Squashed 'third_party/boostorg/odeint/' content from commit 6ff2719
Change-Id: If4892e29c1a5e6cf3a7aa51486a2725c251b0c7d
git-subtree-dir: third_party/boostorg/odeint
git-subtree-split: 6ff2719b6907b86596c3d43e88c1bcfdf29df560
diff --git a/.mailmap b/.mailmap
new file mode 100644
index 0000000..6598614
--- /dev/null
+++ b/.mailmap
@@ -0,0 +1,16 @@
+# git log --all --format='%an <%ae>' | sort -u
+# Proper Name <proper@email> <commit@email>
+Andreas Angelopoulos <andrewtlor@gmail.com> <andrewtlor@gmail.com>
+Christoph Koke <koke@kip.uni-heidelberg.de> <koke@kip.uni-heidelberg.de>
+Daniel James <dnljms@gmail.com> <dnljms@gmail.com>
+Denis Demidov <ddemidov@ksu.ru> <ddemidov@ksu.ru>
+Karsten Ahnert <karsten.ahnert@gmx.de> <karsten.ahnert@gmx.de>
+Karsten Ahnert <karsten.ahnert@gmx.de> <karsten@manta.(none)>
+Karsten Ahnert <karsten.ahnert@gmx.de> <karsten@b8fc166d-592f-0410-95f2-cb63ce0dd405>
+Kyle Lutz <kyle.r.lutz@gmail.com> <kyle.r.lutz@gmail.com>
+Mario Mulansky <mario.mulansky@gmx.net> <mariomulansky@b8fc166d-592f-0410-95f2-cb63ce0dd405>
+Mario Mulansky <mario.mulansky@gmx.net> <mario.mulansky@gmx.net>
+Mario Mulansky <mario.mulansky@gmx.net> <mario@neutrino.stat.physik.uni-potsdam.de>
+Mario Mulansky <mario.mulansky@gmx.net> <mario@.(none)>
+Pascal Germroth <pascal@ensieve.org> <pascal@ensieve.org>
+Sylwester Arabas <slayoo@igf.fuw.edu.pl> <slayoo@igf.fuw.edu.pl>
diff --git a/.travis.yml b/.travis.yml
new file mode 100644
index 0000000..118d3c0
--- /dev/null
+++ b/.travis.yml
@@ -0,0 +1,46 @@
+sudo: false
+language: cpp
+os:
+ - linux
+ - osx
+compiler:
+ - gcc
+ - clang
+install:
+ - if [ "$CXX" = "g++" ]; then export CXX="g++-4.8" CC="gcc-4.8"; fi
+addons:
+ apt:
+ sources:
+ - ubuntu-toolchain-r-test
+ packages:
+ - gcc-4.8
+ - g++-4.8
+ - clang
+
+env:
+ - CXXSTD=""
+ - CXXSTD="-std=c++0x"
+
+# For now disable gcc on osx as g++4.8 is not yet available
+matrix:
+ exclude:
+ - os: osx
+ compiler: gcc
+
+before_install:
+# 1.58: http://downloads.sourceforge.net/project/boost/boost/1.58.0/boost_1_58_0.tar.bz2\?r\=\&ts\=1435589970\&use_mirror\=garr
+# 1.63: https://sourceforge.net/projects/boost/files/boost/1.63.0/boost_1_63_0.tar.bz2/download?use_mirror=superb-dca2
+ - wget https://sourceforge.net/projects/boost/files/boost/1.63.0/boost_1_63_0.tar.bz2/download?use_mirror=superb-dca2 -O /tmp/boost.tar.bz2
+ - tar jxf /tmp/boost.tar.bz2
+ - mv boost_1_63_0 $PWD/boost-trunk
+ - export BOOST_ROOT="$PWD/boost-trunk"
+
+ - cd $BOOST_ROOT
+ - ./bootstrap.sh
+ - cd $TRAVIS_BUILD_DIR
+ - if [ "$TRAVIS_OS_NAME" = "osx" ] && [ "$CC" = "gcc" ]; then export CC=gcc-4.8; fi
+ - echo $CC
+ - $CC --version
+
+script:
+ - $BOOST_ROOT/b2 toolset=$CC cxxflags='$CXXSTD' -j2
\ No newline at end of file
diff --git a/CHANGELOG b/CHANGELOG
new file mode 100644
index 0000000..b1537eb
--- /dev/null
+++ b/CHANGELOG
@@ -0,0 +1,9 @@
+odeint 2.1
+
+* versioning system
+* generation functions
+* bugfixing
+
+odeint 2.2 (still running)
+
+* removing same_size and resize from state_wrapper into separate functions
diff --git a/README.md b/README.md
new file mode 100644
index 0000000..23e4f88
--- /dev/null
+++ b/README.md
@@ -0,0 +1,3 @@
+[](https://travis-ci.org/headmyshoulder/odeint-v2)
+
+odeint is a highly flexible library for solving ordinary differential equations.
diff --git a/doc/Jamfile.v2 b/doc/Jamfile.v2
new file mode 100644
index 0000000..7a7ac95
--- /dev/null
+++ b/doc/Jamfile.v2
@@ -0,0 +1,277 @@
+# Copyright 2009-2013 Karsten Ahnert
+# Copyright 2011-2012 Mario Mulansky
+# Copyright 2012 Daniel James
+# Copyright 2013 Pascal Germroth
+# Distributed under the Boost Software License, Version 1.0.
+# (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+
+using quickbook ;
+using boostbook ;
+using doxygen ;
+import modules ;
+path-constant here : . ;
+
+project : requirements
+ <include>$(BOOST_ROOT)/tools/auto_index/include
+ ;
+
+if --enable-index in [ modules.peek : ARGV ]
+{
+ ECHO "Building the odeint docs with automatic index generation enabled." ;
+
+ using auto-index ;
+
+ project : requirements
+
+ <auto-index>on
+ <auto-index-verbose>on
+
+ # Choose indexing method (separately for html and pdf):
+ <format>html:<auto-index-internal>on # on (or off) to use internally generated indexes.
+ # <format>html:<xsl:param>generate.index=0 # Don't let the XSL stylesheets generate indexes.
+
+ <format>pdf:<auto-index-internal>off # on (or off) to use internally generated indexes.
+ # <auto-index-type>index # Use <index>...</index> as the XML wrapper.
+
+ <format>pdf:<xsl:param>index.on.type=1 # For the native stylesheets to generate the different indexes.
+ # PDF native index support is probably better for PDFs as then you actually get page numbers.
+
+ <auto-index-script>odeint.idx # Specifies the name of the index script to load.
+ <auto-index-prefix>../include
+
+ # Inform Quickbook that there is to be an index(es).
+ <quickbook-define>enable_index
+ ;
+}
+else
+{
+ ECHO "Building the odeint docs with automatic index generation disabled. To get an auto-index, try building with --enable-index." ;
+}
+
+
+
+doxygen reference
+ :
+# [ glob ../include/boost/numeric/odeint/*.hpp ]
+ [ glob ../include/boost/numeric/odeint/stepper/*.hpp ]
+ [ glob ../incude/boost/numeric/odeint/stepper/base/*.hpp ]
+# [ glob ../include/boost/numeric/odeint/stepper/generation/*.hpp ]
+ [ glob ../include/boost/numeric/odeint/integrate/*.hpp : ../include/boost/numeric/odeint/integrate/null_observer.hpp ../include/boost/numeric/odeint/integrate/observer_collection.hpp ]
+ [ glob ../include/boost/numeric/odeint/iterator/*.hpp ]
+# [ glob ../include/boost/numeric/odeint/iterator/impl/*.hpp ]
+# [ glob ../include/boost/numeric/odeint/algebra/*.hpp ]
+# [ glob ../include/boost/numeric/odeint/util/*.hpp ]
+# ../include/boost/numeric/odeint.hpp
+ :
+
+ # Lots of parameters passed to Doxygen. You can see these in the doxygen docs, or the Wizard Expert tab displays them.
+ # If you have successfuly built your Doxygen docs standalone using the Wizard (strongly recommended as it is much quicker).
+ # The values in your project's doxyfile are what to put as the Doxygen parameters passed below.
+ <doxygen:param>WARNINGS=YES
+ <doxygen:param>WARN_LOGFILE=AutoDoxywarnings.log
+ <doxygen:param>WARN_IF_UNDOCUMENTED=NO # Default NO but useful if you aim to Doxygen document *all* members.
+ <doxygen:param>QUIET=NO
+ <doxygen:param>WARN_NO_PARAMDOC=NO # Default no, but YES useful if you aim to document all function parameters.
+ <doxygen:param>DOXYFILE_ENCODING=UTF-8
+ <doxygen:param>PROJECT_NAME="odeint"
+ <doxygen:param>PROJECT_NUMBER=2.2
+ <doxygen:param>TAB_SIZE=2
+ <doxygen:param>SORT_MEMBER_DOCS=NO
+ <doxygen:param>SORT_BRIEF_DOCS=NO
+ <doxygen:param>SORT_MEMBERS_CTORS_1ST=NO
+ <doxygen:param>EXTRACT_PRIVATE=NO
+ <doxygen:param>INLINE_INHERITED_MEMB=YES
+ <doxygen:param>INHERIT_DOCS=YES
+ <doxygen:param>EXTRACT_STATIC=YES
+ <doxygen:param>EXTRACT_ANON_NSPACES=NO
+ <doxygen:param>EXTRACT_LOCAL_CLASSES=YES
+ <doxygen:param>EXTRACT_LOCAL_METHODS=YES
+ <doxygen:param>HIDE_UNDOC_MEMBERS=NO
+ <doxygen:param>HIDE_UNDOC_CLASSES=YES
+ <doxygen:param>HIDE_FRIEND_COMPOUNDS=NO
+ #<doxygen:param>HIDE_INBODY_DOCS=NO
+ <doxygen:param>INTERNAL_DOCS=YES
+ <doxygen:param>CASE_SENSE_NAMES=NO
+ <doxygen:param>HIDE_SCOPE_NAMES=NO
+
+ # Preprocessor settings.
+ # Some ugly examples of predefined macro calls (from Boost.Units library) :(
+ <doxygen:param>"PREDEFINED= \\
+ \"BOOST_UNITS_STATIC_CONSTANT(a,b)=static const b a\" \\
+ \"BOOST_UNITS_TYPEOF(a)=typeof(a)\" \\
+ \"BOOST_PREVENT_MACRO_SUBSTITUTION=\" \\
+ \"BOOST_UNITS_HAS_TYPEOF=1\" \\
+ \"DOXYGEN_SKIP=1\" "
+ <doxygen:param>ENABLE_PREPROCESSING=YES # Evaluates all C-preprocessor directives found in files.
+ <doxygen:param>MACRO_EXPANSION=YES # Will expand all macro names.
+ <doxygen:param>EXPAND_ONLY_PREDEF=YES # Only predefined macros expanded. See units library for an example.
+ <doxygen:param>SEARCH_INCLUDES=YES # Search #include files found.
+ <doxygen:param>INLINE_INFO=YES # If the INLINE_INFO tag is set to YES (the default) then a tag [inline] is inserted in the documentation for inline members.
+
+ <doxygen:param>SHOW_INCLUDE_FILES=NO # List of the files that are included by a file in the documentation of that file.
+ <doxygen:param>REPEAT_BRIEF=YES # Prepend the brief description of a member or function before the detailed description
+ <doxygen:param>BRIEF_MEMBER_DESC=YES # Include brief member descriptions after the members that are listed in the file and class
+ <doxygen:param>MULTILINE_CPP_IS_BRIEF=YES # Treat a multi-line C++ special comment block (i.e. a block of //! or /// comments) as a brief description.
+ # May be best to always use \brief and \details to avoid ambiguity?
+ # <doxygen:param>STRIP_FROM_PATH=NO # Most useful to leave default to strip just the directory from which Doxygen is run.
+ # Yes gives the full path, but NO is more useful, only giving enough to be
+ # <doxygen:param>CPP_CLI_SUPPORT=NO # unless, most unusually, you are compiled for a 'managed' CLI application.
+ <doxygen:param>SHOW_USED_FILES=YES # Default YES to show a list files used to generate documention.
+ <doxygen:param>SHOW_DIRECTORIES=YES # Default NO, but useful to show directory heirarchy.
+ <doxygen:param>SHOW_FILES=YES # Default YES is to include a tab for a page of files listed. Useful.
+ <doxygen:param>SHOW_NAMESPACES=YES # Default YES to include tab for list of namespaces. Useful if you have namespacess other than boost::
+ <doxygen:param>FILE_PATTERNS= # Types of files to be used as input. Default includes *.c *.cc *.cxx *.cpp *.c++ *.ipp *.i++ *.inl *.h *.hh *.hxx *.hpp *.h++ *.py
+ # Might include .qbk?
+
+ <doxygen:param>RECURSIVE=YES # Search recursively down subdirectories.
+ <doxygen:param>EXCLUDE= # Files or directories that should be excluded from INPUT source files.
+ # Headers and footers are actually rather attractive,
+ # <doxygen:param>HTML_HEADER="doxygen/checks_doxygen_header.html" # A sample including a draft stamp and 'Not_Yet_In_Boost' logo.
+ # Take care that if you use this (recommended), you need to ensure that the html
+ # <doxygen:param>HTML_FOOTER="doxygen/checks_doxygen_footer.html" # This is very useful to add copyright, date of revision, versioning etc.
+
+ # A custom stylesheet is also useful, as the default syntax coloring is 'unusual' ;-)
+ <doxygen:param>HTML_STYLESHEET="doxygen/doxygen.css" # Placed in the doxygen directory,
+ # this will change to your choice of C++ syntax coloring when viewing source from Doxygen.
+ # Users can place (or edit) their own personal choice CSS file here.
+
+ # Default is just Reference but you can provide your own title for reference section here.
+ <xsl:param>"boost.doxygen.reftitle=odeint Reference"
+;
+
+
+xml odeint
+ :
+ odeint.qbk
+ :
+;
+
+boostbook standalone
+ :
+ odeint
+ :
+
+ # Path for links to Boost:
+ #<xsl:param>boost.root=\$(local-boost-root) # Link to Boost logo boost.png
+ # Links are relative and trying to make absolute does NOT work.
+ # And remember that all links MUST (unless in quotes) use backslash, not forward that is trip char.
+
+ <xsl:param>boost.root=../../../../.. # OK but link to I:/boost_trunk/boost.png
+
+ # Also control links to admonitions, so need to set separately.
+ #<xsl:param>boost.root=../../../../../../../boost_1_47_0 # OK file:///I:/boost_1_48_0/boost.png
+ # Quickbook [@boost:/boost/units/detail/utility.hpp] should make it relative to xsl parameter boost.root.
+
+ # Use the your own local Boost stylesheet:
+ # <xsl:param>html.stylesheet=../html/boostbook.css
+
+ # Some general style settings:
+ # see http://docbook.sourceforge.net/release/xsl/current/doc/html/index.html
+ <xsl:param>table.footnote.number.format=1 # Identifies the format used for footnote numbers in tables.
+ <xsl:param>footnote.number.format=1 # Identifies the format used for text footnote numbers.
+
+ # Default to not including the Boost logo in the navbar, when one expressly asks to include the navbar.
+ # Boost jamroot now includes
+ # Default to not include a navbar.
+ #<xsl:param>nav.layout=none # No navigation bar (home, prev, next).
+ # defining creates a runtime error: Global parameter nav.layout already defined
+ #<xsl:param>nav.layout=horizontal # to get a horizontal navigation bar (you probably DO want this).
+
+ <xsl:param>boost.image.src=logo.jpg #
+ <xsl:param>boost.image.width=294 # Width of logo in pixels.
+ <xsl:param>boost.image.height=127 # Height of logo in pixels.
+
+
+ # HTML options:
+ # ------------
+ <xsl:param>navig.graphics=1 # Use graphics not text for navigation.
+ <xsl:param>chunk.section.depth=2 # How far down we chunk nested sections, basically all of them.
+ <xsl:param>chunk.first.sections=1 # Don't put the first section on the same page as the TOC.
+ <xsl:param>toc.section.depth=2 # How far down sections get TOCs.
+ <xsl:param>toc.max.depth=2 # Max depth in each TOC.
+ <xsl:param>generate.section.toc.level=3 # How far down we go with TOCs.
+
+ #<format>html:<xsl:param>admon.graphics.extension=".png" # default type for admonitions (important, warning, note ...)
+ #<format>html:<xsl:param>admon.graphics.path=$(nav-images)/ # path to admonition (warning, note...) image (.png) files.
+
+ # <xsl:param name="draft.watermark.image">http://docbook.sourceforge.net/release/images/draft.png</xsl:param>
+ # but use a local copy of draft.png.
+
+ # PDF Options:
+ # -----------
+ # TOC Generation
+ <xsl:param>fop1.extensions=0 # DISable extensions for FOP version 0.90 and later .
+ <format>pdf:<xsl:param>fop.extensions=0 # DISable extensions for FOP version 0.20.5 and earlier.
+ <format>pdf:<xsl:param>xep.extensions=1 # Use XEP extension- PDF bookmarks, document information and better index processing.
+
+ # No indent on body text:
+ <format>pdf:<xsl:param>body.start.indent=0pt #
+ <format>pdf:<xsl:param>paper.type=A4 # Paper type = A4
+ # http://xml.resource.org/public/rfc/html/rfc2346.html
+ # Making Postscript and PDF International, J Palme, RFC 2346 recommends
+ # If you are using US letter paper format, ensure that both left and right margins are at least 21 mm (0.8 in).
+ # If you are using A4 paper, ensure that both the top and bottom margins are at least 33 mm (1.3 in).
+ # Margins sizes:
+ #<format>pdf:<xsl:param>page.margin.top=1.3in
+ #<format>pdf:<xsl:param>page.margin.inner=0.8in
+ #<format>pdf:<xsl:param>page.margin.bottom=1.3in
+ #<format>pdf:<xsl:param>page.margin.outer=0.8in
+
+ # http://docbook.sourceforge.net/release/xsl/current/doc/index.html
+ # DocBook XSL Stylesheets: Reference Documentation.
+
+ # Yes, we want graphics for admonishments:
+ <xsl:param>admon.graphics=1
+ # Set these one for PDF generation *only*:
+ # In PDF format, default PNG graphics are awful, so better use SVG images (type .svg) instead.
+ <format>pdf:<xsl:param>admon.graphics.extension=".svg" #
+ <format>pdf:<xsl:param>use.role.for.mediaobject=1 # Use print role on next line.
+ <format>pdf:<xsl:param>preferred.mediaobject.role=print # pdf role is to be printed.
+ <format>pdf:<xsl:param>img.src.path=$(here)/html/ # Path of image (.svg) files. (Note trailing /) ?
+ #<format>pdf:<xsl:param>admon.graphics.path=$(nav_images)/ # path to admonition (warning, note...) image (.svg) files.
+ #<format>pdf:<xsl:param>draft.mode="yes" # Yes if draft watermark wanted!
+ #<format>pdf:<xsl:param>draft.watermark.image="draft.png" # Watermark (local copy).
+ #<format>pdf:<xsl:param>draft.watermark.image=http://docbook.sourceforge.net/release/images/draft.png # Watermark.
+
+ <dependency>reference # Doxygen reference section
+ # <dependency>pdf-install # final pdf
+ # <dependency>png-install # Boost standard icons in both png
+ # <dependency>svg-install # and svg.
+;
+
+
+# To install a copy of 'master' boostbook.css and logo.
+# install html : ../../../doc/html/boostbook.css ;
+# install ../ : ../../../boost.png ;
+
+
+
+# Install (copy) the 'master' copy of boostbook Cascading Style sheet
+# from your current Boost-root to the /doc/html folder.
+# path-constant boost-root : [ modules.peek : BOOST ] ;
+# install css-install : $(boost-root)/doc/src/boostbook.css : <location>html ;
+
+# path-constant boost-root : [ modules.peek : BOOST ] ;
+
+
+# Install (copy) the 'master' copies of all icon images (both PNG and SVG)
+# and the Boost logo from your current Boost-root
+# to the local /doc/html/images folder so that html is complete and standalone.
+# install png-install : [ glob $(boost-root)/doc/src/images/*.png $(boost-root)/boost.png ] : <location>html/images ;
+# install svg-install : [ glob $(boost-root)/doc/src/images/*.svg ] : <location>html/images ;
+
+# install unordered_pdf : standalone/<format>pdf : <location>. ;
+# explicit unordered_pdf ;
+# The explicit rule is there so that it's only installed when the target is explicitly named.
+
+# Effectively copies the file from \bin folder to the \doc folder.
+# install pdf-install : standalone : <location>. <install-type>PDF ;
+# But will not work as expected if doxygen and/or autoindex is used
+# because a modified pdf file is created, so this command below
+# will rename the file to the expected filename, here quick_auto_dox_index.pdf.
+# <location>. means installed in same place as this jamfile, /doc.
+
+install pdfinstall : standalone : <install-type>PDF <location>. <name>odeint.pdf ;
+
+install callouts : [ glob src/images/callouts/*.png ] : <location>html/images/callouts ;
diff --git a/doc/acknowledgements.qbk b/doc/acknowledgements.qbk
new file mode 100644
index 0000000..90530b1
--- /dev/null
+++ b/doc/acknowledgements.qbk
@@ -0,0 +1,37 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+[section Acknowledgments]
+
+
+[/
+
+* Steven Watanabe for managing the Boost review process.
+* All people who participated in the odeint review process on the Boost mailing list.
+* Paul Bristow for helping with the documentation.
+* The Google Summer Of Code (GSOC) program for funding and Andrew Sutton for supervising us during the GSOC and for lots of useful discussions and feedback about many implementation details..
+* Joachim Faulhaber for motivating us to participate in the Boost review process and many detailed comments about the library.
+* All users of odeint. They are the main motivation for our efforts.
+
+
+[h3 Contributers]
+
+* Andreas Angelopoulos implemented the sparse matrix implicit Euler stepper using the MTL4 library.
+* Rajeev Singh implemented the stiff Van der Pol oscillator example.
+* Sylwester Arabas improved the documentation.
+* Denis Demidov provided the adaption to the VexCL and Viennacl libraries.
+* Christoph Koke provided improved binders.
+* Lee Hodgkinson provided the black hole example.
+]
+
+
+[endsect]
diff --git a/doc/concepts.qbk b/doc/concepts.qbk
new file mode 100644
index 0000000..9adfd08
--- /dev/null
+++ b/doc/concepts.qbk
@@ -0,0 +1,27 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011 Mario Mulansky
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+[section:concepts Concepts]
+[# odeint.concepts]
+
+[include concepts/system.qbk]
+[include concepts/second_order_system.qbk]
+[include concepts/symplectic_system.qbk]
+[include concepts/implicit_system.qbk]
+[include concepts/stepper.qbk]
+[include concepts/error_stepper.qbk]
+[include concepts/controlled_stepper.qbk]
+[include concepts/dense_output_stepper.qbk]
+[include concepts/state_algebra_operations.qbk]
+[include concepts/state_wrapper.qbk]
+
+[endsect]
\ No newline at end of file
diff --git a/doc/concepts/controlled_stepper.qbk b/doc/concepts/controlled_stepper.qbk
new file mode 100644
index 0000000..20afa85
--- /dev/null
+++ b/doc/concepts/controlled_stepper.qbk
@@ -0,0 +1,74 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011 Mario Mulansky
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+[section Controlled Stepper]
+
+This concept specifies the interface a controlled stepper has to fulfill to be used within __integrate_functions.
+
+[heading Description]
+
+A controlled stepper following this Controlled Stepper concept provides the possibility to perform one step of the solution /x(t)/ of an ODE with step-size /dt/ to obtain /x(t+dt)/ with a given step-size /dt/.
+Depending on an error estimate of the solution the step might be rejected and a smaller step-size is suggested.
+
+[heading Associated types]
+
+* '''<para>'''[*state_type]'''</para>'''
+'''<para>'''`Stepper::state_type`'''</para>'''
+'''<para>'''The type characterizing the state of the ODE, hence ['x].'''</para>'''
+
+* '''<para>'''[*deriv_type]'''</para>'''
+'''<para>'''`Stepper::deriv_type`'''</para>'''
+'''<para>'''The type characterizing the derivative of the ODE, hence ['d x/dt].'''</para>'''
+
+* '''<para>'''[*time_type]'''</para>'''
+'''<para>'''`Stepper::time_type`'''</para>'''
+'''<para>'''The type characterizing the dependent variable of the ODE, hence the time ['t].'''</para>'''
+
+* '''<para>'''[*value_type]'''</para>'''
+'''<para>'''`Stepper::value_type`'''</para>'''
+'''<para>'''The numerical data type which is used within the stepper, something like `float`, `double`, `complex< double >`.'''</para>'''
+
+* '''<para>'''[*stepper_category]'''</para>'''
+'''<para>'''`Stepper::stepper_category`'''</para>'''
+'''<para>'''A tag type characterizing the category of the stepper. This type must be convertible to `controlled_stepper_tag`.'''</para>'''
+
+
+
+[heading Notation]
+
+[variablelist
+ [[`ControlledStepper`] [A type that is a model of Controlled Stepper]]
+ [[`State`] [A type representing the state /x/ of the ODE]]
+ [[`Time`] [A type representing the time /t/ of the ODE]]
+ [[`stepper`] [An object of type `ControlledStepper`]]
+ [[`x`] [Object of type `State`]]
+ [[`t`, `dt`] [Objects of type `Time`]]
+ [[`sys`] [An object defining the ODE, should be a model of __system, __symplectic_system, __simple_symplectic_system or __implicit_system.]]
+]
+
+[heading Valid Expressions]
+
+[table
+ [[Name] [Expression] [Type] [Semantics]]
+ [[Do step] [``stepper.try_step( sys , x , t , dt )``] [`controlled_step_result`] [Tries one step of step size `dt`. If the step was successful, `success` is returned, the resulting state is written to `x`, the new time is stored in `t` and `dt` now contains a new (possibly larger) step-size for the next step. If the error was too big, `rejected` is returned and the results are neglected - `x` and `t` are unchanged and `dt` now contains a reduced step-size to be used for the next try.] ]
+ [/ [Do step with reference] [`stepper.try_step( boost::ref(sys) , x , t , dt )`] [`void`] [Same as above with `System` as reference] ]
+]
+
+[heading Models]
+
+* `controlled_error_stepper< runge_kutta_cash_karp54 >`
+* `controlled_error_stepper_fsal< runge_kutta_dopri5 >`
+* `controlled_error_stepper< runge_kutta_fehlberg78 >`
+* `rosenbrock4_controller`
+* `bulirsch_stoer`
+
+[endsect]
\ No newline at end of file
diff --git a/doc/concepts/dense_output_stepper.qbk b/doc/concepts/dense_output_stepper.qbk
new file mode 100644
index 0000000..19d3a25
--- /dev/null
+++ b/doc/concepts/dense_output_stepper.qbk
@@ -0,0 +1,85 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright (c) 2009-2013 Karsten Ahnert
+ Copyright (c) 2009-2013 Mario Mulansky
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+
+[section Dense Output Stepper]
+
+This concept specifies the interface a dense output stepper has to fulfill to be used within __integrate_functions.
+
+[heading Description]
+A dense output stepper following this Dense Output Stepper concept provides the possibility to perform a single step of the solution /x(t)/ of an ODE to obtain /x(t+dt)/.
+The step-size `dt` might be adjusted automatically due to error control.
+Dense output steppers also can interpolate the solution to calculate the state /x(t')/ at any point /t <= t' <= t+dt/.
+
+[heading Associated types]
+
+* '''<para>'''[*state_type]'''</para>'''
+'''<para>'''`Stepper::state_type`'''</para>'''
+'''<para>'''The type characterizing the state of the ODE, hence ['x].'''</para>'''
+
+* '''<para>'''[*deriv_type]'''</para>'''
+'''<para>'''`Stepper::deriv_type`'''</para>'''
+'''<para>'''The type characterizing the derivative of the ODE, hence ['d x/dt].'''</para>'''
+
+* '''<para>'''[*time_type]'''</para>'''
+'''<para>'''`Stepper::time_type`'''</para>'''
+'''<para>'''The type characterizing the dependent variable of the ODE, hence the time ['t].'''</para>'''
+
+* '''<para>'''[*value_type]'''</para>'''
+'''<para>'''`Stepper::value_type`'''</para>'''
+'''<para>'''The numerical data type which is used within the stepper, something like `float`, `double`, `complex< double >`.'''</para>'''
+
+* '''<para>'''[*stepper_category]'''</para>'''
+'''<para>'''`Stepper::stepper_category`'''</para>'''
+'''<para>'''A tag type characterizing the category of the stepper. This type must be convertible to `dense_output_stepper_tag`.'''</para>'''
+
+
+[heading Notation]
+
+[variablelist
+ [[`Stepper`] [A type that is a model of Dense Output Stepper]]
+ [[`State`] [A type representing the state /x/ of the ODE]]
+ [[`stepper`] [An object of type `Stepper`]]
+ [[`x0`, `x`] [Object of type `State`]]
+ [[`t0`, `dt0`, `t`] [Objects of type `Stepper::time_type`]]
+ [[`sys`] [An object defining the ODE, should be a model of __system, __symplectic_system, __simple_symplectic_system or __implicit_system.]]
+]
+
+[heading Valid Expressions]
+
+[table
+ [[Name] [Expression] [Type] [Semantics]]
+
+ [[Initialize integration] [`stepper.initialize( x0 , t0 , dt0 )`] [void] [Initializes the stepper with initial values `x0`, `t0` and `dt0`.]]
+
+ [[Do step] [`stepper.do_step( sys )`] [`std::pair< Stepper::time_type , Stepper::time_type >`] [Performs one step using the ODE defined by `sys`. The step-size might be changed internally due to error control. This function returns a pair containing `t` and `t+dt` representing the interval for which interpolation can be performed.] ]
+
+ [/ [Do step with reference] [`stepper.do_step( boost::ref( sys ) )`] [`std::pair< Stepper::time_type , Stepper::time_type >`] [Same as above with `System` as reference] ]
+
+ [[Do interpolation] [`stepper.calc_state( t_inter , x )`] [`void`] [Performs the interpolation to calculate /x(t[sub inter]/) where /t <= t[sub inter] <= t+dt/.]]
+
+ [[Get current time] [`stepper.current_time()`] [`const Stepper::time_type&`] [Returns the current time /t+dt/ of the stepper, that is the end time of the last step and the starting time for the next call of `do_step`]]
+
+ [[Get current state] [`stepper.current_state()`] [`const Stepper::state_type&`] [Returns the current state of the stepper, that is /x(t+dt)/, the state at the time returned by `stepper.current_time()`]]
+
+ [[Get current time step] [`stepper.current_time_step()`] [`const
+ Stepper::time_type&`] [Returns the current step size of the stepper, that is
+ /dt/]]
+]
+
+[heading Models]
+
+* `dense_output_controlled_explicit_fsal< controlled_error_stepper_fsal< runge_kutta_dopri5 >`
+* `bulirsch_stoer_dense_out`
+* `rosenbrock4_dense_output`
+
+[endsect]
diff --git a/doc/concepts/error_stepper.qbk b/doc/concepts/error_stepper.qbk
new file mode 100644
index 0000000..8ebfde9
--- /dev/null
+++ b/doc/concepts/error_stepper.qbk
@@ -0,0 +1,101 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011 Mario Mulansky
+ Copyright 2012 Sylwester Arabas
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+
+[section Error Stepper]
+
+This concepts specifies the interface an error stepper has to fulfill to be used within a ControlledErrorStepper. An error stepper must always fulfill the stepper concept. This can trivially implemented by
+
+``
+template< class System >
+error_stepper::do_step( System sys , state_type &x , time_type t , time_type dt )
+{
+ state_type xerr;
+ // allocate xerr
+ do_step( sys , x , t , dt , xerr );
+}
+``
+
+[heading Description]
+
+An error stepper following this Error Stepper concept is capable of doing one step of the solution /x(t)/ of an ODE with step-size /dt/ to obtain /x(t+dt)/ and also computing an error estimate ['x[sub err]] of the result.
+Error Steppers can be Runge-Kutta steppers, symplectic steppers as well as implicit steppers.
+Based on the stepper type, the ODE is defined as __system, __symplectic_system, __simple_symplectic_system or __implicit_system.
+
+[heading Refinement of]
+
+* DefaultConstructable
+* CopyConstructable
+* Stepper
+
+[heading Associated types]
+
+* '''<para>'''[*state_type]'''</para>'''
+'''<para>'''`Stepper::state_type`'''</para>'''
+'''<para>'''The type characterizing the state of the ODE, hence ['x].'''</para>'''
+
+* '''<para>'''[*deriv_type]'''</para>'''
+'''<para>'''`Stepper::deriv_type`'''</para>'''
+'''<para>'''The type characterizing the derivative of the ODE, hence ['d x/dt].'''</para>'''
+
+* '''<para>'''[*time_type]'''</para>'''
+'''<para>'''`Stepper::time_type`'''</para>'''
+'''<para>'''The type characterizing the dependent variable of the ODE, hence the time ['t].'''</para>'''
+
+* '''<para>'''[*value_type]'''</para>'''
+'''<para>'''`Stepper::value_type`'''</para>'''
+'''<para>'''The numerical data type which is used within the stepper, something like `float`, `double`, `complex< double >`.'''</para>'''
+
+* '''<para>'''[*order_type]'''</para>'''
+'''<para>'''`Stepper::order_type`'''</para>'''
+'''<para>'''The type characterizing the order of the ODE, typically `unsigned short`.'''</para>'''
+
+* '''<para>'''[*stepper_category]'''</para>'''
+'''<para>'''`Stepper::stepper_category`'''</para>'''
+'''<para>'''A tag type characterizing the category of the stepper. This type must be convertible to `error_stepper_tag`.'''</para>'''
+
+
+[heading Notation]
+
+[variablelist
+ [[`ErrorStepper`] [A type that is a model of Error Stepper]]
+ [[`State`] [A type representing the state /x/ of the ODE]]
+ [[`Error`] [A type representing the error calculated by the stepper, usually same as `State`]]
+ [[`Time`] [A type representing the time /t/ of the ODE]]
+ [[`stepper`] [An object of type `ErrorStepper`]]
+ [[`x`] [Object of type `State`]]
+ [[`xerr`] [Object of type `Error`]]
+ [[`t`, `dt`] [Objects of type `Time`]]
+ [[`sys`] [An object defining the ODE, should be a model of either __system, __symplectic_system, __simple_symplectic_system or __implicit_system.]]
+]
+
+[heading Valid Expressions]
+
+[table
+ [[Name] [Expression] [Type] [Semantics]]
+ [[Get the stepper order] [`stepper.order()`] [`order_type`] [Returns the order of the stepper for one step without error estimation.]]
+ [[Get the stepper order] [`stepper.stepper_order()`] [`order_type`] [Returns the order of the stepper for one error estimation step which is used for error calculation.]]
+ [[Get the error order] [`stepper.errorr_order()`] [`order_type`] [Returns the order of the error step which is used for error calculation.]]
+ [[Do step] [`stepper.do_step( sys , x , t , dt )`] [`void`] [Performs one step of step size `dt`. The newly obtained state is written in-place to `x`.] ]
+ [[Do step with error estimation] [`stepper.do_step( sys , x , t , dt , xerr )`] [`void`] [Performs one step of step size `dt` with error estimation. The newly obtained state is written in-place to `x` and the estimated error to `xerr`.] ]
+ [/ [Do step with reference] [`stepper.do_step( boost::ref(sys) , x , t , dt , xerr )`] [`void`] [Performs one step of step size `dt`. The newly obtained state is written in-place to `x` and the estimated error to `xerr`.] ]
+]
+
+[heading Models]
+
+* `runge_kutta_cash_karp54`
+* `runge_kutta_dopri5`
+* `runge_kutta_fehlberg78`
+* `rosenbrock4`
+
+[endsect]
diff --git a/doc/concepts/implicit_system.qbk b/doc/concepts/implicit_system.qbk
new file mode 100644
index 0000000..e889023
--- /dev/null
+++ b/doc/concepts/implicit_system.qbk
@@ -0,0 +1,43 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011 Mario Mulansky
+ Copyright 2011-2012 Karsten Ahnert
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+
+[section Implicit System]
+
+[heading Description]
+
+This concept describes how to define a ODE that can be solved by an implicit routine.
+Implicit routines need not only the function /f(x,t)/ but also the Jacobian /df/dx = A(x,t)/.
+/A/ is a matrix and implicit routines need to solve the linear problem /Ax = b/.
+In odeint this is implemented with use of __ublas, therefore, the ['state_type] implicit routines is ['ublas::vector] and the matrix is defined as ['ublas::matrix].
+
+[heading Notation]
+
+[variablelist
+ [[`System`] [A type that is a model of `Implicit System`]]
+ [[`Time`] [A type representing the time of the ODE]]
+ [[`sys`] [An object of type `System`]]
+ [[`x`] [Object of type ublas::vector]]
+ [[`dxdt`] [Object of type ublas::vector]]
+ [[`jacobi`] [Object of type ublas::matrix]]
+ [[`t`] [Object of type `Time`]]
+]
+
+[heading Valid Expressions]
+
+[table
+ [[Name] [Expression] [Type] [Semantics]]
+ [[Calculate ['dx/dt := f(x,t)]] [`sys.first( x , dxdt , t )`] [`void`] [Calculates `f(x,t)`, the result is stored into dxdt] ]
+ [[Calculate ['A := df/dx (x,t)]] [`sys.second( x , jacobi , t )`] [`void`] [Calculates the Jacobian of /f/ at /x/,/t/, the result is stored into `jacobi`] ]
+]
+
+[endsect]
\ No newline at end of file
diff --git a/doc/concepts/second_order_system.qbk b/doc/concepts/second_order_system.qbk
new file mode 100644
index 0000000..9ca9009
--- /dev/null
+++ b/doc/concepts/second_order_system.qbk
@@ -0,0 +1,44 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright (c) 2009-2013 Karsten Ahnert
+ Copyright (c) 2009-2013 Mario Mulansky
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+[section Second Order System]
+
+[heading Description]
+
+The Second Order System concept models the algorithmic implementation of the rhs for steppers requirering the second order
+derivative, hence the r.h.s. of the ODE ['x'' = f(x,x',t)]. The only requirement for this concept is that it should be callable
+with a specific parameter syntax (see below). A Second Order System is typically implemented as a function or a functor.
+Systems fulfilling this concept are required by the Velocity Verlet method.
+
+[heading Notation]
+
+[variablelist
+ [[`System`] [A type that is a model of Second Order System]]
+ [[`Space`] [A type representing the state /x/ of the ODE]]
+ [[`Velocity`] [A type representing the derivative /x'/ of the ODE]]
+ [[`Acceleration`] [A type representing the second order derivative /x''/ of the ODE]]
+ [[`Time`] [A type representing the time]]
+ [[`sys`] [An object of type `System`]]
+ [[`x`] [Object of type `Space`]]
+ [[`v`] [Object of type `Velocity`]]
+ [[`a`] [Object of type `Acceleration`]]
+ [[`t`] [Object of type `Time`]]
+]
+
+[heading Valid expressions]
+
+[table
+ [[Name] [Expression] [Type] [Semantics]]
+ [[Calculate ['x'' := f(x,x',t)]] [`sys( x , v , a , t )`] [`void`] [Calculates f(x,x',t), the result is stored into a.] ]
+]
+
+[endsect]
\ No newline at end of file
diff --git a/doc/concepts/state_algebra_operations.qbk b/doc/concepts/state_algebra_operations.qbk
new file mode 100644
index 0000000..d92bb83
--- /dev/null
+++ b/doc/concepts/state_algebra_operations.qbk
@@ -0,0 +1,126 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011 Mario Mulansky
+ Copyright 2012 Karsten Ahnert
+ Copyright 2013 Pascal Germroth
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+
+[section State Algebra Operations]
+
+[note The following does not apply to implicit steppers like implicit_euler or Rosenbrock 4 as there the `state_type` can not be changed from `ublas::vector` and no algebra/operations are used.]
+
+[heading Description]
+
+The `State`, `Algebra` and `Operations` together define a concept describing how the mathematical vector operations required for the stepper algorithms are performed.
+The typical vector operation done within steppers is
+
+['*y* = __Sigma __alpha[sub i] [*x[sub i]]].
+
+The `State` represents the state variable of an ODE, usually denoted with /x/.
+Algorithmically, the state is often realized as a `vector< double >` or `array< double , N >`, however, the genericity of odeint enables you to basically use anything as a state type.
+The algorithmic counterpart of such mathematical expressions is divided into two parts.
+First, the `Algebra` is used to account for the vector character of the equation.
+In the case of a `vector` as state type this means the `Algebra` is responsible for iteration over all vector elements.
+Second, the `Operations` are used to represent the actual operation applied to each of the vector elements.
+So the `Algebra` iterates over all elements of the `State`s and calls an operation taken from the `Operations` for each element.
+This is where `State`, `Algebra` and `Operations` have to work together to make odeint running.
+Please have a look at the `range_algebra` and `default_operations` to see an example how this is implemented.
+
+In the following we describe how `State`, `Algebra` and `Operations` are used together within the stepper implementations.
+
+[section Operations]
+
+[heading Notation]
+
+[variablelist
+ [[`Operations`] [The operations type]]
+ [/[`Time`] [A type representing the time type of steppers]]
+ [[`Value1`, ... , `ValueN`] [Types representing the value or time type of stepper]]
+ [[`Scale`] [Type of the scale operation]]
+ [[`scale`] [Object of type `Scale`]]
+ [[[^ScaleSum['N]]] [Type that represents a general scale_sum operation, [^/N/] should be replaced by a number from 1 to 14.]]
+ [[[^scale_sum['N]]] [Object of type [^ScaleSum['N]], [^/N/] should be replaced by a number from 1 to 14.]]
+ [[`ScaleSumSwap2`] [Type of the scale sum swap operation]]
+ [[`scale_sum_swap2`] [Object of type `ScaleSumSwap2`]]
+ [[`a1, a2, ...`] [Objects of type `Value1`, `Value2`, ...]]
+ [[`y, x1, x2, ...`] [Objects of `State`'s value type]]
+]
+
+[heading Valid Expressions]
+
+[table
+ [[Name] [Expression] [Type] [Semantics]]
+ [[Get scale operation] [`Operations::scale< Value >`] [`Scale`] [Get `Scale` from `Operations`]]
+ [[`Scale` constructor] [`Scale< Value >( a )`] [`Scale`] [Constructs a `Scale` object]]
+ [[`Scale` operation] [`scale( x )`] [`void`] [Calculates `x *= a`]]
+ [[Get general `scale_sum` operation] [[^Operations::scale_sum['N]< Value1 , ... , ValueN >]] [[^ScaleSum['N]]] [Get the [^ScaleSum['N]] type from `Operations`, [^/N/] should be replaced by a number from 1 to 14.]]
+ [[`scale_sum` constructor] [[^ScaleSum['N]< Value1 , ... , ValueN >( a1 , ... , aN )]] [[^ScaleSum['N]]] [Constructs a `scale_sum` object given [^/N/] parameter values with [^/N/] between 1 and 14.]]
+ [[`scale_sum` operation] [[^scale_sum['N]( y , x1 , ... , xN )]] [`void`] [Calculates `y = a1*x1 + a2*x2 + ... + aN*xN`. Note that this is an [^/N/+1]-ary function call.]]
+ [[Get scale sum swap operation] [`Operations::scale_sum_swap2< Value1 , Value2 >`] [`ScaleSumSwap2`] [Get scale sum swap from operations]]
+ [[`ScaleSumSwap2` constructor] [`ScaleSumSwap2< Value1 , Value2 >( a1 , a2 )`] [`ScaleSumSwap2`] [Constructor]]
+ [[`ScaleSumSwap2` operation] [`scale_sum_swap2( x1 , x2 , x3 )`] [`void`] [Calculates `tmp = x1`, `x1 = a1*x2 + a2*x3` and `x2 = tmp`.]]
+]
+
+[endsect]
+
+[section Algebra]
+
+[heading Notation]
+
+[variablelist
+ [[`State`] [The state type]]
+ [[`Algebra`] [The algebra type]]
+ [[[^Operation['N]]] [An [^/N/]-ary operation type, [^/N/] should be a number from 1 to 14.]]
+ [[`algebra`] [Object of type `Algebra`]]
+ [[[^operation['N]]] [Object of type [^Operation['N]]]]
+ [[`y, x1, x2, ...`] [Objects of type `State`]]
+]
+
+
+[heading Valid Expressions]
+
+[table
+ [[Name] [Expression] [Type] [Semantics]]
+ [[Vector Operation with arity 2] [`algebra.for_each2( y , x , operation2 )`] [void] [Calls `operation2( y_i , x_i )` for each element `y_i` of `y` and `x_i` of `x`.]]
+ [[Vector Operation with arity 3] [`algebra.for_each3( y , x1 , x2 , operation3 )`] [void] [Calls `operation3( y_i , x1_i , x2_i )` for each element `y_i` of `y` and `x1_i` of `x1` and `x2_i` of `x2`.]]
+ [[Vector Operation with arity [^/N/]] [[^algebra.for_each['N]( y , x1 , ... , xN , operation['N] )]] [void] [Calls [^operation['N]( y_i , x1_i , ... , xN_i )] for each element `y_i` of `y` and `x1_i` of `x1` and so on. [^/N/] should be replaced by a number between 1 and 14.]]
+]
+
+[endsect]
+
+[section Pre-Defined implementations]
+
+As standard configuration odeint uses the `range_algebra` and `default_operations` which suffices most situations.
+However, a few more possibilities exist either to gain better performance or to ensure interoperability with other libraries.
+In the following we list the existing `Algebra`/`Operations` configurations that can be used in the steppers.
+
+[table
+ [[`State`] [`Algebra`] [`Operations`] [Remarks]]
+ [[Anything supporting __boost_range, like `std::vector`, `std::list`, `boost::array`,... based on a `value_type` that supports operators +,* (typically `double`)] [`range_algebra`] [`default_operations`] [Standard implementation, applicable for most typical situations.]]
+ [[`boost::array` based on a `value_type` that supports operators +,*] [`array_algebra`] [`default_operations`] [Special implementation for boost::array with better performance than `range_algebra`]]
+ [[Anything that defines operators + within itself and * with scalar (Mathematically spoken, anything that is a vector space).] [`vector_space_algebra`] [`default_operations`] [For the use of __controlled_stepper, the template `vector_space_reduce` has to be instantiated.]]
+ [[`thrust::device_vector`, `thrust::host_vector`] [`thrust_algebra`] [`thrust_operations`] [For running odeint on CUDA devices by using __thrust]]
+ [[Any RandomAccessRange] [`openmp_range_algebra`] [`default_operations`] [OpenMP-parallelised range algebra]]
+ [[`openmp_state`] [`openmp_algebra`] [`default_operations`] [OpenMP-parallelised algebra for split data]]
+ [[`boost::array` or anything which allocates the elements in a C-like manner] [`vector_space_algebra`] [`mkl_operations`] [Using the __intel_mkl in odeint for maximum performance. Currently, only the RK4 stepper is supported.]]
+]
+
+[endsect]
+
+[section Example expressions]
+
+[table
+ [[Name] [Expression] [Type] [Semantics]]
+ [[Vector operation] [`algebra.for_each3( y , x1 , x2 , Operations::scale_sum2< Value1 , Value2 >( a1 , a2 ) )`] [void] [Calculates ['*y* = a1 *x1* + a2 *x2*]]]
+]
+
+[endsect]
+
+[endsect]
\ No newline at end of file
diff --git a/doc/concepts/state_wrapper.qbk b/doc/concepts/state_wrapper.qbk
new file mode 100644
index 0000000..768671d
--- /dev/null
+++ b/doc/concepts/state_wrapper.qbk
@@ -0,0 +1,39 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011 Mario Mulansky
+ Copyright 2012 Karsten Ahnert
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+[section State Wrapper]
+
+[heading Description]
+
+The `State Wrapper` concept describes the way odeint creates temporary state objects to store intermediate results within the stepper's `do_step` methods.
+
+[heading Notation]
+
+[variablelist
+ [[`State`] [A type that is the `state_type` of the ODE]]
+ [[`WrappedState`] [A type that is a model of State Wrapper for the state type `State`.]]
+ [[`x`] [Object of type `State`]]
+ [[`w`] [Object of type `WrappedState`]]
+]
+
+[heading Valid Expressions]
+
+[table
+ [[Name] [Expression] [Type] [Semantics]]
+ [[Get resizeability] [`is_resizeable< State >`] [`boost::false_type` or `boost::true_type`] [Returns `boost::true_type` if the `State` is resizeable, `boost::false_type` otherwise.]]
+ [[Create `WrappedState` type] [`state_wrapper< State >`] [`WrappedState`] [Creates the type for a `WrappedState` for the state type `State`]]
+ [[Constructor] [`WrappedState()`] [`WrappedState`] [Constructs a state wrapper with an empty state]]
+ [[Copy Constructor] [`WrappedState( w )`] [`WrappedState`] [Constructs a state wrapper with a state of the same size as the state in `w`]]
+ [[Get state] [`w.m_v`] [`State`] [Returns the `State` object of this state wrapper.]]
+]
+
+[endsect]
\ No newline at end of file
diff --git a/doc/concepts/stepper.qbk b/doc/concepts/stepper.qbk
new file mode 100644
index 0000000..a23c027
--- /dev/null
+++ b/doc/concepts/stepper.qbk
@@ -0,0 +1,93 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011 Mario Mulansky
+ Copyright 2012 Sylwester Arabas
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+[section Stepper]
+
+This concepts specifies the interface a simple stepper has to fulfill to be used within the __integrate_functions.
+
+[heading Description]
+
+The basic stepper concept.
+A basic stepper following this Stepper concept is able to perform a single step of the solution /x(t)/ of an ODE to obtain /x(t+dt)/ using a given step size /dt/.
+Basic steppers can be Runge-Kutta steppers, symplectic steppers as well as implicit steppers.
+Depending on the actual stepper, the ODE is defined as __system, __symplectic_system, __simple_symplectic_system or __implicit_system.
+Note that all error steppers are also basic steppers.
+
+[heading Refinement of]
+
+* DefaultConstructable
+* CopyConstructable
+
+
+[heading Associated types]
+
+* '''<para>'''[*state_type]'''</para>'''
+'''<para>'''`Stepper::state_type`'''</para>'''
+'''<para>'''The type characterizing the state of the ODE, hence ['x].'''</para>'''
+
+* '''<para>'''[*deriv_type]'''</para>'''
+'''<para>'''`Stepper::deriv_type`'''</para>'''
+'''<para>'''The type characterizing the derivative of the ODE, hence ['d x/dt].'''</para>'''
+
+* '''<para>'''[*time_type]'''</para>'''
+'''<para>'''`Stepper::time_type`'''</para>'''
+'''<para>'''The type characterizing the dependent variable of the ODE, hence the time ['t].'''</para>'''
+
+* '''<para>'''[*value_type]'''</para>'''
+'''<para>'''`Stepper::value_type`'''</para>'''
+'''<para>'''The numerical data type which is used within the stepper, something like `float`, `double`, `complex< double >`.'''</para>'''
+
+* '''<para>'''[*order_type]'''</para>'''
+'''<para>'''`Stepper::order_type`'''</para>'''
+'''<para>'''The type characterizing the order of the ODE, typically `unsigned short`.'''</para>'''
+
+* '''<para>'''[*stepper_category]'''</para>'''
+'''<para>'''`Stepper::stepper_category`'''</para>'''
+'''<para>'''A tag type characterizing the category of the stepper. This type must be convertible to `stepper_tag`.'''</para>'''
+
+
+[heading Notation]
+
+[variablelist
+ [[`Stepper`] [A type that is a model of Stepper]]
+ [[`State`] [A type representing the state /x/ of the ODE]]
+ [[`Time`] [A type representing the time /t/ of the ODE]]
+ [[`stepper`] [An object of type `Stepper`]]
+ [[`x`] [Object of type `State`]]
+ [[`t`, `dt`] [Objects of type `Time`]]
+ [[`sys`] [An object defining the ODE. Depending on the Stepper this might be a model of __system, __symplectic_system, __simple_symplectic_system or __implicit_system ]]
+]
+
+[heading Valid Expressions]
+
+[table
+ [[Name] [Expression] [Type] [Semantics]]
+ [[Get the order] [`stepper.order()`] [`order_type`] [Returns the order of the stepper.]]
+ [[Do step] [`stepper.do_step( sys , x , t , dt )`] [`void`] [Performs one step of step size `dt`. The newly obtained state is written in place in `x`.] ]
+
+ [/ [Do step with reference] [`stepper.do_step( boost::ref(sys) , x , t , dt )`] [`void`] [Performs one step of step size `dt`. The newly obtained state is written in place in `x`.] ]
+
+ [/ [Do step out-of-place] [`stepper.do_step( sys , in , t , out , dt )`] [`void`] [Performs one step. The newly obtained state is written to `out`] ]
+]
+
+[heading Models]
+
+* `runge_kutta4`
+* `euler`
+* `runge_kutta_cash_karp54`
+* `runge_kutta_dopri5`
+* `runge_kutta_fehlberg78`
+* `modified_midpoint`
+* `rosenbrock4`
+
+[endsect]
diff --git a/doc/concepts/symplectic_system.qbk b/doc/concepts/symplectic_system.qbk
new file mode 100644
index 0000000..e078597
--- /dev/null
+++ b/doc/concepts/symplectic_system.qbk
@@ -0,0 +1,99 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011 Mario Mulansky
+ Copyright 2011-2012 Karsten Ahnert
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+[section Symplectic System]
+
+[heading Description]
+
+This concept describes how to define a symplectic system written with generalized coordinate `q` and generalized momentum `p`:
+
+[' q'(t) = f(p) ]
+
+[' p'(t) = g(q) ]
+
+Such a situation is typically found for Hamiltonian systems with a separable Hamiltonian:
+
+[' H(p,q) = H[sub kin](p) + V(q) ]
+
+which gives the equations of motion:
+
+[' q'(t) = dH[sub kin] / dp = f(p) ]
+
+[' p'(t) = dV / dq = g(q) ]
+
+
+The algorithmic implementation of this situation is described by a pair of callable objects for /f/ and /g/ with a specific parameter signature.
+Such a system should be implemented as a std::pair of functions or a functors.
+Symplectic systems are used in symplectic steppers like `symplectic_rkn_sb3a_mclachlan`.
+
+[heading Notation]
+
+[variablelist
+ [[`System`] [A type that is a model of SymplecticSystem]]
+ [[`Coor`] [The type of the coordinate ['q]]]
+ [[`Momentum`] [The type of the momentum ['p]]]
+ [[`CoorDeriv`] [The type of the derivative of coordinate ['q']]]
+ [[`MomentumDeriv`] [The type of the derivative of momentum ['p']]]
+ [[`sys`] [An object of the type `System`]]
+ [[`q`] [Object of type Coor]]
+ [[`p`] [Object of type Momentum]]
+ [[`dqdt`] [Object of type CoorDeriv]]
+ [[`dpdt`] [Object of type MomentumDeriv]]
+]
+
+[heading Valid expressions]
+
+[table
+ [[Name] [Expression] [Type] [Semantics]]
+ [[Check for pair] [`boost::is_pair< System >::type`] [`boost::mpl::true_`] [Check if System is a pair]]
+ [[Calculate ['dq/dt = f(p)]] [`sys.first( p , dqdt )`] [`void`] [Calculates ['f(p)], the result is stored into `dqdt`] ]
+ [[Calculate ['dp/dt = g(q)]] [`sys.second( q , dpdt )`] [`void`] [Calculates ['g(q)], the result is stored into `dpdt`] ]
+]
+
+[endsect]
+
+
+[section Simple Symplectic System]
+
+[heading Description]
+
+In most Hamiltonian systems the kinetic term is a quadratic term in the momentum ['H[sub kin] = p^2 / 2m] and in many cases it is possible to rescale coordinates and set /m=1/ which leads to a trivial equation of motion:
+
+[' q'(t) = f(p) = p. ]
+
+while for /p'/ we still have the general form
+
+[' p'(t) = g(q) ]
+
+As this case is very frequent we introduced a concept where only the nontrivial equation for /p'/ has to be provided to the symplectic stepper.
+We call this concept ['SimpleSymplecticSystem]
+
+[heading Notation]
+
+[variablelist
+ [[System] [A type that is a model of SimpleSymplecticSystem]]
+ [[Coor] [The type of the coordinate ['q]]]
+ [[MomentumDeriv] [The type of the derivative of momentum ['p']]]
+ [[sys] [An object that models System]]
+ [[q] [Object of type Coor]]
+ [[dpdt] [Object of type MomentumDeriv]]
+]
+
+[heading Valid Expressions]
+
+[table
+ [[Name] [Expression] [Type] [Semantics]]
+ [[Check for pair] [`boost::is_pair< System >::type`] [`boost::mpl::false_`] [Check if System is a pair, should be evaluated to false in this case.]]
+ [[Calculate ['dp/dt = g(q)]] [`sys( q , dpdt )`] [`void`] [Calculates ['g(q)], the result is stored into `dpdt`] ]
+]
+
+[endsect]
\ No newline at end of file
diff --git a/doc/concepts/system.qbk b/doc/concepts/system.qbk
new file mode 100644
index 0000000..d04c998
--- /dev/null
+++ b/doc/concepts/system.qbk
@@ -0,0 +1,43 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011 Mario Mulansky
+ Copyright 2011-2012 Karsten Ahnert
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+[section System]
+
+[heading Description]
+
+The System concept models the algorithmic implementation of the rhs. of the ODE ['x' = f(x,t)].
+The only requirement for this concept is that it should be callable with a specific parameter syntax (see below).
+A System is typically implemented as a function or a functor.
+Systems fulfilling this concept are required by all Runge-Kutta steppers as well as the Bulirsch-Stoer steppers.
+However, symplectic and implicit steppers work with other system concepts, see __symplectic_system and __implicit_system.
+
+[heading Notation]
+
+[variablelist
+ [[`System`] [A type that is a model of System]]
+ [[`State`] [A type representing the state /x/ of the ODE]]
+ [[`Deriv`] [A type representing the derivative /x'/ of the ODE]]
+ [[`Time`] [A type representing the time]]
+ [[`sys`] [An object of type `System`]]
+ [[`x`] [Object of type `State`]]
+ [[`dxdt`] [Object of type `Deriv`]]
+ [[`t`] [Object of type `Time`]]
+]
+
+[heading Valid expressions]
+
+[table
+ [[Name] [Expression] [Type] [Semantics]]
+ [[Calculate ['dx/dt := f(x,t)]] [`sys( x , dxdt , t )`] [`void`] [Calculates f(x,t), the result is stored into dxdt] ]
+]
+
+[endsect]
\ No newline at end of file
diff --git a/doc/controlled_stepper_table.qbk b/doc/controlled_stepper_table.qbk
new file mode 100644
index 0000000..e422c43
--- /dev/null
+++ b/doc/controlled_stepper_table.qbk
@@ -0,0 +1,55 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+[table Adaptive step size algorithms
+ [ [Stepper] [Tolerance formula] [Norm] [Step size adaption] ]
+ [ [`controlled_runge_kutta`]
+ [
+ ['val = || | err[subl i] | / ( __epsilon[subl abs] + __epsilon[subl rel] * ( a[subl x] | x[subl i] | + a[subl dxdt] | | dxdt[subl i] | )|| ]
+ ]
+ [['||x|| = max( x[subl i] )]]
+ [
+ ['val > 1 : dt[subl new] = dt[subl current] max( 0.9 pow( val , -1 / ( O[subl E] - 1 ) ) , 0.2 )]
+
+ ['val < 0.5 : dt[subl new] = dt[subl current] min( 0.9 pow( val , -1 / O[subl S] ) , 5 )]
+
+ ['else : dt[subl new] = dt[subl current]]
+ ] ]
+ [ [`rosenbrock4_controller`]
+ [
+ ['val = || err[subl i] / ( __epsilon[subl abs] + __epsilon[subl rel] max( | x[subl i] | , | xold[subl i] | ) ) || ]
+ ]
+ [['||x||=(__Sigma[subl i] x[subl i][super 2])[super 1/2]]]
+ [
+ ['fac = max( 1 / 6 , min( 5 , pow( val , 1 / 4 ) / 0.9 ) ]
+
+ ['fac2 = max( 1 / 6 , min( 5 , dt[subl old] / dt[subl current] pow( val[super 2] / val[subl old] , 1 / 4 ) / 0.9 ) ]
+
+ ['val > 1 : dt[subl new] = dt[subl current] / fac ]
+
+ ['val < 1 : dt[subl new] = dt[subl current] / max( fac , fac2 ) ]
+ ]
+ ]
+ [ [bulirsch_stoer] [['tol=1/2]] [-] [['dt[subl new] = dt[subl old][super 1/a]]] ]
+]
+
+[/
+
+safe = 0.9 , fac1 = 5.0 , fac2 = 1.0 / 6.0
+
+value_type fac_pred = ( m_dt_old / dt ) * pow( err * err / m_err_old , 0.25 ) / safe;
+ fac_pred = std::max( fac2 , std::min( fac1 , fac_pred ) );
+ fac = std::max( fac , fac_pred );
+ dt_new = dt / fac;
+
+
+fac = max( fac2 , min( fac1 , pow( err , 0.25 ) / safe ) )
+]
\ No newline at end of file
diff --git a/doc/details.qbk b/doc/details.qbk
new file mode 100644
index 0000000..5c5c5fd
--- /dev/null
+++ b/doc/details.qbk
@@ -0,0 +1,30 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+[section odeint in detail]
+
+[include details_steppers.qbk]
+
+[include details_generation_functions.qbk]
+
+[include details_integrate_functions.qbk]
+
+[include details_iterators.qbk]
+
+[include details_state_types_algebras_operations.qbk]
+
+[include details_boost_ref.qbk]
+
+[include details_boost_range.qbk]
+
+[include details_bind_member_functions.qbk]
+
+[endsect]
diff --git a/doc/details_bind_member_functions.qbk b/doc/details_bind_member_functions.qbk
new file mode 100644
index 0000000..0a10a72
--- /dev/null
+++ b/doc/details_bind_member_functions.qbk
@@ -0,0 +1,36 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+[section Binding member functions]
+
+[import ../examples/bind_member_functions.cpp]
+
+Binding member functions to a function objects suitable for odeint system function is not easy, at least in C++03. The usual way of using __boost_bind does not work because of the forwarding problem. odeint provides two `do_step` method which only differ in the const specifiers of the arguments and __boost_bind binders only provide the specializations up to two argument which is not enough for odeint.
+
+But one can easily implement the according binders themself:
+
+[ode_wrapper]
+
+One can use this binder as follows
+
+[bind_member_function]
+
+[section Binding member functions in C++11]
+
+[import ../examples/bind_member_functions_cpp11.cpp]
+In C++11 one can use `std::bind` and one does not need to implement the bind themself:
+
+[bind_member_function_cpp11]
+
+[endsect]
+
+[endsect]
diff --git a/doc/details_boost_range.qbk b/doc/details_boost_range.qbk
new file mode 100644
index 0000000..172e355
--- /dev/null
+++ b/doc/details_boost_range.qbk
@@ -0,0 +1,60 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+[section Using boost::range]
+
+Most steppers in odeint also accept the state give as a range. A range is
+sequence of values modeled by a range concept. See __boost_range for an
+overview over existing concepts and examples of ranges. This means that the
+`state_type` of the stepper need not necessarily be used to call the `do_step` method.
+
+One use-case for __boost_range in odeint has been shown in __tut_chaotic_system where the state consists of two parts: one for the original system and one for the perturbations. The ranges are used to initialize (solve) only the system part where the perturbation part is not touched, that is a range consisting only of the system part is used. After that the complete state including the perturbations is solved.
+
+Another use case is a system consisting of coupled units where you want to initialize each unit separately with the ODE of the uncoupled unit. An example is a chain of coupled van-der-Pol-oscillators which are initialized uniformly from the uncoupled van-der-Pol-oscillator. Then you can use __boost_range to solve only one individual oscillator in the chain.
+
+In short, you can __boost_range to use one state within two system functions which expect states with different sizes.
+
+An example was given in the __tut_chaotic_system tutorial. Using Boost.Range usually means that your system function needs to adapt to the iterators of Boost.Range. That is, your function is called with a range and you need to get the iterators from that range. This can easily be done. You have to implement your system as a class or a struct and you have to templatize the `operator()`. Then you can use the `range_iterator`-meta function and `boost::begin` and `boost::end` to obtain the iterators of your range:
+
+``
+class sys
+{
+ template< class State , class Deriv >
+ void operator()( const State &x_ , Deriv &dxdt_ , double t ) const
+ {
+ typename boost::range_iterator< const State >::type x = boost::begin( x_ );
+ typename boost::range_iterator< Deriv >::type dxdt = boost::begin( dxdt_ );
+
+ // fill dxdt
+ }
+};
+``
+
+If your range is a random access-range you can also apply the bracket operator to the iterator to access the elements in the range:
+``
+class sys
+{
+ template< class State , class Deriv >
+ void operator()( const State &x_ , Deriv &dxdt_ , double t ) const
+ {
+ typename boost::range_iterator< const State >::type x = boost::begin( x_ );
+ typename boost::range_iterator< Deriv >::type dxdt = boost::begin( dxdt_ );
+
+ dxdt[0] = f1( x[0] , x[1] );
+ dxdt[1] = f2( x[0] , x[1] );
+ }
+};
+``
+
+The following two tables show which steppers and which algebras are compatible with __boost_range.
+[include range_table.qbk]
+
+[endsect]
diff --git a/doc/details_boost_ref.qbk b/doc/details_boost_ref.qbk
new file mode 100644
index 0000000..ccd0847
--- /dev/null
+++ b/doc/details_boost_ref.qbk
@@ -0,0 +1,35 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+[section Using boost::ref]
+
+In odeint all system functions and observers are passed by value. For example, if you call a `do_step` method of a particular stepper or the integration functions, your system and your stepper will be passed by value:
+
+[c++]
+``
+rk4.do_step( sys , x , t , dt ); // pass sys by value
+``
+
+This behavior is suitable for most systems, especially if your system does not contain any data or only a few parameters. However, in some cases you might contain some large amount of data with you system function and passing them by value is not desired since the data would be copied.
+
+In such cases you can easily use `boost::ref` (and its relative `boost::cref`)
+which passes its argument by reference (or constant reference). odeint will
+unpack the arguments and no copying at all of your system object will take place:
+
+``
+rk4.do_step( boost::ref( sys ) , x , t , dt ); // pass sys as references
+``
+
+The same mechanism can be used for the observers in the integrate functions.
+
+[tip If you are using C++11 you can also use `std::ref` and `std::cref`]
+
+[endsect]
diff --git a/doc/details_generation_functions.qbk b/doc/details_generation_functions.qbk
new file mode 100644
index 0000000..208f3bd
--- /dev/null
+++ b/doc/details_generation_functions.qbk
@@ -0,0 +1,45 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+ Copyright 2012 Sylwester Arabas
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+[section Generation functions]
+
+[import ../examples/generation_functions.cpp]
+
+In the __tutorial we have learned how we can use the generation functions `make_controlled` and `make_dense_output` to create controlled and dense output stepper from a simple stepper or an error stepper. The syntax of these two functions is very simple:
+
+[generation_functions_syntax_auto]
+
+The first two parameters are the absolute and the relative error tolerances and the third parameter is the stepper. Additionally, a second version exists where additionally a maximal step size is supplied which ensures the the step size is not increased above this value.
+ In C++03 you can infer the type from the `result_of` mechanism:
+
+[generation_functions_syntax_result_of]
+
+To use your own steppers with the `make_controlled` or `make_dense_output` you need to specialize two class templates. Suppose your steppers are called `custom_stepper`, `custom_controller` and `custom_dense_output`. Then, the first class you need to specialize is `boost::numeric::get_controller`, a meta function returning the type of the controller:
+
+[generation_functions_get_controller]
+
+The second one is a factory class `boost::numeric::odeint::controller_factory` which constructs the controller from the tolerances and the stepper. In our dummy implementation this class is
+
+[generation_functions_controller_factory]
+
+This is all to use the `make_controlled` mechanism. Now you can use your controller via
+
+[generation_functions_example_custom_controller]
+
+For the dense_output_stepper everything works similar. Here you have to specialize `boost::numeric::odeint::get_dense_output` and `boost::numeric::odeint::dense_output_factory`. These two classes have the same syntax as their relatives `get_controller` and `controller_factory`.
+
+All controllers and dense-output steppers in odeint can be used with these mechanisms. In the table below you will find, which steppers is constructed from `make_controlled` or `make_dense_output` if applied on a stepper from odeint:
+
+[include make_controlled_table.qbk]
+[include make_dense_output_table.qbk]
+
+[endsect]
diff --git a/doc/details_integrate_functions.qbk b/doc/details_integrate_functions.qbk
new file mode 100644
index 0000000..47af7ac
--- /dev/null
+++ b/doc/details_integrate_functions.qbk
@@ -0,0 +1,147 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+[def _max_step_checker_ [classref boost::numeric::odeint::max_step_checker `max_step_checker`]]
+
+[section Integrate functions]
+
+Integrate functions perform the time evolution of a given ODE from some
+starting time ['t[sub 0]] to a given end time ['t[sub 1]] and starting at state ['x[sub 0]] by subsequent calls of a given stepper's `do_step` function.
+Additionally, the user can provide an __observer to analyze the state during time evolution, and
+a _max_step_checker_ to throw an exception if too many steps are taken between observer calls (i.e. too
+small step size).
+There are five different integrate functions which have different strategies on when to call the observer function during integration.
+All of the integrate functions except `integrate_n_steps` can be called with any stepper following one of the stepper concepts: __stepper , __error_stepper , __controlled_stepper , __dense_output_stepper.
+Depending on the abilities of the stepper, the integrate functions make use of step-size control or dense output.
+
+[heading Equidistant observer calls]
+
+If observer calls at equidistant time intervals /dt/ are needed, the
+`integrate_const` or `integrate_n_steps` function should be used.
+We start with explaining `integrate_const`:
+
+`integrate_const( stepper , system , x0 , t0 , t1 , dt )`
+
+`integrate_const( stepper , system , x0 , t0 , t1 , dt , observer )`
+
+`integrate_const( stepper , system , x0 , t0 , t1 , dt , observer , max_step_checker )`
+
+These integrate the ODE given by `system` with subsequent steps from `stepper`.
+Integration start at `t0` and `x0` and ends at some ['t' = t[sub 0] + n dt] with /n/ such that ['t[sub 1] - dt < t' <= t[sub 1]].
+`x0` is changed to the approximative solution ['x(t')] at the end of integration.
+If provided, the `observer` is invoked at times ['t[sub 0]], ['t[sub 0] + dt], ['t[sub 0] + 2dt], ... ,['t'].
+If provided, the `max_step_checker` counts the number of steps between observer calls and throws a
+`no_progress_error` this exceeds some limit (default: 500).
+`integrate_const` returns the number of steps performed during the integration.
+Note that if you are using a simple __stepper or __error_stepper and want to make exactly `n` steps you should prefer the `integrate_n_steps` function below.
+
+* If `stepper` is a __stepper or __error_stepper then `dt` is also the step size used for integration and the observer is called just after every step.
+* If `stepper` is a __controlled_stepper then `dt` is the initial step size.
+The actual step size will change due to error control during time evolution.
+However, if an observer is provided the step size will be adjusted such that the algorithm always calculates /x(t)/ at ['t = t[sub 0] + n dt] and calls the observer at that point.
+Note that the use of __controlled_stepper is reasonable here only if `dt` is considerably larger than typical step sizes used by the stepper.
+* If `stepper` is a __dense_output_stepper then `dt` is the initial step size.
+The actual step size will be adjusted during integration due to error control.
+If an observer is provided dense output is used to calculate /x(t)/ at ['t = t[sub 0] + n dt].
+
+[heading Integrate a given number of steps]
+
+This function is very similar to `integrate_const` above. The only difference
+is that it does not take the end time as parameter, but rather the number of
+steps. The integration is then performed until the time `t0+n*dt`.
+
+`integrate_n_steps( stepper , system , x0 , t0 , dt , n )`
+
+`integrate_n_steps( stepper , system , x0 , t0 , dt , n , observer )`
+
+`integrate_n_steps( stepper , system , x0 , t0 , dt , n , observer , max_step_checker )`
+
+Integrates the ODE given by `system` with subsequent steps from `stepper` starting at ['x[sub 0]] and ['t[sub 0]].
+If provided, `observer` is called after every step and at the beginning with
+`t0`, similar as above.
+Again, providing a `max_step_checker` will throw a `no_progress_error` if too many steps are performed
+between observer calls.
+The approximate result for ['x( t[sub 0] + n dt )] is stored in `x0`.
+This function returns the end time `t0 + n*dt`.
+
+
+[heading Observer calls at each step]
+
+If the observer should be called at each time step then the `integrate_adaptive` function should be used.
+Note that in the case of __controlled_stepper or __dense_output_stepper this leads to non-equidistant observer calls as the step size changes.
+
+`integrate_adaptive( stepper , system , x0 , t0 , t1 , dt )`
+
+`integrate_adaptive( stepper , system , x0 , t0 , t1 , dt , observer )`
+
+Integrates the ODE given by `system` with subsequent steps from `stepper`.
+Integration start at `t0` and `x0` and ends at ['t[sub 1]].
+`x0` is changed to the approximative solution ['x(t[sub 1])] at the end of integration.
+If provided, the `observer` is called after each step (and before the first step at `t0`).
+`integrate_adaptive` returns the number of steps performed during the integration.
+
+[note `integrate_adaptive` by design performs an observer call after each time step. Hence
+there is no need for a _max_step_checker_ as only exactly one step is ever performed between
+observer calls.
+]
+
+* If `stepper` is a __stepper or __error_stepper then `dt` is the step size used for integration and `integrate_adaptive` behaves like `integrate_const` except that for the last step the step size is reduced to ensure we end exactly at `t1`.
+If provided, the observer is called at each step.
+* If `stepper` is a __controlled_stepper then `dt` is the initial step size.
+The actual step size is changed according to error control of the stepper.
+For the last step, the step size will be reduced to ensure we end exactly at `t1`.
+If provided, the observer is called after each time step (and before the first step at `t0`).
+* If stepper is a __dense_output_stepper then `dt` is the initial step size and `integrate_adaptive` behaves just like for __controlled_stepper above. No dense output is used.
+
+[heading Observer calls at given time points]
+
+If the observer should be called at some user given time points the `integrate_times` function should be used.
+The times for observer calls are provided as a sequence of time values.
+The sequence is either defined via two iterators pointing to begin and end of the sequence or in terms of a __boost_range object.
+
+`integrate_times( stepper , system , x0 , times_start , times_end , dt , observer )`
+
+`integrate_times( stepper , system , x0 , time_range , dt , observer )`
+
+Integrates the ODE given by `system` with subsequent steps from `stepper`.
+Integration starts at `*times_start` and ends exactly at `*(times_end-1)`.
+`x0` contains the approximate solution at the end point of integration.
+This function requires an observer which is invoked at the subsequent times `*times_start++` until `times_start == times_end`.
+If called with a __boost_range `time_range` the function behaves the same with `times_start = boost::begin( time_range )` and `times_end = boost::end( time_range )`.
+Additionally, a _max_step_checker_ can be provided, e.g.:
+
+`integrate_times( stepper , system , x0 , times_start , times_end , dt , observer , max_step_checker)`
+
+As above, this will throw a `no_progress_error` if too many steps are performed between observer calls.
+
+`integrate_times` returns the number of steps performed during the integration.
+
+* If `stepper` is a __stepper or __error_stepper `dt` is the step size used for integration.
+However, whenever a time point from the sequence is approached the step size `dt` will be reduced to obtain the state /x(t)/ exactly at the time point.
+* If `stepper` is a __controlled_stepper then `dt` is the initial step size.
+The actual step size is adjusted during integration according to error control.
+However, if a time point from the sequence is approached the step size is reduced to obtain the state /x(t)/ exactly at the time point.
+* If `stepper` is a __dense_output_stepper then `dt` is the initial step size.
+The actual step size is adjusted during integration according to error control.
+Dense output is used to obtain the states /x(t)/ at the time points from the sequence.
+
+[heading Convenience integrate function]
+
+Additionally to the sophisticated integrate function above odeint also provides a simple `integrate` routine which uses a dense output stepper based on `runge_kutta_dopri5` with standard error bounds ['10[super -6]] for the steps.
+
+`integrate( system , x0 , t0 , t1 , dt )`
+
+`integrate( system , x0 , t0 , t1 , dt , observer )`
+
+This function behaves exactly like `integrate_adaptive` above but no stepper has to be provided.
+It also returns the number of steps performed during the integration.
+
+[endsect]
diff --git a/doc/details_iterators.qbk b/doc/details_iterators.qbk
new file mode 100644
index 0000000..a4b2fa9
--- /dev/null
+++ b/doc/details_iterators.qbk
@@ -0,0 +1,195 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2012-2013 Karsten Ahnert
+ Copyright 2012-2013 Mario Mulansky
+ Copyright 2012 Sylwester Arabas
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+[section Iterators and Ranges]
+
+[section Examples]
+
+odeint supports iterators that iterate along an approximate solution of an ordinary differential equation. Iterators offer you an alternative to the integrate functions. Furthermore, many of the standard algorithms in the C++ standard library and Boost.Range can be used with the odeint's iterators.
+
+[import ../examples/const_step_iterator.cpp]
+
+Several iterator types are provided, in consistence with the
+__integrate_functions. Hence there are `const_step_iterator`,
+`adaptive_step_iterator`, `n_step_iterator` and `times_iterator` -- each of
+them in two versions: either with only the `state` or with a
+`std::pair<state,time>` as value type. They are all single pass iterators. In
+the following, we show a few examples of how to use those iterators together
+with std algorithms.
+
+[const_step_iterator_accumulate]
+
+In this example all x-values of the solution are accumulated. Note, how
+dereferencing the iterator gives the current state `x` of the ODE (the second
+argument of the accumulate lambda). The iterator
+itself does not occur directly in this example but it is generated by the
+factory functions `make_const_step_iterator_begin` and
+`make_const_step_iterator_end`. odeint also supports Boost.Range, that allows
+to write the above example in a more compact form with the factory function
+`make_const_step_range`, but now using `boost::accumulate` from __bost_range:
+
+[const_step_iterator_accumulate_range]
+
+The second iterator type is also a iterator with const step size. But the value type of this iterator consists here of a pair of the time and the state of the solution of the ODE. An example is
+
+[const_step_time_iterator_accumulate_range]
+
+The factory functions are now `make_const_step_time_iterator_begin`,
+`make_const_step_time_iterator_end` and `make_const_step_time_range`.
+Note, how the lambda now expects a `std::pair` as this is the value type of
+the `const_step_time_iterator`'s.
+
+
+[import ../examples/adaptive_iterator.cpp]
+
+Next, we discuss the adaptive iterators which are completely
+analogous to the const step iterators, but are based on adaptive stepper
+routines and thus adjust the step size during the iteration. Examples are
+
+[adaptive_iterator_accumulate_range]
+
+[adaptive_time_iterator_accumulate_range]
+
+[note 'adaptive_iterator` and `adaptive_time_iterator' can only be used with
+__controlled_stepper or __dense_output_stepper.]
+
+In general one can say that iterating over a range of a `const_step_iterator`
+behaves like an `integrate_const` function call, and similarly for
+`adaptive_iterator` and `integrate_adaptive`, `n_step_iterator` and
+`integrate_n_steps`, and finally `times_iterator` and `integrate_times`.
+
+Below we list the most important properties of the exisiting iterators:
+
+[endsect]
+
+[section const_step_iterator]
+
+* Definition: `const_step_iterator< Stepper , System , State >`
+* `value_type` is `State`
+* `reference_type` is `State const&`
+* Factory functions
+ * `make_const_step_iterator_begin( stepper , system , state , t_start , t_end , dt )`
+ * `make_const_step_iterator_end( stepper , system , state )`
+ * `make_const_step_range( stepper , system , state , t_start , t_end , dt )`
+* This stepper works with all steppers fulfilling the Stepper concept or the DenseOutputStepper concept.
+* The value of `state` is the current state of the ODE during the iteration.
+
+[endsect]
+
+[section const_step_time_iterator]
+
+* Definition: `const_step_time_iterator< Stepper , System , State >`
+* `value_type` is `std::pair< State , Stepper::time_type >`
+* `reference_type` is `std::pair< State const& , Stepper::time_type > const&`
+* Factory functions
+ * `make_const_step_time_iterator_begin( stepper , system , state , t_start , t_end , dt )`
+ * `make_const_step_time_iterator_end( stepper , system , state )`
+ * `make_const_step_time_range( stepper , system , state , t_start , t_end , dt )`
+* This stepper works with all steppers fulfilling the Stepper concept or the DenseOutputStepper concept.
+* This stepper updates the value of `state`. The value of `state` is the current state of the ODE during the iteration.
+
+
+[endsect]
+
+
+[section adaptive_step_iterator]
+
+* Definition: `adaptive_iterator< Stepper , System , State >`
+* `value_type` is `State`
+* `reference_type` is `State const&`
+* Factory functions
+ * `make_adaptive_iterator_begin( stepper , system , state , t_start , t_end , dt )`
+ * `make_adaptive_iterator_end( stepper , system , state )`
+ * `make_adaptive_range( stepper , system , state , t_start , t_end , dt )`
+* This stepper works with all steppers fulfilling the ControlledStepper concept or the DenseOutputStepper concept.
+* For steppers fulfilling the ControlledStepper concept `state` is modified according to the current state of the ODE. For DenseOutputStepper the state is not modified due to performance optimizations, but the steppers itself.
+
+
+[endsect]
+
+[section adaptive_step_time_iterator]
+
+* Definition: `adaptive_iterator< Stepper , System , State >`
+* `value_type` is `std::pair< State , Stepper::time_type >`
+* `reference_type` is `std::pair< State const& , Stepper::time_type > const&`
+* Factory functions
+ * `make_adaptive_time_iterator_begin( stepper , system , state , t_start , t_end , dt )`
+ * `make_adaptive_time_iterator_end( stepper , system , state )`
+ * `make_adaptive_time_range( stepper , system , state , t_start , t_end , dt )`
+* This stepper works with all steppers fulfilling the ControlledStepper concept or the DenseOutputStepper concept.
+* For steppers fulfilling the ControlledStepper concept `state` is modified according to the current state of the ODE. For DenseOutputStepper the state is not modified due to performance optimizations, but the stepper itself.
+
+
+[endsect]
+
+
+[section n_step_iterator]
+
+* Definition: `n_step_iterator< Stepper , System , State >`
+* `value_type` is `State`
+* `reference_type` is `State const&`
+* Factory functions
+ * `make_n_step_iterator_begin( stepper , system , state , t_start , dt , num_of_steps )`
+ * `make_n_step_iterator_end( stepper , system , state )`
+ * `make_n_step_range( stepper , system , state , t_start , dt , num_of_steps )`
+* This stepper works with all steppers fulfilling the Stepper concept or the DenseOutputStepper concept.
+* The value of `state` is the current state of the ODE during the iteration.
+
+[endsect]
+
+[section n_step_time_iterator]
+
+* Definition: `n_step_time_iterator< Stepper , System , State >`
+* `value_type` is `std::pair< State , Stepper::time_type >`
+* `reference_type` is `std::pair< State const& , Stepper::time_type > const&`
+* Factory functions
+ * `make_n_step_time_iterator_begin( stepper , system , state , t_start , dt , num_of_steps )`
+ * `make_n_step_time_iterator_end( stepper , system , state )`
+ * `make_n_step_time_range( stepper , system , state , t_start , dt , num_of_steps )`
+* This stepper works with all steppers fulfilling the Stepper concept or the DenseOutputStepper concept.
+* This stepper updates the value of `state`. The value of `state` is the current state of the ODE during the iteration.
+
+
+[endsect]
+
+
+[section times_iterator]
+
+* Definition: `times_iterator< Stepper , System , State , TimeIterator >`
+* `value_type` is `State`
+* `reference_type` is `State const&`
+* Factory functions
+ * `make_times_iterator_begin( stepper , system , state , t_start , t_end , dt )`
+ * `make_times_iterator_end( stepper , system , state )`
+ * `make_times_range( stepper , system , state , t_start , t_end , dt )`
+* This stepper works with all steppers fulfilling the Stepper concept, the ControlledStepper concept or the DenseOutputStepper concept.
+* The value of `state` is the current state of the ODE during the iteration.
+
+[endsect]
+
+[section times_time_iterator]
+
+* Definition: `times_time_iterator< Stepper , System , State , TimeIterator>`
+* `value_type` is `std::pair< State , Stepper::time_type >`
+* `reference_type` is `std::pair< State const& , Stepper::time_type > const&`
+* Factory functions
+ * `make_times_time_iterator_begin( stepper , system , state , t_start , t_end , dt )`
+ * `make_times_time_step_iterator_end( stepper , system , state )`
+ * `make_times_time_range( stepper , system , state , t_start , t_end , dt )`
+* This stepper works with all steppers fulfilling the Stepper concept, the ControlledStepper concept or the DenseOutputStepper concept.
+* This stepper updates the value of `state`. The value of `state` is the current state of the ODE during the iteration.
+
+[endsect]
+
+
+[endsect]
diff --git a/doc/details_state_types_algebras_operations.qbk b/doc/details_state_types_algebras_operations.qbk
new file mode 100644
index 0000000..274306b
--- /dev/null
+++ b/doc/details_state_types_algebras_operations.qbk
@@ -0,0 +1,482 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2013 Mario Mulansky
+ Copyright 2012 Sylwester Arabas
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+[section State types, algebras and operations]
+
+In odeint the stepper algorithms are implemented independently of the
+underlying fundamental mathematical operations.
+This is realized by giving the user full control over the state type and the
+mathematical operations for this state type.
+Technically, this is done by introducing three concepts: StateType, Algebra,
+Operations.
+Most of the steppers in odeint expect three class types fulfilling these
+concepts as template parameters.
+Note that these concepts are not fully independent of each other but rather a
+valid combination must be provided in order to make the steppers work.
+In the following we will give some examples on reasonable
+state_type-algebra-operations combinations.
+For the most common state types, like `vector<double>` or `array<double,N>`
+the default values range_algebra and default_operations are perfectly fine and
+odeint can be used as is without worrying about algebra/operations at all.
+
+[important state_type, algebra and operations are not independent, a valid
+combination must be provided to make odeint work properly]
+
+Moreover, as odeint handles the memory required for intermediate temporary
+objects itself, it also needs knowledge about how to create state_type objects
+and maybe how to allocate memory (resizing).
+All in all, the following things have to be taken care of when odeint is used
+with non-standard state types:
+
+* construction/destruction
+* resizing (if possible/required)
+* algebraic operations
+
+Again, odeint already provides basic interfaces for most of the usual state
+types.
+So if you use a `std::vector`, or a `boost::array` as state type no additional
+work is required, they just work out of the box.
+
+[section Construction/Resizing]
+
+We distinguish between two basic state types: fixed sized and dynamically
+sized.
+For fixed size state types the default constructor `state_type()` already
+allocates the required memory, prominent example is `boost::array<T,N>`.
+Dynamically sized types have to be resized to make sure enough memory is
+allocated, the standard constructor does not take care of the resizing.
+Examples for this are the STL containers like `vector<double>`.
+
+The most easy way of getting your own state type to work with odeint is to use
+a fixed size state, base calculations on the range_algebra and provide the
+following functionality:
+[table
+ [[Name] [Expression] [Type] [Semantics]]
+ [[Construct State] [`State x()`] [`void`] [Creates an instance of `State`
+ and allocates memory.] ]
+ [[Begin of the sequence] [boost::begin(x)] [Iterator] [Returns an iterator
+ pointing to the begin of the sequence]]
+ [[End of the sequence] [boost::end(x)] [Iterator] [Returns an iterator
+ pointing to the end of the sequence]]
+]
+
+[warning If your state type does not allocate memory by default construction,
+you [*must define it as resizeable] and provide resize functionality (see
+below). Otherwise segmentation faults will occur.]
+
+So fixed sized arrays supported by __boost_range immediately work with odeint.
+For dynamically sized arrays one has to additionally supply the resize
+functionality.
+First, the state has to be tagged as resizeable by specializing the struct
+`is_resizeable` which consists of one typedef and one bool value:
+[table
+ [[Name] [Expression] [Type] [Semantics]]
+ [[Resizability] [`is_resizeable<State>::type`]
+ [`boost::true_type` or `boost::false_type`]
+ [Determines resizeability of the state type, returns `boost::true_type` if
+ the state is resizeable.]]
+ [[Resizability] [`is_resizeable<State>::value`]
+ [`bool`]
+ [Same as above, but with `bool` value.]]
+]
+
+Defining `type` to be `true_type` and `value` as `true` tells odeint that your
+state is resizeable.
+By default, odeint now expects the support of `boost::size(x)` and a
+`x.resize( boost::size(y) )` member function for resizing:
+[table
+ [[Name] [Expression] [Type] [Semantics]]
+ [[Get size] [`boost::size( x )`]
+ [`size_type`] [Returns the current size of x.]]
+ [[Resize] [`x.resize( boost::size( y ) )`]
+ [`void`] [Resizes x to have the same size as y.]]
+]
+
+[section Using the container interface]
+[import ../examples/my_vector.cpp]
+
+As a first example we take the most simple case and implement our own vector
+`my_vector` which will provide a container interface.
+This makes __boost_range working out-of-box.
+We add a little functionality to our vector which makes it allocate some
+default capacity by construction.
+This is helpful when using resizing as then a resize can be assured to not
+require a new allocation.
+
+[my_vector]
+
+
+The only thing that has to be done other than defining is thus declaring
+my_vector as resizeable:
+
+[my_vector_resizeable]
+
+If we wouldn't specialize the `is_resizeable` template, the code would still
+compile but odeint would not adjust the size of temporary internal instances
+of my_vector and hence try to fill zero-sized vectors resulting in
+segmentation faults!
+The full example can be found in [github_link examples/my_vector.cpp my_vector.cpp]
+
+[endsect]
+
+[section std::list]
+
+If your state type does work with __boost_range, but handles resizing
+differently you are required to specialize two implementations used by odeint
+to check a state's size and to resize:
+[table
+ [[Name] [Expression] [Type] [Semantics]]
+ [[Check size] [`same_size_impl<State,State>::same_size(x , y)`]
+ [`bool`] [Returns true if the size of x equals the size of y.]]
+ [[Resize] [`resize_impl<State,State>::resize(x , y)`]
+ [`void`] [Resizes x to have the same size as y.]]
+]
+
+As an example we will use a `std::list` as state type in odeint.
+Because `std::list` is not supported by `boost::size` we have to replace the
+same_size and resize implementation to get list to work with odeint.
+The following code shows the required template specializations:
+
+[import ../examples/list_lattice.cpp]
+
+[list_bindings]
+
+With these definitions odeint knows how to resize `std::list`s and so they can
+be used as state types.
+A complete example can be found in [github_link examples/list_lattice.cpp list_lattice.cpp].
+
+[endsect]
+
+[endsect]
+
+[section Algebras and Operations]
+
+To provide maximum flexibility odeint is implemented in a highly modularized
+way. This means it is possible to change the underlying mathematical
+operations without touching the integration algorithms.
+The fundamental mathematical operations are those of a vector space, that is
+addition of `state_types` and multiplication of `state_type`s with a scalar
+(`time_type`). In odeint this is realized in two concepts: _Algebra_ and
+_Operations_.
+The standard way how this works is by the range algebra which provides
+functions that apply a specific operation to each of the individual elements
+of a container based on the __boost_range library.
+If your state type is not supported by __boost_range there are several
+possibilities to tell odeint how to do algebraic operations:
+
+* Implement `boost::begin` and `boost::end` for your state type so it works
+with __boost_range.
+* Implement vector-vector addition operator `+` and scalar-vector
+multiplication operator `*` and use the non-standard `vector_space_algebra`.
+* Implement your own algebra that implements the required functions.
+
+[section GSL Vector]
+
+In the following example we will try to use the `gsl_vector` type from __gsl (GNU
+Scientific Library) as state type in odeint.
+We will realize this by implementing a wrapper around the gsl_vector that
+takes care of construction/destruction.
+Also, __boost_range is extended such that it works with `gsl_vector`s as well
+which required also the implementation of a new `gsl_iterator`.
+
+[note odeint already includes all the code presented here, see [github_link
+boost/numeric/odeint/external/gsl/gsl_wrapper.hpp gsl_wrapper.hpp], so `gsl_vector`s
+can be used straight out-of-box.
+The following description is just for educational purpose.]
+
+The GSL is a C library, so `gsl_vector` has neither constructor, nor
+destructor or any `begin` or `end` function, no iterators at all.
+So to make it work with odeint plenty of things have to be implemented.
+Note that all of the work shown here is already included in odeint, so using
+`gsl_vector`s in odeint doesn't require any further adjustments.
+We present it here just as an educational example.
+We start with defining appropriate constructors and destructors.
+This is done by specializing the `state_wrapper` for `gsl_vector`.
+State wrappers are used by the steppers internally to create and manage
+temporary instances of state types:
+
+``
+template<>
+struct state_wrapper< gsl_vector* >
+{
+ typedef double value_type;
+ typedef gsl_vector* state_type;
+ typedef state_wrapper< gsl_vector* > state_wrapper_type;
+
+ state_type m_v;
+
+ state_wrapper( )
+ {
+ m_v = gsl_vector_alloc( 1 );
+ }
+
+ state_wrapper( const state_wrapper_type &x )
+ {
+ resize( m_v , x.m_v );
+ gsl_vector_memcpy( m_v , x.m_v );
+ }
+
+
+ ~state_wrapper()
+ {
+ gsl_vector_free( m_v );
+ }
+
+};
+``
+
+This `state_wrapper` specialization tells odeint how gsl_vectors are created,
+copied and destroyed.
+Next we need resizing, this is required because gsl_vectors are dynamically
+sized objects:
+``
+template<>
+struct is_resizeable< gsl_vector* >
+{
+ typedef boost::true_type type;
+ const static bool value = type::value;
+};
+
+template <>
+struct same_size_impl< gsl_vector* , gsl_vector* >
+{
+ static bool same_size( const gsl_vector* x , const gsl_vector* y )
+ {
+ return x->size == y->size;
+ }
+};
+
+template <>
+struct resize_impl< gsl_vector* , gsl_vector* >
+{
+ static void resize( gsl_vector* x , const gsl_vector* y )
+ {
+ gsl_vector_free( x );
+ x = gsl_vector_alloc( y->size );
+ }
+};
+``
+
+Up to now, we defined creation/destruction and resizing, but gsl_vectors also
+don't support iterators, so we first implement a gsl iterator:
+
+``
+/*
+ * defines an iterator for gsl_vector
+ */
+class gsl_vector_iterator
+ : public boost::iterator_facade< gsl_vector_iterator , double ,
+ boost::random_access_traversal_tag >
+{
+public :
+
+ gsl_vector_iterator( void ): m_p(0) , m_stride( 0 ) { }
+ explicit gsl_vector_iterator( gsl_vector *p ) : m_p( p->data ) , m_stride( p->stride ) { }
+ friend gsl_vector_iterator end_iterator( gsl_vector * );
+
+private :
+
+ friend class boost::iterator_core_access;
+ friend class const_gsl_vector_iterator;
+
+ void increment( void ) { m_p += m_stride; }
+ void decrement( void ) { m_p -= m_stride; }
+ void advance( ptrdiff_t n ) { m_p += n*m_stride; }
+ bool equal( const gsl_vector_iterator &other ) const { return this->m_p == other.m_p; }
+ bool equal( const const_gsl_vector_iterator &other ) const;
+ double& dereference( void ) const { return *m_p; }
+
+ double *m_p;
+ size_t m_stride;
+};
+``
+A similar class exists for the `const` version of the iterator.
+Then we have a function returning the end iterator (similarly for `const` again):
+``
+gsl_vector_iterator end_iterator( gsl_vector *x )
+{
+ gsl_vector_iterator iter( x );
+ iter.m_p += iter.m_stride * x->size;
+ return iter;
+}
+``
+
+Finally, the bindings for __boost_range are added:
+``
+// template<>
+inline gsl_vector_iterator range_begin( gsl_vector *x )
+{
+ return gsl_vector_iterator( x );
+}
+
+// template<>
+inline gsl_vector_iterator range_end( gsl_vector *x )
+{
+ return end_iterator( x );
+}
+``
+Again with similar definitions for the `const` versions.
+This eventually makes odeint work with gsl vectors as state types.
+The full code for these bindings is found in [github_link
+boost/numeric/odeint/external/gsl/gsl_wrapper.hpp gsl_wrapper.hpp].
+It might look rather complicated but keep in mind that gsl is a pre-compiled C
+library.
+[endsect]
+
+
+[section Vector Space Algebra]
+
+As seen above, the standard way of performing algebraic operations on
+container-like state types in odeint is to iterate through the elements of the
+container and perform the operations element-wise on the underlying value type.
+This is realized by means of the `range_algebra` that uses __boost_range for
+obtaining iterators of the state types.
+However, there are other ways to implement the algebraic operations on
+containers, one of which is defining the addition/multiplication operators for
+the containers directly and then using the `vector_space_algebra`.
+If you use this algebra, the following operators have to be defined for the
+state_type:
+
+[table
+ [[Name] [Expression] [Type] [Semantics]]
+ [[Addition] [`x + y`] [`state_type`] [Calculates the vector sum 'x+y'.]]
+ [[Assign addition] [`x += y`] [`state_type`] [Performs x+y in place.]]
+ [[Scalar multiplication] [`a * x `] [`state_type`] [Performs multiplication of vector x with scalar a.]]
+ [[Assign scalar multiplication] [`x *= a`] [`state_type`] [Performs in-place multiplication of vector x with scalar a.]]
+]
+
+Defining these operators makes your state type work with any basic Runge-Kutta
+stepper.
+However, if you want to use step-size control, some more functionality is
+required.
+Specifically, operations like
+[' max[sub i]( |err[sub i]| / (alpha * |s[sub i]|) )]
+have to be performed.
+['err] and ['s] are state_types, alpha is a scalar.
+As you can see, we need element wise absolute value and division as well as an
+reduce operation to get the maximum value.
+So for controlled steppers the following things have to be implemented:
+
+[table
+ [[Name] [Expression] [Type] [Semantics]]
+ [[Division] [`x / y`] [`state_type`] [Calculates the element-wise division 'x/y']]
+ [[Absolute value] [`abs( x )`] [`state_type`] [Element wise absolute value]]
+ [[Reduce] [`vector_space_reduce_impl< state_type >::reduce( state , operation , init )`] [`value_type`]
+ [Performs the `operation` for subsequently each element of `state` and returns the aggregate value.
+ E.g.
+
+`init = operator( init , state[0] );`
+
+`init = operator( init , state[1] )`
+
+`...`
+ ]]
+]
+
+[endsect]
+
+[/
+[section Boost.Ublas]
+As an example for the employment of the `vector_space_algebra` we will adopt
+`ublas::vector` from __ublas to work as a state type in odeint.
+This is particularly easy because `ublas::vector` supports vector-vector
+addition and scalar-vector multiplication described above as well as `boost::size`.
+It also has a resize member function so all that has to be done in this case
+is to declare resizability:
+
+[import ../examples/ublas/lorenz_ublas.cpp]
+
+[ublas_resizeable]
+
+Now ublas::vector can be used as state type for simple Runge-Kutta steppers
+in odeint by specifying the `vector_space_algebra` as algebra in the template
+parameter list of the stepper.
+The following code shows the corresponding definitions:
+
+[ublas_main]
+
+Note again, that we haven't supported the requirements for controlled steppers,
+but only for simple Runge-Kutta methods.
+You can find the full example in [github_link
+examples/ublas/lorenz_ublas.cpp lorenz_ublas.cpp].
+
+[endsect]
+/]
+
+[section Point type]
+
+[import ../examples/lorenz_point.cpp]
+
+Here we show how to implement the required operators on a state type.
+As example we define a new class `point3D` representing a three-dimensional
+vector with components x,y,z and define addition and scalar multiplication
+operators for it.
+We use __boost_operators to reduce the amount of code to be written.
+The class for the point type looks as follows:
+
+[point3D]
+
+By deriving from __boost_operators classes we don't have to define outer class
+operators like `operator+( point3D , point3D )` because that is taken care of
+by the operators library.
+Note that for simple Runge-Kutta schemes (like `runge_kutta4`) only the `+`
+and `*` operators are required.
+If, however, a controlled stepper is used one also needs to specify the
+division operator `/` because calculation of the error term involves an
+element wise division of the state types.
+Additionally, controlled steppers require an `abs` function calculating the
+element-wise absolute value for the state type:
+
+[point3D_abs_div]
+
+Finally, we have to provide a specialization to calculate the infintity norm of a state:
+
+[point3D_norm]
+
+Again, note that the two last steps were only required if you want to use
+controlled steppers.
+For simple steppers definition of the simple `+=` and `*=` operators are
+sufficient.
+Having defined such a point type, we can easily perform the integration on a Lorenz
+system by explicitely configuring the `vector_space_algebra` in the stepper's
+template argument list:
+
+[point3D_main]
+
+The whole example can be found in [github_link
+examples/lorenz_point.cpp lorenz_point.cpp]
+
+[note For the most `state_types`, odeint is able to automatically determine
+the correct algebra and operations. But if you want to use your own `state_type`, as in this
+example with `point3D`, you have to manually configure the right
+algebra/operations, unless your `state_type` works with the default choice of
+`range_algebra` and `default_operations`.]
+
+[endsect]
+
+[endsect]
+
+gsl_vector, gsl_matrix, ublas::matrix, blitz::matrix, thrust
+
+[section Adapt your own operations]
+
+to be continued
+
+*thrust
+*gsl_complex
+*min, max, pow
+
+[endsect]
+
+
+
+[endsect]
diff --git a/doc/details_steppers.qbk b/doc/details_steppers.qbk
new file mode 100644
index 0000000..1a83f5c
--- /dev/null
+++ b/doc/details_steppers.qbk
@@ -0,0 +1,421 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+ Copyright 2012 Sylwester Arabas
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+[section Steppers]
+
+[import ../examples/stepper_details.cpp]
+
+Solving ordinary differential equation numerically is usually done iteratively, that is a given state of an ordinary differential equation is iterated forward ['x(t) -> x(t+dt) -> x(t+2dt)]. The steppers in odeint perform one single step. The most general stepper type is described by the __stepper concept. The stepper concepts of odeint are described in detail in section __concepts, here we briefly present the mathematical and numerical details of the steppers. The __stepper has two versions of the `do_step` method, one with an in-place transform of the current state and one with an out-of-place transform:
+
+`do_step( sys , inout , t , dt )`
+
+`do_step( sys , in , t , out , dt )`
+
+The first parameter is always the system function - a function describing the
+ODE. In the first version the second parameter is the step which is here
+updated in-place and the third and the fourth parameters are the time and step
+size (the time step). After a call to `do_step` the state `inout` is updated
+and now represents an approximate solution of the ODE at time ['t+dt]. In the
+second version the second argument is the state of the ODE at time ['t], the
+third argument is t, the fourth argument is the approximate solution at time
+['t+dt] which is filled by `do_step` and the fifth argument is the time step.
+Note that these functions do not change the time `t`.
+
+[* System functions]
+
+Up to now, we have nothing said about the system function. This function
+depends on the stepper. For the explicit Runge-Kutta steppers this function
+can be a simple callable object hence a simple (global) C-function or a
+functor. The parameter syntax is `sys( x , dxdt , t )` and it is assumed that
+it calculates ['dx/dt = f(x,t)].
+The function structure in most cases looks like:
+
+[system_function_structure]
+
+Other types of system functions might represent Hamiltonian systems or systems which also compute the Jacobian needed in implicit steppers. For information which stepper uses which system function see the stepper table below. It might be possible that odeint will introduce new system types in near future. Since the system function is strongly related to the stepper type, such an introduction of a new stepper might result in a new type of system function.
+
+[section Explicit steppers]
+
+A first specialization are the explicit steppers. Explicit means that the new
+state of the ode can be computed explicitly from the current state without
+solving implicit equations. Such steppers have in common that they evaluate the system at time ['t] such that the result of ['f(x,t)] can be passed to the stepper. In odeint, the explicit stepper have two additional methods
+
+`do_step( sys , inout , dxdtin , t , dt )`
+
+`do_step( sys , in , dxdtin , t , out , dt )`
+
+Here, the additional parameter is the value of the function ['f] at state ['x] and time ['t]. An example is the Runge-Kutta stepper of fourth order:
+
+[explicit_stepper_detail_example]
+
+In fact, you do not need to call these two methods. You can always use the
+simpler `do_step( sys , inout , t , dt )`, but sometimes the derivative of the
+state is needed externally to do some external computations or to perform some statistical analysis.
+
+A special class of the explicit steppers are the FSAL (first-same-as-last)
+steppers, where the last evaluation of the system function is also the first
+evaluation of the following step. For such steppers the `do_step` method are
+slightly different:
+
+`do_step( sys , inout , dxdtinout , t , dt )`
+
+`do_step( sys , in , dxdtin , out , dxdtout , t , dt )`
+
+This method takes the derivative at time `t` and also stores
+the derivative at time ['t+dt]. Calling these functions subsequently iterating
+along the solution one saves one function call by passing the result for dxdt
+into the next function call.
+However, when using FSAL steppers without supplying derivatives:
+
+`do_step( sys , inout , t , dt )`
+
+the stepper internally satisfies the FSAL property which means it remembers
+the last `dxdt` and uses it for the next step.
+An example for a FSAL stepper is the Runge-Kutta-Dopri5 stepper. The FSAL trick is sometimes also referred as the Fehlberg trick. An example how the FSAL steppers can be used is
+
+[fsal_stepper_detail_example]
+
+[caution The FSAL-steppers save the derivative at time ['t+dt] internally if
+they are called via `do_step( sys , in , out , t , dt )`. The first call of
+`do_step` will initialize `dxdt` and for all following calls it is assumed
+that the same system and the same state are used. If you use the FSAL stepper
+within the integrate functions this is taken care of automatically. See the __using_steppers section for more details or look into the table below to see which stepper have an internal state.]
+
+
+[endsect]
+
+[section Symplectic solvers]
+
+As mentioned above symplectic solvers are used for Hamiltonian systems. Symplectic solvers conserve the phase space volume exactly and if the Hamiltonian system is energy conservative they also conserve the energy approximately. A special class of symplectic systems are separable systems which can be written in the form ['dqdt/dt = f1(p)], ['dpdt/dt = f2(q)], where ['(q,p)] are the state of system. The space of ['(q,p)] is sometimes referred as the phase space and ['q] and ['p] are said the be the phase space variables. Symplectic systems in this special form occur widely in nature. For example the complete classical mechanics as written down by Newton, Lagrange and Hamilton can be formulated in this framework. The separability of the system depends on the specific choice of coordinates.
+
+Symplectic systems can be solved by odeint by means of the symplectic_euler stepper and a symplectic Runge-Kutta-Nystrom method of fourth order. These steppers assume that the system is autonomous, hence the time will not explicitly occur. Further they fulfill in principle the default Stepper concept, but they expect the system to be a pair of callable objects. The first entry of this pair calculates ['f1(p)] while the second calculates ['f2(q)]. The syntax is `sys.first(p,dqdt)` and `sys.second(q,dpdt)`, where the first and second part can be again simple C-functions of functors. An example is the harmonic oscillator:
+
+[symplectic_stepper_detail_system_function]
+
+The state of such an ODE consist now also of two parts, the part for q (also called the coordinates) and the part for p (the momenta). The full example for the harmonic oscillator is now:
+
+[symplectic_stepper_detail_example]
+
+If you like to represent the system with one class you can easily bind two public method:
+
+[symplectic_stepper_detail_system_class]
+
+[symplectic_stepper_detail_system_class_example]
+
+Many Hamiltonian system can be written as ['dq/dt=p], ['dp/dt=f(q)] which is computationally much easier than the full separable system. Very often, it is also possible to transform the original equations of motion to bring the system in this simplified form. This kind of system can be used in the symplectic solvers, by simply passing ['f(p)] to the `do_step` method, again ['f(p)] will be represented by a simple C-function or a functor. Here, the above example of the harmonic oscillator can be written as
+
+[simplified_symplectic_stepper_example]
+
+In this example the function `harm_osc_f1` is exactly the same function as in the above examples.
+
+Note, that the state of the ODE must not be constructed explicitly via `pair< vector_type , vector_type > x`. One can also use a combination of `make_pair` and `ref`. Furthermore, a convenience version of `do_step` exists which takes q and p without combining them into a pair:
+
+[symplectic_stepper_detail_ref_usage]
+
+[endsect]
+
+[section Implicit solvers]
+
+[caution This section is not up-to-date.]
+
+For some kind of systems the stability properties of the classical Runge-Kutta are not sufficient, especially if the system is said to be stiff. A stiff system possesses two or more time scales of very different order. Solvers for stiff systems are usually implicit, meaning that they solve equations like ['x(t+dt) = x(t) + dt * f(x(t+1))]. This particular scheme is the implicit Euler method. Implicit methods usually solve the system of equations by a root finding algorithm like the Newton method and therefore need to know the Jacobian of the system ['J[subl ij] = df[subl i] / dx[subl j]].
+
+For implicit solvers the system is again a pair, where the first component computes ['f(x,t)] and the second the Jacobian. The syntax is `sys.first( x , dxdt , t )` and `sys.second( x , J , t )`. For the implicit solver the `state_type` is `ublas::vector` and the Jacobian is represented by `ublas::matrix`.
+
+[important Implicit solvers only work with ublas::vector as state type. At
+the moment, no other state types are supported.]
+
+[endsect]
+
+[section Multistep methods]
+
+Another large class of solvers are multi-step method. They save a small part of the history of the solution and compute the next step with the help of this history. Since multi-step methods know a part of their history they do not need to compute the system function very often, usually it is only computed once. This makes multi-step methods preferable if a call of the system function is expensive. Examples are ODEs defined on networks, where the computation of the interaction is usually where expensive (and might be of order O(N^2)).
+
+Multi-step methods differ from the normal steppers. They save a part of their history and this part has to be explicitly calculated and initialized. In the following example an Adams-Bashforth-stepper with a history of 5 steps is instantiated and initialized;
+
+[multistep_detail_example]
+
+The initialization uses a fourth-order Runge-Kutta stepper and after the call
+of `initialize` the state of `inout` has changed to the current state, such
+that it can be immediately used by passing it to following calls of `do_step`. You can also use you own steppers to initialize the internal state of the Adams-Bashforth-Stepper:
+
+[multistep_detail_own_stepper_initialization]
+
+Many multi-step methods are also explicit steppers, hence the parameter of `do_step` method do not differ from the explicit steppers.
+
+[caution The multi-step methods have some internal variables which depend on
+the explicit solution. Hence after any external changes of your state (e.g. size) or
+system the initialize function has to be called again to adjust the internal
+state of the stepper. If you use the integrate functions this will
+be taken into account. See the __using_steppers section for more details.]
+
+
+[endsect]
+
+[section Controlled steppers]
+
+Many of the above introduced steppers possess the possibility to use adaptive step-size control. Adaptive step size integration works in principle as follows:
+
+# The error of one step is calculated. This is usually done by performing two steps with different orders. The difference between these two steps is then used as a measure for the error. Stepper which can calculate the error are __error_stepper and they form an own class with an separate concept.
+# This error is compared against some predefined error tolerances. Are the tolerance violated the step is reject and the step-size is decreases. Otherwise the step is accepted and possibly the step-size is increased.
+
+The class of controlled steppers has their own concept in odeint - the __controlled_stepper concept. They are usually constructed from the underlying error steppers. An example is the controller for the explicit Runge-Kutta steppers. The Runge-Kutta steppers enter the controller as a template argument. Additionally one can pass the Runge-Kutta stepper to the constructor, but this step is not necessary; the stepper is default-constructed if possible.
+
+Different step size controlling mechanism exist. They all have in common that
+they somehow compare predefined error tolerance against the error and that
+they might reject or accept a step. If a step is rejected the step size is
+usually decreased and the step is made again with the reduced step size. This
+procedure is repeated until the step is accepted. This algorithm is
+implemented in the integration functions.
+
+A classical way to decide whether a step is rejected or accepted is to calculate
+
+['val = || | err[subl i] | / ( __epsilon[subl abs] + __epsilon[subl rel] * ( a[subl x] | x[subl i] | + a[subl dxdt] | | dxdt[subl i] | )|| ]
+
+['__epsilon[subl abs]] and ['__epsilon[subl rel]] are the absolute and the relative error tolerances, and ['|| x ||] is a norm, typically ['||x||=(__Sigma[subl i] x[subl i][super 2])[super 1/2]] or the maximum norm. The step is rejected if ['val] is greater then 1, otherwise it is accepted. For details of the used norms and error tolerance see the table below.
+
+For the `controlled_runge_kutta` stepper the new step size is then calculated via
+
+['val > 1 : dt[subl new] = dt[subl current] max( 0.9 pow( val , -1 / ( O[subl E] - 1 ) ) , 0.2 )]
+
+['val < 0.5 : dt[subl new] = dt[subl current] min( 0.9 pow( val , -1 / O[subl S] ) , 5 )]
+
+['else : dt[subl new] = dt[subl current]]
+
+Here, ['O[subl S]] and ['O[subl E]] are the order of the stepper and the error stepper. These formulas also contain some safety factors, avoiding that the step size is reduced or increased to much. For details of the implementations of the controlled steppers in odeint see the table below.
+
+[include controlled_stepper_table.qbk]
+
+To ease to generation of the controlled stepper, generation functions exist which take the absolute and relative error tolerances and a predefined error stepper and construct from this knowledge an appropriate controlled stepper. The generation functions are explained in detail in __generation_functions.
+
+[endsect]
+
+[section Dense output steppers]
+
+A fourth class of stepper exists which are the so called dense output steppers. Dense-output steppers might take larger steps and interpolate the solution between two consecutive points. This interpolated points have usually the same order as the order of the stepper. Dense-output steppers are often composite stepper which take the underlying method as a template parameter. An example is the `dense_output_runge_kutta` stepper which takes a Runge-Kutta stepper with dense-output facilities as argument. Not all Runge-Kutta steppers provide dense-output calculation; at the moment only the Dormand-Prince 5 stepper provides dense output. An example is
+
+[dense_output_detail_example]
+
+Dense output stepper have their own concept. The main difference to usual
+steppers is that they manage the state and time internally. If you call
+`do_step`, only the ODE is passed as argument. Furthermore `do_step` return
+the last time interval: `t` and `t+dt`, hence you can interpolate the solution between these two times points. Another difference is that they must be initialized with `initialize`, otherwise the internal state of the stepper is default constructed which might produce funny errors or bugs.
+
+The construction of the dense output stepper looks a little bit nasty, since in the case of the `dense_output_runge_kutta` stepper a controlled stepper and an error stepper have to be nested. To simplify the generation of the dense output stepper generation functions exist:
+
+[dense_output_detail_generation1]
+
+This statement is also lengthy; it demonstrates how `make_dense_output` can be used with the `result_of` protocol. The parameters to `make_dense_output` are the absolute error tolerance, the relative error tolerance and the stepper. This explicitly assumes that the underlying stepper is a controlled stepper and that this stepper has an absolute and a relative error tolerance. For details about the generation functions see __generation_functions. The generation functions have been designed for easy use with the integrate functions:
+
+[dense_output_detail_generation2]
+
+[endsect]
+
+[section Using steppers]
+
+This section contains some general information about the usage of the steppers in odeint.
+
+[* Steppers are copied by value]
+
+The stepper in odeint are always copied by values. They are copied for the creation of the controlled steppers or the dense output steppers as well as in the integrate functions.
+
+[* Steppers might have a internal state]
+
+[caution Some of the features described in this section are not yet implemented]
+
+Some steppers require to store some information about the state of the ODE between two steps. Examples are the multi-step methods which store a part of the solution during the evolution of the ODE, or the FSAL steppers which store the last derivative at time ['t+dt], to be used in the next step. In both cases the steppers expect that consecutive calls of `do_step` are from the same solution and the same ODE. In this case it is absolutely necessary that you call `do_step` with the same system function and the same state, see also the examples for the FSAL steppers above.
+
+Stepper with an internal state support two additional methods: `reset` which resets the state and `initialize` which initializes the internal state. The parameters of `initialize` depend on the specific stepper. For example the Adams-Bashforth-Moulton stepper provides two initialize methods: `initialize( system , inout , t , dt )` which initializes the internal states with the help of the Runge-Kutta 4 stepper, and `initialize( stepper , system , inout , t , dt )` which initializes with the help of `stepper`. For the case of the FSAL steppers, `initialize` is `initialize( sys , in , t )` which simply calculates the r.h.s. of the ODE and assigns its value to the internal derivative.
+
+All these steppers have in common, that they initially fill their internal state by themselves. Hence you are not required to call initialize. See how this works for the Adams-Bashforth-Moulton stepper: in the example we instantiate a fourth order Adams-Bashforth-Moulton stepper, meaning that it will store 4 internal derivatives of the solution at times `(t-dt,t-2*dt,t-3*dt,t-4*dt)`.
+
+``
+adams_bashforth_moulton< 4 , state_type > stepper;
+stepper.do_step( sys , x , t , dt ); // make one step with the classical Runge-Kutta stepper and initialize the first internal state
+ // the internal array is now [x(t-dt)]
+
+stepper.do_step( sys , x , t , dt ); // make one step with the classical Runge-Kutta stepper and initialize the second internal state
+ // the internal state array is now [x(t-dt), x(t-2*dt)]
+
+stepper.do_step( sys , x , t , dt ); // make one step with the classical Runge-Kutta stepper and initialize the third internal state
+ // the internal state array is now [x(t-dt), x(t-2*dt), x(t-3*dt)]
+
+stepper.do_step( sys , x , t , dt ); // make one step with the classical Runge-Kutta stepper and initialize the fourth internal state
+ // the internal state array is now [x(t-dt), x(t-2*dt), x(t-3*dt), x(t-4*dt)]
+
+stepper.do_step( sys , x , t , dt ); // make one step with Adam-Bashforth-Moulton, the internal array of states is now rotated
+``
+
+In the stepper table at the bottom of this page one can see which stepper have an internal state and hence provide the `reset` and `initialize` methods.
+
+
+[* Stepper might be resizable]
+
+Nearly all steppers in odeint need to store some intermediate results of the
+type `state_type` or `deriv_type`. To do so odeint need some memory management
+for the internal temporaries. As this memory management is typically related
+to adjusting the size of vector-like types, it is called resizing in
+odeint. So, most steppers in odeint provide an additional template parameter
+which controls the size adjustment of the internal variables - the resizer. In
+detail odeint provides three policy classes (resizers) `always_resizer`,
+`initially_resizer`, and `never_resizer`. Furthermore, all stepper have a
+method `adjust_size` which takes a parameter representing a state type and
+which manually adjusts the size of the internal variables matching the size of
+the given instance. Before performing the actual resizing odeint always checks
+if the sizes of the state and the internal variable differ and only resizes if
+they are different.
+
+[note You only have to worry about memory allocation when using dynamically
+sized vector types. If your state type is heap allocated, like `boost::array`,
+no memory allocation is required whatsoever.]
+
+By default the resizing parameter is `initially_resizer`, meaning that the
+first call to `do_step` performs the resizing, hence memory allocation.
+If you have changed the size of your system and your state you have to
+call `adjust_size` by hand in this case. The second resizer is the
+`always_resizer` which tries to resize the internal variables at every call of
+`do_step`. Typical use cases for this kind of resizer are self expanding
+lattices like shown in the tutorial (__resizing_lattice_example) or partial differential equations with an
+adaptive grid. Here, no calls of `adjust_size` are required, the steppers manage
+everything themselves. The third class of resizer is the `never_resizer` which
+means that the internal variables are never adjusted automatically and always
+have to be adjusted by hand .
+
+There is a second mechanism which influences the resizing and which controls if a state type is at least resizeable - a meta-function `is_resizeable`. This meta-function returns a static Boolean value if any type is resizable. For example it will return `true` for `std::vector< T >` but `false` for `boost::array< T >`. By default and for unknown types `is_resizeable` returns `false`, so if you have your own type you need to specialize this meta-function. For more details on the resizing mechanism see the section __adapt_state_types.
+
+
+
+[* Which steppers should be used in which situation]
+
+odeint provides a quite large number of different steppers such that the user is left with the question of which stepper fits his needs. Our personal recommendations are:
+
+* `runge_kutta_dopri5` is maybe the best default stepper. It has step size control as well as dense-output functionality. Simple create a dense-output stepper by `make_dense_output( 1.0e-6 , 1.0e-5 , runge_kutta_dopri5< state_type >() )`.
+* `runge_kutta4` is a good stepper for constant step sizes. It is widely used and very well known. If you need to create artificial time series this stepper should be the first choice.
+* 'runge_kutta_fehlberg78' is similar to the 'runge_kutta4' with the advantage that it has higher precision. It can also be used with step size control.
+* `adams_bashforth_moulton` is very well suited for ODEs where the r.h.s. is expensive (in terms of computation time). It will calculate the system function only once during each step.
+
+[endsect]
+
+[section Stepper overview]
+
+[include stepper_table.qbk]
+
+[endsect]
+
+
+[section Custom steppers]
+
+[import ../examples/stochastic_euler.cpp]
+
+Finally, one can also write new steppers which are fully compatible with odeint. They only have to fulfill one or several of the stepper __concepts of odeint.
+
+We will illustrate how to write your own stepper with the example of the stochastic Euler method. This method is suited to solve stochastic differential equations (SDEs). A SDE has the form
+
+['dx/dt = f(x) + g(x) __xi(t)]
+
+where ['__xi] is Gaussian white noise with zero mean and a standard deviation ['__sigma(t)]. ['f(x)] is said to be the deterministic part while [' g(x) __xi] is the noisy part. In case ['g(x)] is independent of ['x] the SDE is said to have additive noise. It is not possible to solve SDE with the classical solvers for ODEs since the noisy part of the SDE has to be scaled differently then the deterministic part with respect to the time step. But there exist many solvers for SDEs. A classical and easy method is the stochastic Euler solver. It works by iterating
+
+['x(t+__Delta t) = x(t) + __Delta t f(x(t)) + __Delta t[super 1/2] g(x) __xi(t)]
+
+where __xi(t) is an independent normal distributed random variable.
+
+Now we will implement this method. We will call the stepper
+`stochastic_euler`. It models the __stepper concept. For simplicity, we fix
+the state type to be an `array< double , N >` The class definition looks like
+
+[stochastic_euler_class_definition]
+
+The types are needed in order to fulfill the stepper concept. As internal state and deriv type we use simple arrays in the stochastic Euler, they are needed for the temporaries. The stepper has the order one which is returned from the `order()` function.
+
+The system functions needs to calculate the deterministic and the stochastic part of our stochastic differential equation. So it might be suitable that the system function is a pair of functions. The first element of the pair computes the deterministic part and the second the stochastic one. Then, the second part also needs to calculate the random numbers in order to simulate the stochastic process. We can now implement the `do_step` method
+
+[stochastic_euler_do_step]
+
+This is all. It is quite simple and the stochastic Euler stepper implement here is quite general. Of course it can be enhanced, for example
+
+* use of operations and algebras as well as the resizing mechanism for maximal flexibility and portability
+* use of `boost::ref` for the system functions
+* use of `boost::range` for the state type in the `do_step` method
+* ...
+
+Now, lets look how we use the new stepper. A nice example is the Ornstein-Uhlenbeck process. It consists of a simple Brownian motion overlapped with an relaxation process. Its SDE reads
+
+['dx/dt = - x + __xi]
+
+where __xi is Gaussian white noise with standard deviation ['__sigma]. Implementing the Ornstein-Uhlenbeck process is quite simple. We need two functions or functors - one for the deterministic and one for the stochastic part:
+
+[stochastic_euler_ornstein_uhlenbeck_def]
+
+In the stochastic part we have used the Mersenne twister for the random number generation and a Gaussian white noise generator `normal_distribution` with standard deviation ['__sigma]. Now, we can use the stochastic Euler stepper with the integrate functions:
+
+[ornstein_uhlenbeck_main]
+
+Note, how we have used the `make_pair` function for the generation of the system function.
+
+[endsect]
+
+[section Custom Runge-Kutta steppers]
+
+[import ../examples/heun.cpp]
+
+odeint provides a C++ template meta-algorithm for constructing arbitrary
+Runge-Kutta schemes [footnote M. Mulansky, K. Ahnert, Template-Metaprogramming
+applied to numerical problems, [@http://arxiv.org/abs/1110.3233 arxiv:1110.3233]]. Some schemes are predefined in odeint, for
+example the classical Runge-Kutta of fourth order, or the
+Runge-Kutta-Cash-Karp 54 and the Runge-Kutta-Fehlberg 78 method.
+You can use this meta algorithm to construct you own solvers. This has the
+advantage that you can make full use of odeint's algebra and operation system.
+
+Consider for example the method of Heun, defined by the following Butcher tableau:
+
+[pre
+c1 = 0
+
+c2 = 1/3, a21 = 1/3
+
+c3 = 2/3, a31 = 0 , a32 = 2/3
+
+ b1 = 1/4, b2 = 0 , b3 = 3/4
+]
+
+Implementing this method is very easy. First you have to define the constants:
+
+[heun_define_coefficients]
+
+While this might look cumbersome, packing all
+parameters into a templatized class which is not immediately evaluated has the
+advantage that you can change the `value_type` of your stepper to any type you
+like - presumably arbitrary precision types. One could also instantiate
+the coefficients directly
+
+``
+const boost::array< double , 1 > heun_a1 = {{ 1.0 / 3.0 }};
+const boost::array< double , 2 > heun_a2 = {{ 0.0 , 2.0 / 3.0 }};
+const boost::array< double , 3 > heun_b = {{ 1.0 / 4.0 , 0.0 , 3.0 / 4.0 }};
+const boost::array< double , 3 > heun_c = {{ 0.0 , 1.0 / 3.0 , 2.0 / 3.0 }};
+``
+
+But then you are nailed down to use doubles.
+
+Next, you need to define your stepper, note that the Heun method has 3 stages
+and produces approximations of order 3:
+
+[heun_stepper_definition]
+
+That's it. Now, we have a new stepper method and we can use it, for example with the Lorenz system:
+
+[heun_example]
+
+[endsect]
+
+
+[endsect]
diff --git a/doc/examples_table.qbk b/doc/examples_table.qbk
new file mode 100644
index 0000000..e28b7cd
--- /dev/null
+++ b/doc/examples_table.qbk
@@ -0,0 +1,142 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+ Copyright 2012 Sylwester Arabas
+ Copyright 2013 Pascal Germroth
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+[table Examples Overview
+ [[File] [Brief Description]]
+
+ [[[github_link examples/bind_member_functions.cpp bind_member_functions.cpp]]
+ [This examples shows how member functions can be used as system functions in odeint.]]
+
+ [[[github_link examples/bind_member_functions.cpp bind_member_functions_cpp11.cpp]]
+ [This examples shows how member functions can be used as system functions in odeint with `std::bind` in C++11.]]
+
+ [[[github_link examples/bulirsch_stoer.cpp bulirsch_stoer.cpp]]
+ [Shows the usage of the Bulirsch-Stoer method.]]
+
+ [[[github_link examples/chaotic_system.cpp chaotic_system.cpp]]
+ [The chaotic system examples integrates the Lorenz system and calculates the Lyapunov exponents.]]
+
+ [[[github_link examples/elliptic_functions.cpp elliptic_functions.cpp]]
+ [Example calculating the elliptic functions using Bulirsch-Stoer and Runge-Kutta-Dopri5 Steppers with dense output.]]
+
+ [[[github_link examples/fpu.cpp fpu.cpp]]
+ [The Fermi-Pasta-Ulam (FPU) example shows how odeint can be used to integrate lattice systems.]]
+
+ [[[github_link examples/generation_functions.cpp generation_functions.cpp]]
+ [Shows skeletal code on how to implement own factory functions.]]
+
+ [[[github_link examples/harmonic_oscillator.cpp harmonic_oscillator.cpp]]
+ [The harmonic oscillator examples gives a brief introduction to odeint and shows the usage of the classical Runge-Kutta-solvers.]]
+
+ [[[github_link examples/harmonic_oscillator_units.cpp harmonic_oscillator_units.cpp]]
+ [This examples shows how __boost_units can be used with odeint.]]
+
+ [[[github_link examples/heun.cpp heun.cpp]]
+ [The Heun example shows how an custom Runge-Kutta stepper can be created with odeint generic Runge-Kutta method.]]
+
+ [[[github_link examples/list_lattice.cpp list_lattice.cpp]]
+ [Example of a phase lattice integration using `std::list` as state type.]]
+
+ [[[github_link examples/lorenz_point.cpp lorenz_point.cpp]]
+ [Alternative way of integrating lorenz by using a self defined point3d data type as state type.]]
+
+ [[[github_link examples/my_vector.cpp my_vector.cpp]]
+ [Simple example showing how to get odeint to work with a self-defined vector type.]]
+
+ [[[github_link examples/phase_oscillator_ensemble.cpp phase_oscillator_ensemble.cpp]]
+ [The phase oscillator ensemble example shows how globally coupled oscillators can be analyzed and how statistical measures can be computed during integration.]]
+
+ [[[github_link examples/resizing_lattice.cpp resizing_lattice.cpp]]
+ [Shows the strength of odeint's memory management by simulating a Hamiltonian system on an expanding lattice.]]
+
+ [[[github_link examples/simple1d.cpp simple1d.cpp]]
+ [Integrating a simple, one-dimensional ODE showing the usage of integrate- and generate-functions.]]
+
+ [[[github_link examples/solar_system.cpp solar_system.cpp]]
+ [The solar system example shows the usage of the symplectic solvers.]]
+
+ [[[github_link examples/stepper_details.cpp stepper_details.cpp]]
+ [Trivial example showing the usability of the several stepper classes.]]
+
+ [[[github_link examples/stiff_system.cpp stiff_system.cpp]]
+ [The stiff system example shows the usage of the stiff solvers using the Jacobian of the system function.]]
+
+ [[[github_link examples/stochastic_euler.cpp stochastic_euler.cpp]]
+ [Implementation of a custom stepper - the stochastic euler - for solving stochastic differential equations.]]
+
+ [[[github_link examples/stuart_landau.cpp stuart_landau.cpp]]
+ [The Stuart-Landau example shows how odeint can be used with complex state types.]]
+
+ [[[github_link examples/two_dimensional_phase_lattice.cpp two_dimensional_phase_lattice.cpp]]
+ [The 2D phase oscillator example shows how a two-dimensional lattice works with odeint and how matrix types can be used as state types in odeint.]]
+
+ [[[github_link examples/van_der_pol_stiff.cpp van_der_pol_stiff.cpp]]
+ [This stiff system example again shows the usage of the stiff solvers by integrating the van der Pol oscillator.]]
+
+ [[[github_link examples/gmpxx/lorenz_gmpxx.cpp gmpxx/lorenz_gmpxx.cpp]]
+ [This examples integrates the Lorenz system by means of an arbitrary precision type.]]
+
+ [[[github_link examples/mtl/gauss_packet.cpp mtl/gauss_packet.cpp]]
+ [The MTL-Gauss-packet example shows how the MTL can be easily used with odeint.]]
+
+ [[[github_link examples/mtl/implicit_euler_mtl.cpp mtl/implicit_euler_mtl.cpp]]
+ [This examples shows the usage of the MTL implicit Euler method with a sparse matrix type.]]
+
+ [[[github_link examples/thrust/phase_oscillator_ensemble.cu thrust/phase_oscillator_ensemble.cu]]
+ [The Thrust phase oscillator ensemble example shows how globally coupled oscillators can be analyzed with Thrust and CUDA, employing the power of modern graphic devices.]]
+
+ [[[github_link examples/thrust/phase_oscillator_chain.cu thrust/phase_oscillator_chain.cu]]
+ [The Thrust phase oscillator chain example shows how chains of nearest neighbor coupled oscillators can be integrated with Thrust and odeint.]]
+
+ [[[github_link examples/thrust/lorenz_parameters.cu thrust/lorenz_parameters.cu]]
+ [The Lorenz parameters examples show how ensembles of ordinary differential equations can be solved by means of Thrust to study
+ the dependence of an ODE on some parameters.]]
+
+ [[[github_link examples/thrust/relaxation.cu thrust/relaxation.cu]]
+ [Another examples for the usage of Thrust.]]
+
+ [[[github_link examples/ublas/lorenz_ublas.cpp ublas/lorenz_ublas.cpp]]
+ [This example shows how the ublas vector types can be used with odeint.]]
+
+ [[[github_link examples/vexcl/lorenz_ensemble.cpp vexcl/lorenz_ensemble.cpp]]
+ [This example shows how the VexCL - a framework for OpenCL computation - can be used with odeint.]]
+
+ [[[github_link examples/openmp/lorenz_ensemble_simple.cpp openmp/lorenz_ensemble_simple.cpp]]
+ [OpenMP Lorenz attractor parameter study with continuous data.]]
+
+ [[[github_link examples/openmp/lorenz_ensemble.cpp openmp/lorenz_ensemble.cpp]]
+ [OpenMP Lorenz attractor parameter study with split data.]]
+
+ [[[github_link examples/openmp/lorenz_ensemble.cpp openmp/lorenz_ensemble_nested.cpp]]
+ [OpenMP Lorenz attractor parameter study with nested `vector_space_algebra`.]]
+
+ [[[github_link examples/openmp/phase_chain.cpp openmp/phase_chain.cpp]]
+ [OpenMP nearest neighbour coupled phase chain with continuous state.]]
+
+ [[[github_link examples/openmp/phase_chain_omp_state.cpp openmp/phase_chain_omp_state.cpp]]
+ [OpenMP nearest neighbour coupled phase chain with split state.]]
+
+ [[[github_link examples/mpi/phase_chain.cpp mpi/phase_chain.cpp]]
+ [MPI nearest neighbour coupled phase chain.]]
+
+ [[[github_link examples/2d_lattice/spreading.cpp 2d_lattice/spreading.cpp]]
+ [This examples shows how a `vector< vector< T > >` can be used a state type for odeint and how a resizing mechanism of this state can be implemented.]]
+
+ [[[github_link examples/quadmath/black_hole.cpp quadmath/black_hole.cpp]]
+ [This examples shows how gcc libquadmath can be used with odeint. It provides a high precision floating point type which is adapted to odeint in this example.]]
+
+ [[[github_link examples/molecular_dynamics.cpp molecular_dynamics.cpp]]
+ [A very basic molecular dynamics simulation with the Velocity-Verlet method.]]
+
+]
diff --git a/doc/getting_started.qbk b/doc/getting_started.qbk
new file mode 100644
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--- /dev/null
+++ b/doc/getting_started.qbk
@@ -0,0 +1,142 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+ Copyright 2012 Sylwester Arabas
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+
+[section Getting started]
+
+[section Overview]
+
+odeint is a library for solving initial value problems (IVP) of ordinary
+differential equations. Mathematically, these problems are formulated as
+follows:
+
+['x'(t) = f(x,t)], ['x(0) = x0].
+
+['x] and ['f] can be vectors and the solution is some function ['x(t)] fulfilling both equations above. In the following we will refer to ['x'(t)] also `dxdt` which is also our notation for the derivative in the source code.
+
+Ordinary differential equations occur nearly everywhere in natural sciences. For example, the whole Newtonian mechanics are described by second order differential equations. Be sure, you will find them in every discipline. They also occur if partial differential equations (PDEs) are discretized. Then, a system of coupled ordinary differential occurs, sometimes also referred as lattices ODEs.
+
+Numerical approximations for the solution ['x(t)] are calculated iteratively. The easiest algorithm is the Euler scheme, where starting at ['x(0)] one finds ['x(dt) = x(0) + dt f(x(0),0)]. Now one can use ['x(dt)] and obtain ['x(2dt)] in a similar way and so on. The Euler method is of order 1, that means the error at each step is ['~ dt[super 2]]. This is, of course, not very satisfying, which is why the Euler method is rarely used for real life problems and serves just as illustrative example.
+
+The main focus of odeint is to provide numerical methods implemented in a way where the algorithm is completely independent on the data structure used to represent the state /x/.
+In doing so, odeint is applicable for a broad variety of situations and it can be used with many other libraries. Besides the usual case where the state is defined as a `std::vector` or a `boost::array`, we provide native support for the following libraries:
+
+* __ublas
+* __thrust, making odeint naturally running on CUDA devices
+* gsl_vector for compatibility with the many numerical function in the GSL
+* __boost_range
+* __boost_fusion (the state type can be a fusion vector)
+* __boost_units
+* __intel_mkl for maximum performance
+* __vexcl for OpenCL
+* __boost_graph (still experimentally)
+
+In odeint, the following algorithms are implemented:
+
+[include stepper_table.qbk]
+
+[endsect]
+
+
+
+[section Usage, Compilation, Headers]
+
+odeint is a header-only library, no linking against pre-compiled code is required. It can be included by
+
+``
+#include <boost/numeric/odeint.hpp>
+``
+
+which includes all headers of the library. All functions and classes from odeint live in the namespace
+
+``
+ using namespace boost::numeric::odeint;
+``
+
+It is also possible to include only parts of the library. This is the recommended way since it saves a lot of compilation time.
+
+* `#include <boost/numeric/odeint/stepper/XYZ.hpp>` - the include path for all steppers, XYZ is a placeholder for a stepper.
+* `#include <boost/numeric/odeint/algebra/XYZ.hpp>` - all algebras.
+* `#include <boost/numeric/odeint/util/XYZ.hpp>` - the utility functions like `is_resizeable`, `same_size`, or `resize`.
+* `#include <boost/numeric/odeint/integrate/XYZ.hpp>` - the integrate routines.
+* `#include <boost/numeric/odeint/iterator/XYZ.hpp>` - the range and iterator functions.
+* `#include <boost/numeric/odeint/external/XYZ.hpp>` - any binders to external libraries.
+
+
+
+[endsect]
+
+[section Short Example]
+
+Imaging, you want to numerically integrate a harmonic oscillator with
+friction. The equations of motion are given by ['x'' = -x + __gamma x'].
+Odeint only deals with first order ODEs that have no higher derivatives than
+x' involved. However, any higher order ODE can be transformed to a system of
+first order ODEs by introducing the new variables ['q=x] and ['p=x'] such that ['w=(q,p)]. To apply numerical integration one first has to design the right hand side of the equation ['w' = f(w) = (p,-q+__gamma p)]:
+
+[import ../examples/harmonic_oscillator.cpp]
+[rhs_function]
+
+Here we chose `vector<double>` as the state type, but others are also
+possible, for example `boost::array<double,2>`. odeint is designed in such a
+way that you can easily use your own state types. Next, the ODE is defined
+which is in this case a simple function calculating ['f(x)]. The parameter
+signature of this function is crucial: the integration methods will always
+call them in the form `f(x, dxdt, t)` (there are exceptions for some special routines). So, even if there is no explicit time dependence, one has to define `t` as a function parameter.
+
+Now, we have to define the initial state from which the integration should start:
+
+[state_initialization]
+
+For the integration itself we'll use the `integrate` function, which is a convenient way to get quick results. It is based on the error-controlled `runge_kutta54_cash_karp` stepper (5th order) and uses adaptive step-size.
+
+[integration]
+
+The integrate function expects as parameters the rhs of the ode as defined
+above, the initial state `x`, the start-and end-time of the integration as
+well as the initial time step=size. Note, that `integrate` uses an adaptive step-size during
+the integration steps so the time points will not be equally spaced. The
+integration returns the number of steps that were applied and updates x which
+is set to the approximate solution of the ODE at the end of integration.
+
+It is also possible to represent the ode system as a class. The
+rhs must then be implemented as a functor - a class with an overloaded function call operator:
+
+[rhs_class]
+
+which can be used via
+
+[integration_class]
+
+In order to observe the solution
+during the integration steps all you have to do is
+to provide a reasonable observer. An example is
+
+[integrate_observer]
+
+which stores the intermediate steps in a container.
+Note, the argument structure of the ()-operator: odeint calls the observer
+exactly in this way, providing the current state and time. Now, you only have
+to pass this container to the integration function:
+
+[integrate_observ]
+
+That is all. You can use functional libraries like __boost_lambda or __boost_phoenix to ease the creation of observer functions.
+
+The full cpp file for this example can be found here: [github_link examples/harmonic_oscillator.cpp harmonic_oscillator.cpp]
+
+
+
+[endsect]
+
+[endsect]
diff --git a/doc/html/boostbook.css b/doc/html/boostbook.css
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--- /dev/null
+++ b/doc/html/boostbook.css
@@ -0,0 +1,611 @@
+/*=============================================================================
+ Copyright (c) 2004 Joel de Guzman
+ http://spirit.sourceforge.net/
+
+ Distributed under the Boost Software License, Version 1.0. (See accompany-
+ ing file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================*/
+
+/*=============================================================================
+ Body defaults
+=============================================================================*/
+
+ body
+ {
+ margin: 1em;
+ font-family: sans-serif;
+ }
+
+/*=============================================================================
+ Paragraphs
+=============================================================================*/
+
+ p
+ {
+ text-align: left;
+ font-size: 10pt;
+ line-height: 1.15;
+ }
+
+/*=============================================================================
+ Program listings
+=============================================================================*/
+
+ /* Code on paragraphs */
+ p tt.computeroutput
+ {
+ font-size: 9pt;
+ }
+
+ pre.synopsis
+ {
+ font-size: 9pt;
+ margin: 1pc 4% 0pc 4%;
+ padding: 0.5pc 0.5pc 0.5pc 0.5pc;
+ }
+
+ .programlisting,
+ .screen
+ {
+ font-size: 9pt;
+ display: block;
+ margin: 1pc 4% 0pc 4%;
+ padding: 0.5pc 0.5pc 0.5pc 0.5pc;
+ }
+
+ /* Program listings in tables don't get borders */
+ td .programlisting,
+ td .screen
+ {
+ margin: 0pc 0pc 0pc 0pc;
+ padding: 0pc 0pc 0pc 0pc;
+ }
+
+/*=============================================================================
+ Headings
+=============================================================================*/
+
+ h1, h2, h3, h4, h5, h6
+ {
+ text-align: left;
+ margin: 1em 0em 0.5em 0em;
+ font-weight: bold;
+ }
+
+ h1 { font-size: 140%; }
+ h2 { font-weight: bold; font-size: 140%; }
+ h3 { font-weight: bold; font-size: 130%; }
+ h4 { font-weight: bold; font-size: 120%; }
+ h5 { font-weight: normal; font-style: italic; font-size: 110%; }
+ h6 { font-weight: normal; font-style: italic; font-size: 100%; }
+
+ /* Top page titles */
+ title,
+ h1.title,
+ h2.title
+ h3.title,
+ h4.title,
+ h5.title,
+ h6.title,
+ .refentrytitle
+ {
+ font-weight: bold;
+ margin-bottom: 1pc;
+ }
+
+ h1.title { font-size: 140% }
+ h2.title { font-size: 140% }
+ h3.title { font-size: 130% }
+ h4.title { font-size: 120% }
+ h5.title { font-size: 110% }
+ h6.title { font-size: 100% }
+
+ .section h1
+ {
+ margin: 0em 0em 0.5em 0em;
+ font-size: 140%;
+ }
+
+ .section h2 { font-size: 140% }
+ .section h3 { font-size: 130% }
+ .section h4 { font-size: 120% }
+ .section h5 { font-size: 110% }
+ .section h6 { font-size: 100% }
+
+ /* Code on titles */
+ h1 tt.computeroutput { font-size: 140% }
+ h2 tt.computeroutput { font-size: 140% }
+ h3 tt.computeroutput { font-size: 130% }
+ h4 tt.computeroutput { font-size: 130% }
+ h5 tt.computeroutput { font-size: 130% }
+ h6 tt.computeroutput { font-size: 130% }
+
+
+/*=============================================================================
+ Author
+=============================================================================*/
+
+ h3.author
+ {
+ font-size: 100%
+ }
+
+/*=============================================================================
+ Lists
+=============================================================================*/
+
+ li
+ {
+ font-size: 10pt;
+ line-height: 1.3;
+ }
+
+ /* Unordered lists */
+ ul
+ {
+ text-align: left;
+ }
+
+ /* Ordered lists */
+ ol
+ {
+ text-align: left;
+ }
+
+/*=============================================================================
+ Links
+=============================================================================*/
+
+ a
+ {
+ text-decoration: none; /* no underline */
+ }
+
+ a:hover
+ {
+ text-decoration: underline;
+ }
+
+/*=============================================================================
+ Spirit style navigation
+=============================================================================*/
+
+ .spirit-nav
+ {
+ text-align: right;
+ }
+
+ .spirit-nav a
+ {
+ color: white;
+ padding-left: 0.5em;
+ }
+
+ .spirit-nav img
+ {
+ border-width: 0px;
+ }
+
+/*=============================================================================
+ Copyright footer
+=============================================================================*/
+ .copyright-footer
+ {
+ text-align: right;
+ font-size: 70%;
+ }
+
+ .copyright-footer p
+ {
+ text-align: right;
+ font-size: 80%;
+ }
+
+/*=============================================================================
+ Table of contents
+=============================================================================*/
+
+ .toc
+ {
+ margin: 1pc 4% 0pc 4%;
+ padding: 0.1pc 1pc 0.1pc 1pc;
+ font-size: 80%;
+ line-height: 1.15;
+ }
+
+ .boost-toc
+ {
+ float: right;
+ padding: 0.5pc;
+ }
+
+ /* Code on toc */
+ .toc .computeroutput { font-size: 120% }
+
+ /* No margin on nested menus */
+
+ .toc dl dl { margin: 0; }
+
+/*=============================================================================
+ Tables
+=============================================================================*/
+
+ .table-title,
+ div.table p.title
+ {
+ margin-left: 4%;
+ padding-right: 0.5em;
+ padding-left: 0.5em;
+ }
+
+ .informaltable table,
+ .table table
+ {
+ width: 92%;
+ margin-left: 4%;
+ margin-right: 4%;
+ }
+
+ div.informaltable table,
+ div.table table
+ {
+ padding: 4px;
+ }
+
+ /* Table Cells */
+ div.informaltable table tr td,
+ div.table table tr td
+ {
+ padding: 0.5em;
+ text-align: left;
+ font-size: 9pt;
+ }
+
+ div.informaltable table tr th,
+ div.table table tr th
+ {
+ padding: 0.5em 0.5em 0.5em 0.5em;
+ border: 1pt solid white;
+ font-size: 80%;
+ }
+
+ table.simplelist
+ {
+ width: auto !important;
+ margin: 0em !important;
+ padding: 0em !important;
+ border: none !important;
+ }
+ table.simplelist td
+ {
+ margin: 0em !important;
+ padding: 0em !important;
+ text-align: left !important;
+ font-size: 9pt !important;
+ border: none !important;
+ }
+
+/*=============================================================================
+ Blurbs
+=============================================================================*/
+
+ div.note,
+ div.tip,
+ div.important,
+ div.caution,
+ div.warning,
+ p.blurb
+ {
+ font-size: 9pt; /* A little bit smaller than the main text */
+ line-height: 1.2;
+ display: block;
+ margin: 1pc 4% 0pc 4%;
+ padding: 0.5pc 0.5pc 0.5pc 0.5pc;
+ }
+
+ p.blurb img
+ {
+ padding: 1pt;
+ }
+
+/*=============================================================================
+ Variable Lists
+=============================================================================*/
+
+ div.variablelist
+ {
+ margin: 1em 0;
+ }
+
+ /* Make the terms in definition lists bold */
+ div.variablelist dl dt,
+ span.term
+ {
+ font-weight: bold;
+ font-size: 10pt;
+ }
+
+ div.variablelist table tbody tr td
+ {
+ text-align: left;
+ vertical-align: top;
+ padding: 0em 2em 0em 0em;
+ font-size: 10pt;
+ margin: 0em 0em 0.5em 0em;
+ line-height: 1;
+ }
+
+ div.variablelist dl dt
+ {
+ margin-bottom: 0.2em;
+ }
+
+ div.variablelist dl dd
+ {
+ margin: 0em 0em 0.5em 2em;
+ font-size: 10pt;
+ }
+
+ div.variablelist table tbody tr td p,
+ div.variablelist dl dd p
+ {
+ margin: 0em 0em 0.5em 0em;
+ line-height: 1;
+ }
+
+/*=============================================================================
+ Misc
+=============================================================================*/
+
+ /* Title of books and articles in bibliographies */
+ span.title
+ {
+ font-style: italic;
+ }
+
+ span.underline
+ {
+ text-decoration: underline;
+ }
+
+ span.strikethrough
+ {
+ text-decoration: line-through;
+ }
+
+ /* Copyright, Legal Notice */
+ div div.legalnotice p
+ {
+ text-align: left
+ }
+
+/*=============================================================================
+ Colors
+=============================================================================*/
+
+ @media screen
+ {
+ body {
+ background-color: #FFFFFF;
+ color: #000000;
+ }
+
+ /* Syntax Highlighting */
+ .keyword { color: #0000AA; }
+ .identifier { color: #000000; }
+ .special { color: #707070; }
+ .preprocessor { color: #402080; }
+ .char { color: teal; }
+ .comment { color: #800000; }
+ .string { color: teal; }
+ .number { color: teal; }
+ .white_bkd { background-color: #FFFFFF; }
+ .dk_grey_bkd { background-color: #999999; }
+
+ /* Links */
+ a, a .keyword, a .identifier, a .special, a .preprocessor
+ a .char, a .comment, a .string, a .number
+ {
+ color: #005a9c;
+ }
+
+ a:visited, a:visited .keyword, a:visited .identifier,
+ a:visited .special, a:visited .preprocessor a:visited .char,
+ a:visited .comment, a:visited .string, a:visited .number
+ {
+ color: #9c5a9c;
+ }
+
+ h1 a, h2 a, h3 a, h4 a, h5 a, h6 a,
+ h1 a:hover, h2 a:hover, h3 a:hover, h4 a:hover, h5 a:hover, h6 a:hover,
+ h1 a:visited, h2 a:visited, h3 a:visited, h4 a:visited, h5 a:visited, h6 a:visited
+ {
+ text-decoration: none; /* no underline */
+ color: #000000;
+ }
+
+ /* Copyright, Legal Notice */
+ .copyright
+ {
+ color: #666666;
+ font-size: small;
+ }
+
+ div div.legalnotice p
+ {
+ color: #666666;
+ }
+
+ /* Program listing */
+ pre.synopsis
+ {
+ border: 1px solid #DCDCDC;
+ }
+
+ .programlisting,
+ .screen
+ {
+ border: 1px solid #DCDCDC;
+ }
+
+ td .programlisting,
+ td .screen
+ {
+ border: 0px solid #DCDCDC;
+ }
+
+ /* Blurbs */
+ div.note,
+ div.tip,
+ div.important,
+ div.caution,
+ div.warning,
+ p.blurb
+ {
+ border: 1px solid #DCDCDC;
+ }
+
+ /* Table of contents */
+ .toc
+ {
+ border: 1px solid #DCDCDC;
+ }
+
+ /* Tables */
+ div.informaltable table tr td,
+ div.table table tr td
+ {
+ border: 1px solid #DCDCDC;
+ }
+
+ div.informaltable table tr th,
+ div.table table tr th
+ {
+ background-color: #F0F0F0;
+ border: 1px solid #DCDCDC;
+ }
+
+ .copyright-footer
+ {
+ color: #8F8F8F;
+ }
+
+ /* Misc */
+ span.highlight
+ {
+ color: #00A000;
+ }
+ }
+
+ @media print
+ {
+ /* Links */
+ a
+ {
+ color: black;
+ }
+
+ a:visited
+ {
+ color: black;
+ }
+
+ .spirit-nav
+ {
+ display: none;
+ }
+
+ /* Program listing */
+ pre.synopsis
+ {
+ border: 1px solid gray;
+ }
+
+ .programlisting,
+ .screen
+ {
+ border: 1px solid gray;
+ }
+
+ td .programlisting,
+ td .screen
+ {
+ border: 0px solid #DCDCDC;
+ }
+
+ /* Table of contents */
+ .toc
+ {
+ border: 1px solid gray;
+ }
+
+ .informaltable table,
+ .table table
+ {
+ border: 1px solid gray;
+ border-collapse: collapse;
+ }
+
+ /* Tables */
+ div.informaltable table tr td,
+ div.table table tr td
+ {
+ border: 1px solid gray;
+ }
+
+ div.informaltable table tr th,
+ div.table table tr th
+ {
+ border: 1px solid gray;
+ }
+
+ table.simplelist tr td
+ {
+ border: none !important;
+ }
+
+ /* Misc */
+ span.highlight
+ {
+ font-weight: bold;
+ }
+ }
+
+/*=============================================================================
+ Images
+=============================================================================*/
+
+ span.inlinemediaobject img
+ {
+ vertical-align: middle;
+ }
+
+/*==============================================================================
+ Super and Subscript: style so that line spacing isn't effected, see
+ http://www.adobe.com/cfusion/communityengine/index.cfm?event=showdetails&productId=1&postId=5341
+==============================================================================*/
+
+sup,
+sub {
+ height: 0;
+ line-height: 1;
+ vertical-align: baseline;
+ position: relative;
+
+}
+
+/* For internet explorer: */
+
+* html sup,
+* html sub {
+ vertical-align: bottom;
+}
+
+sup {
+ bottom: 1ex;
+}
+
+sub {
+ top: .5ex;
+}
+
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new file mode 100644
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+ style="overflow:visible;enable-background:new 0 0 33 33;" xml:space="preserve">
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new file mode 100644
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+ <path style="&st0;" d="M16.4,42.3L5.7,31.6V16.4L16.4,5.7h15.2l10.7,10.7v15.2L31.6,42.3H16.4z"/>
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+ </g>
+ </g>
+ <g id="crop_x0020_marks" style="&st5;">
+ <path style="&st2;" d="M48,48H0V0h48v48z"/>
+ </g>
+</svg>
diff --git a/doc/html/logo.jpg b/doc/html/logo.jpg
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+++ b/doc/html/logo.jpg
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diff --git a/doc/html/solar_system.jpg b/doc/html/solar_system.jpg
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+++ b/doc/html/solar_system.jpg
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diff --git a/doc/literature.qbk b/doc/literature.qbk
new file mode 100644
index 0000000..c5c7a79
--- /dev/null
+++ b/doc/literature.qbk
@@ -0,0 +1,53 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2010-2012 Karsten Ahnert
+ Copyright 2010-2012 Mario Mulansky
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+[section Literature]
+
+[*General information about numerical integration of ordinary differential equations:]
+
+[#numerical_recipies]
+[1] Press William H et al., Numerical Recipes 3rd Edition: The Art of Scientific Computing, 3rd ed. (Cambridge University Press, 2007).
+
+[#hairer_solving_odes_1]
+[2] Ernst Hairer, Syvert P. Nørsett, and Gerhard Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems, 2nd ed. (Springer, Berlin, 2009).
+
+[#hairer_solving_odes_2]
+[3] Ernst Hairer and Gerhard Wanner, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, 2nd ed. (Springer, Berlin, 2010).
+
+
+[*Symplectic integration of numerical integration:]
+
+[#hairer_geometrical_numeric_integration]
+[4] Ernst Hairer, Gerhard Wanner, and Christian Lubich, Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, 2nd ed. (Springer-Verlag Gmbh, 2006).
+
+[#leimkuhler_reich_simulating_hamiltonian_dynamics]
+[5] Leimkuhler Benedict and Reich Sebastian, Simulating Hamiltonian Dynamics (Cambridge University Press, 2005).
+
+
+[*Special symplectic methods:]
+
+[#symplectic_yoshida_symplectic_integrators]
+[6] Haruo Yoshida, “Construction of higher order symplectic integrators,” Physics Letters A 150, no. 5 (November 12, 1990): 262-268.
+
+[#symplectic_mylachlan_symmetric_composition_mehtods]
+[7] Robert I. McLachlan, “On the numerical integration of ordinary differential equations by symmetric composition methods,” SIAM J. Sci. Comput. 16, no. 1 (1995): 151-168.
+
+
+[*Special systems:]
+
+[#fpu_scholarpedia]
+[8] [@http://www.scholarpedia.org/article/Fermi-Pasta-Ulam_nonlinear_lattice_oscillations Fermi-Pasta-Ulam nonlinear lattice oscillations]
+
+[#synchronization_pikovsky_rosenblum]
+[9] Arkady Pikovsky, Michael Rosemblum, and Jürgen Kurths, Synchronization: A Universal Concept in Nonlinear Sciences. (Cambridge University Press, 2001).
+
+[endsect]
diff --git a/doc/make_controlled_table.qbk b/doc/make_controlled_table.qbk
new file mode 100644
index 0000000..799c019
--- /dev/null
+++ b/doc/make_controlled_table.qbk
@@ -0,0 +1,20 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+
+[table Generation functions make_controlled( abs_error , rel_error , stepper )
+ [[Stepper] [Result of make_controlled] [Remarks]]
+ [[`runge_kutta_cash_karp54`] [`controlled_runge_kutta< runge_kutta_cash_karp54 , default_error_checker<...> >`] [['a[sub x]=1], ['a[sub dxdt]=1]]]
+ [[`runge_kutta_fehlberg78`] [`controlled_runge_kutta< runge_kutta_fehlberg78 , default_error_checker<...> >`] [['a[sub x]=1], ['a[sub dxdt]=1]]]
+ [[`runge_kutta_dopri5`] [`controlled_runge_kutta< runge_kutta_dopri5 , default_error_checker<...> >`] [['a [sub x]=1], ['a[sub dxdt]=1]]]
+ [[`rosenbrock4`] [`rosenbrock4_controlled< rosenbrock4 >`] [-]]
+]
diff --git a/doc/make_dense_output_table.qbk b/doc/make_dense_output_table.qbk
new file mode 100644
index 0000000..be610bc
--- /dev/null
+++ b/doc/make_dense_output_table.qbk
@@ -0,0 +1,19 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+
+[table Generation functions make_dense_output( abs_error , rel_error , stepper )
+ [[Stepper] [Result of make_dense_output] [Remarks]]
+ [[`runge_kutta_dopri5`] [`dense_output_runge_kutta< controlled_runge_kutta< runge_kutta_dopri5 , default_error_checker<...> > >`] [['a [sub x]=1], ['a[sub dxdt]=1]]]
+ [[`rosenbrock4`] [`rosenbrock4_dense_output< rosenbrock4_controller< rosenbrock4 > >`] [-]]
+]
+
diff --git a/doc/odeint.idx b/doc/odeint.idx
new file mode 100644
index 0000000..330e738
--- /dev/null
+++ b/doc/odeint.idx
@@ -0,0 +1,54 @@
+# odeint.idx list of files and keyword to be indexed.
+
+# Copyright 2012 Karsten Ahnert
+# Copyright 2012 Pierre Talbot
+#
+# Use, modification and distribution is subject to the Boost Software
+# License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+# http://www.boost.org/LICENSE_1_0.txt)
+
+!scan-path "boost/numeric/odeint/" ".*\.*pp" true
+# recurse in any sub-directories.
+
+# List of terms in the docbook (from Quickbook) to be indexed.
+# Convenient to order these alphabetically.
+
+# TODO - add more!
+
+acknowledgements
+book
+# C++ \<C|C++\>
+card
+credit
+deprecated
+Doxygen
+example \<example\w*\>
+equations \<equation\w*\>
+graphics \<graphic\w*\>
+Gumm
+links \<link\w*\>
+images \<image\w*\>
+ISBN
+ISSN
+IBM
+italic \<italic\w*\>
+# index index and indexes (assume not using plural indices!)
+index \<index\w*\>
+Luhn
+Mastercard
+modulus
+path \<path\w*\>
+pre-conditions \<pre\w*\>
+post-conditions \<post\w*\>
+remark \<remark\w*\>
+snippet \<snippet\w*\>
+png
+Quickbook
+Verhoeff
+# version \<version\w*\>
+VISA
+warning \<warning\w*\>
+
+# Remove leading "A" or "The" prefixes from section titles.
+# !rewrite-name "(?:A|An|The)\s+(.*)" "\1"
+
diff --git a/doc/odeint.qbk b/doc/odeint.qbk
new file mode 100644
index 0000000..3eda233
--- /dev/null
+++ b/doc/odeint.qbk
@@ -0,0 +1,273 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2009-2012 Karsten Ahnert
+ Copyright 2011-2013 Mario Mulansky
+ Copyright 2012 Sylwester Arabas
+ Copyright 2013 Pascal Germroth
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+
+[library Boost.Numeric.Odeint
+ [quickbook 1.5]
+ [id odeint]
+ [dirname odeint]
+ [authors [Ahnert, Karsten], [Mulansky, Mario]]
+ [copyright 2009-2015 Karsten Ahnert and Mario Mulansky]
+ [category math]
+ [purpose
+ Numerical integration of ordinary differential equations.
+ ]
+ [license
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or copy
+ at [@http://www.boost.org/LICENSE_1_0.txt])
+ ]
+]
+
+[include auto_index_helpers.qbk]
+
+
+
+[def __boost_lambda
+ [@http://www.boost.org/doc/libs/release/libs/lambda/ Boost.Lambda]]
+[def __boost_phoenix
+ [@http://www.boost.org/doc/libs/release/libs/phoenix/ Boost.Phoenix]]
+[def __boost_operators
+ [@http://www.boost.org/doc/libs/release/libs/utility/operators.htm Boost.Operators]]
+[def __boost_ref
+ [@http://www.boost.org/doc/libs/release/libs/bind/ref.html Boost.Ref]]
+[def __boost_range
+ [@http://www.boost.org/doc/libs/release/libs/range/ Boost.Range]]
+[def __boost_units
+ [@http://www.boost.org/doc/libs/release/libs/units/ Boost.Units]]
+[def __boost_fusion
+ [@http://www.boost.org/doc/libs/release/libs/fusion/ Boost.Fusion]]
+[def __boost_graph
+ [@http://www.boost.org/doc/libs/release/libs/graph/ Boost.Graph]]
+[def __boost_multiprecision
+ [@http://www.boost.org/doc/libs/release/libs/multiprecision/ Boost.Multiprecision]]
+[def __boost_mpi
+ [@http://www.boost.org/doc/libs/release/libs/mpi/ Boost.MPI]]
+
+[def __thrust
+ [@http://code.google.com/p/thrust/ Thrust]]
+[def __ublas
+ [@http://www.boost.org/doc/libs/release/libs/numeric/ublas/index.html Boost.uBLAS]]
+[def __intel_mkl
+ [@http://software.intel.com/en-us/articles/intel-mkl/ Intel Math Kernel Library]]
+[def __gsl
+ [@http://www.gsl.org GSL]]
+[def __vexcl
+ [@https://github.com/ddemidov/vexcl VexCL]]
+
+[def __concepts
+ [link boost_numeric_odeint.concepts Concepts]]
+[def __system
+ [link boost_numeric_odeint.concepts.system System]]
+[def __symplectic_system
+ [link boost_numeric_odeint.concepts.symplectic_system Symplectic System]]
+[def __simple_symplectic_system
+ [link boost_numeric_odeint.concepts.simple_symplectic_system Simple Symplectic System]]
+[def __implicit_system
+ [link boost_numeric_odeint.concepts.implicit_system Implicit System]]
+[def __second_order_system
+ [link boost_numeric_odeint.concepts.second_order_system Second Order System]]
+[def __stepper
+ [link boost_numeric_odeint.concepts.stepper Stepper]]
+[def __error_stepper
+ [link boost_numeric_odeint.concepts.error_stepper Error Stepper]]
+[def __controlled_stepper
+ [link boost_numeric_odeint.concepts.controlled_stepper Controlled Stepper]]
+[def __dense_output_stepper
+ [link boost_numeric_odeint.concepts.dense_output_stepper Dense Output Stepper]]
+[def __integrate_functions
+ [link boost_numeric_odeint.odeint_in_detail.integrate_functions integrate functions]]
+[def __tutorial
+ [link boost_numeric_odeint.tutorial Tutorial]]
+[def __tut_solar_system
+ [link boost_numeric_odeint.tutorial.solar_system Solar System]]
+[def __tut_chaotic_system
+ [link boost_numeric_odeint.tutorial.chaotic_systems_and_lyapunov_exponents Chaotic System]]
+[def __tut_harmonic_oscillator
+ [link boost_numeric_odeint.tutorial.harmonic_oscillator Harmonic Oscillator]]
+[def __using_steppers
+ [link boost_numeric_odeint.odeint_in_detail.steppers.using_steppers Using steppers]]
+[def __generation_functions
+ [link boost_numeric_odeint.odeint_in_detail.generation_functions Generation functions]]
+[def __adapt_state_types
+ [link boost_numeric_odeint.odeint_in_detail.state_types__algebras_and_operations Adapt your own state types]]
+[def __resizing_lattice_example
+ [link boost_numeric_odeint.tutorial.self_expanding_lattices Self expanding lattices]]
+[def __odeint_stepper_table
+ [link boost_numeric_odeint.odeint_in_detail.steppers.stepper_overview Stepper overview]]
+
+
+
+[def __nr_ref [link numerical_recipies \[1\] ]]
+[def __hairer_1_ref [link hairer_solving_odes_1 \[2\] ]]
+[def __hairer_2_ref [link hairer_solving_odes_2 \[3\] ]]
+[def __hairer_geom_ref [link hairer_geometrical_numeric_integration \[4\] ]]
+[def __leimkuhler_reich_ref [link leimkuhler_reich_simulating_hamiltonian_dynamics \[5\] ]]
+[def __symplectic_integrator_1_ref [link symplectic_yoshida_symplectic_integrators \[6\] ]]
+[def __symplectic_integrator_2_ref [link symplectic_mylachlan_symmetric_composition_mehtods \[7\] ]]
+[def __fpu_scholarpedia_ref [link fpu_scholarpedia \[8\] ]]
+[def __synchronization_pikovsky_ref [link synchronization_pikovsky_rosenblum \[9\] ]]
+
+
+
+
+
+[def __alpha '''α''']
+[def __Alpha '''Α''']
+[def __beta '''β''']
+[def __Beta '''Β''']
+[def __gamma '''γ''']
+[def __Gamma '''Γ''']
+[def __delta '''δ''']
+[def __Delta '''Δ''']
+[def __epsilon '''ε''']
+[def __Epsilon '''Ε''']
+[def __zeta '''ζ''']
+[def __Zeta '''Ζ''']
+[def __eta '''η''']
+[def __Eta '''Η''']
+[def __theta '''θ''']
+[def __Theta '''Θ''']
+[def __iota '''ι''']
+[def __Iota '''Ι''']
+[def __kappa '''κ''']
+[def __Kappa '''Κ''']
+[def __lambda '''λ'''][/lower case]
+[def __Lambda '''Λ'''][/upper case]
+[def __mu '''μ''']
+[def __Mu '''Μ''']
+[def __nu '''ν''']
+[def __Nu '''Ν''']
+[def __xi '''ξ''']
+[def __Xi '''Ξ''']
+[def __omicron '''ο''']
+[def __Omicron '''Ο''']
+[def __pi '''π''']
+[def __Pi '''Π''']
+[def __rho '''ρ''']
+[def __Rho '''Ρ''']
+[def __sigma '''σ''']
+[def __Sigma '''Σ''']
+[def __tau '''τ''']
+[def __Tau '''Τ''']
+[def __upsilon '''υ''']
+[def __Upsilon '''Υ''']
+[def __phi '''φ''']
+[def __Phi '''Φ''']
+[def __chi '''χ''']
+[def __Chi '''Χ''']
+[def __psi '''ψ''']
+[def __Psi '''Ψ''']
+[def __Omega '''Ω''']
+[def __omega '''ω''']
+
+[def __space '''​''']
+
+
+
+[template super[x]'''<superscript>'''[x]'''</superscript>''']
+[template supl[x]'''<superscript>'''__space[x]'''</superscript>''']
+[template sub[x]'''<subscript>'''[x]'''</subscript>''']
+[template subl[x]'''<subscript>'''__space[x]'''</subscript>''']
+
+[template github_link[url text]'''<ulink url="https://github.com/headmyshoulder/odeint-v2/blob/master/'''[url]'''" target="_blank">'''[text]'''</ulink>''']
+[/ [template github_link[url text]'''<ulink url="../../../../../'''[url]'''" target="_blank">'''[text]'''</ulink>''']]
+
+
+
+
+[include getting_started.qbk]
+
+[include tutorial.qbk]
+
+[include details.qbk]
+
+[include concepts.qbk]
+
+[include literature.qbk]
+
+[include acknowledgements.qbk]
+
+[xinclude reference.xml]
+
+[section:indexes Indexes]
+
+[named_index class_name Class Index]
+[named_index function_name Function Index]
+[/
+[named_index typedef_name Typedef Index]
+[named_index macro_name Macro Index]
+]
+[index]
+
+[endsect]
+
+
+
+
+[/
+# Α Α Α U+0391 Greek capital letter alpha
+# Β Β Β U+0392 Greek capital letter beta
+# Γ Γ Γ U+0393 Greek capital letter gamma ISOgrk3
+# Δ Δ Δ U+0394 Greek capital letter delta ISOgrk3
+# Ε Ε Ε U+0395 Greek capital letter epsilon
+# Ζ Ζ Ζ U+0396 Greek capital letter zeta
+# Η Η Η U+0397 Greek capital letter eta
+# Θ Θ Θ U+0398 Greek capital letter theta ISOgrk3
+# Ι Ι Ι U+0399 Greek capital letter iota
+# Κ Κ Κ U+039A Greek capital letter kappa
+# Λ Λ Λ U+039B Greek capital letter lambda ISOgrk3
+# Μ Μ Μ U+039C Greek capital letter mu
+# Ν Ν Ν U+039D Greek capital letter nu
+# Ξ Ξ Ξ U+039E Greek capital letter xi ISOgrk3
+# Ο Ο Ο U+039F Greek capital letter omicron
+# Π Π Π U+03A0 Greek capital letter pi ISOgrk3
+# Ρ Ρ Ρ U+03A1 Greek capital letter rho
+# Σ Σ Σ U+03A3 Greek capital letter sigma ISOgrk3
+# Τ Τ Τ U+03A4 Greek capital letter tau
+# Υ Υ Υ U+03A5 Greek capital letter upsilon ISOgrk3
+# Φ Φ Φ U+03A6 Greek capital letter phi ISOgrk3
+# Χ Χ Χ U+03A7 Greek capital letter chi
+# Ψ Ψ Ψ U+03A8 Greek capital letter psi ISOgrk3
+# Ω Ω Ω U+03A9 Greek capital letter omega ISOgrk3
+# α α α U+03B1 Greek small letter alpha ISOgrk3
+# β β β U+03B2 Greek small letter beta ISOgrk3
+# γ γ γ U+03B3 Greek small letter gamma ISOgrk3
+# δ δ δ U+03B4 Greek small letter delta ISOgrk3
+# ε ε ε U+03B5 Greek small letter epsilon ISOgrk3
+# ζ ζ ζ U+03B6 Greek small letter zeta ISOgrk3
+# η η η U+03B7 Greek small letter eta ISOgrk3
+# θ θ θ U+03B8 Greek small letter theta ISOgrk3
+# ι ι ι U+03B9 Greek small letter iota ISOgrk3
+# κ κ κ U+03BA Greek small letter kappa ISOgrk3
+# λ λ λ U+03BB Greek small letter lambda ISOgrk3
+# μ μ μ U+03BC Greek small letter mu ISOgrk3
+# ν ν ν U+03BD Greek small letter nu ISOgrk3
+# ξ ξ ξ U+03BE Greek small letter xi ISOgrk3
+# ο ο ο U+03BF Greek small letter omicron New
+# π π π U+03C0 Greek small letter pi ISOgrk3
+# ρ ρ ρ U+03C1 Greek small letter rho ISOgrk3
+# ς ς ς U+03C2 Greek small letter final sigma ISOgrk3
+# σ σ σ U+03C3 Greek small letter sigma ISOgrk3
+# τ τ τ U+03C4 Greek small letter tau ISOgrk3
+# υ υ υ U+03C5 Greek small letter upsilon ISOgrk3
+# φ φ φ U+03C6 Greek small letter phi ISOgrk3
+# χ χ χ U+03C7 Greek small letter chi ISOgrk3
+# ψ ψ ψ U+03C8 Greek small letter psi ISOgrk3
+# ω ω ω U+03C9 Greek small letter omega ISOgrk3
+# ϑ ϑ ϑ U+03D1 Greek small letter theta symbol New
+# ϒ ϒ ϒ U+03D2 Greek upsilon with hook symbol New
+# ϖ ϖ ϖ U+03D6 Greek pi symbol ISOgrk3
+
+/]
diff --git a/doc/range_table.qbk b/doc/range_table.qbk
new file mode 100644
index 0000000..8d88ec9
--- /dev/null
+++ b/doc/range_table.qbk
@@ -0,0 +1,70 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+
+[/
+Steppers supporting __boost_range:
+
+* adams_bashforth_moulton
+* bulirsch_stoer_dense_out
+* bulirsch_stoer
+* controlled_runge_kutta
+* dense_output_runge_kutta
+* euler
+* explicit_error_generic_rk
+* explicit_generic_rk
+* rosenbrock4_controller
+* rosenbrock4_dense_output
+* rosenbrock4
+* runge_kutta4_classic
+* runge_kutta4
+* runge_kutta_cash_karp54_classic
+* runge_kutta_cash_karp54
+* runge_kutta_dopri5
+* runge_kutta_fehlberg78
+* symplectic_euler
+* symplectic_rkn_sb3a_mclachlan
+
+Algebras supporting __boost_range
+
+* range_algebra
+* thrust_algebra
+/]
+
+[table Steppers supporting Boost.Range
+ [[Stepper]]
+ [[adams_bashforth_moulton]]
+ [[bulirsch_stoer_dense_out]]
+ [[bulirsch_stoer]]
+ [[controlled_runge_kutta]]
+ [[dense_output_runge_kutta]]
+ [[euler]]
+ [[explicit_error_generic_rk]]
+ [[explicit_generic_rk]]
+ [[rosenbrock4_controller]]
+ [[rosenbrock4_dense_output]]
+ [[rosenbrock4]]
+ [[runge_kutta4_classic]]
+ [[runge_kutta4]]
+ [[runge_kutta_cash_karp54_classic]]
+ [[runge_kutta_cash_karp54]]
+ [[runge_kutta_dopri5]]
+ [[runge_kutta_fehlberg78]]
+ [[symplectic_euler]]
+ [[symplectic_rkn_sb3a_mclachlan]]
+]
+
+[table Algebras supporting Boost.Range
+ [[algebra]]
+ [[range_algebra]]
+ [[thrust_algebra]]
+]
\ No newline at end of file
diff --git a/doc/stepper_table.qbk b/doc/stepper_table.qbk
new file mode 100644
index 0000000..86e1018
--- /dev/null
+++ b/doc/stepper_table.qbk
@@ -0,0 +1,44 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011-2015 Karsten Ahnert
+ Copyright 2011-2015 Mario Mulansky
+ Copyright 2012 Sylwester Arabas
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+[table Stepper Algorithms
+ [[Algorithm] [Class] [Concept] [System Concept] [Order] [Error Estimation] [Dense Output] [Internal state] [Remarks]]
+ [[Explicit Euler] [`euler`] [__dense_output_stepper] [__system] [1] [No] [Yes] [No] [Very simple, only for demonstrating purpose]]
+ [[Modified Midpoint] [`modified_midpoint`] [__stepper] [__system] [configurable (2)] [No] [No] [No] [Used in Bulirsch-Stoer implementation]]
+ [[Runge-Kutta 4] [`runge_kutta4`] [__stepper] [__system] [4] [No] [No] [No] [The classical Runge-Kutta scheme, good general scheme without error control]]
+ [[Cash-Karp] [`runge_kutta_cash_karp54`] [__error_stepper] [__system] [5] [Yes (4)] [No] [No] [Good general scheme with error estimation, to be used in controlled_error_stepper]]
+ [[Dormand-Prince 5] [`runge_kutta_dopri5`] [__error_stepper] [__system] [5] [Yes (4)] [Yes] [Yes] [Standard method with error control and dense output, to be used in controlled_error_stepper and in dense_output_controlled_explicit_fsal.]]
+ [[Fehlberg 78] [`runge_kutta_fehlberg78`] [__error_stepper] [__system] [8] [Yes (7)] [No] [No] [Good high order method with error estimation, to be used in controlled_error_stepper.]]
+
+ [[Adams Bashforth] [`adams_bashforth`] [__stepper] [__system] [configurable] [No] [No] [Yes] [Multistep method]]
+[/ # removed as it is not an independent algorithm.
+ [[Adams Moulton] [`adams_moulton`] [__stepper] [__system] [configurable] [No] [No] [Yes] [Multistep method]] \]
+ [[Adams Bashforth Moulton] [`adams_bashforth_moulton`] [__stepper] [__system] [configurable] [No] [No] [Yes] [Combined multistep method]]
+
+ [[Controlled Runge-Kutta] [`controlled_runge_kutta`] [__controlled_stepper] [__system] [depends] [Yes] [No] [depends] [Error control for __error_stepper. Requires an __error_stepper from above. Order depends on the given ErrorStepper]]
+ [[Dense Output Runge-Kutta] [`dense_output_runge_kutta`] [__dense_output_stepper] [__system] [depends] [No] [Yes] [Yes] [Dense output for __stepper and __error_stepper from above if they provide dense output functionality (like `euler` and `runge_kutta_dopri5`). Order depends on the given stepper.]]
+
+ [[Bulirsch-Stoer] [`bulirsch_stoer`] [__controlled_stepper] [__system] [variable] [Yes] [No] [No] [Stepper with step size and order control. Very good if high precision is required.]]
+ [[Bulirsch-Stoer Dense Output] [`bulirsch_stoer_dense_out`] [__dense_output_stepper] [__system] [variable] [Yes] [Yes] [No] [Stepper with step size and order control as well as dense output. Very good if high precision and dense output is required.]]
+
+ [[Implicit Euler] [`implicit_euler`] [__stepper] [__implicit_system] [1] [No] [No] [No] [Basic implicit routine. Requires the Jacobian. Works only with __ublas vectors as state types.]]
+ [[Rosenbrock 4] [`rosenbrock4`] [__error_stepper] [__implicit_system] [4] [Yes] [Yes] [No] [Good for stiff systems. Works only with __ublas vectors as state types.]]
+ [[Controlled Rosenbrock 4] [`rosenbrock4_controller`] [__controlled_stepper] [__implicit_system] [4] [Yes] [Yes] [No] [Rosenbrock 4 with error control. Works only with __ublas vectors as state types.]]
+ [[Dense Output Rosenbrock 4] [`rosenbrock4_dense_output`] [__dense_output_stepper] [__implicit_system] [4] [Yes] [Yes] [No] [Controlled Rosenbrock 4 with dense output. Works only with __ublas vectors as state types.]]
+
+ [[Symplectic Euler] [`symplectic_euler`] [__stepper] [__symplectic_system __simple_symplectic_system] [1] [No] [No] [No] [Basic symplectic solver for separable Hamiltonian system]]
+ [[Symplectic RKN McLachlan] [`symplectic_rkn_sb3a_mclachlan`] [__stepper] [__symplectic_system __simple_symplectic_system] [4] [No] [No] [No] [Symplectic solver for separable Hamiltonian system with 6 stages and order 4.]]
+ [[Symplectic RKN McLachlan] [`symplectic_rkn_sb3a_m4_mclachlan`] [__stepper] [__symplectic_system __simple_symplectic_system] [4] [No] [No] [No] [Symplectic solver with 5 stages and order 4, can be used with arbitrary precision types.]]
+
+ [[Velocity Verlet] [`velocity_verlet`] [__stepper] [__second_order_system] [1] [No] [No] [Yes] [Velocity verlet method suitable for molecular dynamics simulation.]]
+]
diff --git a/doc/tutorial.qbk b/doc/tutorial.qbk
new file mode 100644
index 0000000..128437d
--- /dev/null
+++ b/doc/tutorial.qbk
@@ -0,0 +1,46 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2010-2012 Karsten Ahnert
+ Copyright 2010-2013 Mario Mulansky
+ Copyright 2013 Pascal Germroth
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+[section Tutorial]
+
+
+[include tutorial_harmonic_oscillator.qbk]
+
+[include tutorial_solar_system.qbk]
+
+[include tutorial_chaotic_system.qbk]
+
+[include tutorial_stiff_systems.qbk]
+
+[include tutorial_special_topics.qbk]
+
+[include tutorial_thrust_cuda.qbk]
+
+[include tutorial_vexcl_opencl.qbk]
+
+[include tutorial_parallel.qbk]
+
+[section All examples]
+
+The following table gives an overview over all examples.
+
+[include examples_table.qbk]
+
+[endsect]
+
+
+
+
+
+
+[endsect]
diff --git a/doc/tutorial_chaotic_system.qbk b/doc/tutorial_chaotic_system.qbk
new file mode 100644
index 0000000..9305733
--- /dev/null
+++ b/doc/tutorial_chaotic_system.qbk
@@ -0,0 +1,162 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2013 Mario Mulansky
+ Copyright 2012 Sylwester Arabas
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+[section Chaotic systems and Lyapunov exponents]
+
+[import ../examples/chaotic_system.cpp]
+
+In this example we present application of odeint to investigation of the properties of chaotic
+deterministic systems. In mathematical terms chaotic refers to an exponential
+growth of perturbations ['__delta x]. In order to observe this exponential growth one usually solves the equations for the tangential dynamics which is again an ordinary differential equation. These equations are linear but time dependent and can be obtained via
+
+['d __delta x / dt = J(x) __delta x]
+
+where ['J] is the Jacobian of the system under consideration. ['__delta x] can
+also be interpreted as a perturbation of the original system. In principle
+['n] of these perturbations exist, they form a hypercube and evolve in the
+time. The Lyapunov exponents are then defined as logarithmic growth rates of
+the perturbations. If one Lyapunov exponent is larger then zero the nearby
+trajectories diverge exponentially hence they are chaotic. If the largest
+Lyapunov exponent is zero one is usually faced with periodic motion. In the
+case of a largest Lyapunov exponent smaller then zero convergence to a
+fixed point is expected. More information's about Lyapunov exponents and nonlinear
+dynamical systems can be found in many textbooks, see for example: E. Ott "Chaos is
+Dynamical Systems", Cambridge.
+
+To calculate the Lyapunov exponents numerically one usually solves the equations of motion for ['n] perturbations and orthonormalizes them every ['k] steps. The Lyapunov exponent is the average of the logarithm of the stretching factor of each perturbation.
+
+To demonstrate how one can use odeint to determine the Lyapunov exponents we choose the Lorenz system. It is one of the most studied dynamical systems in the nonlinear dynamics community. For the standard parameters it possesses a strange attractor with non-integer dimension. The Lyapunov exponents take values of approximately 0.9, 0 and -12.
+
+The implementation of the Lorenz system is
+
+``
+const double sigma = 10.0;
+const double R = 28.0;
+const double b = 8.0 / 3.0;
+
+typedef boost::array< double , 3 > lorenz_state_type;
+
+void lorenz( const lorenz_state_type &x , lorenz_state_type &dxdt , double t )
+{
+ dxdt[0] = sigma * ( x[1] - x[0] );
+ dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
+ dxdt[2] = -b * x[2] + x[0] * x[1];
+}
+``
+We need also to integrate the set of the perturbations. This is done in parallel to the original system, hence within one system function. Of course, we want to use the above definition of the Lorenz system, hence the definition of the system function including the Lorenz system itself and the perturbation could look like:
+
+``
+const size_t n = 3;
+const size_t num_of_lyap = 3;
+const size_t N = n + n*num_of_lyap;
+
+typedef std::tr1::array< double , N > state_type;
+typedef std::tr1::array< double , num_of_lyap > lyap_type;
+
+void lorenz_with_lyap( const state_type &x , state_type &dxdt , double t )
+{
+ lorenz( x , dxdt , t );
+
+ for( size_t l=0 ; l<num_of_lyap ; ++l )
+ {
+ const double *pert = x.begin() + 3 + l * 3;
+ double *dpert = dxdt.begin() + 3 + l * 3;
+ dpert[0] = - sigma * pert[0] + 10.0 * pert[1];
+ dpert[1] = ( R - x[2] ) * pert[0] - pert[1] - x[0] * pert[2];
+ dpert[2] = x[1] * pert[0] + x[0] * pert[1] - b * pert[2];
+ }
+}
+``
+
+The perturbations are stored linearly in the `state_type` behind the state of the Lorenz system.
+The problem of '''lorenz()''' and '''lorenz_with_lyap()''' having different state types may be solved putting the Lorenz system inside a functor with templatized arguments:
+
+``
+struct lorenz
+{
+ template< class StateIn , class StateOut , class Value >
+ void operator()( const StateIn &x , StateOut &dxdt , Value t )
+ {
+ dxdt[0] = sigma * ( x[1] - x[0] );
+ dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
+ dxdt[2] = -b * x[2] + x[0] * x[1];
+ }
+};
+
+void lorenz_with_lyap( const state_type &x , state_type &dxdt , double t )
+{
+ lorenz()( x , dxdt , t );
+ ...
+}
+
+``
+This works fine and `lorenz_with_lyap` can be used for example via
+``
+state_type x;
+// initialize x..
+
+explicit_rk4< state_type > rk4;
+integrate_n_steps( rk4 , lorenz_with_lyap , x , 0.0 , 0.01 , 1000 );
+``
+This code snippet performs 1000 steps with constant step size 0.01.
+
+A real world use case for the calculation of the Lyapunov exponents of Lorenz system would always include some transient steps, just to ensure that the current state lies on the attractor, hence it would look like
+
+``
+state_type x;
+// initialize x
+explicit_rk4< state_type > rk4;
+integrate_n_steps( rk4 , lorenz , x , 0.0 , 0.01 , 1000 );
+``
+The problem is now, that `x` is the full state containing also the
+perturbations and `integrate_n_steps` does not know that it should only use 3
+elements. In detail, odeint and its steppers determine the length of the
+system under consideration by determining the length of the state. In the
+classical solvers, e.g. from Numerical Recipes, the problem was solved by
+pointer to the state and an appropriate length, something similar to
+
+``
+void lorenz( double* x , double *dxdt , double t, void* params )
+{
+ ...
+}
+
+int system_length = 3;
+rk4( x , system_length , t , dt , lorenz );
+``
+
+But odeint supports a similar and much more sophisticated concept: __boost_range. To make the steppers and the system ready to work with __boost_range the system has to be changed:
+
+[system_function_without_perturbations]
+
+This is in principle all. Now, we only have to call `integrate_n_steps` with a
+range including only the first 3 components of ['x]:
+
+[integrate_transients_with_range]
+
+[note Note that when using __boost_range, we have to explicitly configure the
+stepper to use the `range_algebra` as otherwise odeint would automatically
+chose the `array_algebra`, which is incompatible with the usage of __boost_range, because the original state_type is an `array`.]
+
+Having integrated a sufficient number of transients steps we are now able to calculate the Lyapunov exponents:
+
+# Initialize the perturbations. They are stored linearly behind the state of the Lorenz system. The perturbations are initialized such that [' p [subl ij] = __delta [subl ij]], where ['p [subl ij]] is the ['j]-component of the ['i].-th perturbation and ['__delta [subl ij]] is the Kronecker symbol.
+# Integrate 100 steps of the full system with perturbations
+# Orthonormalize the perturbation using Gram-Schmidt orthonormalization algorithm.
+# Repeat step 2 and 3. Every 10000 steps write the current Lyapunov exponent.
+
+[lyapunov_full_code]
+
+The full code can be found here: [github_link examples/chaotic_system.cpp chaotic_system.cpp]
+
+[endsect]
diff --git a/doc/tutorial_harmonic_oscillator.qbk b/doc/tutorial_harmonic_oscillator.qbk
new file mode 100644
index 0000000..53b8d88
--- /dev/null
+++ b/doc/tutorial_harmonic_oscillator.qbk
@@ -0,0 +1,123 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+ Copyright 2012 Sylwester Arabas
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+
+[section Harmonic oscillator]
+
+[section Define the ODE]
+
+First of all, you have to specify the data type that represents a state ['x] of your system. Mathematically, this usually is an n-dimensional vector with real numbers or complex numbers as scalar objects. For odeint the most natural way is to use `vector< double >` or `vector< complex< double > >` to represent the system state. However, odeint can deal with other container types as well, e.g. `boost::array< double , N >`, as long as it fulfills some requirements defined below.
+
+To integrate a differential equation numerically, one also has to define the rhs of the equation ['x' = f(x)]. In odeint you supply this function in terms of an object that implements the ()-operator with a certain parameter structure. Hence, the straightforward way would be to just define a function, e.g:
+
+[rhs_function]
+
+The parameters of the function must follow the example above where `x` is the
+current state, here a two-component vector containing position ['q] and
+momentum ['p] of the oscillator, `dxdt` is the derivative ['x'] and should be
+filled by the function with ['f(x)], and `t` is the current time.
+Note that in this example ['t] is not required to calculate ['f], however
+odeint expects the function signature to have exactly three parameters (there
+are exception, discussed later).
+
+A more sophisticated approach is to implement the system as a class where the rhs function is defined as the ()-operator of the class with the same parameter structure as above:
+
+[rhs_class]
+
+odeint can deal with instances of such classes instead of pure functions which
+allows for cleaner code.
+
+[endsect]
+
+[section Stepper Types]
+
+Numerical integration works iteratively, that means you start at a state ['x(t)] and perform a time-step of length ['dt] to obtain the approximate state ['x(t+dt)]. There exist many different methods to perform such a time-step each of which has a certain order ['q]. If the order of a method is ['q] than it is accurate up to term ['~dt[super q]] that means the error in ['x] made by such a step is ['~dt[super q+1]]. odeint provides several steppers of different orders, see __odeint_stepper_table.
+
+Some of steppers in the table above are special: Some need the Jacobian of the ODE, others are constructed for special ODE-systems like Hamiltonian systems. We will show typical examples and use-cases in this tutorial and which kind of steppers should be applied.
+
+[endsect]
+
+[section Integration with Constant Step Size]
+
+The basic stepper just performs one time-step and doesn't give you any information about the error that was made (except that you know it is of order ['q+1]). Such steppers are used with constant step size that should be chosen small enough to have reasonable small errors. However, you should apply some sort of validity check of your results (like observing conserved quantities) because you have no other control of the error. The following example defines a basic stepper based on the classical Runge-Kutta scheme of 4th order. The declaration of the stepper requires the state type as template parameter. The integration can now be done by using the `integrate_const( Stepper, System, state, start_time, end_time, step_size )` function from odeint:
+
+[define_const_stepper]
+
+This call integrates the system defined by `harmonic_oscillator` using the RK4 method from ['t=0] to ['10] with a step-size ['dt=0.01] and the initial condition given in `x`. The result, ['x(t=10)] is stored in `x` (in-place). Each stepper defines a `do_step` method which can also be used directly. So, you write down the above example as
+
+[integrate_const_loop]
+
+[tip If you have a C++11 enabled compiler you can easily use lambdas to create the system function :
+
+[define_const_stepper_cpp11]
+
+]
+
+[endsect]
+
+[section Integration with Adaptive Step Size]
+
+To improve the numerical results and additionally minimize the computational
+effort, the application of a step size control is advisable. Step size control
+is realized via stepper algorithms that additionally provide an error
+estimation of the applied step. odeint provides a number of such
+*ErrorSteppers* and we will show their usage on the example of
+`explicit_error_rk54_ck` - a 5th order Runge-Kutta method with 4th order
+error estimation and coefficients introduced by Cash and Karp.
+
+[define_adapt_stepper]
+
+Given the error stepper, one still needs an instance that checks the error and adjusts the step size accordingly. In odeint, this is done by *ControlledSteppers*. For the `runge_kutta_cash_karp54` stepper a `controlled_runge_kutta` stepper exists which can be used via
+
+[integrate_adapt]
+
+As above, this integrates the system defined by `harmonic_oscillator`, but now using an adaptive step size method based on the Runge-Kutta Cash-Karp 54 scheme from ['t=0] to ['10] with an initial step size of ['dt=0.01] (will be adjusted) and the initial condition given in x. The result, ['x(t=10)], will also be stored in x (in-place).
+
+In the above example an error stepper is nested in a controlled stepper. This is a nice technique; however one drawback is that one always needs to define both steppers. One could also write the instantiation of the controlled stepper into the call of the integrate function but a complete knowledge of the underlying stepper types is still necessary. Another point is, that the error tolerances for the step size control are not easily included into the controlled stepper. Both issues can be solved by using `make_controlled`:
+
+[integrate_adapt_make_controlled]
+
+`make_controlled` can be used with many of the steppers of odeint. The first
+parameter is the absolute error tolerance ['eps_abs] and the second is the
+relative error tolerance ['eps_rel] which is used during the integration. The template parameter determines from which error stepper a controlled stepper should be instantiated. An alternative syntax of `make_controlled` is
+
+[integrate_adapt_make_controlled_alternative]
+
+For the Runge-Kutta controller the error made during one step is compared with ['eps_abs + eps_rel * ( a[sub x] * |x| + a[sub dxdt] * dt * |dxdt| )]. If the error is smaller than this value the current step is accepted, otherwise it is rejected and the step size is decreased. Note, that the step size is also increased if the error gets too small compared to the rhs of the above relation. The full instantiation of the `controlled_runge_kutta` with all parameters is therefore
+
+[integrate_adapt_full]
+
+When using `make_controlled` the parameter ['a[sub x]] and ['a[sub dxdt]] are used with their standard values of 1.
+
+In the tables below, one can find all steppers which are working with `make_controlled` and `make_dense_output` which is the analog for the dense output steppers.
+
+[include make_controlled_table.qbk]
+
+[include make_dense_output_table.qbk]
+
+When using `make_controlled` or `make_dense_output` one should be aware which exact type is used and how the step size control works.
+
+[endsect]
+
+[section Using iterators]
+
+odeint supports iterators for solving ODEs. That is, you instantiate a pair of iterators and instead of using the integrate routines with an appropriate observer you put the iterators in one of the algorithm from the C++ standard library or from Boost.Range. An example is
+
+[harm_iterator_const_step]
+
+[endsect]
+
+The full source file for this example can be found here: [github_link examples/harmonic_oscillator.cpp harmonic_oscillator.cpp]
+
+
+[endsect]
diff --git a/doc/tutorial_parallel.qbk b/doc/tutorial_parallel.qbk
new file mode 100644
index 0000000..92f401c
--- /dev/null
+++ b/doc/tutorial_parallel.qbk
@@ -0,0 +1,266 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Pascal Germroth
+ Copyright 2013 Mario Mulansky
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+[section Parallel computation with OpenMP and MPI]
+
+Parallelization is a key feature for modern numerical libraries due to the vast
+availability of many cores nowadays, even on Laptops.
+odeint currently supports parallelization with OpenMP and MPI, as described in
+the following sections.
+However, it should be made clear from the beginning that the difficulty of
+efficiently distributing ODE integration on many cores/machines lies in the
+parallelization of the system function, which is still the user's
+responsibility.
+Simply using a parallel odeint backend without parallelizing the system function
+will bring you almost no performance gains.
+
+[section OpenMP]
+
+[import ../examples/openmp/phase_chain.cpp]
+
+odeint's OpenMP support is implemented as an external backend, which needs to be
+manually included. Depending on the compiler some additional flags may be
+needed, i.e. [^-fopenmp] for GCC.
+[phase_chain_openmp_header]
+
+In the easiest parallelization approach with OpenMP we use a standard `vector`
+as the state type:
+[phase_chain_vector_state]
+
+We initialize the state with some random data:
+[phase_chain_init]
+
+Now we have to configure the stepper to use the OpenMP backend.
+This is done by explicitly providing the `openmp_range_algebra` as a template
+parameter to the stepper.
+This algebra requires the state type to be a model of Random Access Range and
+will be used from multiple threads by the algebra.
+[phase_chain_stepper]
+
+Additional to providing the stepper with OpenMP parallelization we also need
+a parallelized system function to exploit the available cores.
+Here this is shown for a simple one-dimensional chain of phase oscillators with
+nearest neighbor coupling:
+[phase_chain_rhs]
+
+[note In the OpenMP backends the system function will always be called
+sequentially from the thread used to start the integration.]
+
+Finally, we perform the integration by using one of the integrate functions from
+odeint.
+As you can see, the parallelization is completely hidden in the stepper and the
+system function.
+OpenMP will take care of distributing the work among the threads and join them
+automatically.
+[phase_chain_integrate]
+
+After integrating, the data can be accessed immediately and be processed
+further.
+Note, that you can specify the OpenMP scheduling by calling `omp_set_schedule`
+in the beginning of your program:
+[phase_chain_scheduling]
+
+See [github_link examples/openmp/phase_chain.cpp
+openmp/phase_chain.cpp] for the complete example.
+
+[heading Split state]
+
+[import ../examples/openmp/phase_chain_omp_state.cpp]
+
+For advanced cases odeint offers another approach to use OpenMP that allows for
+a more exact control of the parallelization.
+For example, for odd-sized data where OpenMP's thread boundaries don't match
+cache lines and hurt performance it might be advisable to copy the data from the
+continuous `vector<T>` into separate, individually aligned, vectors.
+For this, odeint provides the `openmp_state<T>` type, essentially an alias for
+`vector<vector<T>>`.
+
+Here, the initialization is done with a `vector<double>`, but then we use
+odeint's `split` function to fill an `openmp_state`.
+The splitting is done such that the sizes of the individual regions differ at
+most by 1 to make the computation as uniform as possible.
+[phase_chain_state_init]
+
+Of course, the system function has to be changed to deal with the
+`openmp_state`.
+Note that each sub-region of the state is computed in a single task, but at the
+borders read access to the neighbouring regions is required.
+[phase_chain_state_rhs]
+
+Using the `openmp_state<T>` state type automatically selects `openmp_algebra`
+which executes odeint's internal computations on parallel regions.
+Hence, no manual configuration of the stepper is necessary.
+At the end of the integration, we use `unsplit` to concatenate the sub-regions
+back together into a single vector.
+[phase_chain_state_integrate]
+
+[note You don't actually need to use `openmp_state<T>` for advanced use cases,
+`openmp_algebra` is simply an alias for `openmp_nested_algebra<range_algebra>`
+and supports any model of Random Access Range as the outer, parallel state type,
+and will use the given algebra on its elements.]
+
+See [github_link examples/openmp/phase_chain_omp_state.cpp
+openmp/phase_chain_omp_state.cpp] for the complete example.
+
+[endsect]
+
+[section MPI]
+
+[import ../examples/mpi/phase_chain.cpp]
+
+To expand the parallel computation across multiple machines we can use MPI.
+
+The system function implementation is similar to the OpenMP variant with split
+data, the main difference being that while OpenMP uses a spawn/join model where
+everything not explicitly paralleled is only executed in the main thread, in
+MPI's model each node enters the `main()` method independently, diverging based
+on its rank and synchronizing through message-passing and explicit barriers.
+
+odeint's MPI support is implemented as an external backend, too.
+Depending on the MPI implementation the code might need to be compiled with i.e.
+[^mpic++].
+[phase_chain_mpi_header]
+
+Instead of reading another thread's data, we asynchronously send and receive the
+relevant data from neighbouring nodes, performing some computation in the interim
+to hide the latency.
+[phase_chain_mpi_rhs]
+
+Analogous to `openmp_state<T>` we use `mpi_state< InnerState<T> >`, which
+automatically selects `mpi_nested_algebra` and the appropriate MPI-oblivious
+inner algebra (since our inner state is a `vector`, the inner algebra will be
+`range_algebra` as in the OpenMP example).
+[phase_chain_state]
+
+In the main program we construct a `communicator` which tells us the `size` of
+the cluster and the current node's `rank` within that.
+We generate the input data on the master node only, avoiding unnecessary work on
+the other nodes.
+Instead of simply copying chunks, `split` acts as a MPI collective function here
+and sends/receives regions from master to each slave.
+The input argument is ignored on the slaves, but the master node receives
+a region in its output and will participate in the computation.
+[phase_chain_mpi_init]
+
+Now that `x_split` contains (only) the local chunk for each node, we start the
+integration.
+
+To print the result on the master node, we send the processed data back using
+`unsplit`.
+[phase_chain_mpi_integrate]
+
+[note `mpi_nested_algebra::for_each`[~N] doesn't use any MPI constructs, it
+simply calls the inner algebra on the local chunk and the system function is not
+guarded by any barriers either, so if you don't manually place any (for example
+in parameter studies cases where the elements are completely independent) you
+might see the nodes diverging, returning from this call at different times.]
+
+See [github_link examples/mpi/phase_chain.cpp
+mpi/phase_chain.cpp] for the complete example.
+
+[endsect]
+
+[section Concepts]
+
+[section MPI State]
+As used by `mpi_nested_algebra`.
+[heading Notation]
+[variablelist
+ [[`InnerState`] [The inner state type]]
+ [[`State`] [The MPI-state type]]
+ [[`state`] [Object of type `State`]]
+ [[`world`] [Object of type `boost::mpi::communicator`]]
+]
+[heading Valid Expressions]
+[table
+ [[Name] [Expression] [Type] [Semantics]]
+ [[Construct a state with a communicator]
+ [`State(world)`] [`State`] [Constructs the State.]]
+ [[Construct a state with the default communicator]
+ [`State()`] [`State`] [Constructs the State.]]
+ [[Get the current node's inner state]
+ [`state()`] [`InnerState`] [Returns a (const) reference.]]
+ [[Get the communicator]
+ [`state.world`] [`boost::mpi::communicator`] [See __boost_mpi.]]
+]
+[heading Models]
+* `mpi_state<InnerState>`
+
+[endsect]
+
+[section OpenMP Split State]
+As used by `openmp_nested_algebra`, essentially a Random Access Container with
+`ValueType = InnerState`.
+[heading Notation]
+[variablelist
+ [[`InnerState`] [The inner state type]]
+ [[`State`] [The split state type]]
+ [[`state`] [Object of type `State`]]
+]
+[heading Valid Expressions]
+[table
+ [[Name] [Expression] [Type] [Semantics]]
+ [[Construct a state for `n` chunks]
+ [`State(n)`] [`State`] [Constructs underlying `vector`.]]
+ [[Get a chunk]
+ [`state[i]`] [`InnerState`] [Accesses underlying `vector`.]]
+ [[Get the number of chunks]
+ [`state.size()`] [`size_type`] [Returns size of underlying `vector`.]]
+]
+[heading Models]
+* `openmp_state<ValueType>` with `InnerState = vector<ValueType>`
+
+[endsect]
+
+[section Splitter]
+[heading Notation]
+[variablelist
+ [[`Container1`] [The continuous-data container type]]
+ [[`x`] [Object of type `Container1`]]
+ [[`Container2`] [The chunked-data container type]]
+ [[`y`] [Object of type `Container2`]]
+]
+[heading Valid Expressions]
+[table
+ [[Name] [Expression] [Type] [Semantics]]
+ [[Copy chunks of input to output elements]
+ [`split(x, y)`] [`void`]
+ [Calls `split_impl<Container1, Container2>::split(x, y)`, splits `x` into
+ `y.size()` chunks.]]
+ [[Join chunks of input elements to output]
+ [`unsplit(y, x)`] [`void`]
+ [Calls `unsplit_impl<Container2, Container1>::unsplit(y, x)`, assumes `x`
+ is of the correct size ['__sigma `y[i].size()`], does not resize `x`.]]
+]
+[heading Models]
+* defined for `Container1` = __boost_range and `Container2 = openmp_state`
+* and `Container2 = mpi_state`.
+
+To implement splitters for containers incompatible with __boost_range,
+specialize the `split_impl` and `unsplit_impl` types:
+```
+template< class Container1, class Container2 , class Enabler = void >
+struct split_impl {
+ static void split( const Container1 &from , Container2 &to );
+};
+
+template< class Container2, class Container1 , class Enabler = void >
+struct unsplit_impl {
+ static void unsplit( const Container2 &from , Container1 &to );
+};
+```
+[endsect]
+
+[endsect]
+
+[endsect]
diff --git a/doc/tutorial_solar_system.qbk b/doc/tutorial_solar_system.qbk
new file mode 100644
index 0000000..a9e6677
--- /dev/null
+++ b/doc/tutorial_solar_system.qbk
@@ -0,0 +1,109 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+ Copyright 2012 Sylwester Arabas
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+
+[section Solar system]
+
+[section Gravitation and energy conservation]
+
+The next example in this tutorial is a simulation of the outer solar system, consisting of the sun, Jupiter, Saturn, Uranus, Neptune and Pluto.
+
+[$solar_system.jpg]
+
+Each planet and of course the sun will be represented by mass points. The interaction force between each object is the gravitational force which can be written as
+
+['F[subl ij] = -__gamma m[subl i] m[subl j] ( q[subl i] - q[subl j] ) / | q[subl i] - q[subl j] | [super 3]]
+
+where [' __gamma] is the gravitational constant, ['m[subl i]] and ['m[subl j]] are the masses and ['q[subl i]] and ['q[subl j]] are the locations of the two objects. The equations of motion are then
+
+['dq[subl i] / dt = p[subl i]]
+
+['dp[subl i] / dt = 1 / m[subl i] __Sigma[subl ji] F[subl ij]]
+
+where ['p[subl i]] is the momenta of object ['i]. The equations of motion can also be derived from the Hamiltonian
+
+['H = __Sigma[subl i] p[subl i][super 2] / ( 2 m[subl i] ) + __Sigma[subl j] V( q[subl i] , q[subl j] )]
+
+with the interaction potential ['V(q[subl i],q[subl j])]. The Hamiltonian equations give the
+equations of motion
+
+['dq[subl i] / dt = dH / dp[subl i]]
+
+['dp[subl i] / dt = -dH / dq[subl i]]
+
+In time independent Hamiltonian system the energy and the phase space volume
+are conserved and special integration methods have to be applied in order to
+ensure these conservation laws. The odeint library provides classes for
+separable Hamiltonian systems, which can be written in the form ['H = __Sigma
+p[subl i][super 2] / (2m[subl i]) + H[subl q](q)], where ['H[subl q](q)] only
+depends on the coordinates. Although this functional form might look a bit
+arbitrary, it covers nearly all classical mechanical systems with inertia and
+without dissipation, or where the equations of motion can be written in the
+form ['dq[subl i] / dt = p[subl i]] / m[subl i] , ['dp[subl i] / dt = f(
+q[subl i] )].
+
+[note A short physical note: While the two-body-problem is known to be
+integrable, that means it can be solved with purely analytic techniques,
+already the three-body-problem is not solvable. This was found in the end of the
+19th century by H. Poincare which led to the whole new subject of
+[@http://en.wikipedia.org/wiki/Chaos_theory Chaos Theory].]
+
+[endsect]
+
+
+[section Define the system function]
+
+To implement this system we define a 3D point type which will represent the space as well as the velocity. Therefore, we use the operators from __boost_operators:
+
+[import ../examples/point_type.hpp]
+[point_type]
+
+
+The next step is to define a container type storing the values of ['q] and ['p] and to define system functions. As container type we use `boost::array`
+
+[import ../examples/solar_system.cpp]
+[container_type_definition]
+
+The `container_type` is different from the state type of the ODE. The state type of the ode is simply a `pair< container_type , container_type >` since it needs the information about the coordinates and the momenta.
+
+Next we define the system's equations.
+As we will use a stepper that accounts for the Hamiltonian (energy-preserving)
+character of the system, we have to define the rhs different from the usual
+case where it is just a single function.
+The stepper will make use of the separable character, which means the system
+will be defined by two objects representing ['f(p) = -dH/dq] and ['g(q) = dH/dp]:
+
+[coordinate_function]
+
+[momentum_function]
+
+In general a three body-system is chaotic, hence we can not expect that arbitrary initial conditions of the system will lead to a solution comparable with the solar system dynamics. That is we have to define proper initial conditions, which are taken from the book of Hairer, Wannier, Lubich __hairer_geom_ref.
+
+As mentioned above, we need to use some special integrators in order to
+conserve phase space volume. There is a well known family of such integrators,
+the so-called Runge-Kutta-Nystroem solvers, which we apply here in terms of a
+`symplectic_rkn_sb3a_mclachlan` stepper:
+
+[integration_solar_system]
+
+These integration routine was used to produce the above sketch of the solar system. Note, that there are two particularities in this example. First, the state of the symplectic stepper is not `container_type` but a pair of `container_type`. Hence, we must pass such a pair to the integrate function. Since, we want to pass them as references we can simply pack them into __boost_ref. The second point is the observer, which is called with a state type, hence a pair of `container_type`. The reference wrapper is also passed, but this is not a problem at all:
+
+[streaming_observer]
+
+[tip You can use C++11 lambda to create the observers]
+
+The full example can be found here: [github_link examples/solar_system.cpp solar_system.cpp]
+
+[endsect]
+
+[endsect]
diff --git a/doc/tutorial_special_topics.qbk b/doc/tutorial_special_topics.qbk
new file mode 100644
index 0000000..0e3e9dc
--- /dev/null
+++ b/doc/tutorial_special_topics.qbk
@@ -0,0 +1,274 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2013 Mario Mulansky
+ Copyright 2012 Sylwester Arabas
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+[/ [section Special topics] /]
+
+[section Complex state types]
+
+[import ../examples/stuart_landau.cpp]
+
+Thus far we have seen several examples defined for real values.
+odeint can handle complex state types, hence ODEs which are defined on complex
+vector spaces, as well. An example is the Stuart-Landau oscillator
+
+['d __Psi / dt = ( 1 + i __eta ) __Psi + ( 1 + i __alpha ) | __Psi |[super 2] __Psi ]
+
+where ['__Psi] and ['i] is a complex variable. The definition of this ODE in C++
+using complex< double > as a state type may look as follows
+
+[stuart_landau_system_function]
+
+One can also use a function instead of a functor to implement it
+
+[stuart_landau_system_function_alternative]
+
+We strongly recommend to use the first ansatz. In this case you have explicit control over the parameters of the system and are not restricted to use global variables to parametrize the oscillator.
+
+When choosing the stepper type one has to account for the "unusual" state type:
+it is a single `complex<double>` opposed to the vector types used in the
+previous examples. This means that no iterations over vector elements have to
+be performed inside the stepper algorithm. Odeint already detects that and
+automatically uses the `vector_space_algebra` for computation.
+You can enforce this by supplying additional template arguments to the stepper
+including the `vector_space_algebra`. Details on the usage of algebras can be
+found in the section __adapt_state_types.
+
+[stuart_landau_integration]
+
+The full cpp file for the Stuart-Landau example can be found here [github_link
+examples/stuart_landau.cpp stuart_landau.cpp]
+
+[endsect]
+
+[section Lattice systems]
+
+[import ../examples/fpu.cpp]
+
+
+odeint can also be used to solve ordinary differential equations defined on lattices. A prominent example is the Fermi-Pasta-Ulam system __fpu_scholarpedia_ref. It is a Hamiltonian system of nonlinear coupled harmonic oscillators. The Hamiltonian is
+
+[' H = __Sigma[subl i] p[subl i][super 2]/2 + 1/2 ( q[subl i+1] - q[subl i] )^2 + __beta / 4 ( q[subl i+1] - q[subl i] )^4 ]
+
+Remarkably, the Fermi-Pasta-Ulam system was the first numerical experiment to be implemented on a computer. It was studied at Los Alamos in 1953 on one of the first computers (a MANIAC I) and it triggered a whole new tree of mathematical and physical science.
+
+Like the __tut_solar_system, the FPU is solved again by a symplectic solver, but in this case we can speed up the computation because the ['q] components trivially reduce to ['dq[subl i] / dt = p[subl i]]. odeint is capable of doing this performance improvement. All you have to do is to call the symplectic solver with an state function for the ['p] components. Here is how this function looks like
+
+[fpu_system_function]
+
+You can also use `boost::array< double , N >` for the state type.
+
+Now, you have to define your initial values and perform the integration:
+
+[fpu_integration]
+
+The observer uses a reference to the system object to calculate the local energies:
+
+[fpu_observer]
+
+The full cpp file for this FPU example can be found here [github_link examples/fpu.cpp fpu.cpp]
+
+[endsect]
+
+[section Ensembles of oscillators]
+
+[import ../examples/phase_oscillator_ensemble.cpp]
+
+Another important high dimensional system of coupled ordinary differential equations is an ensemble of ['N] all-to-all coupled phase oscillators __synchronization_pikovsky_ref. It is defined as
+
+[' d__phi[subl k] / dt = __omega[subl k] + __epsilon / N __Sigma[subl j] sin( __phi[subl j] - __phi[subl k] )]
+
+The natural frequencies ['__omega[subl i]] of each oscillator follow some distribution and ['__epsilon] is the coupling strength. We choose here a Lorentzian distribution for ['__omega[subl i]]. Interestingly a phase transition can be observed if the coupling strength exceeds a critical value. Above this value synchronization sets in and some of the oscillators oscillate with the same frequency despite their different natural frequencies. The transition is also called Kuramoto transition. Its behavior can be analyzed by employing the mean field of the phase
+
+['Z = K e[super i __Theta] = 1 / N __Sigma[subl k]e[super i __phi[subl k]]]
+
+The definition of the system function is now a bit more complex since we also need to store the individual frequencies of each oscillator.
+
+[phase_oscillator_ensemble_system_function]
+
+Note, that we have used ['Z] to simplify the equations of motion. Next, we create an observer which computes the value of ['Z] and we record ['Z] for different values of ['__epsilon].
+
+[phase_oscillator_ensemble_observer]
+
+Now, we do several integrations for different values of ['__epsilon] and record ['Z]. The result nicely confirms the analytical result of the phase transition, i.e. in our example the standard deviation of the Lorentzian is 1 such that the transition will be observed at ['__epsilon = 2].
+
+[phase_oscillator_ensemble_integration]
+
+The full cpp file for this example can be found here [github_link examples/phase_oscillator_ensemble.cpp phase_oscillator_ensemble.cpp]
+
+[endsect]
+
+[section Using boost::units]
+
+[import ../examples/harmonic_oscillator_units.cpp]
+
+odeint also works well with __boost_units - a library for compile time unit
+and dimension analysis. It works by decoding unit information into the types
+of values. For a one-dimensional unit you can just use the Boost.Unit types as
+state type, deriv type and time type and hand the `vector_space_algebra` to
+the stepper definition and everything works just fine:
+
+```
+typedef units::quantity< si::time , double > time_type;
+typedef units::quantity< si::length , double > length_type;
+typedef units::quantity< si::velocity , double > velocity_type;
+
+typedef runge_kutta4< length_type , double , velocity_type , time_type ,
+ vector_space_algebra > stepper_type;
+```
+
+If you want to solve more-dimensional problems the individual entries
+typically have different units. That means that the `state_type` is now
+possibly heterogeneous, meaning that every entry might have a different type.
+To solve this problem, compile-time sequences from __boost_fusion can be used.
+
+To illustrate how odeint works with __boost_units we use the harmonic oscillator as primary example. We start with defining all quantities
+
+[units_define_basic_quantities]
+
+Note, that the `state_type` and the `deriv_type` are now a compile-time fusion
+sequences. `deriv_type` represents ['x'] and is now different from the state
+type as it has different unit definitions. Next, we define the ordinary
+differential equation which is completely equivalent to the example in __tut_harmonic_oscillator:
+
+[units_define_ode]
+
+Next, we instantiate an appropriate stepper. We must explicitly parametrize
+the stepper with the `state_type`, `deriv_type`, `time_type`.
+
+[units_define_stepper]
+
+[note When using compile-time sequences, the iteration over vector elements is
+done by the `fusion_algebra`, which is automatically chosen by odeint. For
+more on the state types / algebras see chapter __adapt_state_types.]
+
+It is quite easy but the compilation time might take very long. Furthermore, the observer is defined a bit different
+
+[units_observer]
+
+[caution Using __boost_units works nicely but compilation can be very time and
+memory consuming. For example the unit test for the usage of __boost_units in odeint take up to 4 GB
+of memory at compilation.]
+
+The full cpp file for this example can be found here [github_link examples/harmonic_oscillator_units.cpp harmonic_oscillator_units.cpp].
+
+[endsect]
+
+[section Using matrices as state types]
+
+[import ../examples/two_dimensional_phase_lattice.cpp]
+
+odeint works well with a variety of different state types. It is not restricted to pure vector-wise types, like `vector< double >`, `array< double , N >`, `fusion::vector< double , double >`, etc. but also works with types having a different topology then simple vectors. Here, we show how odeint can be used with matrices as states type, in the next section we will show how can be used to solve ODEs defined on complex networks.
+
+By default, odeint can be used with `ublas::matrix< T >` as state type for matrices. A simple example is a two-dimensional lattice of coupled phase oscillators. Other matrix types like `mtl::dense_matrix` or blitz arrays and matrices can used as well but need some kind of activation in order to work with odeint. This activation is described in following sections,
+
+The definition of the system is
+
+[two_dimensional_phase_lattice_definition]
+
+In principle this is all. Please note, that the above code is far from being optimal. Better performance can be achieved if every interaction is only calculated once and iterators for columns and rows are used. Below are some visualizations of the evolution of this lattice equation.
+
+[$phase_lattice_2d_0000.jpg] [$phase_lattice_2d_0100.jpg] [$phase_lattice_2d_1000.jpg]
+
+The full cpp for this example can be found here [github_link examples/two_dimensional_phase_lattice.cpp two_dimensional_phase_lattice.cpp].
+
+[endsect]
+
+[/
+[section Partial differential equations]
+To be continued:
+*Wave equation
+*KdV
+*Ginzburg-Landau
+[endsect]
+[section Ordinary differential equations on networks]
+to be continued
+[endsect]
+]
+
+[section Using arbitrary precision floating point types]
+
+[import ../examples/multiprecision/lorenz_mp.cpp]
+
+Sometimes one needs results with higher precision than provided by the
+standard floating point types.
+As odeint allows to configure the fundamental numerical type, it is well
+suited to be run with arbitrary precision types.
+Therefore, one only needs a library that provides a type representing values
+with arbitrary precision and the fundamental operations for those values.
+__boost_multiprecision is a boost library that does exactly this.
+Making use of __boost_multiprecision to solve odes with odeint is very simple,
+as the following example shows.
+
+Here we use `cpp_dec_float_50` as the fundamental value type, which ensures
+exact computations up to 50 decimal digits.
+
+
+[mp_lorenz_defs]
+
+As exemplary ODE again the lorenz system is chosen, but here we have to make
+sure all constants are initialized as high precision values.
+
+[mp_lorenz_rhs]
+
+The actual integration then is straight forward:
+
+[mp_lorenz_int]
+
+The full example can be found at [github_link examples/multiprecision/lorenz_mp.cpp lorenz_mp.cpp].
+Another example that compares the accuracy of the high precision type with
+standard double can be found at [github_link examples/multiprecision/cmp_precision.cpp cmp_precision.cpp].
+
+Furthermore, odeint can also be run with other multiprecision libraries,
+e.g. [@http://gmplib.org/ gmp].
+An example for this is given in [github_link examples/gmpxx/lorenz_gmpxx.cpp lorenz_gmpxx.cpp].
+
+[endsect]
+
+[section Self expanding lattices]
+
+[import ../examples/resizing_lattice.cpp]
+
+odeint supports changes of the state size during integration if a state_type
+is used which can be resized, like `std::vector`.
+The adjustment of the state's size has to be done from outside and the stepper
+has to be instantiated with `always_resizer` as the template argument for the
+`resizer_type`.
+In this configuration, the stepper checks for changes in the state size and
+adjust it's internal storage accordingly.
+
+We show this for a Hamiltonian system of nonlinear, disordered oscillators with nonlinear nearest neighbor coupling.
+
+The system function is implemented in terms of a class that also provides functions for calculating the energy.
+Note, that this class stores the random potential internally which is not resized, but rather a start index is kept which should be changed whenever the states' size change.
+
+[resizing_lattice_system_class]
+
+The total size we allow is 1024 and we start with an initial state size of 60.
+
+[resizing_lattice_initialize]
+
+The lattice gets resized whenever the energy distribution comes close to the borders `distr[10] > 1E-150`, `distr[distr.size()-10] > 1E-150`.
+If we increase to the left, `q` and `p` have to be rotated because their resize function always appends at the end.
+Additionally, the start index of the potential changes in this case.
+
+[resizing_lattice_steps_loop]
+
+The `do_resize` function simply calls `vector.resize` of `q` , `p` and `distr`.
+
+[resizing_lattice_resize_function]
+
+The full example can be found in [github_link examples/resizing_lattice.cpp resizing_lattice.cpp]
+
+[endsect]
+
+[/ [endsect] /]
diff --git a/doc/tutorial_stiff_systems.qbk b/doc/tutorial_stiff_systems.qbk
new file mode 100644
index 0000000..6e28257
--- /dev/null
+++ b/doc/tutorial_stiff_systems.qbk
@@ -0,0 +1,62 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+ Copyright 2012 Sylwester Arabas
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+
+[section Stiff systems]
+
+[import ../examples/stiff_system.cpp]
+
+An important class of ordinary differential equations are so called stiff
+system which are characterized by two or more time scales of different
+order. Examples of such systems are found in chemical systems where reaction
+rates of individual sub-reaction might differ over large ranges, for example:
+
+['d S[subl 1] / dt = - 101 S[subl 2] - 100 S[subl 1]]
+
+['d S[subl 2] / dt = S[subl 1]]
+
+
+In order to efficiently solve stiff systems numerically the Jacobian
+
+['J = d f[subl i] / d x[subl j]]
+
+is needed. Here is the definition of the above example
+
+[stiff_system_definition]
+
+The state type has to be a `ublas::vector` and the matrix type must by a
+`ublas::matrix` since the stiff integrator only accepts these types.
+However, you might want use non-stiff integrators on this system, too - we will
+do so later for demonstration. Therefore we want to use the same function also
+with other state_types, realized by templatizing the `operator()`:
+
+[stiff_system_alternative_definition]
+
+Now you can use `stiff_system` in combination with `std::vector` or
+`boost::array`. In the example the explicit time derivative of ['f(x,t)] is
+introduced separately in the Jacobian. If ['df / dt = 0] simply fill `dfdt` with zeros.
+
+A well know solver for stiff systems is the Rosenbrock method. It has a step size control and dense output facilities and can be used like all the other steppers:
+
+[integrate_stiff_system]
+
+During the integration 71 steps have been done. Comparing to a classical Runge-Kutta solver this is a very good result. For example the Dormand-Prince 5 method with step size control and dense output yields 1531 steps.
+
+[integrate_stiff_system_alternative]
+
+Note, that we have used __boost_phoenix, a great functional programming library, to create and compose the observer.
+
+The full example can be found here: [github_link examples/stiff_system.cpp stiff_system.cpp]
+
+
+[endsect]
diff --git a/doc/tutorial_thrust_cuda.qbk b/doc/tutorial_thrust_cuda.qbk
new file mode 100644
index 0000000..4ad6aa0
--- /dev/null
+++ b/doc/tutorial_thrust_cuda.qbk
@@ -0,0 +1,172 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011-2013 Mario Mulansky
+ Copyright 2012 Sylwester Arabas
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+[section Using CUDA (or OpenMP, TBB, ...) via Thrust]
+
+Modern graphic cards (graphic processing units - GPUs) can be used to speed up
+the performance of time consuming algorithms by means of massive
+parallelization. They are designed to execute many operations in
+parallel. odeint can utilize the power of GPUs by means of CUDA and __thrust,
+which is a STL-like interface for the native CUDA API.
+
+[important Thrust also supports parallelization using OpenMP and Intel Threading Building Blocks (TBB). You can switch
+between CUDA, OpenMP and TBB parallelizations by a simple compiler
+switch. Hence, this also provides an easy way to get basic OpenMP
+parallelization into odeint. The examples discussed below are focused on GPU parallelization, though. ]
+
+To use odeint with CUDA a few points have to be taken into account. First of all, the problem has to be well chosen. It makes absolutely no sense to try to parallelize the code for a three dimensional system, it is simply too small and not worth the effort. One single function call (kernel execution) on the GPU is slow but you can do the operation on a huge set of data with only one call. We have experienced that the vector size over which is parallelized should be of the order of ['10[super 6]] to make full use of the GPU. Secondly, you have to use __thrust's algorithms and functors when implementing the rhs the ODE. This might be tricky since it involves some kind of functional programming knowledge.
+
+Typical applications for CUDA and odeint are large systems, like lattices or discretizations of PDE, and parameter studies. We introduce now three examples which show how the power of GPUs can be used in combination with odeint.
+
+[important The full power of CUDA is only available for really large systems where the number of coupled ordinary differential equations is of order ['N=10[super 6]] or larger. For smaller systems the CPU is usually much faster. You can also integrate an ensemble of different uncoupled ODEs in parallel as shown in the last example.]
+
+[section Phase oscillator ensemble]
+
+[import ../examples/thrust/phase_oscillator_ensemble.cu]
+
+The first example is the phase oscillator ensemble from the previous
+section:
+
+[' d__phi[subl k] / dt = __omega[subl k] + __epsilon / N __Sigma[subl j] sin( __phi[subl j] - __phi[subl k] ).]
+
+It has a phase transition at ['__epsilon = 2] in the limit of
+infinite numbers of oscillators ['N]. In the case of finite ['N] this
+transition is smeared out but still clearly visible.
+
+__thrust and CUDA are perfectly suited for such kinds of problems where one needs a large number of particles (oscillators). We start by defining the state type which is a `thrust::device_vector`. The content of this vector lives on the GPU. If you are not familiar with this we recommend reading the ['Getting started] section on the __thrust website.
+
+[thrust_phase_ensemble_state_type]
+
+Thrust follows a functional programming approach. If you want to perform a calculation on the GPU you usually have to call a global function like `thrust::for_each`, `thrust::reduce`, ... with an appropriate local functor which performs the basic operation. An example is
+``
+struct add_two
+{
+ template< class T >
+ __host__ __device__
+ void operator()( T &t ) const
+ {
+ t += T( 2 );
+ }
+};
+
+// ...
+
+thrust::for_each( x.begin() , x.end() , add_two() );
+``
+This code generically adds two to every element in the container `x`.
+
+For the purpose of integrating the phase oscillator ensemble we need
+
+* to calculate the system function, hence the r.h.s. of the ODE.
+* this involves computing the mean field of the oscillator example, i.e. the values of ['R] and ['__theta]
+
+The mean field is calculated in a class `mean_field_calculator`
+
+[thrust_phase_ensemble_mean_field_calculator]
+
+Inside this class two member structures `sin_functor` and `cos_functor` are defined. They compute the sine and the cosine of a value and they are used within a transform iterator to calculate the sum of ['sin(__phi[subl k])] and ['cos(__phi[subl k])]. The classifiers `__host__` and `__device__` are CUDA specific and define a function or operator which can be executed on the GPU as well as on the CPU. The line
+
+[thrust_phase_ensemble_sin_sum]
+
+performs the calculation of this sine-sum on the GPU (or on the CPU, depending on your thrust configuration).
+
+The system function is defined via
+
+[thrust_phase_ensemble_sys_function]
+
+This class is used within the `do_step` and `integrate` method. It defines a member structure `sys_functor` for the r.h.s. of each individual oscillator and the `operator()` for the use in the steppers and integrators of odeint. The functor computes first the mean field of ['__phi[subl k]] and secondly calculates the whole r.h.s. of the ODE using this mean field. Note, how nicely `thrust::tuple` and `thrust::zip_iterator` play together.
+
+Now we are ready to put everything together. All we have to do for making
+odeint ready for using the GPU is to parametrize the stepper with the `state_type`
+and `value_type`:
+
+[thrust_phase_ensemble_define_rk4]
+
+[note We have specifically define four template parameters because we have to
+override the default parameter value `double` with `value_type` to ensure our
+programs runs properly if we use `float` as fundamental data type.]
+
+You can also use a controlled or dense output stepper, e.g.
+
+[thrust_phase_ensemble_define_dopri5]
+
+Then, it is straightforward to integrate the phase ensemble by creating an instance of the rhs class and using an integration function:
+
+[thrust_phase_ensemble_system_instance]
+[thrust_phase_ensemble_integration]
+
+We have to use `boost::ref` here in order to pass the rhs class as reference and not by value. This ensures that the natural frequencies of each oscillator are not copied when calling `integrate_const`. In the full example the performance and results of the Runge-Kutta-4 and the Dopri5 solver are compared.
+
+The full example can be found at [github_link examples/thrust/phase_oscillator_ensemble.cu phase_oscillator_example.cu].
+
+[endsect]
+
+[section Large oscillator chains]
+
+[import ../examples/thrust/phase_oscillator_chain.cu]
+
+The next example is a large, one-dimensional chain of nearest-neighbor coupled phase oscillators with the following equations of motion:
+
+['d __phi[subl k] / dt = __omega[subl k] + sin( __phi[subl k+1] - __phi[subl k] ) + sin( __phi[subl k] - __phi[subl k-1])]
+
+In principle we can use all the techniques from the previous phase oscillator ensemble example, but we have to take special care about the coupling of the oscillators. To efficiently implement the coupling you can use a very elegant way employing Thrust's permutation iterator. A permutation iterator behaves like a normal iterator on a vector but it does not iterate along the usual order of the elements.
+It rather iterates along some permutation of the elements defined by some index map. To realize the nearest neighbor coupling we create one permutation iterator which travels one step behind a usual iterator and another permutation iterator which travels one step in front. The full system class is:
+
+[thrust_phase_chain_system]
+
+Note, how easy you can obtain the value for the left and right neighboring oscillator in the system functor using the permutation iterators. But, the call of the `thrust::for_each` function looks relatively complicated. Every term of the r.h.s. of the ODE is resembled by one iterator packed in exactly the same way as it is unpacked in the functor above.
+
+Now we put everything together. We create random initial conditions and decreasing frequencies such that we should get synchronization. We copy the frequencies and the initial conditions onto the device and finally initialize and perform the integration. As result we simply write out the current state, hence the phase of each oscillator.
+
+[thrust_phase_chain_integration]
+
+The full example can be found at [github_link examples/thrust/phase_oscillator_chain.cu phase_oscillator_chain.cu].
+
+[endsect]
+
+[section Parameter studies]
+
+[import ../examples/thrust/lorenz_parameters.cu]
+
+Another important use case for __thrust and CUDA are parameter studies of relatively small systems. Consider for example the three-dimensional Lorenz system from the chaotic systems example in the previous section which has three parameters. If you want to study the behavior of this system for different parameters you usually have to integrate the system for many parameter values. Using thrust and odeint you can do this integration in parallel, hence you integrate a whole ensemble of Lorenz systems where each individual realization has a different parameter value.
+[/ The Lorenz system is dissipative, such that you can assume that different initial conditions will lead to the same attractor so . For Hamiltonian systems this is not the case. Here it might be interesting to study a range of initial conditions to quantify different regions in the phase space.]
+
+In the following we will show how you can use __thrust to integrate the above mentioned ensemble of Lorenz systems. We will vary only the parameter ['__beta] but it is straightforward to vary other parameters or even two or all three parameters. Furthermore, we will use the largest Lyapunov exponent to quantify the behavior of the system (chaoticity).
+
+We start by defining the range of the parameters we want to study. The state_type is again a `thrust::device_vector< value_type >`.
+
+[thrust_lorenz_parameters_define_beta]
+
+The next thing we have to implement is the Lorenz system without perturbations. Later, a system with perturbations is also implemented in order to calculate the Lyapunov exponent. We will use an ansatz where each device function calculates one particular realization of the Lorenz ensemble
+
+[thrust_lorenz_parameters_define_simple_system]
+
+As `state_type` a `thrust::device_vector` or a __boost_range of a `device_vector` is used. The length of the state is ['3N] where ['N] is the number of systems. The system is encoded into this vector such that all ['x] components come first, then every ['y] components and finally every ['z] components. Implementing the device function is then a simple task, you only have to decompose the tuple originating from the zip iterators.
+
+Besides the system without perturbations we furthermore need to calculate the system including linearized equations governing the time evolution of small perturbations. Using the method from above this is straightforward, with a small difficulty that Thrust's tuples have a maximal arity of 10. But this is only a small problem since we can create a zip iterator packed with zip iterators. So the top level zip iterator contains one zip iterator for the state, one normal iterator for the parameter, and one zip iterator for the derivative. Accessing the elements of this tuple in the system function is then straightforward, you unpack the tuple with `thrust::get<>()`. We will not show the code here, it is to large. It can be found [github_link examples/thrust/lorenz_parameters.cu here] and is easy to understand.
+
+Furthermore, we need an observer which determines the norm of the perturbations, normalizes them and averages the logarithm of the norm. The device functor which is used within this observer is defined
+
+[thrust_lorenz_parameters_observer_functor]
+
+Note, that this functor manipulates the state, i.e. the perturbations.
+
+Now we complete the whole code to calculate the Lyapunov exponents. First, we have to define a state vector. This vector contains ['6N] entries, the state ['x,y,z] and its perturbations ['dx,dy,dz]. We initialize them such that ['x=y=z=10], ['dx=1], and ['dy=dz=0]. We define a stepper type, a controlled Runge-Kutta Dormand-Prince 5 stepper. We start with some integration to overcome the transient behavior. For this, we do not involve the perturbation and run the algorithm only on the state ['x,y,z] without any observer. Note, how __boost_range is used for partial integration of the state vector without perturbations (the first half of the whole state). After the transient, the full system with perturbations is integrated and the Lyapunov exponents are calculated and written to `stdout`.
+
+[thrust_lorenz_parameters_integration]
+
+The full example can be found at [github_link examples/thrust/lorenz_parameters.cu lorenz_parameters.cu].
+
+[endsect]
+
+[endsect]
diff --git a/doc/tutorial_vexcl_opencl.qbk b/doc/tutorial_vexcl_opencl.qbk
new file mode 100644
index 0000000..8e69a77
--- /dev/null
+++ b/doc/tutorial_vexcl_opencl.qbk
@@ -0,0 +1,53 @@
+[/============================================================================
+ Boost.odeint
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012 Sylwester Arabas
+ Copyright 2012-2013 Mario Mulansky
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+
+[section Using OpenCL via VexCL]
+
+[import ../examples/vexcl/lorenz_ensemble.cpp]
+
+In the previous section the usage of odeint in combination with __thrust was shown. In this section we show how one can use OpenCL with odeint. The point of odeint is not to implement its own low-level data structures and algorithms, but to use high level libraries doing this task. Here, we will use the __vexcl framework to use OpenCL. __vexcl is a nice library for general computations and it uses heavily expression templates. With the help of __vexcl it is possible to write very compact and expressive application.
+
+[note vexcl needs C++11 features! So you have to compile with C++11 support enabled.]
+
+To use __vexcl one needs to include one additional header which includes the data-types and algorithms from vexcl and the adaption to odeint. Adaption to odeint means here only to adapt the resizing functionality of __vexcl to odeint.
+
+[vexcl_includes]
+
+To demonstrate the use of __vexcl we integrate an ensemble of Lorenz system. The example is very similar to the parameter study of the Lorenz system in the previous section except that we do not compute the Lyapunov exponents. Again, we vary the parameter R of the Lorenz system an solve a whole ensemble of Lorenz systems in parallel (each with a different parameter R). First, we define the state type and a vector type
+
+[vexcl_state_types ]
+
+The `vector_type` is used to represent the parameter R. The `state_type` is a multi-vector of three sub vectors and is used to represent. The first component of this multi-vector represent all `x` components of the Lorenz system, while the second all `y` components and the third all `z` components. The components of this vector can be obtained via
+
+``
+auto &x = X(0);
+auto &y = X(1);
+auto &z = X(2);
+``
+
+As already mentioned __vexcl supports expression templates and we will use them to implement the system function for the Lorenz ensemble:
+
+[vexcl_system]
+
+It's very easy, isn't it? These three little lines do all the computations for
+you. There is no need to write your own OpenCL kernels. __vexcl does
+everything for you. Next we have to write the main application. We initialize
+the vector of parameters (R) and the initial state. Note that __vexcl requires
+the `vector_space_algebra`, but that is automatically deduced and configured
+by odeint internally, so we only have to specify the `state_type` when
+instantiating the stepper and we are done:
+
+[vexcl_main]
+
+
+[endsect]
diff --git a/examples/2d_lattice/Jamfile.v2 b/examples/2d_lattice/Jamfile.v2
new file mode 100644
index 0000000..c995ec1
--- /dev/null
+++ b/examples/2d_lattice/Jamfile.v2
@@ -0,0 +1,13 @@
+# Copyright 2011 Mario Mulansky
+# Copyright 2012 Karsten Ahnert
+# Distributed under the Boost Software License, Version 1.0. (See
+# accompanying file LICENSE_1_0.txt or copy at
+# http://www.boost.org/LICENSE_1_0.txt)
+
+project
+ : requirements
+ <include>../../../../..
+ <define>BOOST_ALL_NO_LIB=1
+ ;
+
+exe spreading : spreading.cpp ;
\ No newline at end of file
diff --git a/examples/2d_lattice/lattice2d.hpp b/examples/2d_lattice/lattice2d.hpp
new file mode 100644
index 0000000..4fd9c98
--- /dev/null
+++ b/examples/2d_lattice/lattice2d.hpp
@@ -0,0 +1,165 @@
+/*
+ Copyright 2011 Mario Mulansky
+ Copyright 2012-2013 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+/* strongly nonlinear hamiltonian lattice in 2d */
+
+#ifndef LATTICE2D_HPP
+#define LATTICE2D_HPP
+
+#include <vector>
+
+#include <boost/math/special_functions/pow.hpp>
+
+using boost::math::pow;
+
+template< int Kappa , int Lambda >
+struct lattice2d {
+
+ const double m_beta;
+ std::vector< std::vector< double > > m_omega;
+
+ lattice2d( const double beta )
+ : m_beta( beta )
+ { }
+
+ template< class StateIn , class StateOut >
+ void operator()( const StateIn &q , StateOut &dpdt )
+ {
+ // q and dpdt are 2d
+ const int N = q.size();
+
+ int i;
+ for( i = 0 ; i < N ; ++i )
+ {
+ const int i_l = (i-1+N) % N;
+ const int i_r = (i+1) % N;
+ for( int j = 0 ; j < N ; ++j )
+ {
+ const int j_l = (j-1+N) % N;
+ const int j_r = (j+1) % N;
+ dpdt[i][j] = - m_omega[i][j] * pow<Kappa-1>( q[i][j] )
+ - m_beta * pow<Lambda-1>( q[i][j] - q[i][j_l] )
+ - m_beta * pow<Lambda-1>( q[i][j] - q[i][j_r] )
+ - m_beta * pow<Lambda-1>( q[i][j] - q[i_l][j] )
+ - m_beta * pow<Lambda-1>( q[i][j] - q[i_r][j] );
+ }
+ }
+ }
+
+ template< class StateIn >
+ double energy( const StateIn &q , const StateIn &p )
+ {
+ // q and dpdt are 2d
+ const int N = q.size();
+ double energy = 0.0;
+ int i;
+ for( i = 0 ; i < N ; ++i )
+ {
+ const int i_l = (i-1+N) % N;
+ const int i_r = (i+1) % N;
+ for( int j = 0 ; j < N ; ++j )
+ {
+ const int j_l = (j-1+N) % N;
+ const int j_r = (j+1) % N;
+ energy += p[i][j]*p[i][j] / 2.0
+ + m_omega[i][j] * pow<Kappa>( q[i][j] ) / Kappa
+ + m_beta * pow<Lambda>( q[i][j] - q[i][j_l] ) / Lambda / 2
+ + m_beta * pow<Lambda>( q[i][j] - q[i][j_r] ) / Lambda / 2
+ + m_beta * pow<Lambda>( q[i][j] - q[i_l][j] ) / Lambda / 2
+ + m_beta * pow<Lambda>( q[i][j] - q[i_r][j] ) / Lambda / 2;
+ }
+ }
+ return energy;
+ }
+
+
+ template< class StateIn , class StateOut >
+ double local_energy( const StateIn &q , const StateIn &p , StateOut &energy )
+ {
+ // q and dpdt are 2d
+ const int N = q.size();
+ double e = 0.0;
+ int i;
+ for( i = 0 ; i < N ; ++i )
+ {
+ const int i_l = (i-1+N) % N;
+ const int i_r = (i+1) % N;
+ for( int j = 0 ; j < N ; ++j )
+ {
+ const int j_l = (j-1+N) % N;
+ const int j_r = (j+1) % N;
+ energy[i][j] = p[i][j]*p[i][j] / 2.0
+ + m_omega[i][j] * pow<Kappa>( q[i][j] ) / Kappa
+ + m_beta * pow<Lambda>( q[i][j] - q[i][j_l] ) / Lambda / 2
+ + m_beta * pow<Lambda>( q[i][j] - q[i][j_r] ) / Lambda / 2
+ + m_beta * pow<Lambda>( q[i][j] - q[i_l][j] ) / Lambda / 2
+ + m_beta * pow<Lambda>( q[i][j] - q[i_r][j] ) / Lambda / 2;
+ e += energy[i][j];
+ }
+ }
+ //rescale
+ e = 1.0/e;
+ for( i = 0 ; i < N ; ++i )
+ for( int j = 0 ; j < N ; ++j )
+ energy[i][j] *= e;
+ return 1.0/e;
+ }
+
+ void load_pot( const char* filename , const double W , const double gap ,
+ const size_t dim )
+ {
+ std::ifstream in( filename , std::ios::in | std::ios::binary );
+ if( !in.is_open() ) {
+ std::cerr << "pot file not found: " << filename << std::endl;
+ exit(0);
+ } else {
+ std::cout << "using pot file: " << filename << std::endl;
+ }
+
+ m_omega.resize( dim );
+ for( int i = 0 ; i < dim ; ++i )
+ {
+ m_omega[i].resize( dim );
+ for( size_t j = 0 ; j < dim ; ++j )
+ {
+ if( !in.good() )
+ {
+ std::cerr << "I/O Error: " << filename << std::endl;
+ exit(0);
+ }
+ double d;
+ in.read( (char*) &d , sizeof(d) );
+ if( (d < 0) || (d > 1.0) )
+ {
+ std::cerr << "ERROR: " << d << std::endl;
+ exit(0);
+ }
+ m_omega[i][j] = W*d + gap;
+ }
+ }
+
+ }
+
+ void generate_pot( const double W , const double gap , const size_t dim )
+ {
+ m_omega.resize( dim );
+ for( size_t i = 0 ; i < dim ; ++i )
+ {
+ m_omega[i].resize( dim );
+ for( size_t j = 0 ; j < dim ; ++j )
+ {
+ m_omega[i][j] = W*static_cast<double>(rand())/RAND_MAX + gap;
+ }
+ }
+ }
+
+};
+
+#endif
diff --git a/examples/2d_lattice/nested_range_algebra.hpp b/examples/2d_lattice/nested_range_algebra.hpp
new file mode 100644
index 0000000..0afa367
--- /dev/null
+++ b/examples/2d_lattice/nested_range_algebra.hpp
@@ -0,0 +1,46 @@
+/*
+ Copyright 2011 Mario Mulansky
+ Copyright 2012 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+/* nested range algebra */
+
+#ifndef NESTED_RANGE_ALGEBRA
+#define NESTED_RANGE_ALGEBRA
+
+namespace detail {
+
+ template< class Iterator1 , class Iterator2 , class Iterator3 , class Operation , class Algebra >
+ void for_each3( Iterator1 first1 , Iterator1 last1 , Iterator2 first2 , Iterator3 first3, Operation op , Algebra &algebra )
+{
+ for( ; first1 != last1 ; )
+ algebra.for_each3( *first1++ , *first2++ , *first3++ , op );
+}
+}
+
+
+template< class InnerAlgebra >
+struct nested_range_algebra
+{
+
+ nested_range_algebra()
+ : m_inner_algebra()
+ { }
+
+ template< class S1 , class S2 , class S3 , class Op >
+ void for_each3( S1 &s1 , S2 &s2 , S3 &s3 , Op op )
+ {
+ detail::for_each3( boost::begin( s1 ) , boost::end( s1 ) , boost::begin( s2 ) , boost::begin( s3 ) , op , m_inner_algebra );
+ }
+
+
+private:
+ InnerAlgebra m_inner_algebra;
+};
+
+#endif
diff --git a/examples/2d_lattice/spreading.cpp b/examples/2d_lattice/spreading.cpp
new file mode 100644
index 0000000..88c60bf
--- /dev/null
+++ b/examples/2d_lattice/spreading.cpp
@@ -0,0 +1,122 @@
+/*
+ Copyright 2011 Mario Mulansky
+ Copyright 2012 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+/*
+ * Example of a 2D simulation of nonlinearly coupled oscillators.
+ * Program just prints final energy which should be close to the initial energy (1.0).
+ * No parallelization is employed here.
+ * Run time on a 2.3GHz Intel Core-i5: about 10 seconds for 100 steps.
+ * Compile simply via bjam or directly:
+ * g++ -O3 -I${BOOST_ROOT} -I../../../../.. spreading.cpp
+ */
+
+
+#include <iostream>
+#include <fstream>
+#include <vector>
+#include <cstdlib>
+#include <sys/time.h>
+
+#include <boost/ref.hpp>
+#include <boost/numeric/odeint/stepper/symplectic_rkn_sb3a_mclachlan.hpp>
+
+// we use a vector< vector< double > > as state type,
+// for that some functionality has to be added for odeint to work
+#include "nested_range_algebra.hpp"
+#include "vector_vector_resize.hpp"
+
+// defines the rhs of our dynamical equation
+#include "lattice2d.hpp"
+/* dynamical equations (Hamiltonian structure):
+dqdt_{i,j} = p_{i,j}
+dpdt_{i,j} = - omega_{i,j}*q_{i,j} - \beta*[ (q_{i,j} - q_{i,j-1})^3
+ +(q_{i,j} - q_{i,j+1})^3
+ +(q_{i,j} - q_{i-1,j})^3
+ +(q_{i,j} - q_{i+1,j})^3 ]
+*/
+
+
+using namespace std;
+
+static const int MAX_N = 1024;//2048;
+
+static const size_t KAPPA = 2;
+static const size_t LAMBDA = 4;
+static const double W = 1.0;
+static const double gap = 0.0;
+static const size_t steps = 100;
+static const double dt = 0.1;
+
+double initial_e = 1.0;
+double beta = 1.0;
+int realization_index = 0;
+
+//the state type
+typedef vector< vector< double > > state_type;
+
+//the stepper, choose a symplectic one to account for hamiltonian structure
+//use nested_range_algebra for calculations on vector< vector< ... > >
+typedef boost::numeric::odeint::symplectic_rkn_sb3a_mclachlan<
+ state_type , state_type , double , state_type , state_type , double ,
+ nested_range_algebra< boost::numeric::odeint::range_algebra > ,
+ boost::numeric::odeint::default_operations > stepper_type;
+
+double time_diff_in_ms( timeval &t1 , timeval &t2 )
+{ return (t2.tv_sec - t1.tv_sec)*1000.0 + (t2.tv_usec - t1.tv_usec)/1000.0 + 0.5; }
+
+
+int main( int argc, const char* argv[] ) {
+
+ srand( time(NULL) );
+
+ lattice2d< KAPPA , LAMBDA > lattice( beta );
+
+
+ lattice.generate_pot( W , gap , MAX_N );
+
+ state_type q( MAX_N , vector< double >( MAX_N , 0.0 ) );
+
+ state_type p( q );
+
+ state_type energy( q );
+
+ p[MAX_N/2][MAX_N/2] = sqrt( 0.5*initial_e );
+ p[MAX_N/2+1][MAX_N/2] = sqrt( 0.5*initial_e );
+ p[MAX_N/2][MAX_N/2+1] = sqrt( 0.5*initial_e );
+ p[MAX_N/2+1][MAX_N/2+1] = sqrt( 0.5*initial_e );
+
+ cout.precision(10);
+
+ lattice.local_energy( q , p , energy );
+ double e=0.0;
+ for( size_t i=0 ; i<energy.size() ; ++i )
+ for( size_t j=0 ; j<energy[i].size() ; ++j )
+ {
+ e += energy[i][j];
+ }
+
+ cout << "initial energy: " << lattice.energy( q , p ) << endl;
+
+ timeval elapsed_time_start , elapsed_time_end;
+ gettimeofday(&elapsed_time_start , NULL);
+
+ stepper_type stepper;
+
+ for( size_t step=0 ; step<=steps ; ++step )
+ {
+ stepper.do_step( boost::ref( lattice ) ,
+ make_pair( boost::ref( q ) , boost::ref( p ) ) ,
+ 0.0 , 0.1 );
+ }
+
+ gettimeofday(&elapsed_time_end , NULL);
+ double elapsed_time = time_diff_in_ms( elapsed_time_start , elapsed_time_end );
+ cout << steps << " steps in " << elapsed_time/1000 << " s (energy: " << lattice.energy( q , p ) << ")" << endl;
+}
diff --git a/examples/2d_lattice/vector_vector_resize.hpp b/examples/2d_lattice/vector_vector_resize.hpp
new file mode 100644
index 0000000..7132aa5
--- /dev/null
+++ b/examples/2d_lattice/vector_vector_resize.hpp
@@ -0,0 +1,105 @@
+/*
+ Copyright 2011 Mario Mulansky
+ Copyright 2012 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+/* reserved vector */
+
+#ifndef VECTOR_VECTOR_RESIZE_HPP
+#define VECTOR_VECTOR_RESIZE_HPP
+
+#include <vector>
+
+#include <boost/range.hpp>
+
+namespace boost { namespace numeric { namespace odeint {
+
+template<>
+struct is_resizeable< std::vector< std::vector< double > > >
+{
+ typedef boost::true_type type;
+ const static bool value = type::value;
+};
+
+template<>
+struct same_size_impl< std::vector< std::vector< double > > , std::vector< std::vector< double > > >
+{
+ typedef std::vector< std::vector< double > > state_type;
+
+ static bool same_size( const state_type &x1 ,
+ const state_type &x2 )
+ {
+ bool same = ( boost::size( x1 ) == boost::size( x2 ) );
+ if( !same )
+ return false;
+ typename state_type::const_iterator begin1 = boost::begin( x1 );
+ typename state_type::const_iterator begin2 = boost::begin( x2 );
+ while( begin1 != boost::end( x1 ) )
+ same &= ( boost::size( *begin1++ ) == boost::size( *begin2++ ) );
+ return same;
+ }
+};
+
+template<>
+struct resize_impl< std::vector< std::vector< double > > , std::vector< std::vector< double > > >
+{
+ typedef std::vector< std::vector< double > > state_type;
+
+ static void resize( state_type &x1 , const state_type &x2 )
+ {
+ x1.resize( boost::size( x2 ) );
+ typename state_type::iterator begin1 = boost::begin( x1 );
+ typename state_type::const_iterator begin2 = boost::begin( x2 );
+ while( begin1 != boost::end( x1 ) )
+ (*begin1++).resize( boost::size( *begin2++ ) );
+ }
+};
+
+template<>
+struct state_wrapper< std::vector< std::vector< double > > >
+{
+ typedef std::vector< std::vector< double > > state_type;
+ typedef state_wrapper< state_type > state_wrapper_type;
+ typedef boost::true_type is_resizeable;
+
+ state_type m_v;
+
+ template< class State >
+ bool same_size( const State &x )
+ {
+ bool same = ( boost::size( m_v ) == boost::size( x ) );
+ if( !same )
+ return false;
+ typename state_type::iterator begin1 = boost::begin( m_v );
+ typename State::const_iterator begin2 = boost::begin( x );
+ while( begin1 != boost::end( m_v ) )
+ same &= ( boost::size( *begin1++ ) == boost::size( *begin2++ ) );
+ return same;
+ }
+
+ template< class State >
+ bool resize( const State &x )
+ {
+ if( !same_size( x ) )
+ {
+ m_v.resize( boost::size( x ) );
+ typename state_type::iterator begin1 = boost::begin( m_v );
+ typename State::const_iterator begin2 = boost::begin( x );
+ while( begin1 != boost::end( m_v ) )
+ (*begin1++).resize( boost::size( *begin2++ ) );
+
+ return true;
+ } else
+ return false;
+ }
+
+};
+
+} } }
+
+#endif
diff --git a/examples/Jamfile.v2 b/examples/Jamfile.v2
new file mode 100644
index 0000000..11813c8
--- /dev/null
+++ b/examples/Jamfile.v2
@@ -0,0 +1,51 @@
+# Copyright 2009-2013 Karsten Ahnert
+# Copyright 2010-2013 Mario Mulansky
+# Copyright 2013 Pascal Germroth
+# Distributed under the Boost Software License, Version 1.0. (See
+# accompanying file LICENSE_1_0.txt or copy at
+# http://www.boost.org/LICENSE_1_0.txt)
+
+
+project
+ : requirements
+ <define>BOOST_ALL_NO_LIB=1
+ :
+ ;
+
+
+exe harmonic_oscillator : harmonic_oscillator.cpp ;
+exe solar_system : solar_system.cpp ;
+exe chaotic_system : chaotic_system.cpp ;
+exe stiff_system : stiff_system.cpp ;
+exe fpu : fpu.cpp ;
+exe phase_oscillator_ensemble : phase_oscillator_ensemble.cpp ;
+exe harmonic_oscillator_units : harmonic_oscillator_units.cpp : <toolset>clang:<build>no ;
+exe stuart_landau : stuart_landau.cpp ;
+exe two_dimensional_phase_lattice : two_dimensional_phase_lattice.cpp ;
+exe bulirsch_stoer : bulirsch_stoer.cpp ;
+exe elliptic_functions : elliptic_functions.cpp ;
+exe resizing_lattice : resizing_lattice.cpp ;
+exe list_lattice : list_lattice.cpp ;
+exe stepper_details : stepper_details.cpp ;
+exe my_vector : my_vector.cpp ;
+exe lorenz : lorenz.cpp ;
+exe lorenz_point : lorenz_point.cpp ;
+exe van_der_pol_stiff : van_der_pol_stiff.cpp ;
+exe simple1d : simple1d.cpp ;
+exe stochastic_euler : stochastic_euler.cpp ;
+exe generation_functions : generation_functions.cpp ;
+exe heun : heun.cpp ;
+exe bind_member_functions : bind_member_functions.cpp ;
+exe bind_member_functions_cpp11 : bind_member_functions_cpp11.cpp : <cxxflags>-std=c++0x ;
+exe molecular_dynamics : molecular_dynamics.cpp : <cxxflags>-std=c++0x ;
+exe molecular_dynamics_cells : molecular_dynamics_cells.cpp : <cxxflags>-std=c++0x ;
+exe abm_precision : abm_precision.cpp ;
+exe integrate_times : integrate_times.cpp ;
+exe find_crossing : find_crossing.cpp : <cxxflags>-std=c++0x ;
+
+build-project multiprecision ;
+# build-project mtl ;
+# build-project ublas ;
+# build-project gmpxx ;
+# build-project openmp ;
+# build-project mpi ;
diff --git a/examples/abm_precision.cpp b/examples/abm_precision.cpp
new file mode 100644
index 0000000..747919f
--- /dev/null
+++ b/examples/abm_precision.cpp
@@ -0,0 +1,84 @@
+/*
+ * abm_precision.cpp
+ *
+ * example to check the order of the multi-step methods
+ *
+ * Copyright 2009-2013 Karsten Ahnert
+ * Copyright 2009-2013 Mario Mulansky
+ *
+ * Distributed under the Boost Software License, Version 1.0.
+ * (See accompanying file LICENSE_1_0.txt or
+ * copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <iostream>
+#include <cmath>
+
+#include <boost/array.hpp>
+#include <boost/numeric/odeint.hpp>
+
+using namespace boost::numeric::odeint;
+
+const int Steps = 4;
+
+typedef double value_type;
+
+typedef boost::array< double , 2 > state_type;
+
+typedef runge_kutta_fehlberg78<state_type> initializing_stepper_type;
+typedef adams_bashforth_moulton< Steps , state_type > stepper_type;
+//typedef adams_bashforth< Steps , state_type > stepper_type;
+
+// harmonic oscillator, analytic solution x[0] = sin( t )
+struct osc
+{
+ void operator()( const state_type &x , state_type &dxdt , const double t ) const
+ {
+ dxdt[0] = x[1];
+ dxdt[1] = -x[0];
+ }
+};
+
+int main()
+{
+ stepper_type stepper;
+ initializing_stepper_type init_stepper;
+ const int o = stepper.order()+1; //order of the error is order of approximation + 1
+
+ const state_type x0 = {{ 0.0 , 1.0 }};
+ state_type x1 = x0;
+ double t = 0.0;
+ double dt = 0.25;
+ // initialization, does a number of steps already to fill internal buffer, t is increased
+ // we use the rk78 as initializing stepper
+ stepper.initialize( boost::ref(init_stepper) , osc() , x1 , t , dt );
+ // do a number of steps to fill the buffer with results from adams bashforth
+ for( size_t n=0 ; n < stepper.steps ; ++n )
+ {
+ stepper.do_step( osc() , x1 , t , dt );
+ t += dt;
+ }
+ double A = std::sqrt( x1[0]*x1[0] + x1[1]*x1[1] );
+ double phi = std::asin(x1[0]/A) - t;
+ // now we do the actual step
+ stepper.do_step( osc() , x1 , t , dt );
+ // only examine the error of the adams-bashforth-moulton step, not the initialization
+ const double f = 2.0 * std::abs( A*sin(t+dt+phi) - x1[0] ) / std::pow( dt , o ); // upper bound
+
+ std::cout << "# " << o << " , " << f << std::endl;
+
+ /* as long as we have errors above machine precision */
+ while( f*std::pow( dt , o ) > 1E-16 )
+ {
+ x1 = x0;
+ t = 0.0;
+ stepper.initialize( boost::ref(init_stepper) , osc() , x1 , t , dt );
+ A = std::sqrt( x1[0]*x1[0] + x1[1]*x1[1] );
+ phi = std::asin(x1[0]/A) - t;
+ // now we do the actual step
+ stepper.do_step( osc() , x1 , t , dt );
+ // only examine the error of the adams-bashforth-moulton step, not the initialization
+ std::cout << dt << '\t' << std::abs( A*sin(t+dt+phi) - x1[0] ) << std::endl;
+ dt *= 0.5;
+ }
+}
diff --git a/examples/adaptive_iterator.cpp b/examples/adaptive_iterator.cpp
new file mode 100644
index 0000000..343699d
--- /dev/null
+++ b/examples/adaptive_iterator.cpp
@@ -0,0 +1,361 @@
+/*
+ * adaptive_iterator.cpp
+ *
+ * Copyright 2012-2013 Karsten Ahnert
+ * Copyright 2012 Mario Mulansky
+ *
+ * Distributed under the Boost Software License, Version 1.0.
+ * (See accompanying file LICENSE_1_0.txt or
+ * copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+
+#include <iostream>
+#include <iterator>
+#include <utility>
+#include <algorithm>
+#include <cassert>
+
+#include <boost/array.hpp>
+
+#include <boost/range/algorithm.hpp>
+#include <boost/range/adaptor/filtered.hpp>
+#include <boost/range/numeric.hpp>
+
+#include <boost/numeric/odeint/stepper/runge_kutta4.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp>
+#include <boost/numeric/odeint/stepper/generation.hpp>
+
+#include <boost/numeric/odeint/iterator/adaptive_iterator.hpp>
+#include <boost/numeric/odeint/iterator/adaptive_time_iterator.hpp>
+
+#define tab "\t"
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+const double sigma = 10.0;
+const double R = 28.0;
+const double b = 8.0 / 3.0;
+
+struct lorenz
+{
+ template< class State , class Deriv >
+ void operator()( const State &x , Deriv &dxdt , double t ) const
+ {
+ dxdt[0] = sigma * ( x[1] - x[0] );
+ dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
+ dxdt[2] = -b * x[2] + x[0] * x[1];
+ }
+};
+
+#include <typeinfo>
+
+int main( int argc , char **argv )
+{
+ typedef boost::array< double , 3 > state_type;
+
+ /*
+ * Controlled steppers with time iterator
+ */
+
+ // std::for_each
+ {
+ auto stepper = make_controlled( 1.0e-6 , 1.0e-6 , runge_kutta_cash_karp54< state_type >() );
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ std::for_each( make_adaptive_time_iterator_begin( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) ,
+ make_adaptive_time_iterator_end( stepper , lorenz() , x ) ,
+ []( const std::pair< const state_type&, double > &x ) {
+ std::cout << x.second << tab << x.first[0] << tab << x.first[1] << tab << x.first[2] << "\n"; } );
+ }
+
+ // std::copy_if
+ {
+ std::vector< pair< state_type , double > > res;
+ auto stepper = make_controlled( 1.0e-6 , 1.0e-6 , runge_kutta_cash_karp54< state_type >() );
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ std::copy_if( make_adaptive_time_iterator_begin( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) ,
+ make_adaptive_time_iterator_end( stepper , lorenz() , x ) ,
+ std::back_inserter( res ) ,
+ []( const pair< const state_type& , double > &x ) {
+ return ( x.first[0] > 0.0 ) ? true : false; } );
+ for( size_t i=0 ; i<res.size() ; ++i )
+ cout << res[i].first[0] << tab << res[i].first[1] << tab << res[i].first[2] << "\n";
+ }
+
+ // std::accumulate
+ {
+ auto stepper = make_controlled( 1.0e-6 , 1.0e-6 , runge_kutta_cash_karp54< state_type >() );
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ double res = std::accumulate( make_adaptive_time_iterator_begin( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) ,
+ make_adaptive_time_iterator_end( stepper , lorenz() , x ) ,
+ 0.0 ,
+ []( double sum , const pair< const state_type& , double > &x ) {
+ return sum + x.first[0]; } );
+ cout << res << endl;
+ }
+
+
+ // std::transform
+ {
+ auto stepper = make_controlled( 1.0e-6 , 1.0e-6 , runge_kutta_cash_karp54< state_type >() );
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ vector< double > weights;
+ std::transform( make_adaptive_time_iterator_begin( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) ,
+ make_adaptive_time_iterator_end( stepper , lorenz() , x ) ,
+ back_inserter( weights ) ,
+ []( const pair< const state_type& , double > &x ) {
+ return sqrt( x.first[0] * x.first[0] + x.first[1] * x.first[1] + x.first[2] * x.first[2] ); } );
+ for( size_t i=0 ; i<weights.size() ; ++i )
+ cout << weights[i] << "\n";
+ }
+
+
+
+
+
+
+
+
+
+
+
+
+
+ /*
+ * Boost.Range versions of controlled stepper with time iterator
+ */
+
+
+ // boost::range::for_each
+ {
+ auto stepper = make_controlled( 1.0e-6 , 1.0e-6 , runge_kutta_cash_karp54< state_type >() );
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ boost::range::for_each( make_adaptive_time_range( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) ,
+ []( const std::pair< const state_type& , double > &x ) {
+ std::cout << x.second << tab << x.first[0] << tab << x.first[1] << tab << x.first[2] << "\n"; } );
+ }
+
+
+ // boost::range::copy with filtered adaptor (simulating std::copy_if)
+ {
+ auto stepper = make_controlled( 1.0e-6 , 1.0e-6 , runge_kutta_cash_karp54< state_type >() );
+ std::vector< std::pair< state_type , double > > res;
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ boost::range::copy( make_adaptive_time_range( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) |
+ boost::adaptors::filtered( [] ( const pair< const state_type& , double > &x ) { return ( x.first[0] > 0.0 ); } ) ,
+ std::back_inserter( res ) );
+ for( size_t i=0 ; i<res.size() ; ++i )
+ cout << res[i].first[0] << tab << res[i].first[1] << tab << res[i].first[2] << "\n";
+ }
+
+ // boost::range::accumulate
+ {
+ //[adaptive_time_iterator_accumulate_range
+ auto stepper = make_controlled( 1.0e-6 , 1.0e-6 , runge_kutta_cash_karp54< state_type >() );
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ double res = boost::accumulate( make_adaptive_time_range( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) , 0.0 ,
+ []( double sum , const pair< const state_type& , double > &x ) {
+ return sum + x.first[0]; } );
+ cout << res << endl;
+ //]
+ }
+
+
+ // boost::range::transform
+ {
+ auto stepper = make_controlled( 1.0e-6 , 1.0e-6 , runge_kutta_cash_karp54< state_type >() );
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ vector< double > weights;
+ boost::transform( make_adaptive_time_range( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) , back_inserter( weights ) ,
+ []( const pair< const state_type& , double > &x ) {
+ return sqrt( x.first[0] * x.first[0] + x.first[1] * x.first[1] + x.first[2] * x.first[2] ); } );
+ for( size_t i=0 ; i<weights.size() ; ++i )
+ cout << weights[i] << "\n";
+ }
+
+
+ // boost::range::find with time iterator
+ {
+ auto stepper = make_controlled( 1.0e-6 , 1.0e-6 , runge_kutta_cash_karp54< state_type >() );
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ auto iter = boost::find_if( make_adaptive_time_range( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) ,
+ []( const std::pair< const state_type & , double > &x ) {
+ return ( x.first[0] < 0.0 ); } );
+ cout << iter->second << "\t" << iter->first[0] << "\t" << iter->first[1] << "\t" << iter->first[2] << "\n";
+ }
+
+
+
+
+
+
+
+
+
+
+
+
+ // /*
+ // * Boost.Range versions for dense output steppers
+ // */
+
+ // // boost::range::for_each
+ // {
+ // runge_kutta_dopri5< state_type > stepper;
+ // state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ // boost::range::for_each( make_adaptive_range( make_dense_output( 1.0e-6 , 1.0e-6 , stepper ) , lorenz() , x , 0.0 , 1.0 , 0.01 ) ,
+ // []( const state_type &x ) {
+ // std::cout << x[0] << tab << x[1] << tab << x[2] << "\n"; } );
+ // }
+
+
+ // // boost::range::for_each with time iterator
+ // {
+ // runge_kutta_dopri5< state_type > stepper;
+ // state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ // boost::range::for_each( make_adaptive_time_range( make_dense_output( 1.0e-6 , 1.0e-6 , stepper ) , lorenz() , x , 0.0 , 1.0 , 0.01 ) ,
+ // []( const std::pair< state_type& , double > &x ) {
+ // std::cout << x.second << tab << x.first[0] << tab << x.first[1] << tab << x.first[2] << "\n"; } );
+
+ // }
+
+
+
+
+
+ /*
+ * Pure iterators for controlled stepper without time iterator
+ */
+
+ // std::for_each
+ {
+ auto stepper = make_controlled( 1.0e-6 , 1.0e-6 , runge_kutta_cash_karp54< state_type >() );
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ std::for_each( make_adaptive_iterator_begin( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) ,
+ make_adaptive_iterator_end( stepper , lorenz() , x ) ,
+ []( const state_type& x ) {
+ std::cout << x[0] << tab << x[1] << tab << x[2] << "\n"; } );
+ }
+
+ // std::copy_if
+ {
+ std::vector< state_type > res;
+ auto stepper = make_controlled( 1.0e-6 , 1.0e-6 , runge_kutta_cash_karp54< state_type >() );
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ std::copy_if( make_adaptive_iterator_begin( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) ,
+ make_adaptive_iterator_end( stepper , lorenz() , x ) ,
+ std::back_inserter( res ) ,
+ []( const state_type& x ) {
+ return ( x[0] > 0.0 ) ? true : false; } );
+ for( size_t i=0 ; i<res.size() ; ++i )
+ cout << res[i][0] << tab << res[i][1] << tab << res[i][2] << "\n";
+ }
+
+ // std::accumulate
+ {
+ auto stepper = make_controlled( 1.0e-6 , 1.0e-6 , runge_kutta_cash_karp54< state_type >() );
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ double res = std::accumulate( make_adaptive_iterator_begin( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) ,
+ make_adaptive_iterator_end( stepper , lorenz() , x ) ,
+ 0.0 ,
+ []( double sum , const state_type& x ) {
+ return sum + x[0]; } );
+ cout << res << endl;
+ }
+
+
+ // std::transform
+ {
+ auto stepper = make_controlled( 1.0e-6 , 1.0e-6 , runge_kutta_cash_karp54< state_type >() );
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ vector< double > weights;
+ std::transform( make_adaptive_iterator_begin( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) ,
+ make_adaptive_iterator_end( stepper , lorenz() , x ) ,
+ back_inserter( weights ) ,
+ []( const state_type& x ) {
+ return sqrt( x[0] * x[0] + x[1] * x[1] + x[2] * x[2] ); } );
+ for( size_t i=0 ; i<weights.size() ; ++i )
+ cout << weights[i] << "\n";
+ }
+
+
+
+
+
+
+
+
+
+
+ /*
+ * Boost.Range versions of controlled stepper WITHOUT time iterator
+ */
+
+
+ // boost::range::for_each
+ {
+ auto stepper = make_controlled( 1.0e-6 , 1.0e-6 , runge_kutta_cash_karp54< state_type >() );
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ boost::range::for_each( make_adaptive_range( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) ,
+ []( const state_type &x ) {
+ std::cout << x[0] << tab << x[1] << tab << x[2] << "\n"; } );
+ }
+
+
+ // boost::range::copy with filtered adaptor (simulating std::copy_if)
+ {
+ auto stepper = make_controlled( 1.0e-6 , 1.0e-6 , runge_kutta_cash_karp54< state_type >() );
+ std::vector< state_type > res;
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ boost::range::copy( make_adaptive_range( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) |
+ boost::adaptors::filtered( [] ( const state_type& x ) { return ( x[0] > 0.0 ); } ) ,
+ std::back_inserter( res ) );
+ for( size_t i=0 ; i<res.size() ; ++i )
+ cout << res[i][0] << tab << res[i][1] << tab << res[i][2] << "\n";
+ }
+
+ // boost::range::accumulate
+ {
+ //[adaptive_iterator_accumulate_range
+ auto stepper = make_controlled( 1.0e-6 , 1.0e-6 , runge_kutta_cash_karp54< state_type >() );
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ double res = boost::accumulate( make_adaptive_range( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) , 0.0 ,
+ []( double sum , const state_type& x ) {
+ return sum + x[0]; } );
+ cout << res << endl;
+ //]
+ }
+
+
+ // boost::range::transform
+ {
+ auto stepper = make_controlled( 1.0e-6 , 1.0e-6 , runge_kutta_cash_karp54< state_type >() );
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ vector< double > weights;
+ boost::transform( make_adaptive_range( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) , back_inserter( weights ) ,
+ []( const state_type& x ) {
+ return sqrt( x[0] * x[0] + x[1] * x[1] + x[2] * x[2] ); } );
+ for( size_t i=0 ; i<weights.size() ; ++i )
+ cout << weights[i] << "\n";
+ }
+
+
+ // boost::range::find
+ {
+ auto stepper = make_controlled( 1.0e-6 , 1.0e-6 , runge_kutta_cash_karp54< state_type >() );
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ auto iter = boost::find_if( make_adaptive_range( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) ,
+ []( const state_type &x ) {
+ return ( x[0] < 0.0 ); } );
+ cout << (*iter)[0] << "\t" << (*iter)[1] << "\t" << (*iter)[2] << "\n";
+ }
+
+
+
+
+
+ return 0;
+}
diff --git a/examples/bind_member_functions.cpp b/examples/bind_member_functions.cpp
new file mode 100644
index 0000000..51f85e0
--- /dev/null
+++ b/examples/bind_member_functions.cpp
@@ -0,0 +1,126 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/examples/bind_member_functions.hpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <iostream>
+
+#include <boost/numeric/odeint.hpp>
+
+namespace odeint = boost::numeric::odeint;
+
+typedef boost::array< double , 3 > state_type;
+
+//[ ode_wrapper
+template< class Obj , class Mem >
+class ode_wrapper
+{
+ Obj m_obj;
+ Mem m_mem;
+
+public:
+
+ ode_wrapper( Obj obj , Mem mem ) : m_obj( obj ) , m_mem( mem ) { }
+
+ template< class State , class Deriv , class Time >
+ void operator()( const State &x , Deriv &dxdt , Time t )
+ {
+ (m_obj.*m_mem)( x , dxdt , t );
+ }
+};
+
+template< class Obj , class Mem >
+ode_wrapper< Obj , Mem > make_ode_wrapper( Obj obj , Mem mem )
+{
+ return ode_wrapper< Obj , Mem >( obj , mem );
+}
+//]
+
+
+template< class Obj , class Mem >
+class observer_wrapper
+{
+ Obj m_obj;
+ Mem m_mem;
+
+public:
+
+ observer_wrapper( Obj obj , Mem mem ) : m_obj( obj ) , m_mem( mem ) { }
+
+ template< class State , class Time >
+ void operator()( const State &x , Time t )
+ {
+ (m_obj.*m_mem)( x , t );
+ }
+};
+
+template< class Obj , class Mem >
+observer_wrapper< Obj , Mem > make_observer_wrapper( Obj obj , Mem mem )
+{
+ return observer_wrapper< Obj , Mem >( obj , mem );
+}
+
+
+
+//[ bind_member_function
+struct lorenz
+{
+ void ode( const state_type &x , state_type &dxdt , double t ) const
+ {
+ dxdt[0] = 10.0 * ( x[1] - x[0] );
+ dxdt[1] = 28.0 * x[0] - x[1] - x[0] * x[2];
+ dxdt[2] = -8.0 / 3.0 * x[2] + x[0] * x[1];
+ }
+};
+
+int main( int argc , char *argv[] )
+{
+ using namespace boost::numeric::odeint;
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ integrate_const( runge_kutta4< state_type >() , make_ode_wrapper( lorenz() , &lorenz::ode ) ,
+ x , 0.0 , 10.0 , 0.01 );
+ return 0;
+}
+//]
+
+
+/*
+struct lorenz
+{
+ void ode( const state_type &x , state_type &dxdt , double t ) const
+ {
+ dxdt[0] = 10.0 * ( x[1] - x[0] );
+ dxdt[1] = 28.0 * x[0] - x[1] - x[0] * x[2];
+ dxdt[2] = -8.0 / 3.0 * x[2] + x[0] * x[1];
+ }
+
+ void obs( const state_type &x , double t ) const
+ {
+ std::cout << t << " " << x[0] << " " << x[1] << " " << x[2] << "\n";
+ }
+};
+
+int main( int argc , char *argv[] )
+{
+ using namespace boost::numeric::odeint;
+
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ integrate_const( runge_kutta4< state_type >() ,
+ make_ode_wrapper( lorenz() , &lorenz::ode ) ,
+ x , 0.0 , 10.0 , 0.01 ,
+ make_observer_wrapper( lorenz() , &lorenz::obs ) );
+
+ return 0;
+}
+*/
diff --git a/examples/bind_member_functions_cpp11.cpp b/examples/bind_member_functions_cpp11.cpp
new file mode 100644
index 0000000..177dded
--- /dev/null
+++ b/examples/bind_member_functions_cpp11.cpp
@@ -0,0 +1,56 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/examples/bind_member_functions.hpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <iostream>
+#include <array>
+#include <type_traits>
+
+#include <boost/numeric/odeint.hpp>
+
+namespace odeint = boost::numeric::odeint;
+
+
+
+typedef std::array< double , 3 > state_type;
+
+struct lorenz
+{
+ void ode( const state_type &x , state_type &dxdt , double t ) const
+ {
+ const double sigma = 10.0;
+ const double R = 28.0;
+ const double b = 8.0 / 3.0;
+
+ dxdt[0] = sigma * ( x[1] - x[0] );
+ dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
+ dxdt[2] = -b * x[2] + x[0] * x[1];
+ }
+};
+
+int main( int argc , char *argv[] )
+{
+ using namespace boost::numeric::odeint;
+ //[ bind_member_function_cpp11
+ namespace pl = std::placeholders;
+
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ integrate_const( runge_kutta4< state_type >() ,
+ std::bind( &lorenz::ode , lorenz() , pl::_1 , pl::_2 , pl::_3 ) ,
+ x , 0.0 , 10.0 , 0.01 );
+ //]
+ return 0;
+}
+
diff --git a/examples/bulirsch_stoer.cpp b/examples/bulirsch_stoer.cpp
new file mode 100644
index 0000000..0b18f46
--- /dev/null
+++ b/examples/bulirsch_stoer.cpp
@@ -0,0 +1,100 @@
+/*
+ * bulirsch_stoer.cpp
+ *
+ * Copyright 2011-2013 Mario Mulansky
+ * Copyright 2011-2012 Karsten Ahnert
+ *
+ * Distributed under the Boost Software License, Version 1.0.
+ * (See accompanying file LICENSE_1_0.txt or
+ * copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <iostream>
+#include <fstream>
+#define _USE_MATH_DEFINES
+#include <cmath>
+
+#include <boost/array.hpp>
+#include <boost/ref.hpp>
+
+#include <boost/numeric/odeint/config.hpp>
+
+#include <boost/numeric/odeint.hpp>
+#include <boost/numeric/odeint/stepper/bulirsch_stoer.hpp>
+#include <boost/numeric/odeint/stepper/bulirsch_stoer_dense_out.hpp>
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+typedef boost::array< double , 1 > state_type;
+
+/*
+ * x' = ( - x*sin t + 2 tan x ) y
+ * with x( pi/6 ) = 2/sqrt(3) the analytic solution is 1/cos t
+ */
+
+void rhs( const state_type &x , state_type &dxdt , const double t )
+{
+ dxdt[0] = ( - x[0] * sin( t ) + 2.0 * tan( t ) ) * x[0];
+}
+
+void rhs2( const state_type &x , state_type &dxdt , const double t )
+{
+ dxdt[0] = sin(t);
+}
+
+
+ofstream out;
+
+void write_out( const state_type &x , const double t )
+{
+ out << t << '\t' << x[0] << endl;
+}
+
+int main()
+{
+ bulirsch_stoer_dense_out< state_type > stepper( 1E-8 , 0.0 , 0.0 , 0.0 );
+ bulirsch_stoer< state_type > stepper2( 1E-8 , 0.0 , 0.0 , 0.0 );
+
+ state_type x = {{ 2.0 / sqrt(3.0) }};
+
+ double t = M_PI/6.0;
+ //double t = 0.0;
+ double dt = 0.01;
+ double t_end = M_PI/2.0 - 0.1;
+ //double t_end = 100.0;
+
+ out.open( "bs.dat" );
+ out.precision(16);
+ integrate_const( stepper , rhs , x , t , t_end , dt , write_out );
+ out.close();
+
+ x[0] = 2.0 / sqrt(3.0);
+
+ out.open( "bs2.dat" );
+ out.precision(16);
+ integrate_adaptive( stepper , rhs , x , t , t_end , dt , write_out );
+ out.close();
+
+ x[0] = 2.0 / sqrt(3.0);
+
+ out.open( "bs3.dat" );
+ out.precision(16);
+ integrate_adaptive( stepper2 , rhs , x , t , t_end , dt , write_out );
+ out.close();
+
+
+ typedef runge_kutta_dopri5< state_type > dopri5_type;
+ typedef controlled_runge_kutta< dopri5_type > controlled_dopri5_type;
+ typedef dense_output_runge_kutta< controlled_dopri5_type > dense_output_dopri5_type;
+
+ dense_output_dopri5_type dopri5 = make_dense_output( 1E-9 , 1E-9 , dopri5_type() );
+
+ x[0] = 2.0 / sqrt(3.0);
+
+ out.open( "bs4.dat" );
+ out.precision(16);
+ integrate_adaptive( dopri5 , rhs , x , t , t_end , dt , write_out );
+ out.close();
+
+}
diff --git a/examples/chaotic_system.cpp b/examples/chaotic_system.cpp
new file mode 100644
index 0000000..6078468
--- /dev/null
+++ b/examples/chaotic_system.cpp
@@ -0,0 +1,119 @@
+/*
+ * chaotic_system.cpp
+ *
+ * This example demonstrates how one can use odeint to determine the Lyapunov
+ * exponents of a chaotic system namely the well known Lorenz system. Furthermore,
+ * it shows how odeint interacts with boost.range.
+ *
+ * Copyright 2011-2012 Karsten Ahnert
+ * Copyright 2011-2013 Mario Mulansky
+ *
+ * Distributed under the Boost Software License, Version 1.0.
+ * (See accompanying file LICENSE_1_0.txt or
+ * copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#include <iostream>
+#include <boost/array.hpp>
+
+#include <boost/numeric/odeint.hpp>
+
+#include "gram_schmidt.hpp"
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+
+const double sigma = 10.0;
+const double R = 28.0;
+const double b = 8.0 / 3.0;
+
+//[ system_function_without_perturbations
+struct lorenz
+{
+ template< class State , class Deriv >
+ void operator()( const State &x_ , Deriv &dxdt_ , double t ) const
+ {
+ typename boost::range_iterator< const State >::type x = boost::begin( x_ );
+ typename boost::range_iterator< Deriv >::type dxdt = boost::begin( dxdt_ );
+
+ dxdt[0] = sigma * ( x[1] - x[0] );
+ dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
+ dxdt[2] = -b * x[2] + x[0] * x[1];
+ }
+};
+//]
+
+
+
+//[ system_function_with_perturbations
+const size_t n = 3;
+const size_t num_of_lyap = 3;
+const size_t N = n + n*num_of_lyap;
+
+typedef boost::array< double , N > state_type;
+typedef boost::array< double , num_of_lyap > lyap_type;
+
+void lorenz_with_lyap( const state_type &x , state_type &dxdt , double t )
+{
+ lorenz()( x , dxdt , t );
+
+ for( size_t l=0 ; l<num_of_lyap ; ++l )
+ {
+ const double *pert = x.begin() + 3 + l * 3;
+ double *dpert = dxdt.begin() + 3 + l * 3;
+ dpert[0] = - sigma * pert[0] + 10.0 * pert[1];
+ dpert[1] = ( R - x[2] ) * pert[0] - pert[1] - x[0] * pert[2];
+ dpert[2] = x[1] * pert[0] + x[0] * pert[1] - b * pert[2];
+ }
+}
+//]
+
+
+
+
+
+int main( int argc , char **argv )
+{
+ state_type x;
+ lyap_type lyap;
+
+ fill( x.begin() , x.end() , 0.0 );
+ x[0] = 10.0 ; x[1] = 10.0 ; x[2] = 5.0;
+
+ const double dt = 0.01;
+
+ //[ integrate_transients_with_range
+ // explicitly choose range_algebra to override default choice of array_algebra
+ runge_kutta4< state_type , double , state_type , double , range_algebra > rk4;
+
+ // perform 10000 transient steps
+ integrate_n_steps( rk4 , lorenz() , std::make_pair( x.begin() , x.begin() + n ) , 0.0 , dt , 10000 );
+ //]
+
+ //[ lyapunov_full_code
+ fill( x.begin()+n , x.end() , 0.0 );
+ for( size_t i=0 ; i<num_of_lyap ; ++i ) x[n+n*i+i] = 1.0;
+ fill( lyap.begin() , lyap.end() , 0.0 );
+
+ double t = 0.0;
+ size_t count = 0;
+ while( true )
+ {
+
+ t = integrate_n_steps( rk4 , lorenz_with_lyap , x , t , dt , 100 );
+ gram_schmidt< num_of_lyap >( x , lyap , n );
+ ++count;
+
+ if( !(count % 100000) )
+ {
+ cout << t;
+ for( size_t i=0 ; i<num_of_lyap ; ++i ) cout << "\t" << lyap[i] / t ;
+ cout << endl;
+ }
+ }
+ //]
+
+ return 0;
+}
diff --git a/examples/const_step_iterator.cpp b/examples/const_step_iterator.cpp
new file mode 100644
index 0000000..fc39303
--- /dev/null
+++ b/examples/const_step_iterator.cpp
@@ -0,0 +1,296 @@
+/*
+ * const_step_iterator.cpp
+ *
+ * Copyright 2012-2013 Karsten Ahnert
+ * Copyright 2013 Mario Mulansky
+ *
+ * Distributed under the Boost Software License, Version 1.0.
+ * (See accompanying file LICENSE_1_0.txt or
+ * copy at http://www.boost.org/LICENSE_1_0.txt)
+ *
+ * several examples for using iterators
+ */
+
+
+#include <iostream>
+#include <iterator>
+#include <utility>
+#include <algorithm>
+#include <array>
+#include <cassert>
+
+#include <boost/range/algorithm.hpp>
+#include <boost/range/adaptor/filtered.hpp>
+#include <boost/range/numeric.hpp>
+
+#include <boost/numeric/odeint/stepper/runge_kutta4.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp>
+#include <boost/numeric/odeint/stepper/generation.hpp>
+#include <boost/numeric/odeint/iterator/const_step_iterator.hpp>
+#include <boost/numeric/odeint/iterator/const_step_time_iterator.hpp>
+
+#define tab "\t"
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+const double sigma = 10.0;
+const double R = 28.0;
+const double b = 8.0 / 3.0;
+
+struct lorenz
+{
+ template< class State , class Deriv >
+ void operator()( const State &x , Deriv &dxdt , double t ) const
+ {
+ dxdt[0] = sigma * ( x[1] - x[0] );
+ dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
+ dxdt[2] = -b * x[2] + x[0] * x[1];
+ }
+};
+
+
+
+int main( int argc , char **argv )
+{
+ typedef std::array< double , 3 > state_type;
+
+ // std::for_each
+ {
+ runge_kutta4< state_type > stepper;
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ std::for_each( make_const_step_time_iterator_begin( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) ,
+ make_const_step_time_iterator_end( stepper , lorenz() , x ) ,
+ []( const std::pair< const state_type&, double > &x ) {
+ std::cout << x.second << tab << x.first[0] << tab << x.first[1] << tab << x.first[2] << "\n"; } );
+ }
+
+ // std::copy_if
+ {
+ std::vector< state_type > res;
+ runge_kutta4< state_type > stepper;
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ std::copy_if( make_const_step_iterator_begin( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) ,
+ make_const_step_iterator_end( stepper , lorenz() , x ) ,
+ std::back_inserter( res ) ,
+ []( const state_type& x ) {
+ return ( x[0] > 0.0 ) ? true : false; } );
+ for( size_t i=0 ; i<res.size() ; ++i )
+ cout << res[i][0] << tab << res[i][1] << tab << res[i][2] << "\n";
+ }
+
+ // std::accumulate
+ {
+ //[ const_step_iterator_accumulate
+ runge_kutta4< state_type > stepper;
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ double res = std::accumulate( make_const_step_iterator_begin( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) ,
+ make_const_step_iterator_end( stepper , lorenz() , x ) ,
+ 0.0 ,
+ []( double sum , const state_type &x ) {
+ return sum + x[0]; } );
+ cout << res << endl;
+ //]
+ }
+
+
+ // std::transform
+ {
+ runge_kutta4< state_type > stepper;
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ vector< double > weights;
+ std::transform( make_const_step_iterator_begin( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) ,
+ make_const_step_iterator_end( stepper , lorenz() , x ) ,
+ back_inserter( weights ) ,
+ []( const state_type &x ) {
+ return sqrt( x[0] * x[0] + x[1] * x[1] + x[2] * x[2] ); } );
+ for( size_t i=0 ; i<weights.size() ; ++i )
+ cout << weights[i] << "\n";
+ }
+
+
+
+ // std::transform with time_iterator
+ {
+ runge_kutta4< state_type > stepper;
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ vector< double > weights;
+ std::transform( make_const_step_time_iterator_begin( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) ,
+ make_const_step_time_iterator_end( stepper , lorenz() , x ) ,
+ back_inserter( weights ) ,
+ []( const std::pair< const state_type &, double > &x ) {
+ return sqrt( x.first[0] * x.first[0] + x.first[1] * x.first[1] + x.first[2] * x.first[2] ); } );
+ for( size_t i=0 ; i<weights.size() ; ++i )
+ cout << weights[i] << "\n";
+ }
+
+
+
+
+
+
+
+
+
+
+ // /*
+ // * Boost.Range versions
+ // */
+
+
+ // boost::range::for_each
+ {
+ runge_kutta4< state_type > stepper;
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ boost::range::for_each( make_const_step_range( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) ,
+ []( const state_type &x ) {
+ std::cout << x[0] << tab << x[1] << tab << x[2] << "\n"; } );
+ }
+
+ // boost::range::for_each with time iterator
+ {
+ runge_kutta4< state_type > stepper;
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ boost::range::for_each( make_const_step_time_range( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) ,
+ []( const std::pair< const state_type& , double > &x ) {
+ std::cout << x.second << tab << x.first[0] << tab << x.first[1] << tab << x.first[2] << "\n"; } );
+ }
+
+
+ // boost::range::copy with filtered adaptor (simulating std::copy_if)
+ {
+ std::vector< state_type > res;
+ runge_kutta4< state_type > stepper;
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ boost::range::copy( make_const_step_range( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) |
+ boost::adaptors::filtered( [] ( const state_type &x ) { return ( x[0] > 0.0 ); } ) ,
+ std::back_inserter( res ) );
+ for( size_t i=0 ; i<res.size() ; ++i )
+ cout << res[i][0] << tab << res[i][1] << tab << res[i][2] << "\n";
+ }
+
+ // boost::range::accumulate
+ {
+ //[const_step_iterator_accumulate_range
+ runge_kutta4< state_type > stepper;
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ double res = boost::accumulate( make_const_step_range( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) , 0.0 ,
+ []( double sum , const state_type &x ) {
+ return sum + x[0]; } );
+ cout << res << endl;
+ //]
+ }
+
+ // boost::range::accumulate with time iterator
+ {
+ //[const_step_time_iterator_accumulate_range
+ runge_kutta4< state_type > stepper;
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ double res = boost::accumulate( make_const_step_time_range( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) , 0.0 ,
+ []( double sum , const std::pair< const state_type &, double > &x ) {
+ return sum + x.first[0]; } );
+ cout << res << endl;
+ //]
+ }
+
+
+ // boost::range::transform
+ {
+ runge_kutta4< state_type > stepper;
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ vector< double > weights;
+ boost::transform( make_const_step_range( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) , back_inserter( weights ) ,
+ []( const state_type &x ) {
+ return sqrt( x[0] * x[0] + x[1] * x[1] + x[2] * x[2] ); } );
+ for( size_t i=0 ; i<weights.size() ; ++i )
+ cout << weights[i] << "\n";
+ }
+
+
+ // boost::range::find with time iterator
+ {
+ runge_kutta4< state_type > stepper;
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ auto iter = boost::find_if( make_const_step_time_range( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) ,
+ []( const std::pair< const state_type & , double > &x ) {
+ return ( x.first[0] < 0.0 ); } );
+ cout << iter->second << "\t" << iter->first[0] << "\t" << iter->first[1] << "\t" << iter->first[2] << "\n";
+
+ }
+
+
+
+
+
+
+
+
+
+
+
+
+ /*
+ * Boost.Range versions for dense output steppers
+ */
+
+ // boost::range::for_each
+ {
+ runge_kutta_dopri5< state_type > stepper;
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ boost::range::for_each( make_const_step_range( make_dense_output( 1.0e-6 , 1.0e-6 , stepper ) , lorenz() , x , 0.0 , 1.0 , 0.01 ) ,
+ []( const state_type &x ) {
+ std::cout << x[0] << tab << x[1] << tab << x[2] << "\n"; } );
+ }
+
+
+ // boost::range::for_each with time iterator
+ {
+ runge_kutta_dopri5< state_type > stepper;
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ boost::range::for_each( make_const_step_time_range( make_dense_output( 1.0e-6 , 1.0e-6 , stepper ) , lorenz() , x , 0.0 , 1.0 , 0.01 ) ,
+ []( const std::pair< const state_type& , double > &x ) {
+ std::cout << x.second << tab << x.first[0] << tab << x.first[1] << tab << x.first[2] << "\n"; } );
+
+ }
+
+
+
+
+
+ /*
+ * Pure iterators
+ */
+ {
+ runge_kutta4< state_type > stepper;
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ auto first = make_const_step_iterator_begin( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 );
+ auto last = make_const_step_iterator_end( stepper , lorenz() , x );
+ while( first != last )
+ {
+ assert( last != first );
+ cout << (*first)[0] << tab << (*first)[1] << tab << (*first)[2] << "\n";
+ ++first;
+ }
+ }
+
+ {
+ runge_kutta4< state_type > stepper;
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ auto first = make_const_step_time_iterator_begin( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 );
+ auto last = make_const_step_time_iterator_end( stepper , lorenz() , x );
+ while( first != last )
+ {
+ assert( last != first );
+ cout << first->second << tab << first->first[0] << tab << first->first[1] << tab << first->first[2] << "\n";
+ ++first;
+ }
+ }
+
+
+
+
+
+
+
+ return 0;
+}
diff --git a/examples/elliptic.py b/examples/elliptic.py
new file mode 100644
index 0000000..9f5f1d4
--- /dev/null
+++ b/examples/elliptic.py
@@ -0,0 +1,31 @@
+"""
+ Copyright 2011 Mario Mulansky
+ Copyright 2012 Karsten Ahnert
+
+ Stochastic euler stepper example and Ornstein-Uhlenbeck process
+
+ Distributed under the Boost Software License, Version 1.0.
+(See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+"""
+
+
+from pylab import *
+from scipy import special
+
+data1 = loadtxt("elliptic1.dat")
+data2 = loadtxt("elliptic2.dat")
+data3 = loadtxt("elliptic3.dat")
+
+sn1,cn1,dn1,phi1 = special.ellipj( data1[:,0] , 0.51 )
+sn2,cn2,dn2,phi2 = special.ellipj( data2[:,0] , 0.51 )
+sn3,cn3,dn3,phi3 = special.ellipj( data3[:,0] , 0.51 )
+
+semilogy( data1[:,0] , abs(data1[:,1]-sn1) )
+semilogy( data2[:,0] , abs(data2[:,1]-sn2) , 'ro' )
+semilogy( data3[:,0] , abs(data3[:,1]-sn3) , '--' )
+
+show()
+
+
+
diff --git a/examples/elliptic_functions.cpp b/examples/elliptic_functions.cpp
new file mode 100644
index 0000000..97ba59d
--- /dev/null
+++ b/examples/elliptic_functions.cpp
@@ -0,0 +1,89 @@
+/*
+ * elliptic_functions.cpp
+ *
+ * Copyright 2011-2013 Mario Mulansky
+ * Copyright 2011-2012 Karsten Ahnert
+ *
+ * Distributed under the Boost Software License, Version 1.0.
+ * (See accompanying file LICENSE_1_0.txt or
+ * copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+
+
+#include <iostream>
+#include <fstream>
+#include <cmath>
+
+#include <boost/array.hpp>
+
+#include <boost/numeric/odeint/config.hpp>
+
+#include <boost/numeric/odeint.hpp>
+#include <boost/numeric/odeint/stepper/bulirsch_stoer.hpp>
+#include <boost/numeric/odeint/stepper/bulirsch_stoer_dense_out.hpp>
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+typedef boost::array< double , 3 > state_type;
+
+/*
+ * x1' = x2*x3
+ * x2' = -x1*x3
+ * x3' = -m*x1*x2
+ */
+
+void rhs( const state_type &x , state_type &dxdt , const double t )
+{
+ static const double m = 0.51;
+
+ dxdt[0] = x[1]*x[2];
+ dxdt[1] = -x[0]*x[2];
+ dxdt[2] = -m*x[0]*x[1];
+}
+
+ofstream out;
+
+void write_out( const state_type &x , const double t )
+{
+ out << t << '\t' << x[0] << '\t' << x[1] << '\t' << x[2] << endl;
+}
+
+int main()
+{
+ bulirsch_stoer_dense_out< state_type > stepper( 1E-9 , 1E-9 , 1.0 , 0.0 );
+
+ state_type x1 = {{ 0.0 , 1.0 , 1.0 }};
+
+ double t = 0.0;
+ double dt = 0.01;
+
+ out.open( "elliptic1.dat" );
+ out.precision(16);
+ integrate_const( stepper , rhs , x1 , t , 100.0 , dt , write_out );
+ out.close();
+
+ state_type x2 = {{ 0.0 , 1.0 , 1.0 }};
+
+ out.open( "elliptic2.dat" );
+ out.precision(16);
+ integrate_adaptive( stepper , rhs , x2 , t , 100.0 , dt , write_out );
+ out.close();
+
+ typedef runge_kutta_dopri5< state_type > dopri5_type;
+ typedef controlled_runge_kutta< dopri5_type > controlled_dopri5_type;
+ typedef dense_output_runge_kutta< controlled_dopri5_type > dense_output_dopri5_type;
+
+
+ dense_output_dopri5_type dopri5 = make_dense_output( 1E-9 , 1E-9 , dopri5_type() );
+ //dense_output_dopri5_type dopri5( controlled_dopri5_type( default_error_checker< double >( 1E-9 , 0.0 , 0.0 , 0.0 ) ) );
+
+ state_type x3 = {{ 0.0 , 1.0 , 1.0 }};
+
+ out.open( "elliptic3.dat" );
+ out.precision(16);
+ integrate_adaptive( dopri5 , rhs , x3 , t , 100.0 , dt , write_out );
+ out.close();
+}
diff --git a/examples/find_crossing.cpp b/examples/find_crossing.cpp
new file mode 100644
index 0000000..a17ef4f
--- /dev/null
+++ b/examples/find_crossing.cpp
@@ -0,0 +1,134 @@
+/*
+ * find_crossing.cpp
+ *
+ * Finds the energy threshold crossing for a damped oscillator.
+ * The algorithm uses a dense out stepper with find_if to first find an
+ * interval containing the threshold crossing and the utilizes the dense out
+ * functionality with a bisection to further refine the interval until some
+ * desired precision is reached.
+ *
+ * Copyright 2015 Mario Mulansky
+ *
+ * Distributed under the Boost Software License, Version 1.0.
+ * (See accompanying file LICENSE_1_0.txt or
+ * copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+
+#include <iostream>
+#include <utility>
+#include <algorithm>
+#include <array>
+
+#include <boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp>
+#include <boost/numeric/odeint/stepper/generation.hpp>
+#include <boost/numeric/odeint/iterator/adaptive_iterator.hpp>
+
+namespace odeint = boost::numeric::odeint;
+
+typedef std::array<double, 2> state_type;
+
+const double gam = 1.0; // damping strength
+
+void damped_osc(const state_type &x, state_type &dxdt, const double /*t*/)
+{
+ dxdt[0] = x[1];
+ dxdt[1] = -x[0] - gam * x[1];
+}
+
+
+struct energy_condition {
+
+ // defines the threshold crossing in terms of a boolean functor
+
+ double m_min_energy;
+
+ energy_condition(const double min_energy)
+ : m_min_energy(min_energy) { }
+
+ double energy(const state_type &x) {
+ return 0.5 * x[1] * x[1] + 0.5 * x[0] * x[0];
+ }
+
+ bool operator()(const state_type &x) {
+ // becomes true if the energy becomes smaller than the threshold
+ return energy(x) <= m_min_energy;
+ }
+};
+
+
+template<class System, class Condition>
+std::pair<double, state_type>
+find_condition(state_type &x0, System sys, Condition cond,
+ const double t_start, const double t_end, const double dt,
+ const double precision = 1E-6) {
+
+ // integrates an ODE until some threshold is crossed
+ // returns time and state at the point of the threshold crossing
+ // if no threshold crossing is found, some time > t_end is returned
+
+ auto stepper = odeint::make_dense_output(1.0e-6, 1.0e-6,
+ odeint::runge_kutta_dopri5<state_type>());
+
+ auto ode_range = odeint::make_adaptive_range(std::ref(stepper), sys, x0,
+ t_start, t_end, dt);
+
+ // find the step where the condition changes
+ auto found_iter = std::find_if(ode_range.first, ode_range.second, cond);
+
+ if(found_iter == ode_range.second)
+ {
+ // no threshold crossing -> return time after t_end and ic
+ return std::make_pair(t_end + dt, x0);
+ }
+
+ // the dense out stepper now covers the interval where the condition changes
+ // improve the solution by bisection
+ double t0 = stepper.previous_time();
+ double t1 = stepper.current_time();
+ double t_m;
+ state_type x_m;
+ // use odeint's resizing functionality to allocate memory for x_m
+ odeint::adjust_size_by_resizeability(x_m, x0,
+ typename odeint::is_resizeable<state_type>::type());
+ while(std::abs(t1 - t0) > precision) {
+ t_m = 0.5 * (t0 + t1); // get the mid point time
+ stepper.calc_state(t_m, x_m); // obtain the corresponding state
+ if (cond(x_m))
+ t1 = t_m; // condition changer lies before midpoint
+ else
+ t0 = t_m; // condition changer lies after midpoint
+ }
+ // we found the interval of size eps, take it's midpoint as final guess
+ t_m = 0.5 * (t0 + t1);
+ stepper.calc_state(t_m, x_m);
+ return std::make_pair(t_m, x_m);
+}
+
+
+int main(int argc, char **argv)
+{
+ state_type x0 = {{10.0, 0.0}};
+ const double t_start = 0.0;
+ const double t_end = 10.0;
+ const double dt = 0.1;
+ const double threshold = 0.1;
+
+ energy_condition cond(threshold);
+ state_type x_cond;
+ double t_cond;
+ std::tie(t_cond, x_cond) = find_condition(x0, damped_osc, cond,
+ t_start, t_end, dt, 1E-6);
+ if(t_cond > t_end)
+ {
+ // time after t_end -> no threshold crossing within [t_start, t_end]
+ std::cout << "No threshold crossing found." << std::endl;
+ } else
+ {
+ std::cout.precision(16);
+ std::cout << "Time of energy threshold crossing: " << t_cond << std::endl;
+ std::cout << "State: [" << x_cond[0] << " , " << x_cond[1] << "]" << std::endl;
+ std::cout << "Energy: " << cond.energy(x_cond) << std::endl;
+ }
+}
diff --git a/examples/fpu.cpp b/examples/fpu.cpp
new file mode 100644
index 0000000..e3ca9df
--- /dev/null
+++ b/examples/fpu.cpp
@@ -0,0 +1,169 @@
+/*
+ * fpu.cpp
+ *
+ * This example demonstrates how one can use odeint to solve the Fermi-Pasta-Ulam system.
+
+ * Created on: July 13, 2011
+ *
+ * Copyright 2011-2012 Karsten Ahnert
+ * Copyright 2011 Mario Mulansky
+ * Distributed under the Boost Software License, Version 1.0. (See
+ * accompanying file LICENSE_1_0.txt or copy at
+ * http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <iostream>
+#include <numeric>
+#include <cmath>
+#include <vector>
+
+#include <boost/numeric/odeint.hpp>
+
+#ifndef M_PI //not there on windows
+#define M_PI 3.1415927 //...
+#endif
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+//[ fpu_system_function
+typedef vector< double > container_type;
+
+struct fpu
+{
+ const double m_beta;
+
+ fpu( const double beta = 1.0 ) : m_beta( beta ) { }
+
+ // system function defining the ODE
+ void operator()( const container_type &q , container_type &dpdt ) const
+ {
+ size_t n = q.size();
+ double tmp = q[0] - 0.0;
+ double tmp2 = tmp + m_beta * tmp * tmp * tmp;
+ dpdt[0] = -tmp2;
+ for( size_t i=0 ; i<n-1 ; ++i )
+ {
+ tmp = q[i+1] - q[i];
+ tmp2 = tmp + m_beta * tmp * tmp * tmp;
+ dpdt[i] += tmp2;
+ dpdt[i+1] = -tmp2;
+ }
+ tmp = - q[n-1];
+ tmp2 = tmp + m_beta * tmp * tmp * tmp;
+ dpdt[n-1] += tmp2;
+ }
+
+ // calculates the energy of the system
+ double energy( const container_type &q , const container_type &p ) const
+ {
+ // ...
+ //<-
+ double energy = 0.0;
+ size_t n = q.size();
+
+ double tmp = q[0];
+ energy += 0.5 * tmp * tmp + 0.25 * m_beta * tmp * tmp * tmp * tmp;
+ for( size_t i=0 ; i<n-1 ; ++i )
+ {
+ tmp = q[i+1] - q[i];
+ energy += 0.5 * ( p[i] * p[i] + tmp * tmp ) + 0.25 * m_beta * tmp * tmp * tmp * tmp;
+ }
+ energy += 0.5 * p[n-1] * p[n-1];
+ tmp = q[n-1];
+ energy += 0.5 * tmp * tmp + 0.25 * m_beta * tmp * tmp * tmp * tmp;
+
+ return energy;
+ //->
+ }
+
+ // calculates the local energy of the system
+ void local_energy( const container_type &q , const container_type &p , container_type &e ) const
+ {
+ // ...
+ //<-
+ size_t n = q.size();
+ double tmp = q[0];
+ double tmp2 = 0.5 * tmp * tmp + 0.25 * m_beta * tmp * tmp * tmp * tmp;
+ e[0] = tmp2;
+ for( size_t i=0 ; i<n-1 ; ++i )
+ {
+ tmp = q[i+1] - q[i];
+ tmp2 = 0.25 * tmp * tmp + 0.125 * m_beta * tmp * tmp * tmp * tmp;
+ e[i] += 0.5 * p[i] * p[i] + tmp2 ;
+ e[i+1] = tmp2;
+ }
+ tmp = q[n-1];
+ tmp2 = 0.5 * tmp * tmp + 0.25 * m_beta * tmp * tmp * tmp * tmp;
+ e[n-1] += 0.5 * p[n-1] * p[n-1] + tmp2;
+ //->
+ }
+};
+//]
+
+
+
+//[ fpu_observer
+struct streaming_observer
+{
+ std::ostream& m_out;
+ const fpu &m_fpu;
+ size_t m_write_every;
+ size_t m_count;
+
+ streaming_observer( std::ostream &out , const fpu &f , size_t write_every = 100 )
+ : m_out( out ) , m_fpu( f ) , m_write_every( write_every ) , m_count( 0 ) { }
+
+ template< class State >
+ void operator()( const State &x , double t )
+ {
+ if( ( m_count % m_write_every ) == 0 )
+ {
+ container_type &q = x.first;
+ container_type &p = x.second;
+ container_type energy( q.size() );
+ m_fpu.local_energy( q , p , energy );
+ for( size_t i=0 ; i<q.size() ; ++i )
+ {
+ m_out << t << "\t" << i << "\t" << q[i] << "\t" << p[i] << "\t" << energy[i] << "\n";
+ }
+ m_out << "\n";
+ clog << t << "\t" << accumulate( energy.begin() , energy.end() , 0.0 ) << "\n";
+ }
+ ++m_count;
+ }
+};
+//]
+
+
+
+
+
+
+
+
+int main( int argc , char **argv )
+{
+ //[ fpu_integration
+ const size_t n = 64;
+ container_type q( n , 0.0 ) , p( n , 0.0 );
+
+ for( size_t i=0 ; i<n ; ++i )
+ {
+ p[i] = 0.0;
+ q[i] = 32.0 * sin( double( i + 1 ) / double( n + 1 ) * M_PI );
+ }
+
+
+ const double dt = 0.1;
+
+ typedef symplectic_rkn_sb3a_mclachlan< container_type > stepper_type;
+ fpu fpu_instance( 8.0 );
+
+ integrate_const( stepper_type() , fpu_instance ,
+ make_pair( boost::ref( q ) , boost::ref( p ) ) ,
+ 0.0 , 1000.0 , dt , streaming_observer( cout , fpu_instance , 10 ) );
+ //]
+
+ return 0;
+}
diff --git a/examples/generation_functions.cpp b/examples/generation_functions.cpp
new file mode 100644
index 0000000..6baa5f2
--- /dev/null
+++ b/examples/generation_functions.cpp
@@ -0,0 +1,113 @@
+/*
+ libs/numeric/odeint/examples/stochastic_euler.hpp
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012-2013 Mario Mulansky
+ Copyright 2013 Pascal Germroth
+
+ Stochastic euler stepper example and Ornstein-Uhlenbeck process
+
+ Distributed under the Boost Software License, Version 1.0.
+(See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <boost/array.hpp>
+
+#include <boost/numeric/odeint.hpp>
+
+typedef boost::array< double , 1 > state_type;
+
+using namespace boost::numeric::odeint;
+
+
+//[ generation_functions_own_steppers
+class custom_stepper
+{
+public:
+
+ typedef double value_type;
+ // ...
+};
+
+class custom_controller
+{
+ // ...
+};
+
+class custom_dense_output
+{
+ // ...
+};
+//]
+
+
+//[ generation_functions_get_controller
+namespace boost { namespace numeric { namespace odeint {
+
+template<>
+struct get_controller< custom_stepper >
+{
+ typedef custom_controller type;
+};
+
+} } }
+//]
+
+//[ generation_functions_controller_factory
+namespace boost { namespace numeric { namespace odeint {
+
+template<>
+struct controller_factory< custom_stepper , custom_controller >
+{
+ custom_controller operator()( double abs_tol , double rel_tol , const custom_stepper & ) const
+ {
+ return custom_controller();
+ }
+
+ custom_controller operator()( double abs_tol , double rel_tol , double max_dt ,
+ const custom_stepper & ) const
+ {
+ // version with maximal allowed step size max_dt
+ return custom_controller();
+ }
+};
+
+} } }
+//]
+
+int main( int argc , char **argv )
+{
+ {
+ typedef runge_kutta_dopri5< state_type > stepper_type;
+
+ /*
+ //[ generation_functions_syntax_auto
+ auto stepper1 = make_controlled( 1.0e-6 , 1.0e-6 , stepper_type() );
+ // or with max step size limit:
+ // auto stepper1 = make_controlled( 1.0e-6 , 1.0e-6 , 0.01, stepper_type() );
+
+ auto stepper2 = make_dense_output( 1.0e-6 , 1.0e-6 , stepper_type() );
+ //]
+ */
+
+ //[ generation_functions_syntax_result_of
+ boost::numeric::odeint::result_of::make_controlled< stepper_type >::type stepper3 = make_controlled( 1.0e-6 , 1.0e-6 , stepper_type() );
+ (void)stepper3;
+ boost::numeric::odeint::result_of::make_dense_output< stepper_type >::type stepper4 = make_dense_output( 1.0e-6 , 1.0e-6 , stepper_type() );
+ (void)stepper4;
+ //]
+ }
+
+ {
+ /*
+ //[ generation_functions_example_custom_controller
+ auto stepper5 = make_controlled( 1.0e-6 , 1.0e-6 , custom_stepper() );
+ //]
+ */
+
+ boost::numeric::odeint::result_of::make_controlled< custom_stepper >::type stepper5 = make_controlled( 1.0e-6 , 1.0e-6 , custom_stepper() );
+ (void)stepper5;
+ }
+ return 0;
+}
diff --git a/examples/gmpxx/Makefile b/examples/gmpxx/Makefile
new file mode 100644
index 0000000..0a9f7cb
--- /dev/null
+++ b/examples/gmpxx/Makefile
@@ -0,0 +1,5 @@
+CXXFLAGS = -I${BOOST_ROOT} -O2 -static
+LDFLAGS = -lgmpxx -lgmp
+
+lorenz_gmpxx: lorenz_gmpxx.cpp
+ ${CXX} ${CXXFLAGS} lorenz_gmpxx.cpp ${LDFLAGS} -o lorenz_gmpxx
diff --git a/examples/gmpxx/lorenz_gmpxx.cpp b/examples/gmpxx/lorenz_gmpxx.cpp
new file mode 100644
index 0000000..39b4c72
--- /dev/null
+++ b/examples/gmpxx/lorenz_gmpxx.cpp
@@ -0,0 +1,83 @@
+/*
+ * lorenz_gmpxx.cpp
+ *
+ * This example demonstrates how odeint can be used with arbitrary precision types.
+ *
+ * Copyright 2011-2012 Karsten Ahnert
+ * Copyright 2011-2012 Mario Mulansky
+ *
+ * Distributed under the Boost Software License, Version 1.0.
+ * (See accompanying file LICENSE_1_0.txt or
+ * copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+
+#include <iostream>
+#include <boost/array.hpp>
+
+#include <gmpxx.h>
+
+#include <boost/numeric/odeint.hpp>
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+//[ gmpxx_lorenz
+typedef mpf_class value_type;
+typedef boost::array< value_type , 3 > state_type;
+
+struct lorenz
+{
+ void operator()( const state_type &x , state_type &dxdt , value_type t ) const
+ {
+ const value_type sigma( 10.0 );
+ const value_type R( 28.0 );
+ const value_type b( value_type( 8.0 ) / value_type( 3.0 ) );
+
+ dxdt[0] = sigma * ( x[1] - x[0] );
+ dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
+ dxdt[2] = -b * x[2] + x[0] * x[1];
+ }
+};
+//]
+
+
+
+
+struct streaming_observer
+{
+ std::ostream& m_out;
+
+ streaming_observer( std::ostream &out ) : m_out( out ) { }
+
+ template< class State , class Time >
+ void operator()( const State &x , Time t ) const
+ {
+ m_out << t;
+ for( size_t i=0 ; i<x.size() ; ++i ) m_out << "\t" << x[i] ;
+ m_out << "\n";
+ }
+};
+
+
+
+
+
+
+int main( int argc , char **argv )
+{
+ //[ gmpxx_integration
+ const int precision = 1024;
+ mpf_set_default_prec( precision );
+
+ state_type x = {{ value_type( 10.0 ) , value_type( 10.0 ) , value_type( 10.0 ) }};
+
+ cout.precision( 1000 );
+ integrate_const( runge_kutta4< state_type , value_type >() ,
+ lorenz() , x , value_type( 0.0 ) , value_type( 10.0 ) , value_type( value_type( 1.0 ) / value_type( 10.0 ) ) ,
+ streaming_observer( cout ) );
+ //]
+
+ return 0;
+}
diff --git a/examples/gram_schmidt.hpp b/examples/gram_schmidt.hpp
new file mode 100644
index 0000000..f5f5680
--- /dev/null
+++ b/examples/gram_schmidt.hpp
@@ -0,0 +1,89 @@
+/*
+ boost header: numeric/odeint/gram_schmitt.hpp
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#ifndef BOOST_NUMERIC_ODEINT_GRAM_SCHMITT_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_GRAM_SCHMITT_HPP_INCLUDED
+
+#include <boost/throw_exception.hpp>
+#include <iterator>
+#include <algorithm>
+#include <numeric>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template< class Iterator , class T >
+void normalize( Iterator first , Iterator last , T norm )
+{
+ while( first != last ) *first++ /= norm;
+}
+
+template< class Iterator , class T >
+void substract_vector( Iterator first1 , Iterator last1 ,
+ Iterator first2 , T val )
+{
+ while( first1 != last1 ) *first1++ -= val * ( *first2++ );
+}
+
+template< size_t num_of_lyap , class StateType , class LyapType >
+void gram_schmidt( StateType &x , LyapType &lyap , size_t n )
+{
+ if( !num_of_lyap ) return;
+ if( ptrdiff_t( ( num_of_lyap + 1 ) * n ) != std::distance( x.begin() , x.end() ) )
+ BOOST_THROW_EXCEPTION( std::domain_error( "renormalization() : size of state does not match the number of lyapunov exponents." ) );
+
+ typedef typename StateType::value_type value_type;
+ typedef typename StateType::iterator iterator;
+
+ value_type norm[num_of_lyap];
+ value_type tmp[num_of_lyap];
+ iterator first = x.begin() + n;
+ iterator beg1 = first , end1 = first + n ;
+
+ std::fill( norm , norm+num_of_lyap , 0.0 );
+
+ // normalize first vector
+ norm[0] = sqrt( std::inner_product( beg1 , end1 , beg1 , 0.0 ) );
+ normalize( beg1 , end1 , norm[0] );
+
+ beg1 += n;
+ end1 += n;
+
+ for( size_t j=1 ; j<num_of_lyap ; ++j , beg1+=n , end1+=n )
+ {
+ for( size_t k=0 ; k<j ; ++k )
+ {
+ tmp[k] = std::inner_product( beg1 , end1 , first + k*n , 0.0 );
+ // clog << j << " " << k << " " << tmp[k] << "\n";
+ }
+
+
+
+ for( size_t k=0 ; k<j ; ++k )
+ substract_vector( beg1 , end1 , first + k*n , tmp[k] );
+
+ // normalize j-th vector
+ norm[j] = sqrt( std::inner_product( beg1 , end1 , beg1 , 0.0 ) );
+ // clog << j << " " << norm[j] << "\n";
+ normalize( beg1 , end1 , norm[j] );
+ }
+
+ for( size_t j=0 ; j<num_of_lyap ; j++ )
+ lyap[j] += log( norm[j] );
+}
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+#endif //BOOST_NUMERIC_ODEINT_GRAM_SCHMITT_HPP_INCLUDED
diff --git a/examples/harmonic_oscillator.cpp b/examples/harmonic_oscillator.cpp
new file mode 100644
index 0000000..a1f53c4
--- /dev/null
+++ b/examples/harmonic_oscillator.cpp
@@ -0,0 +1,211 @@
+/*
+ Copyright 2010-2012 Karsten Ahnert
+ Copyright 2011-2013 Mario Mulansky
+ Copyright 2013 Pascal Germroth
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#include <iostream>
+#include <vector>
+
+#include <boost/numeric/odeint.hpp>
+
+
+
+//[ rhs_function
+/* The type of container used to hold the state vector */
+typedef std::vector< double > state_type;
+
+const double gam = 0.15;
+
+/* The rhs of x' = f(x) */
+void harmonic_oscillator( const state_type &x , state_type &dxdt , const double /* t */ )
+{
+ dxdt[0] = x[1];
+ dxdt[1] = -x[0] - gam*x[1];
+}
+//]
+
+
+
+
+
+//[ rhs_class
+/* The rhs of x' = f(x) defined as a class */
+class harm_osc {
+
+ double m_gam;
+
+public:
+ harm_osc( double gam ) : m_gam(gam) { }
+
+ void operator() ( const state_type &x , state_type &dxdt , const double /* t */ )
+ {
+ dxdt[0] = x[1];
+ dxdt[1] = -x[0] - m_gam*x[1];
+ }
+};
+//]
+
+
+
+
+
+//[ integrate_observer
+struct push_back_state_and_time
+{
+ std::vector< state_type >& m_states;
+ std::vector< double >& m_times;
+
+ push_back_state_and_time( std::vector< state_type > &states , std::vector< double > × )
+ : m_states( states ) , m_times( times ) { }
+
+ void operator()( const state_type &x , double t )
+ {
+ m_states.push_back( x );
+ m_times.push_back( t );
+ }
+};
+//]
+
+struct write_state
+{
+ void operator()( const state_type &x ) const
+ {
+ std::cout << x[0] << "\t" << x[1] << "\n";
+ }
+};
+
+
+int main(int /* argc */ , char** /* argv */ )
+{
+ using namespace std;
+ using namespace boost::numeric::odeint;
+
+
+ //[ state_initialization
+ state_type x(2);
+ x[0] = 1.0; // start at x=1.0, p=0.0
+ x[1] = 0.0;
+ //]
+
+
+
+ //[ integration
+ size_t steps = integrate( harmonic_oscillator ,
+ x , 0.0 , 10.0 , 0.1 );
+ //]
+
+
+
+ //[ integration_class
+ harm_osc ho(0.15);
+ steps = integrate( ho ,
+ x , 0.0 , 10.0 , 0.1 );
+ //]
+
+
+
+
+
+ //[ integrate_observ
+ vector<state_type> x_vec;
+ vector<double> times;
+
+ steps = integrate( harmonic_oscillator ,
+ x , 0.0 , 10.0 , 0.1 ,
+ push_back_state_and_time( x_vec , times ) );
+
+ /* output */
+ for( size_t i=0; i<=steps; i++ )
+ {
+ cout << times[i] << '\t' << x_vec[i][0] << '\t' << x_vec[i][1] << '\n';
+ }
+ //]
+
+
+
+
+
+
+
+ //[ define_const_stepper
+ runge_kutta4< state_type > stepper;
+ integrate_const( stepper , harmonic_oscillator , x , 0.0 , 10.0 , 0.01 );
+ //]
+
+
+
+
+ //[ integrate_const_loop
+ const double dt = 0.01;
+ for( double t=0.0 ; t<10.0 ; t+= dt )
+ stepper.do_step( harmonic_oscillator , x , t , dt );
+ //]
+
+
+
+
+ //[ define_adapt_stepper
+ typedef runge_kutta_cash_karp54< state_type > error_stepper_type;
+ //]
+
+
+
+ //[ integrate_adapt
+ typedef controlled_runge_kutta< error_stepper_type > controlled_stepper_type;
+ controlled_stepper_type controlled_stepper;
+ integrate_adaptive( controlled_stepper , harmonic_oscillator , x , 0.0 , 10.0 , 0.01 );
+ //]
+
+ {
+ //[integrate_adapt_full
+ double abs_err = 1.0e-10 , rel_err = 1.0e-6 , a_x = 1.0 , a_dxdt = 1.0;
+ controlled_stepper_type controlled_stepper(
+ default_error_checker< double , range_algebra , default_operations >( abs_err , rel_err , a_x , a_dxdt ) );
+ integrate_adaptive( controlled_stepper , harmonic_oscillator , x , 0.0 , 10.0 , 0.01 );
+ //]
+ }
+
+
+ //[integrate_adapt_make_controlled
+ integrate_adaptive( make_controlled< error_stepper_type >( 1.0e-10 , 1.0e-6 ) ,
+ harmonic_oscillator , x , 0.0 , 10.0 , 0.01 );
+ //]
+
+
+
+
+ //[integrate_adapt_make_controlled_alternative
+ integrate_adaptive( make_controlled( 1.0e-10 , 1.0e-6 , error_stepper_type() ) ,
+ harmonic_oscillator , x , 0.0 , 10.0 , 0.01 );
+ //]
+
+ #ifdef BOOST_NUMERIC_ODEINT_CXX11
+ //[ define_const_stepper_cpp11
+ {
+ runge_kutta4< state_type > stepper;
+ integrate_const( stepper , []( const state_type &x , state_type &dxdt , double t ) {
+ dxdt[0] = x[1]; dxdt[1] = -x[0] - gam*x[1]; }
+ , x , 0.0 , 10.0 , 0.01 );
+ }
+ //]
+
+
+
+ //[ harm_iterator_const_step]
+ std::for_each( make_const_step_time_iterator_begin( stepper , harmonic_oscillator, x , 0.0 , 0.1 , 10.0 ) ,
+ make_const_step_time_iterator_end( stepper , harmonic_oscillator, x ) ,
+ []( std::pair< const state_type & , const double & > x ) {
+ cout << x.second << " " << x.first[0] << " " << x.first[1] << "\n"; } );
+ //]
+ #endif
+
+
+
+
+}
diff --git a/examples/harmonic_oscillator_units.cpp b/examples/harmonic_oscillator_units.cpp
new file mode 100644
index 0000000..ceee83d
--- /dev/null
+++ b/examples/harmonic_oscillator_units.cpp
@@ -0,0 +1,121 @@
+/*
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#include <iostream>
+#include <vector>
+
+
+/* WARNING: Compilation in debug mode might consume enormous memory
+ (e.g. ~2GB on gcc 4.4 )
+*/
+
+// first increase fusion macro variables (now done by odeint itself)
+//#define BOOST_FUSION_INVOKE_MAX_ARITY 15
+//#define BOOST_RESULT_OF_NUM_ARGS 15
+
+//[ units_define_basic_quantities
+
+#include <boost/numeric/odeint.hpp>
+#include <boost/numeric/odeint/algebra/fusion_algebra.hpp>
+#include <boost/numeric/odeint/algebra/fusion_algebra_dispatcher.hpp>
+
+#include <boost/units/systems/si/length.hpp>
+#include <boost/units/systems/si/time.hpp>
+#include <boost/units/systems/si/velocity.hpp>
+#include <boost/units/systems/si/acceleration.hpp>
+#include <boost/units/systems/si/io.hpp>
+
+#include <boost/fusion/container.hpp>
+
+using namespace std;
+using namespace boost::numeric::odeint;
+namespace fusion = boost::fusion;
+namespace units = boost::units;
+namespace si = boost::units::si;
+
+typedef units::quantity< si::time , double > time_type;
+typedef units::quantity< si::length , double > length_type;
+typedef units::quantity< si::velocity , double > velocity_type;
+typedef units::quantity< si::acceleration , double > acceleration_type;
+typedef units::quantity< si::frequency , double > frequency_type;
+
+typedef fusion::vector< length_type , velocity_type > state_type;
+typedef fusion::vector< velocity_type , acceleration_type > deriv_type;
+//]
+
+
+
+//[ units_define_ode
+struct oscillator
+{
+ frequency_type m_omega;
+
+ oscillator( const frequency_type &omega = 1.0 * si::hertz ) : m_omega( omega ) { }
+
+ void operator()( const state_type &x , deriv_type &dxdt , time_type t ) const
+ {
+ fusion::at_c< 0 >( dxdt ) = fusion::at_c< 1 >( x );
+ fusion::at_c< 1 >( dxdt ) = - m_omega * m_omega * fusion::at_c< 0 >( x );
+ }
+};
+//]
+
+
+//[ units_observer
+struct streaming_observer
+{
+ std::ostream& m_out;
+
+ streaming_observer( std::ostream &out ) : m_out( out ) { }
+
+ struct write_element
+ {
+ std::ostream &m_out;
+ write_element( std::ostream &out ) : m_out( out ) { };
+
+ template< class T >
+ void operator()( const T &t ) const
+ {
+ m_out << "\t" << t;
+ }
+ };
+
+ template< class State , class Time >
+ void operator()( const State &x , const Time &t ) const
+ {
+ m_out << t;
+ fusion::for_each( x , write_element( m_out ) );
+ m_out << "\n";
+ }
+};
+//]
+
+
+int main( int argc , char**argv )
+{
+// typedef dense_output_runge_kutta
+// <
+// controlled_runge_kutta
+// <
+// runge_kutta_dopri5< state_type , double , deriv_type , time_type , fusion_algebra >
+// >
+// > stepper_type;
+
+ //[ units_define_stepper
+ typedef runge_kutta_dopri5< state_type , double , deriv_type , time_type > stepper_type;
+
+ state_type x( 1.0 * si::meter , 0.0 * si::meter_per_second );
+
+ integrate_const( make_dense_output( 1.0e-6 , 1.0e-6 , stepper_type() ) , oscillator( 2.0 * si::hertz ) ,
+ x , 0.0 * si::second , 100.0 * si::second , 0.1 * si::second , streaming_observer( cout ) );
+ //]
+
+ return 0;
+}
diff --git a/examples/heun.cpp b/examples/heun.cpp
new file mode 100644
index 0000000..34fe12c
--- /dev/null
+++ b/examples/heun.cpp
@@ -0,0 +1,170 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/examples/heun.cpp
+
+ [begin_description]
+ Examplary implementation of the method of Heun.
+ [end_description]
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <iostream>
+
+
+#include <boost/fusion/container/vector.hpp>
+#include <boost/fusion/container/generation/make_vector.hpp>
+
+#include <boost/array.hpp>
+
+#include <boost/numeric/odeint.hpp>
+
+
+
+
+
+
+namespace fusion = boost::fusion;
+
+//[ heun_define_coefficients
+template< class Value = double >
+struct heun_a1 : boost::array< Value , 1 > {
+ heun_a1( void )
+ {
+ (*this)[0] = static_cast< Value >( 1 ) / static_cast< Value >( 3 );
+ }
+};
+
+template< class Value = double >
+struct heun_a2 : boost::array< Value , 2 >
+{
+ heun_a2( void )
+ {
+ (*this)[0] = static_cast< Value >( 0 );
+ (*this)[1] = static_cast< Value >( 2 ) / static_cast< Value >( 3 );
+ }
+};
+
+
+template< class Value = double >
+struct heun_b : boost::array< Value , 3 >
+{
+ heun_b( void )
+ {
+ (*this)[0] = static_cast<Value>( 1 ) / static_cast<Value>( 4 );
+ (*this)[1] = static_cast<Value>( 0 );
+ (*this)[2] = static_cast<Value>( 3 ) / static_cast<Value>( 4 );
+ }
+};
+
+template< class Value = double >
+struct heun_c : boost::array< Value , 3 >
+{
+ heun_c( void )
+ {
+ (*this)[0] = static_cast< Value >( 0 );
+ (*this)[1] = static_cast< Value >( 1 ) / static_cast< Value >( 3 );
+ (*this)[2] = static_cast< Value >( 2 ) / static_cast< Value >( 3 );
+ }
+};
+//]
+
+
+//[ heun_stepper_definition
+template<
+ class State ,
+ class Value = double ,
+ class Deriv = State ,
+ class Time = Value ,
+ class Algebra = boost::numeric::odeint::range_algebra ,
+ class Operations = boost::numeric::odeint::default_operations ,
+ class Resizer = boost::numeric::odeint::initially_resizer
+>
+class heun : public
+boost::numeric::odeint::explicit_generic_rk< 3 , 3 , State , Value , Deriv , Time ,
+ Algebra , Operations , Resizer >
+{
+
+public:
+
+ typedef boost::numeric::odeint::explicit_generic_rk< 3 , 3 , State , Value , Deriv , Time ,
+ Algebra , Operations , Resizer > stepper_base_type;
+
+ typedef typename stepper_base_type::state_type state_type;
+ typedef typename stepper_base_type::wrapped_state_type wrapped_state_type;
+ typedef typename stepper_base_type::value_type value_type;
+ typedef typename stepper_base_type::deriv_type deriv_type;
+ typedef typename stepper_base_type::wrapped_deriv_type wrapped_deriv_type;
+ typedef typename stepper_base_type::time_type time_type;
+ typedef typename stepper_base_type::algebra_type algebra_type;
+ typedef typename stepper_base_type::operations_type operations_type;
+ typedef typename stepper_base_type::resizer_type resizer_type;
+ typedef typename stepper_base_type::stepper_type stepper_type;
+
+ heun( const algebra_type &algebra = algebra_type() )
+ : stepper_base_type(
+ fusion::make_vector(
+ heun_a1<Value>() ,
+ heun_a2<Value>() ) ,
+ heun_b<Value>() , heun_c<Value>() , algebra )
+ { }
+};
+//]
+
+
+const double sigma = 10.0;
+const double R = 28.0;
+const double b = 8.0 / 3.0;
+
+struct lorenz
+{
+ template< class State , class Deriv >
+ void operator()( const State &x_ , Deriv &dxdt_ , double t ) const
+ {
+ typename boost::range_iterator< const State >::type x = boost::begin( x_ );
+ typename boost::range_iterator< Deriv >::type dxdt = boost::begin( dxdt_ );
+
+ dxdt[0] = sigma * ( x[1] - x[0] );
+ dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
+ dxdt[2] = -b * x[2] + x[0] * x[1];
+ }
+};
+
+struct streaming_observer
+{
+ std::ostream &m_out;
+ streaming_observer( std::ostream &out ) : m_out( out ) { }
+ template< typename State , typename Value >
+ void operator()( const State &x , Value t ) const
+ {
+ m_out << t;
+ for( size_t i=0 ; i<x.size() ; ++i ) m_out << "\t" << x[i];
+ m_out << "\n";
+ }
+};
+
+
+
+int main( int argc , char **argv )
+{
+ using namespace std;
+ using namespace boost::numeric::odeint;
+
+
+ //[ heun_example
+ typedef boost::array< double , 3 > state_type;
+ heun< state_type > h;
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+
+ integrate_const( h , lorenz() , x , 0.0 , 100.0 , 0.01 ,
+ streaming_observer( std::cout ) );
+
+ //]
+
+ return 0;
+}
diff --git a/examples/integrate_times.cpp b/examples/integrate_times.cpp
new file mode 100644
index 0000000..9e6b581
--- /dev/null
+++ b/examples/integrate_times.cpp
@@ -0,0 +1,54 @@
+/* Boost libs/numeric/odeint/examples/integrate_times.cpp
+
+ Copyright 2009-2014 Karsten Ahnert
+ Copyright 2009-2014 Mario Mulansky
+
+ example for the use of integrate_times
+
+ Distributed under the Boost Software License, Version 1.0.
+(See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#include <iostream>
+#include <boost/numeric/odeint.hpp>
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+
+/*
+ * simple 1D ODE
+ */
+
+void rhs( const double x , double &dxdt , const double t )
+{
+ dxdt = 3.0/(2.0*t*t) + x/(2.0*t);
+}
+
+void write_cout( const double &x , const double t )
+{
+ cout << t << '\t' << x << endl;
+}
+
+// state_type = double
+typedef runge_kutta_dopri5< double > stepper_type;
+
+const double dt = 0.1;
+
+int main()
+{
+ // create a vector with observation time points
+ std::vector<double> times( 91 );
+ for( size_t i=0 ; i<times.size() ; ++i )
+ times[i] = 1.0 + dt*i;
+
+ double x = 0.0; //initial value x(1) = 0
+ // we can provide the observation time as a boost range (i.e. the vector)
+ integrate_times( make_controlled( 1E-12 , 1E-12 , stepper_type() ) , rhs ,
+ x , times , dt , write_cout );
+ // or as two iterators
+ //integrate_times( make_controlled( 1E-12 , 1E-12 , stepper_type() ) , rhs ,
+ // x , times.begin() , times.end() , dt , write_cout );
+}
diff --git a/examples/list_lattice.cpp b/examples/list_lattice.cpp
new file mode 100644
index 0000000..2c716ca
--- /dev/null
+++ b/examples/list_lattice.cpp
@@ -0,0 +1,78 @@
+/*
+ Copyright 2011-2012 Mario Mulansky
+ Copyright 2012-2013 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+/* example showing how odeint can be used with std::list */
+
+#include <iostream>
+#include <cmath>
+#include <list>
+
+#include <boost/numeric/odeint.hpp>
+
+//[ list_bindings
+typedef std::list< double > state_type;
+
+namespace boost { namespace numeric { namespace odeint {
+
+template< >
+struct is_resizeable< state_type >
+{ // declare resizeability
+ typedef boost::true_type type;
+ const static bool value = type::value;
+};
+
+template< >
+struct same_size_impl< state_type , state_type >
+{ // define how to check size
+ static bool same_size( const state_type &v1 ,
+ const state_type &v2 )
+ {
+ return v1.size() == v2.size();
+ }
+};
+
+template< >
+struct resize_impl< state_type , state_type >
+{ // define how to resize
+ static void resize( state_type &v1 ,
+ const state_type &v2 )
+ {
+ v1.resize( v2.size() );
+ }
+};
+
+} } }
+//]
+
+void lattice( const state_type &x , state_type &dxdt , const double /* t */ )
+{
+ state_type::const_iterator x_begin = x.begin();
+ state_type::const_iterator x_end = x.end();
+ state_type::iterator dxdt_begin = dxdt.begin();
+
+ x_end--; // stop one before last
+ while( x_begin != x_end )
+ {
+ *(dxdt_begin++) = std::sin( *(x_begin) - *(x_begin++) );
+ }
+ *dxdt_begin = sin( *x_begin - *(x.begin()) ); // periodic boundary
+}
+
+using namespace boost::numeric::odeint;
+
+int main()
+{
+ const int N = 32;
+ state_type x;
+ for( int i=0 ; i<N ; ++i )
+ x.push_back( 1.0*i/N );
+
+ integrate_const( runge_kutta4< state_type >() , lattice , x , 0.0 , 10.0 , 0.1 );
+}
diff --git a/examples/lorenz.cpp b/examples/lorenz.cpp
new file mode 100644
index 0000000..37155aa
--- /dev/null
+++ b/examples/lorenz.cpp
@@ -0,0 +1,31 @@
+#include <iostream>
+#include <boost/array.hpp>
+
+#include <boost/numeric/odeint.hpp>
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+const double sigma = 10.0;
+const double R = 28.0;
+const double b = 8.0 / 3.0;
+
+typedef boost::array< double , 3 > state_type;
+
+void lorenz( const state_type &x , state_type &dxdt , double t )
+{
+ dxdt[0] = sigma * ( x[1] - x[0] );
+ dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
+ dxdt[2] = -b * x[2] + x[0] * x[1];
+}
+
+void write_lorenz( const state_type &x , const double t )
+{
+ cout << t << '\t' << x[0] << '\t' << x[1] << '\t' << x[2] << endl;
+}
+
+int main(int argc, char **argv)
+{
+ state_type x = {{ 10.0 , 1.0 , 1.0 }}; // initial conditions
+ integrate( lorenz , x , 0.0 , 25.0 , 0.1 , write_lorenz );
+}
diff --git a/examples/lorenz_point.cpp b/examples/lorenz_point.cpp
new file mode 100644
index 0000000..2616167
--- /dev/null
+++ b/examples/lorenz_point.cpp
@@ -0,0 +1,119 @@
+/*
+ * Copyright 2011-2013 Mario Mulansky
+ * Copyright 2012 Karsten Ahnert
+ *
+ * Distributed under the Boost Software License, Version 1.0.
+ * (See accompanying file LICENSE_1_0.txt or
+ * copy at http://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Example for the lorenz system with a 3D point type
+*/
+
+#include <iostream>
+#include <cmath>
+
+#include <boost/operators.hpp>
+
+#include <boost/numeric/odeint.hpp>
+
+
+//[point3D
+class point3D :
+ boost::additive1< point3D ,
+ boost::additive2< point3D , double ,
+ boost::multiplicative2< point3D , double > > >
+{
+public:
+
+ double x , y , z;
+
+ point3D()
+ : x( 0.0 ) , y( 0.0 ) , z( 0.0 )
+ { }
+
+ point3D( const double val )
+ : x( val ) , y( val ) , z( val )
+ { }
+
+ point3D( const double _x , const double _y , const double _z )
+ : x( _x ) , y( _y ) , z( _z )
+ { }
+
+ point3D& operator+=( const point3D &p )
+ {
+ x += p.x; y += p.y; z += p.z;
+ return *this;
+ }
+
+ point3D& operator*=( const double a )
+ {
+ x *= a; y *= a; z *= a;
+ return *this;
+ }
+
+};
+//]
+
+//[point3D_abs_div
+// only required for steppers with error control
+point3D operator/( const point3D &p1 , const point3D &p2 )
+{
+ return point3D( p1.x/p2.x , p1.y/p2.y , p1.z/p2.z );
+}
+
+point3D abs( const point3D &p )
+{
+ return point3D( std::abs(p.x) , std::abs(p.y) , std::abs(p.z) );
+}
+//]
+
+//[point3D_norm
+// also only for steppers with error control
+namespace boost { namespace numeric { namespace odeint {
+template<>
+struct vector_space_norm_inf< point3D >
+{
+ typedef double result_type;
+ double operator()( const point3D &p ) const
+ {
+ using std::max;
+ using std::abs;
+ return max( max( abs( p.x ) , abs( p.y ) ) , abs( p.z ) );
+ }
+};
+} } }
+//]
+
+std::ostream& operator<<( std::ostream &out , const point3D &p )
+{
+ out << p.x << " " << p.y << " " << p.z;
+ return out;
+}
+
+//[point3D_main
+const double sigma = 10.0;
+const double R = 28.0;
+const double b = 8.0 / 3.0;
+
+void lorenz( const point3D &x , point3D &dxdt , const double t )
+{
+ dxdt.x = sigma * ( x.y - x.x );
+ dxdt.y = R * x.x - x.y - x.x * x.z;
+ dxdt.z = -b * x.z + x.x * x.y;
+}
+
+using namespace boost::numeric::odeint;
+
+int main()
+{
+
+ point3D x( 10.0 , 5.0 , 5.0 );
+ // point type defines it's own operators -> use vector_space_algebra !
+ typedef runge_kutta_dopri5< point3D , double , point3D ,
+ double , vector_space_algebra > stepper;
+ int steps = integrate_adaptive( make_controlled<stepper>( 1E-10 , 1E-10 ) , lorenz , x ,
+ 0.0 , 10.0 , 0.1 );
+ std::cout << x << std::endl;
+ std::cout << "steps: " << steps << std::endl;
+}
+//]
diff --git a/examples/molecular_dynamics.cpp b/examples/molecular_dynamics.cpp
new file mode 100644
index 0000000..e1a82e0
--- /dev/null
+++ b/examples/molecular_dynamics.cpp
@@ -0,0 +1,160 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/examples/molecular_dynamics.cpp
+
+ [begin_description]
+ Molecular dynamics example.
+ [end_description]
+
+ Copyright 2009-2012 Karsten Ahnert
+ Copyright 2009-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <boost/numeric/odeint.hpp>
+
+#include <vector>
+#include <iostream>
+#include <random>
+
+using namespace boost::numeric::odeint;
+
+
+
+using namespace std;
+#define tab "\t"
+
+const size_t n1 = 16;
+const size_t n2 = 16;
+
+struct md_system
+{
+ static const size_t n = n1 * n2;
+ typedef std::vector< double > vector_type;
+
+ md_system( double a = 0.0 , // strength of harmonic oscillator
+ double gamma = 0.0 , // friction
+ double eps = 0.1 , // interaction strenght
+ double sigma = 1.0 , // interaction radius
+ double xmax = 150.0 , double ymax = 150.0 )
+ : m_a( a ) , m_gamma( gamma )
+ , m_eps( eps ) , m_sigma( sigma )
+ , m_xmax( xmax ) , m_ymax( ymax )
+ { }
+
+ static void init_vector_type( vector_type &x ) { x.resize( 2 * n ); }
+
+ void operator()( vector_type const& x , vector_type const& v , vector_type &a , double t ) const
+ {
+ for( size_t i=0 ; i<n ; ++i )
+ {
+ double diffx = x[i] - 0.5 * m_xmax , diffy = x[i+n] - 0.5 * m_ymax;
+ double r2 = diffx * diffx + diffy * diffy ;
+ double r = std::sqrt( r2 );
+ a[ i ] = - m_a * r * diffx - m_gamma * v[ i ] ;
+ a[ n + i ] = - m_a * r * diffy - m_gamma * v[ n + i ] ;
+ }
+
+ for( size_t i=0 ; i<n ; ++i )
+ {
+ double xi = x[i] , yi = x[n+i];
+ xi = periodic_bc( xi , m_xmax );
+ yi = periodic_bc( yi , m_ymax );
+ for( size_t j=0 ; j<i ; ++j )
+ {
+ double xj = x[j] , yj = x[n+j];
+ xj = periodic_bc( xj , m_xmax );
+ yj = periodic_bc( yj , m_ymax );
+
+ double diffx = ( xj - xi ) , diffy = ( yj - yi );
+ double r = sqrt( diffx * diffx + diffy * diffy );
+ double f = lennard_jones( r );
+ a[ i ] += diffx / r * f;
+ a[ n + i ] += diffy / r * f;
+ a[ j ] -= diffx / r * f;
+ a[ n + j ] -= diffy / r * f;
+ }
+ }
+ }
+
+ void bc( vector_type &x )
+ {
+ for( size_t i=0 ; i<n ; ++i )
+ {
+ x[ i ] = periodic_bc( x[ i ] , m_xmax );
+ x[ i + n ] = periodic_bc( x[ i + n ] , m_ymax );
+ }
+ }
+
+ inline double lennard_jones( double r ) const
+ {
+ double c = m_sigma / r;
+ double c3 = c * c * c;
+ double c6 = c3 * c3;
+ return 4.0 * m_eps * ( -12.0 * c6 * c6 / r + 6.0 * c6 / r );
+ }
+
+ static inline double periodic_bc( double x , double xmax )
+ {
+ return ( x < 0.0 ) ? x + xmax : ( x > xmax ) ? x - xmax : x ;
+ }
+
+ double m_a;
+ double m_gamma;
+ double m_eps ;
+ double m_sigma ;
+ double m_xmax , m_ymax;
+};
+
+
+
+
+
+int main( int argc , char *argv[] )
+{
+ const size_t n = md_system::n;
+ typedef md_system::vector_type vector_type;
+
+
+ std::mt19937 rng;
+ std::normal_distribution<> dist( 0.0 , 1.0 );
+
+ vector_type x , v;
+ md_system::init_vector_type( x );
+ md_system::init_vector_type( v );
+
+ for( size_t i=0 ; i<n1 ; ++i )
+ {
+ for( size_t j=0 ; j<n2 ; ++j )
+ {
+ x[i*n2+j ] = 5.0 + i * 4.0 ;
+ x[i*n2+j+n] = 5.0 + j * 4.0 ;
+ v[i] = dist( rng ) ;
+ v[i+n] = dist( rng ) ;
+ }
+ }
+
+ velocity_verlet< vector_type > stepper;
+ const double dt = 0.025;
+ double t = 0.0;
+ md_system sys;
+ for( size_t oi=0 ; oi<100000 ; ++oi )
+ {
+ for( size_t ii=0 ; ii<100 ; ++ii,t+=dt )
+ stepper.do_step( sys , std::make_pair( std::ref( x ) , std::ref( v ) ) , t , dt );
+ sys.bc( x );
+
+ std::cout << "set size square" << "\n";
+ std::cout << "unset key" << "\n";
+ std::cout << "p [0:" << sys.m_xmax << "][0:" << sys.m_ymax << "] '-' pt 7 ps 0.5" << "\n";
+ for( size_t i=0 ; i<n ; ++i )
+ std::cout << x[i] << " " << x[i+n] << " " << v[i] << " " << v[i+n] << "\n";
+ std::cout << "e" << std::endl;
+ }
+
+
+ return 0;
+}
diff --git a/examples/molecular_dynamics_cells.cpp b/examples/molecular_dynamics_cells.cpp
new file mode 100644
index 0000000..d746ca8
--- /dev/null
+++ b/examples/molecular_dynamics_cells.cpp
@@ -0,0 +1,377 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/examples/molecular_dynamics_cells.cpp
+
+ [begin_description]
+ Molecular dynamics example with cells.
+ [end_description]
+
+ Copyright 2009-2012 Karsten Ahnert
+ Copyright 2009-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <boost/numeric/odeint.hpp>
+
+#include <cstddef>
+#include <vector>
+#include <cmath>
+#include <algorithm>
+#include <tuple>
+#include <iostream>
+#include <random>
+
+#include <boost/range/algorithm/for_each.hpp>
+#include <boost/range/algorithm/sort.hpp>
+#include <boost/range/algorithm/unique_copy.hpp>
+#include <boost/range/algorithm_ext/iota.hpp>
+#include <boost/iterator/zip_iterator.hpp>
+#include <boost/iterator/transform_iterator.hpp>
+#include <boost/iterator/permutation_iterator.hpp>
+#include <boost/iterator/counting_iterator.hpp>
+
+#include "point_type.hpp"
+
+
+
+
+
+
+
+
+struct local_force
+{
+ double m_gamma; // friction
+ local_force( double gamma = 0.0 ) : m_gamma( gamma ) { }
+ template< typename Point >
+ Point operator()( Point& x , Point& v ) const
+ {
+ return - m_gamma * v;
+ }
+};
+
+
+struct lennard_jones
+{
+ double m_sigma;
+ double m_eps;
+ lennard_jones( double sigma = 1.0 , double eps = 0.1 ) : m_sigma( sigma ) , m_eps( eps ) { }
+ double operator()( double r ) const
+ {
+ double c = m_sigma / r;
+ double c3 = c * c * c;
+ double c6 = c3 * c3;
+ return 4.0 * m_eps * ( -12.0 * c6 * c6 / r + 6.0 * c6 / r );
+ }
+};
+
+template< typename F >
+struct conservative_interaction
+{
+ F m_f;
+ conservative_interaction( F const &f = F() ) : m_f( f ) { }
+ template< typename Point >
+ Point operator()( Point const& x1 , Point const& x2 ) const
+ {
+ Point diff = x1 - x2;
+ double r = abs( diff );
+ double f = m_f( r );
+ return - diff / r * f;
+ }
+};
+
+template< typename F >
+conservative_interaction< F > make_conservative_interaction( F const &f )
+{
+ return conservative_interaction< F >( f );
+}
+
+
+
+
+
+
+
+// force = interaction( x1 , x2 )
+// force = local_force( x , v )
+template< typename LocalForce , typename Interaction >
+class md_system_bs
+{
+public:
+
+ typedef std::vector< double > vector_type;
+ typedef point< double , 2 > point_type;
+ typedef point< int , 2 > index_type;
+ typedef std::vector< point_type > point_vector;
+ typedef std::vector< index_type > index_vector;
+ typedef std::vector< size_t > hash_vector;
+ typedef LocalForce local_force_type;
+ typedef Interaction interaction_type;
+
+
+ struct params
+ {
+ size_t n;
+ size_t n_cell_x , n_cell_y , n_cells;
+ double x_max , y_max , cell_size;
+ double eps , sigma; // interaction strength, interaction radius
+ interaction_type interaction;
+ local_force_type local_force;
+ };
+
+
+ struct cell_functor
+ {
+ params const &m_p;
+
+ cell_functor( params const& p ) : m_p( p ) { }
+
+ template< typename Tuple >
+ void operator()( Tuple const& t ) const
+ {
+ auto point = boost::get< 0 >( t );
+ size_t i1 = size_t( point[0] / m_p.cell_size ) , i2 = size_t( point[1] / m_p.cell_size );
+ boost::get< 1 >( t ) = index_type( i1 , i2 );
+ boost::get< 2 >( t ) = hash_func( boost::get< 1 >( t ) , m_p );
+ }
+ };
+
+
+
+ struct transform_functor : public std::unary_function< size_t , size_t >
+ {
+ hash_vector const* m_index;
+ transform_functor( hash_vector const& index ) : m_index( &index ) { }
+ size_t operator()( size_t i ) const { return (*m_index)[i]; }
+ };
+
+
+
+ struct interaction_functor
+ {
+ hash_vector const &m_cells_begin;
+ hash_vector const &m_cells_end;
+ hash_vector const &m_order;
+ point_vector const &m_x;
+ point_vector const &m_v;
+ params const &m_p;
+ size_t m_ncellx , m_ncelly;
+
+ interaction_functor( hash_vector const& cells_begin , hash_vector const& cells_end , hash_vector pos_order ,
+ point_vector const&x , point_vector const& v , params const &p )
+ : m_cells_begin( cells_begin ) , m_cells_end( cells_end ) , m_order( pos_order ) , m_x( x ) , m_v( v ) ,
+ m_p( p ) { }
+
+ template< typename Tuple >
+ void operator()( Tuple const &t ) const
+ {
+ point_type x = periodic_bc( boost::get< 0 >( t ) , m_p ) , v = boost::get< 1 >( t );
+ index_type index = boost::get< 3 >( t );
+ size_t pos_hash = boost::get< 4 >( t );
+
+ point_type a = m_p.local_force( x , v );
+
+ for( int i=-1 ; i<=1 ; ++i )
+ {
+ for( int j=-1 ; j<=1 ; ++j )
+ {
+ index_type cell_index = index + index_type( i , j );
+ size_t cell_hash = hash_func( cell_index , m_p );
+ for( size_t ii = m_cells_begin[ cell_hash ] ; ii < m_cells_end[ cell_hash ] ; ++ii )
+ {
+ if( m_order[ ii ] == pos_hash ) continue;
+ point_type x2 = periodic_bc( m_x[ m_order[ ii ] ] , m_p );
+
+ if( cell_index[0] >= m_p.n_cell_x ) x2[0] += m_p.x_max;
+ if( cell_index[0] < 0 ) x2[0] -= m_p.x_max;
+ if( cell_index[1] >= m_p.n_cell_y ) x2[1] += m_p.y_max;
+ if( cell_index[1] < 0 ) x2[1] -= m_p.y_max;
+
+ a += m_p.interaction( x , x2 );
+ }
+ }
+ }
+ boost::get< 2 >( t ) = a;
+ }
+ };
+
+
+
+
+ md_system_bs( size_t n ,
+ local_force_type const& local_force = local_force_type() ,
+ interaction_type const& interaction = interaction_type() ,
+ double xmax = 100.0 , double ymax = 100.0 , double cell_size = 2.0 )
+ : m_p()
+ {
+ m_p.n = n;
+ m_p.x_max = xmax;
+ m_p.y_max = ymax;
+ m_p.interaction = interaction;
+ m_p.local_force = local_force;
+ m_p.n_cell_x = size_t( xmax / cell_size );
+ m_p.n_cell_y = size_t( ymax / cell_size );
+ m_p.n_cells = m_p.n_cell_x * m_p.n_cell_y;
+ m_p.cell_size = cell_size;
+ }
+
+ void init_point_vector( point_vector &x ) const { x.resize( m_p.n ); }
+
+ void operator()( point_vector const& x , point_vector const& v , point_vector &a , double t ) const
+ {
+ // init
+ hash_vector pos_hash( m_p.n , 0 );
+ index_vector pos_index( m_p.n );
+ hash_vector pos_order( m_p.n , 0 );
+ hash_vector cells_begin( m_p.n_cells ) , cells_end( m_p.n_cells ) , cell_order( m_p.n_cells );
+
+ boost::iota( pos_order , 0 );
+ boost::iota( cell_order , 0 );
+
+ // calculate grid hash
+ // calcHash( m_dGridParticleHash, m_dGridParticleIndex, dPos, m_numParticles);
+ std::for_each(
+ boost::make_zip_iterator( boost::make_tuple( x.begin() , pos_index.begin() , pos_hash.begin() ) ) ,
+ boost::make_zip_iterator( boost::make_tuple( x.end() , pos_index.end() , pos_hash.end() ) ) ,
+ cell_functor( m_p ) );
+
+// // sort particles based on hash
+// // sortParticles(m_dGridParticleHash, m_dGridParticleIndex, m_numParticles);
+ boost::sort( pos_order , [&]( size_t i1 , size_t i2 ) -> bool {
+ return pos_hash[i1] < pos_hash[i2]; } );
+
+
+
+ // reorder particle arrays into sorted order and find start and end of each cell
+ std::for_each( cell_order.begin() , cell_order.end() , [&]( size_t i ) {
+ auto pos_begin = boost::make_transform_iterator( pos_order.begin() , transform_functor( pos_hash ) );
+ auto pos_end = boost::make_transform_iterator( pos_order.end() , transform_functor( pos_hash ) );
+ cells_begin[ i ] = std::distance( pos_begin , std::lower_bound( pos_begin , pos_end , i ) );
+ cells_end[ i ] = std::distance( pos_begin , std::upper_bound( pos_begin , pos_end , i ) );
+ } );
+
+ std::for_each(
+ boost::make_zip_iterator( boost::make_tuple(
+ x.begin() ,
+ v.begin() ,
+ a.begin() ,
+ pos_index.begin() ,
+ boost::counting_iterator< size_t >( 0 )
+ ) ) ,
+ boost::make_zip_iterator( boost::make_tuple(
+ x.end() ,
+ v.end() ,
+ a.end() ,
+ pos_index.end() ,
+ boost::counting_iterator< size_t >( m_p.n )
+ ) ) ,
+ interaction_functor( cells_begin , cells_end , pos_order , x , v , m_p ) );
+ }
+
+ void bc( point_vector &x )
+ {
+ for( size_t i=0 ; i<m_p.n ; ++i )
+ {
+ x[i][0] = periodic_bc( x[ i ][0] , m_p.x_max );
+ x[i][1] = periodic_bc( x[ i ][1] , m_p.y_max );
+ }
+ }
+
+ static inline double periodic_bc( double x , double xmax )
+ {
+ double tmp = x - xmax * int( x / xmax );
+ return tmp >= 0.0 ? tmp : tmp + xmax;
+ }
+
+
+ static inline point_type periodic_bc( point_type const& x , params const& p )
+ {
+ return point_type( periodic_bc( x[0] , p.x_max ) , periodic_bc( x[1] , p.y_max ) );
+ }
+
+
+ static inline int check_interval( int i , int max )
+ {
+ int tmp = i % max;
+ return tmp >= 0 ? tmp : tmp + max;
+ }
+
+
+ static inline size_t hash_func( index_type index , params const & p )
+ {
+ size_t i1 = check_interval( index[0] , p.n_cell_x );
+ size_t i2 = check_interval( index[1] , p.n_cell_y );
+ return i1 * p.n_cell_y + i2;
+ }
+
+ params m_p;
+};
+
+
+template< typename LocalForce , typename Interaction >
+md_system_bs< LocalForce , Interaction > make_md_system_bs( size_t n , LocalForce const &f1 , Interaction const &f2 ,
+ double xmax = 100.0 , double ymax = 100.0 , double cell_size = 2.0 )
+{
+ return md_system_bs< LocalForce , Interaction >( n , f1 , f2 , xmax , ymax , cell_size );
+}
+
+
+
+
+
+
+using namespace boost::numeric::odeint;
+
+
+
+int main( int argc , char *argv[] )
+{
+ const size_t n1 = 32;
+ const size_t n2 = 32;
+ const size_t n = n1 * n2;
+ auto sys = make_md_system_bs( n , local_force() , make_conservative_interaction( lennard_jones() ) , 100.0 , 100.0 , 2.0 );
+ typedef decltype( sys ) system_type;
+ typedef system_type::point_vector point_vector;
+
+ std::mt19937 rng;
+ std::normal_distribution<> dist( 0.0 , 1.0 );
+
+ point_vector x , v;
+ sys.init_point_vector( x );
+ sys.init_point_vector( v );
+
+ for( size_t i=0 ; i<n1 ; ++i )
+ {
+ for( size_t j=0 ; j<n2 ; ++j )
+ {
+ size_t index = i * n2 + j;
+ x[index][0] = 10.0 + i * 2.0 ;
+ x[index][1] = 10.0 + j * 2.0 ;
+ v[index][0] = dist( rng ) ;
+ v[index][1] = dist( rng ) ;
+ }
+ }
+
+ velocity_verlet< point_vector > stepper;
+ const double dt = 0.025;
+ double t = 0.0;
+ // std::cout << "set term x11" << endl;
+ for( size_t oi=0 ; oi<10000 ; ++oi )
+ {
+ for( size_t ii=0 ; ii<50 ; ++ii,t+=dt )
+ stepper.do_step( sys , std::make_pair( std::ref( x ) , std::ref( v ) ) , t , dt );
+ sys.bc( x );
+
+ std::cout << "set size square" << "\n";
+ std::cout << "unset key" << "\n";
+ std::cout << "p [0:" << sys.m_p.x_max << "][0:" << sys.m_p.y_max << "] '-' pt 7 ps 0.5" << "\n";
+ for( size_t i=0 ; i<n ; ++i )
+ std::cout << x[i][0] << " " << x[i][1] << " " << v[i][0] << " " << v[i][1] << "\n";
+ std::cout << "e" << std::endl;
+ }
+
+ return 0;
+}
diff --git a/examples/mpi/Jamfile.v2 b/examples/mpi/Jamfile.v2
new file mode 100644
index 0000000..d3f18eb
--- /dev/null
+++ b/examples/mpi/Jamfile.v2
@@ -0,0 +1,15 @@
+# Copyright 2011-2013 Mario Mulansky
+# Copyright 2012 Karsten Ahnert
+# Copyright 2013 Pascal Germroth
+# Distributed under the Boost Software License, Version 1.0. (See
+# accompanying file LICENSE_1_0.txt or copy at
+# http://www.boost.org/LICENSE_1_0.txt)
+
+project
+ : requirements
+ <define>BOOST_ALL_NO_LIB=1
+ <library>/boost//mpi
+ <library>/boost//timer
+ ;
+
+exe phase_chain : phase_chain.cpp ;
diff --git a/examples/mpi/phase_chain.cpp b/examples/mpi/phase_chain.cpp
new file mode 100644
index 0000000..258c2f2
--- /dev/null
+++ b/examples/mpi/phase_chain.cpp
@@ -0,0 +1,120 @@
+/*
+ * phase_chain.cpp
+ *
+ * Example of MPI parallelization with odeint
+ *
+ * Copyright 2013 Karsten Ahnert
+ * Copyright 2013 Mario Mulansky
+ * Copyright 2013 Pascal Germroth
+ * Distributed under the Boost Software License, Version 1.0. (See
+ * accompanying file LICENSE_1_0.txt or copy at
+ * http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <iostream>
+#include <vector>
+#include <boost/random.hpp>
+#include <boost/timer/timer.hpp>
+//[phase_chain_mpi_header
+#include <boost/numeric/odeint.hpp>
+#include <boost/numeric/odeint/external/mpi/mpi.hpp>
+//]
+
+using namespace std;
+using namespace boost::numeric::odeint;
+using boost::timer::cpu_timer;
+using boost::math::double_constants::pi;
+
+//[phase_chain_state
+typedef mpi_state< vector<double> > state_type;
+//]
+
+//[phase_chain_mpi_rhs
+struct phase_chain_mpi_state
+{
+ phase_chain_mpi_state( double gamma = 0.5 )
+ : m_gamma( gamma ) { }
+
+ void operator()( const state_type &x , state_type &dxdt , double /* t */ ) const
+ {
+ const size_t M = x().size();
+ const bool have_left = x.world.rank() > 0,
+ have_right = x.world.rank() < x.world.size()-1;
+ double x_left, x_right;
+ boost::mpi::request r_left, r_right;
+ if( have_left )
+ {
+ x.world.isend( x.world.rank()-1 , 0 , x().front() ); // send to x_right
+ r_left = x.world.irecv( x.world.rank()-1 , 0 , x_left ); // receive from x().back()
+ }
+ if( have_right )
+ {
+ x.world.isend( x.world.rank()+1 , 0 , x().back() ); // send to x_left
+ r_right = x.world.irecv( x.world.rank()+1 , 0 , x_right ); // receive from x().front()
+ }
+ for(size_t m = 1 ; m < M-1 ; ++m)
+ {
+ dxdt()[m] = coupling_func( x()[m+1] - x()[m] ) +
+ coupling_func( x()[m-1] - x()[m] );
+ }
+ dxdt()[0] = coupling_func( x()[1] - x()[0] );
+ if( have_left )
+ {
+ r_left.wait();
+ dxdt()[0] += coupling_func( x_left - x().front() );
+ }
+ dxdt()[M-1] = coupling_func( x()[M-2] - x()[M-1] );
+ if( have_right )
+ {
+ r_right.wait();
+ dxdt()[M-1] += coupling_func( x_right - x().back() );
+ }
+ }
+
+ double coupling_func( double x ) const
+ {
+ return sin( x ) - m_gamma * ( 1.0 - cos( x ) );
+ }
+
+ double m_gamma;
+};
+//]
+
+
+int main( int argc , char **argv )
+{
+ //[phase_chain_mpi_init
+ boost::mpi::environment env( argc , argv );
+ boost::mpi::communicator world;
+
+ const size_t N = 131101;
+ vector<double> x;
+ if( world.rank() == 0 )
+ {
+ x.resize( N );
+ boost::random::uniform_real_distribution<double> distribution( 0.0 , 2.0*pi );
+ boost::random::mt19937 engine( 0 );
+ generate( x.begin() , x.end() , boost::bind( distribution , engine ) );
+ }
+
+ state_type x_split( world );
+ split( x , x_split );
+ //]
+
+
+ cpu_timer timer;
+ //[phase_chain_mpi_integrate
+ integrate_n_steps( runge_kutta4<state_type>() , phase_chain_mpi_state( 1.2 ) ,
+ x_split , 0.0 , 0.01 , 100 );
+ unsplit( x_split , x );
+ //]
+
+ if( world.rank() == 0 )
+ {
+ double run_time = static_cast<double>(timer.elapsed().wall) * 1.0e-9;
+ std::cerr << run_time << "s" << std::endl;
+ // copy(x.begin(), x.end(), ostream_iterator<double>(cout, "\n"));
+ }
+
+ return 0;
+}
diff --git a/examples/mtl/Jamfile.v2 b/examples/mtl/Jamfile.v2
new file mode 100644
index 0000000..9f4ffb0
--- /dev/null
+++ b/examples/mtl/Jamfile.v2
@@ -0,0 +1,17 @@
+# Copyright 2011-2013 Mario Mulansky
+# Copyright 2012 Karsten Ahnert
+# Distributed under the Boost Software License, Version 1.0. (See
+# accompanying file LICENSE_1_0.txt or copy at
+# http://www.boost.org/LICENSE_1_0.txt)
+
+# set your MTL4 directory here
+MTL4_INCLUDE = /home/mario/MTL4 ;
+
+project
+ : requirements
+ <include>$(MTL4_INCLUDE)
+ <define>BOOST_ALL_NO_LIB=1
+ ;
+
+exe gauss_packet : gauss_packet.cpp ;
+exe implicit_euler_mtl : implicit_euler_mtl.cpp ;
\ No newline at end of file
diff --git a/examples/mtl/gauss_packet.cpp b/examples/mtl/gauss_packet.cpp
new file mode 100644
index 0000000..9579e5d
--- /dev/null
+++ b/examples/mtl/gauss_packet.cpp
@@ -0,0 +1,141 @@
+/*
+ * gauss_packet.cpp
+ *
+ * Schroedinger equation with potential barrier and periodic boundary conditions
+ * Initial Gauss packet moving to the right
+ *
+ * pipe output into gnuplot to see animation
+ *
+ * Implementation of Hamilton operator via MTL library
+ *
+ * Copyright 2011-2013 Mario Mulansky
+ * Copyright 2011-2012 Karsten Ahnert
+ *
+ * Distributed under the Boost Software License, Version 1.0.
+ * (See accompanying file LICENSE_1_0.txt or
+ * copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#include <iostream>
+#include <complex>
+
+#include <boost/numeric/odeint.hpp>
+#include <boost/numeric/odeint/external/mtl4/mtl4.hpp>
+
+#include <boost/numeric/mtl/mtl.hpp>
+
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+typedef mtl::dense_vector< complex< double > > state_type;
+
+struct hamiltonian {
+
+ typedef mtl::compressed2D< complex< double > > matrix_type;
+ matrix_type m_H;
+
+ hamiltonian( const int N ) : m_H( N , N )
+ {
+ // constructor with zero potential
+ m_H = 0.0;
+ initialize_kinetic_term();
+ }
+
+ //template< mtl::compressed2D< double > >
+ hamiltonian( mtl::compressed2D< double > &V ) : m_H( num_rows( V ) , num_cols( V ) )
+ {
+ // use potential V in hamiltonian
+ m_H = complex<double>( 0.0 , -1.0 ) * V;
+ initialize_kinetic_term();
+ }
+
+ void initialize_kinetic_term( )
+ {
+ const int N = num_rows( m_H );
+ mtl::matrix::inserter< matrix_type , mtl::update_plus< complex<double> > > ins( m_H );
+ const double z = 1.0;
+ // fill diagonal and upper and lower diagonal
+ for( int i = 0 ; i<N ; ++i )
+ {
+ ins[ i ][ (i+1) % N ] << complex< double >( 0.0 , -z );
+ ins[ i ][ i ] << complex< double >( 0.0 , z );
+ ins[ (i+1) % N ][ i ] << complex< double >( 0.0 , -z );
+ }
+ }
+
+ void operator()( const state_type &psi , state_type &dpsidt , const double t )
+ {
+ dpsidt = m_H * psi;
+ }
+
+};
+
+struct write_for_gnuplot
+{
+ size_t m_every , m_count;
+
+ write_for_gnuplot( size_t every = 10 )
+ : m_every( every ) , m_count( 0 ) { }
+
+ void operator()( const state_type &x , double t )
+ {
+ if( ( m_count % m_every ) == 0 )
+ {
+ //clog << t << endl;
+ cout << "p [0:" << mtl::size(x) << "][0:0.02] '-'" << endl;
+ for( size_t i=0 ; i<mtl::size(x) ; ++i )
+ {
+ cout << i << "\t" << norm(x[i]) << "\n";
+ }
+ cout << "e" << endl;
+ }
+
+ ++m_count;
+ }
+};
+
+static const int N = 1024;
+static const int N0 = 256;
+static const double sigma0 = 20;
+static const double k0 = -1.0;
+
+int main( int argc , char** argv )
+{
+ state_type x( N , 0.0 );
+
+ // initialize gauss packet with nonzero velocity
+ for( int i=0 ; i<N ; ++i )
+ {
+ x[i] = exp( -(i-N0)*(i-N0) / ( 4.0*sigma0*sigma0 ) ) * exp( complex< double >( 0.0 , k0*i ) );
+ //x[i] += 2.0*exp( -(i+N0-N)*(i+N0-N) / ( 4.0*sigma0*sigma0 ) ) * exp( complex< double >( 0.0 , -k0*i ) );
+ }
+ x /= mtl::two_norm( x );
+
+ typedef runge_kutta4< state_type > stepper;
+
+ // create potential barrier
+ mtl::compressed2D< double > V( N , N );
+ V = 0.0;
+ {
+ mtl::matrix::inserter< mtl::compressed2D< double > > ins( V );
+ for( int i=0 ; i<N ; ++i )
+ {
+ //ins[i][i] << 1E-4*(i-N/2)*(i-N/2);
+
+ if( i < N/2 )
+ ins[ i ][ i ] << 0.0 ;
+ else
+ ins[ i ][ i ] << 1.0 ;
+
+ }
+ }
+
+ // perform integration, output can be piped to gnuplot
+ integrate_const( stepper() , hamiltonian( V ) , x , 0.0 , 1000.0 , 0.1 , write_for_gnuplot( 10 ) );
+
+ clog << "Norm: " << mtl::two_norm( x ) << endl;
+
+ return 0;
+}
diff --git a/examples/mtl/implicit_euler_mtl.cpp b/examples/mtl/implicit_euler_mtl.cpp
new file mode 100644
index 0000000..6a1b8e7
--- /dev/null
+++ b/examples/mtl/implicit_euler_mtl.cpp
@@ -0,0 +1,324 @@
+/*
+ * Copyright 2012 Karsten Ahnert
+ * Copyright 2012 Mario Mulansky
+ *
+ * Distributed under the Boost Software License, Version 1.0.
+ * (See accompanying file LICENSE_1_0.txt or
+ * copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#include <iostream>
+#include <fstream>
+#include <utility>
+#include "time.h"
+
+#include <boost/numeric/odeint.hpp>
+#include <boost/phoenix/phoenix.hpp>
+#include <boost/numeric/mtl/mtl.hpp>
+
+#include <boost/numeric/odeint/external/mtl4/implicit_euler_mtl4.hpp>
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+namespace phoenix = boost::phoenix;
+
+
+
+typedef mtl::dense_vector< double > vec_mtl4;
+typedef mtl::compressed2D< double > mat_mtl4;
+
+typedef boost::numeric::ublas::vector< double > vec_ublas;
+typedef boost::numeric::ublas::matrix< double > mat_ublas;
+
+
+// two systems defined 1 & 2 both are mostly sparse with the number of element variable
+struct system1_mtl4
+{
+
+ void operator()( const vec_mtl4 &x , vec_mtl4 &dxdt , double t )
+ {
+ int size = mtl::size(x);
+
+ dxdt[ 0 ] = -0.06*x[0];
+
+ for (int i =1; i< size ; ++i){
+
+ dxdt[ i ] = 4.2*x[i-1]-2.2*x[i]*x[i];
+ }
+
+ }
+};
+
+struct jacobi1_mtl4
+{
+ void operator()( const vec_mtl4 &x , mat_mtl4 &J , const double &t )
+ {
+ int size = mtl::size(x);
+ mtl::matrix::inserter<mat_mtl4> ins(J);
+
+ ins[0][0]=-0.06;
+
+ for (int i =1; i< size ; ++i)
+ {
+ ins[i][i-1] = + 4.2;
+ ins[i][i] = -4.2*x[i];
+ }
+ }
+};
+
+
+
+struct system1_ublas
+{
+
+ void operator()( const vec_ublas &x , vec_ublas &dxdt , double t )
+ {
+ int size = x.size();
+
+ dxdt[ 0 ] = -0.06*x[0];
+
+ for (int i =1; i< size ; ++i){
+
+ dxdt[ i ] = 4.2*x[i-1]-2.2*x[i]*x[i];
+ }
+
+ }
+};
+
+struct jacobi1_ublas
+{
+ void operator()( const vec_ublas &x , mat_ublas &J , const double &t )
+ {
+ int size = x.size();
+// mtl::matrix::inserter<mat_mtl4> ins(J);
+
+ J(0,0)=-0.06;
+
+ for (int i =1; i< size ; ++i){
+//ins[i][0]=120.0*x[i];
+ J(i,i-1) = + 4.2;
+ J(i,i) = -4.2*x[i];
+
+ }
+ }
+};
+
+struct system2_mtl4
+{
+
+ void operator()( const vec_mtl4 &x , vec_mtl4 &dxdt , double t )
+ {
+ int size = mtl::size(x);
+
+
+ for (int i =0; i< size/5 ; i+=5){
+
+ dxdt[ i ] = -0.5*x[i];
+ dxdt[i+1]= +25*x[i+1]*x[i+2]-740*x[i+3]*x[i+3]+4.2e-2*x[i];
+ dxdt[i+2]= +25*x[i]*x[i]-740*x[i+3]*x[i+3];
+ dxdt[i+3]= -25*x[i+1]*x[i+2]+740*x[i+3]*x[i+3];
+ dxdt[i+4] = 0.250*x[i]*x[i+1]-44.5*x[i+3];
+
+ }
+
+ }
+};
+
+struct jacobi2_mtl4
+{
+ void operator()( const vec_mtl4 &x , mat_mtl4 &J , const double &t )
+ {
+ int size = mtl::size(x);
+ mtl::matrix::inserter<mat_mtl4> ins(J);
+
+ for (int i =0; i< size/5 ; i+=5){
+
+ ins[ i ][i] = -0.5;
+ ins[i+1][i+1]=25*x[i+2];
+ ins[i+1][i+2] = 25*x[i+1];
+ ins[i+1][i+3] = -740*2*x[i+3];
+ ins[i+1][i] =+4.2e-2;
+
+ ins[i+2][i]= 50*x[i];
+ ins[i+2][i+3]= -740*2*x[i+3];
+ ins[i+3][i+1] = -25*x[i+2];
+ ins[i+3][i+2] = -25*x[i+1];
+ ins[i+3][i+3] = +740*2*x[i+3];
+ ins[i+4][i] = 0.25*x[i+1];
+ ins[i+4][i+1] =0.25*x[i];
+ ins[i+4][i+3]=-44.5;
+
+
+
+ }
+ }
+};
+
+
+
+struct system2_ublas
+{
+
+ void operator()( const vec_ublas &x , vec_ublas &dxdt , double t )
+ {
+ int size = x.size();
+ for (int i =0; i< size/5 ; i+=5){
+
+ dxdt[ i ] = -4.2e-2*x[i];
+ dxdt[i+1]= +25*x[i+1]*x[i+2]-740*x[i+3]*x[i+3]+4.2e-2*x[i];
+ dxdt[i+2]= +25*x[i]*x[i]-740*x[i+3]*x[i+3];
+ dxdt[i+3]= -25*x[i+1]*x[i+2]+740*x[i+3]*x[i+3];
+ dxdt[i+4] = 0.250*x[i]*x[i+1]-44.5*x[i+3];
+
+ }
+
+ }
+};
+
+struct jacobi2_ublas
+{
+ void operator()( const vec_ublas &x , mat_ublas &J , const double &t )
+ {
+ int size = x.size();
+
+ for (int i =0; i< size/5 ; i+=5){
+
+ J(i ,i) = -4.2e-2;
+ J(i+1,i+1)=25*x[i+2];
+ J(i+1,i+2) = 25*x[i+1];
+ J(i+1,i+3) = -740*2*x[i+3];
+ J(i+1,i) =+4.2e-2;
+
+ J(i+2,i)= 50*x[i];
+ J(i+2,i+3)= -740*2*x[i+3];
+ J(i+3,i+1) = -25*x[i+2];
+ J(i+3,i+2) = -25*x[i+1];
+ J(i+3,i+3) = +740*2*x[i+3];
+ J(i+4,i) = 0.25*x[i+1];
+ J(i+4,i+1) =0.25*x[i];
+ J(i+4,i+3)=-44.5;
+
+
+
+ }
+
+
+ }
+};
+
+
+
+
+void testRidiculouslyMassiveArray( int size )
+{
+ typedef boost::numeric::odeint::implicit_euler_mtl4 < double > mtl4stepper;
+ typedef boost::numeric::odeint::implicit_euler< double > booststepper;
+
+ vec_mtl4 x(size , 0.0);
+ x[0]=1;
+
+
+ double dt = 0.02;
+ double endtime = 10.0;
+
+ clock_t tstart_mtl4 = clock();
+ size_t num_of_steps_mtl4 = integrate_const(
+ mtl4stepper() ,
+ make_pair( system1_mtl4() , jacobi1_mtl4() ) ,
+ x , 0.0 , endtime , dt );
+ clock_t tend_mtl4 = clock() ;
+
+ clog << x[0] << endl;
+ clog << num_of_steps_mtl4 << " time elapsed: " << (double)(tend_mtl4-tstart_mtl4 )/CLOCKS_PER_SEC << endl;
+
+ vec_ublas x_ublas(size , 0.0);
+ x_ublas[0]=1;
+
+ clock_t tstart_boost = clock();
+ size_t num_of_steps_ublas = integrate_const(
+ booststepper() ,
+ make_pair( system1_ublas() , jacobi1_ublas() ) ,
+ x_ublas , 0.0 , endtime , dt );
+ clock_t tend_boost = clock() ;
+
+ clog << x_ublas[0] << endl;
+ clog << num_of_steps_ublas << " time elapsed: " << (double)(tend_boost-tstart_boost)/CLOCKS_PER_SEC<< endl;
+
+ clog << "dt_ublas/dt_mtl4 = " << (double)( tend_boost-tstart_boost )/( tend_mtl4-tstart_mtl4 ) << endl << endl;
+ return ;
+}
+
+
+
+void testRidiculouslyMassiveArray2( int size )
+{
+ typedef boost::numeric::odeint::implicit_euler_mtl4 < double > mtl4stepper;
+ typedef boost::numeric::odeint::implicit_euler< double > booststepper;
+
+
+ vec_mtl4 x(size , 0.0);
+ x[0]=100;
+
+
+ double dt = 0.01;
+ double endtime = 10.0;
+
+ clock_t tstart_mtl4 = clock();
+ size_t num_of_steps_mtl4 = integrate_const(
+ mtl4stepper() ,
+ make_pair( system1_mtl4() , jacobi1_mtl4() ) ,
+ x , 0.0 , endtime , dt );
+
+
+ clock_t tend_mtl4 = clock() ;
+
+ clog << x[0] << endl;
+ clog << num_of_steps_mtl4 << " time elapsed: " << (double)(tend_mtl4-tstart_mtl4 )/CLOCKS_PER_SEC << endl;
+
+ vec_ublas x_ublas(size , 0.0);
+ x_ublas[0]=100;
+
+ clock_t tstart_boost = clock();
+ size_t num_of_steps_ublas = integrate_const(
+ booststepper() ,
+ make_pair( system1_ublas() , jacobi1_ublas() ) ,
+ x_ublas , 0.0 , endtime , dt );
+
+
+ clock_t tend_boost = clock() ;
+
+ clog << x_ublas[0] << endl;
+ clog << num_of_steps_ublas << " time elapsed: " << (double)(tend_boost-tstart_boost)/CLOCKS_PER_SEC<< endl;
+
+ clog << "dt_ublas/dt_mtl4 = " << (double)( tend_boost-tstart_boost )/( tend_mtl4-tstart_mtl4 ) << endl << endl;
+ return ;
+}
+
+
+
+
+int main( int argc , char **argv )
+{
+ std::vector< size_t > length;
+ length.push_back( 8 );
+ length.push_back( 16 );
+ length.push_back( 32 );
+ length.push_back( 64 );
+ length.push_back( 128 );
+ length.push_back( 256 );
+
+ for( size_t i=0 ; i<length.size() ; ++i )
+ {
+ clog << "Testing with size " << length[i] << endl;
+ testRidiculouslyMassiveArray( length[i] );
+ }
+ clog << endl << endl;
+
+ for( size_t i=0 ; i<length.size() ; ++i )
+ {
+ clog << "Testing with size " << length[i] << endl;
+ testRidiculouslyMassiveArray2( length[i] );
+ }
+}
diff --git a/examples/multiprecision/Jamfile b/examples/multiprecision/Jamfile
new file mode 100644
index 0000000..9708d43
--- /dev/null
+++ b/examples/multiprecision/Jamfile
@@ -0,0 +1,16 @@
+# Copyright 2011-2013 Mario Mulansky
+# Copyright 2012 Karsten Ahnert
+# Distributed under the Boost Software License, Version 1.0. (See
+# accompanying file LICENSE_1_0.txt or copy at
+# http://www.boost.org/LICENSE_1_0.txt)
+
+
+project
+ : requirements
+ <define>BOOST_ALL_NO_LIB=1
+ :
+ ;
+
+
+exe lorenz_mp : lorenz_mp.cpp ;
+exe cmp_precision : cmp_precision.cpp ;
diff --git a/examples/multiprecision/cmp_precision.cpp b/examples/multiprecision/cmp_precision.cpp
new file mode 100644
index 0000000..779b5e2
--- /dev/null
+++ b/examples/multiprecision/cmp_precision.cpp
@@ -0,0 +1,68 @@
+/* Boost libs/numeric/odeint/examples/multiprecision/cmp_precision.cpp
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ example comparing double to multiprecision using Boost.Multiprecision
+
+ Distributed under the Boost Software License, Version 1.0.
+(See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#include <iostream>
+#include <boost/numeric/odeint.hpp>
+#include <boost/multiprecision/cpp_dec_float.hpp>
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+typedef boost::multiprecision::cpp_dec_float_50 mp_50;
+
+/* we solve the simple ODE x' = 3/(2t^2) + x/(2t)
+ * with initial condition x(1) = 0.
+ * Analytic solution is x(t) = sqrt(t) - 1/t
+ */
+
+void rhs_m( const mp_50 x , mp_50 &dxdt , const mp_50 t )
+{ // version for multiprecision
+ dxdt = mp_50(3)/(mp_50(2)*t*t) + x/(mp_50(2)*t);
+}
+
+void rhs_d( const double x , double &dxdt , const double t )
+{ // version for double precision
+ dxdt = 3.0/(2.0*t*t) + x/(2.0*t);
+}
+
+// state_type = mp_50 = deriv_type = time_type = mp_50
+typedef runge_kutta4< mp_50 , mp_50 , mp_50 , mp_50 , vector_space_algebra , default_operations , never_resizer > stepper_type_m;
+
+typedef runge_kutta4< double , double , double , double , vector_space_algebra , default_operations , never_resizer > stepper_type_d;
+
+int main()
+{
+
+ stepper_type_m stepper_m;
+ stepper_type_d stepper_d;
+
+ mp_50 dt_m( 0.5 );
+ double dt_d( 0.5 );
+
+ cout << "dt" << '\t' << "mp" << '\t' << "double" << endl;
+
+ while( dt_m > 1E-20 )
+ {
+
+ mp_50 x_m = 0; //initial value x(1) = 0
+ stepper_m.do_step( rhs_m , x_m , mp_50( 1 ) , dt_m );
+ double x_d = 0;
+ stepper_d.do_step( rhs_d , x_d , 1.0 , dt_d );
+
+ cout << dt_m << '\t';
+ cout << abs((x_m - (sqrt(1+dt_m)-mp_50(1)/(1+dt_m)))/x_m) << '\t' ;
+ cout << abs((x_d - (sqrt(1+dt_d)-mp_50(1)/(1+dt_d)))/x_d) << endl ;
+ dt_m /= 2;
+ dt_d /= 2;
+ }
+}
diff --git a/examples/multiprecision/lorenz_mp.cpp b/examples/multiprecision/lorenz_mp.cpp
new file mode 100644
index 0000000..c3e5b82
--- /dev/null
+++ b/examples/multiprecision/lorenz_mp.cpp
@@ -0,0 +1,81 @@
+/*
+ * lorenz_mp.cpp
+ *
+ * This example demonstrates how odeint can be used with boost.multiprecision.
+ *
+ * Copyright 2011-2012 Karsten Ahnert
+ * Copyright 2013 Mario Mulansky
+ *
+ * Distributed under the Boost Software License, Version 1.0.
+ * (See accompanying file LICENSE_1_0.txt or
+ * copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+
+#include <iostream>
+
+//[ mp_lorenz_defs
+#include <boost/numeric/odeint.hpp>
+#include <boost/multiprecision/cpp_dec_float.hpp>
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+typedef boost::multiprecision::cpp_dec_float_50 value_type;
+
+typedef boost::array< value_type , 3 > state_type;
+//]
+
+//[ mp_lorenz_rhs
+struct lorenz
+{
+ void operator()( const state_type &x , state_type &dxdt , value_type t ) const
+ {
+ const value_type sigma( 10 );
+ const value_type R( 28 );
+ const value_type b( value_type( 8 ) / value_type( 3 ) );
+
+ dxdt[0] = sigma * ( x[1] - x[0] );
+ dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
+ dxdt[2] = -b * x[2] + x[0] * x[1];
+ }
+};
+//]
+
+
+
+
+struct streaming_observer
+{
+ std::ostream& m_out;
+
+ streaming_observer( std::ostream &out ) : m_out( out ) { }
+
+ template< class State , class Time >
+ void operator()( const State &x , Time t ) const
+ {
+ m_out << t;
+ for( size_t i=0 ; i<x.size() ; ++i ) m_out << "\t" << x[i] ;
+ m_out << "\n";
+ }
+};
+
+
+
+
+
+
+int main( int argc , char **argv )
+{
+ //[ mp_lorenz_int
+ state_type x = {{ value_type( 10.0 ) , value_type( 10.0 ) , value_type( 10.0 ) }};
+
+ cout.precision( 50 );
+ integrate_const( runge_kutta4< state_type , value_type >() ,
+ lorenz() , x , value_type( 0.0 ) , value_type( 10.0 ) , value_type( value_type( 1.0 ) / value_type( 10.0 ) ) ,
+ streaming_observer( cout ) );
+ //]
+
+ return 0;
+}
diff --git a/examples/my_vector.cpp b/examples/my_vector.cpp
new file mode 100644
index 0000000..746dfaa
--- /dev/null
+++ b/examples/my_vector.cpp
@@ -0,0 +1,114 @@
+/*
+ * Copyright 2011-2012 Mario Mulansky
+ * Copyright 2012-2013 Karsten Ahnert
+ *
+ * Distributed under the Boost Software License, Version 1.0.
+ * (See accompanying file LICENSE_1_0.txt or
+ * copy at http://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Example for self defined vector type.
+ */
+
+#include <vector>
+
+#include <boost/numeric/odeint.hpp>
+
+//[my_vector
+template< size_t MAX_N >
+class my_vector
+{
+ typedef std::vector< double > vector;
+
+public:
+ typedef vector::iterator iterator;
+ typedef vector::const_iterator const_iterator;
+
+public:
+ my_vector( const size_t N )
+ : m_v( N )
+ {
+ m_v.reserve( MAX_N );
+ }
+
+ my_vector()
+ : m_v()
+ {
+ m_v.reserve( MAX_N );
+ }
+
+// ... [ implement container interface ]
+//]
+ const double & operator[]( const size_t n ) const
+ { return m_v[n]; }
+
+ double & operator[]( const size_t n )
+ { return m_v[n]; }
+
+ iterator begin()
+ { return m_v.begin(); }
+
+ const_iterator begin() const
+ { return m_v.begin(); }
+
+ iterator end()
+ { return m_v.end(); }
+
+ const_iterator end() const
+ { return m_v.end(); }
+
+ size_t size() const
+ { return m_v.size(); }
+
+ void resize( const size_t n )
+ { m_v.resize( n ); }
+
+private:
+ std::vector< double > m_v;
+
+};
+
+//[my_vector_resizeable
+// define my_vector as resizeable
+
+namespace boost { namespace numeric { namespace odeint {
+
+template<size_t N>
+struct is_resizeable< my_vector<N> >
+{
+ typedef boost::true_type type;
+ static const bool value = type::value;
+};
+
+} } }
+//]
+
+
+typedef my_vector<3> state_type;
+
+void lorenz( const state_type &x , state_type &dxdt , const double t )
+{
+ const double sigma( 10.0 );
+ const double R( 28.0 );
+ const double b( 8.0 / 3.0 );
+
+ dxdt[0] = sigma * ( x[1] - x[0] );
+ dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
+ dxdt[2] = -b * x[2] + x[0] * x[1];
+}
+
+using namespace boost::numeric::odeint;
+
+int main()
+{
+ state_type x(3);
+ x[0] = 5.0 ; x[1] = 10.0 ; x[2] = 10.0;
+
+ // make sure resizing is ON
+ BOOST_STATIC_ASSERT( is_resizeable<state_type>::value == true );
+
+ // my_vector works with range_algebra as it implements
+ // the required parts of a container interface
+ // no further work is required
+
+ integrate_const( runge_kutta4< state_type >() , lorenz , x , 0.0 , 10.0 , 0.1 );
+}
diff --git a/examples/nt2/Jamfile.v2 b/examples/nt2/Jamfile.v2
new file mode 100644
index 0000000..05847cd
--- /dev/null
+++ b/examples/nt2/Jamfile.v2
@@ -0,0 +1,34 @@
+#==============================================================================
+# Copyright 2014 LRI UMR 8623 CNRS/Univ Paris Sud XI
+# Copyright 2014 NumScale SAS
+#
+# Distributed under the Boost Software License, Version 1.0.
+# See accompanying file LICENSE.txt or copy at
+# http://www.boost.org/LICENSE_1_0.txt
+#==============================================================================
+
+use-project boost : $(BOOST_ROOT) ;
+
+import os ;
+
+# This must be built using an NT2 installation.
+# NT2_ROOT_PATH should point to the build directory.
+# Currently, cxxflags needs to be set to the required architecture
+# if using avx/avx2, set the environemnt variable NT2_SIMD_FLAGS to the
+# required value for your compiler (i.e. -mavx2 on g++)
+# If using sse2/3/4 in 64 bits, this is set automatically.
+
+local NT2_ROOT_PATH = [ os.environ NT2_ROOT_PATH ] ;
+local NT2_SIMD_FLAGS = [ os.environ NT2_SIMD_FLAGS ] ;
+
+project
+ : requirements
+ <define>BOOST_ALL_NO_LIB=1
+ <include>$(NT2_ROOT_PATH)/include/
+ <link>static
+ <toolset>gcc:<cxxflags>-DBOOST_SIMD_NO_STRICT_ALIASING
+ <toolset>gcc:<cxxflags>-fno-strict-aliasing
+ <cxxflags>$(NT2_SIMD_FLAGS)
+ ;
+
+exe phase_oscillator_ensemble : phase_oscillator_ensemble.cpp ;
diff --git a/examples/nt2/phase_oscillator_ensemble.cpp b/examples/nt2/phase_oscillator_ensemble.cpp
new file mode 100644
index 0000000..1f28623
--- /dev/null
+++ b/examples/nt2/phase_oscillator_ensemble.cpp
@@ -0,0 +1,170 @@
+//==============================================================================
+// Copyright 2011-2014 Karsten Ahnert
+// Copyright 2011-2014 Mario Mulansky
+// Copyright 2014 LRI UMR 8623 CNRS/Univ Paris Sud XI
+// Copyright 2014 NumScale SAS
+//
+// Distributed under the Boost Software License, Version 1.0.
+// See accompanying file LICENSE.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt
+//==============================================================================
+
+#include <iostream>
+#include <utility>
+
+#include <boost/numeric/odeint.hpp>
+
+#ifndef M_PI //not there on windows
+#define M_PI 3.141592653589793 //...
+#endif
+
+#include <boost/random.hpp>
+#include <boost/dispatch/meta/as_integer.hpp>
+
+#include <nt2/include/functions/cos.hpp>
+#include <nt2/include/functions/sin.hpp>
+#include <nt2/include/functions/atan2.hpp>
+#include <nt2/table.hpp>
+#include <nt2/include/functions/zeros.hpp>
+#include <nt2/include/functions/sum.hpp>
+#include <nt2/include/functions/mean.hpp>
+#include <nt2/arithmetic/include/functions/hypot.hpp>
+#include <nt2/include/functions/tie.hpp>
+
+#include <boost/numeric/odeint/external/nt2/nt2_algebra_dispatcher.hpp>
+
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+template <typename container_type, typename T>
+pair< T, T > calc_mean_field( const container_type &x )
+
+{
+ T cos_sum = 0.0 , sin_sum = 0.0;
+
+ nt2::tie(cos_sum,sin_sum) = nt2::tie(nt2::mean( nt2::cos(x) ), nt2::mean( nt2::sin(x) ));
+
+ T K = nt2::hypot(sin_sum,cos_sum);
+ T Theta = nt2::atan2( sin_sum , cos_sum );
+
+ return make_pair( K , Theta );
+}
+
+template <typename container_type, typename T>
+struct phase_ensemble
+{
+ typedef typename boost::dispatch::meta::as_integer<T,unsigned>::type int_type;
+ container_type m_omega;
+ T m_epsilon;
+
+ phase_ensemble( const int_type n , T g = 1.0 , T epsilon = 1.0 )
+ : m_epsilon( epsilon )
+ {
+ m_omega = nt2::zeros(nt2::of_size(n), nt2::meta::as_<T>());
+ create_frequencies( g );
+ }
+
+ void create_frequencies( T g )
+ {
+ boost::mt19937 rng;
+ boost::cauchy_distribution<> cauchy( 0.0 , g );
+ boost::variate_generator< boost::mt19937&, boost::cauchy_distribution<> > gen( rng , cauchy );
+ generate( m_omega.begin() , m_omega.end() , gen );
+}
+
+ void set_epsilon( T epsilon ) { m_epsilon = epsilon; }
+
+ T get_epsilon( void ) const { return m_epsilon; }
+
+ void operator()( const container_type &x , container_type &dxdt , T ) const
+ {
+ pair< T, T > mean = calc_mean_field<container_type,T>( x );
+ dxdt = m_omega + m_epsilon * mean.first * nt2::sin( mean.second - x );
+ }
+};
+
+template<typename T>
+struct statistics_observer
+{
+ typedef typename boost::dispatch::meta::as_integer<T,unsigned>::type int_type;
+ T m_K_mean;
+ int_type m_count;
+
+ statistics_observer( void )
+ : m_K_mean( 0.0 ) , m_count( 0 ) { }
+
+ template< class State >
+ void operator()( const State &x , T t )
+ {
+ pair< T, T > mean = calc_mean_field<State,T>( x );
+ m_K_mean += mean.first;
+ ++m_count;
+ }
+
+ T get_K_mean( void ) const { return ( m_count != 0 ) ? m_K_mean / T( m_count ) : 0.0 ; }
+
+ void reset( void ) { m_K_mean = 0.0; m_count = 0; }
+};
+
+template<typename T>
+struct test_ode_table
+{
+ typedef nt2::table<T> array_type;
+ typedef void experiment_is_immutable;
+
+ typedef typename boost::dispatch::meta::as_integer<T,unsigned>::type int_type;
+
+ test_ode_table ( )
+ : size_(16384), ensemble( size_ , 1.0 ), unif( 0.0 , 2.0 * M_PI ), gen( rng , unif ), obs()
+ {
+ x.resize(nt2::of_size(size_));
+ }
+
+ void operator()()
+ {
+ for( T epsilon = 0.0 ; epsilon < 5.0 ; epsilon += 0.1 )
+ {
+ ensemble.set_epsilon( epsilon );
+ obs.reset();
+
+ // start with random initial conditions
+ generate( x.begin() , x.end() , gen );
+ // calculate some transients steps
+ integrate_const( runge_kutta4< array_type, T >() , boost::ref( ensemble ) , x , T(0.0) , T(10.0) , dt );
+
+ // integrate and compute the statistics
+ integrate_const( runge_kutta4< array_type, T >() , boost::ref( ensemble ) , x , T(0.0) , T(100.0) , dt , boost::ref( obs ) );
+ cout << epsilon << "\t" << obs.get_K_mean() << endl;
+ }
+ }
+
+ friend std::ostream& operator<<(std::ostream& os, test_ode_table<T> const& p)
+ {
+ return os << "(" << p.size() << ")";
+ }
+
+ std::size_t size() const { return size_; }
+
+ private:
+ std::size_t size_;
+ phase_ensemble<array_type,T> ensemble;
+ boost::uniform_real<> unif;
+ array_type x;
+ boost::mt19937 rng;
+ boost::variate_generator< boost::mt19937&, boost::uniform_real<> > gen;
+ statistics_observer<T> obs;
+
+ static const T dt = 0.1;
+};
+
+int main()
+{
+ std::cout<< " With T = [double] \n";
+ test_ode_table<double> test_double;
+ test_double();
+
+ std::cout<< " With T = [float] \n";
+ test_ode_table<float> test_float;
+ test_float();
+}
diff --git a/examples/openmp/Jamfile.v2 b/examples/openmp/Jamfile.v2
new file mode 100644
index 0000000..cef4f67
--- /dev/null
+++ b/examples/openmp/Jamfile.v2
@@ -0,0 +1,23 @@
+# Copyright 2011-2013 Mario Mulansky
+# Copyright 2012 Karsten Ahnert
+# Copyright 2013 Pascal Germroth
+# Distributed under the Boost Software License, Version 1.0. (See
+# accompanying file LICENSE_1_0.txt or copy at
+# http://www.boost.org/LICENSE_1_0.txt)
+
+use-project /boost : $(BOOST_ROOT) ;
+import openmp : * ;
+
+project
+ : requirements
+ <include>..
+ <define>BOOST_ALL_NO_LIB=1
+ <library>/boost//timer
+ [ openmp ]
+ ;
+
+exe lorenz_ensemble : lorenz_ensemble.cpp ;
+exe lorenz_ensemble_simple : lorenz_ensemble_simple.cpp ;
+exe lorenz_ensemble_nested : lorenz_ensemble_nested.cpp ;
+exe phase_chain : phase_chain.cpp ;
+exe phase_chain_omp_state : phase_chain_omp_state.cpp ;
diff --git a/examples/openmp/lorenz_ensemble.cpp b/examples/openmp/lorenz_ensemble.cpp
new file mode 100644
index 0000000..6717a50
--- /dev/null
+++ b/examples/openmp/lorenz_ensemble.cpp
@@ -0,0 +1,91 @@
+/* Boost libs/numeric/odeint/examples/openmp/lorenz_ensemble.cpp
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+ Copyright 2013 Pascal Germroth
+
+ Parallelized Lorenz ensembles
+
+ Distributed under the Boost Software License, Version 1.0.
+(See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <omp.h>
+#include <vector>
+#include <iostream>
+#include <iterator>
+#include <boost/numeric/odeint.hpp>
+#include <boost/numeric/odeint/external/openmp/openmp.hpp>
+#include <boost/lexical_cast.hpp>
+#include "point_type.hpp"
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+typedef point<double, 3> point_type;
+typedef vector< point_type > inner_state_type;
+typedef openmp_state<point_type> state_type;
+
+const double sigma = 10.0;
+const double b = 8.0 / 3.0;
+
+
+struct sys_func {
+ const vector<double> &R;
+ sys_func( vector<double> &R ) : R(R) {}
+
+ void operator()( const state_type &x , state_type &dxdt , double t ) const {
+# pragma omp parallel for
+ for(size_t j = 0 ; j < x.size() ; j++) {
+ size_t offset = 0;
+ for(size_t i = 0 ; i < j ; i++)
+ offset += x[i].size();
+
+ for(size_t i = 0 ; i < x[j].size() ; i++) {
+ const point_type &xi = x[j][i];
+ point_type &dxdti = dxdt[j][i];
+ dxdti[0] = -sigma * (xi[0] - xi[1]);
+ dxdti[1] = R[offset + i] * xi[0] - xi[1] - xi[0] * xi[2];
+ dxdti[2] = -b * xi[2] + xi[0] * xi[1];
+ }
+ }
+ }
+};
+
+
+int main(int argc, char **argv) {
+ size_t n = 1024;
+ if(argc > 1) n = boost::lexical_cast<size_t>(argv[1]);
+
+ vector<double> R(n);
+ const double Rmin = 0.1, Rmax = 50.0;
+# pragma omp parallel for
+ for(size_t i = 0 ; i < n ; i++)
+ R[i] = Rmin + (Rmax - Rmin) / (n - 1) * i;
+
+ vector<point_type> inner(n, point_type(10, 10, 10));
+ state_type state;
+ split(inner, state);
+
+ cerr << "openmp_state split " << n << " into";
+ for(size_t i = 0 ; i != state.size() ; i++)
+ cerr << ' ' << state[i].size();
+ cerr << endl;
+
+ typedef runge_kutta4< state_type, double > stepper;
+
+ const double t_max = 10.0, dt = 0.01;
+
+ integrate_const(
+ stepper(),
+ sys_func(R),
+ state,
+ 0.0, t_max, dt
+ );
+
+ unsplit(state, inner);
+ std::copy( inner.begin(), inner.end(), ostream_iterator<point_type>(cout, "\n") );
+
+ return 0;
+}
diff --git a/examples/openmp/lorenz_ensemble_nested.cpp b/examples/openmp/lorenz_ensemble_nested.cpp
new file mode 100644
index 0000000..4609c47
--- /dev/null
+++ b/examples/openmp/lorenz_ensemble_nested.cpp
@@ -0,0 +1,75 @@
+/* Boost libs/numeric/odeint/examples/openmp/lorenz_ensemble_nested.cpp
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Pascal Germroth
+ Copyright 2013 Mario Mulansky
+
+ Parallelized Lorenz ensembles using nested omp algebra
+
+ Distributed under the Boost Software License, Version 1.0.
+(See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <omp.h>
+#include <vector>
+#include <iostream>
+#include <iterator>
+#include <boost/numeric/odeint.hpp>
+#include <boost/numeric/odeint/external/openmp/openmp.hpp>
+#include <boost/lexical_cast.hpp>
+#include "point_type.hpp"
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+typedef point<double, 3> point_type;
+typedef vector< point_type > state_type;
+
+const double sigma = 10.0;
+const double b = 8.0 / 3.0;
+
+
+struct sys_func {
+ const vector<double> &R;
+ sys_func( vector<double> &R ) : R(R) {}
+
+ void operator()( const state_type &x , state_type &dxdt , double t ) const {
+# pragma omp parallel for
+ for(size_t i = 0 ; i < x.size() ; i++) {
+ dxdt[i][0] = -sigma * (x[i][0] - x[i][1]);
+ dxdt[i][1] = R[i] * x[i][0] - x[i][1] - x[i][0] * x[i][2];
+ dxdt[i][2] = -b * x[i][2] + x[i][0] * x[i][1];
+ }
+ }
+};
+
+
+int main(int argc, char **argv) {
+ size_t n = 1024;
+ if(argc > 1) n = boost::lexical_cast<size_t>(argv[1]);
+
+ vector<double> R(n);
+ const double Rmin = 0.1, Rmax = 50.0;
+# pragma omp parallel for
+ for(size_t i = 0 ; i < n ; i++)
+ R[i] = Rmin + (Rmax - Rmin) / (n - 1) * i;
+
+ state_type state( n , point_type(10, 10, 10) );
+
+ typedef runge_kutta4< state_type, double , state_type , double ,
+ openmp_nested_algebra<vector_space_algebra> > stepper;
+
+ const double t_max = 10.0, dt = 0.01;
+
+ integrate_const(
+ stepper(),
+ sys_func(R),
+ state,
+ 0.0, t_max, dt
+ );
+
+ std::copy( state.begin(), state.end(), ostream_iterator<point_type>(cout, "\n") );
+
+ return 0;
+}
diff --git a/examples/openmp/lorenz_ensemble_simple.cpp b/examples/openmp/lorenz_ensemble_simple.cpp
new file mode 100644
index 0000000..fbaf249
--- /dev/null
+++ b/examples/openmp/lorenz_ensemble_simple.cpp
@@ -0,0 +1,79 @@
+/* Boost libs/numeric/odeint/examples/openmp/lorenz_ensemble_simple.cpp
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+ Copyright 2013 Pascal Germroth
+
+ Parallelized Lorenz ensembles
+
+ Distributed under the Boost Software License, Version 1.0.
+(See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <omp.h>
+#include <vector>
+#include <iostream>
+#include <boost/numeric/odeint.hpp>
+#include <boost/numeric/odeint/external/openmp/openmp.hpp>
+#include "point_type.hpp"
+
+using namespace std;
+
+typedef vector<double> vector_type;
+typedef point<double, 3> point_type;
+typedef vector<point_type> state_type;
+
+const double sigma = 10.0;
+const double b = 8.0 / 3.0;
+
+struct sys_func {
+ const vector_type &R;
+ sys_func( const vector_type &_R ) : R( _R ) { }
+
+ void operator()( const state_type &x , state_type &dxdt , double t ) const {
+ const size_t n = x.size();
+# pragma omp parallel for
+ for(size_t i = 0 ; i < n ; i++) {
+ const point_type &xi = x[i];
+ point_type &dxdti = dxdt[i];
+ dxdti[0] = -sigma * (xi[0] - xi[1]);
+ dxdti[1] = R[i] * xi[0] - xi[1] - xi[0] * xi[2];
+ dxdti[2] = -b * xi[2] + xi[0] * xi[1];
+ }
+ }
+};
+
+
+int main() {
+ using namespace boost::numeric::odeint;
+
+ const size_t n = 1024;
+ vector_type R(n);
+ const double Rmin = 0.1, Rmax = 50.0;
+# pragma omp parallel for
+ for(size_t i = 0 ; i < n ; i++)
+ R[i] = Rmin + (Rmax - Rmin) / (n - 1) * i;
+
+ state_type X(n, point_type(10, 10, 10));
+
+ const double t_max = 10.0, dt = 0.01;
+
+ // Simple stepper with constant step size
+ // typedef runge_kutta4<state_type, double, state_type, double,
+ // openmp_range_algebra> stepper;
+
+ // integrate_const(stepper(), sys_func(R), X, 0.0, t_max, dt);
+
+ // Controlled stepper with variable step size
+ typedef runge_kutta_fehlberg78<state_type, double, state_type, double,
+ openmp_range_algebra> error_stepper_type;
+ typedef controlled_runge_kutta<error_stepper_type> controlled_stepper_type;
+ controlled_stepper_type controlled_stepper;
+
+ integrate_adaptive(controlled_stepper, sys_func(R), X, 0.0, t_max, dt);
+
+ copy( X.begin(), X.end(), ostream_iterator<point_type>(cout, "\n") );
+
+ return 0;
+}
diff --git a/examples/openmp/openmp.jam b/examples/openmp/openmp.jam
new file mode 100644
index 0000000..226bcf5
--- /dev/null
+++ b/examples/openmp/openmp.jam
@@ -0,0 +1,52 @@
+# Copyright 2013 Karsten Ahnert
+# Copyright 2013 Mario Mulansky
+# Copyright 2013 Pascal Germroth
+# Distributed under the Boost Software License, Version 1.0. (See
+# accompanying file LICENSE_1_0.txt or copy at
+# http://www.boost.org/LICENSE_1_0.txt)
+
+
+# Only builds target with supported OpenMP enabled toolsets.
+#
+# use as:
+# exe omp : omp.cpp : [ openmp ] ;
+#
+rule openmp return
+ # default
+ <build>no
+ # GNU C++
+ <toolset>gcc:<cxxflags>-fopenmp
+ <toolset>gcc:<linkflags>-fopenmp
+ <toolset>gcc:<build>yes
+ # Microsoft Visual C++
+ <toolset>msvc:<cxxflags>/openmp
+ <toolset>msvc:<linkflags>/openmp
+ <toolset>msvc:<build>yes
+ # Intel C++
+ <toolset>intel-linux:<cxxflags>-openmp
+ <toolset>intel-linux:<linkflags>-openmp
+ <toolset>intel-linux:<build>yes
+ <toolset>intel-win:<cxxflags>-Qopenmp
+ <toolset>intel-win:<linkflags>-Qopenmp
+ <toolset>intel-win:<build>yes
+ # HP aC++
+ <toolset>acc:<cxxflags>+Oopenmp
+ <toolset>acc:<linkflags>+Oopenmp
+ <toolset>acc:<build>yes
+ # Sun Studio
+ <toolset>sun:<cxxflags>-xopenmp
+ <toolset>sun:<linkflags>-xopenmp
+ <toolset>sun:<build>yes
+ # IBM XL
+ <toolset>vacpp:<cxxflags>-qsmp=omp
+ <toolset>vacpp:<linkflags>-qsmp=omp
+ <toolset>vacpp:<build>yes
+ # PG++
+ <toolset>pgi:<cxxflags>-mp
+ <toolset>pgi:<linkflags>-mp
+ <toolset>pgi:<build>yes
+ # Pathscale
+ <toolset>pathscale:<cxxflags>-mp
+ <toolset>pathscale:<linkflags>-mp
+ <toolset>pathscale:<build>yes
+ ;
diff --git a/examples/openmp/phase_chain.cpp b/examples/openmp/phase_chain.cpp
new file mode 100644
index 0000000..08876fc
--- /dev/null
+++ b/examples/openmp/phase_chain.cpp
@@ -0,0 +1,95 @@
+/*
+ * phase_chain.cpp
+ *
+ * Example of OMP parallelization with odeint
+ *
+ * Copyright 2013 Karsten Ahnert
+ * Copyright 2013 Mario Mulansky
+ * Copyright 2013 Pascal Germroth
+ * Distributed under the Boost Software License, Version 1.0. (See
+ * accompanying file LICENSE_1_0.txt or copy at
+ * http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <iostream>
+#include <vector>
+#include <boost/random.hpp>
+#include <boost/timer/timer.hpp>
+//[phase_chain_openmp_header
+#include <omp.h>
+#include <boost/numeric/odeint.hpp>
+#include <boost/numeric/odeint/external/openmp/openmp.hpp>
+//]
+
+using namespace std;
+using namespace boost::numeric::odeint;
+using boost::timer::cpu_timer;
+using boost::math::double_constants::pi;
+
+//[phase_chain_vector_state
+typedef std::vector< double > state_type;
+//]
+
+//[phase_chain_rhs
+struct phase_chain
+{
+ phase_chain( double gamma = 0.5 )
+ : m_gamma( gamma ) { }
+
+ void operator()( const state_type &x , state_type &dxdt , double /* t */ ) const
+ {
+ const size_t N = x.size();
+ #pragma omp parallel for schedule(runtime)
+ for(size_t i = 1 ; i < N - 1 ; ++i)
+ {
+ dxdt[i] = coupling_func( x[i+1] - x[i] ) +
+ coupling_func( x[i-1] - x[i] );
+ }
+ dxdt[0 ] = coupling_func( x[1 ] - x[0 ] );
+ dxdt[N-1] = coupling_func( x[N-2] - x[N-1] );
+ }
+
+ double coupling_func( double x ) const
+ {
+ return sin( x ) - m_gamma * ( 1.0 - cos( x ) );
+ }
+
+ double m_gamma;
+};
+//]
+
+
+int main( int argc , char **argv )
+{
+ //[phase_chain_init
+ size_t N = 131101;
+ state_type x( N );
+ boost::random::uniform_real_distribution<double> distribution( 0.0 , 2.0*pi );
+ boost::random::mt19937 engine( 0 );
+ generate( x.begin() , x.end() , boost::bind( distribution , engine ) );
+ //]
+
+ //[phase_chain_stepper
+ typedef runge_kutta4<
+ state_type , double ,
+ state_type , double ,
+ openmp_range_algebra
+ > stepper_type;
+ //]
+
+ //[phase_chain_scheduling
+ int chunk_size = N/omp_get_max_threads();
+ omp_set_schedule( omp_sched_static , chunk_size );
+ //]
+
+ cpu_timer timer;
+ //[phase_chain_integrate
+ integrate_n_steps( stepper_type() , phase_chain( 1.2 ) ,
+ x , 0.0 , 0.01 , 100 );
+ //]
+ double run_time = static_cast<double>(timer.elapsed().wall) * 1.0e-9;
+ std::cerr << run_time << "s" << std::endl;
+ // copy(x.begin(), x.end(), ostream_iterator<double>(cout, "\n"));
+
+ return 0;
+}
diff --git a/examples/openmp/phase_chain_omp_state.cpp b/examples/openmp/phase_chain_omp_state.cpp
new file mode 100644
index 0000000..8627f58
--- /dev/null
+++ b/examples/openmp/phase_chain_omp_state.cpp
@@ -0,0 +1,98 @@
+/*
+ * phase_chain_omp_state.cpp
+ *
+ * Example of OMP parallelization with odeint
+ *
+ * Copyright 2013 Karsten Ahnert
+ * Copyright 2013 Mario Mulansky
+ * Copyright 2013 Pascal Germroth
+ * Distributed under the Boost Software License, Version 1.0. (See
+ * accompanying file LICENSE_1_0.txt or copy at
+ * http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <iostream>
+#include <vector>
+#include <boost/random.hpp>
+#include <boost/timer/timer.hpp>
+#include <omp.h>
+#include <boost/numeric/odeint.hpp>
+#include <boost/numeric/odeint/external/openmp/openmp.hpp>
+
+#include <boost/numeric/odeint.hpp>
+
+using namespace std;
+using namespace boost::numeric::odeint;
+using boost::timer::cpu_timer;
+using boost::math::double_constants::pi;
+
+typedef openmp_state<double> state_type;
+
+//[phase_chain_state_rhs
+struct phase_chain_omp_state
+{
+ phase_chain_omp_state( double gamma = 0.5 )
+ : m_gamma( gamma ) { }
+
+ void operator()( const state_type &x , state_type &dxdt , double /* t */ ) const
+ {
+ const size_t N = x.size();
+ #pragma omp parallel for schedule(runtime)
+ for(size_t n = 0 ; n < N ; ++n)
+ {
+ const size_t M = x[n].size();
+ for(size_t m = 1 ; m < M-1 ; ++m)
+ {
+ dxdt[n][m] = coupling_func( x[n][m+1] - x[n][m] ) +
+ coupling_func( x[n][m-1] - x[n][m] );
+ }
+ dxdt[n][0] = coupling_func( x[n][1] - x[n][0] );
+ if( n > 0 )
+ {
+ dxdt[n][0] += coupling_func( x[n-1].back() - x[n].front() );
+ }
+ dxdt[n][M-1] = coupling_func( x[n][M-2] - x[n][M-1] );
+ if( n < N-1 )
+ {
+ dxdt[n][M-1] += coupling_func( x[n+1].front() - x[n].back() );
+ }
+ }
+ }
+
+ double coupling_func( double x ) const
+ {
+ return sin( x ) - m_gamma * ( 1.0 - cos( x ) );
+ }
+
+ double m_gamma;
+};
+//]
+
+
+int main( int argc , char **argv )
+{
+ //[phase_chain_state_init
+ const size_t N = 131101;
+ vector<double> x( N );
+ boost::random::uniform_real_distribution<double> distribution( 0.0 , 2.0*pi );
+ boost::random::mt19937 engine( 0 );
+ generate( x.begin() , x.end() , boost::bind( distribution , engine ) );
+ const size_t blocks = omp_get_max_threads();
+ state_type x_split( blocks );
+ split( x , x_split );
+ //]
+
+
+ cpu_timer timer;
+ //[phase_chain_state_integrate
+ integrate_n_steps( runge_kutta4<state_type>() , phase_chain_omp_state( 1.2 ) ,
+ x_split , 0.0 , 0.01 , 100 );
+ unsplit( x_split , x );
+ //]
+
+ double run_time = static_cast<double>(timer.elapsed().wall) * 1.0e-9;
+ std::cerr << run_time << "s" << std::endl;
+ // copy(x.begin(), x.end(), ostream_iterator<double>(cout, "\n"));
+
+ return 0;
+}
diff --git a/examples/phase_oscillator_ensemble.cpp b/examples/phase_oscillator_ensemble.cpp
new file mode 100644
index 0000000..090fd58
--- /dev/null
+++ b/examples/phase_oscillator_ensemble.cpp
@@ -0,0 +1,151 @@
+/*
+ * phase_oscillator_ensemble.cpp
+ *
+ * Demonstrates the phase transition from an unsynchronized to an synchronized state.
+ *
+ * Copyright 2011-2012 Karsten Ahnert
+ * Copyright 2011-2012 Mario Mulansky
+ * Distributed under the Boost Software License, Version 1.0. (See
+ * accompanying file LICENSE_1_0.txt or copy at
+ * http://www.boost.org/LICENSE_1_0.txt)
+ *
+ */
+
+#include <iostream>
+#include <utility>
+
+#include <boost/numeric/odeint.hpp>
+
+#ifndef M_PI //not there on windows
+#define M_PI 3.141592653589793 //...
+#endif
+
+#include <boost/random.hpp>
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+//[ phase_oscillator_ensemble_system_function
+typedef vector< double > container_type;
+
+
+pair< double , double > calc_mean_field( const container_type &x )
+{
+ size_t n = x.size();
+ double cos_sum = 0.0 , sin_sum = 0.0;
+ for( size_t i=0 ; i<n ; ++i )
+ {
+ cos_sum += cos( x[i] );
+ sin_sum += sin( x[i] );
+ }
+ cos_sum /= double( n );
+ sin_sum /= double( n );
+
+ double K = sqrt( cos_sum * cos_sum + sin_sum * sin_sum );
+ double Theta = atan2( sin_sum , cos_sum );
+
+ return make_pair( K , Theta );
+}
+
+
+struct phase_ensemble
+{
+ container_type m_omega;
+ double m_epsilon;
+
+ phase_ensemble( const size_t n , double g = 1.0 , double epsilon = 1.0 )
+ : m_omega( n , 0.0 ) , m_epsilon( epsilon )
+ {
+ create_frequencies( g );
+ }
+
+ void create_frequencies( double g )
+ {
+ boost::mt19937 rng;
+ boost::cauchy_distribution<> cauchy( 0.0 , g );
+ boost::variate_generator< boost::mt19937&, boost::cauchy_distribution<> > gen( rng , cauchy );
+ generate( m_omega.begin() , m_omega.end() , gen );
+ }
+
+ void set_epsilon( double epsilon ) { m_epsilon = epsilon; }
+
+ double get_epsilon( void ) const { return m_epsilon; }
+
+ void operator()( const container_type &x , container_type &dxdt , double /* t */ ) const
+ {
+ pair< double , double > mean = calc_mean_field( x );
+ for( size_t i=0 ; i<x.size() ; ++i )
+ dxdt[i] = m_omega[i] + m_epsilon * mean.first * sin( mean.second - x[i] );
+ }
+};
+//]
+
+
+
+//[ phase_oscillator_ensemble_observer
+struct statistics_observer
+{
+ double m_K_mean;
+ size_t m_count;
+
+ statistics_observer( void )
+ : m_K_mean( 0.0 ) , m_count( 0 ) { }
+
+ template< class State >
+ void operator()( const State &x , double t )
+ {
+ pair< double , double > mean = calc_mean_field( x );
+ m_K_mean += mean.first;
+ ++m_count;
+ }
+
+ double get_K_mean( void ) const { return ( m_count != 0 ) ? m_K_mean / double( m_count ) : 0.0 ; }
+
+ void reset( void ) { m_K_mean = 0.0; m_count = 0; }
+};
+//]
+
+
+
+
+
+
+
+
+int main( int argc , char **argv )
+{
+ //[ phase_oscillator_ensemble_integration
+ const size_t n = 16384;
+ const double dt = 0.1;
+
+ container_type x( n );
+
+ boost::mt19937 rng;
+ boost::uniform_real<> unif( 0.0 , 2.0 * M_PI );
+ boost::variate_generator< boost::mt19937&, boost::uniform_real<> > gen( rng , unif );
+
+ // gamma = 1, the phase transition occurs at epsilon = 2
+ phase_ensemble ensemble( n , 1.0 );
+ statistics_observer obs;
+
+ for( double epsilon = 0.0 ; epsilon < 5.0 ; epsilon += 0.1 )
+ {
+ ensemble.set_epsilon( epsilon );
+ obs.reset();
+
+ // start with random initial conditions
+ generate( x.begin() , x.end() , gen );
+
+ // calculate some transients steps
+ integrate_const( runge_kutta4< container_type >() , boost::ref( ensemble ) , x , 0.0 , 10.0 , dt );
+
+ // integrate and compute the statistics
+ integrate_const( runge_kutta4< container_type >() , boost::ref( ensemble ) , x , 0.0 , 100.0 , dt , boost::ref( obs ) );
+ cout << epsilon << "\t" << obs.get_K_mean() << endl;
+ }
+
+
+ //]
+
+ return 0;
+}
diff --git a/examples/point_type.hpp b/examples/point_type.hpp
new file mode 100644
index 0000000..0887511
--- /dev/null
+++ b/examples/point_type.hpp
@@ -0,0 +1,177 @@
+/* Boost libs/numeric/odeint/examples/point_type.hpp
+
+ Copyright 2010-2012 Karsten Ahnert
+ Copyright 2011 Mario Mulansky
+
+ solar system example for Hamiltonian stepper
+
+ Distributed under the Boost Software License, Version 1.0.
+(See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#ifndef POINT_TYPE_HPP_INCLUDED
+#define POINT_TYPE_HPP_INCLUDED
+
+
+#include <boost/operators.hpp>
+#include <ostream>
+
+
+//[ point_type
+/*the point type */
+template< class T , size_t Dim >
+class point :
+ boost::additive1< point< T , Dim > ,
+ boost::additive2< point< T , Dim > , T ,
+ boost::multiplicative2< point< T , Dim > , T
+ > > >
+ {
+ public:
+
+ const static size_t dim = Dim;
+ typedef T value_type;
+ typedef point< value_type , dim > point_type;
+
+ // ...
+ // constructors
+ //<-
+ point( void )
+ {
+ for( size_t i=0 ; i<dim ; ++i ) m_val[i] = 0.0;
+ }
+
+ point( value_type val )
+ {
+ for( size_t i=0 ; i<dim ; ++i ) m_val[i] = val;
+ }
+
+ point( value_type x , value_type y , value_type z = 0.0 )
+ {
+ if( dim > 0 ) m_val[0] = x;
+ if( dim > 1 ) m_val[1] = y;
+ if( dim > 2 ) m_val[2] = z;
+ }
+ //->
+
+ // ...
+ // operators
+ //<-
+ T operator[]( size_t i ) const { return m_val[i]; }
+ T& operator[]( size_t i ) { return m_val[i]; }
+
+ point_type& operator+=( const point_type& p )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ m_val[i] += p[i];
+ return *this;
+ }
+
+ point_type& operator-=( const point_type& p )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ m_val[i] -= p[i];
+ return *this;
+ }
+
+ point_type& operator+=( const value_type& val )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ m_val[i] += val;
+ return *this;
+ }
+
+ point_type& operator-=( const value_type& val )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ m_val[i] -= val;
+ return *this;
+ }
+
+ point_type& operator*=( const value_type &val )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ m_val[i] *= val;
+ return *this;
+ }
+
+ point_type& operator/=( const value_type &val )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ m_val[i] /= val;
+ return *this;
+ }
+
+ //->
+
+ private:
+
+ T m_val[dim];
+ };
+
+ //...
+ // more operators
+ //]
+
+ //
+ // the - operator
+ //
+ template< class T , size_t Dim >
+ point< T , Dim > operator-( const point< T , Dim > &p )
+ {
+ point< T , Dim > tmp;
+ for( size_t i=0 ; i<Dim ; ++i ) tmp[i] = -p[i];
+ return tmp;
+ }
+
+ //
+ // scalar product
+ //
+ template< class T , size_t Dim >
+ T scalar_prod( const point< T , Dim > &p1 , const point< T , Dim > &p2 )
+ {
+ T tmp = 0.0;
+ for( size_t i=0 ; i<Dim ; ++i ) tmp += p1[i] * p2[i];
+ return tmp;
+ }
+
+
+
+ //
+ // norm
+ //
+ template< class T , size_t Dim >
+ T norm( const point< T , Dim > &p1 )
+ {
+ return scalar_prod( p1 , p1 );
+ }
+
+
+
+
+ //
+ // absolute value
+ //
+ template< class T , size_t Dim >
+ T abs( const point< T , Dim > &p1 )
+ {
+ return sqrt( norm( p1 ) );
+ }
+
+
+
+
+ //
+ // output operator
+ //
+ template< class T , size_t Dim >
+ std::ostream& operator<<( std::ostream &out , const point< T , Dim > &p )
+ {
+ if( Dim > 0 ) out << p[0];
+ for( size_t i=1 ; i<Dim ; ++i ) out << " " << p[i];
+ return out;
+ }
+
+
+
+#endif //POINT_TYPE_HPP_INCLUDED
diff --git a/examples/quadmath/Jamfile.v2 b/examples/quadmath/Jamfile.v2
new file mode 100644
index 0000000..88a0463
--- /dev/null
+++ b/examples/quadmath/Jamfile.v2
@@ -0,0 +1,16 @@
+# Copyright 2011 Mario Mulansky
+# Copyright 2012 Karsten Ahnert
+# Distributed under the Boost Software License, Version 1.0. (See
+# accompanying file LICENSE_1_0.txt or copy at
+# http://www.boost.org/LICENSE_1_0.txt)
+
+
+project
+ : requirements
+ <define>BOOST_ALL_NO_LIB=1
+ :
+ ;
+
+lib quadmath : : <name>quadmath <link>shared ;
+
+exe black_hole : black_hole.cpp quadmath : <cxxflags>-std=c++0x ;
\ No newline at end of file
diff --git a/examples/quadmath/black_hole.cpp b/examples/quadmath/black_hole.cpp
new file mode 100644
index 0000000..5a6802a
--- /dev/null
+++ b/examples/quadmath/black_hole.cpp
@@ -0,0 +1,151 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/examples/black_hole.cpp
+
+ [begin_description]
+ This example shows how the __float128 from gcc libquadmath can be used with odeint.
+ [end_description]
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012 Lee Hodgkinson
+ Copyright 2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <cstdlib>
+#include <cmath>
+#include <iostream>
+#include <iterator>
+#include <utility>
+#include <algorithm>
+#include <cassert>
+#include <vector>
+#include <complex>
+
+extern "C" {
+#include <quadmath.h>
+}
+
+const __float128 zero =strtoflt128 ("0.0", NULL);
+
+namespace std {
+
+ inline __float128 abs( __float128 x )
+ {
+ return fabsq( x );
+ }
+
+ inline __float128 sqrt( __float128 x )
+ {
+ return sqrtq( x );
+ }
+
+ inline __float128 pow( __float128 x , __float128 y )
+ {
+ return powq( x , y );
+ }
+
+ inline __float128 abs( std::complex< __float128 > x )
+ {
+ return sqrtq( x.real() * x.real() + x.imag() * x.imag() );
+ }
+
+ inline std::complex< __float128 > pow( std::complex< __float128> x , __float128 y )
+ {
+ __float128 r = pow( abs(x) , y );
+ __float128 phi = atanq( x.imag() / x.real() );
+ return std::complex< __float128 >( r * cosq( y * phi ) , r * sinq( y * phi ) );
+ }
+}
+
+inline std::ostream& operator<< (std::ostream& os, const __float128& f) {
+
+ char* y = new char[1000];
+ quadmath_snprintf(y, 1000, "%.30Qg", f) ;
+ os.precision(30);
+ os<<y;
+ delete[] y;
+ return os;
+}
+
+
+#include <boost/array.hpp>
+#include <boost/range/algorithm.hpp>
+#include <boost/range/adaptor/filtered.hpp>
+#include <boost/range/numeric.hpp>
+#include <boost/numeric/odeint.hpp>
+
+
+
+using namespace boost::numeric::odeint;
+using namespace std;
+
+typedef __float128 my_float;
+typedef std::vector< std::complex < my_float > > state_type;
+
+struct radMod
+{
+ my_float m_om;
+ my_float m_l;
+
+ radMod( my_float om , my_float l )
+ : m_om( om ) , m_l( l ) { }
+
+ void operator()( const state_type &x , state_type &dxdt , my_float r ) const
+ {
+
+ dxdt[0] = x[1];
+ dxdt[1] = -(2*(r-1)/(r*(r-2)))*x[1]-((m_om*m_om*r*r/((r-2)*(r-2)))-(m_l*(m_l+1)/(r*(r-2))))*x[0];
+ }
+};
+
+
+
+
+
+
+
+int main( int argc , char **argv )
+{
+
+
+ state_type x(2);
+
+ my_float re0 = strtoflt128( "-0.00008944230755601224204687038354994353820468" , NULL );
+ my_float im0 = strtoflt128( "0.00004472229441850588228136889483397204368247" , NULL );
+ my_float re1 = strtoflt128( "-4.464175354293244250869336196695966076150E-6 " , NULL );
+ my_float im1 = strtoflt128( "-8.950483248390306670770345406051469584488E-6" , NULL );
+
+ x[0] = complex< my_float >( re0 ,im0 );
+ x[1] = complex< my_float >( re1 ,im1 );
+
+ const my_float dt =strtoflt128 ("-0.001", NULL);
+ const my_float start =strtoflt128 ("10000.0", NULL);
+ const my_float end =strtoflt128 ("9990.0", NULL);
+ const my_float omega =strtoflt128 ("2.0", NULL);
+ const my_float ell =strtoflt128 ("1.0", NULL);
+
+
+
+ my_float abs_err = strtoflt128( "1.0E-15" , NULL ) , rel_err = strtoflt128( "1.0E-10" , NULL );
+ my_float a_x = strtoflt128( "1.0" , NULL ) , a_dxdt = strtoflt128( "1.0" , NULL );
+
+ typedef runge_kutta_dopri5< state_type, my_float > dopri5_type;
+ typedef controlled_runge_kutta< dopri5_type > controlled_dopri5_type;
+ typedef dense_output_runge_kutta< controlled_dopri5_type > dense_output_dopri5_type;
+
+ dense_output_dopri5_type dopri5( controlled_dopri5_type( default_error_checker< my_float >( abs_err , rel_err , a_x , a_dxdt ) ) );
+
+ std::for_each( make_adaptive_time_iterator_begin(dopri5 , radMod(omega , ell) , x , start , end , dt) ,
+ make_adaptive_time_iterator_end(dopri5 , radMod(omega , ell) , x ) ,
+ []( const std::pair< state_type&, my_float > &x ) {
+ std::cout << x.second << ", " << x.first[0].real() << "\n"; }
+ );
+
+
+
+ return 0;
+}
diff --git a/examples/resizing_lattice.cpp b/examples/resizing_lattice.cpp
new file mode 100644
index 0000000..f77f26e
--- /dev/null
+++ b/examples/resizing_lattice.cpp
@@ -0,0 +1,169 @@
+/*
+ * resizing_lattice.cpp
+ *
+ * Demonstrates the usage of resizing of the state type during integration.
+ * Examplary system is a strongly nonlinear, disordered Hamiltonian lattice
+ * where the spreading of energy is investigated
+ *
+ * Copyright 2011-2012 Mario Mulansky
+ * Copyright 2012-2013 Karsten Ahnert
+ * Distributed under the Boost Software License, Version 1.0. (See
+ * accompanying file LICENSE_1_0.txt or copy at
+ * http://www.boost.org/LICENSE_1_0.txt)
+ *
+ */
+
+#include <iostream>
+#include <utility>
+
+#include <boost/numeric/odeint.hpp>
+
+#include <boost/ref.hpp>
+#include <boost/random.hpp>
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+//[ resizing_lattice_system_class
+typedef vector< double > coord_type;
+typedef pair< coord_type , coord_type > state_type;
+
+struct compacton_lattice
+{
+ const int m_max_N;
+ const double m_beta;
+ int m_pot_start_index;
+ vector< double > m_pot;
+
+ compacton_lattice( int max_N , double beta , int pot_start_index )
+ : m_max_N( max_N ) , m_beta( beta ) , m_pot_start_index( pot_start_index ) , m_pot( max_N )
+ {
+ srand( time( NULL ) );
+ // fill random potential with iid values from [0,1]
+ boost::mt19937 rng;
+ boost::uniform_real<> unif( 0.0 , 1.0 );
+ boost::variate_generator< boost::mt19937&, boost::uniform_real<> > gen( rng , unif );
+ generate( m_pot.begin() , m_pot.end() , gen );
+ }
+
+ void operator()( const coord_type &q , coord_type &dpdt )
+ {
+ // calculate dpdt = -dH/dq of this hamiltonian system
+ // dp_i/dt = - V_i * q_i^3 - beta*(q_i - q_{i-1})^3 + beta*(q_{i+1} - q_i)^3
+ const int N = q.size();
+ double diff = q[0] - q[N-1];
+ for( int i=0 ; i<N ; ++i )
+ {
+ dpdt[i] = - m_pot[m_pot_start_index+i] * q[i]*q[i]*q[i] -
+ m_beta * diff*diff*diff;
+ diff = q[(i+1) % N] - q[i];
+ dpdt[i] += m_beta * diff*diff*diff;
+ }
+ }
+
+ void energy_distribution( const coord_type &q , const coord_type &p , coord_type &energies )
+ {
+ // computes the energy per lattice site normalized by total energy
+ const size_t N = q.size();
+ double en = 0.0;
+ for( size_t i=0 ; i<N ; i++ )
+ {
+ const double diff = q[(i+1) % N] - q[i];
+ energies[i] = p[i]*p[i]/2.0
+ + m_pot[m_pot_start_index+i]*q[i]*q[i]*q[i]*q[i]/4.0
+ + m_beta/4.0 * diff*diff*diff*diff;
+ en += energies[i];
+ }
+ en = 1.0/en;
+ for( size_t i=0 ; i<N ; i++ )
+ {
+ energies[i] *= en;
+ }
+ }
+
+ double energy( const coord_type &q , const coord_type &p )
+ {
+ // calculates the total energy of the excitation
+ const size_t N = q.size();
+ double en = 0.0;
+ for( size_t i=0 ; i<N ; i++ )
+ {
+ const double diff = q[(i+1) % N] - q[i];
+ en += p[i]*p[i]/2.0
+ + m_pot[m_pot_start_index+i]*q[i]*q[i]*q[i]*q[i] / 4.0
+ + m_beta/4.0 * diff*diff*diff*diff;
+ }
+ return en;
+ }
+
+ void change_pot_start( const int delta )
+ {
+ m_pot_start_index += delta;
+ }
+};
+//]
+
+//[ resizing_lattice_resize_function
+void do_resize( coord_type &q , coord_type &p , coord_type &distr , const int N )
+{
+ q.resize( N );
+ p.resize( N );
+ distr.resize( N );
+}
+//]
+
+const int max_N = 1024;
+const double beta = 1.0;
+
+int main()
+{
+ //[ resizing_lattice_initialize
+ //start with 60 sites
+ const int N_start = 60;
+ coord_type q( N_start , 0.0 );
+ q.reserve( max_N );
+ coord_type p( N_start , 0.0 );
+ p.reserve( max_N );
+ // start with uniform momentum distribution over 20 sites
+ fill( p.begin()+20 , p.end()-20 , 1.0/sqrt(20.0) );
+
+ coord_type distr( N_start , 0.0 );
+ distr.reserve( max_N );
+
+ // create the system
+ compacton_lattice lattice( max_N , beta , (max_N-N_start)/2 );
+
+ //create the stepper, note that we use an always_resizer because state size might change during steps
+ typedef symplectic_rkn_sb3a_mclachlan< coord_type , coord_type , double , coord_type , coord_type , double ,
+ range_algebra , default_operations , always_resizer > hamiltonian_stepper;
+ hamiltonian_stepper stepper;
+ hamiltonian_stepper::state_type state = make_pair( q , p );
+ //]
+
+ //[ resizing_lattice_steps_loop
+ double t = 0.0;
+ const double dt = 0.1;
+ const int steps = 10000;
+ for( int step = 0 ; step < steps ; ++step )
+ {
+ stepper.do_step( boost::ref(lattice) , state , t , dt );
+ lattice.energy_distribution( state.first , state.second , distr );
+ if( distr[10] > 1E-150 )
+ {
+ do_resize( state.first , state.second , distr , state.first.size()+20 );
+ rotate( state.first.begin() , state.first.end()-20 , state.first.end() );
+ rotate( state.second.begin() , state.second.end()-20 , state.second.end() );
+ lattice.change_pot_start( -20 );
+ cout << t << ": resized left to " << distr.size() << ", energy = " << lattice.energy( state.first , state.second ) << endl;
+ }
+ if( distr[distr.size()-10] > 1E-150 )
+ {
+ do_resize( state.first , state.second , distr , state.first.size()+20 );
+ cout << t << ": resized right to " << distr.size() << ", energy = " << lattice.energy( state.first , state.second ) << endl;
+ }
+ t += dt;
+ }
+ //]
+
+ cout << "final lattice size: " << distr.size() << ", final energy: " << lattice.energy( state.first , state.second ) << endl;
+}
diff --git a/examples/simple1d.cpp b/examples/simple1d.cpp
new file mode 100644
index 0000000..3a8dfa0
--- /dev/null
+++ b/examples/simple1d.cpp
@@ -0,0 +1,44 @@
+/* Boost libs/numeric/odeint/examples/simple1d.cpp
+
+ Copyright 2012-2013 Mario Mulansky
+ Copyright 2012 Karsten Ahnert
+
+ example for a simple one-dimensional 1st order ODE
+
+ Distributed under the Boost Software License, Version 1.0.
+(See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#include <iostream>
+#include <boost/numeric/odeint.hpp>
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+
+/* we solve the simple ODE x' = 3/(2t^2) + x/(2t)
+ * with initial condition x(1) = 0.
+ * Analytic solution is x(t) = sqrt(t) - 1/t
+ */
+
+void rhs( const double x , double &dxdt , const double t )
+{
+ dxdt = 3.0/(2.0*t*t) + x/(2.0*t);
+}
+
+void write_cout( const double &x , const double t )
+{
+ cout << t << '\t' << x << endl;
+}
+
+// state_type = double
+typedef runge_kutta_dopri5< double > stepper_type;
+
+int main()
+{
+ double x = 0.0; //initial value x(1) = 0
+ // use dopri5 with stepsize control and allowed errors 10^-12, integrate t=1...10
+ integrate_adaptive( make_controlled( 1E-12 , 1E-12 , stepper_type() ) , rhs , x , 1.0 , 10.0 , 0.1 , write_cout );
+}
diff --git a/examples/solar_system.agr b/examples/solar_system.agr
new file mode 100644
index 0000000..87f8c38
--- /dev/null
+++ b/examples/solar_system.agr
@@ -0,0 +1,12672 @@
+# Grace project file
+#
+@version 50122
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diff --git a/examples/solar_system.cpp b/examples/solar_system.cpp
new file mode 100644
index 0000000..3586d5b
--- /dev/null
+++ b/examples/solar_system.cpp
@@ -0,0 +1,201 @@
+/* Boost libs/numeric/odeint/examples/solar_system.cpp
+
+ Copyright 2010-2012 Karsten Ahnert
+ Copyright 2011 Mario Mulansky
+
+ Solar system example for Hamiltonian stepper
+
+ Distributed under the Boost Software License, Version 1.0.
+(See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#include <iostream>
+#include <boost/array.hpp>
+
+#include <boost/numeric/odeint.hpp>
+
+#include "point_type.hpp"
+
+//[ container_type_definition
+// we simulate 5 planets and the sun
+const size_t n = 6;
+
+typedef point< double , 3 > point_type;
+typedef boost::array< point_type , n > container_type;
+typedef boost::array< double , n > mass_type;
+//]
+
+
+
+
+
+
+
+//[ coordinate_function
+const double gravitational_constant = 2.95912208286e-4;
+
+struct solar_system_coor
+{
+ const mass_type &m_masses;
+
+ solar_system_coor( const mass_type &masses ) : m_masses( masses ) { }
+
+ void operator()( const container_type &p , container_type &dqdt ) const
+ {
+ for( size_t i=0 ; i<n ; ++i )
+ dqdt[i] = p[i] / m_masses[i];
+ }
+};
+//]
+
+
+//[ momentum_function
+struct solar_system_momentum
+{
+ const mass_type &m_masses;
+
+ solar_system_momentum( const mass_type &masses ) : m_masses( masses ) { }
+
+ void operator()( const container_type &q , container_type &dpdt ) const
+ {
+ const size_t n = q.size();
+ for( size_t i=0 ; i<n ; ++i )
+ {
+ dpdt[i] = 0.0;
+ for( size_t j=0 ; j<i ; ++j )
+ {
+ point_type diff = q[j] - q[i];
+ double d = abs( diff );
+ diff *= ( gravitational_constant * m_masses[i] * m_masses[j] / d / d / d );
+ dpdt[i] += diff;
+ dpdt[j] -= diff;
+
+ }
+ }
+ }
+};
+//]
+
+
+
+
+
+
+
+//[ some_helpers
+point_type center_of_mass( const container_type &x , const mass_type &m )
+{
+ double overall_mass = 0.0;
+ point_type mean( 0.0 );
+ for( size_t i=0 ; i<x.size() ; ++i )
+ {
+ overall_mass += m[i];
+ mean += m[i] * x[i];
+ }
+ if( !x.empty() ) mean /= overall_mass;
+ return mean;
+}
+
+
+double energy( const container_type &q , const container_type &p , const mass_type &masses )
+{
+ const size_t n = q.size();
+ double en = 0.0;
+ for( size_t i=0 ; i<n ; ++i )
+ {
+ en += 0.5 * norm( p[i] ) / masses[i];
+ for( size_t j=0 ; j<i ; ++j )
+ {
+ double diff = abs( q[i] - q[j] );
+ en -= gravitational_constant * masses[j] * masses[i] / diff;
+ }
+ }
+ return en;
+}
+//]
+
+
+//[ streaming_observer
+struct streaming_observer
+{
+ std::ostream& m_out;
+
+ streaming_observer( std::ostream &out ) : m_out( out ) { }
+
+ template< class State >
+ void operator()( const State &x , double t ) const
+ {
+ container_type &q = x.first;
+ m_out << t;
+ for( size_t i=0 ; i<q.size() ; ++i ) m_out << "\t" << q[i];
+ m_out << "\n";
+ }
+};
+//]
+
+
+int main( int argc , char **argv )
+{
+
+ using namespace std;
+ using namespace boost::numeric::odeint;
+
+ mass_type masses = {{
+ 1.00000597682 , // sun
+ 0.000954786104043 , // jupiter
+ 0.000285583733151 , // saturn
+ 0.0000437273164546 , // uranus
+ 0.0000517759138449 , // neptune
+ 1.0 / ( 1.3e8 ) // pluto
+ }};
+
+ container_type q = {{
+ point_type( 0.0 , 0.0 , 0.0 ) , // sun
+ point_type( -3.5023653 , -3.8169847 , -1.5507963 ) , // jupiter
+ point_type( 9.0755314 , -3.0458353 , -1.6483708 ) , // saturn
+ point_type( 8.3101420 , -16.2901086 , -7.2521278 ) , // uranus
+ point_type( 11.4707666 , -25.7294829 , -10.8169456 ) , // neptune
+ point_type( -15.5387357 , -25.2225594 , -3.1902382 ) // pluto
+ }};
+
+ container_type p = {{
+ point_type( 0.0 , 0.0 , 0.0 ) , // sun
+ point_type( 0.00565429 , -0.00412490 , -0.00190589 ) , // jupiter
+ point_type( 0.00168318 , 0.00483525 , 0.00192462 ) , // saturn
+ point_type( 0.00354178 , 0.00137102 , 0.00055029 ) , // uranus
+ point_type( 0.00288930 , 0.00114527 , 0.00039677 ) , // neptune
+ point_type( 0.00276725 , -0.00170702 , -0.00136504 ) // pluto
+ }};
+
+ point_type qmean = center_of_mass( q , masses );
+ point_type pmean = center_of_mass( p , masses );
+ for( size_t i=0 ; i<n ; ++i )
+ {
+ q[i] -= qmean ;
+ p[i] -= pmean;
+ }
+
+ for( size_t i=0 ; i<n ; ++i ) p[i] *= masses[i];
+
+ //[ integration_solar_system
+ typedef symplectic_rkn_sb3a_mclachlan< container_type > stepper_type;
+ const double dt = 100.0;
+
+ integrate_const(
+ stepper_type() ,
+ make_pair( solar_system_coor( masses ) , solar_system_momentum( masses ) ) ,
+ make_pair( boost::ref( q ) , boost::ref( p ) ) ,
+ 0.0 , 200000.0 , dt , streaming_observer( cout ) );
+ //]
+
+
+ return 0;
+}
+
+
+/*
+Plot with gnuplot:
+p "solar_system.dat" u 2:4 w l,"solar_system.dat" u 5:7 w l,"solar_system.dat" u 8:10 w l,"solar_system.dat" u 11:13 w l,"solar_system.dat" u 14:16 w l,"solar_system.dat" u 17:19 w l
+ */
diff --git a/examples/stepper_details.cpp b/examples/stepper_details.cpp
new file mode 100644
index 0000000..d4ae8bd
--- /dev/null
+++ b/examples/stepper_details.cpp
@@ -0,0 +1,200 @@
+/*
+ * stepper_details.cpp
+ *
+ * This example demonstrates some details about the steppers in odeint.
+ *
+ *
+ * Copyright 2011-2012 Karsten Ahnert
+ * Copyright 2012 Mario Mulansky
+ * Copyright 2013 Pascal Germroth
+ *
+ * Distributed under the Boost Software License, Version 1.0.
+ * (See accompanying file LICENSE_1_0.txt or
+ * copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <iostream>
+#include <boost/array.hpp>
+#include <boost/bind.hpp>
+#include <boost/numeric/odeint.hpp>
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+const size_t N = 3;
+
+typedef boost::array< double , N > state_type;
+
+//[ system_function_structure
+void sys( const state_type & /*x*/ , state_type & /*dxdt*/ , const double /*t*/ )
+{
+ // ...
+}
+//]
+
+void sys1( const state_type &/*x*/ , state_type &/*dxdt*/ , const double /*t*/ )
+{
+}
+
+void sys2( const state_type &/*x*/ , state_type &/*dxdt*/ , const double /*t*/ )
+{
+}
+
+
+//[ symplectic_stepper_detail_system_function
+typedef boost::array< double , 1 > vector_type;
+
+
+struct harm_osc_f1
+{
+ void operator()( const vector_type &p , vector_type &dqdt )
+ {
+ dqdt[0] = p[0];
+ }
+};
+
+struct harm_osc_f2
+{
+ void operator()( const vector_type &q , vector_type &dpdt )
+ {
+ dpdt[0] = -q[0];
+ }
+};
+//]
+
+//[ symplectic_stepper_detail_system_class
+struct harm_osc
+{
+ void f1( const vector_type &p , vector_type &dqdt ) const
+ {
+ dqdt[0] = p[0];
+ }
+
+ void f2( const vector_type &q , vector_type &dpdt ) const
+ {
+ dpdt[0] = -q[0];
+ }
+};
+//]
+
+int main( int argc , char **argv )
+{
+ using namespace std;
+
+ // Explicit stepper example
+ {
+ double t( 0.0 ) , dt( 0.1 );
+ state_type in , out , dxdtin , inout;
+ //[ explicit_stepper_detail_example
+ runge_kutta4< state_type > rk;
+ rk.do_step( sys1 , inout , t , dt ); // In-place transformation of inout
+ rk.do_step( sys2 , inout , t , dt ); // call with different system: Ok
+ rk.do_step( sys1 , in , t , out , dt ); // Out-of-place transformation
+ rk.do_step( sys1 , inout , dxdtin , t , dt ); // In-place tranformation of inout
+ rk.do_step( sys1 , in , dxdtin , t , out , dt ); // Out-of-place transformation
+ //]
+ }
+
+
+
+ // FSAL stepper example
+ {
+ double t( 0.0 ) , dt( 0.1 );
+ state_type in , in2 , in3 , out , dxdtin , dxdtout , inout , dxdtinout;
+ //[ fsal_stepper_detail_example
+ runge_kutta_dopri5< state_type > rk;
+ rk.do_step( sys1 , in , t , out , dt );
+ rk.do_step( sys2 , in , t , out , dt ); // DONT do this, sys1 is assumed
+
+ rk.do_step( sys2 , in2 , t , out , dt );
+ rk.do_step( sys2 , in3 , t , out , dt ); // DONT do this, in2 is assumed
+
+ rk.do_step( sys1 , inout , dxdtinout , t , dt );
+ rk.do_step( sys2 , inout , dxdtinout , t , dt ); // Ok, internal derivative is not used, dxdtinout is updated
+
+ rk.do_step( sys1 , in , dxdtin , t , out , dxdtout , dt );
+ rk.do_step( sys2 , in , dxdtin , t , out , dxdtout , dt ); // Ok, internal derivative is not used
+ //]
+ }
+
+
+ // Symplectic harmonic oscillator example
+ {
+ double t( 0.0 ) , dt( 0.1 );
+ //[ symplectic_stepper_detail_example
+ pair< vector_type , vector_type > x;
+ x.first[0] = 1.0; x.second[0] = 0.0;
+ symplectic_rkn_sb3a_mclachlan< vector_type > rkn;
+ rkn.do_step( make_pair( harm_osc_f1() , harm_osc_f2() ) , x , t , dt );
+ //]
+
+ //[ symplectic_stepper_detail_system_class_example
+ harm_osc h;
+ rkn.do_step( make_pair( boost::bind( &harm_osc::f1 , h , _1 , _2 ) , boost::bind( &harm_osc::f2 , h , _1 , _2 ) ) ,
+ x , t , dt );
+ //]
+ }
+
+ // Simplified harmonic oscillator example
+ {
+ double t = 0.0, dt = 0.1;
+ //[ simplified_symplectic_stepper_example
+ pair< vector_type , vector_type > x;
+ x.first[0] = 1.0; x.second[0] = 0.0;
+ symplectic_rkn_sb3a_mclachlan< vector_type > rkn;
+ rkn.do_step( harm_osc_f1() , x , t , dt );
+ //]
+
+ vector_type q = {{ 1.0 }} , p = {{ 0.0 }};
+ //[ symplectic_stepper_detail_ref_usage
+ rkn.do_step( harm_osc_f1() , make_pair( boost::ref( q ) , boost::ref( p ) ) , t , dt );
+ rkn.do_step( harm_osc_f1() , q , p , t , dt );
+ rkn.do_step( make_pair( harm_osc_f1() , harm_osc_f2() ) , q , p , t , dt );
+ //]
+ }
+
+ // adams_bashforth_moulton stepper example
+ {
+ double t = 0.0 , dt = 0.1;
+ state_type inout;
+ //[ multistep_detail_example
+ adams_bashforth_moulton< 5 , state_type > abm;
+ abm.initialize( sys , inout , t , dt );
+ abm.do_step( sys , inout , t , dt );
+ //]
+
+ //[ multistep_detail_own_stepper_initialization
+ abm.initialize( runge_kutta_fehlberg78< state_type >() , sys , inout , t , dt );
+ //]
+ }
+
+
+
+ // dense output stepper examples
+ {
+ double t = 0.0 , dt = 0.1;
+ state_type in;
+ //[ dense_output_detail_example
+ dense_output_runge_kutta< controlled_runge_kutta< runge_kutta_dopri5< state_type > > > dense;
+ dense.initialize( in , t , dt );
+ pair< double , double > times = dense.do_step( sys );
+ (void)times;
+ //]
+
+ state_type inout;
+ double t_start = 0.0 , t_end = 1.0;
+ //[ dense_output_detail_generation1
+ typedef boost::numeric::odeint::result_of::make_dense_output<
+ runge_kutta_dopri5< state_type > >::type dense_stepper_type;
+ dense_stepper_type dense2 = make_dense_output( 1.0e-6 , 1.0e-6 , runge_kutta_dopri5< state_type >() );
+ (void)dense2;
+ //]
+
+ //[ dense_output_detail_generation2
+ integrate_const( make_dense_output( 1.0e-6 , 1.0e-6 , runge_kutta_dopri5< state_type >() ) , sys , inout , t_start , t_end , dt );
+ //]
+ }
+
+
+ return 0;
+}
diff --git a/examples/stiff_system.cpp b/examples/stiff_system.cpp
new file mode 100644
index 0000000..ca71f66
--- /dev/null
+++ b/examples/stiff_system.cpp
@@ -0,0 +1,118 @@
+/*
+ * rosenbrock4.cpp
+ *
+ * Copyright 2010-2012 Mario Mulansky
+ * Copyright 2011-2012 Karsten Ahnert
+ * Copyright 2012 Andreas Angelopoulos
+ *
+ * Distributed under the Boost Software License, Version 1.0.
+ * (See accompanying file LICENSE_1_0.txt or
+ * copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <iostream>
+#include <fstream>
+#include <utility>
+
+#include <boost/numeric/odeint.hpp>
+
+#include <boost/phoenix/core.hpp>
+
+#include <boost/phoenix/core.hpp>
+#include <boost/phoenix/operator.hpp>
+
+using namespace std;
+using namespace boost::numeric::odeint;
+namespace phoenix = boost::phoenix;
+
+
+
+//[ stiff_system_definition
+typedef boost::numeric::ublas::vector< double > vector_type;
+typedef boost::numeric::ublas::matrix< double > matrix_type;
+
+struct stiff_system
+{
+ void operator()( const vector_type &x , vector_type &dxdt , double /* t */ )
+ {
+ dxdt[ 0 ] = -101.0 * x[ 0 ] - 100.0 * x[ 1 ];
+ dxdt[ 1 ] = x[ 0 ];
+ }
+};
+
+struct stiff_system_jacobi
+{
+ void operator()( const vector_type & /* x */ , matrix_type &J , const double & /* t */ , vector_type &dfdt )
+ {
+ J( 0 , 0 ) = -101.0;
+ J( 0 , 1 ) = -100.0;
+ J( 1 , 0 ) = 1.0;
+ J( 1 , 1 ) = 0.0;
+ dfdt[0] = 0.0;
+ dfdt[1] = 0.0;
+ }
+};
+//]
+
+
+
+/*
+//[ stiff_system_alternative_definition
+typedef boost::numeric::ublas::vector< double > vector_type;
+typedef boost::numeric::ublas::matrix< double > matrix_type;
+
+struct stiff_system
+{
+ template< class State >
+ void operator()( const State &x , State &dxdt , double t )
+ {
+ ...
+ }
+};
+
+struct stiff_system_jacobi
+{
+ template< class State , class Matrix >
+ void operator()( const State &x , Matrix &J , const double &t , State &dfdt )
+ {
+ ...
+ }
+};
+//]
+ */
+
+
+
+int main( int argc , char **argv )
+{
+// typedef rosenbrock4< double > stepper_type;
+// typedef rosenbrock4_controller< stepper_type > controlled_stepper_type;
+// typedef rosenbrock4_dense_output< controlled_stepper_type > dense_output_type;
+ //[ integrate_stiff_system
+ vector_type x( 2 , 1.0 );
+
+ size_t num_of_steps = integrate_const( make_dense_output< rosenbrock4< double > >( 1.0e-6 , 1.0e-6 ) ,
+ make_pair( stiff_system() , stiff_system_jacobi() ) ,
+ x , 0.0 , 50.0 , 0.01 ,
+ cout << phoenix::arg_names::arg2 << " " << phoenix::arg_names::arg1[0] << "\n" );
+ //]
+ clog << num_of_steps << endl;
+
+
+
+// typedef runge_kutta_dopri5< vector_type > dopri5_type;
+// typedef controlled_runge_kutta< dopri5_type > controlled_dopri5_type;
+// typedef dense_output_runge_kutta< controlled_dopri5_type > dense_output_dopri5_type;
+ //[ integrate_stiff_system_alternative
+
+ vector_type x2( 2 , 1.0 );
+
+ size_t num_of_steps2 = integrate_const( make_dense_output< runge_kutta_dopri5< vector_type > >( 1.0e-6 , 1.0e-6 ) ,
+ stiff_system() , x2 , 0.0 , 50.0 , 0.01 ,
+ cout << phoenix::arg_names::arg2 << " " << phoenix::arg_names::arg1[0] << "\n" );
+ //]
+ clog << num_of_steps2 << endl;
+
+
+ return 0;
+}
diff --git a/examples/stochastic_euler.cpp b/examples/stochastic_euler.cpp
new file mode 100644
index 0000000..c98d27b
--- /dev/null
+++ b/examples/stochastic_euler.cpp
@@ -0,0 +1,147 @@
+/*
+ libs/numeric/odeint/examples/stochastic_euler.hpp
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+
+ Stochastic euler stepper example and Ornstein-Uhlenbeck process
+
+ Distributed under the Boost Software License, Version 1.0.
+(See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#include <vector>
+#include <iostream>
+#include <boost/random.hpp>
+#include <boost/array.hpp>
+
+#include <boost/numeric/odeint.hpp>
+
+
+/*
+//[ stochastic_euler_class_definition
+template< size_t N > class stochastic_euler
+{
+public:
+
+ typedef boost::array< double , N > state_type;
+ typedef boost::array< double , N > deriv_type;
+ typedef double value_type;
+ typedef double time_type;
+ typedef unsigned short order_type;
+ typedef boost::numeric::odeint::stepper_tag stepper_category;
+
+ static order_type order( void ) { return 1; }
+
+ // ...
+};
+//]
+*/
+
+
+/*
+//[ stochastic_euler_do_step
+template< size_t N > class stochastic_euler
+{
+public:
+
+ // ...
+
+ template< class System >
+ void do_step( System system , state_type &x , time_type t , time_type dt ) const
+ {
+ deriv_type det , stoch ;
+ system.first( x , det );
+ system.second( x , stoch );
+ for( size_t i=0 ; i<x.size() ; ++i )
+ x[i] += dt * det[i] + sqrt( dt ) * stoch[i];
+ }
+};
+//]
+*/
+
+
+
+
+//[ stochastic_euler_class
+template< size_t N >
+class stochastic_euler
+{
+public:
+
+ typedef boost::array< double , N > state_type;
+ typedef boost::array< double , N > deriv_type;
+ typedef double value_type;
+ typedef double time_type;
+ typedef unsigned short order_type;
+
+ typedef boost::numeric::odeint::stepper_tag stepper_category;
+
+ static order_type order( void ) { return 1; }
+
+ template< class System >
+ void do_step( System system , state_type &x , time_type t , time_type dt ) const
+ {
+ deriv_type det , stoch ;
+ system.first( x , det );
+ system.second( x , stoch );
+ for( size_t i=0 ; i<x.size() ; ++i )
+ x[i] += dt * det[i] + sqrt( dt ) * stoch[i];
+ }
+};
+//]
+
+
+
+//[ stochastic_euler_ornstein_uhlenbeck_def
+const static size_t N = 1;
+typedef boost::array< double , N > state_type;
+
+struct ornstein_det
+{
+ void operator()( const state_type &x , state_type &dxdt ) const
+ {
+ dxdt[0] = -x[0];
+ }
+};
+
+struct ornstein_stoch
+{
+ boost::mt19937 &m_rng;
+ boost::normal_distribution<> m_dist;
+
+ ornstein_stoch( boost::mt19937 &rng , double sigma ) : m_rng( rng ) , m_dist( 0.0 , sigma ) { }
+
+ void operator()( const state_type &x , state_type &dxdt )
+ {
+ dxdt[0] = m_dist( m_rng );
+ }
+};
+//]
+
+struct streaming_observer
+{
+ template< class State >
+ void operator()( const State &x , double t ) const
+ {
+ std::cout << t << "\t" << x[0] << "\n";
+ }
+};
+
+
+int main( int argc , char **argv )
+{
+ using namespace std;
+ using namespace boost::numeric::odeint;
+
+ //[ ornstein_uhlenbeck_main
+ boost::mt19937 rng;
+ double dt = 0.1;
+ state_type x = {{ 1.0 }};
+ integrate_const( stochastic_euler< N >() , make_pair( ornstein_det() , ornstein_stoch( rng , 1.0 ) ),
+ x , 0.0 , 10.0 , dt , streaming_observer() );
+ //]
+ return 0;
+}
diff --git a/examples/stuart_landau.cpp b/examples/stuart_landau.cpp
new file mode 100644
index 0000000..84f9b04
--- /dev/null
+++ b/examples/stuart_landau.cpp
@@ -0,0 +1,87 @@
+/*
+ * stuart_landau.cpp
+ *
+ * This example demonstrates how one can use odeint can be used with state types consisting of complex variables.
+ *
+ * Copyright 2011-2012 Karsten Ahnert
+ * Copyright 2011-2013 Mario Mulansky
+ * Distributed under the Boost Software License, Version 1.0. (See
+ * accompanying file LICENSE_1_0.txt or copy at
+ * http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <iostream>
+#include <complex>
+#include <boost/array.hpp>
+
+#include <boost/numeric/odeint.hpp>
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+//[ stuart_landau_system_function
+typedef complex< double > state_type;
+
+struct stuart_landau
+{
+ double m_eta;
+ double m_alpha;
+
+ stuart_landau( double eta = 1.0 , double alpha = 1.0 )
+ : m_eta( eta ) , m_alpha( alpha ) { }
+
+ void operator()( const state_type &x , state_type &dxdt , double t ) const
+ {
+ const complex< double > I( 0.0 , 1.0 );
+ dxdt = ( 1.0 + m_eta * I ) * x - ( 1.0 + m_alpha * I ) * norm( x ) * x;
+ }
+};
+//]
+
+
+/*
+//[ stuart_landau_system_function_alternative
+double eta = 1.0;
+double alpha = 1.0;
+
+void stuart_landau( const state_type &x , state_type &dxdt , double t )
+{
+ const complex< double > I( 0.0 , 1.0 );
+ dxdt = ( 1.0 + m_eta * I ) * x - ( 1.0 + m_alpha * I ) * norm( x ) * x;
+}
+//]
+*/
+
+
+struct streaming_observer
+{
+ std::ostream& m_out;
+
+ streaming_observer( std::ostream &out ) : m_out( out ) { }
+
+ template< class State >
+ void operator()( const State &x , double t ) const
+ {
+ m_out << t;
+ m_out << "\t" << x.real() << "\t" << x.imag() ;
+ m_out << "\n";
+ }
+};
+
+
+
+
+int main( int argc , char **argv )
+{
+ //[ stuart_landau_integration
+ state_type x = complex< double >( 1.0 , 0.0 );
+
+ const double dt = 0.1;
+
+ typedef runge_kutta4< state_type > stepper_type;
+
+ integrate_const( stepper_type() , stuart_landau( 2.0 , 1.0 ) , x , 0.0 , 10.0 , dt , streaming_observer( cout ) );
+ //]
+
+ return 0;
+}
diff --git a/examples/thrust/Makefile b/examples/thrust/Makefile
new file mode 100644
index 0000000..5a33bdb
--- /dev/null
+++ b/examples/thrust/Makefile
@@ -0,0 +1,34 @@
+# Copyright 2011-2014 Mario Mulansky
+# Copyright 2011-2012 Karsten Ahnert
+#
+# Distributed under the Boost Software License, Version 1.0.
+# (See accompanying file LICENSE_1_0.txt or
+# copy at http://www.boost.org/LICENSE_1_0.txt)
+
+# make sure BOOST_ROOT is pointing to your boost directory
+# otherwise, set it here:
+# BOOST_ROOT = /path/to/boost
+
+# path to the cuda installation
+CUDA_ROOT = /usr/local/cuda
+# target architecture
+ARCH = sm_13
+
+NVCC = $(CUDA_ROOT)/bin/nvcc
+
+INCLUDES += -I../../include/ -I$(BOOST_ROOT)
+
+NVCCFLAGS = -O3 $(INCLUDES) -arch $(ARCH)
+
+%.o : %.cu
+ $(NVCC) $(NVCCFLAGS) -c $< -o $@
+
+% : %.o
+ $(NVCC) $(NVCCFLAGS) -o $@ $<
+
+
+all : phase_oscillator_chain phase_oscillator_ensemble lorenz_parameters relaxation
+
+
+clean :
+ -rm *~ *.o phase_oscillator_chain phase_oscillator_ensemble lorenz_parameters relaxation
diff --git a/examples/thrust/lorenz_parameters.cu b/examples/thrust/lorenz_parameters.cu
new file mode 100644
index 0000000..b332375
--- /dev/null
+++ b/examples/thrust/lorenz_parameters.cu
@@ -0,0 +1,296 @@
+/*
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <iostream>
+#include <cmath>
+#include <utility>
+
+
+#include <thrust/device_vector.h>
+#include <thrust/reduce.h>
+#include <thrust/functional.h>
+
+#include <boost/numeric/odeint.hpp>
+
+#include <boost/numeric/odeint/external/thrust/thrust.hpp>
+
+#include <boost/random/mersenne_twister.hpp>
+#include <boost/random/uniform_real.hpp>
+#include <boost/random/variate_generator.hpp>
+
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+//change this to float if your device does not support double computation
+typedef double value_type;
+
+//change this to host_vector< ... > of you want to run on CPU
+typedef thrust::device_vector< value_type > state_type;
+typedef thrust::device_vector< size_t > index_vector_type;
+// typedef thrust::host_vector< value_type > state_type;
+// typedef thrust::host_vector< size_t > index_vector_type;
+
+
+const value_type sigma = 10.0;
+const value_type b = 8.0 / 3.0;
+
+
+//[ thrust_lorenz_parameters_define_simple_system
+struct lorenz_system
+{
+ struct lorenz_functor
+ {
+ template< class T >
+ __host__ __device__
+ void operator()( T t ) const
+ {
+ // unpack the parameter we want to vary and the Lorenz variables
+ value_type R = thrust::get< 3 >( t );
+ value_type x = thrust::get< 0 >( t );
+ value_type y = thrust::get< 1 >( t );
+ value_type z = thrust::get< 2 >( t );
+ thrust::get< 4 >( t ) = sigma * ( y - x );
+ thrust::get< 5 >( t ) = R * x - y - x * z;
+ thrust::get< 6 >( t ) = -b * z + x * y ;
+
+ }
+ };
+
+ lorenz_system( size_t N , const state_type &beta )
+ : m_N( N ) , m_beta( beta ) { }
+
+ template< class State , class Deriv >
+ void operator()( const State &x , Deriv &dxdt , value_type t ) const
+ {
+ thrust::for_each(
+ thrust::make_zip_iterator( thrust::make_tuple(
+ boost::begin( x ) ,
+ boost::begin( x ) + m_N ,
+ boost::begin( x ) + 2 * m_N ,
+ m_beta.begin() ,
+ boost::begin( dxdt ) ,
+ boost::begin( dxdt ) + m_N ,
+ boost::begin( dxdt ) + 2 * m_N ) ) ,
+ thrust::make_zip_iterator( thrust::make_tuple(
+ boost::begin( x ) + m_N ,
+ boost::begin( x ) + 2 * m_N ,
+ boost::begin( x ) + 3 * m_N ,
+ m_beta.begin() ,
+ boost::begin( dxdt ) + m_N ,
+ boost::begin( dxdt ) + 2 * m_N ,
+ boost::begin( dxdt ) + 3 * m_N ) ) ,
+ lorenz_functor() );
+ }
+ size_t m_N;
+ const state_type &m_beta;
+};
+//]
+
+struct lorenz_perturbation_system
+{
+ struct lorenz_perturbation_functor
+ {
+ template< class T >
+ __host__ __device__
+ void operator()( T t ) const
+ {
+ value_type R = thrust::get< 1 >( t );
+ value_type x = thrust::get< 0 >( thrust::get< 0 >( t ) );
+ value_type y = thrust::get< 1 >( thrust::get< 0 >( t ) );
+ value_type z = thrust::get< 2 >( thrust::get< 0 >( t ) );
+ value_type dx = thrust::get< 3 >( thrust::get< 0 >( t ) );
+ value_type dy = thrust::get< 4 >( thrust::get< 0 >( t ) );
+ value_type dz = thrust::get< 5 >( thrust::get< 0 >( t ) );
+ thrust::get< 0 >( thrust::get< 2 >( t ) ) = sigma * ( y - x );
+ thrust::get< 1 >( thrust::get< 2 >( t ) ) = R * x - y - x * z;
+ thrust::get< 2 >( thrust::get< 2 >( t ) ) = -b * z + x * y ;
+ thrust::get< 3 >( thrust::get< 2 >( t ) ) = sigma * ( dy - dx );
+ thrust::get< 4 >( thrust::get< 2 >( t ) ) = ( R - z ) * dx - dy - x * dz;
+ thrust::get< 5 >( thrust::get< 2 >( t ) ) = y * dx + x * dy - b * dz;
+ }
+ };
+
+ lorenz_perturbation_system( size_t N , const state_type &beta )
+ : m_N( N ) , m_beta( beta ) { }
+
+ template< class State , class Deriv >
+ void operator()( const State &x , Deriv &dxdt , value_type t ) const
+ {
+ thrust::for_each(
+ thrust::make_zip_iterator( thrust::make_tuple(
+ thrust::make_zip_iterator( thrust::make_tuple(
+ boost::begin( x ) ,
+ boost::begin( x ) + m_N ,
+ boost::begin( x ) + 2 * m_N ,
+ boost::begin( x ) + 3 * m_N ,
+ boost::begin( x ) + 4 * m_N ,
+ boost::begin( x ) + 5 * m_N ) ) ,
+ m_beta.begin() ,
+ thrust::make_zip_iterator( thrust::make_tuple(
+ boost::begin( dxdt ) ,
+ boost::begin( dxdt ) + m_N ,
+ boost::begin( dxdt ) + 2 * m_N ,
+ boost::begin( dxdt ) + 3 * m_N ,
+ boost::begin( dxdt ) + 4 * m_N ,
+ boost::begin( dxdt ) + 5 * m_N ) )
+ ) ) ,
+ thrust::make_zip_iterator( thrust::make_tuple(
+ thrust::make_zip_iterator( thrust::make_tuple(
+ boost::begin( x ) + m_N ,
+ boost::begin( x ) + 2 * m_N ,
+ boost::begin( x ) + 3 * m_N ,
+ boost::begin( x ) + 4 * m_N ,
+ boost::begin( x ) + 5 * m_N ,
+ boost::begin( x ) + 6 * m_N ) ) ,
+ m_beta.begin() ,
+ thrust::make_zip_iterator( thrust::make_tuple(
+ boost::begin( dxdt ) + m_N ,
+ boost::begin( dxdt ) + 2 * m_N ,
+ boost::begin( dxdt ) + 3 * m_N ,
+ boost::begin( dxdt ) + 4 * m_N ,
+ boost::begin( dxdt ) + 5 * m_N ,
+ boost::begin( dxdt ) + 6 * m_N ) )
+ ) ) ,
+ lorenz_perturbation_functor() );
+ }
+
+ size_t m_N;
+ const state_type &m_beta;
+};
+
+struct lyap_observer
+{
+ //[thrust_lorenz_parameters_observer_functor
+ struct lyap_functor
+ {
+ template< class T >
+ __host__ __device__
+ void operator()( T t ) const
+ {
+ value_type &dx = thrust::get< 0 >( t );
+ value_type &dy = thrust::get< 1 >( t );
+ value_type &dz = thrust::get< 2 >( t );
+ value_type norm = sqrt( dx * dx + dy * dy + dz * dz );
+ dx /= norm;
+ dy /= norm;
+ dz /= norm;
+ thrust::get< 3 >( t ) += log( norm );
+ }
+ };
+ //]
+
+ lyap_observer( size_t N , size_t every = 100 )
+ : m_N( N ) , m_lyap( N ) , m_every( every ) , m_count( 0 )
+ {
+ thrust::fill( m_lyap.begin() , m_lyap.end() , 0.0 );
+ }
+
+ template< class Lyap >
+ void fill_lyap( Lyap &lyap )
+ {
+ thrust::copy( m_lyap.begin() , m_lyap.end() , lyap.begin() );
+ for( size_t i=0 ; i<lyap.size() ; ++i )
+ lyap[i] /= m_t_overall;
+ }
+
+
+ template< class State >
+ void operator()( State &x , value_type t )
+ {
+ if( ( m_count != 0 ) && ( ( m_count % m_every ) == 0 ) )
+ {
+ thrust::for_each(
+ thrust::make_zip_iterator( thrust::make_tuple(
+ boost::begin( x ) + 3 * m_N ,
+ boost::begin( x ) + 4 * m_N ,
+ boost::begin( x ) + 5 * m_N ,
+ m_lyap.begin() ) ) ,
+ thrust::make_zip_iterator( thrust::make_tuple(
+ boost::begin( x ) + 4 * m_N ,
+ boost::begin( x ) + 5 * m_N ,
+ boost::begin( x ) + 6 * m_N ,
+ m_lyap.end() ) ) ,
+ lyap_functor() );
+ clog << t << "\n";
+ }
+ ++m_count;
+ m_t_overall = t;
+ }
+
+ size_t m_N;
+ state_type m_lyap;
+ size_t m_every;
+ size_t m_count;
+ value_type m_t_overall;
+};
+
+const size_t N = 1024*2;
+const value_type dt = 0.01;
+
+
+int main( int arc , char* argv[] )
+{
+ int driver_version , runtime_version;
+ cudaDriverGetVersion( &driver_version );
+ cudaRuntimeGetVersion ( &runtime_version );
+ cout << driver_version << "\t" << runtime_version << endl;
+
+
+ //[ thrust_lorenz_parameters_define_beta
+ vector< value_type > beta_host( N );
+ const value_type beta_min = 0.0 , beta_max = 56.0;
+ for( size_t i=0 ; i<N ; ++i )
+ beta_host[i] = beta_min + value_type( i ) * ( beta_max - beta_min ) / value_type( N - 1 );
+
+ state_type beta = beta_host;
+ //]
+
+ //[ thrust_lorenz_parameters_integration
+ state_type x( 6 * N );
+
+ // initialize x,y,z
+ thrust::fill( x.begin() , x.begin() + 3 * N , 10.0 );
+
+ // initial dx
+ thrust::fill( x.begin() + 3 * N , x.begin() + 4 * N , 1.0 );
+
+ // initialize dy,dz
+ thrust::fill( x.begin() + 4 * N , x.end() , 0.0 );
+
+
+ // create error stepper, can be used with make_controlled or make_dense_output
+ typedef runge_kutta_dopri5< state_type , value_type , state_type , value_type > stepper_type;
+
+
+ lorenz_system lorenz( N , beta );
+ lorenz_perturbation_system lorenz_perturbation( N , beta );
+ lyap_observer obs( N , 1 );
+
+ // calculate transients
+ integrate_adaptive( make_controlled( 1.0e-6 , 1.0e-6 , stepper_type() ) , lorenz , std::make_pair( x.begin() , x.begin() + 3 * N ) , 0.0 , 10.0 , dt );
+
+ // calculate the Lyapunov exponents -- the main loop
+ double t = 0.0;
+ while( t < 10000.0 )
+ {
+ integrate_adaptive( make_controlled( 1.0e-6 , 1.0e-6 , stepper_type() ) , lorenz_perturbation , x , t , t + 1.0 , 0.1 );
+ t += 1.0;
+ obs( x , t );
+ }
+
+ vector< value_type > lyap( N );
+ obs.fill_lyap( lyap );
+
+ for( size_t i=0 ; i<N ; ++i )
+ cout << beta_host[i] << "\t" << lyap[i] << "\n";
+ //]
+
+ return 0;
+}
diff --git a/examples/thrust/phase_oscillator_chain.cu b/examples/thrust/phase_oscillator_chain.cu
new file mode 100644
index 0000000..0409697
--- /dev/null
+++ b/examples/thrust/phase_oscillator_chain.cu
@@ -0,0 +1,156 @@
+/*
+ Copyright 2011-2013 Mario Mulansky
+ Copyright 2011 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+/*
+ * This example shows how to use odeint on CUDA devices with thrust.
+ * Note that we require at least Version 3.2 of the nVidia CUDA SDK
+ * and the thrust library should be installed in the CUDA include
+ * folder.
+ *
+ * As example we use a chain of phase oscillators with nearest neighbour
+ * coupling, as described in:
+ *
+ * Avis H. Cohen, Philip J. Holmes and Richard H. Rand:
+ * JOURNAL OF MATHEMATICAL BIOLOGY Volume 13, Number 3, 345-369,
+ *
+ */
+
+#include <iostream>
+#include <cmath>
+
+#include <thrust/device_vector.h>
+#include <thrust/iterator/permutation_iterator.h>
+#include <thrust/iterator/counting_iterator.h>
+
+#include <boost/numeric/odeint/stepper/runge_kutta4.hpp>
+#include <boost/numeric/odeint/integrate/integrate_const.hpp>
+#include <boost/numeric/odeint/external/thrust/thrust.hpp>
+
+using namespace std;
+
+using namespace boost::numeric::odeint;
+
+
+//change this to float if your device does not support double computation
+typedef double value_type;
+
+
+//[ thrust_phase_chain_system
+//change this to host_vector< ... > if you want to run on CPU
+typedef thrust::device_vector< value_type > state_type;
+typedef thrust::device_vector< size_t > index_vector_type;
+//typedef thrust::host_vector< value_type > state_type;
+//typedef thrust::host_vector< size_t > index_vector_type;
+
+//<-
+/*
+ * This implements the rhs of the dynamical equation:
+ * \phi'_0 = \omega_0 + sin( \phi_1 - \phi_0 )
+ * \phi'_i = \omega_i + sin( \phi_i+1 - \phi_i ) + sin( \phi_i - \phi_i-1 )
+ * \phi'_N-1 = \omega_N-1 + sin( \phi_N-1 - \phi_N-2 )
+ */
+//->
+class phase_oscillators
+{
+
+public:
+
+ struct sys_functor
+ {
+ template< class Tuple >
+ __host__ __device__
+ void operator()( Tuple t ) // this functor works on tuples of values
+ {
+ // first, unpack the tuple into value, neighbors and omega
+ const value_type phi = thrust::get<0>(t);
+ const value_type phi_left = thrust::get<1>(t); // left neighbor
+ const value_type phi_right = thrust::get<2>(t); // right neighbor
+ const value_type omega = thrust::get<3>(t);
+ // the dynamical equation
+ thrust::get<4>(t) = omega + sin( phi_right - phi ) + sin( phi - phi_left );
+ }
+ };
+
+ phase_oscillators( const state_type &omega )
+ : m_omega( omega ) , m_N( omega.size() ) , m_prev( omega.size() ) , m_next( omega.size() )
+ {
+ // build indices pointing to left and right neighbours
+ thrust::counting_iterator<size_t> c( 0 );
+ thrust::copy( c , c+m_N-1 , m_prev.begin()+1 );
+ m_prev[0] = 0; // m_prev = { 0 , 0 , 1 , 2 , 3 , ... , N-1 }
+
+ thrust::copy( c+1 , c+m_N , m_next.begin() );
+ m_next[m_N-1] = m_N-1; // m_next = { 1 , 2 , 3 , ... , N-1 , N-1 }
+ }
+
+ void operator() ( const state_type &x , state_type &dxdt , const value_type dt )
+ {
+ thrust::for_each(
+ thrust::make_zip_iterator(
+ thrust::make_tuple(
+ x.begin() ,
+ thrust::make_permutation_iterator( x.begin() , m_prev.begin() ) ,
+ thrust::make_permutation_iterator( x.begin() , m_next.begin() ) ,
+ m_omega.begin() ,
+ dxdt.begin()
+ ) ),
+ thrust::make_zip_iterator(
+ thrust::make_tuple(
+ x.end() ,
+ thrust::make_permutation_iterator( x.begin() , m_prev.end() ) ,
+ thrust::make_permutation_iterator( x.begin() , m_next.end() ) ,
+ m_omega.end() ,
+ dxdt.end()) ) ,
+ sys_functor()
+ );
+ }
+
+private:
+
+ const state_type &m_omega;
+ const size_t m_N;
+ index_vector_type m_prev;
+ index_vector_type m_next;
+};
+//]
+
+const size_t N = 32768;
+const value_type pi = 3.1415926535897932384626433832795029;
+const value_type epsilon = 6.0 / ( N * N ); // should be < 8/N^2 to see phase locking
+const value_type dt = 0.1;
+
+int main( int arc , char* argv[] )
+{
+ //[ thrust_phase_chain_integration
+ // create initial conditions and omegas on host:
+ vector< value_type > x_host( N );
+ vector< value_type > omega_host( N );
+ for( size_t i=0 ; i<N ; ++i )
+ {
+ x_host[i] = 2.0 * pi * drand48();
+ omega_host[i] = ( N - i ) * epsilon; // decreasing frequencies
+ }
+
+ // copy to device
+ state_type x = x_host;
+ state_type omega = omega_host;
+
+ // create stepper
+ runge_kutta4< state_type , value_type , state_type , value_type > stepper;
+
+ // create phase oscillator system function
+ phase_oscillators sys( omega );
+
+ // integrate
+ integrate_const( stepper , sys , x , 0.0 , 10.0 , dt );
+
+ thrust::copy( x.begin() , x.end() , std::ostream_iterator< value_type >( std::cout , "\n" ) );
+ std::cout << std::endl;
+ //]
+}
diff --git a/examples/thrust/phase_oscillator_ensemble.cu b/examples/thrust/phase_oscillator_ensemble.cu
new file mode 100644
index 0000000..d678b8f
--- /dev/null
+++ b/examples/thrust/phase_oscillator_ensemble.cu
@@ -0,0 +1,280 @@
+/*
+ The example how the phase_oscillator ensemble can be implemented using CUDA and thrust
+
+ Copyright 2011-2013 Mario Mulansky
+ Copyright 2011 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <iostream>
+#include <fstream>
+#include <cmath>
+#include <utility>
+
+#include <thrust/device_vector.h>
+#include <thrust/reduce.h>
+#include <thrust/functional.h>
+
+#include <boost/numeric/odeint.hpp>
+#include <boost/numeric/odeint/external/thrust/thrust.hpp>
+
+#include <boost/timer.hpp>
+#include <boost/random/cauchy_distribution.hpp>
+
+using namespace std;
+
+using namespace boost::numeric::odeint;
+
+/*
+ * Sorry for that dirty hack, but nvcc has large problems with boost::random.
+ *
+ * Nevertheless we need the cauchy distribution from boost::random, and therefore
+ * we need a generator. Here it is:
+ */
+struct drand48_generator
+{
+ typedef double result_type;
+ result_type operator()( void ) const { return drand48(); }
+ result_type min( void ) const { return 0.0; }
+ result_type max( void ) const { return 1.0; }
+};
+
+//[ thrust_phase_ensemble_state_type
+//change this to float if your device does not support double computation
+typedef double value_type;
+
+//change this to host_vector< ... > of you want to run on CPU
+typedef thrust::device_vector< value_type > state_type;
+// typedef thrust::host_vector< value_type > state_type;
+//]
+
+
+//[ thrust_phase_ensemble_mean_field_calculator
+struct mean_field_calculator
+{
+ struct sin_functor : public thrust::unary_function< value_type , value_type >
+ {
+ __host__ __device__
+ value_type operator()( value_type x) const
+ {
+ return sin( x );
+ }
+ };
+
+ struct cos_functor : public thrust::unary_function< value_type , value_type >
+ {
+ __host__ __device__
+ value_type operator()( value_type x) const
+ {
+ return cos( x );
+ }
+ };
+
+ static std::pair< value_type , value_type > get_mean( const state_type &x )
+ {
+ //[ thrust_phase_ensemble_sin_sum
+ value_type sin_sum = thrust::reduce(
+ thrust::make_transform_iterator( x.begin() , sin_functor() ) ,
+ thrust::make_transform_iterator( x.end() , sin_functor() ) );
+ //]
+ value_type cos_sum = thrust::reduce(
+ thrust::make_transform_iterator( x.begin() , cos_functor() ) ,
+ thrust::make_transform_iterator( x.end() , cos_functor() ) );
+
+ cos_sum /= value_type( x.size() );
+ sin_sum /= value_type( x.size() );
+
+ value_type K = sqrt( cos_sum * cos_sum + sin_sum * sin_sum );
+ value_type Theta = atan2( sin_sum , cos_sum );
+
+ return std::make_pair( K , Theta );
+ }
+};
+//]
+
+
+
+//[ thrust_phase_ensemble_sys_function
+class phase_oscillator_ensemble
+{
+
+public:
+
+ struct sys_functor
+ {
+ value_type m_K , m_Theta , m_epsilon;
+
+ sys_functor( value_type K , value_type Theta , value_type epsilon )
+ : m_K( K ) , m_Theta( Theta ) , m_epsilon( epsilon ) { }
+
+ template< class Tuple >
+ __host__ __device__
+ void operator()( Tuple t )
+ {
+ thrust::get<2>(t) = thrust::get<1>(t) + m_epsilon * m_K * sin( m_Theta - thrust::get<0>(t) );
+ }
+ };
+
+ // ...
+ //<-
+ phase_oscillator_ensemble( size_t N , value_type g = 1.0 , value_type epsilon = 1.0 )
+ : m_omega() , m_N( N ) , m_epsilon( epsilon )
+ {
+ create_frequencies( g );
+ }
+
+ void create_frequencies( value_type g )
+ {
+ boost::cauchy_distribution< value_type > cauchy( 0.0 , g );
+// boost::variate_generator< boost::mt19937&, boost::cauchy_distribution< value_type > > gen( rng , cauchy );
+ drand48_generator d48;
+ vector< value_type > omega( m_N );
+ for( size_t i=0 ; i<m_N ; ++i )
+ omega[i] = cauchy( d48 );
+// generate( omega.begin() , omega.end() , gen );
+ m_omega = omega;
+ }
+
+ void set_epsilon( value_type epsilon ) { m_epsilon = epsilon; }
+
+ value_type get_epsilon( void ) const { return m_epsilon; }
+ //->
+
+ void operator() ( const state_type &x , state_type &dxdt , const value_type dt ) const
+ {
+ std::pair< value_type , value_type > mean_field = mean_field_calculator::get_mean( x );
+
+ thrust::for_each(
+ thrust::make_zip_iterator( thrust::make_tuple( x.begin() , m_omega.begin() , dxdt.begin() ) ),
+ thrust::make_zip_iterator( thrust::make_tuple( x.end() , m_omega.end() , dxdt.end()) ) ,
+ sys_functor( mean_field.first , mean_field.second , m_epsilon )
+ );
+ }
+
+ // ...
+ //<-
+private:
+
+ state_type m_omega;
+ const size_t m_N;
+ value_type m_epsilon;
+ //->
+};
+//]
+
+
+//[ thrust_phase_ensemble_observer
+struct statistics_observer
+{
+ value_type m_K_mean;
+ size_t m_count;
+
+ statistics_observer( void )
+ : m_K_mean( 0.0 ) , m_count( 0 ) { }
+
+ template< class State >
+ void operator()( const State &x , value_type t )
+ {
+ std::pair< value_type , value_type > mean = mean_field_calculator::get_mean( x );
+ m_K_mean += mean.first;
+ ++m_count;
+ }
+
+ value_type get_K_mean( void ) const { return ( m_count != 0 ) ? m_K_mean / value_type( m_count ) : 0.0 ; }
+
+ void reset( void ) { m_K_mean = 0.0; m_count = 0; }
+};
+//]
+
+
+
+// const size_t N = 16384 * 128;
+const size_t N = 16384;
+const value_type pi = 3.1415926535897932384626433832795029;
+const value_type dt = 0.1;
+const value_type d_epsilon = 0.1;
+const value_type epsilon_min = 0.0;
+const value_type epsilon_max = 5.0;
+const value_type t_transients = 10.0;
+const value_type t_max = 100.0;
+
+int main( int arc , char* argv[] )
+{
+ // initial conditions on host
+ vector< value_type > x_host( N );
+ for( size_t i=0 ; i<N ; ++i ) x_host[i] = 2.0 * pi * drand48();
+
+ //[ thrust_phase_ensemble_system_instance
+ phase_oscillator_ensemble ensemble( N , 1.0 );
+ //]
+
+
+
+ boost::timer timer;
+ boost::timer timer_local;
+ double dopri5_time = 0.0 , rk4_time = 0.0;
+ {
+ //[thrust_phase_ensemble_define_dopri5
+ typedef runge_kutta_dopri5< state_type , value_type , state_type , value_type > stepper_type;
+ //]
+
+ ofstream fout( "phase_ensemble_dopri5.dat" );
+ timer.restart();
+ for( value_type epsilon = epsilon_min ; epsilon < epsilon_max ; epsilon += d_epsilon )
+ {
+ ensemble.set_epsilon( epsilon );
+ statistics_observer obs;
+ state_type x = x_host;
+
+ timer_local.restart();
+
+ // calculate some transients steps
+ //[ thrust_phase_ensemble_integration
+ size_t steps1 = integrate_const( make_controlled( 1.0e-6 , 1.0e-6 , stepper_type() ) , boost::ref( ensemble ) , x , 0.0 , t_transients , dt );
+ //]
+
+ // integrate and compute the statistics
+ size_t steps2 = integrate_const( make_dense_output( 1.0e-6 , 1.0e-6 , stepper_type() ) , boost::ref( ensemble ) , x , 0.0 , t_max , dt , boost::ref( obs ) );
+
+ fout << epsilon << "\t" << obs.get_K_mean() << endl;
+ cout << "Dopri5 : " << epsilon << "\t" << obs.get_K_mean() << "\t" << timer_local.elapsed() << "\t" << steps1 << "\t" << steps2 << endl;
+ }
+ dopri5_time = timer.elapsed();
+ }
+
+
+
+ {
+ //[ thrust_phase_ensemble_define_rk4
+ typedef runge_kutta4< state_type , value_type , state_type , value_type > stepper_type;
+ //]
+
+ ofstream fout( "phase_ensemble_rk4.dat" );
+ timer.restart();
+ for( value_type epsilon = epsilon_min ; epsilon < epsilon_max ; epsilon += d_epsilon )
+ {
+ ensemble.set_epsilon( epsilon );
+ statistics_observer obs;
+ state_type x = x_host;
+
+ timer_local.restart();
+
+ // calculate some transients steps
+ size_t steps1 = integrate_const( stepper_type() , boost::ref( ensemble ) , x , 0.0 , t_transients , dt );
+
+ // integrate and compute the statistics
+ size_t steps2 = integrate_const( stepper_type() , boost::ref( ensemble ) , x , 0.0 , t_max , dt , boost::ref( obs ) );
+ fout << epsilon << "\t" << obs.get_K_mean() << endl;
+ cout << "RK4 : " << epsilon << "\t" << obs.get_K_mean() << "\t" << timer_local.elapsed() << "\t" << steps1 << "\t" << steps2 << endl;
+ }
+ rk4_time = timer.elapsed();
+ }
+
+ cout << "Dopri 5 : " << dopri5_time << " s\n";
+ cout << "RK4 : " << rk4_time << "\n";
+
+ return 0;
+}
diff --git a/examples/thrust/relaxation.cu b/examples/thrust/relaxation.cu
new file mode 100644
index 0000000..f1d9f3a
--- /dev/null
+++ b/examples/thrust/relaxation.cu
@@ -0,0 +1,81 @@
+/*
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+/*
+ * Solves many relaxation equations dxdt = - a * x in parallel and for different values of a.
+ * The relaxation equations are completely uncoupled.
+ */
+
+#include <thrust/device_vector.h>
+
+#include <boost/ref.hpp>
+
+#include <boost/numeric/odeint.hpp>
+#include <boost/numeric/odeint/external/thrust/thrust.hpp>
+
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+// change to float if your GPU does not support doubles
+typedef double value_type;
+typedef thrust::device_vector< value_type > state_type;
+typedef runge_kutta4< state_type , value_type , state_type , value_type > stepper_type;
+
+struct relaxation
+{
+ struct relaxation_functor
+ {
+ template< class T >
+ __host__ __device__
+ void operator()( T t ) const
+ {
+ // unpack the parameter we want to vary and the Lorenz variables
+ value_type a = thrust::get< 1 >( t );
+ value_type x = thrust::get< 0 >( t );
+ thrust::get< 2 >( t ) = -a * x;
+ }
+ };
+
+ relaxation( size_t N , const state_type &a )
+ : m_N( N ) , m_a( a ) { }
+
+ void operator()( const state_type &x , state_type &dxdt , value_type t ) const
+ {
+ thrust::for_each(
+ thrust::make_zip_iterator( thrust::make_tuple( x.begin() , m_a.begin() , dxdt.begin() ) ) ,
+ thrust::make_zip_iterator( thrust::make_tuple( x.end() , m_a.end() , dxdt.end() ) ) ,
+ relaxation_functor() );
+ }
+
+ size_t m_N;
+ const state_type &m_a;
+};
+
+const size_t N = 1024 * 1024;
+const value_type dt = 0.01;
+
+int main( int arc , char* argv[] )
+{
+ // initialize the relaxation constants a
+ vector< value_type > a_host( N );
+ for( size_t i=0 ; i<N ; ++i ) a_host[i] = drand48();
+ state_type a = a_host;
+
+ // initialize the intial state x
+ state_type x( N );
+ thrust::fill( x.begin() , x.end() , 1.0 );
+
+ // integrate
+ relaxation relax( N , a );
+ integrate_const( stepper_type() , boost::ref( relax ) , x , 0.0 , 10.0 , dt );
+
+ return 0;
+}
diff --git a/examples/two_dimensional_phase_lattice.cpp b/examples/two_dimensional_phase_lattice.cpp
new file mode 100644
index 0000000..1fe4b95
--- /dev/null
+++ b/examples/two_dimensional_phase_lattice.cpp
@@ -0,0 +1,158 @@
+/*
+ * two_dimensional_phase_lattice.cpp
+ *
+ * This example show how one can use matrices as state types in odeint.
+ *
+ * Copyright 2011-2012 Karsten Ahnert
+ * Copyright 2011-2013 Mario Mulansky
+ * Distributed under the Boost Software License, Version 1.0. (See
+ * accompanying file LICENSE_1_0.txt or copy at
+ * http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <iostream>
+#include <map>
+#include <string>
+#include <fstream>
+
+#ifndef M_PI //not there on windows
+#define M_PI 3.1415927 //...
+#endif
+
+#include <boost/numeric/odeint.hpp>
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+//[ two_dimensional_phase_lattice_definition
+typedef boost::numeric::ublas::matrix< double > state_type;
+
+struct two_dimensional_phase_lattice
+{
+ two_dimensional_phase_lattice( double gamma = 0.5 )
+ : m_gamma( gamma ) { }
+
+ void operator()( const state_type &x , state_type &dxdt , double /* t */ ) const
+ {
+ size_t size1 = x.size1() , size2 = x.size2();
+
+ for( size_t i=1 ; i<size1-1 ; ++i )
+ {
+ for( size_t j=1 ; j<size2-1 ; ++j )
+ {
+ dxdt( i , j ) =
+ coupling_func( x( i + 1 , j ) - x( i , j ) ) +
+ coupling_func( x( i - 1 , j ) - x( i , j ) ) +
+ coupling_func( x( i , j + 1 ) - x( i , j ) ) +
+ coupling_func( x( i , j - 1 ) - x( i , j ) );
+ }
+ }
+
+ for( size_t i=0 ; i<x.size1() ; ++i ) dxdt( i , 0 ) = dxdt( i , x.size2() -1 ) = 0.0;
+ for( size_t j=0 ; j<x.size2() ; ++j ) dxdt( 0 , j ) = dxdt( x.size1() -1 , j ) = 0.0;
+ }
+
+ double coupling_func( double x ) const
+ {
+ return sin( x ) - m_gamma * ( 1.0 - cos( x ) );
+ }
+
+ double m_gamma;
+};
+//]
+
+
+struct write_for_gnuplot
+{
+ size_t m_every , m_count;
+
+ write_for_gnuplot( size_t every = 10 )
+ : m_every( every ) , m_count( 0 ) { }
+
+ void operator()( const state_type &x , double t )
+ {
+ if( ( m_count % m_every ) == 0 )
+ {
+ clog << t << endl;
+ cout << "sp '-'" << endl;
+ for( size_t i=0 ; i<x.size1() ; ++i )
+ {
+ for( size_t j=0 ; j<x.size2() ; ++j )
+ {
+ cout << i << "\t" << j << "\t" << sin( x( i , j ) ) << "\n";
+ }
+ cout << "\n";
+ }
+ cout << "e" << endl;
+ }
+
+ ++m_count;
+ }
+};
+
+class write_snapshots
+{
+public:
+
+ typedef std::map< size_t , std::string > map_type;
+
+ write_snapshots( void ) : m_count( 0 ) { }
+
+ void operator()( const state_type &x , double t )
+ {
+ map< size_t , string >::const_iterator it = m_snapshots.find( m_count );
+ if( it != m_snapshots.end() )
+ {
+ ofstream fout( it->second.c_str() );
+ for( size_t i=0 ; i<x.size1() ; ++i )
+ {
+ for( size_t j=0 ; j<x.size2() ; ++j )
+ {
+ fout << i << "\t" << j << "\t" << x( i , j ) << "\t" << sin( x( i , j ) ) << "\n";
+ }
+ fout << "\n";
+ }
+ }
+ ++m_count;
+ }
+
+ map_type& snapshots( void ) { return m_snapshots; }
+ const map_type& snapshots( void ) const { return m_snapshots; }
+
+private:
+
+ size_t m_count;
+ map_type m_snapshots;
+};
+
+
+int main( int argc , char **argv )
+{
+ size_t size1 = 128 , size2 = 128;
+ state_type x( size1 , size2 , 0.0 );
+
+ for( size_t i=(size1/2-10) ; i<(size1/2+10) ; ++i )
+ for( size_t j=(size2/2-10) ; j<(size2/2+10) ; ++j )
+ x( i , j ) = static_cast<double>( rand() ) / RAND_MAX * 2.0 * M_PI;
+
+ write_snapshots snapshots;
+ snapshots.snapshots().insert( make_pair( size_t( 0 ) , string( "lat_0000.dat" ) ) );
+ snapshots.snapshots().insert( make_pair( size_t( 100 ) , string( "lat_0100.dat" ) ) );
+ snapshots.snapshots().insert( make_pair( size_t( 1000 ) , string( "lat_1000.dat" ) ) );
+ observer_collection< state_type , double > obs;
+ obs.observers().push_back( write_for_gnuplot( 10 ) );
+ obs.observers().push_back( snapshots );
+
+ cout << "set term x11" << endl;
+ cout << "set pm3d map" << endl;
+
+ integrate_const( runge_kutta4<state_type>() , two_dimensional_phase_lattice( 1.2 ) ,
+ x , 0.0 , 1001.0 , 0.1 , boost::ref( obs ) );
+
+ // controlled steppers work only after ublas bugfix
+ //integrate_const( make_dense_output< runge_kutta_dopri5< state_type > >( 1E-6 , 1E-6 ) , two_dimensional_phase_lattice( 1.2 ) ,
+ // x , 0.0 , 1001.0 , 0.1 , boost::ref( obs ) );
+
+
+ return 0;
+}
diff --git a/examples/ublas/Jamfile.v2 b/examples/ublas/Jamfile.v2
new file mode 100644
index 0000000..7abff98
--- /dev/null
+++ b/examples/ublas/Jamfile.v2
@@ -0,0 +1,13 @@
+# Copyright 2011 Mario Mulansky
+# Copyright 2012 Karsten Ahnert
+# Distributed under the Boost Software License, Version 1.0. (See
+# accompanying file LICENSE_1_0.txt or copy at
+# http://www.boost.org/LICENSE_1_0.txt)
+
+
+project
+ : requirements
+ <define>BOOST_ALL_NO_LIB=1
+ ;
+
+exe lorenz_ublas : lorenz_ublas.cpp ;
diff --git a/examples/ublas/lorenz_ublas.cpp b/examples/ublas/lorenz_ublas.cpp
new file mode 100644
index 0000000..0e3958d
--- /dev/null
+++ b/examples/ublas/lorenz_ublas.cpp
@@ -0,0 +1,40 @@
+/*
+ * Copyright 2011-2013 Mario Mulansky
+ * Copyright 2012 Karsten Ahnert
+ *
+ * Distributed under the Boost Software License, Version 1.0.
+ * (See accompanying file LICENSE_1_0.txt or
+ * copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#include <iostream>
+
+#include <boost/numeric/odeint.hpp>
+#include <boost/numeric/ublas/vector.hpp>
+
+typedef boost::numeric::ublas::vector< double > state_type;
+
+void lorenz( const state_type &x , state_type &dxdt , const double t )
+{
+ const double sigma( 10.0 );
+ const double R( 28.0 );
+ const double b( 8.0 / 3.0 );
+
+ dxdt[0] = sigma * ( x[1] - x[0] );
+ dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
+ dxdt[2] = -b * x[2] + x[0] * x[1];
+}
+
+using namespace boost::numeric::odeint;
+
+//[ublas_main
+int main()
+{
+ state_type x(3);
+ x[0] = 10.0; x[1] = 5.0 ; x[2] = 0.0;
+ typedef runge_kutta_dopri5< state_type > stepper;
+ integrate_const( make_dense_output< stepper >( 1E-6 , 1E-6 ) , lorenz , x ,
+ 0.0 , 10.0 , 0.1 );
+}
+//]
diff --git a/examples/van_der_pol_stiff.cpp b/examples/van_der_pol_stiff.cpp
new file mode 100644
index 0000000..a53ae4d
--- /dev/null
+++ b/examples/van_der_pol_stiff.cpp
@@ -0,0 +1,95 @@
+/*
+ * van_der_pol_stiff.cpp
+ *
+ * Created on: Dec 12, 2011
+ *
+ * Copyright 2012 Karsten Ahnert
+ * Copyright 2012-2013 Rajeev Singh
+ * Copyright 2012-2013 Mario Mulansky
+ *
+ * Distributed under the Boost Software License, Version 1.0.
+ * (See accompanying file LICENSE_1_0.txt or
+ * copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <iostream>
+#include <fstream>
+#include <utility>
+
+#include <boost/numeric/odeint.hpp>
+
+#include <boost/phoenix/core.hpp>
+#include <boost/phoenix/operator.hpp>
+
+using namespace std;
+using namespace boost::numeric::odeint;
+namespace phoenix = boost::phoenix;
+
+const double mu = 1000.0;
+
+
+typedef boost::numeric::ublas::vector< double > vector_type;
+typedef boost::numeric::ublas::matrix< double > matrix_type;
+
+struct vdp_stiff
+{
+ void operator()( const vector_type &x , vector_type &dxdt , double t )
+ {
+ dxdt[0] = x[1];
+ dxdt[1] = -x[0] - mu * x[1] * (x[0]*x[0]-1.0);
+ }
+};
+
+struct vdp_stiff_jacobi
+{
+ void operator()( const vector_type &x , matrix_type &J , const double &t , vector_type &dfdt )
+ {
+ J(0, 0) = 0.0;
+ J(0, 1) = 1.0;
+ J(1, 0) = -1.0 - 2.0*mu * x[0] * x[1];
+ J(1, 1) = -mu * ( x[0] * x[0] - 1.0);
+
+ dfdt[0] = 0.0;
+ dfdt[1] = 0.0;
+ }
+};
+
+
+int main( int argc , char **argv )
+{
+ //[ integrate_stiff_system
+ vector_type x( 2 );
+ /* initialize random seed: */
+ srand ( time(NULL) );
+
+ // initial conditions
+ for (int i=0; i<2; i++)
+ x[i] = 1.0; //(1.0 * rand()) / RAND_MAX;
+
+ size_t num_of_steps = integrate_const( make_dense_output< rosenbrock4< double > >( 1.0e-6 , 1.0e-6 ) ,
+ make_pair( vdp_stiff() , vdp_stiff_jacobi() ) ,
+ x , 0.0 , 1000.0 , 1.0
+ , cout << phoenix::arg_names::arg2 << " " << phoenix::arg_names::arg1[0] << " " << phoenix::arg_names::arg1[1] << "\n"
+ );
+ //]
+ clog << num_of_steps << endl;
+
+
+
+ //[ integrate_stiff_system_alternative
+
+ vector_type x2( 2 );
+ // initial conditions
+ for (int i=0; i<2; i++)
+ x2[i] = 1.0; //(1.0 * rand()) / RAND_MAX;
+
+ //size_t num_of_steps2 = integrate_const( make_dense_output< runge_kutta_dopri5< vector_type > >( 1.0e-6 , 1.0e-6 ) ,
+ // vdp_stiff() , x2 , 0.0 , 1000.0 , 1.0
+ // , cout << phoenix::arg_names::arg2 << " " << phoenix::arg_names::arg1[0] << " " << phoenix::arg_names::arg1[1] << "\n"
+ // );
+ //]
+ //clog << num_of_steps2 << endl;
+
+
+ return 0;
+}
diff --git a/examples/vexcl/Jamfile.v2 b/examples/vexcl/Jamfile.v2
new file mode 100644
index 0000000..73dc8da
--- /dev/null
+++ b/examples/vexcl/Jamfile.v2
@@ -0,0 +1,32 @@
+# Copyright 2012 Karsten Ahnert
+# Copyright 2013 Mario Mulansky
+#
+# Distributed under the Boost Software License, Version 1.0.
+# (See accompanying file LICENSE_1_0.txt or
+# copy at http://www.boost.org/LICENSE_1_0.txt)
+
+
+import boost ;
+import os ;
+
+boost.use-project ;
+
+
+# change these lines to fit you configuration
+local HOME = [ os.environ HOME ] ;
+local VEXCL_INCLUDE = [ os.environ VEXCL_ROOT ] ;
+OPENCL_INCLUDE = /usr/local/cuda/include ;
+
+
+
+lib opencl : : <name>OpenCL ;
+
+project : requirements
+ <implicit-dependency>/boost//headers
+ <include>$(VEXCL_INCLUDE)
+ <include>$(OPENCL_INCLUDE)
+ <toolset>gcc:<cxxflags>-std=c++0x
+ <library>/boost//system/
+ ;
+
+exe lorenz_ensemble : lorenz_ensemble.cpp opencl ;
\ No newline at end of file
diff --git a/examples/vexcl/lorenz_ensemble.cpp b/examples/vexcl/lorenz_ensemble.cpp
new file mode 100644
index 0000000..0e7594c
--- /dev/null
+++ b/examples/vexcl/lorenz_ensemble.cpp
@@ -0,0 +1,86 @@
+/*
+ * Copyright 2012 Karsten Ahnert
+ * Copyright 2013 Mario Mulansky
+ *
+ * Distributed under the Boost Software License, Version 1.0.
+ * (See accompanying file LICENSE_1_0.txt or
+ * copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <iostream>
+#include <vector>
+
+#include <vexcl/vexcl.hpp>
+
+#include <boost/numeric/odeint.hpp>
+//[ vexcl_includes
+#include <boost/numeric/odeint/external/vexcl/vexcl.hpp>
+//]
+
+namespace odeint = boost::numeric::odeint;
+
+//[ vexcl_state_types
+typedef vex::vector< double > vector_type;
+typedef vex::multivector< double, 3 > state_type;
+//]
+
+
+//[ vexcl_system
+const double sigma = 10.0;
+const double b = 8.0 / 3.0;
+
+struct sys_func
+{
+ const vector_type &R;
+
+ sys_func( const vector_type &_R ) : R( _R ) { }
+
+ void operator()( const state_type &x , state_type &dxdt , double t ) const
+ {
+ dxdt(0) = -sigma * ( x(0) - x(1) );
+ dxdt(1) = R * x(0) - x(1) - x(0) * x(2);
+ dxdt(2) = - b * x(2) + x(0) * x(1);
+ }
+};
+//]
+
+
+int main( int argc , char **argv )
+{
+ using namespace std;
+ using namespace odeint;
+
+ //[ vexcl_main
+ // setup the opencl context
+ vex::Context ctx( vex::Filter::Type(CL_DEVICE_TYPE_GPU) );
+ std::cout << ctx << std::endl;
+
+ // set up number of system, time step and integration time
+ const size_t n = 1024 * 1024;
+ const double dt = 0.01;
+ const double t_max = 1000.0;
+
+ // initialize R
+ double Rmin = 0.1 , Rmax = 50.0 , dR = ( Rmax - Rmin ) / double( n - 1 );
+ std::vector<double> x( n * 3 ) , r( n );
+ for( size_t i=0 ; i<n ; ++i ) r[i] = Rmin + dR * double( i );
+ vector_type R( ctx.queue() , r );
+
+ // initialize the state of the lorenz ensemble
+ state_type X(ctx.queue(), n);
+ X(0) = 10.0;
+ X(1) = 10.0;
+ X(2) = 10.0;
+
+ // create a stepper
+ runge_kutta4< state_type > stepper;
+
+ // solve the system
+ integrate_const( stepper , sys_func( R ) , X , 0.0 , t_max , dt );
+ //]
+
+ std::vector< double > res( 3 * n );
+ vex::copy( X(0) , res );
+ for( size_t i=0 ; i<n ; ++i )
+ cout << r[i] << "\t" << res[i] << "\t" << "\n";
+}
diff --git a/fix-copyright.py b/fix-copyright.py
new file mode 100755
index 0000000..f484822
--- /dev/null
+++ b/fix-copyright.py
@@ -0,0 +1,71 @@
+#!/usr/bin/env python
+from subprocess import check_output as run
+from datetime import datetime
+from itertools import groupby
+from operator import itemgetter
+import re
+import magic
+
+def authors(filename):
+ log = run(['git', 'log', '--follow',
+ '--date=short','--format=%aN%x09%ad', filename],
+ universal_newlines=True)
+ for line in log.splitlines():
+ author, date = line.split('\t')
+ if author != 'fix-copyright.py':
+ yield author, datetime.strptime(date, '%Y-%m-%d')
+
+def new_copyright(filename, previous):
+ def f():
+ au = list(authors(filename))
+ alldates = map(itemgetter(1), au)
+ aup = sorted(au + map(lambda a: (a, None), previous), key=itemgetter(0))
+ for author, records in groupby(aup, itemgetter(0)):
+ dates = filter(None, map(itemgetter(1), records))
+ if not dates: dates = alldates
+ start = min(dates)
+ end = max(dates)
+ fmt = '{0}' if start.year == end.year else '{0}-{1}'
+ line = 'Copyright ' + fmt.format(start.year, end.year) + ' ' + author
+ key = (start, author)
+ yield key, line
+ return map(itemgetter(1), sorted(f()))
+
+def fix_copyright(filename):
+ # Find copyright block in original file
+ prefix = set()
+ names = []
+ lines = []
+ with open(filename, 'r') as f:
+ content = list(f)
+ for i, line in enumerate(content[:15]):
+ m = re.match(r'^(?P<prefix>\W*)(\(c\))?\s*?copyright\s*(\(c\))?\s+\d{4}(\s*-\s*\d{4})?\s+(?P<name>.+?)\s*$', line, re.IGNORECASE)
+ if m:
+ d = m.groupdict()
+ prefix.add(d['prefix'])
+ lines.append(i)
+ names.append(d['name'].strip())
+ if len(prefix) != 1:
+ print 'Not found:', filename
+ return
+ prefix = list(prefix)[0]
+
+ print filename
+ new = iter(new_copyright(filename, names))
+ with open(filename, 'w') as f:
+ for i, line in enumerate(content):
+ if i in lines:
+ for repl in new:
+ print >>f, prefix + repl
+ else:
+ print >>f, line,
+ pass
+
+def all_files():
+ ls = run(['git', 'ls-files'], universal_newlines=True)
+ for filename in ls.splitlines():
+ if magic.from_file(filename, mime=True).split('/')[0] == 'text':
+ yield filename
+
+for f in all_files():
+ fix_copyright(f)
diff --git a/include/boost/numeric/odeint.hpp b/include/boost/numeric/odeint.hpp
new file mode 100644
index 0000000..e010089
--- /dev/null
+++ b/include/boost/numeric/odeint.hpp
@@ -0,0 +1,84 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint.hpp
+
+ [begin_description]
+ Forward include for odeint. Includes nearly everything.
+ [end_description]
+
+ Copyright 2009-2013 Karsten Ahnert
+ Copyright 2010-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_HPP_INCLUDED
+
+#include <boost/numeric/odeint/version.hpp>
+#include <boost/numeric/odeint/config.hpp>
+
+// start with ublas wrapper because we need its specializations before including state_wrapper.hpp
+#include <boost/numeric/odeint/util/ublas_wrapper.hpp>
+
+#include <boost/numeric/odeint/stepper/euler.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta4_classic.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta4.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54_classic.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_fehlberg78.hpp>
+
+#include <boost/numeric/odeint/stepper/controlled_runge_kutta.hpp>
+
+#include <boost/numeric/odeint/stepper/dense_output_runge_kutta.hpp>
+
+#include <boost/numeric/odeint/stepper/bulirsch_stoer.hpp>
+
+#ifndef __CUDACC__
+/* Bulirsch Stoer with Dense Output does not compile with nvcc
+ * because of the binomial library used there which relies on unsupported SSE functions
+ */
+#include <boost/numeric/odeint/stepper/bulirsch_stoer_dense_out.hpp>
+#endif
+
+#include <boost/numeric/odeint/stepper/symplectic_euler.hpp>
+#include <boost/numeric/odeint/stepper/symplectic_rkn_sb3a_mclachlan.hpp>
+#include <boost/numeric/odeint/stepper/velocity_verlet.hpp>
+
+#include <boost/numeric/odeint/stepper/adams_bashforth_moulton.hpp>
+
+#include <boost/numeric/odeint/stepper/implicit_euler.hpp>
+#include <boost/numeric/odeint/stepper/rosenbrock4.hpp>
+#include <boost/numeric/odeint/stepper/rosenbrock4_controller.hpp>
+#include <boost/numeric/odeint/stepper/rosenbrock4_dense_output.hpp>
+
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/algebra/multi_array_algebra.hpp>
+#include <boost/numeric/odeint/util/multi_array_adaption.hpp>
+/*
+ * Including this algebra slows down the compilation time
+ */
+// #include <boost/numeric/odeint/algebra/fusion_algebra.hpp>
+
+#include <boost/numeric/odeint/integrate/integrate.hpp>
+#include <boost/numeric/odeint/integrate/integrate_adaptive.hpp>
+#include <boost/numeric/odeint/integrate/integrate_const.hpp>
+#include <boost/numeric/odeint/integrate/integrate_n_steps.hpp>
+#include <boost/numeric/odeint/integrate/integrate_times.hpp>
+
+#include <boost/numeric/odeint/integrate/observer_collection.hpp>
+#include <boost/numeric/odeint/integrate/max_step_checker.hpp>
+
+#include <boost/numeric/odeint/stepper/generation.hpp>
+
+#include <boost/numeric/odeint/iterator/adaptive_iterator.hpp>
+#include <boost/numeric/odeint/iterator/adaptive_time_iterator.hpp>
+#include <boost/numeric/odeint/iterator/const_step_iterator.hpp>
+#include <boost/numeric/odeint/iterator/const_step_time_iterator.hpp>
+
+
+#endif // BOOST_NUMERIC_ODEINT_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/algebra/algebra_dispatcher.hpp b/include/boost/numeric/odeint/algebra/algebra_dispatcher.hpp
new file mode 100644
index 0000000..88cf159
--- /dev/null
+++ b/include/boost/numeric/odeint/algebra/algebra_dispatcher.hpp
@@ -0,0 +1,110 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/algebra/algebra_dispatcher.hpp
+
+ [begin_description]
+ Algebra dispatcher to automatically chose suitable algebra.
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#ifndef BOOST_NUMERIC_ODEINT_ALGEBRA_ALGEBRA_DISPATCHER_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_ALGEBRA_ALGEBRA_DISPATCHER_HPP_INCLUDED
+
+#include <boost/numeric/odeint/config.hpp>
+
+#include <complex>
+#include <boost/type_traits/is_floating_point.hpp>
+
+#include <boost/numeric/ublas/vector.hpp>
+#include <boost/numeric/ublas/matrix.hpp>
+
+#include <boost/numeric/odeint/algebra/range_algebra.hpp>
+#include <boost/numeric/odeint/algebra/array_algebra.hpp>
+#include <boost/numeric/odeint/algebra/vector_space_algebra.hpp>
+
+#include <boost/array.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template< class StateType , class Enabler = void >
+struct algebra_dispatcher_sfinae
+{
+ // range_algebra is the standard algebra
+ typedef range_algebra algebra_type;
+};
+
+template< class StateType >
+struct algebra_dispatcher : algebra_dispatcher_sfinae< StateType > { };
+
+// specialize for array
+template< class T , size_t N >
+struct algebra_dispatcher< boost::array< T , N > >
+{
+ typedef array_algebra algebra_type;
+};
+
+//specialize for some integral types
+template< typename T >
+struct algebra_dispatcher_sfinae< T , typename boost::enable_if< typename boost::is_floating_point< T >::type >::type >
+{
+ typedef vector_space_algebra algebra_type;
+};
+
+template< typename T >
+struct algebra_dispatcher< std::complex<T> >
+{
+ typedef vector_space_algebra algebra_type;
+};
+
+///* think about that again....
+// specialize for ublas vector and matrix types
+template< class T , class A >
+struct algebra_dispatcher< boost::numeric::ublas::vector< T , A > >
+{
+ typedef vector_space_algebra algebra_type;
+};
+
+template< class T , class L , class A >
+struct algebra_dispatcher< boost::numeric::ublas::matrix< T , L , A > >
+{
+ typedef vector_space_algebra algebra_type;
+};
+//*/
+
+}
+}
+}
+
+#ifdef BOOST_NUMERIC_ODEINT_CXX11
+
+// c++11 mode: specialization for std::array if available
+
+#include <array>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+// specialize for std::array
+template< class T , size_t N >
+struct algebra_dispatcher< std::array< T , N > >
+{
+ typedef array_algebra algebra_type;
+};
+
+} } }
+
+#endif
+
+
+#endif
diff --git a/include/boost/numeric/odeint/algebra/array_algebra.hpp b/include/boost/numeric/odeint/algebra/array_algebra.hpp
new file mode 100644
index 0000000..471e866
--- /dev/null
+++ b/include/boost/numeric/odeint/algebra/array_algebra.hpp
@@ -0,0 +1,293 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/algebra/array_algebra.hpp
+
+ [begin_description]
+ Algebra for Arrays. Highly specialized for odeint. Const arguments are
+ introduce to work with odeint.
+ The Array algebra can be used for Array structures with two template
+ parameters:
+ Array<T, N>
+ [end_description]
+
+ Copyright 2011-2013 Mario Mulansky
+ Copyright 2011-2012 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_ALGEBRA_ARRAY_ALGEBRA_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_ALGEBRA_ARRAY_ALGEBRA_HPP_INCLUDED
+
+#include <algorithm>
+#include <boost/array.hpp>
+
+#include <boost/numeric/odeint/algebra/norm_result_type.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+struct array_algebra
+{
+ //template< typename T , size_t dim , class Op >
+ template < template < typename, size_t > class Array, typename T,
+ size_t dim, class Op >
+ static void for_each1( Array< T, dim > &s1, Op op )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ op( s1[i] );
+ }
+
+ template < template < typename, size_t > class Array, typename T,
+ size_t dim, class Op >
+ static void for_each2( Array< T, dim > &s1, const Array< T, dim > &s2,
+ Op op )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ op( s1[i] , s2[i] );
+ }
+
+ template < template < typename, size_t > class Array, typename T,
+ size_t dim, class Op >
+ static void for_each3( Array< T , dim > &s1 ,
+ const Array< T , dim > &s2 ,
+ const Array< T , dim > &s3 , Op op )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ op( s1[i] , s2[i] , s3[i] );
+ }
+
+ /* different const signature - required for the scale_sum_swap2 operation */
+ template < template < typename, size_t > class Array, typename T,
+ size_t dim, class Op >
+ static void for_each3( Array< T , dim > &s1 ,
+ Array< T , dim > &s2 ,
+ const Array< T , dim > &s3 , Op op )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ op( s1[i] , s2[i] , s3[i] );
+ }
+
+ template < template < typename, size_t > class Array, typename T,
+ size_t dim, class Op >
+ static void for_each4( Array< T , dim > &s1 ,
+ const Array< T , dim > &s2 ,
+ const Array< T , dim > &s3 ,
+ const Array< T , dim > &s4 , Op op )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ op( s1[i] , s2[i] , s3[i] , s4[i] );
+ }
+
+ template < template < typename, size_t > class Array, typename T,
+ size_t dim, class Op >
+ static void for_each5( Array< T , dim > &s1 ,
+ const Array< T , dim > &s2 ,
+ const Array< T , dim > &s3 ,
+ const Array< T , dim > &s4 ,
+ const Array< T , dim > &s5 , Op op )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ op( s1[i] , s2[i] , s3[i] , s4[i] , s5[i] );
+ }
+
+ template < template < typename, size_t > class Array, typename T,
+ size_t dim, class Op >
+ static void for_each6( Array< T , dim > &s1 ,
+ const Array< T , dim > &s2 ,
+ const Array< T , dim > &s3 ,
+ const Array< T , dim > &s4 ,
+ const Array< T , dim > &s5 ,
+ const Array< T , dim > &s6 , Op op )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ op( s1[i] , s2[i] , s3[i] , s4[i] , s5[i] , s6[i] );
+ }
+
+ template < template < typename, size_t > class Array, typename T,
+ size_t dim, class Op >
+ static void for_each7( Array< T , dim > &s1 ,
+ const Array< T , dim > &s2 ,
+ const Array< T , dim > &s3 ,
+ const Array< T , dim > &s4 ,
+ const Array< T , dim > &s5 ,
+ const Array< T , dim > &s6 ,
+ const Array< T , dim > &s7 , Op op )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ op( s1[i] , s2[i] , s3[i] , s4[i] , s5[i] , s6[i] , s7[i] );
+ }
+
+ template < template < typename, size_t > class Array, typename T,
+ size_t dim, class Op >
+ static void for_each8( Array< T , dim > &s1 ,
+ const Array< T , dim > &s2 ,
+ const Array< T , dim > &s3 ,
+ const Array< T , dim > &s4 ,
+ const Array< T , dim > &s5 ,
+ const Array< T , dim > &s6 ,
+ const Array< T , dim > &s7 ,
+ const Array< T , dim > &s8 , Op op )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ op( s1[i] , s2[i] , s3[i] , s4[i] , s5[i] , s6[i] , s7[i] , s8[i] );
+ }
+
+ template < template < typename, size_t > class Array, typename T,
+ size_t dim, class Op >
+ static void for_each9( Array< T , dim > &s1 ,
+ const Array< T , dim > &s2 ,
+ const Array< T , dim > &s3 ,
+ const Array< T , dim > &s4 ,
+ const Array< T , dim > &s5 ,
+ const Array< T , dim > &s6 ,
+ const Array< T , dim > &s7 ,
+ const Array< T , dim > &s8 ,
+ const Array< T , dim > &s9 , Op op )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ op( s1[i] , s2[i] , s3[i] , s4[i] , s5[i] , s6[i] , s7[i] , s8[i] , s9[i] );
+ }
+
+ template < template < typename, size_t > class Array, typename T,
+ size_t dim, class Op >
+ static void for_each10( Array< T , dim > &s1 ,
+ const Array< T , dim > &s2 ,
+ const Array< T , dim > &s3 ,
+ const Array< T , dim > &s4 ,
+ const Array< T , dim > &s5 ,
+ const Array< T , dim > &s6 ,
+ const Array< T , dim > &s7 ,
+ const Array< T , dim > &s8 ,
+ const Array< T , dim > &s9 ,
+ const Array< T , dim > &s10 , Op op )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ op( s1[i] , s2[i] , s3[i] , s4[i] , s5[i] , s6[i] , s7[i] , s8[i] , s9[i] , s10[i] );
+ }
+
+ template < template < typename, size_t > class Array, typename T,
+ size_t dim, class Op >
+ static void for_each11( Array< T , dim > &s1 ,
+ const Array< T , dim > &s2 ,
+ const Array< T , dim > &s3 ,
+ const Array< T , dim > &s4 ,
+ const Array< T , dim > &s5 ,
+ const Array< T , dim > &s6 ,
+ const Array< T , dim > &s7 ,
+ const Array< T , dim > &s8 ,
+ const Array< T , dim > &s9 ,
+ const Array< T , dim > &s10 ,
+ const Array< T , dim > &s11 , Op op )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ op( s1[i] , s2[i] , s3[i] , s4[i] , s5[i] , s6[i] , s7[i] , s8[i] , s9[i] , s10[i] , s11[i] );
+ }
+
+ template < template < typename, size_t > class Array, typename T,
+ size_t dim, class Op >
+ static void for_each12( Array< T , dim > &s1 ,
+ const Array< T , dim > &s2 ,
+ const Array< T , dim > &s3 ,
+ const Array< T , dim > &s4 ,
+ const Array< T , dim > &s5 ,
+ const Array< T , dim > &s6 ,
+ const Array< T , dim > &s7 ,
+ const Array< T , dim > &s8 ,
+ const Array< T , dim > &s9 ,
+ const Array< T , dim > &s10 ,
+ const Array< T , dim > &s11 ,
+ const Array< T , dim > &s12 , Op op )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ op( s1[i] , s2[i] , s3[i] , s4[i] , s5[i] , s6[i] , s7[i] , s8[i] , s9[i] , s10[i] , s11[i] , s12[i] );
+ }
+
+ template < template < typename, size_t > class Array, typename T,
+ size_t dim, class Op >
+ static void for_each13( Array< T , dim > &s1 ,
+ const Array< T , dim > &s2 ,
+ const Array< T , dim > &s3 ,
+ const Array< T , dim > &s4 ,
+ const Array< T , dim > &s5 ,
+ const Array< T , dim > &s6 ,
+ const Array< T , dim > &s7 ,
+ const Array< T , dim > &s8 ,
+ const Array< T , dim > &s9 ,
+ const Array< T , dim > &s10 ,
+ const Array< T , dim > &s11 ,
+ const Array< T , dim > &s12 ,
+ const Array< T , dim > &s13 , Op op )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ op( s1[i] , s2[i] , s3[i] , s4[i] , s5[i] , s6[i] , s7[i] , s8[i] , s9[i] , s10[i] , s11[i] , s12[i] , s13[i] );
+ }
+
+ template < template < typename, size_t > class Array, typename T,
+ size_t dim, class Op >
+ static void for_each14( Array< T , dim > &s1 ,
+ const Array< T , dim > &s2 ,
+ const Array< T , dim > &s3 ,
+ const Array< T , dim > &s4 ,
+ const Array< T , dim > &s5 ,
+ const Array< T , dim > &s6 ,
+ const Array< T , dim > &s7 ,
+ const Array< T , dim > &s8 ,
+ const Array< T , dim > &s9 ,
+ const Array< T , dim > &s10 ,
+ const Array< T , dim > &s11 ,
+ const Array< T , dim > &s12 ,
+ const Array< T , dim > &s13 ,
+ const Array< T , dim > &s14 , Op op )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ op( s1[i] , s2[i] , s3[i] , s4[i] , s5[i] , s6[i] , s7[i] , s8[i] , s9[i] , s10[i] , s11[i] , s12[i] , s13[i] , s14[i] );
+ }
+
+ template < template < typename, size_t > class Array, typename T,
+ size_t dim, class Op >
+ static void for_each15( Array< T , dim > &s1 ,
+ const Array< T , dim > &s2 ,
+ const Array< T , dim > &s3 ,
+ const Array< T , dim > &s4 ,
+ const Array< T , dim > &s5 ,
+ const Array< T , dim > &s6 ,
+ const Array< T , dim > &s7 ,
+ const Array< T , dim > &s8 ,
+ const Array< T , dim > &s9 ,
+ const Array< T , dim > &s10 ,
+ const Array< T , dim > &s11 ,
+ const Array< T , dim > &s12 ,
+ const Array< T , dim > &s13 ,
+ const Array< T , dim > &s14 ,
+ const Array< T , dim > &s15 , Op op )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ op( s1[i] , s2[i] , s3[i] , s4[i] , s5[i] , s6[i] , s7[i] , s8[i] , s9[i] , s10[i] , s11[i] , s12[i] , s13[i] , s14[i] , s15[i] );
+ }
+
+
+ template < template < typename, size_t > class Array, typename T,
+ size_t dim>
+ static typename norm_result_type< Array< T , dim > >::type norm_inf( const Array< T , dim > &s )
+ {
+ BOOST_USING_STD_MAX();
+ using std::abs;
+ typedef typename norm_result_type< Array< T , dim > >::type result_type;
+ result_type init = static_cast< result_type >( 0 );
+ for( size_t i=0 ; i<dim ; ++i )
+ init = max BOOST_PREVENT_MACRO_SUBSTITUTION ( init , static_cast< result_type >(abs(s[i])) );
+ return init;
+ }
+
+};
+
+}
+}
+}
+
+#endif // BOOST_NUMERIC_ODEINT_ALGEBRA_ARRAY_ALGEBRA_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/algebra/default_operations.hpp b/include/boost/numeric/odeint/algebra/default_operations.hpp
new file mode 100644
index 0000000..5613908
--- /dev/null
+++ b/include/boost/numeric/odeint/algebra/default_operations.hpp
@@ -0,0 +1,599 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/algebra/default_operations.hpp
+
+ [begin_description]
+ Default operations. They work with the default numerical types, like float, double, complex< double> ...
+ [end_description]
+
+ Copyright 2010-2012 Karsten Ahnert
+ Copyright 2010-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_ALGEBRA_DEFAULT_OPERATIONS_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_ALGEBRA_DEFAULT_OPERATIONS_HPP_INCLUDED
+
+#include <algorithm>
+
+#include <boost/config.hpp>
+#include <boost/array.hpp>
+
+#include <boost/numeric/odeint/util/unit_helper.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+
+/*
+ * Notes:
+ *
+ * * the results structs are needed in order to work with fusion_algebra
+ */
+struct default_operations
+{
+
+ template< class Fac1 = double >
+ struct scale
+ {
+ const Fac1 m_alpha1;
+
+ scale( Fac1 alpha1 ) : m_alpha1( alpha1 ) { }
+
+ template< class T1 >
+ void operator()( T1 &t1 ) const
+ {
+ t1 *= m_alpha1;
+ }
+
+ typedef void result_type;
+ };
+
+ template< class Fac1 = double >
+ struct scale_sum1
+ {
+ const Fac1 m_alpha1;
+
+ scale_sum1( Fac1 alpha1 ) : m_alpha1( alpha1 ) { }
+
+ template< class T1 , class T2 >
+ void operator()( T1 &t1 , const T2 &t2 ) const
+ {
+ t1 = m_alpha1 * t2;
+ }
+
+ typedef void result_type;
+ };
+
+
+ template< class Fac1 = double , class Fac2 = Fac1 >
+ struct scale_sum2
+ {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+
+ scale_sum2( Fac1 alpha1 , Fac2 alpha2 ) : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) { }
+
+ template< class T1 , class T2 , class T3 >
+ void operator()( T1 &t1 , const T2 &t2 , const T3 &t3) const
+ {
+ t1 = m_alpha1 * t2 + m_alpha2 * t3;
+ }
+
+ typedef void result_type;
+ };
+
+
+ template< class Fac1 = double , class Fac2 = Fac1 , class Fac3 = Fac2 >
+ struct scale_sum3
+ {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+ const Fac3 m_alpha3;
+
+ scale_sum3( Fac1 alpha1 , Fac2 alpha2 , Fac3 alpha3 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) , m_alpha3( alpha3 ) { }
+
+ template< class T1 , class T2 , class T3 , class T4 >
+ void operator()( T1 &t1 , const T2 &t2 , const T3 &t3 , const T4 &t4 ) const
+ {
+ t1 = m_alpha1 * t2 + m_alpha2 * t3 + m_alpha3 * t4;
+ }
+
+ typedef void result_type;
+ };
+
+
+ template< class Fac1 = double , class Fac2 = Fac1 , class Fac3 = Fac2 , class Fac4 = Fac3 >
+ struct scale_sum4
+ {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+ const Fac3 m_alpha3;
+ const Fac4 m_alpha4;
+
+ scale_sum4( Fac1 alpha1 , Fac2 alpha2 , Fac3 alpha3 , Fac4 alpha4 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) , m_alpha3( alpha3 ) , m_alpha4( alpha4 ) { }
+
+ template< class T1 , class T2 , class T3 , class T4 , class T5 >
+ void operator()( T1 &t1 , const T2 &t2 , const T3 &t3 , const T4 &t4 , const T5 &t5) const
+ {
+ t1 = m_alpha1 * t2 + m_alpha2 * t3 + m_alpha3 * t4 + m_alpha4 * t5;
+ }
+
+ typedef void result_type;
+ };
+
+
+ template< class Fac1 = double , class Fac2 = Fac1 , class Fac3 = Fac2 , class Fac4 = Fac3 , class Fac5 = Fac4 >
+ struct scale_sum5
+ {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+ const Fac3 m_alpha3;
+ const Fac4 m_alpha4;
+ const Fac5 m_alpha5;
+
+ scale_sum5( Fac1 alpha1 , Fac2 alpha2 , Fac3 alpha3 , Fac4 alpha4 , Fac5 alpha5 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) , m_alpha3( alpha3 ) , m_alpha4( alpha4 ) , m_alpha5( alpha5 ) { }
+
+ template< class T1 , class T2 , class T3 , class T4 , class T5 , class T6 >
+ void operator()( T1 &t1 , const T2 &t2 , const T3 &t3 , const T4 &t4 , const T5 &t5 , const T6 &t6) const
+ {
+ t1 = m_alpha1 * t2 + m_alpha2 * t3 + m_alpha3 * t4 + m_alpha4 * t5 + m_alpha5 * t6;
+ }
+
+ typedef void result_type;
+ };
+
+
+ template< class Fac1 = double , class Fac2 = Fac1 , class Fac3 = Fac2 , class Fac4 = Fac3 , class Fac5 = Fac4 , class Fac6 = Fac5 >
+ struct scale_sum6
+ {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+ const Fac3 m_alpha3;
+ const Fac4 m_alpha4;
+ const Fac5 m_alpha5;
+ const Fac6 m_alpha6;
+
+ scale_sum6( Fac1 alpha1 , Fac2 alpha2 , Fac3 alpha3 , Fac4 alpha4 , Fac5 alpha5 , Fac6 alpha6 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) , m_alpha3( alpha3 ) , m_alpha4( alpha4 ) , m_alpha5( alpha5 ) , m_alpha6( alpha6 ){ }
+
+ template< class T1 , class T2 , class T3 , class T4 , class T5 , class T6 , class T7 >
+ void operator()( T1 &t1 , const T2 &t2 , const T3 &t3 , const T4 &t4 , const T5 &t5 , const T6 &t6 ,const T7 &t7) const
+ {
+ t1 = m_alpha1 * t2 + m_alpha2 * t3 + m_alpha3 * t4 + m_alpha4 * t5 + m_alpha5 * t6 + m_alpha6 * t7;
+ }
+
+ typedef void result_type;
+ };
+
+
+ template< class Fac1 = double , class Fac2 = Fac1 , class Fac3 = Fac2 , class Fac4 = Fac3 , class Fac5 = Fac4 , class Fac6 = Fac5 , class Fac7 = Fac6 >
+ struct scale_sum7
+ {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+ const Fac3 m_alpha3;
+ const Fac4 m_alpha4;
+ const Fac5 m_alpha5;
+ const Fac6 m_alpha6;
+ const Fac7 m_alpha7;
+
+ scale_sum7( Fac1 alpha1 , Fac2 alpha2 , Fac3 alpha3 , Fac4 alpha4 ,
+ Fac5 alpha5 , Fac6 alpha6 , Fac7 alpha7 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) , m_alpha3( alpha3 ) , m_alpha4( alpha4 ) , m_alpha5( alpha5 ) , m_alpha6( alpha6 ) , m_alpha7( alpha7 ) { }
+
+ template< class T1 , class T2 , class T3 , class T4 , class T5 , class T6 , class T7 , class T8 >
+ void operator()( T1 &t1 , const T2 &t2 , const T3 &t3 , const T4 &t4 , const T5 &t5 , const T6 &t6 , const T7 &t7 , const T8 &t8 ) const
+ {
+ t1 = m_alpha1 * t2 + m_alpha2 * t3 + m_alpha3 * t4 + m_alpha4 * t5 + m_alpha5 * t6 + m_alpha6 * t7 + m_alpha7 * t8;
+ }
+
+ typedef void result_type;
+ };
+
+
+ template< class Fac1 = double , class Fac2 = Fac1 , class Fac3 = Fac2 , class Fac4 = Fac3 , class Fac5 = Fac4 , class Fac6 = Fac5 , class Fac7 = Fac6 , class Fac8 = Fac7 >
+ struct scale_sum8
+ {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+ const Fac3 m_alpha3;
+ const Fac4 m_alpha4;
+ const Fac5 m_alpha5;
+ const Fac6 m_alpha6;
+ const Fac7 m_alpha7;
+ const Fac8 m_alpha8;
+
+ scale_sum8( Fac1 alpha1 , Fac2 alpha2 , Fac3 alpha3 , Fac4 alpha4 ,
+ Fac5 alpha5 , Fac6 alpha6 , Fac7 alpha7 , Fac8 alpha8 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) , m_alpha3( alpha3 ) , m_alpha4( alpha4 ) , m_alpha5( alpha5 ) , m_alpha6( alpha6 ) , m_alpha7( alpha7 ) , m_alpha8( alpha8 ) { }
+
+ template< class T1 , class T2 , class T3 , class T4 , class T5 , class T6 , class T7 , class T8 , class T9 >
+ void operator()( T1 &t1 , const T2 &t2 , const T3 &t3 , const T4 &t4 , const T5 &t5 , const T6 &t6 , const T7 &t7 , const T8 &t8 , const T9 &t9 ) const
+ {
+ t1 = m_alpha1 * t2 + m_alpha2 * t3 + m_alpha3 * t4 + m_alpha4 * t5 + m_alpha5 * t6 + m_alpha6 * t7 + m_alpha7 * t8 + m_alpha8 * t9;
+ }
+
+ typedef void result_type;
+ };
+
+ template< class Fac1 = double , class Fac2 = Fac1 , class Fac3 = Fac2 , class Fac4 = Fac3 , class Fac5 = Fac4 , class Fac6 = Fac5 , class Fac7 = Fac6 , class Fac8 = Fac7 , class Fac9 = Fac8 >
+ struct scale_sum9
+ {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+ const Fac3 m_alpha3;
+ const Fac4 m_alpha4;
+ const Fac5 m_alpha5;
+ const Fac6 m_alpha6;
+ const Fac7 m_alpha7;
+ const Fac8 m_alpha8;
+ const Fac9 m_alpha9;
+
+ scale_sum9( Fac1 alpha1 , Fac2 alpha2 , Fac3 alpha3 , Fac4 alpha4 ,
+ Fac5 alpha5 , Fac6 alpha6 , Fac7 alpha7 , Fac8 alpha8 , Fac9 alpha9 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) , m_alpha3( alpha3 ) , m_alpha4( alpha4 ) , m_alpha5( alpha5 ) , m_alpha6( alpha6 ) , m_alpha7( alpha7 ) , m_alpha8( alpha8 ) , m_alpha9( alpha9 ) { }
+
+ template< class T1 , class T2 , class T3 , class T4 , class T5 , class T6 , class T7 , class T8 , class T9 , class T10 >
+ void operator()( T1 &t1 , const T2 &t2 , const T3 &t3 , const T4 &t4 , const T5 &t5 , const T6 &t6 , const T7 &t7 , const T8 &t8 , const T9 &t9 , const T10 &t10 ) const
+ {
+ t1 = m_alpha1 * t2 + m_alpha2 * t3 + m_alpha3 * t4 + m_alpha4 * t5 + m_alpha5 * t6 + m_alpha6 * t7 + m_alpha7 * t8 + m_alpha8 * t9 + m_alpha9 * t10;
+ }
+
+ typedef void result_type;
+ };
+
+ template< class Fac1 = double , class Fac2 = Fac1 , class Fac3 = Fac2 , class Fac4 = Fac3 , class Fac5 = Fac4 , class Fac6 = Fac5 , class Fac7 = Fac6 , class Fac8 = Fac7 , class Fac9 = Fac8 , class Fac10 = Fac9 >
+ struct scale_sum10
+ {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+ const Fac3 m_alpha3;
+ const Fac4 m_alpha4;
+ const Fac5 m_alpha5;
+ const Fac6 m_alpha6;
+ const Fac7 m_alpha7;
+ const Fac8 m_alpha8;
+ const Fac9 m_alpha9;
+ const Fac10 m_alpha10;
+
+ scale_sum10( Fac1 alpha1 , Fac2 alpha2 , Fac3 alpha3 , Fac4 alpha4 ,
+ Fac5 alpha5 , Fac6 alpha6 , Fac7 alpha7 , Fac8 alpha8 , Fac9 alpha9 , Fac10 alpha10 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) , m_alpha3( alpha3 ) , m_alpha4( alpha4 ) , m_alpha5( alpha5 ) , m_alpha6( alpha6 ) , m_alpha7( alpha7 ) , m_alpha8( alpha8 ) , m_alpha9( alpha9 ) , m_alpha10( alpha10 ) { }
+
+ template< class T1 , class T2 , class T3 , class T4 , class T5 , class T6 , class T7 , class T8 , class T9 , class T10 , class T11 >
+ void operator()( T1 &t1 , const T2 &t2 , const T3 &t3 , const T4 &t4 , const T5 &t5 , const T6 &t6 , const T7 &t7 , const T8 &t8 , const T9 &t9 , const T10 &t10 , const T11 &t11 ) const
+ {
+ t1 = m_alpha1 * t2 + m_alpha2 * t3 + m_alpha3 * t4 + m_alpha4 * t5 + m_alpha5 * t6 + m_alpha6 * t7 + m_alpha7 * t8 + m_alpha8 * t9 + m_alpha9 * t10 + m_alpha10 * t11;
+ }
+
+ typedef void result_type;
+ };
+
+
+ template< class Fac1 = double , class Fac2 = Fac1 , class Fac3 = Fac2 , class Fac4 = Fac3 , class Fac5 = Fac4 , class Fac6 = Fac5 , class Fac7 = Fac6 , class Fac8 = Fac7 , class Fac9 = Fac8 , class Fac10 = Fac9 , class Fac11 = Fac10 >
+ struct scale_sum11
+ {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+ const Fac3 m_alpha3;
+ const Fac4 m_alpha4;
+ const Fac5 m_alpha5;
+ const Fac6 m_alpha6;
+ const Fac7 m_alpha7;
+ const Fac8 m_alpha8;
+ const Fac9 m_alpha9;
+ const Fac10 m_alpha10;
+ const Fac11 m_alpha11;
+
+ scale_sum11( Fac1 alpha1 , Fac2 alpha2 , Fac3 alpha3 , Fac4 alpha4 ,
+ Fac5 alpha5 , Fac6 alpha6 , Fac7 alpha7 , Fac8 alpha8 , Fac9 alpha9 ,
+ Fac10 alpha10 , Fac11 alpha11 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) , m_alpha3( alpha3 ) , m_alpha4( alpha4 ) , m_alpha5( alpha5 ) , m_alpha6( alpha6 ) , m_alpha7( alpha7 ) , m_alpha8( alpha8 ) , m_alpha9( alpha9 ) , m_alpha10( alpha10 ) , m_alpha11( alpha11 ) { }
+
+ template< class T1 , class T2 , class T3 , class T4 , class T5 , class T6 , class T7 , class T8 , class T9 , class T10 , class T11 , class T12 >
+ void operator()( T1 &t1 , const T2 &t2 , const T3 &t3 , const T4 &t4 , const T5 &t5 , const T6 &t6 , const T7 &t7 , const T8 &t8 , const T9 &t9 , const T10 &t10 , const T11 &t11 , const T12 &t12 ) const
+ {
+ t1 = m_alpha1 * t2 + m_alpha2 * t3 + m_alpha3 * t4 + m_alpha4 * t5 + m_alpha5 * t6 + m_alpha6 * t7 + m_alpha7 * t8 + m_alpha8 * t9 + m_alpha9 * t10 + m_alpha10 * t11 + m_alpha11 * t12;
+ }
+
+ typedef void result_type;
+ };
+
+ template< class Fac1 = double , class Fac2 = Fac1 , class Fac3 = Fac2 , class Fac4 = Fac3 , class Fac5 = Fac4 , class Fac6 = Fac5 , class Fac7 = Fac6 , class Fac8 = Fac7 , class Fac9 = Fac8 , class Fac10 = Fac9 , class Fac11 = Fac10 , class Fac12 = Fac11 >
+ struct scale_sum12
+ {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+ const Fac3 m_alpha3;
+ const Fac4 m_alpha4;
+ const Fac5 m_alpha5;
+ const Fac6 m_alpha6;
+ const Fac7 m_alpha7;
+ const Fac8 m_alpha8;
+ const Fac9 m_alpha9;
+ const Fac10 m_alpha10;
+ const Fac11 m_alpha11;
+ const Fac12 m_alpha12;
+
+ scale_sum12( Fac1 alpha1 , Fac2 alpha2 , Fac3 alpha3 , Fac4 alpha4 ,
+ Fac5 alpha5 , Fac6 alpha6 , Fac7 alpha7 , Fac8 alpha8 , Fac9 alpha9 ,
+ Fac10 alpha10 , Fac11 alpha11 , Fac12 alpha12 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) , m_alpha3( alpha3 ) , m_alpha4( alpha4 ) , m_alpha5( alpha5 ) , m_alpha6( alpha6 ) , m_alpha7( alpha7 ) , m_alpha8( alpha8 ) , m_alpha9( alpha9 ) , m_alpha10( alpha10 ) , m_alpha11( alpha11 ) , m_alpha12( alpha12 ) { }
+
+ template< class T1 , class T2 , class T3 , class T4 , class T5 , class T6 , class T7 , class T8 , class T9 , class T10 , class T11 , class T12 , class T13 >
+ void operator()( T1 &t1 , const T2 &t2 , const T3 &t3 , const T4 &t4 , const T5 &t5 , const T6 &t6 , const T7 &t7 , const T8 &t8 , const T9 &t9 , const T10 &t10 , const T11 &t11 , const T12 &t12 , const T13 &t13 ) const
+ {
+ t1 = m_alpha1 * t2 + m_alpha2 * t3 + m_alpha3 * t4 + m_alpha4 * t5 + m_alpha5 * t6 + m_alpha6 * t7 + m_alpha7 * t8 + m_alpha8 * t9 + m_alpha9 * t10 + m_alpha10 * t11 + m_alpha11 * t12 + m_alpha12 * t13;
+ }
+
+ typedef void result_type;
+ };
+
+ template< class Fac1 = double , class Fac2 = Fac1 , class Fac3 = Fac2 , class Fac4 = Fac3 , class Fac5 = Fac4 , class Fac6 = Fac5 , class Fac7 = Fac6 , class Fac8 = Fac7 , class Fac9 = Fac8 , class Fac10 = Fac9 , class Fac11 = Fac10 , class Fac12 = Fac11 , class Fac13 = Fac12 >
+ struct scale_sum13
+ {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+ const Fac3 m_alpha3;
+ const Fac4 m_alpha4;
+ const Fac5 m_alpha5;
+ const Fac6 m_alpha6;
+ const Fac7 m_alpha7;
+ const Fac8 m_alpha8;
+ const Fac9 m_alpha9;
+ const Fac10 m_alpha10;
+ const Fac11 m_alpha11;
+ const Fac12 m_alpha12;
+ const Fac13 m_alpha13;
+
+ scale_sum13( Fac1 alpha1 , Fac2 alpha2 , Fac3 alpha3 , Fac4 alpha4 ,
+ Fac5 alpha5 , Fac6 alpha6 , Fac7 alpha7 , Fac8 alpha8 , Fac9 alpha9 ,
+ Fac10 alpha10 , Fac11 alpha11 , Fac12 alpha12 , Fac13 alpha13 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) , m_alpha3( alpha3 ) , m_alpha4( alpha4 ) , m_alpha5( alpha5 ) , m_alpha6( alpha6 ) , m_alpha7( alpha7 ) , m_alpha8( alpha8 ) , m_alpha9( alpha9 ) , m_alpha10( alpha10 ) , m_alpha11( alpha11 ) , m_alpha12( alpha12 ) , m_alpha13( alpha13 ) { }
+
+ template< class T1 , class T2 , class T3 , class T4 , class T5 , class T6 , class T7 , class T8 , class T9 , class T10 , class T11 , class T12 , class T13 , class T14 >
+ void operator()( T1 &t1 , const T2 &t2 , const T3 &t3 , const T4 &t4 , const T5 &t5 , const T6 &t6 , const T7 &t7 , const T8 &t8 , const T9 &t9 , const T10 &t10 , const T11 &t11 , const T12 &t12 , const T13 &t13 , const T14 &t14 ) const
+ {
+ t1 = m_alpha1 * t2 + m_alpha2 * t3 + m_alpha3 * t4 + m_alpha4 * t5 + m_alpha5 * t6 + m_alpha6 * t7 + m_alpha7 * t8 + m_alpha8 * t9 + m_alpha9 * t10 + m_alpha10 * t11 + m_alpha11 * t12 + m_alpha12 * t13 + m_alpha13 * t14;
+ }
+
+ typedef void result_type;
+ };
+
+ template< class Fac1 = double , class Fac2 = Fac1 , class Fac3 = Fac2 , class Fac4 = Fac3 , class Fac5 = Fac4 , class Fac6 = Fac5 , class Fac7 = Fac6 , class Fac8 = Fac7 , class Fac9 = Fac8 , class Fac10 = Fac9 , class Fac11 = Fac10 , class Fac12 = Fac11 , class Fac13 = Fac12 , class Fac14 = Fac13 >
+ struct scale_sum14
+ {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+ const Fac3 m_alpha3;
+ const Fac4 m_alpha4;
+ const Fac5 m_alpha5;
+ const Fac6 m_alpha6;
+ const Fac7 m_alpha7;
+ const Fac8 m_alpha8;
+ const Fac9 m_alpha9;
+ const Fac10 m_alpha10;
+ const Fac11 m_alpha11;
+ const Fac12 m_alpha12;
+ const Fac13 m_alpha13;
+ const Fac14 m_alpha14;
+
+ scale_sum14( Fac1 alpha1 , Fac2 alpha2 , Fac3 alpha3 , Fac4 alpha4 ,
+ Fac5 alpha5 , Fac6 alpha6 , Fac7 alpha7 , Fac8 alpha8 , Fac9 alpha9 ,
+ Fac10 alpha10 , Fac11 alpha11 , Fac12 alpha12 , Fac13 alpha13 , Fac14 alpha14 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) , m_alpha3( alpha3 ) , m_alpha4( alpha4 ) , m_alpha5( alpha5 ) , m_alpha6( alpha6 ) , m_alpha7( alpha7 ) , m_alpha8( alpha8 ) , m_alpha9( alpha9 ) , m_alpha10( alpha10 ) , m_alpha11( alpha11 ) , m_alpha12( alpha12 ) , m_alpha13( alpha13 ) , m_alpha14( alpha14 ) { }
+
+ template< class T1 , class T2 , class T3 , class T4 , class T5 , class T6 , class T7 , class T8 , class T9 , class T10 , class T11 , class T12 , class T13 , class T14 , class T15 >
+ void operator()( T1 &t1 , const T2 &t2 , const T3 &t3 , const T4 &t4 , const T5 &t5 , const T6 &t6 , const T7 &t7 , const T8 &t8 , const T9 &t9 , const T10 &t10 , const T11 &t11 , const T12 &t12 , const T13 &t13 , const T14 &t14 , const T15 &t15 ) const
+ {
+ t1 = m_alpha1 * t2 + m_alpha2 * t3 + m_alpha3 * t4 + m_alpha4 * t5 + m_alpha5 * t6 + m_alpha6 * t7 + m_alpha7 * t8 + m_alpha8 * t9 + m_alpha9 * t10 + m_alpha10 * t11 + m_alpha11 * t12 + m_alpha12 * t13 + m_alpha13 * t14 + m_alpha14 * t15;
+ }
+
+ typedef void result_type;
+ };
+
+ template< class Fac1 = double , class Fac2 = Fac1 >
+ struct scale_sum_swap2
+ {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+
+ scale_sum_swap2( Fac1 alpha1 , Fac2 alpha2 ) : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) { }
+
+ template< class T1 , class T2 , class T3 >
+ void operator()( T1 &t1 , T2 &t2 , const T3 &t3) const
+ {
+ const T1 tmp( t1 );
+ t1 = m_alpha1 * t2 + m_alpha2 * t3;
+ t2 = tmp;
+ }
+
+ typedef void result_type;
+ };
+
+ /*
+ * for usage in for_each2
+ *
+ * Works with boost::units by eliminating the unit
+ */
+ template< class Fac1 = double >
+ struct rel_error
+ {
+ const Fac1 m_eps_abs , m_eps_rel , m_a_x , m_a_dxdt;
+
+ rel_error( Fac1 eps_abs , Fac1 eps_rel , Fac1 a_x , Fac1 a_dxdt )
+ : m_eps_abs( eps_abs ) , m_eps_rel( eps_rel ) , m_a_x( a_x ) , m_a_dxdt( a_dxdt ) { }
+
+
+ template< class T1 , class T2 , class T3 >
+ void operator()( T3 &t3 , const T1 &t1 , const T2 &t2 ) const
+ {
+ using std::abs;
+ set_unit_value( t3 , abs( get_unit_value( t3 ) ) / ( m_eps_abs + m_eps_rel * ( m_a_x * abs( get_unit_value( t1 ) ) + m_a_dxdt * abs( get_unit_value( t2 ) ) ) ) );
+ }
+
+ typedef void result_type;
+ };
+
+
+ /*
+ * for usage in for_each3
+ *
+ * used in the controller for the rosenbrock4 method
+ *
+ * Works with boost::units by eliminating the unit
+ */
+ template< class Fac1 = double >
+ struct default_rel_error
+ {
+ const Fac1 m_eps_abs , m_eps_rel ;
+
+ default_rel_error( Fac1 eps_abs , Fac1 eps_rel )
+ : m_eps_abs( eps_abs ) , m_eps_rel( eps_rel ) { }
+
+
+ /*
+ * xerr = xerr / ( eps_abs + eps_rel * max( x , x_old ) )
+ */
+ template< class T1 , class T2 , class T3 >
+ void operator()( T3 &t3 , const T1 &t1 , const T2 &t2 ) const
+ {
+ BOOST_USING_STD_MAX();
+ using std::abs;
+ Fac1 x1 = abs( get_unit_value( t1 ) ) , x2 = abs( get_unit_value( t2 ) );
+ set_unit_value( t3 , abs( get_unit_value( t3 ) ) / ( m_eps_abs + m_eps_rel * max BOOST_PREVENT_MACRO_SUBSTITUTION ( x1 , x2 ) ) );
+ }
+
+ typedef void result_type;
+ };
+
+
+
+ /*
+ * for usage in reduce
+ */
+
+ template< class Value >
+ struct maximum
+ {
+ template< class Fac1 , class Fac2 >
+ Value operator()( Fac1 t1 , const Fac2 t2 ) const
+ {
+ using std::abs;
+ Value a1 = abs( get_unit_value( t1 ) ) , a2 = abs( get_unit_value( t2 ) );
+ return ( a1 < a2 ) ? a2 : a1 ;
+ }
+
+ typedef Value result_type;
+ };
+
+
+ template< class Fac1 = double >
+ struct rel_error_max
+ {
+ const Fac1 m_eps_abs , m_eps_rel;
+
+ rel_error_max( Fac1 eps_abs , Fac1 eps_rel )
+ : m_eps_abs( eps_abs ) , m_eps_rel( eps_rel )
+ { }
+
+ template< class Res , class T1 , class T2 , class T3 >
+ Res operator()( Res r , const T1 &x_old , const T2 &x , const T3 &x_err )
+ {
+ BOOST_USING_STD_MAX();
+ using std::abs;
+ Res tmp = abs( get_unit_value( x_err ) ) / ( m_eps_abs + m_eps_rel * max BOOST_PREVENT_MACRO_SUBSTITUTION ( abs( x_old ) , abs( x ) ) );
+ return max BOOST_PREVENT_MACRO_SUBSTITUTION ( r , tmp );
+ }
+ };
+
+
+ template< class Fac1 = double >
+ struct rel_error_max2
+ {
+ const Fac1 m_eps_abs , m_eps_rel , m_a_x , m_a_dxdt;
+
+ rel_error_max2( Fac1 eps_abs , Fac1 eps_rel , Fac1 a_x , Fac1 a_dxdt )
+ : m_eps_abs( eps_abs ) , m_eps_rel( eps_rel ) , m_a_x( a_x ) , m_a_dxdt( a_dxdt )
+ { }
+
+ template< class Res , class T1 , class T2 , class T3 , class T4 >
+ Res operator()( Res r , const T1 &x_old , const T2 &/*x*/ , const T3 &dxdt_old , const T4 &x_err )
+ {
+ BOOST_USING_STD_MAX();
+ using std::abs;
+ Res tmp = abs( get_unit_value( x_err ) ) /
+ ( m_eps_abs + m_eps_rel * ( m_a_x * abs( get_unit_value( x_old ) ) + m_a_dxdt * abs( get_unit_value( dxdt_old ) ) ) );
+ return max BOOST_PREVENT_MACRO_SUBSTITUTION ( r , tmp );
+ }
+ };
+
+
+
+
+ template< class Fac1 = double >
+ struct rel_error_l2
+ {
+ const Fac1 m_eps_abs , m_eps_rel;
+
+ rel_error_l2( Fac1 eps_abs , Fac1 eps_rel )
+ : m_eps_abs( eps_abs ) , m_eps_rel( eps_rel )
+ { }
+
+ template< class Res , class T1 , class T2 , class T3 >
+ Res operator()( Res r , const T1 &x_old , const T2 &x , const T3 &x_err )
+ {
+ BOOST_USING_STD_MAX();
+ using std::abs;
+ Res tmp = abs( get_unit_value( x_err ) ) / ( m_eps_abs + m_eps_rel * max BOOST_PREVENT_MACRO_SUBSTITUTION ( abs( x_old ) , abs( x ) ) );
+ return r + tmp * tmp;
+ }
+ };
+
+
+
+
+ template< class Fac1 = double >
+ struct rel_error_l2_2
+ {
+ const Fac1 m_eps_abs , m_eps_rel , m_a_x , m_a_dxdt;
+
+ rel_error_l2_2( Fac1 eps_abs , Fac1 eps_rel , Fac1 a_x , Fac1 a_dxdt )
+ : m_eps_abs( eps_abs ) , m_eps_rel( eps_rel ) , m_a_x( a_x ) , m_a_dxdt( a_dxdt )
+ { }
+
+ template< class Res , class T1 , class T2 , class T3 , class T4 >
+ Res operator()( Res r , const T1 &x_old , const T2 &/*x*/ , const T3 &dxdt_old , const T4 &x_err )
+ {
+ using std::abs;
+ Res tmp = abs( get_unit_value( x_err ) ) /
+ ( m_eps_abs + m_eps_rel * ( m_a_x * abs( get_unit_value( x_old ) ) + m_a_dxdt * abs( get_unit_value( dxdt_old ) ) ) );
+ return r + tmp * tmp;
+ }
+ };
+
+
+
+
+
+
+};
+
+
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_ALGEBRA_DEFAULT_OPERATIONS_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/algebra/detail/extract_value_type.hpp b/include/boost/numeric/odeint/algebra/detail/extract_value_type.hpp
new file mode 100644
index 0000000..c5246bb
--- /dev/null
+++ b/include/boost/numeric/odeint/algebra/detail/extract_value_type.hpp
@@ -0,0 +1,52 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/algebra/detail/extract_value_type.hpp
+
+ [begin_description]
+ Extract true value type from complex types (eg. std::complex)
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#ifndef BOOST_NUMERIC_ODEINT_ALGEBRA_DETAIL_EXTRACT_VALUE_TYPE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_ALGEBRA_DETAIL_EXTRACT_VALUE_TYPE_HPP_INCLUDED
+
+#include <boost/utility.hpp>
+#include <boost/mpl/has_xxx.hpp>
+
+BOOST_MPL_HAS_XXX_TRAIT_DEF(value_type)
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+template< typename S , typename Enabler = void >
+struct extract_value_type {};
+
+// as long as value_types are defined we go down the value_type chain
+// e.g. returning S::value_type::value_type::value_type
+
+template< typename S >
+struct extract_value_type<S , typename boost::disable_if< has_value_type<S> >::type >
+{
+ // no value_type defined, return S
+ typedef S type;
+};
+
+template< typename S >
+struct extract_value_type< S , typename boost::enable_if< has_value_type<S> >::type >
+{
+ // go down the value_type
+ typedef typename extract_value_type< typename S::value_type >::type type;
+};
+
+} } } }
+
+#endif
diff --git a/include/boost/numeric/odeint/algebra/detail/for_each.hpp b/include/boost/numeric/odeint/algebra/detail/for_each.hpp
new file mode 100644
index 0000000..5387a47
--- /dev/null
+++ b/include/boost/numeric/odeint/algebra/detail/for_each.hpp
@@ -0,0 +1,165 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/algebra/detail/for_each.hpp
+
+ [begin_description]
+ Default for_each implementations.
+ [end_description]
+
+ Copyright 2010-2012 Karsten Ahnert
+ Copyright 2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_ALGEBRA_DETAIL_FOR_EACH_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_ALGEBRA_DETAIL_FOR_EACH_HPP_INCLUDED
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+
+ template< class Iterator1 , class Operation >
+ inline void for_each1( Iterator1 first1 , Iterator1 last1 , Operation op )
+ {
+ for( ; first1 != last1 ; )
+ op( *first1++ );
+ }
+
+
+ template< class Iterator1 , class Iterator2 , class Operation >
+ inline void for_each2( Iterator1 first1 , Iterator1 last1 , Iterator2 first2 , Operation op )
+ {
+ for( ; first1 != last1 ; )
+ op( *first1++ , *first2++ );
+ }
+
+
+ template< class Iterator1 , class Iterator2 , class Iterator3 , class Operation >
+ inline void for_each3( Iterator1 first1 , Iterator1 last1 , Iterator2 first2 , Iterator3 first3, Operation op )
+ {
+ for( ; first1 != last1 ; )
+ op( *first1++ , *first2++ , *first3++ );
+ }
+
+
+ template< class Iterator1 , class Iterator2 , class Iterator3 , class Iterator4 , class Operation >
+ inline void for_each4( Iterator1 first1 , Iterator1 last1 , Iterator2 first2 , Iterator3 first3, Iterator4 first4, Operation op )
+ {
+ for( ; first1 != last1 ; )
+ op( *first1++ , *first2++ , *first3++ , *first4++ );
+ }
+
+
+ template< class Iterator1 , class Iterator2 , class Iterator3 , class Iterator4 , class Iterator5 , class Operation >
+ inline void for_each5( Iterator1 first1 , Iterator1 last1 , Iterator2 first2 , Iterator3 first3,
+ Iterator4 first4, Iterator5 first5, Operation op )
+ {
+ for( ; first1 != last1 ; )
+ op( *first1++ , *first2++ , *first3++ , *first4++ , *first5++ );
+ }
+
+
+ template< class Iterator1 , class Iterator2 , class Iterator3 , class Iterator4 , class Iterator5 , class Iterator6 , class Operation >
+ inline void for_each6( Iterator1 first1 , Iterator1 last1 , Iterator2 first2 , Iterator3 first3,
+ Iterator4 first4, Iterator5 first5, Iterator6 first6 , Operation op )
+ {
+ for( ; first1 != last1 ; )
+ op( *first1++ , *first2++ , *first3++ , *first4++ , *first5++ , *first6++ );
+ }
+
+
+ template< class Iterator1 , class Iterator2 , class Iterator3 , class Iterator4 , class Iterator5 , class Iterator6 , class Iterator7 , class Operation >
+ inline void for_each7( Iterator1 first1 , Iterator1 last1 , Iterator2 first2 , Iterator3 first3,
+ Iterator4 first4, Iterator5 first5, Iterator6 first6 , Iterator7 first7 , Operation op )
+ {
+ for( ; first1 != last1 ; )
+ op( *first1++ , *first2++ , *first3++ , *first4++ , *first5++ , *first6++ , *first7++ );
+ }
+
+ template< class Iterator1 , class Iterator2 , class Iterator3 , class Iterator4 , class Iterator5 , class Iterator6 , class Iterator7 , class Iterator8 , class Operation >
+ inline void for_each8( Iterator1 first1 , Iterator1 last1 , Iterator2 first2 , Iterator3 first3,
+ Iterator4 first4, Iterator5 first5, Iterator6 first6 , Iterator7 first7 , Iterator8 first8 , Operation op )
+ {
+ for( ; first1 != last1 ; )
+ op( *first1++ , *first2++ , *first3++ , *first4++ , *first5++ , *first6++ , *first7++ , *first8++ );
+ }
+
+ template< class Iterator1 , class Iterator2 , class Iterator3 , class Iterator4 , class Iterator5 , class Iterator6 , class Iterator7 , class Iterator8 , class Iterator9 , class Operation >
+ inline void for_each9( Iterator1 first1 , Iterator1 last1 , Iterator2 first2 , Iterator3 first3,
+ Iterator4 first4, Iterator5 first5, Iterator6 first6 , Iterator7 first7 , Iterator8 first8 ,
+ Iterator9 first9 , Operation op )
+ {
+ for( ; first1 != last1 ; )
+ op( *first1++ , *first2++ , *first3++ , *first4++ , *first5++ , *first6++ , *first7++ , *first8++ , *first9++ );
+ }
+
+ template< class Iterator1 , class Iterator2 , class Iterator3 , class Iterator4 , class Iterator5 , class Iterator6 , class Iterator7 , class Iterator8 , class Iterator9 , class Iterator10 , class Operation >
+ inline void for_each10( Iterator1 first1 , Iterator1 last1 , Iterator2 first2 , Iterator3 first3,
+ Iterator4 first4, Iterator5 first5, Iterator6 first6 , Iterator7 first7 , Iterator8 first8 ,
+ Iterator9 first9 , Iterator10 first10 , Operation op )
+ {
+ for( ; first1 != last1 ; )
+ op( *first1++ , *first2++ , *first3++ , *first4++ , *first5++ , *first6++ , *first7++ , *first8++ , *first9++ , *first10++ );
+ }
+
+ template< class Iterator1 , class Iterator2 , class Iterator3 , class Iterator4 , class Iterator5 , class Iterator6 , class Iterator7 , class Iterator8 , class Iterator9 , class Iterator10 , class Iterator11 , class Operation >
+ inline void for_each11( Iterator1 first1 , Iterator1 last1 , Iterator2 first2 , Iterator3 first3,
+ Iterator4 first4, Iterator5 first5, Iterator6 first6 , Iterator7 first7 , Iterator8 first8 ,
+ Iterator9 first9 , Iterator10 first10 , Iterator11 first11 , Operation op )
+ {
+ for( ; first1 != last1 ; )
+ op( *first1++ , *first2++ , *first3++ , *first4++ , *first5++ , *first6++ , *first7++ , *first8++ , *first9++ , *first10++ , *first11++ );
+ }
+
+ template< class Iterator1 , class Iterator2 , class Iterator3 , class Iterator4 , class Iterator5 , class Iterator6 , class Iterator7 , class Iterator8 , class Iterator9 , class Iterator10 , class Iterator11 , class Iterator12 , class Operation >
+ inline void for_each12( Iterator1 first1 , Iterator1 last1 , Iterator2 first2 , Iterator3 first3,
+ Iterator4 first4, Iterator5 first5, Iterator6 first6 , Iterator7 first7 , Iterator8 first8 ,
+ Iterator9 first9 , Iterator10 first10 , Iterator11 first11 , Iterator12 first12 , Operation op )
+ {
+ for( ; first1 != last1 ; )
+ op( *first1++ , *first2++ , *first3++ , *first4++ , *first5++ , *first6++ , *first7++ , *first8++ , *first9++ , *first10++ , *first11++ , *first12++ );
+ }
+
+ template< class Iterator1 , class Iterator2 , class Iterator3 , class Iterator4 , class Iterator5 , class Iterator6 , class Iterator7 , class Iterator8 , class Iterator9 , class Iterator10 , class Iterator11 , class Iterator12 , class Iterator13 , class Operation >
+ inline void for_each13( Iterator1 first1 , Iterator1 last1 , Iterator2 first2 , Iterator3 first3,
+ Iterator4 first4, Iterator5 first5, Iterator6 first6 , Iterator7 first7 , Iterator8 first8 ,
+ Iterator9 first9 , Iterator10 first10 , Iterator11 first11 , Iterator12 first12 , Iterator13 first13 , Operation op )
+ {
+ for( ; first1 != last1 ; )
+ op( *first1++ , *first2++ , *first3++ , *first4++ , *first5++ , *first6++ , *first7++ , *first8++ , *first9++ , *first10++ , *first11++ , *first12++ , *first13++ );
+ }
+
+ template< class Iterator1 , class Iterator2 , class Iterator3 , class Iterator4 , class Iterator5 , class Iterator6 , class Iterator7 , class Iterator8 , class Iterator9 , class Iterator10 , class Iterator11 , class Iterator12 , class Iterator13 , class Iterator14 , class Operation >
+ inline void for_each14( Iterator1 first1 , Iterator1 last1 , Iterator2 first2 , Iterator3 first3,
+ Iterator4 first4, Iterator5 first5, Iterator6 first6 , Iterator7 first7 , Iterator8 first8 ,
+ Iterator9 first9 , Iterator10 first10 , Iterator11 first11 , Iterator12 first12 , Iterator13 first13 ,
+ Iterator14 first14 , Operation op )
+ {
+ for( ; first1 != last1 ; )
+ op( *first1++ , *first2++ , *first3++ , *first4++ , *first5++ , *first6++ , *first7++ , *first8++ , *first9++ , *first10++ , *first11++ , *first12++ , *first13++ , *first14++ );
+ }
+
+ template< class Iterator1 , class Iterator2 , class Iterator3 , class Iterator4 , class Iterator5 , class Iterator6 , class Iterator7 , class Iterator8 , class Iterator9 , class Iterator10 , class Iterator11 , class Iterator12 , class Iterator13 , class Iterator14 , class Iterator15 , class Operation >
+ inline void for_each15( Iterator1 first1 , Iterator1 last1 , Iterator2 first2 , Iterator3 first3,
+ Iterator4 first4, Iterator5 first5, Iterator6 first6 , Iterator7 first7 , Iterator8 first8 ,
+ Iterator9 first9 , Iterator10 first10 , Iterator11 first11 , Iterator12 first12 , Iterator13 first13 ,
+ Iterator14 first14 , Iterator15 first15 , Operation op )
+ {
+ for( ; first1 != last1 ; )
+ op( *first1++ , *first2++ , *first3++ , *first4++ , *first5++ , *first6++ , *first7++ , *first8++ , *first9++ , *first10++ , *first11++ , *first12++ , *first13++ , *first14++ , *first15++ );
+ }
+
+
+} // detail
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_ALGEBRA_DETAIL_FOR_EACH_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/algebra/detail/macros.hpp b/include/boost/numeric/odeint/algebra/detail/macros.hpp
new file mode 100644
index 0000000..9e18a8a
--- /dev/null
+++ b/include/boost/numeric/odeint/algebra/detail/macros.hpp
@@ -0,0 +1,43 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/algebra/detail/macros.hpp
+
+ [begin_description]
+ Some macros for type checking.
+ [end_description]
+
+ Copyright 2010-2012 Karsten Ahnert
+ Copyright 2010 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_ALGEBRA_DETAIL_MACROS_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_ALGEBRA_DETAIL_MACROS_HPP_INCLUDED
+
+
+//type traits aren't working with nvcc
+#ifndef __CUDACC__
+#include <boost/type_traits.hpp>
+#include <boost/static_assert.hpp>
+
+#define BOOST_ODEINT_CHECK_CONTAINER_TYPE( Type1 , Type2 ) \
+ BOOST_STATIC_ASSERT(( boost::is_same< typename boost::remove_const< Type1 >::type , Type2 >::value ))
+
+#else
+//empty macro for nvcc
+#define BOOST_ODEINT_CHECK_CONTAINER_TYPE( Type1 , Type2 )
+
+#endif // __CUDACC__
+
+
+
+/*
+#define BOOST_ODEINT_CHECK_OPERATION_ARITY( Operation , Arity ) \
+ BOOST_STATIC_ASSERT(( boost::function_traits< Operation >::arity == Arity ))
+ */
+
+#endif // BOOST_NUMERIC_ODEINT_ALGEBRA_DETAIL_MACROS_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/algebra/detail/norm_inf.hpp b/include/boost/numeric/odeint/algebra/detail/norm_inf.hpp
new file mode 100644
index 0000000..3d32c99
--- /dev/null
+++ b/include/boost/numeric/odeint/algebra/detail/norm_inf.hpp
@@ -0,0 +1,45 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/algebra/detail/norm_inf.hpp
+
+ [begin_description]
+ Default reduce implementation.
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_ALGEBRA_DETAIL_NORM_INF_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_ALGEBRA_DETAIL_NORM_INF_HPP_INCLUDED
+
+#include <cmath>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+template< typename Value , class Iterator1 >
+inline Value norm_inf( Iterator1 first1 , Iterator1 last1 , Value init )
+{
+ using std::max;
+ using std::abs;
+ for( ; first1 != last1 ; )
+ init = max( init , abs( *first1++ ) );
+ return init;
+}
+
+
+} // detail
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_ALGEBRA_DETAIL_NORM_INF_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/algebra/fusion_algebra.hpp b/include/boost/numeric/odeint/algebra/fusion_algebra.hpp
new file mode 100644
index 0000000..0055e5d
--- /dev/null
+++ b/include/boost/numeric/odeint/algebra/fusion_algebra.hpp
@@ -0,0 +1,216 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/algebra/fusion_algebra.hpp
+
+ [begin_description]
+ Algebra for boost::fusion sequences.
+ [end_description]
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_ALGEBRA_FUSION_ALGEBRA_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_ALGEBRA_FUSION_ALGEBRA_HPP_INCLUDED
+
+#include <algorithm>
+
+#include <boost/numeric/odeint/config.hpp>
+
+#include <boost/fusion/container/vector.hpp>
+#include <boost/fusion/algorithm/iteration/for_each.hpp>
+#include <boost/fusion/view/zip_view.hpp>
+#include <boost/fusion/functional/generation/make_fused.hpp>
+#include <boost/fusion/algorithm/iteration/accumulate.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+namespace detail {
+
+ template< class Value >
+ struct fusion_maximum
+ {
+ template< class Fac1 , class Fac2 >
+ Value operator()( Fac1 t1 , const Fac2 t2 ) const
+ {
+ using std::abs;
+ Value a1 = abs( get_unit_value( t1 ) ) , a2 = abs( get_unit_value( t2 ) );
+ return ( a1 < a2 ) ? a2 : a1 ;
+ }
+
+ typedef Value result_type;
+ };
+}
+
+/* specialize this if the fundamental numeric type in your fusion sequence is
+ * anything else but double (most likely not)
+ */
+template< typename Sequence >
+struct fusion_traits {
+ typedef double value_type;
+};
+
+struct fusion_algebra
+{
+ template< class S1 , class Op >
+ static void for_each1( S1 &s1 , Op op )
+ {
+ boost::fusion::for_each( s1 , op );
+ };
+
+
+ template< class S1 , class S2 , class Op >
+ static void for_each2( S1 &s1 , S2 &s2 , Op op )
+ {
+ typedef boost::fusion::vector< S1& , S2& > Sequences;
+ Sequences sequences( s1 , s2 );
+ boost::fusion::for_each( boost::fusion::zip_view< Sequences >( sequences ) , boost::fusion::make_fused( op ) );
+ }
+
+
+ template< class S1 , class S2 , class S3 , class Op >
+ static void for_each3( S1 &s1 , S2 &s2 , S3 &s3 , Op op )
+ {
+ typedef boost::fusion::vector< S1& , S2& , S3& > Sequences;
+ Sequences sequences( s1 , s2 , s3 );
+ boost::fusion::for_each( boost::fusion::zip_view< Sequences >( sequences ) , boost::fusion::make_fused( op ) );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class Op >
+ static void for_each4( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , Op op )
+ {
+ typedef boost::fusion::vector< S1& , S2& , S3& , S4& > Sequences;
+ Sequences sequences( s1 , s2 , s3 , s4 );
+ boost::fusion::for_each( boost::fusion::zip_view< Sequences >( sequences ) , boost::fusion::make_fused( op ) );
+ }
+
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class Op >
+ static void for_each5( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , Op op )
+ {
+ typedef boost::fusion::vector< S1& , S2& , S3& , S4& , S5& > Sequences;
+ Sequences sequences( s1 , s2 , s3 , s4 , s5 );
+ boost::fusion::for_each( boost::fusion::zip_view< Sequences >( sequences ) , boost::fusion::make_fused( op ) );
+ }
+
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class Op >
+ static void for_each6( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , Op op )
+ {
+ typedef boost::fusion::vector< S1& , S2& , S3& , S4& , S5& , S6& > Sequences;
+ Sequences sequences( s1 , s2 , s3 , s4 , s5 , s6 );
+ boost::fusion::for_each( boost::fusion::zip_view< Sequences >( sequences ) , boost::fusion::make_fused( op ) );
+ }
+
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class S7 , class Op >
+ static void for_each7( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , Op op )
+ {
+ typedef boost::fusion::vector< S1& , S2& , S3& , S4& , S5& , S6& , S7& > Sequences;
+ Sequences sequences( s1 , s2 , s3 , s4 , s5 , s6 , s7 );
+ boost::fusion::for_each( boost::fusion::zip_view< Sequences >( sequences ) , boost::fusion::make_fused( op ) );
+ }
+
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class S7 , class S8 , class Op >
+ static void for_each8( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , Op op )
+ {
+ BOOST_STATIC_ASSERT_MSG( BOOST_FUSION_INVOKE_MAX_ARITY >= 8 , "Macro Parameter BOOST_FUSION_INVOKE_MAX_ARITY to small!" );
+ typedef boost::fusion::vector< S1& , S2& , S3& , S4& , S5& , S6& , S7& , S8& > Sequences;
+ Sequences sequences( s1 , s2 , s3 , s4 , s5 , s6 , s7 , s8 );
+ boost::fusion::for_each( boost::fusion::zip_view< Sequences >( sequences ) , boost::fusion::make_fused( op ) );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class S7 , class S8 , class S9 , class Op >
+ static void for_each9( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , Op op )
+ {
+ BOOST_STATIC_ASSERT_MSG( BOOST_FUSION_INVOKE_MAX_ARITY >= 9 , "Macro Parameter BOOST_FUSION_INVOKE_MAX_ARITY to small!" );
+ typedef boost::fusion::vector< S1& , S2& , S3& , S4& , S5& , S6& , S7& , S8& , S9& > Sequences;
+ Sequences sequences( s1 , s2 , s3 , s4 , s5 , s6 , s7 , s8 , s9 );
+ boost::fusion::for_each( boost::fusion::zip_view< Sequences >( sequences ) , boost::fusion::make_fused( op ) );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class S7 , class S8 , class S9 , class S10 , class Op >
+ static void for_each10( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , Op op )
+ {
+ BOOST_STATIC_ASSERT_MSG( BOOST_FUSION_INVOKE_MAX_ARITY >= 10 , "Macro Parameter BOOST_FUSION_INVOKE_MAX_ARITY to small!" );
+ typedef boost::fusion::vector< S1& , S2& , S3& , S4& , S5& , S6& , S7& , S8& , S9& , S10& > Sequences;
+ Sequences sequences( s1 , s2 , s3 , s4 , s5 , s6 , s7 , s8 , s9 , s10 );
+ boost::fusion::for_each( boost::fusion::zip_view< Sequences >( sequences ) , boost::fusion::make_fused( op ) );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class S7 , class S8 , class S9 , class S10 , class S11 , class Op >
+ static void for_each11( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , Op op )
+ {
+ BOOST_STATIC_ASSERT_MSG( BOOST_FUSION_INVOKE_MAX_ARITY >= 11 , "Macro Parameter BOOST_FUSION_INVOKE_MAX_ARITY to small!" );
+ BOOST_STATIC_ASSERT_MSG( BOOST_RESULT_OF_NUM_ARGS >= 11 , "Macro Parameter BOOST_RESULT_OF_NUM_ARGS to small!" );
+ typedef boost::fusion::vector< S1& , S2& , S3& , S4& , S5& , S6& , S7& , S8& , S9& , S10& , S11& > Sequences;
+ Sequences sequences( s1 , s2 , s3 , s4 , s5 , s6 , s7 , s8 , s9 , s10 , s11 );
+ boost::fusion::for_each( boost::fusion::zip_view< Sequences >( sequences ) , boost::fusion::make_fused( op ) );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class S7 , class S8 , class S9 , class S10 , class S11 , class S12 , class Op >
+ static void for_each12( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , S12 &s12 , Op op )
+ {
+ BOOST_STATIC_ASSERT_MSG( BOOST_FUSION_INVOKE_MAX_ARITY >= 12 , "Macro Parameter BOOST_FUSION_INVOKE_MAX_ARITY to small!" );
+ BOOST_STATIC_ASSERT_MSG( BOOST_RESULT_OF_NUM_ARGS >= 12 , "Macro Parameter BOOST_RESULT_OF_NUM_ARGS to small!" );
+ typedef boost::fusion::vector< S1& , S2& , S3& , S4& , S5& , S6& , S7& , S8& , S9& , S10& , S11& , S12& > Sequences;
+ Sequences sequences( s1 , s2 , s3 , s4 , s5 , s6 , s7 , s8 , s9 , s10 , s11 , s12 );
+ boost::fusion::for_each( boost::fusion::zip_view< Sequences >( sequences ) , boost::fusion::make_fused( op ) );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class S7 , class S8 , class S9 , class S10 , class S11 , class S12 , class S13 , class Op >
+ static void for_each13( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , S12 &s12 , S13 &s13 , Op op )
+ {
+ BOOST_STATIC_ASSERT_MSG( BOOST_FUSION_INVOKE_MAX_ARITY >= 13 , "Macro Parameter BOOST_FUSION_INVOKE_MAX_ARITY to small!" );
+ BOOST_STATIC_ASSERT_MSG( BOOST_RESULT_OF_NUM_ARGS >= 13 , "Macro Parameter BOOST_RESULT_OF_NUM_ARGS to small!" );
+ typedef boost::fusion::vector< S1& , S2& , S3& , S4& , S5& , S6& , S7& , S8& , S9& , S10& , S11& , S12& , S13& > Sequences;
+ Sequences sequences( s1 , s2 , s3 , s4 , s5 , s6 , s7 , s8 , s9 , s10 , s11 , s12 , s13 );
+ boost::fusion::for_each( boost::fusion::zip_view< Sequences >( sequences ) , boost::fusion::make_fused( op ) );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class S7 , class S8 , class S9 , class S10 , class S11 , class S12 , class S13 , class S14 , class Op >
+ static void for_each14( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , S12 &s12 , S13 &s13 , S14 &s14 , Op op )
+ {
+ BOOST_STATIC_ASSERT_MSG( BOOST_FUSION_INVOKE_MAX_ARITY >= 14 , "Macro Parameter BOOST_FUSION_INVOKE_MAX_ARITY to small!" );
+ BOOST_STATIC_ASSERT_MSG( BOOST_RESULT_OF_NUM_ARGS >= 14 , "Macro Parameter BOOST_RESULT_OF_NUM_ARGS to small!" );
+ typedef boost::fusion::vector< S1& , S2& , S3& , S4& , S5& , S6& , S7& , S8& , S9& , S10& , S11& , S12& , S13& , S14& > Sequences;
+ Sequences sequences( s1 , s2 , s3 , s4 , s5 , s6 , s7 , s8 , s9 , s10 , s11 , s12 , s13 , s14 );
+ boost::fusion::for_each( boost::fusion::zip_view< Sequences >( sequences ) , boost::fusion::make_fused( op ) );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class S7 , class S8 , class S9 , class S10 , class S11 , class S12 , class S13 , class S14 , class S15 , class Op >
+ static void for_each15( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , S12 &s12 , S13 &s13 , S14 &s14 , S15 &s15 , Op op )
+ {
+ BOOST_STATIC_ASSERT_MSG( BOOST_FUSION_INVOKE_MAX_ARITY >= 15 , "Macro Parameter BOOST_FUSION_INVOKE_MAX_ARITY to small!" );
+ BOOST_STATIC_ASSERT_MSG( BOOST_RESULT_OF_NUM_ARGS >= 15 , "Macro Parameter BOOST_RESULT_OF_NUM_ARGS to small!" );
+ typedef boost::fusion::vector< S1& , S2& , S3& , S4& , S5& , S6& , S7& , S8& , S9& , S10& , S11& , S12& , S13& , S14& , S15& > Sequences;
+ Sequences sequences( s1 , s2 , s3 , s4 , s5 , s6 , s7 , s8 , s9 , s10 , s11 , s12 , s13 , s14 , s15 );
+ boost::fusion::for_each( boost::fusion::zip_view< Sequences >( sequences ) , boost::fusion::make_fused( op ) );
+ }
+
+ template< class S >
+ static typename fusion_traits< S >::value_type norm_inf( const S &s )
+ {
+ typedef typename fusion_traits< S >::value_type value_type;
+ return boost::fusion::accumulate( s , static_cast<value_type>(0) ,
+ detail::fusion_maximum<value_type>() );
+ }
+
+};
+
+
+
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_ALGEBRA_FUSION_ALGEBRA_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/algebra/fusion_algebra_dispatcher.hpp b/include/boost/numeric/odeint/algebra/fusion_algebra_dispatcher.hpp
new file mode 100644
index 0000000..4bfc5c2
--- /dev/null
+++ b/include/boost/numeric/odeint/algebra/fusion_algebra_dispatcher.hpp
@@ -0,0 +1,48 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/algebra/fusion_algebra_dispatcher.hpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_ALGEBRA_FUSION_ALGEBRA_DISPATCHER_HPP_DEFINED
+#define BOOST_NUMERIC_ODEINT_ALGEBRA_FUSION_ALGEBRA_DISPATCHER_HPP_DEFINED
+
+#include <boost/numeric/odeint/algebra/fusion_algebra.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+
+#include <boost/utility/enable_if.hpp>
+#include <boost/fusion/include/is_sequence.hpp>
+
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+// specialization for fusion sequences
+template< class FusionSequence >
+struct algebra_dispatcher_sfinae< FusionSequence ,
+ typename boost::enable_if<
+ typename boost::fusion::traits::is_sequence< FusionSequence >::type >::type >
+{
+ typedef fusion_algebra algebra_type;
+};
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_ALGEBRA_FUSION_ALGEBRA_DISPATCHER_HPP_DEFINED
diff --git a/include/boost/numeric/odeint/algebra/multi_array_algebra.hpp b/include/boost/numeric/odeint/algebra/multi_array_algebra.hpp
new file mode 100644
index 0000000..0bc476e
--- /dev/null
+++ b/include/boost/numeric/odeint/algebra/multi_array_algebra.hpp
@@ -0,0 +1,148 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/algebra/multi_array_algebra.hpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2009-2012 Karsten Ahnert
+ Copyright 2009-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_ALGEBRA_MULTI_ARRAY_ALGEBRA_HPP_DEFINED
+#define BOOST_NUMERIC_ODEINT_ALGEBRA_MULTI_ARRAY_ALGEBRA_HPP_DEFINED
+
+
+#include <boost/numeric/odeint/algebra/detail/for_each.hpp>
+#include <boost/numeric/odeint/algebra/detail/norm_inf.hpp>
+#include <boost/numeric/odeint/algebra/norm_result_type.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+// not ready
+struct multi_array_algebra
+{
+ template< class S1 , class Op >
+ static void for_each1( S1 &s1 , Op op )
+ {
+ detail::for_each1( s1.data() , s1.data() + s1.num_elements() , op );
+ }
+
+ template< class S1 , class S2 , class Op >
+ static void for_each2( S1 &s1 , S2 &s2 , Op op )
+ {
+ detail::for_each2( s1.data() , s1.data() + s1.num_elements() , s2.data() , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class Op >
+ static void for_each3( S1 &s1 , S2 &s2 , S3 &s3 , Op op )
+ {
+ detail::for_each3( s1.data() , s1.data() + s1.num_elements() , s2.data() , s3.data() , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class Op >
+ static void for_each4( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , Op op )
+ {
+ detail::for_each4( s1.data() , s1.data() + s1.num_elements() , s2.data() , s3.data() , s4.data() , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class Op >
+ static void for_each5( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , Op op )
+ {
+ detail::for_each5( s1.data() , s1.data() + s1.num_elements() , s2.data() , s3.data() , s4.data() , s5.data() , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class Op >
+ static void for_each6( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , Op op )
+ {
+ detail::for_each6( s1.data() , s1.data() + s1.num_elements() , s2.data() , s3.data() , s4.data() , s5.data() , s6.data() , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class Op >
+ static void for_each7( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , Op op )
+ {
+ detail::for_each7( s1.data() , s1.data() + s1.num_elements() , s2.data() , s3.data() , s4.data() , s5.data() , s6.data() , s7.data() , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class S8 , class Op >
+ static void for_each8( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , Op op )
+ {
+ detail::for_each8( s1.data() , s1.data() + s1.num_elements() , s2.data() , s3.data() , s4.data() , s5.data() , s6.data() , s7.data() , s8.data() , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class S8 , class S9 , class Op >
+ static void for_each9( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , Op op )
+ {
+ detail::for_each9( s1.data() , s1.data() + s1.num_elements() , s2.data() , s3.data() , s4.data() , s5.data() , s6.data() , s7.data() , s8.data() , s9.data() , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class S8 , class S9 , class S10 , class Op >
+ static void for_each10( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , Op op )
+ {
+ detail::for_each10( s1.data() , s1.data() + s1.num_elements() , s2.data() , s3.data() , s4.data() , s5.data() , s6.data() , s7.data() , s8.data() , s9.data() , s10.data() , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class S8 , class S9 , class S10 , class S11 , class Op >
+ static void for_each11( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , Op op )
+ {
+ detail::for_each11( s1.data() , s1.data() + s1.num_elements() , s2.data() , s3.data() , s4.data() , s5.data() , s6.data() , s7.data() , s8.data() , s9.data() , s10.data() , s11.data() , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class S8 , class S9 , class S10 , class S11 , class S12 , class Op >
+ static void for_each12( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , S12 &s12 , Op op )
+ {
+ detail::for_each12( s1.data() , s1.data() + s1.num_elements() , s2.data() , s3.data() , s4.data() , s5.data() , s6.data() , s7.data() , s8.data() , s9.data() , s10.data() , s11.data() , s12.data() , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class S8 , class S9 , class S10 , class S11 , class S12 , class S13 , class Op >
+ static void for_each13( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , S12 &s12 , S13 &s13 , Op op )
+ {
+ detail::for_each13( s1.data() , s1.data() + s1.num_elements() , s2.data() , s3.data() , s4.data() , s5.data() , s6.data() , s7.data() , s8.data() , s9.data() , s10.data() , s11.data() , s12.data() , s13.data() , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class S8 , class S9 , class S10 , class S11 , class S12 , class S13 , class S14 , class Op >
+ static void for_each14( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , S12 &s12 , S13 &s13 , S14 &s14 , Op op )
+ {
+ detail::for_each14( s1.data() , s1.data() + s1.num_elements() , s2.data() , s3.data() , s4.data() , s5.data() , s6.data() , s7.data() , s8.data() , s9.data() , s10.data() , s11.data() , s12.data() , s13.data() , s14.data() , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class S8 , class S9 , class S10 , class S11 , class S12 , class S13 , class S14 , class S15 , class Op >
+ static void for_each15( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , S12 &s12 , S13 &s13 , S14 &s14 , S15 &s15 , Op op )
+ {
+ detail::for_each15( s1.data() , s1.data() + s1.num_elements() , s2.data() , s3.data() , s4.data() , s5.data() , s6.data() , s7.data() , s8.data() , s9.data() , s10.data() , s11.data() , s12.data() , s13.data() , s14.data() , s15.data() , op );
+ }
+
+ template< typename S >
+ static typename norm_result_type<S>::type norm_inf( const S &s )
+ {
+ return detail::norm_inf( s.data() , s.data() + s.num_elements() , static_cast< typename norm_result_type<S>::type >( 0 ) );
+ }
+};
+
+// template< class T , size_t N >
+// struct algebra_dispatcher< boost::array< T , N > >
+// {
+// typedef array_algebra algebra_type;
+// };
+
+
+
+
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_ALGEBRA_MULTI_ARRAY_ALGEBRA_HPP_DEFINED
diff --git a/include/boost/numeric/odeint/algebra/norm_result_type.hpp b/include/boost/numeric/odeint/algebra/norm_result_type.hpp
new file mode 100644
index 0000000..0e99e8f
--- /dev/null
+++ b/include/boost/numeric/odeint/algebra/norm_result_type.hpp
@@ -0,0 +1,33 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/algebra/norm_result_type.hpp
+
+ [begin_description]
+ Calculates the type of the norm_inf operation for container types
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#ifndef BOOST_NUMERIC_ODEINT_ALGEBRA_NORM_RESULT_TYPE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_ALGEBRA_NORM_RESULT_TYPE_HPP_INCLUDED
+
+#include <boost/numeric/odeint/algebra/detail/extract_value_type.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template< typename S , typename Enabler = void >
+struct norm_result_type {
+ typedef typename detail::extract_value_type< S >::type type;
+};
+
+} } }
+
+#endif
diff --git a/include/boost/numeric/odeint/algebra/operations_dispatcher.hpp b/include/boost/numeric/odeint/algebra/operations_dispatcher.hpp
new file mode 100644
index 0000000..faeb5e8
--- /dev/null
+++ b/include/boost/numeric/odeint/algebra/operations_dispatcher.hpp
@@ -0,0 +1,41 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/algebra/operations_dispatcher.hpp
+
+ [begin_description]
+ Operations dispatcher to automatically chose suitable operations.
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#ifndef BOOST_NUMERIC_ODEINT_ALGEBRA_OPERATIONS_DISPATCHER_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_ALGEBRA_OPERATIONS_DISPATCHER_HPP_INCLUDED
+
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template< class StateType , class Enabler = void >
+struct operations_dispatcher_sfinae
+{
+ typedef default_operations operations_type;
+};
+
+template< class StateType >
+struct operations_dispatcher : operations_dispatcher_sfinae< StateType > {};
+
+// no further specializations required
+
+}
+}
+}
+
+#endif
diff --git a/include/boost/numeric/odeint/algebra/range_algebra.hpp b/include/boost/numeric/odeint/algebra/range_algebra.hpp
new file mode 100644
index 0000000..3d7695c
--- /dev/null
+++ b/include/boost/numeric/odeint/algebra/range_algebra.hpp
@@ -0,0 +1,142 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/algebra/range_algebra.hpp
+
+ [begin_description]
+ Default algebra, which works with the most state types, like vector< double >, boost::array< double >, boost::range.
+ Internally is uses boost::range to obtain the begin and end iterator of the according sequence.
+ [end_description]
+
+ Copyright 2010-2013 Karsten Ahnert
+ Copyright 2010-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_ALGEBRA_RANGE_ALGEBRA_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_ALGEBRA_RANGE_ALGEBRA_HPP_INCLUDED
+
+#include <boost/range.hpp>
+#include <boost/mpl/size_t.hpp>
+
+#include <boost/numeric/odeint/algebra/detail/macros.hpp>
+#include <boost/numeric/odeint/algebra/detail/for_each.hpp>
+#include <boost/numeric/odeint/algebra/detail/norm_inf.hpp>
+#include <boost/numeric/odeint/algebra/norm_result_type.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+struct range_algebra
+{
+ template< class S1 , class Op >
+ static void for_each1( S1 &s1 , Op op )
+ {
+ detail::for_each1( boost::begin( s1 ) , boost::end( s1 ) ,
+ op );
+ }
+
+ template< class S1 , class S2 , class Op >
+ static void for_each2( S1 &s1 , S2 &s2 , Op op )
+ {
+ detail::for_each2( boost::begin( s1 ) , boost::end( s1 ) ,
+ boost::begin( s2 ) , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class Op >
+ static void for_each3( S1 &s1 , S2 &s2 , S3 &s3 , Op op )
+ {
+ detail::for_each3( boost::begin( s1 ) , boost::end( s1 ) , boost::begin( s2 ) , boost::begin( s3 ) , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class Op >
+ static void for_each4( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , Op op )
+ {
+ detail::for_each4( boost::begin( s1 ) , boost::end( s1 ) , boost::begin( s2 ) , boost::begin( s3 ) , boost::begin( s4 ) , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class Op >
+ static void for_each5( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , Op op )
+ {
+ detail::for_each5( boost::begin( s1 ) , boost::end( s1 ) , boost::begin( s2 ) , boost::begin( s3 ) , boost::begin( s4 ) , boost::begin( s5 ) , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class Op >
+ static void for_each6( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , Op op )
+ {
+ detail::for_each6( boost::begin( s1 ) , boost::end( s1 ) , boost::begin( s2 ) , boost::begin( s3 ) , boost::begin( s4 ) , boost::begin( s5 ) , boost::begin( s6 ) , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class Op >
+ static void for_each7( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , Op op )
+ {
+ detail::for_each7( boost::begin( s1 ) , boost::end( s1 ) , boost::begin( s2 ) , boost::begin( s3 ) , boost::begin( s4 ) , boost::begin( s5 ) , boost::begin( s6 ) , boost::begin( s7 ) , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class S8 , class Op >
+ static void for_each8( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , Op op )
+ {
+ detail::for_each8( boost::begin( s1 ) , boost::end( s1 ) , boost::begin( s2 ) , boost::begin( s3 ) , boost::begin( s4 ) , boost::begin( s5 ) , boost::begin( s6 ) , boost::begin( s7 ) , boost::begin( s8 ) , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class S8 , class S9 , class Op >
+ static void for_each9( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , Op op )
+ {
+ detail::for_each9( boost::begin( s1 ) , boost::end( s1 ) , boost::begin( s2 ) , boost::begin( s3 ) , boost::begin( s4 ) , boost::begin( s5 ) , boost::begin( s6 ) , boost::begin( s7 ) , boost::begin( s8 ) , boost::begin( s9 ) , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class S8 , class S9 , class S10 , class Op >
+ static void for_each10( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , Op op )
+ {
+ detail::for_each10( boost::begin( s1 ) , boost::end( s1 ) , boost::begin( s2 ) , boost::begin( s3 ) , boost::begin( s4 ) , boost::begin( s5 ) , boost::begin( s6 ) , boost::begin( s7 ) , boost::begin( s8 ) , boost::begin( s9 ) , boost::begin( s10 ) , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class S8 , class S9 , class S10 , class S11 , class Op >
+ static void for_each11( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , Op op )
+ {
+ detail::for_each11( boost::begin( s1 ) , boost::end( s1 ) , boost::begin( s2 ) , boost::begin( s3 ) , boost::begin( s4 ) , boost::begin( s5 ) , boost::begin( s6 ) , boost::begin( s7 ) , boost::begin( s8 ) , boost::begin( s9 ) , boost::begin( s10 ) , boost::begin( s11 ) , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class S8 , class S9 , class S10 , class S11 , class S12 , class Op >
+ static void for_each12( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , S12 &s12 , Op op )
+ {
+ detail::for_each12( boost::begin( s1 ) , boost::end( s1 ) , boost::begin( s2 ) , boost::begin( s3 ) , boost::begin( s4 ) , boost::begin( s5 ) , boost::begin( s6 ) , boost::begin( s7 ) , boost::begin( s8 ) , boost::begin( s9 ) , boost::begin( s10 ) , boost::begin( s11 ) , boost::begin( s12 ) , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class S8 , class S9 , class S10 , class S11 , class S12 , class S13 , class Op >
+ static void for_each13( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , S12 &s12 , S13 &s13 , Op op )
+ {
+ detail::for_each13( boost::begin( s1 ) , boost::end( s1 ) , boost::begin( s2 ) , boost::begin( s3 ) , boost::begin( s4 ) , boost::begin( s5 ) , boost::begin( s6 ) , boost::begin( s7 ) , boost::begin( s8 ) , boost::begin( s9 ) , boost::begin( s10 ) , boost::begin( s11 ) , boost::begin( s12 ) , boost::begin( s13 ) , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class S8 , class S9 , class S10 , class S11 , class S12 , class S13 , class S14 , class Op >
+ static void for_each14( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , S12 &s12 , S13 &s13 , S14 &s14 , Op op )
+ {
+ detail::for_each14( boost::begin( s1 ) , boost::end( s1 ) , boost::begin( s2 ) , boost::begin( s3 ) , boost::begin( s4 ) , boost::begin( s5 ) , boost::begin( s6 ) , boost::begin( s7 ) , boost::begin( s8 ) , boost::begin( s9 ) , boost::begin( s10 ) , boost::begin( s11 ) , boost::begin( s12 ) , boost::begin( s13 ) , boost::begin( s14 ) , op );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class S8 , class S9 , class S10 , class S11 , class S12 , class S13 , class S14 , class S15 , class Op >
+ static void for_each15( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , S12 &s12 , S13 &s13 , S14 &s14 , S15 &s15 , Op op )
+ {
+ detail::for_each15( boost::begin( s1 ) , boost::end( s1 ) , boost::begin( s2 ) , boost::begin( s3 ) , boost::begin( s4 ) , boost::begin( s5 ) , boost::begin( s6 ) , boost::begin( s7 ) , boost::begin( s8 ) , boost::begin( s9 ) , boost::begin( s10 ) , boost::begin( s11 ) , boost::begin( s12 ) , boost::begin( s13 ) , boost::begin( s14 ) , boost::begin( s15 ) , op );
+ }
+
+ template< typename S >
+ static typename norm_result_type<S>::type norm_inf( const S &s )
+ {
+ return detail::norm_inf( boost::begin( s ) , boost::end( s ) ,
+ static_cast< typename norm_result_type<S>::type >( 0 ) );
+ }
+
+};
+
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_ALGEBRA_RANGE_ALGEBRA_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/algebra/vector_space_algebra.hpp b/include/boost/numeric/odeint/algebra/vector_space_algebra.hpp
new file mode 100644
index 0000000..17ff007
--- /dev/null
+++ b/include/boost/numeric/odeint/algebra/vector_space_algebra.hpp
@@ -0,0 +1,178 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/algebra/vector_space_algebra.hpp
+
+ [begin_description]
+ An algebra for types which have vector space semantics, hence types on which the operators +,-,* are well defined.
+ [end_description]
+
+ Copyright 2010-2012 Karsten Ahnert
+ Copyright 2010-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_ALGEBRA_VECTOR_SPACE_ALGEBRA_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_ALGEBRA_VECTOR_SPACE_ALGEBRA_HPP_INCLUDED
+
+#include <complex>
+
+#include <boost/type_traits/remove_reference.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+/*
+ * This class template has to be overload in order to call vector_space_algebra::norm_inf
+ */
+template< class State > struct vector_space_norm_inf;
+
+/*
+ * Example: instantiation for sole doubles and complex
+ */
+template<>
+struct vector_space_norm_inf< double >
+{
+ typedef double result_type;
+ double operator()( double x ) const
+ {
+ using std::abs;
+ return abs(x);
+ }
+};
+
+template<>
+struct vector_space_norm_inf< float >
+{
+ typedef float result_type;
+ result_type operator()( float x ) const
+ {
+ using std::abs;
+ return abs(x);
+ }
+};
+
+template< typename T >
+struct vector_space_norm_inf< std::complex<T> >
+{
+ typedef T result_type;
+ result_type operator()( std::complex<T> x ) const
+ {
+ using std::abs;
+ return abs( x );
+ }
+};
+
+struct vector_space_algebra
+{
+ template< class S1 , class Op >
+ static void for_each1( S1 &s1 , Op op )
+ {
+ // ToDo : build checks, that the +-*/ operators are well defined
+ op( s1 );
+ }
+
+ template< class S1 , class S2 , class Op >
+ static void for_each2( S1 &s1 , S2 &s2 , Op op )
+ {
+ op( s1 , s2 );
+ }
+
+ template< class S1 , class S2 , class S3 , class Op >
+ static void for_each3( S1 &s1 , S2 &s2 , S3 &s3 , Op op )
+ {
+ op( s1 , s2 , s3 );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class Op >
+ static void for_each4( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , Op op )
+ {
+ op( s1 , s2 , s3 , s4 );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class Op >
+ static void for_each5( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , Op op )
+ {
+ op( s1 , s2 , s3 , s4 , s5 );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class Op >
+ static void for_each6( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , Op op )
+ {
+ op( s1 , s2 , s3 , s4 , s5 , s6 );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class Op >
+ static void for_each7( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , Op op )
+ {
+ op( s1 , s2 , s3 , s4 , s5 , s6 , s7 );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class S8 , class Op >
+ static void for_each8( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , Op op )
+ {
+ op( s1 , s2 , s3 , s4 , s5 , s6 , s7 , s8 );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class S8 , class S9 , class Op >
+ static void for_each9( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , Op op )
+ {
+ op( s1 , s2 , s3 , s4 , s5 , s6 , s7 , s8 , s9 );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class S8 , class S9 , class S10 , class Op >
+ static void for_each10( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , Op op )
+ {
+ op( s1 , s2 , s3 , s4 , s5 , s6 , s7 , s8 , s9 , s10 );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class S8 , class S9 , class S10 , class S11 , class Op >
+ static void for_each11( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , Op op )
+ {
+ op( s1 , s2 , s3 , s4 , s5 , s6 , s7 , s8 , s9 , s10 , s11 );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class S8 , class S9 , class S10 , class S11 , class S12 , class Op >
+ static void for_each12( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , S12 &s12 , Op op )
+ {
+ op( s1 , s2 , s3 , s4 , s5 , s6 , s7 , s8 , s9 , s10 , s11 , s12 );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class S8 , class S9 , class S10 , class S11 , class S12 , class S13 , class Op >
+ static void for_each13( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , S12 &s12 , S13 &s13 , Op op )
+ {
+ op( s1 , s2 , s3 , s4 , s5 , s6 , s7 , s8 , s9 , s10 , s11 , s12 , s13 );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class S8 , class S9 , class S10 , class S11 , class S12 , class S13 , class S14 , class Op >
+ static void for_each14( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , S12 &s12 , S13 &s13 , S14 &s14 , Op op )
+ {
+ op( s1 , s2 , s3 , s4 , s5 , s6 , s7 , s8 , s9 , s10 , s11 , s12 , s13 , s14 );
+ }
+
+ template< class S1 , class S2 , class S3 , class S4 , class S5 , class S6 ,class S7 , class S8 , class S9 , class S10 , class S11 , class S12 , class S13 , class S14 , class S15 , class Op >
+ static void for_each15( S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , S12 &s12 , S13 &s13 , S14 &s14 , S15 &s15 , Op op )
+ {
+ op( s1 , s2 , s3 , s4 , s5 , s6 , s7 , s8 , s9 , s10 , s11 , s12 , s13 , s14 , s15 );
+ }
+
+ template< class S >
+ static typename boost::numeric::odeint::vector_space_norm_inf< S >::result_type norm_inf( const S &s )
+ {
+ boost::numeric::odeint::vector_space_norm_inf< S > n;
+ return n( s );
+ }
+};
+
+
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_ALGEBRA_VECTOR_SPACE_ALGEBRA_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/config.hpp b/include/boost/numeric/odeint/config.hpp
new file mode 100644
index 0000000..f191582
--- /dev/null
+++ b/include/boost/numeric/odeint/config.hpp
@@ -0,0 +1,53 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/config.hpp
+
+ [begin_description]
+ Sets configurations for odeint and used libraries. Should be included before any other odeint library
+ [end_description]
+
+ Copyright 2011-2012 Mario Mulansky
+ Copyright 2011-2012 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#ifndef BOOST_NUMERIC_ODEINT_CONFIG_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_CONFIG_HPP_INCLUDED
+
+
+//increase macro variable to allow rk78 scheme
+#ifndef FUSION_MAX_VECTOR_SIZE
+#define FUSION_MAX_VECTOR_SIZE 15
+#endif
+
+
+/*
+ * the following definitions are only required if fusion vectors are used as state types
+ * in the rk78 scheme
+ * they should be defined by the user if required, see e.g. libs/numeric/examples/harmonic_oscillator_units.cpp
+ */
+#ifndef BOOST_FUSION_INVOKE_MAX_ARITY
+#define BOOST_FUSION_INVOKE_MAX_ARITY 15
+#endif
+
+#ifndef BOOST_RESULT_OF_NUM_ARGS
+#define BOOST_RESULT_OF_NUM_ARGS 15
+#endif
+
+
+
+
+
+#include <boost/config.hpp>
+
+#if __cplusplus >= 201103L
+#define BOOST_NUMERIC_ODEINT_CXX11 1
+#endif
+
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_CONFIG_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/external/blaze/blaze_algebra_dispatcher.hpp b/include/boost/numeric/odeint/external/blaze/blaze_algebra_dispatcher.hpp
new file mode 100644
index 0000000..29bf786
--- /dev/null
+++ b/include/boost/numeric/odeint/external/blaze/blaze_algebra_dispatcher.hpp
@@ -0,0 +1,55 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/blaze/blaze_algebra_dispatcher.hpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2009-2012 Karsten Ahnert
+ Copyright 2009-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_BLAZE_BLAZE_ALGEBRA_DISPATCHER_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_BLAZE_BLAZE_ALGEBRA_DISPATCHER_HPP_INCLUDED
+
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <blaze/math/dense/StaticVector.h>
+#include <blaze/math/dense/DynamicVector.h>
+
+
+
+
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template< typename T , size_t N , bool TF >
+struct algebra_dispatcher< blaze::StaticVector< T , N , TF > >
+{
+ typedef vector_space_algebra algebra_type;
+};
+
+template< typename T , bool TF >
+struct algebra_dispatcher< blaze::DynamicVector< T , TF > >
+{
+ typedef vector_space_algebra algebra_type;
+};
+
+
+
+
+
+}
+}
+}
+
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_BLAZE_BLAZE_ALGEBRA_DISPATCHER_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/external/blaze/blaze_resize.hpp b/include/boost/numeric/odeint/external/blaze/blaze_resize.hpp
new file mode 100644
index 0000000..3c5f2d4
--- /dev/null
+++ b/include/boost/numeric/odeint/external/blaze/blaze_resize.hpp
@@ -0,0 +1,62 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/blaze/blaze_resize.hpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2009-2012 Karsten Ahnert
+ Copyright 2009-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_BLAZE_BLAZE_RESIZE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_BLAZE_BLAZE_RESIZE_HPP_INCLUDED
+
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resize.hpp>
+#include <boost/numeric/odeint/util/same_size.hpp>
+
+#include <blaze/math/dense/DynamicVector.h>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template< typename T , bool TF >
+struct is_resizeable< blaze::DynamicVector< T , TF > >
+{
+ typedef boost::true_type type;
+ const static bool value = type::value;
+};
+
+template< typename T1 , bool TF1, typename T2 , bool TF2 >
+struct same_size_impl< blaze::DynamicVector< T1 , TF1 > , blaze::DynamicVector< T2 , TF2 > >
+{
+ static bool same_size( const blaze::DynamicVector< T1 , TF1 > &x1 , const blaze::DynamicVector< T2 , TF2 > &x2 )
+ {
+ return x1.size() == x2.size();
+ }
+};
+
+template< typename T1 , bool TF1, typename T2 , bool TF2 >
+struct resize_impl< blaze::DynamicVector< T1 , TF1 > , blaze::DynamicVector< T2 , TF2 > >
+{
+ static void resize( blaze::DynamicVector< T1 , TF1 > &x1 , const blaze::DynamicVector< T2 , TF2 > &x2 )
+ {
+ x1.resize( x2.size() );
+ }
+};
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_BLAZE_BLAZE_RESIZE_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/external/compute/compute.hpp b/include/boost/numeric/odeint/external/compute/compute.hpp
new file mode 100644
index 0000000..fe04b58
--- /dev/null
+++ b/include/boost/numeric/odeint/external/compute/compute.hpp
@@ -0,0 +1,27 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/compute/compute.hpp
+
+ [begin_description]
+ includes all headers required for using odeint with Boost.Compute
+ [end_description]
+
+ Copyright 2009-2013 Karsten Ahnert
+ Copyright 2009-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_COMPUTE_COMPUTE_HPP_DEFINED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_COMPUTE_COMPUTE_HPP_DEFINED
+
+#include <boost/numeric/odeint/external/compute/compute_algebra.hpp>
+#include <boost/numeric/odeint/external/compute/compute_operations.hpp>
+#include <boost/numeric/odeint/external/compute/compute_algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/external/compute/compute_operations_dispatcher.hpp>
+#include <boost/numeric/odeint/external/compute/compute_resize.hpp>
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_COMPUTE_COMPUTE_HPP_DEFINED
diff --git a/include/boost/numeric/odeint/external/compute/compute_algebra.hpp b/include/boost/numeric/odeint/external/compute/compute_algebra.hpp
new file mode 100644
index 0000000..9cd3912
--- /dev/null
+++ b/include/boost/numeric/odeint/external/compute/compute_algebra.hpp
@@ -0,0 +1,65 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/compute/compute_algebra.hpp
+
+ [begin_description]
+ An algebra for Boost.Compute vectors.
+ [end_description]
+
+ Copyright 2009-2011 Karsten Ahnert
+ Copyright 2009-2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_COMPUTE_COMPUTE_ALGEBRA_HPP_DEFINED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_COMPUTE_COMPUTE_ALGEBRA_HPP_DEFINED
+
+#include <boost/preprocessor/repetition.hpp>
+#include <boost/compute.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+struct compute_algebra
+{
+
+#define BOOST_ODEINT_COMPUTE_STATE_PARAM(z, n, unused) \
+ StateType ## n &s ## n,
+
+#define BOOST_ODEINT_COMPUTE_ALGEBRA(z, n, unused) \
+ template< BOOST_PP_ENUM_PARAMS(n, class StateType), class Operation > \
+ static void for_each ## n( \
+ BOOST_PP_REPEAT(n, BOOST_ODEINT_COMPUTE_STATE_PARAM, ~) \
+ Operation op \
+ ) \
+ { \
+ op( BOOST_PP_ENUM_PARAMS(n, s) ); \
+ }
+
+BOOST_PP_REPEAT_FROM_TO(3, 9, BOOST_ODEINT_COMPUTE_ALGEBRA, ~)
+
+#undef BOOST_ODEINT_COMPUTE_ALGEBRA
+#undef BOOST_ODEINT_COMPUTE_STATE_PARAM
+
+ template < class S >
+ static typename S::value_type norm_inf( const S &s ) {
+ typedef typename S::value_type value_type;
+
+ BOOST_COMPUTE_FUNCTION(value_type, max_abs, (value_type, value_type),
+ {
+ return max(_1, fabs(_2));
+ });
+
+ return boost::compute::accumulate(s.begin(), s.end(), value_type(), max_abs);
+ }
+};
+} // odeint
+} // numeric
+} // boost
+
+#endif
diff --git a/include/boost/numeric/odeint/external/compute/compute_algebra_dispatcher.hpp b/include/boost/numeric/odeint/external/compute/compute_algebra_dispatcher.hpp
new file mode 100644
index 0000000..6df360b
--- /dev/null
+++ b/include/boost/numeric/odeint/external/compute/compute_algebra_dispatcher.hpp
@@ -0,0 +1,41 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/compute/compute_algebra_dispatcher.hpp
+
+ [begin_description]
+ algebra_dispatcher specialization for Boost.Compute
+ [end_description]
+
+ Copyright 2009-2013 Karsten Ahnert
+ Copyright 2009-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_COMPUTE_COMPUTE_ALGEBRA_DISPATCHER_HPP_DEFINED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_COMPUTE_COMPUTE_ALGEBRA_DISPATCHER_HPP_DEFINED
+
+#include <boost/compute/container/vector.hpp>
+
+#include <boost/numeric/odeint/external/compute/compute_algebra.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+// specialization for Boost.Compute vector
+template< class T , class A >
+struct algebra_dispatcher< boost::compute::vector< T , A > >
+{
+ typedef compute_algebra algebra_type;
+};
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_COMPUTE_COMPUTE_ALGEBRA_DISPATCHER_HPP_DEFINED
diff --git a/include/boost/numeric/odeint/external/compute/compute_operations.hpp b/include/boost/numeric/odeint/external/compute/compute_operations.hpp
new file mode 100644
index 0000000..58d5f69
--- /dev/null
+++ b/include/boost/numeric/odeint/external/compute/compute_operations.hpp
@@ -0,0 +1,198 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/compute/compute_operations.hpp
+
+ [begin_description]
+ Operations of Boost.Compute zipped iterators. Is the counterpart of the compute_algebra.
+ [end_description]
+
+ Copyright 2009-2011 Karsten Ahnert
+ Copyright 2009-2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_COMPUTE_COMPUTE_OPERATIONS_HPP_DEFINED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_COMPUTE_COMPUTE_OPERATIONS_HPP_DEFINED
+
+#include <boost/preprocessor/repetition.hpp>
+#include <boost/compute.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+struct compute_operations {
+
+#define BOOST_ODEINT_COMPUTE_TEMPL_FAC(z, n, unused) \
+ , class Fac ## n = BOOST_PP_CAT(Fac, BOOST_PP_DEC(n))
+
+#define BOOST_ODEINT_COMPUTE_MEMB_FAC(z, n, unused) \
+ const Fac ## n m_alpha ## n;
+
+#define BOOST_ODEINT_COMPUTE_PRM_FAC(z, n, unused) \
+ BOOST_PP_COMMA_IF(n) const Fac ## n alpha ## n
+
+#define BOOST_ODEINT_COMPUTE_INIT_FAC(z, n, unused) \
+ BOOST_PP_COMMA_IF(n) m_alpha ## n (alpha ## n)
+
+#define BOOST_ODEINT_COMPUTE_PRM_STATE(z, n, unused) \
+ BOOST_PP_COMMA_IF(n) StateType ## n &s ## n
+
+#define BOOST_ODEINT_COMPUTE_BEGIN_STATE(z, n, unused) \
+ BOOST_PP_COMMA_IF( BOOST_PP_DEC(n) ) s ## n.begin()
+
+#define BOOST_ODEINT_COMPUTE_END_STATE(z, n, unused) \
+ BOOST_PP_COMMA_IF( BOOST_PP_DEC(n) ) s ## n.end()
+
+#define BOOST_ODEINT_COMPUTE_LAMBDA(z, n, unused) \
+ BOOST_PP_EXPR_IF(n, +) m_alpha ## n * bc::lambda::get< n >(bc::_1)
+
+#define BOOST_ODEINT_COMPUTE_OPERATIONS(z, n, unused) \
+ template< \
+ class Fac0 = double \
+ BOOST_PP_REPEAT_FROM_TO(1, n, BOOST_ODEINT_COMPUTE_TEMPL_FAC, ~) \
+ > \
+ struct scale_sum ## n { \
+ BOOST_PP_REPEAT(n, BOOST_ODEINT_COMPUTE_MEMB_FAC, ~) \
+ scale_sum ## n( \
+ BOOST_PP_REPEAT(n, BOOST_ODEINT_COMPUTE_PRM_FAC, ~) \
+ ) \
+ : BOOST_PP_REPEAT(n, BOOST_ODEINT_COMPUTE_INIT_FAC, ~) \
+ { } \
+ template< BOOST_PP_ENUM_PARAMS(BOOST_PP_INC(n), class StateType) > \
+ void operator()( \
+ BOOST_PP_REPEAT( \
+ BOOST_PP_INC(n), \
+ BOOST_ODEINT_COMPUTE_PRM_STATE, ~) \
+ ) const \
+ { \
+ namespace bc = boost::compute; \
+ bc::transform( \
+ bc::make_zip_iterator( \
+ boost::make_tuple( \
+ BOOST_PP_REPEAT_FROM_TO( \
+ 1, BOOST_PP_INC(n), \
+ BOOST_ODEINT_COMPUTE_BEGIN_STATE, ~) \
+ ) \
+ ), \
+ bc::make_zip_iterator( \
+ boost::make_tuple( \
+ BOOST_PP_REPEAT_FROM_TO( \
+ 1, BOOST_PP_INC(n), \
+ BOOST_ODEINT_COMPUTE_END_STATE, ~) \
+ ) \
+ ), \
+ s0.begin(), \
+ BOOST_PP_REPEAT(n, BOOST_ODEINT_COMPUTE_LAMBDA, ~) \
+ ); \
+ } \
+ };
+
+BOOST_PP_REPEAT_FROM_TO(2, 8, BOOST_ODEINT_COMPUTE_OPERATIONS, ~)
+
+#undef BOOST_ODEINT_COMPUTE_TEMPL_FAC
+#undef BOOST_ODEINT_COMPUTE_MEMB_FAC
+#undef BOOST_ODEINT_COMPUTE_PRM_FAC
+#undef BOOST_ODEINT_COMPUTE_INIT_FAC
+#undef BOOST_ODEINT_COMPUTE_PRM_STATE
+#undef BOOST_ODEINT_COMPUTE_BEGIN_STATE
+#undef BOOST_ODEINT_COMPUTE_END_STATE
+#undef BOOST_ODEINT_COMPUTE_LAMBDA
+#undef BOOST_ODEINT_COMPUTE_OPERATIONS
+
+ template<class Fac1 = double, class Fac2 = Fac1>
+ struct scale_sum_swap2 {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+
+ scale_sum_swap2(const Fac1 alpha1, const Fac2 alpha2)
+ : m_alpha1(alpha1), m_alpha2(alpha2) { }
+
+ template<class State0, class State1, class State2>
+ void operator()(State0 &s0, State1 &s1, State2 &s2) const {
+ namespace bc = boost::compute;
+
+ bc::command_queue &queue = bc::system::default_queue();
+ const bc::context &context = queue.get_context();
+
+ const char source[] = BOOST_COMPUTE_STRINGIZE_SOURCE(
+ kernel void scale_sum_swap2(
+ F1 a1, F2 a2,
+ global T0 *x0, global T1 *x1, global T2 *x2,
+ )
+ {
+ uint i = get_global_id(0);
+ T0 tmp = x0[i];
+ x0[i] = a1 * x1[i] + a2 * x2[i];
+ x1[i] = tmp;
+ }
+ );
+
+ std::stringstream options;
+ options
+ << " -DT0=" << bc::type_name<typename State0::value_type>()
+ << " -DT1=" << bc::type_name<typename State1::value_type>()
+ << " -DT2=" << bc::type_name<typename State2::value_type>()
+ << " -DF1=" << bc::type_name<Fac1>()
+ << " -DF2=" << bc::type_name<Fac2>();
+
+ bc::program program =
+ bc::program::build_with_source(source, context, options.str());
+
+ bc::kernel kernel(program, "scale_sum_swap2");
+ kernel.set_arg(0, m_alpha1);
+ kernel.set_arg(1, m_alpha2);
+ kernel.set_arg(2, s0.get_buffer());
+ kernel.set_arg(3, s1.get_buffer());
+ kernel.set_arg(4, s2.get_buffer());
+
+ queue.enqueue_1d_range_kernel(kernel, 0, s0.size());
+
+ }
+ };
+
+ template<class Fac1 = double>
+ struct rel_error {
+ const Fac1 m_eps_abs, m_eps_rel, m_a_x, m_a_dxdt;
+
+ rel_error(const Fac1 eps_abs, const Fac1 eps_rel, const Fac1 a_x, const Fac1 a_dxdt)
+ : m_eps_abs(eps_abs), m_eps_rel(eps_rel), m_a_x(a_x), m_a_dxdt(a_dxdt) { }
+
+
+ template <class State0, class State1, class State2>
+ void operator()(State0 &s0, State1 &s1, State2 &s2) const {
+ namespace bc = boost::compute;
+ using bc::_1;
+ using bc::lambda::get;
+
+ bc::for_each(
+ bc::make_zip_iterator(
+ boost::make_tuple(
+ s0.begin(),
+ s1.begin(),
+ s2.begin()
+ )
+ ),
+ bc::make_zip_iterator(
+ boost::make_tuple(
+ s0.end(),
+ s1.end(),
+ s2.end()
+ )
+ ),
+ get<0>(_1) = abs( get<0>(_1) ) /
+ (m_eps_abs + m_eps_rel * (m_a_x * abs(get<1>(_1) + m_a_dxdt * abs(get<2>(_1)))))
+ );
+ }
+ };
+};
+
+} // odeint
+} // numeric
+} // boost
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_COMPUTE_COMPUTE_OPERATIONS_HPP_DEFINED
diff --git a/include/boost/numeric/odeint/external/compute/compute_operations_dispatcher.hpp b/include/boost/numeric/odeint/external/compute/compute_operations_dispatcher.hpp
new file mode 100644
index 0000000..76df2f3
--- /dev/null
+++ b/include/boost/numeric/odeint/external/compute/compute_operations_dispatcher.hpp
@@ -0,0 +1,44 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/compute/compute_operations_dispatcher.hpp
+
+ [begin_description]
+ operations_dispatcher specialization for Boost.Compute
+ [end_description]
+
+ Copyright 2009-2013 Karsten Ahnert
+ Copyright 2009-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_COMPUTE_COMPUTE_OPERATIONS_DISPATCHER_HPP_DEFINED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_COMPUTE_COMPUTE_OPERATIONS_DISPATCHER_HPP_DEFINED
+
+#include <boost/compute/container/vector.hpp>
+
+#include <boost/numeric/odeint/external/compute/compute_operations.hpp>
+#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+// specialization for Boost.Compute vector
+template< class T , class A >
+struct operations_dispatcher< boost::compute::vector< T , A > >
+{
+ typedef compute_operations operations_type;
+};
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_COMPUTE_COMPUTE_OPERATIONS_DISPATCHER_HPP_DEFINED
diff --git a/include/boost/numeric/odeint/external/compute/compute_resize.hpp b/include/boost/numeric/odeint/external/compute/compute_resize.hpp
new file mode 100644
index 0000000..013a7ac
--- /dev/null
+++ b/include/boost/numeric/odeint/external/compute/compute_resize.hpp
@@ -0,0 +1,90 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/compute/compute_resize.hpp
+
+ [begin_description]
+ Enable resizing for Boost.Compute vector
+ [end_description]
+
+ Copyright 2009-2011 Karsten Ahnert
+ Copyright 2009-2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_COMPUTE_COMPUTE_RESIZE_HPP_DEFINED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_COMPUTE_COMPUTE_RESIZE_HPP_DEFINED
+
+#include <boost/compute/container/vector.hpp>
+
+#include <boost/numeric/odeint/util/copy.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template< class T, class A >
+struct is_resizeable< boost::compute::vector< T , A > >
+{
+ struct type : public boost::true_type { };
+ const static bool value = type::value;
+};
+
+template< class T, class A >
+struct same_size_impl< boost::compute::vector< T, A > , boost::compute::vector< T, A > >
+{
+ static bool same_size( const boost::compute::vector< T, A > &x , const boost::compute::vector< T, A > &y )
+ {
+ return x.size() == y.size();
+ }
+};
+
+template< class T, class A >
+struct resize_impl< boost::compute::vector< T, A > , boost::compute::vector< T, A > >
+{
+ static void resize( boost::compute::vector< T, A > &x , const boost::compute::vector< T, A > &y )
+ {
+ x.resize( y.size() );
+ }
+};
+
+
+template< class Container1, class T, class A >
+struct copy_impl< Container1 , boost::compute::vector< T, A > >
+{
+ static void copy( const Container1 &from , boost::compute::vector< T, A > &to )
+ {
+ boost::compute::copy( boost::begin( from ) , boost::end( from ) , boost::begin( to ) );
+ }
+};
+
+template< class T, class A, class Container2 >
+struct copy_impl< boost::compute::vector< T, A > , Container2 >
+{
+ static void copy( const boost::compute::vector< T, A > &from , Container2 &to )
+ {
+ boost::compute::copy( boost::begin( from ) , boost::end( from ) , boost::begin( to ) );
+ }
+};
+
+template< class T, class A >
+struct copy_impl< boost::compute::vector< T, A > , boost::compute::vector< T, A > >
+{
+ static void copy( const boost::compute::vector< T, A > &from , boost::compute::vector< T, A > &to )
+ {
+ boost::compute::copy( boost::begin( from ) , boost::end( from ) , boost::begin( to ) );
+ }
+};
+
+
+
+
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_COMPUTE_COMPUTE_RESIZE_HPP_DEFINED
diff --git a/include/boost/numeric/odeint/external/eigen/eigen.hpp b/include/boost/numeric/odeint/external/eigen/eigen.hpp
new file mode 100644
index 0000000..620acae
--- /dev/null
+++ b/include/boost/numeric/odeint/external/eigen/eigen.hpp
@@ -0,0 +1,27 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/eigen/eigen.hpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2009-2012 Karsten Ahnert
+ Copyright 2009-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_EIGEN_EIGEN_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_EIGEN_EIGEN_HPP_INCLUDED
+
+
+#include <boost/numeric/odeint/external/eigen/eigen_algebra.hpp>
+#include <boost/numeric/odeint/external/eigen/eigen_algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/external/eigen/eigen_resize.hpp>
+
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_EIGEN_EIGEN_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/external/eigen/eigen_algebra.hpp b/include/boost/numeric/odeint/external/eigen/eigen_algebra.hpp
new file mode 100644
index 0000000..b4ee5c3
--- /dev/null
+++ b/include/boost/numeric/odeint/external/eigen/eigen_algebra.hpp
@@ -0,0 +1,109 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/eigen/eigen_algebra.hpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2013 Christian Shelton
+ Copyright 2013 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_EIGEN_EIGEN_ALGEBRA_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_EIGEN_EIGEN_ALGEBRA_HPP_INCLUDED
+
+#include <Eigen/Dense>
+#include <boost/numeric/odeint/algebra/vector_space_algebra.hpp>
+
+// Necessary routines for Eigen matrices to work with vector_space_algebra
+// from odeint
+// (that is, it lets odeint treat the eigen matrices correctly, knowing
+// how to add, multiply, compute the norm, etc)
+
+namespace Eigen {
+
+
+template<typename D>
+inline const
+typename Eigen::CwiseUnaryOp<
+ typename Eigen::internal::scalar_add_op<
+ typename Eigen::internal::traits<D>::Scalar>,
+ const D >
+operator+(const typename Eigen::MatrixBase<D> &m,
+ const typename Eigen::internal::traits<D>::Scalar &s) {
+ return Eigen::CwiseUnaryOp<
+ typename Eigen::internal::scalar_add_op<
+ typename Eigen::internal::traits<D>::Scalar>,
+ const D >(m.derived(),Eigen::internal::scalar_add_op<
+ typename Eigen::internal::traits<D>::Scalar>(s));
+}
+
+template<typename D>
+inline const
+typename Eigen::CwiseUnaryOp<
+ typename Eigen::internal::scalar_add_op<
+ typename Eigen::internal::traits<D>::Scalar>,
+ const D >
+operator+(const typename Eigen::internal::traits<D>::Scalar &s,
+const typename Eigen::MatrixBase<D> &m) {
+ return Eigen::CwiseUnaryOp<
+ typename Eigen::internal::scalar_add_op<
+ typename Eigen::internal::traits<D>::Scalar>,
+ const D >(m.derived(),Eigen::internal::scalar_add_op<
+ typename Eigen::internal::traits<D>::Scalar>(s));
+}
+
+
+
+template<typename D1,typename D2>
+inline const
+typename Eigen::CwiseBinaryOp<
+ typename Eigen::internal::scalar_quotient_op<
+ typename Eigen::internal::traits<D1>::Scalar>,
+ const D1, const D2>
+operator/(const Eigen::MatrixBase<D1> &x1, const Eigen::MatrixBase<D2> &x2) {
+ return x1.cwiseQuotient(x2);
+}
+
+
+template< typename D >
+inline const
+typename Eigen::CwiseUnaryOp<
+ typename Eigen::internal::scalar_abs_op<
+ typename Eigen::internal::traits< D >::Scalar > ,
+ const D >
+abs( const Eigen::MatrixBase< D > &m ) {
+ return m.cwiseAbs();
+}
+
+
+
+} // end Eigen namespace
+
+
+
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template<typename B,int S1,int S2,int O, int M1, int M2>
+struct vector_space_norm_inf< Eigen::Matrix<B,S1,S2,O,M1,M2> >
+{
+ typedef B result_type;
+ result_type operator()( const Eigen::Matrix<B,S1,S2,O,M1,M2> &m ) const
+ {
+ return m.template lpNorm<Eigen::Infinity>();
+ }
+};
+
+} } } // end boost::numeric::odeint namespace
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_EIGEN_EIGEN_ALGEBRA_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/external/eigen/eigen_algebra_dispatcher.hpp b/include/boost/numeric/odeint/external/eigen/eigen_algebra_dispatcher.hpp
new file mode 100644
index 0000000..6c8a3a2
--- /dev/null
+++ b/include/boost/numeric/odeint/external/eigen/eigen_algebra_dispatcher.hpp
@@ -0,0 +1,49 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/eigen/eigen_algebra_dispatcher.hpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2009-2012 Karsten Ahnert
+ Copyright 2009-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_EIGEN_EIGEN_ALGEBRA_DISPATCHER_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_EIGEN_EIGEN_ALGEBRA_DISPATCHER_HPP_INCLUDED
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+template< class Derived >
+struct algebra_dispatcher_sfinae< Derived ,
+ typename boost::enable_if< typename boost::is_base_of< Eigen::MatrixBase< Derived > , Derived >::type >::type >
+{
+ typedef vector_space_algebra algebra_type;
+};
+
+
+template < class Derived >
+struct algebra_dispatcher_sfinae< Derived ,
+ typename boost::enable_if< typename boost::is_base_of< Eigen::ArrayBase< Derived > , Derived >::type >::type >
+{
+ typedef vector_space_algebra algebra_type;
+};
+
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_EIGEN_EIGEN_ALGEBRA_DISPATCHER_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/external/eigen/eigen_resize.hpp b/include/boost/numeric/odeint/external/eigen/eigen_resize.hpp
new file mode 100644
index 0000000..1989cc3
--- /dev/null
+++ b/include/boost/numeric/odeint/external/eigen/eigen_resize.hpp
@@ -0,0 +1,107 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/eigen/eigen_resize.hpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2013 Ankur Sinha
+ Copyright 2013 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_EIGEN_EIGEN_RESIZE_HPP_DEFINED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_EIGEN_EIGEN_RESIZE_HPP_DEFINED
+
+
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resize.hpp>
+#include <boost/numeric/odeint/util/same_size.hpp>
+
+#include <boost/utility/enable_if.hpp>
+#include <boost/type_traits/is_base_of.hpp>
+
+#include <Eigen/Dense>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+
+template< class Derived >
+struct is_resizeable_sfinae< Derived ,
+ typename boost::enable_if< typename boost::is_base_of< Eigen::MatrixBase< Derived > , Derived >::type >::type >
+{
+ typedef boost::true_type type;
+ const static bool value = type::value;
+};
+
+
+template < class Derived >
+struct is_resizeable_sfinae< Derived ,
+ typename boost::enable_if< typename boost::is_base_of< Eigen::ArrayBase< Derived > , Derived >::type >::type >
+{
+ typedef boost::true_type type;
+ const static bool value = type::value;
+};
+
+
+
+template< class Derived >
+struct same_size_impl_sfinae< Derived , Derived ,
+ typename boost::enable_if< typename boost::is_base_of< Eigen::MatrixBase< Derived > , Derived >::type >::type >
+{
+ static bool same_size( const Eigen::MatrixBase< Derived > &m1 , const Eigen::MatrixBase< Derived > &m2 )
+
+ {
+ return ( ( m1.innerSize () == m2.innerSize () ) && ( m1.outerSize() == m2.outerSize() ) );
+ }
+};
+
+template< class Derived >
+struct same_size_impl_sfinae< Derived , Derived ,
+ typename boost::enable_if< typename boost::is_base_of< Eigen::ArrayBase< Derived > , Derived >::type >::type >
+{
+ static bool same_size( const Eigen::ArrayBase< Derived > &v1 , const Eigen::ArrayBase< Derived > &v2 )
+ {
+ return ( ( v1.innerSize () == v2.innerSize () ) && ( v1.outerSize() == v2.outerSize() ) );
+ }
+};
+
+
+
+
+template< class Derived >
+struct resize_impl_sfinae< Derived , Derived ,
+ typename boost::enable_if< typename boost::is_base_of< Eigen::MatrixBase< Derived > , Derived >::type >::type >
+{
+ static void resize( Eigen::MatrixBase< Derived > &m1 , const Eigen::MatrixBase< Derived > &m2 )
+ {
+ m1.derived().resizeLike(m2);
+ }
+};
+
+template< class Derived >
+struct resize_impl_sfinae< Derived , Derived ,
+ typename boost::enable_if< typename boost::is_base_of< Eigen::ArrayBase< Derived > , Derived >::type >::type >
+{
+ static void resize( Eigen::ArrayBase< Derived > &v1 , const Eigen::ArrayBase< Derived > &v2 )
+ {
+ v1.derived().resizeLike(v2);
+ }
+};
+
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_EIGEN_EIGEN_RESIZE_HPP_DEFINED
diff --git a/include/boost/numeric/odeint/external/gsl/gsl_wrapper.hpp b/include/boost/numeric/odeint/external/gsl/gsl_wrapper.hpp
new file mode 100644
index 0000000..a856f6e
--- /dev/null
+++ b/include/boost/numeric/odeint/external/gsl/gsl_wrapper.hpp
@@ -0,0 +1,229 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/gsl/gsl_wrapper.hpp
+
+ [begin_description]
+ Wrapper for gsl_vector.
+ [end_description]
+
+ Copyright 2011-2012 Mario Mulansky
+ Copyright 2011 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_GSL_GSL_WRAPPER_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_GSL_GSL_WRAPPER_HPP_INCLUDED
+
+#include <new>
+
+#include <gsl/gsl_vector.h>
+
+#include <boost/type_traits/integral_constant.hpp>
+#include <boost/range.hpp>
+#include <boost/iterator/iterator_facade.hpp>
+
+
+#include <boost/numeric/odeint/util/state_wrapper.hpp>
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/copy.hpp>
+
+class const_gsl_vector_iterator;
+
+/*
+ * defines an iterator for gsl_vector
+ */
+class gsl_vector_iterator : public boost::iterator_facade< gsl_vector_iterator , double , boost::random_access_traversal_tag >
+{
+public :
+
+ gsl_vector_iterator( void ): m_p(0) , m_stride( 0 ) { }
+ explicit gsl_vector_iterator( gsl_vector *p ) : m_p( p->data ) , m_stride( p->stride ) { }
+ friend gsl_vector_iterator end_iterator( gsl_vector * );
+
+private :
+
+ friend class boost::iterator_core_access;
+ friend class const_gsl_vector_iterator;
+
+ void increment( void ) { m_p += m_stride; }
+ void decrement( void ) { m_p -= m_stride; }
+ void advance( ptrdiff_t n ) { m_p += n*m_stride; }
+ bool equal( const gsl_vector_iterator &other ) const { return this->m_p == other.m_p; }
+ bool equal( const const_gsl_vector_iterator &other ) const;
+ double& dereference( void ) const { return *m_p; }
+
+ double *m_p;
+ size_t m_stride;
+};
+
+
+
+/*
+ * defines an const iterator for gsl_vector
+ */
+class const_gsl_vector_iterator : public boost::iterator_facade< const_gsl_vector_iterator , const double , boost::random_access_traversal_tag >
+{
+public :
+
+ const_gsl_vector_iterator( void ): m_p(0) , m_stride( 0 ) { }
+ explicit const_gsl_vector_iterator( const gsl_vector *p ) : m_p( p->data ) , m_stride( p->stride ) { }
+ const_gsl_vector_iterator( const gsl_vector_iterator &p ) : m_p( p.m_p ) , m_stride( p.m_stride ) { }
+
+private :
+
+ friend class boost::iterator_core_access;
+ friend class gsl_vector_iterator;
+ friend const_gsl_vector_iterator end_iterator( const gsl_vector * );
+
+ void increment( void ) { m_p += m_stride; }
+ void decrement( void ) { m_p -= m_stride; }
+ void advance( ptrdiff_t n ) { m_p += n*m_stride; }
+ bool equal( const const_gsl_vector_iterator &other ) const { return this->m_p == other.m_p; }
+ bool equal( const gsl_vector_iterator &other ) const { return this->m_p == other.m_p; }
+ const double& dereference( void ) const { return *m_p; }
+
+ const double *m_p;
+ size_t m_stride;
+};
+
+
+bool gsl_vector_iterator::equal( const const_gsl_vector_iterator &other ) const { return this->m_p == other.m_p; }
+
+
+gsl_vector_iterator end_iterator( gsl_vector *x )
+{
+ gsl_vector_iterator iter( x );
+ iter.m_p += iter.m_stride * x->size;
+ return iter;
+}
+
+const_gsl_vector_iterator end_iterator( const gsl_vector *x )
+{
+ const_gsl_vector_iterator iter( x );
+ iter.m_p += iter.m_stride * x->size;
+ return iter;
+}
+
+
+
+
+namespace boost
+{
+template<>
+struct range_mutable_iterator< gsl_vector* >
+{
+ typedef gsl_vector_iterator type;
+};
+
+template<>
+struct range_const_iterator< gsl_vector* >
+{
+ typedef const_gsl_vector_iterator type;
+};
+} // namespace boost
+
+
+
+
+// template<>
+inline gsl_vector_iterator range_begin( gsl_vector *x )
+{
+ return gsl_vector_iterator( x );
+}
+
+// template<>
+inline const_gsl_vector_iterator range_begin( const gsl_vector *x )
+{
+ return const_gsl_vector_iterator( x );
+}
+
+// template<>
+inline gsl_vector_iterator range_end( gsl_vector *x )
+{
+ return end_iterator( x );
+}
+
+// template<>
+inline const_gsl_vector_iterator range_end( const gsl_vector *x )
+{
+ return end_iterator( x );
+}
+
+
+
+
+
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+template<>
+struct is_resizeable< gsl_vector* >
+{
+ //struct type : public boost::true_type { };
+ typedef boost::true_type type;
+ const static bool value = type::value;
+};
+
+template <>
+struct same_size_impl< gsl_vector* , gsl_vector* >
+{
+ static bool same_size( const gsl_vector* x , const gsl_vector* y )
+ {
+ return x->size == y->size;
+ }
+};
+
+template <>
+struct resize_impl< gsl_vector* , gsl_vector* >
+{
+ static void resize( gsl_vector* &x , const gsl_vector* y )
+ {
+ gsl_vector_free( x );
+ x = gsl_vector_alloc( y->size );
+ }
+};
+
+template<>
+struct state_wrapper< gsl_vector* >
+{
+ typedef double value_type;
+ typedef gsl_vector* state_type;
+ typedef state_wrapper< gsl_vector* > state_wrapper_type;
+
+ state_type m_v;
+
+ state_wrapper( )
+ {
+ m_v = gsl_vector_alloc( 1 );
+ }
+
+ state_wrapper( const state_wrapper_type &x )
+ {
+ resize( m_v , x.m_v );
+ gsl_vector_memcpy( m_v , x.m_v );
+ }
+
+
+ ~state_wrapper()
+ {
+ gsl_vector_free( m_v );
+ }
+
+};
+
+} // odeint
+} // numeric
+} // boost
+
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_GSL_GSL_WRAPPER_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/external/mkl/mkl_operations.hpp b/include/boost/numeric/odeint/external/mkl/mkl_operations.hpp
new file mode 100644
index 0000000..59ac4b8
--- /dev/null
+++ b/include/boost/numeric/odeint/external/mkl/mkl_operations.hpp
@@ -0,0 +1,181 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/mkl/mkl_operations.hpp
+
+ [begin_description]
+ Wrapper classes for intel math kernel library types.
+ Get a free, non-commercial download of MKL at
+ http://software.intel.com/en-us/articles/non-commercial-software-download/
+ [end_description]
+
+ Copyright 2010-2011 Mario Mulansky
+ Copyright 2011-2013 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_MKL_MKL_OPERATIONS_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_MKL_MKL_OPERATIONS_HPP_INCLUDED
+
+#include <iostream>
+
+#include <mkl_cblas.h>
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+
+/* exemplary example for writing bindings to the Intel MKL library
+ * see test/mkl for how to use mkl with odeint
+ * this is a quick and dirty implementation showing the general possibility.
+ * It works only with containers based on double and sequential memory allocation.
+ */
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+/* only defined for doubles */
+struct mkl_operations
+{
+ //template< class Fac1 , class Fac2 > struct scale_sum2;
+
+ template< class F1 = double , class F2 = F1 >
+ struct scale_sum2
+ {
+ typedef double Fac1;
+ typedef double Fac2;
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+
+ scale_sum2( const Fac1 alpha1 , const Fac2 alpha2 ) : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) { }
+
+ template< class T1 , class T2 , class T3 >
+ void operator()( T1 &t1 , const T2 &t2 , const T3 &t3) const
+ { // t1 = m_alpha1 * t2 + m_alpha2 * t3;
+ // we get Containers that have size() and [i]-access
+
+ const int n = t1.size();
+ //boost::numeric::odeint::copy( t1 , t3 );
+ if( &(t2[0]) != &(t1[0]) )
+ {
+ cblas_dcopy( n , &(t2[0]) , 1 , &(t1[0]) , 1 );
+ }
+ cblas_dscal( n , m_alpha1 , &(t1[0]) , 1 );
+ cblas_daxpy( n , m_alpha2 , &(t3[0]) , 1 , &(t1[0]) , 1 );
+ //daxpby( &n , &m_alpha2 , &(t3[0]) , &one , &m_alpha1 , &(t1[0]) , &one );
+ }
+ };
+
+ template< class F1 = double , class F2 = F1 , class F3 = F2 >
+ struct scale_sum3
+ {
+ typedef double Fac1;
+ typedef double Fac2;
+ typedef double Fac3;
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+ const Fac3 m_alpha3;
+
+ scale_sum3( const Fac1 alpha1 , const Fac2 alpha2 , const Fac3 alpha3 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) , m_alpha3( alpha3 ) { }
+
+ template< class T1 , class T2 , class T3 , class T4 >
+ void operator()( T1 &t1 , const T2 &t2 , const T3 &t3 , const T4 &t4 ) const
+ { // t1 = m_alpha1 * t2 + m_alpha2 * t3 + m_alpha3 * t4;
+ // we get Containers that have size() and [i]-access
+
+ const int n = t1.size();
+ //boost::numeric::odeint::copy( t1 , t3 );
+ if( &(t2[0]) != &(t1[0]) )
+ {
+ cblas_dcopy( n , &(t2[0]) , 1 , &(t1[0]) , 1 );
+ }
+ cblas_dscal( n , m_alpha1 , &(t1[0]) , 1 );
+ cblas_daxpy( n , m_alpha2 , &(t3[0]) , 1 , &(t1[0]) , 1 );
+ //daxpby( &n , &m_alpha2 , &(t3[0]) , &one , &m_alpha1 , &(t1[0]) , &one );
+ cblas_daxpy( n , m_alpha3 , &(t4[0]) , 1 , &(t1[0]) , 1 );
+ }
+ };
+
+ template< class F1 = double , class F2 = F1 , class F3 = F2 , class F4 = F3 >
+ struct scale_sum4
+ {
+ typedef double Fac1;
+ typedef double Fac2;
+ typedef double Fac3;
+ typedef double Fac4;
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+ const Fac3 m_alpha3;
+ const Fac4 m_alpha4;
+
+ scale_sum4( const Fac1 alpha1 , const Fac2 alpha2 , const Fac3 alpha3 , const Fac4 alpha4 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) , m_alpha3( alpha3 ) , m_alpha4( alpha4 ) { }
+
+ template< class T1 , class T2 , class T3 , class T4 , class T5 >
+ void operator()( T1 &t1 , const T2 &t2 , const T3 &t3 , const T4 &t4 , const T5 &t5 ) const
+ { // t1 = m_alpha1 * t2 + m_alpha2 * t3 + m_alpha3 * t4 + m_alpha4 * t5;
+ // we get Containers that have size() and [i]-access
+
+ const int n = t1.size();
+ //boost::numeric::odeint::copy( t1 , t3 );
+ if( &(t2[0]) != &(t1[0]) )
+ {
+ cblas_dcopy( n , &(t2[0]) , 1 , &(t1[0]) , 1 );
+ }
+
+ cblas_dscal( n , m_alpha1 , &(t1[0]) , 1 );
+ cblas_daxpy( n , m_alpha2 , &(t3[0]) , 1 , &(t1[0]) , 1 );
+ //daxpby( &n , &m_alpha2 , &(t3[0]) , &one , &m_alpha1 , &(t1[0]) , &one );
+ cblas_daxpy( n , m_alpha3 , &(t4[0]) , 1 , &(t1[0]) , 1 );
+ cblas_daxpy( n , m_alpha4 , &(t5[0]) , 1 , &(t1[0]) , 1 );
+ }
+ };
+
+
+ template< class F1 = double , class F2 = F1 , class F3 = F2 , class F4 = F3 , class F5 = F4 >
+ struct scale_sum5
+ {
+ typedef double Fac1;
+ typedef double Fac2;
+ typedef double Fac3;
+ typedef double Fac4;
+ typedef double Fac5;
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+ const Fac3 m_alpha3;
+ const Fac4 m_alpha4;
+ const Fac5 m_alpha5;
+
+ scale_sum5( const Fac1 alpha1 , const Fac2 alpha2 , const Fac3 alpha3 , const Fac4 alpha4 , const Fac5 alpha5 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) , m_alpha3( alpha3 ) , m_alpha4( alpha4 ) , m_alpha5( alpha5 ) { }
+
+ template< class T1 , class T2 , class T3 , class T4 , class T5 , class T6 >
+ void operator()( T1 &t1 , const T2 &t2 , const T3 &t3 , const T4 &t4 , const T5 &t5 , const T6 &t6 ) const
+ { // t1 = m_alpha1 * t2 + m_alpha2 * t3 + m_alpha3 * t4 + m_alpha4 * t5 + m_alpha5 * t6;
+ // we get Containers that have size() and [i]-access
+
+ const int n = t1.size();
+ //boost::numeric::odeint::copy( t1 , t3 );
+ if( &(t2[0]) != &(t1[0]) )
+ {
+ cblas_dcopy( n , &(t2[0]) , 1 , &(t1[0]) , 1 );
+ }
+
+ cblas_dscal( n , m_alpha1 , &(t1[0]) , 1 );
+ cblas_daxpy( n , m_alpha2 , &(t3[0]) , 1 , &(t1[0]) , 1 );
+ //daxpby( &n , &m_alpha2 , &(t3[0]) , &one , &m_alpha1 , &(t1[0]) , &one );
+ cblas_daxpy( n , m_alpha3 , &(t4[0]) , 1 , &(t1[0]) , 1 );
+ cblas_daxpy( n , m_alpha4 , &(t5[0]) , 1 , &(t1[0]) , 1 );
+ cblas_daxpy( n , m_alpha5 , &(t6[0]) , 1 , &(t1[0]) , 1 );
+ }
+ };
+
+};
+
+} // odeint
+} // numeric
+} // boost
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_MKL_MKL_OPERATIONS_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/external/mpi/mpi.hpp b/include/boost/numeric/odeint/external/mpi/mpi.hpp
new file mode 100644
index 0000000..26e1ae9
--- /dev/null
+++ b/include/boost/numeric/odeint/external/mpi/mpi.hpp
@@ -0,0 +1,25 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/mpi/mpi.hpp
+
+ [begin_description]
+ Wrappers for MPI.
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+ Copyright 2013 Pascal Germroth
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_MPI_MPI_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_MPI_MPI_HPP_INCLUDED
+
+#include <boost/numeric/odeint/external/mpi/mpi_vector_state.hpp>
+#include <boost/numeric/odeint/external/mpi/mpi_nested_algebra.hpp>
+
+#endif
diff --git a/include/boost/numeric/odeint/external/mpi/mpi_nested_algebra.hpp b/include/boost/numeric/odeint/external/mpi/mpi_nested_algebra.hpp
new file mode 100644
index 0000000..5d90225
--- /dev/null
+++ b/include/boost/numeric/odeint/external/mpi/mpi_nested_algebra.hpp
@@ -0,0 +1,62 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/mpi/mpi_nested_algebra.hpp
+
+ [begin_description]
+ Nested parallelized algebra for MPI.
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+ Copyright 2013 Pascal Germroth
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_MPI_MPI_NESTED_ALGEBRA_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_MPI_MPI_NESTED_ALGEBRA_HPP_INCLUDED
+
+#include <boost/numeric/odeint/algebra/norm_result_type.hpp>
+#include <boost/numeric/odeint/util/n_ary_helper.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+/** \brief MPI-parallelized algebra, wrapping another algebra.
+ */
+template< class InnerAlgebra >
+struct mpi_nested_algebra
+{
+
+// execute the InnerAlgebra on each node's local data.
+#define BOOST_ODEINT_GEN_BODY(n) \
+ InnerAlgebra::for_each##n( \
+ BOOST_PP_ENUM_BINARY_PARAMS(n, s, () BOOST_PP_INTERCEPT) , \
+ op \
+ );
+BOOST_ODEINT_GEN_FOR_EACH(BOOST_ODEINT_GEN_BODY)
+#undef BOOST_ODEINT_GEN_BODY
+
+
+ template< class NestedState >
+ static typename norm_result_type< typename NestedState::value_type >::type norm_inf( const NestedState &s )
+ {
+ typedef typename norm_result_type< typename NestedState::value_type >::type result_type;
+ // local maximum
+ result_type value = InnerAlgebra::norm_inf( s() );
+ // global maximum
+ return boost::mpi::all_reduce(s.world, value, boost::mpi::maximum<result_type>());
+ }
+
+};
+
+
+}
+}
+}
+
+#endif
diff --git a/include/boost/numeric/odeint/external/mpi/mpi_state.hpp b/include/boost/numeric/odeint/external/mpi/mpi_state.hpp
new file mode 100644
index 0000000..aba179c
--- /dev/null
+++ b/include/boost/numeric/odeint/external/mpi/mpi_state.hpp
@@ -0,0 +1,113 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/mpi/mpi_state.hpp
+
+ [begin_description]
+ A generic split state, storing partial data on each node.
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+ Copyright 2013 Pascal Germroth
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_MPI_MPI_STATE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_MPI_MPI_STATE_HPP_INCLUDED
+
+#include <vector>
+#include <algorithm>
+#include <boost/mpi.hpp>
+#include <boost/numeric/odeint/util/copy.hpp>
+#include <boost/numeric/odeint/util/split.hpp>
+#include <boost/numeric/odeint/util/resize.hpp>
+#include <boost/numeric/odeint/util/same_size.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/external/mpi/mpi_nested_algebra.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+/** \brief A container which has its contents distributed among the nodes.
+ */
+template< class InnerState >
+struct mpi_state
+{
+ typedef InnerState value_type;
+
+ // the node's local data.
+ InnerState m_data;
+
+ boost::mpi::communicator world;
+
+ mpi_state() {}
+ mpi_state(boost::mpi::communicator comm) : world(comm) {}
+
+ inline InnerState &operator()() { return m_data; }
+ inline const InnerState &operator()() const { return m_data; }
+};
+
+
+
+
+template< class InnerState >
+struct is_resizeable< mpi_state< InnerState > >
+ : is_resizeable< InnerState > { };
+
+
+template< class InnerState1 , class InnerState2 >
+struct same_size_impl< mpi_state< InnerState1 > , mpi_state< InnerState2 > >
+{
+ static bool same_size( const mpi_state< InnerState1 > &x , const mpi_state< InnerState2 > &y )
+ {
+ const bool local = boost::numeric::odeint::same_size(x(), y());
+ return boost::mpi::all_reduce(x.world, local, mpi::bitwise_and<bool>());
+ }
+};
+
+
+template< class InnerState1 , class InnerState2 >
+struct resize_impl< mpi_state< InnerState1 > , mpi_state< InnerState2 > >
+{
+ static void resize( mpi_state< InnerState1 > &x , const mpi_state< InnerState2 > &y )
+ {
+ // resize local parts on each node.
+ boost::numeric::odeint::resize(x(), y());
+ }
+};
+
+
+/** \brief Copy data between mpi_states of same size. */
+template< class InnerState1 , class InnerState2 >
+struct copy_impl< mpi_state< InnerState1 > , mpi_state< InnerState2 > >
+{
+ static void copy( const mpi_state< InnerState1 > &from , mpi_state< InnerState2 > &to )
+ {
+ // copy local parts on each node.
+ boost::numeric::odeint::copy(from(), to());
+ }
+};
+
+
+
+/** \brief Use `mpi_algebra` for `mpi_state`. */
+template< class InnerState >
+struct algebra_dispatcher< mpi_state< InnerState > >
+{
+ typedef mpi_nested_algebra<
+ typename algebra_dispatcher< InnerState >::algebra_type
+ > algebra_type;
+};
+
+
+}
+}
+}
+
+
+#endif
diff --git a/include/boost/numeric/odeint/external/mpi/mpi_vector_state.hpp b/include/boost/numeric/odeint/external/mpi/mpi_vector_state.hpp
new file mode 100644
index 0000000..096d40a
--- /dev/null
+++ b/include/boost/numeric/odeint/external/mpi/mpi_vector_state.hpp
@@ -0,0 +1,94 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/mpi/mpi_vector_state.hpp
+
+ [begin_description]
+ Copying a container from/to an mpi_state splits/joins it.
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+ Copyright 2013 Pascal Germroth
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_MPI_MPI_VECTOR_STATE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_MPI_MPI_VECTOR_STATE_HPP_INCLUDED
+
+#include <vector>
+#include <algorithm>
+#include <boost/mpi.hpp>
+#include <boost/numeric/odeint/util/copy.hpp>
+#include <boost/numeric/odeint/util/split_adaptor.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/external/mpi/mpi_state.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+/** \brief Split data from some container on node 0 to the slaves.
+ * Source must be a model of Random Access Range. */
+template< class Source , class InnerState >
+struct split_impl< Source, mpi_state< InnerState >,
+ typename boost::enable_if< boost::has_range_const_iterator<Source> >::type >
+{
+ typedef typename boost::range_iterator<const Source>::type iterator;
+
+ static void split( const Source &from, mpi_state< InnerState > &to )
+ {
+ std::vector< InnerState > pieces;
+ if(to.world.rank() == 0) {
+ const size_t num = static_cast<size_t>(to.world.size());
+ pieces.resize(num);
+ for(size_t i = 0 ; i < num ; i++) {
+ iterator_range<iterator> part = detail::make_split_range(from, i, num);
+ boost::numeric::odeint::resize(pieces[i], part);
+ boost::numeric::odeint::copy(part, pieces[i]);
+ }
+ }
+ // send to nodes
+ boost::mpi::scatter(to.world, pieces, to(), 0);
+ }
+};
+
+/** \brief Merge data from an mpi_state to some container on node 0.
+ * Target must be a model Single Pass Range. */
+template< class Target, class InnerState >
+struct unsplit_impl< mpi_state< InnerState >, Target,
+ typename boost::enable_if< boost::has_range_iterator<Target> >::type >
+{
+ typedef typename boost::range_iterator<Target>::type iterator;
+
+ static void unsplit( const mpi_state< InnerState > &from , Target &to )
+ {
+ std::vector< InnerState > pieces;
+ // send data to root
+ boost::mpi::gather(from.world, from(), pieces, 0);
+ if(from.world.rank() == 0) {
+ // check target size
+ size_t total_size = 0;
+ for(size_t i = 0 ; i < pieces.size() ; i++)
+ total_size += boost::size(pieces[i]);
+ BOOST_ASSERT( total_size <= boost::size(to) );
+ // copy parts
+ iterator out = boost::begin(to);
+ for(size_t i = 0 ; i < pieces.size() ; i++)
+ out = boost::copy(pieces[i], out);
+ }
+ }
+};
+
+
+}
+}
+}
+
+
+#endif
+
diff --git a/include/boost/numeric/odeint/external/mtl4/implicit_euler_mtl4.hpp b/include/boost/numeric/odeint/external/mtl4/implicit_euler_mtl4.hpp
new file mode 100644
index 0000000..a3f0350
--- /dev/null
+++ b/include/boost/numeric/odeint/external/mtl4/implicit_euler_mtl4.hpp
@@ -0,0 +1,162 @@
+/*
+[begin_description]
+Modification of the implicit Euler method, works with the MTL4 matrix library only.
+[end_description]
+
+Copyright 2012-2013 Andreas Angelopoulos
+Copyright 2012-2013 Karsten Ahnert
+Copyright 2012-2013 Mario Mulansky
+
+Distributed under the Boost Software License, Version 1.0.
+(See accompanying file LICENSE_1_0.txt or
+copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_IMPLICIT_EULER_MTL4_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_IMPLICIT_EULER_MTL4_HPP_INCLUDED
+
+
+#include <utility>
+
+#include <boost/numeric/odeint/util/bind.hpp>
+#include <boost/numeric/odeint/util/unwrap_reference.hpp>
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+
+#include <boost/numeric/odeint/external/mtl4/mtl4_resize.hpp>
+
+#include <boost/numeric/mtl/mtl.hpp>
+#include <boost/numeric/itl/itl.hpp>
+
+
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+template< class ValueType , class Resizer = initially_resizer >
+class implicit_euler_mtl4
+{
+
+public:
+
+ typedef ValueType value_type;
+ typedef value_type time_type;
+ typedef mtl::dense_vector<value_type> state_type;
+
+ typedef state_wrapper< state_type > wrapped_state_type;
+ typedef state_type deriv_type;
+ typedef state_wrapper< deriv_type > wrapped_deriv_type;
+ typedef mtl::compressed2D< value_type > matrix_type;
+ typedef state_wrapper< matrix_type > wrapped_matrix_type;
+
+ typedef Resizer resizer_type;
+ typedef stepper_tag stepper_category;
+
+ typedef implicit_euler_mtl4< ValueType , Resizer > stepper_type;
+
+
+ implicit_euler_mtl4( const value_type epsilon = 1E-6 )
+ : m_epsilon( epsilon ) , m_resizer() ,
+ m_dxdt() , m_x() ,
+ m_identity() , m_jacobi()
+ { }
+
+
+ template< class System >
+ void do_step( System system , state_type &x , time_type t , time_type dt )
+ {
+ typedef typename odeint::unwrap_reference< System >::type system_type;
+ typedef typename odeint::unwrap_reference< typename system_type::first_type >::type deriv_func_type;
+ typedef typename odeint::unwrap_reference< typename system_type::second_type >::type jacobi_func_type;
+ system_type &sys = system;
+ deriv_func_type &deriv_func = sys.first;
+ jacobi_func_type &jacobi_func = sys.second;
+
+ m_resizer.adjust_size( x , detail::bind(
+ &stepper_type::template resize_impl< state_type > , detail::ref( *this ) , detail::_1 ) );
+
+ m_identity.m_v = 1;
+
+ t += dt;
+ m_x.m_v = x;
+
+ deriv_func( x , m_dxdt.m_v , t );
+ jacobi_func( x , m_jacobi.m_v , t );
+
+
+ m_dxdt.m_v *= -dt;
+
+ m_jacobi.m_v *= dt;
+ m_jacobi.m_v -= m_identity.m_v ;
+
+
+
+ // using ilu_0 preconditioning -incomplete LU factorisation
+ // itl::pc::diagonal<matrix_type,double> L(m_jacobi.m_v);
+ itl::pc::ilu_0<matrix_type> L( m_jacobi.m_v );
+
+ solve( m_jacobi.m_v , m_x.m_v , m_dxdt.m_v , L );
+ x+= m_x.m_v;
+
+
+ }
+
+
+ template< class StateType >
+ void adjust_size( const StateType &x )
+ {
+ resize_impl( x );
+ }
+
+
+private:
+
+
+ /*
+ Applying approximate iterative linear solvers
+ default solver is Biconjugate gradient stabilized method
+ itl::bicgstab(A, x, b, L, iter);
+ */
+ template < class LinearOperator, class HilbertSpaceX, class HilbertSpaceB, class Preconditioner>
+ void solve(const LinearOperator& A, HilbertSpaceX& x, const HilbertSpaceB& b,
+ const Preconditioner& L, int max_iteractions =500)
+ {
+ // Termination criterion: r < 1e-6 * b or N iterations
+ itl::basic_iteration< double > iter( b , max_iteractions , 1e-6 );
+ itl::bicgstab( A , x , b , L , iter );
+
+ }
+
+
+ template< class StateIn >
+ bool resize_impl( const StateIn &x )
+ {
+ bool resized = false;
+ resized |= adjust_size_by_resizeability( m_dxdt , x , typename is_resizeable<deriv_type>::type() );
+ resized |= adjust_size_by_resizeability( m_x , x , typename is_resizeable<state_type>::type() );
+ resized |= adjust_size_by_resizeability( m_identity , x , typename is_resizeable<matrix_type>::type() );
+ resized |= adjust_size_by_resizeability( m_jacobi , x , typename is_resizeable<matrix_type>::type() );
+ return resized;
+ }
+
+
+private:
+
+ value_type m_epsilon;
+ resizer_type m_resizer;
+ wrapped_deriv_type m_dxdt;
+ wrapped_state_type m_x;
+ wrapped_matrix_type m_identity;
+ wrapped_matrix_type m_jacobi;
+};
+
+
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_IMPLICIT_EULER_MTL4_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/external/mtl4/mtl4.hpp b/include/boost/numeric/odeint/external/mtl4/mtl4.hpp
new file mode 100644
index 0000000..9b9ebf7
--- /dev/null
+++ b/include/boost/numeric/odeint/external/mtl4/mtl4.hpp
@@ -0,0 +1,23 @@
+/*
+ [auto_generated]
+ /boost/numeric/odeint/external/mtl4/mtl4.hpp
+
+ [begin_description]
+ includes all headers required for using mtl4 with odeint
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_MTL4_MTL4_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_MTL4_MTL4_HPP_INCLUDED
+
+#include <boost/numeric/odeint/external/mtl4/mtl4_algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/external/mtl4/mtl4_resize.hpp>
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_MTL4_MTL4_INCLUDED
diff --git a/include/boost/numeric/odeint/external/mtl4/mtl4_algebra_dispatcher.hpp b/include/boost/numeric/odeint/external/mtl4/mtl4_algebra_dispatcher.hpp
new file mode 100644
index 0000000..8f6bfbe
--- /dev/null
+++ b/include/boost/numeric/odeint/external/mtl4/mtl4_algebra_dispatcher.hpp
@@ -0,0 +1,99 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/mtl4/mtl4_algebra_dispatcher.hpp
+
+ [begin_description]
+ specialization of the algebra dispatcher for mtl4
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#ifndef BOOST_NUMERIC_ODEINT_MTL4_MTL4_ALGEBRA_DISPATCHER_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_MTL4_MTL4_ALGEBRA_DISPATCHER_HPP_INCLUDED
+
+#include <boost/numeric/mtl/mtl.hpp>
+
+#include <boost/numeric/odeint/algebra/vector_space_algebra.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template<typename Value, typename Parameters>
+struct algebra_dispatcher< mtl::dense_vector< Value , Parameters > >
+{
+ typedef vector_space_algebra algebra_type;
+};
+
+template<typename Value, typename Parameters>
+struct algebra_dispatcher< mtl::dense2D< Value , Parameters > >
+{
+ typedef vector_space_algebra algebra_type;
+};
+
+template<typename Value , size_t BitMask , typename Parameters>
+struct algebra_dispatcher< mtl::morton_dense< Value , BitMask, Parameters > >
+{
+ typedef vector_space_algebra algebra_type;
+};
+
+template<typename Value, typename Parameters>
+struct algebra_dispatcher< mtl::compressed2D< Value , Parameters > >
+{
+ typedef vector_space_algebra algebra_type;
+};
+
+// specialization of infinity norm calculation
+
+template<typename Value, typename Parameters>
+struct vector_space_norm_inf< mtl::dense_vector< Value , Parameters > >
+{
+ typedef Value result_type;
+ Value operator()( const mtl::dense_vector< Value , Parameters > &x ) const
+ {
+ return mtl::infinity_norm(x);
+ }
+};
+
+template<typename Value, typename Parameters>
+struct vector_space_norm_inf< mtl::dense2D< Value , Parameters > >
+{
+ typedef Value result_type;
+ Value operator()( const mtl::dense2D< Value , Parameters > &x ) const
+ {
+ return mtl::infinity_norm(x);
+ }
+};
+
+template<typename Value , size_t BitMask , typename Parameters>
+struct vector_space_norm_inf< mtl::morton_dense< Value , BitMask , Parameters > >
+{
+ typedef Value result_type;
+ Value operator()( const mtl::morton_dense< Value , BitMask , Parameters > &x ) const
+ {
+ return mtl::infinity_norm(x);
+ }
+};
+
+template<typename Value, typename Parameters>
+struct vector_space_norm_inf< mtl::compressed2D< Value , Parameters > >
+{
+ typedef Value result_type;
+ Value operator()( const mtl::compressed2D< Value , Parameters > &x ) const
+ {
+ return mtl::infinity_norm(x);
+ }
+};
+
+}
+}
+}
+
+#endif // BOOST_NUMERIC_ODEINT_MTL4_MTL4_ALGEBRA_DISPATCHER_INCLUDED
diff --git a/include/boost/numeric/odeint/external/mtl4/mtl4_resize.hpp b/include/boost/numeric/odeint/external/mtl4/mtl4_resize.hpp
new file mode 100644
index 0000000..6295c03
--- /dev/null
+++ b/include/boost/numeric/odeint/external/mtl4/mtl4_resize.hpp
@@ -0,0 +1,133 @@
+/*
+[begin_description]
+Modification of the implicit Euler method, works with the MTL4 matrix library only.
+[end_description]
+
+Copyright 2012-2013 Andreas Angelopoulos
+Copyright 2012-2013 Karsten Ahnert
+Copyright 2012-2013 Mario Mulansky
+
+Distributed under the Boost Software License, Version 1.0.
+(See accompanying file LICENSE_1_0.txt or
+copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_MTL4_RESIZE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_MTL4_RESIZE_HPP_INCLUDED
+
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resize.hpp>
+#include <boost/numeric/odeint/util/same_size.hpp>
+
+#include <boost/numeric/mtl/vector/dense_vector.hpp>
+#include <boost/numeric/mtl/matrix/dense2D.hpp>
+#include <boost/numeric/mtl/matrix/compressed2D.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+template< class Value , class Parameters >
+struct is_resizeable< mtl::dense_vector< Value , Parameters > >
+{
+ typedef boost::true_type type;
+ const static bool value = type::value;
+};
+
+template< class Value , class Parameters >
+struct is_resizeable< mtl::dense2D< Value , Parameters > >
+{
+ typedef boost::true_type type;
+ const static bool value = type::value;
+};
+
+template< class Value , class Parameters >
+struct is_resizeable< mtl::compressed2D< Value , Parameters > >
+{
+ typedef boost::true_type type;
+ const static bool value = type::value;
+};
+
+
+
+
+template< class Value , class Parameters >
+struct same_size_impl< mtl::dense_vector< Value , Parameters > , mtl::dense_vector< Value , Parameters > >
+{
+ static bool same_size( const mtl::dense_vector< Value , Parameters > &v1 ,
+ const mtl::dense_vector< Value , Parameters > &v2 )
+ {
+ return mtl::size( v1 ) == mtl::size( v2 );
+ }
+};
+
+template< class Value , class Parameters >
+struct resize_impl< mtl::dense_vector< Value , Parameters > , mtl::dense_vector< Value , Parameters > >
+{
+ static void resize( mtl::dense_vector< Value , Parameters > &v1 ,
+ const mtl::dense_vector< Value , Parameters > &v2 )
+ {
+ v1.change_dim( mtl::size( v2 ) );
+ }
+};
+
+
+
+template< class Value , class MatrixParameters , class VectorParameters >
+struct same_size_impl< mtl::dense2D< Value , MatrixParameters > , mtl::dense_vector< Value , VectorParameters > >
+{
+ static bool same_size( const mtl::dense2D< Value , MatrixParameters > &m ,
+ const mtl::dense_vector< Value , VectorParameters > &v )
+ {
+ return ( ( mtl::size( v ) == m.num_cols() ) && ( mtl::size( v ) == m.num_rows() ) );
+ }
+};
+
+template< class Value , class MatrixParameters , class VectorParameters >
+struct resize_impl< mtl::dense2D< Value , MatrixParameters > , mtl::dense_vector< Value , VectorParameters > >
+{
+ static void resize( mtl::dense2D< Value , MatrixParameters > &m ,
+ const mtl::dense_vector< Value , VectorParameters > &v )
+ {
+ m.change_dim( mtl::size( v ) , mtl::size( v ) , false );
+ }
+};
+
+
+
+
+template< class Value , class MatrixParameters , class VectorParameters >
+struct same_size_impl< mtl::compressed2D< Value , MatrixParameters > , mtl::dense_vector< Value , VectorParameters > >
+{
+ static bool same_size( const mtl::compressed2D< Value , MatrixParameters > &m ,
+ const mtl::dense_vector< Value , VectorParameters > &v )
+ {
+ return ( ( mtl::size( v ) == m.num_cols() ) && ( mtl::size( v ) == m.num_rows() ) );
+ }
+};
+
+template< class Value , class MatrixParameters , class VectorParameters >
+struct resize_impl< mtl::compressed2D< Value , MatrixParameters > , mtl::dense_vector< Value , VectorParameters > >
+{
+ static void resize( mtl::compressed2D< Value , MatrixParameters > &m ,
+ const mtl::dense_vector< Value , VectorParameters > &v )
+ {
+ m.change_dim( mtl::size( v ) , mtl::size( v ) );
+ }
+};
+
+
+
+
+
+
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_MTL4_RESIZE_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/external/nt2/nt2_algebra_dispatcher.hpp b/include/boost/numeric/odeint/external/nt2/nt2_algebra_dispatcher.hpp
new file mode 100644
index 0000000..7b82a8b
--- /dev/null
+++ b/include/boost/numeric/odeint/external/nt2/nt2_algebra_dispatcher.hpp
@@ -0,0 +1,25 @@
+//==============================================================================
+// Copyright 2014 LRI UMR 8623 CNRS/Univ Paris Sud XI
+// Copyright 2014 NumScale SAS
+//
+// Distributed under the Boost Software License, Version 1.0.
+// See accompanying file LICENSE.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt
+//==============================================================================
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_NT2_NT2_ALGEBRA_DISPATCHER_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_NT2_NT2_ALGEBRA_DISPATCHER_HPP_INCLUDED
+
+#include <nt2/core/container/table/table.hpp>
+
+#include <boost/numeric/odeint/algebra/vector_space_algebra.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+
+namespace boost { namespace numeric { namespace odeint {
+template<typename T, typename S>
+struct algebra_dispatcher<nt2::container::table<T,S> >
+{
+ typedef vector_space_algebra algebra_type;
+};
+} } }
+
+#endif
diff --git a/include/boost/numeric/odeint/external/nt2/nt2_copy.hpp b/include/boost/numeric/odeint/external/nt2/nt2_copy.hpp
new file mode 100644
index 0000000..0fd5588
--- /dev/null
+++ b/include/boost/numeric/odeint/external/nt2/nt2_copy.hpp
@@ -0,0 +1,33 @@
+//==============================================================================
+// Copyright 2014 LASMEA UMR 6602 CNRS/Univ. Clermont II
+// Copyright 2014 LRI UMR 8623 CNRS/Univ Paris Sud XI
+// Copyright 2014 MetaScale SAS
+//
+// Distributed under the Boost Software License, Version 1.0.
+// See accompanying file LICENSE.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt
+//==============================================================================
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_NT2_NT2_COPY_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_NT2_NT2_COPY_HPP_INCLUDED
+
+#include <nt2/core/container/table/table.hpp>
+
+#include <boost/numeric/odeint/util/copy.hpp>
+
+namespace boost { namespace numeric { namespace odeint {
+
+template<typename T, typename S>
+struct copy_impl< nt2::container::table<T,S>
+ , nt2::container::table<T,S>
+ >
+{
+ static void copy ( const nt2::container::table<T,S> &v1
+ , nt2::container::table<T,S> &v2
+ )
+ {
+ v2 = v1;
+ }
+};
+} } }
+
+#endif
diff --git a/include/boost/numeric/odeint/external/nt2/nt2_norm_inf.hpp b/include/boost/numeric/odeint/external/nt2/nt2_norm_inf.hpp
new file mode 100644
index 0000000..81f867e
--- /dev/null
+++ b/include/boost/numeric/odeint/external/nt2/nt2_norm_inf.hpp
@@ -0,0 +1,31 @@
+//==============================================================================
+// Copyright 2014 LRI UMR 8623 CNRS/Univ Paris Sud XI
+// Copyright 2014 NumScale SAS
+//
+// Distributed under the Boost Software License, Version 1.0.
+// See accompanying file LICENSE.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt
+//==============================================================================
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_NT2_NT2_NORM_INF_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_NT2_NT2_NORM_INF_HPP_INCLUDED
+
+#include <nt2/core/container/table/table.hpp>
+#include <nt2/include/functions/globalmax.hpp>
+#include <nt2/include/functions/abs.hpp>
+
+#include <boost/numeric/odeint/algebra/vector_space_algebra.hpp>
+
+namespace boost { namespace numeric { namespace odeint
+{
+ template<typename T, typename S>
+ struct vector_space_norm_inf<nt2::container::table<T,S> >
+ {
+ typedef T result_type;
+ result_type operator()(const nt2::container::table<T,S> &v1) const
+ {
+ return nt2::globalmax(nt2::abs(v1));
+ }
+ };
+} } }
+
+#endif
diff --git a/include/boost/numeric/odeint/external/nt2/nt2_resize.hpp b/include/boost/numeric/odeint/external/nt2/nt2_resize.hpp
new file mode 100644
index 0000000..d9c2359
--- /dev/null
+++ b/include/boost/numeric/odeint/external/nt2/nt2_resize.hpp
@@ -0,0 +1,52 @@
+//==============================================================================
+// Copyright 2014 LRI UMR 8623 CNRS/Univ Paris Sud XI
+// Copyright 2014 NumScale SAS
+//
+// Distributed under the Boost Software License, Version 1.0.
+// See accompanying file LICENSE.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt
+//==============================================================================
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_NT2_NT2_RESIZE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_NT2_NT2_RESIZE_HPP_INCLUDED
+
+#include <nt2/core/container/table/table.hpp>
+
+#include <boost/numeric/odeint/util/same_size.hpp>
+
+namespace boost { namespace numeric { namespace odeint {
+
+template<typename T, typename S>
+struct is_resizeable< nt2::container::table<T,S> >
+{
+ typedef boost::true_type type;
+ static const bool value = type::value;
+};
+
+template<typename T, typename S>
+struct same_size_impl< nt2::container::table<T,S>
+ , nt2::container::table<T,S>
+ >
+{
+ static bool same_size ( const nt2::container::table<T,S> &v1
+ , const nt2::container::table<T,S> &v2
+ )
+ {
+ return v1.extent() == v2.extent();
+ }
+};
+
+template<typename T, typename S>
+struct resize_impl< nt2::container::table<T,S>
+ , nt2::container::table<T,S>
+ >
+{
+ static void resize ( nt2::container::table<T,S> &v1
+ , const nt2::container::table<T,S> &v2
+ )
+ {
+ v1.resize( v2.extent() );
+ }
+};
+} } }
+
+#endif
diff --git a/include/boost/numeric/odeint/external/openmp/openmp.hpp b/include/boost/numeric/odeint/external/openmp/openmp.hpp
new file mode 100644
index 0000000..0d6fb0b
--- /dev/null
+++ b/include/boost/numeric/odeint/external/openmp/openmp.hpp
@@ -0,0 +1,31 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/openmp/openmp.hpp
+
+ [begin_description]
+ Wrappers for OpenMP.
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+ Copyright 2013 Pascal Germroth
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_OPENMP_OPENMP_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_OPENMP_OPENMP_HPP_INCLUDED
+
+// level 1: parallel iteration over random access container
+#include <boost/numeric/odeint/external/openmp/openmp_range_algebra.hpp>
+
+// level 2: split range state
+#include <boost/numeric/odeint/external/openmp/openmp_state.hpp>
+
+// level 3: process a random access container of sub-states in parallel
+#include <boost/numeric/odeint/external/openmp/openmp_nested_algebra.hpp>
+
+#endif
diff --git a/include/boost/numeric/odeint/external/openmp/openmp_nested_algebra.hpp b/include/boost/numeric/odeint/external/openmp/openmp_nested_algebra.hpp
new file mode 100644
index 0000000..a3d299f
--- /dev/null
+++ b/include/boost/numeric/odeint/external/openmp/openmp_nested_algebra.hpp
@@ -0,0 +1,281 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/openmp/openmp_nested_algebra.hpp
+
+ [begin_description]
+ Nested parallelized algebra for OpenMP.
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+ Copyright 2013 Pascal Germroth
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_OPENMP_OPENMP_NESTED_ALGEBRA_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_OPENMP_OPENMP_NESTED_ALGEBRA_HPP_INCLUDED
+
+#include <boost/assert.hpp>
+#include <boost/range.hpp>
+#include <boost/numeric/odeint/algebra/norm_result_type.hpp>
+#include <boost/numeric/odeint/util/n_ary_helper.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+/** \brief OpenMP-parallelized algebra, wrapping another, non-parallelized algebra.
+ *
+ * NestedState must be a model of Random Access Range, where the elements are sub-states
+ * which will be processed in parallel.
+ */
+template< class InnerAlgebra >
+struct openmp_nested_algebra
+{
+
+#if __cplusplus >= 201103L // C++11 supports _Pragma
+
+#define BOOST_ODEINT_GEN_LOCAL(z, n, unused) \
+ BOOST_ASSERT_MSG( len == boost::size(s ## n), "All nested state ranges must have the same size." ); \
+ typename boost::range_iterator<S ## n>::type beg ## n = boost::begin(s ## n);
+#define BOOST_ODEINT_GEN_BODY(n) \
+ const size_t len = boost::size(s0); \
+ BOOST_PP_REPEAT(n, BOOST_ODEINT_GEN_LOCAL, ~) \
+ _Pragma("omp parallel for schedule(runtime)") \
+ for( size_t i = 0 ; i < len ; i++ ) \
+ InnerAlgebra::for_each##n( \
+ BOOST_PP_ENUM_BINARY_PARAMS(n, beg, [i] BOOST_PP_INTERCEPT) , \
+ op \
+ );
+BOOST_ODEINT_GEN_FOR_EACH(BOOST_ODEINT_GEN_BODY)
+#undef BOOST_ODEINT_GEN_BODY
+#undef BOOST_ODEINT_GEN_LOCAL
+
+#else
+
+ template< class S0 , class Op > static void for_each1 ( S0 &s0 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) InnerAlgebra::for_each1( beg0 [i] , op );
+ }
+ template< class S0 , class S1 , class Op > static void for_each2 ( S0 &s0 , S1 &s1 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) InnerAlgebra::for_each2( beg0 [i] , beg1 [i] , op );
+ }
+ template< class S0 , class S1 , class S2 , class Op > static void for_each3 ( S0 &s0 , S1 &s1 , S2 &s2 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) InnerAlgebra::for_each3( beg0 [i] , beg1 [i] , beg2 [i] , op );
+ }
+ template< class S0 , class S1 , class S2 , class S3 , class Op > static void for_each4 ( S0 &s0 , S1 &s1 , S2 &s2 , S3 &s3 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ typename boost::range_iterator<S3>::type beg3 = boost::begin(s3);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) InnerAlgebra::for_each4( beg0 [i] , beg1 [i] , beg2 [i] , beg3 [i] , op );
+ }
+ template< class S0 , class S1 , class S2 , class S3 , class S4 , class Op > static void for_each5 ( S0 &s0 , S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ typename boost::range_iterator<S3>::type beg3 = boost::begin(s3);
+ typename boost::range_iterator<S4>::type beg4 = boost::begin(s4);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) InnerAlgebra::for_each5( beg0 [i] , beg1 [i] , beg2 [i] , beg3 [i] , beg4 [i] , op );
+ }
+ template< class S0 , class S1 , class S2 , class S3 , class S4 , class S5 , class Op > static void for_each6 ( S0 &s0 , S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ typename boost::range_iterator<S3>::type beg3 = boost::begin(s3);
+ typename boost::range_iterator<S4>::type beg4 = boost::begin(s4);
+ typename boost::range_iterator<S5>::type beg5 = boost::begin(s5);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) InnerAlgebra::for_each6( beg0 [i] , beg1 [i] , beg2 [i] , beg3 [i] , beg4 [i] , beg5 [i] , op );
+ }
+ template< class S0 , class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class Op > static void for_each7 ( S0 &s0 , S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ typename boost::range_iterator<S3>::type beg3 = boost::begin(s3);
+ typename boost::range_iterator<S4>::type beg4 = boost::begin(s4);
+ typename boost::range_iterator<S5>::type beg5 = boost::begin(s5);
+ typename boost::range_iterator<S6>::type beg6 = boost::begin(s6);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) InnerAlgebra::for_each7( beg0 [i] , beg1 [i] , beg2 [i] , beg3 [i] , beg4 [i] , beg5 [i] , beg6 [i] , op );
+ }
+ template< class S0 , class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class S7 , class Op > static void for_each8 ( S0 &s0 , S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ typename boost::range_iterator<S3>::type beg3 = boost::begin(s3);
+ typename boost::range_iterator<S4>::type beg4 = boost::begin(s4);
+ typename boost::range_iterator<S5>::type beg5 = boost::begin(s5);
+ typename boost::range_iterator<S6>::type beg6 = boost::begin(s6);
+ typename boost::range_iterator<S7>::type beg7 = boost::begin(s7);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) InnerAlgebra::for_each8( beg0 [i] , beg1 [i] , beg2 [i] , beg3 [i] , beg4 [i] , beg5 [i] , beg6 [i] , beg7 [i] , op );
+ }
+ template< class S0 , class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class S7 , class S8 , class Op > static void for_each9 ( S0 &s0 , S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ typename boost::range_iterator<S3>::type beg3 = boost::begin(s3);
+ typename boost::range_iterator<S4>::type beg4 = boost::begin(s4);
+ typename boost::range_iterator<S5>::type beg5 = boost::begin(s5);
+ typename boost::range_iterator<S6>::type beg6 = boost::begin(s6);
+ typename boost::range_iterator<S7>::type beg7 = boost::begin(s7);
+ typename boost::range_iterator<S8>::type beg8 = boost::begin(s8);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) InnerAlgebra::for_each9( beg0 [i] , beg1 [i] , beg2 [i] , beg3 [i] , beg4 [i] , beg5 [i] , beg6 [i] , beg7 [i] , beg8 [i] , op );
+ }
+ template< class S0 , class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class S7 , class S8 , class S9 , class Op > static void for_each10 ( S0 &s0 , S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ typename boost::range_iterator<S3>::type beg3 = boost::begin(s3);
+ typename boost::range_iterator<S4>::type beg4 = boost::begin(s4);
+ typename boost::range_iterator<S5>::type beg5 = boost::begin(s5);
+ typename boost::range_iterator<S6>::type beg6 = boost::begin(s6);
+ typename boost::range_iterator<S7>::type beg7 = boost::begin(s7);
+ typename boost::range_iterator<S8>::type beg8 = boost::begin(s8);
+ typename boost::range_iterator<S9>::type beg9 = boost::begin(s9);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) InnerAlgebra::for_each10( beg0 [i] , beg1 [i] , beg2 [i] , beg3 [i] , beg4 [i] , beg5 [i] , beg6 [i] , beg7 [i] , beg8 [i] , beg9 [i] , op );
+ }
+ template< class S0 , class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class S7 , class S8 , class S9 , class S10 , class Op > static void for_each11 ( S0 &s0 , S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ typename boost::range_iterator<S3>::type beg3 = boost::begin(s3);
+ typename boost::range_iterator<S4>::type beg4 = boost::begin(s4);
+ typename boost::range_iterator<S5>::type beg5 = boost::begin(s5);
+ typename boost::range_iterator<S6>::type beg6 = boost::begin(s6);
+ typename boost::range_iterator<S7>::type beg7 = boost::begin(s7);
+ typename boost::range_iterator<S8>::type beg8 = boost::begin(s8);
+ typename boost::range_iterator<S9>::type beg9 = boost::begin(s9);
+ typename boost::range_iterator<S10>::type beg10 = boost::begin(s10);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) InnerAlgebra::for_each11( beg0 [i] , beg1 [i] , beg2 [i] , beg3 [i] , beg4 [i] , beg5 [i] , beg6 [i] , beg7 [i] , beg8 [i] , beg9 [i] , beg10 [i] , op );
+ }
+ template< class S0 , class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class S7 , class S8 , class S9 , class S10 , class S11 , class Op > static void for_each12 ( S0 &s0 , S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ typename boost::range_iterator<S3>::type beg3 = boost::begin(s3);
+ typename boost::range_iterator<S4>::type beg4 = boost::begin(s4);
+ typename boost::range_iterator<S5>::type beg5 = boost::begin(s5);
+ typename boost::range_iterator<S6>::type beg6 = boost::begin(s6);
+ typename boost::range_iterator<S7>::type beg7 = boost::begin(s7);
+ typename boost::range_iterator<S8>::type beg8 = boost::begin(s8);
+ typename boost::range_iterator<S9>::type beg9 = boost::begin(s9);
+ typename boost::range_iterator<S10>::type beg10 = boost::begin(s10);
+ typename boost::range_iterator<S11>::type beg11 = boost::begin(s11);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) InnerAlgebra::for_each12( beg0 [i] , beg1 [i] , beg2 [i] , beg3 [i] , beg4 [i] , beg5 [i] , beg6 [i] , beg7 [i] , beg8 [i] , beg9 [i] , beg10 [i] , beg11 [i] , op );
+ }
+ template< class S0 , class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class S7 , class S8 , class S9 , class S10 , class S11 , class S12 , class Op > static void for_each13 ( S0 &s0 , S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , S12 &s12 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ typename boost::range_iterator<S3>::type beg3 = boost::begin(s3);
+ typename boost::range_iterator<S4>::type beg4 = boost::begin(s4);
+ typename boost::range_iterator<S5>::type beg5 = boost::begin(s5);
+ typename boost::range_iterator<S6>::type beg6 = boost::begin(s6);
+ typename boost::range_iterator<S7>::type beg7 = boost::begin(s7);
+ typename boost::range_iterator<S8>::type beg8 = boost::begin(s8);
+ typename boost::range_iterator<S9>::type beg9 = boost::begin(s9);
+ typename boost::range_iterator<S10>::type beg10 = boost::begin(s10);
+ typename boost::range_iterator<S11>::type beg11 = boost::begin(s11);
+ typename boost::range_iterator<S12>::type beg12 = boost::begin(s12);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) InnerAlgebra::for_each13( beg0 [i] , beg1 [i] , beg2 [i] , beg3 [i] , beg4 [i] , beg5 [i] , beg6 [i] , beg7 [i] , beg8 [i] , beg9 [i] , beg10 [i] , beg11 [i] , beg12 [i] , op );
+ }
+ template< class S0 , class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class S7 , class S8 , class S9 , class S10 , class S11 , class S12 , class S13 , class Op > static void for_each14 ( S0 &s0 , S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , S12 &s12 , S13 &s13 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ typename boost::range_iterator<S3>::type beg3 = boost::begin(s3);
+ typename boost::range_iterator<S4>::type beg4 = boost::begin(s4);
+ typename boost::range_iterator<S5>::type beg5 = boost::begin(s5);
+ typename boost::range_iterator<S6>::type beg6 = boost::begin(s6);
+ typename boost::range_iterator<S7>::type beg7 = boost::begin(s7);
+ typename boost::range_iterator<S8>::type beg8 = boost::begin(s8);
+ typename boost::range_iterator<S9>::type beg9 = boost::begin(s9);
+ typename boost::range_iterator<S10>::type beg10 = boost::begin(s10);
+ typename boost::range_iterator<S11>::type beg11 = boost::begin(s11);
+ typename boost::range_iterator<S12>::type beg12 = boost::begin(s12);
+ typename boost::range_iterator<S13>::type beg13 = boost::begin(s13);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) InnerAlgebra::for_each14( beg0 [i] , beg1 [i] , beg2 [i] , beg3 [i] , beg4 [i] , beg5 [i] , beg6 [i] , beg7 [i] , beg8 [i] , beg9 [i] , beg10 [i] , beg11 [i] , beg12 [i] , beg13 [i] , op );
+ }
+ template< class S0 , class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class S7 , class S8 , class S9 , class S10 , class S11 , class S12 , class S13 , class S14 , class Op > static void for_each15 ( S0 &s0 , S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , S12 &s12 , S13 &s13 , S14 &s14 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ typename boost::range_iterator<S3>::type beg3 = boost::begin(s3);
+ typename boost::range_iterator<S4>::type beg4 = boost::begin(s4);
+ typename boost::range_iterator<S5>::type beg5 = boost::begin(s5);
+ typename boost::range_iterator<S6>::type beg6 = boost::begin(s6);
+ typename boost::range_iterator<S7>::type beg7 = boost::begin(s7);
+ typename boost::range_iterator<S8>::type beg8 = boost::begin(s8);
+ typename boost::range_iterator<S9>::type beg9 = boost::begin(s9);
+ typename boost::range_iterator<S10>::type beg10 = boost::begin(s10);
+ typename boost::range_iterator<S11>::type beg11 = boost::begin(s11);
+ typename boost::range_iterator<S12>::type beg12 = boost::begin(s12);
+ typename boost::range_iterator<S13>::type beg13 = boost::begin(s13);
+ typename boost::range_iterator<S14>::type beg14 = boost::begin(s14);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) InnerAlgebra::for_each15( beg0 [i] , beg1 [i] , beg2 [i] , beg3 [i] , beg4 [i] , beg5 [i] , beg6 [i] , beg7 [i] , beg8 [i] , beg9 [i] , beg10 [i] , beg11 [i] , beg12 [i] , beg13 [i] , beg14 [i] , op );
+ }
+
+#endif
+
+
+ template< class NestedState >
+ static typename norm_result_type< typename NestedState::value_type >::type norm_inf( const NestedState &s )
+ {
+ typedef typename boost::range_iterator<const NestedState>::type iterator;
+ typedef typename std::iterator_traits<iterator>::value_type value_type;
+ typedef typename norm_result_type<value_type>::type result_type;
+ result_type init = static_cast< result_type >( 0 );
+ const size_t len = boost::size(s);
+ iterator beg = boost::begin(s);
+# pragma omp parallel for reduction(max: init) schedule(dynamic)
+ for( size_t i = 0 ; i < len ; i++ )
+ init = (std::max)( init , InnerAlgebra::norm_inf( beg[i] ) );
+ return init;
+ }
+
+};
+
+
+}
+}
+}
+
+#endif
diff --git a/include/boost/numeric/odeint/external/openmp/openmp_range_algebra.hpp b/include/boost/numeric/odeint/external/openmp/openmp_range_algebra.hpp
new file mode 100644
index 0000000..295db64
--- /dev/null
+++ b/include/boost/numeric/odeint/external/openmp/openmp_range_algebra.hpp
@@ -0,0 +1,276 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/openmp/openmp_range_algebra.hpp
+
+ [begin_description]
+ Range algebra for OpenMP.
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+ Copyright 2013 Pascal Germroth
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_OPENMP_OPENMP_RANGE_ALGEBRA_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_OPENMP_OPENMP_RANGE_ALGEBRA_HPP_INCLUDED
+
+#include <boost/assert.hpp>
+#include <boost/range.hpp>
+#include <boost/numeric/odeint/algebra/norm_result_type.hpp>
+#include <boost/numeric/odeint/util/n_ary_helper.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+/** \brief OpenMP-parallelized range algebra.
+ *
+ * State must be a model of Random Access Range.
+ */
+struct openmp_range_algebra
+{
+
+#if __cplusplus >= 201103L // C++11 supports _Pragma
+
+#define BOOST_ODEINT_GEN_LOCAL(z, n, unused) \
+ BOOST_ASSERT_MSG( len == boost::size(s ## n), "All state ranges must have the same size." ); \
+ typename boost::range_iterator<S ## n>::type beg ## n = boost::begin(s ## n);
+#define BOOST_ODEINT_GEN_BODY(n) \
+ const size_t len = boost::size(s0); \
+ BOOST_PP_REPEAT(n, BOOST_ODEINT_GEN_LOCAL, ~) \
+ _Pragma("omp parallel for schedule(runtime)") \
+ for( size_t i = 0 ; i < len ; i++ ) \
+ op( BOOST_PP_ENUM_BINARY_PARAMS(n, beg, [i] BOOST_PP_INTERCEPT) );
+BOOST_ODEINT_GEN_FOR_EACH(BOOST_ODEINT_GEN_BODY)
+#undef BOOST_ODEINT_GEN_BODY
+#undef BOOST_ODEINT_GEN_LOCAL
+
+#else
+
+ template< class S0 , class Op > static void for_each1 ( S0 &s0 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) op( beg0 [i] );
+ }
+ template< class S0 , class S1 , class Op > static void for_each2 ( S0 &s0 , S1 &s1 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) op( beg0 [i] , beg1 [i] );
+ }
+ template< class S0 , class S1 , class S2 , class Op > static void for_each3 ( S0 &s0 , S1 &s1 , S2 &s2 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) op( beg0 [i] , beg1 [i] , beg2 [i] );
+ }
+ template< class S0 , class S1 , class S2 , class S3 , class Op > static void for_each4 ( S0 &s0 , S1 &s1 , S2 &s2 , S3 &s3 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ typename boost::range_iterator<S3>::type beg3 = boost::begin(s3);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) op( beg0 [i] , beg1 [i] , beg2 [i] , beg3 [i] );
+ }
+ template< class S0 , class S1 , class S2 , class S3 , class S4 , class Op > static void for_each5 ( S0 &s0 , S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ typename boost::range_iterator<S3>::type beg3 = boost::begin(s3);
+ typename boost::range_iterator<S4>::type beg4 = boost::begin(s4);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) op( beg0 [i] , beg1 [i] , beg2 [i] , beg3 [i] , beg4 [i] );
+ }
+ template< class S0 , class S1 , class S2 , class S3 , class S4 , class S5 , class Op > static void for_each6 ( S0 &s0 , S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ typename boost::range_iterator<S3>::type beg3 = boost::begin(s3);
+ typename boost::range_iterator<S4>::type beg4 = boost::begin(s4);
+ typename boost::range_iterator<S5>::type beg5 = boost::begin(s5);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) op( beg0 [i] , beg1 [i] , beg2 [i] , beg3 [i] , beg4 [i] , beg5 [i] );
+ }
+ template< class S0 , class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class Op > static void for_each7 ( S0 &s0 , S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ typename boost::range_iterator<S3>::type beg3 = boost::begin(s3);
+ typename boost::range_iterator<S4>::type beg4 = boost::begin(s4);
+ typename boost::range_iterator<S5>::type beg5 = boost::begin(s5);
+ typename boost::range_iterator<S6>::type beg6 = boost::begin(s6);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) op( beg0 [i] , beg1 [i] , beg2 [i] , beg3 [i] , beg4 [i] , beg5 [i] , beg6 [i] );
+ }
+ template< class S0 , class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class S7 , class Op > static void for_each8 ( S0 &s0 , S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ typename boost::range_iterator<S3>::type beg3 = boost::begin(s3);
+ typename boost::range_iterator<S4>::type beg4 = boost::begin(s4);
+ typename boost::range_iterator<S5>::type beg5 = boost::begin(s5);
+ typename boost::range_iterator<S6>::type beg6 = boost::begin(s6);
+ typename boost::range_iterator<S7>::type beg7 = boost::begin(s7);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) op( beg0 [i] , beg1 [i] , beg2 [i] , beg3 [i] , beg4 [i] , beg5 [i] , beg6 [i] , beg7 [i] );
+ }
+ template< class S0 , class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class S7 , class S8 , class Op > static void for_each9 ( S0 &s0 , S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ typename boost::range_iterator<S3>::type beg3 = boost::begin(s3);
+ typename boost::range_iterator<S4>::type beg4 = boost::begin(s4);
+ typename boost::range_iterator<S5>::type beg5 = boost::begin(s5);
+ typename boost::range_iterator<S6>::type beg6 = boost::begin(s6);
+ typename boost::range_iterator<S7>::type beg7 = boost::begin(s7);
+ typename boost::range_iterator<S8>::type beg8 = boost::begin(s8);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) op( beg0 [i] , beg1 [i] , beg2 [i] , beg3 [i] , beg4 [i] , beg5 [i] , beg6 [i] , beg7 [i] , beg8 [i] );
+ }
+ template< class S0 , class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class S7 , class S8 , class S9 , class Op > static void for_each10 ( S0 &s0 , S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ typename boost::range_iterator<S3>::type beg3 = boost::begin(s3);
+ typename boost::range_iterator<S4>::type beg4 = boost::begin(s4);
+ typename boost::range_iterator<S5>::type beg5 = boost::begin(s5);
+ typename boost::range_iterator<S6>::type beg6 = boost::begin(s6);
+ typename boost::range_iterator<S7>::type beg7 = boost::begin(s7);
+ typename boost::range_iterator<S8>::type beg8 = boost::begin(s8);
+ typename boost::range_iterator<S9>::type beg9 = boost::begin(s9);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) op( beg0 [i] , beg1 [i] , beg2 [i] , beg3 [i] , beg4 [i] , beg5 [i] , beg6 [i] , beg7 [i] , beg8 [i] , beg9 [i] );
+ }
+ template< class S0 , class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class S7 , class S8 , class S9 , class S10 , class Op > static void for_each11 ( S0 &s0 , S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ typename boost::range_iterator<S3>::type beg3 = boost::begin(s3);
+ typename boost::range_iterator<S4>::type beg4 = boost::begin(s4);
+ typename boost::range_iterator<S5>::type beg5 = boost::begin(s5);
+ typename boost::range_iterator<S6>::type beg6 = boost::begin(s6);
+ typename boost::range_iterator<S7>::type beg7 = boost::begin(s7);
+ typename boost::range_iterator<S8>::type beg8 = boost::begin(s8);
+ typename boost::range_iterator<S9>::type beg9 = boost::begin(s9);
+ typename boost::range_iterator<S10>::type beg10 = boost::begin(s10);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) op( beg0 [i] , beg1 [i] , beg2 [i] , beg3 [i] , beg4 [i] , beg5 [i] , beg6 [i] , beg7 [i] , beg8 [i] , beg9 [i] , beg10 [i] );
+ }
+ template< class S0 , class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class S7 , class S8 , class S9 , class S10 , class S11 , class Op > static void for_each12 ( S0 &s0 , S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ typename boost::range_iterator<S3>::type beg3 = boost::begin(s3);
+ typename boost::range_iterator<S4>::type beg4 = boost::begin(s4);
+ typename boost::range_iterator<S5>::type beg5 = boost::begin(s5);
+ typename boost::range_iterator<S6>::type beg6 = boost::begin(s6);
+ typename boost::range_iterator<S7>::type beg7 = boost::begin(s7);
+ typename boost::range_iterator<S8>::type beg8 = boost::begin(s8);
+ typename boost::range_iterator<S9>::type beg9 = boost::begin(s9);
+ typename boost::range_iterator<S10>::type beg10 = boost::begin(s10);
+ typename boost::range_iterator<S11>::type beg11 = boost::begin(s11);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) op( beg0 [i] , beg1 [i] , beg2 [i] , beg3 [i] , beg4 [i] , beg5 [i] , beg6 [i] , beg7 [i] , beg8 [i] , beg9 [i] , beg10 [i] , beg11 [i] );
+ }
+ template< class S0 , class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class S7 , class S8 , class S9 , class S10 , class S11 , class S12 , class Op > static void for_each13 ( S0 &s0 , S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , S12 &s12 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ typename boost::range_iterator<S3>::type beg3 = boost::begin(s3);
+ typename boost::range_iterator<S4>::type beg4 = boost::begin(s4);
+ typename boost::range_iterator<S5>::type beg5 = boost::begin(s5);
+ typename boost::range_iterator<S6>::type beg6 = boost::begin(s6);
+ typename boost::range_iterator<S7>::type beg7 = boost::begin(s7);
+ typename boost::range_iterator<S8>::type beg8 = boost::begin(s8);
+ typename boost::range_iterator<S9>::type beg9 = boost::begin(s9);
+ typename boost::range_iterator<S10>::type beg10 = boost::begin(s10);
+ typename boost::range_iterator<S11>::type beg11 = boost::begin(s11);
+ typename boost::range_iterator<S12>::type beg12 = boost::begin(s12);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) op( beg0 [i] , beg1 [i] , beg2 [i] , beg3 [i] , beg4 [i] , beg5 [i] , beg6 [i] , beg7 [i] , beg8 [i] , beg9 [i] , beg10 [i] , beg11 [i] , beg12 [i] );
+ }
+ template< class S0 , class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class S7 , class S8 , class S9 , class S10 , class S11 , class S12 , class S13 , class Op > static void for_each14 ( S0 &s0 , S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , S12 &s12 , S13 &s13 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ typename boost::range_iterator<S3>::type beg3 = boost::begin(s3);
+ typename boost::range_iterator<S4>::type beg4 = boost::begin(s4);
+ typename boost::range_iterator<S5>::type beg5 = boost::begin(s5);
+ typename boost::range_iterator<S6>::type beg6 = boost::begin(s6);
+ typename boost::range_iterator<S7>::type beg7 = boost::begin(s7);
+ typename boost::range_iterator<S8>::type beg8 = boost::begin(s8);
+ typename boost::range_iterator<S9>::type beg9 = boost::begin(s9);
+ typename boost::range_iterator<S10>::type beg10 = boost::begin(s10);
+ typename boost::range_iterator<S11>::type beg11 = boost::begin(s11);
+ typename boost::range_iterator<S12>::type beg12 = boost::begin(s12);
+ typename boost::range_iterator<S13>::type beg13 = boost::begin(s13);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) op( beg0 [i] , beg1 [i] , beg2 [i] , beg3 [i] , beg4 [i] , beg5 [i] , beg6 [i] , beg7 [i] , beg8 [i] , beg9 [i] , beg10 [i] , beg11 [i] , beg12 [i] , beg13 [i] );
+ }
+ template< class S0 , class S1 , class S2 , class S3 , class S4 , class S5 , class S6 , class S7 , class S8 , class S9 , class S10 , class S11 , class S12 , class S13 , class S14 , class Op > static void for_each15 ( S0 &s0 , S1 &s1 , S2 &s2 , S3 &s3 , S4 &s4 , S5 &s5 , S6 &s6 , S7 &s7 , S8 &s8 , S9 &s9 , S10 &s10 , S11 &s11 , S12 &s12 , S13 &s13 , S14 &s14 , Op op ) {
+ const size_t len = boost::size(s0);
+ typename boost::range_iterator<S0>::type beg0 = boost::begin(s0);
+ typename boost::range_iterator<S1>::type beg1 = boost::begin(s1);
+ typename boost::range_iterator<S2>::type beg2 = boost::begin(s2);
+ typename boost::range_iterator<S3>::type beg3 = boost::begin(s3);
+ typename boost::range_iterator<S4>::type beg4 = boost::begin(s4);
+ typename boost::range_iterator<S5>::type beg5 = boost::begin(s5);
+ typename boost::range_iterator<S6>::type beg6 = boost::begin(s6);
+ typename boost::range_iterator<S7>::type beg7 = boost::begin(s7);
+ typename boost::range_iterator<S8>::type beg8 = boost::begin(s8);
+ typename boost::range_iterator<S9>::type beg9 = boost::begin(s9);
+ typename boost::range_iterator<S10>::type beg10 = boost::begin(s10);
+ typename boost::range_iterator<S11>::type beg11 = boost::begin(s11);
+ typename boost::range_iterator<S12>::type beg12 = boost::begin(s12);
+ typename boost::range_iterator<S13>::type beg13 = boost::begin(s13);
+ typename boost::range_iterator<S14>::type beg14 = boost::begin(s14);
+ #pragma omp parallel for schedule(runtime)
+ for( size_t i = 0 ; i < len ; i++ ) op( beg0 [i] , beg1 [i] , beg2 [i] , beg3 [i] , beg4 [i] , beg5 [i] , beg6 [i] , beg7 [i] , beg8 [i] , beg9 [i] , beg10 [i] , beg11 [i] , beg12 [i] , beg13 [i] , beg14 [i] );
+ }
+
+#endif
+
+
+ template< class S >
+ static typename norm_result_type< S >::type norm_inf( const S &s )
+ {
+ using std::max;
+ using std::abs;
+ typedef typename norm_result_type< S >::type result_type;
+ result_type init = static_cast< result_type >( 0 );
+ const size_t len = boost::size(s);
+ typename boost::range_iterator<const S>::type beg = boost::begin(s);
+# pragma omp parallel for reduction(max: init) schedule(dynamic)
+ for( size_t i = 0 ; i < len ; ++i )
+ init = max( init , abs( beg[i] ) );
+ return init;
+ }
+
+};
+
+
+}
+}
+}
+
+#endif
diff --git a/include/boost/numeric/odeint/external/openmp/openmp_state.hpp b/include/boost/numeric/odeint/external/openmp/openmp_state.hpp
new file mode 100644
index 0000000..83bbc19
--- /dev/null
+++ b/include/boost/numeric/odeint/external/openmp/openmp_state.hpp
@@ -0,0 +1,171 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/openmp/openmp_state.hpp
+
+ [begin_description]
+ Wrappers for OpenMP.
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+ Copyright 2013 Pascal Germroth
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_OPENMP_OPENMP_STATE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_OPENMP_OPENMP_STATE_HPP_INCLUDED
+
+#include <omp.h>
+#include <vector>
+#include <algorithm>
+#include <boost/range/adaptor/sliced.hpp>
+#include <boost/numeric/odeint/util/copy.hpp>
+#include <boost/numeric/odeint/util/split.hpp>
+#include <boost/numeric/odeint/util/resize.hpp>
+#include <boost/numeric/odeint/external/openmp/openmp_nested_algebra.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+/** \brief A container that is split into distinct parts, for threading.
+ * Just a wrapper for vector<vector<T>>, use `copy` for splitting/joining.
+ */
+template< class T >
+struct openmp_state : public std::vector< std::vector< T > >
+{
+ openmp_state() {}
+
+ openmp_state(size_t n, const std::vector<T>& val = std::vector<T>())
+ : std::vector< std::vector< T > >(n, val) {}
+
+ template<class InputIterator>
+ openmp_state(InputIterator first, InputIterator last)
+ : std::vector< std::vector< T > >(first, last) {}
+
+ openmp_state(const std::vector< std::vector< T > > &orig)
+ : std::vector< std::vector< T > >(orig) {}
+
+};
+
+
+
+
+template< class T >
+struct is_resizeable< openmp_state< T > > : boost::true_type { };
+
+
+template< class T >
+struct same_size_impl< openmp_state< T > , openmp_state< T > >
+{
+ static bool same_size( const openmp_state< T > &x , const openmp_state< T > &y )
+ {
+ if( x.size() != y.size() ) return false;
+ for( size_t i = 0 ; i != x.size() ; i++ )
+ if( x[i].size() != y[i].size() ) return false;
+ return true;
+ }
+};
+
+
+template< class T >
+struct resize_impl< openmp_state< T > , openmp_state< T > >
+{
+ static void resize( openmp_state< T > &x , const openmp_state< T > &y )
+ {
+ x.resize( y.size() );
+# pragma omp parallel for schedule(dynamic)
+ for(size_t i = 0 ; i < x.size() ; i++)
+ x[i].resize( y[i].size() );
+ }
+};
+
+
+/** \brief Copy data between openmp_states of same size. */
+template< class T >
+struct copy_impl< openmp_state< T >, openmp_state< T > >
+{
+ static void copy( const openmp_state< T > &from, openmp_state< T > &to )
+ {
+# pragma omp parallel for schedule(dynamic)
+ for(size_t i = 0 ; i < from.size() ; i++)
+ std::copy( from[i].begin() , from[i].end() , to.begin() );
+ }
+};
+
+
+
+/** \brief Copy data from some container to an openmp_state and resize it.
+ * Target container size will determine number of blocks to split into.
+ * If it is empty, it will be resized to the maximum number of OpenMP threads.
+ * SourceContainer must support `s::value_type`, `s::const_iterator`, `s.begin()`, `s.end()` and `s.size()`,
+ * with Random Access Iterators; i.e. it must be a Random Access Container. */
+template< class SourceContainer >
+struct split_impl< SourceContainer, openmp_state< typename SourceContainer::value_type > >
+{
+ static void split( const SourceContainer &from, openmp_state< typename SourceContainer::value_type > &to )
+ {
+ if(to.size() == 0) to.resize( omp_get_max_threads() );
+ const size_t part = from.size() / to.size();
+# pragma omp parallel for schedule(dynamic)
+ for(size_t i = 0 ; i < to.size() ; i++) {
+ typedef typename SourceContainer::const_iterator it_t;
+ const it_t begin = from.begin() + i * part;
+ it_t end = begin + part;
+ // for cases where from.size() % to.size() > 0
+ if(i + 1 == to.size() || end > from.end()) end = from.end();
+ to[i].resize(end - begin);
+ std::copy(begin, end, to[i].begin());
+ }
+ }
+};
+
+/** \brief Copy data from an openmp_state to some container and resize it.
+ * TargetContainer must support `s::value_type`, `s::iterator`, `s.begin()` and `s.resize(n)`,
+ * i.e. it must be a `std::vector`. */
+template< class TargetContainer >
+struct unsplit_impl< openmp_state< typename TargetContainer::value_type >, TargetContainer >
+{
+ static void unsplit( const openmp_state< typename TargetContainer::value_type > &from , TargetContainer &to )
+ {
+ // resize target
+ size_t total_size = 0;
+ for(size_t i = 0 ; i < from.size() ; i++)
+ total_size += from[i].size();
+ to.resize( total_size );
+ // copy parts
+ typename TargetContainer::iterator out = to.begin();
+ for(size_t i = 0 ; i < from.size() ; i++)
+ out = std::copy(from[i].begin(), from[i].end(), out);
+ }
+};
+
+
+
+
+/** \brief OpenMP-parallelized algebra.
+ * For use with openmp_state.
+ */
+typedef openmp_nested_algebra< range_algebra > openmp_algebra;
+
+
+
+/** \brief Use `openmp_algebra` for `openmp_state`. */
+template< class T >
+struct algebra_dispatcher< openmp_state< T > >
+{
+ typedef openmp_algebra algebra_type;
+};
+
+
+}
+}
+}
+
+
+#endif
+
diff --git a/include/boost/numeric/odeint/external/thrust/thrust.hpp b/include/boost/numeric/odeint/external/thrust/thrust.hpp
new file mode 100644
index 0000000..5c4987c
--- /dev/null
+++ b/include/boost/numeric/odeint/external/thrust/thrust.hpp
@@ -0,0 +1,27 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/thrust/thrust.hpp
+
+ [begin_description]
+ includes all headers required for using odeint with thrust
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_THRUST_HPP_DEFINED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_THRUST_HPP_DEFINED
+
+#include <boost/numeric/odeint/external/thrust/thrust_algebra.hpp>
+#include <boost/numeric/odeint/external/thrust/thrust_operations.hpp>
+#include <boost/numeric/odeint/external/thrust/thrust_algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/external/thrust/thrust_operations_dispatcher.hpp>
+#include <boost/numeric/odeint/external/thrust/thrust_resize.hpp>
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_THRUST_HPP_DEFINED
diff --git a/include/boost/numeric/odeint/external/thrust/thrust_algebra.hpp b/include/boost/numeric/odeint/external/thrust/thrust_algebra.hpp
new file mode 100644
index 0000000..f33e862
--- /dev/null
+++ b/include/boost/numeric/odeint/external/thrust/thrust_algebra.hpp
@@ -0,0 +1,217 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/thrust/thrust_algebra.hpp
+
+ [begin_description]
+ An algebra for thrusts device_vectors.
+ [end_description]
+
+ Copyright 2010-2013 Mario Mulansky
+ Copyright 2010-2011 Karsten Ahnert
+ Copyright 2013 Kyle Lutz
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_THRUST_THRUST_ALGEBRA_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_THRUST_THRUST_ALGEBRA_HPP_INCLUDED
+
+
+#include <thrust/device_vector.h>
+#include <thrust/for_each.h>
+#include <thrust/iterator/zip_iterator.h>
+
+#include <boost/range.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+namespace detail {
+
+ // to use in thrust::reduce
+ template< class Value >
+ struct maximum
+ {
+ template< class Fac1 , class Fac2 >
+ __host__ __device__
+ Value operator()( const Fac1 t1 , const Fac2 t2 ) const
+ {
+ return ( abs( t1 ) < abs( t2 ) ) ? t2 : t1 ;
+ }
+
+ typedef Value result_type;
+ };
+
+}
+
+
+
+
+/** ToDO extend until for_each14 for rk78 */
+
+/*
+ * The const versions are needed for boost.range to work, i.e.
+ * it allows you to do
+ * for_each1( make_pair( vec1.begin() , vec1.begin() + 10 ) , op );
+ */
+
+struct thrust_algebra
+{
+ template< class StateType , class Operation >
+ static void for_each1( StateType &s , Operation op )
+ {
+ thrust::for_each( boost::begin(s) , boost::end(s) , op );
+ }
+
+ template< class StateType1 , class StateType2 , class Operation >
+ static void for_each2( StateType1 &s1 , StateType2 &s2 , Operation op )
+ {
+ thrust::for_each(
+ thrust::make_zip_iterator( thrust::make_tuple( boost::begin(s1) ,
+ boost::begin(s2) ) ) ,
+ thrust::make_zip_iterator( thrust::make_tuple( boost::end(s1) ,
+ boost::end(s2) ) ) ,
+ op);
+ }
+
+ template< class StateType1 , class StateType2 , class StateType3 , class Operation >
+ static void for_each3( StateType1 &s1 , StateType2 &s2 , StateType3 &s3 , Operation op )
+ {
+ thrust::for_each(
+ thrust::make_zip_iterator( thrust::make_tuple( boost::begin(s1) ,
+ boost::begin(s2) ,
+ boost::begin(s3) ) ) ,
+ thrust::make_zip_iterator( thrust::make_tuple( boost::end(s1) ,
+ boost::end(s2) ,
+ boost::end(s3) ) ) ,
+ op);
+ }
+
+ template< class StateType1 , class StateType2 , class StateType3 , class StateType4 ,
+ class Operation >
+ static void for_each4( StateType1 &s1 , StateType2 &s2 , StateType3 &s3 , StateType4 &s4 ,
+ Operation op )
+ {
+ thrust::for_each(
+ thrust::make_zip_iterator( thrust::make_tuple( boost::begin(s1) ,
+ boost::begin(s2) ,
+ boost::begin(s3) ,
+ boost::begin(s4) ) ) ,
+ thrust::make_zip_iterator( thrust::make_tuple( boost::end(s1) ,
+ boost::end(s2) ,
+ boost::end(s3) ,
+ boost::end(s4) ) ) ,
+ op);
+ }
+
+ template< class StateType1 , class StateType2 , class StateType3 ,
+ class StateType4 , class StateType5 ,class Operation >
+ static void for_each5( StateType1 &s1 , StateType2 &s2 , StateType3 &s3 , StateType4 &s4 ,
+ StateType5 &s5 , Operation op )
+ {
+ thrust::for_each(
+ thrust::make_zip_iterator( thrust::make_tuple( boost::begin(s1) ,
+ boost::begin(s2) ,
+ boost::begin(s3) ,
+ boost::begin(s4) ,
+ boost::begin(s5) ) ) ,
+ thrust::make_zip_iterator( thrust::make_tuple( boost::end(s1) ,
+ boost::end(s2) ,
+ boost::end(s3) ,
+ boost::end(s4) ,
+ boost::end(s5) ) ) ,
+ op);
+ }
+
+ template< class StateType1 , class StateType2 , class StateType3 ,
+ class StateType4 , class StateType5 , class StateType6 , class Operation >
+ static void for_each6( StateType1 &s1 , StateType2 &s2 , StateType3 &s3 , StateType4 &s4 ,
+ StateType5 &s5 , StateType6 &s6 , Operation op )
+ {
+ thrust::for_each(
+ thrust::make_zip_iterator( thrust::make_tuple( boost::begin(s1) ,
+ boost::begin(s2) ,
+ boost::begin(s3) ,
+ boost::begin(s4) ,
+ boost::begin(s5) ,
+ boost::begin(s6) ) ) ,
+ thrust::make_zip_iterator( thrust::make_tuple( boost::end(s1) ,
+ boost::end(s2) ,
+ boost::end(s3) ,
+ boost::end(s4) ,
+ boost::end(s5) ,
+ boost::end(s6) ) ) ,
+ op);
+ }
+
+ template< class StateType1 , class StateType2 , class StateType3 , class StateType4 ,
+ class StateType5 , class StateType6 , class StateType7 , class Operation >
+ static void for_each7( StateType1 &s1 , StateType2 &s2 , StateType3 &s3 , StateType4 &s4 ,
+ StateType5 &s5 , StateType6 &s6 , StateType7 &s7 , Operation op )
+ {
+ thrust::for_each(
+ thrust::make_zip_iterator( thrust::make_tuple( boost::begin(s1) ,
+ boost::begin(s2) ,
+ boost::begin(s3) ,
+ boost::begin(s4) ,
+ boost::begin(s5) ,
+ boost::begin(s6) ,
+ boost::begin(s7) ) ) ,
+ thrust::make_zip_iterator( thrust::make_tuple( boost::end(s1) ,
+ boost::end(s2) ,
+ boost::end(s3) ,
+ boost::end(s4) ,
+ boost::end(s5) ,
+ boost::end(s6) ,
+ boost::end(s7) ) ) ,
+ op);
+ }
+
+ template< class StateType1 , class StateType2 , class StateType3 , class StateType4 ,
+ class StateType5 , class StateType6 , class StateType7 , class StateType8 , class Operation >
+ static void for_each8( StateType1 &s1 , StateType2 &s2 , StateType3 &s3 , StateType4 &s4 ,
+ StateType5 &s5 , StateType6 &s6 , StateType7 &s7 , StateType8 &s8 , Operation op )
+ {
+ thrust::for_each(
+ thrust::make_zip_iterator( thrust::make_tuple( boost::begin(s1) ,
+ boost::begin(s2) ,
+ boost::begin(s3) ,
+ boost::begin(s4) ,
+ boost::begin(s5) ,
+ boost::begin(s6) ,
+ boost::begin(s7) ,
+ boost::begin(s8) ) ) ,
+ thrust::make_zip_iterator( thrust::make_tuple( boost::end(s1) ,
+ boost::end(s2) ,
+ boost::end(s3) ,
+ boost::end(s4) ,
+ boost::end(s5) ,
+ boost::end(s6) ,
+ boost::end(s7) ,
+ boost::end(s8) ) ) ,
+ op);
+ }
+
+ template< class S >
+ static typename S::value_type norm_inf( const S &s )
+ {
+ typedef typename S::value_type value_type;
+ return thrust::reduce( boost::begin( s ) , boost::end( s ) ,
+ static_cast<value_type>(0) ,
+ detail::maximum<value_type>() );
+ }
+
+};
+
+
+} // odeint
+} // numeric
+} // boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_THRUST_THRUST_ALGEBRA_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/external/thrust/thrust_algebra_dispatcher.hpp b/include/boost/numeric/odeint/external/thrust/thrust_algebra_dispatcher.hpp
new file mode 100644
index 0000000..0961346
--- /dev/null
+++ b/include/boost/numeric/odeint/external/thrust/thrust_algebra_dispatcher.hpp
@@ -0,0 +1,107 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/thrust/thrust_algebra_dispatcher.hpp
+
+ [begin_description]
+ algebra_dispatcher specialization for thrust
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_THRUST_THRUST_ALGEBRA_DISPATCHER_HPP_DEFINED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_THRUST_THRUST_ALGEBRA_DISPATCHER_HPP_DEFINED
+
+#include <thrust/host_vector.h>
+#include <thrust/device_vector.h>
+
+#include <boost/numeric/odeint/external/thrust/thrust_algebra.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+
+// specializations for the standard thrust containers
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+// specialization for thrust host_vector
+template< class T , class A >
+struct algebra_dispatcher< thrust::host_vector< T , A > >
+{
+ typedef thrust_algebra algebra_type;
+};
+
+// specialization for thrust device_vector
+template< class T , class A >
+struct algebra_dispatcher< thrust::device_vector< T , A > >
+{
+ typedef thrust_algebra algebra_type;
+};
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+// add support for thrust backend vectors, if available
+
+#include <thrust/version.h>
+
+#if THRUST_VERSION >= 100600
+
+// specialization for thrust cpp vector
+#include <thrust/system/cpp/vector.h>
+namespace boost { namespace numeric { namespace odeint {
+ template< class T , class A >
+ struct algebra_dispatcher< thrust::cpp::vector< T , A > >
+ {
+ typedef thrust_algebra algebra_type;
+ };
+} } }
+
+// specialization for thrust omp vector
+#ifdef _OPENMP
+#include <thrust/system/omp/vector.h>
+namespace boost { namespace numeric { namespace odeint {
+ template< class T , class A >
+ struct algebra_dispatcher< thrust::omp::vector< T , A > >
+ {
+ typedef thrust_algebra algebra_type;
+ };
+} } }
+#endif // _OPENMP
+
+// specialization for thrust tbb vector
+#ifdef TBB_VERSION_MAJOR
+#include <thrust/system/tbb/vector.h>
+namespace boost { namespace numeric { namespace odeint {
+ template< class T , class A >
+ struct algebra_dispatcher< thrust::tbb::vector< T , A > >
+ {
+ typedef thrust_algebra algebra_type;
+ };
+} } }
+#endif // TBB_VERSION_MAJOR
+
+// specialization for thrust cuda vector
+#ifdef __CUDACC__
+#include <thrust/system/cuda/vector.h>
+namespace boost { namespace numeric { namespace odeint {
+ template< class T , class A >
+ struct algebra_dispatcher< thrust::cuda::vector< T , A > >
+ {
+ typedef thrust_algebra algebra_type;
+ };
+} } }
+#endif // __CUDACC__
+
+#endif // THRUST_VERSION >= 100600
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_THRUST_THRUST_ALGEBRA_DISPATCHER_HPP_DEFINED
+
diff --git a/include/boost/numeric/odeint/external/thrust/thrust_operations.hpp b/include/boost/numeric/odeint/external/thrust/thrust_operations.hpp
new file mode 100644
index 0000000..ce2d372
--- /dev/null
+++ b/include/boost/numeric/odeint/external/thrust/thrust_operations.hpp
@@ -0,0 +1,233 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/thrust/thrust_operations.hpp
+
+ [begin_description]
+ Operations of thrust zipped iterators. Is the counterpart of the thrust_algebra.
+ [end_description]
+
+ Copyright 2010-2013 Mario Mulansky
+ Copyright 2010-2012 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_THRUST_THRUST_OPERATIONS_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_THRUST_THRUST_OPERATIONS_HPP_INCLUDED
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+#include <thrust/tuple.h>
+#include <thrust/iterator/zip_iterator.h>
+
+/**ToDo extend to scale_sum13 for rk78 */
+
+struct thrust_operations
+{
+ template< class Fac1 = double , class Fac2 = Fac1 >
+ struct scale_sum2
+ {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+
+ scale_sum2( const Fac1 alpha1 , const Fac2 alpha2 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) { }
+
+ template< class Tuple >
+ __host__ __device__
+ void operator()( Tuple t ) const
+ {
+ thrust::get<0>(t) = m_alpha1 * thrust::get<1>(t) + m_alpha2 * thrust::get<2>(t);
+ }
+ };
+
+ template< class Fac1 = double , class Fac2 = Fac1 >
+ struct scale_sum_swap2
+ {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+
+ scale_sum_swap2( const Fac1 alpha1 , const Fac2 alpha2 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) { }
+
+ template< class Tuple >
+ __host__ __device__
+ void operator()( Tuple t ) const
+ {
+ typename thrust::tuple_element<0,Tuple>::type tmp = thrust::get<0>(t);
+ thrust::get<0>(t) = m_alpha1 * thrust::get<1>(t) + m_alpha2 * thrust::get<2>(t);
+ thrust::get<1>(t) = tmp;
+ }
+ };
+
+ template< class Fac1 = double , class Fac2 = Fac1 , class Fac3 = Fac2 >
+ struct scale_sum3
+ {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+ const Fac3 m_alpha3;
+
+ scale_sum3( const Fac1 alpha1 , const Fac2 alpha2 , const Fac3 alpha3 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) , m_alpha3( alpha3 ) { }
+
+ template< class Tuple >
+ __host__ __device__
+ void operator()( Tuple t ) const
+ {
+ thrust::get<0>(t) = m_alpha1 * thrust::get<1>(t) +
+ m_alpha2 * thrust::get<2>(t) +
+ m_alpha3 * thrust::get<3>(t);
+ }
+ };
+
+
+ template< class Fac1 = double , class Fac2 = Fac1 , class Fac3 = Fac2 , class Fac4 = Fac3 >
+ struct scale_sum4
+ {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+ const Fac3 m_alpha3;
+ const Fac4 m_alpha4;
+
+ scale_sum4( const Fac1 alpha1 , const Fac2 alpha2 , const Fac3 alpha3 , const Fac4 alpha4 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) , m_alpha3( alpha3 ) , m_alpha4( alpha4 ){ }
+
+ template< class Tuple >
+ __host__ __device__
+ void operator()( Tuple t ) const
+ {
+ thrust::get<0>(t) = m_alpha1 * thrust::get<1>(t) +
+ m_alpha2 * thrust::get<2>(t) +
+ m_alpha3 * thrust::get<3>(t) +
+ m_alpha4 * thrust::get<4>(t);
+ }
+ };
+
+
+ template< class Fac1 = double , class Fac2 = Fac1 , class Fac3 = Fac2 ,
+ class Fac4 = Fac3 , class Fac5 = Fac4 >
+ struct scale_sum5
+ {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+ const Fac3 m_alpha3;
+ const Fac4 m_alpha4;
+ const Fac5 m_alpha5;
+
+ scale_sum5( const Fac1 alpha1 , const Fac2 alpha2 , const Fac3 alpha3 ,
+ const Fac4 alpha4 , const Fac5 alpha5 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) , m_alpha3( alpha3 ) ,
+ m_alpha4( alpha4 ) , m_alpha5( alpha5 ) { }
+
+ template< class Tuple >
+ __host__ __device__
+ void operator()( Tuple t ) const
+ {
+ thrust::get<0>(t) = m_alpha1 * thrust::get<1>(t) +
+ m_alpha2 * thrust::get<2>(t) +
+ m_alpha3 * thrust::get<3>(t) +
+ m_alpha4 * thrust::get<4>(t) +
+ m_alpha5 * thrust::get<5>(t);
+ }
+ };
+
+
+ template< class Fac1 = double , class Fac2 = Fac1 , class Fac3 = Fac2 ,
+ class Fac4 = Fac3 , class Fac5 = Fac4 , class Fac6 = Fac5 >
+ struct scale_sum6
+ {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+ const Fac3 m_alpha3;
+ const Fac4 m_alpha4;
+ const Fac5 m_alpha5;
+ const Fac6 m_alpha6;
+
+ scale_sum6( const Fac1 alpha1 , const Fac2 alpha2 , const Fac3 alpha3 ,
+ const Fac4 alpha4 , const Fac5 alpha5 , const Fac6 alpha6 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) , m_alpha3( alpha3 ) ,
+ m_alpha4( alpha4 ) , m_alpha5( alpha5 ) , m_alpha6( alpha6 ) { }
+
+ template< class Tuple >
+ __host__ __device__
+ void operator()( Tuple t ) const
+ {
+ thrust::get<0>(t) = m_alpha1 * thrust::get<1>(t) +
+ m_alpha2 * thrust::get<2>(t) +
+ m_alpha3 * thrust::get<3>(t) +
+ m_alpha4 * thrust::get<4>(t) +
+ m_alpha5 * thrust::get<5>(t) +
+ m_alpha6 * thrust::get<6>(t);
+ }
+ };
+
+
+ template< class Fac1 = double , class Fac2 = Fac1 , class Fac3 = Fac2 , class Fac4 = Fac3 ,
+ class Fac5 = Fac4 , class Fac6 = Fac5 , class Fac7 = Fac6 >
+ struct scale_sum7
+ {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+ const Fac3 m_alpha3;
+ const Fac4 m_alpha4;
+ const Fac5 m_alpha5;
+ const Fac6 m_alpha6;
+ const Fac7 m_alpha7;
+
+ scale_sum7( const Fac1 alpha1 , const Fac2 alpha2 , const Fac3 alpha3 ,
+ const Fac4 alpha4 , const Fac5 alpha5 , const Fac6 alpha6 , const Fac7 alpha7 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) , m_alpha3( alpha3 ) ,
+ m_alpha4( alpha4 ) , m_alpha5( alpha5 ) , m_alpha6( alpha6 ) , m_alpha7( alpha7 ) { }
+
+ template< class Tuple >
+ __host__ __device__
+ void operator()( Tuple t ) const
+ {
+ thrust::get<0>(t) = m_alpha1 * thrust::get<1>(t) +
+ m_alpha2 * thrust::get<2>(t) +
+ m_alpha3 * thrust::get<3>(t) +
+ m_alpha4 * thrust::get<4>(t) +
+ m_alpha5 * thrust::get<5>(t) +
+ m_alpha6 * thrust::get<6>(t) +
+ m_alpha7 * thrust::get<7>(t) ;
+ }
+ };
+
+
+
+
+ template< class Fac1 = double >
+ struct rel_error
+ {
+ const Fac1 m_eps_abs , m_eps_rel , m_a_x , m_a_dxdt;
+
+ rel_error( const Fac1 eps_abs , const Fac1 eps_rel , const Fac1 a_x , const Fac1 a_dxdt )
+ : m_eps_abs( eps_abs ) , m_eps_rel( eps_rel ) , m_a_x( a_x ) , m_a_dxdt( a_dxdt ) { }
+
+
+ template< class Tuple >
+ __host__ __device__
+ void operator()( Tuple t ) const
+ {
+ using std::abs;
+ thrust::get< 0 >( t ) = abs( thrust::get< 0 >( t ) ) /
+ ( m_eps_abs + m_eps_rel * ( m_a_x * abs( thrust::get< 1 >( t ) + m_a_dxdt * abs( thrust::get< 2 >( t ) ) ) ) );
+ }
+
+ typedef void result_type;
+ };
+
+
+};
+
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_THRUST_THRUST_OPERATIONS_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/external/thrust/thrust_operations_dispatcher.hpp b/include/boost/numeric/odeint/external/thrust/thrust_operations_dispatcher.hpp
new file mode 100644
index 0000000..e9b3a64
--- /dev/null
+++ b/include/boost/numeric/odeint/external/thrust/thrust_operations_dispatcher.hpp
@@ -0,0 +1,107 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/thrust/thrust_operations_dispatcher.hpp
+
+ [begin_description]
+ operations_dispatcher specialization for thrust
+ [end_description]
+
+ Copyright 2013-2014 Karsten Ahnert
+ Copyright 2013-2014 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_THRUST_THRUST_OPERATIONS_DISPATCHER_HPP_DEFINED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_THRUST_THRUST_OPERATIONS_DISPATCHER_HPP_DEFINED
+
+#include <thrust/host_vector.h>
+#include <thrust/device_vector.h>
+
+#include <boost/numeric/odeint/external/thrust/thrust_operations.hpp>
+#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
+
+// support for the standard thrust containers
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+// specialization for thrust host_vector
+template< class T , class A >
+struct operations_dispatcher< thrust::host_vector< T , A > >
+{
+ typedef thrust_operations operations_type;
+};
+
+// specialization for thrust device_vector
+template< class T , class A >
+struct operations_dispatcher< thrust::device_vector< T , A > >
+{
+ typedef thrust_operations operations_type;
+};
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+// add support for thrust backend vectors, if available
+
+#include <thrust/version.h>
+
+#if THRUST_VERSION >= 100600
+
+// specialization for thrust cpp vector
+#include <thrust/system/cpp/vector.h>
+namespace boost { namespace numeric { namespace odeint {
+ template< class T , class A >
+ struct operations_dispatcher< thrust::cpp::vector< T , A > >
+ {
+ typedef thrust_operations operations_type;
+ };
+} } }
+
+// specialization for thrust omp vector
+#ifdef _OPENMP
+#include <thrust/system/omp/vector.h>
+namespace boost { namespace numeric { namespace odeint {
+ template< class T , class A >
+ struct operations_dispatcher< thrust::omp::vector< T , A > >
+ {
+ typedef thrust_operations operations_type;
+ };
+} } }
+#endif // _OPENMP
+
+// specialization for thrust tbb vector
+#ifdef TBB_VERSION_MAJOR
+#include <thrust/system/tbb/vector.h>
+namespace boost { namespace numeric { namespace odeint {
+ template< class T , class A >
+ struct operations_dispatcher< thrust::tbb::vector< T , A > >
+ {
+ typedef thrust_operations operations_type;
+ };
+} } }
+#endif // TBB_VERSION_MAJOR
+
+// specialization for thrust cuda vector
+#ifdef __CUDACC__
+#include <thrust/system/cuda/vector.h>
+namespace boost { namespace numeric { namespace odeint {
+ template< class T , class A >
+ struct operations_dispatcher< thrust::cuda::vector< T , A > >
+ {
+ typedef thrust_operations operations_type;
+ };
+} } }
+#endif // __CUDACC__
+
+#endif // THRUST_VERSION >= 100600
+
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_THRUST_THRUST_OPERATIONS_DISPATCHER_HPP_DEFINED
+
diff --git a/include/boost/numeric/odeint/external/thrust/thrust_resize.hpp b/include/boost/numeric/odeint/external/thrust/thrust_resize.hpp
new file mode 100644
index 0000000..2f7f7b2
--- /dev/null
+++ b/include/boost/numeric/odeint/external/thrust/thrust_resize.hpp
@@ -0,0 +1,185 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/thrust/thrust_resize.hpp
+
+ [begin_description]
+ Enable resizing for thrusts device and host_vector.
+ [end_description]
+
+ Copyright 2010-2014 Mario Mulansky
+ Copyright 2010-2011 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_THRUST_THRUST_RESIZE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_THRUST_THRUST_RESIZE_HPP_INCLUDED
+
+#include <boost/range.hpp>
+
+#include <thrust/device_vector.h>
+#include <thrust/host_vector.h>
+#include <thrust/distance.h>
+
+#include <boost/numeric/odeint/util/resize.hpp>
+#include <boost/numeric/odeint/util/same_size.hpp>
+#include <boost/numeric/odeint/util/copy.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+// some macros that define the necessary utilities
+
+#define ODEINT_THRUST_VECTOR_IS_RESIZEABLE( THRUST_VECTOR ) \
+template< class T , class A > \
+struct is_resizeable< THRUST_VECTOR<T,A> > \
+{ \
+ struct type : public boost::true_type { }; \
+ const static bool value = type::value; \
+}; \
+
+#define ODEINT_TRHUST_VECTOR_RESIZE_IMPL( THRUST_VECTOR ) \
+template< class T, class A > \
+struct resize_impl< THRUST_VECTOR<T,A> , THRUST_VECTOR<T,A> > \
+{ \
+ static void resize( THRUST_VECTOR<T,A> &x , \
+ const THRUST_VECTOR<T,A> &y ) \
+ { \
+ x.resize( y.size() ); \
+ } \
+}; \
+template< class T, class A, typename Range > \
+struct resize_impl< THRUST_VECTOR<T,A> , Range > \
+{ \
+ static void resize( THRUST_VECTOR<T,A> &x , \
+ const Range &y ) \
+ { \
+ x.resize( thrust::distance(boost::begin(y), \
+ boost::end(y))); \
+ } \
+}; \
+
+
+#define ODEINT_THRUST_SAME_SIZE_IMPL( THRUST_VECTOR ) \
+template< class T , class A > \
+struct same_size_impl< THRUST_VECTOR<T,A> , THRUST_VECTOR<T,A> > \
+{ \
+ static bool same_size( const THRUST_VECTOR<T,A> &x , \
+ const THRUST_VECTOR<T,A> &y ) \
+ { \
+ return x.size() == y.size(); \
+ } \
+}; \
+template< class T , class A, typename Range > \
+struct same_size_impl< THRUST_VECTOR<T,A> , Range > \
+{ \
+ static bool same_size( const THRUST_VECTOR<T,A> &x , \
+ const Range &y ) \
+ { \
+ return x.size() == thrust::distance(boost::begin(y), \
+ boost::end(y)); \
+ } \
+}; \
+
+
+#define ODEINT_THRUST_COPY_IMPL( THRUST_VECTOR ) \
+template< class Container1 , class T , class A > \
+struct copy_impl< Container1 , THRUST_VECTOR<T,A> > \
+{ \
+ static void copy( const Container1 &from , THRUST_VECTOR<T,A> &to ) \
+ { \
+ thrust::copy( boost::begin( from ) , boost::end( from ) , \
+ boost::begin( to ) ); \
+ } \
+}; \
+ \
+template< class T , class A , class Container2 > \
+struct copy_impl< THRUST_VECTOR<T,A> , Container2 > \
+{ \
+ static void copy( const THRUST_VECTOR<T,A> &from , Container2 &to ) \
+ { \
+ thrust::copy( boost::begin( from ) , boost::end( from ) , \
+ boost::begin( to ) ); \
+ } \
+}; \
+ \
+template< class T , class A > \
+struct copy_impl< THRUST_VECTOR<T,A> , THRUST_VECTOR<T,A> > \
+{ \
+ static void copy( const THRUST_VECTOR<T,A> &from , \
+ THRUST_VECTOR<T,A> &to ) \
+ { \
+ thrust::copy( boost::begin( from ) , boost::end( from ) , \
+ boost::begin( to ) ); \
+ } \
+}; \
+
+// add support for the standard thrust containers
+
+ODEINT_THRUST_VECTOR_IS_RESIZEABLE( thrust::device_vector )
+ODEINT_TRHUST_VECTOR_RESIZE_IMPL( thrust::device_vector )
+ODEINT_THRUST_SAME_SIZE_IMPL( thrust::device_vector )
+ODEINT_THRUST_COPY_IMPL( thrust::device_vector )
+
+
+ODEINT_THRUST_VECTOR_IS_RESIZEABLE( thrust::host_vector )
+ODEINT_TRHUST_VECTOR_RESIZE_IMPL( thrust::host_vector )
+ODEINT_THRUST_SAME_SIZE_IMPL( thrust::host_vector )
+ODEINT_THRUST_COPY_IMPL( thrust::host_vector )
+
+
+} // odeint
+} // numeric
+} // boost
+
+// add support for thrust backend vectors, if available
+
+#include <thrust/version.h>
+
+#if THRUST_VERSION >= 100600
+
+#include <thrust/system/cpp/vector.h>
+namespace boost { namespace numeric { namespace odeint {
+ ODEINT_THRUST_VECTOR_IS_RESIZEABLE( thrust::cpp::vector )
+ ODEINT_TRHUST_VECTOR_RESIZE_IMPL( thrust::cpp::vector )
+ ODEINT_THRUST_SAME_SIZE_IMPL( thrust::cpp::vector )
+ ODEINT_THRUST_COPY_IMPL( thrust::cpp::vector )
+} } }
+
+#ifdef _OPENMP
+#include <thrust/system/omp/vector.h>
+namespace boost { namespace numeric { namespace odeint {
+ ODEINT_THRUST_VECTOR_IS_RESIZEABLE( thrust::omp::vector )
+ ODEINT_TRHUST_VECTOR_RESIZE_IMPL( thrust::omp::vector )
+ ODEINT_THRUST_SAME_SIZE_IMPL( thrust::omp::vector )
+ ODEINT_THRUST_COPY_IMPL( thrust::omp::vector )
+} } }
+#endif // _OPENMP
+
+#ifdef TBB_VERSION_MAJOR
+#include <thrust/system/tbb/vector.h>
+namespace boost { namespace numeric { namespace odeint {
+ ODEINT_THRUST_VECTOR_IS_RESIZEABLE( thrust::tbb::vector )
+ ODEINT_TRHUST_VECTOR_RESIZE_IMPL( thrust::tbb::vector )
+ ODEINT_THRUST_SAME_SIZE_IMPL( thrust::tbb::vector )
+ ODEINT_THRUST_COPY_IMPL( thrust::tbb::vector )
+} } }
+#endif // TBB_VERSION_MAJOR
+
+#ifdef __CUDACC__
+#include <thrust/system/cuda/vector.h>
+namespace boost { namespace numeric { namespace odeint {
+ ODEINT_THRUST_VECTOR_IS_RESIZEABLE( thrust::cuda::vector )
+ ODEINT_TRHUST_VECTOR_RESIZE_IMPL( thrust::cuda::vector )
+ ODEINT_THRUST_SAME_SIZE_IMPL( thrust::cuda::vector )
+ ODEINT_THRUST_COPY_IMPL( thrust::cuda::vector )
+} } }
+#endif // __CUDACC__
+
+#endif // THRUST_VERSION >= 100600
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_THRUST_THRUST_RESIZE_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/external/vexcl/vexcl.hpp b/include/boost/numeric/odeint/external/vexcl/vexcl.hpp
new file mode 100644
index 0000000..0a99e27
--- /dev/null
+++ b/include/boost/numeric/odeint/external/vexcl/vexcl.hpp
@@ -0,0 +1,28 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/vexcl/vexcl.hpp
+
+ [begin_description]
+ includes all headers required for using vexcl in odeint
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_VEXCL_VEXCL_HPP_DEFINED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_VEXCL_VEXCL_HPP_DEFINED
+
+#include <boost/numeric/odeint/external/vexcl/vexcl_algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/external/vexcl/vexcl_resize.hpp>
+#include <boost/numeric/odeint/external/vexcl/vexcl_same_instance.hpp>
+#include <boost/numeric/odeint/external/vexcl/vexcl_norm_inf.hpp>
+#include <boost/numeric/odeint/external/vexcl/vexcl_abs.hpp>
+#include <boost/numeric/odeint/external/vexcl/vexcl_copy.hpp>
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_VEXCL_VEXCL_HPP_DEFINED
diff --git a/include/boost/numeric/odeint/external/vexcl/vexcl_abs.hpp b/include/boost/numeric/odeint/external/vexcl/vexcl_abs.hpp
new file mode 100644
index 0000000..c5e5c73
--- /dev/null
+++ b/include/boost/numeric/odeint/external/vexcl/vexcl_abs.hpp
@@ -0,0 +1,61 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/vexcl/vexcl_abs.hpp
+
+ [begin_description]
+ abs() specialization for vexcl
+ [end_description]
+
+ Copyright 2009-2013 Karsten Ahnert
+ Copyright 2009-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_VEXCL_VEXCL_ABS_HPP_DEFINED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_VEXCL_VEXCL_ABS_HPP_DEFINED
+
+#include <vexcl/vector.hpp>
+#include <vexcl/multivector.hpp>
+#include <vexcl/operations.hpp>
+
+namespace vex {
+
+template <typename T, size_t N>
+typename std::enable_if<
+ std::is_integral<T>::value,
+ typename boost::proto::result_of::make_expr<
+ boost::proto::tag::function,
+ abs_func,
+ const vex::multivector<T, N>&
+ >::type const
+>::type
+abs(const multivector<T, N> &arg) {
+ return boost::proto::make_expr<boost::proto::tag::function>(
+ abs_func(),
+ boost::ref(arg)
+ );
+}
+
+template <typename T, size_t N>
+typename std::enable_if<
+ !std::is_integral<T>::value,
+ typename boost::proto::result_of::make_expr<
+ boost::proto::tag::function,
+ fabs_func,
+ const vex::multivector<T, N>&
+ >::type const
+>::type
+abs(const multivector<T, N> &arg) {
+ return boost::proto::make_expr<boost::proto::tag::function>(
+ fabs_func(),
+ boost::ref(arg)
+ );
+}
+
+} // namespace vex
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_VEXCL_VEXCL_ABS_HPP_DEFINED
diff --git a/include/boost/numeric/odeint/external/vexcl/vexcl_algebra_dispatcher.hpp b/include/boost/numeric/odeint/external/vexcl/vexcl_algebra_dispatcher.hpp
new file mode 100644
index 0000000..9511137
--- /dev/null
+++ b/include/boost/numeric/odeint/external/vexcl/vexcl_algebra_dispatcher.hpp
@@ -0,0 +1,51 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/vexcl/vexcl_algebra_dispatcher.hpp
+
+ [begin_description]
+ algebra_dispatcher specialization for vexcl
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_VEXCL_VEXCL_ALGEBRA_DISPATCHER_HPP_DEFINED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_VEXCL_VEXCL_ALGEBRA_DISPATCHER_HPP_DEFINED
+
+#include <vexcl/vector.hpp>
+#include <vexcl/multivector.hpp>
+
+#include <boost/numeric/odeint/algebra/vector_space_algebra.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+// specialization for vexcl vector
+template< typename T >
+struct algebra_dispatcher< vex::vector< T > >
+{
+ typedef vector_space_algebra algebra_type;
+};
+
+// specialization for vexcl multivector
+template< typename T , size_t N >
+struct algebra_dispatcher< vex::multivector< T , N > >
+{
+ typedef vector_space_algebra algebra_type;
+};
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_VEXCL_VEXCL_ALGEBRA_DISPATCHER_HPP_DEFINED
diff --git a/include/boost/numeric/odeint/external/vexcl/vexcl_copy.hpp b/include/boost/numeric/odeint/external/vexcl/vexcl_copy.hpp
new file mode 100644
index 0000000..6a5afac
--- /dev/null
+++ b/include/boost/numeric/odeint/external/vexcl/vexcl_copy.hpp
@@ -0,0 +1,55 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/vexcl/vexcl_copy.hpp
+
+ [begin_description]
+ copy_impl specializations for vexcl
+ [end_description]
+
+ Copyright 2009-2011 Karsten Ahnert
+ Copyright 2009-2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_VEXCL_VEXCL_COPY_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_VEXCL_VEXCL_COPY_HPP_INCLUDED
+
+#include <vexcl/vector.hpp>
+#include <vexcl/multivector.hpp>
+
+#include <boost/numeric/odeint/util/copy.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template< typename T1, typename T2 >
+struct copy_impl< vex::vector<T1>, vex::vector<T2> >
+{
+ static void copy( const vex::vector<T1> &from , vex::vector<T2> &to )
+ {
+ to = from;
+ }
+};
+
+template< typename T1, typename T2, size_t N >
+struct copy_impl< vex::multivector<T1, N>, vex::multivector<T2, N> >
+{
+ static void copy( const vex::multivector<T1, N> &from , vex::multivector<T2, N> &to )
+ {
+ to = from;
+ }
+};
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_VEXCL_VEXCL_COPY_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/external/vexcl/vexcl_norm_inf.hpp b/include/boost/numeric/odeint/external/vexcl/vexcl_norm_inf.hpp
new file mode 100644
index 0000000..a0a62af
--- /dev/null
+++ b/include/boost/numeric/odeint/external/vexcl/vexcl_norm_inf.hpp
@@ -0,0 +1,68 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/vexcl/vexcl_norm_inf.hpp
+
+ [begin_description]
+ vector_space_norm_inf specialization for vexcl
+ [end_description]
+
+ Copyright 2009-2013 Karsten Ahnert
+ Copyright 2009-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_VEXCL_VEXCL_NORM_INF_HPP_DEFINED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_VEXCL_VEXCL_NORM_INF_HPP_DEFINED
+
+#include <map>
+#include <algorithm>
+
+#include <vexcl/vector.hpp>
+#include <vexcl/multivector.hpp>
+#include <vexcl/reductor.hpp>
+
+#include <boost/numeric/odeint/algebra/vector_space_algebra.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+// specialization for vexcl vector
+template <typename T>
+struct vector_space_norm_inf< vex::vector<T> > {
+ typedef T result_type;
+
+ T operator()( const vex::vector<T> &x ) const {
+ const auto &max = vex::get_reductor<T, vex::MAX>(x.queue_list());
+
+ return max( fabs(x) );
+ }
+};
+
+// specialization for vexcl multivector
+template <typename T, size_t N>
+struct vector_space_norm_inf< vex::multivector<T, N> > {
+ typedef T result_type;
+
+ T operator()( const vex::multivector<T, N> &x ) const {
+ const auto &max = vex::get_reductor<T, vex::MAX>(x.queue_list());
+
+ // Reducing a multivector results in std::array<T, N>:
+ auto m = max( fabs(x) );
+
+ // We will need to reduce it even further:
+ return *std::max_element(m.begin(), m.end());
+ }
+};
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_VEXCL_VEXCL_NORM_INF_HPP_DEFINED
diff --git a/include/boost/numeric/odeint/external/vexcl/vexcl_resize.hpp b/include/boost/numeric/odeint/external/vexcl/vexcl_resize.hpp
new file mode 100644
index 0000000..2d6291e
--- /dev/null
+++ b/include/boost/numeric/odeint/external/vexcl/vexcl_resize.hpp
@@ -0,0 +1,94 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/vexcl/vexcl_resize.hpp
+
+ [begin_description]
+ Enable resizing for vexcl vector and multivector.
+ [end_description]
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+ Copyright 2012 Denis Demidov
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_VEXCL_VEXCL_RESIZE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_VEXCL_VEXCL_RESIZE_HPP_INCLUDED
+
+#include <vexcl/vector.hpp>
+#include <vexcl/multivector.hpp>
+
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resize.hpp>
+#include <boost/numeric/odeint/util/same_size.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+
+/*
+ * specializations for vex::vector< T >
+ */
+template< typename T >
+struct is_resizeable< vex::vector< T > > : boost::true_type { };
+
+template< typename T >
+struct resize_impl< vex::vector< T > , vex::vector< T > >
+{
+ static void resize( vex::vector< T > &x1 , const vex::vector< T > &x2 )
+ {
+ x1.resize( x2.queue_list() , x2.size() );
+ }
+};
+
+template< typename T >
+struct same_size_impl< vex::vector< T > , vex::vector< T > >
+{
+ static bool same_size( const vex::vector< T > &x1 , const vex::vector< T > &x2 )
+ {
+ return x1.size() == x2.size();
+ }
+};
+
+
+
+
+
+/*
+ * specializations for vex::multivector< T >
+ */
+template< typename T , size_t N >
+struct is_resizeable< vex::multivector< T , N > > : boost::true_type { };
+
+template< typename T , size_t N >
+struct resize_impl< vex::multivector< T , N > , vex::multivector< T , N > >
+{
+ static void resize( vex::multivector< T , N > &x1 , const vex::multivector< T , N > &x2 )
+ {
+ x1.resize( x2.queue_list() , x2.size() );
+ }
+};
+
+template< typename T , size_t N >
+struct same_size_impl< vex::multivector< T , N > , vex::multivector< T , N > >
+{
+ static bool same_size( const vex::multivector< T , N > &x1 , const vex::multivector< T , N > &x2 )
+ {
+ return x1.size() == x2.size();
+ }
+};
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_VEXCL_VEXCL_RESIZE_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/external/vexcl/vexcl_same_instance.hpp b/include/boost/numeric/odeint/external/vexcl/vexcl_same_instance.hpp
new file mode 100644
index 0000000..f5a7378
--- /dev/null
+++ b/include/boost/numeric/odeint/external/vexcl/vexcl_same_instance.hpp
@@ -0,0 +1,58 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/vexcl/vexcl_same_instance.hpp
+
+ [begin_description]
+ Check if two VexCL containers are the same instance.
+ [end_description]
+
+ Copyright 2009-2011 Karsten Ahnert
+ Copyright 2009-2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_VEXCL_VEXCL_SAME_INSTANCE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_VEXCL_VEXCL_SAME_INSTANCE_HPP_INCLUDED
+
+#include <vexcl/vector.hpp>
+#include <vexcl/multivector.hpp>
+
+#include <boost/numeric/odeint/util/same_instance.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template <typename T>
+struct same_instance_impl< vex::vector<T> , vex::vector<T> >
+{
+ static bool same_instance( const vex::vector<T> &x1 , const vex::vector<T> &x2 )
+ {
+ return
+ static_cast<const vex::vector<T>*>(&x1) ==
+ static_cast<const vex::vector<T>*>(&x2);
+ }
+};
+
+template <typename T, size_t N>
+struct same_instance_impl< vex::multivector<T, N> , vex::multivector<T, N> >
+{
+ static bool same_instance( const vex::multivector<T, N> &x1 , const vex::multivector<T, N> &x2 )
+ {
+ return
+ static_cast<const vex::multivector<T, N>*>(&x1) ==
+ static_cast<const vex::multivector<T, N>*>(&x2);
+ }
+};
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_VEXCL_VEXCL_SAME_INSTANCE_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/external/viennacl/viennacl_operations.hpp b/include/boost/numeric/odeint/external/viennacl/viennacl_operations.hpp
new file mode 100644
index 0000000..662c36a
--- /dev/null
+++ b/include/boost/numeric/odeint/external/viennacl/viennacl_operations.hpp
@@ -0,0 +1,226 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/viennacl_operations.hpp
+
+ [begin_description]
+ ViennaCL operations.
+ [end_description]
+
+ Copyright 2012 Denis Demidov
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_VIENNACL_VIENNACL_OPERATIONS_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_VIENNACL_VIENNACL_OPERATIONS_HPP_INCLUDED
+
+#include <viennacl/vector.hpp>
+
+#ifdef VIENNACL_WITH_OPENCL
+# include <viennacl/generator/custom_operation.hpp>
+#endif
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+#ifdef VIENNACL_WITH_OPENCL
+struct viennacl_operations
+{
+
+ template< class Fac1 = double , class Fac2 = Fac1 >
+ struct scale_sum2
+ {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+
+ scale_sum2( Fac1 alpha1 , Fac2 alpha2 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 )
+ { }
+
+ template< class T1 , class T2 , class T3 >
+ void operator()( viennacl::vector<T1> &v1 ,
+ const viennacl::vector<T2> &v2 ,
+ const viennacl::vector<T3> &v3
+ ) const
+ {
+ using namespace viennacl;
+
+ static generator::symbolic_vector <0, T1> sym_v1;
+ static generator::symbolic_vector <1, T2> sym_v2;
+ static generator::symbolic_vector <2, T3> sym_v3;
+ static generator::cpu_symbolic_scalar<3, Fac1> sym_a1;
+ static generator::cpu_symbolic_scalar<4, Fac2> sym_a2;
+
+ static generator::custom_operation op(
+ sym_v1 = sym_a1 * sym_v2
+ + sym_a2 * sym_v3,
+ "scale_sum2"
+ );
+
+ ocl::enqueue( op(v1, v2, v3, m_alpha1, m_alpha2) );
+ }
+
+ typedef void result_type;
+ };
+
+
+ template< class Fac1 = double , class Fac2 = Fac1 , class Fac3 = Fac2 >
+ struct scale_sum3
+ {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+ const Fac3 m_alpha3;
+
+ scale_sum3( Fac1 alpha1 , Fac2 alpha2 , Fac3 alpha3 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) , m_alpha3( alpha3 )
+ { }
+
+ template< class T1 , class T2 , class T3 , class T4 >
+ void operator()( viennacl::vector<T1> &v1 ,
+ const viennacl::vector<T2> &v2 ,
+ const viennacl::vector<T3> &v3 ,
+ const viennacl::vector<T4> &v4
+ ) const
+ {
+ using namespace viennacl;
+
+ static generator::symbolic_vector <0, T1> sym_v1;
+ static generator::symbolic_vector <1, T2> sym_v2;
+ static generator::symbolic_vector <2, T3> sym_v3;
+ static generator::symbolic_vector <3, T4> sym_v4;
+ static generator::cpu_symbolic_scalar<4, Fac1> sym_a1;
+ static generator::cpu_symbolic_scalar<5, Fac2> sym_a2;
+ static generator::cpu_symbolic_scalar<6, Fac3> sym_a3;
+
+ static generator::custom_operation op(
+ sym_v1 = sym_a1 * sym_v2
+ + sym_a2 * sym_v3
+ + sym_a3 * sym_v4,
+ "scale_sum3"
+ );
+
+ ocl::enqueue( op(v1, v2, v3, v4, m_alpha1, m_alpha2, m_alpha3) );
+ }
+
+ typedef void result_type;
+ };
+
+
+ template< class Fac1 = double , class Fac2 = Fac1 , class Fac3 = Fac2 , class Fac4 = Fac3 >
+ struct scale_sum4
+ {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+ const Fac3 m_alpha3;
+ const Fac4 m_alpha4;
+
+ scale_sum4( Fac1 alpha1 , Fac2 alpha2 , Fac3 alpha3 , Fac4 alpha4 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) , m_alpha3( alpha3 ) , m_alpha4( alpha4 ) { }
+
+ template< class T1 , class T2 , class T3 , class T4 , class T5 >
+ void operator()( viennacl::vector<T1> &v1 ,
+ const viennacl::vector<T2> &v2 ,
+ const viennacl::vector<T3> &v3 ,
+ const viennacl::vector<T4> &v4 ,
+ const viennacl::vector<T5> &v5
+ ) const
+ {
+ using namespace viennacl;
+
+ static generator::symbolic_vector <0, T1> sym_v1;
+ static generator::symbolic_vector <1, T2> sym_v2;
+ static generator::symbolic_vector <2, T3> sym_v3;
+ static generator::symbolic_vector <3, T4> sym_v4;
+ static generator::symbolic_vector <4, T5> sym_v5;
+ static generator::cpu_symbolic_scalar<5, Fac1> sym_a1;
+ static generator::cpu_symbolic_scalar<6, Fac2> sym_a2;
+ static generator::cpu_symbolic_scalar<7, Fac3> sym_a3;
+ static generator::cpu_symbolic_scalar<8, Fac4> sym_a4;
+
+ static generator::custom_operation op(
+ sym_v1 = sym_a1 * sym_v2
+ + sym_a2 * sym_v3
+ + sym_a3 * sym_v4
+ + sym_a4 * sym_v5,
+ "scale_sum4"
+ );
+
+ ocl::enqueue( op(v1, v2, v3, v4, v5,
+ m_alpha1, m_alpha2, m_alpha3, m_alpha4) );
+ }
+
+ typedef void result_type;
+ };
+
+
+ template< class Fac1 = double , class Fac2 = Fac1 , class Fac3 = Fac2 , class Fac4 = Fac3 , class Fac5 = Fac4 >
+ struct scale_sum5
+ {
+ const Fac1 m_alpha1;
+ const Fac2 m_alpha2;
+ const Fac3 m_alpha3;
+ const Fac4 m_alpha4;
+ const Fac5 m_alpha5;
+
+ scale_sum5( Fac1 alpha1 , Fac2 alpha2 , Fac3 alpha3 , Fac4 alpha4 , Fac5 alpha5 )
+ : m_alpha1( alpha1 ) , m_alpha2( alpha2 ) , m_alpha3( alpha3 ) , m_alpha4( alpha4 ) , m_alpha5( alpha5 ) { }
+
+ template< class T1 , class T2 , class T3 , class T4 , class T5 , class T6 >
+ void operator()( viennacl::vector<T1> &v1 ,
+ const viennacl::vector<T2> &v2 ,
+ const viennacl::vector<T3> &v3 ,
+ const viennacl::vector<T4> &v4 ,
+ const viennacl::vector<T5> &v5 ,
+ const viennacl::vector<T6> &v6
+ ) const
+ {
+ using namespace viennacl;
+
+ static generator::symbolic_vector < 0, T1> sym_v1;
+ static generator::symbolic_vector < 1, T2> sym_v2;
+ static generator::symbolic_vector < 2, T3> sym_v3;
+ static generator::symbolic_vector < 3, T4> sym_v4;
+ static generator::symbolic_vector < 4, T5> sym_v5;
+ static generator::symbolic_vector < 5, T6> sym_v6;
+ static generator::cpu_symbolic_scalar< 6, Fac1> sym_a1;
+ static generator::cpu_symbolic_scalar< 7, Fac2> sym_a2;
+ static generator::cpu_symbolic_scalar< 8, Fac3> sym_a3;
+ static generator::cpu_symbolic_scalar< 9, Fac4> sym_a4;
+ static generator::cpu_symbolic_scalar<10, Fac5> sym_a5;
+
+ static generator::custom_operation op(
+ sym_v1 = sym_a1 * sym_v2
+ + sym_a2 * sym_v3
+ + sym_a3 * sym_v4
+ + sym_a4 * sym_v5
+ + sym_a5 * sym_v6,
+ "scale_sum5"
+ );
+
+ ocl::enqueue( op(v1, v2, v3, v4, v5, v6,
+ m_alpha1, m_alpha2, m_alpha3, m_alpha4, m_alpha5) );
+ }
+
+ typedef void result_type;
+ };
+
+
+};
+#else
+struct viennacl_operations : public default_operations {};
+#endif
+
+
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_VIENNACL_VIENNACL_OPERATIONS_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/external/viennacl/viennacl_resize.hpp b/include/boost/numeric/odeint/external/viennacl/viennacl_resize.hpp
new file mode 100644
index 0000000..d324070
--- /dev/null
+++ b/include/boost/numeric/odeint/external/viennacl/viennacl_resize.hpp
@@ -0,0 +1,66 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/external/viennacl/viennacl_resize.hpp
+
+ [begin_description]
+ Enable resizing for viennacl vector.
+ [end_description]
+
+ Copyright 2012 Denis Demidov
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_EXTERNAL_VIENNACL_VIENNACL_RESIZE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_EXTERNAL_VIENNACL_VIENNACL_RESIZE_HPP_INCLUDED
+
+#include <viennacl/vector.hpp>
+
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resize.hpp>
+#include <boost/numeric/odeint/util/same_size.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+
+/*
+ * specializations for viennacl::vector< T >
+ */
+template< typename T >
+struct is_resizeable< viennacl::vector< T > > : boost::true_type { };
+
+template< typename T >
+struct resize_impl< viennacl::vector< T > , viennacl::vector< T > >
+{
+ static void resize( viennacl::vector< T > &x1 , const viennacl::vector< T > &x2 )
+ {
+ x1.resize( x2.size() , false );
+ }
+};
+
+template< typename T >
+struct same_size_impl< viennacl::vector< T > , viennacl::vector< T > >
+{
+ static bool same_size( const viennacl::vector< T > &x1 , const viennacl::vector< T > &x2 )
+ {
+ return x1.size() == x2.size();
+ }
+};
+
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_EXTERNAL_VIENNACL_VIENNACL_RESIZE_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/integrate/check_adapter.hpp b/include/boost/numeric/odeint/integrate/check_adapter.hpp
new file mode 100644
index 0000000..3d3ebd6
--- /dev/null
+++ b/include/boost/numeric/odeint/integrate/check_adapter.hpp
@@ -0,0 +1,222 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/check_adapter.hpp
+
+ [begin_description]
+ Adapters to add checking facility to stepper and observer
+ [end_description]
+
+ Copyright 2015 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_CHECK_ADAPTER_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_CHECK_ADAPTER_HPP_INCLUDED
+
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/stepper/controlled_step_result.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template<class Stepper, class Checker,
+ class StepperCategory = typename base_tag<typename Stepper::stepper_category>::type>
+class checked_stepper;
+
+
+/**
+ * \brief Adapter to combine basic stepper and checker.
+ */
+template<class Stepper, class Checker>
+class checked_stepper<Stepper, Checker, stepper_tag>
+{
+
+public:
+ typedef Stepper stepper_type;
+ typedef Checker checker_type;
+ // forward stepper typedefs
+ typedef typename stepper_type::state_type state_type;
+ typedef typename stepper_type::value_type value_type;
+ typedef typename stepper_type::deriv_type deriv_type;
+ typedef typename stepper_type::time_type time_type;
+
+private:
+ stepper_type &m_stepper;
+ checker_type &m_checker;
+
+public:
+ /**
+ * \brief Construct the checked_stepper.
+ */
+ checked_stepper(stepper_type &stepper, checker_type &checker)
+ : m_stepper(stepper), m_checker(checker) { }
+
+ /**
+ * \brief forward of the do_step method
+ */
+ template<class System, class StateInOut>
+ void do_step(System system, StateInOut &state, const time_type t, const time_type dt)
+ {
+ // do the step
+ m_stepper.do_step(system, state, t, dt);
+ // call the checker
+ m_checker();
+ }
+};
+
+
+/**
+ * \brief Adapter to combine controlled stepper and checker.
+ */
+template<class ControlledStepper, class Checker>
+class checked_stepper<ControlledStepper, Checker, controlled_stepper_tag>
+{
+
+public:
+ typedef ControlledStepper stepper_type;
+ typedef Checker checker_type;
+ // forward stepper typedefs
+ typedef typename stepper_type::state_type state_type;
+ typedef typename stepper_type::value_type value_type;
+ typedef typename stepper_type::deriv_type deriv_type;
+ typedef typename stepper_type::time_type time_type;
+
+private:
+ stepper_type &m_stepper;
+ checker_type &m_checker;
+
+public:
+ /**
+ * \brief Construct the checked_stepper.
+ */
+ checked_stepper(stepper_type &stepper, checker_type &checker)
+ : m_stepper(stepper), m_checker(checker) { }
+
+ /**
+ * \brief forward of the do_step method
+ */
+ template< class System , class StateInOut >
+ controlled_step_result try_step( System system , StateInOut &state , time_type &t , time_type &dt )
+ {
+ // do the step
+ if( m_stepper.try_step(system, state, t, dt) == success )
+ {
+ // call the checker if step was successful
+ m_checker();
+ return success;
+ } else
+ {
+ // step failed -> return fail
+ return fail;
+ }
+ }
+};
+
+
+/**
+ * \brief Adapter to combine dense out stepper and checker.
+ */
+template<class DenseOutStepper, class Checker>
+class checked_stepper<DenseOutStepper, Checker, dense_output_stepper_tag>
+{
+
+public:
+ typedef DenseOutStepper stepper_type;
+ typedef Checker checker_type;
+ // forward stepper typedefs
+ typedef typename stepper_type::state_type state_type;
+ typedef typename stepper_type::value_type value_type;
+ typedef typename stepper_type::deriv_type deriv_type;
+ typedef typename stepper_type::time_type time_type;
+
+private:
+ stepper_type &m_stepper;
+ checker_type &m_checker;
+
+public:
+ /**
+ * \brief Construct the checked_stepper.
+ */
+ checked_stepper(stepper_type &stepper, checker_type &checker)
+ : m_stepper(stepper), m_checker(checker) { }
+
+
+ template< class System >
+ std::pair< time_type , time_type > do_step( System system )
+ {
+ m_checker();
+ return m_stepper.do_step(system);
+ }
+
+ /* provide the remaining dense out stepper interface */
+ template< class StateType >
+ void initialize( const StateType &x0 , time_type t0 , time_type dt0 )
+ { m_stepper.initialize(x0, t0, dt0); }
+
+
+ template< class StateOut >
+ void calc_state( time_type t , StateOut &x ) const
+ { m_stepper.calc_state(t, x); }
+
+ template< class StateOut >
+ void calc_state( time_type t , const StateOut &x ) const
+ { m_stepper.calc_state(t, x); }
+
+ const state_type& current_state( void ) const
+ { return m_stepper.current_state(); }
+
+ time_type current_time( void ) const
+ { return m_stepper.current_time(); }
+
+ const state_type& previous_state( void ) const
+ { return m_stepper.previous_state(); }
+
+ time_type previous_time( void ) const
+ { return m_stepper.previous_time(); }
+
+ time_type current_time_step( void ) const
+ { return m_stepper.current_time_step(); }
+
+};
+
+
+/**
+ * \brief Adapter to combine observer and checker.
+ */
+template<class Observer, class Checker>
+class checked_observer
+{
+public:
+ typedef Observer observer_type;
+ typedef Checker checker_type;
+
+private:
+ observer_type &m_observer;
+ checker_type &m_checker;
+
+public:
+ checked_observer(observer_type &observer, checker_type &checker)
+ : m_observer(observer), m_checker(checker)
+ {}
+
+ template< class State , class Time >
+ void operator()(const State& state, Time t) const
+ {
+ // call the observer
+ m_observer(state, t);
+ // reset the checker
+ m_checker.reset();
+ }
+};
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+#endif
\ No newline at end of file
diff --git a/include/boost/numeric/odeint/integrate/detail/functors.hpp b/include/boost/numeric/odeint/integrate/detail/functors.hpp
new file mode 100644
index 0000000..b239217
--- /dev/null
+++ b/include/boost/numeric/odeint/integrate/detail/functors.hpp
@@ -0,0 +1,70 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/detail/functors.hpp
+
+ [begin_description]
+ some functors for the iterator based integrate routines
+ [end_description]
+
+ Copyright 2009-2013 Karsten Ahnert
+ Copyright 2009-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_FUNCTORS_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_FUNCTORS_HPP_INCLUDED
+
+#include <utility>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+
+template< class Observer >
+struct obs_caller {
+
+ size_t &m_n;
+ Observer m_obs;
+
+ obs_caller( size_t &m , Observer &obs ) : m_n(m) , m_obs( obs ) {}
+
+ template< class State , class Time >
+ void operator()( std::pair< const State & , const Time & > x )
+ {
+ typedef typename odeint::unwrap_reference< Observer >::type observer_type;
+ observer_type &obs = m_obs;
+ obs( x.first , x.second );
+ m_n++;
+ }
+};
+
+template< class Observer , class Time >
+struct obs_caller_time {
+
+ Time &m_t;
+ Observer m_obs;
+
+ obs_caller_time( Time &t , Observer &obs ) : m_t(t) , m_obs( obs ) {}
+
+ template< class State >
+ void operator()( std::pair< const State & , const Time & > x )
+ {
+ typedef typename odeint::unwrap_reference< Observer >::type observer_type;
+ observer_type &obs = m_obs;
+ obs( x.first , x.second );
+ m_t = x.second;
+ }
+};
+
+} // namespace detail
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_FUNCTORS_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/integrate/detail/integrate_adaptive.hpp b/include/boost/numeric/odeint/integrate/detail/integrate_adaptive.hpp
new file mode 100644
index 0000000..7516d44
--- /dev/null
+++ b/include/boost/numeric/odeint/integrate/detail/integrate_adaptive.hpp
@@ -0,0 +1,161 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/detail/integrate_adaptive.hpp
+
+ [begin_description]
+ Default Integrate adaptive implementation.
+ [end_description]
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011-2015 Mario Mulansky
+ Copyright 2012 Christoph Koke
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_ADAPTIVE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_ADAPTIVE_HPP_INCLUDED
+
+#include <stdexcept>
+
+#include <boost/throw_exception.hpp>
+
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/stepper/controlled_step_result.hpp>
+#include <boost/numeric/odeint/integrate/max_step_checker.hpp>
+#include <boost/numeric/odeint/integrate/detail/integrate_const.hpp>
+#include <boost/numeric/odeint/util/bind.hpp>
+#include <boost/numeric/odeint/util/unwrap_reference.hpp>
+#include <boost/numeric/odeint/util/copy.hpp>
+
+#include <boost/numeric/odeint/util/detail/less_with_sign.hpp>
+
+
+#include <iostream>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+// forward declaration
+template< class Stepper , class System , class State , class Time , class Observer >
+size_t integrate_const(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time end_time , Time dt ,
+ Observer observer , stepper_tag );
+
+/*
+ * integrate_adaptive for simple stepper is basically an integrate_const + some last step
+ */
+template< class Stepper , class System , class State , class Time , class Observer >
+size_t integrate_adaptive(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time end_time , Time dt ,
+ Observer observer , stepper_tag
+)
+{
+ size_t steps = detail::integrate_const( stepper , system , start_state , start_time ,
+ end_time , dt , observer , stepper_tag() );
+ typename odeint::unwrap_reference< Observer >::type &obs = observer;
+ typename odeint::unwrap_reference< Stepper >::type &st = stepper;
+
+ Time end = start_time + dt*steps;
+ if( less_with_sign( end , end_time , dt ) )
+ { //make a last step to end exactly at end_time
+ st.do_step( system , start_state , end , end_time - end );
+ steps++;
+ obs( start_state , end_time );
+ }
+ return steps;
+}
+
+
+/*
+ * integrate adaptive for controlled stepper
+ */
+template< class Stepper , class System , class State , class Time , class Observer >
+size_t integrate_adaptive(
+ Stepper stepper , System system , State &start_state ,
+ Time &start_time , Time end_time , Time &dt ,
+ Observer observer , controlled_stepper_tag
+)
+{
+ typename odeint::unwrap_reference< Observer >::type &obs = observer;
+ typename odeint::unwrap_reference< Stepper >::type &st = stepper;
+
+ failed_step_checker fail_checker; // to throw a runtime_error if step size adjustment fails
+ size_t count = 0;
+ while( less_with_sign( start_time , end_time , dt ) )
+ {
+ obs( start_state , start_time );
+ if( less_with_sign( end_time , static_cast<Time>(start_time + dt) , dt ) )
+ {
+ dt = end_time - start_time;
+ }
+
+ controlled_step_result res;
+ do
+ {
+ res = st.try_step( system , start_state , start_time , dt );
+ fail_checker(); // check number of failed steps
+ }
+ while( res == fail );
+ fail_checker.reset(); // if we reach here, the step was successful -> reset fail checker
+
+ ++count;
+ }
+ obs( start_state , start_time );
+ return count;
+}
+
+
+/*
+ * integrate adaptive for dense output steppers
+ *
+ * step size control is used if the stepper supports it
+ */
+template< class Stepper , class System , class State , class Time , class Observer >
+size_t integrate_adaptive(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time end_time , Time dt ,
+ Observer observer , dense_output_stepper_tag )
+{
+ typename odeint::unwrap_reference< Observer >::type &obs = observer;
+ typename odeint::unwrap_reference< Stepper >::type &st = stepper;
+
+ size_t count = 0;
+ st.initialize( start_state , start_time , dt );
+
+ while( less_with_sign( st.current_time() , end_time , st.current_time_step() ) )
+ {
+ while( less_eq_with_sign( static_cast<Time>(st.current_time() + st.current_time_step()) ,
+ end_time ,
+ st.current_time_step() ) )
+ { //make sure we don't go beyond the end_time
+ obs( st.current_state() , st.current_time() );
+ st.do_step( system );
+ ++count;
+ }
+ // calculate time step to arrive exactly at end time
+ st.initialize( st.current_state() , st.current_time() , static_cast<Time>(end_time - st.current_time()) );
+ }
+ obs( st.current_state() , st.current_time() );
+ // overwrite start_state with the final point
+ boost::numeric::odeint::copy( st.current_state() , start_state );
+ return count;
+}
+
+
+
+
+} // namespace detail
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_ADAPTIVE_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/integrate/detail/integrate_const.hpp b/include/boost/numeric/odeint/integrate/detail/integrate_const.hpp
new file mode 100644
index 0000000..7a86b32
--- /dev/null
+++ b/include/boost/numeric/odeint/integrate/detail/integrate_const.hpp
@@ -0,0 +1,167 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/detail/integrate_const.hpp
+
+ [begin_description]
+ integrate const implementation
+ [end_description]
+
+ Copyright 2012-2015 Mario Mulansky
+ Copyright 2012 Christoph Koke
+ Copyright 2012 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_CONST_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_CONST_HPP_INCLUDED
+
+#include <boost/numeric/odeint/util/unwrap_reference.hpp>
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/util/unit_helper.hpp>
+#include <boost/numeric/odeint/integrate/detail/integrate_adaptive.hpp>
+
+#include <boost/numeric/odeint/util/detail/less_with_sign.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+// forward declaration
+template< class Stepper , class System , class State , class Time , class Observer >
+size_t integrate_adaptive(
+ Stepper stepper , System system , State &start_state ,
+ Time &start_time , Time end_time , Time &dt ,
+ Observer observer , controlled_stepper_tag
+);
+
+
+template< class Stepper , class System , class State , class Time , class Observer >
+size_t integrate_const(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time end_time , Time dt ,
+ Observer observer , stepper_tag
+)
+{
+
+ typename odeint::unwrap_reference< Observer >::type &obs = observer;
+ typename odeint::unwrap_reference< Stepper >::type &st = stepper;
+
+ Time time = start_time;
+ int step = 0;
+ // cast time+dt explicitely in case of expression templates (e.g. multiprecision)
+ while( less_eq_with_sign( static_cast<Time>(time+dt) , end_time , dt ) )
+ {
+ obs( start_state , time );
+ st.do_step( system , start_state , time , dt );
+ // direct computation of the time avoids error propagation happening when using time += dt
+ // we need clumsy type analysis to get boost units working here
+ ++step;
+ time = start_time + static_cast< typename unit_value_type<Time>::type >(step) * dt;
+ }
+ obs( start_state , time );
+
+ return step;
+}
+
+
+
+template< class Stepper , class System , class State , class Time , class Observer >
+size_t integrate_const(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time end_time , Time dt ,
+ Observer observer , controlled_stepper_tag
+)
+{
+ typename odeint::unwrap_reference< Observer >::type &obs = observer;
+
+ Time time = start_time;
+ const Time time_step = dt;
+ int real_steps = 0;
+ int step = 0;
+
+ while( less_eq_with_sign( static_cast<Time>(time+time_step) , end_time , dt ) )
+ {
+ obs( start_state , time );
+ // integrate_adaptive_checked uses the given checker to throw if an overflow occurs
+ real_steps += detail::integrate_adaptive(stepper, system, start_state, time,
+ static_cast<Time>(time + time_step), dt,
+ null_observer(), controlled_stepper_tag());
+ // direct computation of the time avoids error propagation happening when using time += dt
+ // we need clumsy type analysis to get boost units working here
+ step++;
+ time = start_time + static_cast< typename unit_value_type<Time>::type >(step) * time_step;
+ }
+ obs( start_state , time );
+
+ return real_steps;
+}
+
+
+template< class Stepper , class System , class State , class Time , class Observer >
+size_t integrate_const(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time end_time , Time dt ,
+ Observer observer , dense_output_stepper_tag
+)
+{
+ typename odeint::unwrap_reference< Observer >::type &obs = observer;
+ typename odeint::unwrap_reference< Stepper >::type &st = stepper;
+
+ Time time = start_time;
+
+ st.initialize( start_state , time , dt );
+ obs( start_state , time );
+ time += dt;
+
+ int obs_step( 1 );
+ int real_step( 0 );
+
+ while( less_eq_with_sign( static_cast<Time>(time+dt) , end_time , dt ) )
+ {
+ while( less_eq_with_sign( time , st.current_time() , dt ) )
+ {
+ st.calc_state( time , start_state );
+ obs( start_state , time );
+ ++obs_step;
+ // direct computation of the time avoids error propagation happening when using time += dt
+ // we need clumsy type analysis to get boost units working here
+ time = start_time + static_cast< typename unit_value_type<Time>::type >(obs_step) * dt;
+ }
+ // we have not reached the end, do another real step
+ if( less_with_sign( static_cast<Time>(st.current_time()+st.current_time_step()) ,
+ end_time ,
+ st.current_time_step() ) )
+ {
+ while( less_eq_with_sign( st.current_time() , time , dt ) )
+ {
+ st.do_step( system );
+ ++real_step;
+ }
+ }
+ else if( less_with_sign( st.current_time() , end_time , st.current_time_step() ) )
+ { // do the last step ending exactly on the end point
+ st.initialize( st.current_state() , st.current_time() , end_time - st.current_time() );
+ st.do_step( system );
+ ++real_step;
+ }
+
+ }
+ // last observation, if we are still in observation interval
+ // might happen due to finite precision problems when computing the the time
+ if( less_eq_with_sign( time , end_time , dt ) )
+ {
+ st.calc_state( time , start_state );
+ obs( start_state , time );
+ }
+
+ return real_step;
+}
+
+
+} } } }
+
+#endif
diff --git a/include/boost/numeric/odeint/integrate/detail/integrate_n_steps.hpp b/include/boost/numeric/odeint/integrate/detail/integrate_n_steps.hpp
new file mode 100644
index 0000000..2ef490d
--- /dev/null
+++ b/include/boost/numeric/odeint/integrate/detail/integrate_n_steps.hpp
@@ -0,0 +1,161 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/detail/integrate_n_steps.hpp
+
+ [begin_description]
+ integrate steps implementation
+ [end_description]
+
+ Copyright 2012-2015 Mario Mulansky
+ Copyright 2012 Christoph Koke
+ Copyright 2012 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_N_STEPS_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_N_STEPS_HPP_INCLUDED
+
+#include <boost/numeric/odeint/util/unwrap_reference.hpp>
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/integrate/detail/integrate_adaptive.hpp>
+#include <boost/numeric/odeint/util/unit_helper.hpp>
+
+#include <boost/numeric/odeint/util/detail/less_with_sign.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+// forward declaration
+template< class Stepper , class System , class State , class Time , class Observer >
+size_t integrate_adaptive_checked(
+ Stepper stepper , System system , State &start_state ,
+ Time &start_time , Time end_time , Time &dt ,
+ Observer observer, controlled_stepper_tag
+);
+
+
+/* basic version */
+template< class Stepper , class System , class State , class Time , class Observer>
+Time integrate_n_steps(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time dt , size_t num_of_steps ,
+ Observer observer , stepper_tag )
+{
+ typename odeint::unwrap_reference< Observer >::type &obs = observer;
+ typename odeint::unwrap_reference< Stepper >::type &st = stepper;
+
+ Time time = start_time;
+
+ for( size_t step = 0; step < num_of_steps ; ++step )
+ {
+ obs( start_state , time );
+ st.do_step( system , start_state , time , dt );
+ // direct computation of the time avoids error propagation happening when using time += dt
+ // we need clumsy type analysis to get boost units working here
+ time = start_time + static_cast< typename unit_value_type<Time>::type >( step+1 ) * dt;
+ }
+ obs( start_state , time );
+
+ return time;
+}
+
+
+/* controlled version */
+template< class Stepper , class System , class State , class Time , class Observer >
+Time integrate_n_steps(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time dt , size_t num_of_steps ,
+ Observer observer , controlled_stepper_tag )
+{
+ typename odeint::unwrap_reference< Observer >::type &obs = observer;
+
+ Time time = start_time;
+ Time time_step = dt;
+
+ for( size_t step = 0; step < num_of_steps ; ++step )
+ {
+ obs( start_state , time );
+ // integrate_adaptive_checked uses the given checker to throw if an overflow occurs
+ detail::integrate_adaptive(stepper, system, start_state, time, static_cast<Time>(time + time_step), dt,
+ null_observer(), controlled_stepper_tag());
+ // direct computation of the time avoids error propagation happening when using time += dt
+ // we need clumsy type analysis to get boost units working here
+ time = start_time + static_cast< typename unit_value_type<Time>::type >(step+1) * time_step;
+ }
+ obs( start_state , time );
+
+ return time;
+}
+
+
+/* dense output version */
+template< class Stepper , class System , class State , class Time , class Observer >
+Time integrate_n_steps(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time dt , size_t num_of_steps ,
+ Observer observer , dense_output_stepper_tag )
+{
+ typename odeint::unwrap_reference< Observer >::type &obs = observer;
+ typename odeint::unwrap_reference< Stepper >::type &st = stepper;
+
+ Time time = start_time;
+ const Time end_time = start_time + static_cast< typename unit_value_type<Time>::type >(num_of_steps) * dt;
+
+ st.initialize( start_state , time , dt );
+
+ size_t step = 0;
+
+ while( step < num_of_steps )
+ {
+ while( less_with_sign( time , st.current_time() , st.current_time_step() ) )
+ {
+ st.calc_state( time , start_state );
+ obs( start_state , time );
+ ++step;
+ // direct computation of the time avoids error propagation happening when using time += dt
+ // we need clumsy type analysis to get boost units working here
+ time = start_time + static_cast< typename unit_value_type<Time>::type >(step) * dt;
+ }
+
+ // we have not reached the end, do another real step
+ if( less_with_sign( static_cast<Time>(st.current_time()+st.current_time_step()) ,
+ end_time ,
+ st.current_time_step() ) )
+ {
+ st.do_step( system );
+ }
+ else if( less_with_sign( st.current_time() , end_time , st.current_time_step() ) )
+ { // do the last step ending exactly on the end point
+ st.initialize( st.current_state() , st.current_time() , static_cast<Time>(end_time - st.current_time()) );
+ st.do_step( system );
+ }
+ }
+
+ // make sure we really end exactly where we should end
+ while( st.current_time() < end_time )
+ {
+ if( less_with_sign( end_time ,
+ static_cast<Time>(st.current_time()+st.current_time_step()) ,
+ st.current_time_step() ) )
+ st.initialize( st.current_state() , st.current_time() , static_cast<Time>(end_time - st.current_time()) );
+ st.do_step( system );
+ }
+
+ // observation at final point
+ obs( st.current_state() , end_time );
+
+ return time;
+}
+
+
+}
+}
+}
+}
+
+#endif /* BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_N_STEPS_HPP_INCLUDED */
diff --git a/include/boost/numeric/odeint/integrate/detail/integrate_times.hpp b/include/boost/numeric/odeint/integrate/detail/integrate_times.hpp
new file mode 100644
index 0000000..2e27990
--- /dev/null
+++ b/include/boost/numeric/odeint/integrate/detail/integrate_times.hpp
@@ -0,0 +1,179 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/detail/integrate_times.hpp
+
+ [begin_description]
+ Default integrate times implementation.
+ [end_description]
+
+ Copyright 2011-2015 Mario Mulansky
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012 Christoph Koke
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_TIMES_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_TIMES_HPP_INCLUDED
+
+#include <stdexcept>
+
+#include <boost/config.hpp>
+#include <boost/throw_exception.hpp>
+#include <boost/numeric/odeint/util/unwrap_reference.hpp>
+#include <boost/numeric/odeint/stepper/controlled_step_result.hpp>
+#include <boost/numeric/odeint/util/detail/less_with_sign.hpp>
+#include <boost/numeric/odeint/integrate/max_step_checker.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+
+
+/*
+ * integrate_times for simple stepper
+ */
+template<class Stepper, class System, class State, class TimeIterator, class Time, class Observer>
+size_t integrate_times(
+ Stepper stepper , System system , State &start_state ,
+ TimeIterator start_time , TimeIterator end_time , Time dt ,
+ Observer observer , stepper_tag
+)
+{
+ typedef typename odeint::unwrap_reference< Stepper >::type stepper_type;
+ typedef typename odeint::unwrap_reference< Observer >::type observer_type;
+
+ stepper_type &st = stepper;
+ observer_type &obs = observer;
+ typedef typename unit_value_type<Time>::type time_type;
+
+ size_t steps = 0;
+ Time current_dt = dt;
+ while( true )
+ {
+ Time current_time = *start_time++;
+ obs( start_state , current_time );
+ if( start_time == end_time )
+ break;
+ while( less_with_sign( current_time , static_cast<time_type>(*start_time) , current_dt ) )
+ {
+ current_dt = min_abs( dt , *start_time - current_time );
+ st.do_step( system , start_state , current_time , current_dt );
+ current_time += current_dt;
+ steps++;
+ }
+ }
+ return steps;
+}
+
+/*
+ * integrate_times for controlled stepper
+ */
+template< class Stepper , class System , class State , class TimeIterator , class Time , class Observer >
+size_t integrate_times(
+ Stepper stepper , System system , State &start_state ,
+ TimeIterator start_time , TimeIterator end_time , Time dt ,
+ Observer observer , controlled_stepper_tag
+)
+{
+ typename odeint::unwrap_reference< Observer >::type &obs = observer;
+ typename odeint::unwrap_reference< Stepper >::type &st = stepper;
+ typedef typename unit_value_type<Time>::type time_type;
+
+ failed_step_checker fail_checker; // to throw a runtime_error if step size adjustment fails
+ size_t steps = 0;
+ while( true )
+ {
+ Time current_time = *start_time++;
+ obs( start_state , current_time );
+ if( start_time == end_time )
+ break;
+ while( less_with_sign( current_time , static_cast<time_type>(*start_time) , dt ) )
+ {
+ // adjust stepsize to end up exactly at the observation point
+ Time current_dt = min_abs( dt , *start_time - current_time );
+ if( st.try_step( system , start_state , current_time , current_dt ) == success )
+ {
+ ++steps;
+ // successful step -> reset the fail counter, see #173
+ fail_checker.reset();
+ // continue with the original step size if dt was reduced due to observation
+ dt = max_abs( dt , current_dt );
+ }
+ else
+ {
+ fail_checker(); // check for possible overflow of failed steps in step size adjustment
+ dt = current_dt;
+ }
+ }
+ }
+ return steps;
+}
+
+/*
+ * integrate_times for dense output stepper
+ */
+template< class Stepper , class System , class State , class TimeIterator , class Time , class Observer >
+size_t integrate_times(
+ Stepper stepper , System system , State &start_state ,
+ TimeIterator start_time , TimeIterator end_time , Time dt ,
+ Observer observer , dense_output_stepper_tag
+)
+{
+ typename odeint::unwrap_reference< Observer >::type &obs = observer;
+ typename odeint::unwrap_reference< Stepper >::type &st = stepper;
+
+ typedef typename unit_value_type<Time>::type time_type;
+
+ if( start_time == end_time )
+ return 0;
+
+ TimeIterator last_time_iterator = end_time;
+ --last_time_iterator;
+ Time last_time_point = static_cast<time_type>(*last_time_iterator);
+
+ st.initialize( start_state , *start_time , dt );
+ obs( start_state , *start_time++ );
+
+ size_t count = 0;
+ while( start_time != end_time )
+ {
+ while( ( start_time != end_time ) && less_eq_with_sign( static_cast<time_type>(*start_time) , st.current_time() , st.current_time_step() ) )
+ {
+ st.calc_state( *start_time , start_state );
+ obs( start_state , *start_time );
+ start_time++;
+ }
+
+ // we have not reached the end, do another real step
+ if( less_eq_with_sign( st.current_time() + st.current_time_step() ,
+ last_time_point ,
+ st.current_time_step() ) )
+ {
+ st.do_step( system );
+ ++count;
+ }
+ else if( start_time != end_time )
+ { // do the last step ending exactly on the end point
+ st.initialize( st.current_state() , st.current_time() , last_time_point - st.current_time() );
+ st.do_step( system );
+ ++count;
+ }
+ }
+ return count;
+}
+
+
+} // namespace detail
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_ADAPTIVE_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/integrate/integrate.hpp b/include/boost/numeric/odeint/integrate/integrate.hpp
new file mode 100644
index 0000000..446656b
--- /dev/null
+++ b/include/boost/numeric/odeint/integrate/integrate.hpp
@@ -0,0 +1,133 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/integrate.hpp
+
+ [begin_description]
+ Convenience methods which choose the stepper for the current ODE.
+ [end_description]
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_HPP_INCLUDED
+
+#include <boost/utility/enable_if.hpp>
+
+#include <boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp>
+#include <boost/numeric/odeint/stepper/controlled_runge_kutta.hpp>
+#include <boost/numeric/odeint/integrate/null_observer.hpp>
+#include <boost/numeric/odeint/integrate/integrate_adaptive.hpp>
+
+// for has_value_type trait
+#include <boost/numeric/odeint/algebra/detail/extract_value_type.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+/*
+ * ToDo :
+ *
+ * determine type of dxdt for units
+ *
+ */
+template< class System , class State , class Time , class Observer >
+typename boost::enable_if< typename has_value_type<State>::type , size_t >::type
+integrate( System system , State &start_state , Time start_time , Time end_time , Time dt , Observer observer )
+{
+ typedef controlled_runge_kutta< runge_kutta_dopri5< State , typename State::value_type , State , Time > > stepper_type;
+ return integrate_adaptive( stepper_type() , system , start_state , start_time , end_time , dt , observer );
+}
+
+template< class Value , class System , class State , class Time , class Observer >
+size_t
+integrate( System system , State &start_state , Time start_time , Time end_time , Time dt , Observer observer )
+{
+ typedef controlled_runge_kutta< runge_kutta_dopri5< State , Value , State , Time > > stepper_type;
+ return integrate_adaptive( stepper_type() , system , start_state , start_time , end_time , dt , observer );
+}
+
+
+
+
+/*
+ * the two overloads are needed in order to solve the forwarding problem
+ */
+template< class System , class State , class Time >
+size_t integrate( System system , State &start_state , Time start_time , Time end_time , Time dt )
+{
+ return integrate( system , start_state , start_time , end_time , dt , null_observer() );
+}
+
+template< class Value , class System , class State , class Time >
+size_t integrate( System system , State &start_state , Time start_time , Time end_time , Time dt )
+{
+ return integrate< Value >( system , start_state , start_time , end_time , dt , null_observer() );
+}
+
+
+
+/**
+ * \fn integrate( System system , State &start_state , Time start_time , Time end_time , Time dt , Observer observer )
+ * \brief Integrates the ODE.
+ *
+ * Integrates the ODE given by system from start_time to end_time starting
+ * with start_state as initial condition and dt as initial time step.
+ * This function uses a dense output dopri5 stepper and performs an adaptive
+ * integration with step size control, thus dt changes during the integration.
+ * This method uses standard error bounds of 1E-6.
+ * After each step, the observer is called.
+ *
+ * \attention A second version of this function template exists which explicitly
+ * expects the value type as template parameter, i.e. integrate< double >( sys , x , t0 , t1 , dt , obs );
+ *
+ * \param system The system function to solve, hence the r.h.s. of the
+ * ordinary differential equation.
+ * \param start_state The initial state.
+ * \param start_time Start time of the integration.
+ * \param end_time End time of the integration.
+ * \param dt Initial step size, will be adjusted during the integration.
+ * \param observer Observer that will be called after each time step.
+ * \return The number of steps performed.
+ */
+
+
+/**
+ * \fn integrate( System system , State &start_state , Time start_time , Time end_time , Time dt )
+ * \brief Integrates the ODE without observer calls.
+ *
+ * Integrates the ODE given by system from start_time to end_time starting
+ * with start_state as initial condition and dt as initial time step.
+ * This function uses a dense output dopri5 stepper and performs an adaptive
+ * integration with step size control, thus dt changes during the integration.
+ * This method uses standard error bounds of 1E-6.
+ * No observer is called.
+ *
+ * \attention A second version of this function template exists which explicitly
+ * expects the value type as template parameter, i.e. integrate< double >( sys , x , t0 , t1 , dt );
+ *
+ * \param system The system function to solve, hence the r.h.s. of the
+ * ordinary differential equation.
+ * \param start_state The initial state.
+ * \param start_time Start time of the integration.
+ * \param end_time End time of the integration.
+ * \param dt Initial step size, will be adjusted during the integration.
+ * \return The number of steps performed.
+ */
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/integrate/integrate_adaptive.hpp b/include/boost/numeric/odeint/integrate/integrate_adaptive.hpp
new file mode 100644
index 0000000..0999714
--- /dev/null
+++ b/include/boost/numeric/odeint/integrate/integrate_adaptive.hpp
@@ -0,0 +1,129 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/integrate_adaptive.hpp
+
+ [begin_description]
+ Adaptive integration of ODEs.
+ [end_description]
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011-2015 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_ADAPTIVE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_ADAPTIVE_HPP_INCLUDED
+
+#include <boost/type_traits/is_same.hpp>
+
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/integrate/null_observer.hpp>
+#include <boost/numeric/odeint/integrate/detail/integrate_adaptive.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+/*
+ * the two overloads are needed in order to solve the forwarding problem
+ */
+template< class Stepper , class System , class State , class Time , class Observer >
+size_t integrate_adaptive(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time end_time , Time dt ,
+ Observer observer )
+{
+ typedef typename odeint::unwrap_reference< Stepper >::type::stepper_category stepper_category;
+ return detail::integrate_adaptive(
+ stepper , system , start_state ,
+ start_time , end_time , dt ,
+ observer , stepper_category() );
+
+ /*
+ * Suggestion for a new extendable version:
+ *
+ * integrator_adaptive< Stepper , System, State , Time , Observer , typename Stepper::stepper_category > integrator;
+ * return integrator.run( stepper , system , start_state , start_time , end_time , dt , observer );
+ */
+}
+
+/**
+ * \brief Second version to solve the forwarding problem,
+ * can be called with Boost.Range as start_state.
+ */
+template< class Stepper , class System , class State , class Time , class Observer >
+size_t integrate_adaptive(
+ Stepper stepper , System system , const State &start_state ,
+ Time start_time , Time end_time , Time dt ,
+ Observer observer )
+{
+ typedef typename odeint::unwrap_reference< Stepper >::type::stepper_category stepper_category;
+ return detail::integrate_adaptive(
+ stepper , system , start_state ,
+ start_time , end_time , dt ,
+ observer , stepper_category() );
+}
+
+
+
+
+/**
+ * \brief integrate_adaptive without an observer.
+ */
+template< class Stepper , class System , class State , class Time >
+size_t integrate_adaptive(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time end_time , Time dt )
+{
+ return integrate_adaptive( stepper , system , start_state , start_time , end_time , dt , null_observer() );
+}
+
+/**
+ * \brief Second version to solve the forwarding problem,
+ * can be called with Boost.Range as start_state.
+ */
+template< class Stepper , class System , class State , class Time >
+size_t integrate_adaptive(
+ Stepper stepper , System system , const State &start_state ,
+ Time start_time , Time end_time , Time dt )
+{
+ return integrate_adaptive( stepper , system , start_state , start_time , end_time , dt , null_observer() );
+}
+
+
+/************* DOXYGEN ************/
+
+ /**
+ * \fn integrate_adaptive( Stepper stepper , System system , State &start_state , Time start_time , Time end_time , Time dt , Observer observer )
+ * \brief Integrates the ODE with adaptive step size.
+ *
+ * This function integrates the ODE given by system with the given stepper.
+ * The observer is called after each step. If the stepper has no error
+ * control, the step size remains constant and the observer is called at
+ * equidistant time points t0+n*dt. If the stepper is a ControlledStepper,
+ * the step size is adjusted and the observer is called in non-equidistant
+ * intervals.
+ *
+ * \param stepper The stepper to be used for numerical integration.
+ * \param system Function/Functor defining the rhs of the ODE.
+ * \param start_state The initial condition x0.
+ * \param start_time The initial time t0.
+ * \param end_time The final integration time tend.
+ * \param dt The time step between observer calls, _not_ necessarily the
+ * time step of the integration.
+ * \param observer Function/Functor called at equidistant time intervals.
+ * \return The number of steps performed.
+ */
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_ADAPTIVE_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/integrate/integrate_const.hpp b/include/boost/numeric/odeint/integrate/integrate_const.hpp
new file mode 100644
index 0000000..fae683f
--- /dev/null
+++ b/include/boost/numeric/odeint/integrate/integrate_const.hpp
@@ -0,0 +1,195 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/integrate_const.hpp
+
+ [begin_description]
+ Constant integration of ODEs, meaning that the state of the ODE is observed on constant time intervals.
+ The routines makes full use of adaptive and dense-output methods.
+ [end_description]
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011-2015 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_CONST_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_CONST_HPP_INCLUDED
+
+#include <boost/type_traits/is_same.hpp>
+
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/integrate/null_observer.hpp>
+#include <boost/numeric/odeint/integrate/check_adapter.hpp>
+#include <boost/numeric/odeint/integrate/detail/integrate_const.hpp>
+#include <boost/numeric/odeint/integrate/detail/integrate_adaptive.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+/*
+ * Integrates with constant time step dt.
+ */
+template<class Stepper, class System, class State, class Time, class Observer, class StepOverflowChecker>
+size_t integrate_const(
+ Stepper stepper, System system, State &start_state,
+ Time start_time, Time end_time, Time dt,
+ Observer observer, StepOverflowChecker checker
+) {
+ typedef typename odeint::unwrap_reference<Stepper>::type::stepper_category stepper_category;
+ // we want to get as fast as possible to the end
+ // no overflow checks needed
+ if (boost::is_same<null_observer, Observer>::value) {
+ return detail::integrate_adaptive(
+ stepper, system, start_state,
+ start_time, end_time, dt,
+ observer, stepper_category());
+ }
+ else {
+ // unwrap references
+ typedef typename odeint::unwrap_reference< Stepper >::type stepper_type;
+ typedef typename odeint::unwrap_reference< Observer >::type observer_type;
+ typedef typename odeint::unwrap_reference< StepOverflowChecker >::type checker_type;
+
+ return detail::integrate_const(checked_stepper<stepper_type, checker_type>(stepper, checker),
+ system, start_state,
+ start_time, end_time, dt,
+ checked_observer<observer_type, checker_type>(observer, checker),
+ stepper_category());
+ }
+}
+
+/**
+* \brief Second version to solve the forwarding problem,
+* can be called with Boost.Range as start_state.
+*/
+template<class Stepper, class System, class State, class Time, class Observer, class StepOverflowChecker >
+size_t integrate_const(
+ Stepper stepper, System system, const State &start_state,
+ Time start_time, Time end_time, Time dt,
+ Observer observer, StepOverflowChecker checker
+) {
+ typedef typename odeint::unwrap_reference<Stepper>::type::stepper_category stepper_category;
+ // we want to get as fast as possible to the end
+
+ if (boost::is_same<null_observer, Observer>::value) {
+ return detail::integrate_adaptive(
+ stepper, system, start_state,
+ start_time, end_time, dt,
+ observer, stepper_category());
+ }
+ else {
+ typedef typename odeint::unwrap_reference< Stepper >::type stepper_type;
+ typedef typename odeint::unwrap_reference< Observer >::type observer_type;
+ typedef typename odeint::unwrap_reference< StepOverflowChecker >::type checker_type;
+
+ return detail::integrate_const(checked_stepper<stepper_type, checker_type>(stepper, checker),
+ system, start_state,
+ start_time, end_time, dt,
+ checked_observer<observer_type, checker_type>(observer, checker),
+ stepper_category());
+ }
+}
+
+
+/**
+* \brief integrate_const without step overflow checker
+*/
+template<class Stepper, class System, class State, class Time, class Observer>
+size_t integrate_const(
+ Stepper stepper, System system, State &start_state,
+ Time start_time, Time end_time, Time dt, Observer observer)
+{
+ typedef typename odeint::unwrap_reference<Stepper>::type::stepper_category stepper_category;
+ return detail::integrate_const(stepper, system, start_state,
+ start_time, end_time, dt, observer, stepper_category());
+}
+
+/**
+* \brief Second version to solve the forwarding problem,
+* can be called with Boost.Range as start_state.
+*/
+template<class Stepper, class System, class State, class Time, class Observer>
+size_t integrate_const(
+ Stepper stepper, System system, const State &start_state,
+ Time start_time, Time end_time, Time dt, Observer observer
+) {
+ typedef typename odeint::unwrap_reference<Stepper>::type::stepper_category stepper_category;
+ return detail::integrate_const(stepper, system, start_state,
+ start_time, end_time, dt, observer, stepper_category());
+}
+
+
+/**
+* \brief integrate_const without observer calls
+*/
+template<class Stepper, class System, class State, class Time>
+size_t integrate_const(
+ Stepper stepper, System system, State &start_state,
+ Time start_time, Time end_time, Time dt
+) {
+ return integrate_const(stepper, system, start_state, start_time, end_time, dt, null_observer());
+}
+
+/**
+* \brief Second version to solve the forwarding problem,
+* can be called with Boost.Range as start_state.
+*/
+template<class Stepper, class System, class State, class Time>
+size_t integrate_const(
+ Stepper stepper, System system, const State &start_state,
+ Time start_time, Time end_time, Time dt
+) {
+ return integrate_const(stepper, system, start_state, start_time, end_time, dt, null_observer());
+}
+
+
+
+
+
+
+/********* DOXYGEN *********/
+/**
+ * \fn integrate_const( Stepper stepper , System system , State &start_state , Time start_time ,
+ * Time end_time , Time dt , Observer observer , StepOverflowChecker checker )
+ * \brief Integrates the ODE with constant step size.
+ *
+ * Integrates the ODE defined by system using the given stepper.
+ * This method ensures that the observer is called at constant intervals dt.
+ * If the Stepper is a normal stepper without step size control, dt is also
+ * used for the numerical scheme. If a ControlledStepper is provided, the
+ * algorithm might reduce the step size to meet the error bounds, but it is
+ * ensured that the observer is always called at equidistant time points
+ * t0 + n*dt. If a DenseOutputStepper is used, the step size also may vary
+ * and the dense output is used to call the observer at equidistant time
+ * points.
+ * If a max_step_checker is provided as StepOverflowChecker, a
+ * no_progress_error is thrown if too many steps (default: 500) are performed
+ * without progress, i.e. in between observer calls. If no checker is provided,
+ * no such overflow check is performed.
+ *
+ * \param stepper The stepper to be used for numerical integration.
+ * \param system Function/Functor defining the rhs of the ODE.
+ * \param start_state The initial condition x0.
+ * \param start_time The initial time t0.
+ * \param end_time The final integration time tend.
+ * \param dt The time step between observer calls, _not_ necessarily the
+ * time step of the integration.
+ * \param observer [optional] Function/Functor called at equidistant time intervals.
+ * \param checker [optional] Functor to check for step count overflows, if no
+ * checker is provided, no exception is thrown.
+ * \return The number of steps performed.
+ */
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_CONST_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/integrate/integrate_n_steps.hpp b/include/boost/numeric/odeint/integrate/integrate_n_steps.hpp
new file mode 100644
index 0000000..5cc8aa0
--- /dev/null
+++ b/include/boost/numeric/odeint/integrate/integrate_n_steps.hpp
@@ -0,0 +1,180 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/integrate_n_steps.hpp
+
+ [begin_description]
+ Integration of n steps with constant time size. Adaptive and dense-output methods are fully supported.
+ [end_description]
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011-2015 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_N_STEPS_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_N_STEPS_HPP_INCLUDED
+
+#include <boost/type_traits/is_same.hpp>
+
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/integrate/null_observer.hpp>
+#include <boost/numeric/odeint/integrate/detail/integrate_n_steps.hpp>
+#include <boost/numeric/odeint/integrate/check_adapter.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+/*
+ * Integrates n steps
+ *
+ * the two overloads are needed in order to solve the forwarding problem
+ */
+template< class Stepper , class System , class State , class Time , class Observer , class StepOverflowChecker >
+Time integrate_n_steps(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time dt , size_t num_of_steps ,
+ Observer observer , StepOverflowChecker checker )
+{
+ // unwrap references
+ typedef typename odeint::unwrap_reference< Stepper >::type stepper_type;
+ typedef typename odeint::unwrap_reference< Observer >::type observer_type;
+ typedef typename odeint::unwrap_reference< StepOverflowChecker >::type checker_type;
+ typedef typename stepper_type::stepper_category stepper_category;
+
+ return detail::integrate_n_steps(
+ checked_stepper<stepper_type, checker_type>(stepper, checker),
+ system , start_state ,
+ start_time , dt , num_of_steps ,
+ checked_observer<observer_type, checker_type>(observer, checker),
+ stepper_category() );
+}
+
+/**
+ * \brief Solves the forwarding problem, can be called with Boost.Range as start_state.
+ */
+template< class Stepper , class System , class State , class Time , class Observer , class StepOverflowChecker >
+Time integrate_n_steps(
+ Stepper stepper , System system , const State &start_state ,
+ Time start_time , Time dt , size_t num_of_steps ,
+ Observer observer , StepOverflowChecker checker )
+{
+ typedef typename odeint::unwrap_reference< Stepper >::type stepper_type;
+ typedef typename odeint::unwrap_reference< Observer >::type observer_type;
+ typedef typename odeint::unwrap_reference< StepOverflowChecker >::type checker_type;
+ typedef typename stepper_type::stepper_category stepper_category;
+
+ return detail::integrate_n_steps(
+ checked_stepper<stepper_type, checker_type>(stepper, checker),
+ system , start_state ,
+ start_time , dt , num_of_steps ,
+ checked_observer<observer_type, checker_type>(observer, checker),
+ stepper_category() );
+}
+
+
+/**
+* \brief The same function as above, but without checker.
+*/
+template< class Stepper , class System , class State , class Time , class Observer >
+Time integrate_n_steps(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time dt , size_t num_of_steps , Observer observer )
+{
+ typedef typename odeint::unwrap_reference<Stepper>::type::stepper_category stepper_category;
+
+ return detail::integrate_n_steps(
+ stepper , system , start_state ,
+ start_time , dt , num_of_steps ,
+ observer , stepper_category() );
+}
+
+/**
+* \brief Solves the forwarding problem, can be called with Boost.Range as start_state.
+*/
+template< class Stepper , class System , class State , class Time , class Observer >
+Time integrate_n_steps(
+ Stepper stepper , System system , const State &start_state ,
+ Time start_time , Time dt , size_t num_of_steps , Observer observer )
+{
+ typedef typename odeint::unwrap_reference<Stepper>::type::stepper_category stepper_category;
+
+ return detail::integrate_n_steps(
+ stepper , system , start_state ,
+ start_time , dt , num_of_steps ,
+ observer , stepper_category() );
+}
+
+/**
+ * \brief The same function as above, but without observer calls.
+ */
+template< class Stepper , class System , class State , class Time >
+Time integrate_n_steps(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time dt , size_t num_of_steps )
+{
+ return integrate_n_steps(stepper, system, start_state, start_time,
+ dt, num_of_steps, null_observer());
+}
+
+/**
+ * \brief Solves the forwarding problem, can be called with Boost.Range as start_state.
+ */
+template< class Stepper , class System , class State , class Time >
+Time integrate_n_steps(
+ Stepper stepper , System system , const State &start_state ,
+ Time start_time , Time dt , size_t num_of_steps )
+{
+ return integrate_n_steps(stepper, system, start_state, start_time,
+ dt, num_of_steps, null_observer());
+}
+
+
+
+/************* DOXYGEN *************/
+ /**
+ * \fn Time integrate_n_steps( Stepper stepper , System system , State &start_state , Time start_time , Time dt , size_t num_of_steps , Observer observer )
+ * \brief Integrates the ODE with constant step size.
+ *
+ * This function is similar to integrate_const. The observer is called at
+ * equidistant time intervals t0 + n*dt.
+ * If the Stepper is a normal stepper without step size control, dt is also
+ * used for the numerical scheme. If a ControlledStepper is provided, the
+ * algorithm might reduce the step size to meet the error bounds, but it is
+ * ensured that the observer is always called at equidistant time points
+ * t0 + n*dt. If a DenseOutputStepper is used, the step size also may vary
+ * and the dense output is used to call the observer at equidistant time
+ * points. The final integration time is always t0 + num_of_steps*dt.
+ * If a max_step_checker is provided as StepOverflowChecker, a
+ * no_progress_errror is thrown if too many steps (default: 500) are
+ * performed without progress, i.e. in between observer calls. If no
+ * checker is provided, no such overflow check is performed.
+
+ *
+ * \param stepper The stepper to be used for numerical integration.
+ * \param system Function/Functor defining the rhs of the ODE.
+ * \param start_state The initial condition x0.
+ * \param start_time The initial time t0.
+ * \param dt The time step between observer calls, _not_ necessarily the
+ * time step of the integration.
+ * \param num_of_steps Number of steps to be performed
+ * \param observer Function/Functor called at equidistant time intervals.
+ * \param checker [optional] Functor to check for step count overflows, if no
+ * checker is provided, no exception is thrown.
+ * \return The number of steps performed.
+ */
+
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_N_STEPS_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/integrate/integrate_times.hpp b/include/boost/numeric/odeint/integrate/integrate_times.hpp
new file mode 100644
index 0000000..79fba4f
--- /dev/null
+++ b/include/boost/numeric/odeint/integrate/integrate_times.hpp
@@ -0,0 +1,222 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/integrate_times.hpp
+
+ [begin_description]
+ Integration of ODEs with observation at user defined points
+ [end_description]
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011-2015 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_TIMES_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_TIMES_HPP_INCLUDED
+
+#include <boost/type_traits/is_same.hpp>
+
+#include <boost/range.hpp>
+
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/integrate/null_observer.hpp>
+#include <boost/numeric/odeint/integrate/check_adapter.hpp>
+#include <boost/numeric/odeint/integrate/detail/integrate_times.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+/*
+ * \brief Integrates while calling the observer at the time points given by sequence [times_start, time_end)
+ * the two overloads are needed in order to solve the forwarding problem
+ */
+template< class Stepper , class System , class State , class TimeIterator , class Time , class Observer , class StepOverflowChecker >
+size_t integrate_times(
+ Stepper stepper , System system , State &start_state ,
+ TimeIterator times_start , TimeIterator times_end , Time dt ,
+ Observer observer , StepOverflowChecker checker )
+{
+ // unwrap references
+ typedef typename odeint::unwrap_reference< Stepper >::type stepper_type;
+ typedef typename odeint::unwrap_reference< Observer >::type observer_type;
+ typedef typename odeint::unwrap_reference< StepOverflowChecker >::type checker_type;
+ typedef typename stepper_type::stepper_category stepper_category;
+
+ // pass on checked stepper and observer
+ // checked_stepper/observer use references internally, so passing by value is fine
+ return detail::integrate_times(
+ checked_stepper<stepper_type, checker_type>(stepper, checker) ,
+ system , start_state ,
+ times_start , times_end , dt ,
+ checked_observer<observer_type, checker_type>(observer, checker),
+ stepper_category() );
+}
+
+/**
+ * \brief Solves the forwarding problem, can be called with Boost.Range as start_state.
+ */
+template< class Stepper , class System , class State , class TimeIterator , class Time , class Observer , class StepOverflowChecker >
+size_t integrate_times(
+ Stepper stepper , System system , const State &start_state ,
+ TimeIterator times_start , TimeIterator times_end , Time dt ,
+ Observer observer , StepOverflowChecker checker )
+{
+ typedef typename odeint::unwrap_reference< Stepper >::type stepper_type;
+ typedef typename odeint::unwrap_reference< Observer >::type observer_type;
+ typedef typename odeint::unwrap_reference< StepOverflowChecker >::type checker_type;
+ typedef typename stepper_type::stepper_category stepper_category;
+
+ stepper_type &st = stepper;
+ observer_type &obs = observer;
+ checker_type &chk = checker;
+
+ return detail::integrate_times(
+ checked_stepper<stepper_type, checker_type>(stepper, checker) ,
+ system , start_state ,
+ times_start , times_end , dt ,
+ checked_observer<observer_type, checker_type>(observer, checker),
+ stepper_category() );
+}
+
+/**
+ * \brief The same function as above, but with the observation times given as range.
+ */
+template< class Stepper , class System , class State , class TimeRange , class Time , class Observer , class StepOverflowChecker >
+size_t integrate_times(
+ Stepper stepper , System system , State &start_state ,
+ const TimeRange × , Time dt ,
+ Observer observer , StepOverflowChecker checker )
+{
+ return integrate_times(
+ stepper , system , start_state ,
+ boost::begin( times ) , boost::end( times ) , dt , observer , checker );
+}
+
+/**
+ * \brief Solves the forwarding problem, can be called with Boost.Range as start_state.
+ */
+template< class Stepper , class System , class State , class TimeRange , class Time , class Observer , class StepOverflowChecker >
+size_t integrate_times(
+ Stepper stepper , System system , const State &start_state ,
+ const TimeRange × , Time dt ,
+ Observer observer , StepOverflowChecker checker )
+{
+ return integrate_times(
+ stepper , system , start_state ,
+ boost::begin( times ) , boost::end( times ) , dt , observer , checker );
+}
+
+
+
+
+/*
+* The same functions as above, but without a StepOverflowChecker
+*/
+template< class Stepper , class System , class State , class TimeIterator , class Time , class Observer >
+size_t integrate_times(
+ Stepper stepper , System system , State &start_state ,
+ TimeIterator times_start , TimeIterator times_end , Time dt ,
+ Observer observer )
+{
+ typedef typename odeint::unwrap_reference< Stepper >::type::stepper_category stepper_category;
+ // simply don't use checked_* adapters
+ return detail::integrate_times(
+ stepper , system , start_state ,
+ times_start , times_end , dt ,
+ observer , stepper_category() );
+}
+
+/**
+* \brief Solves the forwarding problem, can be called with Boost.Range as start_state.
+*/
+template< class Stepper , class System , class State , class TimeIterator , class Time , class Observer >
+size_t integrate_times(
+ Stepper stepper , System system , const State &start_state ,
+ TimeIterator times_start , TimeIterator times_end , Time dt ,
+ Observer observer )
+{
+ typedef typename odeint::unwrap_reference< Stepper >::type::stepper_category stepper_category;
+ return detail::integrate_times(
+ stepper , system , start_state ,
+ times_start , times_end , dt ,
+ observer , stepper_category() );
+}
+
+/**
+* \brief The same function as above, but with the observation times given as range.
+*/
+template< class Stepper , class System , class State , class TimeRange , class Time , class Observer >
+size_t integrate_times(
+ Stepper stepper , System system , State &start_state ,
+ const TimeRange × , Time dt ,
+ Observer observer )
+{
+ return integrate_times(
+ stepper , system , start_state ,
+ boost::begin( times ) , boost::end( times ) , dt , observer );
+}
+
+/**
+* \brief Solves the forwarding problem, can be called with Boost.Range as start_state.
+*/
+template< class Stepper , class System , class State , class TimeRange , class Time , class Observer >
+size_t integrate_times(
+ Stepper stepper , System system , const State &start_state ,
+ const TimeRange × , Time dt ,
+ Observer observer )
+{
+ return integrate_times(
+ stepper , system , start_state ,
+ boost::begin( times ) , boost::end( times ) , dt , observer);
+}
+
+
+/********* DOXYGEN ***********/
+
+ /**
+ * \fn size_t integrate_times( Stepper stepper , System system , State &start_state , TimeIterator times_start , TimeIterator times_end , Time dt , Observer observer )
+ * \brief Integrates the ODE with observer calls at given time points.
+ *
+ * Integrates the ODE given by system using the given stepper. This function
+ * does observer calls at the subsequent time points given by the range
+ * times_start, times_end. If the stepper has not step size control, the
+ * step size might be reduced occasionally to ensure observer calls exactly
+ * at the time points from the given sequence. If the stepper is a
+ * ControlledStepper, the step size is adjusted to meet the error bounds,
+ * but also might be reduced occasionally to ensure correct observer calls.
+ * If a DenseOutputStepper is provided, the dense output functionality is
+ * used to call the observer at the given times. The end time of the
+ * integration is always *(end_time-1).
+ * If a max_step_checker is provided as StepOverflowChecker, a
+ * no_progress_error is thrown if too many steps (default: 500) are
+ * performed without progress, i.e. in between observer calls. If no
+ * checker is provided, no such overflow check is performed.
+ *
+ * \param stepper The stepper to be used for numerical integration.
+ * \param system Function/Functor defining the rhs of the ODE.
+ * \param start_state The initial condition x0.
+ * \param times_start Iterator to the start time
+ * \param times_end Iterator to the end time
+ * \param dt The time step between observer calls, _not_ necessarily the
+ * time step of the integration.
+ * \param observer Function/Functor called at equidistant time intervals.
+ * \param checker [optional] Functor to check for step count overflows, if no
+ * checker is provided, no exception is thrown.
+ * \return The number of steps performed.
+ */
+
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_TIMES_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/integrate/max_step_checker.hpp b/include/boost/numeric/odeint/integrate/max_step_checker.hpp
new file mode 100644
index 0000000..654c95b
--- /dev/null
+++ b/include/boost/numeric/odeint/integrate/max_step_checker.hpp
@@ -0,0 +1,114 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/max_step_checker.hpp
+
+ [begin_description]
+ Throws exception if too many steps are performed.
+ [end_description]
+
+ Copyright 2015 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_MAX_STEP_CHECKER_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_MAX_STEP_CHECKER_HPP_INCLUDED
+
+#include <stdexcept>
+#include <cstdio>
+
+#include <boost/throw_exception.hpp>
+#include <boost/numeric/odeint/util/odeint_error.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+/**
+ * \brief A class for performing overflow checks on the step count in integrate functions.
+ *
+ * Provide an instance of this class to integrate functions if you want to throw a runtime error if
+ * too many steps are performed without progress during the integrate routine.
+ */
+class max_step_checker
+{
+public:
+
+protected:
+ const int m_max_steps;
+ int m_steps;
+
+public:
+ /**
+ * \brief Construct the max_step_checker.
+ * max_steps is the maximal number of iterations allowed before runtime_error is thrown.
+ */
+ max_step_checker(const int max_steps = 500)
+ : m_max_steps(max_steps)
+ {
+ reset();
+ }
+
+ /**
+ * \brief Resets the max_step_checker by setting the internal counter to 0.
+ */
+ void reset()
+ {
+ m_steps = 0;
+ }
+
+ /**
+ * \brief Increases the counter and performs the iteration check
+ */
+ void operator()(void)
+ {
+ if( m_steps++ >= m_max_steps )
+ {
+ char error_msg[200];
+ std::sprintf(error_msg, "Max number of iterations exceeded (%d).", m_max_steps);
+ BOOST_THROW_EXCEPTION( no_progress_error(error_msg) );
+ }
+ }
+};
+
+
+/**
+ * \brief A class for performing overflow checks on the failed step count in step size adjustments.
+ *
+ * Used internally within the dense output stepper and integrate routines.
+ */
+class failed_step_checker : public max_step_checker
+{
+
+public:
+ /**
+ * \brief Construct the failed_step_checker.
+ * max_steps is the maximal number of iterations allowed before runtime_error is thrown.
+ */
+ failed_step_checker(const int max_steps = 500)
+ : max_step_checker(max_steps)
+ {}
+
+ /**
+ * \brief Increases the counter and performs the iteration check
+ */
+ void operator()(void)
+ {
+ if( m_steps++ >= m_max_steps )
+ {
+ char error_msg[200];
+ std::sprintf(error_msg, "Max number of iterations exceeded (%d). A new step size was not found.", m_max_steps);
+ BOOST_THROW_EXCEPTION( step_adjustment_error(error_msg) );
+ }
+ }
+};
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+#endif
diff --git a/include/boost/numeric/odeint/integrate/null_observer.hpp b/include/boost/numeric/odeint/integrate/null_observer.hpp
new file mode 100644
index 0000000..82b86b4
--- /dev/null
+++ b/include/boost/numeric/odeint/integrate/null_observer.hpp
@@ -0,0 +1,38 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/null_observer.hpp
+
+ [begin_description]
+ null_observer
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_NULL_OBSERVER_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_NULL_OBSERVER_HPP_INCLUDED
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+struct null_observer
+{
+ template< class State , class Time >
+ void operator()( const State& /* x */ , Time /* t */ ) const
+ {
+
+ }
+};
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_NULL_OBSERVER_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/integrate/observer_collection.hpp b/include/boost/numeric/odeint/integrate/observer_collection.hpp
new file mode 100644
index 0000000..f8c9af8
--- /dev/null
+++ b/include/boost/numeric/odeint/integrate/observer_collection.hpp
@@ -0,0 +1,56 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/observer_collection.hpp
+
+ [begin_description]
+ Collection of observers, which are all called during the evolution of the ODE.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_OBSERVER_COLLECTION_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_OBSERVER_COLLECTION_HPP_INCLUDED
+
+#include <vector>
+
+#include <boost/function.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template< class State , class Time >
+class observer_collection
+{
+public:
+
+ typedef boost::function< void( const State& , const Time& ) > observer_type;
+ typedef std::vector< observer_type > collection_type;
+
+ void operator()( const State& x , Time t )
+ {
+ for( size_t i=0 ; i<m_observers.size() ; ++i )
+ m_observers[i]( x , t );
+ }
+
+ collection_type& observers( void ) { return m_observers; }
+ const collection_type& observers( void ) const { return m_observers; }
+
+private:
+
+ collection_type m_observers;
+};
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_OBSERVER_COLLECTION_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/iterator/adaptive_iterator.hpp b/include/boost/numeric/odeint/iterator/adaptive_iterator.hpp
new file mode 100644
index 0000000..e8313e7
--- /dev/null
+++ b/include/boost/numeric/odeint/iterator/adaptive_iterator.hpp
@@ -0,0 +1,183 @@
+
+/*
+ [auto_generated]
+ boost/numeric/odeint/iterator/adaptive_iterator.hpp
+
+ [begin_description]
+ Iterator for iterating throught the solution of an ODE with adaptive step size. The dereferenced types containes also the time.
+ [end_description]
+
+ Copyright 2012-2013 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_ITERATOR_ADAPTIVE_ITERATOR_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_ITERATOR_ADAPTIVE_ITERATOR_HPP_INCLUDED
+
+#include <boost/numeric/odeint/util/stepper_traits.hpp>
+#include <boost/numeric/odeint/util/unit_helper.hpp>
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/stepper/controlled_step_result.hpp>
+#include <boost/numeric/odeint/iterator/impl/adaptive_iterator_impl.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+ /* use the adaptive_iterator_impl with the right tags */
+ template< class Stepper , class System , class State
+#ifndef DOXYGEN_SKIP
+ , class StepperTag = typename base_tag< typename traits::stepper_category< Stepper >::type >::type
+#endif
+ >
+ class adaptive_iterator : public adaptive_iterator_impl<
+ adaptive_iterator< Stepper , System , State , StepperTag > ,
+ Stepper , System , State , detail::ode_state_iterator_tag , StepperTag
+ >
+ {
+ typedef typename traits::time_type< Stepper >::type time_type;
+ typedef adaptive_iterator< Stepper , System , State , StepperTag > iterator_type;
+
+ public:
+ adaptive_iterator( Stepper stepper , System sys , State &s , time_type t_start , time_type t_end , time_type dt )
+ : adaptive_iterator_impl< iterator_type , Stepper , System , State , detail::ode_state_iterator_tag , StepperTag >( stepper , sys , s , t_start , t_end , dt )
+ {}
+
+ adaptive_iterator( Stepper stepper , System sys , State &s )
+ : adaptive_iterator_impl< iterator_type , Stepper , System , State , detail::ode_state_iterator_tag , StepperTag >( stepper , sys , s )
+ {}
+ };
+
+
+
+
+ template< class Stepper , class System , class State >
+ adaptive_iterator< Stepper , System , State > make_adaptive_iterator_begin(
+ Stepper stepper ,
+ System system ,
+ State &x ,
+ typename traits::time_type< Stepper >::type t_start ,
+ typename traits::time_type< Stepper >::type t_end ,
+ typename traits::time_type< Stepper >::type dt )
+ {
+ return adaptive_iterator< Stepper , System , State >( stepper , system , x , t_start , t_end , dt );
+ }
+
+
+ template< class Stepper , class System , class State >
+ adaptive_iterator< Stepper , System , State > make_adaptive_iterator_end(
+ Stepper stepper ,
+ System system ,
+ State &x )
+ {
+ return adaptive_iterator< Stepper , System , State >( stepper , system , x );
+ }
+
+
+ template< class Stepper , class System , class State >
+ std::pair< adaptive_iterator< Stepper , System , State > , adaptive_iterator< Stepper , System , State > >
+ make_adaptive_range(
+ Stepper stepper ,
+ System system ,
+ State &x ,
+ typename traits::time_type< Stepper >::type t_start ,
+ typename traits::time_type< Stepper >::type t_end ,
+ typename traits::time_type< Stepper >::type dt )
+ {
+ return std::make_pair(
+ adaptive_iterator< Stepper , System , State >( stepper , system , x , t_start , t_end , dt ) ,
+ adaptive_iterator< Stepper , System , State >( stepper , system , x )
+ );
+ }
+
+ /**
+ * \class adaptive_iterator
+ *
+ * \brief ODE Iterator with adaptive step size. The value type of this iterator is the state type of the stepper.
+ *
+ * Implements an iterator representing the solution of an ODE from t_start
+ * to t_end evaluated at steps with an adaptive step size dt.
+ * After each iteration the iterator dereferences to the state x at the next
+ * time t+dt where dt is controlled by the stepper.
+ * This iterator can be used with ControlledSteppers and
+ * DenseOutputSteppers and it always makes use of the all the given steppers
+ * capabilities. A for_each over such an iterator range behaves similar to
+ * the integrate_adaptive routine.
+ *
+ * adaptive_iterator is a model of single-pass iterator.
+ *
+ * The value type of this iterator is the state type of the stepper. Hence one can only access the state and not the current time.
+ *
+ * \tparam Stepper The stepper type which should be used during the iteration.
+ * \tparam System The type of the system function (ODE) which should be solved.
+ * \tparam State The state type of the ODE.
+ */
+
+
+
+
+
+
+ /**
+ * \fn make_adaptive_iterator_begin( Stepper stepper , System system , State &x ,
+ typename traits::time_type< Stepper >::type t_start ,
+ typename traits::time_type< Stepper >::type t_end ,
+ typename traits::time_type< Stepper >::type dt )
+ *
+ * \brief Factory function for adaptive_iterator. Constructs a begin iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param system The system function (ODE) to solve.
+ * \param x The initial state.
+ * \param t_start The initial time.
+ * \param t_end The end time, at which the iteration should stop.
+ * \param dt The initial time step.
+ * \returns The adaptive iterator.
+ */
+
+
+ /**
+ * \fn make_adaptive_iterator_end( Stepper stepper , System system , State &x )
+ * \brief Factory function for adaptive_iterator. Constructs a end iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param system The system function (ODE) to solve.
+ * \param x The initial state.
+ * \returns The adaptive iterator.
+ */
+
+
+ /**
+ * \fn make_adaptive_range( Stepper stepper , System system , State &x ,
+ typename traits::time_type< Stepper >::type t_start ,
+ typename traits::time_type< Stepper >::type t_end ,
+ typename traits::time_type< Stepper >::type dt )
+ *
+ * \brief Factory function to construct a single pass range of adaptive iterators. A range is here a pair of adaptive_iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param system The system function (ODE) to solve.
+ * \param x The initial state.
+ * \param t_start The initial time.
+ * \param t_end The end time, at which the iteration should stop.
+ * \param dt The initial time step.
+ * \returns The adaptive range.
+ */
+
+
+
+
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_ITERATOR_ADAPTIVE_ITERATOR_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/iterator/adaptive_time_iterator.hpp b/include/boost/numeric/odeint/iterator/adaptive_time_iterator.hpp
new file mode 100644
index 0000000..f70d34a
--- /dev/null
+++ b/include/boost/numeric/odeint/iterator/adaptive_time_iterator.hpp
@@ -0,0 +1,175 @@
+
+/*
+ [auto_generated]
+ boost/numeric/odeint/iterator/adaptive_time_iterator.hpp
+
+ [begin_description]
+ Iterator for iterating throught the solution of an ODE with adaptive step size. The dereferenced types containes also the time.
+ [end_description]
+
+ Copyright 2012-2013 Karsten Ahnert
+ Copyright 2012-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_ITERATOR_ADAPTIVE_TIME_ITERATOR_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_ITERATOR_ADAPTIVE_TIME_ITERATOR_HPP_INCLUDED
+
+
+
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/util/stepper_traits.hpp>
+#include <boost/numeric/odeint/iterator/impl/adaptive_iterator_impl.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+ /* use the adaptive_iterator_impl with the right tags */
+ template< class Stepper , class System , class State
+#ifndef DOXYGEN_SKIP
+ , class StepperTag = typename base_tag< typename traits::stepper_category< Stepper >::type >::type
+#endif
+ >
+ class adaptive_time_iterator : public adaptive_iterator_impl<
+ adaptive_time_iterator< Stepper , System , State , StepperTag > ,
+ Stepper , System , State , detail::ode_state_time_iterator_tag , StepperTag
+ >
+ {
+ typedef typename traits::time_type< Stepper >::type time_type;
+ typedef adaptive_time_iterator< Stepper , System , State , StepperTag > iterator_type;
+
+ public:
+ adaptive_time_iterator( Stepper stepper , System sys , State &s , time_type t_start , time_type t_end , time_type dt )
+ : adaptive_iterator_impl< iterator_type , Stepper , System , State , detail::ode_state_time_iterator_tag , StepperTag >( stepper , sys , s , t_start , t_end , dt )
+ {}
+
+ adaptive_time_iterator( Stepper stepper , System sys , State &s )
+ : adaptive_iterator_impl< iterator_type , Stepper , System , State , detail::ode_state_time_iterator_tag , StepperTag >( stepper , sys , s )
+ {}
+ };
+
+
+
+
+ template< class Stepper , class System , class State >
+ adaptive_time_iterator< Stepper , System , State > make_adaptive_time_iterator_begin(
+ Stepper stepper ,
+ System system ,
+ State &x ,
+ typename traits::time_type< Stepper >::type t_start ,
+ typename traits::time_type< Stepper >::type t_end ,
+ typename traits::time_type< Stepper >::type dt )
+ {
+ return adaptive_time_iterator< Stepper , System , State >( stepper , system , x , t_start , t_end , dt );
+ }
+
+ template< class Stepper , class System , class State >
+ adaptive_time_iterator< Stepper , System , State > make_adaptive_time_iterator_end(
+ Stepper stepper ,
+ System system ,
+ State &x )
+ {
+ return adaptive_time_iterator< Stepper , System , State >( stepper , system , x );
+ }
+
+
+ template< class Stepper , class System , class State >
+ std::pair< adaptive_time_iterator< Stepper , System , State > , adaptive_time_iterator< Stepper , System , State > >
+ make_adaptive_time_range(
+ Stepper stepper ,
+ System system ,
+ State &x ,
+ typename traits::time_type< Stepper >::type t_start ,
+ typename traits::time_type< Stepper >::type t_end ,
+ typename traits::time_type< Stepper >::type dt )
+ {
+ return std::make_pair(
+ adaptive_time_iterator< Stepper , System , State >( stepper , system , x , t_start , t_end , dt ) ,
+ adaptive_time_iterator< Stepper , System , State >( stepper , system , x ) );
+ }
+
+
+
+ /**
+ * \class adaptive_time_iterator
+ *
+ * \brief ODE Iterator with adaptive step size. The value type of this iterator is a std::pair containing state and time.
+ *
+ * Implements an iterator representing the solution of an ODE from t_start
+ * to t_end evaluated at steps with an adaptive step size dt.
+ * After each iteration the iterator dereferences to a pair containing state
+ * and time at the next time point t+dt where dt is controlled by the stepper.
+ * This iterator can be used with ControlledSteppers and
+ * DenseOutputSteppers and it always makes use of the all the given steppers
+ * capabilities. A for_each over such an iterator range behaves similar to
+ * the integrate_adaptive routine.
+ *
+ * adaptive_iterator is a model of single-pass iterator.
+ *
+ * The value type of this iterator is a std::pair of state and time of the stepper.
+ *
+ * \tparam Stepper The stepper type which should be used during the iteration.
+ * \tparam System The type of the system function (ODE) which should be solved.
+ * \tparam State The state type of the ODE.
+ */
+
+
+
+ /**
+ * \fn make_adaptive_time_iterator_begin( Stepper stepper , System system , State &x ,
+ typename traits::time_type< Stepper >::type t_start ,
+ typename traits::time_type< Stepper >::type t_end ,
+ typename traits::time_type< Stepper >::type dt )
+ *
+ * \brief Factory function for adaptive_time_iterator. Constructs a begin iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param system The system function (ODE) to solve.
+ * \param x The initial state. adaptive_time_iterator stores a reference of s and changes its value during the iteration.
+ * \param t_start The initial time.
+ * \param t_end The end time, at which the iteration should stop.
+ * \param dt The initial time step.
+ * \returns The adaptive time iterator.
+ */
+
+
+ /**
+ * \fn make_adaptive_time_iterator_end( Stepper stepper , System system , State &x )
+ * \brief Factory function for adaptive_time_iterator. Constructs a end iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param system The system function (ODE) to solve.
+ * \param x The initial state. adaptive_time_iterator stores a reference of s and changes its value during the iteration.
+ * \returns The adaptive time iterator.
+ */
+
+
+ /**
+ * \fn make_adaptive_time_range( Stepper stepper , System system , State &x ,
+ typename traits::time_type< Stepper >::type t_start ,
+ typename traits::time_type< Stepper >::type t_end ,
+ typename traits::time_type< Stepper >::type dt )
+ *
+ * \brief Factory function to construct a single pass range of adaptive time iterators. A range is here a pair of adaptive_time_iterators.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param system The system function (ODE) to solve.
+ * \param x The initial state. adaptive_time_iterator stores a reference of s and changes its value during the iteration.
+ * \param t_start The initial time.
+ * \param t_end The end time, at which the iteration should stop.
+ * \param dt The initial time step.
+ * \returns The adaptive time range.
+ */
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_ITERATOR_ADAPTIVE_TIME_ITERATOR_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/iterator/const_step_iterator.hpp b/include/boost/numeric/odeint/iterator/const_step_iterator.hpp
new file mode 100644
index 0000000..fb1bbb1
--- /dev/null
+++ b/include/boost/numeric/odeint/iterator/const_step_iterator.hpp
@@ -0,0 +1,180 @@
+
+/*
+ [auto_generated]
+ boost/numeric/odeint/iterator/const_step_iterator.hpp
+
+ [begin_description]
+ Iterator for iterating through the solution of an ODE with constant step size.
+ [end_description]
+
+ Copyright 2012-2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_ITERATOR_CONST_STEP_ODE_ITERATOR_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_ITERATOR_CONST_STEP_ODE_ITERATOR_HPP_INCLUDED
+
+
+#include <boost/numeric/odeint/util/stepper_traits.hpp>
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/iterator/detail/ode_iterator_base.hpp>
+#include <boost/numeric/odeint/iterator/impl/const_step_iterator_impl.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+ /* use the const_step_iterator_impl with the right tags */
+ template< class Stepper , class System , class State
+#ifndef DOXYGEN_SKIP
+ , class StepperTag = typename base_tag< typename traits::stepper_category< Stepper >::type >::type
+#endif
+ >
+ class const_step_iterator : public const_step_iterator_impl<
+ const_step_iterator< Stepper , System , State , StepperTag > ,
+ Stepper , System , State , detail::ode_state_iterator_tag , StepperTag
+ >
+ {
+ typedef typename traits::time_type< Stepper >::type time_type;
+ typedef const_step_iterator< Stepper , System , State , StepperTag > iterator_type;
+
+ public:
+ const_step_iterator( Stepper stepper , System sys , State &s , time_type t_start , time_type t_end , time_type dt )
+ : const_step_iterator_impl< iterator_type , Stepper , System , State , detail::ode_state_iterator_tag , StepperTag >( stepper , sys , s , t_start , t_end , dt )
+ {}
+
+ const_step_iterator( Stepper stepper , System sys , State &s )
+ : const_step_iterator_impl< iterator_type , Stepper , System , State , detail::ode_state_iterator_tag , StepperTag >( stepper , sys , s )
+ {}
+ };
+
+ /* make functions */
+
+ template< class Stepper , class System , class State >
+ const_step_iterator< Stepper , System, State > make_const_step_iterator_begin(
+ Stepper stepper ,
+ System system ,
+ State &x ,
+ typename traits::time_type< Stepper >::type t_start ,
+ typename traits::time_type< Stepper >::type t_end ,
+ typename traits::time_type< Stepper >::type dt )
+ {
+ return const_step_iterator< Stepper , System , State >( stepper , system , x , t_start , t_end , dt );
+ }
+
+ template< class Stepper , class System , class State >
+ const_step_iterator< Stepper , System , State > make_const_step_iterator_end(
+ Stepper stepper ,
+ System system ,
+ State &x )
+ {
+ return const_step_iterator< Stepper , System , State >( stepper , system , x );
+ }
+
+ template< class Stepper , class System , class State >
+ std::pair< const_step_iterator< Stepper , System , State > , const_step_iterator< Stepper , System , State > >
+ make_const_step_range(
+ Stepper stepper ,
+ System system ,
+ State &x ,
+ typename traits::time_type< Stepper >::type t_start ,
+ typename traits::time_type< Stepper >::type t_end ,
+ typename traits::time_type< Stepper >::type dt )
+ {
+ return std::make_pair(
+ const_step_iterator< Stepper , System , State >( stepper , system , x , t_start , t_end , dt ) ,
+ const_step_iterator< Stepper , System , State >( stepper , system , x )
+ );
+ }
+
+
+
+ /**
+ * \class const_step_iterator
+ *
+ * \brief ODE Iterator with constant step size. The value type of this iterator is the state type of the stepper.
+ *
+ * Implements an iterator representing the solution of an ODE from t_start
+ * to t_end evaluated at steps with constant step size dt.
+ * After each iteration the iterator dereferences to the state x at the next
+ * time t+dt.
+ * This iterator can be used with Steppers and
+ * DenseOutputSteppers and it always makes use of the all the given steppers
+ * capabilities. A for_each over such an iterator range behaves similar to
+ * the integrate_const routine.
+ *
+ * const_step_iterator is a model of single-pass iterator.
+ *
+ * The value type of this iterator is the state type of the stepper. Hence one can only access the state and not the current time.
+ *
+ * \tparam Stepper The stepper type which should be used during the iteration.
+ * \tparam System The type of the system function (ODE) which should be solved.
+ * \tparam State The state type of the ODE.
+ */
+
+
+ /**
+ * \fn make_const_step_iterator_begin(
+ Stepper stepper ,
+ System system ,
+ State &x ,
+ typename traits::time_type< Stepper >::type t_start ,
+ typename traits::time_type< Stepper >::type t_end ,
+ typename traits::time_type< Stepper >::type dt )
+ *
+ * \brief Factory function for const_step_iterator. Constructs a begin iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param system The system function (ODE) to solve.
+ * \param x The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.
+ * \param t_start The initial time.
+ * \param t_end The end time, at which the iteration should stop.
+ * \param dt The initial time step.
+ * \returns The const step iterator.
+ */
+
+
+ /**
+ * \fn make_const_step_iterator_end( Stepper stepper , System system , State &x )
+ * \brief Factory function for const_step_iterator. Constructs a end iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param system The system function (ODE) to solve.
+ * \param x The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.
+ * \returns The const_step_iterator.
+ */
+
+
+ /**
+ * \fn make_const_step_range( Stepper stepper , System system , State &x ,
+ typename traits::time_type< Stepper >::type t_start ,
+ typename traits::time_type< Stepper >::type t_end ,
+ typename traits::time_type< Stepper >::type dt )
+ *
+ * \brief Factory function to construct a single pass range of const step iterators. A range is here a pair
+ * of const_step_iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param system The system function (ODE) to solve.
+ * \param x The initial state. const_step_iterator store a reference of s and changes its value during the iteration.
+ * \param t_start The initial time.
+ * \param t_end The end time, at which the iteration should stop.
+ * \param dt The initial time step.
+ * \returns The const step range.
+ */
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+//#include <boost/numeric/odeint/iterator/impl/const_step_iterator_dense_output_impl.hpp>
+
+#endif // BOOST_NUMERIC_ODEINT_ITERATOR_CONST_STEP_ODE_ITERATOR_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/iterator/const_step_time_iterator.hpp b/include/boost/numeric/odeint/iterator/const_step_time_iterator.hpp
new file mode 100644
index 0000000..94ec5dd
--- /dev/null
+++ b/include/boost/numeric/odeint/iterator/const_step_time_iterator.hpp
@@ -0,0 +1,173 @@
+
+/*
+ [auto_generated]
+ boost/numeric/odeint/iterator/const_step_time_iterator.hpp
+
+ [begin_description]
+ Iterator for iterating throught the solution of an ODE with constant step size. The dereferences types containes also the time.
+ [end_description]
+
+ Copyright 2012-2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_ITERATOR_CONST_STEP_TIME_ITERATOR_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_ITERATOR_CONST_STEP_TIME_ITERATOR_HPP_INCLUDED
+
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/util/stepper_traits.hpp>
+#include <boost/numeric/odeint/iterator/detail/ode_iterator_base.hpp>
+#include <boost/numeric/odeint/iterator/impl/const_step_iterator_impl.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+ /* use the const_step_iterator_impl with the right tags */
+ template< class Stepper , class System , class State
+#ifndef DOXYGEN_SKIP
+ , class StepperTag = typename base_tag< typename traits::stepper_category< Stepper >::type >::type
+#endif
+ >
+ class const_step_time_iterator : public const_step_iterator_impl<
+ const_step_time_iterator< Stepper , System , State , StepperTag > ,
+ Stepper , System , State , detail::ode_state_time_iterator_tag , StepperTag
+ >
+ {
+ typedef typename traits::time_type< Stepper >::type time_type;
+ typedef const_step_time_iterator< Stepper , System , State , StepperTag > iterator_type;
+
+ public:
+ const_step_time_iterator( Stepper stepper , System sys , State &s , time_type t_start , time_type t_end , time_type dt )
+ : const_step_iterator_impl< iterator_type , Stepper , System , State , detail::ode_state_time_iterator_tag , StepperTag >( stepper , sys , s , t_start , t_end , dt )
+ {}
+
+ const_step_time_iterator( Stepper stepper , System sys , State &s )
+ : const_step_iterator_impl< iterator_type , Stepper , System , State , detail::ode_state_time_iterator_tag , StepperTag >( stepper , sys , s )
+ {}
+ };
+
+ template< class Stepper , class System , class State >
+ const_step_time_iterator< Stepper , System , State > make_const_step_time_iterator_begin(
+ Stepper stepper ,
+ System system ,
+ State &x ,
+ typename traits::time_type< Stepper >::type t_start ,
+ typename traits::time_type< Stepper >::type t_end ,
+ typename traits::time_type< Stepper >::type dt )
+ {
+ return const_step_time_iterator< Stepper , System , State >( stepper , system , x , t_start , t_end , dt );
+ }
+
+ template< class Stepper , class System , class State >
+ const_step_time_iterator< Stepper , System , State > make_const_step_time_iterator_end(
+ Stepper stepper ,
+ System system ,
+ State &x )
+ {
+ return const_step_time_iterator< Stepper , System , State >( stepper , system , x );
+ }
+
+
+ template< class Stepper , class System , class State >
+ std::pair< const_step_time_iterator< Stepper , System , State > , const_step_time_iterator< Stepper , System , State > >
+ make_const_step_time_range(
+ Stepper stepper ,
+ System system ,
+ State &x ,
+ typename traits::time_type< Stepper >::type t_start ,
+ typename traits::time_type< Stepper >::type t_end ,
+ typename traits::time_type< Stepper >::type dt )
+ {
+ return std::make_pair(
+ const_step_time_iterator< Stepper , System , State >( stepper , system , x , t_start , t_end , dt ) ,
+ const_step_time_iterator< Stepper , System , State >( stepper , system , x ) );
+ }
+
+ /**
+ * \class const_step_time_iterator
+ *
+ * \brief ODE Iterator with constant step size. The value type of this iterator is a std::pair containing state and time.
+ *
+ * Implements an iterator representing the solution of an ODE from t_start
+ * to t_end evaluated at steps with constant step size dt.
+ * After each iteration the iterator dereferences to a pair containing
+ * state and time at the next time point t+dt..
+ * This iterator can be used with Steppers and
+ * DenseOutputSteppers and it always makes use of the all the given steppers
+ * capabilities. A for_each over such an iterator range behaves similar to
+ * the integrate_const routine.
+ *
+ * const_step_time_iterator is a model of single-pass iterator.
+ *
+ * The value type of this iterator is a pair with the state type and time type of the stepper.
+ *
+ * \tparam Stepper The stepper type which should be used during the iteration.
+ * \tparam System The type of the system function (ODE) which should be solved.
+ * \tparam State The state type of the ODE.
+ */
+
+
+ /**
+ * \fn make_const_step_time_iterator_begin( Stepper stepper , System system , State &x ,
+ typename traits::time_type< Stepper >::type t_start ,
+ typename traits::time_type< Stepper >::type t_end ,
+ typename traits::time_type< Stepper >::type dt )
+ *
+ * \brief Factory function for const_step_time_iterator. Constructs a begin iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param system The system function (ODE) to solve.
+ * \param x The initial state. const_step_time_iterator stores a reference of s and changes its value during the iteration.
+ * \param t_start The initial time.
+ * \param t_end The end time, at which the iteration should stop.
+ * \param dt The initial time step.
+ * \returns The const step time iterator.
+ */
+
+
+ /**
+ * \fn make_const_step_time_iterator_end( Stepper stepper , System system , State &x )
+ * \brief Factory function for const_step_time_iterator. Constructs a end iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param system The system function (ODE) to solve.
+ * \param x The initial state. const_step_time_iterator store a reference of s and changes its value during the iteration.
+ * \returns The const step time iterator.
+ */
+
+
+ /**
+ * \fn make_const_step_time_range( Stepper stepper , System system , State &x ,
+ typename traits::time_type< Stepper >::type t_start ,
+ typename traits::time_type< Stepper >::type t_end ,
+ typename traits::time_type< Stepper >::type dt)
+ *
+ * \brief Factory function to construct a single pass range of const_step_time_iterator. A range is here a pair of const_step_time_iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param system The system function (ODE) to solve.
+ * \param x The initial state. const_step_time_iterator stores a reference of s and changes its value during the iteration.
+ * \param t The initial time.
+ * \param t_end The end time, at which the iteration should stop.
+ * \param dt The initial time step.
+ * \returns The const step time range.
+ */
+
+
+
+
+
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_ITERATOR_CONST_STEP_TIME_ITERATOR_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/iterator/detail/ode_iterator_base.hpp b/include/boost/numeric/odeint/iterator/detail/ode_iterator_base.hpp
new file mode 100644
index 0000000..5960e18
--- /dev/null
+++ b/include/boost/numeric/odeint/iterator/detail/ode_iterator_base.hpp
@@ -0,0 +1,199 @@
+
+/*
+ [auto_generated]
+ boost/numeric/odeint/iterator/detail/ode_iterator_base.hpp
+
+ [begin_description]
+ Base class for const_step_iterator and adaptive_iterator.
+ [end_description]
+
+ Copyright 2012-2013 Karsten Ahnert
+ Copyright 2012-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_ITERATOR_DETAIL_ODE_ITERATOR_BASE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_ITERATOR_DETAIL_ODE_ITERATOR_BASE_HPP_INCLUDED
+
+#include <boost/iterator/iterator_facade.hpp>
+
+#include <boost/numeric/odeint/util/unwrap_reference.hpp>
+#include <boost/numeric/odeint/util/detail/less_with_sign.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+ struct ode_state_iterator_tag {};
+ struct ode_state_time_iterator_tag {};
+
+ template< class Iterator , class Stepper , class System , class State , typename Tag >
+ class ode_iterator_base;
+
+
+ /* Specialization for the state iterator that has only state_type as its value_type */
+ template< class Iterator , class Stepper , class System , class State >
+ class ode_iterator_base< Iterator , Stepper , System , State , ode_state_iterator_tag >
+ : public boost::iterator_facade
+ <
+ Iterator ,
+ typename traits::state_type< Stepper >::type const ,
+ boost::single_pass_traversal_tag
+ >
+ {
+ private:
+
+ typedef Stepper stepper_type;
+ typedef System system_type;
+ typedef typename boost::numeric::odeint::unwrap_reference< stepper_type >::type unwrapped_stepper_type;
+ typedef State state_type;
+ typedef typename unwrapped_stepper_type::time_type time_type;
+ typedef typename unwrapped_stepper_type::value_type ode_value_type;
+
+ public:
+
+ ode_iterator_base( stepper_type stepper , system_type sys , time_type t , time_type dt )
+ : m_stepper( stepper ) , m_system( sys ) ,
+ m_t( t ) , m_dt( dt ) , m_at_end( false )
+ { }
+
+ ode_iterator_base( stepper_type stepper , system_type sys )
+ : m_stepper( stepper ) , m_system( sys ) ,
+ m_t() , m_dt() , m_at_end( true )
+ { }
+
+ // this function is only for testing
+ bool same( const ode_iterator_base &iter ) const
+ {
+ return (
+ //( static_cast<Iterator>(*this).get_state() ==
+ // static_cast<Iterator>(iter).get_state ) &&
+ ( m_t == iter.m_t ) &&
+ ( m_dt == iter.m_dt ) &&
+ ( m_at_end == iter.m_at_end )
+ );
+ }
+
+
+ protected:
+
+ friend class boost::iterator_core_access;
+
+ bool equal( ode_iterator_base const& other ) const
+ {
+ if( m_at_end == other.m_at_end )
+ {
+ return true;
+ }
+ else
+ {
+ return false;
+ }
+ }
+
+ const state_type& dereference() const
+ {
+ return static_cast<const Iterator*>(this)->get_state();
+ }
+
+ protected:
+
+ stepper_type m_stepper;
+ system_type m_system;
+ time_type m_t;
+ time_type m_dt;
+ bool m_at_end;
+ };
+
+
+
+ /* Specialization for the state-time iterator that has pair<state_type,time_type> as its value_type */
+
+ template< class Iterator , class Stepper , class System , class State >
+ class ode_iterator_base< Iterator , Stepper , System , State , ode_state_time_iterator_tag >
+ : public boost::iterator_facade
+ <
+ Iterator ,
+ std::pair< const State , const typename traits::time_type< Stepper >::type > ,
+ boost::single_pass_traversal_tag ,
+ std::pair< const State& , const typename traits::time_type< Stepper >::type& >
+ >
+ {
+ private:
+
+ typedef Stepper stepper_type;
+ typedef System system_type;
+ typedef typename boost::numeric::odeint::unwrap_reference< stepper_type >::type unwrapped_stepper_type;
+ typedef State state_type;
+ typedef typename unwrapped_stepper_type::time_type time_type;
+ typedef typename unwrapped_stepper_type::value_type ode_value_type;
+
+ public:
+
+ ode_iterator_base( stepper_type stepper , system_type sys ,
+ time_type t , time_type dt )
+ : m_stepper( stepper ) , m_system( sys ) ,
+ m_t( t ) , m_dt( dt ) , m_at_end( false )
+ { }
+
+ ode_iterator_base( stepper_type stepper , system_type sys )
+ : m_stepper( stepper ) , m_system( sys ) , m_at_end( true )
+ { }
+
+ bool same( ode_iterator_base const& iter )
+ {
+ return (
+ //( static_cast<Iterator>(*this).get_state() ==
+ // static_cast<Iterator>(iter).get_state ) &&
+ ( m_t == iter.m_t ) &&
+ ( m_dt == iter.m_dt ) &&
+ ( m_at_end == iter.m_at_end )
+ );
+ }
+
+
+ protected:
+
+ friend class boost::iterator_core_access;
+
+ bool equal( ode_iterator_base const& other ) const
+ {
+ if( m_at_end == other.m_at_end )
+ {
+ return true;
+ }
+ else
+ {
+ return false;
+ }
+ }
+
+ std::pair< const state_type& , const time_type& > dereference() const
+ {
+ return std::pair< const state_type & , const time_type & >(
+ static_cast<const Iterator*>(this)->get_state() , m_t );
+ }
+
+ stepper_type m_stepper;
+ system_type m_system;
+ time_type m_t;
+ time_type m_dt;
+ bool m_at_end;
+
+ };
+
+
+
+} // namespace detail
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_ITERATOR_DETAIL_ODE_ITERATOR_BASE_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/iterator/impl/adaptive_iterator_impl.hpp b/include/boost/numeric/odeint/iterator/impl/adaptive_iterator_impl.hpp
new file mode 100644
index 0000000..e5b4b3c
--- /dev/null
+++ b/include/boost/numeric/odeint/iterator/impl/adaptive_iterator_impl.hpp
@@ -0,0 +1,253 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/iterator/detail/adaptive_iterator_impl.hpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2009-2012 Karsten Ahnert
+ Copyright 2009-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_ITERATOR_DETAIL_ADAPTIVE_ITERATOR_IMPL_HPP_DEFINED
+#define BOOST_NUMERIC_ODEINT_ITERATOR_DETAIL_ADAPTIVE_ITERATOR_IMPL_HPP_DEFINED
+
+#include <boost/utility/enable_if.hpp>
+#include <boost/type_traits/is_same.hpp>
+#include <boost/throw_exception.hpp>
+
+#include <boost/numeric/odeint/util/unit_helper.hpp>
+#include <boost/numeric/odeint/util/copy.hpp>
+#include <boost/numeric/odeint/stepper/controlled_step_result.hpp>
+#include <boost/numeric/odeint/iterator/detail/ode_iterator_base.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+ template< class Iterator , class Stepper , class System , class State , typename Tag , typename StepperTag >
+ class adaptive_iterator_impl;
+
+ /*
+ * Specilization for controlled steppers
+ */
+ /**
+ * \brief ODE Iterator with adaptive step size control. The value type of this iterator is the state type of the stepper.
+ *
+ * Implements an ODE iterator with adaptive step size control. Uses controlled steppers. adaptive_iterator is a model
+ * of single-pass iterator.
+ *
+ * The value type of this iterator is the state type of the stepper. Hence one can only access the state and not the current time.
+ *
+ * \tparam Stepper The stepper type which should be used during the iteration.
+ * \tparam System The type of the system function (ODE) which should be solved.
+ */
+ template< class Iterator , class Stepper , class System , class State , typename Tag >
+ class adaptive_iterator_impl< Iterator , Stepper , System , State , Tag , controlled_stepper_tag >
+ : public detail::ode_iterator_base< Iterator , Stepper , System , State , Tag >
+ {
+ private:
+
+
+ typedef Stepper stepper_type;
+ typedef System system_type;
+ typedef typename boost::numeric::odeint::unwrap_reference< stepper_type >::type unwrapped_stepper_type;
+ typedef State state_type;
+ typedef typename traits::time_type< stepper_type >::type time_type;
+ typedef typename traits::value_type< stepper_type >::type ode_value_type;
+ #ifndef DOXYGEN_SKIP
+ typedef detail::ode_iterator_base< Iterator , Stepper , System , State , Tag > base_type;
+ #endif
+
+ public:
+
+ /**
+ * \brief Constructs an adaptive_iterator. This constructor should be used to construct the begin iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param sys The system function (ODE) to solve.
+ * \param s The initial state. adaptive_iterator stores a reference of s and changes its value during the iteration.
+ * \param t The initial time.
+ * \param t_end The end time, at which the iteration should stop.
+ * \param dt The initial time step.
+ */
+ adaptive_iterator_impl( stepper_type stepper , system_type sys , state_type &s , time_type t , time_type t_end , time_type dt )
+ : base_type( stepper , sys , t , dt ) , m_t_end( t_end ) , m_state( &s )
+ {
+ if( detail::less_with_sign( this->m_t_end , this->m_t , this->m_dt ) )
+ this->m_at_end = true;
+ }
+
+ /**
+ * \brief Constructs an adaptive_iterator. This constructor should be used to construct the end iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param sys The system function (ODE) to solve.
+ * \param s The initial state. adaptive_iterator store a reference of s and changes its value during the iteration.
+ */
+ adaptive_iterator_impl( stepper_type stepper , system_type sys , state_type &s )
+ : base_type( stepper , sys ) , m_state( &s ) { }
+
+ protected:
+
+ friend class boost::iterator_core_access;
+
+ void increment()
+ {
+ if( detail::less_with_sign( this->m_t , this->m_t_end , this->m_dt) )
+ {
+ if( detail::less_with_sign( this->m_t_end ,
+ static_cast<time_type>(this->m_t + this->m_dt) ,
+ this->m_dt ) )
+ {
+ this->m_dt = this->m_t_end - this->m_t;
+ }
+ unwrapped_stepper_type &stepper = this->m_stepper;
+ const size_t max_attempts = 1000;
+ size_t trials = 0;
+ controlled_step_result res = success;
+ do
+ {
+ res = stepper.try_step( this->m_system , *( this->m_state ) , this->m_t , this->m_dt );
+ ++trials;
+ }
+ while( ( res == fail ) && ( trials < max_attempts ) );
+ if( trials == max_attempts )
+ {
+ BOOST_THROW_EXCEPTION( std::overflow_error( "Adaptive iterator : Maximal number of iterations reached. A step size could not be found." ));
+ }
+ } else {
+ this->m_at_end = true;
+ }
+ }
+ public:
+ const state_type& get_state() const
+ {
+ return *this->m_state;
+ }
+
+ private:
+ time_type m_t_end;
+ state_type* m_state;
+ };
+
+
+
+ /*
+ * Specilization for dense outputer steppers
+ */
+ /**
+ * \brief ODE Iterator with adaptive step size control. The value type of this iterator is the state type of the stepper.
+ *
+ * Implements an ODE iterator with adaptive step size control. Uses dense-output steppers. adaptive_iterator is a model
+ * of single-pass iterator.
+ *
+ * The value type of this iterator is the state type of the stepper. Hence one can only access the state and not the current time.
+ *
+ * \tparam Stepper The stepper type which should be used during the iteration.
+ * \tparam System The type of the system function (ODE) which should be solved.
+ */
+ template< class Iterator , class Stepper , class System , class State , typename Tag >
+ class adaptive_iterator_impl< Iterator , Stepper , System , State , Tag , dense_output_stepper_tag >
+ : public detail::ode_iterator_base< Iterator , Stepper , System , State , Tag >
+ {
+ private:
+
+
+ typedef Stepper stepper_type;
+ typedef System system_type;
+ typedef typename boost::numeric::odeint::unwrap_reference< stepper_type >::type unwrapped_stepper_type;
+ typedef State state_type;
+ typedef typename traits::time_type< stepper_type >::type time_type;
+ typedef typename traits::value_type< stepper_type >::type ode_value_type;
+ #ifndef DOXYGEN_SKIP
+ typedef detail::ode_iterator_base< Iterator , Stepper , System , State , Tag > base_type;
+ #endif
+
+
+ public:
+
+
+ /**
+ * \brief Constructs an adaptive_iterator. This constructor should be used to construct the begin iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param sys The system function (ODE) to solve.
+ * \param s The initial state.
+ * \param t The initial time.
+ * \param t_end The end time, at which the iteration should stop.
+ * \param dt The initial time step.
+ */
+ adaptive_iterator_impl( stepper_type stepper , system_type sys , state_type &s , time_type t , time_type t_end , time_type dt )
+ : base_type( stepper , sys , t , dt ) , m_t_end( t_end )
+ {
+ if( detail::less_eq_with_sign( this->m_t , this->m_t_end , this->m_dt ) )
+ {
+ unwrapped_stepper_type &st = this->m_stepper;
+ st.initialize( s , this->m_t , this->m_dt );
+ } else {
+ this->m_at_end = true;
+ }
+ }
+
+ /**
+ * \brief Constructs an adaptive_iterator. This constructor should be used to construct the end iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param sys The system function (ODE) to solve.
+ * \param s The initial state.
+ */
+ adaptive_iterator_impl( stepper_type stepper , system_type sys , state_type& /* s */ )
+ : base_type( stepper , sys ) { }
+
+ protected:
+
+ friend class boost::iterator_core_access;
+
+ void increment()
+ {
+ unwrapped_stepper_type &stepper = this->m_stepper;
+ if( detail::less_with_sign( this->m_t ,
+ this->m_t_end ,
+ stepper.current_time_step() ) )
+ {
+ if( detail::less_with_sign( this->m_t_end ,
+ static_cast<time_type>(this->m_t + stepper.current_time_step()) ,
+ stepper.current_time_step() ) )
+ {
+ // make stpper to end exactly at t_end
+ stepper.initialize( stepper.current_state() , stepper.current_time() ,
+ static_cast<time_type>(this->m_t_end-this->m_t) );
+ }
+ stepper.do_step( this->m_system );
+ this->m_t = stepper.current_time();
+ } else { // we have reached t_end
+ this->m_at_end = true;
+ }
+ }
+
+ public:
+ const state_type& get_state() const
+ {
+ const unwrapped_stepper_type &stepper = this->m_stepper;
+ return stepper.current_state();
+ }
+
+ private:
+ time_type m_t_end;
+ };
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_ITERATOR_DETAIL_ADAPTIVE_ITERATOR_IMPL_HPP_DEFINED
diff --git a/include/boost/numeric/odeint/iterator/impl/const_step_iterator_impl.hpp b/include/boost/numeric/odeint/iterator/impl/const_step_iterator_impl.hpp
new file mode 100644
index 0000000..e23474c
--- /dev/null
+++ b/include/boost/numeric/odeint/iterator/impl/const_step_iterator_impl.hpp
@@ -0,0 +1,228 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/iterator/detail/const_step_iterator_impl.hpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_ITERATOR_DETAIL_CONST_STEP_ITERATOR_IMPL_HPP_DEFINED
+#define BOOST_NUMERIC_ODEINT_ITERATOR_DETAIL_CONST_STEP_ITERATOR_IMPL_HPP_DEFINED
+
+#include <boost/numeric/odeint/iterator/detail/ode_iterator_base.hpp>
+#include <boost/numeric/odeint/util/unit_helper.hpp>
+
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+ template< class Iterator , class Stepper , class System , class State , typename Tag , class StepperTag >
+ class const_step_iterator_impl;
+
+
+ /*
+ * Specilization for steppers and error steppers
+ */
+ template< class Iterator , class Stepper , class System , class State , typename Tag >
+ class const_step_iterator_impl< Iterator , Stepper , System , State , Tag , stepper_tag >
+ : public detail::ode_iterator_base< Iterator , Stepper , System , State , Tag >
+ {
+ private:
+
+ typedef Stepper stepper_type;
+ typedef System system_type;
+ typedef typename boost::numeric::odeint::unwrap_reference< stepper_type >::type unwrapped_stepper_type;
+ typedef State state_type;
+ typedef typename traits::time_type< stepper_type >::type time_type;
+ typedef typename traits::value_type< stepper_type >::type ode_value_type;
+ #ifndef DOXYGEN_SKIP
+ typedef detail::ode_iterator_base< Iterator , Stepper , System , State , Tag > base_type;
+ #endif
+
+ public:
+
+ /**
+ * \brief Constructs a const_step_iterator. This constructor should be used to construct the begin iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param sys The system function (ODE) to solve.
+ * \param s The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.
+ * \param t The initial time.
+ * \param t_end The end time, at which the iteration should stop.
+ * \param dt The initial time step.
+ */
+ const_step_iterator_impl( stepper_type stepper , system_type sys , state_type &s , time_type t , time_type t_end , time_type dt )
+ : base_type( stepper , sys , t , dt ) , m_t_start( t ) , m_t_end( t_end ) , m_state( &s ) , m_step( 0 )
+ {
+ if( detail::less_with_sign( this->m_t_end , this->m_t , this->m_dt ) )
+ this->m_at_end = true;
+ }
+
+ /**
+ * \brief Constructs a const_step_iterator. This constructor should be used to construct the end iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param sys The system function (ODE) to solve.
+ * \param s The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.
+ */
+ const_step_iterator_impl( stepper_type stepper , system_type sys , state_type& /* s */ )
+ : base_type( stepper , sys ) { }
+
+ protected:
+
+ friend class boost::iterator_core_access;
+
+ void increment()
+ {
+ if( detail::less_eq_with_sign( static_cast<time_type>(this->m_t+this->m_dt) ,
+ this->m_t_end , this->m_dt ) )
+ {
+ unwrapped_stepper_type &stepper = this->m_stepper;
+ stepper.do_step( this->m_system , *this->m_state , this->m_t , this->m_dt );
+ // use integer to compute current time to reduce roundoff errors
+ this->m_step++;
+ this->m_t = this->m_t_start + static_cast< typename unit_value_type<time_type>::type >(this->m_step)*this->m_dt;
+ } else {
+ this->m_at_end = true;
+ }
+ }
+
+ public:
+ const state_type& get_state() const
+ {
+ return *m_state;
+ }
+
+ private:
+ time_type m_t_start;
+ time_type m_t_end;
+ state_type* m_state;
+ size_t m_step;
+
+ };
+
+
+
+ /*
+ * Specilization for dense output stepper
+ */
+ /**
+ * \brief ODE Iterator with constant step size. The value type of this iterator is the state type of the stepper.
+ *
+ * Implements an ODE iterator solving the ODE with constant steps. Uses dense-output steppers.
+ * const_step_iterator is a model of single-pass iterator.
+ *
+ * The value type of this iterator is the state type of the stepper. Hence one can only access the state and not the current time.
+ *
+ * \tparam Stepper The stepper type which should be used during the iteration.
+ * \tparam System The type of the system function (ODE) which should be solved.
+ */
+ template< class Iterator , class Stepper , class System , class State , typename Tag >
+ class const_step_iterator_impl< Iterator , Stepper , System , State , Tag , dense_output_stepper_tag >
+ : public detail::ode_iterator_base< Iterator , Stepper , System , State , Tag >
+ {
+ private:
+
+ typedef Stepper stepper_type;
+ typedef System system_type;
+ typedef typename boost::numeric::odeint::unwrap_reference< stepper_type >::type unwrapped_stepper_type;
+ typedef State state_type;
+ typedef typename traits::time_type< stepper_type >::type time_type;
+ typedef typename traits::value_type< stepper_type >::type ode_value_type;
+ #ifndef DOXYGEN_SKIP
+ typedef detail::ode_iterator_base< Iterator , Stepper , System , State , Tag > base_type;
+ #endif
+
+ public:
+
+ /**
+ * \brief Constructs a const_step_iterator. This constructor should be used to construct the begin iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param sys The system function (ODE) to solve.
+ * \param s The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.
+ * \param t The initial time.
+ * \param t_end The end time, at which the iteration should stop.
+ * \param dt The initial time step.
+ */
+ const_step_iterator_impl( stepper_type stepper , system_type sys , state_type &s , time_type t , time_type t_end , time_type dt )
+ : base_type( stepper , sys , t , dt ) , m_t_start( t ) , m_t_end( t_end ) , m_state( &s ) , m_step( 0 )
+ {
+ if( detail::less_eq_with_sign( this->m_t , this->m_t_end , this->m_dt ) )
+ {
+ unwrapped_stepper_type &st = this->m_stepper;
+ st.initialize( * ( this->m_state ) , this->m_t , this->m_dt );
+ } else {
+ this->m_at_end = true;
+ }
+ }
+
+ /**
+ * \brief Constructs a const_step_iterator. This constructor should be used to construct the end iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param sys The system function (ODE) to solve.
+ * \param s The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.
+ */
+ const_step_iterator_impl( stepper_type stepper , system_type sys , state_type &s )
+ : base_type( stepper , sys ) , m_state( &s )
+ {
+ }
+
+
+
+ protected:
+
+ friend class boost::iterator_core_access;
+
+ void increment( void )
+ {
+ if( detail::less_eq_with_sign( static_cast<time_type>(this->m_t+this->m_dt) ,
+ this->m_t_end , this->m_dt ) )
+ {
+ unwrapped_stepper_type &stepper = this->m_stepper;
+ // use integer to compute current time to reduce roundoff errors
+ this->m_step++;
+ this->m_t = this->m_t_start + static_cast< typename unit_value_type<time_type>::type >(this->m_step)*this->m_dt;
+ while( detail::less_with_sign( stepper.current_time() , this->m_t ,
+ stepper.current_time_step() ) )
+ {
+ stepper.do_step( this->m_system );
+ }
+ stepper.calc_state( this->m_t , *( this->m_state ) );
+ } else {
+ this->m_at_end = true;
+ }
+ }
+
+ public:
+ const state_type& get_state() const
+ {
+ return *m_state;
+ }
+
+ private:
+ time_type m_t_start;
+ time_type m_t_end;
+ state_type* m_state;
+ size_t m_step;
+ };
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_ITERATOR_DETAIL_CONST_STEP_ITERATOR_IMPL_HPP_DEFINED
diff --git a/include/boost/numeric/odeint/iterator/impl/n_step_iterator_impl.hpp b/include/boost/numeric/odeint/iterator/impl/n_step_iterator_impl.hpp
new file mode 100644
index 0000000..7dd167f
--- /dev/null
+++ b/include/boost/numeric/odeint/iterator/impl/n_step_iterator_impl.hpp
@@ -0,0 +1,239 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/iterator/detail/n_step_iterator_impl.hpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2009-2013 Karsten Ahnert
+ Copyright 2009-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_ITERATOR_DETAIL_N_STEP_ITERATOR_IMPL_HPP_DEFINED
+#define BOOST_NUMERIC_ODEINT_ITERATOR_DETAIL_N_STEP_ITERATOR_IMPL_HPP_DEFINED
+
+#include <boost/numeric/odeint/iterator/detail/ode_iterator_base.hpp>
+#include <boost/numeric/odeint/util/unit_helper.hpp>
+
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+ template< class Iterator , class Stepper , class System , class State , typename Tag , class StepperTag >
+ class n_step_iterator_impl;
+
+
+ /*
+ * Specilization for steppers and error steppers
+ */
+ /**
+ * \brief ODE Iterator performing exactly n steps with constant step size. The value type of this iterator is the state type of the stepper.
+ *
+ * Implements an ODE iterator solving the ODE with constant step size. Uses steppers fulfilling the Stepper concept.
+ * n_step_iterator is a model of single-pass iterator.
+ *
+ * The value type of this iterator is the state type of the stepper. Hence one can only access the state and not the current time.
+ *
+ * \tparam Stepper The stepper type which should be used during the iteration.
+ * \tparam System The type of the system function (ODE) which should be solved.
+ */
+ template< class Iterator , class Stepper , class System , class State , typename Tag >
+ class n_step_iterator_impl< Iterator , Stepper , System , State , Tag , stepper_tag >
+ : public detail::ode_iterator_base< Iterator , Stepper , System , State , Tag >
+ {
+ private:
+
+ typedef Stepper stepper_type;
+ typedef System system_type;
+ typedef typename boost::numeric::odeint::unwrap_reference< stepper_type >::type unwrapped_stepper_type;
+ typedef State state_type;
+ typedef typename traits::time_type< stepper_type >::type time_type;
+ typedef typename traits::value_type< stepper_type >::type ode_value_type;
+ #ifndef DOXYGEN_SKIP
+ typedef detail::ode_iterator_base< Iterator , Stepper , System , State , Tag > base_type;
+ #endif
+
+ public:
+
+ /**
+ * \brief Constructs a n_step_iterator. This constructor should be used to construct the begin iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param sys The system function (ODE) to solve.
+ * \param s The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.
+ * \param t The initial time.
+ * \param dt The initial time step.
+ * \param num_of_steps the number of steps to be executed.
+ */
+ n_step_iterator_impl( stepper_type stepper , system_type sys , state_type &s ,
+ time_type t , time_type dt , size_t num_of_steps )
+ : base_type( stepper , sys , t , dt ) , m_t_start( t ) , m_state( &s ) ,
+ m_steps(num_of_steps) , m_step( 0 )
+ { }
+
+ /**
+ * \brief Constructs a const_step_iterator. This constructor should be used to construct the end iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param sys The system function (ODE) to solve.
+ * \param s The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.
+ */
+ n_step_iterator_impl( stepper_type stepper , system_type sys , state_type &s )
+ : base_type( stepper , sys ) , m_state( &s ) { }
+
+ protected:
+
+ friend class boost::iterator_core_access;
+
+ void increment()
+ {
+ if( this->m_step < this->m_steps )
+ {
+ unwrapped_stepper_type &stepper = this->m_stepper;
+ stepper.do_step( this->m_system , *this->m_state , this->m_t , this->m_dt );
+ // use integer to compute current time to reduce roundoff errors
+ this->m_step++;
+ this->m_t = this->m_t_start + static_cast< typename unit_value_type<time_type>::type >(this->m_step)*this->m_dt;
+ } else {
+ this->m_at_end = true;
+
+ }
+ }
+
+ public:
+ const state_type& get_state() const
+ {
+ return *m_state;
+ }
+
+
+ private:
+ time_type m_t_start;
+ time_type m_t_end;
+ state_type* m_state;
+ size_t m_steps;
+ size_t m_step;
+
+ };
+
+
+
+
+ /*
+ * Specilization for dense output stepper
+ */
+ /**
+ * \brief ODE Iterator with step-size control and dense output.
+ *
+ * Implements an ODE iterator solving the ODE with constant steps. Uses dense-output steppers.
+ * n_step_iterator is a model of single-pass iterator.
+ *
+ * The value type of this iterator is the state type of the stepper. Hence one can only access the state and not the current time.
+ *
+ * \tparam Stepper The stepper type which should be used during the iteration.
+ * \tparam System The type of the system function (ODE) which should be solved.
+ */
+ template< class Iterator , class Stepper , class System , class State , typename Tag >
+ class n_step_iterator_impl< Iterator , Stepper , System , State , Tag , dense_output_stepper_tag >
+ : public detail::ode_iterator_base< Iterator , Stepper , System , State , Tag >
+ {
+ private:
+
+ typedef Stepper stepper_type;
+ typedef System system_type;
+ typedef typename boost::numeric::odeint::unwrap_reference< stepper_type >::type unwrapped_stepper_type;
+ typedef State state_type;
+ typedef typename traits::time_type< stepper_type >::type time_type;
+ typedef typename traits::value_type< stepper_type >::type ode_value_type;
+ #ifndef DOXYGEN_SKIP
+ typedef detail::ode_iterator_base< Iterator , Stepper , System , State , Tag > base_type;
+ #endif
+
+ public:
+
+ /**
+ * \brief Constructs a const_step_iterator. This constructor should be used to construct the begin iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param sys The system function (ODE) to solve.
+ * \param s The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.
+ * \param t The initial time.
+ * \param dt The initial time step.
+ * \param num_of_steps the number of steps to be executed.
+ */
+ n_step_iterator_impl( stepper_type stepper , system_type sys , state_type &s ,
+ time_type t , time_type dt , size_t num_of_steps )
+ : base_type( stepper , sys , t , dt ) , m_t_start( t ) , m_state( &s ) ,
+ m_steps( num_of_steps ) , m_step( 0 )
+ {
+ unwrapped_stepper_type &st = this->m_stepper;
+ st.initialize( * ( this->m_state ) , this->m_t , this->m_dt );
+ }
+
+ /**
+ * \brief Constructs a const_step_iterator. This constructor should be used to construct the end iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param sys The system function (ODE) to solve.
+ * \param s The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.
+ */
+ n_step_iterator_impl( stepper_type stepper , system_type sys , state_type &s )
+ : base_type( stepper , sys ) , m_state( &s )
+ {
+ }
+
+
+
+ protected:
+
+ friend class boost::iterator_core_access;
+
+ void increment( void )
+ {
+ if( this->m_step < this->m_steps )
+ {
+ unwrapped_stepper_type &stepper = this->m_stepper;
+ // use integer to compute current time to reduce roundoff errors
+ this->m_step++;
+ this->m_t = this->m_t_start + static_cast< typename unit_value_type<time_type>::type >(this->m_step)*this->m_dt;
+ while( detail::less_with_sign( stepper.current_time() , this->m_t ,
+ stepper.current_time_step() ) )
+ {
+ stepper.do_step( this->m_system );
+ }
+ stepper.calc_state( this->m_t , *( this->m_state ) );
+ } else {
+ this->m_at_end = true;
+ }
+ }
+
+ public:
+ const state_type& get_state() const
+ {
+ return *m_state;
+ }
+
+
+ private:
+ time_type m_t_start;
+ time_type m_t_end;
+ state_type* m_state;
+ size_t m_steps;
+ size_t m_step;
+ };
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_ITERATOR_DETAIL_N_STEP_ITERATOR_IMPL_HPP_DEFINED
diff --git a/include/boost/numeric/odeint/iterator/impl/times_iterator_impl.hpp b/include/boost/numeric/odeint/iterator/impl/times_iterator_impl.hpp
new file mode 100644
index 0000000..7a2b48d
--- /dev/null
+++ b/include/boost/numeric/odeint/iterator/impl/times_iterator_impl.hpp
@@ -0,0 +1,371 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/iterator/detail/times_iterator_impl.hpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2009-2013 Karsten Ahnert
+ Copyright 2009-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_ITERATOR_DETAIL_TIMES_ITERATOR_IMPL_HPP_DEFINED
+#define BOOST_NUMERIC_ODEINT_ITERATOR_DETAIL_TIMES_ITERATOR_IMPL_HPP_DEFINED
+
+#include <boost/utility/enable_if.hpp>
+#include <boost/type_traits/is_same.hpp>
+#include <boost/throw_exception.hpp>
+
+#include <boost/numeric/odeint/util/unit_helper.hpp>
+#include <boost/numeric/odeint/util/copy.hpp>
+#include <boost/numeric/odeint/stepper/controlled_step_result.hpp>
+#include <boost/numeric/odeint/iterator/detail/ode_iterator_base.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+ template< class Iterator , class Stepper , class System , class State , class TimeIterator ,
+ typename Tag , typename StepperTag >
+ class times_iterator_impl;
+
+ /*
+ * Specilization for basic steppers
+ */
+ /**
+ * \brief ODE Iterator with constant step size.
+ *
+ * Implements an ODE iterator with observer calls at predefined times.
+ * Uses controlled steppers. times_iterator is a model of single-pass iterator.
+ *
+ * The value type of this iterator is the state type of the stepper. Hence one can only access the state and not the current time.
+ *
+ * \tparam Stepper The stepper type which should be used during the iteration.
+ * \tparam System The type of the system function (ODE) which should be solved.
+ */
+ template< class Iterator , class Stepper , class System , class State , class TimeIterator , typename Tag >
+ class times_iterator_impl< Iterator , Stepper , System , State , TimeIterator , Tag , stepper_tag >
+ : public detail::ode_iterator_base< Iterator , Stepper , System , State , Tag >
+ {
+ private:
+
+
+ typedef Stepper stepper_type;
+ typedef System system_type;
+ typedef typename boost::numeric::odeint::unwrap_reference< stepper_type >::type unwrapped_stepper_type;
+ typedef State state_type;
+ typedef TimeIterator time_iterator_type;
+ typedef typename traits::time_type< stepper_type >::type time_type;
+ typedef typename traits::value_type< stepper_type >::type ode_value_type;
+ #ifndef DOXYGEN_SKIP
+ typedef detail::ode_iterator_base< Iterator , Stepper , System , State , Tag > base_type;
+ #endif
+
+ public:
+
+ /**
+ * \brief Constructs a times_iterator. This constructor should be used to construct the begin iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param sys The system function (ODE) to solve.
+ * \param s The initial state. adaptive_iterator stores a reference of s and changes its value during the iteration.
+ * \param t_start Iterator to the begin of a sequence of time values.
+ * \param t_end Iterator to the begin of a sequence of time values.
+ * \param dt The (initial) time step.
+ */
+ times_iterator_impl( stepper_type stepper , system_type sys , state_type &s ,
+ time_iterator_type t_start , time_iterator_type t_end , time_type dt )
+ : base_type( stepper , sys , *t_start , dt ) ,
+ m_t_start( t_start ) , m_t_end( t_end ) , m_state( &s )
+ {
+ if( t_start == t_end )
+ this->m_at_end = true;
+ }
+
+ /**
+ * \brief Constructs an adaptive_iterator. This constructor should be used to construct the end iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param sys The system function (ODE) to solve.
+ * \param s The initial state. adaptive_iterator store a reference of s and changes its value during the iteration.
+ */
+ times_iterator_impl( stepper_type stepper , system_type sys , state_type &s )
+ : base_type( stepper , sys ) , m_state( &s ) { }
+
+ protected:
+
+ friend class boost::iterator_core_access;
+
+ void increment()
+ {
+ unwrapped_stepper_type &stepper = this->m_stepper;
+ if( ++m_t_start != m_t_end )
+ {
+ while( detail::less_with_sign( this->m_t , static_cast<time_type>(*m_t_start) , this->m_dt ) )
+ {
+ const time_type current_dt = detail::min_abs( this->m_dt , static_cast<time_type>(*m_t_start) - this->m_t );
+ stepper.do_step( this->m_system , *( this->m_state ) , this->m_t , current_dt );
+ this->m_t += current_dt;
+ }
+
+ } else {
+ this->m_at_end = true;
+ }
+ }
+
+ public:
+ const state_type& get_state() const
+ {
+ return *m_state;
+ }
+
+ private:
+ time_iterator_type m_t_start;
+ time_iterator_type m_t_end;
+ state_type* m_state;
+ };
+
+
+
+ /*
+ * Specilization for controlled steppers
+ */
+ /**
+ * \brief ODE Iterator with adaptive step size control. The value type of this iterator is the state type of the stepper.
+ *
+ * Implements an ODE iterator with observer calls at predefined times.
+ * Uses controlled steppers. times_iterator is a model of single-pass iterator.
+ *
+ * The value type of this iterator is the state type of the stepper. Hence one can only access the state and not the current time.
+ *
+ * \tparam Stepper The stepper type which should be used during the iteration.
+ * \tparam System The type of the system function (ODE) which should be solved.
+ */
+ template< class Iterator , class Stepper , class System , class State , class TimeIterator , typename Tag >
+ class times_iterator_impl< Iterator , Stepper , System , State , TimeIterator , Tag , controlled_stepper_tag >
+ : public detail::ode_iterator_base< Iterator , Stepper , System , State , Tag >
+ {
+ private:
+
+
+ typedef Stepper stepper_type;
+ typedef System system_type;
+ typedef typename boost::numeric::odeint::unwrap_reference< stepper_type >::type unwrapped_stepper_type;
+ typedef State state_type;
+ typedef TimeIterator time_iterator_type;
+ typedef typename traits::time_type< stepper_type >::type time_type;
+ typedef typename traits::value_type< stepper_type >::type ode_value_type;
+ #ifndef DOXYGEN_SKIP
+ typedef detail::ode_iterator_base< Iterator , Stepper , System , State , Tag > base_type;
+ #endif
+
+ public:
+
+ /**
+ * \brief Constructs a times_iterator. This constructor should be used to construct the begin iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param sys The system function (ODE) to solve.
+ * \param s The initial state. adaptive_iterator stores a reference of s and changes its value during the iteration.
+ * \param t_start Iterator to the begin of a sequence of time values.
+ * \param t_end Iterator to the begin of a sequence of time values.
+ * \param dt The (initial) time step.
+ */
+ times_iterator_impl( stepper_type stepper , system_type sys , state_type &s ,
+ time_iterator_type t_start , time_iterator_type t_end , time_type dt )
+ : base_type( stepper , sys , *t_start , dt ) ,
+ m_t_start( t_start ) , m_t_end( t_end ) , m_state( &s )
+ {
+ if( t_start == t_end )
+ this->m_at_end = true;
+ }
+
+ /**
+ * \brief Constructs an adaptive_iterator. This constructor should be used to construct the end iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param sys The system function (ODE) to solve.
+ * \param s The initial state. adaptive_iterator store a reference of s and changes its value during the iteration.
+ */
+ times_iterator_impl( stepper_type stepper , system_type sys , state_type &s )
+ : base_type( stepper , sys ) , m_state( &s ) { }
+
+ protected:
+
+ friend class boost::iterator_core_access;
+
+ void increment()
+ {
+ if( ++m_t_start != m_t_end )
+ {
+ while( detail::less_with_sign( this->m_t , static_cast<time_type>(*m_t_start) , this->m_dt ) )
+ {
+ if( detail::less_with_sign( static_cast<time_type>(*m_t_start) - this->m_t , this->m_dt , this->m_dt ) )
+ {
+ // we want to end exactly at the time point
+ time_type current_dt = static_cast<time_type>(*m_t_start) - this->m_t;
+ step_loop( current_dt );
+ } else {
+ step_loop( this->m_dt );
+ }
+ }
+
+ } else {
+ this->m_at_end = true;
+ }
+ }
+
+ private:
+ void step_loop( time_type &dt )
+ {
+ unwrapped_stepper_type &stepper = this->m_stepper;
+ const size_t max_attempts = 1000;
+ size_t trials = 0;
+ controlled_step_result res = success;
+ do
+ {
+ res = stepper.try_step( this->m_system , *( this->m_state ) , this->m_t , dt );
+ ++trials;
+ }
+ while( ( res == fail ) && ( trials < max_attempts ) );
+ if( trials == max_attempts )
+ {
+ BOOST_THROW_EXCEPTION( std::overflow_error( "Adaptive iterator : Maximal number of iterations reached. A step size could not be found." ) );
+ }
+ }
+
+ public:
+ const state_type& get_state() const
+ {
+ return *m_state;
+ }
+
+
+ private:
+ time_iterator_type m_t_start;
+ time_iterator_type m_t_end;
+ state_type* m_state;
+ };
+
+
+ /*
+ * Specilization for dense outputer steppers
+ */
+ /**
+ * \brief ODE Iterator with step size control and dense output.
+ * Implements an ODE iterator with adaptive step size control. Uses dense-output steppers.
+ * times_iterator is a model of single-pass iterator.
+ *
+ * \tparam Stepper The stepper type which should be used during the iteration.
+ * \tparam System The type of the system function (ODE) which should be solved.
+ */
+ template< class Iterator , class Stepper , class System , class State , class TimeIterator , typename Tag >
+ class times_iterator_impl< Iterator , Stepper , System , State , TimeIterator , Tag , dense_output_stepper_tag >
+ : public detail::ode_iterator_base< Iterator , Stepper , System , State , Tag >
+ {
+ private:
+
+
+ typedef Stepper stepper_type;
+ typedef System system_type;
+ typedef typename boost::numeric::odeint::unwrap_reference< stepper_type >::type unwrapped_stepper_type;
+ typedef State state_type;
+ typedef TimeIterator time_iterator_type;
+ typedef typename traits::time_type< stepper_type >::type time_type;
+ typedef typename traits::value_type< stepper_type >::type ode_value_type;
+ #ifndef DOXYGEN_SKIP
+ typedef detail::ode_iterator_base< Iterator , Stepper , System , State , Tag > base_type;
+ #endif
+
+
+ public:
+
+
+ /**
+ * \brief Constructs a times_iterator. This constructor should be used to construct the begin iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param sys The system function (ODE) to solve.
+ * \param s The initial state.
+ * \param t_start Iterator to the begin of a sequence of time values.
+ * \param t_end Iterator to the begin of a sequence of time values.
+ * \param dt The (initial) time step.
+ */
+ times_iterator_impl( stepper_type stepper , system_type sys , state_type &s ,
+ time_iterator_type t_start , time_iterator_type t_end , time_type dt )
+ : base_type( stepper , sys , *t_start , dt ) ,
+ m_t_start( t_start ) , m_t_end( t_end ) , m_final_time( *(t_end-1) ) ,
+ m_state( &s )
+ {
+ if( t_start != t_end )
+ {
+ unwrapped_stepper_type &st = this->m_stepper;
+ st.initialize( *( this->m_state ) , this->m_t , this->m_dt );
+ } else {
+ this->m_at_end = true;
+ }
+ }
+
+ /**
+ * \brief Constructs a times_iterator. This constructor should be used to construct the end iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param sys The system function (ODE) to solve.
+ * \param s The initial state.
+ */
+ times_iterator_impl( stepper_type stepper , system_type sys , state_type &s )
+ : base_type( stepper , sys ) , m_state( &s ) { }
+
+ protected:
+
+ friend class boost::iterator_core_access;
+
+ void increment()
+ {
+ unwrapped_stepper_type &st = this->m_stepper;
+ if( ++m_t_start != m_t_end )
+ {
+ this->m_t = static_cast<time_type>(*m_t_start);
+ while( detail::less_with_sign( st.current_time() , this->m_t , this->m_dt ) )
+ {
+ // make sure we don't go beyond the last point
+ if( detail::less_with_sign( m_final_time-st.current_time() , st.current_time_step() , st.current_time_step() ) )
+ {
+ st.initialize( st.current_state() , st.current_time() , m_final_time-st.current_time() );
+ }
+ st.do_step( this->m_system );
+ }
+ st.calc_state( this->m_t , *( this->m_state ) );
+ } else {
+ this->m_at_end = true;
+ }
+ }
+
+ public:
+ const state_type& get_state() const
+ {
+ return *m_state;
+ }
+
+
+ private:
+ time_iterator_type m_t_start;
+ time_iterator_type m_t_end;
+ time_type m_final_time;
+ state_type* m_state;
+ };
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_ITERATOR_DETAIL_TIMES_ITERATOR_IMPL_HPP_DEFINED
diff --git a/include/boost/numeric/odeint/iterator/integrate/detail/functors.hpp b/include/boost/numeric/odeint/iterator/integrate/detail/functors.hpp
new file mode 100644
index 0000000..b239217
--- /dev/null
+++ b/include/boost/numeric/odeint/iterator/integrate/detail/functors.hpp
@@ -0,0 +1,70 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/detail/functors.hpp
+
+ [begin_description]
+ some functors for the iterator based integrate routines
+ [end_description]
+
+ Copyright 2009-2013 Karsten Ahnert
+ Copyright 2009-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_FUNCTORS_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_FUNCTORS_HPP_INCLUDED
+
+#include <utility>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+
+template< class Observer >
+struct obs_caller {
+
+ size_t &m_n;
+ Observer m_obs;
+
+ obs_caller( size_t &m , Observer &obs ) : m_n(m) , m_obs( obs ) {}
+
+ template< class State , class Time >
+ void operator()( std::pair< const State & , const Time & > x )
+ {
+ typedef typename odeint::unwrap_reference< Observer >::type observer_type;
+ observer_type &obs = m_obs;
+ obs( x.first , x.second );
+ m_n++;
+ }
+};
+
+template< class Observer , class Time >
+struct obs_caller_time {
+
+ Time &m_t;
+ Observer m_obs;
+
+ obs_caller_time( Time &t , Observer &obs ) : m_t(t) , m_obs( obs ) {}
+
+ template< class State >
+ void operator()( std::pair< const State & , const Time & > x )
+ {
+ typedef typename odeint::unwrap_reference< Observer >::type observer_type;
+ observer_type &obs = m_obs;
+ obs( x.first , x.second );
+ m_t = x.second;
+ }
+};
+
+} // namespace detail
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_FUNCTORS_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/iterator/integrate/detail/integrate_adaptive.hpp b/include/boost/numeric/odeint/iterator/integrate/detail/integrate_adaptive.hpp
new file mode 100644
index 0000000..ccbbf49
--- /dev/null
+++ b/include/boost/numeric/odeint/iterator/integrate/detail/integrate_adaptive.hpp
@@ -0,0 +1,121 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/detail/integrate_adaptive.hpp
+
+ [begin_description]
+ Default Integrate adaptive implementation.
+ [end_description]
+
+ Copyright 2009-2011 Karsten Ahnert
+ Copyright 2009-2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_ADAPTIVE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_ADAPTIVE_HPP_INCLUDED
+
+#include <stdexcept>
+
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/stepper/controlled_step_result.hpp>
+#include <boost/numeric/odeint/iterator/integrate/detail/integrate_const.hpp>
+#include <boost/numeric/odeint/iterator/adaptive_time_iterator.hpp>
+#include <boost/numeric/odeint/iterator/integrate/detail/functors.hpp>
+#include <boost/numeric/odeint/util/bind.hpp>
+#include <boost/numeric/odeint/util/unwrap_reference.hpp>
+#include <boost/numeric/odeint/util/copy.hpp>
+
+#include <boost/numeric/odeint/util/detail/less_with_sign.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+// forward declaration
+template< class Stepper , class System , class State , class Time , class Observer>
+size_t integrate_const(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time end_time , Time dt ,
+ Observer observer , stepper_tag );
+
+/*
+ * integrate_adaptive for simple stepper is basically an integrate_const + some last step
+ */
+template< class Stepper , class System , class State , class Time , class Observer >
+size_t integrate_adaptive(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time end_time , Time dt ,
+ Observer observer , stepper_tag
+)
+{
+ size_t steps = detail::integrate_const( stepper , system , start_state , start_time ,
+ end_time , dt , observer , stepper_tag() );
+ typename odeint::unwrap_reference< Observer >::type &obs = observer;
+ typename odeint::unwrap_reference< Stepper >::type &st = stepper;
+
+ Time end = start_time + dt*steps;
+ if( less_with_sign( end , end_time , dt ) )
+ { //make a last step to end exactly at end_time
+ st.do_step( system , start_state , end , end_time - end );
+ steps++;
+ obs( start_state , end_time );
+ }
+ return steps;
+}
+
+
+/*
+ * classical integrate adaptive
+ */
+template< class Stepper , class System , class State , class Time , class Observer >
+size_t integrate_adaptive(
+ Stepper stepper , System system , State &start_state ,
+ Time &start_time , Time end_time , Time &dt ,
+ Observer observer , controlled_stepper_tag
+)
+{
+ size_t obs_calls = 0;
+
+ boost::for_each( make_adaptive_time_range( stepper , system , start_state ,
+ start_time , end_time , dt ) ,
+ obs_caller< Observer >( obs_calls , observer ) );
+
+ return obs_calls-1;
+}
+
+
+/*
+ * integrate adaptive for dense output steppers
+ *
+ * step size control is used if the stepper supports it
+ */
+template< class Stepper , class System , class State , class Time , class Observer >
+size_t integrate_adaptive(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time end_time , Time dt ,
+ Observer observer , dense_output_stepper_tag )
+{
+ size_t obs_calls = 0;
+
+ boost::for_each( make_adaptive_time_range( stepper , system , start_state ,
+ start_time , end_time , dt ) ,
+ obs_caller< Observer >( obs_calls , observer ) );
+
+ return obs_calls-1;
+}
+
+
+
+
+} // namespace detail
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_ADAPTIVE_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/iterator/integrate/detail/integrate_const.hpp b/include/boost/numeric/odeint/iterator/integrate/detail/integrate_const.hpp
new file mode 100644
index 0000000..1065036
--- /dev/null
+++ b/include/boost/numeric/odeint/iterator/integrate/detail/integrate_const.hpp
@@ -0,0 +1,111 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/detail/integrate_const.hpp
+
+ [begin_description]
+ integrate const implementation
+ [end_description]
+
+ Copyright 2009-2012 Karsten Ahnert
+ Copyright 2009-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_CONST_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_CONST_HPP_INCLUDED
+
+#include <boost/range/algorithm/for_each.hpp>
+
+#include <boost/numeric/odeint/util/unwrap_reference.hpp>
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/util/unit_helper.hpp>
+#include <boost/numeric/odeint/iterator/const_step_time_iterator.hpp>
+#include <boost/numeric/odeint/iterator/integrate/detail/integrate_adaptive.hpp>
+#include <boost/numeric/odeint/iterator/integrate/detail/functors.hpp>
+#include <boost/numeric/odeint/util/detail/less_with_sign.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+// forward declaration
+template< class Stepper , class System , class State , class Time , class Observer >
+size_t integrate_adaptive(
+ Stepper stepper , System system , State &start_state ,
+ Time &start_time , Time end_time , Time &dt ,
+ Observer observer , controlled_stepper_tag
+);
+
+
+template< class Stepper , class System , class State , class Time , class Observer >
+size_t integrate_const(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time end_time , Time dt ,
+ Observer observer , stepper_tag
+)
+{
+ size_t obs_calls = 0;
+
+ boost::for_each( make_const_step_time_range( stepper , system , start_state ,
+ start_time , end_time , dt ) ,
+ // should we use traits<Stepper>::state_type here instead of State? NO!
+ obs_caller< Observer >( obs_calls , observer ) );
+
+ // step integration steps gives step+1 observer calls
+ return obs_calls-1;
+}
+
+
+
+template< class Stepper , class System , class State , class Time , class Observer >
+size_t integrate_const(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time end_time , Time dt ,
+ Observer observer , controlled_stepper_tag
+)
+{
+ typename odeint::unwrap_reference< Observer >::type &obs = observer;
+
+ Time time = start_time;
+ const Time time_step = dt;
+ int step = 0;
+
+ while( less_eq_with_sign( static_cast<Time>(time+time_step) , end_time , dt ) )
+ {
+ obs( start_state , time );
+ detail::integrate_adaptive( stepper , system , start_state , time , time+time_step , dt ,
+ null_observer() , controlled_stepper_tag() );
+ // direct computation of the time avoids error propagation happening when using time += dt
+ // we need clumsy type analysis to get boost units working here
+ ++step;
+ time = start_time + static_cast< typename unit_value_type<Time>::type >(step) * time_step;
+ }
+ obs( start_state , time );
+
+ return step;
+}
+
+
+template< class Stepper , class System , class State , class Time , class Observer >
+size_t integrate_const(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time end_time , Time dt ,
+ Observer observer , dense_output_stepper_tag
+)
+{
+ size_t obs_calls = 0;
+
+ boost::for_each( make_const_step_time_range( stepper , system , start_state ,
+ start_time , end_time , dt ) ,
+ obs_caller< Observer >( obs_calls , observer ) );
+ return obs_calls-1;
+}
+
+
+} } } }
+
+#endif
diff --git a/include/boost/numeric/odeint/iterator/integrate/detail/integrate_n_steps.hpp b/include/boost/numeric/odeint/iterator/integrate/detail/integrate_n_steps.hpp
new file mode 100644
index 0000000..f90f887
--- /dev/null
+++ b/include/boost/numeric/odeint/iterator/integrate/detail/integrate_n_steps.hpp
@@ -0,0 +1,107 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/detail/integrate_n_steps.hpp
+
+ [begin_description]
+ integrate steps implementation
+ [end_description]
+
+ Copyright 2009-2012 Karsten Ahnert
+ Copyright 2009-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_N_STEPS_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_N_STEPS_HPP_INCLUDED
+
+#include <boost/numeric/odeint/util/unwrap_reference.hpp>
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/iterator/integrate/detail/integrate_adaptive.hpp>
+#include <boost/numeric/odeint/iterator/integrate/detail/functors.hpp>
+#include <boost/numeric/odeint/iterator/n_step_time_iterator.hpp>
+#include <boost/numeric/odeint/util/unit_helper.hpp>
+
+#include <boost/numeric/odeint/util/detail/less_with_sign.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+// forward declaration
+template< class Stepper , class System , class State , class Time , class Observer >
+size_t integrate_adaptive(
+ Stepper stepper , System system , State &start_state ,
+ Time &start_time , Time end_time , Time &dt ,
+ Observer observer , controlled_stepper_tag
+);
+
+
+/* basic version */
+template< class Stepper , class System , class State , class Time , class Observer>
+Time integrate_n_steps(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time dt , size_t num_of_steps ,
+ Observer observer , stepper_tag )
+{
+ // ToDo: is there a better way to extract the final time?
+ Time t = start_time; // Assignment is only here to avoid warnings.
+ boost::for_each( make_n_step_time_range( stepper , system , start_state ,
+ start_time , dt , num_of_steps ) ,
+ obs_caller_time< Observer , Time >( t , observer ) );
+ return t;
+}
+
+
+/* controlled version */
+template< class Stepper , class System , class State , class Time , class Observer>
+Time integrate_n_steps(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time dt , size_t num_of_steps ,
+ Observer observer , controlled_stepper_tag )
+{
+ typename odeint::unwrap_reference< Observer >::type &obs = observer;
+
+ Time time = start_time;
+ Time time_step = dt;
+
+ for( size_t step = 0; step < num_of_steps ; ++step )
+ {
+ obs( start_state , time );
+ detail::integrate_adaptive( stepper , system , start_state , time , static_cast<Time>(time+time_step) , dt ,
+ null_observer() , controlled_stepper_tag() );
+ // direct computation of the time avoids error propagation happening when using time += dt
+ // we need clumsy type analysis to get boost units working here
+ time = start_time + static_cast< typename unit_value_type<Time>::type >(step+1) * time_step;
+ }
+ obs( start_state , time );
+
+ return time;
+}
+
+
+/* dense output version */
+template< class Stepper , class System , class State , class Time , class Observer>
+Time integrate_n_steps(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time dt , size_t num_of_steps ,
+ Observer observer , dense_output_stepper_tag )
+{
+ // ToDo: is there a better way to extract the final time?
+ Time t = start_time; // Assignment is only here to avoid warnings.
+ boost::for_each( make_n_step_time_range( stepper , system , start_state ,
+ start_time , dt , num_of_steps ) ,
+ obs_caller_time< Observer , Time >( t , observer ) );
+ return t;
+}
+
+
+}
+}
+}
+}
+
+#endif /* BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_N_STEPS_HPP_INCLUDED */
diff --git a/include/boost/numeric/odeint/iterator/integrate/detail/integrate_times.hpp b/include/boost/numeric/odeint/iterator/integrate/detail/integrate_times.hpp
new file mode 100644
index 0000000..bccc7c6
--- /dev/null
+++ b/include/boost/numeric/odeint/iterator/integrate/detail/integrate_times.hpp
@@ -0,0 +1,67 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/detail/integrate_times.hpp
+
+ [begin_description]
+ Default integrate times implementation.
+ [end_description]
+
+ Copyright 2009-2012 Karsten Ahnert
+ Copyright 2009-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_TIMES_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_TIMES_HPP_INCLUDED
+
+#include <stdexcept>
+
+#include <boost/config.hpp>
+#include <boost/range/algorithm/for_each.hpp>
+
+#include <boost/numeric/odeint/util/unwrap_reference.hpp>
+#include <boost/numeric/odeint/stepper/controlled_step_result.hpp>
+#include <boost/numeric/odeint/util/detail/less_with_sign.hpp>
+#include <boost/numeric/odeint/iterator/times_time_iterator.hpp>
+#include <boost/numeric/odeint/iterator/integrate/detail/functors.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+
+
+/*
+ * integrate_times for all steppers
+ */
+template< class Stepper , class System , class State , class TimeIterator , class Time , class Observer , class StepperTag >
+size_t integrate_times(
+ Stepper stepper , System system , State &start_state ,
+ TimeIterator start_time , TimeIterator end_time , Time dt ,
+ Observer observer , StepperTag
+)
+{
+ size_t obs_calls = 0;
+
+ boost::for_each( make_times_time_range( stepper , system , start_state ,
+ start_time , end_time , dt ) ,
+ // should we use traits<Stepper>::state_type here instead of State? NO!
+ obs_caller< Observer >( obs_calls , observer ) );
+
+ // step integration steps gives step+1 observer calls
+ return obs_calls-1;
+}
+
+
+} // namespace detail
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_ADAPTIVE_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/iterator/integrate/integrate.hpp b/include/boost/numeric/odeint/iterator/integrate/integrate.hpp
new file mode 100644
index 0000000..9d88ef9
--- /dev/null
+++ b/include/boost/numeric/odeint/iterator/integrate/integrate.hpp
@@ -0,0 +1,111 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/integrate.hpp
+
+ [begin_description]
+ Convenience methods which choose the stepper for the current ODE.
+ [end_description]
+
+ Copyright 2009-2011 Karsten Ahnert
+ Copyright 2009-2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_HPP_INCLUDED
+
+#include <boost/utility/enable_if.hpp>
+
+#include <boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp>
+#include <boost/numeric/odeint/stepper/controlled_runge_kutta.hpp>
+#include <boost/numeric/odeint/iterator/integrate/null_observer.hpp>
+#include <boost/numeric/odeint/iterator/integrate/integrate_adaptive.hpp>
+
+// for has_value_type trait
+#include <boost/numeric/odeint/algebra/detail/extract_value_type.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+/*
+ * ToDo :
+ *
+ * determine type of dxdt for units
+ *
+ */
+template< class System , class State , class Time , class Observer >
+typename boost::enable_if< typename has_value_type<State>::type , size_t >::type
+integrate( System system , State &start_state , Time start_time , Time end_time , Time dt , Observer observer )
+{
+ typedef controlled_runge_kutta< runge_kutta_dopri5< State , typename State::value_type , State , Time > > stepper_type;
+ return integrate_adaptive( stepper_type() , system , start_state , start_time , end_time , dt , observer );
+}
+
+
+
+/*
+ * the two overloads are needed in order to solve the forwarding problem
+ */
+template< class System , class State , class Time >
+size_t integrate( System system , State &start_state , Time start_time , Time end_time , Time dt )
+{
+ return integrate( system , start_state , start_time , end_time , dt , null_observer() );
+}
+
+
+/**
+ * \fn integrate( System system , State &start_state , Time start_time , Time end_time , Time dt , Observer observer )
+ * \brief Integrates the ODE.
+ *
+ * Integrates the ODE given by system from start_time to end_time starting
+ * with start_state as initial condition and dt as initial time step.
+ * This function uses a dense output dopri5 stepper and performs an adaptive
+ * integration with step size control, thus dt changes during the integration.
+ * This method uses standard error bounds of 1E-6.
+ * After each step, the observer is called.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the
+ * ordinary differential equation.
+ * \param start_state The initial state.
+ * \param start_time Start time of the integration.
+ * \param end_time End time of the integration.
+ * \param dt Initial step size, will be adjusted during the integration.
+ * \param observer Observer that will be called after each time step.
+ * \return The number of steps performed.
+ */
+
+
+/**
+ * \fn integrate( System system , State &start_state , Time start_time , Time end_time , Time dt )
+ * \brief Integrates the ODE without observer calls.
+ *
+ * Integrates the ODE given by system from start_time to end_time starting
+ * with start_state as initial condition and dt as initial time step.
+ * This function uses a dense output dopri5 stepper and performs an adaptive
+ * integration with step size control, thus dt changes during the integration.
+ * This method uses standard error bounds of 1E-6.
+ * No observer is called.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the
+ * ordinary differential equation.
+ * \param start_state The initial state.
+ * \param start_time Start time of the integration.
+ * \param end_time End time of the integration.
+ * \param dt Initial step size, will be adjusted during the integration.
+ * \return The number of steps performed.
+ */
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/iterator/integrate/integrate_adaptive.hpp b/include/boost/numeric/odeint/iterator/integrate/integrate_adaptive.hpp
new file mode 100644
index 0000000..3229a00
--- /dev/null
+++ b/include/boost/numeric/odeint/iterator/integrate/integrate_adaptive.hpp
@@ -0,0 +1,129 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/integrate_adaptive.hpp
+
+ [begin_description]
+ Adaptive integration of ODEs.
+ [end_description]
+
+ Copyright 2009-2011 Karsten Ahnert
+ Copyright 2009-2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_ADAPTIVE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_ADAPTIVE_HPP_INCLUDED
+
+#include <boost/type_traits/is_same.hpp>
+
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/iterator/integrate/null_observer.hpp>
+#include <boost/numeric/odeint/iterator/integrate/detail/integrate_adaptive.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+/*
+ * the two overloads are needed in order to solve the forwarding problem
+ */
+template< class Stepper , class System , class State , class Time , class Observer >
+size_t integrate_adaptive(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time end_time , Time dt ,
+ Observer observer )
+{
+ typedef typename odeint::unwrap_reference< Stepper >::type::stepper_category stepper_category;
+ return detail::integrate_adaptive(
+ stepper , system , start_state ,
+ start_time , end_time , dt ,
+ observer , stepper_category() );
+
+ /*
+ * Suggestion for a new extendable version:
+ *
+ * integrator_adaptive< Stepper , System, State , Time , Observer , typename Stepper::stepper_category > integrator;
+ * return integrator.run( stepper , system , start_state , start_time , end_time , dt , observer );
+ */
+}
+
+/**
+ * \brief Second version to solve the forwarding problem,
+ * can be called with Boost.Range as start_state.
+ */
+template< class Stepper , class System , class State , class Time , class Observer >
+size_t integrate_adaptive(
+ Stepper stepper , System system , const State &start_state ,
+ Time start_time , Time end_time , Time dt ,
+ Observer observer )
+{
+ typedef typename odeint::unwrap_reference< Stepper >::type::stepper_category stepper_category;
+ return detail::integrate_adaptive(
+ stepper , system , start_state ,
+ start_time , end_time , dt ,
+ observer , stepper_category() );
+}
+
+
+
+
+/**
+ * \brief integrate_adaptive without an observer.
+ */
+template< class Stepper , class System , class State , class Time >
+size_t integrate_adaptive(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time end_time , Time dt )
+{
+ return integrate_adaptive( stepper , system , start_state , start_time , end_time , dt , null_observer() );
+}
+
+/**
+ * \brief Second version to solve the forwarding problem,
+ * can be called with Boost.Range as start_state.
+ */
+template< class Stepper , class System , class State , class Time >
+size_t integrate_adaptive(
+ Stepper stepper , System system , const State &start_state ,
+ Time start_time , Time end_time , Time dt )
+{
+ return integrate_adaptive( stepper , system , start_state , start_time , end_time , dt , null_observer() );
+}
+
+
+/************* DOXYGEN ************/
+
+ /**
+ * \fn integrate_adaptive( Stepper stepper , System system , State &start_state , Time start_time , Time end_time , Time dt , Observer observer )
+ * \brief Integrates the ODE with adaptive step size.
+ *
+ * This function integrates the ODE given by system with the given stepper.
+ * The observer is called after each step. If the stepper has no error
+ * control, the step size remains constant and the observer is called at
+ * equidistant time points t0+n*dt. If the stepper is a ControlledStepper,
+ * the step size is adjusted and the observer is called in non-equidistant
+ * intervals.
+ *
+ * \param stepper The stepper to be used for numerical integration.
+ * \param system Function/Functor defining the rhs of the ODE.
+ * \param start_state The initial condition x0.
+ * \param start_time The initial time t0.
+ * \param end_time The final integration time tend.
+ * \param dt The time step between observer calls, _not_ necessarily the
+ * time step of the integration.
+ * \param observer Function/Functor called at equidistant time intervals.
+ * \return The number of steps performed.
+ */
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_ADAPTIVE_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/iterator/integrate/integrate_const.hpp b/include/boost/numeric/odeint/iterator/integrate/integrate_const.hpp
new file mode 100644
index 0000000..ffcea6c
--- /dev/null
+++ b/include/boost/numeric/odeint/iterator/integrate/integrate_const.hpp
@@ -0,0 +1,158 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/integrate_const.hpp
+
+ [begin_description]
+ Constant integration of ODEs, meaning that the state of the ODE is observed on constant time intervals.
+ The routines makes full use of adaptive and dense-output methods.
+ [end_description]
+
+ Copyright 2009-2011 Karsten Ahnert
+ Copyright 2009-2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_CONST_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_CONST_HPP_INCLUDED
+
+#include <boost/type_traits/is_same.hpp>
+
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/iterator/integrate/null_observer.hpp>
+#include <boost/numeric/odeint/iterator/integrate/detail/integrate_const.hpp>
+#include <boost/numeric/odeint/iterator/integrate/detail/integrate_adaptive.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+
+
+
+/*
+ * Integrates with constant time step dt.
+ */
+template< class Stepper , class System , class State , class Time , class Observer >
+size_t integrate_const(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time end_time , Time dt ,
+ Observer observer
+)
+{
+ typedef typename odeint::unwrap_reference< Stepper >::type::stepper_category stepper_category;
+ // we want to get as fast as possible to the end
+ if( boost::is_same< null_observer , Observer >::value )
+ {
+ return detail::integrate_adaptive(
+ stepper , system , start_state ,
+ start_time , end_time , dt ,
+ observer , stepper_category() );
+ }
+ else
+ {
+ return detail::integrate_const( stepper , system , start_state ,
+ start_time , end_time , dt ,
+ observer , stepper_category() );
+ }
+}
+
+/**
+ * \brief Second version to solve the forwarding problem,
+ * can be called with Boost.Range as start_state.
+ */
+template< class Stepper , class System , class State , class Time , class Observer >
+size_t integrate_const(
+ Stepper stepper , System system , const State &start_state ,
+ Time start_time , Time end_time , Time dt ,
+ Observer observer
+)
+{
+ typedef typename odeint::unwrap_reference< Stepper >::type::stepper_category stepper_category;
+ // we want to get as fast as possible to the end
+ if( boost::is_same< null_observer , Observer >::value )
+ {
+ return detail::integrate_adaptive(
+ stepper , system , start_state ,
+ start_time , end_time , dt ,
+ observer , stepper_category() );
+ }
+ else
+ {
+ return detail::integrate_const( stepper , system , start_state ,
+ start_time , end_time , dt ,
+ observer , stepper_category() );
+ }
+}
+
+
+
+
+
+/**
+ * \brief integrate_const without observer calls
+ */
+template< class Stepper , class System , class State , class Time >
+size_t integrate_const(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time end_time , Time dt
+)
+{
+ return integrate_const( stepper , system , start_state , start_time , end_time , dt , null_observer() );
+}
+
+/**
+ * \brief Second version to solve the forwarding problem,
+ * can be called with Boost.Range as start_state.
+ */
+template< class Stepper , class System , class State , class Time >
+size_t integrate_const(
+ Stepper stepper , System system , const State &start_state ,
+ Time start_time , Time end_time , Time dt
+)
+{
+ return integrate_const( stepper , system , start_state , start_time , end_time , dt , null_observer() );
+}
+
+
+
+
+
+
+/********* DOXYGEN *********/
+ /**
+ * \fn integrate_const( Stepper stepper , System system , State &start_state , Time start_time , Time end_time , Time dt , Observer observer )
+ * \brief Integrates the ODE with constant step size.
+ *
+ * Integrates the ODE defined by system using the given stepper.
+ * This method ensures that the observer is called at constant intervals dt.
+ * If the Stepper is a normal stepper without step size control, dt is also
+ * used for the numerical scheme. If a ControlledStepper is provided, the
+ * algorithm might reduce the step size to meet the error bounds, but it is
+ * ensured that the observer is always called at equidistant time points
+ * t0 + n*dt. If a DenseOutputStepper is used, the step size also may vary
+ * and the dense output is used to call the observer at equidistant time
+ * points.
+ *
+ * \param stepper The stepper to be used for numerical integration.
+ * \param system Function/Functor defining the rhs of the ODE.
+ * \param start_state The initial condition x0.
+ * \param start_time The initial time t0.
+ * \param end_time The final integration time tend.
+ * \param dt The time step between observer calls, _not_ necessarily the
+ * time step of the integration.
+ * \param observer Function/Functor called at equidistant time intervals.
+ * \return The number of steps performed.
+ */
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_CONST_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/iterator/integrate/integrate_n_steps.hpp b/include/boost/numeric/odeint/iterator/integrate/integrate_n_steps.hpp
new file mode 100644
index 0000000..8f30c77
--- /dev/null
+++ b/include/boost/numeric/odeint/iterator/integrate/integrate_n_steps.hpp
@@ -0,0 +1,125 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/integrate_n_steps.hpp
+
+ [begin_description]
+ Integration of n steps with constant time size. Adaptive and dense-output methods are fully supported.
+ [end_description]
+
+ Copyright 2009-2011 Karsten Ahnert
+ Copyright 2009-2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_N_STEPS_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_N_STEPS_HPP_INCLUDED
+
+#include <boost/type_traits/is_same.hpp>
+
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/iterator/integrate/null_observer.hpp>
+#include <boost/numeric/odeint/iterator/integrate/detail/integrate_n_steps.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+/*
+ * Integrates n steps
+ *
+ * the two overloads are needed in order to solve the forwarding problem
+ */
+template< class Stepper , class System , class State , class Time , class Observer>
+Time integrate_n_steps(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time dt , size_t num_of_steps ,
+ Observer observer )
+{
+ typedef typename odeint::unwrap_reference< Stepper >::type::stepper_category stepper_category;
+ return detail::integrate_n_steps(
+ stepper , system , start_state ,
+ start_time , dt , num_of_steps ,
+ observer , stepper_category() );
+}
+
+/**
+ * \brief Solves the forwarding problem, can be called with Boost.Range as start_state.
+ */
+template< class Stepper , class System , class State , class Time , class Observer >
+Time integrate_n_steps(
+ Stepper stepper , System system , const State &start_state ,
+ Time start_time , Time dt , size_t num_of_steps ,
+ Observer observer )
+{
+ typedef typename odeint::unwrap_reference< Stepper >::type::stepper_category stepper_category;
+ return detail::integrate_n_steps(
+ stepper , system , start_state ,
+ start_time , dt , num_of_steps ,
+ observer , stepper_category() );
+}
+
+
+/**
+ * \brief The same function as above, but without observer calls.
+ */
+template< class Stepper , class System , class State , class Time >
+Time integrate_n_steps(
+ Stepper stepper , System system , State &start_state ,
+ Time start_time , Time dt , size_t num_of_steps )
+{
+ return integrate_n_steps( stepper , system , start_state , start_time , dt , num_of_steps , null_observer() );
+}
+
+/**
+ * \brief Solves the forwarding problem, can be called with Boost.Range as start_state.
+ */
+template< class Stepper , class System , class State , class Time >
+Time integrate_n_steps(
+ Stepper stepper , System system , const State &start_state ,
+ Time start_time , Time dt , size_t num_of_steps )
+{
+ return integrate_n_steps( stepper , system , start_state , start_time , dt , num_of_steps , null_observer() );
+}
+
+
+
+/************* DOXYGEN *************/
+ /**
+ * \fn Time integrate_n_steps( Stepper stepper , System system , State &start_state , Time start_time , Time dt , size_t num_of_steps , Observer observer )
+ * \brief Integrates the ODE with constant step size.
+ *
+ * This function is similar to integrate_const. The observer is called at
+ * equidistant time intervals t0 + n*dt.
+ * If the Stepper is a normal stepper without step size control, dt is also
+ * used for the numerical scheme. If a ControlledStepper is provided, the
+ * algorithm might reduce the step size to meet the error bounds, but it is
+ * ensured that the observer is always called at equidistant time points
+ * t0 + n*dt. If a DenseOutputStepper is used, the step size also may vary
+ * and the dense output is used to call the observer at equidistant time
+ * points. The final integration time is always t0 + num_of_steps*dt.
+ *
+ * \param stepper The stepper to be used for numerical integration.
+ * \param system Function/Functor defining the rhs of the ODE.
+ * \param start_state The initial condition x0.
+ * \param start_time The initial time t0.
+ * \param dt The time step between observer calls, _not_ necessarily the
+ * time step of the integration.
+ * \param num_of_steps Number of steps to be performed
+ * \param observer Function/Functor called at equidistant time intervals.
+ * \return The number of steps performed.
+ */
+
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_N_STEPS_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/iterator/integrate/integrate_times.hpp b/include/boost/numeric/odeint/iterator/integrate/integrate_times.hpp
new file mode 100644
index 0000000..1bbd836
--- /dev/null
+++ b/include/boost/numeric/odeint/iterator/integrate/integrate_times.hpp
@@ -0,0 +1,133 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/integrate_times.hpp
+
+ [begin_description]
+ Integration of ODEs with observation at user defined points
+ [end_description]
+
+ Copyright 2009-2011 Karsten Ahnert
+ Copyright 2009-2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_TIMES_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_TIMES_HPP_INCLUDED
+
+#include <boost/type_traits/is_same.hpp>
+
+#include <boost/range.hpp>
+
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/iterator/integrate/null_observer.hpp>
+#include <boost/numeric/odeint/iterator/integrate/detail/integrate_times.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+/*
+ * the two overloads are needed in order to solve the forwarding problem
+ */
+template< class Stepper , class System , class State , class TimeIterator , class Time , class Observer >
+size_t integrate_times(
+ Stepper stepper , System system , State &start_state ,
+ TimeIterator times_start , TimeIterator times_end , Time dt ,
+ Observer observer )
+{
+ typedef typename odeint::unwrap_reference< Stepper >::type::stepper_category stepper_category;
+ return detail::integrate_times(
+ stepper , system , start_state ,
+ times_start , times_end , dt ,
+ observer , stepper_category() );
+}
+
+/**
+ * \brief Solves the forwarding problem, can be called with Boost.Range as start_state.
+ */
+template< class Stepper , class System , class State , class TimeIterator , class Time , class Observer >
+size_t integrate_times(
+ Stepper stepper , System system , const State &start_state ,
+ TimeIterator times_start , TimeIterator times_end , Time dt ,
+ Observer observer )
+{
+ typedef typename odeint::unwrap_reference< Stepper >::type::stepper_category stepper_category;
+ return detail::integrate_times(
+ stepper , system , start_state ,
+ times_start , times_end , dt ,
+ observer , stepper_category() );
+}
+
+/**
+ * \brief The same function as above, but without observer calls.
+ */
+template< class Stepper , class System , class State , class TimeRange , class Time , class Observer >
+size_t integrate_times(
+ Stepper stepper , System system , State &start_state ,
+ const TimeRange × , Time dt ,
+ Observer observer )
+{
+ return integrate_times(
+ stepper , system , start_state ,
+ boost::begin( times ) , boost::end( times ) , dt , observer );
+}
+
+/**
+ * \brief Solves the forwarding problem, can be called with Boost.Range as start_state.
+ */
+template< class Stepper , class System , class State , class TimeRange , class Time , class Observer >
+size_t integrate_times(
+ Stepper stepper , System system , const State &start_state ,
+ const TimeRange × , Time dt ,
+ Observer observer )
+{
+ return integrate_times(
+ stepper , system , start_state ,
+ boost::begin( times ) , boost::end( times ) , dt , observer );
+}
+
+
+
+
+/********* DOXYGEN ***********/
+
+ /**
+ * \fn size_t integrate_times( Stepper stepper , System system , State &start_state , TimeIterator times_start , TimeIterator times_end , Time dt , Observer observer )
+ * \brief Integrates the ODE with observer calls at given time points.
+ *
+ * Integrates the ODE given by system using the given stepper. This function
+ * does observer calls at the subsequent time points given by the range
+ * times_start, times_end. If the stepper has not step size control, the
+ * step size might be reduced occasionally to ensure observer calls exactly
+ * at the time points from the given sequence. If the stepper is a
+ * ControlledStepper, the step size is adjusted to meet the error bounds,
+ * but also might be reduced occasionally to ensure correct observer calls.
+ * If a DenseOutputStepper is provided, the dense output functionality is
+ * used to call the observer at the given times. The end time of the
+ * integration is always *(end_time-1).
+ *
+ * \param stepper The stepper to be used for numerical integration.
+ * \param system Function/Functor defining the rhs of the ODE.
+ * \param start_state The initial condition x0.
+ * \param times_start Iterator to the start time
+ * \param times_end Iterator to the end time
+ * \param dt The time step between observer calls, _not_ necessarily the
+ * time step of the integration.
+ * \param observer Function/Functor called at equidistant time intervals.
+ * \return The number of steps performed.
+ */
+
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_TIMES_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/iterator/integrate/null_observer.hpp b/include/boost/numeric/odeint/iterator/integrate/null_observer.hpp
new file mode 100644
index 0000000..4d9a070
--- /dev/null
+++ b/include/boost/numeric/odeint/iterator/integrate/null_observer.hpp
@@ -0,0 +1,38 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/null_observer.hpp
+
+ [begin_description]
+ null_observer
+ [end_description]
+
+ Copyright 2009-2011 Karsten Ahnert
+ Copyright 2009-2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_NULL_OBSERVER_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_NULL_OBSERVER_HPP_INCLUDED
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+struct null_observer
+{
+ template< class State , class Time >
+ void operator()( const State& /* x */ , Time /* t */ ) const
+ {
+
+ }
+};
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_NULL_OBSERVER_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/iterator/integrate/observer_collection.hpp b/include/boost/numeric/odeint/iterator/integrate/observer_collection.hpp
new file mode 100644
index 0000000..26101a3
--- /dev/null
+++ b/include/boost/numeric/odeint/iterator/integrate/observer_collection.hpp
@@ -0,0 +1,56 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/integrate/observer_collection.hpp
+
+ [begin_description]
+ Collection of observers, which are all called during the evolution of the ODE.
+ [end_description]
+
+ Copyright 2009-2011 Karsten Ahnert
+ Copyright 2009-2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_OBSERVER_COLLECTION_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_OBSERVER_COLLECTION_HPP_INCLUDED
+
+#include <vector>
+
+#include <boost/function.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template< class State , class Time >
+class observer_collection
+{
+public:
+
+ typedef boost::function< void( const State& , const Time& ) > observer_type;
+ typedef std::vector< observer_type > collection_type;
+
+ void operator()( const State& x , Time t )
+ {
+ for( size_t i=0 ; i<m_observers.size() ; ++i )
+ m_observers[i]( x , t );
+ }
+
+ collection_type& observers( void ) { return m_observers; }
+ const collection_type& observers( void ) const { return m_observers; }
+
+private:
+
+ collection_type m_observers;
+};
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_OBSERVER_COLLECTION_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/iterator/n_step_iterator.hpp b/include/boost/numeric/odeint/iterator/n_step_iterator.hpp
new file mode 100644
index 0000000..195e981
--- /dev/null
+++ b/include/boost/numeric/odeint/iterator/n_step_iterator.hpp
@@ -0,0 +1,168 @@
+
+/*
+ [auto_generated]
+ boost/numeric/odeint/iterator/n_step_iterator.hpp
+
+ [begin_description]
+ Iterator for iterating through the solution of an ODE with constant step size performing exactly n steps.
+ [end_description]
+
+ Copyright 2009-2013 Karsten Ahnert
+ Copyright 2009-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_ITERATOR_N_STEP_ITERATOR_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_ITERATOR_N_STEP_ITERATOR_HPP_INCLUDED
+
+
+#include <boost/numeric/odeint/util/stepper_traits.hpp>
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/iterator/detail/ode_iterator_base.hpp>
+#include <boost/numeric/odeint/iterator/impl/n_step_iterator_impl.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+ /* use the n_step_iterator_impl with the right tags */
+ template< class Stepper , class System , class State
+#ifndef DOXYGEN_SKIP
+ , class StepperTag = typename base_tag< typename traits::stepper_category< Stepper >::type >::type
+#endif
+ >
+ class n_step_iterator : public n_step_iterator_impl<
+ n_step_iterator< Stepper , System , State , StepperTag > ,
+ Stepper , System , State , detail::ode_state_iterator_tag , StepperTag
+ >
+ {
+ typedef typename traits::time_type< Stepper >::type time_type;
+ typedef n_step_iterator< Stepper , System , State , StepperTag > iterator_type;
+
+ public:
+ n_step_iterator( Stepper stepper , System sys , State &s , time_type t , time_type dt , size_t num_of_steps )
+ : n_step_iterator_impl< iterator_type , Stepper , System , State , detail::ode_state_iterator_tag , StepperTag >( stepper , sys , s , t , dt , num_of_steps )
+ {}
+
+ n_step_iterator( Stepper stepper , System sys , State &s )
+ : n_step_iterator_impl< iterator_type , Stepper , System , State , detail::ode_state_iterator_tag , StepperTag >( stepper , sys , s )
+ {}
+ };
+
+ /* make functions */
+
+ template< class Stepper , class System , class State >
+ n_step_iterator< Stepper , System, State > make_n_step_iterator_begin(
+ Stepper stepper ,
+ System system ,
+ State &x ,
+ typename traits::time_type< Stepper >::type t ,
+ typename traits::time_type< Stepper >::type dt ,
+ size_t num_of_steps )
+ {
+ return n_step_iterator< Stepper , System , State >( stepper , system , x , t , dt , num_of_steps );
+ }
+
+ template< class Stepper , class System , class State >
+ n_step_iterator< Stepper , System , State > make_n_step_iterator_end(
+ Stepper stepper ,
+ System system ,
+ State &x )
+ {
+ return n_step_iterator< Stepper , System , State >( stepper , system , x );
+ }
+
+ template< class Stepper , class System , class State >
+ std::pair< n_step_iterator< Stepper , System , State > , n_step_iterator< Stepper , System , State > >
+ make_n_step_range(
+ Stepper stepper ,
+ System system ,
+ State &x ,
+ typename traits::time_type< Stepper >::type t ,
+ typename traits::time_type< Stepper >::type dt ,
+ size_t num_of_steps )
+ {
+ return std::make_pair(
+ n_step_iterator< Stepper , System , State >( stepper , system , x , t , dt , num_of_steps ) ,
+ n_step_iterator< Stepper , System , State >( stepper , system , x )
+ );
+ }
+
+
+ /**
+ * \class n_step_iterator
+ *
+ * \brief ODE Iterator with constant step size. The value type of this iterator is the state type of the stepper.
+ *
+ * Implements an iterator representing the solution of an ODE starting from t
+ * with n steps and a constant step size dt.
+ * After each iteration the iterator dereferences to the state x at the next
+ * time t+dt.
+ * This iterator can be used with Steppers and
+ * DenseOutputSteppers and it always makes use of the all the given steppers
+ * capabilities. A for_each over such an iterator range behaves similar to
+ * the integrate_n_steps routine.
+ *
+ * n_step_iterator is a model of single-pass iterator.
+ *
+ * The value type of this iterator is the state type of the stepper. Hence one can only access the state and not the current time.
+ *
+ * \tparam Stepper The stepper type which should be used during the iteration.
+ * \tparam System The type of the system function (ODE) which should be solved.
+ * \tparam State The state type of the ODE.
+ */
+
+
+ /**
+ * \fn make_n_step_iterator_begin( Stepper stepper , System system , State &x , typename traits::time_type< Stepper >::type t , typename traits::time_type< Stepper >::type dt , size_t num_of_steps )
+ *
+ * \brief Factory function for n_step_iterator. Constructs a begin iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param system The system function (ODE) to solve.
+ * \param x The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.
+ * \param t The initial time.
+ * \param dt The initial time step.
+ * \param num_of_steps The number of steps to be executed.
+ * \returns The n-step iterator.
+ */
+
+
+ /**
+ * \fn make_n_step_iterator_end( Stepper stepper , System system , State &x )
+ * \brief Factory function for n_step_iterator. Constructs an end iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param system The system function (ODE) to solve.
+ * \param x The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.
+ * \returns The const_step_iterator.
+ */
+
+
+ /**
+ * \fn make_n_step_range( Stepper stepper , System system , State &x , typename traits::time_type< Stepper >::type t , typename traits::time_type< Stepper >::type dt , , size_t num_of_steps )
+ *
+ * \brief Factory function to construct a single pass range of n-step iterators. A range is here a pair
+ * of n_step_iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param system The system function (ODE) to solve.
+ * \param x The initial state. const_step_iterator store a reference of s and changes its value during the iteration.
+ * \param t The initial time.
+ * \param dt The initial time step.
+ * \param num_of_steps The number of steps to be executed.
+ * \returns The n-step range.
+ */
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_ODEINT_ITERATOR_CONST_N_STEP_ITERATOR_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/iterator/n_step_time_iterator.hpp b/include/boost/numeric/odeint/iterator/n_step_time_iterator.hpp
new file mode 100644
index 0000000..8ed17de
--- /dev/null
+++ b/include/boost/numeric/odeint/iterator/n_step_time_iterator.hpp
@@ -0,0 +1,169 @@
+
+/*
+ [auto_generated]
+ boost/numeric/odeint/iterator/n_step_time_iterator.hpp
+
+ [begin_description]
+ Iterator for iterating through the solution of an ODE with constant step size performing exactly n steps.
+ The dereferenced type contains also the time.
+ [end_description]
+
+ Copyright 2009-2013 Karsten Ahnert
+ Copyright 2009-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_ITERATOR_N_STEP_TIME_ITERATOR_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_ITERATOR_N_STEP_TIME_ITERATOR_HPP_INCLUDED
+
+
+#include <boost/numeric/odeint/util/stepper_traits.hpp>
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/iterator/detail/ode_iterator_base.hpp>
+#include <boost/numeric/odeint/iterator/impl/n_step_iterator_impl.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+ /* use the n_step_iterator_impl with the right tags */
+ template< class Stepper , class System , class State
+#ifndef DOXYGEN_SKIP
+ , class StepperTag = typename base_tag< typename traits::stepper_category< Stepper >::type >::type
+#endif
+ >
+ class n_step_time_iterator : public n_step_iterator_impl<
+ n_step_time_iterator< Stepper , System , State , StepperTag > ,
+ Stepper , System , State , detail::ode_state_time_iterator_tag , StepperTag
+ >
+ {
+ typedef typename traits::time_type< Stepper >::type time_type;
+ typedef n_step_time_iterator< Stepper , System , State , StepperTag > iterator_type;
+
+ public:
+ n_step_time_iterator( Stepper stepper , System sys , State &s , time_type t , time_type dt , size_t num_of_steps )
+ : n_step_iterator_impl< iterator_type , Stepper , System , State , detail::ode_state_time_iterator_tag , StepperTag >( stepper , sys , s , t , dt , num_of_steps )
+ {}
+
+ n_step_time_iterator( Stepper stepper , System sys , State &s )
+ : n_step_iterator_impl< iterator_type , Stepper , System , State , detail::ode_state_time_iterator_tag , StepperTag >( stepper , sys , s )
+ {}
+ };
+
+ /* make functions */
+
+ template< class Stepper , class System , class State >
+ n_step_time_iterator< Stepper , System, State > make_n_step_time_iterator_begin(
+ Stepper stepper ,
+ System system ,
+ State &x ,
+ typename traits::time_type< Stepper >::type t ,
+ typename traits::time_type< Stepper >::type dt ,
+ size_t num_of_steps )
+ {
+ return n_step_time_iterator< Stepper , System , State >( stepper , system , x , t , dt , num_of_steps );
+ }
+
+ template< class Stepper , class System , class State >
+ n_step_time_iterator< Stepper , System , State > make_n_step_time_iterator_end(
+ Stepper stepper ,
+ System system ,
+ State &x )
+ {
+ return n_step_time_iterator< Stepper , System , State >( stepper , system , x );
+ }
+
+ template< class Stepper , class System , class State >
+ std::pair< n_step_time_iterator< Stepper , System , State > , n_step_time_iterator< Stepper , System , State > >
+ make_n_step_time_range(
+ Stepper stepper ,
+ System system ,
+ State &x ,
+ typename traits::time_type< Stepper >::type t ,
+ typename traits::time_type< Stepper >::type dt ,
+ size_t num_of_steps )
+ {
+ return std::make_pair(
+ n_step_time_iterator< Stepper , System , State >( stepper , system , x , t , dt , num_of_steps ) ,
+ n_step_time_iterator< Stepper , System , State >( stepper , system , x )
+ );
+ }
+
+
+ /**
+ * \class n_step_time_iterator
+ *
+ * \brief ODE Iterator with constant step size. The value type of this iterator is a std::pair containing state and time.
+ *
+ * Implements an iterator representing the solution of an ODE starting from t
+ * with n steps and a constant step size dt.
+ * After each iteration the iterator dereferences to a pair of state and time at the next
+ * time t+dt.
+ * This iterator can be used with Steppers and
+ * DenseOutputSteppers and it always makes use of the all the given steppers
+ * capabilities. A for_each over such an iterator range behaves similar to
+ * the integrate_n_steps routine.
+ *
+ * n_step_time_iterator is a model of single-pass iterator.
+ *
+ * The value type of this iterator is pair of state and time.
+ *
+ * \tparam Stepper The stepper type which should be used during the iteration.
+ * \tparam System The type of the system function (ODE) which should be solved.
+ * \tparam State The state type of the ODE.
+ */
+
+
+ /**
+ * \fn make_n_step_time_iterator_begin( Stepper stepper , System system , State &x , typename traits::time_type< Stepper >::type t , typename traits::time_type< Stepper >::type dt , size_t num_of_steps )
+ *
+ * \brief Factory function for n_step_time_iterator. Constructs a begin iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param system The system function (ODE) to solve.
+ * \param x The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.
+ * \param t The initial time.
+ * \param dt The initial time step.
+ * \param num_of_steps The number of steps to be executed.
+ * \returns The n-step iterator.
+ */
+
+
+ /**
+ * \fn make_n_step_time_iterator_end( Stepper stepper , System system , State &x )
+ * \brief Factory function for n_step_time_iterator. Constructs an end iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param system The system function (ODE) to solve.
+ * \param x The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.
+ * \returns The const_step_iterator.
+ */
+
+
+ /**
+ * \fn make_n_step_time_range( Stepper stepper , System system , State &x , typename traits::time_type< Stepper >::type t , typename traits::time_type< Stepper >::type dt , size_t num_of_steps )
+ *
+ * \brief Factory function to construct a single pass range of n-step iterators. A range is here a pair
+ * of n_step_time_iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param system The system function (ODE) to solve.
+ * \param x The initial state. const_step_iterator store a reference of s and changes its value during the iteration.
+ * \param t The initial time.
+ * \param dt The initial time step.
+ * \param num_of_steps The number of steps to be executed.
+ * \returns The n-step range.
+ */
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_ODEINT_ITERATOR_CONST_N_STEP_TIME_ITERATOR_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/iterator/times_iterator.hpp b/include/boost/numeric/odeint/iterator/times_iterator.hpp
new file mode 100644
index 0000000..e6c9b85
--- /dev/null
+++ b/include/boost/numeric/odeint/iterator/times_iterator.hpp
@@ -0,0 +1,189 @@
+
+/*
+ [auto_generated]
+ boost/numeric/odeint/iterator/times_iterator.hpp
+
+ [begin_description]
+ Iterator for iterating through the solution of an ODE with oscillator calls at times from a given sequence.
+ [end_description]
+
+ Copyright 2009-2013 Karsten Ahnert
+ Copyright 2009-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_ITERATOR_TIMES_ITERATOR_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_ITERATOR_TIMES_ITERATOR_HPP_INCLUDED
+
+
+#include <boost/numeric/odeint/util/stepper_traits.hpp>
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/iterator/detail/ode_iterator_base.hpp>
+#include <boost/numeric/odeint/iterator/impl/times_iterator_impl.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+ /* use the times_iterator_impl with the right tags */
+ template< class Stepper , class System , class State , class TimeIterator
+#ifndef DOXYGEN_SKIP
+ , class StepperTag = typename base_tag< typename traits::stepper_category< Stepper >::type >::type
+#endif
+ >
+ class times_iterator : public times_iterator_impl<
+ times_iterator< Stepper , System , State , TimeIterator , StepperTag > ,
+ Stepper , System , State , TimeIterator , detail::ode_state_iterator_tag , StepperTag
+ >
+ {
+ typedef typename traits::time_type< Stepper >::type time_type;
+ typedef times_iterator< Stepper , System , State , TimeIterator , StepperTag > iterator_type;
+
+ public:
+ times_iterator( Stepper stepper , System sys , State &s ,
+ TimeIterator t_start , TimeIterator t_end , time_type dt )
+ : times_iterator_impl< iterator_type , Stepper , System , State , TimeIterator, detail::ode_state_iterator_tag , StepperTag >( stepper , sys , s , t_start , t_end , dt )
+ {}
+
+ times_iterator( Stepper stepper , System sys , State &s )
+ : times_iterator_impl< iterator_type , Stepper , System , State , TimeIterator , detail::ode_state_iterator_tag , StepperTag >( stepper , sys , s )
+ {}
+ };
+
+ /* make functions */
+
+ template< class Stepper , class System , class State , class TimeIterator >
+ times_iterator< Stepper , System, State , TimeIterator > make_times_iterator_begin(
+ Stepper stepper ,
+ System system ,
+ State &x ,
+ TimeIterator t_start ,
+ TimeIterator t_end ,
+ typename traits::time_type< Stepper >::type dt )
+ {
+ return times_iterator< Stepper , System , State , TimeIterator >( stepper , system , x , t_start , t_end , dt );
+ }
+
+ // ToDo: requires to specifically provide the TimeIterator template parameter, can this be improved?
+ template< class TimeIterator , class Stepper , class System , class State >
+ times_iterator< Stepper , System , State , TimeIterator > make_times_iterator_end(
+ Stepper stepper ,
+ System system ,
+ State &x )
+ //TimeIterator t_end )
+ {
+ return times_iterator< Stepper , System , State , TimeIterator >( stepper , system , x );
+ }
+
+ template< class Stepper , class System , class State , class TimeIterator >
+ std::pair< times_iterator< Stepper , System , State , TimeIterator > ,
+ times_iterator< Stepper , System , State , TimeIterator > >
+ make_times_range(
+ Stepper stepper ,
+ System system ,
+ State &x ,
+ TimeIterator t_start ,
+ TimeIterator t_end ,
+ typename traits::time_type< Stepper >::type dt )
+ {
+ return std::make_pair(
+ times_iterator< Stepper , System , State , TimeIterator >( stepper , system , x , t_start , t_end , dt ) ,
+ times_iterator< Stepper , System , State , TimeIterator >( stepper , system , x )
+ );
+ }
+
+
+ /**
+ * \class times_iterator
+ *
+ * \brief ODE Iterator with given evaluation points. The value type of this iterator is the state type of the stepper.
+ *
+ * Implements an iterator representing the solution of an ODE from *t_start
+ * to *t_end evaluated at time points given by the sequence t_start to t_end.
+ * t_start and t_end are iterators representing a sequence of time points
+ * where the solution of the ODE should be evaluated.
+ * After each iteration the iterator dereferences to the state x at the next
+ * time *t_start++ until t_end is reached.
+ * This iterator can be used with Steppers, ControlledSteppers and
+ * DenseOutputSteppers and it always makes use of the all the given steppers
+ * capabilities. A for_each over such an iterator range behaves similar to
+ * the integrate_times routine.
+ *
+ * times_iterator is a model of single-pass iterator.
+ *
+ * The value type of this iterator is the state type of the stepper. Hence one can only access the state and not the current time.
+ *
+ * \tparam Stepper The stepper type which should be used during the iteration.
+ * \tparam System The type of the system function (ODE) which should be solved.
+ * \tparam State The state type of the ODE.
+ * \tparam TimeIterator The iterator type for the sequence of time points.
+ */
+
+
+
+ /**
+ * \fn make_times_iterator_begin( Stepper stepper ,
+ System system ,
+ State &x ,
+ TimeIterator t_start ,
+ TimeIterator t_end ,
+ typename traits::time_type< Stepper >::type dt )
+ *
+ * \brief Factory function for times_iterator. Constructs a begin iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param system The system function (ODE) to solve.
+ * \param x The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.
+ * \param t_start Begin iterator of the sequence of evaluation time points.
+ * \param t_end End iterator of the sequence of evaluation time points.
+ * \param dt The initial time step.
+ * \returns The times iterator.
+ */
+
+
+ /**
+ * \fn make_times_iterator_end( Stepper stepper , System system , State &x )
+ * \brief Factory function for times_iterator. Constructs an end iterator.
+ *
+ * \tparam TimesIterator The iterator type of the time sequence, must be specifically provided.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param system The system function (ODE) to solve.
+ * \param x The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.
+ * \returns The times iterator.
+ *
+ * This function needs the TimeIterator type specifically defined as a
+ * template parameter.
+ */
+
+
+ /**
+ * \fn make_times_range( Stepper stepper , System system , State &x ,
+ TimeIterator t_start ,
+ TimeIterator t_end ,
+ typename traits::time_type< Stepper >::type dt )
+ *
+ * \brief Factory function to construct a single pass range of times iterators. A range is here a pair
+ * of times_iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param system The system function (ODE) to solve.
+ * \param x The initial state. const_step_iterator store a reference of s and changes its value during the iteration.
+ * \param t_start Begin iterator of the sequence of evaluation time points.
+ * \param t_end End iterator of the sequence of evaluation time points.
+ * \param dt The initial time step.
+ * \returns The times iterator range.
+ */
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_ODEINT_ITERATOR_TIMES_ITERATOR_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/iterator/times_time_iterator.hpp b/include/boost/numeric/odeint/iterator/times_time_iterator.hpp
new file mode 100644
index 0000000..94fd9a3
--- /dev/null
+++ b/include/boost/numeric/odeint/iterator/times_time_iterator.hpp
@@ -0,0 +1,193 @@
+
+/*
+ [auto_generated]
+ boost/numeric/odeint/iterator/times_time_iterator.hpp
+
+ [begin_description]
+ Iterator for iterating through the solution of an ODE with oscillator calls at times from a given sequence.
+ The dereferenced type contains also the time.
+ [end_description]
+
+ Copyright 2009-2013 Karsten Ahnert
+ Copyright 2009-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_ITERATOR_TIMES_TIME_ITERATOR_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_ITERATOR_TIMES_TIME_ITERATOR_HPP_INCLUDED
+
+
+#include <boost/numeric/odeint/util/stepper_traits.hpp>
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/iterator/detail/ode_iterator_base.hpp>
+#include <boost/numeric/odeint/iterator/impl/times_iterator_impl.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+ /* use the times_iterator_impl with the right tags */
+ template< class Stepper , class System , class State , class TimeIterator
+#ifndef DOXYGEN_SKIP
+ , class StepperTag = typename base_tag< typename traits::stepper_category< Stepper >::type >::type
+#endif
+ >
+ class times_time_iterator : public times_iterator_impl<
+ times_time_iterator< Stepper , System , State , TimeIterator , StepperTag > ,
+ Stepper , System , State , TimeIterator , detail::ode_state_time_iterator_tag , StepperTag
+ >
+ {
+ typedef typename traits::time_type< Stepper >::type time_type;
+ typedef times_time_iterator< Stepper , System , State , TimeIterator , StepperTag > iterator_type;
+
+ public:
+ times_time_iterator( Stepper stepper , System sys , State &s ,
+ TimeIterator t_start , TimeIterator t_end , time_type dt )
+ : times_iterator_impl< iterator_type , Stepper , System , State , TimeIterator, detail::ode_state_time_iterator_tag , StepperTag >( stepper , sys , s , t_start , t_end , dt )
+ {}
+
+ times_time_iterator( Stepper stepper , System sys , State &s )
+ : times_iterator_impl< iterator_type , Stepper , System , State , TimeIterator , detail::ode_state_time_iterator_tag , StepperTag >( stepper , sys , s )
+ {}
+ };
+
+ /* make functions */
+
+ template< class Stepper , class System , class State , class TimeIterator >
+ times_time_iterator< Stepper , System, State , TimeIterator > make_times_time_iterator_begin(
+ Stepper stepper ,
+ System system ,
+ State &x ,
+ TimeIterator t_start ,
+ TimeIterator t_end ,
+ typename traits::time_type< Stepper >::type dt )
+ {
+ return times_time_iterator< Stepper , System , State , TimeIterator >( stepper , system , x , t_start , t_end , dt );
+ }
+
+ // ToDo: requires to specifically provide the TimeIterator template parameter, can this be improved?
+ template< class TimeIterator , class Stepper , class System , class State >
+ times_time_iterator< Stepper , System , State , TimeIterator > make_times_time_iterator_end(
+ Stepper stepper ,
+ System system ,
+ State &x )
+ //TimeIterator t_end )
+ {
+ return times_time_iterator< Stepper , System , State , TimeIterator >( stepper , system , x );
+ }
+
+ template< class Stepper , class System , class State , class TimeIterator >
+ std::pair< times_time_iterator< Stepper , System , State , TimeIterator > ,
+ times_time_iterator< Stepper , System , State , TimeIterator > >
+ make_times_time_range(
+ Stepper stepper ,
+ System system ,
+ State &x ,
+ TimeIterator t_start ,
+ TimeIterator t_end ,
+ typename traits::time_type< Stepper >::type dt )
+ {
+ return std::make_pair(
+ times_time_iterator< Stepper , System , State , TimeIterator >( stepper , system , x , t_start , t_end , dt ) ,
+ times_time_iterator< Stepper , System , State , TimeIterator >( stepper , system , x )
+ );
+ }
+
+
+
+
+
+ /**
+ * \class times_time_iterator
+ *
+ * \brief ODE Iterator with given evaluation points. The value type of this iterator is a std::pair containing state and time.
+ *
+ * Implements an iterator representing the solution of an ODE from *t_start
+ * to *t_end evaluated at time points given by the sequence t_start to t_end.
+ * t_start and t_end are iterators representing a sequence of time points
+ * where the solution of the ODE should be evaluated.
+ * After each iteration the iterator dereferences to a pair with the state
+ * and the time at the next evaluation point *t_start++ until t_end is reached.
+ * This iterator can be used with Steppers, ControlledSteppers and
+ * DenseOutputSteppers and it always makes use of the all the given steppers
+ * capabilities. A for_each over such an iterator range behaves similar to
+ * the integrate_times routine.
+ *
+ * times_time_iterator is a model of single-pass iterator.
+ *
+ * The value type of this iterator is a pair of state and time type.
+ *
+ * \tparam Stepper The stepper type which should be used during the iteration.
+ * \tparam System The type of the system function (ODE) which should be solved.
+ * \tparam State The state type of the ODE.
+ * \tparam TimeIterator The iterator type for the sequence of time points.
+ */
+
+
+
+ /**
+ * \fn make_times_time_iterator_begin( Stepper stepper ,
+ System system ,
+ State &x ,
+ TimeIterator t_start ,
+ TimeIterator t_end ,
+ typename traits::time_type< Stepper >::type dt )
+ *
+ * \brief Factory function for times_time_iterator. Constructs a begin iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param system The system function (ODE) to solve.
+ * \param x The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.
+ * \param t_start Begin iterator of the sequence of evaluation time points.
+ * \param t_end End iterator of the sequence of evaluation time points.
+ * \param dt The initial time step.
+ * \returns The times_time iterator.
+ */
+
+
+ /**
+ * \fn make_times_time_iterator_end( Stepper stepper , System system , State &x )
+ * \brief Factory function for times_time_iterator. Constructs an end iterator.
+ *
+ * \tparam TimesIterator The iterator type of the time sequence, must be specifically provided.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param system The system function (ODE) to solve.
+ * \param x The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.
+ * \returns The times_time iterator.
+ *
+ * This function needs the TimeIterator type specifically defined as a
+ * template parameter.
+ */
+
+
+ /**
+ * \fn make_times_time_range( Stepper stepper , System system , State &x ,
+ TimeIterator t_start ,
+ TimeIterator t_end ,
+ typename traits::time_type< Stepper >::type dt )
+ *
+ * \brief Factory function to construct a single pass range of times_time iterators. A range is here a pair
+ * of times_iterator.
+ *
+ * \param stepper The stepper to use during the iteration.
+ * \param system The system function (ODE) to solve.
+ * \param x The initial state. const_step_iterator store a reference of s and changes its value during the iteration.
+ * \param t_start Begin iterator of the sequence of evaluation time points.
+ * \param t_end End iterator of the sequence of evaluation time points.
+ * \param dt The initial time step.
+ * \returns The times_time iterator range.
+ */
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_ODEINT_ITERATOR_TIMES_TIME_ITERATOR_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/adams_bashforth.hpp b/include/boost/numeric/odeint/stepper/adams_bashforth.hpp
new file mode 100644
index 0000000..5ff1e83
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/adams_bashforth.hpp
@@ -0,0 +1,420 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/adams_bashforth.hpp
+
+ [begin_description]
+ Implementaton of the Adam-Bashforth method a multistep method used for the predictor step in the
+ Adams-Bashforth-Moulton method.
+ [end_description]
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011-2013 Mario Mulansky
+ Copyright 2012 Christoph Koke
+ Copyright 2013 Pascal Germroth
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_ADAMS_BASHFORTH_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_ADAMS_BASHFORTH_HPP_INCLUDED
+
+#include <boost/static_assert.hpp>
+
+#include <boost/numeric/odeint/util/bind.hpp>
+#include <boost/numeric/odeint/util/unwrap_reference.hpp>
+
+#include <boost/numeric/odeint/algebra/range_algebra.hpp>
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
+
+#include <boost/numeric/odeint/util/state_wrapper.hpp>
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resizer.hpp>
+
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta4.hpp>
+#include <boost/numeric/odeint/stepper/extrapolation_stepper.hpp>
+
+#include <boost/numeric/odeint/stepper/base/algebra_stepper_base.hpp>
+
+#include <boost/numeric/odeint/stepper/detail/adams_bashforth_coefficients.hpp>
+#include <boost/numeric/odeint/stepper/detail/adams_bashforth_call_algebra.hpp>
+#include <boost/numeric/odeint/stepper/detail/rotating_buffer.hpp>
+
+#include <boost/mpl/arithmetic.hpp>
+#include <boost/mpl/min_max.hpp>
+#include <boost/mpl/equal_to.hpp>
+
+namespace mpl = boost::mpl;
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+ using mpl::int_;
+
+ /* if N >= 4, returns the smallest even number > N, otherwise returns 4 */
+ template < int N >
+ struct order_helper
+ : mpl::max< typename mpl::eval_if<
+ mpl::equal_to< mpl::modulus< int_< N >, int_< 2 > >,
+ int_< 0 > >,
+ int_< N >, int_< N + 1 > >::type,
+ int_< 4 > >::type
+ { };
+
+template<
+size_t Steps ,
+class State ,
+class Value = double ,
+class Deriv = State ,
+class Time = Value ,
+class Algebra = typename algebra_dispatcher< State >::algebra_type ,
+class Operations = typename operations_dispatcher< State >::operations_type ,
+class Resizer = initially_resizer ,
+class InitializingStepper = extrapolation_stepper< order_helper<Steps>::value,
+ State, Value, Deriv, Time,
+ Algebra, Operations, Resizer >
+>
+class adams_bashforth : public algebra_stepper_base< Algebra , Operations >
+{
+
+#ifndef DOXYGEN_SKIP
+ BOOST_STATIC_ASSERT(( Steps > 0 ));
+ BOOST_STATIC_ASSERT(( Steps < 9 ));
+#endif
+
+public :
+
+ typedef State state_type;
+ typedef state_wrapper< state_type > wrapped_state_type;
+ typedef Value value_type;
+ typedef Deriv deriv_type;
+ typedef state_wrapper< deriv_type > wrapped_deriv_type;
+ typedef Time time_type;
+ typedef Resizer resizer_type;
+ typedef stepper_tag stepper_category;
+
+ typedef InitializingStepper initializing_stepper_type;
+
+ typedef algebra_stepper_base< Algebra , Operations > algebra_stepper_base_type;
+ typedef typename algebra_stepper_base_type::algebra_type algebra_type;
+ typedef typename algebra_stepper_base_type::operations_type operations_type;
+#ifndef DOXYGEN_SKIP
+ typedef adams_bashforth< Steps , State , Value , Deriv , Time , Algebra , Operations , Resizer , InitializingStepper > stepper_type;
+#endif
+ static const size_t steps = Steps;
+
+
+
+ typedef unsigned short order_type;
+ static const order_type order_value = steps;
+
+ typedef detail::rotating_buffer< wrapped_deriv_type , steps > step_storage_type;
+
+
+
+ order_type order( void ) const { return order_value; }
+
+ adams_bashforth( const algebra_type &algebra = algebra_type() )
+ : algebra_stepper_base_type( algebra ) ,
+ m_step_storage() , m_resizer() , m_coefficients() ,
+ m_steps_initialized( 0 ) , m_initializing_stepper()
+ { }
+
+
+
+ /*
+ * Version 1 : do_step( system , x , t , dt );
+ *
+ * solves the forwarding problem
+ */
+ template< class System , class StateInOut >
+ void do_step( System system , StateInOut &x , time_type t , time_type dt )
+ {
+ do_step( system , x , t , x , dt );
+ }
+
+ /**
+ * \brief Second version to solve the forwarding problem, can be called with Boost.Range as StateInOut.
+ */
+ template< class System , class StateInOut >
+ void do_step( System system , const StateInOut &x , time_type t , time_type dt )
+ {
+ do_step( system , x , t , x , dt );
+ }
+
+
+
+ /*
+ * Version 2 : do_step( system , in , t , out , dt );
+ *
+ * solves the forwarding problem
+ */
+
+ template< class System , class StateIn , class StateOut >
+ void do_step( System system , const StateIn &in , time_type t , StateOut &out , time_type dt )
+ {
+ do_step_impl( system , in , t , out , dt );
+ }
+
+ /**
+ * \brief Second version to solve the forwarding problem, can be called with Boost.Range as StateOut.
+ */
+ template< class System , class StateIn , class StateOut >
+ void do_step( System system , const StateIn &in , time_type t , const StateOut &out , time_type dt )
+ {
+ do_step_impl( system , in , t , out , dt );
+ }
+
+
+ template< class StateType >
+ void adjust_size( const StateType &x )
+ {
+ resize_impl( x );
+ }
+
+ const step_storage_type& step_storage( void ) const
+ {
+ return m_step_storage;
+ }
+
+ step_storage_type& step_storage( void )
+ {
+ return m_step_storage;
+ }
+
+ template< class ExplicitStepper , class System , class StateIn >
+ void initialize( ExplicitStepper explicit_stepper , System system , StateIn &x , time_type &t , time_type dt )
+ {
+ typename odeint::unwrap_reference< ExplicitStepper >::type &stepper = explicit_stepper;
+ typename odeint::unwrap_reference< System >::type &sys = system;
+
+ m_resizer.adjust_size( x , detail::bind( &stepper_type::template resize_impl<StateIn> , detail::ref( *this ) , detail::_1 ) );
+
+ for( size_t i=0 ; i+1<steps ; ++i )
+ {
+ if( i != 0 ) m_step_storage.rotate();
+ sys( x , m_step_storage[0].m_v , t );
+ stepper.do_step_dxdt_impl( system, x, m_step_storage[0].m_v, t,
+ dt );
+ t += dt;
+ }
+ m_steps_initialized = steps;
+ }
+
+ template< class System , class StateIn >
+ void initialize( System system , StateIn &x , time_type &t , time_type dt )
+ {
+ initialize( detail::ref( m_initializing_stepper ) , system , x , t , dt );
+ }
+
+ void reset( void )
+ {
+ m_steps_initialized = 0;
+ }
+
+ bool is_initialized( void ) const
+ {
+ return m_steps_initialized >= ( steps - 1 );
+ }
+
+ const initializing_stepper_type& initializing_stepper( void ) const { return m_initializing_stepper; }
+
+ initializing_stepper_type& initializing_stepper( void ) { return m_initializing_stepper; }
+
+private:
+
+ template< class System , class StateIn , class StateOut >
+ void do_step_impl( System system , const StateIn &in , time_type t , StateOut &out , time_type dt )
+ {
+ typename odeint::unwrap_reference< System >::type &sys = system;
+ if( m_resizer.adjust_size( in , detail::bind( &stepper_type::template resize_impl<StateIn> , detail::ref( *this ) , detail::_1 ) ) )
+ {
+ m_steps_initialized = 0;
+ }
+
+ if( m_steps_initialized + 1 < steps )
+ {
+ if( m_steps_initialized != 0 ) m_step_storage.rotate();
+ sys( in , m_step_storage[0].m_v , t );
+ m_initializing_stepper.do_step_dxdt_impl(
+ system, in, m_step_storage[0].m_v, t, out, dt );
+ ++m_steps_initialized;
+ }
+ else
+ {
+ m_step_storage.rotate();
+ sys( in , m_step_storage[0].m_v , t );
+ detail::adams_bashforth_call_algebra< steps , algebra_type , operations_type >()( this->m_algebra , in , out , m_step_storage , m_coefficients , dt );
+ }
+ }
+
+
+ template< class StateIn >
+ bool resize_impl( const StateIn &x )
+ {
+ bool resized( false );
+ for( size_t i=0 ; i<steps ; ++i )
+ {
+ resized |= adjust_size_by_resizeability( m_step_storage[i] , x , typename is_resizeable<deriv_type>::type() );
+ }
+ return resized;
+ }
+
+ step_storage_type m_step_storage;
+ resizer_type m_resizer;
+ detail::adams_bashforth_coefficients< value_type , steps > m_coefficients;
+ size_t m_steps_initialized;
+ initializing_stepper_type m_initializing_stepper;
+
+};
+
+
+/***** DOXYGEN *****/
+
+/**
+ * \class adams_bashforth
+ * \brief The Adams-Bashforth multistep algorithm.
+ *
+ * The Adams-Bashforth method is a multi-step algorithm with configurable step
+ * number. The step number is specified as template parameter Steps and it
+ * then uses the result from the previous Steps steps. See also
+ * <a href="http://en.wikipedia.org/wiki/Linear_multistep_method">en.wikipedia.org/wiki/Linear_multistep_method</a>.
+ * Currently, a maximum of Steps=8 is supported.
+ * The method is explicit and fulfills the Stepper concept. Step size control
+ * or continuous output are not provided.
+ *
+ * This class derives from algebra_base and inherits its interface via
+ * CRTP (current recurring template pattern). For more details see
+ * algebra_stepper_base.
+ *
+ * \tparam Steps The number of steps (maximal 8).
+ * \tparam State The state type.
+ * \tparam Value The value type.
+ * \tparam Deriv The type representing the time derivative of the state.
+ * \tparam Time The time representing the independent variable - the time.
+ * \tparam Algebra The algebra type.
+ * \tparam Operations The operations type.
+ * \tparam Resizer The resizer policy type.
+ * \tparam InitializingStepper The stepper for the first two steps.
+ */
+
+ /**
+ * \fn adams_bashforth::adams_bashforth( const algebra_type &algebra )
+ * \brief Constructs the adams_bashforth class. This constructor can be used as a default
+ * constructor if the algebra has a default constructor.
+ * \param algebra A copy of algebra is made and stored.
+ */
+
+ /**
+ * \fn order_type adams_bashforth::order( void ) const
+ * \brief Returns the order of the algorithm, which is equal to the number of steps.
+ * \return order of the method.
+ */
+
+ /**
+ * \fn void adams_bashforth::do_step( System system , StateInOut &x , time_type t , time_type dt )
+ * \brief This method performs one step. It transforms the result in-place.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the
+ * Simple System concept.
+ * \param x The state of the ODE which should be solved. After calling do_step the result is updated in x.
+ * \param t The value of the time, at which the step should be performed.
+ * \param dt The step size.
+ */
+
+ /**
+ * \fn void adams_bashforth::do_step( System system , const StateIn &in , time_type t , StateOut &out , time_type dt )
+ * \brief The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param in The state of the ODE which should be solved. in is not modified in this method
+ * \param t The value of the time, at which the step should be performed.
+ * \param out The result of the step is written in out.
+ * \param dt The step size.
+ */
+
+ /**
+ * \fn void adams_bashforth::adjust_size( const StateType &x )
+ * \brief Adjust the size of all temporaries in the stepper manually.
+ * \param x A state from which the size of the temporaries to be resized is deduced.
+ */
+
+
+ /**
+ * \fn const step_storage_type& adams_bashforth::step_storage( void ) const
+ * \brief Returns the storage of intermediate results.
+ * \return The storage of intermediate results.
+ */
+
+ /**
+ * \fn step_storage_type& adams_bashforth::step_storage( void )
+ * \brief Returns the storage of intermediate results.
+ * \return The storage of intermediate results.
+ */
+
+ /**
+ * \fn void adams_bashforth::initialize( ExplicitStepper explicit_stepper , System system , StateIn &x , time_type &t , time_type dt )
+ * \brief Initialized the stepper. Does Steps-1 steps with the explicit_stepper to fill the buffer.
+ * \param explicit_stepper the stepper used to fill the buffer of previous step results
+ * \param system The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the
+ * Simple System concept.
+ * \param x The state of the ODE which should be solved. After calling do_step the result is updated in x.
+ * \param t The value of the time, at which the step should be performed.
+ * \param dt The step size.
+ */
+
+ /**
+ * \fn void adams_bashforth::initialize( System system , StateIn &x , time_type &t , time_type dt )
+ * \brief Initialized the stepper. Does Steps-1 steps with an internal instance of InitializingStepper to fill the buffer.
+ * \note The state x and time t are updated to the values after Steps-1 initial steps.
+ * \param system The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the
+ * Simple System concept.
+ * \param x The initial state of the ODE which should be solved, updated in this method.
+ * \param t The initial value of the time, updated in this method.
+ * \param dt The step size.
+ */
+
+ /**
+ * \fn void adams_bashforth::reset( void )
+ * \brief Resets the internal buffer of the stepper.
+ */
+
+ /**
+ * \fn bool adams_bashforth::is_initialized( void ) const
+ * \brief Returns true if the stepper has been initialized.
+ * \return bool true if stepper is initialized, false otherwise
+ */
+
+ /**
+ * \fn const initializing_stepper_type& adams_bashforth::initializing_stepper( void ) const
+ * \brief Returns the internal initializing stepper instance.
+ * \return initializing_stepper
+ */
+
+ /**
+ * \fn const initializing_stepper_type& adams_bashforth::initializing_stepper( void ) const
+ * \brief Returns the internal initializing stepper instance.
+ * \return initializing_stepper
+ */
+
+ /**
+ * \fn initializing_stepper_type& adams_bashforth::initializing_stepper( void )
+ * \brief Returns the internal initializing stepper instance.
+ * \return initializing_stepper
+ */
+
+} // odeint
+} // numeric
+} // boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_ADAMS_BASHFORTH_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/adams_bashforth_moulton.hpp b/include/boost/numeric/odeint/stepper/adams_bashforth_moulton.hpp
new file mode 100644
index 0000000..f3edce1
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/adams_bashforth_moulton.hpp
@@ -0,0 +1,314 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/adams_bashforth_moulton.hpp
+
+ [begin_description]
+ Implementation of the Adams-Bashforth-Moulton method, a predictor-corrector multistep method.
+ [end_description]
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011-2013 Mario Mulansky
+ Copyright 2012 Christoph Koke
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_ADAMS_BASHFORTH_MOULTON_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_ADAMS_BASHFORTH_MOULTON_HPP_INCLUDED
+
+
+#include <boost/numeric/odeint/util/bind.hpp>
+
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/algebra/range_algebra.hpp>
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
+
+#include <boost/numeric/odeint/util/state_wrapper.hpp>
+#include <boost/numeric/odeint/util/resizer.hpp>
+
+#include <boost/numeric/odeint/stepper/adams_bashforth.hpp>
+#include <boost/numeric/odeint/stepper/adams_moulton.hpp>
+
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+template<
+size_t Steps ,
+class State ,
+class Value = double ,
+class Deriv = State ,
+class Time = Value ,
+class Algebra = typename algebra_dispatcher< State >::algebra_type ,
+class Operations = typename operations_dispatcher< State >::operations_type ,
+class Resizer = initially_resizer,
+class InitializingStepper = runge_kutta4< State , Value , Deriv , Time , Algebra , Operations, Resizer >
+>
+class adams_bashforth_moulton
+{
+
+#ifndef DOXYGEN_SKIP
+ BOOST_STATIC_ASSERT(( Steps > 0 ));
+ BOOST_STATIC_ASSERT(( Steps < 9 ));
+#endif
+
+public :
+
+ typedef State state_type;
+ typedef state_wrapper< state_type > wrapped_state_type;
+ typedef Value value_type;
+ typedef Deriv deriv_type;
+ typedef state_wrapper< deriv_type > wrapped_deriv_type;
+ typedef Time time_type;
+ typedef Algebra algebra_type;
+ typedef Operations operations_type;
+ typedef Resizer resizer_type;
+ typedef stepper_tag stepper_category;
+ typedef InitializingStepper initializing_stepper_type;
+
+ static const size_t steps = Steps;
+#ifndef DOXYGEN_SKIP
+ typedef adams_bashforth< steps , state_type , value_type , deriv_type , time_type , algebra_type , operations_type , resizer_type, initializing_stepper_type > adams_bashforth_type;
+ typedef adams_moulton< steps , state_type , value_type , deriv_type , time_type , algebra_type , operations_type , resizer_type > adams_moulton_type;
+ typedef adams_bashforth_moulton< steps , state_type , value_type , deriv_type , time_type , algebra_type , operations_type , resizer_type , initializing_stepper_type> stepper_type;
+#endif //DOXYGEN_SKIP
+ typedef unsigned short order_type;
+ static const order_type order_value = steps;
+
+ /** \brief Constructs the adams_bashforth class. */
+ adams_bashforth_moulton( void )
+ : m_adams_bashforth() , m_adams_moulton( m_adams_bashforth.algebra() )
+ , m_x() , m_resizer()
+ { }
+
+ adams_bashforth_moulton( const algebra_type &algebra )
+ : m_adams_bashforth( algebra ) , m_adams_moulton( m_adams_bashforth.algebra() )
+ , m_x() , m_resizer()
+ { }
+
+ order_type order( void ) const { return order_value; }
+
+ template< class System , class StateInOut >
+ void do_step( System system , StateInOut &x , time_type t , time_type dt )
+ {
+ do_step_impl1( system , x , t , dt );
+ }
+
+ /**
+ * \brief Second version to solve the forwarding problem, can be called with Boost.Range as StateInOut.
+ */
+ template< class System , class StateInOut >
+ void do_step( System system , const StateInOut &x , time_type t , time_type dt )
+ {
+ do_step_impl1( system , x , t , dt );
+ }
+
+ template< class System , class StateIn , class StateOut >
+ void do_step( System system , const StateIn &in , time_type t , const StateOut &out , time_type dt )
+ {
+ do_step_impl2( system , in , t , out , dt );
+ }
+
+ /**
+ * \brief Second version to solve the forwarding problem, can be called with Boost.Range as StateOut.
+ */
+ template< class System , class StateIn , class StateOut >
+ void do_step( System system , const StateIn &in , time_type t , StateOut &out , time_type dt )
+ {
+ do_step_impl2( system , in ,t , out , dt );
+ }
+
+
+ template< class StateType >
+ void adjust_size( const StateType &x )
+ {
+ m_adams_bashforth.adjust_size( x );
+ m_adams_moulton.adjust_size( x );
+ resize_impl( x );
+ }
+
+
+ template< class ExplicitStepper , class System , class StateIn >
+ void initialize( ExplicitStepper explicit_stepper , System system , StateIn &x , time_type &t , time_type dt )
+ {
+ m_adams_bashforth.initialize( explicit_stepper , system , x , t , dt );
+ }
+
+
+ template< class System , class StateIn >
+ void initialize( System system , StateIn &x , time_type &t , time_type dt )
+ {
+ m_adams_bashforth.initialize( system , x , t , dt );
+ }
+
+
+ void reset(void)
+ {
+ m_adams_bashforth.reset();
+ }
+
+
+
+private:
+
+ template< typename System , typename StateInOut >
+ void do_step_impl1( System system , StateInOut &x , time_type t , time_type dt )
+ {
+ if( m_adams_bashforth.is_initialized() )
+ {
+ m_resizer.adjust_size( x , detail::bind( &stepper_type::template resize_impl< StateInOut > , detail::ref( *this ) , detail::_1 ) );
+ m_adams_bashforth.do_step( system , x , t , m_x.m_v , dt );
+ m_adams_moulton.do_step( system , x , m_x.m_v , t+dt , x , dt , m_adams_bashforth.step_storage() );
+ }
+ else
+ {
+ m_adams_bashforth.do_step( system , x , t , dt );
+ }
+ }
+
+ template< typename System , typename StateIn , typename StateInOut >
+ void do_step_impl2( System system , StateIn const &in , time_type t , StateInOut & out , time_type dt )
+ {
+ if( m_adams_bashforth.is_initialized() )
+ {
+ m_resizer.adjust_size( in , detail::bind( &stepper_type::template resize_impl< StateInOut > , detail::ref( *this ) , detail::_1 ) );
+ m_adams_bashforth.do_step( system , in , t , m_x.m_v , dt );
+ m_adams_moulton.do_step( system , in , m_x.m_v , t+dt , out , dt , m_adams_bashforth.step_storage() );
+ }
+ else
+ {
+ m_adams_bashforth.do_step( system , in , t , out , dt );
+ }
+ }
+
+
+ template< class StateIn >
+ bool resize_impl( const StateIn &x )
+ {
+ return adjust_size_by_resizeability( m_x , x , typename is_resizeable< state_type >::type() );
+ }
+
+ adams_bashforth_type m_adams_bashforth;
+ adams_moulton_type m_adams_moulton;
+ wrapped_state_type m_x;
+ resizer_type m_resizer;
+};
+
+
+/********* DOXYGEN ********/
+
+/**
+ * \class adams_bashforth_moulton
+ * \brief The Adams-Bashforth-Moulton multistep algorithm.
+ *
+ * The Adams-Bashforth method is a multi-step predictor-corrector algorithm
+ * with configurable step number. The step number is specified as template
+ * parameter Steps and it then uses the result from the previous Steps steps.
+ * See also
+ * <a href="http://en.wikipedia.org/wiki/Linear_multistep_method">en.wikipedia.org/wiki/Linear_multistep_method</a>.
+ * Currently, a maximum of Steps=8 is supported.
+ * The method is explicit and fulfills the Stepper concept. Step size control
+ * or continuous output are not provided.
+ *
+ * This class derives from algebra_base and inherits its interface via
+ * CRTP (current recurring template pattern). For more details see
+ * algebra_stepper_base.
+ *
+ * \tparam Steps The number of steps (maximal 8).
+ * \tparam State The state type.
+ * \tparam Value The value type.
+ * \tparam Deriv The type representing the time derivative of the state.
+ * \tparam Time The time representing the independent variable - the time.
+ * \tparam Algebra The algebra type.
+ * \tparam Operations The operations type.
+ * \tparam Resizer The resizer policy type.
+ * \tparam InitializingStepper The stepper for the first two steps.
+ */
+
+ /**
+ * \fn adams_bashforth_moulton::adams_bashforth_moulton( const algebra_type &algebra )
+ * \brief Constructs the adams_bashforth class. This constructor can be used as a default
+ * constructor if the algebra has a default constructor.
+ * \param algebra A copy of algebra is made and stored.
+ */
+
+ /**
+ * \fn adams_bashforth_moulton::order( void ) const
+ * \brief Returns the order of the algorithm, which is equal to the number of steps+1.
+ * \return order of the method.
+ */
+
+ /**
+ * \fn adams_bashforth_moulton::do_step( System system , StateInOut &x , time_type t , time_type dt )
+ * \brief This method performs one step. It transforms the result in-place.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the
+ * Simple System concept.
+ * \param x The state of the ODE which should be solved. After calling do_step the result is updated in x.
+ * \param t The value of the time, at which the step should be performed.
+ * \param dt The step size.
+ */
+
+
+ /**
+ * \fn adams_bashforth_moulton::do_step( System system , const StateIn &in , time_type t , const StateOut &out , time_type dt )
+ * \brief The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param in The state of the ODE which should be solved. in is not modified in this method
+ * \param t The value of the time, at which the step should be performed.
+ * \param out The result of the step is written in out.
+ * \param dt The step size.
+ */
+
+ /**
+ * \fn adams_bashforth_moulton::adjust_size( const StateType &x )
+ * \brief Adjust the size of all temporaries in the stepper manually.
+ * \param x A state from which the size of the temporaries to be resized is deduced.
+ */
+
+ /**
+ * \fn adams_bashforth_moulton::initialize( ExplicitStepper explicit_stepper , System system , StateIn &x , time_type &t , time_type dt )
+ * \brief Initialized the stepper. Does Steps-1 steps with the explicit_stepper to fill the buffer.
+ * \note The state x and time t are updated to the values after Steps-1 initial steps.
+ * \param explicit_stepper the stepper used to fill the buffer of previous step results
+ * \param system The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the
+ * Simple System concept.
+ * \param x The initial state of the ODE which should be solved, updated after in this method.
+ * \param t The initial time, updated in this method.
+ * \param dt The step size.
+ */
+
+ /**
+ * \fn adams_bashforth_moulton::initialize( System system , StateIn &x , time_type &t , time_type dt )
+ * \brief Initialized the stepper. Does Steps-1 steps using the standard initializing stepper
+ * of the underlying adams_bashforth stepper.
+ * \param system The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the
+ * Simple System concept.
+ * \param x The state of the ODE which should be solved. After calling do_step the result is updated in x.
+ * \param t The value of the time, at which the step should be performed.
+ * \param dt The step size.
+ */
+
+ /**
+ * \fn adams_bashforth_moulton::reset( void )
+ * \brief Resets the internal buffers of the stepper.
+ */
+
+
+} // odeint
+} // numeric
+} // boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_ADAMS_BASHFORTH_MOULTON_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/adams_moulton.hpp b/include/boost/numeric/odeint/stepper/adams_moulton.hpp
new file mode 100644
index 0000000..05b4277
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/adams_moulton.hpp
@@ -0,0 +1,201 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/adams_moulton.hpp
+
+ [begin_description]
+ Implementation of the Adams-Moulton method. This is method is not a real stepper, it is more a helper class
+ which computes the corrector step in the Adams-Bashforth-Moulton method.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2013 Mario Mulansky
+ Copyright 2012 Christoph Koke
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_ADAMS_MOULTON_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_ADAMS_MOULTON_HPP_INCLUDED
+
+
+#include <boost/numeric/odeint/util/bind.hpp>
+
+#include <boost/numeric/odeint/algebra/range_algebra.hpp>
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
+
+#include <boost/numeric/odeint/util/state_wrapper.hpp>
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resizer.hpp>
+
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta4_classic.hpp>
+
+#include <boost/numeric/odeint/stepper/detail/adams_moulton_call_algebra.hpp>
+#include <boost/numeric/odeint/stepper/detail/adams_moulton_coefficients.hpp>
+#include <boost/numeric/odeint/stepper/detail/rotating_buffer.hpp>
+
+
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+/*
+ * Static implicit Adams-Moulton multistep-solver without step size control and without dense output.
+ */
+template<
+size_t Steps ,
+class State ,
+class Value = double ,
+class Deriv = State ,
+class Time = Value ,
+class Algebra = typename algebra_dispatcher< State >::algebra_type ,
+class Operations = typename operations_dispatcher< State >::operations_type ,
+class Resizer = initially_resizer
+>
+class adams_moulton
+{
+private:
+
+
+public :
+
+ typedef State state_type;
+ typedef state_wrapper< state_type > wrapped_state_type;
+ typedef Value value_type;
+ typedef Deriv deriv_type;
+ typedef state_wrapper< deriv_type > wrapped_deriv_type;
+ typedef Time time_type;
+ typedef Algebra algebra_type;
+ typedef Operations operations_type;
+ typedef Resizer resizer_type;
+ typedef stepper_tag stepper_category;
+
+ typedef adams_moulton< Steps , State , Value , Deriv , Time , Algebra , Operations , Resizer > stepper_type;
+
+ static const size_t steps = Steps;
+
+ typedef unsigned short order_type;
+ static const order_type order_value = steps + 1;
+
+ typedef detail::rotating_buffer< wrapped_deriv_type , steps > step_storage_type;
+
+ adams_moulton( )
+ : m_coefficients() , m_dxdt() , m_resizer() ,
+ m_algebra_instance() , m_algebra( m_algebra_instance )
+ { }
+
+ adams_moulton( algebra_type &algebra )
+ : m_coefficients() , m_dxdt() , m_resizer() ,
+ m_algebra_instance() , m_algebra( algebra )
+ { }
+
+ adams_moulton& operator=( const adams_moulton &stepper )
+ {
+ m_dxdt = stepper.m_dxdt;
+ m_resizer = stepper.m_resizer;
+ m_algebra = stepper.m_algebra;
+ return *this;
+ }
+
+ order_type order( void ) const { return order_value; }
+
+
+ /*
+ * Version 1 : do_step( system , x , t , dt , buf );
+ *
+ * solves the forwarding problem
+ */
+ template< class System , class StateInOut , class StateIn , class ABBuf >
+ void do_step( System system , StateInOut &x , StateIn const & pred , time_type t , time_type dt , const ABBuf &buf )
+ {
+ do_step( system , x , pred , t , x , dt , buf );
+ }
+
+ template< class System , class StateInOut , class StateIn , class ABBuf >
+ void do_step( System system , const StateInOut &x , StateIn const & pred , time_type t , time_type dt , const ABBuf &buf )
+ {
+ do_step( system , x , pred , t , x , dt , buf );
+ }
+
+
+
+ /*
+ * Version 2 : do_step( system , in , t , out , dt , buf );
+ *
+ * solves the forwarding problem
+ */
+ template< class System , class StateIn , class PredIn , class StateOut , class ABBuf >
+ void do_step( System system , const StateIn &in , const PredIn &pred , time_type t , StateOut &out , time_type dt , const ABBuf &buf )
+ {
+ do_step_impl( system , in , pred , t , out , dt , buf );
+ }
+
+ template< class System , class StateIn , class PredIn , class StateOut , class ABBuf >
+ void do_step( System system , const StateIn &in , const PredIn &pred , time_type t , const StateOut &out , time_type dt , const ABBuf &buf )
+ {
+ do_step_impl( system , in , pred , t , out , dt , buf );
+ }
+
+
+
+ template< class StateType >
+ void adjust_size( const StateType &x )
+ {
+ resize_impl( x );
+ }
+
+ algebra_type& algebra()
+ { return m_algebra; }
+
+ const algebra_type& algebra() const
+ { return m_algebra; }
+
+
+private:
+
+
+ template< class System , class StateIn , class PredIn , class StateOut , class ABBuf >
+ void do_step_impl( System system , const StateIn &in , const PredIn &pred , time_type t , StateOut &out , time_type dt , const ABBuf &buf )
+ {
+ typename odeint::unwrap_reference< System >::type &sys = system;
+ m_resizer.adjust_size( in , detail::bind( &stepper_type::template resize_impl<StateIn> , detail::ref( *this ) , detail::_1 ) );
+ sys( pred , m_dxdt.m_v , t );
+ detail::adams_moulton_call_algebra< steps , algebra_type , operations_type >()( m_algebra , in , out , m_dxdt.m_v , buf , m_coefficients , dt );
+ }
+
+
+ template< class StateIn >
+ bool resize_impl( const StateIn &x )
+ {
+ return adjust_size_by_resizeability( m_dxdt , x , typename is_resizeable<deriv_type>::type() );
+ }
+
+
+ const detail::adams_moulton_coefficients< value_type , steps > m_coefficients;
+ wrapped_deriv_type m_dxdt;
+ resizer_type m_resizer;
+
+protected:
+
+ algebra_type m_algebra_instance;
+ algebra_type &m_algebra;
+};
+
+
+
+
+} // odeint
+} // numeric
+} // boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_ADAMS_MOULTON_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/base/algebra_stepper_base.hpp b/include/boost/numeric/odeint/stepper/base/algebra_stepper_base.hpp
new file mode 100644
index 0000000..3b014f8
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/base/algebra_stepper_base.hpp
@@ -0,0 +1,91 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/base/algebra_stepper_base.hpp
+
+ [begin_description]
+ Base class for all steppers with an algebra and operations.
+ [end_description]
+
+ Copyright 2012-2013 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_BASE_ALGEBRA_STEPPER_BASE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_BASE_ALGEBRA_STEPPER_BASE_HPP_INCLUDED
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template< class Algebra , class Operations >
+class algebra_stepper_base
+{
+public:
+
+ typedef Algebra algebra_type;
+ typedef Operations operations_type;
+
+ algebra_stepper_base( const algebra_type &algebra = algebra_type() )
+ : m_algebra( algebra ) { }
+
+ algebra_type& algebra()
+ {
+ return m_algebra;
+ }
+
+ const algebra_type& algebra() const
+ {
+ return m_algebra;
+ }
+
+protected:
+
+ algebra_type m_algebra;
+};
+
+
+/******* DOXYGEN *******/
+
+/**
+ * \class algebra_stepper_base
+ * \brief Base class for all steppers with algebra and operations.
+ *
+ * This class serves a base class for all steppers with algebra and operations. It holds the
+ * algebra and provides access to the algebra. The operations are not instantiated, since they are
+ * static classes inside the operations class.
+ *
+ * \tparam Algebra The type of the algebra. Must fulfill the Algebra Concept, at least partially to work
+ * with the stepper.
+ * \tparam Operations The type of the operations. Must fulfill the Operations Concept, at least partially
+ * to work with the stepper.
+ */
+
+ /**
+ * \fn algebra_stepper_base::algebra_stepper_base( const algebra_type &algebra = algebra_type() )
+ * \brief Constructs a algebra_stepper_base and creates the algebra. This constructor can be used as a default
+ * constructor if the algebra has a default constructor.
+ * \param algebra The algebra_stepper_base stores and uses a copy of algebra.
+ */
+
+ /**
+ * \fn algebra_type& algebra_stepper_base::algebra()
+ * \return A reference to the algebra which is held by this class.
+ */
+
+ /**
+ * \fn const algebra_type& algebra_stepper_base::algebra() const
+ * \return A const reference to the algebra which is held by this class.
+ */
+
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_BASE_ALGEBRA_STEPPER_BASE_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/base/explicit_error_stepper_base.hpp b/include/boost/numeric/odeint/stepper/base/explicit_error_stepper_base.hpp
new file mode 100644
index 0000000..08009dc
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/base/explicit_error_stepper_base.hpp
@@ -0,0 +1,588 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/base/explicit_error_stepper_base.hpp
+
+ [begin_description]
+ Base class for all explicit Runge Kutta stepper which are also error steppers.
+ [end_description]
+
+ Copyright 2010-2013 Karsten Ahnert
+ Copyright 2010-2012 Mario Mulansky
+ Copyright 2012 Christoph Koke
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_BASE_EXPLICIT_ERROR_STEPPER_BASE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_BASE_EXPLICIT_ERROR_STEPPER_BASE_HPP_INCLUDED
+
+#include <boost/utility/enable_if.hpp>
+#include <boost/type_traits/is_same.hpp>
+
+
+#include <boost/numeric/odeint/util/bind.hpp>
+#include <boost/numeric/odeint/util/unwrap_reference.hpp>
+#include <boost/numeric/odeint/util/state_wrapper.hpp>
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resizer.hpp>
+
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+
+#include <boost/numeric/odeint/stepper/base/algebra_stepper_base.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+/*
+ * base class for explicit stepper and error steppers
+ * models the stepper AND the error stepper concept
+ *
+ * this class provides the following do_step variants:
+ * do_step( sys , x , t , dt )
+ * do_step( sys , x , dxdt , t , dt )
+ * do_step( sys , in , t , out , dt )
+ * do_step( sys , in , dxdt , t , out , dt )
+ * do_step( sys , x , t , dt , xerr )
+ * do_step( sys , x , dxdt , t , dt , xerr )
+ * do_step( sys , in , t , out , dt , xerr )
+ * do_step( sys , in , dxdt , t , out , dt , xerr )
+ */
+template<
+class Stepper ,
+unsigned short Order ,
+unsigned short StepperOrder ,
+unsigned short ErrorOrder ,
+class State ,
+class Value ,
+class Deriv ,
+class Time ,
+class Algebra ,
+class Operations ,
+class Resizer
+>
+class explicit_error_stepper_base : public algebra_stepper_base< Algebra , Operations >
+{
+public:
+
+ typedef algebra_stepper_base< Algebra , Operations > algebra_stepper_base_type;
+ typedef typename algebra_stepper_base_type::algebra_type algebra_type;
+
+
+ typedef State state_type;
+ typedef Value value_type;
+ typedef Deriv deriv_type;
+ typedef Time time_type;
+ typedef Resizer resizer_type;
+ typedef Stepper stepper_type;
+ typedef explicit_error_stepper_tag stepper_category;
+ #ifndef DOXYGEN_SKIP
+ typedef state_wrapper< state_type > wrapped_state_type;
+ typedef state_wrapper< deriv_type > wrapped_deriv_type;
+ typedef explicit_error_stepper_base< Stepper , Order , StepperOrder , ErrorOrder ,
+ State , Value , Deriv , Time , Algebra , Operations , Resizer > internal_stepper_base_type;
+ #endif
+
+ typedef unsigned short order_type;
+ static const order_type order_value = Order;
+ static const order_type stepper_order_value = StepperOrder;
+ static const order_type error_order_value = ErrorOrder;
+
+
+ explicit_error_stepper_base( const algebra_type &algebra = algebra_type() )
+ : algebra_stepper_base_type( algebra )
+ { }
+
+ order_type order( void ) const
+ {
+ return order_value;
+ }
+
+ order_type stepper_order( void ) const
+ {
+ return stepper_order_value;
+ }
+
+ order_type error_order( void ) const
+ {
+ return error_order_value;
+ }
+
+
+
+ /*
+ * Version 1 : do_step( sys , x , t , dt )
+ *
+ * the two overloads are needed in order to solve the forwarding problem
+ */
+ template< class System , class StateInOut >
+ void do_step( System system , StateInOut &x , time_type t , time_type dt )
+ {
+ do_step_v1( system , x , t , dt );
+ }
+
+ /**
+ * \brief Second version to solve the forwarding problem, can be called with Boost.Range as StateInOut.
+ */
+ template< class System , class StateInOut >
+ void do_step( System system , const StateInOut &x , time_type t , time_type dt )
+ {
+ do_step_v1( system , x , t , dt );
+ }
+
+
+
+ /*
+ * Version 2 : do_step( sys , x , dxdt , t , dt )
+ *
+ * this version does not solve the forwarding problem, boost.range can not be used
+ *
+ * the disable is needed to avoid ambiguous overloads if state_type = time_type
+ */
+ template< class System , class StateInOut , class DerivIn >
+ typename boost::disable_if< boost::is_same< DerivIn , time_type > , void >::type
+ do_step( System system , StateInOut &x , const DerivIn &dxdt , time_type t , time_type dt )
+ {
+ this->stepper().do_step_impl( system , x , dxdt , t , x , dt );
+ }
+
+
+ /*
+ * named Version 2: do_step_dxdt_impl( sys , in , dxdt , t , dt )
+ *
+ * this version is needed when this stepper is used for initializing
+ * multistep stepper like adams-bashforth. Hence we provide an explicitely
+ * named version that is not disabled. Meant for internal use only.
+ */
+ template < class System, class StateInOut, class DerivIn >
+ void do_step_dxdt_impl( System system, StateInOut &x, const DerivIn &dxdt,
+ time_type t, time_type dt )
+ {
+ this->stepper().do_step_impl( system , x , dxdt , t , x , dt );
+ }
+
+
+
+ /*
+ * Version 3 : do_step( sys , in , t , out , dt )
+ *
+ * this version does not solve the forwarding problem, boost.range can not be used
+ *
+ * the disable is needed to avoid ambiguous overloads if state_type = time_type
+ */
+ template< class System , class StateIn , class StateOut >
+ typename boost::disable_if< boost::is_same< StateIn , time_type > , void >::type
+ do_step( System system , const StateIn &in , time_type t , StateOut &out , time_type dt )
+ {
+ typename odeint::unwrap_reference< System >::type &sys = system;
+ m_resizer.adjust_size( in , detail::bind( &internal_stepper_base_type::template resize_impl<StateIn> , detail::ref( *this ) , detail::_1 ) );
+ sys( in , m_dxdt.m_v ,t );
+ this->stepper().do_step_impl( system , in , m_dxdt.m_v , t , out , dt );
+ }
+
+ /*
+ * Version 4 :do_step( sys , in , dxdt , t , out , dt )
+ *
+ * this version does not solve the forwarding problem, boost.range can not be used
+ *
+ * the disable is needed to avoid ambiguous overloads if state_type = time_type
+ */
+ template< class System , class StateIn , class DerivIn , class StateOut >
+ typename boost::disable_if< boost::is_same< DerivIn , time_type > , void >::type
+ do_step( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt )
+ {
+ this->stepper().do_step_impl( system , in , dxdt , t , out , dt );
+ }
+
+ /*
+ * named Version 4: do_step_dxdt_impl( sys , in , dxdt , t , out, dt )
+ *
+ * this version is needed when this stepper is used for initializing
+ * multistep stepper like adams-bashforth. Hence we provide an explicitely
+ * named version that is not disabled. Meant for internal use only.
+ */
+ template < class System, class StateIn, class DerivIn, class StateOut >
+ void do_step_dxdt_impl( System system, const StateIn &in,
+ const DerivIn &dxdt, time_type t, StateOut &out,
+ time_type dt )
+ {
+ this->stepper().do_step_impl( system , in , dxdt , t , out , dt );
+ }
+
+ /*
+ * Version 5 :do_step( sys , x , t , dt , xerr )
+ *
+ * the two overloads are needed in order to solve the forwarding problem
+ */
+ template< class System , class StateInOut , class Err >
+ void do_step( System system , StateInOut &x , time_type t , time_type dt , Err &xerr )
+ {
+ do_step_v5( system , x , t , dt , xerr );
+ }
+
+ /**
+ * \brief Second version to solve the forwarding problem, can be called with Boost.Range as StateInOut.
+ */
+ template< class System , class StateInOut , class Err >
+ void do_step( System system , const StateInOut &x , time_type t , time_type dt , Err &xerr )
+ {
+ do_step_v5( system , x , t , dt , xerr );
+ }
+
+
+ /*
+ * Version 6 :do_step( sys , x , dxdt , t , dt , xerr )
+ *
+ * this version does not solve the forwarding problem, boost.range can not be used
+ *
+ * the disable is needed to avoid ambiguous overloads if state_type = time_type
+ */
+ template< class System , class StateInOut , class DerivIn , class Err >
+ typename boost::disable_if< boost::is_same< DerivIn , time_type > , void >::type
+ do_step( System system , StateInOut &x , const DerivIn &dxdt , time_type t , time_type dt , Err &xerr )
+ {
+ this->stepper().do_step_impl( system , x , dxdt , t , x , dt , xerr );
+ }
+
+
+ /*
+ * Version 7 : do_step( sys , in , t , out , dt , xerr )
+ *
+ * this version does not solve the forwarding problem, boost.range can not be used
+ */
+ template< class System , class StateIn , class StateOut , class Err >
+ void do_step( System system , const StateIn &in , time_type t , StateOut &out , time_type dt , Err &xerr )
+ {
+ typename odeint::unwrap_reference< System >::type &sys = system;
+ m_resizer.adjust_size( in , detail::bind( &internal_stepper_base_type::template resize_impl<StateIn> , detail::ref( *this ) , detail::_1 ) );
+ sys( in , m_dxdt.m_v ,t );
+ this->stepper().do_step_impl( system , in , m_dxdt.m_v , t , out , dt , xerr );
+ }
+
+
+ /*
+ * Version 8 : do_step( sys , in , dxdt , t , out , dt , xerr )
+ *
+ * this version does not solve the forwarding problem, boost.range can not be used
+ */
+ template< class System , class StateIn , class DerivIn , class StateOut , class Err >
+ void do_step( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt , Err &xerr )
+ {
+ this->stepper().do_step_impl( system , in , dxdt , t , out , dt , xerr );
+ }
+
+ template< class StateIn >
+ void adjust_size( const StateIn &x )
+ {
+ resize_impl( x );
+ }
+
+
+
+private:
+
+ template< class System , class StateInOut >
+ void do_step_v1( System system , StateInOut &x , time_type t , time_type dt )
+ {
+ typename odeint::unwrap_reference< System >::type &sys = system;
+ m_resizer.adjust_size( x , detail::bind( &internal_stepper_base_type::template resize_impl<StateInOut> , detail::ref( *this ) , detail::_1 ) );
+ sys( x , m_dxdt.m_v , t );
+ this->stepper().do_step_impl( system , x , m_dxdt.m_v , t , x , dt );
+ }
+
+ template< class System , class StateInOut , class Err >
+ void do_step_v5( System system , StateInOut &x , time_type t , time_type dt , Err &xerr )
+ {
+ typename odeint::unwrap_reference< System >::type &sys = system;
+ m_resizer.adjust_size( x , detail::bind( &internal_stepper_base_type::template resize_impl<StateInOut> , detail::ref( *this ) , detail::_1 ) );
+ sys( x , m_dxdt.m_v ,t );
+ this->stepper().do_step_impl( system , x , m_dxdt.m_v , t , x , dt , xerr );
+ }
+
+ template< class StateIn >
+ bool resize_impl( const StateIn &x )
+ {
+ return adjust_size_by_resizeability( m_dxdt , x , typename is_resizeable<deriv_type>::type() );
+ }
+
+ stepper_type& stepper( void )
+ {
+ return *static_cast< stepper_type* >( this );
+ }
+
+ const stepper_type& stepper( void ) const
+ {
+ return *static_cast< const stepper_type* >( this );
+ }
+
+
+ resizer_type m_resizer;
+
+protected:
+
+ wrapped_deriv_type m_dxdt;
+};
+
+
+
+
+/******** DOXYGEN *******/
+
+/**
+ * \class explicit_error_stepper_base
+ * \brief Base class for explicit steppers with error estimation. This class can used with
+ * controlled steppers for step size control.
+ *
+ * This class serves as the base class for all explicit steppers with algebra and operations. In contrast to
+ * explicit_stepper_base it also estimates the error and can be used in a controlled stepper to provide
+ * step size control.
+ *
+ * \note This stepper provides `do_step` methods with and without error estimation. It has therefore three orders,
+ * one for the order of a step if the error is not estimated. The other two orders are the orders of the step and
+ * the error step if the error estimation is performed.
+ *
+ * explicit_error_stepper_base is used as the interface in a CRTP (currently recurring template
+ * pattern). In order to work correctly the parent class needs to have a method
+ * `do_step_impl( system , in , dxdt_in , t , out , dt , xerr )`.
+ * explicit_error_stepper_base derives from algebra_stepper_base.
+ *
+ * explicit_error_stepper_base provides several overloaded `do_step` methods, see the list below. Only two of them
+ * are needed to fulfill the Error Stepper concept. The other ones are for convenience and for performance. Some
+ * of them simply update the state out-of-place, while other expect that the first derivative at `t` is passed to the
+ * stepper.
+ *
+ * - `do_step( sys , x , t , dt )` - The classical `do_step` method needed to fulfill the Error Stepper concept. The
+ * state is updated in-place. A type modelling a Boost.Range can be used for x.
+ * - `do_step( sys , x , dxdt , t , dt )` - This method updates the state in-place, but the derivative at the point `t`
+ * must be explicitly passed in `dxdt`.
+ * - `do_step( sys , in , t , out , dt )` - This method updates the state out-of-place, hence the result of the step
+ * is stored in `out`.
+ * - `do_step( sys , in , dxdt , t , out , dt )` - This method update the state out-of-place and expects that the
+ * derivative at the point `t` is explicitly passed in `dxdt`. It is a combination of the two `do_step` methods
+ * above.
+ * - `do_step( sys , x , t , dt , xerr )` - This `do_step` method is needed to fulfill the Error Stepper concept. The
+ * state is updated in-place and an error estimate is calculated. A type modelling a Boost.Range can be used for x.
+ * - `do_step( sys , x , dxdt , t , dt , xerr )` - This method updates the state in-place, but the derivative at the
+ * point `t` must be passed in `dxdt`. An error estimate is calculated.
+ * - `do_step( sys , in , t , out , dt , xerr )` - This method updates the state out-of-place and estimates the error
+ * during the step.
+ * - `do_step( sys , in , dxdt , t , out , dt , xerr )` - This methods updates the state out-of-place and estimates
+ * the error during the step. Furthermore, the derivative at `t` must be passed in `dxdt`.
+ *
+ * \note The system is always passed as value, which might result in poor performance if it contains data. In this
+ * case it can be used with `boost::ref` or `std::ref`, for example `stepper.do_step( boost::ref( sys ) , x , t , dt );`
+ *
+ * \note The time `t` is not advanced by the stepper. This has to done manually, or by the appropriate `integrate`
+ * routines or `iterator`s.
+ *
+ * \tparam Stepper The stepper on which this class should work. It is used via CRTP, hence explicit_stepper_base
+ * provides the interface for the Stepper.
+ * \tparam Order The order of a stepper if the stepper is used without error estimation.
+ * \tparam StepperOrder The order of a step if the stepper is used with error estimation. Usually Order and StepperOrder have
+ * the same value.
+ * \tparam ErrorOrder The order of the error step if the stepper is used with error estimation.
+ * \tparam State The state type for the stepper.
+ * \tparam Value The value type for the stepper. This should be a floating point type, like float,
+ * double, or a multiprecision type. It must not necessary be the value_type of the State. For example
+ * the State can be a `vector< complex< double > >` in this case the Value must be double.
+ * The default value is double.
+ * \tparam Deriv The type representing time derivatives of the state type. It is usually the same type as the
+ * state type, only if used with Boost.Units both types differ.
+ * \tparam Time The type representing the time. Usually the same type as the value type. When Boost.Units is
+ * used, this type has usually a unit.
+ * \tparam Algebra The algebra type which must fulfill the Algebra Concept.
+ * \tparam Operations The type for the operations which must fulfill the Operations Concept.
+ * \tparam Resizer The resizer policy class.
+ */
+
+
+ /**
+ * \fn explicit_error_stepper_base::explicit_error_stepper_base( const algebra_type &algebra = algebra_type() )
+ *
+ * \brief Constructs a explicit_error_stepper_base class. This constructor can be used as a default
+ * constructor if the algebra has a default constructor.
+ * \param algebra A copy of algebra is made and stored inside explicit_stepper_base.
+ */
+
+ /**
+ * \fn explicit_error_stepper_base::order( void ) const
+ * \return Returns the order of the stepper if it used without error estimation.
+ */
+
+ /**
+ * \fn explicit_error_stepper_base::stepper_order( void ) const
+ * \return Returns the order of a step if the stepper is used without error estimation.
+ */
+
+ /**
+ * \fn explicit_error_stepper_base::error_order( void ) const
+ * \return Returns the order of an error step if the stepper is used without error estimation.
+ */
+
+ /**
+ * \fn explicit_error_stepper_base::do_step( System system , StateInOut &x , time_type t , time_type dt )
+ * \brief This method performs one step. It transforms the result in-place.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the
+ * Simple System concept.
+ * \param x The state of the ODE which should be solved. After calling do_step the result is updated in x.
+ * \param t The value of the time, at which the step should be performed.
+ * \param dt The step size.
+ */
+
+ /**
+ * \fn explicit_error_stepper_base::do_step( System system , StateInOut &x , const DerivIn &dxdt , time_type t , time_type dt )
+ * \brief The method performs one step with the stepper passed by Stepper. Additionally to the other method
+ * the derivative of x is also passed to this method. It is supposed to be used in the following way:
+ *
+ * \code
+ * sys( x , dxdt , t );
+ * stepper.do_step( sys , x , dxdt , t , dt );
+ * \endcode
+ *
+ * The result is updated in place in x. This method is disabled if Time and Deriv are of the same type. In this
+ * case the method could not be distinguished from other `do_step` versions.
+ *
+ * \note This method does not solve the forwarding problem.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param x The state of the ODE which should be solved. After calling do_step the result is updated in x.
+ * \param dxdt The derivative of x at t.
+ * \param t The value of the time, at which the step should be performed.
+ * \param dt The step size.
+ */
+
+ /**
+ * \fn explicit_error_stepper_base::do_step( System system , const StateIn &in , time_type t , StateOut &out , time_type dt )
+ * \brief The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place.
+ * This method is disabled if StateIn and Time are the same type. In this case the method can not be distinguished from
+ * other `do_step` variants.
+ * \note This method does not solve the forwarding problem.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param in The state of the ODE which should be solved. in is not modified in this method
+ * \param t The value of the time, at which the step should be performed.
+ * \param out The result of the step is written in out.
+ * \param dt The step size.
+ */
+
+
+ /**
+ * \fn explicit_error_stepper_base::do_step( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt )
+ * \brief The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place.
+ * Furthermore, the derivative of x at t is passed to the stepper. It is supposed to be used in the following way:
+ *
+ * \code
+ * sys( in , dxdt , t );
+ * stepper.do_step( sys , in , dxdt , t , out , dt );
+ * \endcode
+ *
+ * This method is disabled if DerivIn and Time are of same type.
+ *
+ * \note This method does not solve the forwarding problem.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param in The state of the ODE which should be solved. in is not modified in this method
+ * \param dxdt The derivative of x at t.
+ * \param t The value of the time, at which the step should be performed.
+ * \param out The result of the step is written in out.
+ * \param dt The step size.
+ */
+
+ /**
+ * \fn explicit_error_stepper_base::do_step( System system , StateInOut &x , time_type t , time_type dt , Err &xerr )
+ * \brief The method performs one step with the stepper passed by Stepper and estimates the error. The state of the ODE
+ * is updated in-place.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param x The state of the ODE which should be solved. x is updated by this method.
+ * \param t The value of the time, at which the step should be performed.
+ * \param dt The step size.
+ * \param xerr The estimation of the error is stored in xerr.
+ */
+
+ /**
+ * \fn explicit_error_stepper_base::do_step( System system , StateInOut &x , const DerivIn &dxdt , time_type t , time_type dt , Err &xerr )
+ * \brief The method performs one step with the stepper passed by Stepper. Additionally to the other method
+ * the derivative of x is also passed to this method. It is supposed to be used in the following way:
+ *
+ * \code
+ * sys( x , dxdt , t );
+ * stepper.do_step( sys , x , dxdt , t , dt , xerr );
+ * \endcode
+ *
+ * The result is updated in place in x. This method is disabled if Time and DerivIn are of the same type. In this
+ * case the method could not be distinguished from other `do_step` versions.
+ *
+ * \note This method does not solve the forwarding problem.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param x The state of the ODE which should be solved. After calling do_step the result is updated in x.
+ * \param dxdt The derivative of x at t.
+ * \param t The value of the time, at which the step should be performed.
+ * \param dt The step size.
+ * \param xerr The error estimate is stored in xerr.
+ */
+
+ /**
+ * \fn explicit_error_stepper_base::do_step( System system , const StateIn &in , time_type t , StateOut &out , time_type dt , Err &xerr )
+ * \brief The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place.
+ * Furthermore, the error is estimated.
+ *
+ * \note This method does not solve the forwarding problem.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param in The state of the ODE which should be solved. in is not modified in this method
+ * \param t The value of the time, at which the step should be performed.
+ * \param out The result of the step is written in out.
+ * \param dt The step size.
+ * \param xerr The error estimate.
+ */
+
+
+ /**
+ * \fn explicit_error_stepper_base::do_step( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt , Err &xerr )
+ * \brief The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place.
+ * Furthermore, the derivative of x at t is passed to the stepper and the error is estimated. It is supposed to be used in the following way:
+ *
+ * \code
+ * sys( in , dxdt , t );
+ * stepper.do_step( sys , in , dxdt , t , out , dt );
+ * \endcode
+ *
+ * This method is disabled if DerivIn and Time are of same type.
+ *
+ * \note This method does not solve the forwarding problem.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param in The state of the ODE which should be solved. in is not modified in this method
+ * \param dxdt The derivative of x at t.
+ * \param t The value of the time, at which the step should be performed.
+ * \param out The result of the step is written in out.
+ * \param dt The step size.
+ * \param xerr The error estimate.
+ */
+
+
+ /**
+ * \fn explicit_error_stepper_base::adjust_size( const StateIn &x )
+ * \brief Adjust the size of all temporaries in the stepper manually.
+ * \param x A state from which the size of the temporaries to be resized is deduced.
+ */
+
+} // odeint
+} // numeric
+} // boost
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_BASE_EXPLICIT_ERROR_STEPPER_BASE_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/base/explicit_error_stepper_fsal_base.hpp b/include/boost/numeric/odeint/stepper/base/explicit_error_stepper_fsal_base.hpp
new file mode 100644
index 0000000..b1d751a
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/base/explicit_error_stepper_fsal_base.hpp
@@ -0,0 +1,677 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/base/explicit_error_stepper_fsal_base.hpp
+
+ [begin_description]
+ Base class for all explicit first-same-as-last Runge Kutta steppers.
+ [end_description]
+
+ Copyright 2010-2013 Karsten Ahnert
+ Copyright 2010-2012 Mario Mulansky
+ Copyright 2012 Christoph Koke
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_BASE_EXPLICIT_ERROR_STEPPER_FSAL_BASE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_BASE_EXPLICIT_ERROR_STEPPER_FSAL_BASE_HPP_INCLUDED
+
+#include <boost/utility/enable_if.hpp>
+#include <boost/type_traits/is_same.hpp>
+
+
+#include <boost/numeric/odeint/util/bind.hpp>
+#include <boost/numeric/odeint/util/unwrap_reference.hpp>
+#include <boost/numeric/odeint/util/state_wrapper.hpp>
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resizer.hpp>
+#include <boost/numeric/odeint/util/copy.hpp>
+
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+
+#include <boost/numeric/odeint/stepper/base/algebra_stepper_base.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+/*
+ * base class for explicit stepper and error steppers with the fsal property
+ * models the stepper AND the error stepper fsal concept
+ *
+ * this class provides the following do_step overloads
+ * do_step( sys , x , t , dt )
+ * do_step( sys , x , dxdt , t , dt )
+ * do_step( sys , in , t , out , dt )
+ * do_step( sys , in , dxdt_in , t , out , dxdt_out , dt )
+ * do_step( sys , x , t , dt , xerr )
+ * do_step( sys , x , dxdt , t , dt , xerr )
+ * do_step( sys , in , t , out , dt , xerr )
+ * do_step( sys , in , dxdt_in , t , out , dxdt_out , dt , xerr )
+ */
+template<
+class Stepper ,
+unsigned short Order ,
+unsigned short StepperOrder ,
+unsigned short ErrorOrder ,
+class State ,
+class Value ,
+class Deriv ,
+class Time ,
+class Algebra ,
+class Operations ,
+class Resizer
+>
+class explicit_error_stepper_fsal_base : public algebra_stepper_base< Algebra , Operations >
+{
+public:
+
+ typedef algebra_stepper_base< Algebra , Operations > algebra_stepper_base_type;
+ typedef typename algebra_stepper_base_type::algebra_type algebra_type;
+
+ typedef State state_type;
+ typedef Value value_type;
+ typedef Deriv deriv_type;
+ typedef Time time_type;
+ typedef Resizer resizer_type;
+ typedef Stepper stepper_type;
+ typedef explicit_error_stepper_fsal_tag stepper_category;
+
+ #ifndef DOXYGEN_SKIP
+ typedef state_wrapper< state_type > wrapped_state_type;
+ typedef state_wrapper< deriv_type > wrapped_deriv_type;
+ typedef explicit_error_stepper_fsal_base< Stepper , Order , StepperOrder , ErrorOrder ,
+ State , Value , Deriv , Time , Algebra , Operations , Resizer > internal_stepper_base_type;
+ #endif
+
+
+ typedef unsigned short order_type;
+ static const order_type order_value = Order;
+ static const order_type stepper_order_value = StepperOrder;
+ static const order_type error_order_value = ErrorOrder;
+
+ explicit_error_stepper_fsal_base( const algebra_type &algebra = algebra_type() )
+ : algebra_stepper_base_type( algebra ) , m_first_call( true )
+ { }
+
+ order_type order( void ) const
+ {
+ return order_value;
+ }
+
+ order_type stepper_order( void ) const
+ {
+ return stepper_order_value;
+ }
+
+ order_type error_order( void ) const
+ {
+ return error_order_value;
+ }
+
+
+ /*
+ * version 1 : do_step( sys , x , t , dt )
+ *
+ * the two overloads are needed in order to solve the forwarding problem
+ */
+ template< class System , class StateInOut >
+ void do_step( System system , StateInOut &x , time_type t , time_type dt )
+ {
+ do_step_v1( system , x , t , dt );
+ }
+
+ /**
+ * \brief Second version to solve the forwarding problem, can be called with Boost.Range as StateInOut.
+ */
+ template< class System , class StateInOut >
+ void do_step( System system , const StateInOut &x , time_type t , time_type dt )
+ {
+ do_step_v1( system , x , t , dt );
+ }
+
+
+ /*
+ * version 2 : do_step( sys , x , dxdt , t , dt )
+ *
+ * this version does not solve the forwarding problem, boost.range can not be used
+ *
+ * the disable is needed to avoid ambiguous overloads if state_type = time_type
+ */
+ template< class System , class StateInOut , class DerivInOut >
+ typename boost::disable_if< boost::is_same< StateInOut , time_type > , void >::type
+ do_step( System system , StateInOut &x , DerivInOut &dxdt , time_type t , time_type dt )
+ {
+ m_first_call = true;
+ this->stepper().do_step_impl( system , x , dxdt , t , x , dxdt , dt );
+ }
+
+
+ /*
+ * named Version 2: do_step_dxdt_impl( sys , in , dxdt , t , dt )
+ *
+ * this version is needed when this stepper is used for initializing
+ * multistep stepper like adams-bashforth. Hence we provide an explicitely
+ * named version that is not disabled. Meant for internal use only.
+ */
+ template< class System , class StateInOut , class DerivInOut >
+ void do_step_dxdt_impl( System system , StateInOut &x , DerivInOut &dxdt , time_type t , time_type dt )
+ {
+ m_first_call = true;
+ this->stepper().do_step_impl( system , x , dxdt , t , x , dxdt , dt );
+ }
+
+ /*
+ * version 3 : do_step( sys , in , t , out , dt )
+ *
+ * this version does not solve the forwarding problem, boost.range can not
+ * be used.
+ *
+ * the disable is needed to avoid ambiguous overloads if
+ * state_type = time_type
+ */
+ template< class System , class StateIn , class StateOut >
+ typename boost::disable_if< boost::is_same< StateIn , time_type > , void >::type
+ do_step( System system , const StateIn &in , time_type t , StateOut &out , time_type dt )
+ {
+ if( m_resizer.adjust_size( in , detail::bind( &internal_stepper_base_type::template resize_impl< StateIn > , detail::ref( *this ) , detail::_1 ) ) || m_first_call )
+ {
+ initialize( system , in , t );
+ }
+ this->stepper().do_step_impl( system , in , m_dxdt.m_v , t , out , m_dxdt.m_v , dt );
+ }
+
+
+ /*
+ * version 4 : do_step( sys , in , dxdt_in , t , out , dxdt_out , dt )
+ *
+ * this version does not solve the forwarding problem, boost.range can not be used
+ */
+ template< class System, class StateIn, class DerivIn, class StateOut,
+ class DerivOut >
+ void do_step( System system, const StateIn &in, const DerivIn &dxdt_in,
+ time_type t, StateOut &out, DerivOut &dxdt_out, time_type dt )
+ {
+ m_first_call = true;
+ this->stepper().do_step_impl( system, in, dxdt_in, t, out, dxdt_out,
+ dt );
+ }
+
+
+
+
+
+ /*
+ * version 5 : do_step( sys , x , t , dt , xerr )
+ *
+ * the two overloads are needed in order to solve the forwarding problem
+ */
+ template< class System , class StateInOut , class Err >
+ void do_step( System system , StateInOut &x , time_type t , time_type dt , Err &xerr )
+ {
+ do_step_v5( system , x , t , dt , xerr );
+ }
+
+ /**
+ * \brief Second version to solve the forwarding problem, can be called with Boost.Range as StateInOut.
+ */
+ template< class System , class StateInOut , class Err >
+ void do_step( System system , const StateInOut &x , time_type t , time_type dt , Err &xerr )
+ {
+ do_step_v5( system , x , t , dt , xerr );
+ }
+
+
+ /*
+ * version 6 : do_step( sys , x , dxdt , t , dt , xerr )
+ *
+ * this version does not solve the forwarding problem, boost.range can not be used
+ *
+ * the disable is needed to avoid ambiguous overloads if state_type = time_type
+ */
+ template< class System , class StateInOut , class DerivInOut , class Err >
+ typename boost::disable_if< boost::is_same< StateInOut , time_type > , void >::type
+ do_step( System system , StateInOut &x , DerivInOut &dxdt , time_type t , time_type dt , Err &xerr )
+ {
+ m_first_call = true;
+ this->stepper().do_step_impl( system , x , dxdt , t , x , dxdt , dt , xerr );
+ }
+
+
+
+
+ /*
+ * version 7 : do_step( sys , in , t , out , dt , xerr )
+ *
+ * this version does not solve the forwarding problem, boost.range can not be used
+ */
+ template< class System , class StateIn , class StateOut , class Err >
+ void do_step( System system , const StateIn &in , time_type t , StateOut &out , time_type dt , Err &xerr )
+ {
+ if( m_resizer.adjust_size( in , detail::bind( &internal_stepper_base_type::template resize_impl< StateIn > , detail::ref( *this ) , detail::_1 ) ) || m_first_call )
+ {
+ initialize( system , in , t );
+ }
+ this->stepper().do_step_impl( system , in , m_dxdt.m_v , t , out , m_dxdt.m_v , dt , xerr );
+ }
+
+
+ /*
+ * version 8 : do_step( sys , in , dxdt_in , t , out , dxdt_out , dt , xerr )
+ *
+ * this version does not solve the forwarding problem, boost.range can not be used
+ */
+ template< class System , class StateIn , class DerivIn , class StateOut , class DerivOut , class Err >
+ void do_step( System system , const StateIn &in , const DerivIn &dxdt_in , time_type t ,
+ StateOut &out , DerivOut &dxdt_out , time_type dt , Err &xerr )
+ {
+ m_first_call = true;
+ this->stepper().do_step_impl( system , in , dxdt_in , t , out , dxdt_out , dt , xerr );
+ }
+
+ template< class StateIn >
+ void adjust_size( const StateIn &x )
+ {
+ resize_impl( x );
+ }
+
+ void reset( void )
+ {
+ m_first_call = true;
+ }
+
+ template< class DerivIn >
+ void initialize( const DerivIn &deriv )
+ {
+ boost::numeric::odeint::copy( deriv , m_dxdt.m_v );
+ m_first_call = false;
+ }
+
+ template< class System , class StateIn >
+ void initialize( System system , const StateIn &x , time_type t )
+ {
+ typename odeint::unwrap_reference< System >::type &sys = system;
+ sys( x , m_dxdt.m_v , t );
+ m_first_call = false;
+ }
+
+ bool is_initialized( void ) const
+ {
+ return ! m_first_call;
+ }
+
+
+
+private:
+
+ template< class System , class StateInOut >
+ void do_step_v1( System system , StateInOut &x , time_type t , time_type dt )
+ {
+ if( m_resizer.adjust_size( x , detail::bind( &internal_stepper_base_type::template resize_impl< StateInOut > , detail::ref( *this ) , detail::_1 ) ) || m_first_call )
+ {
+ initialize( system , x , t );
+ }
+ this->stepper().do_step_impl( system , x , m_dxdt.m_v , t , x , m_dxdt.m_v , dt );
+ }
+
+ template< class System , class StateInOut , class Err >
+ void do_step_v5( System system , StateInOut &x , time_type t , time_type dt , Err &xerr )
+ {
+ if( m_resizer.adjust_size( x , detail::bind( &internal_stepper_base_type::template resize_impl< StateInOut > , detail::ref( *this ) , detail::_1 ) ) || m_first_call )
+ {
+ initialize( system , x , t );
+ }
+ this->stepper().do_step_impl( system , x , m_dxdt.m_v , t , x , m_dxdt.m_v , dt , xerr );
+ }
+
+ template< class StateIn >
+ bool resize_impl( const StateIn &x )
+ {
+ return adjust_size_by_resizeability( m_dxdt , x , typename is_resizeable<deriv_type>::type() );
+ }
+
+
+ stepper_type& stepper( void )
+ {
+ return *static_cast< stepper_type* >( this );
+ }
+
+ const stepper_type& stepper( void ) const
+ {
+ return *static_cast< const stepper_type* >( this );
+ }
+
+
+ resizer_type m_resizer;
+ bool m_first_call;
+
+protected:
+
+
+ wrapped_deriv_type m_dxdt;
+};
+
+
+/******* DOXYGEN *******/
+
+/**
+ * \class explicit_error_stepper_fsal_base
+ * \brief Base class for explicit steppers with error estimation and stepper fulfilling the FSAL (first-same-as-last)
+ * property. This class can be used with controlled steppers for step size control.
+ *
+ * This class serves as the base class for all explicit steppers with algebra and operations and which fulfill the FSAL
+ * property. In contrast to explicit_stepper_base it also estimates the error and can be used in a controlled stepper
+ * to provide step size control.
+ *
+ * The FSAL property means that the derivative of the system at t+dt is already used in the current step going from
+ * t to t +dt. Therefore, some more do_steps method can be introduced and the controlled steppers can explicitly make use
+ * of this property.
+ *
+ * \note This stepper provides `do_step` methods with and without error estimation. It has therefore three orders,
+ * one for the order of a step if the error is not estimated. The other two orders are the orders of the step and
+ * the error step if the error estimation is performed.
+ *
+ * explicit_error_stepper_fsal_base is used as the interface in a CRTP (currently recurring template
+ * pattern). In order to work correctly the parent class needs to have a method
+ * `do_step_impl( system , in , dxdt_in , t , out , dxdt_out , dt , xerr )`.
+ * explicit_error_stepper_fsal_base derives from algebra_stepper_base.
+ *
+ * This class can have an intrinsic state depending on the explicit usage of the `do_step` method. This means that some
+ * `do_step` methods are expected to be called in order. For example the `do_step( sys , x , t , dt , xerr )` will keep track
+ * of the derivative of `x` which is the internal state. The first call of this method is recognized such that one
+ * does not explicitly initialize the internal state, so it is safe to use this method like
+ *
+ * \code
+ * stepper_type stepper;
+ * stepper.do_step( sys , x , t , dt , xerr );
+ * stepper.do_step( sys , x , t , dt , xerr );
+ * stepper.do_step( sys , x , t , dt , xerr );
+ * \endcode
+ *
+ * But it is unsafe to call this method with different system functions after each other. Do do so, one must initialize the
+ * internal state with the `initialize` method or reset the internal state with the `reset` method.
+ *
+ * explicit_error_stepper_fsal_base provides several overloaded `do_step` methods, see the list below. Only two of them are needed
+ * to fulfill the Error Stepper concept. The other ones are for convenience and for better performance. Some of them
+ * simply update the state out-of-place, while other expect that the first derivative at `t` is passed to the stepper.
+ *
+ * - `do_step( sys , x , t , dt )` - The classical `do_step` method needed to fulfill the Error Stepper concept. The
+ * state is updated in-place. A type modelling a Boost.Range can be used for x.
+ * - `do_step( sys , x , dxdt , t , dt )` - This method updates the state x and the derivative dxdt in-place. It is expected
+ * that dxdt has the value of the derivative of x at time t.
+ * - `do_step( sys , in , t , out , dt )` - This method updates the state out-of-place, hence the result of the step
+ * is stored in `out`.
+ * - `do_step( sys , in , dxdt_in , t , out , dxdt_out , dt )` - This method updates the state and the derivative
+ * out-of-place. It expects that the derivative at the point `t` is explicitly passed in `dxdt_in`.
+ * - `do_step( sys , x , t , dt , xerr )` - This `do_step` method is needed to fulfill the Error Stepper concept. The
+ * state is updated in-place and an error estimate is calculated. A type modelling a Boost.Range can be used for x.
+ * - `do_step( sys , x , dxdt , t , dt , xerr )` - This method updates the state and the derivative in-place. It is assumed
+ * that the dxdt has the value of the derivative of x at time t. An error estimate is calculated.
+ * - `do_step( sys , in , t , out , dt , xerr )` - This method updates the state out-of-place and estimates the error
+ * during the step.
+ * - `do_step( sys , in , dxdt_in , t , out , dxdt_out , dt , xerr )` - This methods updates the state and the derivative
+ * out-of-place and estimates the error during the step. It is assumed the dxdt_in is derivative of in at time t.
+ *
+ * \note The system is always passed as value, which might result in poor performance if it contains data. In this
+ * case it can be used with `boost::ref` or `std::ref`, for example `stepper.do_step( boost::ref( sys ) , x , t , dt );`
+ *
+ * \note The time `t` is not advanced by the stepper. This has to done manually, or by the appropriate `integrate`
+ * routines or `iterator`s.
+ *
+ * \tparam Stepper The stepper on which this class should work. It is used via CRTP, hence explicit_stepper_base
+ * provides the interface for the Stepper.
+ * \tparam Order The order of a stepper if the stepper is used without error estimation.
+ * \tparam StepperOrder The order of a step if the stepper is used with error estimation. Usually Order and StepperOrder have
+ * the same value.
+ * \tparam ErrorOrder The order of the error step if the stepper is used with error estimation.
+ * \tparam State The state type for the stepper.
+ * \tparam Value The value type for the stepper. This should be a floating point type, like float,
+ * double, or a multiprecision type. It must not necessary be the value_type of the State. For example
+ * the State can be a `vector< complex< double > >` in this case the Value must be double.
+ * The default value is double.
+ * \tparam Deriv The type representing time derivatives of the state type. It is usually the same type as the
+ * state type, only if used with Boost.Units both types differ.
+ * \tparam Time The type representing the time. Usually the same type as the value type. When Boost.Units is
+ * used, this type has usually a unit.
+ * \tparam Algebra The algebra type which must fulfill the Algebra Concept.
+ * \tparam Operations The type for the operations which must fulfill the Operations Concept.
+ * \tparam Resizer The resizer policy class.
+ */
+
+
+
+ /**
+ * \fn explicit_error_stepper_fsal_base::explicit_error_stepper_fsal_base( const algebra_type &algebra )
+ * \brief Constructs a explicit_stepper_fsal_base class. This constructor can be used as a default
+ * constructor if the algebra has a default constructor.
+ * \param algebra A copy of algebra is made and stored inside explicit_stepper_base.
+ */
+
+
+ /**
+ * \fn explicit_error_stepper_fsal_base::order( void ) const
+ * \return Returns the order of the stepper if it used without error estimation.
+ */
+
+ /**
+ * \fn explicit_error_stepper_fsal_base::stepper_order( void ) const
+ * \return Returns the order of a step if the stepper is used without error estimation.
+ */
+
+
+ /**
+ * \fn explicit_error_stepper_fsal_base::error_order( void ) const
+ * \return Returns the order of an error step if the stepper is used without error estimation.
+ */
+
+ /**
+ * \fn explicit_error_stepper_fsal_base::do_step( System system , StateInOut &x , time_type t , time_type dt )
+ * \brief This method performs one step. It transforms the result in-place.
+ *
+ * \note This method uses the internal state of the stepper.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the
+ * Simple System concept.
+ * \param x The state of the ODE which should be solved. After calling do_step the result is updated in x.
+ * \param t The value of the time, at which the step should be performed.
+ * \param dt The step size.
+ */
+
+
+ /**
+ * \fn explicit_error_stepper_fsal_base::do_step( System system , StateInOut &x , DerivInOut &dxdt , time_type t , time_type dt )
+ * \brief The method performs one step with the stepper passed by Stepper. Additionally to the other methods
+ * the derivative of x is also passed to this method. Therefore, dxdt must be evaluated initially:
+ *
+ * \code
+ * ode( x , dxdt , t );
+ * for( ... )
+ * {
+ * stepper.do_step( ode , x , dxdt , t , dt );
+ * t += dt;
+ * }
+ * \endcode
+ *
+ * \note This method does NOT use the initial state, since the first derivative is explicitly passed to this method.
+ *
+ * The result is updated in place in x as well as the derivative dxdt. This method is disabled if
+ * Time and StateInOut are of the same type. In this case the method could not be distinguished from other `do_step`
+ * versions.
+ *
+ * \note This method does not solve the forwarding problem.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param x The state of the ODE which should be solved. After calling do_step the result is updated in x.
+ * \param dxdt The derivative of x at t. After calling `do_step` dxdt is updated to the new value.
+ * \param t The value of the time, at which the step should be performed.
+ * \param dt The step size.
+ */
+
+ /**
+ * \fn explicit_error_stepper_fsal_base::do_step( System system , const StateIn &in , time_type t , StateOut &out , time_type dt )
+ * \brief The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place.
+ * This method is disabled if StateIn and Time are the same type. In this case the method can not be distinguished from
+ * other `do_step` variants.
+ *
+ * \note This method uses the internal state of the stepper.
+ *
+ * \note This method does not solve the forwarding problem.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param in The state of the ODE which should be solved. in is not modified in this method
+ * \param t The value of the time, at which the step should be performed.
+ * \param out The result of the step is written in out.
+ * \param dt The step size.
+ */
+
+ /**
+ * \fn explicit_error_stepper_fsal_base::do_step( System system , const StateIn &in , const DerivIn &dxdt_in , time_type t , StateOut &out , DerivOut &dxdt_out , time_type dt )
+ * \brief The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place.
+ * Furthermore, the derivative of x at t is passed to the stepper and updated by the stepper to its new value at
+ * t+dt.
+ *
+ * \note This method does not solve the forwarding problem.
+ *
+ * \note This method does NOT use the internal state of the stepper.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param in The state of the ODE which should be solved. in is not modified in this method
+ * \param dxdt_in The derivative of x at t.
+ * \param t The value of the time, at which the step should be performed.
+ * \param out The result of the step is written in out.
+ * \param dxdt_out The updated derivative of `out` at `t+dt`.
+ * \param dt The step size.
+ */
+
+ /**
+ * \fn explicit_error_stepper_fsal_base::do_step( System system , StateInOut &x , time_type t , time_type dt , Err &xerr )
+ * \brief The method performs one step with the stepper passed by Stepper and estimates the error. The state of the ODE
+ * is updated in-place.
+ *
+ *
+ * \note This method uses the internal state of the stepper.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param x The state of the ODE which should be solved. x is updated by this method.
+ * \param t The value of the time, at which the step should be performed.
+ * \param dt The step size.
+ * \param xerr The estimation of the error is stored in xerr.
+ */
+
+ /**
+ * \fn explicit_error_stepper_fsal_base::do_step( System system , StateInOut &x , DerivInOut &dxdt , time_type t , time_type dt , Err &xerr )
+ * \brief The method performs one step with the stepper passed by Stepper. Additionally to the other method
+ * the derivative of x is also passed to this method and updated by this method.
+ *
+ * \note This method does NOT use the internal state of the stepper.
+ *
+ * The result is updated in place in x. This method is disabled if Time and Deriv are of the same type. In this
+ * case the method could not be distinguished from other `do_step` versions. This method is disabled if StateInOut and
+ * Time are of the same type.
+ *
+ * \note This method does NOT use the internal state of the stepper.
+ *
+ * \note This method does not solve the forwarding problem.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param x The state of the ODE which should be solved. After calling do_step the result is updated in x.
+ * \param dxdt The derivative of x at t. After calling `do_step` this value is updated to the new value at `t+dt`.
+ * \param t The value of the time, at which the step should be performed.
+ * \param dt The step size.
+ * \param xerr The error estimate is stored in xerr.
+ */
+
+
+ /**
+ * \fn explicit_error_stepper_fsal_base::do_step( System system , const StateIn &in , time_type t , StateOut &out , time_type dt , Err &xerr )
+ * \brief The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place.
+ * Furthermore, the error is estimated.
+ *
+ * \note This method uses the internal state of the stepper.
+ *
+ * \note This method does not solve the forwarding problem.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param in The state of the ODE which should be solved. in is not modified in this method
+ * \param t The value of the time, at which the step should be performed.
+ * \param out The result of the step is written in out.
+ * \param dt The step size.
+ * \param xerr The error estimate.
+ */
+
+ /**
+ * \fn explicit_error_stepper_fsal_base::do_step( System system , const StateIn &in , const DerivIn &dxdt_in , time_type t , StateOut &out , DerivOut &dxdt_out , time_type dt , Err &xerr )
+ * \brief The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place.
+ * Furthermore, the derivative of x at t is passed to the stepper and the error is estimated.
+ *
+ * \note This method does NOT use the internal state of the stepper.
+ *
+ * \note This method does not solve the forwarding problem.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param in The state of the ODE which should be solved. in is not modified in this method
+ * \param dxdt_in The derivative of x at t.
+ * \param t The value of the time, at which the step should be performed.
+ * \param out The result of the step is written in out.
+ * \param dxdt_out The new derivative at `t+dt` is written into this variable.
+ * \param dt The step size.
+ * \param xerr The error estimate.
+ */
+
+ /**
+ * \fn explicit_error_stepper_fsal_base::adjust_size( const StateIn &x )
+ * \brief Adjust the size of all temporaries in the stepper manually.
+ * \param x A state from which the size of the temporaries to be resized is deduced.
+ */
+
+ /**
+ * \fn explicit_error_stepper_fsal_base::reset( void )
+ * \brief Resets the internal state of this stepper. After calling this method it is safe to use all
+ * `do_step` method without explicitly initializing the stepper.
+ */
+
+ /**
+ * \fn explicit_error_stepper_fsal_base::initialize( const DerivIn &deriv )
+ * \brief Initializes the internal state of the stepper.
+ * \param deriv The derivative of x. The next call of `do_step` expects that the derivative of `x` passed to `do_step`
+ * has the value of `deriv`.
+ */
+
+ /**
+ * \fn explicit_error_stepper_fsal_base::initialize( System system , const StateIn &x , time_type t )
+ * \brief Initializes the internal state of the stepper.
+ *
+ * This method is equivalent to
+ * \code
+ * Deriv dxdt;
+ * system( x , dxdt , t );
+ * stepper.initialize( dxdt );
+ * \endcode
+ *
+ * \param system The system function for the next calls of `do_step`.
+ * \param x The current state of the ODE.
+ * \param t The current time of the ODE.
+ */
+
+ /**
+ * \fn explicit_error_stepper_fsal_base::is_initialized( void ) const
+ * \brief Returns if the stepper is already initialized. If the stepper is not initialized, the first
+ * call of `do_step` will initialize the state of the stepper. If the stepper is already initialized
+ * the system function can not be safely exchanged between consecutive `do_step` calls.
+ */
+
+} // odeint
+} // numeric
+} // boost
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_BASE_EXPLICIT_ERROR_STEPPER_FSAL_BASE_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/base/explicit_stepper_base.hpp b/include/boost/numeric/odeint/stepper/base/explicit_stepper_base.hpp
new file mode 100644
index 0000000..d81c8c7
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/base/explicit_stepper_base.hpp
@@ -0,0 +1,415 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/base/explicit_stepper_base.hpp
+
+ [begin_description]
+ Base class for all explicit Runge Kutta steppers.
+ [end_description]
+
+ Copyright 2010-2013 Karsten Ahnert
+ Copyright 2010-2012 Mario Mulansky
+ Copyright 2012 Christoph Koke
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_BASE_EXPLICIT_STEPPER_BASE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_BASE_EXPLICIT_STEPPER_BASE_HPP_INCLUDED
+
+
+#include <boost/utility/enable_if.hpp>
+#include <boost/type_traits/is_same.hpp>
+
+#include <boost/numeric/odeint/util/bind.hpp>
+#include <boost/numeric/odeint/util/unwrap_reference.hpp>
+
+#include <boost/numeric/odeint/util/state_wrapper.hpp>
+#include <boost/numeric/odeint/util/resizer.hpp>
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+
+#include <boost/numeric/odeint/stepper/base/algebra_stepper_base.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+/*
+ * base class for explicit steppers
+ * models the stepper concept
+ *
+ * this class provides the following overloads
+ * do_step( sys , x , t , dt )
+ * do_step( sys , in , t , out , dt )
+ * do_step( sys , x , dxdt_in , t , dt )
+ * do_step( sys , in , dxdt_in , t , out , dt )
+ */
+
+template<
+class Stepper ,
+unsigned short Order ,
+class State ,
+class Value ,
+class Deriv ,
+class Time ,
+class Algebra ,
+class Operations ,
+class Resizer
+>
+class explicit_stepper_base : public algebra_stepper_base< Algebra , Operations >
+{
+public:
+
+ #ifndef DOXYGEN_SKIP
+ typedef explicit_stepper_base< Stepper , Order , State , Value , Deriv , Time , Algebra , Operations , Resizer > internal_stepper_base_type;
+ #endif // DOXYGEN_SKIP
+
+
+ typedef State state_type;
+ typedef Value value_type;
+ typedef Deriv deriv_type;
+ typedef Time time_type;
+ typedef Resizer resizer_type;
+ typedef Stepper stepper_type;
+ typedef stepper_tag stepper_category;
+ typedef algebra_stepper_base< Algebra , Operations > algebra_stepper_base_type;
+ typedef typename algebra_stepper_base_type::algebra_type algebra_type;
+ typedef typename algebra_stepper_base_type::operations_type operations_type;
+ typedef unsigned short order_type;
+
+ #ifndef DOXYGEN_SKIP
+ typedef state_wrapper< state_type > wrapped_state_type;
+ typedef state_wrapper< deriv_type > wrapped_deriv_type;
+ #endif // DOXYGEN_SKIP
+
+
+ static const order_type order_value = Order;
+
+
+ explicit_stepper_base( const algebra_type &algebra = algebra_type() )
+ : algebra_stepper_base_type( algebra )
+ { }
+
+ /**
+ * \return Returns the order of the stepper.
+ */
+ order_type order( void ) const
+ {
+ return order_value;
+ }
+
+
+ /*
+ * Version 1 : do_step( sys , x , t , dt )
+ *
+ * the two overloads are needed in order to solve the forwarding problem
+ */
+ template< class System , class StateInOut >
+ void do_step( System system , StateInOut &x , time_type t , time_type dt )
+ {
+ do_step_v1( system , x , t , dt );
+ }
+
+ /**
+ * \brief Second version to solve the forwarding problem, can be called with Boost.Range as StateInOut.
+ */
+ template< class System , class StateInOut >
+ void do_step( System system , const StateInOut &x , time_type t , time_type dt )
+ {
+ do_step_v1( system , x , t , dt );
+ }
+
+ /*
+ * Version 2 : do_step( sys , x , dxdt , t , dt )
+ *
+ * this version does not solve the forwarding problem, boost.range can not be used
+ *
+ * the disable is needed to avoid ambiguous overloads if state_type = time_type
+ */
+ template< class System , class StateInOut , class DerivIn >
+ typename boost::disable_if< boost::is_same< DerivIn , time_type > , void >::type
+ do_step( System system , StateInOut &x , const DerivIn &dxdt , time_type t , time_type dt )
+ {
+ this->stepper().do_step_impl( system , x , dxdt , t , x , dt );
+ }
+
+
+ /*
+ * named Version 2: do_step_dxdt_impl( sys , in , dxdt , t , dt )
+ *
+ * this version is needed when this stepper is used for initializing
+ * multistep stepper like adams-bashforth. Hence we provide an explicitely
+ * named version that is not disabled. Meant for internal use only.
+ */
+ template < class System, class StateInOut, class DerivIn >
+ void do_step_dxdt_impl( System system, StateInOut &x, const DerivIn &dxdt,
+ time_type t, time_type dt )
+ {
+ this->stepper().do_step_impl( system , x , dxdt , t , x , dt );
+ }
+
+
+ /*
+ * Version 3 : do_step( sys , in , t , out , dt )
+ *
+ * this version does not solve the forwarding problem, boost.range can not be used
+ */
+ template< class System , class StateIn , class StateOut >
+ void do_step( System system , const StateIn &in , time_type t , StateOut &out , time_type dt )
+ {
+ typename odeint::unwrap_reference< System >::type &sys = system;
+ m_resizer.adjust_size( in , detail::bind( &internal_stepper_base_type::template resize_impl<StateIn> , detail::ref( *this ) , detail::_1 ) );
+ sys( in , m_dxdt.m_v ,t );
+ this->stepper().do_step_impl( system , in , m_dxdt.m_v , t , out , dt );
+ }
+
+
+ /*
+ * Version 4 : do_step( sys , in , dxdt , t , out , dt )
+ *
+ * this version does not solve the forwarding problem, boost.range can not be used
+ */
+ template< class System , class StateIn , class DerivIn , class StateOut >
+ void do_step( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt )
+ {
+ this->stepper().do_step_impl( system , in , dxdt , t , out , dt );
+ }
+
+
+ /*
+ * named Version 4: do_step_dxdt_impl( sys , in , dxdt , t , out, dt )
+ *
+ * this version is needed when this stepper is used for initializing
+ * multistep stepper like adams-bashforth. Hence we provide an explicitely
+ * named version. Meant for internal use only.
+ */
+ template < class System, class StateIn, class DerivIn, class StateOut >
+ void do_step_dxdt_impl( System system, const StateIn &in,
+ const DerivIn &dxdt, time_type t, StateOut &out,
+ time_type dt )
+ {
+ this->stepper().do_step_impl( system , in , dxdt , t , out , dt );
+ }
+
+ template< class StateIn >
+ void adjust_size( const StateIn &x )
+ {
+ resize_impl( x );
+ }
+
+private:
+
+ stepper_type& stepper( void )
+ {
+ return *static_cast< stepper_type* >( this );
+ }
+
+ const stepper_type& stepper( void ) const
+ {
+ return *static_cast< const stepper_type* >( this );
+ }
+
+
+ template< class StateIn >
+ bool resize_impl( const StateIn &x )
+ {
+ return adjust_size_by_resizeability( m_dxdt , x , typename is_resizeable<deriv_type>::type() );
+ }
+
+
+ template< class System , class StateInOut >
+ void do_step_v1( System system , StateInOut &x , time_type t , time_type dt )
+ {
+ typename odeint::unwrap_reference< System >::type &sys = system;
+ m_resizer.adjust_size( x , detail::bind( &internal_stepper_base_type::template resize_impl< StateInOut > , detail::ref( *this ) , detail::_1 ) );
+ sys( x , m_dxdt.m_v ,t );
+ this->stepper().do_step_impl( system , x , m_dxdt.m_v , t , x , dt );
+ }
+
+
+ resizer_type m_resizer;
+
+protected:
+
+ wrapped_deriv_type m_dxdt;
+};
+
+
+/******* DOXYGEN *********/
+
+/**
+ * \class explicit_stepper_base
+ * \brief Base class for explicit steppers without step size control and without dense output.
+ *
+ * This class serves as the base class for all explicit steppers with algebra and operations.
+ * Step size control and error estimation as well as dense output are not provided. explicit_stepper_base
+ * is used as the interface in a CRTP (currently recurring template pattern). In order to work
+ * correctly the parent class needs to have a method `do_step_impl( system , in , dxdt_in , t , out , dt )`.
+ * This is method is used by explicit_stepper_base. explicit_stepper_base derives from
+ * algebra_stepper_base. An example how this class can be used is
+ *
+ * \code
+ * template< class State , class Value , class Deriv , class Time , class Algebra , class Operations , class Resizer >
+ * class custom_euler : public explicit_stepper_base< 1 , State , Value , Deriv , Time , Algebra , Operations , Resizer >
+ * {
+ * public:
+ *
+ * typedef explicit_stepper_base< 1 , State , Value , Deriv , Time , Algebra , Operations , Resizer > base_type;
+ *
+ * custom_euler( const Algebra &algebra = Algebra() ) { }
+ *
+ * template< class Sys , class StateIn , class DerivIn , class StateOut >
+ * void do_step_impl( Sys sys , const StateIn &in , const DerivIn &dxdt , Time t , StateOut &out , Time dt )
+ * {
+ * m_algebra.for_each3( out , in , dxdt , Operations::scale_sum2< Value , Time >( 1.0 , dt );
+ * }
+ *
+ * template< class State >
+ * void adjust_size( const State &x )
+ * {
+ * base_type::adjust_size( x );
+ * }
+ * };
+ * \endcode
+ *
+ * For the Stepper concept only the `do_step( sys , x , t , dt )` needs to be implemented. But this class
+ * provides additional `do_step` variants since the stepper is explicit. These methods can be used to increase
+ * the performance in some situation, for example if one needs to analyze `dxdt` during each step. In this case
+ * one can use
+ *
+ * \code
+ * sys( x , dxdt , t );
+ * stepper.do_step( sys , x , dxdt , t , dt ); // the value of dxdt is used here
+ * t += dt;
+ * \endcode
+ *
+ * In detail explicit_stepper_base provides the following `do_step` variants
+ * - `do_step( sys , x , t , dt )` - The classical `do_step` method needed to fulfill the Stepper concept. The state is updated in-place.
+ * A type modelling a Boost.Range can be used for x.
+ * - `do_step( sys , in , t , out , dt )` - This method updates the state out-of-place, hence the result of the step is stored in `out`.
+ * - `do_step( sys , x , dxdt , t , dt )` - This method updates the state in-place, but the derivative at the point `t` must be
+ * explicitly passed in `dxdt`. For an example see the code snippet above.
+ * - `do_step( sys , in , dxdt , t , out , dt )` - This method update the state out-of-place and expects that the derivative at the point
+ * `t` is explicitly passed in `dxdt`. It is a combination of the two `do_step` methods above.
+ *
+ * \note The system is always passed as value, which might result in poor performance if it contains data. In this case it can be used with `boost::ref`
+ * or `std::ref`, for example `stepper.do_step( boost::ref( sys ) , x , t , dt );`
+ *
+ * \note The time `t` is not advanced by the stepper. This has to done manually, or by the appropriate `integrate` routines or `iterator`s.
+ *
+ * \tparam Stepper The stepper on which this class should work. It is used via CRTP, hence explicit_stepper_base
+ * provides the interface for the Stepper.
+ * \tparam Order The order of the stepper.
+ * \tparam State The state type for the stepper.
+ * \tparam Value The value type for the stepper. This should be a floating point type, like float,
+ * double, or a multiprecision type. It must not necessary be the value_type of the State. For example
+ * the State can be a `vector< complex< double > >` in this case the Value must be double.
+ * The default value is double.
+ * \tparam Deriv The type representing time derivatives of the state type. It is usually the same type as the
+ * state type, only if used with Boost.Units both types differ.
+ * \tparam Time The type representing the time. Usually the same type as the value type. When Boost.Units is
+ * used, this type has usually a unit.
+ * \tparam Algebra The algebra type which must fulfill the Algebra Concept.
+ * \tparam Operations The type for the operations which must fulfill the Operations Concept.
+ * \tparam Resizer The resizer policy class.
+ */
+
+
+ /**
+ * \fn explicit_stepper_base::explicit_stepper_base( const algebra_type &algebra )
+ * \brief Constructs a explicit_stepper_base class. This constructor can be used as a default
+ * constructor if the algebra has a default constructor.
+ * \param algebra A copy of algebra is made and stored inside explicit_stepper_base.
+ */
+
+ /**
+ * \fn explicit_stepper_base::order_type order( void ) const
+ * \return Returns the order of the stepper.
+ */
+
+ /**
+ * \fn explicit_stepper_base::do_step( System system , StateInOut &x , time_type t , time_type dt )
+ * \brief This method performs one step. It transforms the result in-place.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the
+ * Simple System concept.
+ * \param x The state of the ODE which should be solved. After calling do_step the result is updated in x.
+ * \param t The value of the time, at which the step should be performed.
+ * \param dt The step size.
+ */
+
+
+ /**
+ * \fn explicit_stepper_base::do_step( System system , StateInOut &x , const DerivIn &dxdt , time_type t , time_type dt )
+
+ * \brief The method performs one step. Additionally to the other method
+ * the derivative of x is also passed to this method. It is supposed to be used in the following way:
+ *
+ * \code
+ * sys( x , dxdt , t );
+ * stepper.do_step( sys , x , dxdt , t , dt );
+ * \endcode
+ *
+ * The result is updated in place in x. This method is disabled if Time and Deriv are of the same type. In this
+ * case the method could not be distinguished from other `do_step` versions.
+ *
+ * \note This method does not solve the forwarding problem.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param x The state of the ODE which should be solved. After calling do_step the result is updated in x.
+ * \param dxdt The derivative of x at t.
+ * \param t The value of the time, at which the step should be performed.
+ * \param dt The step size.
+ */
+
+ /**
+ * \fn void explicit_stepper_base::do_step( System system , const StateIn &in , time_type t , StateOut &out , time_type dt )
+ * \brief The method performs one step. The state of the ODE is updated out-of-place.
+ * \note This method does not solve the forwarding problem.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param in The state of the ODE which should be solved. in is not modified in this method
+ * \param t The value of the time, at which the step should be performed.
+ * \param out The result of the step is written in out.
+ * \param dt The step size.
+ */
+
+ /**
+ * \fn void explicit_stepper_base::do_step( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt )
+ * \brief The method performs one step. The state of the ODE is updated out-of-place.
+ * Furthermore, the derivative of x at t is passed to the stepper.
+ * It is supposed to be used in the following way:
+ *
+ * \code
+ * sys( in , dxdt , t );
+ * stepper.do_step( sys , in , dxdt , t , out , dt );
+ * \endcode
+ *
+ * \note This method does not solve the forwarding problem.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param in The state of the ODE which should be solved. in is not modified in this method
+ * \param dxdt The derivative of x at t.
+ * \param t The value of the time, at which the step should be performed.
+ * \param out The result of the step is written in out.
+ * \param dt The step size.
+ */
+
+ /**
+ * \fn void explicit_stepper_base::adjust_size( const StateIn &x )
+ * \brief Adjust the size of all temporaries in the stepper manually.
+ * \param x A state from which the size of the temporaries to be resized is deduced.
+ */
+
+} // odeint
+} // numeric
+} // boost
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_BASE_EXPLICIT_STEPPER_BASE_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/base/symplectic_rkn_stepper_base.hpp b/include/boost/numeric/odeint/stepper/base/symplectic_rkn_stepper_base.hpp
new file mode 100644
index 0000000..eb09aef
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/base/symplectic_rkn_stepper_base.hpp
@@ -0,0 +1,431 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/base/symplectic_rkn_stepper_base.hpp
+
+ [begin_description]
+ Base class for symplectic Runge-Kutta-Nystrom steppers.
+ [end_description]
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011-2013 Mario Mulansky
+ Copyright 2012 Christoph Koke
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_BASE_SYMPLECTIC_RKN_STEPPER_BASE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_BASE_SYMPLECTIC_RKN_STEPPER_BASE_HPP_INCLUDED
+
+#include <boost/array.hpp>
+
+#include <boost/numeric/odeint/util/bind.hpp>
+#include <boost/numeric/odeint/util/unwrap_reference.hpp>
+
+#include <boost/numeric/odeint/util/copy.hpp>
+#include <boost/numeric/odeint/util/is_pair.hpp>
+
+#include <boost/numeric/odeint/util/state_wrapper.hpp>
+#include <boost/numeric/odeint/util/resizer.hpp>
+
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+
+#include <boost/numeric/odeint/stepper/base/algebra_stepper_base.hpp>
+
+
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+template<
+size_t NumOfStages ,
+unsigned short Order ,
+class Coor ,
+class Momentum ,
+class Value ,
+class CoorDeriv ,
+class MomentumDeriv ,
+class Time ,
+class Algebra ,
+class Operations ,
+class Resizer
+>
+class symplectic_nystroem_stepper_base : public algebra_stepper_base< Algebra , Operations >
+{
+
+public:
+
+ typedef algebra_stepper_base< Algebra , Operations > algebra_stepper_base_type;
+ typedef typename algebra_stepper_base_type::algebra_type algebra_type;
+ typedef typename algebra_stepper_base_type::operations_type operations_type;
+
+ const static size_t num_of_stages = NumOfStages;
+ typedef Coor coor_type;
+ typedef Momentum momentum_type;
+ typedef std::pair< coor_type , momentum_type > state_type;
+ typedef CoorDeriv coor_deriv_type;
+ typedef state_wrapper< coor_deriv_type> wrapped_coor_deriv_type;
+ typedef MomentumDeriv momentum_deriv_type;
+ typedef state_wrapper< momentum_deriv_type > wrapped_momentum_deriv_type;
+ typedef std::pair< coor_deriv_type , momentum_deriv_type > deriv_type;
+ typedef Value value_type;
+ typedef Time time_type;
+ typedef Resizer resizer_type;
+ typedef stepper_tag stepper_category;
+
+ #ifndef DOXYGEN_SKIP
+ typedef symplectic_nystroem_stepper_base< NumOfStages , Order , Coor , Momentum , Value ,
+ CoorDeriv , MomentumDeriv , Time , Algebra , Operations , Resizer > internal_stepper_base_type;
+ #endif
+ typedef unsigned short order_type;
+
+ static const order_type order_value = Order;
+
+ typedef boost::array< value_type , num_of_stages > coef_type;
+
+ symplectic_nystroem_stepper_base( const coef_type &coef_a , const coef_type &coef_b , const algebra_type &algebra = algebra_type() )
+ : algebra_stepper_base_type( algebra ) , m_coef_a( coef_a ) , m_coef_b( coef_b ) ,
+ m_dqdt_resizer() , m_dpdt_resizer() , m_dqdt() , m_dpdt()
+ { }
+
+
+ order_type order( void ) const
+ {
+ return order_value;
+ }
+
+ /*
+ * Version 1 : do_step( system , x , t , dt )
+ *
+ * This version does not solve the forwarding problem, boost.range can not be used.
+ */
+ template< class System , class StateInOut >
+ void do_step( System system , const StateInOut &state , time_type t , time_type dt )
+ {
+ typedef typename odeint::unwrap_reference< System >::type system_type;
+ do_step_impl( system , state , t , state , dt , typename is_pair< system_type >::type() );
+ }
+
+ /**
+ * \brief Same function as above. It differs only in a different const specifier in order
+ * to solve the forwarding problem, can be used with Boost.Range.
+ */
+ template< class System , class StateInOut >
+ void do_step( System system , StateInOut &state , time_type t , time_type dt )
+ {
+ typedef typename odeint::unwrap_reference< System >::type system_type;
+ do_step_impl( system , state , t , state , dt , typename is_pair< system_type >::type() );
+ }
+
+
+
+
+ /*
+ * Version 2 : do_step( system , q , p , t , dt );
+ *
+ * For Convenience
+ *
+ * The two overloads are needed in order to solve the forwarding problem.
+ */
+ template< class System , class CoorInOut , class MomentumInOut >
+ void do_step( System system , CoorInOut &q , MomentumInOut &p , time_type t , time_type dt )
+ {
+ do_step( system , std::make_pair( detail::ref( q ) , detail::ref( p ) ) , t , dt );
+ }
+
+ /**
+ * \brief Same function as do_step( system , q , p , t , dt ). It differs only in a different const specifier in order
+ * to solve the forwarding problem, can be called with Boost.Range.
+ */
+ template< class System , class CoorInOut , class MomentumInOut >
+ void do_step( System system , const CoorInOut &q , const MomentumInOut &p , time_type t , time_type dt )
+ {
+ do_step( system , std::make_pair( detail::ref( q ) , detail::ref( p ) ) , t , dt );
+ }
+
+
+
+
+
+ /*
+ * Version 3 : do_step( system , in , t , out , dt )
+ *
+ * The forwarding problem is not solved in this version
+ */
+ template< class System , class StateIn , class StateOut >
+ void do_step( System system , const StateIn &in , time_type t , StateOut &out , time_type dt )
+ {
+ typedef typename odeint::unwrap_reference< System >::type system_type;
+ do_step_impl( system , in , t , out , dt , typename is_pair< system_type >::type() );
+ }
+
+
+ template< class StateType >
+ void adjust_size( const StateType &x )
+ {
+ resize_dqdt( x );
+ resize_dpdt( x );
+ }
+
+ /** \brief Returns the coefficients a. */
+ const coef_type& coef_a( void ) const { return m_coef_a; }
+
+ /** \brief Returns the coefficients b. */
+ const coef_type& coef_b( void ) const { return m_coef_b; }
+
+private:
+
+ // stepper for systems with function for dq/dt = f(p) and dp/dt = -f(q)
+ template< class System , class StateIn , class StateOut >
+ void do_step_impl( System system , const StateIn &in , time_type /* t */ , StateOut &out , time_type dt , boost::mpl::true_ )
+ {
+ typedef typename odeint::unwrap_reference< System >::type system_type;
+ typedef typename odeint::unwrap_reference< typename system_type::first_type >::type coor_deriv_func_type;
+ typedef typename odeint::unwrap_reference< typename system_type::second_type >::type momentum_deriv_func_type;
+ system_type &sys = system;
+ coor_deriv_func_type &coor_func = sys.first;
+ momentum_deriv_func_type &momentum_func = sys.second;
+
+ typedef typename odeint::unwrap_reference< StateIn >::type state_in_type;
+ typedef typename odeint::unwrap_reference< typename state_in_type::first_type >::type coor_in_type;
+ typedef typename odeint::unwrap_reference< typename state_in_type::second_type >::type momentum_in_type;
+ const state_in_type &state_in = in;
+ const coor_in_type &coor_in = state_in.first;
+ const momentum_in_type &momentum_in = state_in.second;
+
+ typedef typename odeint::unwrap_reference< StateOut >::type state_out_type;
+ typedef typename odeint::unwrap_reference< typename state_out_type::first_type >::type coor_out_type;
+ typedef typename odeint::unwrap_reference< typename state_out_type::second_type >::type momentum_out_type;
+ state_out_type &state_out = out;
+ coor_out_type &coor_out = state_out.first;
+ momentum_out_type &momentum_out = state_out.second;
+
+ m_dqdt_resizer.adjust_size( coor_in , detail::bind( &internal_stepper_base_type::template resize_dqdt< coor_in_type > , detail::ref( *this ) , detail::_1 ) );
+ m_dpdt_resizer.adjust_size( momentum_in , detail::bind( &internal_stepper_base_type::template resize_dpdt< momentum_in_type > , detail::ref( *this ) , detail::_1 ) );
+
+ // ToDo: check sizes?
+
+ for( size_t l=0 ; l<num_of_stages ; ++l )
+ {
+ if( l == 0 )
+ {
+ coor_func( momentum_in , m_dqdt.m_v );
+ this->m_algebra.for_each3( coor_out , coor_in , m_dqdt.m_v ,
+ typename operations_type::template scale_sum2< value_type , time_type >( 1.0 , m_coef_a[l] * dt ) );
+ momentum_func( coor_out , m_dpdt.m_v );
+ this->m_algebra.for_each3( momentum_out , momentum_in , m_dpdt.m_v ,
+ typename operations_type::template scale_sum2< value_type , time_type >( 1.0 , m_coef_b[l] * dt ) );
+ }
+ else
+ {
+ coor_func( momentum_out , m_dqdt.m_v );
+ this->m_algebra.for_each3( coor_out , coor_out , m_dqdt.m_v ,
+ typename operations_type::template scale_sum2< value_type , time_type >( 1.0 , m_coef_a[l] * dt ) );
+ momentum_func( coor_out , m_dpdt.m_v );
+ this->m_algebra.for_each3( momentum_out , momentum_out , m_dpdt.m_v ,
+ typename operations_type::template scale_sum2< value_type , time_type >( 1.0 , m_coef_b[l] * dt ) );
+ }
+ }
+ }
+
+
+ // stepper for systems with only function dp /dt = -f(q), dq/dt = p, time not required but still expected for compatibility reasons
+ template< class System , class StateIn , class StateOut >
+ void do_step_impl( System system , const StateIn &in , time_type /* t */ , StateOut &out , time_type dt , boost::mpl::false_ )
+ {
+ typedef typename odeint::unwrap_reference< System >::type momentum_deriv_func_type;
+ momentum_deriv_func_type &momentum_func = system;
+
+ typedef typename odeint::unwrap_reference< StateIn >::type state_in_type;
+ typedef typename odeint::unwrap_reference< typename state_in_type::first_type >::type coor_in_type;
+ typedef typename odeint::unwrap_reference< typename state_in_type::second_type >::type momentum_in_type;
+ const state_in_type &state_in = in;
+ const coor_in_type &coor_in = state_in.first;
+ const momentum_in_type &momentum_in = state_in.second;
+
+ typedef typename odeint::unwrap_reference< StateOut >::type state_out_type;
+ typedef typename odeint::unwrap_reference< typename state_out_type::first_type >::type coor_out_type;
+ typedef typename odeint::unwrap_reference< typename state_out_type::second_type >::type momentum_out_type;
+ state_out_type &state_out = out;
+ coor_out_type &coor_out = state_out.first;
+ momentum_out_type &momentum_out = state_out.second;
+
+
+ // m_dqdt not required when called with momentum_func only - don't resize
+ // m_dqdt_resizer.adjust_size( coor_in , detail::bind( &internal_stepper_base_type::template resize_dqdt< coor_in_type > , detail::ref( *this ) , detail::_1 ) );
+ m_dpdt_resizer.adjust_size( momentum_in , detail::bind( &internal_stepper_base_type::template resize_dpdt< momentum_in_type > , detail::ref( *this ) , detail::_1 ) );
+
+
+ // ToDo: check sizes?
+
+ // step 0
+ this->m_algebra.for_each3( coor_out , coor_in , momentum_in ,
+ typename operations_type::template scale_sum2< value_type , time_type >( 1.0 , m_coef_a[0] * dt ) );
+ momentum_func( coor_out , m_dpdt.m_v );
+ this->m_algebra.for_each3( momentum_out , momentum_in , m_dpdt.m_v ,
+ typename operations_type::template scale_sum2< value_type , time_type >( 1.0 , m_coef_b[0] * dt ) );
+
+ for( size_t l=1 ; l<num_of_stages ; ++l )
+ {
+ this->m_algebra.for_each3( coor_out , coor_out , momentum_out ,
+ typename operations_type::template scale_sum2< value_type , time_type >( 1.0 , m_coef_a[l] * dt ) );
+ momentum_func( coor_out , m_dpdt.m_v );
+ this->m_algebra.for_each3( momentum_out , momentum_out , m_dpdt.m_v ,
+ typename operations_type::template scale_sum2< value_type , time_type >( 1.0 , m_coef_b[l] * dt ) );
+ }
+ }
+
+ template< class StateIn >
+ bool resize_dqdt( const StateIn &x )
+ {
+ return adjust_size_by_resizeability( m_dqdt , x , typename is_resizeable<coor_deriv_type>::type() );
+ }
+
+ template< class StateIn >
+ bool resize_dpdt( const StateIn &x )
+ {
+ return adjust_size_by_resizeability( m_dpdt , x , typename is_resizeable<momentum_deriv_type>::type() );
+ }
+
+
+ const coef_type m_coef_a;
+ const coef_type m_coef_b;
+
+ resizer_type m_dqdt_resizer;
+ resizer_type m_dpdt_resizer;
+ wrapped_coor_deriv_type m_dqdt;
+ wrapped_momentum_deriv_type m_dpdt;
+
+};
+
+/********* DOXYGEN *********/
+
+/**
+ * \class symplectic_nystroem_stepper_base
+ * \brief Base class for all symplectic steppers of Nystroem type.
+ *
+ * This class is the base class for the symplectic Runge-Kutta-Nystroem steppers. Symplectic steppers are usually
+ * used to solve Hamiltonian systems and they conserve the phase space volume, see
+ * <a href="http://en.wikipedia.org/wiki/Symplectic_integrator">en.wikipedia.org/wiki/Symplectic_integrator</a>.
+ * Furthermore, the energy is conserved
+ * in average. In detail this class of steppers can be used to solve separable Hamiltonian systems which can be written
+ * in the form H(q,p) = H1(p) + H2(q). q is usually called the coordinate, while p is the momentum. The equations of motion
+ * are dq/dt = dH1/dp, dp/dt = -dH2/dq.
+ *
+ * ToDo : add formula for solver and explanation of the coefficients
+ *
+ * symplectic_nystroem_stepper_base uses odeints algebra and operation system. Step size and error estimation are not
+ * provided for this class of solvers. It derives from algebra_stepper_base. Several `do_step` variants are provided:
+ *
+ * - `do_step( sys , x , t , dt )` - The classical `do_step` method. The sys can be either a pair of function objects
+ * for the coordinate or the momentum part or one function object for the momentum part. `x` is a pair of coordinate
+ * and momentum. The state is updated in-place.
+ * - `do_step( sys , q , p , t , dt )` - This method is similar to the method above with the difference that the coordinate
+ * and the momentum are passed explicitly and not packed into a pair.
+ * - `do_step( sys , x_in , t , x_out , dt )` - This method transforms the state out-of-place. `x_in` and `x_out` are here pairs
+ * of coordinate and momentum.
+ *
+ * \tparam NumOfStages Number of stages.
+ * \tparam Order The order of the stepper.
+ * \tparam Coor The type representing the coordinates q.
+ * \tparam Momentum The type representing the coordinates p.
+ * \tparam Value The basic value type. Should be something like float, double or a high-precision type.
+ * \tparam CoorDeriv The type representing the time derivative of the coordinate dq/dt.
+ * \tparam MomemtnumDeriv The type representing the time derivative of the momentum dp/dt.
+ * \tparam Time The type representing the time t.
+ * \tparam Algebra The algebra.
+ * \tparam Operations The operations.
+ * \tparam Resizer The resizer policy.
+ */
+
+ /**
+ * \fn symplectic_nystroem_stepper_base::symplectic_nystroem_stepper_base( const coef_type &coef_a , const coef_type &coef_b , const algebra_type &algebra )
+ * \brief Constructs a symplectic_nystroem_stepper_base class. The parameters of the specific Nystroem method and the
+ * algebra have to be passed.
+ * \param coef_a The coefficients a.
+ * \param coef_b The coefficients b.
+ * \param algebra A copy of algebra is made and stored inside explicit_stepper_base.
+ */
+
+ /**
+ * \fn symplectic_nystroem_stepper_base::order( void ) const
+ * \return Returns the order of the stepper.
+ */
+
+ /**
+ * \fn symplectic_nystroem_stepper_base::do_step( System system , const StateInOut &state , time_type t , time_type dt )
+ * \brief This method performs one step. The system can be either a pair of two function object
+ * describing the momentum part and the coordinate part or one function object describing only
+ * the momentum part. In this case the coordinate is assumed to be trivial dq/dt = p. The state
+ * is updated in-place.
+ *
+ * \note boost::ref or std::ref can be used for the system as well as for the state. So, it is correct
+ * to write `stepper.do_step( make_pair( std::ref( fq ) , std::ref( fp ) ) , make_pair( std::ref( q ) , std::ref( p ) ) , t , dt )`.
+ *
+ * \note This method solves the forwarding problem.
+ *
+ * \param system The system, can be represented as a pair of two function object or one function object. See above.
+ * \param state The state of the ODE. It is a pair of Coor and Momentum. The state is updated in-place, therefore, the
+ * new value of the state will be written into this variable.
+ * \param t The time of the ODE. It is not advanced by this method.
+ * \param dt The time step.
+ */
+
+ /**
+ * \fn symplectic_nystroem_stepper_base::do_step( System system , CoorInOut &q , MomentumInOut &p , time_type t , time_type dt )
+ * \brief This method performs one step. The system can be either a pair of two function object
+ * describing the momentum part and the coordinate part or one function object describing only
+ * the momentum part. In this case the coordinate is assumed to be trivial dq/dt = p. The state
+ * is updated in-place.
+ *
+ * \note boost::ref or std::ref can be used for the system. So, it is correct
+ * to write `stepper.do_step( make_pair( std::ref( fq ) , std::ref( fp ) ) , q , p , t , dt )`.
+ *
+ * \note This method solves the forwarding problem.
+ *
+ * \param system The system, can be represented as a pair of two function object or one function object. See above.
+ * \param q The coordinate of the ODE. It is updated in-place. Therefore, the new value of the coordinate will be written
+ * into this variable.
+ * \param p The momentum of the ODE. It is updated in-place. Therefore, the new value of the momentum will be written info
+ * this variable.
+ * \param t The time of the ODE. It is not advanced by this method.
+ * \param dt The time step.
+ */
+
+ /**
+ * \fn symplectic_nystroem_stepper_base::do_step( System system , const StateIn &in , time_type t , StateOut &out , time_type dt )
+ * \brief This method performs one step. The system can be either a pair of two function object
+ * describing the momentum part and the coordinate part or one function object describing only
+ * the momentum part. In this case the coordinate is assumed to be trivial dq/dt = p. The state
+ * is updated out-of-place.
+ *
+ * \note boost::ref or std::ref can be used for the system. So, it is correct
+ * to write `stepper.do_step( make_pair( std::ref( fq ) , std::ref( fp ) ) , x_in , t , x_out , dt )`.
+ *
+ * \note This method NOT solve the forwarding problem.
+ *
+ * \param system The system, can be represented as a pair of two function object or one function object. See above.
+ * \param in The state of the ODE, which is a pair of coordinate and momentum. The state is updated out-of-place, therefore the
+ * new value is written into out
+ * \param t The time of the ODE. It is not advanced by this method.
+ * \param out The new state of the ODE.
+ * \param dt The time step.
+ */
+
+ /**
+ * \fn symplectic_nystroem_stepper_base::adjust_size( const StateType &x )
+ * \brief Adjust the size of all temporaries in the stepper manually.
+ * \param x A state from which the size of the temporaries to be resized is deduced.
+ */
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_BASE_SYMPLECTIC_RKN_STEPPER_BASE_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/bulirsch_stoer.hpp b/include/boost/numeric/odeint/stepper/bulirsch_stoer.hpp
new file mode 100644
index 0000000..02c3749
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/bulirsch_stoer.hpp
@@ -0,0 +1,642 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/bulirsch_stoer.hpp
+
+ [begin_description]
+ Implementation of the Burlish-Stoer method. As described in
+ Ernst Hairer, Syvert Paul Norsett, Gerhard Wanner
+ Solving Ordinary Differential Equations I. Nonstiff Problems.
+ Springer Series in Comput. Mathematics, Vol. 8, Springer-Verlag 1987, Second revised edition 1993.
+ [end_description]
+
+ Copyright 2011-2013 Mario Mulansky
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2012 Christoph Koke
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_BULIRSCH_STOER_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_BULIRSCH_STOER_HPP_INCLUDED
+
+
+#include <iostream>
+
+#include <algorithm>
+
+#include <boost/config.hpp> // for min/max guidelines
+
+#include <boost/numeric/odeint/util/bind.hpp>
+#include <boost/numeric/odeint/util/unwrap_reference.hpp>
+
+#include <boost/numeric/odeint/stepper/controlled_runge_kutta.hpp>
+#include <boost/numeric/odeint/stepper/modified_midpoint.hpp>
+#include <boost/numeric/odeint/stepper/controlled_step_result.hpp>
+#include <boost/numeric/odeint/algebra/range_algebra.hpp>
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
+
+#include <boost/numeric/odeint/util/state_wrapper.hpp>
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resizer.hpp>
+#include <boost/numeric/odeint/util/unit_helper.hpp>
+#include <boost/numeric/odeint/util/detail/less_with_sign.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template<
+ class State ,
+ class Value = double ,
+ class Deriv = State ,
+ class Time = Value ,
+ class Algebra = typename algebra_dispatcher< State >::algebra_type ,
+ class Operations = typename operations_dispatcher< State >::operations_type ,
+ class Resizer = initially_resizer
+ >
+class bulirsch_stoer {
+
+public:
+
+ typedef State state_type;
+ typedef Value value_type;
+ typedef Deriv deriv_type;
+ typedef Time time_type;
+ typedef Algebra algebra_type;
+ typedef Operations operations_type;
+ typedef Resizer resizer_type;
+#ifndef DOXYGEN_SKIP
+ typedef state_wrapper< state_type > wrapped_state_type;
+ typedef state_wrapper< deriv_type > wrapped_deriv_type;
+ typedef controlled_stepper_tag stepper_category;
+
+ typedef bulirsch_stoer< State , Value , Deriv , Time , Algebra , Operations , Resizer > controlled_error_bs_type;
+
+ typedef typename inverse_time< time_type >::type inv_time_type;
+
+ typedef std::vector< value_type > value_vector;
+ typedef std::vector< time_type > time_vector;
+ typedef std::vector< inv_time_type > inv_time_vector; //should be 1/time_type for boost.units
+ typedef std::vector< value_vector > value_matrix;
+ typedef std::vector< size_t > int_vector;
+ typedef std::vector< wrapped_state_type > state_table_type;
+#endif //DOXYGEN_SKIP
+ const static size_t m_k_max = 8;
+
+ bulirsch_stoer(
+ value_type eps_abs = 1E-6 , value_type eps_rel = 1E-6 ,
+ value_type factor_x = 1.0 , value_type factor_dxdt = 1.0 ,
+ time_type max_dt = static_cast<time_type>(0))
+ : m_error_checker( eps_abs , eps_rel , factor_x, factor_dxdt ) , m_midpoint() ,
+ m_last_step_rejected( false ) , m_first( true ) ,
+ m_max_dt(max_dt) ,
+ m_interval_sequence( m_k_max+1 ) ,
+ m_coeff( m_k_max+1 ) ,
+ m_cost( m_k_max+1 ) ,
+ m_facmin_table( m_k_max+1 ) ,
+ m_table( m_k_max ) ,
+ STEPFAC1( 0.65 ) , STEPFAC2( 0.94 ) , STEPFAC3( 0.02 ) , STEPFAC4( 4.0 ) , KFAC1( 0.8 ) , KFAC2( 0.9 )
+ {
+ BOOST_USING_STD_MIN();
+ BOOST_USING_STD_MAX();
+ /* initialize sequence of stage numbers and work */
+ for( unsigned short i = 0; i < m_k_max+1; i++ )
+ {
+ m_interval_sequence[i] = 2 * (i+1);
+ if( i == 0 )
+ m_cost[i] = m_interval_sequence[i];
+ else
+ m_cost[i] = m_cost[i-1] + m_interval_sequence[i];
+ m_coeff[i].resize(i);
+ m_facmin_table[i] = pow BOOST_PREVENT_MACRO_SUBSTITUTION( STEPFAC3 , static_cast< value_type >(1) / static_cast< value_type >( 2*i+1 ) );
+ for( size_t k = 0 ; k < i ; ++k )
+ {
+ const value_type r = static_cast< value_type >( m_interval_sequence[i] ) / static_cast< value_type >( m_interval_sequence[k] );
+ m_coeff[i][k] = 1.0 / ( r*r - static_cast< value_type >( 1.0 ) ); // coefficients for extrapolation
+ }
+ }
+ reset();
+ }
+
+
+ /*
+ * Version 1 : try_step( sys , x , t , dt )
+ *
+ * The overloads are needed to solve the forwarding problem
+ */
+ template< class System , class StateInOut >
+ controlled_step_result try_step( System system , StateInOut &x , time_type &t , time_type &dt )
+ {
+ return try_step_v1( system , x , t, dt );
+ }
+
+ /**
+ * \brief Second version to solve the forwarding problem, can be used with Boost.Range as StateInOut.
+ */
+ template< class System , class StateInOut >
+ controlled_step_result try_step( System system , const StateInOut &x , time_type &t , time_type &dt )
+ {
+ return try_step_v1( system , x , t, dt );
+ }
+
+ /*
+ * Version 2 : try_step( sys , x , dxdt , t , dt )
+ *
+ * this version does not solve the forwarding problem, boost.range can not be used
+ */
+ template< class System , class StateInOut , class DerivIn >
+ controlled_step_result try_step( System system , StateInOut &x , const DerivIn &dxdt , time_type &t , time_type &dt )
+ {
+ m_xnew_resizer.adjust_size( x , detail::bind( &controlled_error_bs_type::template resize_m_xnew< StateInOut > , detail::ref( *this ) , detail::_1 ) );
+ controlled_step_result res = try_step( system , x , dxdt , t , m_xnew.m_v , dt );
+ if( res == success )
+ {
+ boost::numeric::odeint::copy( m_xnew.m_v , x );
+ }
+ return res;
+ }
+
+ /*
+ * Version 3 : try_step( sys , in , t , out , dt )
+ *
+ * this version does not solve the forwarding problem, boost.range can not be used
+ */
+ template< class System , class StateIn , class StateOut >
+ typename boost::disable_if< boost::is_same< StateIn , time_type > , controlled_step_result >::type
+ try_step( System system , const StateIn &in , time_type &t , StateOut &out , time_type &dt )
+ {
+ typename odeint::unwrap_reference< System >::type &sys = system;
+ m_dxdt_resizer.adjust_size( in , detail::bind( &controlled_error_bs_type::template resize_m_dxdt< StateIn > , detail::ref( *this ) , detail::_1 ) );
+ sys( in , m_dxdt.m_v , t );
+ return try_step( system , in , m_dxdt.m_v , t , out , dt );
+ }
+
+
+ /*
+ * Full version : try_step( sys , in , dxdt_in , t , out , dt )
+ *
+ * contains the actual implementation
+ */
+ template< class System , class StateIn , class DerivIn , class StateOut >
+ controlled_step_result try_step( System system , const StateIn &in , const DerivIn &dxdt , time_type &t , StateOut &out , time_type &dt )
+ {
+ if( m_max_dt != static_cast<time_type>(0) && detail::less_with_sign(m_max_dt, dt, dt) )
+ {
+ // given step size is bigger then max_dt
+ // set limit and return fail
+ dt = m_max_dt;
+ return fail;
+ }
+
+ BOOST_USING_STD_MIN();
+ BOOST_USING_STD_MAX();
+
+ static const value_type val1( 1.0 );
+
+ if( m_resizer.adjust_size( in , detail::bind( &controlled_error_bs_type::template resize_impl< StateIn > , detail::ref( *this ) , detail::_1 ) ) )
+ {
+ reset(); // system resized -> reset
+ }
+
+ if( dt != m_dt_last )
+ {
+ reset(); // step size changed from outside -> reset
+ }
+
+ bool reject( true );
+
+ time_vector h_opt( m_k_max+1 );
+ inv_time_vector work( m_k_max+1 );
+
+ time_type new_h = dt;
+
+ /* m_current_k_opt is the estimated current optimal stage number */
+ for( size_t k = 0 ; k <= m_current_k_opt+1 ; k++ )
+ {
+ /* the stage counts are stored in m_interval_sequence */
+ m_midpoint.set_steps( m_interval_sequence[k] );
+ if( k == 0 )
+ {
+ m_midpoint.do_step( system , in , dxdt , t , out , dt );
+ /* the first step, nothing more to do */
+ }
+ else
+ {
+ m_midpoint.do_step( system , in , dxdt , t , m_table[k-1].m_v , dt );
+ extrapolate( k , m_table , m_coeff , out );
+ // get error estimate
+ m_algebra.for_each3( m_err.m_v , out , m_table[0].m_v ,
+ typename operations_type::template scale_sum2< value_type , value_type >( val1 , -val1 ) );
+ const value_type error = m_error_checker.error( m_algebra , in , dxdt , m_err.m_v , dt );
+ h_opt[k] = calc_h_opt( dt , error , k );
+ work[k] = static_cast<value_type>( m_cost[k] ) / h_opt[k];
+
+ if( (k == m_current_k_opt-1) || m_first )
+ { // convergence before k_opt ?
+ if( error < 1.0 )
+ {
+ //convergence
+ reject = false;
+ if( (work[k] < KFAC2*work[k-1]) || (m_current_k_opt <= 2) )
+ {
+ // leave order as is (except we were in first round)
+ m_current_k_opt = min BOOST_PREVENT_MACRO_SUBSTITUTION( static_cast<int>(m_k_max)-1 , max BOOST_PREVENT_MACRO_SUBSTITUTION( 2 , static_cast<int>(k)+1 ) );
+ new_h = h_opt[k];
+ new_h *= static_cast<value_type>( m_cost[k+1] ) / static_cast<value_type>( m_cost[k] );
+ } else {
+ m_current_k_opt = min BOOST_PREVENT_MACRO_SUBSTITUTION( static_cast<int>(m_k_max)-1 , max BOOST_PREVENT_MACRO_SUBSTITUTION( 2 , static_cast<int>(k) ) );
+ new_h = h_opt[k];
+ }
+ break;
+ }
+ else if( should_reject( error , k ) && !m_first )
+ {
+ reject = true;
+ new_h = h_opt[k];
+ break;
+ }
+ }
+ if( k == m_current_k_opt )
+ { // convergence at k_opt ?
+ if( error < 1.0 )
+ {
+ //convergence
+ reject = false;
+ if( (work[k-1] < KFAC2*work[k]) )
+ {
+ m_current_k_opt = max BOOST_PREVENT_MACRO_SUBSTITUTION( 2 , static_cast<int>(m_current_k_opt)-1 );
+ new_h = h_opt[m_current_k_opt];
+ }
+ else if( (work[k] < KFAC2*work[k-1]) && !m_last_step_rejected )
+ {
+ m_current_k_opt = min BOOST_PREVENT_MACRO_SUBSTITUTION( static_cast<int>(m_k_max-1) , static_cast<int>(m_current_k_opt)+1 );
+ new_h = h_opt[k];
+ new_h *= static_cast<value_type>(m_cost[m_current_k_opt])/static_cast<value_type>(m_cost[k]);
+ } else
+ new_h = h_opt[m_current_k_opt];
+ break;
+ }
+ else if( should_reject( error , k ) )
+ {
+ reject = true;
+ new_h = h_opt[m_current_k_opt];
+ break;
+ }
+ }
+ if( k == m_current_k_opt+1 )
+ { // convergence at k_opt+1 ?
+ if( error < 1.0 )
+ { //convergence
+ reject = false;
+ if( work[k-2] < KFAC2*work[k-1] )
+ m_current_k_opt = max BOOST_PREVENT_MACRO_SUBSTITUTION( 2 , static_cast<int>(m_current_k_opt)-1 );
+ if( (work[k] < KFAC2*work[m_current_k_opt]) && !m_last_step_rejected )
+ m_current_k_opt = min BOOST_PREVENT_MACRO_SUBSTITUTION( static_cast<int>(m_k_max)-1 , static_cast<int>(k) );
+ new_h = h_opt[m_current_k_opt];
+ } else
+ {
+ reject = true;
+ new_h = h_opt[m_current_k_opt];
+ }
+ break;
+ }
+ }
+ }
+
+ if( !reject )
+ {
+ t += dt;
+ }
+
+ if( !m_last_step_rejected || boost::numeric::odeint::detail::less_with_sign(new_h, dt, dt) )
+ {
+ // limit step size
+ if( m_max_dt != static_cast<time_type>(0) )
+ {
+ new_h = detail::min_abs(m_max_dt, new_h);
+ }
+ m_dt_last = new_h;
+ dt = new_h;
+ }
+
+ m_last_step_rejected = reject;
+ m_first = false;
+
+ if( reject )
+ return fail;
+ else
+ return success;
+ }
+
+ /** \brief Resets the internal state of the stepper */
+ void reset()
+ {
+ m_first = true;
+ m_last_step_rejected = false;
+ // crude estimate of optimal order
+ m_current_k_opt = 4;
+ /* no calculation because log10 might not exist for value_type!
+ const value_type logfact( -log10( max BOOST_PREVENT_MACRO_SUBSTITUTION( eps_rel , static_cast< value_type >(1.0E-12) ) ) * 0.6 + 0.5 );
+ m_current_k_opt = max BOOST_PREVENT_MACRO_SUBSTITUTION( static_cast<value_type>( 1 ) , min BOOST_PREVENT_MACRO_SUBSTITUTION( static_cast<value_type>( m_k_max-1 ) , logfact ));
+ */
+ }
+
+
+ /* Resizer methods */
+
+ template< class StateIn >
+ void adjust_size( const StateIn &x )
+ {
+ resize_m_dxdt( x );
+ resize_m_xnew( x );
+ resize_impl( x );
+ m_midpoint.adjust_size( x );
+ }
+
+
+private:
+
+ template< class StateIn >
+ bool resize_m_dxdt( const StateIn &x )
+ {
+ return adjust_size_by_resizeability( m_dxdt , x , typename is_resizeable<deriv_type>::type() );
+ }
+
+ template< class StateIn >
+ bool resize_m_xnew( const StateIn &x )
+ {
+ return adjust_size_by_resizeability( m_xnew , x , typename is_resizeable<state_type>::type() );
+ }
+
+ template< class StateIn >
+ bool resize_impl( const StateIn &x )
+ {
+ bool resized( false );
+ for( size_t i = 0 ; i < m_k_max ; ++i )
+ resized |= adjust_size_by_resizeability( m_table[i] , x , typename is_resizeable<state_type>::type() );
+ resized |= adjust_size_by_resizeability( m_err , x , typename is_resizeable<state_type>::type() );
+ return resized;
+ }
+
+
+ template< class System , class StateInOut >
+ controlled_step_result try_step_v1( System system , StateInOut &x , time_type &t , time_type &dt )
+ {
+ typename odeint::unwrap_reference< System >::type &sys = system;
+ m_dxdt_resizer.adjust_size( x , detail::bind( &controlled_error_bs_type::template resize_m_dxdt< StateInOut > , detail::ref( *this ) , detail::_1 ) );
+ sys( x , m_dxdt.m_v ,t );
+ return try_step( system , x , m_dxdt.m_v , t , dt );
+ }
+
+
+ template< class StateInOut >
+ void extrapolate( size_t k , state_table_type &table , const value_matrix &coeff , StateInOut &xest )
+ /* polynomial extrapolation, see http://www.nr.com/webnotes/nr3web21.pdf
+ uses the obtained intermediate results to extrapolate to dt->0
+ */
+ {
+ static const value_type val1 = static_cast< value_type >( 1.0 );
+ for( int j=k-1 ; j>0 ; --j )
+ {
+ m_algebra.for_each3( table[j-1].m_v , table[j].m_v , table[j-1].m_v ,
+ typename operations_type::template scale_sum2< value_type , value_type >( val1 + coeff[k][j] , -coeff[k][j] ) );
+ }
+ m_algebra.for_each3( xest , table[0].m_v , xest ,
+ typename operations_type::template scale_sum2< value_type , value_type >( val1 + coeff[k][0] , -coeff[k][0]) );
+ }
+
+ time_type calc_h_opt( time_type h , value_type error , size_t k ) const
+ /* calculates the optimal step size for a given error and stage number */
+ {
+ BOOST_USING_STD_MIN();
+ BOOST_USING_STD_MAX();
+ using std::pow;
+ value_type expo( 1.0/(2*k+1) );
+ value_type facmin = m_facmin_table[k];
+ value_type fac;
+ if (error == 0.0)
+ fac=1.0/facmin;
+ else
+ {
+ fac = STEPFAC2 / pow BOOST_PREVENT_MACRO_SUBSTITUTION( error / STEPFAC1 , expo );
+ fac = max BOOST_PREVENT_MACRO_SUBSTITUTION( static_cast<value_type>(facmin/STEPFAC4) , min BOOST_PREVENT_MACRO_SUBSTITUTION( static_cast<value_type>(1.0/facmin) , fac ) );
+ }
+ return h*fac;
+ }
+
+ controlled_step_result set_k_opt( size_t k , const inv_time_vector &work , const time_vector &h_opt , time_type &dt )
+ /* calculates the optimal stage number */
+ {
+ if( k == 1 )
+ {
+ m_current_k_opt = 2;
+ return success;
+ }
+ if( (work[k-1] < KFAC1*work[k]) || (k == m_k_max) )
+ { // order decrease
+ m_current_k_opt = k-1;
+ dt = h_opt[ m_current_k_opt ];
+ return success;
+ }
+ else if( (work[k] < KFAC2*work[k-1]) || m_last_step_rejected || (k == m_k_max-1) )
+ { // same order - also do this if last step got rejected
+ m_current_k_opt = k;
+ dt = h_opt[ m_current_k_opt ];
+ return success;
+ }
+ else
+ { // order increase - only if last step was not rejected
+ m_current_k_opt = k+1;
+ dt = h_opt[ m_current_k_opt-1 ] * m_cost[ m_current_k_opt ] / m_cost[ m_current_k_opt-1 ] ;
+ return success;
+ }
+ }
+
+ bool in_convergence_window( size_t k ) const
+ {
+ if( (k == m_current_k_opt-1) && !m_last_step_rejected )
+ return true; // decrease stepsize only if last step was not rejected
+ return ( (k == m_current_k_opt) || (k == m_current_k_opt+1) );
+ }
+
+ bool should_reject( value_type error , size_t k ) const
+ {
+ if( k == m_current_k_opt-1 )
+ {
+ const value_type d = m_interval_sequence[m_current_k_opt] * m_interval_sequence[m_current_k_opt+1] /
+ (m_interval_sequence[0]*m_interval_sequence[0]);
+ //step will fail, criterion 17.3.17 in NR
+ return ( error > d*d );
+ }
+ else if( k == m_current_k_opt )
+ {
+ const value_type d = m_interval_sequence[m_current_k_opt] / m_interval_sequence[0];
+ return ( error > d*d );
+ } else
+ return error > 1.0;
+ }
+
+ default_error_checker< value_type, algebra_type , operations_type > m_error_checker;
+ modified_midpoint< state_type , value_type , deriv_type , time_type , algebra_type , operations_type , resizer_type > m_midpoint;
+
+ bool m_last_step_rejected;
+ bool m_first;
+
+ time_type m_dt_last;
+ time_type m_t_last;
+ time_type m_max_dt;
+
+ size_t m_current_k_opt;
+
+ algebra_type m_algebra;
+
+ resizer_type m_dxdt_resizer;
+ resizer_type m_xnew_resizer;
+ resizer_type m_resizer;
+
+ wrapped_state_type m_xnew;
+ wrapped_state_type m_err;
+ wrapped_deriv_type m_dxdt;
+
+ int_vector m_interval_sequence; // stores the successive interval counts
+ value_matrix m_coeff;
+ int_vector m_cost; // costs for interval count
+ value_vector m_facmin_table; // for precomputed facmin to save pow calls
+
+ state_table_type m_table; // sequence of states for extrapolation
+
+ value_type STEPFAC1 , STEPFAC2 , STEPFAC3 , STEPFAC4 , KFAC1 , KFAC2;
+};
+
+
+/******** DOXYGEN ********/
+/**
+ * \class bulirsch_stoer
+ * \brief The Bulirsch-Stoer algorithm.
+ *
+ * The Bulirsch-Stoer is a controlled stepper that adjusts both step size
+ * and order of the method. The algorithm uses the modified midpoint and
+ * a polynomial extrapolation compute the solution.
+ *
+ * \tparam State The state type.
+ * \tparam Value The value type.
+ * \tparam Deriv The type representing the time derivative of the state.
+ * \tparam Time The time representing the independent variable - the time.
+ * \tparam Algebra The algebra type.
+ * \tparam Operations The operations type.
+ * \tparam Resizer The resizer policy type.
+ */
+
+ /**
+ * \fn bulirsch_stoer::bulirsch_stoer( value_type eps_abs , value_type eps_rel , value_type factor_x , value_type factor_dxdt )
+ * \brief Constructs the bulirsch_stoer class, including initialization of
+ * the error bounds.
+ *
+ * \param eps_abs Absolute tolerance level.
+ * \param eps_rel Relative tolerance level.
+ * \param factor_x Factor for the weight of the state.
+ * \param factor_dxdt Factor for the weight of the derivative.
+ */
+
+ /**
+ * \fn bulirsch_stoer::try_step( System system , StateInOut &x , time_type &t , time_type &dt )
+ * \brief Tries to perform one step.
+ *
+ * This method tries to do one step with step size dt. If the error estimate
+ * is to large, the step is rejected and the method returns fail and the
+ * step size dt is reduced. If the error estimate is acceptably small, the
+ * step is performed, success is returned and dt might be increased to make
+ * the steps as large as possible. This method also updates t if a step is
+ * performed. Also, the internal order of the stepper is adjusted if required.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE.
+ * It must fulfill the Simple System concept.
+ * \param x The state of the ODE which should be solved. Overwritten if
+ * the step is successful.
+ * \param t The value of the time. Updated if the step is successful.
+ * \param dt The step size. Updated.
+ * \return success if the step was accepted, fail otherwise.
+ */
+
+ /**
+ * \fn bulirsch_stoer::try_step( System system , StateInOut &x , const DerivIn &dxdt , time_type &t , time_type &dt )
+ * \brief Tries to perform one step.
+ *
+ * This method tries to do one step with step size dt. If the error estimate
+ * is to large, the step is rejected and the method returns fail and the
+ * step size dt is reduced. If the error estimate is acceptably small, the
+ * step is performed, success is returned and dt might be increased to make
+ * the steps as large as possible. This method also updates t if a step is
+ * performed. Also, the internal order of the stepper is adjusted if required.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE.
+ * It must fulfill the Simple System concept.
+ * \param x The state of the ODE which should be solved. Overwritten if
+ * the step is successful.
+ * \param dxdt The derivative of state.
+ * \param t The value of the time. Updated if the step is successful.
+ * \param dt The step size. Updated.
+ * \return success if the step was accepted, fail otherwise.
+ */
+
+ /**
+ * \fn bulirsch_stoer::try_step( System system , const StateIn &in , time_type &t , StateOut &out , time_type &dt )
+ * \brief Tries to perform one step.
+ *
+ * \note This method is disabled if state_type=time_type to avoid ambiguity.
+ *
+ * This method tries to do one step with step size dt. If the error estimate
+ * is to large, the step is rejected and the method returns fail and the
+ * step size dt is reduced. If the error estimate is acceptably small, the
+ * step is performed, success is returned and dt might be increased to make
+ * the steps as large as possible. This method also updates t if a step is
+ * performed. Also, the internal order of the stepper is adjusted if required.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE.
+ * It must fulfill the Simple System concept.
+ * \param in The state of the ODE which should be solved.
+ * \param t The value of the time. Updated if the step is successful.
+ * \param out Used to store the result of the step.
+ * \param dt The step size. Updated.
+ * \return success if the step was accepted, fail otherwise.
+ */
+
+
+ /**
+ * \fn bulirsch_stoer::try_step( System system , const StateIn &in , const DerivIn &dxdt , time_type &t , StateOut &out , time_type &dt )
+ * \brief Tries to perform one step.
+ *
+ * This method tries to do one step with step size dt. If the error estimate
+ * is to large, the step is rejected and the method returns fail and the
+ * step size dt is reduced. If the error estimate is acceptably small, the
+ * step is performed, success is returned and dt might be increased to make
+ * the steps as large as possible. This method also updates t if a step is
+ * performed. Also, the internal order of the stepper is adjusted if required.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE.
+ * It must fulfill the Simple System concept.
+ * \param in The state of the ODE which should be solved.
+ * \param dxdt The derivative of state.
+ * \param t The value of the time. Updated if the step is successful.
+ * \param out Used to store the result of the step.
+ * \param dt The step size. Updated.
+ * \return success if the step was accepted, fail otherwise.
+ */
+
+
+ /**
+ * \fn bulirsch_stoer::adjust_size( const StateIn &x )
+ * \brief Adjust the size of all temporaries in the stepper manually.
+ * \param x A state from which the size of the temporaries to be resized is deduced.
+ */
+
+}
+}
+}
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_BULIRSCH_STOER_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/bulirsch_stoer_dense_out.hpp b/include/boost/numeric/odeint/stepper/bulirsch_stoer_dense_out.hpp
new file mode 100644
index 0000000..6a1eed1
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/bulirsch_stoer_dense_out.hpp
@@ -0,0 +1,838 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/bulirsch_stoer_dense_out.hpp
+
+ [begin_description]
+ Implementaiton of the Burlish-Stoer method with dense output
+ [end_description]
+
+ Copyright 2011-2015 Mario Mulansky
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2012 Christoph Koke
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_BULIRSCH_STOER_DENSE_OUT_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_BULIRSCH_STOER_DENSE_OUT_HPP_INCLUDED
+
+
+#include <iostream>
+
+#include <algorithm>
+
+#include <boost/config.hpp> // for min/max guidelines
+
+#include <boost/numeric/odeint/util/bind.hpp>
+
+#include <boost/math/special_functions/binomial.hpp>
+
+#include <boost/numeric/odeint/stepper/controlled_runge_kutta.hpp>
+#include <boost/numeric/odeint/stepper/modified_midpoint.hpp>
+#include <boost/numeric/odeint/stepper/controlled_step_result.hpp>
+#include <boost/numeric/odeint/algebra/range_algebra.hpp>
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
+
+#include <boost/numeric/odeint/util/state_wrapper.hpp>
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resizer.hpp>
+#include <boost/numeric/odeint/util/unit_helper.hpp>
+
+#include <boost/numeric/odeint/integrate/max_step_checker.hpp>
+
+#include <boost/type_traits.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template<
+ class State ,
+ class Value = double ,
+ class Deriv = State ,
+ class Time = Value ,
+ class Algebra = typename algebra_dispatcher< State >::algebra_type ,
+ class Operations = typename operations_dispatcher< State >::operations_type ,
+ class Resizer = initially_resizer
+ >
+class bulirsch_stoer_dense_out {
+
+
+public:
+
+ typedef State state_type;
+ typedef Value value_type;
+ typedef Deriv deriv_type;
+ typedef Time time_type;
+ typedef Algebra algebra_type;
+ typedef Operations operations_type;
+ typedef Resizer resizer_type;
+ typedef dense_output_stepper_tag stepper_category;
+#ifndef DOXYGEN_SKIP
+ typedef state_wrapper< state_type > wrapped_state_type;
+ typedef state_wrapper< deriv_type > wrapped_deriv_type;
+
+ typedef bulirsch_stoer_dense_out< State , Value , Deriv , Time , Algebra , Operations , Resizer > controlled_error_bs_type;
+
+ typedef typename inverse_time< time_type >::type inv_time_type;
+
+ typedef std::vector< value_type > value_vector;
+ typedef std::vector< time_type > time_vector;
+ typedef std::vector< inv_time_type > inv_time_vector; //should be 1/time_type for boost.units
+ typedef std::vector< value_vector > value_matrix;
+ typedef std::vector< size_t > int_vector;
+ typedef std::vector< wrapped_state_type > state_vector_type;
+ typedef std::vector< wrapped_deriv_type > deriv_vector_type;
+ typedef std::vector< deriv_vector_type > deriv_table_type;
+#endif //DOXYGEN_SKIP
+
+ const static size_t m_k_max = 8;
+
+
+
+ bulirsch_stoer_dense_out(
+ value_type eps_abs = 1E-6 , value_type eps_rel = 1E-6 ,
+ value_type factor_x = 1.0 , value_type factor_dxdt = 1.0 ,
+ time_type max_dt = static_cast<time_type>(0) ,
+ bool control_interpolation = false )
+ : m_error_checker( eps_abs , eps_rel , factor_x, factor_dxdt ) ,
+ m_max_dt(max_dt) ,
+ m_control_interpolation( control_interpolation) ,
+ m_last_step_rejected( false ) , m_first( true ) ,
+ m_current_state_x1( true ) ,
+ m_error( m_k_max ) ,
+ m_interval_sequence( m_k_max+1 ) ,
+ m_coeff( m_k_max+1 ) ,
+ m_cost( m_k_max+1 ) ,
+ m_facmin_table( m_k_max+1 ) ,
+ m_table( m_k_max ) ,
+ m_mp_states( m_k_max+1 ) ,
+ m_derivs( m_k_max+1 ) ,
+ m_diffs( 2*m_k_max+2 ) ,
+ STEPFAC1( 0.65 ) , STEPFAC2( 0.94 ) , STEPFAC3( 0.02 ) , STEPFAC4( 4.0 ) , KFAC1( 0.8 ) , KFAC2( 0.9 )
+ {
+ BOOST_USING_STD_MIN();
+ BOOST_USING_STD_MAX();
+
+ for( unsigned short i = 0; i < m_k_max+1; i++ )
+ {
+ /* only this specific sequence allows for dense output */
+ m_interval_sequence[i] = 2 + 4*i; // 2 6 10 14 ...
+ m_derivs[i].resize( m_interval_sequence[i] );
+ if( i == 0 )
+ {
+ m_cost[i] = m_interval_sequence[i];
+ } else
+ {
+ m_cost[i] = m_cost[i-1] + m_interval_sequence[i];
+ }
+ m_facmin_table[i] = pow BOOST_PREVENT_MACRO_SUBSTITUTION( STEPFAC3 , static_cast< value_type >(1) / static_cast< value_type >( 2*i+1 ) );
+ m_coeff[i].resize(i);
+ for( size_t k = 0 ; k < i ; ++k )
+ {
+ const value_type r = static_cast< value_type >( m_interval_sequence[i] ) / static_cast< value_type >( m_interval_sequence[k] );
+ m_coeff[i][k] = 1.0 / ( r*r - static_cast< value_type >( 1.0 ) ); // coefficients for extrapolation
+ }
+ // crude estimate of optimal order
+
+ m_current_k_opt = 4;
+ /* no calculation because log10 might not exist for value_type!
+ const value_type logfact( -log10( max BOOST_PREVENT_MACRO_SUBSTITUTION( eps_rel , static_cast< value_type >( 1.0E-12 ) ) ) * 0.6 + 0.5 );
+ m_current_k_opt = max BOOST_PREVENT_MACRO_SUBSTITUTION( 1 , min BOOST_PREVENT_MACRO_SUBSTITUTION( static_cast<int>( m_k_max-1 ) , static_cast<int>( logfact ) ));
+ */
+ }
+ int num = 1;
+ for( int i = 2*(m_k_max)+1 ; i >=0 ; i-- )
+ {
+ m_diffs[i].resize( num );
+ num += (i+1)%2;
+ }
+ }
+
+ template< class System , class StateIn , class DerivIn , class StateOut , class DerivOut >
+ controlled_step_result try_step( System system , const StateIn &in , const DerivIn &dxdt , time_type &t , StateOut &out , DerivOut &dxdt_new , time_type &dt )
+ {
+ if( m_max_dt != static_cast<time_type>(0) && detail::less_with_sign(m_max_dt, dt, dt) )
+ {
+ // given step size is bigger then max_dt
+ // set limit and return fail
+ dt = m_max_dt;
+ return fail;
+ }
+
+ BOOST_USING_STD_MIN();
+ BOOST_USING_STD_MAX();
+ using std::pow;
+
+ static const value_type val1( 1.0 );
+
+ bool reject( true );
+
+ time_vector h_opt( m_k_max+1 );
+ inv_time_vector work( m_k_max+1 );
+
+ m_k_final = 0;
+ time_type new_h = dt;
+
+ //std::cout << "t=" << t <<", dt=" << dt << ", k_opt=" << m_current_k_opt << ", first: " << m_first << std::endl;
+
+ for( size_t k = 0 ; k <= m_current_k_opt+1 ; k++ )
+ {
+ m_midpoint.set_steps( m_interval_sequence[k] );
+ if( k == 0 )
+ {
+ m_midpoint.do_step( system , in , dxdt , t , out , dt , m_mp_states[k].m_v , m_derivs[k]);
+ }
+ else
+ {
+ m_midpoint.do_step( system , in , dxdt , t , m_table[k-1].m_v , dt , m_mp_states[k].m_v , m_derivs[k] );
+ extrapolate( k , m_table , m_coeff , out );
+ // get error estimate
+ m_algebra.for_each3( m_err.m_v , out , m_table[0].m_v ,
+ typename operations_type::template scale_sum2< value_type , value_type >( val1 , -val1 ) );
+ const value_type error = m_error_checker.error( m_algebra , in , dxdt , m_err.m_v , dt );
+ h_opt[k] = calc_h_opt( dt , error , k );
+ work[k] = static_cast<value_type>( m_cost[k] ) / h_opt[k];
+
+ m_k_final = k;
+
+ if( (k == m_current_k_opt-1) || m_first )
+ { // convergence before k_opt ?
+ if( error < 1.0 )
+ {
+ //convergence
+ reject = false;
+ if( (work[k] < KFAC2*work[k-1]) || (m_current_k_opt <= 2) )
+ {
+ // leave order as is (except we were in first round)
+ m_current_k_opt = min BOOST_PREVENT_MACRO_SUBSTITUTION( static_cast<int>(m_k_max)-1 , max BOOST_PREVENT_MACRO_SUBSTITUTION( 2 , static_cast<int>(k)+1 ) );
+ new_h = h_opt[k] * static_cast<value_type>( m_cost[k+1] ) / static_cast<value_type>( m_cost[k] );
+ } else {
+ m_current_k_opt = min BOOST_PREVENT_MACRO_SUBSTITUTION( static_cast<int>(m_k_max)-1 , max BOOST_PREVENT_MACRO_SUBSTITUTION( 2 , static_cast<int>(k) ) );
+ new_h = h_opt[k];
+ }
+ break;
+ }
+ else if( should_reject( error , k ) && !m_first )
+ {
+ reject = true;
+ new_h = h_opt[k];
+ break;
+ }
+ }
+ if( k == m_current_k_opt )
+ { // convergence at k_opt ?
+ if( error < 1.0 )
+ {
+ //convergence
+ reject = false;
+ if( (work[k-1] < KFAC2*work[k]) )
+ {
+ m_current_k_opt = max BOOST_PREVENT_MACRO_SUBSTITUTION( 2 , static_cast<int>(m_current_k_opt)-1 );
+ new_h = h_opt[m_current_k_opt];
+ }
+ else if( (work[k] < KFAC2*work[k-1]) && !m_last_step_rejected )
+ {
+ m_current_k_opt = min BOOST_PREVENT_MACRO_SUBSTITUTION( static_cast<int>(m_k_max)-1 , static_cast<int>(m_current_k_opt)+1 );
+ new_h = h_opt[k]*static_cast<value_type>( m_cost[m_current_k_opt] ) / static_cast<value_type>( m_cost[k] );
+ } else
+ new_h = h_opt[m_current_k_opt];
+ break;
+ }
+ else if( should_reject( error , k ) )
+ {
+ reject = true;
+ new_h = h_opt[m_current_k_opt];
+ break;
+ }
+ }
+ if( k == m_current_k_opt+1 )
+ { // convergence at k_opt+1 ?
+ if( error < 1.0 )
+ { //convergence
+ reject = false;
+ if( work[k-2] < KFAC2*work[k-1] )
+ m_current_k_opt = max BOOST_PREVENT_MACRO_SUBSTITUTION( 2 , static_cast<int>(m_current_k_opt)-1 );
+ if( (work[k] < KFAC2*work[m_current_k_opt]) && !m_last_step_rejected )
+ m_current_k_opt = min BOOST_PREVENT_MACRO_SUBSTITUTION( static_cast<int>(m_k_max)-1 , static_cast<int>(k) );
+ new_h = h_opt[m_current_k_opt];
+ } else
+ {
+ reject = true;
+ new_h = h_opt[m_current_k_opt];
+ }
+ break;
+ }
+ }
+ }
+
+ if( !reject )
+ {
+
+ //calculate dxdt for next step and dense output
+ typename odeint::unwrap_reference< System >::type &sys = system;
+ sys( out , dxdt_new , t+dt );
+
+ //prepare dense output
+ value_type error = prepare_dense_output( m_k_final , in , dxdt , out , dxdt_new , dt );
+
+ if( error > static_cast<value_type>(10) ) // we are not as accurate for interpolation as for the steps
+ {
+ reject = true;
+ new_h = dt * pow BOOST_PREVENT_MACRO_SUBSTITUTION( error , static_cast<value_type>(-1)/(2*m_k_final+2) );
+ } else {
+ t += dt;
+ }
+ }
+ //set next stepsize
+ if( !m_last_step_rejected || (new_h < dt) )
+ {
+ // limit step size
+ if( m_max_dt != static_cast<time_type>(0) )
+ {
+ new_h = detail::min_abs(m_max_dt, new_h);
+ }
+ dt = new_h;
+ }
+
+ m_last_step_rejected = reject;
+ if( reject )
+ return fail;
+ else
+ return success;
+ }
+
+ template< class StateType >
+ void initialize( const StateType &x0 , const time_type &t0 , const time_type &dt0 )
+ {
+ m_resizer.adjust_size( x0 , detail::bind( &controlled_error_bs_type::template resize_impl< StateType > , detail::ref( *this ) , detail::_1 ) );
+ boost::numeric::odeint::copy( x0 , get_current_state() );
+ m_t = t0;
+ m_dt = dt0;
+ reset();
+ }
+
+
+ /* =======================================================
+ * the actual step method that should be called from outside (maybe make try_step private?)
+ */
+ template< class System >
+ std::pair< time_type , time_type > do_step( System system )
+ {
+ if( m_first )
+ {
+ typename odeint::unwrap_reference< System >::type &sys = system;
+ sys( get_current_state() , get_current_deriv() , m_t );
+ }
+
+ failed_step_checker fail_checker; // to throw a runtime_error if step size adjustment fails
+ controlled_step_result res = fail;
+ m_t_last = m_t;
+ while( res == fail )
+ {
+ res = try_step( system , get_current_state() , get_current_deriv() , m_t , get_old_state() , get_old_deriv() , m_dt );
+ m_first = false;
+ fail_checker(); // check for overflow of failed steps
+ }
+ toggle_current_state();
+ return std::make_pair( m_t_last , m_t );
+ }
+
+ /* performs the interpolation from a calculated step */
+ template< class StateOut >
+ void calc_state( time_type t , StateOut &x ) const
+ {
+ do_interpolation( t , x );
+ }
+
+ const state_type& current_state( void ) const
+ {
+ return get_current_state();
+ }
+
+ time_type current_time( void ) const
+ {
+ return m_t;
+ }
+
+ const state_type& previous_state( void ) const
+ {
+ return get_old_state();
+ }
+
+ time_type previous_time( void ) const
+ {
+ return m_t_last;
+ }
+
+ time_type current_time_step( void ) const
+ {
+ return m_dt;
+ }
+
+ /** \brief Resets the internal state of the stepper. */
+ void reset()
+ {
+ m_first = true;
+ m_last_step_rejected = false;
+ }
+
+ template< class StateIn >
+ void adjust_size( const StateIn &x )
+ {
+ resize_impl( x );
+ m_midpoint.adjust_size( x );
+ }
+
+
+private:
+
+ template< class StateInOut , class StateVector >
+ void extrapolate( size_t k , StateVector &table , const value_matrix &coeff , StateInOut &xest , size_t order_start_index = 0 )
+ //polynomial extrapolation, see http://www.nr.com/webnotes/nr3web21.pdf
+ {
+ static const value_type val1( 1.0 );
+ for( int j=k-1 ; j>0 ; --j )
+ {
+ m_algebra.for_each3( table[j-1].m_v , table[j].m_v , table[j-1].m_v ,
+ typename operations_type::template scale_sum2< value_type , value_type >( val1 + coeff[k + order_start_index][j + order_start_index] ,
+ -coeff[k + order_start_index][j + order_start_index] ) );
+ }
+ m_algebra.for_each3( xest , table[0].m_v , xest ,
+ typename operations_type::template scale_sum2< value_type , value_type >( val1 + coeff[k + order_start_index][0 + order_start_index] ,
+ -coeff[k + order_start_index][0 + order_start_index]) );
+ }
+
+
+ template< class StateVector >
+ void extrapolate_dense_out( size_t k , StateVector &table , const value_matrix &coeff , size_t order_start_index = 0 )
+ //polynomial extrapolation, see http://www.nr.com/webnotes/nr3web21.pdf
+ {
+ // result is written into table[0]
+ static const value_type val1( 1.0 );
+ for( int j=k ; j>1 ; --j )
+ {
+ m_algebra.for_each3( table[j-1].m_v , table[j].m_v , table[j-1].m_v ,
+ typename operations_type::template scale_sum2< value_type , value_type >( val1 + coeff[k + order_start_index][j + order_start_index - 1] ,
+ -coeff[k + order_start_index][j + order_start_index - 1] ) );
+ }
+ m_algebra.for_each3( table[0].m_v , table[1].m_v , table[0].m_v ,
+ typename operations_type::template scale_sum2< value_type , value_type >( val1 + coeff[k + order_start_index][order_start_index] ,
+ -coeff[k + order_start_index][order_start_index]) );
+ }
+
+ time_type calc_h_opt( time_type h , value_type error , size_t k ) const
+ {
+ BOOST_USING_STD_MIN();
+ BOOST_USING_STD_MAX();
+ using std::pow;
+
+ value_type expo = static_cast<value_type>(1)/(m_interval_sequence[k-1]);
+ value_type facmin = m_facmin_table[k];
+ value_type fac;
+ if (error == 0.0)
+ fac = static_cast<value_type>(1)/facmin;
+ else
+ {
+ fac = STEPFAC2 / pow BOOST_PREVENT_MACRO_SUBSTITUTION( error / STEPFAC1 , expo );
+ fac = max BOOST_PREVENT_MACRO_SUBSTITUTION( static_cast<value_type>( facmin/STEPFAC4 ) , min BOOST_PREVENT_MACRO_SUBSTITUTION( static_cast<value_type>(static_cast<value_type>(1)/facmin) , fac ) );
+ }
+ return h*fac;
+ }
+
+ bool in_convergence_window( size_t k ) const
+ {
+ if( (k == m_current_k_opt-1) && !m_last_step_rejected )
+ return true; // decrease order only if last step was not rejected
+ return ( (k == m_current_k_opt) || (k == m_current_k_opt+1) );
+ }
+
+ bool should_reject( value_type error , size_t k ) const
+ {
+ if( k == m_current_k_opt-1 )
+ {
+ const value_type d = m_interval_sequence[m_current_k_opt] * m_interval_sequence[m_current_k_opt+1] /
+ (m_interval_sequence[0]*m_interval_sequence[0]);
+ //step will fail, criterion 17.3.17 in NR
+ return ( error > d*d );
+ }
+ else if( k == m_current_k_opt )
+ {
+ const value_type d = m_interval_sequence[m_current_k_opt+1] / m_interval_sequence[0];
+ return ( error > d*d );
+ } else
+ return error > 1.0;
+ }
+
+ template< class StateIn1 , class DerivIn1 , class StateIn2 , class DerivIn2 >
+ value_type prepare_dense_output( int k , const StateIn1 &x_start , const DerivIn1 &dxdt_start ,
+ const StateIn2 & /* x_end */ , const DerivIn2 & /*dxdt_end */ , time_type dt )
+ /* k is the order to which the result was approximated */
+ {
+
+ /* compute the coefficients of the interpolation polynomial
+ * we parametrize the interval t .. t+dt by theta = -1 .. 1
+ * we use 2k+3 values at the interval center theta=0 to obtain the interpolation coefficients
+ * the values are x(t+dt/2) and the derivatives dx/dt , ... d^(2k+2) x / dt^(2k+2) at the midpoints
+ * the derivatives are approximated via finite differences
+ * all values are obtained from interpolation of the results from the increasing orders of the midpoint calls
+ */
+
+ // calculate finite difference approximations to derivatives at the midpoint
+ for( int j = 0 ; j<=k ; j++ )
+ {
+ /* not working with boost units... */
+ const value_type d = m_interval_sequence[j] / ( static_cast<value_type>(2) * dt );
+ value_type f = 1.0; //factor 1/2 here because our interpolation interval has length 2 !!!
+ for( int kappa = 0 ; kappa <= 2*j+1 ; ++kappa )
+ {
+ calculate_finite_difference( j , kappa , f , dxdt_start );
+ f *= d;
+ }
+
+ if( j > 0 )
+ extrapolate_dense_out( j , m_mp_states , m_coeff );
+ }
+
+ time_type d = dt/2;
+
+ // extrapolate finite differences
+ for( int kappa = 0 ; kappa<=2*k+1 ; kappa++ )
+ {
+ for( int j=1 ; j<=(k-kappa/2) ; ++j )
+ extrapolate_dense_out( j , m_diffs[kappa] , m_coeff , kappa/2 );
+
+ // extrapolation results are now stored in m_diffs[kappa][0]
+
+ // divide kappa-th derivative by kappa because we need these terms for dense output interpolation
+ m_algebra.for_each1( m_diffs[kappa][0].m_v , typename operations_type::template scale< time_type >( static_cast<time_type>(d) ) );
+
+ d *= dt/(2*(kappa+2));
+ }
+
+ // dense output coefficients a_0 is stored in m_mp_states[0], a_i for i = 1...2k are stored in m_diffs[i-1][0]
+
+ // the error is just the highest order coefficient of the interpolation polynomial
+ // this is because we use only the midpoint theta=0 as support for the interpolation (remember that theta = -1 .. 1)
+
+ value_type error = 0.0;
+ if( m_control_interpolation )
+ {
+ boost::numeric::odeint::copy( m_diffs[2*k+1][0].m_v , m_err.m_v );
+ error = m_error_checker.error( m_algebra , x_start , dxdt_start , m_err.m_v , dt );
+ }
+
+ return error;
+ }
+
+ template< class DerivIn >
+ void calculate_finite_difference( size_t j , size_t kappa , value_type fac , const DerivIn &dxdt )
+ {
+ const int m = m_interval_sequence[j]/2-1;
+ if( kappa == 0) // no calculation required for 0th derivative of f
+ {
+ m_algebra.for_each2( m_diffs[0][j].m_v , m_derivs[j][m].m_v ,
+ typename operations_type::template scale_sum1< value_type >( fac ) );
+ }
+ else
+ {
+ // calculate the index of m_diffs for this kappa-j-combination
+ const int j_diffs = j - kappa/2;
+
+ m_algebra.for_each2( m_diffs[kappa][j_diffs].m_v , m_derivs[j][m+kappa].m_v ,
+ typename operations_type::template scale_sum1< value_type >( fac ) );
+ value_type sign = -1.0;
+ int c = 1;
+ //computes the j-th order finite difference for the kappa-th derivative of f at t+dt/2 using function evaluations stored in m_derivs
+ for( int i = m+static_cast<int>(kappa)-2 ; i >= m-static_cast<int>(kappa) ; i -= 2 )
+ {
+ if( i >= 0 )
+ {
+ m_algebra.for_each3( m_diffs[kappa][j_diffs].m_v , m_diffs[kappa][j_diffs].m_v , m_derivs[j][i].m_v ,
+ typename operations_type::template scale_sum2< value_type , value_type >( 1.0 ,
+ sign * fac * boost::math::binomial_coefficient< value_type >( kappa , c ) ) );
+ }
+ else
+ {
+ m_algebra.for_each3( m_diffs[kappa][j_diffs].m_v , m_diffs[kappa][j_diffs].m_v , dxdt ,
+ typename operations_type::template scale_sum2< value_type , value_type >( 1.0 , sign * fac ) );
+ }
+ sign *= -1;
+ ++c;
+ }
+ }
+ }
+
+ template< class StateOut >
+ void do_interpolation( time_type t , StateOut &out ) const
+ {
+ // interpolation polynomial is defined for theta = -1 ... 1
+ // m_k_final is the number of order-iterations done for the last step - it governs the order of the interpolation polynomial
+ const value_type theta = 2 * get_unit_value( (t - m_t_last) / (m_t - m_t_last) ) - 1;
+ // we use only values at interval center, that is theta=0, for interpolation
+ // our interpolation polynomial is thus of order 2k+2, hence we have 2k+3 terms
+
+ boost::numeric::odeint::copy( m_mp_states[0].m_v , out );
+ // add remaining terms: x += a_1 theta + a2 theta^2 + ... + a_{2k} theta^{2k}
+ value_type theta_pow( theta );
+ for( size_t i=0 ; i<=2*m_k_final+1 ; ++i )
+ {
+ m_algebra.for_each3( out , out , m_diffs[i][0].m_v ,
+ typename operations_type::template scale_sum2< value_type >( static_cast<value_type>(1) , theta_pow ) );
+ theta_pow *= theta;
+ }
+ }
+
+ /* Resizer methods */
+ template< class StateIn >
+ bool resize_impl( const StateIn &x )
+ {
+ bool resized( false );
+
+ resized |= adjust_size_by_resizeability( m_x1 , x , typename is_resizeable<state_type>::type() );
+ resized |= adjust_size_by_resizeability( m_x2 , x , typename is_resizeable<state_type>::type() );
+ resized |= adjust_size_by_resizeability( m_dxdt1 , x , typename is_resizeable<state_type>::type() );
+ resized |= adjust_size_by_resizeability( m_dxdt2 , x , typename is_resizeable<state_type>::type() );
+ resized |= adjust_size_by_resizeability( m_err , x , typename is_resizeable<state_type>::type() );
+
+ for( size_t i = 0 ; i < m_k_max ; ++i )
+ resized |= adjust_size_by_resizeability( m_table[i] , x , typename is_resizeable<state_type>::type() );
+ for( size_t i = 0 ; i < m_k_max+1 ; ++i )
+ resized |= adjust_size_by_resizeability( m_mp_states[i] , x , typename is_resizeable<state_type>::type() );
+ for( size_t i = 0 ; i < m_k_max+1 ; ++i )
+ for( size_t j = 0 ; j < m_derivs[i].size() ; ++j )
+ resized |= adjust_size_by_resizeability( m_derivs[i][j] , x , typename is_resizeable<deriv_type>::type() );
+ for( size_t i = 0 ; i < 2*m_k_max+2 ; ++i )
+ for( size_t j = 0 ; j < m_diffs[i].size() ; ++j )
+ resized |= adjust_size_by_resizeability( m_diffs[i][j] , x , typename is_resizeable<deriv_type>::type() );
+
+ return resized;
+ }
+
+
+ state_type& get_current_state( void )
+ {
+ return m_current_state_x1 ? m_x1.m_v : m_x2.m_v ;
+ }
+
+ const state_type& get_current_state( void ) const
+ {
+ return m_current_state_x1 ? m_x1.m_v : m_x2.m_v ;
+ }
+
+ state_type& get_old_state( void )
+ {
+ return m_current_state_x1 ? m_x2.m_v : m_x1.m_v ;
+ }
+
+ const state_type& get_old_state( void ) const
+ {
+ return m_current_state_x1 ? m_x2.m_v : m_x1.m_v ;
+ }
+
+ deriv_type& get_current_deriv( void )
+ {
+ return m_current_state_x1 ? m_dxdt1.m_v : m_dxdt2.m_v ;
+ }
+
+ const deriv_type& get_current_deriv( void ) const
+ {
+ return m_current_state_x1 ? m_dxdt1.m_v : m_dxdt2.m_v ;
+ }
+
+ deriv_type& get_old_deriv( void )
+ {
+ return m_current_state_x1 ? m_dxdt2.m_v : m_dxdt1.m_v ;
+ }
+
+ const deriv_type& get_old_deriv( void ) const
+ {
+ return m_current_state_x1 ? m_dxdt2.m_v : m_dxdt1.m_v ;
+ }
+
+
+ void toggle_current_state( void )
+ {
+ m_current_state_x1 = ! m_current_state_x1;
+ }
+
+
+
+ default_error_checker< value_type, algebra_type , operations_type > m_error_checker;
+ modified_midpoint_dense_out< state_type , value_type , deriv_type , time_type , algebra_type , operations_type , resizer_type > m_midpoint;
+
+ time_type m_max_dt;
+
+ bool m_control_interpolation;
+
+ bool m_last_step_rejected;
+ bool m_first;
+
+ time_type m_t;
+ time_type m_dt;
+ time_type m_dt_last;
+ time_type m_t_last;
+
+ size_t m_current_k_opt;
+ size_t m_k_final;
+
+ algebra_type m_algebra;
+
+ resizer_type m_resizer;
+
+ wrapped_state_type m_x1 , m_x2;
+ wrapped_deriv_type m_dxdt1 , m_dxdt2;
+ wrapped_state_type m_err;
+ bool m_current_state_x1;
+
+
+
+ value_vector m_error; // errors of repeated midpoint steps and extrapolations
+ int_vector m_interval_sequence; // stores the successive interval counts
+ value_matrix m_coeff;
+ int_vector m_cost; // costs for interval count
+ value_vector m_facmin_table; // for precomputed facmin to save pow calls
+
+ state_vector_type m_table; // sequence of states for extrapolation
+
+ //for dense output:
+ state_vector_type m_mp_states; // sequence of approximations of x at distance center
+ deriv_table_type m_derivs; // table of function values
+ deriv_table_type m_diffs; // table of function values
+
+ //wrapped_state_type m_a1 , m_a2 , m_a3 , m_a4;
+
+ value_type STEPFAC1 , STEPFAC2 , STEPFAC3 , STEPFAC4 , KFAC1 , KFAC2;
+};
+
+
+
+/********** DOXYGEN **********/
+
+/**
+ * \class bulirsch_stoer_dense_out
+ * \brief The Bulirsch-Stoer algorithm.
+ *
+ * The Bulirsch-Stoer is a controlled stepper that adjusts both step size
+ * and order of the method. The algorithm uses the modified midpoint and
+ * a polynomial extrapolation compute the solution. This class also provides
+ * dense output facility.
+ *
+ * \tparam State The state type.
+ * \tparam Value The value type.
+ * \tparam Deriv The type representing the time derivative of the state.
+ * \tparam Time The time representing the independent variable - the time.
+ * \tparam Algebra The algebra type.
+ * \tparam Operations The operations type.
+ * \tparam Resizer The resizer policy type.
+ */
+
+ /**
+ * \fn bulirsch_stoer_dense_out::bulirsch_stoer_dense_out( value_type eps_abs , value_type eps_rel , value_type factor_x , value_type factor_dxdt , bool control_interpolation )
+ * \brief Constructs the bulirsch_stoer class, including initialization of
+ * the error bounds.
+ *
+ * \param eps_abs Absolute tolerance level.
+ * \param eps_rel Relative tolerance level.
+ * \param factor_x Factor for the weight of the state.
+ * \param factor_dxdt Factor for the weight of the derivative.
+ * \param control_interpolation Set true to additionally control the error of
+ * the interpolation.
+ */
+
+ /**
+ * \fn bulirsch_stoer_dense_out::try_step( System system , const StateIn &in , const DerivIn &dxdt , time_type &t , StateOut &out , DerivOut &dxdt_new , time_type &dt )
+ * \brief Tries to perform one step.
+ *
+ * This method tries to do one step with step size dt. If the error estimate
+ * is to large, the step is rejected and the method returns fail and the
+ * step size dt is reduced. If the error estimate is acceptably small, the
+ * step is performed, success is returned and dt might be increased to make
+ * the steps as large as possible. This method also updates t if a step is
+ * performed. Also, the internal order of the stepper is adjusted if required.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE.
+ * It must fulfill the Simple System concept.
+ * \param in The state of the ODE which should be solved.
+ * \param dxdt The derivative of state.
+ * \param t The value of the time. Updated if the step is successful.
+ * \param out Used to store the result of the step.
+ * \param dt The step size. Updated.
+ * \return success if the step was accepted, fail otherwise.
+ */
+
+ /**
+ * \fn bulirsch_stoer_dense_out::initialize( const StateType &x0 , const time_type &t0 , const time_type &dt0 )
+ * \brief Initializes the dense output stepper.
+ *
+ * \param x0 The initial state.
+ * \param t0 The initial time.
+ * \param dt0 The initial time step.
+ */
+
+ /**
+ * \fn bulirsch_stoer_dense_out::do_step( System system )
+ * \brief Does one time step. This is the main method that should be used to
+ * integrate an ODE with this stepper.
+ * \note initialize has to be called before using this method to set the
+ * initial conditions x,t and the stepsize.
+ * \param system The system function to solve, hence the r.h.s. of the
+ * ordinary differential equation. It must fulfill the Simple System concept.
+ * \return Pair with start and end time of the integration step.
+ */
+
+ /**
+ * \fn bulirsch_stoer_dense_out::calc_state( time_type t , StateOut &x ) const
+ * \brief Calculates the solution at an intermediate point within the last step
+ * \param t The time at which the solution should be calculated, has to be
+ * in the current time interval.
+ * \param x The output variable where the result is written into.
+ */
+
+ /**
+ * \fn bulirsch_stoer_dense_out::current_state( void ) const
+ * \brief Returns the current state of the solution.
+ * \return The current state of the solution x(t).
+ */
+
+ /**
+ * \fn bulirsch_stoer_dense_out::current_time( void ) const
+ * \brief Returns the current time of the solution.
+ * \return The current time of the solution t.
+ */
+
+ /**
+ * \fn bulirsch_stoer_dense_out::previous_state( void ) const
+ * \brief Returns the last state of the solution.
+ * \return The last state of the solution x(t-dt).
+ */
+
+ /**
+ * \fn bulirsch_stoer_dense_out::previous_time( void ) const
+ * \brief Returns the last time of the solution.
+ * \return The last time of the solution t-dt.
+ */
+
+ /**
+ * \fn bulirsch_stoer_dense_out::current_time_step( void ) const
+ * \brief Returns the current step size.
+ * \return The current step size.
+ */
+
+ /**
+ * \fn bulirsch_stoer_dense_out::adjust_size( const StateIn &x )
+ * \brief Adjust the size of all temporaries in the stepper manually.
+ * \param x A state from which the size of the temporaries to be resized is deduced.
+ */
+
+}
+}
+}
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_BULIRSCH_STOER_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/controlled_runge_kutta.hpp b/include/boost/numeric/odeint/stepper/controlled_runge_kutta.hpp
new file mode 100644
index 0000000..aac2b02
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/controlled_runge_kutta.hpp
@@ -0,0 +1,1014 @@
+/* [auto_generated]
+ boost/numeric/odeint/stepper/controlled_runge_kutta.hpp
+
+ [begin_description]
+ The default controlled stepper which can be used with all explicit Runge-Kutta error steppers.
+ [end_description]
+
+ Copyright 2010-2013 Karsten Ahnert
+ Copyright 2010-2015 Mario Mulansky
+ Copyright 2012 Christoph Koke
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_CONTROLLED_RUNGE_KUTTA_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_CONTROLLED_RUNGE_KUTTA_HPP_INCLUDED
+
+
+
+#include <cmath>
+
+#include <boost/config.hpp>
+#include <boost/utility/enable_if.hpp>
+#include <boost/type_traits/is_same.hpp>
+
+#include <boost/numeric/odeint/util/bind.hpp>
+#include <boost/numeric/odeint/util/unwrap_reference.hpp>
+#include <boost/numeric/odeint/util/copy.hpp>
+
+#include <boost/numeric/odeint/util/state_wrapper.hpp>
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resizer.hpp>
+#include <boost/numeric/odeint/util/detail/less_with_sign.hpp>
+
+#include <boost/numeric/odeint/algebra/range_algebra.hpp>
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+
+#include <boost/numeric/odeint/stepper/controlled_step_result.hpp>
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+template
+<
+class Value ,
+class Algebra ,
+class Operations
+>
+class default_error_checker
+{
+public:
+
+ typedef Value value_type;
+ typedef Algebra algebra_type;
+ typedef Operations operations_type;
+
+ default_error_checker(
+ value_type eps_abs = static_cast< value_type >( 1.0e-6 ) ,
+ value_type eps_rel = static_cast< value_type >( 1.0e-6 ) ,
+ value_type a_x = static_cast< value_type >( 1 ) ,
+ value_type a_dxdt = static_cast< value_type >( 1 ))
+ : m_eps_abs( eps_abs ) , m_eps_rel( eps_rel ) , m_a_x( a_x ) , m_a_dxdt( a_dxdt )
+ { }
+
+
+ template< class State , class Deriv , class Err, class Time >
+ value_type error( const State &x_old , const Deriv &dxdt_old , Err &x_err , Time dt ) const
+ {
+ return error( algebra_type() , x_old , dxdt_old , x_err , dt );
+ }
+
+ template< class State , class Deriv , class Err, class Time >
+ value_type error( algebra_type &algebra , const State &x_old , const Deriv &dxdt_old , Err &x_err , Time dt ) const
+ {
+ using std::abs;
+ // this overwrites x_err !
+ algebra.for_each3( x_err , x_old , dxdt_old ,
+ typename operations_type::template rel_error< value_type >( m_eps_abs , m_eps_rel , m_a_x , m_a_dxdt * abs(get_unit_value( dt )) ) );
+
+ // value_type res = algebra.reduce( x_err ,
+ // typename operations_type::template maximum< value_type >() , static_cast< value_type >( 0 ) );
+ return algebra.norm_inf( x_err );
+ }
+
+private:
+
+ value_type m_eps_abs;
+ value_type m_eps_rel;
+ value_type m_a_x;
+ value_type m_a_dxdt;
+
+};
+
+
+template< typename Value, typename Time >
+class default_step_adjuster
+{
+public:
+ typedef Time time_type;
+ typedef Value value_type;
+
+ default_step_adjuster(const time_type max_dt=static_cast<time_type>(0))
+ : m_max_dt(max_dt)
+ {}
+
+
+ time_type decrease_step(time_type dt, const value_type error, const int error_order) const
+ {
+ // returns the decreased time step
+ BOOST_USING_STD_MIN();
+ BOOST_USING_STD_MAX();
+ using std::pow;
+
+ dt *= max
+ BOOST_PREVENT_MACRO_SUBSTITUTION(
+ static_cast<value_type>( static_cast<value_type>(9) / static_cast<value_type>(10) *
+ pow(error, static_cast<value_type>(-1) / (error_order - 1))),
+ static_cast<value_type>( static_cast<value_type>(1) / static_cast<value_type> (5)));
+ if(m_max_dt != static_cast<time_type >(0))
+ // limit to maximal stepsize even when decreasing
+ dt = detail::min_abs(dt, m_max_dt);
+ return dt;
+ }
+
+ time_type increase_step(time_type dt, value_type error, const int stepper_order) const
+ {
+ // returns the increased time step
+ BOOST_USING_STD_MIN();
+ BOOST_USING_STD_MAX();
+ using std::pow;
+
+ // adjust the size if dt is smaller than max_dt (providede max_dt is not zero)
+ if(error < 0.5)
+ {
+ // error should be > 0
+ error = max BOOST_PREVENT_MACRO_SUBSTITUTION (
+ static_cast<value_type>( pow( static_cast<value_type>(5.0) , -static_cast<value_type>(stepper_order) ) ) ,
+ error);
+ // time_type dt_old = dt; unused variable warning
+ //error too small - increase dt and keep the evolution and limit scaling factor to 5.0
+ dt *= static_cast<value_type>(9)/static_cast<value_type>(10) *
+ pow(error, static_cast<value_type>(-1) / stepper_order);
+ if(m_max_dt != static_cast<time_type >(0))
+ // limit to maximal stepsize
+ dt = detail::min_abs(dt, m_max_dt);
+ }
+ return dt;
+ }
+
+ bool check_step_size_limit(const time_type dt)
+ {
+ if(m_max_dt != static_cast<time_type >(0))
+ return detail::less_eq_with_sign(dt, m_max_dt, dt);
+ return true;
+ }
+
+ time_type get_max_dt() { return m_max_dt; }
+
+private:
+ time_type m_max_dt;
+};
+
+
+
+/*
+ * error stepper category dispatcher
+ */
+template<
+class ErrorStepper ,
+class ErrorChecker = default_error_checker< typename ErrorStepper::value_type ,
+ typename ErrorStepper::algebra_type ,
+ typename ErrorStepper::operations_type > ,
+class StepAdjuster = default_step_adjuster< typename ErrorStepper::value_type ,
+ typename ErrorStepper::time_type > ,
+class Resizer = typename ErrorStepper::resizer_type ,
+class ErrorStepperCategory = typename ErrorStepper::stepper_category
+>
+class controlled_runge_kutta ;
+
+
+
+/*
+ * explicit stepper version
+ *
+ * this class introduces the following try_step overloads
+ * try_step( sys , x , t , dt )
+ * try_step( sys , x , dxdt , t , dt )
+ * try_step( sys , in , t , out , dt )
+ * try_step( sys , in , dxdt , t , out , dt )
+ */
+/**
+ * \brief Implements step size control for Runge-Kutta steppers with error
+ * estimation.
+ *
+ * This class implements the step size control for standard Runge-Kutta
+ * steppers with error estimation.
+ *
+ * \tparam ErrorStepper The stepper type with error estimation, has to fulfill the ErrorStepper concept.
+ * \tparam ErrorChecker The error checker
+ * \tparam Resizer The resizer policy type.
+ */
+template<
+class ErrorStepper,
+class ErrorChecker,
+class StepAdjuster,
+class Resizer
+>
+class controlled_runge_kutta< ErrorStepper , ErrorChecker , StepAdjuster, Resizer ,
+ explicit_error_stepper_tag >
+{
+
+public:
+
+ typedef ErrorStepper stepper_type;
+ typedef typename stepper_type::state_type state_type;
+ typedef typename stepper_type::value_type value_type;
+ typedef typename stepper_type::deriv_type deriv_type;
+ typedef typename stepper_type::time_type time_type;
+ typedef typename stepper_type::algebra_type algebra_type;
+ typedef typename stepper_type::operations_type operations_type;
+ typedef Resizer resizer_type;
+ typedef ErrorChecker error_checker_type;
+ typedef StepAdjuster step_adjuster_type;
+ typedef explicit_controlled_stepper_tag stepper_category;
+
+#ifndef DOXYGEN_SKIP
+ typedef typename stepper_type::wrapped_state_type wrapped_state_type;
+ typedef typename stepper_type::wrapped_deriv_type wrapped_deriv_type;
+
+ typedef controlled_runge_kutta< ErrorStepper , ErrorChecker , StepAdjuster ,
+ Resizer , explicit_error_stepper_tag > controlled_stepper_type;
+#endif //DOXYGEN_SKIP
+
+
+ /**
+ * \brief Constructs the controlled Runge-Kutta stepper.
+ * \param error_checker An instance of the error checker.
+ * \param stepper An instance of the underlying stepper.
+ */
+ controlled_runge_kutta(
+ const error_checker_type &error_checker = error_checker_type( ) ,
+ const step_adjuster_type &step_adjuster = step_adjuster_type() ,
+ const stepper_type &stepper = stepper_type( )
+ )
+ : m_stepper(stepper), m_error_checker(error_checker) , m_step_adjuster(step_adjuster)
+ { }
+
+
+
+ /*
+ * Version 1 : try_step( sys , x , t , dt )
+ *
+ * The overloads are needed to solve the forwarding problem
+ */
+ /**
+ * \brief Tries to perform one step.
+ *
+ * This method tries to do one step with step size dt. If the error estimate
+ * is to large, the step is rejected and the method returns fail and the
+ * step size dt is reduced. If the error estimate is acceptably small, the
+ * step is performed, success is returned and dt might be increased to make
+ * the steps as large as possible. This method also updates t if a step is
+ * performed.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param x The state of the ODE which should be solved. Overwritten if
+ * the step is successful.
+ * \param t The value of the time. Updated if the step is successful.
+ * \param dt The step size. Updated.
+ * \return success if the step was accepted, fail otherwise.
+ */
+ template< class System , class StateInOut >
+ controlled_step_result try_step( System system , StateInOut &x , time_type &t , time_type &dt )
+ {
+ return try_step_v1( system , x , t, dt );
+ }
+
+ /**
+ * \brief Tries to perform one step. Solves the forwarding problem and
+ * allows for using boost range as state_type.
+ *
+ * This method tries to do one step with step size dt. If the error estimate
+ * is to large, the step is rejected and the method returns fail and the
+ * step size dt is reduced. If the error estimate is acceptably small, the
+ * step is performed, success is returned and dt might be increased to make
+ * the steps as large as possible. This method also updates t if a step is
+ * performed.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param x The state of the ODE which should be solved. Overwritten if
+ * the step is successful. Can be a boost range.
+ * \param t The value of the time. Updated if the step is successful.
+ * \param dt The step size. Updated.
+ * \return success if the step was accepted, fail otherwise.
+ */
+ template< class System , class StateInOut >
+ controlled_step_result try_step( System system , const StateInOut &x , time_type &t , time_type &dt )
+ {
+ return try_step_v1( system , x , t, dt );
+ }
+
+
+
+ /*
+ * Version 2 : try_step( sys , x , dxdt , t , dt )
+ *
+ * this version does not solve the forwarding problem, boost.range can not be used
+ */
+ /**
+ * \brief Tries to perform one step.
+ *
+ * This method tries to do one step with step size dt. If the error estimate
+ * is to large, the step is rejected and the method returns fail and the
+ * step size dt is reduced. If the error estimate is acceptably small, the
+ * step is performed, success is returned and dt might be increased to make
+ * the steps as large as possible. This method also updates t if a step is
+ * performed.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param x The state of the ODE which should be solved. Overwritten if
+ * the step is successful.
+ * \param dxdt The derivative of state.
+ * \param t The value of the time. Updated if the step is successful.
+ * \param dt The step size. Updated.
+ * \return success if the step was accepted, fail otherwise.
+ */
+ template< class System , class StateInOut , class DerivIn >
+ controlled_step_result try_step( System system , StateInOut &x , const DerivIn &dxdt , time_type &t , time_type &dt )
+ {
+ m_xnew_resizer.adjust_size( x , detail::bind( &controlled_runge_kutta::template resize_m_xnew_impl< StateInOut > , detail::ref( *this ) , detail::_1 ) );
+ controlled_step_result res = try_step( system , x , dxdt , t , m_xnew.m_v , dt );
+ if( res == success )
+ {
+ boost::numeric::odeint::copy( m_xnew.m_v , x );
+ }
+ return res;
+ }
+
+ /*
+ * Version 3 : try_step( sys , in , t , out , dt )
+ *
+ * this version does not solve the forwarding problem, boost.range can not be used
+ *
+ * the disable is needed to avoid ambiguous overloads if state_type = time_type
+ */
+ /**
+ * \brief Tries to perform one step.
+ *
+ * \note This method is disabled if state_type=time_type to avoid ambiguity.
+ *
+ * This method tries to do one step with step size dt. If the error estimate
+ * is to large, the step is rejected and the method returns fail and the
+ * step size dt is reduced. If the error estimate is acceptably small, the
+ * step is performed, success is returned and dt might be increased to make
+ * the steps as large as possible. This method also updates t if a step is
+ * performed.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param in The state of the ODE which should be solved.
+ * \param t The value of the time. Updated if the step is successful.
+ * \param out Used to store the result of the step.
+ * \param dt The step size. Updated.
+ * \return success if the step was accepted, fail otherwise.
+ */
+ template< class System , class StateIn , class StateOut >
+ typename boost::disable_if< boost::is_same< StateIn , time_type > , controlled_step_result >::type
+ try_step( System system , const StateIn &in , time_type &t , StateOut &out , time_type &dt )
+ {
+ typename odeint::unwrap_reference< System >::type &sys = system;
+ m_dxdt_resizer.adjust_size( in , detail::bind( &controlled_runge_kutta::template resize_m_dxdt_impl< StateIn > , detail::ref( *this ) , detail::_1 ) );
+ sys( in , m_dxdt.m_v , t );
+ return try_step( system , in , m_dxdt.m_v , t , out , dt );
+ }
+
+
+ /*
+ * Version 4 : try_step( sys , in , dxdt , t , out , dt )
+ *
+ * this version does not solve the forwarding problem, boost.range can not be used
+ */
+ /**
+ * \brief Tries to perform one step.
+ *
+ * This method tries to do one step with step size dt. If the error estimate
+ * is to large, the step is rejected and the method returns fail and the
+ * step size dt is reduced. If the error estimate is acceptably small, the
+ * step is performed, success is returned and dt might be increased to make
+ * the steps as large as possible. This method also updates t if a step is
+ * performed.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param in The state of the ODE which should be solved.
+ * \param dxdt The derivative of state.
+ * \param t The value of the time. Updated if the step is successful.
+ * \param out Used to store the result of the step.
+ * \param dt The step size. Updated.
+ * \return success if the step was accepted, fail otherwise.
+ */
+ template< class System , class StateIn , class DerivIn , class StateOut >
+ controlled_step_result try_step( System system , const StateIn &in , const DerivIn &dxdt , time_type &t , StateOut &out , time_type &dt )
+ {
+ if( !m_step_adjuster.check_step_size_limit(dt) )
+ {
+ // given dt was above step size limit - adjust and return fail;
+ dt = m_step_adjuster.get_max_dt();
+ return fail;
+ }
+
+ m_xerr_resizer.adjust_size( in , detail::bind( &controlled_runge_kutta::template resize_m_xerr_impl< StateIn > , detail::ref( *this ) , detail::_1 ) );
+
+ // do one step with error calculation
+ m_stepper.do_step( system , in , dxdt , t , out , dt , m_xerr.m_v );
+
+ value_type max_rel_err = m_error_checker.error( m_stepper.algebra() , in , dxdt , m_xerr.m_v , dt );
+
+ if( max_rel_err > 1.0 )
+ {
+ // error too big, decrease step size and reject this step
+ dt = m_step_adjuster.decrease_step(dt, max_rel_err, m_stepper.error_order());
+ return fail;
+ } else
+ {
+ // otherwise, increase step size and accept
+ t += dt;
+ dt = m_step_adjuster.increase_step(dt, max_rel_err, m_stepper.stepper_order());
+ return success;
+ }
+ }
+
+ /**
+ * \brief Adjust the size of all temporaries in the stepper manually.
+ * \param x A state from which the size of the temporaries to be resized is deduced.
+ */
+ template< class StateType >
+ void adjust_size( const StateType &x )
+ {
+ resize_m_xerr_impl( x );
+ resize_m_dxdt_impl( x );
+ resize_m_xnew_impl( x );
+ m_stepper.adjust_size( x );
+ }
+
+ /**
+ * \brief Returns the instance of the underlying stepper.
+ * \returns The instance of the underlying stepper.
+ */
+ stepper_type& stepper( void )
+ {
+ return m_stepper;
+ }
+
+ /**
+ * \brief Returns the instance of the underlying stepper.
+ * \returns The instance of the underlying stepper.
+ */
+ const stepper_type& stepper( void ) const
+ {
+ return m_stepper;
+ }
+
+private:
+
+
+ template< class System , class StateInOut >
+ controlled_step_result try_step_v1( System system , StateInOut &x , time_type &t , time_type &dt )
+ {
+ typename odeint::unwrap_reference< System >::type &sys = system;
+ m_dxdt_resizer.adjust_size( x , detail::bind( &controlled_runge_kutta::template resize_m_dxdt_impl< StateInOut > , detail::ref( *this ) , detail::_1 ) );
+ sys( x , m_dxdt.m_v ,t );
+ return try_step( system , x , m_dxdt.m_v , t , dt );
+ }
+
+ template< class StateIn >
+ bool resize_m_xerr_impl( const StateIn &x )
+ {
+ return adjust_size_by_resizeability( m_xerr , x , typename is_resizeable<state_type>::type() );
+ }
+
+ template< class StateIn >
+ bool resize_m_dxdt_impl( const StateIn &x )
+ {
+ return adjust_size_by_resizeability( m_dxdt , x , typename is_resizeable<deriv_type>::type() );
+ }
+
+ template< class StateIn >
+ bool resize_m_xnew_impl( const StateIn &x )
+ {
+ return adjust_size_by_resizeability( m_xnew , x , typename is_resizeable<state_type>::type() );
+ }
+
+
+
+ stepper_type m_stepper;
+ error_checker_type m_error_checker;
+ step_adjuster_type m_step_adjuster;
+
+ resizer_type m_dxdt_resizer;
+ resizer_type m_xerr_resizer;
+ resizer_type m_xnew_resizer;
+
+ wrapped_deriv_type m_dxdt;
+ wrapped_state_type m_xerr;
+ wrapped_state_type m_xnew;
+};
+
+
+
+
+
+
+
+
+
+
+/*
+ * explicit stepper fsal version
+ *
+ * the class introduces the following try_step overloads
+ * try_step( sys , x , t , dt )
+ * try_step( sys , in , t , out , dt )
+ * try_step( sys , x , dxdt , t , dt )
+ * try_step( sys , in , dxdt_in , t , out , dxdt_out , dt )
+ */
+/**
+ * \brief Implements step size control for Runge-Kutta FSAL steppers with
+ * error estimation.
+ *
+ * This class implements the step size control for FSAL Runge-Kutta
+ * steppers with error estimation.
+ *
+ * \tparam ErrorStepper The stepper type with error estimation, has to fulfill the ErrorStepper concept.
+ * \tparam ErrorChecker The error checker
+ * \tparam Resizer The resizer policy type.
+ */
+template<
+class ErrorStepper ,
+class ErrorChecker ,
+class StepAdjuster ,
+class Resizer
+>
+class controlled_runge_kutta< ErrorStepper , ErrorChecker , StepAdjuster , Resizer , explicit_error_stepper_fsal_tag >
+{
+
+public:
+
+ typedef ErrorStepper stepper_type;
+ typedef typename stepper_type::state_type state_type;
+ typedef typename stepper_type::value_type value_type;
+ typedef typename stepper_type::deriv_type deriv_type;
+ typedef typename stepper_type::time_type time_type;
+ typedef typename stepper_type::algebra_type algebra_type;
+ typedef typename stepper_type::operations_type operations_type;
+ typedef Resizer resizer_type;
+ typedef ErrorChecker error_checker_type;
+ typedef StepAdjuster step_adjuster_type;
+ typedef explicit_controlled_stepper_fsal_tag stepper_category;
+
+#ifndef DOXYGEN_SKIP
+ typedef typename stepper_type::wrapped_state_type wrapped_state_type;
+ typedef typename stepper_type::wrapped_deriv_type wrapped_deriv_type;
+
+ typedef controlled_runge_kutta< ErrorStepper , ErrorChecker , StepAdjuster , Resizer , explicit_error_stepper_tag > controlled_stepper_type;
+#endif // DOXYGEN_SKIP
+
+ /**
+ * \brief Constructs the controlled Runge-Kutta stepper.
+ * \param error_checker An instance of the error checker.
+ * \param stepper An instance of the underlying stepper.
+ */
+ controlled_runge_kutta(
+ const error_checker_type &error_checker = error_checker_type() ,
+ const step_adjuster_type &step_adjuster = step_adjuster_type() ,
+ const stepper_type &stepper = stepper_type()
+ )
+ : m_stepper( stepper ) , m_error_checker( error_checker ) , m_step_adjuster(step_adjuster) ,
+ m_first_call( true )
+ { }
+
+ /*
+ * Version 1 : try_step( sys , x , t , dt )
+ *
+ * The two overloads are needed in order to solve the forwarding problem
+ */
+ /**
+ * \brief Tries to perform one step.
+ *
+ * This method tries to do one step with step size dt. If the error estimate
+ * is to large, the step is rejected and the method returns fail and the
+ * step size dt is reduced. If the error estimate is acceptably small, the
+ * step is performed, success is returned and dt might be increased to make
+ * the steps as large as possible. This method also updates t if a step is
+ * performed.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param x The state of the ODE which should be solved. Overwritten if
+ * the step is successful.
+ * \param t The value of the time. Updated if the step is successful.
+ * \param dt The step size. Updated.
+ * \return success if the step was accepted, fail otherwise.
+ */
+ template< class System , class StateInOut >
+ controlled_step_result try_step( System system , StateInOut &x , time_type &t , time_type &dt )
+ {
+ return try_step_v1( system , x , t , dt );
+ }
+
+
+ /**
+ * \brief Tries to perform one step. Solves the forwarding problem and
+ * allows for using boost range as state_type.
+ *
+ * This method tries to do one step with step size dt. If the error estimate
+ * is to large, the step is rejected and the method returns fail and the
+ * step size dt is reduced. If the error estimate is acceptably small, the
+ * step is performed, success is returned and dt might be increased to make
+ * the steps as large as possible. This method also updates t if a step is
+ * performed.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param x The state of the ODE which should be solved. Overwritten if
+ * the step is successful. Can be a boost range.
+ * \param t The value of the time. Updated if the step is successful.
+ * \param dt The step size. Updated.
+ * \return success if the step was accepted, fail otherwise.
+ */
+ template< class System , class StateInOut >
+ controlled_step_result try_step( System system , const StateInOut &x , time_type &t , time_type &dt )
+ {
+ return try_step_v1( system , x , t , dt );
+ }
+
+
+
+ /*
+ * Version 2 : try_step( sys , in , t , out , dt );
+ *
+ * This version does not solve the forwarding problem, boost::range can not be used.
+ *
+ * The disabler is needed to solve ambiguous overloads
+ */
+ /**
+ * \brief Tries to perform one step.
+ *
+ * \note This method is disabled if state_type=time_type to avoid ambiguity.
+ *
+ * This method tries to do one step with step size dt. If the error estimate
+ * is to large, the step is rejected and the method returns fail and the
+ * step size dt is reduced. If the error estimate is acceptably small, the
+ * step is performed, success is returned and dt might be increased to make
+ * the steps as large as possible. This method also updates t if a step is
+ * performed.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param in The state of the ODE which should be solved.
+ * \param t The value of the time. Updated if the step is successful.
+ * \param out Used to store the result of the step.
+ * \param dt The step size. Updated.
+ * \return success if the step was accepted, fail otherwise.
+ */
+ template< class System , class StateIn , class StateOut >
+ typename boost::disable_if< boost::is_same< StateIn , time_type > , controlled_step_result >::type
+ try_step( System system , const StateIn &in , time_type &t , StateOut &out , time_type &dt )
+ {
+ if( m_dxdt_resizer.adjust_size( in , detail::bind( &controlled_runge_kutta::template resize_m_dxdt_impl< StateIn > , detail::ref( *this ) , detail::_1 ) ) || m_first_call )
+ {
+ initialize( system , in , t );
+ }
+ return try_step( system , in , m_dxdt.m_v , t , out , dt );
+ }
+
+
+ /*
+ * Version 3 : try_step( sys , x , dxdt , t , dt )
+ *
+ * This version does not solve the forwarding problem, boost::range can not be used.
+ */
+ /**
+ * \brief Tries to perform one step.
+ *
+ * This method tries to do one step with step size dt. If the error estimate
+ * is to large, the step is rejected and the method returns fail and the
+ * step size dt is reduced. If the error estimate is acceptably small, the
+ * step is performed, success is returned and dt might be increased to make
+ * the steps as large as possible. This method also updates t if a step is
+ * performed.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param x The state of the ODE which should be solved. Overwritten if
+ * the step is successful.
+ * \param dxdt The derivative of state.
+ * \param t The value of the time. Updated if the step is successful.
+ * \param dt The step size. Updated.
+ * \return success if the step was accepted, fail otherwise.
+ */
+ template< class System , class StateInOut , class DerivInOut >
+ controlled_step_result try_step( System system , StateInOut &x , DerivInOut &dxdt , time_type &t , time_type &dt )
+ {
+ m_xnew_resizer.adjust_size( x , detail::bind( &controlled_runge_kutta::template resize_m_xnew_impl< StateInOut > , detail::ref( *this ) , detail::_1 ) );
+ m_dxdt_new_resizer.adjust_size( x , detail::bind( &controlled_runge_kutta::template resize_m_dxdt_new_impl< StateInOut > , detail::ref( *this ) , detail::_1 ) );
+ controlled_step_result res = try_step( system , x , dxdt , t , m_xnew.m_v , m_dxdtnew.m_v , dt );
+ if( res == success )
+ {
+ boost::numeric::odeint::copy( m_xnew.m_v , x );
+ boost::numeric::odeint::copy( m_dxdtnew.m_v , dxdt );
+ }
+ return res;
+ }
+
+
+ /*
+ * Version 4 : try_step( sys , in , dxdt_in , t , out , dxdt_out , dt )
+ *
+ * This version does not solve the forwarding problem, boost::range can not be used.
+ */
+ /**
+ * \brief Tries to perform one step.
+ *
+ * This method tries to do one step with step size dt. If the error estimate
+ * is to large, the step is rejected and the method returns fail and the
+ * step size dt is reduced. If the error estimate is acceptably small, the
+ * step is performed, success is returned and dt might be increased to make
+ * the steps as large as possible. This method also updates t if a step is
+ * performed.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param in The state of the ODE which should be solved.
+ * \param dxdt The derivative of state.
+ * \param t The value of the time. Updated if the step is successful.
+ * \param out Used to store the result of the step.
+ * \param dt The step size. Updated.
+ * \return success if the step was accepted, fail otherwise.
+ */
+ template< class System , class StateIn , class DerivIn , class StateOut , class DerivOut >
+ controlled_step_result try_step( System system , const StateIn &in , const DerivIn &dxdt_in , time_type &t ,
+ StateOut &out , DerivOut &dxdt_out , time_type &dt )
+ {
+ if( !m_step_adjuster.check_step_size_limit(dt) )
+ {
+ // given dt was above step size limit - adjust and return fail;
+ dt = m_step_adjuster.get_max_dt();
+ return fail;
+ }
+
+ m_xerr_resizer.adjust_size( in , detail::bind( &controlled_runge_kutta::template resize_m_xerr_impl< StateIn > , detail::ref( *this ) , detail::_1 ) );
+
+ //fsal: m_stepper.get_dxdt( dxdt );
+ //fsal: m_stepper.do_step( sys , x , dxdt , t , dt , m_x_err );
+ m_stepper.do_step( system , in , dxdt_in , t , out , dxdt_out , dt , m_xerr.m_v );
+
+ // this potentially overwrites m_x_err! (standard_error_checker does, at least)
+ value_type max_rel_err = m_error_checker.error( m_stepper.algebra() , in , dxdt_in , m_xerr.m_v , dt );
+
+ if( max_rel_err > 1.0 )
+ {
+ // error too big, decrease step size and reject this step
+ dt = m_step_adjuster.decrease_step(dt, max_rel_err, m_stepper.error_order());
+ return fail;
+ }
+ // otherwise, increase step size and accept
+ t += dt;
+ dt = m_step_adjuster.increase_step(dt, max_rel_err, m_stepper.stepper_order());
+ return success;
+ }
+
+
+ /**
+ * \brief Resets the internal state of the underlying FSAL stepper.
+ */
+ void reset( void )
+ {
+ m_first_call = true;
+ }
+
+ /**
+ * \brief Initializes the internal state storing an internal copy of the derivative.
+ *
+ * \param deriv The initial derivative of the ODE.
+ */
+ template< class DerivIn >
+ void initialize( const DerivIn &deriv )
+ {
+ boost::numeric::odeint::copy( deriv , m_dxdt.m_v );
+ m_first_call = false;
+ }
+
+ /**
+ * \brief Initializes the internal state storing an internal copy of the derivative.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param x The initial state of the ODE which should be solved.
+ * \param t The initial time.
+ */
+ template< class System , class StateIn >
+ void initialize( System system , const StateIn &x , time_type t )
+ {
+ typename odeint::unwrap_reference< System >::type &sys = system;
+ sys( x , m_dxdt.m_v , t );
+ m_first_call = false;
+ }
+
+ /**
+ * \brief Returns true if the stepper has been initialized, false otherwise.
+ *
+ * \return true, if the stepper has been initialized, false otherwise.
+ */
+ bool is_initialized( void ) const
+ {
+ return ! m_first_call;
+ }
+
+
+ /**
+ * \brief Adjust the size of all temporaries in the stepper manually.
+ * \param x A state from which the size of the temporaries to be resized is deduced.
+ */
+ template< class StateType >
+ void adjust_size( const StateType &x )
+ {
+ resize_m_xerr_impl( x );
+ resize_m_dxdt_impl( x );
+ resize_m_dxdt_new_impl( x );
+ resize_m_xnew_impl( x );
+ }
+
+
+ /**
+ * \brief Returns the instance of the underlying stepper.
+ * \returns The instance of the underlying stepper.
+ */
+ stepper_type& stepper( void )
+ {
+ return m_stepper;
+ }
+
+ /**
+ * \brief Returns the instance of the underlying stepper.
+ * \returns The instance of the underlying stepper.
+ */
+ const stepper_type& stepper( void ) const
+ {
+ return m_stepper;
+ }
+
+
+
+private:
+
+
+ template< class StateIn >
+ bool resize_m_xerr_impl( const StateIn &x )
+ {
+ return adjust_size_by_resizeability( m_xerr , x , typename is_resizeable<state_type>::type() );
+ }
+
+ template< class StateIn >
+ bool resize_m_dxdt_impl( const StateIn &x )
+ {
+ return adjust_size_by_resizeability( m_dxdt , x , typename is_resizeable<deriv_type>::type() );
+ }
+
+ template< class StateIn >
+ bool resize_m_dxdt_new_impl( const StateIn &x )
+ {
+ return adjust_size_by_resizeability( m_dxdtnew , x , typename is_resizeable<deriv_type>::type() );
+ }
+
+ template< class StateIn >
+ bool resize_m_xnew_impl( const StateIn &x )
+ {
+ return adjust_size_by_resizeability( m_xnew , x , typename is_resizeable<state_type>::type() );
+ }
+
+
+ template< class System , class StateInOut >
+ controlled_step_result try_step_v1( System system , StateInOut &x , time_type &t , time_type &dt )
+ {
+ if( m_dxdt_resizer.adjust_size( x , detail::bind( &controlled_runge_kutta::template resize_m_dxdt_impl< StateInOut > , detail::ref( *this ) , detail::_1 ) ) || m_first_call )
+ {
+ initialize( system , x , t );
+ }
+ return try_step( system , x , m_dxdt.m_v , t , dt );
+ }
+
+
+ stepper_type m_stepper;
+ error_checker_type m_error_checker;
+ step_adjuster_type m_step_adjuster;
+
+ resizer_type m_dxdt_resizer;
+ resizer_type m_xerr_resizer;
+ resizer_type m_xnew_resizer;
+ resizer_type m_dxdt_new_resizer;
+
+ wrapped_deriv_type m_dxdt;
+ wrapped_state_type m_xerr;
+ wrapped_state_type m_xnew;
+ wrapped_deriv_type m_dxdtnew;
+ bool m_first_call;
+};
+
+
+/********** DOXYGEN **********/
+
+/**** DEFAULT ERROR CHECKER ****/
+
+/**
+ * \class default_error_checker
+ * \brief The default error checker to be used with Runge-Kutta error steppers
+ *
+ * This class provides the default mechanism to compare the error estimates
+ * reported by Runge-Kutta error steppers with user defined error bounds.
+ * It is used by the controlled_runge_kutta steppers.
+ *
+ * \tparam Value The value type.
+ * \tparam Time The time type.
+ * \tparam Algebra The algebra type.
+ * \tparam Operations The operations type.
+ */
+
+ /**
+ * \fn default_error_checker( value_type eps_abs , value_type eps_rel , value_type a_x , value_type a_dxdt ,
+ * time_type max_dt)
+ * \brief Constructs the error checker.
+ *
+ * The error is calculated as follows: ????
+ *
+ * \param eps_abs Absolute tolerance level.
+ * \param eps_rel Relative tolerance level.
+ * \param a_x Factor for the weight of the state.
+ * \param a_dxdt Factor for the weight of the derivative.
+ * \param max_dt Maximum allowed step size.
+ */
+
+ /**
+ * \fn error( const State &x_old , const Deriv &dxdt_old , Err &x_err , time_type dt ) const
+ * \brief Calculates the error level.
+ *
+ * If the returned error level is greater than 1, the estimated error was
+ * larger than the permitted error bounds and the step should be repeated
+ * with a smaller step size.
+ *
+ * \param x_old State at the beginning of the step.
+ * \param dxdt_old Derivative at the beginning of the step.
+ * \param x_err Error estimate.
+ * \param dt Time step.
+ * \return error
+ */
+
+ /**
+ * \fn error( algebra_type &algebra , const State &x_old , const Deriv &dxdt_old , Err &x_err , time_type dt ) const
+ * \brief Calculates the error level using a given algebra.
+ *
+ * If the returned error level is greater than 1, the estimated error was
+ * larger than the permitted error bounds and the step should be repeated
+ * with a smaller step size.
+ *
+ * \param algebra The algebra used for calculation of the error.
+ * \param x_old State at the beginning of the step.
+ * \param dxdt_old Derivative at the beginning of the step.
+ * \param x_err Error estimate.
+ * \param dt Time step.
+ * \return error
+ */
+
+ /**
+ * \fn time_type decrease_step(const time_type dt, const value_type error, const int error_order)
+ * \brief Returns a decreased step size based on the given error and order
+ *
+ * Calculates a new smaller step size based on the given error and its order.
+ *
+ * \param dt The old step size.
+ * \param error The computed error estimate.
+ * \param error_order The error order of the stepper.
+ * \return dt_new The new, reduced step size.
+ */
+
+ /**
+ * \fn time_type increase_step(const time_type dt, const value_type error, const int error_order)
+ * \brief Returns an increased step size based on the given error and order.
+ *
+ * Calculates a new bigger step size based on the given error and its order. If max_dt != 0, the
+ * new step size is limited to max_dt.
+ *
+ * \param dt The old step size.
+ * \param error The computed error estimate.
+ * \param error_order The order of the stepper.
+ * \return dt_new The new, increased step size.
+ */
+
+
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_CONTROLLED_RUNGE_KUTTA_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/controlled_step_result.hpp b/include/boost/numeric/odeint/stepper/controlled_step_result.hpp
new file mode 100644
index 0000000..7f17726
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/controlled_step_result.hpp
@@ -0,0 +1,42 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/controlled_step_result.hpp
+
+ [begin_description]
+ Defines the result type for all controlled stepper.
+ [end_description]
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_CONTROLLED_STEP_RESULT_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_CONTROLLED_STEP_RESULT_HPP_INCLUDED
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+/**
+ * \enum controlled_step_result
+ *
+ * \brief Enum representing the return values of the controlled steppers.
+ */
+typedef enum
+{
+ success , /**< The trial step was successful, hence the state and the time have been advanced. */
+ fail /**< The step was not successful and might possibly be repeated with a small step size. */
+} controlled_step_result;
+
+} // namespace odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_CONTROLLED_STEP_RESULT_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/dense_output_runge_kutta.hpp b/include/boost/numeric/odeint/stepper/dense_output_runge_kutta.hpp
new file mode 100644
index 0000000..94abc5a
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/dense_output_runge_kutta.hpp
@@ -0,0 +1,476 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/dense_output_runge_kutta.hpp
+
+ [begin_description]
+ Implementation of the Dense-output stepper for all steppers. Note, that this class does
+ not computes the result but serves as an interface.
+ [end_description]
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011-2015 Mario Mulansky
+ Copyright 2012 Christoph Koke
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_DENSE_OUTPUT_RUNGE_KUTTA_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_DENSE_OUTPUT_RUNGE_KUTTA_HPP_INCLUDED
+
+
+#include <utility>
+#include <stdexcept>
+
+#include <boost/throw_exception.hpp>
+
+#include <boost/numeric/odeint/util/bind.hpp>
+
+#include <boost/numeric/odeint/util/copy.hpp>
+
+#include <boost/numeric/odeint/util/state_wrapper.hpp>
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resizer.hpp>
+
+#include <boost/numeric/odeint/stepper/controlled_step_result.hpp>
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+
+#include <boost/numeric/odeint/integrate/max_step_checker.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template< class Stepper , class StepperCategory = typename Stepper::stepper_category >
+class dense_output_runge_kutta;
+
+
+/**
+ * \brief The class representing dense-output Runge-Kutta steppers.
+ * \note In this stepper, the initialize method has to be called before using
+ * the do_step method.
+ *
+ * The dense-output functionality allows to interpolate the solution between
+ * subsequent integration points using intermediate results obtained during the
+ * computation. This version works based on a normal stepper without step-size
+ * control.
+ *
+ *
+ * \tparam Stepper The stepper type of the underlying algorithm.
+ */
+template< class Stepper >
+class dense_output_runge_kutta< Stepper , stepper_tag >
+{
+
+public:
+
+ /*
+ * We do not need all typedefs.
+ */
+ typedef Stepper stepper_type;
+ typedef typename stepper_type::state_type state_type;
+ typedef typename stepper_type::wrapped_state_type wrapped_state_type;
+ typedef typename stepper_type::value_type value_type;
+ typedef typename stepper_type::deriv_type deriv_type;
+ typedef typename stepper_type::wrapped_deriv_type wrapped_deriv_type;
+ typedef typename stepper_type::time_type time_type;
+ typedef typename stepper_type::algebra_type algebra_type;
+ typedef typename stepper_type::operations_type operations_type;
+ typedef typename stepper_type::resizer_type resizer_type;
+ typedef dense_output_stepper_tag stepper_category;
+ typedef dense_output_runge_kutta< Stepper > dense_output_stepper_type;
+
+
+ /**
+ * \brief Constructs the dense_output_runge_kutta class. An instance of the
+ * underlying stepper can be provided.
+ * \param stepper An instance of the underlying stepper.
+ */
+ dense_output_runge_kutta( const stepper_type &stepper = stepper_type() )
+ : m_stepper( stepper ) , m_resizer() ,
+ m_x1() , m_x2() , m_current_state_x1( true ) ,
+ m_t() , m_t_old() , m_dt()
+ { }
+
+
+ /**
+ * \brief Initializes the stepper. Has to be called before do_step can be
+ * used to set the initial conditions and the step size.
+ * \param x0 The initial state of the ODE which should be solved.
+ * \param t0 The initial time, at which the step should be performed.
+ * \param dt0 The step size.
+ */
+ template< class StateType >
+ void initialize( const StateType &x0 , time_type t0 , time_type dt0 )
+ {
+ m_resizer.adjust_size( x0 , detail::bind( &dense_output_stepper_type::template resize_impl< StateType > , detail::ref( *this ) , detail::_1 ) );
+ boost::numeric::odeint::copy( x0 , get_current_state() );
+ m_t = t0;
+ m_dt = dt0;
+ }
+
+ /**
+ * \brief Does one time step.
+ * \note initialize has to be called before using this method to set the
+ * initial conditions x,t and the stepsize.
+ * \param system The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the
+ * Simple System concept.
+ * \return Pair with start and end time of the integration step.
+ */
+ template< class System >
+ std::pair< time_type , time_type > do_step( System system )
+ {
+ m_stepper.do_step( system , get_current_state() , m_t , get_old_state() , m_dt );
+ m_t_old = m_t;
+ m_t += m_dt;
+ toggle_current_state();
+ return std::make_pair( m_t_old , m_dt );
+ }
+
+ /*
+ * The next two overloads are needed to solve the forwarding problem
+ */
+
+ /**
+ * \brief Calculates the solution at an intermediate point.
+ * \param t The time at which the solution should be calculated, has to be
+ * in the current time interval.
+ * \param x The output variable where the result is written into.
+ */
+ template< class StateOut >
+ void calc_state( time_type t , StateOut &x ) const
+ {
+ if( t == current_time() )
+ {
+ boost::numeric::odeint::copy( get_current_state() , x );
+ }
+ m_stepper.calc_state( x , t , get_old_state() , m_t_old , get_current_state() , m_t );
+ }
+
+ /**
+ * \brief Calculates the solution at an intermediate point. Solves the forwarding problem
+ * \param t The time at which the solution should be calculated, has to be
+ * in the current time interval.
+ * \param x The output variable where the result is written into, can be a boost range.
+ */
+ template< class StateOut >
+ void calc_state( time_type t , const StateOut &x ) const
+ {
+ m_stepper.calc_state( x , t , get_old_state() , m_t_old , get_current_state() , m_t );
+ }
+
+ /**
+ * \brief Adjust the size of all temporaries in the stepper manually.
+ * \param x A state from which the size of the temporaries to be resized is deduced.
+ */
+ template< class StateType >
+ void adjust_size( const StateType &x )
+ {
+ resize_impl( x );
+ m_stepper.stepper().resize( x );
+ }
+
+ /**
+ * \brief Returns the current state of the solution.
+ * \return The current state of the solution x(t).
+ */
+ const state_type& current_state( void ) const
+ {
+ return get_current_state();
+ }
+
+ /**
+ * \brief Returns the current time of the solution.
+ * \return The current time of the solution t.
+ */
+ time_type current_time( void ) const
+ {
+ return m_t;
+ }
+
+ /**
+ * \brief Returns the last state of the solution.
+ * \return The last state of the solution x(t-dt).
+ */
+ const state_type& previous_state( void ) const
+ {
+ return get_old_state();
+ }
+
+ /**
+ * \brief Returns the last time of the solution.
+ * \return The last time of the solution t-dt.
+ */
+ time_type previous_time( void ) const
+ {
+ return m_t_old;
+ }
+
+ /**
+ * \brief Returns the current time step.
+ * \return dt.
+ */
+ time_type current_time_step( void ) const
+ {
+ return m_dt;
+ }
+
+
+private:
+
+ state_type& get_current_state( void )
+ {
+ return m_current_state_x1 ? m_x1.m_v : m_x2.m_v ;
+ }
+
+ const state_type& get_current_state( void ) const
+ {
+ return m_current_state_x1 ? m_x1.m_v : m_x2.m_v ;
+ }
+
+ state_type& get_old_state( void )
+ {
+ return m_current_state_x1 ? m_x2.m_v : m_x1.m_v ;
+ }
+
+ const state_type& get_old_state( void ) const
+ {
+ return m_current_state_x1 ? m_x2.m_v : m_x1.m_v ;
+ }
+
+ void toggle_current_state( void )
+ {
+ m_current_state_x1 = ! m_current_state_x1;
+ }
+
+
+ template< class StateIn >
+ bool resize_impl( const StateIn &x )
+ {
+ bool resized = false;
+ resized |= adjust_size_by_resizeability( m_x1 , x , typename is_resizeable<state_type>::type() );
+ resized |= adjust_size_by_resizeability( m_x2 , x , typename is_resizeable<state_type>::type() );
+ return resized;
+ }
+
+
+ stepper_type m_stepper;
+ resizer_type m_resizer;
+ wrapped_state_type m_x1 , m_x2;
+ bool m_current_state_x1; // if true, the current state is m_x1
+ time_type m_t , m_t_old , m_dt;
+
+};
+
+
+
+
+
+/**
+ * \brief The class representing dense-output Runge-Kutta steppers with FSAL property.
+ *
+ * The interface is the same as for dense_output_runge_kutta< Stepper , stepper_tag >.
+ * This class provides dense output functionality based on methods with step size controlled
+ *
+ *
+ * \tparam Stepper The stepper type of the underlying algorithm.
+ */
+template< class Stepper >
+class dense_output_runge_kutta< Stepper , explicit_controlled_stepper_fsal_tag >
+{
+public:
+
+ /*
+ * We do not need all typedefs.
+ */
+ typedef Stepper controlled_stepper_type;
+
+ typedef typename controlled_stepper_type::stepper_type stepper_type;
+ typedef typename stepper_type::state_type state_type;
+ typedef typename stepper_type::wrapped_state_type wrapped_state_type;
+ typedef typename stepper_type::value_type value_type;
+ typedef typename stepper_type::deriv_type deriv_type;
+ typedef typename stepper_type::wrapped_deriv_type wrapped_deriv_type;
+ typedef typename stepper_type::time_type time_type;
+ typedef typename stepper_type::algebra_type algebra_type;
+ typedef typename stepper_type::operations_type operations_type;
+ typedef typename stepper_type::resizer_type resizer_type;
+ typedef dense_output_stepper_tag stepper_category;
+ typedef dense_output_runge_kutta< Stepper > dense_output_stepper_type;
+
+
+ dense_output_runge_kutta( const controlled_stepper_type &stepper = controlled_stepper_type() )
+ : m_stepper( stepper ) , m_resizer() ,
+ m_current_state_x1( true ) ,
+ m_x1() , m_x2() , m_dxdt1() , m_dxdt2() ,
+ m_t() , m_t_old() , m_dt() ,
+ m_is_deriv_initialized( false )
+ { }
+
+
+ template< class StateType >
+ void initialize( const StateType &x0 , time_type t0 , time_type dt0 )
+ {
+ m_resizer.adjust_size( x0 , detail::bind( &dense_output_stepper_type::template resize< StateType > , detail::ref( *this ) , detail::_1 ) );
+ boost::numeric::odeint::copy( x0 , get_current_state() );
+ m_t = t0;
+ m_dt = dt0;
+ m_is_deriv_initialized = false;
+ }
+
+ template< class System >
+ std::pair< time_type , time_type > do_step( System system )
+ {
+ if( !m_is_deriv_initialized )
+ {
+ typename odeint::unwrap_reference< System >::type &sys = system;
+ sys( get_current_state() , get_current_deriv() , m_t );
+ m_is_deriv_initialized = true;
+ }
+
+ failed_step_checker fail_checker; // to throw a runtime_error if step size adjustment fails
+ controlled_step_result res = fail;
+ m_t_old = m_t;
+ do
+ {
+ res = m_stepper.try_step( system , get_current_state() , get_current_deriv() , m_t ,
+ get_old_state() , get_old_deriv() , m_dt );
+ fail_checker(); // check for overflow of failed steps
+ }
+ while( res == fail );
+ toggle_current_state();
+ return std::make_pair( m_t_old , m_t );
+ }
+
+
+ /*
+ * The two overloads are needed in order to solve the forwarding problem.
+ */
+ template< class StateOut >
+ void calc_state( time_type t , StateOut &x ) const
+ {
+ m_stepper.stepper().calc_state( t , x , get_old_state() , get_old_deriv() , m_t_old ,
+ get_current_state() , get_current_deriv() , m_t );
+ }
+
+ template< class StateOut >
+ void calc_state( time_type t , const StateOut &x ) const
+ {
+ m_stepper.stepper().calc_state( t , x , get_old_state() , get_old_deriv() , m_t_old ,
+ get_current_state() , get_current_deriv() , m_t );
+ }
+
+
+ template< class StateIn >
+ bool resize( const StateIn &x )
+ {
+ bool resized = false;
+ resized |= adjust_size_by_resizeability( m_x1 , x , typename is_resizeable<state_type>::type() );
+ resized |= adjust_size_by_resizeability( m_x2 , x , typename is_resizeable<state_type>::type() );
+ resized |= adjust_size_by_resizeability( m_dxdt1 , x , typename is_resizeable<deriv_type>::type() );
+ resized |= adjust_size_by_resizeability( m_dxdt2 , x , typename is_resizeable<deriv_type>::type() );
+ return resized;
+ }
+
+
+ template< class StateType >
+ void adjust_size( const StateType &x )
+ {
+ resize( x );
+ m_stepper.stepper().resize( x );
+ }
+
+ const state_type& current_state( void ) const
+ {
+ return get_current_state();
+ }
+
+ time_type current_time( void ) const
+ {
+ return m_t;
+ }
+
+ const state_type& previous_state( void ) const
+ {
+ return get_old_state();
+ }
+
+ time_type previous_time( void ) const
+ {
+ return m_t_old;
+ }
+
+ time_type current_time_step( void ) const
+ {
+ return m_dt;
+ }
+
+
+private:
+
+ state_type& get_current_state( void )
+ {
+ return m_current_state_x1 ? m_x1.m_v : m_x2.m_v ;
+ }
+
+ const state_type& get_current_state( void ) const
+ {
+ return m_current_state_x1 ? m_x1.m_v : m_x2.m_v ;
+ }
+
+ state_type& get_old_state( void )
+ {
+ return m_current_state_x1 ? m_x2.m_v : m_x1.m_v ;
+ }
+
+ const state_type& get_old_state( void ) const
+ {
+ return m_current_state_x1 ? m_x2.m_v : m_x1.m_v ;
+ }
+
+ deriv_type& get_current_deriv( void )
+ {
+ return m_current_state_x1 ? m_dxdt1.m_v : m_dxdt2.m_v ;
+ }
+
+ const deriv_type& get_current_deriv( void ) const
+ {
+ return m_current_state_x1 ? m_dxdt1.m_v : m_dxdt2.m_v ;
+ }
+
+ deriv_type& get_old_deriv( void )
+ {
+ return m_current_state_x1 ? m_dxdt2.m_v : m_dxdt1.m_v ;
+ }
+
+ const deriv_type& get_old_deriv( void ) const
+ {
+ return m_current_state_x1 ? m_dxdt2.m_v : m_dxdt1.m_v ;
+ }
+
+
+ void toggle_current_state( void )
+ {
+ m_current_state_x1 = ! m_current_state_x1;
+ }
+
+
+ controlled_stepper_type m_stepper;
+ resizer_type m_resizer;
+ bool m_current_state_x1;
+ wrapped_state_type m_x1 , m_x2;
+ wrapped_deriv_type m_dxdt1 , m_dxdt2;
+ time_type m_t , m_t_old , m_dt;
+ bool m_is_deriv_initialized;
+
+};
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_DENSE_OUTPUT_RUNGE_KUTTA_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/detail/adams_bashforth_call_algebra.hpp b/include/boost/numeric/odeint/stepper/detail/adams_bashforth_call_algebra.hpp
new file mode 100644
index 0000000..cc279ab
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/detail/adams_bashforth_call_algebra.hpp
@@ -0,0 +1,151 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/detail/adams_bashforth_call_algebra.hpp
+
+ [begin_description]
+ Algebra caller for the Adams Bashforth stepper.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_ADAMS_BASHFORTH_CALL_ALGEBRA_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_ADAMS_BASHFORTH_CALL_ALGEBRA_HPP_INCLUDED
+
+#include <boost/assert.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+template< size_t Step , class Algebra , class Operations >
+struct adams_bashforth_call_algebra;
+
+template< class Algebra , class Operations >
+struct adams_bashforth_call_algebra< 1 , Algebra , Operations >
+{
+ template< class StateIn , class StateOut , class StepStorage , class Coefficients , class Time >
+ void operator()( Algebra &algebra , const StateIn &in , StateOut &out , const StepStorage &steps , const Coefficients &coef , Time dt ) const
+ {
+ typedef typename Coefficients::value_type value_type;
+ algebra.for_each3( out , in , steps[0].m_v , typename Operations::template scale_sum2< value_type , Time >( 1.0 , dt * coef[0] ) );
+ }
+};
+
+
+template< class Algebra , class Operations >
+struct adams_bashforth_call_algebra< 2 , Algebra , Operations >
+{
+ template< class StateIn , class StateOut , class StepStorage , class Coefficients , class Time >
+ void operator()( Algebra &algebra , const StateIn &in , StateOut &out , const StepStorage &steps , const Coefficients &coef , Time dt ) const
+ {
+ typedef typename Coefficients::value_type value_type;
+ algebra.for_each4( out , in , steps[0].m_v , steps[1].m_v ,
+ typename Operations::template scale_sum3< value_type , Time , Time >( 1.0 , dt * coef[0] , dt * coef[1] ) );
+ }
+};
+
+
+template< class Algebra , class Operations >
+struct adams_bashforth_call_algebra< 3 , Algebra , Operations >
+{
+ template< class StateIn , class StateOut , class StepStorage , class Coefficients , class Time >
+ void operator()( Algebra &algebra , const StateIn &in , StateOut &out , const StepStorage &steps , const Coefficients &coef , Time dt ) const
+ {
+ typedef typename Coefficients::value_type value_type;
+ algebra.for_each5( out , in , steps[0].m_v , steps[1].m_v , steps[2].m_v ,
+ typename Operations::template scale_sum4< value_type , Time , Time , Time >( 1.0 , dt * coef[0] , dt * coef[1] , dt * coef[2] ) );
+ }
+};
+
+
+template< class Algebra , class Operations >
+struct adams_bashforth_call_algebra< 4 , Algebra , Operations >
+{
+ template< class StateIn , class StateOut , class StepStorage , class Coefficients , class Time >
+ void operator()( Algebra &algebra , const StateIn &in , StateOut &out , const StepStorage &steps , const Coefficients &coef , Time dt ) const
+ {
+ typedef typename Coefficients::value_type value_type;
+ algebra.for_each6( out , in , steps[0].m_v , steps[1].m_v , steps[2].m_v , steps[3].m_v ,
+ typename Operations::template scale_sum5< value_type , Time , Time , Time >(
+ 1.0 , dt * coef[0] , dt * coef[1] , dt * coef[2] , dt * coef[3] ) );
+ }
+};
+
+
+template< class Algebra , class Operations >
+struct adams_bashforth_call_algebra< 5 , Algebra , Operations >
+{
+ template< class StateIn , class StateOut , class StepStorage , class Coefficients , class Time >
+ void operator()( Algebra &algebra , const StateIn &in , StateOut &out , const StepStorage &steps , const Coefficients &coef , Time dt ) const
+ {
+ typedef typename Coefficients::value_type value_type;
+ algebra.for_each7( out , in , steps[0].m_v , steps[1].m_v , steps[2].m_v , steps[3].m_v , steps[4].m_v ,
+ typename Operations::template scale_sum6< value_type , Time , Time , Time , Time >(
+ 1.0 , dt * coef[0] , dt * coef[1] , dt * coef[2] , dt * coef[3] , dt * coef[4] ) );
+ }
+};
+
+
+template< class Algebra , class Operations >
+struct adams_bashforth_call_algebra< 6 , Algebra , Operations >
+{
+ template< class StateIn , class StateOut , class StepStorage , class Coefficients , class Time >
+ void operator()( Algebra &algebra , const StateIn &in , StateOut &out , const StepStorage &steps , const Coefficients &coef , Time dt ) const
+ {
+ typedef typename Coefficients::value_type value_type;
+ algebra.for_each8( out , in , steps[0].m_v , steps[1].m_v , steps[2].m_v , steps[3].m_v , steps[4].m_v , steps[5].m_v ,
+ typename Operations::template scale_sum7< value_type , Time , Time , Time , Time , Time >(
+ 1.0 , dt * coef[0] , dt * coef[1] , dt * coef[2] , dt * coef[3] , dt * coef[4] , dt * coef[5] ) );
+ }
+};
+
+
+template< class Algebra , class Operations >
+struct adams_bashforth_call_algebra< 7 , Algebra , Operations >
+{
+ template< class StateIn , class StateOut , class StepStorage , class Coefficients , class Time >
+ void operator()( Algebra &algebra , const StateIn &in , StateOut &out , const StepStorage &steps , const Coefficients &coef , Time dt ) const
+ {
+ //BOOST_ASSERT( false ); // not implemented
+ typedef typename Coefficients::value_type value_type;
+ algebra.for_each9( out , in , steps[0].m_v , steps[1].m_v , steps[2].m_v , steps[3].m_v , steps[4].m_v , steps[5].m_v , steps[6].m_v ,
+ typename Operations::template scale_sum8< value_type , Time , Time , Time , Time , Time , Time >(
+ 1.0 , dt * coef[0] , dt * coef[1] , dt * coef[2] , dt * coef[3] , dt * coef[4] , dt * coef[5] , dt * coef[6] ) );
+ }
+};
+
+
+template< class Algebra , class Operations >
+struct adams_bashforth_call_algebra< 8 , Algebra , Operations >
+{
+ template< class StateIn , class StateOut , class StepStorage , class Coefficients , class Time >
+ void operator()( Algebra &algebra , const StateIn &in , StateOut &out , const StepStorage &steps , const Coefficients &coef , Time dt ) const
+ {
+ //BOOST_ASSERT( false ); // not implemented
+ typedef typename Coefficients::value_type value_type;
+ algebra.for_each10( out , in , steps[0].m_v , steps[1].m_v , steps[2].m_v , steps[3].m_v , steps[4].m_v , steps[5].m_v , steps[6].m_v , steps[7].m_v ,
+ typename Operations::template scale_sum9< value_type , Time , Time , Time , Time , Time , Time , Time >(
+ 1.0 , dt * coef[0] , dt * coef[1] , dt * coef[2] , dt * coef[3] , dt * coef[4] , dt * coef[5] , dt * coef[6] , dt * coef[7] ) );
+ }
+};
+
+
+
+
+} // detail
+} // odeint
+} // numeric
+} // boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_ADAMS_BASHFORTH_CALL_ALGEBRA_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/detail/adams_bashforth_coefficients.hpp b/include/boost/numeric/odeint/stepper/detail/adams_bashforth_coefficients.hpp
new file mode 100644
index 0000000..26a9f9a
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/detail/adams_bashforth_coefficients.hpp
@@ -0,0 +1,168 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/detail/adams_bashforth_coefficients.hpp
+
+ [begin_description]
+ Definition of the coefficients for the Adams-Bashforth method.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_ADAMS_BASHFORTH_COEFFICIENTS_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_ADAMS_BASHFORTH_COEFFICIENTS_HPP_INCLUDED
+
+#include <boost/array.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+template< class Value , size_t Steps >
+class adams_bashforth_coefficients ;
+
+template< class Value >
+class adams_bashforth_coefficients< Value , 1 > : public boost::array< Value , 1 >
+{
+public:
+ adams_bashforth_coefficients( void )
+ : boost::array< Value , 1 >()
+ {
+ (*this)[0] = static_cast< Value >( 1 );
+ }
+};
+
+
+template< class Value >
+class adams_bashforth_coefficients< Value , 2 > : public boost::array< Value , 2 >
+{
+public:
+ adams_bashforth_coefficients( void )
+ : boost::array< Value , 2 >()
+ {
+ (*this)[0] = static_cast< Value >( 3 ) / static_cast< Value >( 2 );
+ (*this)[1] = -static_cast< Value >( 1 ) / static_cast< Value >( 2 );
+ }
+};
+
+
+template< class Value >
+class adams_bashforth_coefficients< Value , 3 > : public boost::array< Value , 3 >
+{
+public:
+ adams_bashforth_coefficients( void )
+ : boost::array< Value , 3 >()
+ {
+ (*this)[0] = static_cast< Value >( 23 ) / static_cast< Value >( 12 );
+ (*this)[1] = -static_cast< Value >( 4 ) / static_cast< Value >( 3 );
+ (*this)[2] = static_cast< Value >( 5 ) / static_cast< Value >( 12 );
+ }
+};
+
+
+template< class Value >
+class adams_bashforth_coefficients< Value , 4 > : public boost::array< Value , 4 >
+{
+public:
+ adams_bashforth_coefficients( void )
+ : boost::array< Value , 4 >()
+ {
+ (*this)[0] = static_cast< Value >( 55 ) / static_cast< Value >( 24 );
+ (*this)[1] = -static_cast< Value >( 59 ) / static_cast< Value >( 24 );
+ (*this)[2] = static_cast< Value >( 37 ) / static_cast< Value >( 24 );
+ (*this)[3] = -static_cast< Value >( 3 ) / static_cast< Value >( 8 );
+ }
+};
+
+
+template< class Value >
+class adams_bashforth_coefficients< Value , 5 > : public boost::array< Value , 5 >
+{
+public:
+ adams_bashforth_coefficients( void )
+ : boost::array< Value , 5 >()
+ {
+ (*this)[0] = static_cast< Value >( 1901 ) / static_cast< Value >( 720 );
+ (*this)[1] = -static_cast< Value >( 1387 ) / static_cast< Value >( 360 );
+ (*this)[2] = static_cast< Value >( 109 ) / static_cast< Value >( 30 );
+ (*this)[3] = -static_cast< Value >( 637 ) / static_cast< Value >( 360 );
+ (*this)[4] = static_cast< Value >( 251 ) / static_cast< Value >( 720 );
+ }
+};
+
+
+template< class Value >
+class adams_bashforth_coefficients< Value , 6 > : public boost::array< Value , 6 >
+{
+public:
+ adams_bashforth_coefficients( void )
+ : boost::array< Value , 6 >()
+ {
+ (*this)[0] = static_cast< Value >( 4277 ) / static_cast< Value >( 1440 );
+ (*this)[1] = -static_cast< Value >( 2641 ) / static_cast< Value >( 480 );
+ (*this)[2] = static_cast< Value >( 4991 ) / static_cast< Value >( 720 );
+ (*this)[3] = -static_cast< Value >( 3649 ) / static_cast< Value >( 720 );
+ (*this)[4] = static_cast< Value >( 959 ) / static_cast< Value >( 480 );
+ (*this)[5] = -static_cast< Value >( 95 ) / static_cast< Value >( 288 );
+ }
+};
+
+
+template< class Value >
+class adams_bashforth_coefficients< Value , 7 > : public boost::array< Value , 7 >
+{
+public:
+ adams_bashforth_coefficients( void )
+ : boost::array< Value , 7 >()
+ {
+ (*this)[0] = static_cast< Value >( 198721 ) / static_cast< Value >( 60480 );
+ (*this)[1] = -static_cast< Value >( 18637 ) / static_cast< Value >( 2520 );
+ (*this)[2] = static_cast< Value >( 235183 ) / static_cast< Value >( 20160 );
+ (*this)[3] = -static_cast< Value >( 10754 ) / static_cast< Value >( 945 );
+ (*this)[4] = static_cast< Value >( 135713 ) / static_cast< Value >( 20160 );
+ (*this)[5] = -static_cast< Value >( 5603 ) / static_cast< Value >( 2520 );
+ (*this)[6] = static_cast< Value >( 19087 ) / static_cast< Value >( 60480 );
+ }
+};
+
+
+template< class Value >
+class adams_bashforth_coefficients< Value , 8 > : public boost::array< Value , 8 >
+{
+public:
+ adams_bashforth_coefficients( void )
+ : boost::array< Value , 8 >()
+ {
+ (*this)[0] = static_cast< Value >( 16083 ) / static_cast< Value >( 4480 );
+ (*this)[1] = -static_cast< Value >( 1152169 ) / static_cast< Value >( 120960 );
+ (*this)[2] = static_cast< Value >( 242653 ) / static_cast< Value >( 13440 );
+ (*this)[3] = -static_cast< Value >( 296053 ) / static_cast< Value >( 13440 );
+ (*this)[4] = static_cast< Value >( 2102243 ) / static_cast< Value >( 120960 );
+ (*this)[5] = -static_cast< Value >( 115747 ) / static_cast< Value >( 13440 );
+ (*this)[6] = static_cast< Value >( 32863 ) / static_cast< Value >( 13440 );
+ (*this)[7] = -static_cast< Value >( 5257 ) / static_cast< Value >( 17280 );
+ }
+};
+
+
+
+
+
+
+
+} // detail
+} // odeint
+} // numeric
+} // boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_ADAMS_BASHFORTH_COEFFICIENTS_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/detail/adams_moulton_call_algebra.hpp b/include/boost/numeric/odeint/stepper/detail/adams_moulton_call_algebra.hpp
new file mode 100644
index 0000000..b6f5f2a
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/detail/adams_moulton_call_algebra.hpp
@@ -0,0 +1,148 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/detail/adams_moulton_call_algebra.hpp
+
+ [begin_description]
+ Algebra caller for the Adams Moulton method.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_ADAMS_MOULTON_CALL_ALGEBRA_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_ADAMS_MOULTON_CALL_ALGEBRA_HPP_INCLUDED
+
+#include <boost/assert.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+template< size_t Step , class Algebra , class Operations >
+struct adams_moulton_call_algebra;
+
+template< class Algebra , class Operations >
+struct adams_moulton_call_algebra< 1 , Algebra , Operations >
+{
+ template< class StateIn , class StateOut , class DerivIn , class StepStorage , class Coefficients , class Time >
+ void operator()( Algebra &algebra , const StateIn &in , StateOut &out , const DerivIn &dxdt , const StepStorage& /* steps */ , const Coefficients &coef , Time dt ) const
+ {
+ typedef typename Coefficients::value_type value_type;
+ algebra.for_each3( out , in , dxdt , typename Operations::template scale_sum2< value_type , Time >( 1.0 , dt * coef[0] ) );
+ }
+};
+
+
+template< class Algebra , class Operations >
+struct adams_moulton_call_algebra< 2 , Algebra , Operations >
+{
+ template< class StateIn , class StateOut , class DerivIn , class StepStorage , class Coefficients , class Time >
+ void operator()( Algebra &algebra , const StateIn &in , StateOut &out , const DerivIn &dxdt , const StepStorage &steps , const Coefficients &coef , Time dt ) const
+ {
+ typedef typename Coefficients::value_type value_type;
+ algebra.for_each4( out , in , dxdt , steps[0].m_v ,
+ typename Operations::template scale_sum3< value_type , Time , Time >( 1.0 , dt * coef[0] , dt * coef[1] ) );
+ }
+};
+
+
+template< class Algebra , class Operations >
+struct adams_moulton_call_algebra< 3 , Algebra , Operations >
+{
+ template< class StateIn , class StateOut , class DerivIn , class StepStorage , class Coefficients , class Time >
+ void operator()( Algebra &algebra , const StateIn &in , StateOut &out , const DerivIn &dxdt , const StepStorage &steps , const Coefficients &coef , Time dt ) const
+ {
+ typedef typename Coefficients::value_type value_type;
+ algebra.for_each5( out , in , dxdt , steps[0].m_v , steps[1].m_v ,
+ typename Operations::template scale_sum4< value_type , Time , Time >( 1.0 , dt * coef[0] , dt * coef[1] , dt * coef[2] ) );
+ }
+};
+
+
+template< class Algebra , class Operations >
+struct adams_moulton_call_algebra< 4 , Algebra , Operations >
+{
+ template< class StateIn , class StateOut , class DerivIn , class StepStorage , class Coefficients , class Time >
+ void operator()( Algebra &algebra , const StateIn &in , StateOut &out , const DerivIn &dxdt , const StepStorage &steps , const Coefficients &coef , Time dt ) const
+ {
+ typedef typename Coefficients::value_type value_type;
+ algebra.for_each6( out , in , dxdt , steps[0].m_v , steps[1].m_v , steps[2].m_v ,
+ typename Operations::template scale_sum5< value_type , Time , Time , Time >(
+ 1.0 , dt * coef[0] , dt * coef[1] , dt * coef[2] , dt * coef[3] ) );
+ }
+};
+
+
+template< class Algebra , class Operations >
+struct adams_moulton_call_algebra< 5 , Algebra , Operations >
+{
+ template< class StateIn , class StateOut , class DerivIn , class StepStorage , class Coefficients , class Time >
+ void operator()( Algebra &algebra , const StateIn &in , StateOut &out , const DerivIn &dxdt , const StepStorage &steps , const Coefficients &coef , Time dt ) const
+ {
+ typedef typename Coefficients::value_type value_type;
+ algebra.for_each7( out , in , dxdt , steps[0].m_v , steps[1].m_v , steps[2].m_v , steps[3].m_v ,
+ typename Operations::template scale_sum6< value_type , Time , Time , Time , Time >(
+ 1.0 , dt * coef[0] , dt * coef[1] , dt * coef[2] , dt * coef[3] , dt * coef[4] ) );
+ }
+};
+
+
+template< class Algebra , class Operations >
+struct adams_moulton_call_algebra< 6 , Algebra , Operations >
+{
+ template< class StateIn , class StateOut , class DerivIn , class StepStorage , class Coefficients , class Time >
+ void operator()( Algebra &algebra , const StateIn &in , StateOut &out , const DerivIn &dxdt , const StepStorage &steps , const Coefficients &coef , Time dt ) const
+ {
+ typedef typename Coefficients::value_type value_type;
+ algebra.for_each8( out , in , dxdt , steps[0].m_v , steps[1].m_v , steps[2].m_v , steps[3].m_v , steps[4].m_v ,
+ typename Operations::template scale_sum7< value_type , Time , Time , Time , Time , Time >(
+ 1.0 , dt * coef[0] , dt * coef[1] , dt * coef[2] , dt * coef[3] , dt * coef[4] , dt * coef[5] ) );
+ }
+};
+
+
+template< class Algebra , class Operations >
+struct adams_moulton_call_algebra< 7 , Algebra , Operations >
+{
+ template< class StateIn , class StateOut , class DerivIn , class StepStorage , class Coefficients , class Time >
+ void operator()( Algebra &algebra , const StateIn &in , StateOut &out , const DerivIn &dxdt , const StepStorage &steps , const Coefficients &coef , Time dt ) const
+ {
+ typedef typename Coefficients::value_type value_type;
+ algebra.for_each9( out , in , dxdt , steps[0].m_v , steps[1].m_v , steps[2].m_v , steps[3].m_v , steps[4].m_v , steps[5].m_v ,
+ typename Operations::template scale_sum8< value_type , Time , Time , Time , Time , Time , Time >(
+ 1.0 , dt * coef[0] , dt * coef[1] , dt * coef[2] , dt * coef[3] , dt * coef[4] , dt * coef[5] , dt * coef[6] ) );
+ }
+};
+
+
+template< class Algebra , class Operations >
+struct adams_moulton_call_algebra< 8 , Algebra , Operations >
+{
+ template< class StateIn , class StateOut , class DerivIn , class StepStorage , class Coefficients , class Time >
+ void operator()( Algebra &algebra , const StateIn &in , StateOut &out , const DerivIn &dxdt , const StepStorage &steps , const Coefficients &coef , Time dt ) const
+ {
+ typedef typename Coefficients::value_type value_type;
+ algebra.for_each10( out , in , dxdt , steps[0].m_v , steps[1].m_v , steps[2].m_v , steps[3].m_v , steps[4].m_v , steps[5].m_v , steps[6].m_v ,
+ typename Operations::template scale_sum9< value_type , Time , Time , Time , Time , Time , Time , Time >(
+ 1.0 , dt * coef[0] , dt * coef[1] , dt * coef[2] , dt * coef[3] , dt * coef[4] , dt * coef[5] , dt * coef[6] , dt * coef[7] ) );
+ }
+};
+
+
+
+
+} // detail
+} // odeint
+} // numeric
+} // boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_ADAMS_MOULTON_CALL_ALGEBRA_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/detail/adams_moulton_coefficients.hpp b/include/boost/numeric/odeint/stepper/detail/adams_moulton_coefficients.hpp
new file mode 100644
index 0000000..8047fa8
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/detail/adams_moulton_coefficients.hpp
@@ -0,0 +1,168 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/detail/adams_moulton_coefficients.hpp
+
+ [begin_description]
+ Coefficients for the Adams Moulton method.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_ADAMS_MOULTON_COEFFICIENTS_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_ADAMS_MOULTON_COEFFICIENTS_HPP_INCLUDED
+
+
+#include <boost/array.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+template< class Value , size_t Steps >
+class adams_moulton_coefficients ;
+
+template< class Value >
+class adams_moulton_coefficients< Value , 1 > : public boost::array< Value , 1 >
+{
+public:
+ adams_moulton_coefficients( void )
+ : boost::array< Value , 1 >()
+ {
+ (*this)[0] = static_cast< Value >( 1 );
+ }
+};
+
+
+template< class Value >
+class adams_moulton_coefficients< Value , 2 > : public boost::array< Value , 2 >
+{
+public:
+ adams_moulton_coefficients( void )
+ : boost::array< Value , 2 >()
+ {
+ (*this)[0] = static_cast< Value >( 1 ) / static_cast< Value >( 2 );
+ (*this)[1] = static_cast< Value >( 1 ) / static_cast< Value >( 2 );
+ }
+};
+
+
+template< class Value >
+class adams_moulton_coefficients< Value , 3 > : public boost::array< Value , 3 >
+{
+public:
+ adams_moulton_coefficients( void )
+ : boost::array< Value , 3 >()
+ {
+ (*this)[0] = static_cast< Value >( 5 ) / static_cast< Value >( 12 );
+ (*this)[1] = static_cast< Value >( 2 ) / static_cast< Value >( 3 );
+ (*this)[2] = -static_cast< Value >( 1 ) / static_cast< Value >( 12 );
+ }
+};
+
+
+template< class Value >
+class adams_moulton_coefficients< Value , 4 > : public boost::array< Value , 4 >
+{
+public:
+ adams_moulton_coefficients( void )
+ : boost::array< Value , 4 >()
+ {
+ (*this)[0] = static_cast< Value >( 3 ) / static_cast< Value >( 8 );
+ (*this)[1] = static_cast< Value >( 19 ) / static_cast< Value >( 24 );
+ (*this)[2] = -static_cast< Value >( 5 ) / static_cast< Value >( 24 );
+ (*this)[3] = static_cast< Value >( 1 ) / static_cast< Value >( 24 );
+ }
+};
+
+
+template< class Value >
+class adams_moulton_coefficients< Value , 5 > : public boost::array< Value , 5 >
+{
+public:
+ adams_moulton_coefficients( void )
+ : boost::array< Value , 5 >()
+ {
+ (*this)[0] = static_cast< Value >( 251 ) / static_cast< Value >( 720 );
+ (*this)[1] = static_cast< Value >( 323 ) / static_cast< Value >( 360 );
+ (*this)[2] = -static_cast< Value >( 11 ) / static_cast< Value >( 30 );
+ (*this)[3] = static_cast< Value >( 53 ) / static_cast< Value >( 360 );
+ (*this)[4] = -static_cast< Value >( 19 ) / static_cast< Value >( 720 );
+ }
+};
+
+
+template< class Value >
+class adams_moulton_coefficients< Value , 6 > : public boost::array< Value , 6 >
+{
+public:
+ adams_moulton_coefficients( void )
+ : boost::array< Value , 6 >()
+ {
+ (*this)[0] = static_cast< Value >( 95 ) / static_cast< Value >( 288 );
+ (*this)[1] = static_cast< Value >( 1427 ) / static_cast< Value >( 1440 );
+ (*this)[2] = -static_cast< Value >( 133 ) / static_cast< Value >( 240 );
+ (*this)[3] = static_cast< Value >( 241 ) / static_cast< Value >( 720 );
+ (*this)[4] = -static_cast< Value >( 173 ) / static_cast< Value >( 1440 );
+ (*this)[5] = static_cast< Value >( 3 ) / static_cast< Value >( 160 );
+ }
+};
+
+template< class Value >
+class adams_moulton_coefficients< Value , 7 > : public boost::array< Value , 7 >
+{
+public:
+ adams_moulton_coefficients( void )
+ : boost::array< Value , 7 >()
+ {
+ (*this)[0] = static_cast< Value >( 19087 ) / static_cast< Value >( 60480 );
+ (*this)[1] = static_cast< Value >( 2713 ) / static_cast< Value >( 2520 );
+ (*this)[2] = -static_cast< Value >( 15487 ) / static_cast< Value >( 20160 );
+ (*this)[3] = static_cast< Value >( 586 ) / static_cast< Value >( 945 );
+ (*this)[4] = -static_cast< Value >( 6737 ) / static_cast< Value >( 20160 );
+ (*this)[5] = static_cast< Value >( 263 ) / static_cast< Value >( 2520 );
+ (*this)[6] = -static_cast< Value >( 863 ) / static_cast< Value >( 60480 );
+ }
+};
+
+
+template< class Value >
+class adams_moulton_coefficients< Value , 8 > : public boost::array< Value , 8 >
+{
+public:
+ adams_moulton_coefficients( void )
+ : boost::array< Value , 8 >()
+ {
+ (*this)[0] = static_cast< Value >( 5257 ) / static_cast< Value >( 17280 );
+ (*this)[1] = static_cast< Value >( 139849 ) / static_cast< Value >( 120960 );
+ (*this)[2] = -static_cast< Value >( 4511 ) / static_cast< Value >( 4480 );
+ (*this)[3] = static_cast< Value >( 123133 ) / static_cast< Value >( 120960 );
+ (*this)[4] = -static_cast< Value >( 88547 ) / static_cast< Value >( 120960 );
+ (*this)[5] = static_cast< Value >( 1537 ) / static_cast< Value >( 4480 );
+ (*this)[6] = -static_cast< Value >( 11351 ) / static_cast< Value >( 120960 );
+ (*this)[7] = static_cast< Value >( 275 ) / static_cast< Value >( 24192 );
+ }
+};
+
+
+
+
+
+
+
+} // detail
+} // odeint
+} // numeric
+} // boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_ADAMS_MOULTON_COEFFICIENTS_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/detail/generic_rk_algorithm.hpp b/include/boost/numeric/odeint/stepper/detail/generic_rk_algorithm.hpp
new file mode 100644
index 0000000..ab74b24
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/detail/generic_rk_algorithm.hpp
@@ -0,0 +1,247 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/detail/generic_rk_algorithm.hpp
+
+ [begin_description]
+ Implementation of the generic Runge-Kutta method.
+ [end_description]
+
+ Copyright 2011-2013 Mario Mulansky
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2012 Christoph Koke
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_GENERIC_RK_ALGORITHM_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_GENERIC_RK_ALGORITHM_HPP_INCLUDED
+
+#include <boost/static_assert.hpp>
+
+#include <boost/mpl/vector.hpp>
+#include <boost/mpl/push_back.hpp>
+#include <boost/mpl/for_each.hpp>
+#include <boost/mpl/range_c.hpp>
+#include <boost/mpl/copy.hpp>
+#include <boost/mpl/size_t.hpp>
+
+#include <boost/fusion/algorithm.hpp>
+#include <boost/fusion/iterator.hpp>
+#include <boost/fusion/mpl.hpp>
+#include <boost/fusion/sequence.hpp>
+
+#include <boost/array.hpp>
+
+#include <boost/numeric/odeint/algebra/range_algebra.hpp>
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+#include <boost/numeric/odeint/stepper/detail/generic_rk_call_algebra.hpp>
+#include <boost/numeric/odeint/stepper/detail/generic_rk_operations.hpp>
+#include <boost/numeric/odeint/util/bind.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+template< class T , class Constant >
+struct array_wrapper
+{
+ typedef const typename boost::array< T , Constant::value > type;
+};
+
+template< class T , size_t i >
+struct stage
+{
+ T c;
+ boost::array< T , i > a;
+};
+
+
+template< class T , class Constant >
+struct stage_wrapper
+{
+ typedef stage< T , Constant::value > type;
+};
+
+
+template<
+size_t StageCount,
+class Value ,
+class Algebra ,
+class Operations
+>
+class generic_rk_algorithm {
+
+public:
+ typedef mpl::range_c< size_t , 1 , StageCount > stage_indices;
+
+ typedef typename boost::fusion::result_of::as_vector
+ <
+ typename boost::mpl::copy
+ <
+ stage_indices ,
+ boost::mpl::inserter
+ <
+ boost::mpl::vector0< > ,
+ boost::mpl::push_back< boost::mpl::_1 , array_wrapper< Value , boost::mpl::_2 > >
+ >
+ >::type
+ >::type coef_a_type;
+
+ typedef boost::array< Value , StageCount > coef_b_type;
+ typedef boost::array< Value , StageCount > coef_c_type;
+
+ typedef typename boost::fusion::result_of::as_vector
+ <
+ typename boost::mpl::push_back
+ <
+ typename boost::mpl::copy
+ <
+ stage_indices,
+ boost::mpl::inserter
+ <
+ boost::mpl::vector0<> ,
+ boost::mpl::push_back< boost::mpl::_1 , stage_wrapper< Value , boost::mpl::_2 > >
+ >
+ >::type ,
+ stage< Value , StageCount >
+ >::type
+ >::type stage_vector_base;
+
+
+ struct stage_vector : public stage_vector_base
+ {
+ struct do_insertion
+ {
+ stage_vector_base &m_base;
+ const coef_a_type &m_a;
+ const coef_c_type &m_c;
+
+ do_insertion( stage_vector_base &base , const coef_a_type &a , const coef_c_type &c )
+ : m_base( base ) , m_a( a ) , m_c( c ) { }
+
+ template< class Index >
+ void operator()( Index ) const
+ {
+ //boost::fusion::at< Index >( m_base ) = stage< double , Index::value+1 , intermediate_stage >( m_c[ Index::value ] , boost::fusion::at< Index >( m_a ) );
+ boost::fusion::at< Index >( m_base ).c = m_c[ Index::value ];
+ boost::fusion::at< Index >( m_base ).a = boost::fusion::at< Index >( m_a );
+ }
+ };
+
+ struct print_butcher
+ {
+ const stage_vector_base &m_base;
+ std::ostream &m_os;
+
+ print_butcher( const stage_vector_base &base , std::ostream &os )
+ : m_base( base ) , m_os( os )
+ { }
+
+ template<class Index>
+ void operator()(Index) const {
+ m_os << boost::fusion::at<Index>(m_base).c << " | ";
+ for( size_t i=0 ; i<Index::value ; ++i )
+ m_os << boost::fusion::at<Index>(m_base).a[i] << " ";
+ m_os << std::endl;
+ }
+ };
+
+
+ stage_vector( const coef_a_type &a , const coef_b_type &b , const coef_c_type &c )
+ {
+ typedef boost::mpl::range_c< size_t , 0 , StageCount-1 > indices;
+ boost::mpl::for_each< indices >( do_insertion( *this , a , c ) );
+ boost::fusion::at_c< StageCount - 1 >( *this ).c = c[ StageCount - 1 ];
+ boost::fusion::at_c< StageCount - 1 >( *this ).a = b;
+ }
+
+ void print( std::ostream &os ) const
+ {
+ typedef boost::mpl::range_c< size_t , 0 , StageCount > indices;
+ boost::mpl::for_each< indices >( print_butcher( *this , os ) );
+ }
+ };
+
+
+
+ template< class System , class StateIn , class StateTemp , class DerivIn , class Deriv ,
+ class StateOut , class Time >
+ struct calculate_stage
+ {
+ Algebra &algebra;
+ System &system;
+ const StateIn &x;
+ StateTemp &x_tmp;
+ StateOut &x_out;
+ const DerivIn &dxdt;
+ Deriv *F;
+ Time t;
+ Time dt;
+
+ calculate_stage( Algebra &_algebra , System &_system , const StateIn &_x , const DerivIn &_dxdt , StateOut &_out ,
+ StateTemp &_x_tmp , Deriv *_F , Time _t , Time _dt )
+ : algebra( _algebra ) , system( _system ) , x( _x ) , x_tmp( _x_tmp ) , x_out( _out) , dxdt( _dxdt ) , F( _F ) , t( _t ) , dt( _dt )
+ {}
+
+
+ template< typename T , size_t stage_number >
+ void inline operator()( stage< T , stage_number > const &stage ) const
+ //typename stage_fusion_wrapper< T , mpl::size_t< stage_number > , intermediate_stage >::type const &stage ) const
+ {
+ if( stage_number > 1 )
+ {
+#ifdef BOOST_MSVC
+#pragma warning( disable : 4307 34 )
+#endif
+ system( x_tmp , F[stage_number-2].m_v , t + stage.c * dt );
+#ifdef BOOST_MSVC
+#pragma warning( default : 4307 34 )
+#endif
+ }
+ //std::cout << stage_number-2 << ", t': " << t + stage.c * dt << std::endl;
+
+ if( stage_number < StageCount )
+ detail::template generic_rk_call_algebra< stage_number , Algebra >()( algebra , x_tmp , x , dxdt , F ,
+ detail::generic_rk_scale_sum< stage_number , Operations , Value , Time >( stage.a , dt) );
+ // algebra_type::template for_eachn<stage_number>( x_tmp , x , dxdt , F ,
+ // typename operations_type::template scale_sumn< stage_number , time_type >( stage.a , dt ) );
+ else
+ detail::template generic_rk_call_algebra< stage_number , Algebra >()( algebra , x_out , x , dxdt , F ,
+ detail::generic_rk_scale_sum< stage_number , Operations , Value , Time >( stage.a , dt ) );
+ // algebra_type::template for_eachn<stage_number>( x_out , x , dxdt , F ,
+ // typename operations_type::template scale_sumn< stage_number , time_type >( stage.a , dt ) );
+ }
+
+ };
+
+ generic_rk_algorithm( const coef_a_type &a , const coef_b_type &b , const coef_c_type &c )
+ : m_stages( a , b , c )
+ { }
+
+ template< class System , class StateIn , class DerivIn , class Time , class StateOut , class StateTemp , class Deriv >
+ void inline do_step( Algebra &algebra , System system , const StateIn &in , const DerivIn &dxdt ,
+ Time t , StateOut &out , Time dt ,
+ StateTemp &x_tmp , Deriv F[StageCount-1] ) const
+ {
+ typedef typename odeint::unwrap_reference< System >::type unwrapped_system_type;
+ unwrapped_system_type &sys = system;
+ boost::fusion::for_each( m_stages , calculate_stage<
+ unwrapped_system_type , StateIn , StateTemp , DerivIn , Deriv , StateOut , Time >
+ ( algebra , sys , in , dxdt , out , x_tmp , F , t , dt ) );
+ }
+
+private:
+ stage_vector m_stages;
+};
+
+
+}
+}
+}
+}
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_GENERIC_RK_ALGORITHM_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/detail/generic_rk_call_algebra.hpp b/include/boost/numeric/odeint/stepper/detail/generic_rk_call_algebra.hpp
new file mode 100644
index 0000000..0249d86
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/detail/generic_rk_call_algebra.hpp
@@ -0,0 +1,263 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/detail/generic_rk_call_algebra.hpp
+
+ [begin_description]
+ Algebra caller for the generic Runge-Kutta methods.
+ [end_description]
+
+ Copyright 2011-2012 Mario Mulansky
+ Copyright 2011-2012 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_GENERIC_RK_CALL_ALGEBRA_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_GENERIC_RK_CALL_ALGEBRA_HPP_INCLUDED
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+template< size_t StageNumber , class Algebra >
+struct generic_rk_call_algebra;
+
+template< class Algebra >
+struct generic_rk_call_algebra< 1 , Algebra >
+{
+ typedef Algebra algebra_type;
+
+ template< class S1 , class S2 , class S3 , class S4 , class Op>
+ void operator()( algebra_type &algebra , S1 &s1 , S2 &s2 , S3 &s3 , S4 * /* s4_array */ , Op op ) const
+ {
+ algebra.for_each3( s1 , s2 , s3 , op );
+ }
+
+ template< class S1 , class S2 , class S4 , class Op>
+ void operator()( algebra_type &algebra , S1 &s1 , S2 &s2 , S4 * /* s4_array */ , Op op ) const
+ {
+ algebra.for_each2( s1 , s2 , op );
+ }
+};
+
+template< class Algebra >
+struct generic_rk_call_algebra< 2 , Algebra >
+{
+ template< class S1 , class S2 , class S3 , class S4 , class Op>
+ void operator()( Algebra &algebra , S1 &s1 , S2 &s2 , S3 &s3 , S4 s4_array[1] , Op op ) const
+ {
+ algebra.for_each4( s1 , s2 , s3 , s4_array[0].m_v , op );
+ }
+
+ template< class S1 , class S2 , class S4 , class Op>
+ void operator()( Algebra &algebra , S1 &s1 , S2 &s2 , S4 s4_array[1] , Op op ) const
+ {
+ algebra.for_each3( s1 , s2 , s4_array[0].m_v , op );
+ }
+};
+
+
+template< class Algebra >
+struct generic_rk_call_algebra< 3 , Algebra >
+{
+ template< class S1 , class S2 , class S3 , class S4 , class Op>
+ void operator()( Algebra &algebra , S1 &s1 , S2 &s2 , S3 &s3 , S4 s4_array[2] , Op op ) const
+ {
+ algebra.for_each5( s1 , s2 , s3 , s4_array[0].m_v , s4_array[1].m_v , op );
+ }
+
+ template< class S1 , class S2 , class S4 , class Op>
+ void operator()( Algebra &algebra , S1 &s1 , S2 &s2 , S4 s4_array[2] , Op op ) const
+ {
+ algebra.for_each4( s1 , s2 , s4_array[0].m_v , s4_array[1].m_v , op );
+ }
+};
+
+
+template< class Algebra >
+struct generic_rk_call_algebra< 4 , Algebra >
+{
+ template< class S1 , class S2 , class S3 , class S4 , class Op>
+ void operator()( Algebra &algebra , S1 &s1 , S2 &s2 , S3 &s3 , S4 s4_array[3] , Op op ) const
+ {
+ algebra.for_each6( s1 , s2 , s3 , s4_array[0].m_v , s4_array[1].m_v , s4_array[2].m_v , op );
+ }
+
+ template< class S1 , class S2 , class S4 , class Op>
+ void operator()( Algebra &algebra , S1 &s1 , S2 &s2 , S4 s4_array[3] , Op op ) const
+ {
+ algebra.for_each5( s1 , s2 , s4_array[0].m_v , s4_array[1].m_v , s4_array[2].m_v , op );
+ }
+};
+
+
+template< class Algebra >
+struct generic_rk_call_algebra< 5 , Algebra >
+{
+ template< class S1 , class S2 , class S3 , class S4 , class Op>
+ void operator()( Algebra &algebra , S1 &s1 , S2 &s2 , S3 &s3 , S4 s4_array[4] , Op op ) const
+ {
+ algebra.for_each7( s1 , s2 , s3 , s4_array[0].m_v , s4_array[1].m_v , s4_array[2].m_v , s4_array[3].m_v , op );
+ }
+
+ template< class S1 , class S2 , class S4 , class Op>
+ void operator()( Algebra &algebra , S1 &s1 , S2 &s2 , S4 s4_array[4] , Op op ) const
+ {
+ algebra.for_each6( s1 , s2 , s4_array[0].m_v , s4_array[1].m_v , s4_array[2].m_v , s4_array[3].m_v , op );
+ }
+};
+
+template< class Algebra >
+struct generic_rk_call_algebra< 6 , Algebra >
+{
+ template< class S1 , class S2 , class S3 , class S4 , class Op>
+ void operator()( Algebra &algebra , S1 &s1 , S2 &s2 , S3 &s3 , S4 s4_array[5] , Op op ) const
+ {
+ algebra.for_each8( s1 , s2 , s3 , s4_array[0].m_v , s4_array[1].m_v , s4_array[2].m_v , s4_array[3].m_v , s4_array[4].m_v , op );
+ }
+
+ template< class S1 , class S2 , class S4 , class Op>
+ void operator()( Algebra &algebra , S1 &s1 , S2 &s2 , S4 s4_array[5] , Op op ) const
+ {
+ algebra.for_each7( s1 , s2 , s4_array[0].m_v , s4_array[1].m_v , s4_array[2].m_v , s4_array[3].m_v , s4_array[4].m_v , op );
+ }
+};
+
+template< class Algebra >
+struct generic_rk_call_algebra< 7 , Algebra >
+{
+ template< class S1 , class S2 , class S3 , class S4 , class Op>
+ void operator()( Algebra &algebra , S1 &s1 , S2 &s2 , S3 &s3 , S4 s4_array[6] , Op op ) const
+ {
+ algebra.for_each9( s1 , s2 , s3 , s4_array[0].m_v , s4_array[1].m_v , s4_array[2].m_v , s4_array[3].m_v , s4_array[4].m_v ,
+ s4_array[5].m_v , op );
+ }
+
+ template< class S1 , class S2 , class S4 , class Op>
+ void operator()( Algebra &algebra , S1 &s1 , S2 &s2 , S4 s4_array[6] , Op op ) const
+ {
+ algebra.for_each8( s1 , s2 , s4_array[0].m_v , s4_array[1].m_v , s4_array[2].m_v , s4_array[3].m_v , s4_array[4].m_v ,
+ s4_array[5].m_v , op );
+ }
+};
+
+template< class Algebra >
+struct generic_rk_call_algebra< 8 , Algebra >
+{
+ template< class S1 , class S2 , class S3 , class S4 , class Op>
+ void operator()( Algebra &algebra , S1 &s1 , S2 &s2 , S3 &s3 , S4 s4_array[7] , Op op ) const
+ {
+ algebra.for_each10( s1 , s2 , s3 , s4_array[0].m_v , s4_array[1].m_v , s4_array[2].m_v , s4_array[3].m_v , s4_array[4].m_v ,
+ s4_array[5].m_v , s4_array[6].m_v , op );
+ }
+
+ template< class S1 , class S2 , class S4 , class Op>
+ void operator()( Algebra &algebra , S1 &s1 , S2 &s2 , S4 s4_array[7] , Op op ) const
+ {
+ algebra.for_each9( s1 , s2 , s4_array[0].m_v , s4_array[1].m_v , s4_array[2].m_v , s4_array[3].m_v , s4_array[4].m_v ,
+ s4_array[5].m_v , s4_array[6].m_v , op );
+ }
+};
+
+template< class Algebra >
+struct generic_rk_call_algebra< 9 , Algebra >
+{
+ template< class S1 , class S2 , class S3 , class S4 , class Op>
+ void operator()( Algebra &algebra , S1 &s1 , S2 &s2 , S3 &s3 , S4 s4_array[8] , Op op ) const
+ {
+ algebra.for_each11( s1 , s2 , s3 , s4_array[0].m_v , s4_array[1].m_v , s4_array[2].m_v , s4_array[3].m_v , s4_array[4].m_v ,
+ s4_array[5].m_v , s4_array[6].m_v , s4_array[7].m_v , op );
+ }
+
+ template< class S1 , class S2 , class S4 , class Op>
+ void operator()( Algebra &algebra , S1 &s1 , S2 &s2 , S4 s4_array[8] , Op op ) const
+ {
+ algebra.for_each10( s1 , s2 , s4_array[0].m_v , s4_array[1].m_v , s4_array[2].m_v , s4_array[3].m_v , s4_array[4].m_v ,
+ s4_array[5].m_v , s4_array[6].m_v , s4_array[7].m_v , op );
+ }
+};
+
+template< class Algebra >
+struct generic_rk_call_algebra< 10 , Algebra >
+{
+ template< class S1 , class S2 , class S3 , class S4 , class Op>
+ void operator()( Algebra &algebra , S1 &s1 , S2 &s2 , S3 &s3 , S4 s4_array[9] , Op op ) const
+ {
+ algebra.for_each12( s1 , s2 , s3 , s4_array[0].m_v , s4_array[1].m_v , s4_array[2].m_v , s4_array[3].m_v , s4_array[4].m_v ,
+ s4_array[5].m_v , s4_array[6].m_v , s4_array[7].m_v , s4_array[8].m_v , op );
+ }
+
+ template< class S1 , class S2 , class S4 , class Op>
+ void operator()( Algebra &algebra , S1 &s1 , S2 &s2 , S4 s4_array[9] , Op op ) const
+ {
+ algebra.for_each11( s1 , s2 , s4_array[0].m_v , s4_array[1].m_v , s4_array[2].m_v , s4_array[3].m_v , s4_array[4].m_v ,
+ s4_array[5].m_v , s4_array[6].m_v , s4_array[7].m_v , s4_array[8].m_v , op );
+ }
+};
+
+
+template< class Algebra >
+struct generic_rk_call_algebra< 11 , Algebra >
+{
+ template< class S1 , class S2 , class S3 , class S4 , class Op>
+ void operator()( Algebra &algebra , S1 &s1 , S2 &s2 , S3 &s3 , S4 s4_array[10] , Op op ) const
+ {
+ algebra.for_each13( s1 , s2 , s3 , s4_array[0].m_v , s4_array[1].m_v , s4_array[2].m_v , s4_array[3].m_v , s4_array[4].m_v ,
+ s4_array[5].m_v , s4_array[6].m_v , s4_array[7].m_v , s4_array[8].m_v , s4_array[9].m_v , op );
+ }
+
+ template< class S1 , class S2 , class S4 , class Op>
+ void operator()( Algebra &algebra , S1 &s1 , S2 &s2 , S4 s4_array[10] , Op op ) const
+ {
+ algebra.for_each12( s1 , s2 , s4_array[0].m_v , s4_array[1].m_v , s4_array[2].m_v , s4_array[3].m_v , s4_array[4].m_v ,
+ s4_array[5].m_v , s4_array[6].m_v , s4_array[7].m_v , s4_array[8].m_v , s4_array[9].m_v , op );
+ }
+};
+
+template< class Algebra >
+struct generic_rk_call_algebra< 12 , Algebra >
+{
+ template< class S1 , class S2 , class S3 , class S4 , class Op>
+ void operator()( Algebra &algebra , S1 &s1 , S2 &s2 , S3 &s3 , S4 s4_array[11] , Op op ) const
+ {
+ algebra.for_each14( s1 , s2 , s3 , s4_array[0].m_v , s4_array[1].m_v , s4_array[2].m_v , s4_array[3].m_v , s4_array[4].m_v ,
+ s4_array[5].m_v , s4_array[6].m_v , s4_array[7].m_v , s4_array[8].m_v , s4_array[9].m_v , s4_array[10].m_v , op );
+ }
+
+ template< class S1 , class S2 , class S4 , class Op>
+ void operator()( Algebra &algebra , S1 &s1 , S2 &s2 , S4 s4_array[11] , Op op ) const
+ {
+ algebra.for_each13( s1 , s2 , s4_array[0].m_v , s4_array[1].m_v , s4_array[2].m_v , s4_array[3].m_v , s4_array[4].m_v ,
+ s4_array[5].m_v , s4_array[6].m_v , s4_array[7].m_v , s4_array[8].m_v , s4_array[9].m_v , s4_array[10].m_v , op );
+ }
+};
+
+template< class Algebra >
+struct generic_rk_call_algebra< 13 , Algebra >
+{
+ template< class S1 , class S2 , class S3 , class S4 , class Op>
+ void operator()( Algebra &algebra , S1 &s1 , S2 &s2 , S3 &s3 , S4 s4_array[12] , Op op ) const
+ {
+ algebra.for_each15( s1 , s2 , s3 , s4_array[0].m_v , s4_array[1].m_v , s4_array[2].m_v , s4_array[3].m_v , s4_array[4].m_v ,
+ s4_array[5].m_v , s4_array[6].m_v , s4_array[7].m_v , s4_array[8].m_v , s4_array[9].m_v , s4_array[10].m_v , s4_array[11].m_v , op );
+ }
+
+ template< class S1 , class S2 , class S4 , class Op>
+ void operator()( Algebra &algebra , S1 &s1 , S2 &s2 , S4 s4_array[12] , Op op ) const
+ {
+ algebra.for_each14( s1 , s2 , s4_array[0].m_v , s4_array[1].m_v , s4_array[2].m_v , s4_array[3].m_v , s4_array[4].m_v ,
+ s4_array[5].m_v , s4_array[6].m_v , s4_array[7].m_v , s4_array[8].m_v , s4_array[9].m_v , s4_array[10].m_v , s4_array[11].m_v , op );
+ }
+};
+
+}
+}
+}
+}
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_GENERIC_RK_CALL_ALGEBRA_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/detail/generic_rk_operations.hpp b/include/boost/numeric/odeint/stepper/detail/generic_rk_operations.hpp
new file mode 100644
index 0000000..2cce3f4
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/detail/generic_rk_operations.hpp
@@ -0,0 +1,252 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/detail/generic_rk_operations.hpp
+
+ [begin_description]
+ Operations caller for the generic Runge Kutta method.
+ [end_description]
+
+ Copyright 2011 Mario Mulansky
+ Copyright 2011-2012 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_GENERIC_RK_OPERATIONS_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_GENERIC_RK_OPERATIONS_HPP_INCLUDED
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+template< size_t StageNumber , class Operations , class Fac , class Time >
+struct generic_rk_scale_sum;
+
+template< class Operations , class Fac , class Time >
+struct generic_rk_scale_sum< 1 , Operations , Fac , Time > : public Operations::template scale_sum2< Fac , Time >
+{
+ generic_rk_scale_sum( const boost::array<Fac,1> &a , Time dt ) : Operations::template scale_sum2< Fac , Time >( 1.0 , a[0]*dt )
+ { }
+
+ typedef void result_type;
+};
+
+
+template< class Operations , class Fac , class Time >
+struct generic_rk_scale_sum< 2 , Operations , Fac , Time > : public Operations::template scale_sum3< Fac , Time >
+{
+ generic_rk_scale_sum( const boost::array<Fac,2> &a , Time dt )
+ : Operations::template scale_sum3< Fac , Time >( 1.0 , a[0]*dt , a[1]*dt )
+ { }
+
+ typedef void result_type;
+};
+
+template< class Operations , class Fac , class Time >
+struct generic_rk_scale_sum< 3 , Operations , Fac , Time > : public Operations::template scale_sum4< Fac , Time >
+{
+ generic_rk_scale_sum( const boost::array<Fac,3> &a , Time dt )
+ : Operations::template scale_sum4< Fac , Time >( 1.0 , a[0]*dt , a[1]*dt , a[2]*dt )
+ { }
+
+ typedef void result_type;
+};
+
+template< class Operations , class Fac , class Time >
+struct generic_rk_scale_sum< 4 , Operations , Fac , Time > : public Operations::template scale_sum5< Fac , Time >
+{
+ generic_rk_scale_sum( const boost::array<Fac,4> &a , Time dt )
+ : Operations::template scale_sum5< Fac , Time >( 1.0 , a[0]*dt , a[1]*dt , a[2]*dt , a[3]*dt )
+ { }
+
+ typedef void result_type;
+};
+
+template< class Operations , class Fac , class Time >
+struct generic_rk_scale_sum< 5 , Operations , Fac , Time > : public Operations::template scale_sum6< Fac , Time >
+{
+ generic_rk_scale_sum( const boost::array<Fac,5> &a , Time dt )
+ : Operations::template scale_sum6< Fac , Time >( 1.0 , a[0]*dt , a[1]*dt , a[2]*dt , a[3]*dt , a[4]*dt )
+ { }
+
+ typedef void result_type;
+};
+
+template< class Operations , class Fac , class Time >
+struct generic_rk_scale_sum< 6 , Operations , Fac , Time > : public Operations::template scale_sum7< Fac , Time >
+{
+ generic_rk_scale_sum( const boost::array<Fac,6> &a , Time dt )
+ : Operations::template scale_sum7< Fac , Time >( 1.0 , a[0]*dt , a[1]*dt , a[2]*dt , a[3]*dt , a[4]*dt , a[5]*dt )
+ { }
+
+ typedef void result_type;
+};
+
+template< class Operations , class Fac , class Time >
+struct generic_rk_scale_sum< 7 , Operations , Fac , Time > : public Operations::template scale_sum8< Fac , Time >
+{
+ generic_rk_scale_sum( const boost::array<Fac,7> &a , Time dt )
+ : Operations::template scale_sum8< Fac , Time >( 1.0 , a[0]*dt , a[1]*dt , a[2]*dt , a[3]*dt , a[4]*dt , a[5]*dt , a[6]*dt )
+ { }
+
+ typedef void result_type;
+};
+
+template< class Operations , class Fac , class Time >
+struct generic_rk_scale_sum< 8 , Operations , Fac , Time > : public Operations::template scale_sum9< Fac , Time >
+{
+ generic_rk_scale_sum( const boost::array<Fac,8> &a , Time dt )
+ : Operations::template scale_sum9< Fac , Time >( 1.0 , a[0]*dt , a[1]*dt , a[2]*dt , a[3]*dt , a[4]*dt ,
+ a[5]*dt , a[6]*dt , a[7]*dt )
+ { }
+
+ typedef void result_type;
+};
+
+template< class Operations , class Fac , class Time >
+struct generic_rk_scale_sum< 9 , Operations , Fac , Time > : public Operations::template scale_sum10< Fac , Time >
+{
+ generic_rk_scale_sum( const boost::array<Fac,9> &a , Time dt )
+ : Operations::template scale_sum10< Fac , Time >( 1.0 , a[0]*dt , a[1]*dt , a[2]*dt , a[3]*dt , a[4]*dt ,
+ a[5]*dt , a[6]*dt , a[7]*dt , a[8]*dt )
+ { }
+
+ typedef void result_type;
+};
+
+template< class Operations , class Fac , class Time >
+struct generic_rk_scale_sum< 10 , Operations , Fac , Time > : public Operations::template scale_sum11< Fac , Time >
+{
+ generic_rk_scale_sum( const boost::array<Fac,10> &a , Time dt )
+ : Operations::template scale_sum11< Fac , Time >( 1.0 , a[0]*dt , a[1]*dt , a[2]*dt , a[3]*dt , a[4]*dt ,
+ a[5]*dt , a[6]*dt , a[7]*dt , a[8]*dt , a[9]*dt )
+ { }
+
+ typedef void result_type;
+};
+
+template< class Operations , class Fac , class Time >
+struct generic_rk_scale_sum< 11 , Operations , Fac , Time > : public Operations::template scale_sum12< Fac , Time >
+{
+ generic_rk_scale_sum( const boost::array<Fac,11> &a , Time dt )
+ : Operations::template scale_sum12< Fac , Time >( 1.0 , a[0]*dt , a[1]*dt , a[2]*dt , a[3]*dt , a[4]*dt ,
+ a[5]*dt , a[6]*dt , a[7]*dt , a[8]*dt , a[9]*dt , a[10]*dt )
+ { }
+
+ typedef void result_type;
+};
+
+template< class Operations , class Fac , class Time >
+struct generic_rk_scale_sum< 12 , Operations , Fac , Time > : public Operations::template scale_sum13< Fac , Time >
+{
+ generic_rk_scale_sum( const boost::array<Fac,12> &a , Time dt )
+ : Operations::template scale_sum13< Fac , Time >( 1.0 , a[0]*dt , a[1]*dt , a[2]*dt , a[3]*dt , a[4]*dt ,
+ a[5]*dt , a[6]*dt , a[7]*dt , a[8]*dt , a[9]*dt , a[10]*dt , a[11]*dt )
+ { }
+
+ typedef void result_type;
+};
+
+template< class Operations , class Fac , class Time >
+struct generic_rk_scale_sum< 13 , Operations , Fac , Time > : public Operations::template scale_sum14< Fac , Time >
+{
+ generic_rk_scale_sum( const boost::array<Fac,13> &a , Time dt )
+ : Operations::template scale_sum14< Fac , Time >( 1.0 , a[0]*dt , a[1]*dt , a[2]*dt , a[3]*dt , a[4]*dt ,
+ a[5]*dt , a[6]*dt , a[7]*dt , a[8]*dt , a[9]*dt , a[10]*dt , a[11]*dt , a[12]*dt )
+ { }
+
+ typedef void result_type;
+};
+
+
+// for error estimates
+template< size_t StageNumber , class Operations , class Fac , class Time >
+struct generic_rk_scale_sum_err;
+
+template< class Operations , class Fac , class Time >
+struct generic_rk_scale_sum_err< 1 , Operations , Fac , Time > : public Operations::template scale_sum1< Time >
+{
+ generic_rk_scale_sum_err( const boost::array<Fac,1> &a , Time dt ) : Operations::template scale_sum1< Time >( a[0]*dt )
+ { }
+
+ typedef void result_type;
+};
+
+
+template< class Operations , class Fac , class Time >
+struct generic_rk_scale_sum_err< 2 , Operations , Fac , Time > : public Operations::template scale_sum2< Time >
+{
+ generic_rk_scale_sum_err( const boost::array<Fac,2> &a , Time dt )
+ : Operations::template scale_sum2< Time >( a[0]*dt , a[1]*dt )
+ { }
+
+ typedef void result_type;
+};
+
+template< class Operations , class Fac , class Time >
+struct generic_rk_scale_sum_err< 3 , Operations , Fac , Time > : public Operations::template scale_sum3< Time >
+{
+ generic_rk_scale_sum_err( const boost::array<Fac,3> &a , Time dt )
+ : Operations::template scale_sum3< Time >( a[0]*dt , a[1]*dt , a[2]*dt )
+ { }
+
+ typedef void result_type;
+};
+
+template< class Operations , class Fac , class Time >
+struct generic_rk_scale_sum_err< 4 , Operations , Fac , Time > : public Operations::template scale_sum4< Time >
+{
+ generic_rk_scale_sum_err( const boost::array<Fac,4> &a , Time dt )
+ : Operations::template scale_sum4< Time >( a[0]*dt , a[1]*dt , a[2]*dt , a[3]*dt )
+ { }
+
+ typedef void result_type;
+};
+
+template< class Operations , class Fac , class Time >
+struct generic_rk_scale_sum_err< 5 , Operations , Fac , Time > : public Operations::template scale_sum5< Fac >
+{
+ generic_rk_scale_sum_err( const boost::array<Fac,5> &a , Time dt )
+ : Operations::template scale_sum5< Time >( a[0]*dt , a[1]*dt , a[2]*dt , a[3]*dt , a[4]*dt )
+ { }
+
+ typedef void result_type;
+};
+
+
+template< class Operations , class Fac , class Time >
+struct generic_rk_scale_sum_err< 6 , Operations , Fac , Time > : public Operations::template scale_sum6< Time >
+{
+ generic_rk_scale_sum_err( const boost::array<Fac,6> &a , Time dt )
+ : Operations::template scale_sum6< Time >( a[0]*dt , a[1]*dt , a[2]*dt , a[3]*dt , a[4]*dt , a[5]*dt )
+ { }
+
+ typedef void result_type;
+};
+
+
+// for rk87
+template< class Operations , class Fac , class Time >
+struct generic_rk_scale_sum_err< 13 , Operations , Fac , Time > : public Operations::template scale_sum13< Time >
+{
+ generic_rk_scale_sum_err( const boost::array<Fac,13> &a , Time dt )
+ : Operations::template scale_sum13< Time >( a[0]*dt , a[1]*dt , a[2]*dt , a[3]*dt , a[4]*dt , a[5]*dt ,
+ a[6]*dt , a[7]*dt , a[8]*dt , a[9]*dt , a[10]*dt , a[11]*dt , a[12]*dt )
+ { }
+
+ typedef void result_type;
+};
+
+
+}
+}
+}
+}
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_GENERIC_RK_OPERATIONS_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/detail/rotating_buffer.hpp b/include/boost/numeric/odeint/stepper/detail/rotating_buffer.hpp
new file mode 100644
index 0000000..2338afd
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/detail/rotating_buffer.hpp
@@ -0,0 +1,84 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/detail/rotating_buffer.hpp
+
+ [begin_description]
+ Implemetation of a rotating (cyclic) buffer for use in the Adam Bashforth stepper
+ [end_description]
+
+ Copyright 2011 Karsten Ahnert
+ Copyright 2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_ROTATING_BUFFER_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_ROTATING_BUFFER_HPP_INCLUDED
+
+#include <boost/array.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+template< class T , size_t N >
+class rotating_buffer
+{
+public:
+
+ typedef T value_type;
+ const static size_t dim = N;
+
+ rotating_buffer( void ) : m_first( 0 )
+ { }
+
+ size_t size( void ) const
+ {
+ return dim;
+ }
+
+ value_type& operator[]( size_t i )
+ {
+ return m_data[ get_index( i ) ];
+ }
+
+ const value_type& operator[]( size_t i ) const
+ {
+ return m_data[ get_index( i ) ];
+ }
+
+ void rotate( void )
+ {
+ if( m_first == 0 )
+ m_first = dim-1;
+ else
+ --m_first;
+ }
+
+protected:
+
+ value_type m_data[N];
+
+private:
+
+ size_t get_index( size_t i ) const
+ {
+ return ( ( i + m_first ) % dim );
+ }
+
+ size_t m_first;
+
+};
+
+
+} // detail
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_ROTATING_BUFFER_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/euler.hpp b/include/boost/numeric/odeint/stepper/euler.hpp
new file mode 100644
index 0000000..1c7c126
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/euler.hpp
@@ -0,0 +1,166 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/euler.hpp
+
+ [begin_description]
+ Implementation of the classical explicit Euler stepper. This method is really simple and should only
+ be used for demonstration purposes.
+ [end_description]
+
+ Copyright 2010-2013 Karsten Ahnert
+ Copyright 2010-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_EULER_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_EULER_HPP_INCLUDED
+
+
+#include <boost/numeric/odeint/stepper/base/explicit_stepper_base.hpp>
+#include <boost/numeric/odeint/util/resizer.hpp>
+#include <boost/numeric/odeint/algebra/range_algebra.hpp>
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+template<
+class State ,
+class Value = double ,
+class Deriv = State ,
+class Time = Value ,
+class Algebra = typename algebra_dispatcher< State >::algebra_type ,
+class Operations = typename operations_dispatcher< State >::operations_type ,
+class Resizer = initially_resizer
+>
+#ifndef DOXYGEN_SKIP
+class euler
+: public explicit_stepper_base<
+ euler< State , Value , Deriv , Time , Algebra , Operations , Resizer > ,
+ 1 , State , Value , Deriv , Time , Algebra , Operations , Resizer >
+#else
+class euler : public explicit_stepper_base
+#endif
+{
+public :
+
+ #ifndef DOXYGEN_SKIP
+ typedef explicit_stepper_base< euler< State , Value , Deriv , Time , Algebra , Operations , Resizer > , 1 , State , Value , Deriv , Time , Algebra , Operations , Resizer > stepper_base_type;
+ #else
+ typedef explicit_stepper_base< euler< ... > , ... > stepper_base_type;
+ #endif
+ typedef typename stepper_base_type::state_type state_type;
+ typedef typename stepper_base_type::value_type value_type;
+ typedef typename stepper_base_type::deriv_type deriv_type;
+ typedef typename stepper_base_type::time_type time_type;
+ typedef typename stepper_base_type::algebra_type algebra_type;
+ typedef typename stepper_base_type::operations_type operations_type;
+ typedef typename stepper_base_type::resizer_type resizer_type;
+
+ #ifndef DOXYGEN_SKIP
+ typedef typename stepper_base_type::stepper_type stepper_type;
+ typedef typename stepper_base_type::wrapped_state_type wrapped_state_type;
+ typedef typename stepper_base_type::wrapped_deriv_type wrapped_deriv_type;
+ #endif
+
+
+ euler( const algebra_type &algebra = algebra_type() ) : stepper_base_type( algebra )
+ { }
+
+ template< class System , class StateIn , class DerivIn , class StateOut >
+ void do_step_impl( System /* system */ , const StateIn &in , const DerivIn &dxdt , time_type /* t */ , StateOut &out , time_type dt )
+ {
+ stepper_base_type::m_algebra.for_each3( out , in , dxdt ,
+ typename operations_type::template scale_sum2< value_type , time_type >( 1.0 , dt ) );
+
+ }
+
+ template< class StateOut , class StateIn1 , class StateIn2 >
+ void calc_state( StateOut &x , time_type t , const StateIn1 &old_state , time_type t_old , const StateIn2 & /*current_state*/ , time_type /* t_new */ ) const
+ {
+ const time_type delta = t - t_old;
+ stepper_base_type::m_algebra.for_each3( x , old_state , stepper_base_type::m_dxdt.m_v ,
+ typename operations_type::template scale_sum2< value_type , time_type >( 1.0 , delta ) );
+ }
+
+ template< class StateType >
+ void adjust_size( const StateType &x )
+ {
+ stepper_base_type::adjust_size( x );
+ }
+};
+
+
+
+/********** DOXYGEN ***********/
+
+/**
+ * \class euler
+ * \brief An implementation of the Euler method.
+ *
+ * The Euler method is a very simply solver for ordinary differential equations. This method should not be used
+ * for real applications. It is only useful for demonstration purposes. Step size control is not provided but
+ * trivial continuous output is available.
+ *
+ * This class derives from explicit_stepper_base and inherits its interface via CRTP (current recurring template pattern),
+ * see explicit_stepper_base
+ *
+ * \tparam State The state type.
+ * \tparam Value The value type.
+ * \tparam Deriv The type representing the time derivative of the state.
+ * \tparam Time The time representing the independent variable - the time.
+ * \tparam Algebra The algebra type.
+ * \tparam Operations The operations type.
+ * \tparam Resizer The resizer policy type.
+ */
+
+ /**
+ * \fn euler::euler( const algebra_type &algebra )
+ * \brief Constructs the euler class. This constructor can be used as a default
+ * constructor of the algebra has a default constructor.
+ * \param algebra A copy of algebra is made and stored inside explicit_stepper_base.
+ */
+
+ /**
+ * \fn euler::do_step_impl( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt )
+ * \brief This method performs one step. The derivative `dxdt` of `in` at the time `t` is passed to the method.
+ * The result is updated out of place, hence the input is in `in` and the output in `out`.
+ * Access to this step functionality is provided by explicit_stepper_base and
+ * `do_step_impl` should not be called directly.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param in The state of the ODE which should be solved. in is not modified in this method
+ * \param dxdt The derivative of x at t.
+ * \param t The value of the time, at which the step should be performed.
+ * \param out The result of the step is written in out.
+ * \param dt The step size.
+ */
+
+
+ /**
+ * \fn euler::calc_state( StateOut &x , time_type t , const StateIn1 &old_state , time_type t_old , const StateIn2 ¤t_state , time_type t_new ) const
+ * \brief This method is used for continuous output and it calculates the state `x` at a time `t` from the
+ * knowledge of two states `old_state` and `current_state` at time points `t_old` and `t_new`.
+ */
+
+ /**
+ * \fn euler::adjust_size( const StateType &x )
+ * \brief Adjust the size of all temporaries in the stepper manually.
+ * \param x A state from which the size of the temporaries to be resized is deduced.
+ */
+
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_EULER_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/explicit_error_generic_rk.hpp b/include/boost/numeric/odeint/stepper/explicit_error_generic_rk.hpp
new file mode 100644
index 0000000..3c59810
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/explicit_error_generic_rk.hpp
@@ -0,0 +1,255 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/explicit_error_generic_rk.hpp
+
+ [begin_description]
+ Implementation of the generic Runge Kutta error stepper. Base class for many RK error steppers.
+ [end_description]
+
+ Copyright 2011-2013 Mario Mulansky
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2012 Christoph Koke
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_EXPLICIT_ERROR_GENERIC_RK_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_EXPLICIT_ERROR_GENERIC_RK_HPP_INCLUDED
+
+#include <boost/numeric/odeint/stepper/base/explicit_error_stepper_base.hpp>
+
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+#include <boost/numeric/odeint/algebra/range_algebra.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
+#include <boost/numeric/odeint/stepper/detail/generic_rk_algorithm.hpp>
+#include <boost/numeric/odeint/stepper/detail/generic_rk_call_algebra.hpp>
+#include <boost/numeric/odeint/stepper/detail/generic_rk_operations.hpp>
+
+#include <boost/numeric/odeint/util/state_wrapper.hpp>
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resizer.hpp>
+
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+template<
+size_t StageCount,
+size_t Order,
+size_t StepperOrder ,
+size_t ErrorOrder ,
+class State ,
+class Value = double ,
+class Deriv = State ,
+class Time = Value ,
+class Algebra = typename algebra_dispatcher< State >::algebra_type ,
+class Operations = typename operations_dispatcher< State >::operations_type ,
+class Resizer = initially_resizer
+>
+#ifndef DOXYGEN_SKIP
+class explicit_error_generic_rk
+: public explicit_error_stepper_base<
+ explicit_error_generic_rk< StageCount , Order , StepperOrder , ErrorOrder , State ,
+ Value , Deriv , Time , Algebra , Operations , Resizer > ,
+ Order , StepperOrder , ErrorOrder , State , Value , Deriv , Time , Algebra ,
+ Operations , Resizer >
+#else
+class explicit_error_generic_rk : public explicit_error_stepper_base
+#endif
+{
+
+public:
+#ifndef DOXYGEN_SKIP
+ typedef explicit_error_stepper_base<
+ explicit_error_generic_rk< StageCount , Order , StepperOrder , ErrorOrder , State ,
+ Value , Deriv , Time , Algebra , Operations , Resizer > ,
+ Order , StepperOrder , ErrorOrder , State , Value , Deriv , Time , Algebra ,
+ Operations , Resizer > stepper_base_type;
+#else
+ typedef explicit_stepper_base< ... > stepper_base_type;
+#endif
+ typedef typename stepper_base_type::state_type state_type;
+ typedef typename stepper_base_type::wrapped_state_type wrapped_state_type;
+ typedef typename stepper_base_type::value_type value_type;
+ typedef typename stepper_base_type::deriv_type deriv_type;
+ typedef typename stepper_base_type::wrapped_deriv_type wrapped_deriv_type;
+ typedef typename stepper_base_type::time_type time_type;
+ typedef typename stepper_base_type::algebra_type algebra_type;
+ typedef typename stepper_base_type::operations_type operations_type;
+ typedef typename stepper_base_type::resizer_type resizer_type;
+#ifndef DOXYGEN_SKIP
+ typedef explicit_error_generic_rk< StageCount , Order , StepperOrder , ErrorOrder , State ,
+ Value , Deriv , Time , Algebra , Operations , Resizer > stepper_type;
+#endif
+ typedef detail::generic_rk_algorithm< StageCount , Value , Algebra , Operations > rk_algorithm_type;
+
+ typedef typename rk_algorithm_type::coef_a_type coef_a_type;
+ typedef typename rk_algorithm_type::coef_b_type coef_b_type;
+ typedef typename rk_algorithm_type::coef_c_type coef_c_type;
+
+ static const size_t stage_count = StageCount;
+
+private:
+
+
+public:
+
+ // we use an explicit_generic_rk to do the normal rk step
+ // and add a separate calculation of the error estimate afterwards
+ explicit_error_generic_rk( const coef_a_type &a ,
+ const coef_b_type &b ,
+ const coef_b_type &b2 ,
+ const coef_c_type &c ,
+ const algebra_type &algebra = algebra_type() )
+ : stepper_base_type( algebra ) , m_rk_algorithm( a , b , c ) , m_b2( b2 )
+ { }
+
+
+ template< class System , class StateIn , class DerivIn , class StateOut , class Err >
+ void do_step_impl( System system , const StateIn &in , const DerivIn &dxdt ,
+ time_type t , StateOut &out , time_type dt , Err &xerr )
+ {
+ // normal step
+ do_step_impl( system , in , dxdt , t , out , dt );
+
+ // additionally, perform the error calculation
+ detail::template generic_rk_call_algebra< StageCount , algebra_type >()( stepper_base_type::m_algebra ,
+ xerr , dxdt , m_F , detail::generic_rk_scale_sum_err< StageCount , operations_type , value_type , time_type >( m_b2 , dt) );
+ }
+
+
+ template< class System , class StateIn , class DerivIn , class StateOut >
+ void do_step_impl( System system , const StateIn &in , const DerivIn &dxdt ,
+ time_type t , StateOut &out , time_type dt )
+ {
+ m_resizer.adjust_size( in , detail::bind( &stepper_type::template resize_impl< StateIn > , detail::ref( *this ) , detail::_1 ) );
+
+ // actual calculation done in generic_rk.hpp
+ m_rk_algorithm.do_step( stepper_base_type::m_algebra , system , in , dxdt , t , out , dt , m_x_tmp.m_v , m_F );
+ }
+
+
+ template< class StateIn >
+ void adjust_size( const StateIn &x )
+ {
+ resize_impl( x );
+ stepper_base_type::adjust_size( x );
+ }
+
+
+private:
+
+ template< class StateIn >
+ bool resize_impl( const StateIn &x )
+ {
+ bool resized( false );
+ resized |= adjust_size_by_resizeability( m_x_tmp , x , typename is_resizeable<state_type>::type() );
+ for( size_t i = 0 ; i < StageCount-1 ; ++i )
+ {
+ resized |= adjust_size_by_resizeability( m_F[i] , x , typename is_resizeable<deriv_type>::type() );
+ }
+ return resized;
+ }
+
+
+ rk_algorithm_type m_rk_algorithm;
+ coef_b_type m_b2;
+
+ resizer_type m_resizer;
+
+ wrapped_state_type m_x_tmp;
+ wrapped_deriv_type m_F[StageCount-1];
+
+};
+
+
+/********* DOXYGEN *********/
+
+/**
+ * \class explicit_error_generic_rk
+ * \brief A generic implementation of explicit Runge-Kutta algorithms with error estimation. This class is as a
+ * base class for all explicit Runge-Kutta steppers with error estimation.
+ *
+ * This class implements the explicit Runge-Kutta algorithms with error estimation in a generic way.
+ * The Butcher tableau is passed to the stepper which constructs the stepper scheme with the help of a
+ * template-metaprogramming algorithm. ToDo : Add example!
+ *
+ * This class derives explicit_error_stepper_base which provides the stepper interface.
+ *
+ * \tparam StageCount The number of stages of the Runge-Kutta algorithm.
+ * \tparam Order The order of a stepper if the stepper is used without error estimation.
+ * \tparam StepperOrder The order of a step if the stepper is used with error estimation. Usually Order and StepperOrder have
+ * the same value.
+ * \tparam ErrorOrder The order of the error step if the stepper is used with error estimation.
+ * \tparam State The type representing the state of the ODE.
+ * \tparam Value The floating point type which is used in the computations.
+ * \tparam Time The type representing the independent variable - the time - of the ODE.
+ * \tparam Algebra The algebra type.
+ * \tparam Operations The operations type.
+ * \tparam Resizer The resizer policy type.
+ */
+
+
+ /**
+ * \fn explicit_error_generic_rk::explicit_error_generic_rk( const coef_a_type &a , const coef_b_type &b , const coef_b_type &b2 , const coef_c_type &c , const algebra_type &algebra )
+ * \brief Constructs the explicit_error_generik_rk class with the given parameters a, b, b2 and c. See examples section for details on the coefficients.
+ *
+ * \param a Triangular matrix of parameters b in the Butcher tableau.
+ * \param b Last row of the butcher tableau.
+ * \param b2 Parameters for lower-order evaluation to estimate the error.
+ * \param c Parameters to calculate the time points in the Butcher tableau.
+ * \param algebra A copy of algebra is made and stored inside explicit_stepper_base.
+ */
+
+
+ /**
+ * \fn explicit_error_generic_rk::do_step_impl( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt , Err &xerr )
+ * \brief This method performs one step. The derivative `dxdt` of `in` at the time `t` is passed to the method.
+ * The result is updated out-of-place, hence the input is in `in` and the output in `out`. Futhermore, an
+ * estimation of the error is stored in `xerr`. `do_step_impl` is used by explicit_error_stepper_base.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param in The state of the ODE which should be solved. in is not modified in this method
+ * \param dxdt The derivative of x at t.
+ * \param t The value of the time, at which the step should be performed.
+ * \param out The result of the step is written in out.
+ * \param dt The step size.
+ * \param xerr The result of the error estimation is written in xerr.
+ */
+
+ /**
+ * \fn explicit_error_generic_rk::do_step_impl( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt )
+ * \brief This method performs one step. The derivative `dxdt` of `in` at the time `t` is passed to the method.
+ * The result is updated out-of-place, hence the input is in `in` and the output in `out`.
+ * Access to this step functionality is provided by explicit_stepper_base and
+ * `do_step_impl` should not be called directly.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param in The state of the ODE which should be solved. in is not modified in this method
+ * \param dxdt The derivative of x at t.
+ * \param t The value of the time, at which the step should be performed.
+ * \param out The result of the step is written in out.
+ * \param dt The step size.
+ */
+
+ /**
+ * \fn explicit_error_generic_rk::adjust_size( const StateIn &x )
+ * \brief Adjust the size of all temporaries in the stepper manually.
+ * \param x A state from which the size of the temporaries to be resized is deduced.
+ */
+
+}
+}
+}
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_EXPLICIT_ERROR_GENERIC_RK_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/explicit_generic_rk.hpp b/include/boost/numeric/odeint/stepper/explicit_generic_rk.hpp
new file mode 100644
index 0000000..f8edc20
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/explicit_generic_rk.hpp
@@ -0,0 +1,246 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/explicit_generic_rk.hpp
+
+ [begin_description]
+ Implementation of the generic Runge-Kutta steppers. This is the base class for many Runge-Kutta steppers.
+ [end_description]
+
+ Copyright 2011-2013 Mario Mulansky
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2012 Christoph Koke
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_EXPLICIT_GENERIC_RK_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_EXPLICIT_GENERIC_RK_HPP_INCLUDED
+
+
+#include <boost/array.hpp>
+
+
+#include <boost/numeric/odeint/stepper/base/explicit_stepper_base.hpp>
+#include <boost/numeric/odeint/algebra/range_algebra.hpp>
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
+#include <boost/numeric/odeint/stepper/detail/generic_rk_algorithm.hpp>
+
+#include <boost/numeric/odeint/util/state_wrapper.hpp>
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resizer.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+//forward declarations
+
+#ifndef DOXYGEN_SKIP
+template<
+size_t StageCount,
+size_t Order,
+class State ,
+class Value = double ,
+class Deriv = State ,
+class Time = Value ,
+class Algebra = typename algebra_dispatcher< State >::algebra_type ,
+class Operations = typename operations_dispatcher< State >::operations_type ,
+class Resizer = initially_resizer
+>
+class explicit_generic_rk;
+
+
+struct stage_vector;
+
+template< class T , class Constant >
+struct array_wrapper
+{
+ typedef const typename boost::array< T , Constant::value > type;
+};
+
+template< class T , size_t i >
+struct stage
+{
+ T c;
+ boost::array< T , i > a;
+};
+
+
+template< class T , class Constant >
+struct stage_wrapper
+{
+ typedef stage< T , Constant::value > type;
+};
+#endif
+
+
+template<
+size_t StageCount,
+size_t Order,
+class State ,
+class Value ,
+class Deriv ,
+class Time ,
+class Algebra ,
+class Operations ,
+class Resizer
+>
+#ifndef DOXYGEN_SKIP
+class explicit_generic_rk : public explicit_stepper_base<
+explicit_generic_rk< StageCount , Order , State , Value , Deriv , Time , Algebra , Operations , Resizer > ,
+Order , State , Value , Deriv , Time , Algebra , Operations , Resizer >
+#else
+class explicit_generic_rk : public explicit_stepper_base
+#endif
+{
+
+public:
+
+ #ifndef DOXYGEN_SKIP
+ typedef explicit_stepper_base<
+ explicit_generic_rk< StageCount , Order , State , Value , Deriv ,Time , Algebra , Operations , Resizer > ,
+ Order , State , Value , Deriv , Time , Algebra ,
+ Operations , Resizer > stepper_base_type;
+ #else
+ typedef explicit_stepper_base< ... > stepper_base_type;
+ #endif
+
+ typedef typename stepper_base_type::state_type state_type;
+ typedef typename stepper_base_type::wrapped_state_type wrapped_state_type;
+ typedef typename stepper_base_type::value_type value_type;
+ typedef typename stepper_base_type::deriv_type deriv_type;
+ typedef typename stepper_base_type::wrapped_deriv_type wrapped_deriv_type;
+ typedef typename stepper_base_type::time_type time_type;
+ typedef typename stepper_base_type::algebra_type algebra_type;
+ typedef typename stepper_base_type::operations_type operations_type;
+ typedef typename stepper_base_type::resizer_type resizer_type;
+
+ #ifndef DOXYGEN_SKIP
+ typedef explicit_generic_rk< StageCount , Order , State , Value , Deriv ,Time , Algebra , Operations , Resizer > stepper_type;
+ #endif
+
+ typedef detail::generic_rk_algorithm< StageCount , Value , Algebra , Operations > rk_algorithm_type;
+
+ typedef typename rk_algorithm_type::coef_a_type coef_a_type;
+ typedef typename rk_algorithm_type::coef_b_type coef_b_type;
+ typedef typename rk_algorithm_type::coef_c_type coef_c_type;
+
+ #ifndef DOXYGEN_SKIP
+ static const size_t stage_count = StageCount;
+ #endif
+
+public:
+
+ explicit_generic_rk( const coef_a_type &a , const coef_b_type &b , const coef_c_type &c ,
+ const algebra_type &algebra = algebra_type() )
+ : stepper_base_type( algebra ) , m_rk_algorithm( a , b , c )
+ { }
+
+
+ template< class System , class StateIn , class DerivIn , class StateOut >
+ void do_step_impl( System system , const StateIn &in , const DerivIn &dxdt ,
+ time_type t , StateOut &out , time_type dt )
+ {
+ m_resizer.adjust_size( in , detail::bind( &stepper_type::template resize_impl< StateIn > , detail::ref( *this ) , detail::_1 ) );
+
+ // actual calculation done in generic_rk.hpp
+ m_rk_algorithm.do_step( stepper_base_type::m_algebra , system , in , dxdt , t , out , dt , m_x_tmp.m_v , m_F );
+ }
+
+ template< class StateIn >
+ void adjust_size( const StateIn &x )
+ {
+ resize_impl( x );
+ stepper_base_type::adjust_size( x );
+ }
+
+private:
+
+ template< class StateIn >
+ bool resize_impl( const StateIn &x )
+ {
+ bool resized( false );
+ resized |= adjust_size_by_resizeability( m_x_tmp , x , typename is_resizeable<state_type>::type() );
+ for( size_t i = 0 ; i < StageCount-1 ; ++i )
+ {
+ resized |= adjust_size_by_resizeability( m_F[i] , x , typename is_resizeable<deriv_type>::type() );
+ }
+ return resized;
+ }
+
+
+ rk_algorithm_type m_rk_algorithm;
+
+ resizer_type m_resizer;
+
+ wrapped_state_type m_x_tmp;
+ wrapped_deriv_type m_F[StageCount-1];
+
+};
+
+
+
+/*********** DOXYGEN *************/
+
+/**
+ * \class explicit_generic_rk
+ * \brief A generic implementation of explicit Runge-Kutta algorithms. This class is as a base class
+ * for all explicit Runge-Kutta steppers.
+ *
+ * This class implements the explicit Runge-Kutta algorithms without error estimation in a generic way.
+ * The Butcher tableau is passed to the stepper which constructs the stepper scheme with the help of a
+ * template-metaprogramming algorithm. ToDo : Add example!
+ *
+ * This class derives explicit_stepper_base which provides the stepper interface.
+ *
+ * \tparam StageCount The number of stages of the Runge-Kutta algorithm.
+ * \tparam Order The order of the stepper.
+ * \tparam State The type representing the state of the ODE.
+ * \tparam Value The floating point type which is used in the computations.
+ * \tparam Time The type representing the independent variable - the time - of the ODE.
+ * \tparam Algebra The algebra type.
+ * \tparam Operations The operations type.
+ * \tparam Resizer The resizer policy type.
+ */
+
+ /**
+ * \fn explicit_generic_rk::explicit_generic_rk( const coef_a_type &a , const coef_b_type &b , const coef_c_type &c , const algebra_type &algebra )
+ * \brief Constructs the explicit_generic_rk class. See examples section for details on the coefficients.
+ * \param a Triangular matrix of parameters b in the Butcher tableau.
+ * \param b Last row of the butcher tableau.
+ * \param c Parameters to calculate the time points in the Butcher tableau.
+ * \param algebra A copy of algebra is made and stored inside explicit_stepper_base.
+ */
+
+ /**
+ * \fn explicit_generic_rk::do_step_impl( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt )
+ * \brief This method performs one step. The derivative `dxdt` of `in` at the time `t` is passed to the method.
+ * The result is updated out of place, hence the input is in `in` and the output in `out`.
+ * Access to this step functionality is provided by explicit_stepper_base and
+ * `do_step_impl` should not be called directly.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param in The state of the ODE which should be solved. in is not modified in this method
+ * \param dxdt The derivative of x at t.
+ * \param t The value of the time, at which the step should be performed.
+ * \param out The result of the step is written in out.
+ * \param dt The step size.
+ */
+
+
+ /**
+ * \fn explicit_generic_rk::adjust_size( const StateIn &x )
+ * \brief Adjust the size of all temporaries in the stepper manually.
+ * \param x A state from which the size of the temporaries to be resized is deduced.
+ */
+
+}
+}
+}
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_EXPLICIT_GENERIC_RK_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/extrapolation_stepper.hpp b/include/boost/numeric/odeint/stepper/extrapolation_stepper.hpp
new file mode 100644
index 0000000..3b688e9
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/extrapolation_stepper.hpp
@@ -0,0 +1,293 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/extrapolation_stepper.hpp
+
+ [begin_description]
+ extrapolation stepper
+ [end_description]
+
+ Copyright 2009-2015 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_EXTRAPOLATION_STEPPER_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_EXTRAPOLATION_STEPPER_HPP_INCLUDED
+
+#include <iostream>
+
+#include <algorithm>
+
+#include <boost/config.hpp> // for min/max guidelines
+#include <boost/static_assert.hpp>
+
+#include <boost/numeric/odeint/util/bind.hpp>
+#include <boost/numeric/odeint/util/unwrap_reference.hpp>
+
+#include <boost/numeric/odeint/stepper/base/explicit_error_stepper_base.hpp>
+#include <boost/numeric/odeint/stepper/modified_midpoint.hpp>
+#include <boost/numeric/odeint/stepper/controlled_step_result.hpp>
+#include <boost/numeric/odeint/algebra/range_algebra.hpp>
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
+
+#include <boost/numeric/odeint/util/state_wrapper.hpp>
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resizer.hpp>
+#include <boost/numeric/odeint/util/unit_helper.hpp>
+#include <boost/numeric/odeint/util/detail/less_with_sign.hpp>
+
+namespace boost
+{
+namespace numeric
+{
+namespace odeint
+{
+
+template < unsigned short Order, class State, class Value = double,
+ class Deriv = State, class Time = Value,
+ class Algebra = typename algebra_dispatcher< State >::algebra_type,
+ class Operations =
+ typename operations_dispatcher< State >::operations_type,
+ class Resizer = initially_resizer >
+#ifndef DOXYGEN_SKIP
+class extrapolation_stepper
+ : public explicit_error_stepper_base<
+ extrapolation_stepper< Order, State, Value, Deriv, Time, Algebra,
+ Operations, Resizer >,
+ Order, Order, Order - 2, State, Value, Deriv, Time, Algebra,
+ Operations, Resizer >
+#else
+class extrapolation_stepper : public explicit_error_stepper_base
+#endif
+{
+
+ private:
+ // check for Order being odd
+ BOOST_STATIC_ASSERT_MSG(
+ ( ( Order % 2 ) == 0 ) && ( Order > 2 ),
+ "extrapolation_stepper requires even Order larger than 2" );
+
+ public:
+#ifndef DOXYGEN_SKIP
+ typedef explicit_error_stepper_base<
+ extrapolation_stepper< Order, State, Value, Deriv, Time, Algebra,
+ Operations, Resizer >,
+ Order, Order, Order - 2, State, Value, Deriv, Time, Algebra, Operations,
+ Resizer > stepper_base_type;
+#else
+ typedef explicit_error_stepper_base< extrapolation_stepper< ... >, ... >
+ stepper_base_type;
+#endif
+
+ typedef typename stepper_base_type::state_type state_type;
+ typedef typename stepper_base_type::value_type value_type;
+ typedef typename stepper_base_type::deriv_type deriv_type;
+ typedef typename stepper_base_type::time_type time_type;
+ typedef typename stepper_base_type::algebra_type algebra_type;
+ typedef typename stepper_base_type::operations_type operations_type;
+ typedef typename stepper_base_type::resizer_type resizer_type;
+
+#ifndef DOXYGEN_SKIP
+ typedef typename stepper_base_type::stepper_type stepper_type;
+ typedef typename stepper_base_type::wrapped_state_type wrapped_state_type;
+ typedef typename stepper_base_type::wrapped_deriv_type wrapped_deriv_type;
+
+ typedef std::vector< value_type > value_vector;
+ typedef std::vector< value_vector > value_matrix;
+ typedef std::vector< size_t > int_vector;
+ typedef std::vector< wrapped_state_type > state_table_type;
+ typedef modified_midpoint< state_type, value_type, deriv_type, time_type,
+ algebra_type, operations_type,
+ resizer_type > midpoint_stepper_type;
+
+#endif // DOXYGEN_SKIP
+
+ typedef unsigned short order_type;
+ static const order_type order_value = stepper_base_type::order_value;
+ static const order_type stepper_order_value =
+ stepper_base_type::stepper_order_value;
+ static const order_type error_order_value =
+ stepper_base_type::error_order_value;
+
+ const static size_t m_k_max = ( order_value - 2 ) / 2;
+
+ extrapolation_stepper( const algebra_type &algebra = algebra_type() )
+ : stepper_base_type( algebra ), m_interval_sequence( m_k_max + 1 ),
+ m_coeff( m_k_max + 1 ), m_table( m_k_max )
+ {
+ for ( unsigned short i = 0; i < m_k_max + 1; i++ )
+ {
+ m_interval_sequence[i] = 2 * ( i + 1 );
+ m_coeff[i].resize( i );
+ for ( size_t k = 0; k < i; ++k )
+ {
+ const value_type r =
+ static_cast< value_type >( m_interval_sequence[i] ) /
+ static_cast< value_type >( m_interval_sequence[k] );
+ m_coeff[i][k] =
+ static_cast< value_type >( 1 ) /
+ ( r * r - static_cast< value_type >(
+ 1 ) ); // coefficients for extrapolation
+ }
+ }
+ }
+
+ template < class System, class StateIn, class DerivIn, class StateOut,
+ class Err >
+ void do_step_impl( System system, const StateIn &in, const DerivIn &dxdt,
+ time_type t, StateOut &out, time_type dt, Err &xerr )
+ {
+ // std::cout << "dt: " << dt << std::endl;
+ // normal step
+ do_step_impl( system, in, dxdt, t, out, dt );
+
+ static const value_type val1( 1.0 );
+ // additionally, perform the error calculation
+ stepper_base_type::m_algebra.for_each3(
+ xerr, out, m_table[0].m_v,
+ typename operations_type::template scale_sum2<
+ value_type, value_type >( val1, -val1 ) );
+ }
+
+ template < class System, class StateInOut, class DerivIn, class Err >
+ void do_step_impl_io( System system, StateInOut &inout, const DerivIn &dxdt,
+ time_type t, time_type dt, Err &xerr )
+ {
+ // normal step
+ do_step_impl_io( system, inout, dxdt, t, dt );
+
+ static const value_type val1( 1.0 );
+ // additionally, perform the error calculation
+ stepper_base_type::m_algebra.for_each3(
+ xerr, inout, m_table[0].m_v,
+ typename operations_type::template scale_sum2<
+ value_type, value_type >( val1, -val1 ) );
+ }
+
+ template < class System, class StateIn, class DerivIn, class StateOut >
+ void do_step_impl( System system, const StateIn &in, const DerivIn &dxdt,
+ time_type t, StateOut &out, time_type dt )
+ {
+ m_resizer.adjust_size(
+ in, detail::bind( &stepper_type::template resize_impl< StateIn >,
+ detail::ref( *this ), detail::_1 ) );
+ size_t k = 0;
+ m_midpoint.set_steps( m_interval_sequence[k] );
+ m_midpoint.do_step( system, in, dxdt, t, out, dt );
+ for ( k = 1; k <= m_k_max; ++k )
+ {
+ m_midpoint.set_steps( m_interval_sequence[k] );
+ m_midpoint.do_step( system, in, dxdt, t, m_table[k - 1].m_v, dt );
+ extrapolate( k, m_table, m_coeff, out );
+ }
+ }
+
+ template < class System, class StateInOut, class DerivIn >
+ void do_step_impl_io( System system, StateInOut &inout, const DerivIn &dxdt,
+ time_type t, time_type dt )
+ {
+ // special care for inout
+ m_xout_resizer.adjust_size(
+ inout,
+ detail::bind( &stepper_type::template resize_m_xout< StateInOut >,
+ detail::ref( *this ), detail::_1 ) );
+ do_step_impl( system, inout, dxdt, t, m_xout.m_v, dt );
+ boost::numeric::odeint::copy( m_xout.m_v, inout );
+ }
+
+ template < class System, class StateInOut, class DerivIn >
+ void do_step_dxdt_impl( System system, StateInOut &x, const DerivIn &dxdt,
+ time_type t, time_type dt )
+ {
+ do_step_impl_io( system , x , dxdt , t , dt );
+ }
+
+ template < class System, class StateIn, class DerivIn, class StateOut >
+ void do_step_dxdt_impl( System system, const StateIn &in,
+ const DerivIn &dxdt, time_type t, StateOut &out,
+ time_type dt )
+ {
+ do_step_impl( system , in , dxdt , t , out , dt );
+ }
+
+
+ template < class StateIn > void adjust_size( const StateIn &x )
+ {
+ resize_impl( x );
+ m_midpoint.adjust_size( x );
+ }
+
+ private:
+ template < class StateIn > bool resize_impl( const StateIn &x )
+ {
+ bool resized( false );
+ for ( size_t i = 0; i < m_k_max; ++i )
+ resized |= adjust_size_by_resizeability(
+ m_table[i], x, typename is_resizeable< state_type >::type() );
+ return resized;
+ }
+
+ template < class StateIn > bool resize_m_xout( const StateIn &x )
+ {
+ return adjust_size_by_resizeability(
+ m_xout, x, typename is_resizeable< state_type >::type() );
+ }
+
+ template < class StateInOut >
+ void extrapolate( size_t k, state_table_type &table,
+ const value_matrix &coeff, StateInOut &xest )
+ /* polynomial extrapolation, see http://www.nr.com/webnotes/nr3web21.pdf
+ uses the obtained intermediate results to extrapolate to dt->0
+ */
+ {
+ static const value_type val1 = static_cast< value_type >( 1.0 );
+
+ for ( int j = k - 1; j > 0; --j )
+ {
+ stepper_base_type::m_algebra.for_each3(
+ table[j - 1].m_v, table[j].m_v, table[j - 1].m_v,
+ typename operations_type::template scale_sum2<
+ value_type, value_type >( val1 + coeff[k][j],
+ -coeff[k][j] ) );
+ }
+ stepper_base_type::m_algebra.for_each3(
+ xest, table[0].m_v, xest,
+ typename operations_type::template scale_sum2<
+ value_type, value_type >( val1 + coeff[k][0], -coeff[k][0] ) );
+ }
+
+ private:
+ midpoint_stepper_type m_midpoint;
+
+ resizer_type m_resizer;
+ resizer_type m_xout_resizer;
+
+ int_vector m_interval_sequence; // stores the successive interval counts
+ value_matrix m_coeff;
+
+ wrapped_state_type m_xout;
+ state_table_type m_table; // sequence of states for extrapolation
+};
+
+/******** DOXYGEN *******/
+
+/**
+ * \class extrapolation_stepper
+ * \brief Extrapolation stepper with configurable order, and error estimation.
+ *
+ * The extrapolation stepper is a stepper with error estimation and configurable
+ * order. The order is given as template parameter and needs to be an _odd_
+ * number. The stepper is based on several executions of the modified midpoint
+ * method and a Richardson extrapolation. This is essentially the same technique
+ * as for bulirsch_stoer, but without the variable order.
+ *
+ * \note The Order parameter has to be an even number greater 2.
+ */
+}
+}
+}
+#endif
diff --git a/include/boost/numeric/odeint/stepper/generation.hpp b/include/boost/numeric/odeint/stepper/generation.hpp
new file mode 100644
index 0000000..90ad2b9
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/generation.hpp
@@ -0,0 +1,36 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/generation.hpp
+
+ [begin_description]
+ Forward header for the factory functions. Includes all files from the generation directory.
+ [end_description]
+
+ Copyright 2011 Karsten Ahnert
+ Copyright 2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_HPP_INCLUDED
+
+#include <boost/numeric/odeint/stepper/generation/make_controlled.hpp>
+#include <boost/numeric/odeint/stepper/generation/make_dense_output.hpp>
+
+#include <boost/numeric/odeint/stepper/generation/generation_controlled_runge_kutta.hpp>
+#include <boost/numeric/odeint/stepper/generation/generation_dense_output_runge_kutta.hpp>
+
+#include <boost/numeric/odeint/stepper/generation/generation_runge_kutta_cash_karp54_classic.hpp>
+#include <boost/numeric/odeint/stepper/generation/generation_runge_kutta_cash_karp54.hpp>
+#include <boost/numeric/odeint/stepper/generation/generation_runge_kutta_dopri5.hpp>
+#include <boost/numeric/odeint/stepper/generation/generation_runge_kutta_fehlberg78.hpp>
+
+
+#include <boost/numeric/odeint/stepper/generation/generation_rosenbrock4.hpp>
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/generation/generation_controlled_runge_kutta.hpp b/include/boost/numeric/odeint/stepper/generation/generation_controlled_runge_kutta.hpp
new file mode 100644
index 0000000..bad2bed
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/generation/generation_controlled_runge_kutta.hpp
@@ -0,0 +1,61 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/generation/generation_controlled_runge_kutta.hpp
+
+ [begin_description]
+ Specialization of the controller factory for the controlled_runge_kutta class.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_GENERATION_CONTROLLED_RUNGE_KUTTA_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_GENERATION_CONTROLLED_RUNGE_KUTTA_HPP_INCLUDED
+
+#include <boost/numeric/odeint/stepper/controlled_runge_kutta.hpp>
+#include <boost/numeric/odeint/stepper/generation/make_controlled.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+// controller factory for controlled_runge_kutta
+template< class Stepper >
+struct controller_factory< Stepper , controlled_runge_kutta< Stepper > >
+{
+ typedef Stepper stepper_type;
+ typedef controlled_runge_kutta< stepper_type > controller_type;
+ typedef typename controller_type::error_checker_type error_checker_type;
+ typedef typename controller_type::step_adjuster_type step_adjuster_type;
+ typedef typename stepper_type::value_type value_type;
+ typedef typename stepper_type::value_type time_type;
+
+ controller_type operator()( value_type abs_error , value_type rel_error , const stepper_type &stepper )
+ {
+ return controller_type( error_checker_type( abs_error , rel_error ) ,
+ step_adjuster_type() , stepper );
+ }
+
+ controller_type operator()( value_type abs_error , value_type rel_error ,
+ time_type max_dt, const stepper_type &stepper )
+ {
+ return controller_type( error_checker_type( abs_error , rel_error ) ,
+ step_adjuster_type(max_dt) , stepper );
+ }
+};
+
+
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_GENERATION_CONTROLLED_RUNGE_KUTTA_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/generation/generation_dense_output_runge_kutta.hpp b/include/boost/numeric/odeint/stepper/generation/generation_dense_output_runge_kutta.hpp
new file mode 100644
index 0000000..276358a
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/generation/generation_dense_output_runge_kutta.hpp
@@ -0,0 +1,65 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/generation/generation_dense_output_runge_kutta.hpp
+
+ [begin_description]
+ Specialization of the controller factory for the dense_output_runge_kutta class.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_GENERATION_DENSE_OUTPUT_RUNGE_KUTTA_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_GENERATION_DENSE_OUTPUT_RUNGE_KUTTA_HPP_INCLUDED
+
+#include <boost/numeric/odeint/stepper/controlled_runge_kutta.hpp>
+#include <boost/numeric/odeint/stepper/dense_output_runge_kutta.hpp>
+#include <boost/numeric/odeint/stepper/generation/make_dense_output.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+// controller factory for controlled_runge_kutta
+template< class Stepper >
+struct dense_output_factory< Stepper , dense_output_runge_kutta< controlled_runge_kutta< Stepper > > >
+{
+ typedef Stepper stepper_type;
+ typedef controlled_runge_kutta< stepper_type > controller_type;
+ typedef typename controller_type::error_checker_type error_checker_type;
+ typedef typename controller_type::step_adjuster_type step_adjuster_type;
+ typedef typename stepper_type::value_type value_type;
+ typedef typename stepper_type::time_type time_type;
+ typedef dense_output_runge_kutta< controller_type > dense_output_type;
+
+ dense_output_type operator()( value_type abs_error , value_type rel_error , const stepper_type &stepper )
+ {
+ return dense_output_type( controller_type( error_checker_type( abs_error , rel_error ) ,
+ step_adjuster_type() , stepper ) );
+ }
+
+ dense_output_type operator()( value_type abs_error , value_type rel_error ,
+ time_type max_dt , const stepper_type &stepper )
+ {
+ return dense_output_type(
+ controller_type( error_checker_type( abs_error , rel_error) ,
+ step_adjuster_type( max_dt ) , stepper ) );
+ }
+};
+
+
+
+
+
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_GENERATION_DENSE_OUTPUT_RUNGE_KUTTA_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/generation/generation_rosenbrock4.hpp b/include/boost/numeric/odeint/stepper/generation/generation_rosenbrock4.hpp
new file mode 100644
index 0000000..366cb5e
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/generation/generation_rosenbrock4.hpp
@@ -0,0 +1,79 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/generation/generation_rosenbrock4.hpp
+
+ [begin_description]
+ Enable the factory functions for the controller and the dense output of the Rosenbrock4 method.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_GENERATION_ROSENBROCK4_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_GENERATION_ROSENBROCK4_HPP_INCLUDED
+
+#include <boost/numeric/odeint/stepper/rosenbrock4.hpp>
+#include <boost/numeric/odeint/stepper/rosenbrock4_controller.hpp>
+#include <boost/numeric/odeint/stepper/rosenbrock4_dense_output.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+template< class Value , class Coefficients , class Resize >
+struct get_controller< rosenbrock4< Value , Coefficients , Resize > >
+{
+ typedef rosenbrock4< Value , Coefficients , Resize > stepper_type;
+ typedef rosenbrock4_controller< stepper_type > type;
+};
+
+
+
+template< class Value , class Coefficients , class Resize >
+struct get_dense_output< rosenbrock4< Value , Coefficients , Resize > >
+{
+ typedef rosenbrock4< Value , Coefficients , Resize > stepper_type;
+ typedef rosenbrock4_controller< stepper_type > controller_type;
+ typedef rosenbrock4_dense_output< controller_type > type;
+};
+
+
+
+// controller factory for controlled_runge_kutta
+template< class Stepper >
+struct dense_output_factory< Stepper , rosenbrock4_dense_output< rosenbrock4_controller< Stepper > > >
+{
+ typedef Stepper stepper_type;
+ typedef rosenbrock4_controller< stepper_type > controller_type;
+ typedef typename stepper_type::value_type value_type;
+ typedef typename stepper_type::time_type time_type;
+ typedef rosenbrock4_dense_output< controller_type > dense_output_type;
+
+ dense_output_type operator()( value_type abs_error , value_type rel_error , const stepper_type &stepper )
+ {
+ return dense_output_type( controller_type( abs_error , rel_error , stepper ) );
+ }
+
+ dense_output_type operator()( value_type abs_error , value_type rel_error ,
+ time_type max_dt, const stepper_type &stepper )
+ {
+ return dense_output_type( controller_type( abs_error , rel_error , max_dt , stepper ) );
+ }
+};
+
+
+
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_GENERATION_ROSENBROCK4_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/generation/generation_runge_kutta_cash_karp54.hpp b/include/boost/numeric/odeint/stepper/generation/generation_runge_kutta_cash_karp54.hpp
new file mode 100644
index 0000000..24ae547
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/generation/generation_runge_kutta_cash_karp54.hpp
@@ -0,0 +1,47 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/generation/generation_runge_kutta_cash_karp54.hpp
+
+ [begin_description]
+ Enable the factory functions for the controller and the dense output of the Runge-Kutta-Cash-Karp 54 method.
+ [end_description]
+
+ Copyright 2011 Karsten Ahnert
+ Copyright 2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_GENERATION_RUNGE_KUTTA_CASH_KARP54_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_GENERATION_RUNGE_KUTTA_CASH_KARP54_HPP_INCLUDED
+
+#include <boost/numeric/odeint/stepper/controlled_runge_kutta.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp>
+#include <boost/numeric/odeint/stepper/generation/make_controlled.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+// Specializations for runge_kutta_cash_karp54
+template< class State , class Value , class Deriv , class Time , class Algebra , class Operations , class Resize >
+struct get_controller< runge_kutta_cash_karp54< State , Value , Deriv , Time , Algebra , Operations , Resize > >
+{
+ typedef runge_kutta_cash_karp54< State , Value , Deriv , Time , Algebra , Operations , Resize > stepper_type;
+ typedef controlled_runge_kutta< stepper_type > type;
+};
+
+
+
+
+
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_GENERATION_RUNGE_KUTTA_CASH_KARP54_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/generation/generation_runge_kutta_cash_karp54_classic.hpp b/include/boost/numeric/odeint/stepper/generation/generation_runge_kutta_cash_karp54_classic.hpp
new file mode 100644
index 0000000..1cc0f91
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/generation/generation_runge_kutta_cash_karp54_classic.hpp
@@ -0,0 +1,48 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/generation/generation_runge_kutta_cash_karp54_classic.hpp
+
+ [begin_description]
+ Enable the factory functions for the controller and the dense output of the
+ Runge-Kutta-Cash-Karp 54 method with the classical implementation.
+ [end_description]
+
+ Copyright 2011 Karsten Ahnert
+ Copyright 2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_GENERATION_RUNGE_KUTTA_CASH_KARP54_CLASSIC_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_GENERATION_RUNGE_KUTTA_CASH_KARP54_CLASSIC_HPP_INCLUDED
+
+#include <boost/numeric/odeint/stepper/controlled_runge_kutta.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54_classic.hpp>
+#include <boost/numeric/odeint/stepper/generation/make_controlled.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+// Specializations for runge_kutta_cash_karp54
+template< class State , class Value , class Deriv , class Time , class Algebra , class Operations , class Resize >
+struct get_controller< runge_kutta_cash_karp54_classic< State , Value , Deriv , Time , Algebra , Operations , Resize > >
+{
+ typedef runge_kutta_cash_karp54_classic< State , Value , Deriv , Time , Algebra , Operations , Resize > stepper_type;
+ typedef controlled_runge_kutta< stepper_type > type;
+};
+
+
+
+
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_GENERATION_RUNGE_KUTTA_CASH_KARP54_CLASSIC_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/generation/generation_runge_kutta_dopri5.hpp b/include/boost/numeric/odeint/stepper/generation/generation_runge_kutta_dopri5.hpp
new file mode 100644
index 0000000..1a607f3
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/generation/generation_runge_kutta_dopri5.hpp
@@ -0,0 +1,56 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/generation/generation_runge_kutta_dopri5.hpp
+
+ [begin_description]
+ Enable the factory functions for the controller and the dense output of the Runge-Kutta-Dormand-Prince5 method.
+ [end_description]
+
+ Copyright 2011 Karsten Ahnert
+ Copyright 2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_GENERATION_RUNGE_KUTTA_DOPRI5_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_GENERATION_RUNGE_KUTTA_DOPRI5_HPP_INCLUDED
+
+#include <boost/numeric/odeint/stepper/controlled_runge_kutta.hpp>
+#include <boost/numeric/odeint/stepper/dense_output_runge_kutta.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp>
+#include <boost/numeric/odeint/stepper/generation/make_controlled.hpp>
+#include <boost/numeric/odeint/stepper/generation/make_dense_output.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+template< class State , class Value , class Deriv , class Time , class Algebra , class Operations , class Resize >
+struct get_controller< runge_kutta_dopri5< State , Value , Deriv , Time , Algebra , Operations , Resize > >
+{
+ typedef runge_kutta_dopri5< State , Value , Deriv , Time , Algebra , Operations , Resize > stepper_type;
+ typedef controlled_runge_kutta< stepper_type > type;
+};
+
+
+template< class State , class Value , class Deriv , class Time , class Algebra , class Operations , class Resize >
+struct get_dense_output< runge_kutta_dopri5< State , Value , Deriv , Time , Algebra , Operations , Resize > >
+{
+ typedef runge_kutta_dopri5< State , Value , Deriv , Time , Algebra , Operations , Resize > stepper_type;
+ typedef controlled_runge_kutta< stepper_type > controller_type;
+ typedef dense_output_runge_kutta< controller_type > type;
+};
+
+
+
+
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_GENERATION_RUNGE_KUTTA_DOPRI5_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/generation/generation_runge_kutta_fehlberg78.hpp b/include/boost/numeric/odeint/stepper/generation/generation_runge_kutta_fehlberg78.hpp
new file mode 100644
index 0000000..d89343b
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/generation/generation_runge_kutta_fehlberg78.hpp
@@ -0,0 +1,46 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/generation/generation_runge_kutta_fehlberg78.hpp
+
+ [begin_description]
+ Enable the factory functions for the controller and the dense output of the Runge-Kutta-Fehlberg 78 method.
+ [end_description]
+
+ Copyright 2011 Karsten Ahnert
+ Copyright 2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_GENERATION_RUNGE_KUTTA_FEHLBERG78_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_GENERATION_RUNGE_KUTTA_FEHLBERG78_HPP_INCLUDED
+
+#include <boost/numeric/odeint/stepper/controlled_runge_kutta.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_fehlberg78.hpp>
+#include <boost/numeric/odeint/stepper/generation/make_controlled.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+template< class State , class Value , class Deriv , class Time , class Algebra , class Operations , class Resize >
+struct get_controller< runge_kutta_fehlberg78< State , Value , Deriv , Time , Algebra , Operations , Resize > >
+{
+ typedef runge_kutta_fehlberg78< State , Value , Deriv , Time , Algebra , Operations , Resize > stepper_type;
+ typedef controlled_runge_kutta< stepper_type > type;
+};
+
+
+
+
+
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_GENERATION_RUNGE_KUTTA_FEHLBERG78_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/generation/make_controlled.hpp b/include/boost/numeric/odeint/stepper/generation/make_controlled.hpp
new file mode 100644
index 0000000..61bc8f1
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/generation/make_controlled.hpp
@@ -0,0 +1,103 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/generation/make_controlled.hpp
+
+ [begin_description]
+ Factory function to simplify the creation of controlled steppers from error steppers.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_MAKE_CONTROLLED_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_MAKE_CONTROLLED_HPP_INCLUDED
+
+
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+
+// default template for the controller
+template< class Stepper > struct get_controller { };
+
+
+
+// default controller factory
+template< class Stepper , class Controller >
+struct controller_factory
+{
+ Controller operator()(
+ typename Stepper::value_type abs_error ,
+ typename Stepper::value_type rel_error ,
+ const Stepper &stepper )
+ {
+ return Controller( abs_error , rel_error , stepper );
+ }
+
+ Controller operator()(
+ typename Stepper::value_type abs_error ,
+ typename Stepper::value_type rel_error ,
+ typename Stepper::time_type max_dt ,
+ const Stepper &stepper )
+ {
+ return Controller( abs_error , rel_error , max_dt, stepper );
+ }
+};
+
+
+
+
+namespace result_of
+{
+ template< class Stepper >
+ struct make_controlled
+ {
+ typedef typename get_controller< Stepper >::type type;
+ };
+}
+
+
+template< class Stepper >
+typename result_of::make_controlled< Stepper >::type make_controlled(
+ typename Stepper::value_type abs_error ,
+ typename Stepper::value_type rel_error ,
+ const Stepper & stepper = Stepper() )
+{
+ typedef Stepper stepper_type;
+ typedef typename result_of::make_controlled< stepper_type >::type controller_type;
+ typedef controller_factory< stepper_type , controller_type > factory_type;
+ factory_type factory;
+ return factory( abs_error , rel_error , stepper );
+}
+
+
+template< class Stepper >
+typename result_of::make_controlled< Stepper >::type make_controlled(
+ typename Stepper::value_type abs_error ,
+ typename Stepper::value_type rel_error ,
+ typename Stepper::time_type max_dt ,
+ const Stepper & stepper = Stepper() )
+{
+ typedef Stepper stepper_type;
+ typedef typename result_of::make_controlled< stepper_type >::type controller_type;
+ typedef controller_factory< stepper_type , controller_type > factory_type;
+ factory_type factory;
+ return factory( abs_error , rel_error , max_dt, stepper );
+}
+
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_MAKE_CONTROLLED_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/generation/make_dense_output.hpp b/include/boost/numeric/odeint/stepper/generation/make_dense_output.hpp
new file mode 100644
index 0000000..fff3590
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/generation/make_dense_output.hpp
@@ -0,0 +1,100 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/generation/make_dense_output.hpp
+
+ [begin_description]
+ Factory function to simplify the creation of dense output steppers from error steppers.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_MAKE_DENSE_OUTPUT_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_MAKE_DENSE_OUTPUT_HPP_INCLUDED
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+// default template for the dense output
+template< class Stepper > struct get_dense_output { };
+
+
+
+// default dense output factory
+template< class Stepper , class DenseOutput >
+struct dense_output_factory
+{
+ DenseOutput operator()(
+ typename Stepper::value_type abs_error ,
+ typename Stepper::value_type rel_error ,
+ const Stepper &stepper )
+ {
+ return DenseOutput( abs_error , rel_error , stepper );
+ }
+
+ DenseOutput operator()(
+ typename Stepper::value_type abs_error ,
+ typename Stepper::value_type rel_error ,
+ typename Stepper::time_type max_dt ,
+ const Stepper &stepper )
+ {
+ return DenseOutput( abs_error , rel_error , max_dt , stepper );
+ }
+};
+
+
+
+namespace result_of
+{
+ template< class Stepper >
+ struct make_dense_output
+ {
+ typedef typename get_dense_output< Stepper >::type type;
+ };
+}
+
+
+
+template< class Stepper >
+typename result_of::make_dense_output< Stepper >::type make_dense_output(
+ typename Stepper::value_type abs_error ,
+ typename Stepper::value_type rel_error ,
+ const Stepper &stepper = Stepper() )
+{
+ typedef Stepper stepper_type;
+ typedef typename result_of::make_dense_output< stepper_type >::type dense_output_type;
+ typedef dense_output_factory< stepper_type , dense_output_type > factory_type;
+ factory_type factory;
+ return factory( abs_error , rel_error , stepper );
+}
+
+
+template< class Stepper >
+typename result_of::make_dense_output< Stepper >::type make_dense_output(
+ typename Stepper::value_type abs_error ,
+ typename Stepper::value_type rel_error ,
+ typename Stepper::time_type max_dt ,
+ const Stepper &stepper = Stepper() )
+{
+ typedef Stepper stepper_type;
+ typedef typename result_of::make_dense_output< stepper_type >::type dense_output_type;
+ typedef dense_output_factory< stepper_type , dense_output_type > factory_type;
+ factory_type factory;
+ return factory( abs_error , rel_error , max_dt, stepper );
+}
+
+
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_GENERATION_MAKE_DENSE_OUTPUT_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/implicit_euler.hpp b/include/boost/numeric/odeint/stepper/implicit_euler.hpp
new file mode 100644
index 0000000..e1c6416
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/implicit_euler.hpp
@@ -0,0 +1,170 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/implicit_euler.hpp
+
+ [begin_description]
+ Impementation of the implicit Euler method. Works with ublas::vector as state type.
+ [end_description]
+
+ Copyright 2010-2012 Mario Mulansky
+ Copyright 2010-2012 Karsten Ahnert
+ Copyright 2012 Christoph Koke
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_IMPLICIT_EULER_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_IMPLICIT_EULER_HPP_INCLUDED
+
+
+#include <utility>
+
+#include <boost/numeric/odeint/util/bind.hpp>
+#include <boost/numeric/odeint/util/unwrap_reference.hpp>
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+
+#include <boost/numeric/odeint/util/ublas_wrapper.hpp>
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resizer.hpp>
+
+#include <boost/numeric/ublas/vector.hpp>
+#include <boost/numeric/ublas/matrix.hpp>
+#include <boost/numeric/ublas/lu.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+
+
+
+
+
+
+template< class ValueType , class Resizer = initially_resizer >
+class implicit_euler
+{
+
+public:
+
+ typedef ValueType value_type;
+ typedef value_type time_type;
+ typedef boost::numeric::ublas::vector< value_type > state_type;
+ typedef state_wrapper< state_type > wrapped_state_type;
+ typedef state_type deriv_type;
+ typedef state_wrapper< deriv_type > wrapped_deriv_type;
+ typedef boost::numeric::ublas::matrix< value_type > matrix_type;
+ typedef state_wrapper< matrix_type > wrapped_matrix_type;
+ typedef boost::numeric::ublas::permutation_matrix< size_t > pmatrix_type;
+ typedef state_wrapper< pmatrix_type > wrapped_pmatrix_type;
+ typedef Resizer resizer_type;
+ typedef stepper_tag stepper_category;
+ typedef implicit_euler< ValueType , Resizer > stepper_type;
+
+ implicit_euler( value_type epsilon = 1E-6 )
+ : m_epsilon( epsilon )
+ { }
+
+
+ template< class System >
+ void do_step( System system , state_type &x , time_type t , time_type dt )
+ {
+ typedef typename odeint::unwrap_reference< System >::type system_type;
+ typedef typename odeint::unwrap_reference< typename system_type::first_type >::type deriv_func_type;
+ typedef typename odeint::unwrap_reference< typename system_type::second_type >::type jacobi_func_type;
+ system_type &sys = system;
+ deriv_func_type &deriv_func = sys.first;
+ jacobi_func_type &jacobi_func = sys.second;
+
+ m_resizer.adjust_size( x , detail::bind( &stepper_type::template resize_impl<state_type> , detail::ref( *this ) , detail::_1 ) );
+
+ for( size_t i=0 ; i<x.size() ; ++i )
+ m_pm.m_v[i] = i;
+
+ t += dt;
+
+ // apply first Newton step
+ deriv_func( x , m_dxdt.m_v , t );
+
+ m_b.m_v = dt * m_dxdt.m_v;
+
+ jacobi_func( x , m_jacobi.m_v , t );
+ m_jacobi.m_v *= dt;
+ m_jacobi.m_v -= boost::numeric::ublas::identity_matrix< value_type >( x.size() );
+
+ solve( m_b.m_v , m_jacobi.m_v );
+
+ m_x.m_v = x - m_b.m_v;
+
+ // iterate Newton until some precision is reached
+ // ToDo: maybe we should apply only one Newton step -> linear implicit one-step scheme
+ while( boost::numeric::ublas::norm_2( m_b.m_v ) > m_epsilon )
+ {
+ deriv_func( m_x.m_v , m_dxdt.m_v , t );
+ m_b.m_v = x - m_x.m_v + dt*m_dxdt.m_v;
+
+ // simplified version, only the first Jacobian is used
+ // jacobi( m_x , m_jacobi , t );
+ // m_jacobi *= dt;
+ // m_jacobi -= boost::numeric::ublas::identity_matrix< value_type >( x.size() );
+
+ solve( m_b.m_v , m_jacobi.m_v );
+
+ m_x.m_v -= m_b.m_v;
+ }
+ x = m_x.m_v;
+ }
+
+ template< class StateType >
+ void adjust_size( const StateType &x )
+ {
+ resize_impl( x );
+ }
+
+
+private:
+
+ template< class StateIn >
+ bool resize_impl( const StateIn &x )
+ {
+ bool resized = false;
+ resized |= adjust_size_by_resizeability( m_dxdt , x , typename is_resizeable<deriv_type>::type() );
+ resized |= adjust_size_by_resizeability( m_x , x , typename is_resizeable<state_type>::type() );
+ resized |= adjust_size_by_resizeability( m_b , x , typename is_resizeable<deriv_type>::type() );
+ resized |= adjust_size_by_resizeability( m_jacobi , x , typename is_resizeable<matrix_type>::type() );
+ resized |= adjust_size_by_resizeability( m_pm , x , typename is_resizeable<pmatrix_type>::type() );
+ return resized;
+ }
+
+
+ void solve( state_type &x , matrix_type &m )
+ {
+ int res = boost::numeric::ublas::lu_factorize( m , m_pm.m_v );
+ if( res != 0 ) std::exit(0);
+ boost::numeric::ublas::lu_substitute( m , m_pm.m_v , x );
+ }
+
+private:
+
+ value_type m_epsilon;
+ resizer_type m_resizer;
+ wrapped_deriv_type m_dxdt;
+ wrapped_state_type m_x;
+ wrapped_deriv_type m_b;
+ wrapped_matrix_type m_jacobi;
+ wrapped_pmatrix_type m_pm;
+
+
+};
+
+
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_IMPLICIT_EULER_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/modified_midpoint.hpp b/include/boost/numeric/odeint/stepper/modified_midpoint.hpp
new file mode 100644
index 0000000..9e34c7d
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/modified_midpoint.hpp
@@ -0,0 +1,315 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/modified_midpoint.hpp
+
+ [begin_description]
+ Modified midpoint method for the use in Burlish-Stoer stepper.
+ [end_description]
+
+ Copyright 2011-2013 Mario Mulansky
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2012 Christoph Koke
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_MODIFIED_MIDPOINT_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_MODIFIED_MIDPOINT_HPP_INCLUDED
+
+#include <vector>
+
+#include <boost/numeric/odeint/stepper/base/explicit_stepper_base.hpp>
+#include <boost/numeric/odeint/util/resizer.hpp>
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/algebra/range_algebra.hpp>
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
+#include <boost/numeric/odeint/util/copy.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template<
+class State ,
+class Value = double ,
+class Deriv = State ,
+class Time = Value ,
+class Algebra = typename algebra_dispatcher< State >::algebra_type ,
+class Operations = typename operations_dispatcher< State >::operations_type ,
+class Resizer = initially_resizer
+>
+#ifndef DOXYGEN_SKIP
+class modified_midpoint
+: public explicit_stepper_base<
+ modified_midpoint< State , Value , Deriv , Time , Algebra , Operations , Resizer > ,
+ 2 , State , Value , Deriv , Time , Algebra , Operations , Resizer >
+#else
+class modified_midpoint : public explicit_stepper_base
+#endif
+{
+
+public :
+
+ typedef explicit_stepper_base<
+ modified_midpoint< State , Value , Deriv , Time , Algebra , Operations , Resizer > ,
+ 2 , State , Value , Deriv , Time , Algebra , Operations , Resizer > stepper_base_type;
+
+ typedef typename stepper_base_type::state_type state_type;
+ typedef typename stepper_base_type::wrapped_state_type wrapped_state_type;
+ typedef typename stepper_base_type::value_type value_type;
+ typedef typename stepper_base_type::deriv_type deriv_type;
+ typedef typename stepper_base_type::wrapped_deriv_type wrapped_deriv_type;
+ typedef typename stepper_base_type::time_type time_type;
+ typedef typename stepper_base_type::algebra_type algebra_type;
+ typedef typename stepper_base_type::operations_type operations_type;
+ typedef typename stepper_base_type::resizer_type resizer_type;
+ typedef typename stepper_base_type::stepper_type stepper_type;
+
+
+ modified_midpoint( unsigned short steps = 2 , const algebra_type &algebra = algebra_type() )
+ : stepper_base_type( algebra ) , m_steps( steps )
+ { }
+
+ template< class System , class StateIn , class DerivIn , class StateOut >
+ void do_step_impl( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt )
+ {
+ static const value_type val1 = static_cast< value_type >( 1 );
+ static const value_type val05 = static_cast< value_type >( 1 ) / static_cast< value_type >( 2 );
+
+ m_resizer.adjust_size( in , detail::bind( &stepper_type::template resize_impl< StateIn > , detail::ref( *this ) , detail::_1 ) );
+
+ const time_type h = dt / static_cast<value_type>( m_steps );
+ const time_type h2 = static_cast<value_type>(2) * h;
+
+ typename odeint::unwrap_reference< System >::type &sys = system;
+
+ time_type th = t + h;
+
+ // m_x1 = x + h*dxdt
+ stepper_base_type::m_algebra.for_each3( m_x1.m_v , in , dxdt ,
+ typename operations_type::template scale_sum2< value_type , time_type >( val1 , h ) );
+
+ sys( m_x1.m_v , m_dxdt.m_v , th );
+
+ boost::numeric::odeint::copy( in , m_x0.m_v );
+
+ unsigned short i = 1;
+ while( i != m_steps )
+ {
+ // general step
+ //tmp = m_x1; m_x1 = m_x0 + h2*m_dxdt; m_x0 = tmp
+ stepper_base_type::m_algebra.for_each3( m_x1.m_v , m_x0.m_v , m_dxdt.m_v ,
+ typename operations_type::template scale_sum_swap2< value_type , time_type >( val1 , h2 ) );
+ th += h;
+ sys( m_x1.m_v , m_dxdt.m_v , th);
+ i++;
+ }
+
+ // last step
+ // x = 0.5*( m_x0 + m_x1 + h*m_dxdt )
+ stepper_base_type::m_algebra.for_each4( out , m_x0.m_v , m_x1.m_v , m_dxdt.m_v ,
+ typename operations_type::template scale_sum3< value_type , value_type , time_type >( val05 , val05 , val05*h ) );
+ }
+
+
+ void set_steps( unsigned short steps )
+ { m_steps = steps; }
+
+
+ unsigned short steps( void ) const
+ { return m_steps; }
+
+
+ template< class StateIn >
+ void adjust_size( const StateIn &x )
+ {
+ resize_impl( x );
+ stepper_base_type::adjust_size( x );
+ }
+
+private:
+
+ template< class StateIn >
+ bool resize_impl( const StateIn &x )
+ {
+ bool resized( false );
+ resized |= adjust_size_by_resizeability( m_x0 , x , typename is_resizeable<state_type>::type() );
+ resized |= adjust_size_by_resizeability( m_x1 , x , typename is_resizeable<state_type>::type() );
+ resized |= adjust_size_by_resizeability( m_dxdt , x , typename is_resizeable<deriv_type>::type() );
+ return resized;
+ }
+
+
+ unsigned short m_steps;
+
+ resizer_type m_resizer;
+
+ wrapped_state_type m_x0;
+ wrapped_state_type m_x1;
+ wrapped_deriv_type m_dxdt;
+
+};
+
+
+/* Modified midpoint which stores derivatives and state at dt/2 in some external storage for later usage in dense output calculation
+ * This Stepper is for use in Bulirsch Stoer only. It DOES NOT meet any stepper concept.
+ */
+template<
+class State ,
+class Value = double ,
+class Deriv = State ,
+class Time = Value ,
+class Algebra = typename algebra_dispatcher< State >::algebra_type ,
+class Operations = typename operations_dispatcher< State >::operations_type ,
+class Resizer = initially_resizer
+>
+class modified_midpoint_dense_out
+{
+
+public :
+
+ typedef State state_type;
+ typedef Value value_type;
+ typedef Deriv deriv_type;
+ typedef Time time_type;
+ typedef Algebra algebra_type;
+ typedef Operations operations_type;
+ typedef Resizer resizer_type;
+ typedef state_wrapper< state_type > wrapped_state_type;
+ typedef state_wrapper< deriv_type > wrapped_deriv_type;
+
+ typedef modified_midpoint_dense_out< State , Value , Deriv , Time , Algebra , Operations , Resizer > stepper_type;
+ typedef std::vector< wrapped_deriv_type > deriv_table_type;
+
+ modified_midpoint_dense_out( unsigned short steps = 2 , const algebra_type &algebra = algebra_type() )
+ : m_algebra( algebra ) , m_steps( steps )
+ { }
+
+ /*
+ * performs a modified midpoint step with m_steps intermediate points
+ * stores approximation for x(t+dt/2) in x_mp and all evaluated function results in derivs
+ *
+ */
+
+ template< class System , class StateIn , class DerivIn , class StateOut >
+ void do_step( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt ,
+ state_type &x_mp , deriv_table_type &derivs )
+ {
+
+ static const value_type val1 = static_cast< value_type >( 1 );
+ static const value_type val05 = static_cast< value_type >( 1 ) / static_cast< value_type >( 2 );
+
+ m_resizer.adjust_size( in , detail::bind( &stepper_type::template resize< StateIn > , detail::ref( *this ) , detail::_1 ) );
+
+ const time_type h = dt / static_cast<value_type>( m_steps );
+ const time_type h2 = static_cast<value_type>( 2 ) * h;
+
+ typename odeint::unwrap_reference< System >::type &sys = system;
+
+ time_type th = t + h;
+
+ // m_x1 = x + h*dxdt
+ m_algebra.for_each3( m_x1.m_v , in , dxdt ,
+ typename operations_type::template scale_sum2< value_type , time_type >( val1 , h ) );
+
+ if( m_steps == 2 )
+ // result of first step already gives approximation at the center of the interval
+ boost::numeric::odeint::copy( m_x1.m_v , x_mp );
+
+ sys( m_x1.m_v , derivs[0].m_v , th );
+
+ boost::numeric::odeint::copy( in , m_x0.m_v );
+
+ unsigned short i = 1;
+ while( i != m_steps )
+ {
+ // general step
+ //tmp = m_x1; m_x1 = m_x0 + h2*m_dxdt; m_x0 = tmp
+ m_algebra.for_each3( m_x1.m_v , m_x0.m_v , derivs[i-1].m_v ,
+ typename operations_type::template scale_sum_swap2< value_type , time_type >( val1 , h2 ) );
+ if( i == m_steps/2-1 )
+ // save approximation at the center of the interval
+ boost::numeric::odeint::copy( m_x1.m_v , x_mp );
+
+ th += h;
+ sys( m_x1.m_v , derivs[i].m_v , th);
+ i++;
+ }
+
+ // last step
+ // x = 0.5*( m_x0 + m_x1 + h*m_dxdt )
+ m_algebra.for_each4( out , m_x0.m_v , m_x1.m_v , derivs[m_steps-1].m_v ,
+ typename operations_type::template scale_sum3< value_type , value_type , time_type >( val05 , val05 , val05*h ) );
+ }
+
+
+ void set_steps( unsigned short steps )
+ { m_steps = steps; }
+
+
+ unsigned short steps( void ) const
+ { return m_steps; }
+
+
+ template< class StateIn >
+ bool resize( const StateIn &x )
+ {
+ bool resized( false );
+ resized |= adjust_size_by_resizeability( m_x0 , x , typename is_resizeable<state_type>::type() );
+ resized |= adjust_size_by_resizeability( m_x1 , x , typename is_resizeable<state_type>::type() );
+ return resized;
+ }
+
+ template< class StateIn >
+ void adjust_size( const StateIn &x )
+ {
+ resize( x );
+ }
+
+private:
+
+ algebra_type m_algebra;
+
+ unsigned short m_steps;
+
+ resizer_type m_resizer;
+
+ wrapped_state_type m_x0;
+ wrapped_state_type m_x1;
+
+};
+
+
+
+/********** DOXYGEN ***********/
+
+/**
+ * \class modified_midpoint
+ *
+ * Implementation of the modified midpoint method with a configurable
+ * number of intermediate steps. This class is used by the Bulirsch-Stoer
+ * algorithm and is not meant for direct usage.
+ */
+
+
+/**
+ * \class modified_midpoint_dense_out
+ *
+ * Implementation of the modified midpoint method with a configurable
+ * number of intermediate steps. This class is used by the dense output
+ * Bulirsch-Stoer algorithm and is not meant for direct usage.
+ * \note This stepper is for internal use only and does not meet
+ * any stepper concept.
+ */
+
+
+}
+}
+}
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_MODIFIED_MIDPOINT_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/rosenbrock4.hpp b/include/boost/numeric/odeint/stepper/rosenbrock4.hpp
new file mode 100644
index 0000000..8613698
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/rosenbrock4.hpp
@@ -0,0 +1,346 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/rosenbrock4.hpp
+
+ [begin_description]
+ Implementation of the Rosenbrock 4 method for solving stiff ODEs. Note, that a
+ controller and a dense-output stepper exist for this method,
+ [end_description]
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+ Copyright 2012 Christoph Koke
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_ROSENBROCK4_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_ROSENBROCK4_HPP_INCLUDED
+
+
+#include <boost/numeric/odeint/util/bind.hpp>
+#include <boost/numeric/odeint/util/unwrap_reference.hpp>
+#include <boost/numeric/ublas/vector.hpp>
+#include <boost/numeric/ublas/matrix.hpp>
+#include <boost/numeric/ublas/lu.hpp>
+
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+
+#include <boost/numeric/odeint/util/ublas_wrapper.hpp>
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resizer.hpp>
+
+#include <boost/numeric/ublas/vector.hpp>
+#include <boost/numeric/ublas/matrix.hpp>
+#include <boost/numeric/ublas/lu.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+/*
+ * ToDo:
+ *
+ * 2. Interfacing for odeint, check if controlled_error_stepper can be used
+ * 3. dense output
+ */
+
+
+
+template< class Value >
+struct default_rosenbrock_coefficients
+{
+ typedef Value value_type;
+ typedef unsigned short order_type;
+
+ default_rosenbrock_coefficients( void )
+ : gamma ( static_cast< value_type >( 0.25 ) ) ,
+ d1 ( static_cast< value_type >( 0.25 ) ) ,
+ d2 ( static_cast< value_type >( -0.1043 ) ) ,
+ d3 ( static_cast< value_type >( 0.1035 ) ) ,
+ d4 ( static_cast< value_type >( 0.3620000000000023e-01 ) ) ,
+ c2 ( static_cast< value_type >( 0.386 ) ) ,
+ c3 ( static_cast< value_type >( 0.21 ) ) ,
+ c4 ( static_cast< value_type >( 0.63 ) ) ,
+ c21 ( static_cast< value_type >( -0.5668800000000000e+01 ) ) ,
+ a21 ( static_cast< value_type >( 0.1544000000000000e+01 ) ) ,
+ c31 ( static_cast< value_type >( -0.2430093356833875e+01 ) ) ,
+ c32 ( static_cast< value_type >( -0.2063599157091915e+00 ) ) ,
+ a31 ( static_cast< value_type >( 0.9466785280815826e+00 ) ) ,
+ a32 ( static_cast< value_type >( 0.2557011698983284e+00 ) ) ,
+ c41 ( static_cast< value_type >( -0.1073529058151375e+00 ) ) ,
+ c42 ( static_cast< value_type >( -0.9594562251023355e+01 ) ) ,
+ c43 ( static_cast< value_type >( -0.2047028614809616e+02 ) ) ,
+ a41 ( static_cast< value_type >( 0.3314825187068521e+01 ) ) ,
+ a42 ( static_cast< value_type >( 0.2896124015972201e+01 ) ) ,
+ a43 ( static_cast< value_type >( 0.9986419139977817e+00 ) ) ,
+ c51 ( static_cast< value_type >( 0.7496443313967647e+01 ) ) ,
+ c52 ( static_cast< value_type >( -0.1024680431464352e+02 ) ) ,
+ c53 ( static_cast< value_type >( -0.3399990352819905e+02 ) ) ,
+ c54 ( static_cast< value_type >( 0.1170890893206160e+02 ) ) ,
+ a51 ( static_cast< value_type >( 0.1221224509226641e+01 ) ) ,
+ a52 ( static_cast< value_type >( 0.6019134481288629e+01 ) ) ,
+ a53 ( static_cast< value_type >( 0.1253708332932087e+02 ) ) ,
+ a54 ( static_cast< value_type >( -0.6878860361058950e+00 ) ) ,
+ c61 ( static_cast< value_type >( 0.8083246795921522e+01 ) ) ,
+ c62 ( static_cast< value_type >( -0.7981132988064893e+01 ) ) ,
+ c63 ( static_cast< value_type >( -0.3152159432874371e+02 ) ) ,
+ c64 ( static_cast< value_type >( 0.1631930543123136e+02 ) ) ,
+ c65 ( static_cast< value_type >( -0.6058818238834054e+01 ) ) ,
+ d21 ( static_cast< value_type >( 0.1012623508344586e+02 ) ) ,
+ d22 ( static_cast< value_type >( -0.7487995877610167e+01 ) ) ,
+ d23 ( static_cast< value_type >( -0.3480091861555747e+02 ) ) ,
+ d24 ( static_cast< value_type >( -0.7992771707568823e+01 ) ) ,
+ d25 ( static_cast< value_type >( 0.1025137723295662e+01 ) ) ,
+ d31 ( static_cast< value_type >( -0.6762803392801253e+00 ) ) ,
+ d32 ( static_cast< value_type >( 0.6087714651680015e+01 ) ) ,
+ d33 ( static_cast< value_type >( 0.1643084320892478e+02 ) ) ,
+ d34 ( static_cast< value_type >( 0.2476722511418386e+02 ) ) ,
+ d35 ( static_cast< value_type >( -0.6594389125716872e+01 ) )
+ {}
+
+ const value_type gamma;
+ const value_type d1 , d2 , d3 , d4;
+ const value_type c2 , c3 , c4;
+ const value_type c21 ;
+ const value_type a21;
+ const value_type c31 , c32;
+ const value_type a31 , a32;
+ const value_type c41 , c42 , c43;
+ const value_type a41 , a42 , a43;
+ const value_type c51 , c52 , c53 , c54;
+ const value_type a51 , a52 , a53 , a54;
+ const value_type c61 , c62 , c63 , c64 , c65;
+ const value_type d21 , d22 , d23 , d24 , d25;
+ const value_type d31 , d32 , d33 , d34 , d35;
+
+ static const order_type stepper_order = 4;
+ static const order_type error_order = 3;
+};
+
+
+
+template< class Value , class Coefficients = default_rosenbrock_coefficients< Value > , class Resizer = initially_resizer >
+class rosenbrock4
+{
+private:
+
+public:
+
+ typedef Value value_type;
+ typedef boost::numeric::ublas::vector< value_type > state_type;
+ typedef state_type deriv_type;
+ typedef value_type time_type;
+ typedef boost::numeric::ublas::matrix< value_type > matrix_type;
+ typedef boost::numeric::ublas::permutation_matrix< size_t > pmatrix_type;
+ typedef Resizer resizer_type;
+ typedef Coefficients rosenbrock_coefficients;
+ typedef stepper_tag stepper_category;
+ typedef unsigned short order_type;
+
+ typedef state_wrapper< state_type > wrapped_state_type;
+ typedef state_wrapper< deriv_type > wrapped_deriv_type;
+ typedef state_wrapper< matrix_type > wrapped_matrix_type;
+ typedef state_wrapper< pmatrix_type > wrapped_pmatrix_type;
+
+ typedef rosenbrock4< Value , Coefficients , Resizer > stepper_type;
+
+ const static order_type stepper_order = rosenbrock_coefficients::stepper_order;
+ const static order_type error_order = rosenbrock_coefficients::error_order;
+
+ rosenbrock4( void )
+ : m_resizer() , m_x_err_resizer() ,
+ m_jac() , m_pm() ,
+ m_dfdt() , m_dxdt() , m_dxdtnew() ,
+ m_g1() , m_g2() , m_g3() , m_g4() , m_g5() ,
+ m_cont3() , m_cont4() , m_xtmp() , m_x_err() ,
+ m_coef()
+ { }
+
+
+ order_type order() const { return stepper_order; }
+
+ template< class System >
+ void do_step( System system , const state_type &x , time_type t , state_type &xout , time_type dt , state_type &xerr )
+ {
+ // get the system and jacobi function
+ typedef typename odeint::unwrap_reference< System >::type system_type;
+ typedef typename odeint::unwrap_reference< typename system_type::first_type >::type deriv_func_type;
+ typedef typename odeint::unwrap_reference< typename system_type::second_type >::type jacobi_func_type;
+ system_type &sys = system;
+ deriv_func_type &deriv_func = sys.first;
+ jacobi_func_type &jacobi_func = sys.second;
+
+ const size_t n = x.size();
+
+ m_resizer.adjust_size( x , detail::bind( &stepper_type::template resize_impl<state_type> , detail::ref( *this ) , detail::_1 ) );
+
+ for( size_t i=0 ; i<n ; ++i )
+ m_pm.m_v( i ) = i;
+
+ deriv_func( x , m_dxdt.m_v , t );
+ jacobi_func( x , m_jac.m_v , t , m_dfdt.m_v );
+
+ m_jac.m_v *= -1.0;
+ m_jac.m_v += 1.0 / m_coef.gamma / dt * boost::numeric::ublas::identity_matrix< value_type >( n );
+ boost::numeric::ublas::lu_factorize( m_jac.m_v , m_pm.m_v );
+
+ for( size_t i=0 ; i<n ; ++i )
+ m_g1.m_v[i] = m_dxdt.m_v[i] + dt * m_coef.d1 * m_dfdt.m_v[i];
+ boost::numeric::ublas::lu_substitute( m_jac.m_v , m_pm.m_v , m_g1.m_v );
+
+
+ for( size_t i=0 ; i<n ; ++i )
+ m_xtmp.m_v[i] = x[i] + m_coef.a21 * m_g1.m_v[i];
+ deriv_func( m_xtmp.m_v , m_dxdtnew.m_v , t + m_coef.c2 * dt );
+ for( size_t i=0 ; i<n ; ++i )
+ m_g2.m_v[i] = m_dxdtnew.m_v[i] + dt * m_coef.d2 * m_dfdt.m_v[i] + m_coef.c21 * m_g1.m_v[i] / dt;
+ boost::numeric::ublas::lu_substitute( m_jac.m_v , m_pm.m_v , m_g2.m_v );
+
+
+ for( size_t i=0 ; i<n ; ++i )
+ m_xtmp.m_v[i] = x[i] + m_coef.a31 * m_g1.m_v[i] + m_coef.a32 * m_g2.m_v[i];
+ deriv_func( m_xtmp.m_v , m_dxdtnew.m_v , t + m_coef.c3 * dt );
+ for( size_t i=0 ; i<n ; ++i )
+ m_g3.m_v[i] = m_dxdtnew.m_v[i] + dt * m_coef.d3 * m_dfdt.m_v[i] + ( m_coef.c31 * m_g1.m_v[i] + m_coef.c32 * m_g2.m_v[i] ) / dt;
+ boost::numeric::ublas::lu_substitute( m_jac.m_v , m_pm.m_v , m_g3.m_v );
+
+
+ for( size_t i=0 ; i<n ; ++i )
+ m_xtmp.m_v[i] = x[i] + m_coef.a41 * m_g1.m_v[i] + m_coef.a42 * m_g2.m_v[i] + m_coef.a43 * m_g3.m_v[i];
+ deriv_func( m_xtmp.m_v , m_dxdtnew.m_v , t + m_coef.c4 * dt );
+ for( size_t i=0 ; i<n ; ++i )
+ m_g4.m_v[i] = m_dxdtnew.m_v[i] + dt * m_coef.d4 * m_dfdt.m_v[i] + ( m_coef.c41 * m_g1.m_v[i] + m_coef.c42 * m_g2.m_v[i] + m_coef.c43 * m_g3.m_v[i] ) / dt;
+ boost::numeric::ublas::lu_substitute( m_jac.m_v , m_pm.m_v , m_g4.m_v );
+
+
+ for( size_t i=0 ; i<n ; ++i )
+ m_xtmp.m_v[i] = x[i] + m_coef.a51 * m_g1.m_v[i] + m_coef.a52 * m_g2.m_v[i] + m_coef.a53 * m_g3.m_v[i] + m_coef.a54 * m_g4.m_v[i];
+ deriv_func( m_xtmp.m_v , m_dxdtnew.m_v , t + dt );
+ for( size_t i=0 ; i<n ; ++i )
+ m_g5.m_v[i] = m_dxdtnew.m_v[i] + ( m_coef.c51 * m_g1.m_v[i] + m_coef.c52 * m_g2.m_v[i] + m_coef.c53 * m_g3.m_v[i] + m_coef.c54 * m_g4.m_v[i] ) / dt;
+ boost::numeric::ublas::lu_substitute( m_jac.m_v , m_pm.m_v , m_g5.m_v );
+
+ for( size_t i=0 ; i<n ; ++i )
+ m_xtmp.m_v[i] += m_g5.m_v[i];
+ deriv_func( m_xtmp.m_v , m_dxdtnew.m_v , t + dt );
+ for( size_t i=0 ; i<n ; ++i )
+ xerr[i] = m_dxdtnew.m_v[i] + ( m_coef.c61 * m_g1.m_v[i] + m_coef.c62 * m_g2.m_v[i] + m_coef.c63 * m_g3.m_v[i] + m_coef.c64 * m_g4.m_v[i] + m_coef.c65 * m_g5.m_v[i] ) / dt;
+ boost::numeric::ublas::lu_substitute( m_jac.m_v , m_pm.m_v , xerr );
+
+ for( size_t i=0 ; i<n ; ++i )
+ xout[i] = m_xtmp.m_v[i] + xerr[i];
+ }
+
+ template< class System >
+ void do_step( System system , state_type &x , time_type t , time_type dt , state_type &xerr )
+ {
+ do_step( system , x , t , x , dt , xerr );
+ }
+
+ /*
+ * do_step without error output - just calls above functions with and neglects the error estimate
+ */
+ template< class System >
+ void do_step( System system , const state_type &x , time_type t , state_type &xout , time_type dt )
+ {
+ m_x_err_resizer.adjust_size( x , detail::bind( &stepper_type::template resize_x_err<state_type> , detail::ref( *this ) , detail::_1 ) );
+ do_step( system , x , t , xout , dt , m_x_err.m_v );
+ }
+
+ template< class System >
+ void do_step( System system , state_type &x , time_type t , time_type dt )
+ {
+ m_x_err_resizer.adjust_size( x , detail::bind( &stepper_type::template resize_x_err<state_type> , detail::ref( *this ) , detail::_1 ) );
+ do_step( system , x , t , dt , m_x_err.m_v );
+ }
+
+ void prepare_dense_output()
+ {
+ const size_t n = m_g1.m_v.size();
+ for( size_t i=0 ; i<n ; ++i )
+ {
+ m_cont3.m_v[i] = m_coef.d21 * m_g1.m_v[i] + m_coef.d22 * m_g2.m_v[i] + m_coef.d23 * m_g3.m_v[i] + m_coef.d24 * m_g4.m_v[i] + m_coef.d25 * m_g5.m_v[i];
+ m_cont4.m_v[i] = m_coef.d31 * m_g1.m_v[i] + m_coef.d32 * m_g2.m_v[i] + m_coef.d33 * m_g3.m_v[i] + m_coef.d34 * m_g4.m_v[i] + m_coef.d35 * m_g5.m_v[i];
+ }
+ }
+
+
+ void calc_state( time_type t , state_type &x ,
+ const state_type &x_old , time_type t_old ,
+ const state_type &x_new , time_type t_new )
+ {
+ const size_t n = m_g1.m_v.size();
+ time_type dt = t_new - t_old;
+ time_type s = ( t - t_old ) / dt;
+ time_type s1 = 1.0 - s;
+ for( size_t i=0 ; i<n ; ++i )
+ x[i] = x_old[i] * s1 + s * ( x_new[i] + s1 * ( m_cont3.m_v[i] + s * m_cont4.m_v[i] ) );
+ }
+
+
+
+ template< class StateType >
+ void adjust_size( const StateType &x )
+ {
+ resize_impl( x );
+ resize_x_err( x );
+ }
+
+
+protected:
+
+ template< class StateIn >
+ bool resize_impl( const StateIn &x )
+ {
+ bool resized = false;
+ resized |= adjust_size_by_resizeability( m_dxdt , x , typename is_resizeable<deriv_type>::type() );
+ resized |= adjust_size_by_resizeability( m_dfdt , x , typename is_resizeable<deriv_type>::type() );
+ resized |= adjust_size_by_resizeability( m_dxdtnew , x , typename is_resizeable<deriv_type>::type() );
+ resized |= adjust_size_by_resizeability( m_xtmp , x , typename is_resizeable<state_type>::type() );
+ resized |= adjust_size_by_resizeability( m_g1 , x , typename is_resizeable<state_type>::type() );
+ resized |= adjust_size_by_resizeability( m_g2 , x , typename is_resizeable<state_type>::type() );
+ resized |= adjust_size_by_resizeability( m_g3 , x , typename is_resizeable<state_type>::type() );
+ resized |= adjust_size_by_resizeability( m_g4 , x , typename is_resizeable<state_type>::type() );
+ resized |= adjust_size_by_resizeability( m_g5 , x , typename is_resizeable<state_type>::type() );
+ resized |= adjust_size_by_resizeability( m_cont3 , x , typename is_resizeable<state_type>::type() );
+ resized |= adjust_size_by_resizeability( m_cont4 , x , typename is_resizeable<state_type>::type() );
+ resized |= adjust_size_by_resizeability( m_jac , x , typename is_resizeable<matrix_type>::type() );
+ resized |= adjust_size_by_resizeability( m_pm , x , typename is_resizeable<pmatrix_type>::type() );
+ return resized;
+ }
+
+ template< class StateIn >
+ bool resize_x_err( const StateIn &x )
+ {
+ return adjust_size_by_resizeability( m_x_err , x , typename is_resizeable<state_type>::type() );
+ }
+
+private:
+
+
+ resizer_type m_resizer;
+ resizer_type m_x_err_resizer;
+
+ wrapped_matrix_type m_jac;
+ wrapped_pmatrix_type m_pm;
+ wrapped_deriv_type m_dfdt , m_dxdt , m_dxdtnew;
+ wrapped_state_type m_g1 , m_g2 , m_g3 , m_g4 , m_g5;
+ wrapped_state_type m_cont3 , m_cont4;
+ wrapped_state_type m_xtmp;
+ wrapped_state_type m_x_err;
+
+ const rosenbrock_coefficients m_coef;
+};
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_ROSENBROCK4_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/rosenbrock4_controller.hpp b/include/boost/numeric/odeint/stepper/rosenbrock4_controller.hpp
new file mode 100644
index 0000000..61d6e51
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/rosenbrock4_controller.hpp
@@ -0,0 +1,240 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/rosenbrock4_controller.hpp
+
+ [begin_description]
+ Controller for the Rosenbrock4 method.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+ Copyright 2012 Christoph Koke
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_ROSENBROCK4_CONTROLLER_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_ROSENBROCK4_CONTROLLER_HPP_INCLUDED
+
+#include <boost/config.hpp>
+#include <boost/numeric/odeint/util/bind.hpp>
+
+#include <boost/numeric/odeint/stepper/controlled_step_result.hpp>
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+
+#include <boost/numeric/odeint/util/copy.hpp>
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/detail/less_with_sign.hpp>
+
+#include <boost/numeric/odeint/stepper/rosenbrock4.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template< class Stepper >
+class rosenbrock4_controller
+{
+private:
+
+
+public:
+
+ typedef Stepper stepper_type;
+ typedef typename stepper_type::value_type value_type;
+ typedef typename stepper_type::state_type state_type;
+ typedef typename stepper_type::wrapped_state_type wrapped_state_type;
+ typedef typename stepper_type::time_type time_type;
+ typedef typename stepper_type::deriv_type deriv_type;
+ typedef typename stepper_type::wrapped_deriv_type wrapped_deriv_type;
+ typedef typename stepper_type::resizer_type resizer_type;
+ typedef controlled_stepper_tag stepper_category;
+
+ typedef rosenbrock4_controller< Stepper > controller_type;
+
+
+ rosenbrock4_controller( value_type atol = 1.0e-6 , value_type rtol = 1.0e-6 ,
+ const stepper_type &stepper = stepper_type() )
+ : m_stepper( stepper ) , m_atol( atol ) , m_rtol( rtol ) ,
+ m_max_dt( static_cast<time_type>(0) ) ,
+ m_first_step( true ) , m_err_old( 0.0 ) , m_dt_old( 0.0 ) ,
+ m_last_rejected( false )
+ { }
+
+ rosenbrock4_controller( value_type atol, value_type rtol, time_type max_dt,
+ const stepper_type &stepper = stepper_type() )
+ : m_stepper( stepper ) , m_atol( atol ) , m_rtol( rtol ) , m_max_dt( max_dt ) ,
+ m_first_step( true ) , m_err_old( 0.0 ) , m_dt_old( 0.0 ) ,
+ m_last_rejected( false )
+ { }
+
+ value_type error( const state_type &x , const state_type &xold , const state_type &xerr )
+ {
+ BOOST_USING_STD_MAX();
+ using std::abs;
+ using std::sqrt;
+
+ const size_t n = x.size();
+ value_type err = 0.0 , sk = 0.0;
+ for( size_t i=0 ; i<n ; ++i )
+ {
+ sk = m_atol + m_rtol * max BOOST_PREVENT_MACRO_SUBSTITUTION ( abs( xold[i] ) , abs( x[i] ) );
+ err += xerr[i] * xerr[i] / sk / sk;
+ }
+ return sqrt( err / value_type( n ) );
+ }
+
+ value_type last_error( void ) const
+ {
+ return m_err_old;
+ }
+
+
+
+
+ template< class System >
+ boost::numeric::odeint::controlled_step_result
+ try_step( System sys , state_type &x , time_type &t , time_type &dt )
+ {
+ m_xnew_resizer.adjust_size( x , detail::bind( &controller_type::template resize_m_xnew< state_type > , detail::ref( *this ) , detail::_1 ) );
+ boost::numeric::odeint::controlled_step_result res = try_step( sys , x , t , m_xnew.m_v , dt );
+ if( res == success )
+ {
+ boost::numeric::odeint::copy( m_xnew.m_v , x );
+ }
+ return res;
+ }
+
+
+ template< class System >
+ boost::numeric::odeint::controlled_step_result
+ try_step( System sys , const state_type &x , time_type &t , state_type &xout , time_type &dt )
+ {
+ if( m_max_dt != static_cast<time_type>(0) && detail::less_with_sign(m_max_dt, dt, dt) )
+ {
+ // given step size is bigger then max_dt
+ // set limit and return fail
+ dt = m_max_dt;
+ return fail;
+ }
+
+ BOOST_USING_STD_MIN();
+ BOOST_USING_STD_MAX();
+ using std::pow;
+
+ static const value_type safe = 0.9 , fac1 = 5.0 , fac2 = 1.0 / 6.0;
+
+ m_xerr_resizer.adjust_size( x , detail::bind( &controller_type::template resize_m_xerr< state_type > , detail::ref( *this ) , detail::_1 ) );
+
+ m_stepper.do_step( sys , x , t , xout , dt , m_xerr.m_v );
+ value_type err = error( xout , x , m_xerr.m_v );
+
+ value_type fac = max BOOST_PREVENT_MACRO_SUBSTITUTION (
+ fac2 , min BOOST_PREVENT_MACRO_SUBSTITUTION (
+ fac1 ,
+ static_cast< value_type >( pow( err , 0.25 ) / safe ) ) );
+ value_type dt_new = dt / fac;
+ if ( err <= 1.0 )
+ {
+ if( m_first_step )
+ {
+ m_first_step = false;
+ }
+ else
+ {
+ value_type fac_pred = ( m_dt_old / dt ) * pow( err * err / m_err_old , 0.25 ) / safe;
+ fac_pred = max BOOST_PREVENT_MACRO_SUBSTITUTION (
+ fac2 , min BOOST_PREVENT_MACRO_SUBSTITUTION ( fac1 , fac_pred ) );
+ fac = max BOOST_PREVENT_MACRO_SUBSTITUTION ( fac , fac_pred );
+ dt_new = dt / fac;
+ }
+
+ m_dt_old = dt;
+ m_err_old = max BOOST_PREVENT_MACRO_SUBSTITUTION ( static_cast< value_type >( 0.01 ) , err );
+ if( m_last_rejected )
+ dt_new = ( dt >= 0.0 ?
+ min BOOST_PREVENT_MACRO_SUBSTITUTION ( dt_new , dt ) :
+ max BOOST_PREVENT_MACRO_SUBSTITUTION ( dt_new , dt ) );
+ t += dt;
+ // limit step size to max_dt
+ if( m_max_dt != static_cast<time_type>(0) )
+ {
+ dt = detail::min_abs(m_max_dt, dt_new);
+ } else {
+ dt = dt_new;
+ }
+ m_last_rejected = false;
+ return success;
+ }
+ else
+ {
+ dt = dt_new;
+ m_last_rejected = true;
+ return fail;
+ }
+ }
+
+
+ template< class StateType >
+ void adjust_size( const StateType &x )
+ {
+ resize_m_xerr( x );
+ resize_m_xnew( x );
+ }
+
+
+
+ stepper_type& stepper( void )
+ {
+ return m_stepper;
+ }
+
+ const stepper_type& stepper( void ) const
+ {
+ return m_stepper;
+ }
+
+
+
+
+private:
+
+ template< class StateIn >
+ bool resize_m_xerr( const StateIn &x )
+ {
+ return adjust_size_by_resizeability( m_xerr , x , typename is_resizeable<state_type>::type() );
+ }
+
+ template< class StateIn >
+ bool resize_m_xnew( const StateIn &x )
+ {
+ return adjust_size_by_resizeability( m_xnew , x , typename is_resizeable<state_type>::type() );
+ }
+
+
+ stepper_type m_stepper;
+ resizer_type m_xerr_resizer;
+ resizer_type m_xnew_resizer;
+ wrapped_state_type m_xerr;
+ wrapped_state_type m_xnew;
+ value_type m_atol , m_rtol;
+ time_type m_max_dt;
+ bool m_first_step;
+ value_type m_err_old , m_dt_old;
+ bool m_last_rejected;
+};
+
+
+
+
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_ROSENBROCK4_CONTROLLER_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/rosenbrock4_dense_output.hpp b/include/boost/numeric/odeint/stepper/rosenbrock4_dense_output.hpp
new file mode 100644
index 0000000..6695ba6
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/rosenbrock4_dense_output.hpp
@@ -0,0 +1,199 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/rosenbrock4_dense_output.hpp
+
+ [begin_description]
+ Dense output for Rosenbrock 4.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2015 Mario Mulansky
+ Copyright 2012 Christoph Koke
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_ROSENBROCK4_DENSE_OUTPUT_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_ROSENBROCK4_DENSE_OUTPUT_HPP_INCLUDED
+
+
+#include <utility>
+
+#include <boost/numeric/odeint/util/bind.hpp>
+
+#include <boost/numeric/odeint/stepper/rosenbrock4_controller.hpp>
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+
+#include <boost/numeric/odeint/integrate/max_step_checker.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template< class ControlledStepper >
+class rosenbrock4_dense_output
+{
+
+public:
+
+ typedef ControlledStepper controlled_stepper_type;
+ typedef typename controlled_stepper_type::stepper_type stepper_type;
+ typedef typename stepper_type::value_type value_type;
+ typedef typename stepper_type::state_type state_type;
+ typedef typename stepper_type::wrapped_state_type wrapped_state_type;
+ typedef typename stepper_type::time_type time_type;
+ typedef typename stepper_type::deriv_type deriv_type;
+ typedef typename stepper_type::wrapped_deriv_type wrapped_deriv_type;
+ typedef typename stepper_type::resizer_type resizer_type;
+ typedef dense_output_stepper_tag stepper_category;
+
+ typedef rosenbrock4_dense_output< ControlledStepper > dense_output_stepper_type;
+
+ rosenbrock4_dense_output( const controlled_stepper_type &stepper = controlled_stepper_type() )
+ : m_stepper( stepper ) ,
+ m_x1() , m_x2() ,
+ m_current_state_x1( true ) ,
+ m_t() , m_t_old() , m_dt()
+ {
+ }
+
+
+
+ template< class StateType >
+ void initialize( const StateType &x0 , time_type t0 , time_type dt0 )
+ {
+ m_resizer.adjust_size( x0 , detail::bind( &dense_output_stepper_type::template resize_impl< StateType > , detail::ref( *this ) , detail::_1 ) );
+ get_current_state() = x0;
+ m_t = t0;
+ m_dt = dt0;
+ }
+
+ template< class System >
+ std::pair< time_type , time_type > do_step( System system )
+ {
+ failed_step_checker fail_checker; // to throw a runtime_error if step size adjustment fails
+ controlled_step_result res = fail;
+ m_t_old = m_t;
+ do
+ {
+ res = m_stepper.try_step( system , get_current_state() , m_t , get_old_state() , m_dt );
+ fail_checker(); // check for overflow of failed steps
+ }
+ while( res == fail );
+ m_stepper.stepper().prepare_dense_output();
+ this->toggle_current_state();
+ return std::make_pair( m_t_old , m_t );
+ }
+
+
+ /*
+ * The two overloads are needed in order to solve the forwarding problem.
+ */
+ template< class StateOut >
+ void calc_state( time_type t , StateOut &x )
+ {
+ m_stepper.stepper().calc_state( t , x , get_old_state() , m_t_old , get_current_state() , m_t );
+ }
+
+ template< class StateOut >
+ void calc_state( time_type t , const StateOut &x )
+ {
+ m_stepper.stepper().calc_state( t , x , get_old_state() , m_t_old , get_current_state() , m_t );
+ }
+
+
+ template< class StateType >
+ void adjust_size( const StateType &x )
+ {
+ m_stepper.adjust_size( x );
+ resize_impl( x );
+ }
+
+
+
+
+ const state_type& current_state( void ) const
+ {
+ return get_current_state();
+ }
+
+ time_type current_time( void ) const
+ {
+ return m_t;
+ }
+
+ const state_type& previous_state( void ) const
+ {
+ return get_old_state();
+ }
+
+ time_type previous_time( void ) const
+ {
+ return m_t_old;
+ }
+
+ time_type current_time_step( void ) const
+ {
+ return m_dt;
+ }
+
+
+
+
+private:
+
+ state_type& get_current_state( void )
+ {
+ return m_current_state_x1 ? m_x1.m_v : m_x2.m_v ;
+ }
+
+ const state_type& get_current_state( void ) const
+ {
+ return m_current_state_x1 ? m_x1.m_v : m_x2.m_v ;
+ }
+
+ state_type& get_old_state( void )
+ {
+ return m_current_state_x1 ? m_x2.m_v : m_x1.m_v ;
+ }
+
+ const state_type& get_old_state( void ) const
+ {
+ return m_current_state_x1 ? m_x2.m_v : m_x1.m_v ;
+ }
+
+ void toggle_current_state( void )
+ {
+ m_current_state_x1 = ! m_current_state_x1;
+ }
+
+
+ template< class StateIn >
+ bool resize_impl( const StateIn &x )
+ {
+ bool resized = false;
+ resized |= adjust_size_by_resizeability( m_x1 , x , typename is_resizeable<state_type>::type() );
+ resized |= adjust_size_by_resizeability( m_x2 , x , typename is_resizeable<state_type>::type() );
+ return resized;
+ }
+
+
+ controlled_stepper_type m_stepper;
+ resizer_type m_resizer;
+ wrapped_state_type m_x1 , m_x2;
+ bool m_current_state_x1;
+ time_type m_t , m_t_old , m_dt;
+};
+
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_ROSENBROCK4_DENSE_OUTPUT_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/runge_kutta4.hpp b/include/boost/numeric/odeint/stepper/runge_kutta4.hpp
new file mode 100644
index 0000000..2410774
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/runge_kutta4.hpp
@@ -0,0 +1,181 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/runge_kutta4.hpp
+
+ [begin_description]
+ Implementation of the classical Runge-Kutta stepper with the generic stepper.
+ [end_description]
+
+ Copyright 2011-2013 Mario Mulansky
+ Copyright 2011-2013 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA4_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA4_HPP_INCLUDED
+
+
+
+
+#include <boost/fusion/container/vector.hpp>
+#include <boost/fusion/container/generation/make_vector.hpp>
+
+#include <boost/numeric/odeint/stepper/explicit_generic_rk.hpp>
+#include <boost/numeric/odeint/algebra/range_algebra.hpp>
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
+
+#include <boost/array.hpp>
+
+#include <boost/numeric/odeint/util/resizer.hpp>
+
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+#ifndef DOXYGEN_SKIP
+template< class Value = double >
+struct rk4_coefficients_a1 : boost::array< Value , 1 >
+{
+ rk4_coefficients_a1( void )
+ {
+ (*this)[0] = static_cast< Value >( 1 ) / static_cast< Value >( 2 );
+ }
+};
+
+template< class Value = double >
+struct rk4_coefficients_a2 : boost::array< Value , 2 >
+{
+ rk4_coefficients_a2( void )
+ {
+ (*this)[0] = static_cast<Value>(0);
+ (*this)[1] = static_cast< Value >( 1 ) / static_cast< Value >( 2 );
+ }
+};
+
+
+template< class Value = double >
+struct rk4_coefficients_a3 : boost::array< Value , 3 >
+{
+ rk4_coefficients_a3( void )
+ {
+ (*this)[0] = static_cast<Value>(0);
+ (*this)[1] = static_cast<Value>(0);
+ (*this)[2] = static_cast<Value>(1);
+ }
+};
+
+template< class Value = double >
+struct rk4_coefficients_b : boost::array< Value , 4 >
+{
+ rk4_coefficients_b( void )
+ {
+ (*this)[0] = static_cast<Value>(1)/static_cast<Value>(6);
+ (*this)[1] = static_cast<Value>(1)/static_cast<Value>(3);
+ (*this)[2] = static_cast<Value>(1)/static_cast<Value>(3);
+ (*this)[3] = static_cast<Value>(1)/static_cast<Value>(6);
+ }
+};
+
+template< class Value = double >
+struct rk4_coefficients_c : boost::array< Value , 4 >
+{
+ rk4_coefficients_c( void )
+ {
+ (*this)[0] = static_cast<Value>(0);
+ (*this)[1] = static_cast< Value >( 1 ) / static_cast< Value >( 2 );
+ (*this)[2] = static_cast< Value >( 1 ) / static_cast< Value >( 2 );
+ (*this)[3] = static_cast<Value>(1);
+ }
+};
+#endif
+
+
+
+template<
+class State ,
+class Value = double ,
+class Deriv = State ,
+class Time = Value ,
+class Algebra = typename algebra_dispatcher< State >::algebra_type ,
+class Operations = typename operations_dispatcher< State >::operations_type ,
+class Resizer = initially_resizer
+>
+#ifndef DOXYGEN_SKIP
+class runge_kutta4 : public explicit_generic_rk< 4 , 4 , State , Value , Deriv , Time ,
+Algebra , Operations , Resizer >
+#else
+class runge_kutta4 : public explicit_generic_rk
+#endif
+{
+
+public:
+
+#ifndef DOXYGEN_SKIP
+ typedef explicit_generic_rk< 4 , 4 , State , Value , Deriv , Time ,
+ Algebra , Operations , Resizer > stepper_base_type;
+#endif
+ typedef typename stepper_base_type::state_type state_type;
+ typedef typename stepper_base_type::value_type value_type;
+ typedef typename stepper_base_type::deriv_type deriv_type;
+ typedef typename stepper_base_type::time_type time_type;
+ typedef typename stepper_base_type::algebra_type algebra_type;
+ typedef typename stepper_base_type::operations_type operations_type;
+ typedef typename stepper_base_type::resizer_type resizer_type;
+
+ #ifndef DOXYGEN_SKIP
+ typedef typename stepper_base_type::wrapped_state_type wrapped_state_type;
+ typedef typename stepper_base_type::wrapped_deriv_type wrapped_deriv_type;
+ typedef typename stepper_base_type::stepper_type stepper_type;
+ #endif
+
+ runge_kutta4( const algebra_type &algebra = algebra_type() ) : stepper_base_type(
+ boost::fusion::make_vector( rk4_coefficients_a1<Value>() , rk4_coefficients_a2<Value>() , rk4_coefficients_a3<Value>() ) ,
+ rk4_coefficients_b<Value>() , rk4_coefficients_c<Value>() , algebra )
+ { }
+
+};
+
+/**
+ * \class runge_kutta4
+ * \brief The classical Runge-Kutta stepper of fourth order.
+ *
+ * The Runge-Kutta method of fourth order is one standard method for
+ * solving ordinary differential equations and is widely used, see also
+ * <a href="http://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods">en.wikipedia.org/wiki/Runge-Kutta_methods</a>
+ * The method is explicit and fulfills the Stepper concept. Step size control
+ * or continuous output are not provided.
+ *
+ * This class derives from explicit_stepper_base and inherits its interface via CRTP (current recurring template pattern).
+ * Furthermore, it derivs from explicit_generic_rk which is a generic Runge-Kutta algorithm. For more details see
+ * explicit_stepper_base and explicit_generic_rk.
+ *
+ * \tparam State The state type.
+ * \tparam Value The value type.
+ * \tparam Deriv The type representing the time derivative of the state.
+ * \tparam Time The time representing the independent variable - the time.
+ * \tparam Algebra The algebra type.
+ * \tparam Operations The operations type.
+ * \tparam Resizer The resizer policy type.
+ */
+
+/**
+ * \fn runge_kutta4::runge_kutta4( const algebra_type &algebra = algebra_type() )
+ * \brief Constructs the runge_kutta4 class. This constructor can be used as a default
+ * constructor if the algebra has a default constructor.
+ * \param algebra A copy of algebra is made and stored inside explicit_stepper_base.
+ */
+
+}
+}
+}
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA4_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/runge_kutta4_classic.hpp b/include/boost/numeric/odeint/stepper/runge_kutta4_classic.hpp
new file mode 100644
index 0000000..32bda0b
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/runge_kutta4_classic.hpp
@@ -0,0 +1,232 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/runge_kutta4_classic.hpp
+
+ [begin_description]
+ Implementation for the classical Runge Kutta stepper.
+ [end_description]
+
+ Copyright 2010-2013 Karsten Ahnert
+ Copyright 2010-2013 Mario Mulansky
+ Copyright 2012 Christoph Koke
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA4_CLASSIC_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA4_CLASSIC_HPP_INCLUDED
+
+
+
+#include <boost/numeric/odeint/stepper/base/explicit_stepper_base.hpp>
+#include <boost/numeric/odeint/algebra/range_algebra.hpp>
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
+
+#include <boost/numeric/odeint/util/state_wrapper.hpp>
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resizer.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template<
+class State ,
+class Value = double ,
+class Deriv = State ,
+class Time = Value ,
+class Algebra = typename algebra_dispatcher< State >::algebra_type ,
+class Operations = typename operations_dispatcher< State >::operations_type ,
+class Resizer = initially_resizer
+>
+#ifndef DOXYGEN_SKIP
+class runge_kutta4_classic
+: public explicit_stepper_base<
+ runge_kutta4_classic< State , Value , Deriv , Time , Algebra , Operations , Resizer > ,
+ 4 , State , Value , Deriv , Time , Algebra , Operations , Resizer >
+#else
+class runge_kutta4_classic : public explicit_stepper_base
+#endif
+{
+
+public :
+
+ #ifndef DOXYGEN_SKIP
+ typedef explicit_stepper_base<
+ runge_kutta4_classic< State , Value , Deriv , Time , Algebra , Operations , Resizer > ,
+ 4 , State , Value , Deriv , Time , Algebra , Operations , Resizer > stepper_base_type;
+ #else
+ typedef explicit_stepper_base< runge_kutta4_classic< ... > , ... > stepper_base_type;
+ #endif
+
+ typedef typename stepper_base_type::state_type state_type;
+ typedef typename stepper_base_type::value_type value_type;
+ typedef typename stepper_base_type::deriv_type deriv_type;
+ typedef typename stepper_base_type::time_type time_type;
+ typedef typename stepper_base_type::algebra_type algebra_type;
+ typedef typename stepper_base_type::operations_type operations_type;
+ typedef typename stepper_base_type::resizer_type resizer_type;
+
+ #ifndef DOXYGEN_SKIP
+ typedef typename stepper_base_type::stepper_type stepper_type;
+ typedef typename stepper_base_type::wrapped_state_type wrapped_state_type;
+ typedef typename stepper_base_type::wrapped_deriv_type wrapped_deriv_type;
+ #endif // DOXYGEN_SKIP
+
+
+
+ runge_kutta4_classic( const algebra_type &algebra = algebra_type() ) : stepper_base_type( algebra )
+ { }
+
+
+ template< class System , class StateIn , class DerivIn , class StateOut >
+ void do_step_impl( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt )
+ {
+ // ToDo : check if size of in,dxdt,out are equal?
+
+ static const value_type val1 = static_cast< value_type >( 1 );
+
+ m_resizer.adjust_size( in , detail::bind( &stepper_type::template resize_impl< StateIn > , detail::ref( *this ) , detail::_1 ) );
+
+ typename odeint::unwrap_reference< System >::type &sys = system;
+
+ const time_type dh = dt / static_cast< value_type >( 2 );
+ const time_type th = t + dh;
+
+ // dt * dxdt = k1
+ // m_x_tmp = x + dh*dxdt
+ stepper_base_type::m_algebra.for_each3( m_x_tmp.m_v , in , dxdt ,
+ typename operations_type::template scale_sum2< value_type , time_type >( val1 , dh ) );
+
+
+ // dt * m_dxt = k2
+ sys( m_x_tmp.m_v , m_dxt.m_v , th );
+
+ // m_x_tmp = x + dh*m_dxt
+ stepper_base_type::m_algebra.for_each3( m_x_tmp.m_v , in , m_dxt.m_v ,
+ typename operations_type::template scale_sum2< value_type , time_type >( val1 , dh ) );
+
+
+ // dt * m_dxm = k3
+ sys( m_x_tmp.m_v , m_dxm.m_v , th );
+ //m_x_tmp = x + dt*m_dxm
+ stepper_base_type::m_algebra.for_each3( m_x_tmp.m_v , in , m_dxm.m_v ,
+ typename operations_type::template scale_sum2< value_type , time_type >( val1 , dt ) );
+
+
+ // dt * m_dxh = k4
+ sys( m_x_tmp.m_v , m_dxh.m_v , t + dt );
+
+ //x += dt/6 * ( m_dxdt + m_dxt + val2*m_dxm )
+ time_type dt6 = dt / static_cast< value_type >( 6 );
+ time_type dt3 = dt / static_cast< value_type >( 3 );
+ stepper_base_type::m_algebra.for_each6( out , in , dxdt , m_dxt.m_v , m_dxm.m_v , m_dxh.m_v ,
+ typename operations_type::template scale_sum5< value_type , time_type , time_type , time_type , time_type >( 1.0 , dt6 , dt3 , dt3 , dt6 ) );
+
+ // x += dt/6 * m_dxdt + dt/3 * m_dxt )
+ // stepper_base_type::m_algebra.for_each4( out , in , dxdt , m_dxt.m_v ,
+ // typename operations_type::template scale_sum3< value_type , time_type , time_type >( 1.0 , dt6 , dt3 ) );
+ // // x += dt/3 * m_dxm + dt/6 * m_dxh )
+ // stepper_base_type::m_algebra.for_each4( out , out , m_dxm.m_v , m_dxh.m_v ,
+ // typename operations_type::template scale_sum3< value_type , time_type , time_type >( 1.0 , dt3 , dt6 ) );
+
+ }
+
+ template< class StateType >
+ void adjust_size( const StateType &x )
+ {
+ resize_impl( x );
+ stepper_base_type::adjust_size( x );
+ }
+
+private:
+
+ template< class StateIn >
+ bool resize_impl( const StateIn &x )
+ {
+ bool resized = false;
+ resized |= adjust_size_by_resizeability( m_x_tmp , x , typename is_resizeable<state_type>::type() );
+ resized |= adjust_size_by_resizeability( m_dxm , x , typename is_resizeable<deriv_type>::type() );
+ resized |= adjust_size_by_resizeability( m_dxt , x , typename is_resizeable<deriv_type>::type() );
+ resized |= adjust_size_by_resizeability( m_dxh , x , typename is_resizeable<deriv_type>::type() );
+ return resized;
+ }
+
+
+ resizer_type m_resizer;
+
+ wrapped_deriv_type m_dxt;
+ wrapped_deriv_type m_dxm;
+ wrapped_deriv_type m_dxh;
+ wrapped_state_type m_x_tmp;
+
+};
+
+
+/********* DOXYGEN *********/
+
+/**
+ * \class runge_kutta4_classic
+ * \brief The classical Runge-Kutta stepper of fourth order.
+ *
+ * The Runge-Kutta method of fourth order is one standard method for
+ * solving ordinary differential equations and is widely used, see also
+ * <a href="http://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods">en.wikipedia.org/wiki/Runge-Kutta_methods</a>
+ * The method is explicit and fulfills the Stepper concept. Step size control
+ * or continuous output are not provided. This class implements the method directly, hence the
+ * generic Runge-Kutta algorithm is not used.
+ *
+ * This class derives from explicit_stepper_base and inherits its interface via
+ * CRTP (current recurring template pattern). For more details see
+ * explicit_stepper_base.
+ *
+ * \tparam State The state type.
+ * \tparam Value The value type.
+ * \tparam Deriv The type representing the time derivative of the state.
+ * \tparam Time The time representing the independent variable - the time.
+ * \tparam Algebra The algebra type.
+ * \tparam Operations The operations type.
+ * \tparam Resizer The resizer policy type.
+ */
+
+ /**
+ * \fn runge_kutta4_classic::runge_kutta4_classic( const algebra_type &algebra )
+ * \brief Constructs the runge_kutta4_classic class. This constructor can be used as a default
+ * constructor if the algebra has a default constructor.
+ * \param algebra A copy of algebra is made and stored inside explicit_stepper_base.
+ */
+
+
+ /**
+ * \fn runge_kutta4_classic::do_step_impl( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt )
+ * \brief This method performs one step. The derivative `dxdt` of `in` at the time `t` is passed to the method.
+ * The result is updated out of place, hence the input is in `in` and the output in `out`.
+ * Access to this step functionality is provided by explicit_stepper_base and
+ * `do_step_impl` should not be called directly.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param in The state of the ODE which should be solved. in is not modified in this method
+ * \param dxdt The derivative of x at t.
+ * \param t The value of the time, at which the step should be performed.
+ * \param out The result of the step is written in out.
+ * \param dt The step size.
+ */
+
+ /**
+ * \fn runge_kutta4_classic::adjust_size( const StateType &x )
+ * \brief Adjust the size of all temporaries in the stepper manually.
+ * \param x A state from which the size of the temporaries to be resized is deduced.
+ */
+
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA4_CLASSIC_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp b/include/boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp
new file mode 100644
index 0000000..beecb3f
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp
@@ -0,0 +1,231 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp
+
+ [begin_description]
+ Implementation of the Runge Kutta Cash Karp 5(4) method. It uses the generic error stepper.
+ [end_description]
+
+ Copyright 2011-2013 Mario Mulansky
+ Copyright 2011-2013 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_CASH_KARP54_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_CASH_KARP54_HPP_INCLUDED
+
+#include <boost/fusion/container/vector.hpp>
+#include <boost/fusion/container/generation/make_vector.hpp>
+
+#include <boost/numeric/odeint/stepper/explicit_error_generic_rk.hpp>
+#include <boost/numeric/odeint/algebra/range_algebra.hpp>
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
+
+#include <boost/numeric/odeint/util/state_wrapper.hpp>
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resizer.hpp>
+
+#include <boost/array.hpp>
+
+
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+#ifndef DOXYGEN_SKIP
+template< class Value = double >
+struct rk54_ck_coefficients_a1 : boost::array< Value , 1 >
+{
+ rk54_ck_coefficients_a1( void )
+ {
+ (*this)[0] = static_cast< Value >( 1 )/static_cast< Value >( 5 );
+ }
+};
+
+template< class Value = double >
+struct rk54_ck_coefficients_a2 : boost::array< Value , 2 >
+{
+ rk54_ck_coefficients_a2( void )
+ {
+ (*this)[0] = static_cast<Value>( 3 )/static_cast<Value>( 40 );
+ (*this)[1] = static_cast<Value>( 9 )/static_cast<Value>( 40 );
+ }
+};
+
+
+template< class Value = double >
+struct rk54_ck_coefficients_a3 : boost::array< Value , 3 >
+{
+ rk54_ck_coefficients_a3( void )
+ {
+ (*this)[0] = static_cast<Value>( 3 )/static_cast<Value>( 10 );
+ (*this)[1] = static_cast<Value>( -9 )/static_cast<Value>( 10 );
+ (*this)[2] = static_cast<Value>( 6 )/static_cast<Value>( 5 );
+ }
+};
+
+template< class Value = double >
+struct rk54_ck_coefficients_a4 : boost::array< Value , 4 >
+{
+ rk54_ck_coefficients_a4( void )
+ {
+ (*this)[0] = static_cast<Value>( -11 )/static_cast<Value>( 54 );
+ (*this)[1] = static_cast<Value>( 5 )/static_cast<Value>( 2 );
+ (*this)[2] = static_cast<Value>( -70 )/static_cast<Value>( 27 );
+ (*this)[3] = static_cast<Value>( 35 )/static_cast<Value>( 27 );
+ }
+};
+
+template< class Value = double >
+struct rk54_ck_coefficients_a5 : boost::array< Value , 5 >
+{
+ rk54_ck_coefficients_a5( void )
+ {
+ (*this)[0] = static_cast<Value>( 1631 )/static_cast<Value>( 55296 );
+ (*this)[1] = static_cast<Value>( 175 )/static_cast<Value>( 512 );
+ (*this)[2] = static_cast<Value>( 575 )/static_cast<Value>( 13824 );
+ (*this)[3] = static_cast<Value>( 44275 )/static_cast<Value>( 110592 );
+ (*this)[4] = static_cast<Value>( 253 )/static_cast<Value>( 4096 );
+ }
+};
+
+template< class Value = double >
+struct rk54_ck_coefficients_b : boost::array< Value , 6 >
+{
+ rk54_ck_coefficients_b( void )
+ {
+ (*this)[0] = static_cast<Value>( 37 )/static_cast<Value>( 378 );
+ (*this)[1] = static_cast<Value>( 0 );
+ (*this)[2] = static_cast<Value>( 250 )/static_cast<Value>( 621 );
+ (*this)[3] = static_cast<Value>( 125 )/static_cast<Value>( 594 );
+ (*this)[4] = static_cast<Value>( 0 );
+ (*this)[5] = static_cast<Value>( 512 )/static_cast<Value>( 1771 );
+ }
+};
+
+template< class Value = double >
+struct rk54_ck_coefficients_db : boost::array< Value , 6 >
+{
+ rk54_ck_coefficients_db( void )
+ {
+ (*this)[0] = static_cast<Value>( 37 )/static_cast<Value>( 378 ) - static_cast<Value>( 2825 )/static_cast<Value>( 27648 );
+ (*this)[1] = static_cast<Value>( 0 );
+ (*this)[2] = static_cast<Value>( 250 )/static_cast<Value>( 621 ) - static_cast<Value>( 18575 )/static_cast<Value>( 48384 );
+ (*this)[3] = static_cast<Value>( 125 )/static_cast<Value>( 594 ) - static_cast<Value>( 13525 )/static_cast<Value>( 55296 );
+ (*this)[4] = static_cast<Value>( -277 )/static_cast<Value>( 14336 );
+ (*this)[5] = static_cast<Value>( 512 )/static_cast<Value>( 1771 ) - static_cast<Value>( 1 )/static_cast<Value>( 4 );
+ }
+};
+
+
+template< class Value = double >
+struct rk54_ck_coefficients_c : boost::array< Value , 6 >
+{
+ rk54_ck_coefficients_c( void )
+ {
+ (*this)[0] = static_cast<Value>(0);
+ (*this)[1] = static_cast<Value>( 1 )/static_cast<Value>( 5 );
+ (*this)[2] = static_cast<Value>( 3 )/static_cast<Value>( 10 );
+ (*this)[3] = static_cast<Value>( 3 )/static_cast<Value>( 5 );
+ (*this)[4] = static_cast<Value>( 1 );
+ (*this)[5] = static_cast<Value>( 7 )/static_cast<Value>( 8 );
+ }
+};
+#endif
+
+
+template<
+ class State ,
+ class Value = double ,
+ class Deriv = State ,
+ class Time = Value ,
+ class Algebra = typename algebra_dispatcher< State >::algebra_type ,
+ class Operations = typename operations_dispatcher< State >::operations_type ,
+ class Resizer = initially_resizer
+ >
+#ifndef DOXYGEN_SKIP
+class runge_kutta_cash_karp54 : public explicit_error_generic_rk< 6 , 5 , 5 , 4 ,
+ State , Value , Deriv , Time , Algebra , Operations , Resizer >
+#else
+class runge_kutta_cash_karp54 : public explicit_error_generic_rk
+#endif
+{
+
+public:
+#ifndef DOXYGEN_SKIP
+ typedef explicit_error_generic_rk< 6 , 5 , 5 , 4 , State , Value , Deriv , Time ,
+ Algebra , Operations , Resizer > stepper_base_type;
+#endif
+ typedef typename stepper_base_type::state_type state_type;
+ typedef typename stepper_base_type::value_type value_type;
+ typedef typename stepper_base_type::deriv_type deriv_type;
+ typedef typename stepper_base_type::time_type time_type;
+ typedef typename stepper_base_type::algebra_type algebra_type;
+ typedef typename stepper_base_type::operations_type operations_type;
+ typedef typename stepper_base_type::resizer_type resizer_typ;
+
+ #ifndef DOXYGEN_SKIP
+ typedef typename stepper_base_type::stepper_type stepper_type;
+ typedef typename stepper_base_type::wrapped_state_type wrapped_state_type;
+ typedef typename stepper_base_type::wrapped_deriv_type wrapped_deriv_type;
+ #endif
+
+
+ runge_kutta_cash_karp54( const algebra_type &algebra = algebra_type() ) : stepper_base_type(
+ boost::fusion::make_vector( rk54_ck_coefficients_a1<Value>() ,
+ rk54_ck_coefficients_a2<Value>() ,
+ rk54_ck_coefficients_a3<Value>() ,
+ rk54_ck_coefficients_a4<Value>() ,
+ rk54_ck_coefficients_a5<Value>() ) ,
+ rk54_ck_coefficients_b<Value>() , rk54_ck_coefficients_db<Value>() , rk54_ck_coefficients_c<Value>() ,
+ algebra )
+ { }
+};
+
+
+/********** DOXYGEN **********/
+
+/**
+ * \class runge_kutta_cash_karp54
+ * \brief The Runge-Kutta Cash-Karp method.
+ *
+ * The Runge-Kutta Cash-Karp method is one of the standard methods for
+ * solving ordinary differential equations, see
+ * <a href="http://en.wikipedia.org/wiki/Cash%E2%80%93Karp_methods">en.wikipedia.org/wiki/Cash-Karp_methods</a>.
+ * The method is explicit and fulfills the Error Stepper concept. Step size control
+ * is provided but continuous output is not available for this method.
+ *
+ * This class derives from explicit_error_stepper_base and inherits its interface via CRTP (current recurring template pattern).
+ * Furthermore, it derivs from explicit_error_generic_rk which is a generic Runge-Kutta algorithm with error estimation.
+ * For more details see explicit_error_stepper_base and explicit_error_generic_rk.
+ *
+ * \tparam State The state type.
+ * \tparam Value The value type.
+ * \tparam Deriv The type representing the time derivative of the state.
+ * \tparam Time The time representing the independent variable - the time.
+ * \tparam Algebra The algebra type.
+ * \tparam Operations The operations type.
+ * \tparam Resizer The resizer policy type.
+ */
+
+
+ /**
+ * \fn runge_kutta_cash_karp54::runge_kutta_cash_karp54( const algebra_type &algebra )
+ * \brief Constructs the runge_kutta_cash_karp54 class. This constructor can be used as a default
+ * constructor if the algebra has a default constructor.
+ * \param algebra A copy of algebra is made and stored inside explicit_stepper_base.
+ */
+}
+}
+}
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_CASH_KARP54_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/runge_kutta_cash_karp54_classic.hpp b/include/boost/numeric/odeint/stepper/runge_kutta_cash_karp54_classic.hpp
new file mode 100644
index 0000000..80f1a3c
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/runge_kutta_cash_karp54_classic.hpp
@@ -0,0 +1,289 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/runge_kutta_cash_karp54_classic.hpp
+
+ [begin_description]
+ Classical implementation of the Runge-Kutta Cash-Karp 5(4) method.
+ [end_description]
+
+ Copyright 2010-2013 Mario Mulansky
+ Copyright 2010-2013 Karsten Ahnert
+ Copyright 2012 Christoph Koke
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_CASH_KARP54_CLASSIC_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_CASH_KARP54_CLASSIC_HPP_INCLUDED
+
+
+#include <boost/numeric/odeint/util/bind.hpp>
+
+#include <boost/numeric/odeint/stepper/base/explicit_error_stepper_base.hpp>
+#include <boost/numeric/odeint/algebra/range_algebra.hpp>
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/util/state_wrapper.hpp>
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resizer.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+
+
+template<
+class State ,
+class Value = double ,
+class Deriv = State ,
+class Time = Value ,
+class Algebra = typename algebra_dispatcher< State >::algebra_type ,
+class Operations = typename operations_dispatcher< State >::operations_type ,
+class Resizer = initially_resizer
+>
+#ifndef DOXYGEN_SKIP
+class runge_kutta_cash_karp54_classic
+: public explicit_error_stepper_base<
+ runge_kutta_cash_karp54_classic< State , Value , Deriv , Time , Algebra , Operations , Resizer > ,
+ 5 , 5 , 4 , State , Value , Deriv , Time , Algebra , Operations , Resizer >
+#else
+class runge_kutta_cash_karp54_classic : public explicit_error_stepper_base
+#endif
+{
+
+
+public :
+
+ #ifndef DOXYGEN_SKIP
+ typedef explicit_error_stepper_base<
+ runge_kutta_cash_karp54_classic< State , Value , Deriv , Time , Algebra , Operations , Resizer > ,
+ 5 , 5 , 4 , State , Value , Deriv , Time , Algebra , Operations , Resizer > stepper_base_type;
+ #else
+ typedef explicit_error_stepper_base< runge_kutta_cash_karp54_classic< ... > , ... > stepper_base_type;
+ #endif
+
+ typedef typename stepper_base_type::state_type state_type;
+ typedef typename stepper_base_type::value_type value_type;
+ typedef typename stepper_base_type::deriv_type deriv_type;
+ typedef typename stepper_base_type::time_type time_type;
+ typedef typename stepper_base_type::algebra_type algebra_type;
+ typedef typename stepper_base_type::operations_type operations_type;
+ typedef typename stepper_base_type::resizer_type resizer_type;
+
+ #ifndef DOXYGEN_SKIP
+ typedef typename stepper_base_type::wrapped_state_type wrapped_state_type;
+ typedef typename stepper_base_type::wrapped_deriv_type wrapped_deriv_type;
+ typedef typename stepper_base_type::stepper_type stepper_type;
+ #endif
+
+
+ runge_kutta_cash_karp54_classic( const algebra_type &algebra = algebra_type() ) : stepper_base_type( algebra )
+ { }
+
+
+
+ template< class System , class StateIn , class DerivIn , class StateOut , class Err >
+ void do_step_impl( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt , Err &xerr )
+ {
+ const value_type c1 = static_cast<value_type> ( 37 ) / static_cast<value_type>( 378 );
+ const value_type c3 = static_cast<value_type> ( 250 ) / static_cast<value_type>( 621 );
+ const value_type c4 = static_cast<value_type> ( 125 ) / static_cast<value_type>( 594 );
+ const value_type c6 = static_cast<value_type> ( 512 ) / static_cast<value_type>( 1771 );
+
+ const value_type dc1 = c1 - static_cast<value_type> ( 2825 ) / static_cast<value_type>( 27648 );
+ const value_type dc3 = c3 - static_cast<value_type> ( 18575 ) / static_cast<value_type>( 48384 );
+ const value_type dc4 = c4 - static_cast<value_type> ( 13525 ) / static_cast<value_type>( 55296 );
+ const value_type dc5 = static_cast<value_type> ( -277 ) / static_cast<value_type>( 14336 );
+ const value_type dc6 = c6 - static_cast<value_type> ( 1 ) / static_cast<value_type> ( 4 );
+
+ do_step_impl( system , in , dxdt , t , out , dt );
+
+ //error estimate
+ stepper_base_type::m_algebra.for_each6( xerr , dxdt , m_k3.m_v , m_k4.m_v , m_k5.m_v , m_k6.m_v ,
+ typename operations_type::template scale_sum5< time_type , time_type , time_type , time_type , time_type >( dt*dc1 , dt*dc3 , dt*dc4 , dt*dc5 , dt*dc6 ));
+
+ }
+
+
+
+ template< class System , class StateIn , class DerivIn , class StateOut >
+ void do_step_impl( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt )
+ {
+ const value_type a2 = static_cast<value_type> ( 1 ) / static_cast<value_type> ( 5 );
+ const value_type a3 = static_cast<value_type> ( 3 ) / static_cast<value_type> ( 10 );
+ const value_type a4 = static_cast<value_type> ( 3 ) / static_cast<value_type> ( 5 );
+ const value_type a5 = static_cast<value_type> ( 1 );
+ const value_type a6 = static_cast<value_type> ( 7 ) / static_cast<value_type> ( 8 );
+
+ const value_type b21 = static_cast<value_type> ( 1 ) / static_cast<value_type> ( 5 );
+ const value_type b31 = static_cast<value_type> ( 3 ) / static_cast<value_type>( 40 );
+ const value_type b32 = static_cast<value_type> ( 9 ) / static_cast<value_type>( 40 );
+ const value_type b41 = static_cast<value_type> ( 3 ) / static_cast<value_type> ( 10 );
+ const value_type b42 = static_cast<value_type> ( -9 ) / static_cast<value_type> ( 10 );
+ const value_type b43 = static_cast<value_type> ( 6 ) / static_cast<value_type> ( 5 );
+ const value_type b51 = static_cast<value_type> ( -11 ) / static_cast<value_type>( 54 );
+ const value_type b52 = static_cast<value_type> ( 5 ) / static_cast<value_type> ( 2 );
+ const value_type b53 = static_cast<value_type> ( -70 ) / static_cast<value_type>( 27 );
+ const value_type b54 = static_cast<value_type> ( 35 ) / static_cast<value_type>( 27 );
+ const value_type b61 = static_cast<value_type> ( 1631 ) / static_cast<value_type>( 55296 );
+ const value_type b62 = static_cast<value_type> ( 175 ) / static_cast<value_type>( 512 );
+ const value_type b63 = static_cast<value_type> ( 575 ) / static_cast<value_type>( 13824 );
+ const value_type b64 = static_cast<value_type> ( 44275 ) / static_cast<value_type>( 110592 );
+ const value_type b65 = static_cast<value_type> ( 253 ) / static_cast<value_type>( 4096 );
+
+ const value_type c1 = static_cast<value_type> ( 37 ) / static_cast<value_type>( 378 );
+ const value_type c3 = static_cast<value_type> ( 250 ) / static_cast<value_type>( 621 );
+ const value_type c4 = static_cast<value_type> ( 125 ) / static_cast<value_type>( 594 );
+ const value_type c6 = static_cast<value_type> ( 512 ) / static_cast<value_type>( 1771 );
+
+ typename odeint::unwrap_reference< System >::type &sys = system;
+
+ m_resizer.adjust_size( in , detail::bind( &stepper_type::template resize_impl<StateIn> , detail::ref( *this ) , detail::_1 ) );
+
+ //m_x1 = x + dt*b21*dxdt
+ stepper_base_type::m_algebra.for_each3( m_x_tmp.m_v , in , dxdt ,
+ typename operations_type::template scale_sum2< value_type , time_type >( 1.0 , dt*b21 ) );
+
+ sys( m_x_tmp.m_v , m_k2.m_v , t + dt*a2 );
+ // m_x_tmp = x + dt*b31*dxdt + dt*b32*m_x2
+ stepper_base_type::m_algebra.for_each4( m_x_tmp.m_v , in , dxdt , m_k2.m_v ,
+ typename operations_type::template scale_sum3< value_type , time_type , time_type >( 1.0 , dt*b31 , dt*b32 ));
+
+ sys( m_x_tmp.m_v , m_k3.m_v , t + dt*a3 );
+ // m_x_tmp = x + dt * (b41*dxdt + b42*m_x2 + b43*m_x3)
+ stepper_base_type::m_algebra.for_each5( m_x_tmp.m_v , in , dxdt , m_k2.m_v , m_k3.m_v ,
+ typename operations_type::template scale_sum4< value_type , time_type , time_type , time_type >( 1.0 , dt*b41 , dt*b42 , dt*b43 ));
+
+ sys( m_x_tmp.m_v, m_k4.m_v , t + dt*a4 );
+ stepper_base_type::m_algebra.for_each6( m_x_tmp.m_v , in , dxdt , m_k2.m_v , m_k3.m_v , m_k4.m_v ,
+ typename operations_type::template scale_sum5< value_type , time_type , time_type , time_type , time_type >( 1.0 , dt*b51 , dt*b52 , dt*b53 , dt*b54 ));
+
+ sys( m_x_tmp.m_v , m_k5.m_v , t + dt*a5 );
+ stepper_base_type::m_algebra.for_each7( m_x_tmp.m_v , in , dxdt , m_k2.m_v , m_k3.m_v , m_k4.m_v , m_k5.m_v ,
+ typename operations_type::template scale_sum6< value_type , time_type , time_type , time_type , time_type , time_type >( 1.0 , dt*b61 , dt*b62 , dt*b63 , dt*b64 , dt*b65 ));
+
+ sys( m_x_tmp.m_v , m_k6.m_v , t + dt*a6 );
+ stepper_base_type::m_algebra.for_each6( out , in , dxdt , m_k3.m_v , m_k4.m_v , m_k6.m_v ,
+ typename operations_type::template scale_sum5< value_type , time_type , time_type , time_type , time_type >( 1.0 , dt*c1 , dt*c3 , dt*c4 , dt*c6 ));
+
+ }
+
+ /**
+ * \brief Adjust the size of all temporaries in the stepper manually.
+ * \param x A state from which the size of the temporaries to be resized is deduced.
+ */
+ template< class StateIn >
+ void adjust_size( const StateIn &x )
+ {
+ resize_impl( x );
+ stepper_base_type::adjust_size( x );
+ }
+
+private:
+
+ template< class StateIn >
+ bool resize_impl( const StateIn &x )
+ {
+ bool resized = false;
+ resized |= adjust_size_by_resizeability( m_x_tmp , x , typename is_resizeable<state_type>::type() );
+ resized |= adjust_size_by_resizeability( m_k2 , x , typename is_resizeable<deriv_type>::type() );
+ resized |= adjust_size_by_resizeability( m_k3 , x , typename is_resizeable<deriv_type>::type() );
+ resized |= adjust_size_by_resizeability( m_k4 , x , typename is_resizeable<deriv_type>::type() );
+ resized |= adjust_size_by_resizeability( m_k5 , x , typename is_resizeable<deriv_type>::type() );
+ resized |= adjust_size_by_resizeability( m_k6 , x , typename is_resizeable<deriv_type>::type() );
+ return resized;
+ }
+
+
+ wrapped_state_type m_x_tmp;
+ wrapped_deriv_type m_k2, m_k3, m_k4, m_k5, m_k6;
+ resizer_type m_resizer;
+
+};
+
+
+
+/************ DOXYGEN *************/
+
+/**
+ * \class runge_kutta_cash_karp54_classic
+ * \brief The Runge-Kutta Cash-Karp method implemented without the generic Runge-Kutta algorithm.
+ *
+ * The Runge-Kutta Cash-Karp method is one of the standard methods for
+ * solving ordinary differential equations, see
+ * <a href="http://en.wikipedia.org/wiki/Cash%E2%80%93Karp_method">en.wikipedia.org/wiki/Cash-Karp_method</a>.
+ * The method is explicit and fulfills the Error Stepper concept. Step size control
+ * is provided but continuous output is not available for this method.
+ *
+ * This class derives from explicit_error_stepper_base and inherits its interface via CRTP (current recurring
+ * template pattern). This class implements the method directly, hence the generic Runge-Kutta algorithm is not used.
+ *
+ * \tparam State The state type.
+ * \tparam Value The value type.
+ * \tparam Deriv The type representing the time derivative of the state.
+ * \tparam Time The time representing the independent variable - the time.
+ * \tparam Algebra The algebra type.
+ * \tparam Operations The operations type.
+ * \tparam Resizer The resizer policy type.
+ */
+
+
+ /**
+ * \fn runge_kutta_cash_karp54_classic::runge_kutta_cash_karp54_classic( const algebra_type &algebra )
+ * \brief Constructs the runge_kutta_cash_karp54_classic class. This constructor can be used as a default
+ * constructor if the algebra has a default constructor.
+ * \param algebra A copy of algebra is made and stored inside explicit_stepper_base.
+ */
+
+
+ /**
+ * \fn runge_kutta_cash_karp54_classic::do_step_impl( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt , Err &xerr )
+ * \brief This method performs one step. The derivative `dxdt` of `in` at the time `t` is passed to the method.
+ *
+ * The result is updated out-of-place, hence the input is in `in` and the output in `out`. Futhermore, an
+ * estimation of the error is stored in `xerr`.
+ * Access to this step functionality is provided by explicit_error_stepper_base and
+ * `do_step_impl` should not be called directly.
+
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param in The state of the ODE which should be solved. in is not modified in this method
+ * \param dxdt The derivative of x at t.
+ * \param t The value of the time, at which the step should be performed.
+ * \param out The result of the step is written in out.
+ * \param dt The step size.
+ * \param xerr The result of the error estimation is written in xerr.
+ */
+
+ /**
+ * \fn runge_kutta_cash_karp54_classic::do_step_impl( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt )
+ * \brief This method performs one step. The derivative `dxdt` of `in` at the time `t` is passed to the method.
+ * The result is updated out-of-place, hence the input is in `in` and the output in `out`.
+ * Access to this step functionality is provided by explicit_error_stepper_base and
+ * `do_step_impl` should not be called directly.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param in The state of the ODE which should be solved. in is not modified in this method
+ * \param dxdt The derivative of x at t.
+ * \param t The value of the time, at which the step should be performed.
+ * \param out The result of the step is written in out.
+ * \param dt The step size.
+ */
+
+} // odeint
+} // numeric
+} // boost
+
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_CASH_KARP54_CLASSIC_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp b/include/boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp
new file mode 100644
index 0000000..260cd74
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp
@@ -0,0 +1,403 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp
+
+ [begin_description]
+ Implementation of the Dormand-Prince 5(4) method. This stepper can also be used with the dense-output controlled stepper.
+ [end_description]
+
+ Copyright 2010-2013 Karsten Ahnert
+ Copyright 2010-2013 Mario Mulansky
+ Copyright 2012 Christoph Koke
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_DOPRI5_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_DOPRI5_HPP_INCLUDED
+
+
+#include <boost/numeric/odeint/util/bind.hpp>
+
+#include <boost/numeric/odeint/stepper/base/explicit_error_stepper_fsal_base.hpp>
+#include <boost/numeric/odeint/algebra/range_algebra.hpp>
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+
+#include <boost/numeric/odeint/util/state_wrapper.hpp>
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resizer.hpp>
+#include <boost/numeric/odeint/util/same_instance.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+
+template<
+class State ,
+class Value = double ,
+class Deriv = State ,
+class Time = Value ,
+class Algebra = typename algebra_dispatcher< State >::algebra_type ,
+class Operations = typename operations_dispatcher< State >::operations_type ,
+class Resizer = initially_resizer
+>
+class runge_kutta_dopri5
+#ifndef DOXYGEN_SKIP
+: public explicit_error_stepper_fsal_base<
+ runge_kutta_dopri5< State , Value , Deriv , Time , Algebra , Operations , Resizer > ,
+ 5 , 5 , 4 , State , Value , Deriv , Time , Algebra , Operations , Resizer >
+#else
+: public explicit_error_stepper_fsal_base
+#endif
+{
+
+public :
+
+ #ifndef DOXYGEN_SKIP
+ typedef explicit_error_stepper_fsal_base<
+ runge_kutta_dopri5< State , Value , Deriv , Time , Algebra , Operations , Resizer > ,
+ 5 , 5 , 4 , State , Value , Deriv , Time , Algebra , Operations , Resizer > stepper_base_type;
+ #else
+ typedef explicit_error_stepper_fsal_base< runge_kutta_dopri5< ... > , ... > stepper_base_type;
+ #endif
+
+ typedef typename stepper_base_type::state_type state_type;
+ typedef typename stepper_base_type::value_type value_type;
+ typedef typename stepper_base_type::deriv_type deriv_type;
+ typedef typename stepper_base_type::time_type time_type;
+ typedef typename stepper_base_type::algebra_type algebra_type;
+ typedef typename stepper_base_type::operations_type operations_type;
+ typedef typename stepper_base_type::resizer_type resizer_type;
+
+ #ifndef DOXYGEN_SKIP
+ typedef typename stepper_base_type::stepper_type stepper_type;
+ typedef typename stepper_base_type::wrapped_state_type wrapped_state_type;
+ typedef typename stepper_base_type::wrapped_deriv_type wrapped_deriv_type;
+ #endif // DOXYGEN_SKIP
+
+
+ runge_kutta_dopri5( const algebra_type &algebra = algebra_type() ) : stepper_base_type( algebra )
+ { }
+
+
+ template< class System , class StateIn , class DerivIn , class StateOut , class DerivOut >
+ void do_step_impl( System system , const StateIn &in , const DerivIn &dxdt_in , time_type t ,
+ StateOut &out , DerivOut &dxdt_out , time_type dt )
+ {
+ const value_type a2 = static_cast<value_type> ( 1 ) / static_cast<value_type>( 5 );
+ const value_type a3 = static_cast<value_type> ( 3 ) / static_cast<value_type> ( 10 );
+ const value_type a4 = static_cast<value_type> ( 4 ) / static_cast<value_type> ( 5 );
+ const value_type a5 = static_cast<value_type> ( 8 )/static_cast<value_type> ( 9 );
+
+ const value_type b21 = static_cast<value_type> ( 1 ) / static_cast<value_type> ( 5 );
+
+ const value_type b31 = static_cast<value_type> ( 3 ) / static_cast<value_type>( 40 );
+ const value_type b32 = static_cast<value_type> ( 9 ) / static_cast<value_type>( 40 );
+
+ const value_type b41 = static_cast<value_type> ( 44 ) / static_cast<value_type> ( 45 );
+ const value_type b42 = static_cast<value_type> ( -56 ) / static_cast<value_type> ( 15 );
+ const value_type b43 = static_cast<value_type> ( 32 ) / static_cast<value_type> ( 9 );
+
+ const value_type b51 = static_cast<value_type> ( 19372 ) / static_cast<value_type>( 6561 );
+ const value_type b52 = static_cast<value_type> ( -25360 ) / static_cast<value_type> ( 2187 );
+ const value_type b53 = static_cast<value_type> ( 64448 ) / static_cast<value_type>( 6561 );
+ const value_type b54 = static_cast<value_type> ( -212 ) / static_cast<value_type>( 729 );
+
+ const value_type b61 = static_cast<value_type> ( 9017 ) / static_cast<value_type>( 3168 );
+ const value_type b62 = static_cast<value_type> ( -355 ) / static_cast<value_type>( 33 );
+ const value_type b63 = static_cast<value_type> ( 46732 ) / static_cast<value_type>( 5247 );
+ const value_type b64 = static_cast<value_type> ( 49 ) / static_cast<value_type>( 176 );
+ const value_type b65 = static_cast<value_type> ( -5103 ) / static_cast<value_type>( 18656 );
+
+ const value_type c1 = static_cast<value_type> ( 35 ) / static_cast<value_type>( 384 );
+ const value_type c3 = static_cast<value_type> ( 500 ) / static_cast<value_type>( 1113 );
+ const value_type c4 = static_cast<value_type> ( 125 ) / static_cast<value_type>( 192 );
+ const value_type c5 = static_cast<value_type> ( -2187 ) / static_cast<value_type>( 6784 );
+ const value_type c6 = static_cast<value_type> ( 11 ) / static_cast<value_type>( 84 );
+
+ typename odeint::unwrap_reference< System >::type &sys = system;
+
+ m_k_x_tmp_resizer.adjust_size( in , detail::bind( &stepper_type::template resize_k_x_tmp_impl<StateIn> , detail::ref( *this ) , detail::_1 ) );
+
+ //m_x_tmp = x + dt*b21*dxdt
+ stepper_base_type::m_algebra.for_each3( m_x_tmp.m_v , in , dxdt_in ,
+ typename operations_type::template scale_sum2< value_type , time_type >( 1.0 , dt*b21 ) );
+
+ sys( m_x_tmp.m_v , m_k2.m_v , t + dt*a2 );
+ // m_x_tmp = x + dt*b31*dxdt + dt*b32*m_k2
+ stepper_base_type::m_algebra.for_each4( m_x_tmp.m_v , in , dxdt_in , m_k2.m_v ,
+ typename operations_type::template scale_sum3< value_type , time_type , time_type >( 1.0 , dt*b31 , dt*b32 ));
+
+ sys( m_x_tmp.m_v , m_k3.m_v , t + dt*a3 );
+ // m_x_tmp = x + dt * (b41*dxdt + b42*m_k2 + b43*m_k3)
+ stepper_base_type::m_algebra.for_each5( m_x_tmp.m_v , in , dxdt_in , m_k2.m_v , m_k3.m_v ,
+ typename operations_type::template scale_sum4< value_type , time_type , time_type , time_type >( 1.0 , dt*b41 , dt*b42 , dt*b43 ));
+
+ sys( m_x_tmp.m_v, m_k4.m_v , t + dt*a4 );
+ stepper_base_type::m_algebra.for_each6( m_x_tmp.m_v , in , dxdt_in , m_k2.m_v , m_k3.m_v , m_k4.m_v ,
+ typename operations_type::template scale_sum5< value_type , time_type , time_type , time_type , time_type >( 1.0 , dt*b51 , dt*b52 , dt*b53 , dt*b54 ));
+
+ sys( m_x_tmp.m_v , m_k5.m_v , t + dt*a5 );
+ stepper_base_type::m_algebra.for_each7( m_x_tmp.m_v , in , dxdt_in , m_k2.m_v , m_k3.m_v , m_k4.m_v , m_k5.m_v ,
+ typename operations_type::template scale_sum6< value_type , time_type , time_type , time_type , time_type , time_type >( 1.0 , dt*b61 , dt*b62 , dt*b63 , dt*b64 , dt*b65 ));
+
+ sys( m_x_tmp.m_v , m_k6.m_v , t + dt );
+ stepper_base_type::m_algebra.for_each7( out , in , dxdt_in , m_k3.m_v , m_k4.m_v , m_k5.m_v , m_k6.m_v ,
+ typename operations_type::template scale_sum6< value_type , time_type , time_type , time_type , time_type , time_type >( 1.0 , dt*c1 , dt*c3 , dt*c4 , dt*c5 , dt*c6 ));
+
+ // the new derivative
+ sys( out , dxdt_out , t + dt );
+ }
+
+
+
+ template< class System , class StateIn , class DerivIn , class StateOut , class DerivOut , class Err >
+ void do_step_impl( System system , const StateIn &in , const DerivIn &dxdt_in , time_type t ,
+ StateOut &out , DerivOut &dxdt_out , time_type dt , Err &xerr )
+ {
+ const value_type c1 = static_cast<value_type> ( 35 ) / static_cast<value_type>( 384 );
+ const value_type c3 = static_cast<value_type> ( 500 ) / static_cast<value_type>( 1113 );
+ const value_type c4 = static_cast<value_type> ( 125 ) / static_cast<value_type>( 192 );
+ const value_type c5 = static_cast<value_type> ( -2187 ) / static_cast<value_type>( 6784 );
+ const value_type c6 = static_cast<value_type> ( 11 ) / static_cast<value_type>( 84 );
+
+ const value_type dc1 = c1 - static_cast<value_type> ( 5179 ) / static_cast<value_type>( 57600 );
+ const value_type dc3 = c3 - static_cast<value_type> ( 7571 ) / static_cast<value_type>( 16695 );
+ const value_type dc4 = c4 - static_cast<value_type> ( 393 ) / static_cast<value_type>( 640 );
+ const value_type dc5 = c5 - static_cast<value_type> ( -92097 ) / static_cast<value_type>( 339200 );
+ const value_type dc6 = c6 - static_cast<value_type> ( 187 ) / static_cast<value_type>( 2100 );
+ const value_type dc7 = static_cast<value_type>( -1 ) / static_cast<value_type> ( 40 );
+
+ /* ToDo: copy only if &dxdt_in == &dxdt_out ? */
+ if( same_instance( dxdt_in , dxdt_out ) )
+ {
+ m_dxdt_tmp_resizer.adjust_size( in , detail::bind( &stepper_type::template resize_dxdt_tmp_impl<StateIn> , detail::ref( *this ) , detail::_1 ) );
+ boost::numeric::odeint::copy( dxdt_in , m_dxdt_tmp.m_v );
+ do_step_impl( system , in , dxdt_in , t , out , dxdt_out , dt );
+ //error estimate
+ stepper_base_type::m_algebra.for_each7( xerr , m_dxdt_tmp.m_v , m_k3.m_v , m_k4.m_v , m_k5.m_v , m_k6.m_v , dxdt_out ,
+ typename operations_type::template scale_sum6< time_type , time_type , time_type , time_type , time_type , time_type >( dt*dc1 , dt*dc3 , dt*dc4 , dt*dc5 , dt*dc6 , dt*dc7 ) );
+
+ }
+ else
+ {
+ do_step_impl( system , in , dxdt_in , t , out , dxdt_out , dt );
+ //error estimate
+ stepper_base_type::m_algebra.for_each7( xerr , dxdt_in , m_k3.m_v , m_k4.m_v , m_k5.m_v , m_k6.m_v , dxdt_out ,
+ typename operations_type::template scale_sum6< time_type , time_type , time_type , time_type , time_type , time_type >( dt*dc1 , dt*dc3 , dt*dc4 , dt*dc5 , dt*dc6 , dt*dc7 ) );
+
+ }
+
+ }
+
+
+ /*
+ * Calculates Dense-Output for Dopri5
+ *
+ * See Hairer, Norsett, Wanner: Solving Ordinary Differential Equations, Nonstiff Problems. I, p.191/192
+ *
+ * y(t+theta) = y(t) + h * sum_i^7 b_i(theta) * k_i
+ *
+ * A = theta^2 * ( 3 - 2 theta )
+ * B = theta^2 * ( theta - 1 )
+ * C = theta^2 * ( theta - 1 )^2
+ * D = theta * ( theta - 1 )^2
+ *
+ * b_1( theta ) = A * b_1 - C * X1( theta ) + D
+ * b_2( theta ) = 0
+ * b_3( theta ) = A * b_3 + C * X3( theta )
+ * b_4( theta ) = A * b_4 - C * X4( theta )
+ * b_5( theta ) = A * b_5 + C * X5( theta )
+ * b_6( theta ) = A * b_6 - C * X6( theta )
+ * b_7( theta ) = B + C * X7( theta )
+ *
+ * An alternative Method is described in:
+ *
+ * www-m2.ma.tum.de/homepages/simeon/numerik3/kap3.ps
+ */
+ template< class StateOut , class StateIn1 , class DerivIn1 , class StateIn2 , class DerivIn2 >
+ void calc_state( time_type t , StateOut &x ,
+ const StateIn1 &x_old , const DerivIn1 &deriv_old , time_type t_old ,
+ const StateIn2 & /* x_new */ , const DerivIn2 &deriv_new , time_type t_new ) const
+ {
+ const value_type b1 = static_cast<value_type> ( 35 ) / static_cast<value_type>( 384 );
+ const value_type b3 = static_cast<value_type> ( 500 ) / static_cast<value_type>( 1113 );
+ const value_type b4 = static_cast<value_type> ( 125 ) / static_cast<value_type>( 192 );
+ const value_type b5 = static_cast<value_type> ( -2187 ) / static_cast<value_type>( 6784 );
+ const value_type b6 = static_cast<value_type> ( 11 ) / static_cast<value_type>( 84 );
+
+ const time_type dt = ( t_new - t_old );
+ const value_type theta = ( t - t_old ) / dt;
+ const value_type X1 = static_cast< value_type >( 5 ) * ( static_cast< value_type >( 2558722523LL ) - static_cast< value_type >( 31403016 ) * theta ) / static_cast< value_type >( 11282082432LL );
+ const value_type X3 = static_cast< value_type >( 100 ) * ( static_cast< value_type >( 882725551 ) - static_cast< value_type >( 15701508 ) * theta ) / static_cast< value_type >( 32700410799LL );
+ const value_type X4 = static_cast< value_type >( 25 ) * ( static_cast< value_type >( 443332067 ) - static_cast< value_type >( 31403016 ) * theta ) / static_cast< value_type >( 1880347072LL ) ;
+ const value_type X5 = static_cast< value_type >( 32805 ) * ( static_cast< value_type >( 23143187 ) - static_cast< value_type >( 3489224 ) * theta ) / static_cast< value_type >( 199316789632LL );
+ const value_type X6 = static_cast< value_type >( 55 ) * ( static_cast< value_type >( 29972135 ) - static_cast< value_type >( 7076736 ) * theta ) / static_cast< value_type >( 822651844 );
+ const value_type X7 = static_cast< value_type >( 10 ) * ( static_cast< value_type >( 7414447 ) - static_cast< value_type >( 829305 ) * theta ) / static_cast< value_type >( 29380423 );
+
+ const value_type theta_m_1 = theta - static_cast< value_type >( 1 );
+ const value_type theta_sq = theta * theta;
+ const value_type A = theta_sq * ( static_cast< value_type >( 3 ) - static_cast< value_type >( 2 ) * theta );
+ const value_type B = theta_sq * theta_m_1;
+ const value_type C = theta_sq * theta_m_1 * theta_m_1;
+ const value_type D = theta * theta_m_1 * theta_m_1;
+
+ const value_type b1_theta = A * b1 - C * X1 + D;
+ const value_type b3_theta = A * b3 + C * X3;
+ const value_type b4_theta = A * b4 - C * X4;
+ const value_type b5_theta = A * b5 + C * X5;
+ const value_type b6_theta = A * b6 - C * X6;
+ const value_type b7_theta = B + C * X7;
+
+ // const state_type &k1 = *m_old_deriv;
+ // const state_type &k3 = dopri5().m_k3;
+ // const state_type &k4 = dopri5().m_k4;
+ // const state_type &k5 = dopri5().m_k5;
+ // const state_type &k6 = dopri5().m_k6;
+ // const state_type &k7 = *m_current_deriv;
+
+ stepper_base_type::m_algebra.for_each8( x , x_old , deriv_old , m_k3.m_v , m_k4.m_v , m_k5.m_v , m_k6.m_v , deriv_new ,
+ typename operations_type::template scale_sum7< value_type , time_type , time_type , time_type , time_type , time_type , time_type >( 1.0 , dt * b1_theta , dt * b3_theta , dt * b4_theta , dt * b5_theta , dt * b6_theta , dt * b7_theta ) );
+ }
+
+
+ template< class StateIn >
+ void adjust_size( const StateIn &x )
+ {
+ resize_k_x_tmp_impl( x );
+ resize_dxdt_tmp_impl( x );
+ stepper_base_type::adjust_size( x );
+ }
+
+
+private:
+
+ template< class StateIn >
+ bool resize_k_x_tmp_impl( const StateIn &x )
+ {
+ bool resized = false;
+ resized |= adjust_size_by_resizeability( m_x_tmp , x , typename is_resizeable<state_type>::type() );
+ resized |= adjust_size_by_resizeability( m_k2 , x , typename is_resizeable<deriv_type>::type() );
+ resized |= adjust_size_by_resizeability( m_k3 , x , typename is_resizeable<deriv_type>::type() );
+ resized |= adjust_size_by_resizeability( m_k4 , x , typename is_resizeable<deriv_type>::type() );
+ resized |= adjust_size_by_resizeability( m_k5 , x , typename is_resizeable<deriv_type>::type() );
+ resized |= adjust_size_by_resizeability( m_k6 , x , typename is_resizeable<deriv_type>::type() );
+ return resized;
+ }
+
+ template< class StateIn >
+ bool resize_dxdt_tmp_impl( const StateIn &x )
+ {
+ return adjust_size_by_resizeability( m_dxdt_tmp , x , typename is_resizeable<deriv_type>::type() );
+ }
+
+
+
+ wrapped_state_type m_x_tmp;
+ wrapped_deriv_type m_k2 , m_k3 , m_k4 , m_k5 , m_k6 ;
+ wrapped_deriv_type m_dxdt_tmp;
+ resizer_type m_k_x_tmp_resizer;
+ resizer_type m_dxdt_tmp_resizer;
+};
+
+
+
+/************* DOXYGEN ************/
+/**
+ * \class runge_kutta_dopri5
+ * \brief The Runge-Kutta Dormand-Prince 5 method.
+ *
+ * The Runge-Kutta Dormand-Prince 5 method is a very popular method for solving ODEs, see
+ * <a href=""></a>.
+ * The method is explicit and fulfills the Error Stepper concept. Step size control
+ * is provided but continuous output is available which make this method favourable for many applications.
+ *
+ * This class derives from explicit_error_stepper_fsal_base and inherits its interface via CRTP (current recurring
+ * template pattern). The method possesses the FSAL (first-same-as-last) property. See
+ * explicit_error_stepper_fsal_base for more details.
+ *
+ * \tparam State The state type.
+ * \tparam Value The value type.
+ * \tparam Deriv The type representing the time derivative of the state.
+ * \tparam Time The time representing the independent variable - the time.
+ * \tparam Algebra The algebra type.
+ * \tparam Operations The operations type.
+ * \tparam Resizer The resizer policy type.
+ */
+
+
+ /**
+ * \fn runge_kutta_dopri5::runge_kutta_dopri5( const algebra_type &algebra )
+ * \brief Constructs the runge_kutta_dopri5 class. This constructor can be used as a default
+ * constructor if the algebra has a default constructor.
+ * \param algebra A copy of algebra is made and stored inside explicit_stepper_base.
+ */
+
+ /**
+ * \fn runge_kutta_dopri5::do_step_impl( System system , const StateIn &in , const DerivIn &dxdt_in , time_type t , StateOut &out , DerivOut &dxdt_out , time_type dt )
+ * \brief This method performs one step. The derivative `dxdt_in` of `in` at the time `t` is passed to the
+ * method. The result is updated out-of-place, hence the input is in `in` and the output in `out`. Furthermore,
+ * the derivative is update out-of-place, hence the input is assumed to be in `dxdt_in` and the output in
+ * `dxdt_out`.
+ * Access to this step functionality is provided by explicit_error_stepper_fsal_base and
+ * `do_step_impl` should not be called directly.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param in The state of the ODE which should be solved. in is not modified in this method
+ * \param dxdt_in The derivative of x at t. dxdt_in is not modified by this method
+ * \param t The value of the time, at which the step should be performed.
+ * \param out The result of the step is written in out.
+ * \param dxdt_out The result of the new derivative at time t+dt.
+ * \param dt The step size.
+ */
+
+ /**
+ * \fn runge_kutta_dopri5::do_step_impl( System system , const StateIn &in , const DerivIn &dxdt_in , time_type t , StateOut &out , DerivOut &dxdt_out , time_type dt , Err &xerr )
+ * \brief This method performs one step. The derivative `dxdt_in` of `in` at the time `t` is passed to the
+ * method. The result is updated out-of-place, hence the input is in `in` and the output in `out`. Furthermore,
+ * the derivative is update out-of-place, hence the input is assumed to be in `dxdt_in` and the output in
+ * `dxdt_out`.
+ * Access to this step functionality is provided by explicit_error_stepper_fsal_base and
+ * `do_step_impl` should not be called directly.
+ * An estimation of the error is calculated.
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
+ * Simple System concept.
+ * \param in The state of the ODE which should be solved. in is not modified in this method
+ * \param dxdt_in The derivative of x at t. dxdt_in is not modified by this method
+ * \param t The value of the time, at which the step should be performed.
+ * \param out The result of the step is written in out.
+ * \param dxdt_out The result of the new derivative at time t+dt.
+ * \param dt The step size.
+ * \param xerr An estimation of the error.
+ */
+
+ /**
+ * \fn runge_kutta_dopri5::calc_state( time_type t , StateOut &x , const StateIn1 &x_old , const DerivIn1 &deriv_old , time_type t_old , const StateIn2 & , const DerivIn2 &deriv_new , time_type t_new ) const
+ * \brief This method is used for continuous output and it calculates the state `x` at a time `t` from the
+ * knowledge of two states `old_state` and `current_state` at time points `t_old` and `t_new`. It also uses
+ * internal variables to calculate the result. Hence this method must be called after two successful `do_step`
+ * calls.
+ */
+
+ /**
+ * \fn runge_kutta_dopri5::adjust_size( const StateIn &x )
+ * \brief Adjust the size of all temporaries in the stepper manually.
+ * \param x A state from which the size of the temporaries to be resized is deduced.
+ */
+
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_DOPRI5_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/runge_kutta_fehlberg78.hpp b/include/boost/numeric/odeint/stepper/runge_kutta_fehlberg78.hpp
new file mode 100644
index 0000000..f2f8251
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/runge_kutta_fehlberg78.hpp
@@ -0,0 +1,374 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/runge_kutta_fehlberg87.hpp
+
+ [begin_description]
+ Implementation of the Runge-Kutta-Fehlberg stepper with the generic stepper.
+ [end_description]
+
+ Copyright 2011-2013 Mario Mulansky
+ Copyright 2012-2013 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_FEHLBERG87_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_FEHLBERG87_HPP_INCLUDED
+
+
+#include <boost/fusion/container/vector.hpp>
+#include <boost/fusion/container/generation/make_vector.hpp>
+
+#include <boost/numeric/odeint/stepper/explicit_error_generic_rk.hpp>
+#include <boost/numeric/odeint/algebra/range_algebra.hpp>
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
+
+#include <boost/array.hpp>
+
+#include <boost/numeric/odeint/util/state_wrapper.hpp>
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resizer.hpp>
+
+
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+#ifndef DOXYGEN_SKIP
+template< class Value = double >
+struct rk78_coefficients_a1 : boost::array< Value , 1 >
+{
+ rk78_coefficients_a1( void )
+ {
+ (*this)[0] = static_cast< Value >( 2 )/static_cast< Value >( 27 );
+ }
+};
+
+template< class Value = double >
+struct rk78_coefficients_a2 : boost::array< Value , 2 >
+{
+ rk78_coefficients_a2( void )
+ {
+ (*this)[0] = static_cast< Value >( 1 )/static_cast< Value >( 36 );
+ (*this)[1] = static_cast< Value >( 1 )/static_cast< Value >( 12 );
+ }
+};
+
+
+template< class Value = double >
+struct rk78_coefficients_a3 : boost::array< Value , 3 >
+{
+ rk78_coefficients_a3( void )
+ {
+ (*this)[0] = static_cast< Value >( 1 )/static_cast< Value >( 24 );
+ (*this)[1] = static_cast< Value >( 0 );
+ (*this)[2] = static_cast< Value >( 1 )/static_cast< Value >( 8 );
+ }
+};
+
+template< class Value = double >
+struct rk78_coefficients_a4 : boost::array< Value , 4 >
+{
+ rk78_coefficients_a4( void )
+ {
+ (*this)[0] = static_cast< Value >( 5 )/static_cast< Value >( 12 );
+ (*this)[1] = static_cast< Value >( 0 );
+ (*this)[2] = static_cast< Value >( -25 )/static_cast< Value >( 16 );
+ (*this)[3] = static_cast< Value >( 25 )/static_cast< Value >( 16 );
+ }
+};
+
+template< class Value = double >
+struct rk78_coefficients_a5 : boost::array< Value , 5 >
+{
+ rk78_coefficients_a5( void )
+ {
+ (*this)[0] = static_cast< Value >( 1 )/static_cast< Value >( 20 );
+ (*this)[1] = static_cast< Value >( 0 );
+ (*this)[2] = static_cast< Value >( 0 );
+ (*this)[3] = static_cast< Value >( 1 )/static_cast< Value >( 4 );
+ (*this)[4] = static_cast< Value >( 1 )/static_cast< Value >( 5 );
+ }
+};
+
+
+template< class Value = double >
+struct rk78_coefficients_a6 : boost::array< Value , 6 >
+{
+ rk78_coefficients_a6( void )
+ {
+ (*this)[0] = static_cast< Value >( -25 )/static_cast< Value >( 108 );
+ (*this)[1] = static_cast< Value >( 0 );
+ (*this)[2] = static_cast< Value >( 0 );
+ (*this)[3] = static_cast< Value >( 125 )/static_cast< Value >( 108 );
+ (*this)[4] = static_cast< Value >( -65 )/static_cast< Value >( 27 );
+ (*this)[5] = static_cast< Value >( 125 )/static_cast< Value >( 54 );
+ }
+};
+
+template< class Value = double >
+struct rk78_coefficients_a7 : boost::array< Value , 7 >
+{
+ rk78_coefficients_a7( void )
+ {
+ (*this)[0] = static_cast< Value >( 31 )/static_cast< Value >( 300 );
+ (*this)[1] = static_cast< Value >( 0 );
+ (*this)[2] = static_cast< Value >( 0 );
+ (*this)[3] = static_cast< Value >( 0 );
+ (*this)[4] = static_cast< Value >( 61 )/static_cast< Value >( 225 );
+ (*this)[5] = static_cast< Value >( -2 )/static_cast< Value >( 9 );
+ (*this)[6] = static_cast< Value >( 13 )/static_cast< Value >( 900 );
+ }
+};
+
+template< class Value = double >
+struct rk78_coefficients_a8 : boost::array< Value , 8 >
+{
+ rk78_coefficients_a8( void )
+ {
+ (*this)[0] = static_cast< Value >( 2 );
+ (*this)[1] = static_cast< Value >( 0 );
+ (*this)[2] = static_cast< Value >( 0 );
+ (*this)[3] = static_cast< Value >( -53 )/static_cast< Value >( 6 );
+ (*this)[4] = static_cast< Value >( 704 )/static_cast< Value >( 45 );
+ (*this)[5] = static_cast< Value >( -107 )/static_cast< Value >( 9 );
+ (*this)[6] = static_cast< Value >( 67 )/static_cast< Value >( 90 );
+ (*this)[7] = static_cast< Value >( 3 );
+ }
+};
+
+template< class Value = double >
+struct rk78_coefficients_a9 : boost::array< Value , 9 >
+{
+ rk78_coefficients_a9( void )
+ {
+ (*this)[0] = static_cast< Value >( -91 )/static_cast< Value >( 108 );
+ (*this)[1] = static_cast< Value >( 0 );
+ (*this)[2] = static_cast< Value >( 0 );
+ (*this)[3] = static_cast< Value >( 23 )/static_cast< Value >( 108 );
+ (*this)[4] = static_cast< Value >( -976 )/static_cast< Value >( 135 );
+ (*this)[5] = static_cast< Value >( 311 )/static_cast< Value >( 54 );
+ (*this)[6] = static_cast< Value >( -19 )/static_cast< Value >( 60 );
+ (*this)[7] = static_cast< Value >( 17 )/static_cast< Value >( 6 );
+ (*this)[8] = static_cast< Value >( -1 )/static_cast< Value >( 12 );
+ }
+};
+
+template< class Value = double >
+struct rk78_coefficients_a10 : boost::array< Value , 10 >
+{
+ rk78_coefficients_a10( void )
+ {
+ (*this)[0] = static_cast< Value >( 2383 )/static_cast< Value >( 4100 );
+ (*this)[1] = static_cast< Value >( 0 );
+ (*this)[2] = static_cast< Value >( 0 );
+ (*this)[3] = static_cast< Value >( -341 )/static_cast< Value >( 164 );
+ (*this)[4] = static_cast< Value >( 4496 )/static_cast< Value >( 1025 );
+ (*this)[5] = static_cast< Value >( -301 )/static_cast< Value >( 82 );
+ (*this)[6] = static_cast< Value >( 2133 )/static_cast< Value >( 4100 );
+ (*this)[7] = static_cast< Value >( 45 )/static_cast< Value >( 82 );
+ (*this)[8] = static_cast< Value >( 45 )/static_cast< Value >( 164 );
+ (*this)[9] = static_cast< Value >( 18 )/static_cast< Value >( 41 );
+ }
+};
+
+template< class Value = double >
+struct rk78_coefficients_a11 : boost::array< Value , 11 >
+{
+ rk78_coefficients_a11( void )
+ {
+ (*this)[0] = static_cast< Value >( 3 )/static_cast< Value >( 205 );
+ (*this)[1] = static_cast< Value >( 0 );
+ (*this)[2] = static_cast< Value >( 0 );
+ (*this)[3] = static_cast< Value >( 0 );
+ (*this)[4] = static_cast< Value >( 0 );
+ (*this)[5] = static_cast< Value >( -6 )/static_cast< Value >( 41 );
+ (*this)[6] = static_cast< Value >( -3 )/static_cast< Value >( 205 );
+ (*this)[7] = static_cast< Value >( -3 )/static_cast< Value >( 41 );
+ (*this)[8] = static_cast< Value >( 3 )/static_cast< Value >( 41 );
+ (*this)[9] = static_cast< Value >( 6 )/static_cast< Value >( 41 );
+ (*this)[10] = static_cast< Value >( 0 );
+ }
+};
+
+template< class Value = double >
+struct rk78_coefficients_a12 : boost::array< Value , 12 >
+{
+ rk78_coefficients_a12( void )
+ {
+ (*this)[0] = static_cast< Value >( -1777 )/static_cast< Value >( 4100 );
+ (*this)[1] = static_cast< Value >( 0 );
+ (*this)[2] = static_cast< Value >( 0 );
+ (*this)[3] = static_cast< Value >( -341 )/static_cast< Value >( 164 );
+ (*this)[4] = static_cast< Value >( 4496 )/static_cast< Value >( 1025 );
+ (*this)[5] = static_cast< Value >( -289 )/static_cast< Value >( 82 );
+ (*this)[6] = static_cast< Value >( 2193 )/static_cast< Value >( 4100 );
+ (*this)[7] = static_cast< Value >( 51 )/static_cast< Value >( 82 );
+ (*this)[8] = static_cast< Value >( 33 )/static_cast< Value >( 164 );
+ (*this)[9] = static_cast< Value >( 12 )/static_cast< Value >( 41 );
+ (*this)[10] = static_cast< Value >( 0 );
+ (*this)[11] = static_cast< Value >( 1 );
+ }
+};
+
+template< class Value = double >
+struct rk78_coefficients_b : boost::array< Value , 13 >
+{
+ rk78_coefficients_b( void )
+ {
+ (*this)[0] = static_cast< Value >( 0 );
+ (*this)[1] = static_cast< Value >( 0 );
+ (*this)[2] = static_cast< Value >( 0 );
+ (*this)[3] = static_cast< Value >( 0 );
+ (*this)[4] = static_cast< Value >( 0 );
+ (*this)[5] = static_cast< Value >( 34 )/static_cast<Value>( 105 );
+ (*this)[6] = static_cast< Value >( 9 )/static_cast<Value>( 35 );
+ (*this)[7] = static_cast< Value >( 9 )/static_cast<Value>( 35 );
+ (*this)[8] = static_cast< Value >( 9 )/static_cast<Value>( 280 );
+ (*this)[9] = static_cast< Value >( 9 )/static_cast<Value>( 280 );
+ (*this)[10] = static_cast< Value >( 0 );
+ (*this)[11] = static_cast< Value >( 41 )/static_cast<Value>( 840 );
+ (*this)[12] = static_cast< Value >( 41 )/static_cast<Value>( 840 );
+ }
+};
+
+template< class Value = double >
+struct rk78_coefficients_db : boost::array< Value , 13 >
+{
+ rk78_coefficients_db( void )
+ {
+ (*this)[0] = static_cast< Value >( 0 ) - static_cast< Value >( 41 )/static_cast<Value>( 840 );
+ (*this)[1] = static_cast< Value >( 0 );
+ (*this)[2] = static_cast< Value >( 0 );
+ (*this)[3] = static_cast< Value >( 0 );
+ (*this)[4] = static_cast< Value >( 0 );
+ (*this)[5] = static_cast< Value >( 0 );
+ (*this)[6] = static_cast< Value >( 0 );
+ (*this)[7] = static_cast< Value >( 0 );
+ (*this)[8] = static_cast< Value >( 0 );
+ (*this)[9] = static_cast< Value >( 0 );
+ (*this)[10] = static_cast< Value >( 0 ) - static_cast< Value >( 41 )/static_cast<Value>( 840 );
+ (*this)[11] = static_cast< Value >( 41 )/static_cast<Value>( 840 );
+ (*this)[12] = static_cast< Value >( 41 )/static_cast<Value>( 840 );
+ }
+};
+
+
+template< class Value = double >
+struct rk78_coefficients_c : boost::array< Value , 13 >
+{
+ rk78_coefficients_c( void )
+ {
+ (*this)[0] = static_cast< Value >( 0 );
+ (*this)[1] = static_cast< Value >( 2 )/static_cast< Value >( 27 );
+ (*this)[2] = static_cast< Value >( 1 )/static_cast< Value >( 9 );
+ (*this)[3] = static_cast< Value >( 1 )/static_cast<Value>( 6 );
+ (*this)[4] = static_cast< Value >( 5 )/static_cast<Value>( 12 );
+ (*this)[5] = static_cast< Value >( 1 )/static_cast<Value>( 2 );
+ (*this)[6] = static_cast< Value >( 5 )/static_cast<Value>( 6 );
+ (*this)[7] = static_cast< Value >( 1 )/static_cast<Value>( 6 );
+ (*this)[8] = static_cast< Value >( 2 )/static_cast<Value>( 3 );
+ (*this)[9] = static_cast< Value >( 1 )/static_cast<Value>( 3 );
+ (*this)[10] = static_cast< Value >( 1 );
+ (*this)[11] = static_cast< Value >( 0 );
+ (*this)[12] = static_cast< Value >( 1 );
+ }
+};
+#endif // DOXYGEN_SKIP
+
+
+
+
+
+template<
+class State ,
+class Value = double ,
+class Deriv = State ,
+class Time = Value ,
+class Algebra = typename algebra_dispatcher< State >::algebra_type ,
+class Operations = typename operations_dispatcher< State >::operations_type ,
+class Resizer = initially_resizer
+>
+#ifndef DOXYGEN_SKIP
+class runge_kutta_fehlberg78 : public explicit_error_generic_rk< 13 , 8 , 8 , 7 , State , Value , Deriv , Time ,
+Algebra , Operations , Resizer >
+#else
+class runge_kutta_fehlberg78 : public explicit_error_generic_rk
+#endif
+{
+
+public:
+#ifndef DOXYGEN_SKIP
+ typedef explicit_error_generic_rk< 13 , 8 , 8 , 7 , State , Value , Deriv , Time ,
+ Algebra , Operations , Resizer > stepper_base_type;
+#endif
+ typedef typename stepper_base_type::state_type state_type;
+ typedef typename stepper_base_type::value_type value_type;
+ typedef typename stepper_base_type::deriv_type deriv_type;
+ typedef typename stepper_base_type::time_type time_type;
+ typedef typename stepper_base_type::algebra_type algebra_type;
+ typedef typename stepper_base_type::operations_type operations_type;
+ typedef typename stepper_base_type::resizer_type resizer_type;
+
+ #ifndef DOXYGEN_SKIP
+ typedef typename stepper_base_type::stepper_type stepper_type;
+ typedef typename stepper_base_type::wrapped_state_type wrapped_state_type;
+ typedef typename stepper_base_type::wrapped_deriv_type wrapped_deriv_type;
+ #endif // DOXYGEN_SKIP
+
+
+ runge_kutta_fehlberg78( const algebra_type &algebra = algebra_type() ) : stepper_base_type(
+ boost::fusion::make_vector( rk78_coefficients_a1<Value>() , rk78_coefficients_a2<Value>() , rk78_coefficients_a3<Value>() ,
+ rk78_coefficients_a4<Value>() , rk78_coefficients_a5<Value>() , rk78_coefficients_a6<Value>() ,
+ rk78_coefficients_a7<Value>() , rk78_coefficients_a8<Value>() , rk78_coefficients_a9<Value>() ,
+ rk78_coefficients_a10<Value>() , rk78_coefficients_a11<Value>() , rk78_coefficients_a12<Value>() ) ,
+ rk78_coefficients_b<Value>() , rk78_coefficients_db<Value>() , rk78_coefficients_c<Value>() , algebra )
+ { }
+};
+
+
+
+/************* DOXYGEN *************/
+
+/**
+ * \class runge_kutta_fehlberg78
+ * \brief The Runge-Kutta Fehlberg 78 method.
+ *
+ * The Runge-Kutta Fehlberg 78 method is a standard method for high-precision applications.
+ * The method is explicit and fulfills the Error Stepper concept. Step size control
+ * is provided but continuous output is not available for this method.
+ *
+ * This class derives from explicit_error_stepper_base and inherits its interface via CRTP (current recurring template pattern).
+ * Furthermore, it derivs from explicit_error_generic_rk which is a generic Runge-Kutta algorithm with error estimation.
+ * For more details see explicit_error_stepper_base and explicit_error_generic_rk.
+ *
+ * \tparam State The state type.
+ * \tparam Value The value type.
+ * \tparam Deriv The type representing the time derivative of the state.
+ * \tparam Time The time representing the independent variable - the time.
+ * \tparam Algebra The algebra type.
+ * \tparam Operations The operations type.
+ * \tparam Resizer The resizer policy type.
+ */
+
+
+ /**
+ * \fn runge_kutta_fehlberg78::runge_kutta_fehlberg78( const algebra_type &algebra )
+ * \brief Constructs the runge_kutta_cash_fehlberg78 class. This constructor can be used as a default
+ * constructor if the algebra has a default constructor.
+ * \param algebra A copy of algebra is made and stored inside explicit_stepper_base.
+ */
+
+}
+}
+}
+
+#endif //BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_FEHLBERG87_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/stepper_categories.hpp b/include/boost/numeric/odeint/stepper/stepper_categories.hpp
new file mode 100644
index 0000000..9bc5372
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/stepper_categories.hpp
@@ -0,0 +1,68 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/stepper_categories.hpp
+
+ [begin_description]
+ Definition of all stepper categories.
+ [end_description]
+
+ Copyright 2010-2011 Mario Mulansky
+ Copyright 2010-2012 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_STEPPER_CATEGORIES_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_STEPPER_CATEGORIES_HPP_INCLUDED
+
+#include <boost/type_traits/integral_constant.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+/*
+ * Tags to specify stepper types
+ *
+ * These tags are used by integrate() to choose which integration method is used
+ */
+
+struct stepper_tag {};
+// struct explicit_stepper_tag : stepper_tag {};
+// struct implicit_stepper_tag : stepper_tag {};
+
+
+struct error_stepper_tag : stepper_tag {};
+struct explicit_error_stepper_tag : error_stepper_tag {};
+struct explicit_error_stepper_fsal_tag : error_stepper_tag {};
+
+struct controlled_stepper_tag {};
+struct explicit_controlled_stepper_tag : controlled_stepper_tag {};
+struct explicit_controlled_stepper_fsal_tag : controlled_stepper_tag {};
+
+struct dense_output_stepper_tag {};
+
+
+template< class tag > struct base_tag ;
+template< > struct base_tag< stepper_tag > { typedef stepper_tag type; };
+template< > struct base_tag< error_stepper_tag > { typedef stepper_tag type; };
+template< > struct base_tag< explicit_error_stepper_tag > { typedef stepper_tag type; };
+template< > struct base_tag< explicit_error_stepper_fsal_tag > { typedef stepper_tag type; };
+
+template< > struct base_tag< controlled_stepper_tag > { typedef controlled_stepper_tag type; };
+template< > struct base_tag< explicit_controlled_stepper_tag > { typedef controlled_stepper_tag type; };
+template< > struct base_tag< explicit_controlled_stepper_fsal_tag > { typedef controlled_stepper_tag type; };
+
+template< > struct base_tag< dense_output_stepper_tag > { typedef dense_output_stepper_tag type; };
+
+
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_STEPPER_CATEGORIES_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/symplectic_euler.hpp b/include/boost/numeric/odeint/stepper/symplectic_euler.hpp
new file mode 100644
index 0000000..bd40860
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/symplectic_euler.hpp
@@ -0,0 +1,136 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/symplectic_euler.hpp
+
+ [begin_description]
+ Implementation of the symplectic Euler for separable Hamiltonian systems.
+ [end_description]
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_SYMPLECTIC_EULER_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_SYMPLECTIC_EULER_HPP_INCLUDED
+
+
+#include <boost/numeric/odeint/stepper/base/symplectic_rkn_stepper_base.hpp>
+
+#include <boost/numeric/odeint/algebra/range_algebra.hpp>
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
+
+#include <boost/array.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+#ifndef DOXYGEN_SKIP
+namespace detail {
+namespace symplectic_euler_coef {
+
+template< class Value >
+struct coef_a_type : public boost::array< Value , 1 >
+{
+ coef_a_type( void )
+ {
+ (*this)[0] = static_cast< Value >( 1 );
+ }
+};
+
+template< class Value >
+struct coef_b_type : public boost::array< Value , 1 >
+{
+ coef_b_type( void )
+ {
+ (*this)[0] = static_cast< Value >( 1 );
+ }
+};
+
+} // namespace symplectic_euler_coef
+} // namespace detail
+#endif
+
+
+
+template<
+class Coor ,
+class Momentum = Coor ,
+class Value = double ,
+class CoorDeriv = Coor ,
+class MomentumDeriv = Coor ,
+class Time = Value ,
+class Algebra = typename algebra_dispatcher< Coor >::algebra_type ,
+class Operations = typename operations_dispatcher< Coor >::operations_type ,
+class Resizer = initially_resizer
+>
+#ifndef DOXYGEN_SKIP
+class symplectic_euler :
+public symplectic_nystroem_stepper_base
+<
+1 , 1 ,
+Coor , Momentum , Value , CoorDeriv , MomentumDeriv , Time , Algebra , Operations , Resizer
+>
+#else
+class symplectic_euler : public symplectic_nystroem_stepper_base
+#endif
+{
+public:
+
+#ifndef DOXYGEN_SKIP
+ typedef symplectic_nystroem_stepper_base<
+ 1 , 1 , Coor , Momentum , Value , CoorDeriv , MomentumDeriv , Time , Algebra , Operations , Resizer > stepper_base_type;
+#endif
+ typedef typename stepper_base_type::algebra_type algebra_type;
+ typedef typename stepper_base_type::value_type value_type;
+
+
+ symplectic_euler( const algebra_type &algebra = algebra_type() )
+ : stepper_base_type( detail::symplectic_euler_coef::coef_a_type< value_type >() ,
+ detail::symplectic_euler_coef::coef_b_type< value_type >() ,
+ algebra )
+ { }
+};
+
+
+/*************** DOXYGEN ***************/
+
+/**
+ * \class symplectic_euler
+ * \brief Implementation of the symplectic Euler method.
+ *
+ * The method is of first order and has one stage. It is described HERE.
+ *
+ * \tparam Order The order of the stepper.
+ * \tparam Coor The type representing the coordinates q.
+ * \tparam Momentum The type representing the coordinates p.
+ * \tparam Value The basic value type. Should be something like float, double or a high-precision type.
+ * \tparam CoorDeriv The type representing the time derivative of the coordinate dq/dt.
+ * \tparam MomemtnumDeriv The type representing the time derivative of the momentum dp/dt.
+ * \tparam Time The type representing the time t.
+ * \tparam Algebra The algebra.
+ * \tparam Operations The operations.
+ * \tparam Resizer The resizer policy.
+ */
+
+ /**
+ * \fn symplectic_euler::symplectic_euler( const algebra_type &algebra )
+ * \brief Constructs the symplectic_euler. This constructor can be used as a default
+ * constructor if the algebra has a default constructor.
+ * \param algebra A copy of algebra is made and stored inside explicit_stepper_base.
+ */
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_SYMPLECTIC_EULER_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/symplectic_rkn_sb3a_m4_mclachlan.hpp b/include/boost/numeric/odeint/stepper/symplectic_rkn_sb3a_m4_mclachlan.hpp
new file mode 100644
index 0000000..b33773e
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/symplectic_rkn_sb3a_m4_mclachlan.hpp
@@ -0,0 +1,160 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/symplectic_rkn_sb3a_m4_mclachlan.hpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2012-2013 Karsten Ahnert
+ Copyright 2012-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_SYMPLECTIC_RKN_SB3A_M4_MCLACHLAN_HPP_DEFINED
+#define BOOST_NUMERIC_ODEINT_STEPPER_SYMPLECTIC_RKN_SB3A_M4_MCLACHLAN_HPP_DEFINED
+
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
+
+#include <boost/numeric/odeint/util/resizer.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+#ifndef DOXYGEN_SKIP
+namespace detail {
+namespace symplectic_rkn_sb3a_m4_mclachlan {
+
+ /*
+ exp( a1 t A ) exp( b1 t B )
+ exp( a2 t A ) exp( b2 t B )
+ exp( a3 t A )
+ exp( b2 t B ) exp( a2 t A )
+ exp( b1 t B ) exp( a1 t A )
+ */
+
+
+
+ template< class Value >
+ struct coef_a_type : public boost::array< Value , 5 >
+ {
+ coef_a_type( void )
+ {
+ using std::sqrt;
+
+ Value z = sqrt( static_cast< Value >( 7 ) / static_cast< Value >( 8 ) ) / static_cast< Value >( 3 );
+ (*this)[0] = static_cast< Value >( 1 ) / static_cast< Value >( 2 ) - z ;
+ (*this)[1] = static_cast< Value >( -1 ) / static_cast< Value >( 3 ) + z ;
+ (*this)[2] = static_cast< Value >( 2 ) / static_cast< Value >( 3 );
+ (*this)[3] = (*this)[1];
+ (*this)[4] = (*this)[0];
+ }
+ };
+
+ template< class Value >
+ struct coef_b_type : public boost::array< Value , 5 >
+ {
+ coef_b_type( void )
+ {
+ (*this)[0] = static_cast< Value >( 1 );
+ (*this)[1] = static_cast< Value >( -1 ) / static_cast< Value >( 2 );
+ (*this)[2] = (*this)[1];
+ (*this)[3] = (*this)[0];
+ (*this)[4] = static_cast< Value >( 0 );
+ }
+ };
+
+} // namespace symplectic_rkn_sb3a_m4_mclachlan
+} // namespace detail
+#endif // DOXYGEN_SKIP
+
+
+
+
+template<
+ class Coor ,
+ class Momentum = Coor ,
+ class Value = double ,
+ class CoorDeriv = Coor ,
+ class MomentumDeriv = Coor ,
+ class Time = Value ,
+ class Algebra = typename algebra_dispatcher< Coor >::algebra_type ,
+ class Operations = typename operations_dispatcher< Coor >::operations_type ,
+ class Resizer = initially_resizer
+ >
+#ifndef DOXYGEN_SKIP
+class symplectic_rkn_sb3a_m4_mclachlan :
+ public symplectic_nystroem_stepper_base
+<
+ 5 , 4 ,
+ Coor , Momentum , Value , CoorDeriv , MomentumDeriv , Time , Algebra , Operations , Resizer
+ >
+#else
+class symplectic_rkn_sb3a_m4_mclachlan : public symplectic_nystroem_stepper_base
+#endif
+{
+public:
+#ifndef DOXYGEN_SKIP
+ typedef symplectic_nystroem_stepper_base
+ <
+ 5 , 4 ,
+ Coor , Momentum , Value , CoorDeriv , MomentumDeriv , Time , Algebra , Operations , Resizer
+ > stepper_base_type;
+#endif
+ typedef typename stepper_base_type::algebra_type algebra_type;
+ typedef typename stepper_base_type::value_type value_type;
+
+
+ symplectic_rkn_sb3a_m4_mclachlan( const algebra_type &algebra = algebra_type() )
+ : stepper_base_type(
+ detail::symplectic_rkn_sb3a_m4_mclachlan::coef_a_type< value_type >() ,
+ detail::symplectic_rkn_sb3a_m4_mclachlan::coef_b_type< value_type >() ,
+ algebra )
+ { }
+};
+
+
+/***************** DOXYGEN ***************/
+
+/**
+ * \class symplectic_rkn_sb3a_m4_mclachlan
+ * \brief Implementation of the symmetric B3A Runge-Kutta Nystroem method of fifth order.
+ *
+ * The method is of fourth order and has five stages. It is described HERE. This method can be used
+ * with multiprecision types since the coefficients are defined analytically.
+ *
+ * ToDo: add reference to paper.
+ *
+ * \tparam Order The order of the stepper.
+ * \tparam Coor The type representing the coordinates q.
+ * \tparam Momentum The type representing the coordinates p.
+ * \tparam Value The basic value type. Should be something like float, double or a high-precision type.
+ * \tparam CoorDeriv The type representing the time derivative of the coordinate dq/dt.
+ * \tparam MomemtnumDeriv The type representing the time derivative of the momentum dp/dt.
+ * \tparam Time The type representing the time t.
+ * \tparam Algebra The algebra.
+ * \tparam Operations The operations.
+ * \tparam Resizer The resizer policy.
+ */
+
+ /**
+ * \fn symplectic_rkn_sb3a_m4_mclachlan::symplectic_rkn_sb3a_m4_mclachlan( const algebra_type &algebra )
+ * \brief Constructs the symplectic_rkn_sb3a_m4_mclachlan. This constructor can be used as a default
+ * constructor if the algebra has a default constructor.
+ * \param algebra A copy of algebra is made and stored inside explicit_stepper_base.
+ */
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_SYMPLECTIC_RKN_SB3A_M4_MCLACHLAN_HPP_DEFINED
diff --git a/include/boost/numeric/odeint/stepper/symplectic_rkn_sb3a_mclachlan.hpp b/include/boost/numeric/odeint/stepper/symplectic_rkn_sb3a_mclachlan.hpp
new file mode 100644
index 0000000..d75c535
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/symplectic_rkn_sb3a_mclachlan.hpp
@@ -0,0 +1,162 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/symplectic_rkn_sb3a_mclachlan.hpp
+
+ [begin_description]
+ Implementation of the symplectic MacLachlan stepper for separable Hamiltonian system.
+ [end_description]
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_SYMPLECTIC_RKN_SB3A_MCLACHLAN_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_SYMPLECTIC_RKN_SB3A_MCLACHLAN_HPP_INCLUDED
+
+
+#include <boost/numeric/odeint/stepper/base/symplectic_rkn_stepper_base.hpp>
+
+#include <boost/numeric/odeint/algebra/range_algebra.hpp>
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
+
+#include <boost/numeric/odeint/util/resizer.hpp>
+
+#include <boost/array.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+#ifndef DOXYGEN_SKIP
+namespace detail {
+namespace symplectic_rkn_sb3a_mclachlan {
+
+ /*
+ exp( a1 t A ) exp( b1 t B )
+ exp( a2 t A ) exp( b2 t B )
+ exp( a3 t A ) exp( b3 t B ) exp( a3 t A )
+ exp( b2 t B ) exp( a2 t A )
+ exp( b1 t B ) exp( a1 t A )
+ */
+
+ template< class Value >
+ struct coef_a_type : public boost::array< Value , 6 >
+ {
+ coef_a_type( void )
+ {
+ (*this)[0] = static_cast< Value >( 0.40518861839525227722 );
+ (*this)[1] = static_cast< Value >( -0.28714404081652408900 );
+ (*this)[2] = static_cast< Value >( 1 ) / static_cast< Value >( 2 ) - ( (*this)[0] + (*this)[1] );
+ (*this)[3] = (*this)[2];
+ (*this)[4] = (*this)[1];
+ (*this)[5] = (*this)[0];
+
+ }
+ };
+
+ template< class Value >
+ struct coef_b_type : public boost::array< Value , 6 >
+ {
+ coef_b_type( void )
+ {
+ (*this)[0] = static_cast< Value >( -3 ) / static_cast< Value >( 73 );
+ (*this)[1] = static_cast< Value >( 17 ) / static_cast< Value >( 59 );
+ (*this)[2] = static_cast< Value >( 1 ) - static_cast< Value >( 2 ) * ( (*this)[0] + (*this)[1] );
+ (*this)[3] = (*this)[1];
+ (*this)[4] = (*this)[0];
+ (*this)[5] = static_cast< Value >( 0 );
+ }
+ };
+
+} // namespace symplectic_rkn_sb3a_mclachlan
+} // namespace detail
+#endif // DOXYGEN_SKIP
+
+
+
+template<
+ class Coor ,
+ class Momentum = Coor ,
+ class Value = double ,
+ class CoorDeriv = Coor ,
+ class MomentumDeriv = Coor ,
+ class Time = Value ,
+ class Algebra = typename algebra_dispatcher< Coor >::algebra_type ,
+ class Operations = typename operations_dispatcher< Coor >::operations_type ,
+ class Resizer = initially_resizer
+ >
+#ifndef DOXYGEN_SKIP
+class symplectic_rkn_sb3a_mclachlan :
+ public symplectic_nystroem_stepper_base
+<
+ 6 , 4 ,
+ Coor , Momentum , Value , CoorDeriv , MomentumDeriv , Time , Algebra , Operations , Resizer
+ >
+#else
+class symplectic_rkn_sb3a_mclachlan : public symplectic_nystroem_stepper_base
+#endif
+{
+public:
+#ifndef DOXYGEN_SKIP
+ typedef symplectic_nystroem_stepper_base
+ <
+ 6 , 4 ,
+ Coor , Momentum , Value , CoorDeriv , MomentumDeriv , Time , Algebra , Operations , Resizer
+ > stepper_base_type;
+#endif
+ typedef typename stepper_base_type::algebra_type algebra_type;
+ typedef typename stepper_base_type::value_type value_type;
+
+
+ symplectic_rkn_sb3a_mclachlan( const algebra_type &algebra = algebra_type() )
+ : stepper_base_type(
+ detail::symplectic_rkn_sb3a_mclachlan::coef_a_type< value_type >() ,
+ detail::symplectic_rkn_sb3a_mclachlan::coef_b_type< value_type >() ,
+ algebra )
+ { }
+};
+
+
+/************* DOXYGEN ***********/
+
+/**
+ * \class symplectic_rkn_sb3a_mclachlan
+ * \brief Implement of the symmetric B3A method of Runge-Kutta-Nystroem method of sixth order.
+ *
+ * The method is of fourth order and has six stages. It is described HERE. This method cannot be used
+ * with multiprecision types since the coefficients are not defined analytically.
+ *
+ * ToDo Add reference to the paper.
+ *
+ * \tparam Order The order of the stepper.
+ * \tparam Coor The type representing the coordinates q.
+ * \tparam Momentum The type representing the coordinates p.
+ * \tparam Value The basic value type. Should be something like float, double or a high-precision type.
+ * \tparam CoorDeriv The type representing the time derivative of the coordinate dq/dt.
+ * \tparam MomemtnumDeriv The type representing the time derivative of the momentum dp/dt.
+ * \tparam Time The type representing the time t.
+ * \tparam Algebra The algebra.
+ * \tparam Operations The operations.
+ * \tparam Resizer The resizer policy.
+ */
+
+ /**
+ * \fn symplectic_rkn_sb3a_mclachlan::symplectic_rkn_sb3a_mclachlan( const algebra_type &algebra )
+ * \brief Constructs the symplectic_rkn_sb3a_mclachlan. This constructor can be used as a default
+ * constructor if the algebra has a default constructor.
+ * \param algebra A copy of algebra is made and stored inside explicit_stepper_base.
+ */
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_SYMPLECTIC_RKN_SB3A_MCLACHLAN_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/stepper/velocity_verlet.hpp b/include/boost/numeric/odeint/stepper/velocity_verlet.hpp
new file mode 100644
index 0000000..3a20fc2
--- /dev/null
+++ b/include/boost/numeric/odeint/stepper/velocity_verlet.hpp
@@ -0,0 +1,381 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/velocity_verlet.hpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2009-2012 Karsten Ahnert
+ Copyright 2009-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_STEPPER_VELOCITY_VERLET_HPP_DEFINED
+#define BOOST_NUMERIC_ODEINT_STEPPER_VELOCITY_VERLET_HPP_DEFINED
+
+#include <boost/numeric/odeint/stepper/base/algebra_stepper_base.hpp>
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
+#include <boost/numeric/odeint/util/resizer.hpp>
+#include <boost/numeric/odeint/util/state_wrapper.hpp>
+#include <boost/numeric/odeint/util/unwrap_reference.hpp>
+
+#include <boost/numeric/odeint/util/bind.hpp>
+#include <boost/numeric/odeint/util/copy.hpp>
+#include <boost/numeric/odeint/util/resizer.hpp>
+// #include <boost/numeric/odeint/util/is_pair.hpp>
+// #include <boost/array.hpp>
+
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+
+template <
+ class Coor ,
+ class Velocity = Coor ,
+ class Value = double ,
+ class Acceleration = Coor ,
+ class Time = Value ,
+ class TimeSq = Time ,
+ class Algebra = typename algebra_dispatcher< Coor >::algebra_type ,
+ class Operations = typename operations_dispatcher< Coor >::operations_type ,
+ class Resizer = initially_resizer
+ >
+class velocity_verlet : public algebra_stepper_base< Algebra , Operations >
+{
+public:
+
+ typedef algebra_stepper_base< Algebra , Operations > algebra_stepper_base_type;
+ typedef typename algebra_stepper_base_type::algebra_type algebra_type;
+ typedef typename algebra_stepper_base_type::operations_type operations_type;
+
+ typedef Coor coor_type;
+ typedef Velocity velocity_type;
+ typedef Acceleration acceleration_type;
+ typedef std::pair< coor_type , velocity_type > state_type;
+ typedef std::pair< velocity_type , acceleration_type > deriv_type;
+ typedef state_wrapper< acceleration_type > wrapped_acceleration_type;
+ typedef Value value_type;
+ typedef Time time_type;
+ typedef TimeSq time_square_type;
+ typedef Resizer resizer_type;
+ typedef stepper_tag stepper_category;
+
+ typedef unsigned short order_type;
+
+ static const order_type order_value = 1;
+
+ /**
+ * \return Returns the order of the stepper.
+ */
+ order_type order( void ) const
+ {
+ return order_value;
+ }
+
+
+ velocity_verlet( const algebra_type & algebra = algebra_type() )
+ : algebra_stepper_base_type( algebra ) , m_first_call( true )
+ , m_a1() , m_a2() , m_current_a1( true ) { }
+
+
+ template< class System , class StateInOut >
+ void do_step( System system , StateInOut & x , time_type t , time_type dt )
+ {
+ do_step_v1( system , x , t , dt );
+ }
+
+
+ template< class System , class StateInOut >
+ void do_step( System system , const StateInOut & x , time_type t , time_type dt )
+ {
+ do_step_v1( system , x , t , dt );
+ }
+
+
+ template< class System , class CoorIn , class VelocityIn , class AccelerationIn ,
+ class CoorOut , class VelocityOut , class AccelerationOut >
+ void do_step( System system , CoorIn const & qin , VelocityIn const & pin , AccelerationIn const & ain ,
+ CoorOut & qout , VelocityOut & pout , AccelerationOut & aout , time_type t , time_type dt )
+ {
+ const value_type one = static_cast< value_type >( 1.0 );
+ const value_type one_half = static_cast< value_type >( 0.5 );
+
+ algebra_stepper_base_type::m_algebra.for_each4(
+ qout , qin , pin , ain ,
+ typename operations_type::template scale_sum3< value_type , time_type , time_square_type >( one , one * dt , one_half * dt * dt ) );
+
+ typename odeint::unwrap_reference< System >::type & sys = system;
+
+ sys( qout , pin , aout , t + dt );
+
+ algebra_stepper_base_type::m_algebra.for_each4(
+ pout , pin , ain , aout ,
+ typename operations_type::template scale_sum3< value_type , time_type , time_type >( one , one_half * dt , one_half * dt ) );
+ }
+
+
+ template< class StateIn >
+ void adjust_size( const StateIn & x )
+ {
+ if( resize_impl( x ) )
+ m_first_call = true;
+ }
+
+ void reset( void )
+ {
+ m_first_call = true;
+ }
+
+
+ /**
+ * \fn velocity_verlet::initialize( const AccelerationIn &qin )
+ * \brief Initializes the internal state of the stepper.
+ * \param deriv The acceleration of x. The next call of `do_step` expects that the acceleration of `x` passed to `do_step`
+ * has the value of `qin`.
+ */
+ template< class AccelerationIn >
+ void initialize( const AccelerationIn & ain )
+ {
+ // alloc a
+ m_resizer.adjust_size( ain ,
+ detail::bind( &velocity_verlet::template resize_impl< AccelerationIn > ,
+ detail::ref( *this ) , detail::_1 ) );
+ boost::numeric::odeint::copy( ain , get_current_acc() );
+ m_first_call = false;
+ }
+
+
+ template< class System , class CoorIn , class VelocityIn >
+ void initialize( System system , const CoorIn & qin , const VelocityIn & pin , time_type t )
+ {
+ m_resizer.adjust_size( qin ,
+ detail::bind( &velocity_verlet::template resize_impl< CoorIn > ,
+ detail::ref( *this ) , detail::_1 ) );
+ initialize_acc( system , qin , pin , t );
+ }
+
+ bool is_initialized( void ) const
+ {
+ return ! m_first_call;
+ }
+
+
+private:
+
+ template< class System , class CoorIn , class VelocityIn >
+ void initialize_acc( System system , const CoorIn & qin , const VelocityIn & pin , time_type t )
+ {
+ typename odeint::unwrap_reference< System >::type & sys = system;
+ sys( qin , pin , get_current_acc() , t );
+ m_first_call = false;
+ }
+
+ template< class System , class StateInOut >
+ void do_step_v1( System system , StateInOut & x , time_type t , time_type dt )
+ {
+ typedef typename odeint::unwrap_reference< StateInOut >::type state_in_type;
+ typedef typename odeint::unwrap_reference< typename state_in_type::first_type >::type coor_in_type;
+ typedef typename odeint::unwrap_reference< typename state_in_type::second_type >::type momentum_in_type;
+
+ typedef typename boost::remove_reference< coor_in_type >::type xyz_type;
+ state_in_type & statein = x;
+ coor_in_type & qinout = statein.first;
+ momentum_in_type & pinout = statein.second;
+
+ // alloc a
+ if( m_resizer.adjust_size( qinout ,
+ detail::bind( &velocity_verlet::template resize_impl< xyz_type > ,
+ detail::ref( *this ) , detail::_1 ) )
+ || m_first_call )
+ {
+ initialize_acc( system , qinout , pinout , t );
+ }
+
+ // check first
+ do_step( system , qinout , pinout , get_current_acc() , qinout , pinout , get_old_acc() , t , dt );
+ toggle_current_acc();
+ }
+
+ template< class StateIn >
+ bool resize_impl( const StateIn & x )
+ {
+ bool resized = false;
+ resized |= adjust_size_by_resizeability( m_a1 , x , typename is_resizeable< acceleration_type >::type() );
+ resized |= adjust_size_by_resizeability( m_a2 , x , typename is_resizeable< acceleration_type >::type() );
+ return resized;
+ }
+
+ acceleration_type & get_current_acc( void )
+ {
+ return m_current_a1 ? m_a1.m_v : m_a2.m_v ;
+ }
+
+ const acceleration_type & get_current_acc( void ) const
+ {
+ return m_current_a1 ? m_a1.m_v : m_a2.m_v ;
+ }
+
+ acceleration_type & get_old_acc( void )
+ {
+ return m_current_a1 ? m_a2.m_v : m_a1.m_v ;
+ }
+
+ const acceleration_type & get_old_acc( void ) const
+ {
+ return m_current_a1 ? m_a2.m_v : m_a1.m_v ;
+ }
+
+ void toggle_current_acc( void )
+ {
+ m_current_a1 = ! m_current_a1;
+ }
+
+ resizer_type m_resizer;
+ bool m_first_call;
+ wrapped_acceleration_type m_a1 , m_a2;
+ bool m_current_a1;
+};
+
+/**
+ * \class velocity_verlet
+ * \brief The Velocity-Verlet algorithm.
+ *
+ * <a href="http://en.wikipedia.org/wiki/Verlet_integration" >The Velocity-Verlet algorithm</a> is a method for simulation of molecular dynamics systems. It solves the ODE
+ * a=f(r,v',t) where r are the coordinates, v are the velocities and a are the accelerations, hence v = dr/dt, a=dv/dt.
+ *
+ * \tparam Coor The type representing the coordinates.
+ * \tparam Velocity The type representing the velocities.
+ * \tparam Value The type value type.
+ * \tparam Acceleration The type representing the acceleration.
+ * \tparam Time The time representing the independent variable - the time.
+ * \tparam TimeSq The time representing the square of the time.
+ * \tparam Algebra The algebra.
+ * \tparam Operations The operations type.
+ * \tparam Resizer The resizer policy type.
+ */
+
+
+ /**
+ * \fn velocity_verlet::velocity_verlet( const algebra_type &algebra )
+ * \brief Constructs the velocity_verlet class. This constructor can be used as a default
+ * constructor if the algebra has a default constructor.
+ * \param algebra A copy of algebra is made and stored.
+ */
+
+
+ /**
+ * \fn velocity_verlet::do_step( System system , StateInOut &x , time_type t , time_type dt )
+ * \brief This method performs one step. It transforms the result in-place.
+ *
+ * It can be used like
+ * \code
+ * pair< coordinates , velocities > state;
+ * stepper.do_step( sys , x , t , dt );
+ * \endcode
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the
+ * Second Order System concept.
+ * \param x The state of the ODE which should be solved. The state is pair of Coor and Velocity.
+ * \param t The value of the time, at which the step should be performed.
+ * \param dt The step size.
+ */
+
+ /**
+ * \fn velocity_verlet::do_step( System system , const StateInOut &x , time_type t , time_type dt )
+ * \brief This method performs one step. It transforms the result in-place.
+ *
+ * It can be used like
+ * \code
+ * pair< coordinates , velocities > state;
+ * stepper.do_step( sys , x , t , dt );
+ * \endcode
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the
+ * Second Order System concept.
+ * \param x The state of the ODE which should be solved. The state is pair of Coor and Velocity.
+ * \param t The value of the time, at which the step should be performed.
+ * \param dt The step size.
+ */
+
+
+
+ /**
+ * \fn velocity_verlet::do_step( System system , CoorIn const & qin , VelocityIn const & pin , AccelerationIn const & ain , CoorOut & qout , VelocityOut & pout , AccelerationOut & aout , time_type t , time_type dt )
+ * \brief This method performs one step. It transforms the result in-place. Additionally to the other methods
+ * the coordinates, velocities and accelerations are passed directly to do_step and they are transformed out-of-place.
+ *
+ * It can be used like
+ * \code
+ * coordinates qin , qout;
+ * velocities pin , pout;
+ * accelerations ain, aout;
+ * stepper.do_step( sys , qin , pin , ain , qout , pout , aout , t , dt );
+ * \endcode
+ *
+ * \param system The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the
+ * Second Order System concept.
+ * \param x The state of the ODE which should be solved. The state is pair of Coor and Velocity.
+ * \param t The value of the time, at which the step should be performed.
+ * \param dt The step size.
+ */
+
+
+ /**
+ * \fn void velocity_verlet::adjust_size( const StateIn &x )
+ * \brief Adjust the size of all temporaries in the stepper manually.
+ * \param x A state from which the size of the temporaries to be resized is deduced.
+ */
+
+
+ /**
+ * \fn velocity_verlet::reset( void )
+ * \brief Resets the internal state of this stepper. After calling this method it is safe to use all
+ * `do_step` method without explicitly initializing the stepper.
+ */
+
+
+
+ /**
+ * \fn velocity_verlet::initialize( System system , const CoorIn &qin , const VelocityIn &pin , time_type t )
+ * \brief Initializes the internal state of the stepper.
+ *
+ * This method is equivalent to
+ * \code
+ * Acceleration a;
+ * system( qin , pin , a , t );
+ * stepper.initialize( a );
+ * \endcode
+ *
+ * \param system The system function for the next calls of `do_step`.
+ * \param qin The current coordinates of the ODE.
+ * \param pin The current velocities of the ODE.
+ * \param t The current time of the ODE.
+ */
+
+
+ /**
+ * \fn velocity_verlet::is_initialized()
+ * \returns Returns if the stepper is initialized.
+ */
+
+
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_VELOCITY_VERLET_HPP_DEFINED
diff --git a/include/boost/numeric/odeint/util/bind.hpp b/include/boost/numeric/odeint/util/bind.hpp
new file mode 100644
index 0000000..1201afa
--- /dev/null
+++ b/include/boost/numeric/odeint/util/bind.hpp
@@ -0,0 +1,101 @@
+/*
+ * [begin_description]
+ * Boost bind pull the placeholders, _1, _2, ... into global
+ * namespace. This can conflict with the C++03 TR1 and C++11
+ * std::placeholders. This header provides a workaround for
+ * this problem.
+ * [end_description]
+ *
+ * Copyright 2012 Christoph Koke
+ * Copyright 2012 Karsten Ahnert
+ *
+ * Distributed under the Boost Software License, Version 1.0.
+ * (See accompanying file LICENSE_1_0.txt or
+ * copy at http://www.boost.org/LICENSE_1_0.txt)
+ * */
+
+#ifndef BOOST_NUMERIC_ODEINT_UTIL_BIND_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_UTIL_BIND_HPP_INCLUDED
+
+
+#include <boost/numeric/odeint/config.hpp>
+
+
+#if BOOST_NUMERIC_ODEINT_CXX11
+ #include <functional>
+#else
+#define BOOST_BIND_NO_PLACEHOLDERS
+#include <boost/bind.hpp>
+#endif
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+#if BOOST_NUMERIC_ODEINT_CXX11
+
+using ::std::bind;
+using namespace ::std::placeholders;
+
+
+#else
+
+// unnamed namespace to avoid multiple declarations (#138)
+namespace {
+using ::boost::bind;
+boost::arg<1> _1;
+boost::arg<2> _2;
+}
+// using ::boost::bind;
+// using ::_1;
+// using ::_2;
+
+#endif
+
+}
+}
+}
+}
+
+
+
+
+
+/*
+
+// the following is the suggested way. Unfortunately it does not work with all compilers.
+
+#ifdef BOOST_NO_CXX11_HDR_FUNCTIONAL
+#include <boost/bind.hpp>
+#else
+#include <functional>
+#endif
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+
+#ifdef BOOST_NO_CXX11_HDR_FUNCTIONAL
+
+using ::boost::bind;
+using ::_1;
+using ::_2;
+
+#else
+
+using ::std::bind;
+using namespace ::std::placeholders;
+
+#endif
+
+
+}
+}
+}
+}*/
+
+#endif // BOOST_NUMERIC_ODEINT_UTIL_BIND_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/util/copy.hpp b/include/boost/numeric/odeint/util/copy.hpp
new file mode 100644
index 0000000..161f135
--- /dev/null
+++ b/include/boost/numeric/odeint/util/copy.hpp
@@ -0,0 +1,87 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/util/copy.hpp
+
+ [begin_description]
+ Copy abstraction for the usage in the steppers.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_UTIL_COPY_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_UTIL_COPY_HPP_INCLUDED
+
+
+#include <boost/range/algorithm/copy.hpp>
+
+#include <boost/utility/enable_if.hpp>
+
+#include <boost/numeric/odeint/util/detail/is_range.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+namespace detail {
+
+ template< class Container1 , class Container2 >
+ void do_copying( const Container1 &from , Container2 &to , boost::mpl::true_ )
+ {
+ boost::range::copy( from , boost::begin( to ) );
+ }
+
+ template< class Container1 , class Container2 >
+ void do_copying( const Container1 &from , Container2 &to , boost::mpl::false_ )
+ {
+ to = from;
+ }
+
+} // namespace detail
+
+
+
+/*
+ * Default implementation of the copy operation used the assign operator
+ * gsl_vector must copied differently
+ */
+template< class Container1 , class Container2 , class Enabler = void >
+struct copy_impl_sfinae
+{
+ static void copy( const Container1 &from , Container2 &to )
+ {
+ typedef typename boost::numeric::odeint::detail::is_range< Container1 >::type is_range_type;
+ detail::do_copying( from , to , is_range_type() );
+ }
+
+};
+
+template< class Container1, class Container2 >
+struct copy_impl
+{
+ static void copy( const Container1 &from , Container2 &to )
+ {
+ copy_impl_sfinae< Container1 , Container2 >::copy( from , to );
+ }
+};
+
+// ToDo: allow also to copy INTO a range, not only from a range! Needs "const Container2 &to"
+template< class Container1 , class Container2 >
+void copy( const Container1 &from , Container2 &to )
+{
+ copy_impl< Container1 , Container2 >::copy( from , to );
+}
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_UTIL_COPY_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/util/detail/is_range.hpp b/include/boost/numeric/odeint/util/detail/is_range.hpp
new file mode 100644
index 0000000..a176855
--- /dev/null
+++ b/include/boost/numeric/odeint/util/detail/is_range.hpp
@@ -0,0 +1,134 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/util/detail/is_range.hpp
+
+ [begin_description]
+ is_range implementation. Taken from the boost::range library.
+ [end_description]
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011-2013 Thorsten Ottosen
+
+
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_UTIL_DETAIL_IS_RANGE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_UTIL_DETAIL_IS_RANGE_HPP_INCLUDED
+
+
+#if defined(_MSC_VER) && (_MSC_VER >= 1200)
+# pragma once
+#endif
+
+#include <cstddef>
+#include <boost/range/config.hpp>
+#include <boost/mpl/has_xxx.hpp>
+#include <boost/mpl/bool.hpp>
+#include <boost/mpl/and.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+
+namespace range_detail
+{
+BOOST_MPL_HAS_XXX_TRAIT_DEF(iterator)
+ BOOST_MPL_HAS_XXX_TRAIT_DEF(const_iterator)
+}
+
+namespace detail
+{
+
+template< typename Range >
+struct is_range : boost::mpl::and_<range_detail::has_iterator<Range>, range_detail::has_const_iterator<Range> >
+{
+};
+
+//////////////////////////////////////////////////////////////////////////
+// pair
+//////////////////////////////////////////////////////////////////////////
+
+template< typename iteratorT >
+struct is_range< std::pair<iteratorT,iteratorT> > : boost::mpl::true_
+{
+};
+
+template< typename iteratorT >
+struct is_range< const std::pair<iteratorT,iteratorT> > : boost::mpl::true_
+{
+};
+
+//////////////////////////////////////////////////////////////////////////
+// array
+//////////////////////////////////////////////////////////////////////////
+
+template< typename elementT, std::size_t sz >
+struct is_range< elementT[sz] > : boost::mpl::true_
+{
+};
+
+template< typename elementT, std::size_t sz >
+struct is_range< const elementT[sz] > : boost::mpl::true_
+{
+};
+
+//////////////////////////////////////////////////////////////////////////
+// string
+//////////////////////////////////////////////////////////////////////////
+
+template<>
+struct is_range< char* > : boost::mpl::true_
+{
+};
+
+template<>
+struct is_range< wchar_t* > : boost::mpl::true_
+{
+};
+
+template<>
+struct is_range< const char* > : boost::mpl::true_
+{
+};
+
+template<>
+struct is_range< const wchar_t* > : boost::mpl::true_
+{
+};
+
+template<>
+struct is_range< char* const > : boost::mpl::true_
+{
+};
+
+template<>
+struct is_range< wchar_t* const > : boost::mpl::true_
+{
+};
+
+template<>
+struct is_range< const char* const > : boost::mpl::true_
+{
+};
+
+template<>
+struct is_range< const wchar_t* const > : boost::mpl::true_
+{
+};
+
+} // namespace detail
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_UTIL_DETAIL_IS_RANGE_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/util/detail/less_with_sign.hpp b/include/boost/numeric/odeint/util/detail/less_with_sign.hpp
new file mode 100644
index 0000000..3ffa7ca
--- /dev/null
+++ b/include/boost/numeric/odeint/util/detail/less_with_sign.hpp
@@ -0,0 +1,78 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/util/detail/less_with_sign.hpp
+
+ [begin_description]
+ Helper function to compare times taking into account the sign of dt
+ [end_description]
+
+ Copyright 2012-2015 Mario Mulansky
+ Copyright 2012 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#ifndef BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_LESS_WITH_SIGN_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_LESS_WITH_SIGN_HPP_INCLUDED
+
+#include <limits>
+
+#include <boost/numeric/odeint/util/unit_helper.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+/**
+ * return t1 < t2 if dt > 0 and t1 > t2 if dt < 0 with epsilon accuracy
+ */
+template< typename T >
+bool less_with_sign( T t1 , T t2 , T dt )
+{
+ if( get_unit_value(dt) > 0 )
+ //return t1 < t2;
+ return t2-t1 > std::numeric_limits<T>::epsilon();
+ else
+ //return t1 > t2;
+ return t1-t2 > std::numeric_limits<T>::epsilon();
+}
+
+/**
+ * return t1 <= t2 if dt > 0 and t1 => t2 if dt < 0 with epsilon accuracy
+ */
+template< typename T >
+bool less_eq_with_sign( T t1 , T t2 , T dt )
+{
+ if( get_unit_value(dt) > 0 )
+ return t1-t2 <= std::numeric_limits<T>::epsilon();
+ else
+ return t2-t1 <= std::numeric_limits<T>::epsilon();
+}
+
+template< typename T >
+T min_abs( T t1 , T t2 )
+{
+ BOOST_USING_STD_MIN();
+ BOOST_USING_STD_MAX();
+ if( get_unit_value(t1)>0 )
+ return min BOOST_PREVENT_MACRO_SUBSTITUTION ( t1 , t2 );
+ else
+ return max BOOST_PREVENT_MACRO_SUBSTITUTION ( t1 , t2 );
+}
+
+template< typename T >
+T max_abs( T t1 , T t2 )
+{
+ BOOST_USING_STD_MIN();
+ BOOST_USING_STD_MAX();
+ if( get_unit_value(t1)>0 )
+ return max BOOST_PREVENT_MACRO_SUBSTITUTION ( t1 , t2 );
+ else
+ return min BOOST_PREVENT_MACRO_SUBSTITUTION ( t1 , t2 );
+}
+} } } }
+
+#endif
diff --git a/include/boost/numeric/odeint/util/is_pair.hpp b/include/boost/numeric/odeint/util/is_pair.hpp
new file mode 100644
index 0000000..1827840
--- /dev/null
+++ b/include/boost/numeric/odeint/util/is_pair.hpp
@@ -0,0 +1,45 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/util/is_pair.hpp
+
+ [begin_description]
+ Metafunction to determine if a type is a std::pair<>.
+ [end_description]
+
+ Copyright 2011 Karsten Ahnert
+ Copyright 2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_UTIL_IS_PAIR_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_UTIL_IS_PAIR_HPP_INCLUDED
+
+
+#include <boost/mpl/bool.hpp>
+#include <utility>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template< class T >
+struct is_pair : public boost::mpl::false_
+{
+};
+
+template< class T1 , class T2 >
+struct is_pair< std::pair< T1 , T2 > > : public boost::mpl::true_
+{
+};
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_UTIL_IS_PAIR_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/util/is_resizeable.hpp b/include/boost/numeric/odeint/util/is_resizeable.hpp
new file mode 100644
index 0000000..ad7332d
--- /dev/null
+++ b/include/boost/numeric/odeint/util/is_resizeable.hpp
@@ -0,0 +1,83 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/util/is_resizeable.hpp
+
+ [begin_description]
+ Metafunction to determine if a state type can resized. For usage in the steppers.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_UTIL_IS_RESIZEABLE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_UTIL_IS_RESIZEABLE_HPP_INCLUDED
+
+
+#include <vector>
+
+#include <boost/type_traits/integral_constant.hpp>
+#include <boost/type_traits/remove_reference.hpp>
+#include <boost/fusion/include/front.hpp>
+#include <boost/fusion/include/is_sequence.hpp>
+
+#include <boost/mpl/find_if.hpp>
+#include <boost/mpl/end.hpp>
+#include <boost/mpl/placeholders.hpp>
+#include <boost/mpl/if.hpp>
+#include <boost/type_traits/is_same.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+/*
+ * by default any type is not resizable
+ */
+template< typename Container , typename Enabler = void >
+struct is_resizeable_sfinae : boost::false_type {};
+
+template< typename Container >
+struct is_resizeable : is_resizeable_sfinae< Container > {};
+
+
+
+/*
+ * specialization for std::vector
+ */
+template< class V, class A >
+struct is_resizeable< std::vector< V , A > > : boost::true_type {};
+
+
+/*
+ * sfinae specialization for fusion sequences
+ */
+template< typename FusionSequence >
+struct is_resizeable_sfinae<
+ FusionSequence ,
+ typename boost::enable_if< typename boost::fusion::traits::is_sequence< FusionSequence >::type >::type >
+{
+ typedef typename boost::mpl::find_if< FusionSequence , is_resizeable< boost::mpl::_1 > >::type iter;
+ typedef typename boost::mpl::end< FusionSequence >::type last;
+
+ typedef typename boost::mpl::if_< boost::is_same< iter , last > , boost::false_type , boost::true_type >::type type;
+ const static bool value = type::value;
+};
+
+
+
+
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_UTIL_IS_RESIZEABLE_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/util/multi_array_adaption.hpp b/include/boost/numeric/odeint/util/multi_array_adaption.hpp
new file mode 100644
index 0000000..e2c0a48
--- /dev/null
+++ b/include/boost/numeric/odeint/util/multi_array_adaption.hpp
@@ -0,0 +1,130 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/util/multi_array_adaption.hpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2009-2012 Karsten Ahnert
+ Copyright 2009-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_UTIL_MULTI_ARRAY_ADAPTION_HPP_DEFINED
+#define BOOST_NUMERIC_ODEINT_UTIL_MULTI_ARRAY_ADAPTION_HPP_DEFINED
+
+
+
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resize.hpp>
+#include <boost/numeric/odeint/util/same_size.hpp>
+
+#include <boost/mpl/and.hpp>
+#include <boost/mpl/bool.hpp>
+#include <boost/multi_array.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template< typename T >
+struct is_multi_array
+{
+ typedef boost::false_type type;
+ const static bool value = type::value;
+};
+
+template< typename T >
+struct is_resizeable_multi_array
+{
+ typedef boost::false_type type;
+ const static bool value = type::value;
+};
+
+
+
+template< typename V , size_t Dim , typename A >
+struct is_multi_array< boost::multi_array< V , Dim , A > >
+{
+ typedef boost::true_type type;
+ const static bool value = type::value;
+};
+
+template< typename V , size_t Dim , typename A >
+struct is_resizeable_multi_array< boost::multi_array< V , Dim , A > >
+{
+ typedef boost::true_type type;
+ const static bool value = type::value;
+};
+
+
+
+
+template< typename T >
+struct is_resizeable_sfinae< T , typename boost::enable_if< typename is_resizeable_multi_array< T >::type >::type >
+{
+ typedef boost::true_type type;
+ const static bool value = type::value;
+};
+
+
+
+
+
+template< typename T1 , typename T2 >
+struct same_size_impl_sfinae< T1 , T2 ,
+ typename boost::enable_if<
+ typename boost::mpl::and_<
+ is_multi_array< T1 > ,
+ is_multi_array< T2 > ,
+ boost::mpl::bool_< T1::dimensionality == T2::dimensionality >
+ >::type
+ >::type >
+{
+ static bool same_size( T1 const &x1 , T2 const &x2 )
+ {
+ for( size_t i=0 ; i<T1::dimensionality ; ++i )
+ {
+ if( x1.shape()[i] != x2.shape()[i] ) return false;
+ if( x1.index_bases()[i] != x2.index_bases()[i] ) return false;
+ }
+ return true;
+ }
+};
+
+
+template< typename T1 , typename T2 >
+struct resize_impl_sfinae< T1 , T2 ,
+ typename boost::enable_if<
+ typename boost::mpl::and_<
+ is_resizeable_multi_array< T1 > ,
+ is_multi_array< T2 > ,
+ boost::mpl::bool_< T1::dimensionality == T2::dimensionality >
+ >::type
+ >::type >
+{
+ static void resize( T1 &x1 , const T2 &x2 )
+ {
+ boost::array< int , T1::dimensionality > extents;
+ for( size_t i=0 ; i<T1::dimensionality ; ++i ) extents[i] = x2.shape()[i];
+ x1.resize( extents );
+ boost::array< int , T1::dimensionality > origins;
+ for( size_t i=0 ; i<T1::dimensionality ; ++i ) origins[i] = x2.index_bases()[i];
+ x1.reindex( origins );
+ }
+};
+
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_UTIL_MULTI_ARRAY_ADAPTION_HPP_DEFINED
diff --git a/include/boost/numeric/odeint/util/n_ary_helper.hpp b/include/boost/numeric/odeint/util/n_ary_helper.hpp
new file mode 100644
index 0000000..6138074
--- /dev/null
+++ b/include/boost/numeric/odeint/util/n_ary_helper.hpp
@@ -0,0 +1,96 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/util/n_ary_helper.hpp
+
+ Macros to generate scale_sumN and for_eachN functors.
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+ Copyright 2013 Pascal Germroth
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#ifndef BOOST_NUMERIC_ODEINT_UTIL_N_ARY_HELPER_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_UTIL_N_ARY_HELPER_HPP_INCLUDED
+
+#include <boost/preprocessor/repetition.hpp>
+
+// like BOOST_PP_ENUM_SHIFTED but with a comma in front like _TRAILING
+#define BOOST_ODEINT_ENUM_TRAILING_SHIFTED_PARAMS(count, param) \
+ BOOST_PP_COMMA_IF(BOOST_PP_DEC(count)) \
+ BOOST_PP_ENUM_SHIFTED_PARAMS(count, param)
+
+#define BOOST_ODEINT_ENUM_TRAILING_SHIFTED_BINARY_PARAMS(count, p1, p2) \
+ BOOST_PP_COMMA_IF(BOOST_PP_DEC(count)) \
+ BOOST_PP_ENUM_SHIFTED_BINARY_PARAMS(count, p1, p2)
+
+// like BOOST_PP_ENUM_SHIFTED_BINARY_PARAMS(n, p1, p2) but p2 is shifted left.
+// generate "p1 ## 0 = p2, p1 ## 1 = p3 ## 0, p1 ## 2 = p3 ## 1"
+#define BOOST_ODEINT_ENUM_LSHIFTED_BINARY_PARAMS(count, p1, p2, p3) \
+ BOOST_PP_ENUM(count, BOOST_ODEINT_ENUM_LSHIFTED_BINARY_PARAMS_, (p1, p2, p3))
+#define BOOST_ODEINT_ENUM_LSHIFTED_BINARY_PARAMS_(z, n, data) \
+ BOOST_PP_CAT(BOOST_PP_TUPLE_ELEM(3, 0, data), n) \
+ BOOST_PP_IF(n, \
+ BOOST_PP_CAT(BOOST_PP_TUPLE_ELEM(3, 2, data), BOOST_PP_DEC(n)), \
+ BOOST_PP_TUPLE_ELEM(3, 1, data))
+
+// like BOOST_PP_ENUM_BINARY_PARAMS(n, p1, p2) but with statements.
+// "p1 ## 0 p2 ## 0 ; p1 ## 1 p2 ## 1 ; ..."
+#define BOOST_ODEINT_ENUM_BINARY_STATEMENTS(count, p1, p2) \
+ BOOST_PP_REPEAT(count, BOOST_ODEINT_ENUM_BINARY_STATEMENTS_, (p1, p2))
+#define BOOST_ODEINT_ENUM_BINARY_STATEMENTS_(z, n, data) \
+ BOOST_PP_CAT(BOOST_PP_TUPLE_ELEM(2, 0, data), n) \
+ BOOST_PP_CAT(BOOST_PP_TUPLE_ELEM(2, 1, data), n) ;
+
+// like BOOST_PP_ENUM_BINARY_PARAMS(n, p1, p2) but p2 is in parens.
+// "p1 ## 0 (p2 ## 0) , p1 ## 1 (p2 ## 1) , ..."
+#define BOOST_ODEINT_ENUM_UNARY_CALLS(count, p1, p2) \
+ BOOST_PP_ENUM(count, BOOST_ODEINT_ENUM_UNARY_CALLS_, (p1, p2))
+#define BOOST_ODEINT_ENUM_SHIFTED_UNARY_CALLS(count, p1, p2) \
+ BOOST_PP_ENUM_SHIFTED(count, BOOST_ODEINT_ENUM_UNARY_CALLS_, (p1, p2))
+#define BOOST_ODEINT_ENUM_TRAILING_SHIFTED_UNARY_CALLS(count, p1, p2) \
+ BOOST_PP_COMMA_IF(BOOST_PP_DEC(count)) \
+ BOOST_PP_ENUM_SHIFTED(count, BOOST_ODEINT_ENUM_UNARY_CALLS_, (p1, p2))
+#define BOOST_ODEINT_ENUM_UNARY_CALLS_(z, n, data) \
+ BOOST_PP_CAT(BOOST_PP_TUPLE_ELEM(2, 0, data), n) \
+ ( BOOST_PP_CAT(BOOST_PP_TUPLE_ELEM(2, 1, data), n) )
+
+
+// maximum arity + 1 for scale_sum and for_each
+#define BOOST_ODEINT_N_ARY_MAX 16
+
+
+// generate scale_sum1 to scale_sumN, operator body generated by macro(N)
+#define BOOST_ODEINT_GEN_SCALE_SUM(macro) \
+ BOOST_PP_REPEAT_FROM_TO(1, BOOST_ODEINT_N_ARY_MAX, BOOST_ODEINT_GEN_SCALE_SUM_, macro)
+#define BOOST_ODEINT_GEN_SCALE_SUM_(z, n, macro) \
+ template< BOOST_ODEINT_ENUM_LSHIFTED_BINARY_PARAMS(n, class Fac, = double, = Fac) > \
+ struct BOOST_PP_CAT(scale_sum, n) \
+ { \
+ BOOST_ODEINT_ENUM_BINARY_STATEMENTS(n, const Fac, m_alpha) \
+ \
+ BOOST_PP_CAT(scale_sum, n) \
+ ( BOOST_PP_ENUM_BINARY_PARAMS(n, Fac, alpha) ) \
+ : BOOST_ODEINT_ENUM_UNARY_CALLS(n, m_alpha, alpha) {} \
+ \
+ template< BOOST_PP_ENUM_PARAMS(BOOST_PP_INC(n), class T) > \
+ void operator()( T0 &t0 \
+ BOOST_ODEINT_ENUM_TRAILING_SHIFTED_BINARY_PARAMS(BOOST_PP_INC(n), const T, &t) \
+ ) const \
+ { macro(n) } \
+ typedef void result_type; \
+ };
+
+// generate for_each1 to for_eachN, body generated by macro(N)
+#define BOOST_ODEINT_GEN_FOR_EACH(macro) \
+ BOOST_PP_REPEAT_FROM_TO(1, BOOST_ODEINT_N_ARY_MAX, BOOST_ODEINT_GEN_FOR_EACH_, macro)
+#define BOOST_ODEINT_GEN_FOR_EACH_(z, n, macro) \
+ template< BOOST_PP_ENUM_PARAMS(n, class S) , class Op > \
+ static void for_each##n ( BOOST_PP_ENUM_BINARY_PARAMS(n, S, &s) , Op op ) \
+ { macro(n) }
+
+
+#endif
diff --git a/include/boost/numeric/odeint/util/odeint_error.hpp b/include/boost/numeric/odeint/util/odeint_error.hpp
new file mode 100644
index 0000000..312e5b1
--- /dev/null
+++ b/include/boost/numeric/odeint/util/odeint_error.hpp
@@ -0,0 +1,77 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/util/odeint_error.hpp
+
+ [begin_description]
+ Runtime Exceptions thrown by odeint
+ [end_description]
+
+ Copyright 2015 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_UTIL_ODEINT_ERROR_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_UTIL_ODEINT_ERROR_HPP_INCLUDED
+
+#include <stdexcept>
+#include <string>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+/**
+ * \brief Runtime error thrown by odeint
+ */
+class odeint_error : public std::runtime_error
+{
+public:
+ odeint_error(const std::string &s)
+ : std::runtime_error(s)
+ { }
+};
+
+
+/**
+ * \brief Runtime error thrown from integrate routines
+ *
+ * This Error occures when too many iterations are performed in between two
+ * observer calls in the integrate routines.
+ */
+class no_progress_error : public odeint_error
+{
+public:
+ no_progress_error(const std::string &s)
+ : odeint_error(s)
+ { }
+};
+
+
+/**
+ * \brief Runtime error thrown during stepsize adjustment
+ *
+ * This Error occures when too many iterations are performed without finding
+ * an appropriate new step size. This usually indicates non-continuous points
+ * in the ODE.
+ */
+class step_adjustment_error : public odeint_error
+{
+public:
+ step_adjustment_error(const std::string &s)
+ : odeint_error(s)
+ { }
+};
+
+}
+}
+}
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_UTIL_ODEINT_ERROR_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/util/resize.hpp b/include/boost/numeric/odeint/util/resize.hpp
new file mode 100644
index 0000000..3645782
--- /dev/null
+++ b/include/boost/numeric/odeint/util/resize.hpp
@@ -0,0 +1,118 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/util/state_wrapper.hpp
+
+ [begin_description]
+ State wrapper for the state type in all stepper. The state wrappers are responsible for construction,
+ destruction, copying construction, assignment and resizing.
+ [end_description]
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_UTIL_RESIZE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_UTIL_RESIZE_HPP_INCLUDED
+
+#include <boost/range.hpp>
+
+#include <boost/utility/enable_if.hpp>
+#include <boost/fusion/include/is_sequence.hpp>
+#include <boost/fusion/include/zip_view.hpp>
+#include <boost/fusion/include/vector.hpp>
+#include <boost/fusion/include/make_fused.hpp>
+#include <boost/fusion/include/for_each.hpp>
+
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+template< class StateOut , class StateIn , class Enabler = void >
+struct resize_impl_sfinae
+{
+ static void resize( StateOut &x1 , const StateIn &x2 )
+ {
+ x1.resize( boost::size( x2 ) );
+ }
+};
+
+// resize function
+// standard implementation relies on boost.range and resize member function
+template< class StateOut , class StateIn >
+struct resize_impl
+{
+ static void resize( StateOut &x1 , const StateIn &x2 )
+ {
+ resize_impl_sfinae< StateOut , StateIn >::resize( x1 , x2 );
+ }
+};
+
+
+// do not overload or specialize this function, specialize resize_impl<> instead
+template< class StateOut , class StateIn >
+void resize( StateOut &x1 , const StateIn &x2 )
+{
+ resize_impl< StateOut , StateIn >::resize( x1 , x2 );
+}
+
+
+namespace detail {
+
+ struct resizer
+ {
+ typedef void result_type;
+
+ template< class StateOut , class StateIn >
+ void operator()( StateOut &x1 , const StateIn &x2 ) const
+ {
+ resize_op( x1 , x2 , typename is_resizeable< StateOut >::type() );
+ }
+
+ template< class StateOut , class StateIn >
+ void resize_op( StateOut &x1 , const StateIn &x2 , boost::true_type ) const
+ {
+ resize( x1 , x2 );
+ }
+
+ template< class StateOut , class StateIn >
+ void resize_op( StateOut &/*x1*/ , const StateIn &/*x2*/ , boost::false_type ) const
+ {
+ }
+
+ };
+} // namespace detail
+
+
+/*
+ * specialization for fusion sequences
+ */
+template< class FusionSeq >
+struct resize_impl_sfinae< FusionSeq , FusionSeq ,
+ typename boost::enable_if< typename boost::fusion::traits::is_sequence< FusionSeq >::type >::type >
+{
+ static void resize( FusionSeq &x1 , const FusionSeq &x2 )
+ {
+ typedef boost::fusion::vector< FusionSeq& , const FusionSeq& > Sequences;
+ Sequences sequences( x1 , x2 );
+ boost::fusion::for_each( boost::fusion::zip_view< Sequences >( sequences ) , boost::fusion::make_fused( detail::resizer() ) );
+ }
+};
+
+
+
+
+}
+}
+}
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_UTIL_RESIZE_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/util/resizer.hpp b/include/boost/numeric/odeint/util/resizer.hpp
new file mode 100644
index 0000000..cd27990
--- /dev/null
+++ b/include/boost/numeric/odeint/util/resizer.hpp
@@ -0,0 +1,93 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/util/resizer.hpp
+
+ [begin_description]
+ Implementation of the resizers.
+ [end_description]
+
+ Copyright 2011-2012 Mario Mulansky
+ Copyright 2011 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_UTIL_RESIZER_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_UTIL_RESIZER_HPP_INCLUDED
+
+
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/same_size.hpp>
+#include <boost/numeric/odeint/util/resize.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template< class ResizeWrappedState , class State >
+bool adjust_size_by_resizeability( ResizeWrappedState &x , const State &y , boost::true_type )
+{
+ if ( !same_size( x.m_v , y ) )
+ {
+ resize( x.m_v , y );
+ return true;
+ }
+ else
+ return false;
+}
+
+template< class ResizeWrappedState , class State >
+bool adjust_size_by_resizeability( ResizeWrappedState & /* x */ , const State & /* y */ , boost::false_type )
+{
+ return false;
+}
+
+struct always_resizer
+{
+ template< class State , class ResizeFunction >
+ bool adjust_size( const State &x , ResizeFunction f )
+ {
+ return f( x );
+ }
+};
+
+
+struct initially_resizer
+{
+
+ bool m_initialized;
+
+ initially_resizer() : m_initialized( false )
+ { }
+
+ template< class State , class ResizeFunction >
+ bool adjust_size( const State &x , ResizeFunction f )
+ {
+ if( !m_initialized )
+ {
+ m_initialized = true;
+ return f( x );
+ } else
+ return false;
+ }
+};
+
+
+struct never_resizer
+{
+ template< class State , class ResizeFunction >
+ bool adjust_size( const State &/*x*/ , ResizeFunction /*f*/ )
+ {
+ return false;
+ }
+};
+
+
+}
+}
+}
+
+#endif // BOOST_NUMERIC_ODEINT_UTIL_RESIZER_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/util/same_instance.hpp b/include/boost/numeric/odeint/util/same_instance.hpp
new file mode 100644
index 0000000..a889ee1
--- /dev/null
+++ b/include/boost/numeric/odeint/util/same_instance.hpp
@@ -0,0 +1,56 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/util/same_instance.hpp
+
+ [begin_description]
+ Basic check if two variables are the same instance
+ [end_description]
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_UTIL_SAME_INSTANCE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_UTIL_SAME_INSTANCE_HPP_INCLUDED
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template< class T1 , class T2 , class Enabler=void >
+struct same_instance_impl
+{
+ static bool same_instance( const T1& /* x1 */ , const T2& /* x2 */ )
+ {
+ return false;
+ }
+};
+
+template< class T >
+struct same_instance_impl< T , T >
+{
+ static bool same_instance( const T &x1 , const T &x2 )
+ {
+ // check pointers
+ return (&x1 == &x2);
+ }
+};
+
+
+template< class T1 , class T2 >
+bool same_instance( const T1 &x1 , const T2 &x2 )
+{
+ return same_instance_impl< T1 , T2 >::same_instance( x1 , x2 );
+}
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+#endif
diff --git a/include/boost/numeric/odeint/util/same_size.hpp b/include/boost/numeric/odeint/util/same_size.hpp
new file mode 100644
index 0000000..81ae249
--- /dev/null
+++ b/include/boost/numeric/odeint/util/same_size.hpp
@@ -0,0 +1,115 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/util/state_wrapper.hpp
+
+ [begin_description]
+ State wrapper for the state type in all stepper. The state wrappers are responsible for construction,
+ destruction, copying construction, assignment and resizing.
+ [end_description]
+
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_UTIL_SAME_SIZE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_UTIL_SAME_SIZE_HPP_INCLUDED
+
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+
+#include <boost/utility/enable_if.hpp>
+#include <boost/fusion/include/is_sequence.hpp>
+#include <boost/fusion/include/zip_view.hpp>
+#include <boost/fusion/include/vector.hpp>
+#include <boost/fusion/include/make_fused.hpp>
+#include <boost/fusion/include/all.hpp>
+
+#include <boost/range.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template< typename State1 , typename State2 , class Enabler = void >
+struct same_size_impl_sfinae
+{
+ static bool same_size( const State1 &x1 , const State2 &x2 )
+ {
+ return ( boost::size( x1 ) == boost::size( x2 ) );
+ }
+
+};
+
+// same_size function
+// standard implementation relies on boost.range
+template< class State1 , class State2 >
+struct same_size_impl
+{
+ static bool same_size( const State1 &x1 , const State2 &x2 )
+ {
+ return same_size_impl_sfinae< State1 , State2 >::same_size( x1 , x2 );
+ }
+};
+
+
+// do not overload or specialize this function, specialize resize_impl<> instead
+template< class State1 , class State2 >
+bool same_size( const State1 &x1 , const State2 &x2 )
+{
+ return same_size_impl< State1 , State2 >::same_size( x1 , x2 );
+}
+
+namespace detail {
+
+struct same_size_fusion
+{
+ typedef bool result_type;
+
+ template< class S1 , class S2 >
+ bool operator()( const S1 &x1 , const S2 &x2 ) const
+ {
+ return same_size_op( x1 , x2 , typename is_resizeable< S1 >::type() );
+ }
+
+ template< class S1 , class S2 >
+ bool same_size_op( const S1 &x1 , const S2 &x2 , boost::true_type ) const
+ {
+ return same_size( x1 , x2 );
+ }
+
+ template< class S1 , class S2 >
+ bool same_size_op( const S1 &/*x1*/ , const S2 &/*x2*/ , boost::false_type ) const
+ {
+ return true;
+ }
+};
+
+} // namespace detail
+
+
+
+template< class FusionSeq >
+struct same_size_impl_sfinae< FusionSeq , FusionSeq , typename boost::enable_if< typename boost::fusion::traits::is_sequence< FusionSeq >::type >::type >
+{
+ static bool same_size( const FusionSeq &x1 , const FusionSeq &x2 )
+ {
+ typedef boost::fusion::vector< const FusionSeq& , const FusionSeq& > Sequences;
+ Sequences sequences( x1 , x2 );
+ return boost::fusion::all( boost::fusion::zip_view< Sequences >( sequences ) ,
+ boost::fusion::make_fused( detail::same_size_fusion() ) );
+ }
+};
+
+
+}
+}
+}
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_UTIL_SAME_SIZE_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/util/split.hpp b/include/boost/numeric/odeint/util/split.hpp
new file mode 100644
index 0000000..ba9875a
--- /dev/null
+++ b/include/boost/numeric/odeint/util/split.hpp
@@ -0,0 +1,64 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/util/split.hpp
+
+ [begin_description]
+ Split abstraction for parallel backends.
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+ Copyright 2013 Pascal Germroth
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_UTIL_SPLIT_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_UTIL_SPLIT_HPP_INCLUDED
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+/*
+ * No default implementation of the split operation
+ */
+template< class Container1, class Container2 , class Enabler = void >
+struct split_impl
+{
+ static void split( const Container1 &from , Container2 &to );
+};
+
+template< class Container1 , class Container2 >
+void split( const Container1 &from , Container2 &to )
+{
+ split_impl< Container1 , Container2 >::split( from , to );
+}
+
+
+/*
+ * No default implementation of the unsplit operation
+ */
+template< class Container1, class Container2 , class Enabler = void >
+struct unsplit_impl
+{
+ static void unsplit( const Container1 &from , Container2 &to );
+};
+
+template< class Container1 , class Container2 >
+void unsplit( const Container1 &from , Container2 &to )
+{
+ unsplit_impl< Container1 , Container2 >::unsplit( from , to );
+}
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_UTIL_COPY_HPP_INCLUDED
+
diff --git a/include/boost/numeric/odeint/util/split_adaptor.hpp b/include/boost/numeric/odeint/util/split_adaptor.hpp
new file mode 100644
index 0000000..cf0d623
--- /dev/null
+++ b/include/boost/numeric/odeint/util/split_adaptor.hpp
@@ -0,0 +1,102 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/util/split_adaptor.hpp
+
+ [begin_description]
+ A range adaptor which returns even-sized slices.
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+ Copyright 2013 Pascal Germroth
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_UTIL_SPLIT_ADAPTOR_INCLUDED
+#define BOOST_NUMERIC_ODEINT_UTIL_SPLIT_ADAPTOR_INCLUDED
+
+#include <boost/range/adaptor/argument_fwd.hpp>
+#include <boost/range/size_type.hpp>
+#include <boost/range/iterator_range.hpp>
+#include <algorithm>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+/** \brief Returns the begin and end offset for a sub-range */
+inline std::pair<std::size_t, std::size_t>
+split_offsets( std::size_t total_length, std::size_t index, std::size_t parts )
+{
+ BOOST_ASSERT( parts > 0 );
+ BOOST_ASSERT( index < parts );
+ const std::size_t
+ slice = total_length / parts,
+ partial = total_length % parts,
+ lo = (std::min)(index, partial),
+ hi = (std::max<std::ptrdiff_t>)(0, index - partial),
+ begin_offset = lo * (slice + 1) + hi * slice,
+ length = slice + (index < partial ? 1 : 0),
+ end_offset = begin_offset + length;
+ return std::make_pair( begin_offset, end_offset );
+}
+
+/** \brief Return the sub-range `index` from a range which is split into `parts`.
+ *
+ * For example, splitting a range into three about equal-sized sub-ranges:
+ * \code
+ * sub0 = make_split_range(rng, 0, 3);
+ * sub1 = rng | split(1, 3);
+ * sub2 = rng | split(2, 3);
+ * \endcode
+ */
+template< class RandomAccessRange >
+inline iterator_range< typename range_iterator<RandomAccessRange>::type >
+make_split_range( RandomAccessRange& rng, std::size_t index, std::size_t parts )
+{
+ const std::pair<std::size_t, std::size_t> off = split_offsets(boost::size(rng), index, parts);
+ return make_iterator_range( boost::begin(rng) + off.first, boost::begin(rng) + off.second );
+}
+
+template< class RandomAccessRange >
+inline iterator_range< typename range_iterator<const RandomAccessRange>::type >
+make_split_range( const RandomAccessRange& rng, std::size_t index, std::size_t parts )
+{
+ const std::pair<std::size_t, std::size_t> off = split_offsets(boost::size(rng), index, parts);
+ return make_iterator_range( boost::begin(rng) + off.first, boost::begin(rng) + off.second );
+}
+
+
+struct split
+{
+ split(std::size_t index, std::size_t parts)
+ : index(index), parts(parts) {}
+ std::size_t index, parts;
+};
+
+template< class RandomAccessRange >
+inline iterator_range< typename range_iterator<RandomAccessRange>::type >
+operator|( RandomAccessRange& rng, const split& f )
+{
+ return make_split_range( rng, f.index, f.parts );
+}
+
+template< class RandomAccessRange >
+inline iterator_range< typename range_iterator<const RandomAccessRange>::type >
+operator|( const RandomAccessRange& rng, const split& f )
+{
+ return make_split_range( rng, f.index, f.parts );
+}
+
+
+}
+}
+}
+}
+
+#endif
diff --git a/include/boost/numeric/odeint/util/state_wrapper.hpp b/include/boost/numeric/odeint/util/state_wrapper.hpp
new file mode 100644
index 0000000..10f8ecd
--- /dev/null
+++ b/include/boost/numeric/odeint/util/state_wrapper.hpp
@@ -0,0 +1,50 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/util/state_wrapper.hpp
+
+ [begin_description]
+ State wrapper for the state type in all stepper. The state wrappers are responsible for construction,
+ destruction, copying construction, assignment and resizing.
+ [end_description]
+
+ Copyright 2011-2012 Mario Mulansky
+ Copyright 2011-2013 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_UTIL_STATE_WRAPPER_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_UTIL_STATE_WRAPPER_HPP_INCLUDED
+
+
+#include <boost/type_traits/integral_constant.hpp>
+
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resize.hpp>
+#include <boost/numeric/odeint/util/same_size.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+template< class V , class Enabler = void >
+struct state_wrapper
+{
+ typedef state_wrapper< V > state_wrapper_type;
+
+ V m_v;
+};
+
+
+}
+}
+}
+
+
+
+#endif // BOOST_NUMERIC_ODEINT_UTIL_STATE_WRAPPER_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/util/stepper_traits.hpp b/include/boost/numeric/odeint/util/stepper_traits.hpp
new file mode 100644
index 0000000..5d1d31a
--- /dev/null
+++ b/include/boost/numeric/odeint/util/stepper_traits.hpp
@@ -0,0 +1,63 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/util/stepper_traits.hpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_UTIL_STEPPER_TRAITS_HPP_DEFINED
+#define BOOST_NUMERIC_ODEINT_UTIL_STEPPER_TRAITS_HPP_DEFINED
+
+#include <boost/numeric/odeint/util/unwrap_reference.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace traits {
+
+template< class Stepper >
+struct state_type
+{
+ typedef typename boost::numeric::odeint::unwrap_reference< Stepper >::type stepper_type;
+ typedef typename stepper_type::state_type type;
+};
+
+template< class Stepper >
+struct time_type
+{
+ typedef typename boost::numeric::odeint::unwrap_reference< Stepper >::type stepper_type;
+ typedef typename stepper_type::time_type type;
+};
+
+template< class Stepper >
+struct stepper_category
+{
+ typedef typename boost::numeric::odeint::unwrap_reference< Stepper >::type stepper_type;
+ typedef typename stepper_type::stepper_category type;
+};
+
+template< class Stepper >
+struct value_type
+{
+ typedef typename boost::numeric::odeint::unwrap_reference< Stepper >::type stepper_type;
+ typedef typename stepper_type::value_type type;
+};
+
+} // namespace traits
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_UTIL_STEPPER_TRAITS_HPP_DEFINED
diff --git a/include/boost/numeric/odeint/util/ublas_matrix_expression.patch b/include/boost/numeric/odeint/util/ublas_matrix_expression.patch
new file mode 100644
index 0000000..4e8ac6c
--- /dev/null
+++ b/include/boost/numeric/odeint/util/ublas_matrix_expression.patch
@@ -0,0 +1,6 @@
+3390,3392c3390
+< typename enable_if< is_convertible<typename E1::value_type , T2>,
+< typename matrix_binary_scalar2_traits<E1, const T2, scalar_divides<typename E1::value_type, T2> >::result_type
+< > ::result_type
+---
+> typename matrix_binary_scalar2_traits<E1, const T2, scalar_divides<typename E1::value_type, T2> >::result_type
diff --git a/include/boost/numeric/odeint/util/ublas_wrapper.hpp b/include/boost/numeric/odeint/util/ublas_wrapper.hpp
new file mode 100644
index 0000000..c8facfc
--- /dev/null
+++ b/include/boost/numeric/odeint/util/ublas_wrapper.hpp
@@ -0,0 +1,297 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/util/ublas_wrapper.hpp
+
+ [begin_description]
+ Resizing for ublas::vector and ublas::matrix
+ [end_description]
+
+ Copyright 2011-2013 Mario Mulansky
+ Copyright 2011-2013 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_UTIL_UBLAS_WRAPPER_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_UTIL_UBLAS_WRAPPER_HPP_INCLUDED
+
+
+#include <boost/type_traits/integral_constant.hpp>
+#include <boost/numeric/ublas/vector.hpp>
+#include <boost/numeric/ublas/matrix.hpp>
+#include <boost/numeric/ublas/lu.hpp>
+#include <boost/numeric/ublas/vector_expression.hpp>
+#include <boost/numeric/ublas/matrix_expression.hpp>
+
+#include <boost/numeric/odeint/algebra/vector_space_algebra.hpp>
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/state_wrapper.hpp>
+
+
+/* extend ublas by a few operations */
+
+/* map norm_inf onto reduce( v , default_operations::maximum ) */
+namespace boost { namespace numeric { namespace odeint {
+
+ template< typename T , typename A >
+ struct vector_space_norm_inf< boost::numeric::ublas::vector<T,A> >
+ {
+ typedef T result_type;
+
+ result_type operator()( const boost::numeric::ublas::vector<T,A> &x ) const
+ {
+ return boost::numeric::ublas::norm_inf( x );
+ }
+ };
+
+
+ template< class T , class L , class A >
+ struct vector_space_norm_inf< boost::numeric::ublas::matrix<T,L,A> >
+ {
+ typedef T result_type;
+
+ result_type operator()( const boost::numeric::ublas::matrix<T,L,A> &x ) const
+ {
+ return boost::numeric::ublas::norm_inf( x );
+ }
+ };
+} } }
+
+/* additional operations:
+ * abs( v )
+ * v / w
+ * a + v
+ */
+namespace boost { namespace numeric { namespace ublas {
+
+
+ // elementwise abs - calculates absolute values of the elements
+ template<class T>
+ struct scalar_abs: public scalar_unary_functor<T> {
+ typedef typename scalar_unary_functor<T>::value_type value_type;
+ typedef typename scalar_unary_functor<T>::argument_type argument_type;
+ typedef typename scalar_unary_functor<T>::result_type result_type;
+
+ static BOOST_UBLAS_INLINE
+ result_type apply (argument_type t) {
+ using std::abs;
+ return abs (t);
+ }
+ };
+
+
+ // (abs v) [i] = abs (v [i])
+ template<class E>
+ BOOST_UBLAS_INLINE
+ typename vector_unary_traits<E, scalar_abs<typename E::value_type> >::result_type
+ abs (const vector_expression<E> &e) {
+ typedef typename vector_unary_traits<E, scalar_abs<typename E::value_type> >::expression_type expression_type;
+ return expression_type (e ());
+ }
+
+ // (abs m) [i] = abs (m [i])
+ template<class E>
+ BOOST_UBLAS_INLINE
+ typename matrix_unary1_traits<E, scalar_abs<typename E::value_type> >::result_type
+ abs (const matrix_expression<E> &e) {
+ typedef typename matrix_unary1_traits<E, scalar_abs<typename E::value_type> >::expression_type expression_type;
+ return expression_type (e ());
+ }
+
+
+ // elementwise division (v1 / v2) [i] = v1 [i] / v2 [i]
+ template<class E1, class E2>
+ BOOST_UBLAS_INLINE
+ typename vector_binary_traits<E1, E2, scalar_divides<typename E1::value_type,
+ typename E2::value_type> >::result_type
+ operator / (const vector_expression<E1> &e1,
+ const vector_expression<E2> &e2) {
+ typedef typename vector_binary_traits<E1, E2, scalar_divides<typename E1::value_type,
+ typename E2::value_type> >::expression_type expression_type;
+ return expression_type (e1 (), e2 ());
+ }
+
+
+ // elementwise division (m1 / m2) [i] = m1 [i] / m2 [i]
+ template<class E1, class E2>
+ BOOST_UBLAS_INLINE
+ typename matrix_binary_traits<E1, E2, scalar_divides<typename E1::value_type,
+ typename E2::value_type> >::result_type
+ operator / (const matrix_expression<E1> &e1,
+ const matrix_expression<E2> &e2) {
+ typedef typename matrix_binary_traits<E1, E2, scalar_divides<typename E1::value_type,
+ typename E2::value_type> >::expression_type expression_type;
+ return expression_type (e1 (), e2 ());
+ }
+
+ // addition with scalar
+ // (t + v) [i] = t + v [i]
+ template<class T1, class E2>
+ BOOST_UBLAS_INLINE
+ typename enable_if< is_convertible<T1, typename E2::value_type >,
+ typename vector_binary_scalar1_traits<const T1, E2, scalar_plus<T1, typename E2::value_type> >::result_type
+ >::type
+ operator + (const T1 &e1,
+ const vector_expression<E2> &e2) {
+ typedef typename vector_binary_scalar1_traits<const T1, E2, scalar_plus<T1, typename E2::value_type> >::expression_type expression_type;
+ return expression_type (e1, e2 ());
+ }
+
+ // addition with scalar
+ // (t + m) [i] = t + m [i]
+ template<class T1, class E2>
+ BOOST_UBLAS_INLINE
+ typename enable_if< is_convertible<T1, typename E2::value_type >,
+ typename matrix_binary_scalar1_traits<const T1, E2, scalar_plus<T1, typename E2::value_type> >::result_type
+ >::type
+ operator + (const T1 &e1,
+ const matrix_expression<E2> &e2) {
+ typedef typename matrix_binary_scalar1_traits<const T1, E2, scalar_plus<T1, typename E2::value_type> >::expression_type expression_type;
+ return expression_type (e1, e2 ());
+ }
+
+} } }
+
+
+
+
+/* add resize functionality */
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+/*
+ * resizeable specialization for boost::numeric::ublas::vector
+ */
+template< class T , class A >
+struct is_resizeable< boost::numeric::ublas::vector< T , A > >
+{
+ typedef boost::true_type type;
+ const static bool value = type::value;
+};
+
+
+/*
+ * resizeable specialization for boost::numeric::ublas::matrix
+ */
+template< class T , class L , class A >
+struct is_resizeable< boost::numeric::ublas::matrix< T , L , A > >
+{
+ typedef boost::true_type type;
+ const static bool value = type::value;
+};
+
+
+/*
+ * resizeable specialization for boost::numeric::ublas::permutation_matrix
+ */
+template< class T , class A >
+struct is_resizeable< boost::numeric::ublas::permutation_matrix< T , A > >
+{
+ typedef boost::true_type type;
+ const static bool value = type::value;
+};
+
+
+// specialization for ublas::matrix
+// same size and resize specialization for matrix-matrix resizing
+template< class T , class L , class A , class T2 , class L2 , class A2 >
+struct same_size_impl< boost::numeric::ublas::matrix< T , L , A > , boost::numeric::ublas::matrix< T2 , L2 , A2 > >
+{
+ static bool same_size( const boost::numeric::ublas::matrix< T , L , A > &m1 ,
+ const boost::numeric::ublas::matrix< T2 , L2 , A2 > &m2 )
+ {
+ return ( ( m1.size1() == m2.size1() ) && ( m1.size2() == m2.size2() ) );
+ }
+};
+
+template< class T , class L , class A , class T2 , class L2 , class A2 >
+struct resize_impl< boost::numeric::ublas::matrix< T , L , A > , boost::numeric::ublas::matrix< T2 , L2 , A2 > >
+{
+ static void resize( boost::numeric::ublas::matrix< T , L , A > &m1 ,
+ const boost::numeric::ublas::matrix< T2 , L2 , A2 > &m2 )
+ {
+ m1.resize( m2.size1() , m2.size2() );
+ }
+};
+
+
+
+// same size and resize specialization for matrix-vector resizing
+template< class T , class L , class A , class T_V , class A_V >
+struct same_size_impl< boost::numeric::ublas::matrix< T , L , A > , boost::numeric::ublas::vector< T_V , A_V > >
+{
+ static bool same_size( const boost::numeric::ublas::matrix< T , L , A > &m ,
+ const boost::numeric::ublas::vector< T_V , A_V > &v )
+ {
+ return ( ( m.size1() == v.size() ) && ( m.size2() == v.size() ) );
+ }
+};
+
+template< class T , class L , class A , class T_V , class A_V >
+struct resize_impl< boost::numeric::ublas::matrix< T , L , A > , boost::numeric::ublas::vector< T_V , A_V > >
+{
+ static void resize( boost::numeric::ublas::matrix< T , L , A > &m ,
+ const boost::numeric::ublas::vector< T_V , A_V > &v )
+ {
+ m.resize( v.size() , v.size() );
+ }
+};
+
+
+
+// specialization for ublas::permutation_matrix
+// same size and resize specialization for matrix-vector resizing
+template< class T , class A , class T_V , class A_V >
+struct same_size_impl< boost::numeric::ublas::permutation_matrix< T , A > ,
+ boost::numeric::ublas::vector< T_V , A_V > >
+{
+ static bool same_size( const boost::numeric::ublas::permutation_matrix< T , A > &m ,
+ const boost::numeric::ublas::vector< T_V , A_V > &v )
+ {
+ return ( m.size() == v.size() ); // && ( m.size2() == v.size() ) );
+ }
+};
+
+template< class T , class A , class T_V , class A_V >
+struct resize_impl< boost::numeric::ublas::vector< T_V , A_V > ,
+ boost::numeric::ublas::permutation_matrix< T , A > >
+{
+ static void resize( const boost::numeric::ublas::vector< T_V , A_V > &v,
+ boost::numeric::ublas::permutation_matrix< T , A > &m )
+ {
+ m.resize( v.size() , v.size() );
+ }
+};
+
+
+
+
+
+
+
+template< class T , class A >
+struct state_wrapper< boost::numeric::ublas::permutation_matrix< T , A > > // with resizing
+{
+ typedef boost::numeric::ublas::permutation_matrix< T , A > state_type;
+ typedef state_wrapper< state_type > state_wrapper_type;
+
+ state_type m_v;
+
+ state_wrapper() : m_v( 1 ) // permutation matrix constructor requires a size, choose 1 as default
+ { }
+
+};
+
+
+
+
+} } }
+
+
+#endif // BOOST_NUMERIC_ODEINT_UTIL_UBLAS_WRAPPER_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/util/unit_helper.hpp b/include/boost/numeric/odeint/util/unit_helper.hpp
new file mode 100644
index 0000000..736b3e5
--- /dev/null
+++ b/include/boost/numeric/odeint/util/unit_helper.hpp
@@ -0,0 +1,151 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/util/unit_helper.hpp
+
+ [begin_description]
+ Get and set the value of a unit.
+ [end_description]
+
+ Copyright 2012-2013 Karsten Ahnert
+ Copyright 2012-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef BOOST_NUMERIC_ODEINT_UTIL_UNIT_HELPER_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_UTIL_UNIT_HELPER_HPP_INCLUDED
+
+
+#ifndef __CUDACC__
+#include <boost/units/quantity.hpp>
+#include <boost/units/get_dimension.hpp>
+#include <boost/units/get_system.hpp>
+#endif
+
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+namespace detail {
+
+ template<class T , class Enabler = void >
+ struct get_unit_value_impl
+ {
+ static T value(const T &t)
+ {
+ return t;
+ }
+ typedef T result_type;
+ };
+
+#ifndef __CUDACC__
+ template<class Unit , class T>
+ struct get_unit_value_impl< boost::units::quantity< Unit , T> >
+ {
+ static T value( const boost::units::quantity< Unit , T> &t )
+ {
+ return t.value();
+ }
+ typedef T result_type;
+ };
+#endif
+
+
+
+
+
+ template<class T , class V , class Enabler = void >
+ struct set_unit_value_impl
+ {
+ static void set_value(T &t , const V &v)
+ {
+ t = v;
+ }
+ };
+
+#ifndef __CUDACC__
+ template<class Unit , class T , class V>
+ struct set_unit_value_impl<boost::units::quantity<Unit , T> , V>
+ {
+ static void set_value(boost::units::quantity<Unit , T> &t , const V &v)
+ {
+ t = boost::units::quantity<Unit , T>::from_value(v);
+ }
+ };
+#endif
+
+
+
+} // namespace detail
+
+
+ template<class T>
+ typename detail::get_unit_value_impl<T>::result_type get_unit_value(const T &t)
+ {
+ return detail::get_unit_value_impl<T>::value(t);
+ }
+
+
+ template<class T , class V>
+ void set_unit_value(T &t , const V &v)
+ {
+ return detail::set_unit_value_impl<T , V>::set_value(t , v);
+ }
+
+
+
+ template< class T >
+ struct unit_value_type
+ {
+ typedef T type;
+ };
+
+#ifndef __CUDACC__
+ template< class Unit , class Y >
+ struct unit_value_type< boost::units::quantity< Unit , Y > >
+ {
+ typedef Y type;
+ };
+#endif
+
+
+
+
+
+
+
+
+
+
+ template< typename Time >
+ struct inverse_time
+ {
+ typedef Time type;
+ };
+
+#ifndef __CUDACC__
+ template< typename Unit , typename Value >
+ struct inverse_time< boost::units::quantity< Unit , Value > >
+ {
+ typedef boost::units::quantity< Unit , Value > time_type;
+ typedef typename boost::units::get_dimension< time_type >::type dimension;
+ typedef typename boost::units::get_system< time_type >::type system;
+ typedef typename boost::mpl::divides< boost::units::dimensionless_type , dimension >::type inv_dimension;
+ typedef boost::units::unit< inv_dimension , system > inv_unit;
+ typedef boost::units::quantity< inv_unit , Value > type;
+ };
+#endif
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_UTIL_UNIT_HELPER_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/util/unwrap_reference.hpp b/include/boost/numeric/odeint/util/unwrap_reference.hpp
new file mode 100644
index 0000000..e160878
--- /dev/null
+++ b/include/boost/numeric/odeint/util/unwrap_reference.hpp
@@ -0,0 +1,166 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/util/unwrap_reference.hpp
+
+ [begin_description]
+ unwrap_reference
+ [end_description]
+
+ Copyright 2012-2013 Karsten Ahnert
+ Copyright 2012-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_NUMERIC_ODEINT_UTIL_UNWRAP_REFERENCE_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_UTIL_UNWRAP_REFERENCE_HPP_INCLUDED
+
+
+#include <boost/numeric/odeint/config.hpp>
+
+
+#if BOOST_NUMERIC_ODEINT_CXX11
+#include <functional>
+#else
+#include <boost/ref.hpp>
+#endif
+
+namespace boost {
+
+#if BOOST_NUMERIC_ODEINT_CXX11
+template<typename T> class reference_wrapper;
+
+template<typename T> struct unwrap_reference;
+#endif
+
+namespace numeric {
+namespace odeint {
+
+
+#if BOOST_NUMERIC_ODEINT_CXX11
+
+template<typename T>
+struct unwrap_reference
+{
+ typedef typename std::remove_reference<T>::type type;
+};
+
+template<typename T>
+struct unwrap_reference< std::reference_wrapper<T> >
+{
+ typedef typename std::remove_reference<T>::type type;
+};
+
+template<typename T>
+struct unwrap_reference< boost::reference_wrapper<T> >
+{
+ typedef typename boost::unwrap_reference<T>::type type;
+};
+
+#else
+
+using ::boost::unwrap_reference;
+
+#endif
+
+namespace detail
+{
+
+#if BOOST_NUMERIC_ODEINT_CXX11
+
+using ::std::ref;
+
+#else
+
+using ::boost::ref;
+
+#endif
+}
+
+}
+}
+}
+
+
+
+/*
+ *
+ * the following is the suggested way, but unfortunately it does not work with all compilers.
+ */
+
+/*
+
+#include <boost/config.hpp>
+
+
+#ifdef BOOST_NO_CXX11_HDR_FUNCTIONAL
+#include <boost/ref.hpp>
+#else
+#include <functional>
+#endif
+
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+#ifndef BOOST_NO_CXX11_HDR_FUNCTIONAL
+
+template<typename T>
+struct unwrap_reference
+{
+ typedef typename std::remove_reference<T>::type type;
+};
+
+template<typename T>
+struct unwrap_reference< std::reference_wrapper<T> >
+{
+ typedef typename std::remove_reference<T>::type type;
+};
+
+template<typename T>
+struct unwrap_reference< boost::reference_wrapper<T> >
+{
+ typedef typename boost::unwrap_reference<T>::type type;
+};
+
+#else
+
+using ::boost::unwrap_reference;
+
+#endif
+
+}
+}
+}
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+namespace detail {
+
+
+#ifndef BOOST_NO_CXX11_HDR_FUNCTIONAL
+
+using ::std::ref;
+
+#else
+
+using ::boost::ref;
+
+#endif
+
+
+}
+}
+}
+}
+
+*/
+
+#endif // BOOST_NUMERIC_ODEINT_UTIL_UNWRAP_REFERENCE_HPP_INCLUDED
diff --git a/include/boost/numeric/odeint/version.hpp b/include/boost/numeric/odeint/version.hpp
new file mode 100644
index 0000000..379c906
--- /dev/null
+++ b/include/boost/numeric/odeint/version.hpp
@@ -0,0 +1,55 @@
+/*
+ [auto_generated]
+ boost/numeric/odeint/version.hpp
+
+ [begin_description]
+ Defines the current version of odeint.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#ifndef BOOST_NUMERIC_ODEINT_VERSION_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_VERSION_HPP_INCLUDED
+
+#include <string>
+#include <sstream>
+
+
+#define ODEINT_MAJOR_VERSION 2
+#define ODEINT_MINOR_VERSION 2
+#define ODEINT_PATCH_LEVEL 0
+#define ODEINT_VERSION ( ODEINT_MAJOR_VERSION * 100000 + ODEINT_MINOR_VERSION * 100 + ODEINT_PATCH_LEVEL )
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+namespace version {
+
+const int major = ODEINT_MAJOR_VERSION ;
+const int minor = ODEINT_MINOR_VERSION ;
+const int patch_level = ODEINT_PATCH_LEVEL ;
+
+}
+
+inline std::string get_version_string( void )
+{
+ std::ostringstream str;
+ str << "v" << version::major << "." << version::minor;
+ if( version::patch_level != 0 ) str << "_" << version::patch_level;
+ return str.str();
+}
+
+
+}
+}
+}
+
+#endif // BOOST_NUMERIC_ODEINT_VERSION_HPP_INCLUDED
diff --git a/index.html b/index.html
new file mode 100644
index 0000000..20c1314
--- /dev/null
+++ b/index.html
@@ -0,0 +1,20 @@
+<!--
+Copyright 2012 Beman Daves
+Copyright 2012 Karsten Ahnert
+Distributed under the Boost Software License, Version 1.0. (See accompanying
+file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+-->
+<html>
+<head>
+<meta http-equiv="refresh" content="0; URL=doc/html/index.html">
+</head>
+<body>
+Automatic redirection failed, please go to
+<a href="doc/html/index.html">doc/html/index.html</a>
+<hr>
+<p>© Copyright Beman Dawes, 2001</p>
+<p> Distributed under the Boost Software
+License, Version 1.0. (See accompanying file <a href="../../../LICENSE_1_0.txt">LICENSE_1_0.txt</a> or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
+www.boost.org/LICENSE_1_0.txt</a>)</p>
+</body>
+</html>
diff --git a/meta/libraries.json b/meta/libraries.json
new file mode 100644
index 0000000..7825fec
--- /dev/null
+++ b/meta/libraries.json
@@ -0,0 +1,16 @@
+{
+ "key": "numeric/odeint",
+ "name": "Odeint",
+ "authors": [
+ "Karsten Ahnert",
+ "Mario Mulansky"
+ ],
+ "description": "Solving ordinary differential equations.",
+ "category": [
+ "Math"
+ ],
+ "maintainers": [
+ "Karsten Ahnert <karsten.ahnert -at- gmx.de>",
+ "Mario Mulansky <mario.mulansky -at- gmx.net>"
+ ]
+}
diff --git a/performance/Jamfile.v2 b/performance/Jamfile.v2
new file mode 100644
index 0000000..e60e4ea
--- /dev/null
+++ b/performance/Jamfile.v2
@@ -0,0 +1,32 @@
+# Copyright 2012 Karsten Ahnert
+# Copyright 2012 Mario Mulansky
+# Distributed under the Boost Software License, Version 1.0.
+# (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+import os ;
+import modules ;
+import path ;
+
+project
+ : requirements
+ <define>BOOST_ALL_NO_LIB=1
+ <include>../../../..
+ <cxxflags>-std=c++11
+ <toolset>gcc:<cxxflags>-ffast-math
+ <toolset>intel:<cxxflags>"-fast -inline-forceinline"
+ : default-build release
+ ;
+
+
+lib libgsl : : <name>gsl ;
+lib libgslcblas : : <name>gslcblas ;
+
+lib libmkl : : <name>mkl_intel_lp64 <link>shared ;
+lib libmkl_core : : <name>mkl_core <link>shared ;
+lib libmkl_intel_thread : : <name>mkl_intel_thread ;
+lib libiomp5 : : <name>iomp5 ;
+lib libpthread : : <name>pthread ;
+
+exe odeint_rk4_array
+ : odeint_rk4_array.cpp
+ ;
diff --git a/performance/Makefile b/performance/Makefile
new file mode 100644
index 0000000..641cb03
--- /dev/null
+++ b/performance/Makefile
@@ -0,0 +1,43 @@
+# Copyright 2011-2014 Mario Mulansky
+# Copyright 2011-2014 Karsten Ahnert
+#
+# Distributed under the Boost Software License, Version 1.0.
+# (See accompanying file LICENSE_1_0.txt or
+# copy at http://www.boost.org/LICENSE_1_0.txt)
+
+# make sure BOOST_ROOT is pointing to your boost directory
+# otherwise, set it here:
+# BOOST_ROOT = /path/to/boost
+
+INCLUDES += -I../../include/ -I$(BOOST_ROOT)
+GCCFLAGS = -O3 -ffast-math -DNDEBUG
+# disabling -ffast-math might give slightly better performance
+ICCFLAGS = -Ofast -xHost -ip -inline-forceinline -DNDEBUG
+# Possible options: -fp-model source -no-fma
+GFORTFLAGS = -Ofast
+
+bin/gcc:
+ mkdir -p bin/gcc
+
+bin/intel:
+ mkdir -p bin/intel
+
+bin/gfort:
+ mkdir -p bin/gfort
+
+bin/gcc/odeint_rk4_array: odeint_rk4_array.cpp bin/gcc
+ g++ ${GCCFLAGS} ${INCLUDES} -o bin/gcc/odeint_rk4_array odeint_rk4_array.cpp
+
+bin/gcc/c_lorenz: c_lorenz.c bin/gcc
+ gcc -std=c99 -Ofast -mtune=corei7-avx c_lorenz.c -o bin/gcc/c_lorenz
+
+bin/intel/odeint_rk4_array: odeint_rk4_array.cpp bin/intel
+ icpc ${ICCFLAGS} ${INCLUDES} -o bin/intel/odeint_rk4_array odeint_rk4_array.cpp
+
+bin/intel/c_lorenz: c_lorenz.c bin/intel
+ icc -std=c99 -Ofast -xHost -ansi-alias -o bin/intel/c_lorenz c_lorenz.c
+
+bin/gfort/fortran_lorenz: fortran_lorenz.f90 bin/gfort
+ gfortran ${GFORTFLAGS} fortran_lorenz.f90 -o bin/gfort/fortran_lorenz
+
+all: bin/gcc/odeint_rk4_array bin/intel/odeint_rk4_array bin/gcc/c_lorenz bin/intel/c_lorenz bin/gfort/fortran_lorenz
diff --git a/performance/SIMD/Makefile b/performance/SIMD/Makefile
new file mode 100644
index 0000000..811acd9
--- /dev/null
+++ b/performance/SIMD/Makefile
@@ -0,0 +1,33 @@
+# Copyright 2014 Mario Mulansky
+#
+# Distributed under the Boost Software License, Version 1.0.
+# (See accompanying file LICENSE_1_0.txt or
+# copy at http://www.boost.org/LICENSE_1_0.txt)
+
+# make sure BOOST_ROOT is pointing to your boost directory
+# otherwise, set it here:
+# BOOST_ROOT = /path/to/boost
+# you also need NT2s SIMD libary available set the include path here:
+# SIMD_INCLUDE = /path/to/simd/include
+
+INCLUDES = -I$(BOOST_ROOT) -I${SIMD_INCLUDE}
+
+# INTEL COMPILER
+# change this if you want to cross-compile
+ARCH = Host
+# ARCH = AVX
+# ARCH = SSE4.2
+
+CXX = icpc
+CC = icpc
+CXXFLAGS = -O3 -x${ARCH} -std=c++0x -fno-alias -inline-forceinline -DNDEBUG ${INCLUDES}
+# -ip
+
+# GCC COMPILER
+# change this if you want to cross-compile
+# ARCH = native
+# # ARCH = core-avx-i
+
+# CXX = g++
+# CC = g++
+# CXXFLAGS = -O3 -ffast-math -mtune=${ARCH} -march=${ARCH} -std=c++0x -DNDEBUG ${INCLUDES}
diff --git a/performance/SIMD/perf_roessler.sh b/performance/SIMD/perf_roessler.sh
new file mode 100755
index 0000000..a1094f6
--- /dev/null
+++ b/performance/SIMD/perf_roessler.sh
@@ -0,0 +1,22 @@
+#!/bin/bash
+echo "Running on ${HOSTNAME}"
+
+out_dir=perf_${HOSTNAME}
+mkdir -p ${out_dir}
+
+for N in 256 1024 4096 16384 65536 262144 1048576 4194304 16777216 67108864
+do
+ steps=`expr 4 \* 67108864 / ${N}`
+ for exe in "roessler" "roessler_simd"
+ do
+ rm -f ${out_dir}/${exe}_N${N}.times
+ for i in {0..4}
+ do
+ likwid-pin -cS0:0 ./${exe} ${N} ${steps} >> ${out_dir}/${exe}_N${N}.times
+ done
+ for perf_ctr in "FLOPS_DP" "FLOPS_AVX" "L2" "L3" "MEM"
+ do
+ likwid-perfctr -CS0:0 -g ${perf_ctr} ./${exe} ${N} ${steps} > ${out_dir}/${exe}_N${N}_${perf_ctr}.perf
+ done
+ done
+done
diff --git a/performance/SIMD/roessler.cpp b/performance/SIMD/roessler.cpp
new file mode 100644
index 0000000..4e6cc42
--- /dev/null
+++ b/performance/SIMD/roessler.cpp
@@ -0,0 +1,125 @@
+/*
+ * Simulation of an ensemble of Roessler attractors
+ *
+ * Copyright 2014 Mario Mulansky
+ *
+ * Distributed under the Boost Software License, Version 1.0.
+ * (See accompanying file LICENSE_1_0.txt or
+ * copy at http://www.boost.org/LICENSE_1_0.txt)
+ *
+ */
+
+
+#include <iostream>
+#include <vector>
+#include <random>
+
+#include <boost/timer.hpp>
+#include <boost/array.hpp>
+
+#include <boost/numeric/odeint.hpp>
+
+namespace odeint = boost::numeric::odeint;
+
+typedef boost::timer timer_type;
+
+typedef double fp_type;
+//typedef float fp_type;
+
+typedef boost::array<fp_type, 3> state_type;
+typedef std::vector<state_type> state_vec;
+
+//---------------------------------------------------------------------------
+struct roessler_system {
+ const fp_type m_a, m_b, m_c;
+
+ roessler_system(const fp_type a, const fp_type b, const fp_type c)
+ : m_a(a), m_b(b), m_c(c)
+ {}
+
+ void operator()(const state_type &x, state_type &dxdt, const fp_type t) const
+ {
+ dxdt[0] = -x[1] - x[2];
+ dxdt[1] = x[0] + m_a * x[1];
+ dxdt[2] = m_b + x[2] * (x[0] - m_c);
+ }
+};
+
+//---------------------------------------------------------------------------
+int main(int argc, char *argv[]) {
+if(argc<3)
+{
+ std::cerr << "Expected size and steps as parameter" << std::endl;
+ exit(1);
+}
+const size_t n = atoi(argv[1]);
+const size_t steps = atoi(argv[2]);
+//const size_t steps = 50;
+
+const fp_type dt = 0.01;
+
+const fp_type a = 0.2;
+const fp_type b = 1.0;
+const fp_type c = 9.0;
+
+// random initial conditions on the device
+std::vector<fp_type> x(n), y(n), z(n);
+std::default_random_engine generator;
+std::uniform_real_distribution<fp_type> distribution_xy(-8.0, 8.0);
+std::uniform_real_distribution<fp_type> distribution_z(0.0, 20.0);
+auto rand_xy = std::bind(distribution_xy, std::ref(generator));
+auto rand_z = std::bind(distribution_z, std::ref(generator));
+std::generate(x.begin(), x.end(), rand_xy);
+std::generate(y.begin(), y.end(), rand_xy);
+std::generate(z.begin(), z.end(), rand_z);
+
+state_vec state(n);
+for(size_t i=0; i<n; ++i)
+{
+ state[i][0] = x[i];
+ state[i][1] = y[i];
+ state[i][2] = z[i];
+}
+
+std::cout.precision(16);
+
+std::cout << "# n: " << n << std::endl;
+
+std::cout << x[0] << std::endl;
+
+
+// Stepper type - use never_resizer for slight performance improvement
+odeint::runge_kutta4_classic<state_type, fp_type, state_type, fp_type,
+ odeint::array_algebra,
+ odeint::default_operations,
+ odeint::never_resizer> stepper;
+
+roessler_system sys(a, b, c);
+
+timer_type timer;
+
+fp_type t = 0.0;
+
+for (int step = 0; step < steps; step++)
+{
+ for(size_t i=0; i<n; ++i)
+ {
+ stepper.do_step(sys, state[i], t, dt);
+ }
+ t += dt;
+}
+
+std::cout << "Integration finished, runtime for " << steps << " steps: ";
+std::cout << timer.elapsed() << " s" << std::endl;
+
+// compute some accumulation to make sure all results have been computed
+fp_type s = 0.0;
+for(size_t i = 0; i < n; ++i)
+{
+ s += state[i][0];
+}
+
+std::cout << state[0][0] << std::endl;
+std::cout << s/n << std::endl;
+
+}
diff --git a/performance/SIMD/roessler_simd.cpp b/performance/SIMD/roessler_simd.cpp
new file mode 100644
index 0000000..d79af4d
--- /dev/null
+++ b/performance/SIMD/roessler_simd.cpp
@@ -0,0 +1,149 @@
+/*
+ * Simulation of an ensemble of Roessler attractors using NT2 SIMD library
+ * This requires the SIMD library headers.
+ *
+ * Copyright 2014 Mario Mulansky
+ *
+ * Distributed under the Boost Software License, Version 1.0.
+ * (See accompanying file LICENSE_1_0.txt or
+ * copy at http://www.boost.org/LICENSE_1_0.txt)
+ *
+ */
+
+
+#include <iostream>
+#include <vector>
+#include <random>
+
+#include <boost/timer.hpp>
+#include <boost/array.hpp>
+
+#include <boost/numeric/odeint.hpp>
+#include <boost/simd/sdk/simd/pack.hpp>
+#include <boost/simd/sdk/simd/io.hpp>
+#include <boost/simd/memory/allocator.hpp>
+#include <boost/simd/include/functions/splat.hpp>
+#include <boost/simd/include/functions/plus.hpp>
+#include <boost/simd/include/functions/multiplies.hpp>
+
+
+namespace odeint = boost::numeric::odeint;
+namespace simd = boost::simd;
+
+typedef boost::timer timer_type;
+
+static const size_t dim = 3; // roessler is 3D
+
+typedef double fp_type;
+//typedef float fp_type;
+
+typedef simd::pack<fp_type> simd_pack;
+typedef boost::array<simd_pack, dim> state_type;
+// use the simd allocator to get properly aligned memory
+typedef std::vector< state_type, simd::allocator< state_type > > state_vec;
+
+static const size_t pack_size = simd_pack::static_size;
+
+//---------------------------------------------------------------------------
+struct roessler_system {
+ const fp_type m_a, m_b, m_c;
+
+ roessler_system(const fp_type a, const fp_type b, const fp_type c)
+ : m_a(a), m_b(b), m_c(c)
+ {}
+
+ void operator()(const state_type &x, state_type &dxdt, const fp_type t) const
+ {
+ dxdt[0] = -1.0*x[1] - x[2];
+ dxdt[1] = x[0] + m_a * x[1];
+ dxdt[2] = m_b + x[2] * (x[0] - m_c);
+ }
+};
+
+//---------------------------------------------------------------------------
+int main(int argc, char *argv[]) {
+if(argc<3)
+{
+ std::cerr << "Expected size and steps as parameter" << std::endl;
+ exit(1);
+}
+const size_t n = atoi(argv[1]);
+const size_t steps = atoi(argv[2]);
+
+const fp_type dt = 0.01;
+
+const fp_type a = 0.2;
+const fp_type b = 1.0;
+const fp_type c = 9.0;
+
+// random initial conditions on the device
+std::vector<fp_type> x(n), y(n), z(n);
+std::default_random_engine generator;
+std::uniform_real_distribution<fp_type> distribution_xy(-8.0, 8.0);
+std::uniform_real_distribution<fp_type> distribution_z(0.0, 20.0);
+auto rand_xy = std::bind(distribution_xy, std::ref(generator));
+auto rand_z = std::bind(distribution_z, std::ref(generator));
+std::generate(x.begin(), x.end(), rand_xy);
+std::generate(y.begin(), y.end(), rand_xy);
+std::generate(z.begin(), z.end(), rand_z);
+
+state_vec state(n/pack_size);
+for(size_t i=0; i<n/pack_size; ++i)
+{
+ for(size_t p=0; p<pack_size; ++p)
+ {
+ state[i][0][p] = x[i*pack_size+p];
+ state[i][1][p] = y[i*pack_size+p];
+ state[i][2][p] = z[i*pack_size+p];
+ }
+}
+
+std::cout << "Systems: " << n << std::endl;
+std::cout << "Steps: " << steps << std::endl;
+std::cout << "SIMD pack size: " << pack_size << std::endl;
+
+std::cout << state[0][0] << std::endl;
+
+// Stepper type
+odeint::runge_kutta4_classic<state_type, fp_type, state_type, fp_type,
+ odeint::array_algebra, odeint::default_operations,
+ odeint::never_resizer> stepper;
+
+roessler_system sys(a, b, c);
+
+timer_type timer;
+
+fp_type t = 0.0;
+
+for(int step = 0; step < steps; step++)
+{
+ for(size_t i = 0; i < n/pack_size; ++i)
+ {
+ stepper.do_step(sys, state[i], t, dt);
+ }
+ t += dt;
+}
+
+std::cout.precision(16);
+
+std::cout << "Integration finished, runtime for " << steps << " steps: ";
+std::cout << timer.elapsed() << " s" << std::endl;
+
+// compute some accumulation to make sure all results have been computed
+simd_pack s_pack = 0.0;
+for(size_t i = 0; i < n/pack_size; ++i)
+{
+ s_pack += state[i][0];
+}
+
+fp_type s = 0.0;
+for(size_t p=0; p<pack_size; ++p)
+{
+ s += s_pack[p];
+}
+
+
+std::cout << state[0][0] << std::endl;
+std::cout << s/n << std::endl;
+
+}
diff --git a/performance/c_lorenz.c b/performance/c_lorenz.c
new file mode 100644
index 0000000..85aba7f
--- /dev/null
+++ b/performance/c_lorenz.c
@@ -0,0 +1,57 @@
+#include <stdio.h>
+#include <time.h>
+#include <math.h>
+
+void lorenz(const double *x, double *restrict y) {
+ y[0] = 10.0 * (x[1] - x[0]);
+ y[1] = 28.0 * x[0] - x[1] - x[0] * x[2];
+ y[2] = x[0] * x[1] - (8.0 / 3.0) * x[2];
+}
+
+int main(int argc, const char *argv[])
+{
+ const int nb_steps = 20000000;
+ const double h = 1.0e-10;
+ const double h2 = 0.5 * h;
+ const double nb_loops = 21;
+ double x[3];
+ double y[3];
+ double f1[3];
+ double f2[3];
+ double f3[3];
+ double f4[3];
+ double min_time = 1E6;
+ clock_t begin, end;
+ double time_spent;
+
+ for (int j = 0; j < nb_loops; j++) {
+ x[0] = 8.5;
+ x[1] = 3.1;
+ x[2] = 1.2;
+ begin = clock();
+ for (int k = 0; k < nb_steps; k++) {
+ lorenz(x, f1);
+ for (int i = 0; i < 3; i++) {
+ y[i] = x[i] + h2 * f1[i];
+ }
+ lorenz(y, f2);
+ for (int i = 0; i < 3; i++) {
+ y[i] = x[i] + h2 * f2[i];
+ }
+ lorenz(y, f3);
+ for (int i = 0; i < 3; i++) {
+ y[i] = x[i] + h * f3[i];
+ }
+ lorenz(y, f4);
+ for (int i = 0; i < 3; i++) {
+ x[i] = x[i] + h * (f1[i] + 2 * (f2[i] + f3[i]) + f4[i]) / 6.0;
+ }
+ }
+ end = clock();
+ min_time = fmin(min_time, (double)(end-begin)/CLOCKS_PER_SEC);
+ printf("Result: %f\t runtime: %f\n", x[0], (double)(end-begin)/CLOCKS_PER_SEC);
+ }
+ printf("Minimal Runtime: %f\n", min_time);
+
+ return 0;
+}
diff --git a/performance/fortran_lorenz.f90 b/performance/fortran_lorenz.f90
new file mode 100644
index 0000000..2686997
--- /dev/null
+++ b/performance/fortran_lorenz.f90
@@ -0,0 +1,60 @@
+program main
+ implicit none
+
+ integer, parameter :: dp = 8
+ real(dp), dimension(1:3) :: x
+ integer, parameter :: nstep = 20000000
+ real(dp) :: t = 0.0_dp
+ real(dp) :: h = 1.0e-10_dp
+ integer, parameter :: nb_loops = 21
+ integer, parameter :: n = 3
+ integer :: k
+ integer :: time_begin
+ integer :: time_end
+ integer :: count_rate
+ real(dp) :: time
+ real(dp) :: min_time = 100.0
+
+ do k = 1, nb_loops
+ x = [ 8.5_dp, 3.1_dp, 1.2_dp ]
+ call system_clock(time_begin, count_rate)
+ call rk4sys(n, t, x, h, nstep)
+ call system_clock(time_end, count_rate)
+ time = real(time_end - time_begin, dp) / real(count_rate, dp)
+ min_time = min(time, min_time)
+ write (*,*) time, x(1)
+ end do
+ write (*,*) "Minimal Runtime:", min_time
+contains
+ subroutine xpsys(x,f)
+ real(dp), dimension(1:3), intent(in) :: x
+ real(dp), dimension(1:3), intent(out) :: f
+ f(1) = 10.0_dp * ( x(2) - x(1) )
+ f(2) = 28.0_dp * x(1) - x(2) - x(1) * x(3)
+ f(3) = x(1) * x(2) - (8.0_dp / 3.0_dp) * x(3)
+ end subroutine xpsys
+
+ subroutine rk4sys(n, t, x, h, nstep)
+ integer, intent(in) :: n
+ real(dp), intent(in) :: t
+ real(dp), dimension(1:n), intent(inout) :: x
+ real(dp), intent(in) :: h
+ integer, intent(in) :: nstep
+ ! Local variables
+ real(dp) :: h2
+ real(dp), dimension(1:n) :: y, f1, f2, f3, f4
+ integer :: i, k
+
+ h2 = 0.5_dp * h
+ do k = 1, nstep
+ call xpsys(x, f1)
+ y = x + h2 * f1
+ call xpsys(y, f2)
+ y = x + h2 * f2
+ call xpsys(y, f3)
+ y = x + h * f3
+ call xpsys(y, f4)
+ x = x + h * (f1 + 2.0_dp * (f2 + f3) + f4) / 6.0_dp
+ end do
+ end subroutine rk4sys
+end program main
diff --git a/performance/lorenz.hpp b/performance/lorenz.hpp
new file mode 100644
index 0000000..c1ea37c
--- /dev/null
+++ b/performance/lorenz.hpp
@@ -0,0 +1,33 @@
+/*
+ * lorenz.hpp
+ *
+ * Copyright 2011 Mario Mulansky
+ * Copyright 2012 Karsten Ahnert
+ *
+ * Distributed under the Boost Software License, Version 1.0.
+ * (See accompanying file LICENSE_1_0.txt or
+ * copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef LORENZ_HPP_
+#define LORENZ_HPP_
+
+#include <boost/array.hpp>
+
+struct lorenz
+{
+ template< class state_type >
+ void inline operator()( const state_type &x , state_type &dxdt , const double t ) const
+ {
+ const double sigma = 10.0;
+ const double R = 28.0;
+ const double b = 8.0 / 3.0;
+ dxdt[0] = sigma * ( x[1] - x[0] );
+ dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
+ dxdt[2] = x[0]*x[1] - b * x[2];
+ }
+};
+
+
+#endif /* LORENZ_HPP_ */
diff --git a/performance/odeint_rk4_array.cpp b/performance/odeint_rk4_array.cpp
new file mode 100644
index 0000000..6d60296
--- /dev/null
+++ b/performance/odeint_rk4_array.cpp
@@ -0,0 +1,63 @@
+/*
+ * odeint_rk4_array
+ *
+ * Copyright 2011 Mario Mulansky
+ * Copyright 2012 Karsten Ahnert
+ *
+ * Distributed under the Boost Software License, Version 1.0.
+ * (See accompanying file LICENSE_1_0.txt or
+ * copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <iostream>
+
+#include <boost/timer.hpp>
+#include <boost/array.hpp>
+
+#include <boost/numeric/odeint/stepper/runge_kutta4_classic.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta4.hpp>
+#include <boost/numeric/odeint/algebra/array_algebra.hpp>
+
+#include "lorenz.hpp"
+
+typedef boost::timer timer_type;
+
+typedef boost::array< double , 3 > state_type;
+
+using namespace boost::numeric::odeint;
+
+//typedef boost::numeric::odeint::runge_kutta4_classic< state_type > rk4_odeint_type;
+
+// use the never resizer explicitely for optimal performance with gcc,
+// for the intel compiler this doesnt matter and the above definition
+// gives the same performance
+typedef runge_kutta4_classic< state_type , double , state_type , double ,
+ array_algebra, default_operations, never_resizer > rk4_odeint_type;
+
+
+const int loops = 21;
+const int num_of_steps = 20000000;
+const double dt = 1E-10;
+
+
+int main()
+{
+ double min_time = 1E6; // something big
+ rk4_odeint_type stepper;
+ std::clog.precision(16);
+ std::cout.precision(16);
+ for( int n=0; n<loops; n++ )
+ {
+ state_type x = {{ 8.5, 3.1, 1.2 }};
+ double t = 0.0;
+ timer_type timer;
+ for( size_t i = 0 ; i < num_of_steps ; ++i )
+ {
+ stepper.do_step( lorenz(), x, t, dt );
+ t += dt;
+ }
+ min_time = std::min( timer.elapsed() , min_time );
+ std::clog << timer.elapsed() << '\t' << x[0] << std::endl;
+ }
+ std::cout << "Minimal Runtime: " << min_time << std::endl;
+}
diff --git a/performance/plot_result.py b/performance/plot_result.py
new file mode 100644
index 0000000..f39e49f
--- /dev/null
+++ b/performance/plot_result.py
@@ -0,0 +1,64 @@
+"""
+ Copyright 2011-2014 Mario Mulansky
+ Copyright 2011-2014 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+"""
+
+import numpy as np
+from matplotlib import pyplot as plt
+
+plt.rc("font", size=16)
+
+
+def get_runtime_from_file(filename):
+ gcc_perf_file = open(filename, 'r')
+ for line in gcc_perf_file:
+ if "Minimal Runtime:" in line:
+ return float(line.split(":")[-1])
+
+
+t_gcc = [get_runtime_from_file("perf_workbook/odeint_rk4_array_gcc.perf"),
+ get_runtime_from_file("perf_ariel/odeint_rk4_array_gcc.perf"),
+ get_runtime_from_file("perf_lyra/odeint_rk4_array_gcc.perf")]
+
+t_intel = [get_runtime_from_file("perf_workbook/odeint_rk4_array_intel.perf"),
+ get_runtime_from_file("perf_ariel/odeint_rk4_array_intel.perf"),
+ get_runtime_from_file("perf_lyra/odeint_rk4_array_intel.perf")]
+
+t_gfort = [get_runtime_from_file("perf_workbook/rk4_gfort.perf"),
+ get_runtime_from_file("perf_ariel/rk4_gfort.perf"),
+ get_runtime_from_file("perf_lyra/rk4_gfort.perf")]
+
+t_c_intel = [get_runtime_from_file("perf_workbook/rk4_c_intel.perf"),
+ get_runtime_from_file("perf_ariel/rk4_c_intel.perf"),
+ get_runtime_from_file("perf_lyra/rk4_c_intel.perf")]
+
+print t_c_intel
+
+
+ind = np.arange(3) # the x locations for the groups
+width = 0.15 # the width of the bars
+
+fig = plt.figure()
+ax = fig.add_subplot(111)
+rects1 = ax.bar(ind, t_gcc, width, color='b', label="odeint gcc")
+rects2 = ax.bar(ind+width, t_intel, width, color='g', label="odeint intel")
+rects3 = ax.bar(ind+2*width, t_c_intel, width, color='y', label="C intel")
+rects4 = ax.bar(ind+3*width, t_gfort, width, color='c', label="gfort")
+
+ax.axis([-width, 2.0+5*width, 0.0, 0.85])
+ax.set_ylabel('Runtime (s)')
+ax.set_title('Performance for integrating the Lorenz system')
+ax.set_xticks(ind + 1.5*width)
+ax.set_xticklabels(('Core i5-3210M\n3.1 GHz',
+ 'Xeon E5-2690\n3.8 GHz',
+ 'Opteron 8431\n 2.4 GHz'))
+ax.legend(loc='upper left', prop={'size': 16})
+
+plt.savefig("perf.pdf")
+plt.savefig("perf.png", dpi=50)
+
+plt.show()
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
new file mode 100644
index 0000000..502ee41
--- /dev/null
+++ b/test/Jamfile.v2
@@ -0,0 +1,102 @@
+# Copyright 2012-2013 Karsten Ahnert
+# Copyright 2012-2013 Mario Mulansky
+# Copyright 2013 Pascal Germroth
+# Distributed under the Boost Software License, Version 1.0.
+# (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+# bring in rules for testing
+
+import testing ;
+
+# make sure you are using a new version of boost.build, otherwise the local
+# odeint will not be included properly
+# you can fix older boost.build versions by applying the patch provided in
+# odeint's root, e.g.:
+# cd ~/odeint-v2
+# sudo patch /usr/share/boost-build/build/toolset.jam toolset.jam.patch
+
+use-project boost : $(BOOST_ROOT) ;
+
+project
+ : requirements
+ <define>BOOST_ALL_NO_LIB=1
+ # use test library
+ <library>/boost//unit_test_framework
+ <link>static
+ <toolset>clang:<cxxflags>-Wno-unused-variable
+ # <cxxflags>-D_SCL_SECURE_NO_WARNINGS
+ ;
+
+test-suite "odeint"
+ :
+ [ run euler_stepper.cpp ]
+ [ run runge_kutta_concepts.cpp ]
+ [ run runge_kutta_error_concepts.cpp ]
+ [ run runge_kutta_controlled_concepts.cpp ]
+ [ run resizing.cpp ]
+ [ run default_operations.cpp ]
+ [ run range_algebra.cpp ]
+ [ run implicit_euler.cpp ]
+# disable in clang
+ [ run fusion_algebra.cpp : : : <toolset>clang:<build>no ]
+ [ run stepper_with_units.cpp : : : <toolset>clang:<build>no ]
+ [ run stepper_copying.cpp ]
+ [ run stepper_with_ranges.cpp ]
+ [ run rosenbrock4.cpp ]
+ [ run rosenbrock4_mp.cpp ]
+ [ run is_pair.cpp ]
+ [ run adams_bashforth.cpp ]
+ [ run adams_moulton.cpp ]
+ [ run adams_bashforth_moulton.cpp ]
+ [ run generic_stepper.cpp ]
+ [ run generic_error_stepper.cpp ]
+ [ run bulirsch_stoer.cpp ]
+ [ run integrate_times.cpp ]
+ [ run integrate_times.cpp : : : <define>ODEINT_INTEGRATE_ITERATOR : integrate_times_iterator ]
+ [ run integrate.cpp ]
+ [ run integrate.cpp : : : <define>ODEINT_INTEGRATE_ITERATOR : integrate_iterator ]
+ [ run integrate_implicit.cpp ]
+ [ run integrate_implicit.cpp : : : <define>ODEINT_INTEGRATE_ITERATOR : integrate_implicit_iterator ]
+ [ run generation.cpp ]
+ [ run trivial_state.cpp ]
+ [ run is_resizeable.cpp ]
+ [ run resize.cpp ]
+ [ run same_size.cpp ]
+ [ run split.cpp ]
+ [ run symplectic_steppers.cpp ]
+ [ run integrators_symplectic.cpp ]
+ [ run integrators_symplectic.cpp : : : <define>ODEINT_INTEGRATE_ITERATOR : integrators_symplectic_iterator ]
+ [ run velocity_verlet.cpp ]
+ [ run multi_array.cpp ]
+ [ compile algebra_dispatcher.cpp ]
+ [ run integrate_stepper_refs.cpp ]
+ [ run const_step_iterator.cpp ]
+ [ run const_step_time_iterator.cpp ]
+ [ run adaptive_iterator.cpp ]
+ [ run adaptive_time_iterator.cpp ]
+ [ run n_step_iterator.cpp ]
+ [ run n_step_time_iterator.cpp ]
+ [ run times_iterator.cpp ]
+ [ run times_time_iterator.cpp ]
+ [ run step_size_limitation.cpp ]
+ [ run integrate_overflow.cpp ]
+ [ compile unwrap_boost_reference.cpp ]
+ [ compile unwrap_reference.cpp : <cxxflags>-std=c++0x : unwrap_reference_C++11 ]
+ [ compile-fail unwrap_reference.cpp : <cxxflags>-std=c++98 : unwrap_reference_C++98 ]
+ [ compile std_array.cpp : <cxxflags>-std=c++0x ]
+ :
+ <testing.launcher>valgrind
+ ;
+
+# also run numeric tests
+build-project numeric ;
+
+build-project regression ;
+
+# test-suite "odeint-iterator_integrate"
+# :
+# [ run integrate.cpp : : : : integrate_iterator ]
+# : <testing.launcher>valgrind
+# <define>ODEINT_ITERATOR_INTEGRATE
+# ;
+
diff --git a/test/adams_bashforth.cpp b/test/adams_bashforth.cpp
new file mode 100644
index 0000000..7574346
--- /dev/null
+++ b/test/adams_bashforth.cpp
@@ -0,0 +1,237 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/adams_bashforth.cpp
+
+ [begin_description]
+ This file tests the use of the adams bashforth stepper.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+// disable checked iterator warning for msvc
+
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_adams_bashforth
+
+#include <utility>
+
+#include <boost/array.hpp>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/mpl/list.hpp>
+#include <boost/mpl/size_t.hpp>
+#include <boost/mpl/range_c.hpp>
+
+
+#include <boost/numeric/odeint/stepper/adams_bashforth.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta4.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+typedef double value_type;
+
+struct lorenz
+{
+ template< class State , class Deriv , class Value >
+ void operator()( const State &_x , Deriv &_dxdt , const Value &dt ) const
+ {
+ const value_type sigma = 10.0;
+ const value_type R = 28.0;
+ const value_type b = 8.0 / 3.0;
+
+ typename boost::range_iterator< const State >::type x = boost::begin( _x );
+ typename boost::range_iterator< Deriv >::type dxdt = boost::begin( _dxdt );
+
+ dxdt[0] = sigma * ( x[1] - x[0] );
+ dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
+ dxdt[2] = x[0]*x[1] - b * x[2];
+ }
+};
+
+template< class State >
+class rk4_decorator
+{
+public:
+
+ size_t do_count;
+
+ template< class System , class StateIn , class DerivIn , class StateOut >
+ void do_step_dxdt_impl( System system , const StateIn &in , const DerivIn &dxdt , value_type t , StateOut &out , value_type dt )
+ {
+ m_stepper.do_step( system , in , dxdt , t , out , dt );
+ ++do_count;
+ }
+
+ template< class System , class StateInOut , class DerivIn >
+ void do_step_dxdt_impl( System system , StateInOut &x , const DerivIn &dxdt , value_type t , value_type dt )
+ {
+ m_stepper.do_step( system , x , dxdt , t , dt );
+ ++do_count;
+ }
+
+
+ runge_kutta4< State > m_stepper;
+
+private:
+
+
+};
+
+
+BOOST_AUTO_TEST_SUITE( adams_bashforth_test )
+
+BOOST_AUTO_TEST_CASE( test_adams_bashforth_coefficients )
+{
+ detail::adams_bashforth_coefficients< value_type , 1 > c1;
+ detail::adams_bashforth_coefficients< value_type , 2 > c2;
+ detail::adams_bashforth_coefficients< value_type , 3 > c3;
+ detail::adams_bashforth_coefficients< value_type , 4 > c4;
+ detail::adams_bashforth_coefficients< value_type , 5 > c5;
+ detail::adams_bashforth_coefficients< value_type , 6 > c6;
+ detail::adams_bashforth_coefficients< value_type , 7 > c7;
+ detail::adams_bashforth_coefficients< value_type , 8 > c8;
+}
+
+BOOST_AUTO_TEST_CASE( test_rotating_buffer )
+{
+ const size_t N = 5;
+ detail::rotating_buffer< size_t , N > buffer;
+ for( size_t i=0 ; i<N ; ++i ) buffer[i] = i;
+
+ for( size_t i=0 ; i<N ; ++i )
+ BOOST_CHECK_EQUAL( buffer[i] , i );
+
+ buffer.rotate();
+
+ for( size_t i=1 ; i<N ; ++i )
+ BOOST_CHECK_EQUAL( buffer[i] , i - 1 );
+ BOOST_CHECK_EQUAL( buffer[0] , size_t( N-1 ) );
+}
+
+BOOST_AUTO_TEST_CASE( test_copying )
+{
+ typedef boost::array< double , 1 > state_type;
+ typedef adams_bashforth< 2 , state_type > stepper_type;
+
+ stepper_type s1;
+ s1.step_storage()[0].m_v[0] = 1.5;
+ s1.step_storage()[1].m_v[0] = 2.25;
+
+ stepper_type s2( s1 );
+ BOOST_CHECK_CLOSE( s1.step_storage()[0].m_v[0] , s2.step_storage()[0].m_v[0] , 1.0e-14 );
+ BOOST_CHECK_CLOSE( s1.step_storage()[1].m_v[0] , s2.step_storage()[1].m_v[0] , 1.0e-14 );
+ BOOST_CHECK( ( &(s1.step_storage()[0]) ) != ( &(s2.step_storage()[0]) ) );
+
+ stepper_type s3;
+ state_type *p1 = &( s3.step_storage()[0].m_v ) , *p2 = &( s3.step_storage()[1].m_v );
+ s3 = s1;
+ BOOST_CHECK( p1 == ( &( s3.step_storage()[0].m_v ) ) );
+ BOOST_CHECK( p2 == ( &( s3.step_storage()[1].m_v ) ) );
+
+ BOOST_CHECK_CLOSE( s1.step_storage()[0].m_v[0] , s3.step_storage()[0].m_v[0] , 1.0e-14 );
+ BOOST_CHECK_CLOSE( s1.step_storage()[1].m_v[0] , s3.step_storage()[1].m_v[0] , 1.0e-14 );
+}
+
+typedef boost::mpl::range_c< size_t , 1 , 6 > vector_of_steps;
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( test_init_and_steps , step_type , vector_of_steps )
+{
+ const static size_t steps = step_type::value;
+ typedef boost::array< value_type , 3 > state_type;
+
+ adams_bashforth< steps , state_type > stepper;
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ const value_type dt = 0.01;
+ value_type t = 0.0;
+
+ stepper.initialize( lorenz() , x , t , dt );
+ BOOST_CHECK_CLOSE( t , value_type( steps - 1 ) * dt , 1.0e-14 );
+
+ stepper.do_step( lorenz() , x , t , dt );
+}
+
+BOOST_AUTO_TEST_CASE( test_instantiation )
+{
+ typedef boost::array< double , 3 > state_type;
+ adams_bashforth< 1 , state_type > s1;
+ adams_bashforth< 2 , state_type > s2;
+ adams_bashforth< 3 , state_type > s3;
+ adams_bashforth< 4 , state_type > s4;
+ adams_bashforth< 5 , state_type > s5;
+ adams_bashforth< 6 , state_type > s6;
+ adams_bashforth< 7 , state_type > s7;
+ adams_bashforth< 8 , state_type > s8;
+
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ value_type t = 0.0 , dt = 0.01;
+ s1.do_step( lorenz() , x , t , dt );
+ s2.do_step( lorenz() , x , t , dt );
+ s3.do_step( lorenz() , x , t , dt );
+ s4.do_step( lorenz() , x , t , dt );
+ s5.do_step( lorenz() , x , t , dt );
+ s6.do_step( lorenz() , x , t , dt );
+// s7.do_step( lorenz() , x , t , dt );
+// s8.do_step( lorenz() , x , t , dt );
+}
+
+BOOST_AUTO_TEST_CASE( test_auto_initialization )
+{
+ typedef boost::array< double , 3 > state_type;
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+
+ adams_bashforth< 3 , state_type , value_type , state_type , value_type , range_algebra , default_operations ,
+ initially_resizer , rk4_decorator< state_type > > adams;
+
+ adams.initializing_stepper().do_count = 0;
+ adams.do_step( lorenz() , x , 0.0 , x , 0.1 );
+ BOOST_CHECK_EQUAL( adams.initializing_stepper().do_count , size_t( 1 ) );
+
+ adams.do_step( lorenz() , x , 0.0 , x , 0.1 );
+ BOOST_CHECK_EQUAL( adams.initializing_stepper().do_count , size_t( 2 ) );
+
+ adams.do_step( lorenz() , x , 0.0 , x , 0.1 );
+ BOOST_CHECK_EQUAL( adams.initializing_stepper().do_count , size_t( 2 ) );
+
+ adams.do_step( lorenz() , x , 0.0 , x , 0.1 );
+ BOOST_CHECK_EQUAL( adams.initializing_stepper().do_count , size_t( 2 ) );
+
+ adams.reset();
+
+ adams.do_step( lorenz() , x , 0.0 , x , 0.1 );
+ BOOST_CHECK_EQUAL( adams.initializing_stepper().do_count , size_t( 3 ) );
+
+ adams.do_step( lorenz() , x , 0.0 , x , 0.1 );
+ BOOST_CHECK_EQUAL( adams.initializing_stepper().do_count , size_t( 4 ) );
+}
+
+BOOST_AUTO_TEST_CASE( test_manual_initialization )
+{
+ typedef boost::array< double , 3 > state_type;
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+
+ adams_bashforth< 3 , state_type , value_type , state_type , value_type , range_algebra , default_operations ,
+ initially_resizer , rk4_decorator< state_type > > adams;
+
+ adams.initializing_stepper().do_count = 0;
+ double t = 0.0 , dt = 0.1;
+ adams.initialize( lorenz() , x , t , dt );
+ BOOST_CHECK_EQUAL( adams.initializing_stepper().do_count , size_t( 2 ) );
+
+ adams.do_step( lorenz() , x , 0.0 , x , 0.1 );
+ BOOST_CHECK_EQUAL( adams.initializing_stepper().do_count , size_t( 2 ) );
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/adams_bashforth_moulton.cpp b/test/adams_bashforth_moulton.cpp
new file mode 100644
index 0000000..8e7688b
--- /dev/null
+++ b/test/adams_bashforth_moulton.cpp
@@ -0,0 +1,112 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/adams_bashforth_moulton.cpp
+
+ [begin_description]
+ This file tests the use of the Adams-Bashforth-Moulton.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#define BOOST_TEST_MODULE odeint_adams_bashforth_moulton
+
+#include <utility>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/mpl/list.hpp>
+#include <boost/mpl/size_t.hpp>
+#include <boost/mpl/range_c.hpp>
+
+#include <boost/numeric/odeint/stepper/adams_bashforth_moulton.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+typedef double value_type;
+
+struct lorenz
+{
+ template< class State , class Deriv , class Value >
+ void operator()( const State &_x , Deriv &_dxdt , const Value &dt ) const
+ {
+ const value_type sigma = 10.0;
+ const value_type R = 28.0;
+ const value_type b = 8.0 / 3.0;
+
+ typename boost::range_iterator< const State >::type x = boost::begin( _x );
+ typename boost::range_iterator< Deriv >::type dxdt = boost::begin( _dxdt );
+
+ dxdt[0] = sigma * ( x[1] - x[0] );
+ dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
+ dxdt[2] = x[0]*x[1] - b * x[2];
+ }
+};
+
+BOOST_AUTO_TEST_SUITE( adams_bashforth_moulton_test )
+
+typedef boost::mpl::range_c< size_t , 1 , 6 > vector_of_steps;
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( test_init_and_steps , step_type , vector_of_steps )
+{
+ const static size_t steps = step_type::value;
+ typedef boost::array< value_type , 3 > state_type;
+
+ adams_bashforth_moulton< steps , state_type > stepper;
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ const value_type dt = 0.01;
+ value_type t = 0.0;
+
+ stepper.initialize( lorenz() , x , t , dt );
+ BOOST_CHECK_CLOSE( t , value_type( steps - 1 ) * dt , 1.0e-14 );
+
+ stepper.do_step( lorenz() , x , t , dt );
+}
+
+
+BOOST_AUTO_TEST_CASE( test_copying )
+{
+ typedef boost::array< double , 1 > state_type;
+ typedef adams_bashforth_moulton< 2 , state_type > stepper_type;
+
+ stepper_type s1;
+
+ stepper_type s2( s1 );
+
+ stepper_type s3;
+ s3 = s1;
+ }
+
+
+BOOST_AUTO_TEST_CASE( test_instantiation )
+{
+ typedef boost::array< double , 3 > state_type;
+ adams_bashforth_moulton< 1 , state_type > s1;
+ adams_bashforth_moulton< 2 , state_type > s2;
+ adams_bashforth_moulton< 3 , state_type > s3;
+ adams_bashforth_moulton< 4 , state_type > s4;
+ adams_bashforth_moulton< 5 , state_type > s5;
+ adams_bashforth_moulton< 6 , state_type > s6;
+ adams_bashforth_moulton< 7 , state_type > s7;
+ adams_bashforth_moulton< 8 , state_type > s8;
+
+ state_type x = {{ 10.0 , 10.0 , 10.0 }};
+ value_type t = 0.0 , dt = 0.01;
+ s1.do_step( lorenz() , x , t , dt );
+ s2.do_step( lorenz() , x , t , dt );
+ s3.do_step( lorenz() , x , t , dt );
+ s4.do_step( lorenz() , x , t , dt );
+ s5.do_step( lorenz() , x , t , dt );
+ s6.do_step( lorenz() , x , t , dt );
+// s7.do_step( lorenz() , x , t , dt );
+// s8.do_step( lorenz() , x , t , dt );
+}
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/adams_moulton.cpp b/test/adams_moulton.cpp
new file mode 100644
index 0000000..faccdda
--- /dev/null
+++ b/test/adams_moulton.cpp
@@ -0,0 +1,104 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/adams_moulton.cpp
+
+ [begin_description]
+ This file tests the use of the Adams-Moulton stepper.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#define BOOST_TEST_MODULE odeint_adams_moulton
+
+#include <utility>
+
+#include <boost/array.hpp>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/mpl/list.hpp>
+#include <boost/mpl/size_t.hpp>
+#include <boost/mpl/range_c.hpp>
+
+
+#include <boost/numeric/odeint/stepper/detail/adams_moulton_coefficients.hpp>
+#include <boost/numeric/odeint/stepper/detail/rotating_buffer.hpp>
+#include <boost/numeric/odeint/stepper/adams_moulton.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+typedef double value_type;
+
+struct lorenz
+{
+ template< class State , class Deriv , class Value >
+ void operator()( const State &_x , Deriv &_dxdt , const Value &dt ) const
+ {
+ const value_type sigma = 10.0;
+ const value_type R = 28.0;
+ const value_type b = 8.0 / 3.0;
+
+ typename boost::range_iterator< const State >::type x = boost::begin( _x );
+ typename boost::range_iterator< Deriv >::type dxdt = boost::begin( _dxdt );
+
+ dxdt[0] = sigma * ( x[1] - x[0] );
+ dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
+ dxdt[2] = x[0]*x[1] - b * x[2];
+ }
+};
+
+BOOST_AUTO_TEST_SUITE( adams_moulton_test )
+
+BOOST_AUTO_TEST_CASE( test_adams_moulton_coefficients )
+{
+ detail::adams_moulton_coefficients< value_type , 1 > c1;
+ detail::adams_moulton_coefficients< value_type , 2 > c2;
+ detail::adams_moulton_coefficients< value_type , 3 > c3;
+ detail::adams_moulton_coefficients< value_type , 4 > c4;
+ detail::adams_moulton_coefficients< value_type , 5 > c5;
+ detail::adams_moulton_coefficients< value_type , 6 > c6;
+ detail::adams_moulton_coefficients< value_type , 7 > c7;
+ detail::adams_moulton_coefficients< value_type , 8 > c8;
+}
+
+typedef boost::mpl::range_c< size_t , 1 , 6 > vector_of_steps;
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( test_init_and_steps , step_type , vector_of_steps )
+{
+ const static size_t steps = step_type::value;
+ typedef boost::array< value_type , 3 > state_type;
+
+ adams_moulton< steps , state_type > stepper;
+// state_type x = {{ 10.0 , 10.0 , 10.0 }};
+// const value_type dt = 0.01;
+// value_type t = 0.0;
+
+// stepper.do_step( lorenz() , x , t , dt );
+}
+
+BOOST_AUTO_TEST_CASE( test_instantiation )
+{
+ typedef boost::array< double , 3 > state_type;
+ adams_moulton< 1 , state_type > s1;
+ adams_moulton< 2 , state_type > s2;
+ adams_moulton< 3 , state_type > s3;
+ adams_moulton< 4 , state_type > s4;
+ adams_moulton< 5 , state_type > s5;
+ adams_moulton< 6 , state_type > s6;
+ adams_moulton< 7 , state_type > s7;
+ adams_moulton< 8 , state_type > s8;
+
+// state_type x = {{ 10.0 , 10.0 , 10.0 }};
+// value_type t = 0.0 , dt = 0.01;
+}
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/adaptive_iterator.cpp b/test/adaptive_iterator.cpp
new file mode 100644
index 0000000..8f3cfa7
--- /dev/null
+++ b/test/adaptive_iterator.cpp
@@ -0,0 +1,346 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/adaptive_iterator.cpp
+
+ [begin_description]
+ This file tests the adaptive iterators.
+ [end_description]
+
+ Copyright 2012-2013 Karsten Ahnert
+ Copyright 2012-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#define BOOST_TEST_MODULE odeint_adaptive_iterator
+
+#include <iterator>
+#include <algorithm>
+#include <vector>
+
+#include <boost/numeric/odeint/config.hpp>
+#include <boost/array.hpp>
+#include <boost/range/algorithm/copy.hpp>
+#include <boost/range/algorithm/for_each.hpp>
+#include <boost/mpl/vector.hpp>
+
+#include <boost/test/unit_test.hpp>
+#include <boost/test/floating_point_comparison.hpp>
+
+#include <boost/numeric/odeint/iterator/adaptive_iterator.hpp>
+#include "dummy_steppers.hpp"
+#include "dummy_odes.hpp"
+#include "dummy_observers.hpp"
+
+namespace mpl = boost::mpl;
+using namespace boost::numeric::odeint;
+
+typedef dummy_stepper::state_type state_type;
+typedef dummy_stepper::value_type value_type;
+
+BOOST_AUTO_TEST_SUITE( adaptive_iterator_test )
+
+typedef mpl::vector<
+ dummy_controlled_stepper
+ , dummy_dense_output_stepper
+ > dummy_steppers;
+
+
+BOOST_AUTO_TEST_CASE( copy_controlled_stepper_iterator )
+{
+ typedef adaptive_iterator< dummy_controlled_stepper , empty_system , state_type > iterator_type;
+
+ state_type x = {{ 1.0 }};
+ iterator_type iter1( dummy_controlled_stepper() , empty_system() , x );
+ iterator_type iter2( iter1 );
+
+ BOOST_CHECK_EQUAL( &( *iter1 ) , &x );
+ BOOST_CHECK_EQUAL( &( *iter2 ) , &x );
+ BOOST_CHECK_EQUAL( &( *iter1 ) , &( *iter2 ) );
+ BOOST_CHECK( iter1.same( iter2 ) );
+
+ ++iter1;
+ ++iter2;
+
+ BOOST_CHECK_EQUAL( &( *iter1 ) , &x );
+ BOOST_CHECK_EQUAL( &( *iter2 ) , &x );
+ BOOST_CHECK_EQUAL( &( *iter1 ) , &( *iter2 ) );
+ BOOST_CHECK( iter1.same( iter2 ) );
+
+}
+
+BOOST_AUTO_TEST_CASE( copy_dense_output_stepper_iterator )
+{
+ typedef adaptive_iterator< dummy_dense_output_stepper , empty_system , state_type > iterator_type;
+
+ state_type x = {{ 1.0 }};
+ // fix by mario: do not dereference iterators at the end - made iter1 start iterator
+ iterator_type iter1( dummy_dense_output_stepper() , empty_system() , x , 0.0 , 1.0 , 0.1 );
+ iterator_type iter2( iter1 );
+
+ // fix by mario: iterator dereference now always gives internal state also for dense output, consistent with other iterator implementations
+ // changed: iterators with dense output stepper do not have an internal state now to avoid a copy
+ BOOST_CHECK_NE( & (*iter1) , & (*iter2) );
+ BOOST_CHECK( iter1.same( iter2 ) );
+
+ ++iter1;
+ ++iter2;
+
+ BOOST_CHECK_NE( & (*iter1) , & (*iter2) );
+ BOOST_CHECK( iter1.same( iter2 ) );
+}
+
+BOOST_AUTO_TEST_CASE( copy_dense_output_stepper_iterator_with_reference_wrapper )
+{
+ // bad use case, the same stepper is iterated twice
+ typedef adaptive_iterator< boost::reference_wrapper< dummy_dense_output_stepper > , empty_system , state_type > iterator_type;
+
+ state_type x = {{ 1.0 }};
+ dummy_dense_output_stepper stepper;
+ iterator_type iter1( boost::ref( stepper ) , empty_system() , x , 0.0 , 0.9 , 0.1 );
+ iterator_type iter2( iter1 );
+
+ BOOST_CHECK_EQUAL( & (*iter1) , & (*iter2) );
+ BOOST_CHECK( iter1.same( iter2 ) );
+
+ ++iter1;
+ ++iter2;
+
+ BOOST_CHECK_EQUAL( & (*iter1) , & (*iter2) );
+ BOOST_CHECK( !iter1.same( iter2 ) ); // they point to the same stepper, there the times will be different
+}
+
+
+
+BOOST_AUTO_TEST_CASE( assignment_controlled_stepper_iterator )
+{
+ typedef adaptive_iterator< dummy_controlled_stepper , empty_system , state_type > iterator_type;
+ state_type x1 = {{ 1.0 }} , x2 = {{ 2.0 }};
+ iterator_type iter1 = iterator_type( dummy_controlled_stepper() , empty_system() , x1 , 0.0 , 1.0 , 0.1 );
+ iterator_type iter2 = iterator_type( dummy_controlled_stepper() , empty_system() , x2 , 0.0 , 1.0 , 0.2 );
+ BOOST_CHECK_EQUAL( &(*iter1) , &x1 );
+ BOOST_CHECK_EQUAL( &(*iter2) , &x2 );
+ // the iterators are indeed the same as this only checks the time values
+ BOOST_CHECK( !iter1.same( iter2 ) );
+ iter2 = iter1;
+ BOOST_CHECK_EQUAL( &(*iter1) , &x1 );
+ BOOST_CHECK_EQUAL( &(*iter2) , &x1 );
+ BOOST_CHECK( iter1.same( iter2 ) );
+}
+
+
+
+BOOST_AUTO_TEST_CASE( assignment_dense_output_stepper_iterator )
+{
+ typedef adaptive_iterator< dummy_dense_output_stepper , empty_system , state_type > iterator_type;
+ state_type x1 = {{ 1.0 }};
+ iterator_type iter1 = iterator_type( dummy_dense_output_stepper() , empty_system() , x1 , 0.0 , 1.0 , 0.1 );
+ iterator_type iter2 = iterator_type( dummy_dense_output_stepper() , empty_system() , x1 , 0.0 , 1.0 , 0.2 );
+
+ BOOST_CHECK_NE( & (*iter1) , & (*iter2) );
+ BOOST_CHECK( !iter1.same( iter2 ) );
+
+ iter2 = iter1;
+ // fix by mario: iterator dereference now always gives internal state also for dense output, consistent with other iterator implementations
+ // changed: iterators with dense output stepper do not have an internal state now to avoid a copy
+ BOOST_CHECK_NE( & (*iter1) , & (*iter2) );
+ BOOST_CHECK( iter1.same( iter2 ) );
+}
+
+BOOST_AUTO_TEST_CASE( assignment_dense_output_stepper_iterator_with_reference_wrapper )
+{
+ typedef adaptive_iterator< boost::reference_wrapper< dummy_dense_output_stepper > , empty_system , state_type > iterator_type;
+ state_type x1 = {{ 1.0 }};
+
+ dummy_dense_output_stepper stepper;
+ iterator_type iter1 = iterator_type( boost::ref( stepper ) , empty_system() , x1 , 0.0 , 1.0 , 0.1 );
+ iterator_type iter2 = iterator_type( boost::ref( stepper ) , empty_system() , x1 , 0.0 , 1.0 , 0.2 );
+
+ BOOST_CHECK_EQUAL( & (*iter1) , & (*iter2) );
+ BOOST_CHECK( !iter1.same( iter2 ) );
+
+ iter2 = iter1;
+
+ BOOST_CHECK_EQUAL( & (*iter1) , & (*iter2) );
+ BOOST_CHECK( iter1.same( iter2 ) );
+}
+
+
+
+BOOST_AUTO_TEST_CASE( controlled_stepper_iterator_factory )
+{
+ dummy_controlled_stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ std::for_each(
+ make_adaptive_iterator_begin( stepper , boost::ref( system ) , x , 0.0 , 1.0 , 0.1 ) ,
+ make_adaptive_iterator_end( stepper , boost::ref( system ) , x ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 3.5 , 1.0e-14 );
+}
+
+// just test if it compiles
+BOOST_AUTO_TEST_CASE( dense_output_stepper_iterator_factory )
+{
+ dummy_dense_output_stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ std::for_each(
+ make_adaptive_iterator_begin( stepper , boost::ref( system ) , x , 0.0 , 1.0 , 0.1 ) ,
+ make_adaptive_iterator_end( stepper , boost::ref( system ) , x ) ,
+ dummy_observer() );
+}
+
+
+
+BOOST_AUTO_TEST_CASE( controlled_stepper_range )
+{
+ dummy_controlled_stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ boost::for_each( make_adaptive_range( stepper , boost::ref( system ) , x , 0.0 , 1.0 , 0.1 ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 3.5 , 1.0e-14 );
+}
+
+// just test if it compiles
+BOOST_AUTO_TEST_CASE( dense_output_stepper_range )
+{
+ dummy_dense_output_stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ boost::for_each( make_adaptive_range( stepper , boost::ref( system ) , x , 0.0 , 1.0 , 0.1 ) ,
+ dummy_observer() );
+}
+
+
+BOOST_AUTO_TEST_CASE( controlled_stepper_iterator_with_reference_wrapper_factory )
+{
+ dummy_controlled_stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ std::for_each(
+ make_adaptive_iterator_begin( boost::ref( stepper ) , boost::ref( system ) , x , 0.0 , 1.0 , 0.1 ) ,
+ make_adaptive_iterator_end( boost::ref( stepper ) , boost::ref( system ) , x ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 3.5 , 1.0e-14 );
+}
+
+// just test if it compiles
+BOOST_AUTO_TEST_CASE( dense_output_stepper_iterator_with_reference_wrapper_factory )
+{
+ dummy_dense_output_stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ std::for_each(
+ make_adaptive_iterator_begin( boost::ref( stepper ) , boost::ref( system ) , x , 0.0 , 1.0 , 0.1 ) ,
+ make_adaptive_iterator_end( boost::ref( stepper ) , boost::ref( system ) , x ) ,
+ dummy_observer() );
+}
+
+BOOST_AUTO_TEST_CASE( controlled_stepper_range_with_reference_wrapper )
+{
+ dummy_controlled_stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ boost::for_each( make_adaptive_range( boost::ref( stepper ) , boost::ref( system ) , x , 0.0 , 1.0 , 0.1 ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 3.5 , 1.0e-14 );
+}
+
+// just test if it compiles
+BOOST_AUTO_TEST_CASE( dense_output_stepper_range_with_reference_wrapper )
+{
+ dummy_dense_output_stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ boost::for_each( make_adaptive_range( boost::ref( stepper ) , boost::ref( system ) , x , 0.0 , 1.0 , 0.1 ) ,
+ dummy_observer() );
+}
+
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( transitivity1 , Stepper , dummy_steppers )
+{
+ typedef adaptive_iterator< Stepper , empty_system , state_type > stepper_iterator;
+
+ state_type x = {{ 1.0 }};
+ stepper_iterator first1( Stepper() , empty_system() , x , 2.5 , 2.0 , 0.1 );
+ stepper_iterator last1( Stepper() , empty_system() , x );
+ stepper_iterator last2( Stepper() , empty_system() , x );
+
+ BOOST_CHECK( first1 == last1 );
+ BOOST_CHECK( first1 == last2 );
+ BOOST_CHECK( last1 == last2 );
+}
+
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm , Stepper , dummy_steppers )
+{
+ typedef adaptive_iterator< Stepper , empty_system , state_type > stepper_iterator;
+ state_type x = {{ 1.0 }};
+ std::vector< state_type > res;
+ stepper_iterator first( Stepper() , empty_system() , x , 0.0 , 0.35 , 0.1 );
+ stepper_iterator last( Stepper() , empty_system() , x );
+
+ std::copy( first , last , std::back_insert_iterator< std::vector< state_type > >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 5 ) );
+ BOOST_CHECK_CLOSE( res[0][0] , 1.0 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[1][0] , 1.25 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[2][0] , 1.5 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[3][0] , 1.75 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[4][0] , 2.0 , 1.0e-14 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm_with_factory , Stepper , dummy_steppers )
+{
+ state_type x = {{ 1.0 }};
+ std::vector< state_type > res;
+ std::copy( make_adaptive_iterator_begin( Stepper() , empty_system() , x , 0.0 , 0.35 , 0.1 ) ,
+ make_adaptive_iterator_end( Stepper() , empty_system() , x ) ,
+ std::back_insert_iterator< std::vector< state_type > >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 5 ) );
+ BOOST_CHECK_CLOSE( res[0][0] , 1.0 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[1][0] , 1.25 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[2][0] , 1.5 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[3][0] , 1.75 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[4][0] , 2.0 , 1.0e-14 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm_with_range_factory , Stepper , dummy_steppers )
+{
+ state_type x = {{ 1.0 }};
+ std::vector< state_type > res;
+ boost::range::copy( make_adaptive_range( Stepper() , empty_system() , x , 0.0 , 0.35 , 0.1 ) ,
+ std::back_insert_iterator< std::vector< state_type > >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 5 ) );
+ BOOST_CHECK_CLOSE( res[0][0] , 1.0 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[1][0] , 1.25 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[2][0] , 1.5 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[3][0] , 1.75 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[4][0] , 2.0 , 1.0e-14 );
+}
+
+
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/adaptive_time_iterator.cpp b/test/adaptive_time_iterator.cpp
new file mode 100644
index 0000000..406a71c
--- /dev/null
+++ b/test/adaptive_time_iterator.cpp
@@ -0,0 +1,332 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/adaptive_time_iterator.cpp
+
+ [begin_description]
+ This file tests the adaptive time iterator.
+ [end_description]
+
+ Copyright 2012-2013 Karsten Ahnert
+ Copyright 2012-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#define BOOST_TEST_MODULE odeint_adaptive_time_iterator
+
+#include <iterator>
+#include <algorithm>
+#include <vector>
+
+#include <boost/numeric/odeint/config.hpp>
+#include <boost/array.hpp>
+#include <boost/range/algorithm/copy.hpp>
+#include <boost/range/algorithm/for_each.hpp>
+#include <boost/mpl/vector.hpp>
+
+#include <boost/test/unit_test.hpp>
+#include <boost/test/floating_point_comparison.hpp>
+
+#include <boost/numeric/odeint/iterator/adaptive_time_iterator.hpp>
+#include "dummy_steppers.hpp"
+#include "dummy_odes.hpp"
+#include "dummy_observers.hpp"
+
+namespace mpl = boost::mpl;
+using namespace boost::numeric::odeint;
+
+
+
+typedef dummy_stepper::state_type state_type;
+typedef dummy_stepper::value_type value_type;
+typedef dummy_stepper::time_type time_type;
+typedef std::vector< std::pair< state_type , time_type > > result_vector;
+
+BOOST_AUTO_TEST_SUITE( adaptive_time_iterator_test )
+
+typedef mpl::vector<
+ dummy_controlled_stepper
+ , dummy_dense_output_stepper
+ > dummy_steppers;
+
+
+BOOST_AUTO_TEST_CASE( copy_stepper_iterator )
+{
+ typedef adaptive_time_iterator< dummy_controlled_stepper , empty_system , state_type > iterator_type;
+ state_type x = {{ 1.0 }};
+ iterator_type iter1 = iterator_type( dummy_controlled_stepper() , empty_system() , x , 0.0 , 1.0 , 0.1 );
+ iterator_type iter2 = iter1;
+ BOOST_CHECK_EQUAL( &( iter1->first ) , &( iter2->first ) );
+ BOOST_CHECK_EQUAL( &( iter1->first ) , &x );
+ BOOST_CHECK( iter1.same( iter2 ) );
+}
+
+BOOST_AUTO_TEST_CASE( copy_dense_output_stepper_iterator )
+{
+ typedef adaptive_time_iterator< dummy_dense_output_stepper , empty_system , state_type > iterator_type;
+ state_type x = {{ 1.0 }};
+ iterator_type iter1 = iterator_type( dummy_dense_output_stepper() , empty_system() , x , 0.0 , 1.0 , 0.1 );
+ iterator_type iter2 = iter1;
+ BOOST_CHECK_NE( &( iter1->first ) , &( iter2->first ) );
+ BOOST_CHECK( iter1.same( iter2 ) );
+}
+
+BOOST_AUTO_TEST_CASE( copy_dense_output_stepper_iterator_with_reference_wrapper )
+{
+ typedef adaptive_time_iterator< boost::reference_wrapper< dummy_dense_output_stepper > , empty_system , state_type > iterator_type;
+ state_type x = {{ 1.0 }};
+ dummy_dense_output_stepper stepper;
+ iterator_type iter1 = iterator_type( boost::ref( stepper ) , empty_system() , x , 0.0 , 1.0 , 0.1 );
+ iterator_type iter2 = iter1;
+ BOOST_CHECK_EQUAL( &( iter1->first ) , &( iter2->first ) );
+ BOOST_CHECK( iter1.same( iter2 ) );
+}
+
+
+BOOST_AUTO_TEST_CASE( assignment_stepper_iterator )
+{
+ typedef adaptive_time_iterator< dummy_controlled_stepper , empty_system , state_type > iterator_type;
+ state_type x1 = {{ 1.0 }} , x2 = {{ 2.0 }};
+ iterator_type iter1 = iterator_type( dummy_controlled_stepper() , empty_system() , x1 , 0.0 , 1.0 , 0.1 );
+ iterator_type iter2 = iterator_type( dummy_controlled_stepper() , empty_system() , x2 , 0.0 , 1.0 , 0.2 );
+ BOOST_CHECK_EQUAL( &( iter1->first ) , &x1 );
+ BOOST_CHECK_EQUAL( &( iter2->first ) , &x2 );
+ BOOST_CHECK( !iter1.same( iter2 ) );
+ iter2 = iter1;
+ BOOST_CHECK_EQUAL( &( iter1->first ) , &x1 );
+ BOOST_CHECK_EQUAL( &( iter2->first ) , &x1 );
+ BOOST_CHECK( iter1.same( iter2 ) );
+}
+
+BOOST_AUTO_TEST_CASE( assignment_dense_output_stepper_iterator )
+{
+ typedef adaptive_time_iterator< dummy_dense_output_stepper , empty_system , state_type > iterator_type;
+ state_type x1 = {{ 1.0 }} , x2 = {{ 2.0 }};
+ iterator_type iter1 = iterator_type( dummy_dense_output_stepper() , empty_system() , x1 , 0.0 , 1.0 , 0.1 );
+ iterator_type iter2 = iterator_type( dummy_dense_output_stepper() , empty_system() , x2 , 0.0 , 1.0 , 0.2 );
+ BOOST_CHECK_NE( &( iter1->first ) , &x1 );
+ BOOST_CHECK_NE( &( iter2->first ) , &x2 );
+ BOOST_CHECK( !iter1.same( iter2 ) );
+ iter2 = iter1;
+ BOOST_CHECK_NE( &( iter1->first ) , &x1 );
+ BOOST_CHECK_NE( &( iter2->first ) , &x1 );
+ BOOST_CHECK( iter1.same( iter2 ) );
+ BOOST_CHECK_EQUAL( (iter1->first)[0] , (iter1->first)[0] );
+}
+
+BOOST_AUTO_TEST_CASE( assignment_dense_output_stepper_iterator_with_reference_wrapper )
+{
+ typedef adaptive_time_iterator< boost::reference_wrapper< dummy_dense_output_stepper > , empty_system , state_type > iterator_type;
+ state_type x1 = {{ 1.0 }} , x2 = {{ 2.0 }};
+ dummy_dense_output_stepper stepper;
+ iterator_type iter1 = iterator_type( boost::ref( stepper ) , empty_system() , x1 , 0.0 , 1.0 , 0.1 );
+ iterator_type iter2 = iterator_type( boost::ref( stepper ) , empty_system() , x2 , 0.0 , 1.0 , 0.2 );
+
+ BOOST_CHECK_NE( &( iter1->first ) , &x1 );
+ BOOST_CHECK_NE( &( iter2->first ) , &x2 );
+ // same stepper instance -> same internal state
+ BOOST_CHECK_EQUAL( &( iter1->first ) , &( iter2->first ) );
+ BOOST_CHECK( !iter1.same( iter2 ) );
+ iter2 = iter1;
+ BOOST_CHECK_NE( &( iter1->first ) , &x1 );
+ BOOST_CHECK_NE( &( iter2->first ) , &x1 );
+ BOOST_CHECK( iter1.same( iter2 ) );
+ BOOST_CHECK_EQUAL( &( iter1->first ) , &( iter2->first ) );
+}
+
+
+BOOST_AUTO_TEST_CASE( stepper_iterator_factory )
+{
+ dummy_controlled_stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ std::for_each(
+ make_adaptive_time_iterator_begin( stepper , boost::ref( system ) , x , 0.0 , 1.0 , 0.1 ) ,
+ make_adaptive_time_iterator_end( stepper , boost::ref( system ) , x ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 3.5 , 1.0e-14 );
+}
+
+// just test if it compiles
+BOOST_AUTO_TEST_CASE( dense_output_stepper_iterator_factory )
+{
+ dummy_dense_output_stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ std::for_each(
+ make_adaptive_time_iterator_begin( stepper , boost::ref( system ) , x , 0.0 , 1.0 , 0.1 ) ,
+ make_adaptive_time_iterator_end( stepper , boost::ref( system ) , x ) ,
+ dummy_observer() );
+}
+
+
+BOOST_AUTO_TEST_CASE( stepper_range )
+{
+ dummy_controlled_stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ boost::for_each( make_adaptive_time_range( stepper , boost::ref( system ) , x , 0.0 , 1.0 , 0.1 ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 3.5 , 1.0e-14 );
+}
+
+// just test if it compiles
+BOOST_AUTO_TEST_CASE( dense_output_stepper_range )
+{
+ dummy_dense_output_stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ boost::for_each( make_adaptive_time_range( stepper , boost::ref( system ) , x , 0.0 , 1.0 , 0.1 ) ,
+ dummy_observer() );
+}
+
+
+BOOST_AUTO_TEST_CASE( stepper_iterator_with_reference_wrapper_factory )
+{
+ dummy_controlled_stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ std::for_each(
+ make_adaptive_time_iterator_begin( boost::ref( stepper ) , boost::ref( system ) , x , 0.0 , 1.0 , 0.1 ) ,
+ make_adaptive_time_iterator_end( boost::ref( stepper ) , boost::ref( system ) , x ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 3.5 , 1.0e-14 );
+}
+
+// just test if it compiles
+BOOST_AUTO_TEST_CASE( dense_output_stepper_iterator_with_reference_wrapper_factory )
+{
+ dummy_dense_output_stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ std::for_each(
+ make_adaptive_time_iterator_begin( boost::ref( stepper ) , boost::ref( system ) , x , 0.0 , 1.0 , 0.1 ) ,
+ make_adaptive_time_iterator_end( boost::ref( stepper ) , boost::ref( system ) , x ) ,
+ dummy_observer() );
+}
+
+
+
+BOOST_AUTO_TEST_CASE( stepper_range_with_reference_wrapper )
+{
+ dummy_controlled_stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ boost::for_each( make_adaptive_time_range( boost::ref( stepper ) , boost::ref( system ) , x , 0.0 , 1.0 , 0.1 ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 3.5 , 1.0e-14 );
+}
+
+// just test if it compiles
+BOOST_AUTO_TEST_CASE( dense_output_stepper_range_with_reference_wrapper )
+{
+ dummy_dense_output_stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ boost::for_each( make_adaptive_time_range( boost::ref( stepper ) , boost::ref( system ) , x , 0.0 , 1.0 , 0.1 ) ,
+ dummy_observer() );
+}
+
+
+
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( transitivity1 , Stepper , dummy_steppers )
+{
+ typedef adaptive_time_iterator< Stepper , empty_system , state_type > stepper_iterator;
+
+ state_type x = {{ 1.0 }};
+ stepper_iterator first1( Stepper() , empty_system() , x , 1.5 , 1.0 , 0.1 );
+ stepper_iterator last1( Stepper() , empty_system() , x );
+ stepper_iterator last2( Stepper() , empty_system() , x );
+
+ BOOST_CHECK( first1 == last1 );
+ BOOST_CHECK( first1 == last2 );
+ BOOST_CHECK( last1 == last2 );
+}
+
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm , Stepper , dummy_steppers )
+{
+ typedef adaptive_time_iterator< Stepper , empty_system , state_type > stepper_iterator;
+ state_type x = {{ 1.0 }};
+ result_vector res;
+ stepper_iterator first( Stepper() , empty_system() , x , 0.0 , 0.35 , 0.1 );
+ stepper_iterator last( Stepper() , empty_system() , x );
+
+ std::copy( first , last , std::back_insert_iterator< result_vector >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 5 ) );
+ BOOST_CHECK_CLOSE( res[0].first[0] , 1.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[0].second , 0.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1].first[0] , 1.25 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1].second , 0.1 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2].first[0] , 1.5 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2].second , 0.2 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3].first[0] , 1.75 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3].second , 0.3 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[4].first[0] , 2.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[4].second , 0.35 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm_with_factory , Stepper , dummy_steppers )
+{
+ state_type x = {{ 1.0 }};
+ result_vector res;
+ std::copy( make_adaptive_time_iterator_begin( Stepper() , empty_system() , x , 0.0 , 0.35 , 0.1 ) ,
+ make_adaptive_time_iterator_end( Stepper() , empty_system() , x ) ,
+ std::back_insert_iterator< result_vector >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 5 ) );
+ BOOST_CHECK_CLOSE( res[0].first[0] , 1.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[0].second , 0.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1].first[0] , 1.25 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1].second , 0.1 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2].first[0] , 1.5 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2].second , 0.2 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3].first[0] , 1.75 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3].second , 0.3 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[4].first[0] , 2.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[4].second , 0.35 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm_with_range_factory , Stepper , dummy_steppers )
+{
+ state_type x = {{ 1.0 }};
+ result_vector res;
+ boost::range::copy( make_adaptive_time_range( Stepper() , empty_system() , x , 0.0 , 0.35 , 0.1 ) ,
+ std::back_insert_iterator< result_vector >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 5 ) );
+ BOOST_CHECK_CLOSE( res[0].first[0] , 1.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[0].second , 0.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1].first[0] , 1.25 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1].second , 0.1 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2].first[0] , 1.5 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2].second , 0.2 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3].first[0] , 1.75 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3].second , 0.3 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[4].first[0] , 2.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[4].second , 0.35 , 1.0e-13 );
+}
+
+
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/algebra_dispatcher.cpp b/test/algebra_dispatcher.cpp
new file mode 100644
index 0000000..66a292f
--- /dev/null
+++ b/test/algebra_dispatcher.cpp
@@ -0,0 +1,82 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/algebra_dispatcher.cpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+ Copyright 2013 Pascal Germroth
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_algebra_dispatcher
+
+#include <boost/numeric/odeint/config.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta4.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_fehlberg78.hpp>
+#include <boost/numeric/odeint/algebra/fusion_algebra_dispatcher.hpp>
+
+#include <boost/test/unit_test.hpp>
+#include <boost/static_assert.hpp>
+#include <boost/type_traits/is_same.hpp>
+#include <boost/array.hpp>
+#include <boost/mpl/list.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+
+BOOST_AUTO_TEST_SUITE( algebra_dispatcher_test )
+
+BOOST_AUTO_TEST_CASE( range_algebra_with_vector )
+{
+ typedef runge_kutta4< std::vector< double > > stepper_type;
+ BOOST_STATIC_ASSERT(( boost::is_same< stepper_type::algebra_type , range_algebra >::value ));
+}
+
+BOOST_AUTO_TEST_CASE( array_algebra_with_array )
+{
+ typedef runge_kutta4< boost::array< double , 2 > > stepper_type;
+ BOOST_STATIC_ASSERT(( boost::is_same< stepper_type::algebra_type , array_algebra >::value ));
+}
+
+BOOST_AUTO_TEST_CASE( range_algebra_with_array )
+{
+ typedef runge_kutta4< boost::array< double , 2 > , double , boost::array< double , 2 > , double , range_algebra > stepper_type;
+ BOOST_STATIC_ASSERT(( boost::is_same< stepper_type::algebra_type , range_algebra >::value ));
+}
+
+BOOST_AUTO_TEST_CASE( fusion_algebra_with_fusion_vector )
+{
+ typedef runge_kutta4< boost::fusion::vector< double > > stepper_type;
+ BOOST_STATIC_ASSERT(( boost::is_same< stepper_type::algebra_type , fusion_algebra >::value ));
+}
+
+BOOST_AUTO_TEST_CASE( fusion_algebra_with_fusion_vector2 )
+{
+ typedef runge_kutta_fehlberg78< boost::fusion::vector< double > > stepper_type;
+ BOOST_STATIC_ASSERT(( boost::is_same< stepper_type::algebra_type , fusion_algebra >::value ));
+}
+
+typedef boost::mpl::list< float , double , long double , std::complex< double > , std::complex< float > > fp_types;
+BOOST_AUTO_TEST_CASE_TEMPLATE( vector_space_algebra_with_floating_point , T , fp_types )
+{
+ typedef runge_kutta_fehlberg78< T > stepper_type;
+ BOOST_STATIC_ASSERT(( boost::is_same< typename stepper_type::algebra_type , vector_space_algebra >::value ));
+}
+
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/boost_units_helpers.hpp b/test/boost_units_helpers.hpp
new file mode 100644
index 0000000..7ff4275
--- /dev/null
+++ b/test/boost_units_helpers.hpp
@@ -0,0 +1,59 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/dummy_boost_units.hpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef LIBS_NUMERIC_ODEINT_TEST_DUMMY_BOOST_UNITS_HPP_DEFINED
+#define LIBS_NUMERIC_ODEINT_TEST_DUMMY_BOOST_UNITS_HPP_DEFINED
+
+#include <boost/units/systems/si/length.hpp>
+#include <boost/units/systems/si/time.hpp>
+#include <boost/units/systems/si/velocity.hpp>
+#include <boost/units/systems/si/acceleration.hpp>
+#include <boost/units/systems/si/io.hpp>
+
+#include <boost/fusion/container.hpp>
+
+
+
+typedef double value_type;
+typedef boost::units::quantity< boost::units::si::time , value_type > time_type;
+typedef boost::units::quantity< boost::units::si::length , value_type > length_type;
+typedef boost::units::quantity< boost::units::si::velocity , value_type > velocity_type;
+typedef boost::units::quantity< boost::units::si::acceleration , value_type > acceleration_type;
+
+
+
+struct oscillator_mom_func_units
+{
+ template< class Coor , class MomDeriv >
+ void operator()( const Coor &q , MomDeriv &dp ) const
+ {
+ const boost::units::quantity< boost::units::si::frequency , value_type > omega = 1.0 * boost::units::si::hertz;
+ boost::fusion::at_c< 0 >( dp ) = - omega * omega * boost::fusion::at_c< 0 >( q );
+ }
+};
+
+struct oscillator_coor_func_units
+{
+ template< class Mom , class CoorDeriv >
+ void operator()( const Mom &p , CoorDeriv &dq ) const
+ {
+ boost::fusion::at_c< 0 >( dq ) = boost::fusion::at_c< 0 >( p );
+ }
+};
+
+
+#endif // LIBS_NUMERIC_ODEINT_TEST_DUMMY_BOOST_UNITS_HPP_DEFINED
diff --git a/test/bulirsch_stoer.cpp b/test/bulirsch_stoer.cpp
new file mode 100644
index 0000000..2c6a0c9
--- /dev/null
+++ b/test/bulirsch_stoer.cpp
@@ -0,0 +1,155 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/bulirsch_stoer.cpp
+
+ [begin_description]
+ This file tests the Bulirsch-Stoer stepper.
+ [end_description]
+
+ Copyright 2011 Mario Mulansky
+ Copyright 2012 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+// disable checked iterator warning for msvc
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_bulirsch_stoer
+
+#include <utility>
+#include <iostream>
+
+#include <boost/array.hpp>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/numeric/odeint/stepper/bulirsch_stoer.hpp>
+#include <boost/numeric/odeint/stepper/bulirsch_stoer_dense_out.hpp>
+
+#include <boost/numeric/odeint/integrate/integrate_adaptive.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+typedef double value_type;
+typedef boost::array< value_type , 3 > state_type;
+
+const double sigma = 10.0;
+const double R = 28.0;
+const double b = 8.0 / 3.0;
+
+struct lorenz
+{
+ template< class State , class Deriv >
+ void operator()( const State &x , Deriv &dxdt , double t ) const
+ {
+ dxdt[0] = sigma * ( x[1] - x[0] );
+ dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
+ dxdt[2] = -b * x[2] + x[0] * x[1];
+ }
+};
+
+struct const_system
+{
+ template< class State , class Deriv >
+ void operator()( const State &x , Deriv &dxdt , double t ) const
+ {
+ dxdt[0] = 1.0;
+ dxdt[1] = 1.0;
+ dxdt[2] = 1.0;
+ }
+};
+
+struct sin_system
+{
+ template< class State , class Deriv >
+ void operator()( const State &x , Deriv &dxdt , double t ) const
+ {
+ dxdt[0] = sin( x[0] );
+ dxdt[1] = cos( x[1] );
+ dxdt[2] = sin( x[2] ) + cos( x[2] );
+ }
+};
+
+BOOST_AUTO_TEST_SUITE( bulirsch_stoer_test )
+
+BOOST_AUTO_TEST_CASE( test_bulirsch_stoer )
+{
+ typedef bulirsch_stoer< state_type > stepper_type;
+ stepper_type stepper( 1E-9 , 1E-9 , 1.0 , 0.0 );
+
+ state_type x;
+ x[0] = 10.0 ; x[1] = 10.0 ; x[2] = 5.0;
+
+ double dt = 0.1;
+
+ //stepper.try_step( lorenz() , x , t , dt );
+
+ std::cout << "starting integration..." << std::endl;
+
+ size_t steps = integrate_adaptive( stepper , lorenz() , x , 0.0 , 10.0 , dt );
+
+ std::cout << "required steps: " << steps << std::endl;
+
+ bulirsch_stoer_dense_out< state_type > bs_do( 1E-9 , 1E-9 , 1.0 , 0.0 );
+ x[0] = 10.0 ; x[1] = 10.0 ; x[2] = 5.0;
+ double t = 0.0;
+ dt = 1E-1;
+ bs_do.initialize( x , t , dt );
+ bs_do.do_step( sin_system() );
+ std::cout << "one step successful, new time: " << bs_do.current_time() << " (" << t << ")" << std::endl;
+
+ x = bs_do.current_state();
+ std::cout << "x( " << bs_do.current_time() << " ) = [ " << x[0] << " , " << x[1] << " , " << x[2] << " ]" << std::endl;
+
+ bs_do.calc_state( bs_do.current_time()/3 , x );
+ std::cout << "x( " << bs_do.current_time()/3 << " ) = [ " << x[0] << " , " << x[1] << " , " << x[2] << " ]" << std::endl;
+
+ std::cout << std::endl << "=======================================================================" << std::endl << std::endl;
+
+ x[0] = 10.0 ; x[1] = 10.0 ; x[2] = 5.0;
+ t = 0.0; dt /= 3;
+ bs_do.initialize( x , t , dt );
+ bs_do.do_step( sin_system() );
+ x = bs_do.current_state();
+ std::cout << "x( " << bs_do.current_time() << " ) = [ " << x[0] << " , " << x[1] << " , " << x[2] << " ]" << std::endl;
+
+ t = dt;
+ bs_do.initialize( x , t , dt );
+ bs_do.do_step( sin_system() );
+ x = bs_do.current_state();
+
+ t = 2*dt;
+ bs_do.initialize( x , t , dt );
+ bs_do.do_step( sin_system() );
+ x = bs_do.current_state();
+
+ std::cout << "x( " << bs_do.current_time() << " ) = [ " << x[0] << " , " << x[1] << " , " << x[2] << " ]" << std::endl << std::endl << std::endl;
+}
+
+BOOST_AUTO_TEST_CASE( test_bulirsch_stoer_adjust_size )
+{
+ typedef bulirsch_stoer< state_type > stepper_type;
+ stepper_type stepper( 1E-9 , 1E-9 , 1.0 , 0.0 );
+
+ state_type x; x[0] = 10.0 ; x[1] = 10.0 ; x[2] = 5.0;
+
+ stepper.adjust_size( x );
+
+
+ double dt = 0.1;
+
+ size_t steps = integrate_adaptive( stepper , lorenz() , x , 0.0 , 10.0 , dt );
+
+ std::cout << "required steps: " << steps << std::endl;
+}
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/const_range.hpp b/test/const_range.hpp
new file mode 100644
index 0000000..d646b1d
--- /dev/null
+++ b/test/const_range.hpp
@@ -0,0 +1,50 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/const_range.hpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef LIBS_NUMERIC_ODEINT_TEST_CONST_RANGE_HPP_DEFINED
+#define LIBS_NUMERIC_ODEINT_TEST_CONST_RANGE_HPP_DEFINED
+
+#include <boost/mpl/copy.hpp>
+#include <boost/mpl/inserter.hpp>
+#include <boost/mpl/insert.hpp>
+#include <boost/mpl/end.hpp>
+#include <boost/mpl/vector.hpp>
+#include <boost/mpl/range_c.hpp>
+#include <boost/mpl/placeholders.hpp>
+
+
+namespace mpl = boost::mpl;
+
+
+
+template< class N , class T >
+struct const_range
+{
+ typedef typename mpl::copy<
+ mpl::range_c< typename N::value_type , 0 , N::value > ,
+ mpl::inserter<
+ mpl::vector0<> ,
+ mpl::insert<
+ mpl::_1 ,
+ mpl::end< mpl::_1 > ,
+ T
+ >
+ >
+ >::type type;
+};
+
+#endif // LIBS_NUMERIC_ODEINT_TEST_CONST_RANGE_HPP_DEFINED
diff --git a/test/const_step_iterator.cpp b/test/const_step_iterator.cpp
new file mode 100644
index 0000000..2d0ac9d
--- /dev/null
+++ b/test/const_step_iterator.cpp
@@ -0,0 +1,232 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/const_step_iterator.cpp
+
+ [begin_description]
+ This file tests the const step iterator.
+ [end_description]
+
+ Copyright 2012-2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#define BOOST_TEST_MODULE odeint_const_step_iterator
+
+#include <iterator>
+#include <algorithm>
+#include <vector>
+
+#include <boost/numeric/odeint/config.hpp>
+#include <boost/array.hpp>
+#include <boost/range/algorithm/for_each.hpp>
+#include <boost/range/algorithm/copy.hpp>
+#include <boost/mpl/vector.hpp>
+
+#include <boost/test/unit_test.hpp>
+#include <boost/test/floating_point_comparison.hpp>
+
+#include <boost/numeric/odeint/iterator/const_step_iterator.hpp>
+#include "dummy_steppers.hpp"
+#include "dummy_odes.hpp"
+#include "dummy_observers.hpp"
+
+namespace mpl = boost::mpl;
+using namespace boost::numeric::odeint;
+
+typedef dummy_stepper::state_type state_type;
+typedef dummy_stepper::value_type value_type;
+
+
+BOOST_AUTO_TEST_SUITE( const_step_iterator_test )
+
+typedef mpl::vector<
+ dummy_stepper
+ , dummy_dense_output_stepper
+ > dummy_steppers;
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_stepper_iterator , Stepper , dummy_steppers )
+{
+ typedef const_step_iterator< Stepper , empty_system , state_type > iterator_type;
+ state_type x = {{ 1.0 }};
+ iterator_type iter1 = iterator_type( Stepper() , empty_system() , x , 0.0 , 0.999 , 0.1 );
+ iterator_type iter2 = iter1;
+ BOOST_CHECK_EQUAL( &(*iter1) , &(*iter2) );
+ BOOST_CHECK_EQUAL( &(*iter1) , &x );
+ BOOST_CHECK( iter1.same( iter2 ) );
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( assignment_stepper_iterator , Stepper , dummy_steppers )
+{
+ typedef const_step_iterator< Stepper , empty_system , state_type > iterator_type;
+ state_type x1 = {{ 1.0 }} , x2 = {{ 2.0 }};
+ iterator_type iter1 = iterator_type( Stepper() , empty_system() , x1 , 0.0 , 1.0 , 0.1 );
+ iterator_type iter2 = iterator_type( Stepper() , empty_system() , x2 , 0.0 , 1.0 , 0.2 );
+ BOOST_CHECK_EQUAL( &(*iter1) , &x1 );
+ BOOST_CHECK_EQUAL( &(*iter2) , &x2 );
+ BOOST_CHECK( !iter1.same( iter2 ) );
+ iter2 = iter1;
+ BOOST_CHECK_EQUAL( &(*iter1) , &x1 );
+ BOOST_CHECK_EQUAL( &(*iter2) , &x1 );
+ BOOST_CHECK( iter1.same( iter2 ) );
+}
+
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_iterator_factory , Stepper , dummy_steppers )
+{
+ Stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ std::for_each(
+ make_const_step_iterator_begin( stepper , boost::ref( system ) , x , 0.0 , 1.0 , 0.1 ) ,
+ make_const_step_iterator_end( stepper , boost::ref( system ) , x ) ,
+ dummy_observer() );
+
+ // dummy_steppers just add 0.25 at each step, the above for_each leads to 10 do_step calls so x should be 3.5
+ BOOST_CHECK_CLOSE( x[0] , 3.5 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_range , Stepper , dummy_steppers )
+{
+ Stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ boost::for_each( make_const_step_range( stepper , boost::ref( system ) , x , 0.0 , 1.0 , 0.1 ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 3.5 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_iterator_with_reference_wrapper_factory , Stepper , dummy_steppers )
+{
+ Stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ std::for_each(
+ make_const_step_iterator_begin( boost::ref( stepper ) , boost::ref( system ) , x , 0.0 , 1.0 , 0.1 ) ,
+ make_const_step_iterator_end( boost::ref( stepper ) , boost::ref( system ) , x ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 3.5 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_range_with_reference_wrapper , Stepper , dummy_steppers )
+{
+ Stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ boost::for_each( make_const_step_range( boost::ref( stepper ) , boost::ref( system ) , x , 0.0 , 1.0 , 0.1 ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 3.5 , 1.0e-13 );
+}
+
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( transitivity1 , Stepper , dummy_steppers )
+{
+ typedef const_step_iterator< Stepper , empty_system , state_type > stepper_iterator;
+
+ state_type x = {{ 1.0 }};
+ stepper_iterator first1( Stepper() , empty_system() , x , 2.5 , 2.0 , 0.1 );
+ stepper_iterator last1( Stepper() , empty_system() , x );
+ stepper_iterator last2( Stepper() , empty_system() , x );
+
+ BOOST_CHECK( first1 == last1 );
+ BOOST_CHECK( first1 == last2 );
+ BOOST_CHECK( last1 == last2 );
+
+ first1 = stepper_iterator( Stepper() , empty_system() , x , 2.0 , 2.0 , 0.1 );
+ last1 = stepper_iterator( Stepper() , empty_system() , x );
+ BOOST_CHECK( first1 != last1 );
+ BOOST_CHECK( ++first1 == last1 );
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm , Stepper , dummy_steppers )
+{
+ typedef const_step_iterator< Stepper , empty_system , state_type > stepper_iterator;
+ state_type x = {{ 1.0 }};
+ std::vector< state_type > res;
+ stepper_iterator first( Stepper() , empty_system() , x , 0.0 , 0.35 , 0.1 );
+ stepper_iterator last( Stepper() , empty_system() , x );
+
+ std::copy( first , last , std::back_insert_iterator< std::vector< state_type > >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 4 ) );
+ BOOST_CHECK_CLOSE( res[0][0] , 1.0 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[1][0] , 1.25 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[2][0] , 1.5 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[3][0] , 1.75 , 1.0e-14 );
+
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-14 ); // the iterator should not iterate over the end
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm_negative_time_step , Stepper , dummy_steppers )
+{
+ typedef const_step_iterator< Stepper , empty_system , state_type > stepper_iterator;
+ state_type x = {{ 1.0 }};
+ std::vector< state_type > res;
+ stepper_iterator first( Stepper() , empty_system() , x , 0.3 , -0.05 , -0.1 );
+ stepper_iterator last( Stepper() , empty_system() , x );
+
+ std::copy( first , last , std::back_insert_iterator< std::vector< state_type > >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 4 ) );
+ BOOST_CHECK_CLOSE( res[0][0] , 1.0 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[1][0] , 1.25 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[2][0] , 1.5 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[3][0] , 1.75 , 1.0e-14 );
+
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-14 );
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm_with_factory , Stepper , dummy_steppers )
+{
+ state_type x = {{ 1.0 }};
+ std::vector< state_type > res;
+ std::copy( make_const_step_iterator_begin( Stepper() , empty_system() , x , 0.0 , 0.35 , 0.1 ) ,
+ make_const_step_iterator_end( Stepper() , empty_system() , x ) ,
+ std::back_insert_iterator< std::vector< state_type > >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 4 ) );
+ BOOST_CHECK_CLOSE( res[0][0] , 1.0 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[1][0] , 1.25 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[2][0] , 1.5 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[3][0] , 1.75 , 1.0e-14 );
+
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-14 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm_with_range_factory , Stepper , dummy_steppers )
+{
+ state_type x = {{ 1.0 }};
+ std::vector< state_type > res;
+ boost::range::copy( make_const_step_range( Stepper() , empty_system() , x , 0.0 , 0.35 , 0.1 ) ,
+ std::back_insert_iterator< std::vector< state_type > >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 4 ) );
+ BOOST_CHECK_CLOSE( res[0][0] , 1.0 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[1][0] , 1.25 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[2][0] , 1.5 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[3][0] , 1.75 , 1.0e-14 );
+
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-14 );
+}
+
+
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/const_step_time_iterator.cpp b/test/const_step_time_iterator.cpp
new file mode 100644
index 0000000..9227f5c
--- /dev/null
+++ b/test/const_step_time_iterator.cpp
@@ -0,0 +1,218 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/const_step_time_iterator.cpp
+
+ [begin_description]
+ This file tests the const step time iterator.
+ [end_description]
+
+ Copyright 2012-2013 Karsten Ahnert
+ Copyright 2012-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#define BOOST_TEST_MODULE odeint_const_step_time_iterator
+
+#include <iterator>
+#include <algorithm>
+#include <vector>
+
+#include <boost/numeric/odeint/config.hpp>
+#include <boost/array.hpp>
+#include <boost/range/algorithm/copy.hpp>
+#include <boost/range/algorithm/for_each.hpp>
+#include <boost/mpl/vector.hpp>
+
+#include <boost/test/unit_test.hpp>
+#include <boost/test/floating_point_comparison.hpp>
+
+#include <boost/numeric/odeint/iterator/const_step_time_iterator.hpp>
+#include "dummy_steppers.hpp"
+#include "dummy_odes.hpp"
+#include "dummy_observers.hpp"
+
+namespace mpl = boost::mpl;
+using namespace boost::numeric::odeint;
+
+typedef dummy_stepper::state_type state_type;
+typedef dummy_stepper::value_type value_type;
+typedef dummy_stepper::time_type time_type;
+typedef std::vector< std::pair< state_type , time_type > > result_vector;
+
+BOOST_AUTO_TEST_SUITE( const_step_time_iterator_test )
+
+typedef mpl::vector<
+ dummy_stepper
+ , dummy_dense_output_stepper
+ > dummy_steppers;
+
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_stepper_iterator , Stepper , dummy_steppers )
+{
+ typedef const_step_time_iterator< Stepper , empty_system , state_type > iterator_type;
+ state_type x = {{ 1.0 }};
+ iterator_type iter1 = iterator_type( Stepper() , empty_system() , x , 0.0 , 1.0 , 0.1 );
+ iterator_type iter2 = iter1;
+ BOOST_CHECK_EQUAL( &( iter1->first ) , &( iter2->first ) );
+ BOOST_CHECK_EQUAL( &( iter1->first ) , &x );
+ BOOST_CHECK( iter1.same( iter2 ) );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( assignment_stepper_iterator , Stepper , dummy_steppers )
+{
+ typedef const_step_time_iterator< Stepper , empty_system , state_type > iterator_type;
+ state_type x1 = {{ 1.0 }} , x2 = {{ 2.0 }};
+ iterator_type iter1 = iterator_type( Stepper() , empty_system() , x1 , 0.0 , 1.0 , 0.1 );
+ iterator_type iter2 = iterator_type( Stepper() , empty_system() , x2 , 0.0 , 1.0 , 0.2 );
+ BOOST_CHECK_EQUAL( &( iter1->first ) , &x1 );
+ BOOST_CHECK_EQUAL( &( iter2->first ) , &x2 );
+ BOOST_CHECK( !iter1.same( iter2 ) );
+ iter2 = iter1;
+ BOOST_CHECK_EQUAL( &( iter1->first ) , &x1 );
+ BOOST_CHECK_EQUAL( &( iter2->first ) , &x1 );
+ BOOST_CHECK( iter1.same( iter2 ) );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_iterator_factory , Stepper , dummy_steppers )
+{
+ Stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ std::for_each(
+ make_const_step_time_iterator_begin( stepper , boost::ref( system ) , x , 0.0 , 1.0 , 0.1 ) ,
+ make_const_step_time_iterator_end( stepper , boost::ref( system ) , x ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 3.5 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_range , Stepper , dummy_steppers )
+{
+ Stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ boost::for_each( make_const_step_time_range( stepper , boost::ref( system ) , x , 0.0 , 1.0 , 0.1 ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 3.5 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_iterator_with_reference_wrapper_factory , Stepper , dummy_steppers )
+{
+ Stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ std::for_each(
+ make_const_step_time_iterator_begin( boost::ref( stepper ) , boost::ref( system ) , x , 0.0 , 1.0 , 0.1 ) ,
+ make_const_step_time_iterator_end( boost::ref( stepper ) , boost::ref( system ) , x ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 3.5 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_range_with_reference_wrapper , Stepper , dummy_steppers )
+{
+ Stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ boost::for_each( make_const_step_time_range( boost::ref( stepper ) , boost::ref( system ) , x , 0.0 , 1.0 , 0.1 ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 3.5 , 1.0e-13 );
+}
+
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( transitivity1 , Stepper , dummy_steppers )
+{
+ typedef const_step_time_iterator< Stepper , empty_system , state_type > stepper_iterator;
+
+ state_type x = {{ 1.0 }};
+ stepper_iterator first1( Stepper() , empty_system() , x , 1.5 , 1.0 , 0.1 );
+ stepper_iterator last1( Stepper() , empty_system() , x );
+ stepper_iterator last2( Stepper() , empty_system() , x );
+
+ BOOST_CHECK( first1 == last1 );
+ BOOST_CHECK( first1 == last2 );
+ BOOST_CHECK( last1 == last2 );
+
+ first1 = stepper_iterator( Stepper() , empty_system() , x , 2.0 , 2.0 , 0.1 );
+ last1 = stepper_iterator( Stepper() , empty_system() , x );
+ BOOST_CHECK( first1 != last1 );
+ BOOST_CHECK( ++first1 == last1 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm , Stepper , dummy_steppers )
+{
+ typedef const_step_time_iterator< Stepper , empty_system , state_type > stepper_iterator;
+ state_type x = {{ 1.0 }};
+ result_vector res;
+ stepper_iterator first( Stepper() , empty_system() , x , 0.0 , 0.35 , 0.1 );
+ stepper_iterator last( Stepper() , empty_system() , x );
+
+ std::copy( first , last , std::back_insert_iterator< result_vector >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 4 ) );
+ BOOST_CHECK_CLOSE( res[0].first[0] , 1.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[0].second , 0.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1].first[0] , 1.25 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1].second , 0.1 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2].first[0] , 1.5 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2].second , 0.2 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3].first[0] , 1.75 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3].second , 0.3 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm_with_factory , Stepper , dummy_steppers )
+{
+ state_type x = {{ 1.0 }};
+ result_vector res;
+ std::copy( make_const_step_time_iterator_begin( Stepper() , empty_system() , x , 0.0 , 0.35 , 0.1 ) ,
+ make_const_step_time_iterator_end( Stepper() , empty_system() , x ) ,
+ std::back_insert_iterator< result_vector >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 4 ) );
+ BOOST_CHECK_CLOSE( res[0].first[0] , 1.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[0].second , 0.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1].first[0] , 1.25 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1].second , 0.1 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2].first[0] , 1.5 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2].second , 0.2 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3].first[0] , 1.75 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3].second , 0.3 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm_with_range_factory , Stepper , dummy_steppers )
+{
+ state_type x = {{ 1.0 }};
+ result_vector res;
+ boost::range::copy( make_const_step_time_range( Stepper() , empty_system() , x , 0.0 , 0.35 , 0.1 ) ,
+ std::back_insert_iterator< result_vector >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 4 ) );
+ BOOST_CHECK_CLOSE( res[0].first[0] , 1.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[0].second , 0.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1].first[0] , 1.25 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1].second , 0.1 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2].first[0] , 1.5 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2].second , 0.2 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3].first[0] , 1.75 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3].second , 0.3 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-13 );
+}
+
+
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/default_operations.cpp b/test/default_operations.cpp
new file mode 100644
index 0000000..a2634b7
--- /dev/null
+++ b/test/default_operations.cpp
@@ -0,0 +1,257 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/default_operations.cpp
+
+ [begin_description]
+ This file tests default_operations.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#define BOOST_TEST_MODULE odeint_standard_operations
+
+#include <cmath>
+#include <complex>
+
+#include <boost/test/unit_test.hpp>
+#include <boost/test/floating_point_comparison.hpp>
+
+#include <boost/units/systems/si/length.hpp>
+#include <boost/units/systems/si/time.hpp>
+#include <boost/units/systems/si/velocity.hpp>
+#include <boost/units/systems/si/acceleration.hpp>
+#include <boost/units/systems/si/io.hpp>
+
+#include <boost/mpl/list.hpp>
+
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+
+namespace units = boost::units;
+namespace si = boost::units::si;
+namespace mpl = boost::mpl;
+using boost::numeric::odeint::default_operations;
+
+
+template< class Value > struct internal_value_type { typedef Value type; };
+template< class T > struct internal_value_type< std::complex< T > > { typedef T type; };
+
+template< class T > struct default_eps;
+template<> struct default_eps< double > { static double def_eps( void ) { return 1.0e-10; } };
+template<> struct default_eps< float > { static float def_eps( void ) { return 1.0e-5; } };
+
+
+typedef units::unit< units::derived_dimension< units::time_base_dimension , 2 >::type , si::system > time_2;
+typedef units::unit< units::derived_dimension< units::time_base_dimension , 3 >::type , si::system > time_3;
+typedef units::unit< units::derived_dimension< units::time_base_dimension , 4 >::type , si::system > time_4;
+typedef units::unit< units::derived_dimension< units::time_base_dimension , 5 >::type , si::system > time_5;
+typedef units::unit< units::derived_dimension< units::time_base_dimension , 6 >::type , si::system > time_6;
+typedef units::unit< units::derived_dimension< units::time_base_dimension , 7 >::type , si::system > time_7;
+
+const time_2 second2 = si::second * si::second;
+const time_3 second3 = second2 * si::second;
+const time_4 second4 = second3 * si::second;
+const time_5 second5 = second4 * si::second;
+const time_6 second6 = second5 * si::second;
+const time_7 second7 = second6 * si::second;
+
+
+
+
+template< class Value , class Compare = typename internal_value_type< Value >::type >
+struct double_fixture
+{
+ typedef Value value_type;
+ typedef Compare compare_type;
+
+ double_fixture( const compare_type &eps_ = default_eps< compare_type >::def_eps() )
+ : m_eps( eps_ ) , res( 0.0 ) , x1( 1.0 ) , x2( 2.0 ) , x3( 3.0 ) , x4( 4.0 ) , x5( 5.0 ) , x6( 6.0 ) , x7( 7.0 ) , x8( 8.0 )
+ {}
+
+ ~double_fixture( void )
+ {
+ using std::abs;
+ BOOST_CHECK_SMALL( abs( x1 - value_type( 1.0 ) ) , m_eps );
+ BOOST_CHECK_SMALL( abs( x2 - value_type( 2.0 ) ) , m_eps );
+ BOOST_CHECK_SMALL( abs( x3 - value_type( 3.0 ) ) , m_eps );
+ BOOST_CHECK_SMALL( abs( x4 - value_type( 4.0 ) ) , m_eps );
+ BOOST_CHECK_SMALL( abs( x5 - value_type( 5.0 ) ) , m_eps );
+ BOOST_CHECK_SMALL( abs( x6 - value_type( 6.0 ) ) , m_eps );
+ BOOST_CHECK_SMALL( abs( x7 - value_type( 7.0 ) ) , m_eps );
+ }
+
+ const compare_type m_eps;
+ value_type res;
+ value_type x1 , x2 , x3 , x4 , x5 , x6 , x7 , x8;
+};
+
+template< class Value , class Compare = typename internal_value_type< Value >::type >
+struct unit_fixture
+{
+ typedef Value value_type;
+ typedef Compare compare_type;
+ typedef units::quantity< si::length , value_type > length_type;
+
+ typedef units::quantity< si::time , value_type > time_type;
+ typedef units::quantity< time_2 , value_type > time_2_type;
+ typedef units::quantity< time_3 , value_type > time_3_type;
+ typedef units::quantity< time_4 , value_type > time_4_type;
+ typedef units::quantity< time_5 , value_type > time_5_type;
+ typedef units::quantity< time_6 , value_type > time_6_type;
+ typedef units::quantity< time_7 , value_type > time_7_type;
+
+ typedef units::quantity< si::velocity , value_type > velocity_type;
+ typedef units::quantity< si::acceleration , value_type > acceleration_type;
+
+ unit_fixture( const compare_type &eps_ = default_eps< compare_type >::def_eps() )
+ : m_eps( eps_ )
+ , res( 0.0 * si::meter )
+ , x( 1.0 * si::meter )
+ , d1x( 2.0 * si::meter / si::second )
+ , d2x( 3.0 * si::meter / si::second / si::second )
+ {}
+
+ ~unit_fixture( void )
+ {
+ using std::abs;
+ BOOST_CHECK_SMALL( abs( x.value() - value_type( 1.0 ) ) , m_eps );
+ BOOST_CHECK_SMALL( abs( d1x.value() - value_type( 2.0 ) ) , m_eps );
+ BOOST_CHECK_SMALL( abs( d2x.value() - value_type( 3.0 ) ) , m_eps );
+ }
+
+ compare_type m_eps;
+ length_type res;
+ length_type x;
+ velocity_type d1x;
+ acceleration_type d2x;
+};
+
+
+typedef mpl::list< float , double , std::complex< double > > test_types;
+
+BOOST_AUTO_TEST_SUITE( check_operations_test )
+
+using std::abs;
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( scale_sum2_test , T , test_types )
+{
+ typedef double_fixture< T > fix_type;
+ fix_type f;
+ typedef typename default_operations::scale_sum2< T , T > Op;
+ Op op( 1.25 , 9.81 );
+ op( f.res , f.x1 , f.x2 );
+ BOOST_CHECK_SMALL( abs( f.res - T( 20.87 ) ) , f.m_eps );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( scale_sum3_test , T , test_types )
+{
+ typedef double_fixture< T > fix_type;
+ fix_type f;
+ typedef default_operations::scale_sum3< T , T , T > Op;
+ Op op( 1.25 , 9.81 , 0.87 );
+ op( f.res , f.x1 , f.x2 , f.x3 );
+ BOOST_CHECK_SMALL( abs( f.res - T( 23.48 ) ) , f.m_eps );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( scale_sum4_test , T , test_types )
+{
+ typedef double_fixture< T > fix_type;
+ fix_type f;
+ typedef default_operations::scale_sum4< T , T , T , T > Op;
+ Op op( 1.25 , 9.81 , 0.87 , -0.15 );
+ op( f.res , f.x1 , f.x2 , f.x3 , f.x4 );
+ BOOST_CHECK_SMALL( abs( f.res - T( 22.88 ) ) , f.m_eps );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( scale_sum5_test , T , test_types )
+{
+ typedef double_fixture< T > fix_type;
+ fix_type f;
+ typedef default_operations::scale_sum5< T , T , T , T , T > Op;
+ Op op( 1.25 , 9.81 , 0.87 , -0.15 , -3.3 );
+ op( f.res , f.x1 , f.x2 , f.x3 , f.x4 , f.x5 );
+ BOOST_CHECK_SMALL( abs( f.res - T( 6.38 ) ) , f.m_eps );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( scale_sum6_test , T , test_types )
+{
+ typedef double_fixture< T > fix_type;
+ fix_type f;
+ typedef default_operations::scale_sum6< T , T , T , T , T , T > Op;
+ Op op( 1.25 , 9.81 , 0.87 , -0.15 , -3.3 , 4.2 );
+ op( f.res , f.x1 , f.x2 , f.x3 , f.x4 , f.x5 , f.x6 );
+ BOOST_CHECK_SMALL( abs( f.res - T( 31.58 ) ) , f.m_eps );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( scale_sum7_test , T , test_types )
+{
+ typedef double_fixture< T > fix_type;
+ fix_type f;
+ typedef default_operations::scale_sum7< T , T , T , T , T , T , T > Op;
+ Op op( 1.25 , 9.81 , 0.87 , -0.15 , -3.3 , 4.2 , -0.22 );
+ op( f.res , f.x1 , f.x2 , f.x3 , f.x4 , f.x5 , f.x6 , f.x7 );
+ BOOST_CHECK_SMALL( abs( f.res - T( 30.04 ) ) , f.m_eps );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( rel_error_test , T , test_types )
+{
+ typedef double_fixture< T > fix_type;
+ fix_type f;
+ f.res = -1.1;
+ typedef default_operations::rel_error< T > Op;
+ Op op( 0.1 , 0.2 , 0.15 , 0.12 );
+ op( f.res , -f.x1 , -f.x2 );
+ BOOST_CHECK_SMALL( abs( f.res - T( 6.17978 ) ) , typename fix_type::compare_type( 1.0e-4 ) );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( maximum_test , T , test_types )
+{
+ typedef double_fixture< T > fix_type;
+ fix_type f;
+ typedef default_operations::maximum< typename fix_type::compare_type > Op;
+ Op op;
+ f.res = op( f.x1 , f.x2 );
+ BOOST_CHECK_SMALL( abs( f.res - T( 2.0 ) ) , f.m_eps );
+}
+
+
+
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( scale_sum2_units_test , T , test_types )
+{
+ typedef unit_fixture< T > fix_type;
+ typedef typename fix_type::value_type value_type;
+ typedef typename fix_type::time_type time_type;
+
+ fix_type f;
+ typedef default_operations::scale_sum2< value_type , time_type > Op;
+ Op op( 1.0 , time_type( 1.0 * si::second ) );
+ op( f.res , f.x , f.d1x );
+ BOOST_CHECK_SMALL( abs( f.res.value() - T( 3.0 ) ) , f.m_eps );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( scale_sum3_units_test , T , test_types )
+{
+ typedef unit_fixture< T > fix_type;
+ typedef typename fix_type::value_type value_type;
+ typedef typename fix_type::time_type time_type;
+ typedef typename fix_type::time_2_type time_2_type;
+
+ fix_type f;
+ typedef default_operations::scale_sum3< value_type , time_type , time_2_type > Op;
+ Op op( 1.0 , time_type( 1.0 * si::second ) , time_2_type( 1.0 * second2 ) );
+ op( f.res , f.x , f.d1x , f.d2x );
+ BOOST_CHECK_SMALL( abs( f.res.value() - T( 6.0 ) ) , f.m_eps );
+}
+
+
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/diagnostic_state_type.hpp b/test/diagnostic_state_type.hpp
new file mode 100644
index 0000000..0c21013
--- /dev/null
+++ b/test/diagnostic_state_type.hpp
@@ -0,0 +1,185 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/diagnostic_state_type.hpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef LIBS_NUMERIC_ODEINT_TEST_DIAGNOSTIC_STATE_TYPE_HPP_DEFINED
+#define LIBS_NUMERIC_ODEINT_TEST_DIAGNOSTIC_STATE_TYPE_HPP_DEFINED
+
+#include <boost/array.hpp>
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/same_size.hpp>
+#include <boost/numeric/odeint/util/resize.hpp>
+#include <boost/numeric/odeint/util/state_wrapper.hpp>
+
+template< size_t N >
+struct counter
+{
+ static size_t& adjust_size_count( void )
+ {
+ static size_t m_adjust_size_count;
+ return m_adjust_size_count;
+ }
+
+ static size_t& construct_count( void )
+ {
+ static size_t m_construct_count;
+ return m_construct_count;
+ }
+
+ static size_t& copy_count( void )
+ {
+ static size_t m_copy_count;
+ return m_copy_count;
+ }
+
+ static size_t& destroy_count( void )
+ {
+ static size_t m_destroy_count;
+ return m_destroy_count;
+ }
+
+
+ static void init_counter( void )
+ {
+ counter< N >::adjust_size_count() = 0;
+ counter< N >::construct_count() = 0;
+ counter< N >::copy_count() = 0;
+ counter< N >::destroy_count() = 0;
+ }
+};
+
+template< size_t N >
+class diagnostic_type : public boost::array< double , 1 > { };
+
+
+typedef diagnostic_type< 0 > diagnostic_state_type;
+typedef diagnostic_type< 1 > diagnostic_deriv_type;
+typedef diagnostic_type< 2 > diagnostic_state_type2;
+typedef diagnostic_type< 3 > diagnostic_deriv_type2;
+
+typedef counter< 0 > counter_state;
+typedef counter< 1 > counter_deriv;
+typedef counter< 2 > counter_state2;
+typedef counter< 3 > counter_deriv2;
+
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+ template< size_t N >
+ struct is_resizeable< diagnostic_type< N > >
+ {
+ typedef boost::true_type type;
+ const static bool value = type::value;
+ };
+
+ template< size_t N , size_t M >
+ struct same_size_impl< diagnostic_type< N > , diagnostic_type< M > >
+ {
+ static bool same_size( const diagnostic_type< N > &x1 , const diagnostic_type< M > &x2 )
+ {
+ return false;
+ }
+ };
+
+ template< size_t N , class State1 >
+ struct same_size_impl< diagnostic_type< N > , State1 >
+ {
+ static bool same_size( const diagnostic_type< N > &x1 , const State1 &x2 )
+ {
+ return false;
+ }
+ };
+
+ template< class State1 , size_t N >
+ struct same_size_impl< State1 , diagnostic_type< N > >
+ {
+ static bool same_size( const State1 &x1 , const diagnostic_type< N > &x2 )
+ {
+ return false;
+ }
+ };
+
+
+
+ template< size_t N , class StateIn >
+ struct resize_impl< diagnostic_type< N > , StateIn >
+ {
+ static void resize( diagnostic_type< N > &x1 , const StateIn &x2 )
+ {
+ counter< N >::adjust_size_count()++;
+ }
+ };
+
+ template< size_t N >
+ struct state_wrapper< diagnostic_type< N > >
+ {
+ typedef state_wrapper< diagnostic_type< N > > state_wrapper_type;
+ typedef diagnostic_type< N > state_type;
+ typedef double value_type;
+
+ state_type m_v;
+
+ state_wrapper() : m_v()
+ {
+ counter< N >::construct_count()++;
+ }
+
+ state_wrapper( const state_type &v ) : m_v( v )
+ {
+ counter< N >::construct_count()++;
+ counter< N >::copy_count()++;
+ }
+
+ state_wrapper( const state_wrapper_type &x ) : m_v( x.m_v )
+ {
+ counter< N >::construct_count()++;
+ counter< N >::copy_count()++;
+ }
+
+ state_wrapper_type& operator=( const state_wrapper_type &x )
+ {
+ counter< N >::copy_count()++;
+ return *this;
+ }
+
+ ~state_wrapper()
+ {
+ counter< N >::destroy_count()++;
+ }
+ };
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+#define TEST_COUNTERS( c , s1 , s2 , s3 ,s4 ) \
+ BOOST_CHECK_EQUAL( c::adjust_size_count() , size_t( s1 ) ); \
+ BOOST_CHECK_EQUAL( c::construct_count() , size_t( s2 ) ); \
+ BOOST_CHECK_EQUAL( c::copy_count() , size_t( s3 ) ); \
+ BOOST_CHECK_EQUAL( c::destroy_count() , size_t( s4 ) );
+
+#define TEST_COUNTERS_MSG( c , s1 , s2 , s3 ,s4 , msg ) \
+ BOOST_CHECK_EQUAL( c::adjust_size_count() , size_t( s1 ) ); \
+ BOOST_CHECK_EQUAL( c::construct_count() , size_t( s2 ) ); \
+ BOOST_CHECK_EQUAL( c::copy_count() , size_t( s3 ) ); \
+ BOOST_CHECK_EQUAL( c::destroy_count() , size_t( s4 ) );
+
+
+#endif // LIBS_NUMERIC_ODEINT_TEST_DIAGNOSTIC_STATE_TYPE_HPP_DEFINED
diff --git a/test/dummy_observers.hpp b/test/dummy_observers.hpp
new file mode 100644
index 0000000..744c374
--- /dev/null
+++ b/test/dummy_observers.hpp
@@ -0,0 +1,41 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/dummy_observers.hpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef LIBS_NUMERIC_ODEINT_TEST_DUMMY_OBSERVERS_HPP_DEFINED
+#define LIBS_NUMERIC_ODEINT_TEST_DUMMY_OBSERVERS_HPP_DEFINED
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+struct dummy_observer
+{
+ template< class State >
+ void operator()( const State &s ) const
+ {
+ }
+};
+
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // LIBS_NUMERIC_ODEINT_TEST_DUMMY_OBSERVERS_HPP_DEFINED
diff --git a/test/dummy_odes.hpp b/test/dummy_odes.hpp
new file mode 100644
index 0000000..7a92363
--- /dev/null
+++ b/test/dummy_odes.hpp
@@ -0,0 +1,151 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/dummy_odes.hpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2012-2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef LIBS_NUMERIC_ODEINT_TEST_DUMMY_ODES_HPP_DEFINED
+#define LIBS_NUMERIC_ODEINT_TEST_DUMMY_ODES_HPP_DEFINED
+
+#include <boost/fusion/include/at_c.hpp>
+
+
+
+
+
+
+/*
+ * rhs functors/functions for different state types
+ */
+struct constant_system_functor_standard
+{
+ template< class State , class Deriv , class Time >
+ void operator()( const State &x , Deriv &dxdt , const Time t ) const
+ {
+ dxdt[0] = 1.0;
+ }
+};
+
+struct constant_system_functor_vector_space
+{
+ template< class State , class Deriv , class Time >
+ void operator()( const State &x , Deriv &dxdt , const Time t ) const
+ {
+ dxdt = 1.0;
+ }
+};
+
+struct constant_system_functor_fusion
+{
+ template< class State , class Deriv , class Time >
+ void operator()( const State &x , Deriv &dxdt , const Time t ) const
+ {
+ boost::fusion::at_c< 0 >( dxdt ) = boost::fusion::at_c< 0 >( x ) / Time( 1.0 );
+ }
+};
+
+struct lorenz
+{
+ template< typename State , typename Deriv , typename Time >
+ void operator()( const State& x , Deriv& dxdt , const Time& t ) const
+ {
+ const Time sigma = 10.0;
+ const Time R = 28.0;
+ const Time b = 8.0 / 3.0;
+ dxdt[0] = sigma * ( x[1] - x[0] );
+ dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
+ dxdt[2] = -b * x[2] + x[0] * x[1];
+ }
+};
+
+template< class State , class Deriv , class Time >
+void constant_system_standard( const State &x , Deriv &dxdt , const Time t )
+{
+ dxdt[0] = 1.0;
+}
+
+template< class State , class Deriv , class Time >
+void constant_system_vector_space( const State &x , Deriv &dxdt , const Time t )
+{
+ dxdt = 1.0;
+}
+
+template< class State , class Deriv , class Time >
+void constant_system_fusion( const State &x , Deriv &dxdt , const Time t )
+{
+ boost::fusion::at_c< 0 >( dxdt ) = boost::fusion::at_c< 0 >( x ) / Time( 1.0 );
+}
+
+
+
+
+/*
+ * rhs functors for symplectic steppers
+ */
+struct constant_mom_func
+{
+ template< class StateIn , class StateOut >
+ void operator()( const StateIn &q , StateOut &dp ) const
+ {
+ dp[0] = 1.0;
+ }
+};
+
+struct default_coor_func
+{
+ template< class StateIn , class StateOut >
+ void operator()( const StateIn &p , StateOut &dq ) const
+ {
+ dq[0] = p[0];
+ }
+};
+
+
+
+struct constant_mom_func_vector_space_1d
+{
+ template< class T >
+ void operator()( const T &q , T &dp ) const
+ {
+ dp = 1.0;
+ }
+};
+
+struct default_coor_func_vector_space_1d
+{
+ template< class T >
+ void operator()( const T &p , T &dq ) const
+ {
+ dq = p;
+ }
+};
+
+
+
+
+
+
+
+struct empty_system
+{
+ template <class State >
+ void operator()( const State &x , State &dxdt , double t ) const
+ {
+ }
+};
+
+
+
+
+#endif // LIBS_NUMERIC_ODEINT_TEST_DUMMY_ODES_HPP_DEFINED
diff --git a/test/dummy_steppers.hpp b/test/dummy_steppers.hpp
new file mode 100644
index 0000000..5f8d749
--- /dev/null
+++ b/test/dummy_steppers.hpp
@@ -0,0 +1,122 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/dummy_steppers.hpp
+
+ [begin_description]
+ Dummy steppers for several tests.
+ [end_description]
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#ifndef BOOST_LIBS_NUMERIC_ODEINT_TEST_DUMMY_STEPPER_HPP_INCLUDED
+#define BOOST_LIBS_NUMERIC_ODEINT_TEST_DUMMY_STEPPER_HPP_INCLUDED
+
+#include <boost/array.hpp>
+#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
+#include <boost/numeric/odeint/stepper/controlled_step_result.hpp>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+struct dummy_stepper
+{
+ typedef double value_type;
+ typedef value_type time_type;
+ typedef boost::array< value_type , 1 > state_type;
+ typedef state_type deriv_type;
+ typedef unsigned short order_type;
+ typedef stepper_tag stepper_category;
+
+ order_type order( void ) const { return 1; }
+
+ template< class System >
+ void do_step( System sys , state_type &x , time_type t , time_type dt ) const
+ {
+ x[0] += 0.25;
+ }
+};
+
+struct dummy_dense_output_stepper
+{
+ typedef double value_type;
+ typedef value_type time_type;
+ typedef boost::array< value_type , 1 > state_type;
+ typedef state_type deriv_type;
+ typedef dense_output_stepper_tag stepper_category;
+
+ void initialize( const state_type &x0 , time_type t0 , time_type dt0 )
+ {
+ m_x = x0;
+ m_t = t0;
+ m_dt = dt0;
+ }
+
+ template< class System >
+ std::pair< time_type , time_type > do_step( System sys )
+ {
+ m_x[0] += 0.25;
+ m_t += m_dt;
+ return std::make_pair( m_t - m_dt , m_t );
+ }
+
+ void calc_state( time_type t_inter , state_type &x ) const
+ {
+ value_type theta = ( m_t - t_inter ) / m_dt;
+ x[0] = m_x[0] - 0.25 * theta;
+
+ }
+
+ const time_type& current_time( void ) const
+ {
+ return m_t;
+ }
+
+ const state_type& current_state( void ) const
+ {
+ return m_x;
+ }
+
+ const time_type& current_time_step( void ) const
+ {
+ return m_dt;
+ }
+
+ state_type m_x;
+ time_type m_t;
+ time_type m_dt;
+};
+
+
+
+struct dummy_controlled_stepper
+{
+ typedef double value_type;
+ typedef value_type time_type;
+ typedef boost::array< value_type , 1 > state_type;
+ typedef state_type deriv_type;
+ typedef controlled_stepper_tag stepper_category;
+
+ template< class Sys >
+ controlled_step_result try_step( Sys sys , state_type &x , time_type &t , time_type &dt ) const
+ {
+ x[0] += 0.25;
+ t += dt;
+ return success;
+ }
+};
+
+
+} // odeint
+} // numeric
+} // boost
+
+
+#endif // BOOST_LIBS_NUMERIC_ODEINT_TEST_DUMMY_STEPPER_HPP_INCLUDED
diff --git a/test/euler_stepper.cpp b/test/euler_stepper.cpp
new file mode 100644
index 0000000..a274de4
--- /dev/null
+++ b/test/euler_stepper.cpp
@@ -0,0 +1,105 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/euler_stepper.cpp
+
+ [begin_description]
+ This file tests explicit Euler stepper.
+ [end_description]
+
+ Copyright 2011 Mario Mulansky
+ Copyright 2012 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#define BOOST_TEST_MODULE odeint_explicit_euler
+
+#include <boost/test/unit_test.hpp>
+
+#include <utility>
+#include <iostream>
+#include <vector>
+
+#include <boost/numeric/odeint/stepper/euler.hpp>
+#include <boost/numeric/odeint/algebra/range_algebra.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+// test with own vector implementation
+
+class my_vec : public std::vector< double > {
+
+public:
+
+ my_vec() : std::vector< double >()
+ { }
+
+ my_vec( const my_vec &x ) : std::vector< double >( x )
+ { }
+
+
+ my_vec( size_t dim )
+ : std::vector< double >( dim )
+ { }
+
+};
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+template<>
+struct is_resizeable< my_vec >
+{
+ //struct type : public boost::true_type { };
+ typedef boost::true_type type;
+ const static bool value = type::value;
+};
+} } }
+
+typedef double value_type;
+//typedef std::vector< value_type > state_type;
+typedef my_vec state_type;
+
+/* use functors, because functions don't work with msvc 10, I guess this is a bug */
+struct sys
+{
+ void operator()( const state_type &x , state_type &dxdt , const value_type t ) const
+ {
+ std::cout << "sys start " << dxdt.size() << std::endl;
+ dxdt[0] = x[0] + 2 * x[1];
+ dxdt[1] = x[1];
+ std::cout << "sys done" << std::endl;
+ }
+};
+
+
+BOOST_AUTO_TEST_SUITE( explicit_euler_test )
+
+BOOST_AUTO_TEST_CASE( test_euler )
+{
+ range_algebra algebra;
+ euler< state_type > stepper( algebra );
+ state_type x( 2 );
+ x[0] = 0.0; x[1] = 1.0;
+
+ std::cout << "initialized" << std::endl;
+
+ const value_type eps = 1E-12;
+ const value_type dt = 0.1;
+
+ stepper.do_step( sys() , x , 0.0 , dt );
+
+ using std::abs;
+
+ // compare with analytic solution of above system
+ BOOST_CHECK_MESSAGE( abs( x[0] - 2.0*1.0*dt ) < eps , x[0] - 2.0*1.0*dt );
+ BOOST_CHECK_MESSAGE( abs( x[1] - (1.0 + dt) ) < eps , x[1] - (1.0+dt) );
+
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/fusion_algebra.cpp b/test/fusion_algebra.cpp
new file mode 100644
index 0000000..cc63fa9
--- /dev/null
+++ b/test/fusion_algebra.cpp
@@ -0,0 +1,184 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/fusion_algebra.cpp
+
+ [begin_description]
+ This file tests the Fusion algebra.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#define BOOST_TEST_MODULE odeint_fusion_algebra
+
+// using fusion vectors as state types requires increased macro variables
+#define BOOST_FUSION_INVOKE_MAX_ARITY 15
+#define BOOST_RESULT_OF_NUM_ARGS 15
+
+#include <cmath>
+#include <complex>
+#include <utility>
+#include <functional>
+
+#include <boost/numeric/odeint/config.hpp>
+
+#include <boost/test/unit_test.hpp>
+#include <boost/test/floating_point_comparison.hpp>
+
+#include <boost/units/systems/si/length.hpp>
+#include <boost/units/systems/si/time.hpp>
+#include <boost/units/systems/si/velocity.hpp>
+#include <boost/units/systems/si/acceleration.hpp>
+#include <boost/units/systems/si/io.hpp>
+
+#include <boost/fusion/container.hpp>
+
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+#include <boost/numeric/odeint/algebra/fusion_algebra.hpp>
+
+namespace units = boost::units;
+namespace si = boost::units::si;
+namespace fusion = boost::fusion;
+
+using boost::numeric::odeint::default_operations;
+using boost::numeric::odeint::fusion_algebra;
+
+typedef double value_type;
+typedef units::quantity< si::time , value_type > time_type;
+typedef units::quantity< si::length , value_type > length_type;
+typedef units::quantity< si::velocity , value_type > velocity_type;
+typedef units::quantity< si::acceleration , value_type > acceleration_type;
+typedef fusion::vector< length_type , velocity_type > state_type;
+typedef fusion::vector< velocity_type , acceleration_type > deriv_type;
+
+const time_type dt = 0.1 * si::second;
+
+
+struct fusion_fixture
+{
+ fusion_fixture( void )
+ : res( 0.0 * si::meter , 0.0 * si::meter_per_second ) ,
+ x( 1.0 * si::meter , 1.0 * si::meter_per_second ) ,
+ k1( 1.0 * si::meter_per_second , 1.0 * si::meter_per_second_squared ) ,
+ k2( 2.0 * si::meter_per_second , 2.0 * si::meter_per_second_squared ) ,
+ k3( 3.0 * si::meter_per_second , 3.0 * si::meter_per_second_squared ) ,
+ k4( 4.0 * si::meter_per_second , 4.0 * si::meter_per_second_squared ) ,
+ k5( 5.0 * si::meter_per_second , 5.0 * si::meter_per_second_squared ) ,
+ k6( 6.0 * si::meter_per_second , 6.0 * si::meter_per_second_squared ) { }
+
+ ~fusion_fixture( void )
+ {
+ BOOST_CHECK_CLOSE( fusion::at_c< 0 >( x ).value() , 1.0 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( fusion::at_c< 1 >( x ).value() , 1.0 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( fusion::at_c< 0 >( k1 ).value() , 1.0 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( fusion::at_c< 1 >( k1 ).value() , 1.0 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( fusion::at_c< 0 >( k2 ).value() , 2.0 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( fusion::at_c< 1 >( k2 ).value() , 2.0 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( fusion::at_c< 0 >( k3 ).value() , 3.0 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( fusion::at_c< 1 >( k3 ).value() , 3.0 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( fusion::at_c< 0 >( k4 ).value() , 4.0 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( fusion::at_c< 1 >( k4 ).value() , 4.0 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( fusion::at_c< 0 >( k5 ).value() , 5.0 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( fusion::at_c< 1 >( k5 ).value() , 5.0 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( fusion::at_c< 0 >( k6 ).value() , 6.0 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( fusion::at_c< 1 >( k6 ).value() , 6.0 , 1.0e-10 );
+ }
+
+ state_type res , x;
+ deriv_type k1 , k2 , k3 , k4 , k5 , k6 ;
+};
+
+
+
+BOOST_AUTO_TEST_SUITE( fusion_algebra_test )
+
+fusion_algebra algebra;
+
+BOOST_AUTO_TEST_CASE( for_each2 )
+{
+ fusion_fixture f;
+ algebra.for_each2( f.res , f.k1 ,
+ default_operations::scale_sum1< time_type >( dt ) );
+ BOOST_CHECK_CLOSE( fusion::at_c< 0 >( f.res ).value() , 0.1 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( fusion::at_c< 1 >( f.res ).value() , 0.1 , 1.0e-10 );
+}
+
+BOOST_AUTO_TEST_CASE( for_each3 )
+{
+ fusion_fixture f;
+ algebra.for_each3( f.res , f.x , f.k1 ,
+ default_operations::scale_sum2< value_type , time_type >( 1.0 , dt ) );
+ BOOST_CHECK_CLOSE( fusion::at_c< 0 >( f.res ).value() , 1.1 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( fusion::at_c< 1 >( f.res ).value() , 1.1 , 1.0e-10 );
+}
+
+BOOST_AUTO_TEST_CASE( for_each4 )
+{
+ fusion_fixture f;
+ algebra.for_each4( f.res , f.x , f.k1 , f.k2 ,
+ default_operations::scale_sum3< value_type , time_type , time_type >( 1.0 , dt , dt ) );
+ BOOST_CHECK_CLOSE( fusion::at_c< 0 >( f.res ).value() , 1.3 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( fusion::at_c< 1 >( f.res ).value() , 1.3 , 1.0e-10 );
+}
+
+BOOST_AUTO_TEST_CASE( for_each5 )
+{
+ fusion_fixture f;
+ algebra.for_each5( f.res , f.x , f.k1 , f.k2 , f.k3 ,
+ default_operations::scale_sum4< value_type , time_type , time_type , time_type >( 1.0 , dt , dt , dt ) );
+ BOOST_CHECK_CLOSE( fusion::at_c< 0 >( f.res ).value() , 1.6 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( fusion::at_c< 1 >( f.res ).value() , 1.6 , 1.0e-10 );
+}
+
+BOOST_AUTO_TEST_CASE( for_each6 )
+{
+ fusion_fixture f;
+ algebra.for_each6( f.res , f.x , f.k1 , f.k2 , f.k3 , f.k4 ,
+ default_operations::scale_sum5< value_type , time_type , time_type , time_type , time_type >( 1.0 , dt , dt , dt , dt ) );
+ BOOST_CHECK_CLOSE( fusion::at_c< 0 >( f.res ).value() , 2.0 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( fusion::at_c< 1 >( f.res ).value() , 2.0 , 1.0e-10 );
+}
+
+BOOST_AUTO_TEST_CASE( for_each7 )
+{
+ fusion_fixture f;
+ algebra.for_each7( f.res , f.x , f.k1 , f.k2 , f.k3 , f.k4 , f.k5 ,
+ default_operations::scale_sum6< value_type , time_type , time_type , time_type , time_type , time_type >( 1.0 , dt , dt , dt , dt , dt ) );
+ BOOST_CHECK_CLOSE( fusion::at_c< 0 >( f.res ).value() , 2.5 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( fusion::at_c< 1 >( f.res ).value() , 2.5 , 1.0e-10 );
+}
+
+BOOST_AUTO_TEST_CASE( for_each8 )
+{
+ fusion_fixture f;
+ algebra.for_each8( f.res , f.x , f.k1 , f.k2 , f.k3 , f.k4 , f.k5 , f.k6 ,
+ default_operations::scale_sum7< value_type , time_type , time_type , time_type , time_type , time_type , time_type >( 1.0 , dt , dt , dt , dt , dt , dt ) );
+ BOOST_CHECK_CLOSE( fusion::at_c< 0 >( f.res ).value() , 3.1 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( fusion::at_c< 1 >( f.res ).value() , 3.1 , 1.0e-10 );
+}
+
+BOOST_AUTO_TEST_CASE( for_each15 )
+{
+ fusion_fixture f;
+ algebra.for_each15( f.res , f.x , f.k1 , f.k2 , f.k3 , f.k4 , f.k5 , f.k6 , f.k1 , f.k2 , f.k3 , f.k4 , f.k5 , f.k6 , f.k1 ,
+ default_operations::scale_sum14< value_type , time_type , time_type , time_type , time_type , time_type , time_type ,
+ time_type , time_type , time_type , time_type , time_type , time_type , time_type >( 1.0 , dt , dt , dt , dt , dt , dt , dt , dt , dt , dt , dt , dt , dt ) );
+ //BOOST_CHECK_CLOSE( fusion::at_c< 0 >( f.res ).value() , 3.1 , 1.0e-10 );
+ //BOOST_CHECK_CLOSE( fusion::at_c< 1 >( f.res ).value() , 3.1 , 1.0e-10 );
+}
+
+
+BOOST_AUTO_TEST_CASE( norm_inf )
+{
+ double nrm = algebra.norm_inf( fusion::make_vector( 1.0 , 2.0 , 3.0 ) );
+ BOOST_CHECK_CLOSE( nrm , 3.0 , 1.0e-10 );
+}
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/generation.cpp b/test/generation.cpp
new file mode 100644
index 0000000..6432692
--- /dev/null
+++ b/test/generation.cpp
@@ -0,0 +1,87 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/generation.cpp
+
+ [begin_description]
+ This file tests the generation functions.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#define BOOST_TEST_MODULE odeint_generation
+
+#include <vector>
+
+#include <boost/test/unit_test.hpp>
+#include <boost/static_assert.hpp>
+#include <boost/type_traits/is_same.hpp>
+
+#include <boost/numeric/odeint/config.hpp>
+#include <boost/numeric/odeint/stepper/generation.hpp>
+
+using namespace boost::numeric::odeint;
+
+template< class Stepper1 , class Stepper2 >
+void check_stepper_type( const Stepper1 &s1 , const Stepper2 &s2 )
+{
+ BOOST_STATIC_ASSERT(( boost::is_same< Stepper1 , Stepper2 >::value ));
+}
+
+BOOST_AUTO_TEST_SUITE( generation_test )
+
+typedef std::vector< double > state_type;
+
+typedef runge_kutta_cash_karp54< state_type > rk54_type;
+typedef runge_kutta_cash_karp54_classic< state_type > rk54_classic_type;
+typedef runge_kutta_dopri5< state_type > dopri5_type;
+typedef runge_kutta_fehlberg78< state_type > fehlberg78_type;
+typedef rosenbrock4< double > rosenbrock4_type;
+
+
+BOOST_AUTO_TEST_CASE( test_generation_dopri5 )
+{
+ check_stepper_type( make_controlled( 1.0e-6 , 1.0e-10 , dopri5_type() ) , controlled_runge_kutta< dopri5_type >() );
+ check_stepper_type( make_controlled< dopri5_type >( 1.0e-6 , 1.0e-10 ) , controlled_runge_kutta< dopri5_type >() );
+
+ check_stepper_type( make_dense_output( 1.0e-6 , 1.0e-10 , dopri5_type() ) , dense_output_runge_kutta< controlled_runge_kutta< dopri5_type > >() );
+ check_stepper_type( make_dense_output< dopri5_type >( 1.0e-6 , 1.0e-10 ) , dense_output_runge_kutta< controlled_runge_kutta< dopri5_type > >() );
+}
+
+BOOST_AUTO_TEST_CASE( test_generation_cash_karp54 )
+{
+ check_stepper_type( make_controlled( 1.0e-6 , 1.0e-10 , rk54_type() ) , controlled_runge_kutta< rk54_type >() );
+ check_stepper_type( make_controlled< rk54_type >( 1.0e-6 , 1.0e-10 ) , controlled_runge_kutta< rk54_type >() );
+}
+
+BOOST_AUTO_TEST_CASE( test_generation_cash_karp54_classic )
+{
+ check_stepper_type( make_controlled( 1.0e-6 , 1.0e-10 , rk54_classic_type() ) , controlled_runge_kutta< rk54_classic_type >() );
+ check_stepper_type( make_controlled< rk54_classic_type >( 1.0e-6 , 1.0e-10 ) , controlled_runge_kutta< rk54_classic_type >() );
+}
+
+
+BOOST_AUTO_TEST_CASE( test_generation_fehlberg78 )
+{
+ check_stepper_type( make_controlled( 1.0e-6 , 1.0e-10 , fehlberg78_type() ) , controlled_runge_kutta< fehlberg78_type >() );
+ check_stepper_type( make_controlled< fehlberg78_type >( 1.0e-6 , 1.0e-10 ) , controlled_runge_kutta< fehlberg78_type >() );
+}
+
+
+BOOST_AUTO_TEST_CASE( test_generation_rosenbrock4 )
+{
+ check_stepper_type( make_controlled( 1.0e-6 , 1.0e-10 , rosenbrock4_type() ) , rosenbrock4_controller< rosenbrock4_type >() );
+ check_stepper_type( make_controlled< rosenbrock4_type >( 1.0e-6 , 1.0e-10 ) , rosenbrock4_controller< rosenbrock4_type >() );
+
+ check_stepper_type( make_dense_output( 1.0e-6 , 1.0e-10 , rosenbrock4_type() ) , rosenbrock4_dense_output< rosenbrock4_controller< rosenbrock4_type > >() );
+ check_stepper_type( make_dense_output< rosenbrock4_type >( 1.0e-6 , 1.0e-10 ) , rosenbrock4_dense_output< rosenbrock4_controller< rosenbrock4_type > >() );
+}
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/generic_error_stepper.cpp b/test/generic_error_stepper.cpp
new file mode 100644
index 0000000..0b18da8
--- /dev/null
+++ b/test/generic_error_stepper.cpp
@@ -0,0 +1,111 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/generic_error_stepper.cpp
+
+ [begin_description]
+ This file tests the generic error stepper.
+ [end_description]
+
+ Copyright 2011 Mario Mulansky
+ Copyright 2012 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+// disable checked iterator warning for msvc
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_generic_error_stepper
+
+#include <iostream>
+#include <utility>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/numeric/odeint/stepper/explicit_error_generic_rk.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54_classic.hpp>
+
+#include <boost/array.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+namespace fusion = boost::fusion;
+
+typedef double value_type;
+typedef boost::array< value_type , 2 > state_type;
+
+void sys( const state_type &x , state_type &dxdt , const value_type &t )
+{
+ dxdt[ 0 ] = x[ 0 ] + 2 * x[ 1 ];
+ dxdt[ 1 ] = x[ 1 ];
+}
+
+typedef explicit_error_generic_rk< 6 , 5 , 4 , 5 , state_type> error_rk_generic_type;
+
+const boost::array< double , 1 > a1 = {{ 0.2 }};
+const boost::array< double , 2 > a2 = {{ 3.0/40.0 , 9.0/40 }};
+const boost::array< double , 3 > a3 = {{ 0.3 , -0.9 , 1.2 }};
+const boost::array< double , 4 > a4 = {{ -11.0/54.0 , 2.5 , -70.0/27.0 , 35.0/27.0 }};
+const boost::array< double , 5 > a5 = {{ 1631.0/55296.0 , 175.0/512.0 , 575.0/13824.0 , 44275.0/110592.0 , 253.0/4096.0 }};
+
+const error_rk_generic_type::coef_a_type a = fusion::make_vector( a1 , a2 , a3 , a4 , a5 );
+const error_rk_generic_type::coef_b_type b = {{ 37.0/378.0 , 0.0 , 250.0/621.0 , 125.0/594.0 , 0.0 , 512.0/1771.0 }};
+const error_rk_generic_type::coef_b_type b2 = {{ b[0]-2825.0/27648.0 , b[1]-0.0 , b[2]-18575.0/48384.0 , b[3]-13525.0/55296.0 , b[4]-277.0/14336.0 , b[5]-0.25 }};
+const error_rk_generic_type::coef_c_type c = {{ 0.0 , 0.2 , 0.3 , 0.6 , 1.0 , 7.0/8 }};
+
+typedef runge_kutta_cash_karp54< state_type > error_rk54_ck_generic_type;
+typedef runge_kutta_cash_karp54_classic< state_type > rk54_ck_type;
+
+BOOST_AUTO_TEST_SUITE( generic_error_stepper_test )
+
+BOOST_AUTO_TEST_CASE( test_generic_error_stepper )
+{
+ //simultaneously test copying
+ error_rk_generic_type rk_generic_( a , b , b2 , c );
+ error_rk_generic_type rk_generic = rk_generic_;
+
+ error_rk54_ck_generic_type rk54_ck_generic_;
+ error_rk54_ck_generic_type rk54_ck_generic = rk54_ck_generic_;
+
+ //std::cout << stepper;
+
+ rk54_ck_type rk54_ck_;
+ rk54_ck_type rk54_ck = rk54_ck_;
+
+ typedef error_rk_generic_type::state_type state_type;
+ typedef error_rk_generic_type::value_type stepper_value_type;
+ typedef error_rk_generic_type::deriv_type deriv_type;
+ typedef error_rk_generic_type::time_type time_type;
+
+ state_type x = {{ 0.0 , 1.0 }};
+ state_type y = x;
+ state_type z = x;
+ state_type x_err , y_err , z_err;
+
+ rk_generic.do_step( sys , x , 0.0 , 0.1 , x_err );
+
+ rk54_ck_generic.do_step( sys , y , 0.0 , 0.1 , y_err);
+
+ rk54_ck.do_step( sys , z , 0.0 , 0.1 , z_err );
+
+ BOOST_CHECK_NE( 0.0 , x[0] );
+ BOOST_CHECK_NE( 1.0 , x[1] );
+ BOOST_CHECK_NE( 0.0 , x_err[0] );
+ BOOST_CHECK_NE( 0.0 , x_err[1] );
+ // compare with analytic solution of above system
+ BOOST_CHECK_EQUAL( x[0] , y[0] );
+ BOOST_CHECK_EQUAL( x[1] , y[1] );
+ BOOST_CHECK_EQUAL( x[0] , z[0] );
+ BOOST_CHECK_EQUAL( x[1] , z[1] );
+
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/generic_stepper.cpp b/test/generic_stepper.cpp
new file mode 100644
index 0000000..e2c1827
--- /dev/null
+++ b/test/generic_stepper.cpp
@@ -0,0 +1,104 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/generic_stepper.cpp
+
+ [begin_description]
+ This file tests the generic stepper.
+ [end_description]
+
+ Copyright 2011 Mario Mulansky
+ Copyright 2012 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+// disable checked iterator warning for msvc
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_generic_stepper
+
+#include <iostream>
+#include <utility>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/numeric/odeint/stepper/explicit_generic_rk.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta4.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta4_classic.hpp>
+
+#include <boost/array.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+namespace fusion = boost::fusion;
+
+typedef double value_type;
+typedef boost::array< value_type , 2 > state_type;
+
+void sys( const state_type &x , state_type &dxdt , const value_type &t )
+{
+ dxdt[ 0 ] = x[ 0 ] + 2 * x[ 1 ];
+ dxdt[ 1 ] = x[ 1 ];
+}
+
+typedef explicit_generic_rk< 4 , 4 , state_type> rk_generic_type;
+typedef runge_kutta4< state_type > rk4_generic_type;
+
+const boost::array< double , 1 > a1 = {{ 0.5 }};
+const boost::array< double , 2 > a2 = {{ 0.0 , 0.5 }};
+const boost::array< double , 3 > a3 = {{ 0.0 , 0.0 , 1.0 }};
+
+const rk_generic_type::coef_a_type a = fusion::make_vector( a1 , a2 , a3 );
+const rk_generic_type::coef_b_type b = {{ 1.0/6 , 1.0/3 , 1.0/3 , 1.0/6 }};
+const rk_generic_type::coef_c_type c = {{ 0.0 , 0.5 , 0.5 , 1.0 }};
+
+typedef runge_kutta4_classic< state_type > rk4_type;
+
+BOOST_AUTO_TEST_SUITE( generic_stepper_test )
+
+BOOST_AUTO_TEST_CASE( test_generic_stepper )
+{
+ //simultaneously test copying
+ rk_generic_type rk_generic_( a , b , c );
+ rk_generic_type rk_generic = rk_generic_;
+
+ rk4_generic_type rk4_generic_;
+ rk4_generic_type rk4_generic = rk4_generic_;
+
+ //std::cout << stepper;
+
+ rk4_type rk4_;
+ rk4_type rk4 = rk4_;
+
+ typedef rk_generic_type::state_type state_type;
+ typedef rk_generic_type::value_type stepper_value_type;
+ typedef rk_generic_type::deriv_type deriv_type;
+ typedef rk_generic_type::time_type time_type;
+
+ state_type x = {{ 0.0 , 1.0 }};
+ state_type y = x;
+ state_type z = x;
+
+ rk_generic.do_step( sys , x , 0.0 , 0.1 );
+
+ rk4_generic.do_step( sys , y , 0.0 , 0.1 );
+
+ rk4.do_step( sys , z , 0.0 , 0.1 );
+
+ BOOST_CHECK_NE( 0.0 , x[0] );
+ BOOST_CHECK_NE( 1.0 , x[1] );
+ // compare with analytic solution of above system
+ BOOST_CHECK_EQUAL( x[0] , y[0] );
+ BOOST_CHECK_EQUAL( x[1] , y[1] );
+ BOOST_CHECK_EQUAL( x[0] , z[0] );
+ BOOST_CHECK_EQUAL( x[1] , z[1] );
+
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/implicit_euler.cpp b/test/implicit_euler.cpp
new file mode 100644
index 0000000..575c896
--- /dev/null
+++ b/test/implicit_euler.cpp
@@ -0,0 +1,86 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/implicit_euler.cpp
+
+ [begin_description]
+ This file tests the implicit Euler stepper.
+ [end_description]
+
+ Copyright 2010-2011 Mario Mulansky
+ Copyright 2010-2012 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+// disable checked iterator warning for msvc
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_implicit_euler
+
+#include <boost/test/unit_test.hpp>
+
+#include <utility>
+#include <iostream>
+
+#include <boost/numeric/odeint/stepper/implicit_euler.hpp>
+//#include <boost/numeric/odeint/util/ublas_resize.hpp>
+
+#include <boost/numeric/ublas/vector.hpp>
+#include <boost/numeric/ublas/matrix.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+typedef double value_type;
+typedef boost::numeric::ublas::vector< value_type > state_type;
+typedef boost::numeric::ublas::matrix< value_type > matrix_type;
+
+/* use functors, because functions don't work with msvc 10, I guess this is a bug */
+struct sys
+{
+ void operator()( const state_type &x , state_type &dxdt , const value_type t ) const
+ {
+ dxdt( 0 ) = x( 0 ) + 2 * x( 1 );
+ dxdt( 1 ) = x( 1 );
+ }
+};
+
+struct jacobi
+{
+ void operator()( const state_type &x , matrix_type &jacobi , const value_type t ) const
+ {
+ jacobi( 0 , 0 ) = 1;
+ jacobi( 0 , 1 ) = 2;
+ jacobi( 1 , 0 ) = 0;
+ jacobi( 1 , 1 ) = 1;
+ }
+};
+
+BOOST_AUTO_TEST_SUITE( implicit_euler_test )
+
+BOOST_AUTO_TEST_CASE( test_euler )
+{
+ implicit_euler< value_type > stepper;
+ state_type x( 2 );
+ x(0) = 0.0; x(1) = 1.0;
+
+ value_type eps = 1E-12;
+
+ /* make_pair doesn't work with function pointers on msvc 10 */
+ stepper.do_step( std::make_pair( sys() , jacobi() ) , x , 0.0 , 0.1 );
+
+ using std::abs;
+
+ // compare with analytic solution of above system
+ BOOST_CHECK_MESSAGE( abs( x(0) - 20.0/81.0 ) < eps , x(0) - 20.0/81.0 );
+ BOOST_CHECK_MESSAGE( abs( x(1) - 10.0/9.0 ) < eps , x(0) - 10.0/9.0 );
+
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/integrate.cpp b/test/integrate.cpp
new file mode 100644
index 0000000..a90e8b3
--- /dev/null
+++ b/test/integrate.cpp
@@ -0,0 +1,285 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/integrate.cpp
+
+ [begin_description]
+ This file tests the integrate function and its variants.
+ [end_description]
+
+ Copyright 2011-2012 Mario Mulansky
+ Copyright 2011-2012 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#define BOOST_TEST_MODULE odeint_integrate_functions
+
+#include <vector>
+#include <cmath>
+#include <iostream>
+
+#include <boost/numeric/odeint/config.hpp>
+
+#include <boost/array.hpp>
+#include <boost/ref.hpp>
+#include <boost/iterator/counting_iterator.hpp>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/mpl/vector.hpp>
+
+// nearly everything from odeint is used in these tests
+#ifndef ODEINT_INTEGRATE_ITERATOR
+#include <boost/numeric/odeint/integrate/integrate_const.hpp>
+#include <boost/numeric/odeint/integrate/integrate_adaptive.hpp>
+#include <boost/numeric/odeint/integrate/integrate_times.hpp>
+#include <boost/numeric/odeint/integrate/integrate_n_steps.hpp>
+#else
+#include <boost/numeric/odeint/iterator/integrate/integrate_const.hpp>
+#include <boost/numeric/odeint/iterator/integrate/integrate_adaptive.hpp>
+#include <boost/numeric/odeint/iterator/integrate/integrate_times.hpp>
+#include <boost/numeric/odeint/iterator/integrate/integrate_n_steps.hpp>
+#endif
+#include <boost/numeric/odeint/stepper/euler.hpp>
+#include <boost/numeric/odeint/stepper/modified_midpoint.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta4.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_fehlberg78.hpp>
+#include <boost/numeric/odeint/stepper/controlled_runge_kutta.hpp>
+#include <boost/numeric/odeint/stepper/bulirsch_stoer.hpp>
+#include <boost/numeric/odeint/stepper/dense_output_runge_kutta.hpp>
+#include <boost/numeric/odeint/stepper/bulirsch_stoer_dense_out.hpp>
+
+#include <boost/numeric/odeint/util/detail/less_with_sign.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+namespace mpl = boost::mpl;
+
+
+typedef double value_type;
+typedef std::vector< value_type > state_type;
+
+void lorenz( const state_type &x , state_type &dxdt , const value_type t )
+{
+ //const value_type sigma( 10.0 );
+ const value_type R( 28.0 );
+ const value_type b( value_type( 8.0 ) / value_type( 3.0 ) );
+
+ // first component trivial
+ dxdt[0] = 1.0; //sigma * ( x[1] - x[0] );
+ dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
+ dxdt[2] = -b * x[2] + x[0] * x[1];
+}
+
+struct push_back_time
+{
+ std::vector< double >& m_times;
+
+ state_type& m_x;
+
+ push_back_time( std::vector< double > × , state_type &x )
+ : m_times( times ) , m_x( x ) { }
+
+ void operator()( const state_type &x , double t )
+ {
+ m_times.push_back( t );
+ boost::numeric::odeint::copy( x , m_x );
+ }
+};
+
+template< class Stepper >
+struct perform_integrate_const_test
+{
+ void operator()( const value_type t_end , const value_type dt )
+ {
+ // std::cout << "Testing integrate_const with " << typeid( Stepper ).name() << std::endl;
+
+ state_type x( 3 , 10.0 ) , x_end( 3 );
+
+ std::vector< value_type > times;
+
+ size_t steps = integrate_const( Stepper() , lorenz , x , 0.0 , t_end ,
+ dt , push_back_time( times , x_end ) );
+
+ std::cout.precision(16);
+ std::cout << t_end << " (" << dt << "), " << steps << " , " << times.size() << " , " << 10.0+dt*steps << "=" << x_end[0] << std::endl;
+
+ std::cout << static_cast<int>(floor(t_end/dt)) << " , " << t_end/dt << std::endl;
+
+ BOOST_CHECK_EQUAL( static_cast<int>(times.size()) , static_cast<int>(floor(t_end/dt))+1 );
+
+ for( size_t i=0 ; i<times.size() ; ++i )
+ {
+ //std::cout << i << " , " << times[i] << " , " << static_cast< value_type >(i)*dt << std::endl;
+ // check if observer was called at times 0,1,2,...
+ BOOST_CHECK_SMALL( times[i] - static_cast< value_type >(i)*dt , (i+1) * 2E-16 );
+ }
+
+ // check first, trivial, component
+ BOOST_CHECK_SMALL( (10.0 + times[times.size()-1]) - x_end[0] , 1E-6 ); // precision of steppers: 1E-6
+ //BOOST_CHECK_EQUAL( x[1] , x_end[1] );
+ //BOOST_CHECK_EQUAL( x[2] , x_end[2] );
+ }
+};
+
+template< class Stepper >
+struct perform_integrate_adaptive_test
+{
+ void operator()( const value_type t_end = 10.0 , const value_type dt = 0.03 )
+ {
+ // std::cout << "Testing integrate_adaptive with " << typeid( Stepper ).name() << std::endl;
+
+ state_type x( 3 , 10.0 ) , x_end( 3 );
+
+ std::vector< value_type > times;
+
+ size_t steps = integrate_adaptive( Stepper() , lorenz , x , 0.0 , t_end ,
+ dt , push_back_time( times , x_end ) );
+
+ // std::cout << t_end << " , " << steps << " , " << times.size() << " , " << dt << " , " << 10.0+t_end << "=" << x_end[0] << std::endl;
+
+ BOOST_CHECK_EQUAL( times.size() , steps+1 );
+
+ BOOST_CHECK_SMALL( times[0] - 0.0 , 2E-16 );
+ BOOST_CHECK_SMALL( times[times.size()-1] - t_end , times.size() * 2E-16 );
+
+ // check first, trivial, component
+ BOOST_CHECK_SMALL( (10.0 + t_end) - x_end[0] , 1E-6 ); // precision of steppers: 1E-6
+// BOOST_CHECK_EQUAL( x[1] , x_end[1] );
+// BOOST_CHECK_EQUAL( x[2] , x_end[2] );
+ }
+};
+
+
+template< class Stepper >
+struct perform_integrate_times_test
+{
+ void operator()( const int n = 10 , const int dn=1 , const value_type dt = 0.03 )
+ {
+ // std::cout << "Testing integrate_times with " << typeid( Stepper ).name() << std::endl;
+
+ state_type x( 3 ) , x_end( 3 );
+ x[0] = x[1] = x[2] = 10.0;
+
+ std::vector< double > times;
+
+ std::vector< double > obs_times( abs(n) );
+ for( int i=0 ; boost::numeric::odeint::detail::less_with_sign( static_cast<double>(i) ,
+ static_cast<double>(obs_times.size()) ,
+ dt ) ; i+=dn )
+ {
+ obs_times[i] = i;
+ }
+ // simple stepper
+ integrate_times( Stepper() , lorenz , x , obs_times.begin() , obs_times.end() ,
+ dt , push_back_time( times , x_end ) );
+
+ BOOST_CHECK_EQUAL( static_cast<int>(times.size()) , abs(n) );
+
+ for( size_t i=0 ; i<times.size() ; ++i )
+ // check if observer was called at times 0,1,2,...
+ BOOST_CHECK_EQUAL( times[i] , static_cast<double>(i) );
+
+ // check first, trivial, component
+ BOOST_CHECK_SMALL( (10.0 + 1.0*times[times.size()-1]) - x_end[0] , 1E-6 ); // precision of steppers: 1E-6
+// BOOST_CHECK_EQUAL( x[1] , x_end[1] );
+// BOOST_CHECK_EQUAL( x[2] , x_end[2] );
+ }
+};
+
+template< class Stepper >
+struct perform_integrate_n_steps_test
+{
+ void operator()( const int n = 200 , const value_type dt = 0.01 )
+ {
+ // std::cout << "Testing integrate_n_steps with " << typeid( Stepper ).name() << ". ";
+ // std::cout << "dt=" << dt << std::endl;
+
+ state_type x( 3 ) , x_end( 3 );
+ x[0] = x[1] = x[2] = 10.0;
+
+ std::vector< double > times;
+
+ // simple stepper
+ value_type end_time = integrate_n_steps( Stepper() , lorenz , x , 0.0 , dt , n , push_back_time( times , x_end ) );
+
+ BOOST_CHECK_SMALL( end_time - n*dt , 2E-16 );
+ BOOST_CHECK_EQUAL( static_cast<int>(times.size()) , n+1 );
+
+ for( size_t i=0 ; i<times.size() ; ++i )
+ {
+ // check if observer was called at times 0,1,2,...
+ BOOST_CHECK_SMALL(times[i] - static_cast< value_type >(i) * dt, 2E-16);
+ }
+ // check first, trivial, component
+ BOOST_CHECK_SMALL( (10.0 + end_time) - x_end[0] , 1E-6 ); // precision of steppers: 1E-6
+// BOOST_CHECK_EQUAL( x[1] , x_end[1] );
+// BOOST_CHECK_EQUAL( x[2] , x_end[2] );
+
+ }
+};
+
+
+
+class stepper_methods : public mpl::vector<
+ euler< state_type > ,
+ modified_midpoint< state_type > ,
+ runge_kutta4< state_type > ,
+ runge_kutta_cash_karp54< state_type > ,
+ runge_kutta_dopri5< state_type > ,
+ runge_kutta_fehlberg78< state_type > ,
+ controlled_runge_kutta< runge_kutta_cash_karp54< state_type > > ,
+ controlled_runge_kutta< runge_kutta_dopri5< state_type > > ,
+ controlled_runge_kutta< runge_kutta_fehlberg78< state_type > > ,
+ bulirsch_stoer< state_type > ,
+ dense_output_runge_kutta< controlled_runge_kutta< runge_kutta_dopri5< state_type > > >
+ //bulirsch_stoer_dense_out< state_type >
+> { };
+
+
+
+BOOST_AUTO_TEST_SUITE( integrate_test )
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( integrate_const_test_case , Stepper, stepper_methods )
+{
+ perform_integrate_const_test< Stepper > tester;
+ tester( 1.005 , 0.01 );
+ tester( 1.0 , 0.01 );
+ tester( 1.1 , 0.01 );
+ tester( -1.005 , -0.01 );
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( integrate_adaptive_test_case , Stepper, stepper_methods )
+{
+ perform_integrate_adaptive_test< Stepper > tester;
+ tester( 1.005 , 0.01 );
+ tester( 1.0 , 0.01 );
+ tester( 1.1 , 0.01 );
+ tester( -1.005 , -0.01 );
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( integrate_times_test_case , Stepper, stepper_methods )
+{
+ perform_integrate_times_test< Stepper > tester;
+ tester();
+ //tester( -10 , -0.01 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( integrate_n_steps_test_case , Stepper, stepper_methods )
+{
+ perform_integrate_n_steps_test< Stepper > tester;
+ tester();
+ tester( 200 , 0.01 );
+ tester( 200 , 0.01 );
+ tester( 200 , 0.01 );
+ tester( 200 , -0.01 );
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/integrate_implicit.cpp b/test/integrate_implicit.cpp
new file mode 100644
index 0000000..4bff200
--- /dev/null
+++ b/test/integrate_implicit.cpp
@@ -0,0 +1,233 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/integrate_implicit.cpp
+
+ [begin_description]
+ This file tests the integrate function and its variants with the implicit steppers.
+ [end_description]
+
+ Copyright 2011 Mario Mulansky
+ Copyright 2011-2013 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#define BOOST_TEST_MODULE odeint_integrate_functions_implicit
+
+#include <vector>
+#include <cmath>
+#include <iostream>
+
+#include <boost/numeric/odeint/config.hpp>
+
+#include <boost/array.hpp>
+#include <boost/ref.hpp>
+#include <boost/iterator/counting_iterator.hpp>
+#include <boost/numeric/ublas/vector.hpp>
+#include <boost/numeric/ublas/matrix.hpp>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/mpl/vector.hpp>
+
+#ifndef ODEINT_INTEGRATE_ITERATOR
+#include <boost/numeric/odeint/integrate/integrate_const.hpp>
+#include <boost/numeric/odeint/integrate/integrate_adaptive.hpp>
+#include <boost/numeric/odeint/integrate/integrate_times.hpp>
+#include <boost/numeric/odeint/integrate/integrate_n_steps.hpp>
+#else
+#include <boost/numeric/odeint/iterator/integrate/integrate_const.hpp>
+#include <boost/numeric/odeint/iterator/integrate/integrate_adaptive.hpp>
+#include <boost/numeric/odeint/iterator/integrate/integrate_times.hpp>
+#include <boost/numeric/odeint/iterator/integrate/integrate_n_steps.hpp>
+#endif
+#include <boost/numeric/odeint/stepper/rosenbrock4.hpp>
+#include <boost/numeric/odeint/stepper/rosenbrock4_controller.hpp>
+#include <boost/numeric/odeint/stepper/rosenbrock4_dense_output.hpp>
+
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+namespace mpl = boost::mpl;
+namespace ublas = boost::numeric::ublas;
+
+typedef double value_type;
+typedef ublas::vector< value_type > state_type;
+typedef boost::numeric::ublas::matrix< value_type > matrix_type;
+
+struct sys
+{
+ void operator()( const state_type &x , state_type &dxdt , const value_type &t ) const
+ {
+ dxdt( 0 ) = x( 0 ) + 2 * x( 1 );
+ dxdt( 1 ) = x( 1 );
+ }
+};
+
+struct jacobi
+{
+ void operator()( const state_type &x , matrix_type &jacobi , const value_type &t , state_type &dfdt ) const
+ {
+ jacobi( 0 , 0 ) = 1;
+ jacobi( 0 , 1 ) = 2;
+ jacobi( 1 , 0 ) = 0;
+ jacobi( 1 , 1 ) = 1;
+ dfdt( 0 ) = 0.0;
+ dfdt( 1 ) = 0.0;
+ }
+};
+
+struct push_back_time
+{
+ std::vector< double >& m_times;
+
+ push_back_time( std::vector< double > × )
+ : m_times( times ) { }
+
+ void operator()( const state_type &x , double t )
+ {
+ m_times.push_back( t );
+ }
+};
+
+template< class Stepper >
+struct perform_integrate_const_test
+{
+ void operator()( void )
+ {
+ state_type x( 2 , 1.0 );
+ const value_type dt = 0.03;
+ const value_type t_end = 10.0;
+
+ std::vector< value_type > times;
+
+ integrate_const( Stepper() , std::make_pair( sys() , jacobi() ) , x , 0.0 , t_end ,
+ dt , push_back_time( times ) );
+
+ BOOST_CHECK_EQUAL( static_cast<int>(times.size()) , static_cast<int>(std::floor(t_end/dt))+1 );
+
+ for( size_t i=0 ; i<times.size() ; ++i )
+ {
+ //std::cout << i << std::endl;
+ // check if observer was called at times 0,1,2,...
+ BOOST_CHECK_SMALL( times[i] - static_cast< value_type >(i)*dt , (i+1) * 2.0e-16 );
+ }
+ }
+};
+
+template< class Stepper >
+struct perform_integrate_adaptive_test
+{
+ void operator()( void )
+ {
+ state_type x( 2 , 1.0 );
+ const value_type dt = 0.03;
+ const value_type t_end = 10.0;
+
+ std::vector< value_type > times;
+
+ size_t steps = integrate_adaptive( Stepper() , std::make_pair( sys() , jacobi() ) , x , 0.0 , t_end ,
+ dt , push_back_time( times ) );
+
+ BOOST_CHECK_EQUAL( times.size() , steps+1 );
+
+ BOOST_CHECK_SMALL( times[0] - 0.0 , 2.0e-16 );
+ BOOST_CHECK_SMALL( times[times.size()-1] - t_end , times.size() * 3.0e-16 );
+ }
+};
+
+
+template< class Stepper >
+struct perform_integrate_times_test
+{
+ void operator()( void )
+ {
+ state_type x( 2 , 1.0 );
+
+ const value_type dt = 0.03;
+
+ std::vector< double > times;
+
+ // simple stepper
+ integrate_times( Stepper() , std::make_pair( sys() , jacobi() ) , x ,
+ boost::counting_iterator<int>(0) , boost::counting_iterator<int>(10) ,
+ dt , push_back_time( times ) );
+
+ BOOST_CHECK_EQUAL( static_cast<int>(times.size()) , 10 );
+
+ for( size_t i=0 ; i<times.size() ; ++i )
+ // check if observer was called at times 0,1,2,...
+ BOOST_CHECK_EQUAL( times[i] , static_cast<double>(i) );
+ }
+};
+
+template< class Stepper >
+struct perform_integrate_n_steps_test
+{
+ void operator()( void )
+ {
+ state_type x( 2 , 1.0 );
+
+ const value_type dt = 0.03;
+ const int n = 200;
+
+ std::vector< double > times;
+
+ // simple stepper
+ value_type end_time = integrate_n_steps( Stepper() , std::make_pair( sys() , jacobi() ) , x , 0.0 , dt , n , push_back_time( times ) );
+
+ BOOST_CHECK_SMALL( end_time - n*dt , 3.0e-16 );
+ BOOST_CHECK_EQUAL( static_cast<int>(times.size()) , n+1 );
+
+ for( size_t i=0 ; i<times.size() ; ++i )
+ // check if observer was called at times 0,1,2,...
+ BOOST_CHECK_SMALL( times[i] - static_cast< value_type >(i)*dt , (i+1) * 2.0e-16 );
+ }
+};
+
+
+
+class stepper_methods : public mpl::vector<
+ rosenbrock4< value_type > ,
+ rosenbrock4_controller< rosenbrock4< value_type > > ,
+ rosenbrock4_dense_output< rosenbrock4_controller< rosenbrock4< value_type > > >
+> { };
+
+
+
+BOOST_AUTO_TEST_SUITE( integrate_test )
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( integrate_const_test_case , Stepper, stepper_methods )
+{
+ perform_integrate_const_test< Stepper > tester;
+ tester();
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( integrate_adaptive_test_case , Stepper, stepper_methods )
+{
+ perform_integrate_adaptive_test< Stepper > tester;
+ tester();
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( integrate_times_test_case , Stepper, stepper_methods )
+{
+ perform_integrate_times_test< Stepper > tester;
+ tester();
+}
+
+
+class simple_stepper_methods : public mpl::vector<
+ rosenbrock4< value_type >
+> { };
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( integrate_n_steps_test_case , Stepper, simple_stepper_methods )
+{
+ perform_integrate_n_steps_test< Stepper > tester;
+ tester();
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/integrate_overflow.cpp b/test/integrate_overflow.cpp
new file mode 100644
index 0000000..0dba404
--- /dev/null
+++ b/test/integrate_overflow.cpp
@@ -0,0 +1,200 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/integrate_overflow.cpp
+
+ [begin_description]
+ This file tests the overflow exception of the integrate functions.
+ [end_description]
+
+ Copyright 2015 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#define BOOST_TEST_MODULE odeint_integrate_overflow
+
+#include <boost/test/unit_test.hpp>
+
+#include <utility>
+#include <iostream>
+#include <vector>
+
+
+#include <vector>
+#include <cmath>
+#include <iostream>
+
+#include <boost/iterator/counting_iterator.hpp>
+
+#include <boost/numeric/odeint.hpp>
+
+
+using namespace boost::numeric::odeint;
+
+
+typedef double value_type;
+typedef std::vector< value_type > state_type;
+
+// the famous lorenz system as usual
+void lorenz( const state_type &x , state_type &dxdt , const value_type t )
+{
+ //const value_type sigma( 10.0 );
+ const value_type R( 28.0 );
+ const value_type b( value_type( 8.0 ) / value_type( 3.0 ) );
+
+ // first component trivial
+ dxdt[0] = 1.0; //sigma * ( x[1] - x[0] );
+ dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
+ dxdt[2] = -b * x[2] + x[0] * x[1];
+}
+
+struct push_back_time
+{
+ std::vector< double >& m_times;
+
+ push_back_time( std::vector< double > × )
+ : m_times( times ) { }
+
+ void operator()( const state_type &x , double t )
+ {
+ m_times.push_back( t );
+ }
+};
+
+typedef runge_kutta_dopri5<state_type> stepper_type;
+typedef runge_kutta_cash_karp54<state_type> cash_karp_type;
+
+
+BOOST_AUTO_TEST_SUITE( integrate_overflow )
+
+BOOST_AUTO_TEST_CASE( test_integrate_const )
+{
+ state_type x(3, 5.0);
+ std::vector<double> times;
+
+ // check the function signatures with normal stepper
+ integrate_const(stepper_type(), lorenz, x, 0.0, 10.0, 1.0);
+ integrate_const(stepper_type(), lorenz, x, 0.0, 10.0, 1.0, null_observer());
+ // no exceptions expected for normal steppers
+ integrate_const(stepper_type(), lorenz, x, 0.0, 10.0, 1.0, null_observer(), max_step_checker(10));
+
+
+ // check exceptions for controlled stepper
+ integrate_const(make_controlled<stepper_type>(1E-5, 1E-5), lorenz, x, 0.0, 10.0, 1.0);
+ // very small error terms -> standard overflow threshold of 500 should fire an exception
+ BOOST_CHECK_THROW(integrate_const(make_controlled<stepper_type>(1E-15, 1E-15), lorenz, x,
+ 0.0, 10.0, 1.0, push_back_time(times), max_step_checker()),
+ std::runtime_error);
+ // small threshold of 10 -> larger error still gives an exception
+ BOOST_CHECK_THROW(integrate_const(make_controlled<stepper_type>(1E-5, 1E-5), lorenz, x,
+ 0.0, 10.0, 1.0, push_back_time(times), max_step_checker(10)),
+ std::runtime_error);
+
+ // check exceptions for dense output stepper
+ integrate_const(make_dense_output<stepper_type>(1E-5, 1E-5), lorenz, x, 0.0, 10.0, 1.0);
+ integrate_const(make_dense_output<stepper_type>(1E-5, 1E-5), lorenz, x, 0.0, 10.0, 1.0);
+ // very small error terms -> standard overflow threshold of 500 should fire an exception
+ BOOST_CHECK_THROW(integrate_const(make_dense_output<stepper_type>(1E-15, 1E-15), lorenz, x,
+ 0.0, 10.0, 1.0, push_back_time(times), max_step_checker()),
+ std::runtime_error);
+ // small threshold of 10 -> larger error still gives an exception
+ BOOST_CHECK_THROW(integrate_const(make_dense_output<stepper_type>(1E-5, 1E-5), lorenz, x,
+ 0.0, 10.0, 1.0, push_back_time(times), max_step_checker(10)),
+ std::runtime_error);
+}
+
+BOOST_AUTO_TEST_CASE( test_integrate_n_steps )
+{
+ state_type x(3, 5.0);
+ std::vector<double> times;
+
+ // check the function signatures with normal stepper
+ integrate_n_steps(stepper_type(), lorenz, x, 0.0, 1.0, 10);
+ integrate_n_steps(stepper_type(), lorenz, x, 0.0, 1.0, 10, null_observer());
+ // no exceptions expected for normal steppers
+ integrate_n_steps(stepper_type(), lorenz, x, 0.0, 1.0, 10, null_observer(), max_step_checker(10));
+
+
+ // check exceptions for controlled stepper
+ integrate_n_steps(make_controlled<stepper_type>(1E-5, 1E-5), lorenz, x, 0.0, 1.0, 10);
+ // very small error terms -> standard overflow threshold of 500 should fire an exception
+ BOOST_CHECK_THROW(integrate_n_steps(make_controlled<stepper_type>(1E-15, 1E-15), lorenz, x,
+ 0.0, 1.0, 10, push_back_time(times), max_step_checker()),
+ std::runtime_error);
+ // small threshold of 10 -> larger error still gives an exception
+ BOOST_CHECK_THROW(integrate_n_steps(make_controlled<stepper_type>(1E-5, 1E-5), lorenz, x,
+ 0.0, 1.0, 10, push_back_time(times), max_step_checker(10)),
+ std::runtime_error);
+
+ // check exceptions for dense output stepper
+ integrate_n_steps(make_dense_output<stepper_type>(1E-5, 1E-5), lorenz, x, 0.0, 1.0, 10);
+ integrate_n_steps(make_dense_output<stepper_type>(1E-5, 1E-5), lorenz, x, 0.0, 1.0, 10, push_back_time(times));
+ // very small error terms -> standard overflow threshold of 500 should fire an exception
+ BOOST_CHECK_THROW(integrate_n_steps(make_dense_output<stepper_type>(1E-15, 1E-15), lorenz, x,
+ 0.0, 1.0, 10, push_back_time(times), max_step_checker()),
+ std::runtime_error);
+ // small threshold of 10 -> larger error still gives an exception
+ BOOST_CHECK_THROW(integrate_n_steps(make_dense_output<stepper_type>(1E-5, 1E-5), lorenz, x,
+ 0.0, 1.0, 10, push_back_time(times), max_step_checker(10)),
+ std::runtime_error);
+}
+
+BOOST_AUTO_TEST_CASE( test_integrate_times )
+{
+ state_type x(3, 5.0);
+ std::vector<double> times;
+ boost::counting_iterator<int> t0(0);
+ boost::counting_iterator<int> t1(10);
+
+ // check the function signatures with normal stepper
+ integrate_times(stepper_type(), lorenz, x, t0, t1, 1.0 , push_back_time(times));
+ // no exceptions expected for big enough step size
+ integrate_times(stepper_type(), lorenz, x, t0, t1, 1.0 , push_back_time(times), max_step_checker(10));
+ // if dt*max_steps < observer time difference we expect an exception
+ BOOST_CHECK_THROW(integrate_times(stepper_type(), lorenz, x, t0, t1, 0.01, push_back_time(times),
+ max_step_checker(10)),
+ std::runtime_error);
+
+ // check exceptions for controlled stepper
+ // no exception if no checker is provided
+ integrate_times(make_controlled<stepper_type>(1E-5, 1E-5), lorenz, x, t0, t1, 1.0 , push_back_time(times));
+ // very small error terms -> standard overflow threshold of 500 should fire an exception
+ BOOST_CHECK_THROW(integrate_times(make_controlled<stepper_type>(1E-15, 1E-15), lorenz, x,
+ t0, t1, 1.0 , push_back_time(times), max_step_checker()),
+ std::runtime_error);
+
+ // small threshold of 10 -> larger error still gives an exception
+ BOOST_CHECK_THROW(integrate_times(make_controlled<stepper_type>(1E-5, 1E-5), lorenz, x,
+ t0, t1, 1.0 , push_back_time(times), max_step_checker(10)),
+ std::runtime_error);
+
+ // check cash karp controlled stepper
+ // no exception if no checker is provided
+ integrate_times(make_controlled<cash_karp_type>(1E-5, 1E-5), lorenz, x, t0, t1, 1.0 , push_back_time(times));
+ // very small error terms -> standard overflow threshold of 500 should fire an exception
+ BOOST_CHECK_THROW(integrate_times(make_controlled<cash_karp_type>(1E-15, 1E-15), lorenz, x,
+ t0, t1, 1.0 , push_back_time(times), max_step_checker()),
+ std::runtime_error);
+
+ // small threshold of 10 -> larger error still gives an exception
+ BOOST_CHECK_THROW(integrate_times(make_controlled<cash_karp_type>(1E-5, 1E-5), lorenz, x,
+ t0, t1, 1.0 , push_back_time(times), max_step_checker(10)),
+ std::runtime_error);
+
+ // check exceptions for dense output stepper
+ integrate_times(make_dense_output<stepper_type>(1E-5, 1E-5), lorenz, x, t0, t1, 1.0 ,
+ push_back_time(times));
+ // very small error terms -> standard overflow threshold of 500 should fire an exception
+ BOOST_CHECK_THROW(integrate_times(make_dense_output<stepper_type>(1E-15, 1E-15), lorenz, x,
+ t0, t1, 1.0 , push_back_time(times), max_step_checker()),
+ std::runtime_error);
+ // small threshold of 10 -> larger error still gives an exception
+ BOOST_CHECK_THROW(integrate_times(make_dense_output<stepper_type>(1E-5, 1E-5), lorenz, x,
+ t0, t1, 1.0 , push_back_time(times), max_step_checker(10)),
+ std::runtime_error);
+}
+
+BOOST_AUTO_TEST_SUITE_END()
\ No newline at end of file
diff --git a/test/integrate_stepper_refs.cpp b/test/integrate_stepper_refs.cpp
new file mode 100644
index 0000000..5d6d34c
--- /dev/null
+++ b/test/integrate_stepper_refs.cpp
@@ -0,0 +1,271 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/integrate_stepper_refs.cpp
+
+ [begin_description]
+ Tests the integrate functions with boost::ref( stepper)
+ [end_description]
+
+ Copyright 2009-2013 Karsten Ahnert
+ Copyright 2009-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#define BOOST_TEST_MODULE odeint_integrate_stepper_refs
+
+#include <vector>
+#include <cmath>
+#include <iostream>
+
+#include <boost/numeric/odeint/config.hpp>
+
+#include <boost/noncopyable.hpp>
+#include <boost/test/unit_test.hpp>
+#include <boost/iterator/counting_iterator.hpp>
+
+#include <boost/mpl/vector.hpp>
+
+#include <boost/numeric/odeint/integrate/integrate_const.hpp>
+#include <boost/numeric/odeint/integrate/integrate_adaptive.hpp>
+#include <boost/numeric/odeint/integrate/integrate_times.hpp>
+#include <boost/numeric/odeint/integrate/integrate_n_steps.hpp>
+#include <boost/numeric/odeint/stepper/controlled_step_result.hpp>
+
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+namespace mpl = boost::mpl;
+
+typedef double value_type;
+typedef std::vector< value_type > state_type;
+
+// minimal non-copyable basic stepper
+template<
+class State
+>
+class simple_stepper_nc : boost::noncopyable
+{
+public :
+ typedef State state_type;
+ typedef double value_type;
+ typedef state_type deriv_type;
+ typedef double time_type;
+ typedef size_t order_type;
+ typedef stepper_tag stepper_category;
+
+ template< class System >
+ void do_step( System system , state_type &in , time_type t , time_type dt )
+ {
+ // empty
+
+ }
+};
+
+// minimal non-copyable controlled stepper
+template<
+class State
+>
+class controlled_stepper_nc : boost::noncopyable
+{
+public :
+ typedef State state_type;
+ typedef double value_type;
+ typedef state_type deriv_type;
+ typedef double time_type;
+ typedef size_t order_type;
+ typedef controlled_stepper_tag stepper_category;
+
+ template< class System >
+ controlled_step_result try_step( System system , state_type &in , time_type &t , time_type &dt )
+ {
+ std::cout << "dense out stepper: " << t << " , " << dt << std::endl;
+ t += dt;
+ return success;
+ }
+};
+
+// minimal non-copyable dense_output stepper
+template<
+class State
+>
+class dense_out_stepper_nc : boost::noncopyable
+{
+public :
+ typedef State state_type;
+ typedef double value_type;
+ typedef state_type deriv_type;
+ typedef double time_type;
+ typedef size_t order_type;
+ typedef dense_output_stepper_tag stepper_category;
+
+ void initialize( const state_type &x0 , const time_type t0 , const time_type dt0 )
+ {
+ m_x = x0;
+ m_t = t0;
+ m_dt = dt0;
+ std::cout << "initialize: " << m_t << " , " << m_dt << std::endl;
+ }
+
+ template< class System >
+ void do_step( System system )
+ {
+ std::cout << "dense out stepper: " << m_t << " , " << m_dt << std::endl;
+ m_t += m_dt;
+ }
+
+ void calc_state( const time_type t_inter , state_type &x )
+ {
+ x = m_x;
+ }
+
+ const state_type& current_state() const
+ { return m_x; }
+
+ time_type current_time() const
+ { return m_t; }
+
+ time_type current_time_step() const
+ { return m_dt; }
+
+
+private :
+ time_type m_t;
+ time_type m_dt;
+ state_type m_x;
+};
+
+
+void lorenz( const state_type &x , state_type &dxdt , const value_type t )
+{
+ //const value_type sigma( 10.0 );
+ const value_type R( 28.0 );
+ const value_type b( value_type( 8.0 ) / value_type( 3.0 ) );
+
+ // first component trivial
+ dxdt[0] = 1.0; //sigma * ( x[1] - x[0] );
+ dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
+ dxdt[2] = -b * x[2] + x[0] * x[1];
+}
+
+struct push_back_time
+{
+ std::vector< double >& m_times;
+
+ state_type& m_x;
+
+ push_back_time( std::vector< double > × , state_type &x )
+ : m_times( times ) , m_x( x ) { }
+
+ void operator()( const state_type &x , double t )
+ {
+ m_times.push_back( t );
+ boost::numeric::odeint::copy( x , m_x );
+ }
+};
+
+template< class Stepper >
+struct perform_integrate_const_test
+{
+ void operator()()
+ {
+ state_type x( 3 , 10.0 ) , x_end( 3 );
+
+ std::vector< value_type > times;
+
+ Stepper stepper;
+
+ integrate_const( boost::ref(stepper) , lorenz , x , 0.0 , 1.0 ,
+ 0.1, push_back_time( times , x_end ) );
+ }
+};
+
+template< class Stepper >
+struct perform_integrate_adaptive_test
+{
+ void operator()()
+ {
+ state_type x( 3 , 10.0 ) , x_end( 3 );
+
+ std::vector< value_type > times;
+
+ Stepper stepper;
+
+ integrate_adaptive( boost::ref(stepper) , lorenz , x , 0.0 , 1.0 ,
+ 0.1, push_back_time( times , x_end ) );
+ }
+};
+
+template< class Stepper >
+struct perform_integrate_n_steps_test
+{
+ void operator()()
+ {
+ state_type x( 3 , 10.0 ) , x_end( 3 );
+
+ std::vector< value_type > times;
+
+ Stepper stepper;
+
+ integrate_n_steps( boost::ref(stepper) , lorenz , x , 0.0 , 0.1 ,
+ 10 , push_back_time( times , x_end ) );
+ }
+};
+
+template< class Stepper >
+struct perform_integrate_times_test
+{
+ void operator()()
+ {
+ state_type x( 3 , 10.0 ) , x_end( 3 );
+
+ std::vector< value_type > times;
+
+ Stepper stepper;
+
+ integrate_times( boost::ref(stepper) , lorenz , x ,
+ boost::counting_iterator<int>(0) , boost::counting_iterator<int>(10) , 0.1 ,
+ push_back_time( times , x_end ) );
+ }
+};
+
+class stepper_methods : public mpl::vector<
+ simple_stepper_nc< state_type > ,
+ controlled_stepper_nc< state_type >,
+ dense_out_stepper_nc< state_type > > { };
+
+BOOST_AUTO_TEST_SUITE( integrate_stepper_refs )
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( integrate_const_test_case , Stepper, stepper_methods )
+{
+ std::cout << "integrate const" << std::endl;
+ perform_integrate_const_test< Stepper > tester;
+ tester();
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( integrate_adaptive_test_case , Stepper, stepper_methods )
+{
+ std::cout << "integrate adaptive" << std::endl;
+ perform_integrate_adaptive_test< Stepper > tester;
+ tester();
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( integrate_n_steps_test_case , Stepper, stepper_methods )
+{
+ std::cout << "integrate n steps" << std::endl;
+ perform_integrate_n_steps_test< Stepper > tester;
+ tester();
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( integrate_times_test_case , Stepper, stepper_methods )
+{
+ std::cout << "integrate times" << std::endl;
+ perform_integrate_times_test< Stepper > tester;
+ tester();
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/integrate_times.cpp b/test/integrate_times.cpp
new file mode 100644
index 0000000..2837f09
--- /dev/null
+++ b/test/integrate_times.cpp
@@ -0,0 +1,247 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/integrate_times.cpp
+
+ [begin_description]
+ This file tests the integrate_times function and its variants.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#define BOOST_TEST_MODULE odeint_integrate_times
+
+#include <boost/test/unit_test.hpp>
+
+#include <utility>
+#include <iostream>
+#include <vector>
+
+#include <boost/ref.hpp>
+#include <boost/iterator/counting_iterator.hpp>
+
+#ifndef ODEINT_INTEGRATE_ITERATOR
+#include <boost/numeric/odeint/integrate/integrate_times.hpp>
+#include <boost/numeric/odeint/integrate/integrate_adaptive.hpp>
+#else
+#include <boost/numeric/odeint/iterator/integrate/integrate_times.hpp>
+#include <boost/numeric/odeint/iterator/integrate/integrate_adaptive.hpp>
+#endif
+#include <boost/numeric/odeint/stepper/runge_kutta4.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp>
+#include <boost/numeric/odeint/stepper/controlled_runge_kutta.hpp>
+#include <boost/numeric/odeint/stepper/bulirsch_stoer.hpp>
+#include <boost/numeric/odeint/stepper/bulirsch_stoer_dense_out.hpp>
+#include <boost/numeric/odeint/stepper/dense_output_runge_kutta.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+typedef double value_type;
+typedef std::vector< value_type > state_type;
+
+
+void lorenz( const state_type &x , state_type &dxdt , const value_type t )
+{
+ BOOST_CHECK( t >= 0.0 );
+
+ const value_type sigma( 10.0 );
+ const value_type R( 28.0 );
+ const value_type b( value_type( 8.0 ) / value_type( 3.0 ) );
+
+ dxdt[0] = sigma * ( x[1] - x[0] );
+ dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
+ dxdt[2] = -b * x[2] + x[0] * x[1];
+}
+
+struct push_back_time
+{
+ std::vector< double >& m_times;
+
+ push_back_time( std::vector< double > × )
+ : m_times( times ) { }
+
+ void operator()( const state_type &x , double t )
+ {
+ m_times.push_back( t );
+ }
+};
+
+BOOST_AUTO_TEST_SUITE( integrate_times_test )
+
+BOOST_AUTO_TEST_CASE( test_integrate_times )
+{
+
+ state_type x( 3 );
+ x[0] = x[1] = x[2] = 10.0;
+
+ const value_type dt = 0.03;
+
+ std::vector< double > times;
+
+ std::cout << "test rk4 stepper" << std::endl;
+
+ // simple stepper
+ integrate_times( runge_kutta4< state_type >() , lorenz , x , boost::counting_iterator<int>(0) , boost::counting_iterator<int>(10) ,
+ dt , push_back_time( times ) );
+
+ for( int i=0 ; i<10 ; ++i )
+ // check if observer was called at times 0,1,2,...
+ BOOST_CHECK_EQUAL( times[i] , static_cast<double>(i) );
+ times.clear();
+
+ std::cout << "test dopri5 stepper" << std::endl;
+
+ // controlled stepper
+ integrate_times( controlled_runge_kutta< runge_kutta_dopri5< state_type > >() , lorenz , x ,
+ boost::counting_iterator<int>(0) , boost::counting_iterator<int>(10) ,
+ dt , push_back_time( times ) );
+
+ for( int i=0 ; i<10 ; ++i )
+ // check if observer was called at times 0,1,2,...
+ BOOST_CHECK_EQUAL( times[i] , static_cast<double>(i) );
+ times.clear();
+
+ std::cout << "test BS stepper" << std::endl;
+
+ //another controlled stepper
+ integrate_times( bulirsch_stoer< state_type >() , lorenz , x ,
+ boost::counting_iterator<int>(0) , boost::counting_iterator<int>(10) ,
+ dt , push_back_time( times ) );
+
+ for( int i=0 ; i<10 ; ++i )
+ // check if observer was called at times 0,1,2,...
+ BOOST_CHECK_EQUAL( times[i] , static_cast<double>(i) );
+ times.clear();
+
+ std::cout << "test dense_out stepper" << std::endl;
+
+ // dense output stepper
+ integrate_times( dense_output_runge_kutta< controlled_runge_kutta< runge_kutta_dopri5< state_type > > >() ,
+ lorenz , x ,
+ boost::counting_iterator<int>(0) , boost::counting_iterator<int>(10) ,
+ dt , push_back_time( times ) );
+
+ for( int i=0 ; i<10 ; ++i )
+ // check if observer was called at times 0,1,2,...
+ BOOST_CHECK_EQUAL( times[i] , static_cast<double>(i) );
+
+ std::cout << "test BS_do stepper" << std::endl;
+
+ integrate_times( bulirsch_stoer_dense_out< state_type >() , lorenz , x ,
+ boost::counting_iterator<int>(0) , boost::counting_iterator<int>(10) ,
+ dt , push_back_time( times ) );
+
+ for( int i=0 ; i<10 ; ++i )
+ // check if observer was called at times 0,1,2,...
+ BOOST_CHECK_EQUAL( times[i] , static_cast<double>(i) );
+
+}
+
+
+BOOST_AUTO_TEST_CASE( test_integrate_times_ranges )
+{
+
+ state_type x( 3 );
+ x[0] = x[1] = x[2] = 10.0;
+
+ const value_type dt = 0.03;
+
+ std::vector< double > times;
+
+ // simple stepper
+ integrate_times( runge_kutta4< state_type >() , lorenz , x ,
+ std::make_pair( boost::counting_iterator<int>(0) , boost::counting_iterator<int>(10) ) ,
+ dt , push_back_time( times ) );
+
+ for( int i=0 ; i<10 ; ++i )
+ // check if observer was called at times 0,1,2,...
+ BOOST_CHECK_EQUAL( times[i] , static_cast<double>(i) );
+ times.clear();
+
+ // controlled stepper
+ integrate_times( controlled_runge_kutta< runge_kutta_dopri5< state_type > >() , lorenz , x ,
+ std::make_pair( boost::counting_iterator<int>(0) , boost::counting_iterator<int>(10) ) ,
+ dt , push_back_time( times ) );
+
+ for( int i=0 ; i<10 ; ++i )
+ // check if observer was called at times 0,1,2,...
+ BOOST_CHECK_EQUAL( times[i] , static_cast<double>(i) );
+ times.clear();
+
+ //another controlled stepper
+ integrate_times( bulirsch_stoer< state_type >() , lorenz , x ,
+ std::make_pair( boost::counting_iterator<int>(0) , boost::counting_iterator<int>(10) ) ,
+ dt , push_back_time( times ) );
+
+ for( int i=0 ; i<10 ; ++i )
+ // check if observer was called at times 0,1,2,...
+ BOOST_CHECK_EQUAL( times[i] , static_cast<double>(i) );
+ times.clear();
+
+
+ // dense output stepper
+ integrate_times( bulirsch_stoer_dense_out< state_type >() , lorenz , x ,
+ std::make_pair( boost::counting_iterator<int>(0) , boost::counting_iterator<int>(10) ) ,
+ dt , push_back_time( times ) );
+
+ for( int i=0 ; i<10 ; ++i )
+ // check if observer was called at times 0,1,2,...
+ BOOST_CHECK_EQUAL( times[i] , static_cast<double>(i) );
+
+}
+
+BOOST_AUTO_TEST_CASE( test_integrate_times_overshoot )
+{
+ state_type x( 3 );
+ x[0] = x[1] = x[2] = 10.0;
+ double dt = -0.1;
+
+ std::vector<double> times( 10 );
+ for( int i=0 ; i<10 ; ++i )
+ times[i] = 1.0-i*1.0/9.0;
+
+ std::cout << "test rk4 stepper" << std::endl;
+ // simple stepper
+ std::vector<double> obs_times;
+ int steps = integrate_times( runge_kutta4< state_type >() , lorenz , x ,
+ times.begin() , times.end() ,
+ dt , push_back_time( obs_times ) );
+// different behavior for the iterator based integrate implementaton
+#ifndef ODEINT_INTEGRATE_ITERATOR
+ BOOST_CHECK_EQUAL( steps , 18 ); // we really need 18 steps because dt and
+ // the difference of the observation times
+ // are so out of sync
+#else
+ // iterator based implementation can only return the number of iteration steps
+ BOOST_CHECK_EQUAL( steps , 9 );
+#endif
+ for( int i=0 ; i<10 ; ++i )
+ BOOST_CHECK_EQUAL( times[i] , obs_times[i] );
+
+ std::cout << "test rk_ck stepper" << std::endl;
+ // controlled stepper
+ obs_times.clear();
+ integrate_times( controlled_runge_kutta< runge_kutta_cash_karp54< state_type > >() , lorenz , x ,
+ times.begin() , times.end() ,
+ dt , push_back_time( obs_times ) );
+ for( int i=0 ; i<10 ; ++i )
+ BOOST_CHECK_EQUAL( times[i] , obs_times[i] );
+
+ std::cout << "test dopri5 stepper" << std::endl;
+ // controlled stepper
+ obs_times.clear();
+ integrate_times( dense_output_runge_kutta< controlled_runge_kutta< runge_kutta_dopri5< state_type > > >() , lorenz , x ,
+ times.begin() , times.end() ,
+ dt , push_back_time( obs_times ) );
+ for( int i=0 ; i<10 ; ++i )
+ BOOST_CHECK_EQUAL( times[i] , obs_times[i] );
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/integrators_symplectic.cpp b/test/integrators_symplectic.cpp
new file mode 100644
index 0000000..2c28619
--- /dev/null
+++ b/test/integrators_symplectic.cpp
@@ -0,0 +1,74 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/integrators_symplectic.cpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2009-2013 Karsten Ahnert
+ Copyright 2009-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_iterators_symplectic
+
+#define BOOST_FUSION_INVOKE_MAX_ARITY 15
+#define BOOST_RESULT_OF_NUM_ARGS 15
+#define FUSION_MAX_VECTOR_SIZE 15
+
+#include <cmath>
+
+#include <boost/test/unit_test.hpp>
+
+#ifndef ODEINT_INTEGRATE_ITERATOR
+#include <boost/numeric/odeint/integrate/integrate_const.hpp>
+#else
+#include <boost/numeric/odeint/iterator/integrate/integrate_const.hpp>
+#endif
+#include <boost/numeric/odeint/stepper/symplectic_euler.hpp>
+#include <boost/numeric/odeint/stepper/symplectic_rkn_sb3a_mclachlan.hpp>
+#include <boost/numeric/odeint/stepper/symplectic_rkn_sb3a_m4_mclachlan.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+namespace mpl = boost::mpl;
+namespace fusion = boost::fusion;
+
+typedef std::vector<double> container_type;
+
+struct harm_osc {
+ void operator()( const container_type &q , container_type &dpdt )
+ {
+ dpdt[0] = -q[0];
+ }
+};
+
+class complete_steppers : public mpl::vector<
+ symplectic_euler< container_type >
+ , symplectic_rkn_sb3a_mclachlan< container_type >
+ , symplectic_rkn_sb3a_m4_mclachlan< container_type >
+ > {};
+
+BOOST_AUTO_TEST_SUITE( symplectic_steppers_test )
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( test_integrate_const , Stepper , complete_steppers )
+{
+ container_type q( 1 , 1.0 ) , p( 1 , 0.0 );
+ size_t steps = integrate_const( Stepper() , harm_osc() ,
+ std::make_pair( boost::ref(q) , boost::ref(p) ) ,
+ 0.0 , 1.0 , 0.1 );
+ BOOST_CHECK( steps == 10 );
+ BOOST_CHECK_CLOSE( q[0] , std::cos(1.0) , 100*std::pow( 0.1 , Stepper::order_value ) );
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/is_pair.cpp b/test/is_pair.cpp
new file mode 100644
index 0000000..bf3bc35
--- /dev/null
+++ b/test/is_pair.cpp
@@ -0,0 +1,49 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/is_pair.cpp
+
+ [begin_description]
+ This file tests the is_pair meta-function.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+#define BOOST_TEST_MODULE odeint_is_pair
+
+#include <utility>
+
+#include <boost/test/unit_test.hpp>
+#include <boost/static_assert.hpp>
+
+#include <boost/numeric/odeint/util/is_pair.hpp>
+
+using namespace boost::numeric::odeint;
+
+
+
+BOOST_AUTO_TEST_SUITE( is_pair_test )
+
+BOOST_AUTO_TEST_CASE( test_is_pair )
+{
+ typedef std::pair< int , int > type1;
+ typedef std::pair< int& , int > type2;
+ typedef std::pair< int , int& > type3;
+ typedef std::pair< int& , int& > type4;
+ typedef std::pair< const int , int > type5;
+ typedef std::pair< const int& , int > type6;
+
+ BOOST_STATIC_ASSERT(( is_pair< type1 >::value ));
+ BOOST_STATIC_ASSERT(( is_pair< type2 >::value ));
+ BOOST_STATIC_ASSERT(( is_pair< type3 >::value ));
+ BOOST_STATIC_ASSERT(( is_pair< type4 >::value ));
+ BOOST_STATIC_ASSERT(( is_pair< type5 >::value ));
+ BOOST_STATIC_ASSERT(( is_pair< type6 >::value ));
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/is_resizeable.cpp b/test/is_resizeable.cpp
new file mode 100644
index 0000000..cb8e9c1
--- /dev/null
+++ b/test/is_resizeable.cpp
@@ -0,0 +1,116 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/is_resizeable.cpp
+
+ [begin_description]
+ This file tests is_resizeable meta-function of odeint.
+ [end_description]
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+// disable checked iterator warning for msvc
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_is_resizeable
+
+#include <vector>
+#include <cmath>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/fusion/include/vector.hpp>
+#include <boost/units/systems/si/length.hpp>
+#include <boost/units/systems/si/time.hpp>
+#include <boost/units/systems/si/velocity.hpp>
+#include <boost/units/systems/si/acceleration.hpp>
+#include <boost/units/systems/si/io.hpp>
+
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+template< typename T > struct my_seq1 {};
+template< typename T > struct my_seq2 {};
+
+namespace boost { namespace fusion { namespace traits {
+
+ template< typename T > struct is_sequence< my_seq1< T > > : boost::true_type {};
+ template< typename T > struct is_sequence< my_seq2< T > > : boost::true_type {};
+} } } // boost::fusion::traits
+
+namespace boost { namespace numeric { namespace odeint {
+
+ template< typename T >
+ struct is_resizeable< my_seq2< T > > : boost::true_type {};
+
+} } } // boost::numeric::odeint
+
+
+
+BOOST_AUTO_TEST_CASE( test_vector )
+{
+ BOOST_CHECK( is_resizeable< std::vector< int > >::value );
+}
+
+BOOST_AUTO_TEST_CASE( test_double )
+{
+ BOOST_CHECK( !( is_resizeable< double >::value ) );
+}
+
+BOOST_AUTO_TEST_CASE( test_fusion_vector_of_vector )
+{
+ typedef boost::fusion::vector< std::vector< double > , std::vector< double > > state_type;
+ BOOST_CHECK( is_resizeable< state_type >::value );
+}
+
+BOOST_AUTO_TEST_CASE( test_fusion_vector_of_double )
+{
+ typedef boost::fusion::vector< double , double > state_type;
+ BOOST_CHECK( !( is_resizeable< state_type >::value ) );
+}
+
+BOOST_AUTO_TEST_CASE( test_fusion_vector_mixed1 )
+{
+ typedef boost::fusion::vector< double , std::vector< double > > state_type;
+ BOOST_CHECK( is_resizeable< state_type >::value);
+}
+
+BOOST_AUTO_TEST_CASE( test_fusion_vector_mixed2 )
+{
+ typedef boost::fusion::vector< std::vector< double > , double > state_type;
+ BOOST_CHECK( is_resizeable< state_type >::value );
+}
+
+BOOST_AUTO_TEST_CASE( test_fusion_quantity_sequence )
+{
+ namespace units = boost::units;
+ namespace si = boost::units::si;
+
+ typedef double value_type;
+ typedef units::quantity< si::time , value_type > time_type;
+ typedef units::quantity< si::length , value_type > length_type;
+ typedef units::quantity< si::velocity , value_type > velocity_type;
+ typedef boost::fusion::vector< length_type , velocity_type > state_type;
+
+ BOOST_CHECK( !( is_resizeable< state_type >::value ) );
+}
+
+BOOST_AUTO_TEST_CASE( test_my_seq1 )
+{
+ BOOST_CHECK( !is_resizeable< my_seq1< double > >::value );
+}
+
+BOOST_AUTO_TEST_CASE( test_my_seq2 )
+{
+ BOOST_CHECK( is_resizeable< my_seq2< double > >::value );
+}
\ No newline at end of file
diff --git a/test/multi_array.cpp b/test/multi_array.cpp
new file mode 100644
index 0000000..67b7f96
--- /dev/null
+++ b/test/multi_array.cpp
@@ -0,0 +1,211 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/multi_array.cpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2009-2012 Karsten Ahnert
+ Copyright 2009-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_multi_array
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/numeric/odeint/algebra/multi_array_algebra.hpp>
+#include <boost/numeric/odeint/util/multi_array_adaption.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta4.hpp>
+#include <boost/numeric/odeint/integrate/integrate_const.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp>
+#include <boost/numeric/odeint/stepper/generation.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+typedef boost::multi_array< double , 1 > vector_type;
+typedef boost::multi_array< double , 2 > matrix_type;
+typedef boost::multi_array< double , 3 > tensor_type;
+
+
+BOOST_AUTO_TEST_SUITE( multi_array_test )
+
+BOOST_AUTO_TEST_CASE( test_resizeable )
+{
+ BOOST_CHECK( is_resizeable< vector_type >::value );
+ BOOST_CHECK( is_resizeable< matrix_type >::value );
+ BOOST_CHECK( is_resizeable< tensor_type >::value );
+}
+
+BOOST_AUTO_TEST_CASE( test_same_size_vector1 )
+{
+ vector_type v1( boost::extents[12] );
+ vector_type v2( boost::extents[12] );
+ BOOST_CHECK( same_size( v1 , v2 ) );
+}
+
+BOOST_AUTO_TEST_CASE( test_same_size_vector2 )
+{
+ vector_type v1( boost::extents[12] );
+ vector_type v2( boost::extents[13] );
+ BOOST_CHECK( !same_size( v1 , v2 ) );
+}
+
+BOOST_AUTO_TEST_CASE( test_same_size_vector3 )
+{
+ vector_type v1( boost::extents[12] );
+ vector_type v2( boost::extents[vector_type::extent_range(-1,11)] );
+ BOOST_CHECK( !same_size( v1 , v2 ) );
+}
+
+BOOST_AUTO_TEST_CASE( test_same_size_vector4 )
+{
+ vector_type v1( boost::extents[12] );
+ vector_type v2( boost::extents[vector_type::extent_range(-1,10)] );
+ BOOST_CHECK( !same_size( v1 , v2 ) );
+}
+
+BOOST_AUTO_TEST_CASE( test_same_size_vector5 )
+{
+ vector_type v1( boost::extents[vector_type::extent_range(-1,10)] );
+ vector_type v2( boost::extents[vector_type::extent_range(-1,10)] );
+ BOOST_CHECK( same_size( v1 , v2 ) );
+}
+
+
+
+BOOST_AUTO_TEST_CASE( test_same_size_matrix1 )
+{
+ matrix_type m1( boost::extents[12][4] );
+ matrix_type m2( boost::extents[12][4] );
+ BOOST_CHECK( same_size( m1 , m2 ) );
+}
+
+BOOST_AUTO_TEST_CASE( test_same_size_matrix2 )
+{
+ matrix_type m1( boost::extents[12][4] );
+ matrix_type m2( boost::extents[12][3] );
+ BOOST_CHECK( !same_size( m1 , m2 ) );
+}
+
+BOOST_AUTO_TEST_CASE( test_same_size_matrix3 )
+{
+ matrix_type m1( boost::extents[12][matrix_type::extent_range(-1,2)] );
+ matrix_type m2( boost::extents[12][3] );
+ BOOST_CHECK( !same_size( m1 , m2 ) );
+}
+
+BOOST_AUTO_TEST_CASE( test_same_size_matrix4 )
+{
+ matrix_type m1( boost::extents[12][matrix_type::extent_range(-1,1)] );
+ matrix_type m2( boost::extents[12][3] );
+ BOOST_CHECK( !same_size( m1 , m2 ) );
+}
+
+BOOST_AUTO_TEST_CASE( test_same_size_tensor1 )
+{
+ tensor_type t1( boost::extents[ tensor_type::extent_range( -2 , 9 ) ]
+ [ tensor_type::extent_range( 5 , 11 ) ]
+ [ tensor_type::extent_range( -1 , 2 ) ] );
+ tensor_type t2( boost::extents[ tensor_type::extent_range( 2 , 13 ) ]
+ [ tensor_type::extent_range( -1 , 5 ) ]
+ [ tensor_type::extent_range( 1 , 4 ) ] );
+ BOOST_CHECK( !same_size( t1 , t2 ) );
+}
+
+BOOST_AUTO_TEST_CASE( test_same_size_tensor2 )
+{
+ tensor_type t1( boost::extents[ tensor_type::extent_range( -2 , 9 ) ]
+ [ tensor_type::extent_range( 5 , 11 ) ]
+ [ tensor_type::extent_range( -1 , 2 ) ] );
+ tensor_type t2( boost::extents[ tensor_type::extent_range( -2 , 9 ) ]
+ [ tensor_type::extent_range( 5 , 11 ) ]
+ [ tensor_type::extent_range( -1 , 2 ) ] );
+ BOOST_CHECK( same_size( t1 , t2 ) );
+}
+
+
+// Tests for tensor_type
+
+BOOST_AUTO_TEST_CASE( test_resize_vector1 )
+{
+ vector_type v1( boost::extents[4] );
+ vector_type v2;
+ resize( v2 , v1 );
+ BOOST_CHECK( same_size( v1 , v2 ) );
+}
+
+BOOST_AUTO_TEST_CASE( test_resize_vector2 )
+{
+ vector_type v1( boost::extents[ vector_type::extent_range( -2 , 9 ) ] );
+ vector_type v2;
+ resize( v2 , v1 );
+ BOOST_CHECK( same_size( v1 , v2 ) );
+}
+
+BOOST_AUTO_TEST_CASE( test_resize_vector3 )
+{
+ vector_type v1( boost::extents[ vector_type::extent_range( -2 , 9 ) ] );
+ vector_type v2( boost::extents[ vector_type::extent_range( 2 , 9 ) ] );
+ BOOST_CHECK( !same_size( v1 , v2 ) );
+ resize( v2 , v1 );
+ BOOST_CHECK( same_size( v1 , v2 ) );
+}
+
+struct mult4
+{
+ void operator()( double &a , double const &b ) const
+ {
+ a = b * 4.0;
+ }
+};
+
+BOOST_AUTO_TEST_CASE( test_for_each2_vector )
+{
+ vector_type v1( boost::extents[ vector_type::extent_range( -2 , 9 ) ] );
+ vector_type v2( boost::extents[ vector_type::extent_range( 2 , 13 ) ] );
+ for( int i=-2 ; i<9 ; ++i )
+ v1[i] = i * 2;
+ multi_array_algebra::for_each2( v2 , v1 , mult4() );
+ for( int i=2 ; i<13 ; ++i )
+ BOOST_CHECK_EQUAL( v2[i] , v1[i-4]*4.0 );
+}
+
+struct vector_ode
+{
+ const static size_t n = 128;
+ void operator()( const vector_type &x , vector_type &dxdt , double t ) const
+ {
+ dxdt[-1] = x[n] - 2.0 * x[-1] + x[0];
+ for( size_t i=0 ; i<n ; ++i )
+ dxdt[i] = x[i-1] - 2.0 * x[i] + x[i+1];
+ dxdt[n] = x[-1] - 2.0 * x[n] + x[n-1];
+ }
+};
+
+
+BOOST_AUTO_TEST_CASE( test_rk4_vector )
+{
+ vector_type v1( boost::extents[ vector_type::extent_range( -1 , vector_ode::n+1 ) ] );
+ integrate_const( runge_kutta4< vector_type >() , vector_ode() , v1 , 0.0 , 1.0 , 0.01 );
+}
+
+BOOST_AUTO_TEST_CASE( test_dopri5_vector )
+{
+ vector_type v1( boost::extents[ vector_type::extent_range( -1 , vector_ode::n+1 ) ] );
+ integrate_const( make_dense_output( 1.0e-6 , 1.0e-6 , runge_kutta_dopri5< vector_type >() ) , vector_ode() , v1 , 0.0 , 1.0 , 0.01 );
+}
+
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/n_step_iterator.cpp b/test/n_step_iterator.cpp
new file mode 100644
index 0000000..bebcf6d
--- /dev/null
+++ b/test/n_step_iterator.cpp
@@ -0,0 +1,225 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/n_step_iterator.cpp
+
+ [begin_description]
+ This file tests the n-step iterator.
+ [end_description]
+
+ Copyright 2009-2013 Karsten Ahnert
+ Copyright 2009-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#define BOOST_TEST_MODULE odeint_n_step_iterator
+
+#include <iterator>
+#include <algorithm>
+#include <vector>
+
+#include <boost/numeric/odeint/config.hpp>
+#include <boost/array.hpp>
+#include <boost/range/algorithm/for_each.hpp>
+#include <boost/range/algorithm/copy.hpp>
+#include <boost/mpl/vector.hpp>
+
+#include <boost/test/unit_test.hpp>
+#include <boost/test/floating_point_comparison.hpp>
+
+#include <boost/numeric/odeint/iterator/n_step_iterator.hpp>
+#include "dummy_steppers.hpp"
+#include "dummy_odes.hpp"
+#include "dummy_observers.hpp"
+
+namespace mpl = boost::mpl;
+using namespace boost::numeric::odeint;
+
+typedef dummy_stepper::state_type state_type;
+typedef dummy_stepper::value_type value_type;
+
+
+BOOST_AUTO_TEST_SUITE( n_step_iterator_test )
+
+typedef mpl::vector<
+ dummy_stepper
+ , dummy_dense_output_stepper
+ > dummy_steppers;
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_stepper_iterator , Stepper , dummy_steppers )
+{
+ typedef n_step_iterator< Stepper , empty_system , state_type > iterator_type;
+ state_type x = {{ 1.0 }};
+ iterator_type iter1 = iterator_type( Stepper() , empty_system() , x , 0.0 , 0.1 , 10 );
+ iterator_type iter2 = iter1;
+ BOOST_CHECK_EQUAL( &(*iter1) , &(*iter2) );
+ BOOST_CHECK_EQUAL( &(*iter1) , &x );
+ BOOST_CHECK( iter1.same( iter2 ) );
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( assignment_stepper_iterator , Stepper , dummy_steppers )
+{
+ typedef n_step_iterator< Stepper , empty_system , state_type > iterator_type;
+ state_type x1 = {{ 1.0 }} , x2 = {{ 2.0 }};
+ iterator_type iter1 = iterator_type( Stepper() , empty_system() , x1 , 0.0 , 0.1 , 10 );
+ iterator_type iter2 = iterator_type( Stepper() , empty_system() , x2 , 0.0 , 0.2 , 10 );
+ BOOST_CHECK_EQUAL( &(*iter1) , &x1 );
+ BOOST_CHECK_EQUAL( &(*iter2) , &x2 );
+ BOOST_CHECK( !iter1.same( iter2 ) );
+ iter2 = iter1;
+ BOOST_CHECK_EQUAL( &(*iter1) , &x1 );
+ BOOST_CHECK_EQUAL( &(*iter2) , &x1 );
+ BOOST_CHECK( iter1.same( iter2 ) );
+}
+
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_iterator_factory , Stepper , dummy_steppers )
+{
+ Stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ std::for_each(
+ make_n_step_iterator_begin( stepper , boost::ref( system ) , x , 0.0 , 0.1 , 10 ) ,
+ make_n_step_iterator_end( stepper , boost::ref( system ) , x ) ,
+ dummy_observer() );
+
+ // dummy_steppers just add 0.25 at each step, the above for_each leads to 10 do_step calls so x should be 3.5
+ BOOST_CHECK_CLOSE( x[0] , 3.5 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_range , Stepper , dummy_steppers )
+{
+ Stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ boost::for_each( make_n_step_range( stepper , boost::ref( system ) , x , 0.0 , 0.1 , 10 ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 3.5 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_iterator_with_reference_wrapper_factory , Stepper , dummy_steppers )
+{
+ Stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ std::for_each(
+ make_n_step_iterator_begin( boost::ref( stepper ) , boost::ref( system ) , x , 0.0 , 0.1 , 10 ) ,
+ make_n_step_iterator_end( boost::ref( stepper ) , boost::ref( system ) , x ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 3.5 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_range_with_reference_wrapper , Stepper , dummy_steppers )
+{
+ Stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ boost::for_each( make_n_step_range( boost::ref( stepper ) , boost::ref( system ) , x , 0.0 , 0.1 , 10 ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 3.5 , 1.0e-13 );
+}
+
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( transitivity1 , Stepper , dummy_steppers )
+{
+ typedef n_step_iterator< Stepper , empty_system , state_type > stepper_iterator;
+
+ state_type x = {{ 1.0 }};
+ stepper_iterator first1( Stepper() , empty_system() , x , 2.5 , 0.1 , 0 );
+ stepper_iterator last1( Stepper() , empty_system() , x );
+ stepper_iterator last2( Stepper() , empty_system() , x );
+
+ BOOST_CHECK( last1 == last2 );
+ BOOST_CHECK( first1 != last1 );
+ BOOST_CHECK( ++first1 == last1 );
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm , Stepper , dummy_steppers )
+{
+ typedef n_step_iterator< Stepper , empty_system , state_type > stepper_iterator;
+ state_type x = {{ 1.0 }};
+ std::vector< state_type > res;
+ stepper_iterator first( Stepper() , empty_system() , x , 0.0 , 0.1 , 3 );
+ stepper_iterator last( Stepper() , empty_system() , x );
+
+ std::copy( first , last , std::back_insert_iterator< std::vector< state_type > >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 4 ) );
+ BOOST_CHECK_CLOSE( res[0][0] , 1.0 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[1][0] , 1.25 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[2][0] , 1.5 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[3][0] , 1.75 , 1.0e-14 );
+
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-14 ); // the iterator should not iterate over the end
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm_negative_time_step , Stepper , dummy_steppers )
+{
+ typedef n_step_iterator< Stepper , empty_system , state_type > stepper_iterator;
+ state_type x = {{ 1.0 }};
+ std::vector< state_type > res;
+ stepper_iterator first( Stepper() , empty_system() , x , 0.3 , -0.1 , 3 );
+ stepper_iterator last( Stepper() , empty_system() , x );
+
+ std::copy( first , last , std::back_insert_iterator< std::vector< state_type > >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 4 ) );
+ BOOST_CHECK_CLOSE( res[0][0] , 1.0 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[1][0] , 1.25 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[2][0] , 1.5 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[3][0] , 1.75 , 1.0e-14 );
+
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-14 );
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm_with_factory , Stepper , dummy_steppers )
+{
+ state_type x = {{ 1.0 }};
+ std::vector< state_type > res;
+ std::copy( make_n_step_iterator_begin( Stepper() , empty_system() , x , 0.0 , 0.1 , 3 ) ,
+ make_n_step_iterator_end( Stepper() , empty_system() , x ) ,
+ std::back_insert_iterator< std::vector< state_type > >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 4 ) );
+ BOOST_CHECK_CLOSE( res[0][0] , 1.0 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[1][0] , 1.25 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[2][0] , 1.5 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[3][0] , 1.75 , 1.0e-14 );
+
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-14 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm_with_range_factory , Stepper , dummy_steppers )
+{
+ state_type x = {{ 1.0 }};
+ std::vector< state_type > res;
+ boost::range::copy( make_n_step_range( Stepper() , empty_system() , x , 0.0 , 0.1 , 3 ) ,
+ std::back_insert_iterator< std::vector< state_type > >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 4 ) );
+ BOOST_CHECK_CLOSE( res[0][0] , 1.0 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[1][0] , 1.25 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[2][0] , 1.5 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( res[3][0] , 1.75 , 1.0e-14 );
+
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-14 );
+}
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/n_step_time_iterator.cpp b/test/n_step_time_iterator.cpp
new file mode 100644
index 0000000..fbce867
--- /dev/null
+++ b/test/n_step_time_iterator.cpp
@@ -0,0 +1,213 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/n_step_time_iterator.cpp
+
+ [begin_description]
+ This file tests the n-step time iterator.
+ [end_description]
+
+ Copyright 2009-2013 Karsten Ahnert
+ Copyright 2009-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#define BOOST_TEST_MODULE odeint_n_step_time_iterator
+
+#include <iterator>
+#include <algorithm>
+#include <vector>
+
+#include <boost/numeric/odeint/config.hpp>
+#include <boost/array.hpp>
+#include <boost/range/algorithm/copy.hpp>
+#include <boost/range/algorithm/for_each.hpp>
+#include <boost/mpl/vector.hpp>
+
+#include <boost/test/unit_test.hpp>
+#include <boost/test/floating_point_comparison.hpp>
+
+#include <boost/numeric/odeint/iterator/n_step_time_iterator.hpp>
+#include "dummy_steppers.hpp"
+#include "dummy_odes.hpp"
+#include "dummy_observers.hpp"
+
+namespace mpl = boost::mpl;
+using namespace boost::numeric::odeint;
+
+typedef dummy_stepper::state_type state_type;
+typedef dummy_stepper::value_type value_type;
+typedef dummy_stepper::time_type time_type;
+typedef std::vector< std::pair< state_type , time_type > > result_vector;
+
+BOOST_AUTO_TEST_SUITE( n_step_time_iterator_test )
+
+typedef mpl::vector<
+ dummy_stepper
+ , dummy_dense_output_stepper
+ > dummy_steppers;
+
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_stepper_iterator , Stepper , dummy_steppers )
+{
+ typedef n_step_time_iterator< Stepper , empty_system , state_type > iterator_type;
+ state_type x = {{ 1.0 }};
+ iterator_type iter1 = iterator_type( Stepper() , empty_system() , x , 0.0 , 0.1 , 10 );
+ iterator_type iter2 = iter1;
+ BOOST_CHECK_EQUAL( &( iter1->first ) , &( iter2->first ) );
+ BOOST_CHECK_EQUAL( &( iter1->first ) , &x );
+ BOOST_CHECK( iter1.same( iter2 ) );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( assignment_stepper_iterator , Stepper , dummy_steppers )
+{
+ typedef n_step_time_iterator< Stepper , empty_system , state_type > iterator_type;
+ state_type x1 = {{ 1.0 }} , x2 = {{ 2.0 }};
+ iterator_type iter1 = iterator_type( Stepper() , empty_system() , x1 , 0.0 , 0.1 , 10 );
+ iterator_type iter2 = iterator_type( Stepper() , empty_system() , x2 , 0.0 , 0.2 , 10 );
+ BOOST_CHECK_EQUAL( &( iter1->first ) , &x1 );
+ BOOST_CHECK_EQUAL( &( iter2->first ) , &x2 );
+ BOOST_CHECK( !iter1.same( iter2 ) );
+ iter2 = iter1;
+ BOOST_CHECK_EQUAL( &( iter1->first ) , &x1 );
+ BOOST_CHECK_EQUAL( &( iter2->first ) , &x1 );
+ BOOST_CHECK( iter1.same( iter2 ) );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_iterator_factory , Stepper , dummy_steppers )
+{
+ Stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ std::for_each(
+ make_n_step_time_iterator_begin( stepper , boost::ref( system ) , x , 0.0 , 0.1 , 10 ) ,
+ make_n_step_time_iterator_end( stepper , boost::ref( system ) , x ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 3.5 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_range , Stepper , dummy_steppers )
+{
+ Stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ boost::for_each( make_n_step_time_range( stepper , boost::ref( system ) , x , 0.0 , 0.1 , 10 ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 3.5 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_iterator_with_reference_wrapper_factory , Stepper , dummy_steppers )
+{
+ Stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ std::for_each(
+ make_n_step_time_iterator_begin( boost::ref( stepper ) , boost::ref( system ) , x , 0.0 , 0.1 , 10 ) ,
+ make_n_step_time_iterator_end( boost::ref( stepper ) , boost::ref( system ) , x ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 3.5 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_range_with_reference_wrapper , Stepper , dummy_steppers )
+{
+ Stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ boost::for_each( make_n_step_time_range( boost::ref( stepper ) , boost::ref( system ) , x , 0.0 , 0.1 , 10 ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 3.5 , 1.0e-13 );
+}
+
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( transitivity1 , Stepper , dummy_steppers )
+{
+ typedef n_step_time_iterator< Stepper , empty_system , state_type > stepper_iterator;
+
+ state_type x = {{ 1.0 }};
+ stepper_iterator first1( Stepper() , empty_system() , x , 0.0 , 0.1 , 0 );
+ stepper_iterator last1( Stepper() , empty_system() , x );
+ stepper_iterator last2( Stepper() , empty_system() , x );
+
+ BOOST_CHECK( last1 == last2 );
+ BOOST_CHECK( first1 != last1 );
+ BOOST_CHECK( ++first1 == last1 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm , Stepper , dummy_steppers )
+{
+ typedef n_step_time_iterator< Stepper , empty_system , state_type > stepper_iterator;
+ state_type x = {{ 1.0 }};
+ result_vector res;
+ stepper_iterator first( Stepper() , empty_system() , x , 0.0 , 0.1 , 3 );
+ stepper_iterator last( Stepper() , empty_system() , x );
+
+ std::copy( first , last , std::back_insert_iterator< result_vector >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 4 ) );
+ BOOST_CHECK_CLOSE( res[0].first[0] , 1.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[0].second , 0.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1].first[0] , 1.25 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1].second , 0.1 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2].first[0] , 1.5 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2].second , 0.2 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3].first[0] , 1.75 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3].second , 0.3 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm_with_factory , Stepper , dummy_steppers )
+{
+ state_type x = {{ 1.0 }};
+ result_vector res;
+ std::copy( make_n_step_time_iterator_begin( Stepper() , empty_system() , x , 0.0 , 0.1 , 3 ) ,
+ make_n_step_time_iterator_end( Stepper() , empty_system() , x ) ,
+ std::back_insert_iterator< result_vector >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 4 ) );
+ BOOST_CHECK_CLOSE( res[0].first[0] , 1.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[0].second , 0.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1].first[0] , 1.25 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1].second , 0.1 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2].first[0] , 1.5 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2].second , 0.2 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3].first[0] , 1.75 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3].second , 0.3 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm_with_range_factory , Stepper , dummy_steppers )
+{
+ state_type x = {{ 1.0 }};
+ result_vector res;
+ boost::range::copy( make_n_step_time_range( Stepper() , empty_system() , x , 0.0 , 0.1 , 3 ) ,
+ std::back_insert_iterator< result_vector >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 4 ) );
+ BOOST_CHECK_CLOSE( res[0].first[0] , 1.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[0].second , 0.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1].first[0] , 1.25 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1].second , 0.1 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2].first[0] , 1.5 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2].second , 0.2 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3].first[0] , 1.75 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3].second , 0.3 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-13 );
+}
+
+
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/numeric/Jamfile.v2 b/test/numeric/Jamfile.v2
new file mode 100644
index 0000000..1915a32
--- /dev/null
+++ b/test/numeric/Jamfile.v2
@@ -0,0 +1,35 @@
+# Copyright 2012 Karsten Ahnert
+# Copyright 2012 Mario Mulansky
+# Distributed under the Boost Software License, Version 1.0.
+# (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+# bring in rules for testing
+
+
+import testing ;
+
+use-project boost : $(BOOST_ROOT) ;
+
+project
+ : requirements
+ <library>/boost/test//boost_unit_test_framework
+ <define>BOOST_ALL_NO_LIB=1
+ <include>../../include
+ <link>static
+ <toolset>clang:<cxxflags>-Wno-unused-variable
+
+# <cxxflags>-D_SCL_SECURE_NO_WARNINGS
+ ;
+
+test-suite "odeint"
+ :
+ [ run runge_kutta.cpp ]
+ [ run symplectic.cpp ]
+ [ run rosenbrock.cpp ]
+ [ run adams_bashforth.cpp ]
+ [ run adams_bashforth_moulton.cpp ]
+ [ run abm_time_dependent.cpp ]
+ [ run order_quadrature_formula.cpp ]
+ [ run velocity_verlet.cpp ]
+ : <testing.launcher>valgrind
+ ;
diff --git a/test/numeric/abm_time_dependent.cpp b/test/numeric/abm_time_dependent.cpp
new file mode 100644
index 0000000..019a17d
--- /dev/null
+++ b/test/numeric/abm_time_dependent.cpp
@@ -0,0 +1,85 @@
+/* Boost numeric test of the adams-bashforth-moulton steppers test file
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013-2015 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+// disable checked iterator warning for msvc
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE numeric_adams_bashforth_moulton
+
+#include <iostream>
+#include <cmath>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/mpl/vector.hpp>
+
+#include <boost/numeric/odeint.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+namespace mpl = boost::mpl;
+
+typedef double value_type;
+
+typedef value_type state_type;
+
+
+// simple time-dependent rhs, analytic solution x = 0.5*t^2
+struct simple_rhs
+{
+ void operator()( const state_type& x , state_type &dxdt , const double t ) const
+ {
+ dxdt = t;
+ }
+};
+
+BOOST_AUTO_TEST_SUITE( numeric_abm_time_dependent_test )
+
+
+/* generic test for all adams bashforth moulton steppers */
+template< class Stepper >
+struct perform_abm_time_dependent_test
+{
+ void operator()( void )
+ {
+ Stepper stepper;
+ const int o = stepper.order()+1; //order of the error is order of approximation + 1
+
+ const state_type x0 = 0.0;
+ state_type x1 = x0;
+ double t = 0.0;
+ double dt = 0.1;
+ const int steps = 10;
+
+ integrate_n_steps( boost::ref(stepper) , simple_rhs(), x1 , t , dt , steps );
+ BOOST_CHECK_LT( std::abs( 0.5 - x1 ) , std::pow( dt , o ) );
+ }
+};
+
+typedef mpl::vector<
+ adams_bashforth_moulton< 2 , state_type > ,
+ adams_bashforth_moulton< 3 , state_type > ,
+ adams_bashforth_moulton< 4 , state_type > ,
+ adams_bashforth_moulton< 5 , state_type > ,
+ adams_bashforth_moulton< 6 , state_type > ,
+ adams_bashforth_moulton< 7 , state_type > ,
+ adams_bashforth_moulton< 8 , state_type >
+ > adams_bashforth_moulton_steppers;
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( abm_time_dependent_test , Stepper, adams_bashforth_moulton_steppers )
+{
+ perform_abm_time_dependent_test< Stepper > tester;
+ tester();
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/numeric/adams_bashforth.cpp b/test/numeric/adams_bashforth.cpp
new file mode 100644
index 0000000..ca8a6ce
--- /dev/null
+++ b/test/numeric/adams_bashforth.cpp
@@ -0,0 +1,117 @@
+/* Boost numeric test of the adams-bashforth steppers test file
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013-2015 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+// disable checked iterator warning for msvc
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE numeric_adams_bashforth
+
+#include <iostream>
+#include <cmath>
+
+#include <boost/array.hpp>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/mpl/vector.hpp>
+
+#include <boost/numeric/odeint.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+namespace mpl = boost::mpl;
+
+typedef double value_type;
+
+typedef boost::array< double , 2 > state_type;
+
+// harmonic oscillator, analytic solution x[0] = sin( t )
+struct osc
+{
+ void operator()( const state_type &x , state_type &dxdt , const double t ) const
+ {
+ dxdt[0] = x[1];
+ dxdt[1] = -x[0];
+ }
+};
+
+BOOST_AUTO_TEST_SUITE( numeric_adams_bashforth_test )
+
+
+/* generic test for all adams bashforth steppers */
+template< class Stepper >
+struct perform_adams_bashforth_test
+{
+ void operator()( void )
+ {
+ Stepper stepper;
+ const int o = stepper.order()+1; //order of the error is order of approximation + 1
+
+ const state_type x0 = {{ 0.0 , 1.0 }};
+ state_type x1 = x0;
+ double t = 0.0;
+ double dt = 0.2;
+ // initialization, does a number of steps already to fill internal buffer, t is increased
+ stepper.initialize( osc() , x1 , t , dt );
+ double A = std::sqrt( x1[0]*x1[0] + x1[1]*x1[1] );
+ double phi = std::asin(x1[0]/A) - t;
+ // do a number of steps to fill the buffer with results from adams bashforth
+ for( size_t n=0 ; n < stepper.steps ; ++n )
+ {
+ stepper.do_step( osc() , x1 , t , dt );
+ t += dt;
+ }
+ // now we do the actual step
+ stepper.do_step( osc() , x1 , t , dt );
+ // only examine the error of the adams-bashforth step, not the initialization
+ const double f = 2.0 * std::abs( A*sin(t+dt+phi) - x1[0] ) / std::pow( dt , o ); // upper bound
+
+ std::cout << o << " , "
+ << Stepper::initializing_stepper_type::order_value+1 << " , "
+ << f << std::endl;
+
+ /* as long as we have errors above machine precision */
+ while( f*std::pow( dt , o ) > 1E-16 )
+ {
+ x1 = x0;
+ t = 0.0;
+ stepper.initialize( osc() , x1 , t , dt );
+ A = std::sqrt( x1[0]*x1[0] + x1[1]*x1[1] );
+ phi = std::asin(x1[0]/A) - t;
+ // now we do the actual step
+ stepper.do_step( osc() , x1 , t , dt );
+ // only examine the error of the adams-bashforth step, not the initialization
+ std::cout << "Testing dt=" << dt << " , " << std::abs( A*sin(t+dt+phi) - x1[0] ) << std::endl;
+ BOOST_CHECK_LT( std::abs( A*sin(t+dt+phi) - x1[0] ) , f*std::pow( dt , o ) );
+ dt *= 0.5;
+ }
+ }
+};
+
+typedef mpl::vector<
+ adams_bashforth< 2 , state_type > ,
+ adams_bashforth< 3 , state_type > ,
+ adams_bashforth< 4 , state_type > ,
+ adams_bashforth< 5 , state_type > ,
+ adams_bashforth< 6 , state_type > ,
+ adams_bashforth< 7 , state_type > ,
+ adams_bashforth< 8 , state_type >
+ > adams_bashforth_steppers;
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( adams_bashforth_test , Stepper, adams_bashforth_steppers )
+{
+ perform_adams_bashforth_test< Stepper > tester;
+ tester();
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/numeric/adams_bashforth_moulton.cpp b/test/numeric/adams_bashforth_moulton.cpp
new file mode 100644
index 0000000..dea5718
--- /dev/null
+++ b/test/numeric/adams_bashforth_moulton.cpp
@@ -0,0 +1,119 @@
+/* Boost numeric test of the adams-bashforth-moulton steppers test file
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+// disable checked iterator warning for msvc
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE numeric_adams_bashforth_moulton
+
+#include <iostream>
+#include <cmath>
+
+#include <boost/array.hpp>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/mpl/vector.hpp>
+
+#include <boost/numeric/odeint.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+namespace mpl = boost::mpl;
+
+typedef double value_type;
+
+typedef boost::array< double , 2 > state_type;
+typedef runge_kutta_fehlberg78<state_type> initializing_stepper;
+
+// harmonic oscillator, analytic solution x[0] = sin( t )
+struct osc
+{
+ void operator()( const state_type &x , state_type &dxdt , const double t ) const
+ {
+ dxdt[0] = x[1];
+ dxdt[1] = -x[0];
+ }
+};
+
+BOOST_AUTO_TEST_SUITE( numeric_adams_bashforth_moulton_test )
+
+
+/* generic test for all adams bashforth moulton steppers */
+template< class Stepper >
+struct perform_adams_bashforth_moulton_test
+{
+ void operator()( void )
+ {
+ Stepper stepper;
+ initializing_stepper init_stepper;
+ const int o = stepper.order()+1; //order of the error is order of approximation + 1
+
+ const state_type x0 = {{ 0.0 , 1.0 }};
+ state_type x1 = x0;
+ double t = 0.0;
+ double dt = 0.25;
+ // initialization, does a number of steps already to fill internal buffer, t is increased
+ // we use the rk78 as initializing stepper
+ stepper.initialize( boost::ref(init_stepper) , osc() , x1 , t , dt );
+ // do a number of steps to fill the buffer with results from adams bashforth
+ for( size_t n=0 ; n < stepper.steps ; ++n )
+ {
+ stepper.do_step( osc() , x1 , t , dt );
+ t += dt;
+ }
+ double A = std::sqrt( x1[0]*x1[0] + x1[1]*x1[1] );
+ double phi = std::asin(x1[0]/A) - t;
+ // now we do the actual step
+ stepper.do_step( osc() , x1 , t , dt );
+ // only examine the error of the adams-bashforth-moulton step, not the initialization
+ const double f = 2.0 * std::abs( A*sin(t+dt+phi) - x1[0] ) / std::pow( dt , o ); // upper bound
+
+ std::cout << o << " , " << f << std::endl;
+
+ /* as long as we have errors above machine precision */
+ while( f*std::pow( dt , o ) > 1E-16 )
+ {
+ x1 = x0;
+ t = 0.0;
+ stepper.initialize( boost::ref(init_stepper) , osc() , x1 , t , dt );
+ A = std::sqrt( x1[0]*x1[0] + x1[1]*x1[1] );
+ phi = std::asin(x1[0]/A) - t;
+ // now we do the actual step
+ stepper.do_step( osc() , x1 , t , dt );
+ // only examine the error of the adams-bashforth-moulton step, not the initialization
+ std::cout << "Testing dt=" << dt << " , " << std::abs( A*sin(t+dt+phi) - x1[0] ) << std::endl;
+ BOOST_CHECK_LT( std::abs( A*sin(t+dt+phi) - x1[0] ) , f*std::pow( dt , o ) );
+ dt *= 0.5;
+ }
+ }
+};
+
+typedef mpl::vector<
+ adams_bashforth_moulton< 1 , state_type > ,
+ adams_bashforth_moulton< 2 , state_type > ,
+ adams_bashforth_moulton< 3 , state_type > ,
+ adams_bashforth_moulton< 4 , state_type > ,
+ adams_bashforth_moulton< 5 , state_type > ,
+ adams_bashforth_moulton< 6 , state_type > ,
+ adams_bashforth_moulton< 7 , state_type > ,
+ adams_bashforth_moulton< 8 , state_type >
+ > adams_bashforth_moulton_steppers;
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( adams_bashforth_moulton_test , Stepper, adams_bashforth_moulton_steppers )
+{
+ perform_adams_bashforth_moulton_test< Stepper > tester;
+ tester();
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/numeric/order_quadrature_formula.cpp b/test/numeric/order_quadrature_formula.cpp
new file mode 100644
index 0000000..cefab4d
--- /dev/null
+++ b/test/numeric/order_quadrature_formula.cpp
@@ -0,0 +1,195 @@
+/* Boost numeric test for orders of quadrature formulas test file
+
+ Copyright 2015 Gregor de Cillia
+ Copyright 2015 Mario Mulansky <mario.mulansky@gmx.net>
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+// disable checked iterator warning for msvc
+#include <boost/config.hpp>
+
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE order_quadrature_formula
+
+#include <iostream>
+#include <cmath>
+
+#include "boost/format.hpp"
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/mpl/vector.hpp>
+
+#include <boost/numeric/odeint.hpp>
+
+#include <boost/numeric/ublas/vector.hpp>
+
+#include <boost/format.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+namespace mpl = boost::mpl;
+
+typedef double value_type;
+typedef value_type time_type;
+typedef value_type state_type;
+
+BOOST_AUTO_TEST_SUITE( order_of_convergence_test )
+
+/* defines the simple monomial f(t) = (p+1) * t^p.*/
+struct monomial
+{
+ int power;
+
+ monomial(int p = 0) : power( p ){};
+
+ void operator()( const state_type &x , state_type &dxdt , const time_type t )
+ {
+ dxdt = ( 1.0 + power ) * pow( t, power );
+ }
+};
+
+
+/* generic test for all steppers that support integrate_const */
+template< class Stepper >
+struct stepper_order_test
+{
+ void operator()( int steps = 1 )
+ {
+ const int estimated_order = estimate_order( steps );
+ const int defined_order = Stepper::order_value;
+
+ std::cout << boost::format( "%-20i%-20i\n" )
+ % estimated_order % defined_order;
+
+ BOOST_REQUIRE_EQUAL( estimated_order, defined_order );
+ }
+
+ /*
+ the order of the stepper is estimated by trying to solve the ODE
+ x'(t) = (p+1) * t^p
+ until the errors are too big to be justified by finite precision.
+ the first value p for which the problem is *not* solved within the
+ finite precision tolerance is the estimate for the order of the scheme.
+ */
+ int estimate_order( int steps )
+ {
+ const double dt = 1.0/steps;
+ const double tolerance = steps*1E-15;
+ int p;
+ for( p = 0; true; p++ )
+ {
+ // begin with x'(t) = t^0 = 1
+ // => x (t) = t
+ // then use x'(t) = 2*t^1
+ // => x (t) = t^2
+ // ...
+ state_type x = 0.0;
+
+ double t = integrate_n_steps( Stepper(), monomial( p ), x, 0.0, dt,
+ steps );
+ if( fabs( x - pow( t, ( 1.0 + p ) ) ) > tolerance )
+ break;
+ }
+ // the smallest power p for which the test failed is the estimated order,
+ // as the solution for this power is x(t) = t^{p+1}
+ return p;
+ }
+};
+
+
+typedef mpl::vector<
+ euler< state_type > ,
+ modified_midpoint< state_type > ,
+ runge_kutta4< state_type > ,
+ runge_kutta4_classic< state_type > ,
+ runge_kutta_cash_karp54_classic< state_type > ,
+ runge_kutta_cash_karp54< state_type > ,
+ runge_kutta_dopri5< state_type > ,
+ runge_kutta_fehlberg78< state_type >
+ > runge_kutta_steppers;
+
+typedef mpl::vector<
+ adams_bashforth< 2, state_type, double, state_type, double,
+ vector_space_algebra, default_operations,
+ initially_resizer, runge_kutta_fehlberg78< state_type > >,
+ adams_bashforth< 3, state_type, double, state_type, double,
+ vector_space_algebra, default_operations,
+ initially_resizer, runge_kutta_fehlberg78< state_type > >,
+ adams_bashforth< 4, state_type, double, state_type, double,
+ vector_space_algebra, default_operations,
+ initially_resizer, runge_kutta_fehlberg78< state_type > >,
+ adams_bashforth< 5, state_type, double, state_type, double,
+ vector_space_algebra, default_operations,
+ initially_resizer, runge_kutta_fehlberg78< state_type > >,
+ adams_bashforth< 6, state_type, double, state_type, double,
+ vector_space_algebra, default_operations,
+ initially_resizer, runge_kutta_fehlberg78< state_type > >,
+ adams_bashforth< 7, state_type, double, state_type, double,
+ vector_space_algebra, default_operations,
+ initially_resizer, runge_kutta_fehlberg78< state_type > >,
+ adams_bashforth< 8, state_type, double, state_type, double,
+ vector_space_algebra, default_operations,
+ initially_resizer, runge_kutta_fehlberg78< state_type > >
+ > ab_steppers;
+
+
+typedef mpl::vector<
+ adams_bashforth_moulton< 2, state_type, double, state_type, double,
+ vector_space_algebra, default_operations,
+ initially_resizer,
+ runge_kutta_fehlberg78< state_type > >,
+ adams_bashforth_moulton< 3, state_type, double, state_type, double,
+ vector_space_algebra, default_operations,
+ initially_resizer,
+ runge_kutta_fehlberg78< state_type > >,
+ adams_bashforth_moulton< 4, state_type, double, state_type, double,
+ vector_space_algebra, default_operations,
+ initially_resizer,
+ runge_kutta_fehlberg78< state_type > >,
+ adams_bashforth_moulton< 5, state_type, double, state_type, double,
+ vector_space_algebra, default_operations,
+ initially_resizer,
+ runge_kutta_fehlberg78< state_type > >,
+ adams_bashforth_moulton< 6, state_type, double, state_type, double,
+ vector_space_algebra, default_operations,
+ initially_resizer,
+ runge_kutta_fehlberg78< state_type > >,
+ adams_bashforth_moulton< 7, state_type, double, state_type, double,
+ vector_space_algebra, default_operations,
+ initially_resizer,
+ runge_kutta_fehlberg78< state_type > >,
+ adams_bashforth_moulton< 8, state_type, double, state_type, double,
+ vector_space_algebra, default_operations,
+ initially_resizer,
+ runge_kutta_fehlberg78< state_type > >
+ > abm_steppers;
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( runge_kutta_test , Stepper, runge_kutta_steppers )
+{
+ stepper_order_test< Stepper > tester;
+ tester(10);
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( adams_bashforth_test , Stepper, ab_steppers )
+{
+ stepper_order_test< Stepper > tester;
+ tester(16);
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( adams_bashforth_moultion_test , Stepper, abm_steppers )
+{
+ stepper_order_test< Stepper > tester;
+ tester(16);
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/numeric/rosenbrock.cpp b/test/numeric/rosenbrock.cpp
new file mode 100644
index 0000000..2b6a267
--- /dev/null
+++ b/test/numeric/rosenbrock.cpp
@@ -0,0 +1,89 @@
+/* Boost numeric test of the rosenbrock4 stepper test file
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+// disable checked iterator warning for msvc
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE numeric_rosenbrock
+
+#include <iostream>
+#include <cmath>
+
+#include <boost/array.hpp>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/numeric/odeint/stepper/rosenbrock4.hpp>
+#include <boost/numeric/ublas/vector.hpp>
+#include <boost/numeric/ublas/matrix.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+typedef double value_type;
+typedef boost::numeric::ublas::vector< value_type > state_type;
+typedef boost::numeric::ublas::matrix< value_type > matrix_type;
+
+// harmonic oscillator, analytic solution x[0] = sin( t )
+struct sys
+{
+ void operator()( const state_type &x , state_type &dxdt , const value_type &t ) const
+ {
+ dxdt( 0 ) = x( 1 );
+ dxdt( 1 ) = -x( 0 );
+ }
+};
+
+struct jacobi
+{
+ void operator()( const state_type &x , matrix_type &jacobi , const value_type &t , state_type &dfdt ) const
+ {
+ jacobi( 0 , 0 ) = 0;
+ jacobi( 0 , 1 ) = 1;
+ jacobi( 1 , 0 ) = -1;
+ jacobi( 1 , 1 ) = 0;
+ dfdt( 0 ) = 0.0;
+ dfdt( 1 ) = 0.0;
+ }
+};
+
+
+BOOST_AUTO_TEST_SUITE( numeric_rosenbrock4 )
+
+BOOST_AUTO_TEST_CASE( rosenbrock4_numeric_test )
+{
+ typedef rosenbrock4< value_type > stepper_type;
+ stepper_type stepper;
+
+ const int o = stepper.order()+1;
+
+ state_type x0( 2 ) , x1( 2 );
+ x0(0) = 0.0; x0(1) = 1.0;
+
+ double dt = 0.5;
+
+ stepper.do_step( std::make_pair( sys() , jacobi() ) , x0 , 0.0 , x1 , dt );
+ const double f = 2.0 * std::abs( std::sin(dt) - x1(0) ) / std::pow( dt , o );
+
+ std::cout << o << " , " << f << std::endl;
+
+ while( f*std::pow( dt , o ) > 1E-16 )
+ {
+ stepper.do_step( std::make_pair( sys() , jacobi() ) , x0 , 0.0 , x1 , dt );
+ std::cout << "Testing dt=" << dt << std::endl;
+ BOOST_CHECK_SMALL( std::abs( std::sin(dt) - x1(0) ) , f*std::pow( dt , o ) );
+ dt *= 0.5;
+ }
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/numeric/runge_kutta.cpp b/test/numeric/runge_kutta.cpp
new file mode 100644
index 0000000..a71701b
--- /dev/null
+++ b/test/numeric/runge_kutta.cpp
@@ -0,0 +1,177 @@
+/* Boost numeric test of the runge kutta steppers test file
+
+ Copyright 2012 Mario Mulansky
+ Copyright 2012 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+// disable checked iterator warning for msvc
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE numeric_runge_kutta
+
+#include <iostream>
+#include <cmath>
+
+#include <boost/array.hpp>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/mpl/vector.hpp>
+
+#include <boost/numeric/odeint.hpp>
+#include <boost/numeric/odeint/stepper/extrapolation_stepper.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+namespace mpl = boost::mpl;
+
+typedef double value_type;
+
+typedef boost::array< double , 2 > state_type;
+
+// harmonic oscillator, analytic solution x[0] = sin( t )
+struct osc
+{
+ void operator()( const state_type &x , state_type &dxdt , const double t ) const
+ {
+ dxdt[0] = x[1];
+ dxdt[1] = -x[0];
+ }
+};
+
+/* reset dispatcher */
+template< class StepperCategory >
+struct resetter
+{
+ template< class Stepper >
+ static void reset( Stepper &stepper ) { }
+};
+
+template< >
+struct resetter< explicit_error_stepper_fsal_tag >
+{
+ template< class Stepper >
+ static void reset( Stepper &stepper )
+ { stepper.reset(); }
+};
+
+
+BOOST_AUTO_TEST_SUITE( numeric_runge_kutta_test )
+
+
+/* generic test for all runge kutta steppers */
+template< class Stepper >
+struct perform_runge_kutta_test
+{
+ void operator()( void )
+ {
+
+ Stepper stepper;
+ const int o = stepper.order()+1; //order of the error is order of approximation + 1
+
+ const state_type x0 = {{ 0.0 , 1.0 }};
+ state_type x1;
+ const double t = 0.0;
+ /* do a first step with dt=0.1 to get an estimate on the prefactor of the error dx = f * dt^(order+1) */
+ double dt = 0.5;
+ stepper.do_step( osc() , x0 , t , x1 , dt );
+ const double f = 2.0 * std::abs( sin(dt) - x1[0] ) / std::pow( dt , o ); // upper bound
+
+ std::cout << o << " , " << f << std::endl;
+
+ /* as long as we have errors above machine precision */
+ while( f*std::pow( dt , o ) > 1E-16 )
+ {
+ // reset stepper which require resetting (fsal steppers)
+ resetter< typename Stepper::stepper_category >::reset( stepper );
+
+ stepper.do_step( osc() , x0 , t , x1 , dt );
+ std::cout << "Testing dt=" << dt << std::endl;
+ BOOST_CHECK_LT( std::abs( sin(dt) - x1[0] ) , f*std::pow( dt , o ) );
+ dt *= 0.5;
+ }
+ }
+};
+
+
+/* generic error test for all runge kutta steppers */
+template< class Stepper >
+struct perform_runge_kutta_error_test
+{
+ void operator()( void )
+ {
+ Stepper stepper;
+ const int o = stepper.error_order()+1; //order of the error is order of approximation + 1
+
+ const state_type x0 = {{ 0.0 , 1.0 }};
+ state_type x1 , x_err;
+ const double t = 0.0;
+ /* do a first step with dt=0.1 to get an estimate on the prefactor of the error dx = f * dt^(order+1) */
+ double dt = 0.5;
+ stepper.do_step( osc() , x0 , t , x1 , dt , x_err );
+ const double f = 2.0 * std::abs( x_err[0] ) / std::pow( dt , o );
+
+ std::cout << o << " , " << f << " , " << x0[0] << std::endl;
+
+ /* as long as we have errors above machine precision */
+ while( f*std::pow( dt , o ) > 1E-16 )
+ {
+ // reset stepper which require resetting (fsal steppers)
+ resetter< typename Stepper::stepper_category >::reset( stepper );
+
+ stepper.do_step( osc() , x0 , t , x1 , dt , x_err );
+ std::cout << "Testing dt=" << dt << ": " << x_err[1] << std::endl;
+ BOOST_CHECK_SMALL( std::abs( x_err[0] ) , f*std::pow( dt , o ) );
+ dt *= 0.5;
+ }
+ }
+};
+
+
+typedef mpl::vector<
+ euler< state_type > ,
+ modified_midpoint< state_type > ,
+ runge_kutta4< state_type > ,
+ runge_kutta4_classic< state_type > ,
+ runge_kutta_cash_karp54_classic< state_type > ,
+ runge_kutta_cash_karp54< state_type > ,
+ runge_kutta_dopri5< state_type > ,
+ runge_kutta_fehlberg78< state_type > ,
+ extrapolation_stepper< 4, state_type > ,
+ extrapolation_stepper< 6, state_type > ,
+ extrapolation_stepper< 8, state_type > ,
+ extrapolation_stepper< 10, state_type >
+ > runge_kutta_steppers;
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( runge_kutta_test , Stepper, runge_kutta_steppers )
+{
+ perform_runge_kutta_test< Stepper > tester;
+ tester();
+}
+
+
+typedef mpl::vector<
+ runge_kutta_cash_karp54_classic< state_type > ,
+ runge_kutta_cash_karp54< state_type > ,
+ runge_kutta_dopri5< state_type > ,
+ runge_kutta_fehlberg78< state_type > ,
+ extrapolation_stepper< 4, state_type > ,
+ extrapolation_stepper< 6, state_type > ,
+ extrapolation_stepper< 8, state_type > ,
+ extrapolation_stepper< 10, state_type >
+ > runge_kutta_error_steppers;
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( runge_kutta_error_test , Stepper, runge_kutta_error_steppers )
+{
+ perform_runge_kutta_error_test< Stepper > tester;
+ tester();
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/numeric/symplectic.cpp b/test/numeric/symplectic.cpp
new file mode 100644
index 0000000..6d3f75b
--- /dev/null
+++ b/test/numeric/symplectic.cpp
@@ -0,0 +1,95 @@
+/* Boost numeric test of the symplectic steppers test file
+
+ Copyright 2012 Mario Mulansky
+ Copyright 2012 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+// disable checked iterator warning for msvc
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE numeric_symplectic
+
+#include <iostream>
+#include <cmath>
+
+#include <boost/array.hpp>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/mpl/vector.hpp>
+
+#include <boost/numeric/odeint.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+namespace mpl = boost::mpl;
+
+typedef double value_type;
+
+typedef boost::array< double ,1 > state_type;
+
+// harmonic oscillator, analytic solution x[0] = sin( t )
+struct osc
+{
+ void operator()( const state_type &q , state_type &dpdt ) const
+ {
+ dpdt[0] = -q[0];
+ }
+};
+
+BOOST_AUTO_TEST_SUITE( numeric_symplectic_test )
+
+
+/* generic test for all symplectic steppers */
+template< class Stepper >
+struct perform_symplectic_test
+{
+ void operator()( void )
+ {
+
+ Stepper stepper;
+ const int o = stepper.order()+1; //order of the error is order of approximation + 1
+
+ const state_type q0 = {{ 0.0 }};
+ const state_type p0 = {{ 1.0 }};
+ state_type q1,p1;
+ std::pair< state_type , state_type >x1( q1 , p1 );
+ const double t = 0.0;
+ /* do a first step with dt=0.1 to get an estimate on the prefactor of the error dx = f * dt^(order+1) */
+ double dt = 0.5;
+ stepper.do_step( osc() , std::make_pair( q0 , p0 ) , t , x1 , dt );
+ const double f = 2.0 * std::abs( sin(dt) - x1.first[0] ) / std::pow( dt , o );
+
+ std::cout << o << " , " << f << std::endl;
+
+ /* as long as we have errors above machine precision */
+ while( f*std::pow( dt , o ) > 1E-16 )
+ {
+ stepper.do_step( osc() , std::make_pair( q0 , p0 ) , t , x1 , dt );
+ std::cout << "Testing dt=" << dt << std::endl;
+ BOOST_CHECK_SMALL( std::abs( sin(dt) - x1.first[0] ) , f*std::pow( dt , o ) );
+ dt *= 0.5;
+ }
+ }
+};
+
+
+typedef mpl::vector<
+ symplectic_euler< state_type > ,
+ symplectic_rkn_sb3a_mclachlan< state_type >
+ > symplectic_steppers;
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( symplectic_test , Stepper, symplectic_steppers )
+{
+ perform_symplectic_test< Stepper > tester;
+ tester();
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/numeric/velocity_verlet.cpp b/test/numeric/velocity_verlet.cpp
new file mode 100644
index 0000000..5ac7780
--- /dev/null
+++ b/test/numeric/velocity_verlet.cpp
@@ -0,0 +1,93 @@
+/* Boost numeric test of the runge kutta steppers test file
+
+ Copyright 2012 Mario Mulansky
+ Copyright 2012 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+// disable checked iterator warning for msvc
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE numeric_runge_kutta
+
+#include <iostream>
+#include <cmath>
+
+#include <boost/array.hpp>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/mpl/vector.hpp>
+
+#include <boost/numeric/odeint.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+namespace mpl = boost::mpl;
+
+typedef double value_type;
+
+typedef boost::array< double , 1 > state_type;
+
+// harmonic oscillator, analytic solution x[0] = sin( t )
+struct osc
+{
+ void operator()( const state_type &x, const state_type &v, state_type &a,
+ const double t ) const
+ {
+ a[0] = -x[0];
+ }
+};
+
+BOOST_AUTO_TEST_SUITE( velocity_verlet_test )
+
+BOOST_AUTO_TEST_CASE( numeric_velocity_verlet_test )
+{
+
+ velocity_verlet<state_type> stepper;
+ const int steps = 10;
+ // order of the error is order of approximation + 1
+ const int o = stepper.order() + 1;
+
+ const state_type x0 = {{ 0.0 }};
+ const state_type v0 = {{ 1.0 }};
+ state_type x = x0;
+ state_type v = v0;
+ const double t = 0.0;
+ /* do a first step with dt=0.1 to get an estimate on the prefactor of the error dx = f * dt^(order+1) */
+ double dt = 0.5;
+ for ( int step = 0; step < steps; ++step )
+ {
+ stepper.do_step(
+ osc(), std::make_pair( boost::ref( x ), boost::ref( v ) ), t, dt );
+ }
+ const double f = steps * std::abs( sin( steps * dt ) - x[0] ) /
+ std::pow( dt, o ); // upper bound
+
+ std::cout << o << " , " << f << std::endl;
+
+ /* as long as we have errors above machine precision */
+ while( f*std::pow( dt , o ) > 1E-16 )
+ {
+ x = x0;
+ v = v0;
+ stepper.reset();
+ for ( int step = 0; step < steps; ++step )
+ {
+ stepper.do_step( osc() , std::make_pair(boost::ref(x), boost::ref(v)) , t , dt );
+ }
+ std::cout << "Testing dt=" << dt << std::endl;
+ BOOST_CHECK_LT( std::abs( sin( steps * dt ) - x[0] ),
+ f * std::pow( dt, o ) );
+ dt *= 0.5;
+ }
+};
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/prepare_stepper_testing.hpp b/test/prepare_stepper_testing.hpp
new file mode 100644
index 0000000..10c0c84
--- /dev/null
+++ b/test/prepare_stepper_testing.hpp
@@ -0,0 +1,74 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/prepare_stepper_testing.hpp
+
+ [begin_description]
+ This file defines some helper functions for the stepper tests.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2012-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#ifndef PREPARE_STEPPER_TESTING_HPP_
+#define PREPARE_STEPPER_TESTING_HPP_
+
+#include <boost/array.hpp>
+#include <vector>
+#include <complex>
+
+#include <boost/fusion/sequence.hpp>
+#include <boost/mpl/vector.hpp>
+#include <boost/multiprecision/cpp_dec_float.hpp>
+
+#include <boost/numeric/odeint/algebra/vector_space_algebra.hpp>
+#include <boost/numeric/odeint/algebra/array_algebra.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+
+namespace mpl = boost::mpl;
+namespace fusion = boost::fusion;
+
+using namespace boost::numeric::odeint;
+
+/* the state types that will be tested */
+typedef std::vector< double > vector_type;
+typedef std::vector< std::complex<double> > complex_vector_type;
+typedef double vector_space_type;
+typedef boost::array< double , 1 > array_type;
+typedef boost::array< std::complex<double> , 1 > complex_array_type;
+
+typedef boost::multiprecision::cpp_dec_float_50 mp_type;
+typedef boost::array< mp_type , 1 > mp_array_type;
+
+typedef mpl::vector< vector_type , complex_vector_type , vector_space_type ,
+ array_type , complex_array_type , mp_type , mp_array_type
+ >::type container_types;
+
+namespace boost { namespace numeric { namespace odeint {
+
+ // mp_type forms a vector space
+ template<>
+ struct algebra_dispatcher< mp_type >
+ {
+ typedef vector_space_algebra algebra_type;
+ };
+
+ // add norm computation
+ template<>
+ struct vector_space_norm_inf< mp_type >
+ {
+ typedef mp_type result_type;
+ mp_type operator()( mp_type x ) const
+ {
+ using std::abs;
+ return abs(x);
+ }
+ };
+
+} } }
+
+#endif /* PREPARE_STEPPER_TESTING_HPP_ */
diff --git a/test/range_algebra.cpp b/test/range_algebra.cpp
new file mode 100644
index 0000000..d80e951
--- /dev/null
+++ b/test/range_algebra.cpp
@@ -0,0 +1,143 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/check_operations.cpp
+
+ [begin_description]
+ This file tests interaction between the algebras and the operations.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#define BOOST_TEST_MODULE odeint_standard_algebra
+
+#include <cmath>
+#include <complex>
+#include <utility>
+#include <functional>
+#include <boost/array.hpp>
+
+#include <boost/test/unit_test.hpp>
+#include <boost/test/floating_point_comparison.hpp>
+
+#include <boost/units/systems/si/length.hpp>
+#include <boost/units/systems/si/time.hpp>
+#include <boost/units/systems/si/velocity.hpp>
+#include <boost/units/systems/si/io.hpp>
+
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+#include <boost/numeric/odeint/algebra/range_algebra.hpp>
+#include <boost/numeric/odeint/algebra/array_algebra.hpp>
+
+#include <boost/mpl/list.hpp>
+
+namespace units = boost::units;
+namespace si = boost::units::si;
+
+using boost::numeric::odeint::default_operations;
+using boost::numeric::odeint::range_algebra;
+using boost::numeric::odeint::array_algebra;
+
+
+BOOST_AUTO_TEST_SUITE( standard_algebra_test )
+
+typedef boost::mpl::list< range_algebra , array_algebra > algebra_types;
+range_algebra algebra;
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( for_each2 , algebra_type , algebra_types )
+{
+ algebra_type algebra;
+ boost::array< double , 2 > x1 = {{ 1.0 , 1.0 }} , x2 = {{ 2.0 , 2.0 }};
+ algebra.for_each2( x1 , x2 , default_operations::scale_sum1<>( 1.0 ) );
+ BOOST_CHECK_CLOSE( x1[0] , 2.0 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( x1[1] , 2.0 , 1.0e-10 );
+}
+
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( for_each3 , algebra_type , algebra_types )
+{
+ algebra_type algebra;
+ boost::array< double , 2 > x1 = {{ 1.0 , 1.0 }} , x2 = {{ 2.0 , 2.0 }} , x3 = {{ 3.0 , 3.0 }};
+ algebra.for_each3( x1 , x2 , x3 , default_operations::scale_sum2<>( 1.0 , 2.0 ) );
+ BOOST_CHECK_CLOSE( x1[0] , 8.0 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( x1[1] , 8.0 , 1.0e-10 );
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( for_each4 , algebra_type , algebra_types )
+{
+ algebra_type algebra;
+ boost::array< double , 2 > x1 = {{ 1.0 , 1.0 }} , x2 = {{ 2.0 , 2.0 }} , x3 = {{ 3.0 , 3.0 }} , x4 = {{ 4.0 , 4.0 }};
+ algebra.for_each4( x1 , x2 , x3 , x4 , default_operations::scale_sum3<>( 1.0 , 2.0 , 3.0 ) );
+ BOOST_CHECK_CLOSE( x1[0] , 20.0 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( x1[1] , 20.0 , 1.0e-10 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( for_each5 , algebra_type , algebra_types )
+{
+ algebra_type algebra;
+ boost::array< double , 2 > x1 = {{ 1.0 , 1.0 }} , x2 = {{ 2.0 , 2.0 }} , x3 = {{ 3.0 , 3.0 }} , x4 = {{ 4.0 , 4.0 }} , x5 = {{ 5.0 , 5.0 }};
+ algebra.for_each5( x1 , x2 , x3 , x4 , x5 , default_operations::scale_sum4<>( 1.0 , 2.0 , 3.0 , 4.0 ) );
+ BOOST_CHECK_CLOSE( x1[0] , 40.0 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( x1[1] , 40.0 , 1.0e-10 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( for_each6 , algebra_type , algebra_types )
+{
+ algebra_type algebra;
+ boost::array< double , 2 > x1 = {{ 1.0 , 1.0 }} , x2 = {{ 2.0 , 2.0 }} , x3 = {{ 3.0 , 3.0 }} , x4 = {{ 4.0 , 4.0 }} , x5 = {{ 5.0 , 5.0 }} , x6 = {{ 6.0 , 6.0 }};
+ algebra.for_each6( x1 , x2 , x3 , x4 , x5 , x6 ,default_operations::scale_sum5<>( 1.0 , 2.0 , 3.0 , 4.0 , 5.0 ) );
+ BOOST_CHECK_CLOSE( x1[0] , 70.0 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( x1[1] , 70.0 , 1.0e-10 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( for_each7 , algebra_type , algebra_types )
+{
+ algebra_type algebra;
+ boost::array< double , 2 > x1 = {{ 1.0 , 1.0 }} , x2 = {{ 2.0 , 2.0 }} , x3 = {{ 3.0 , 3.0 }} , x4 = {{ 4.0 , 4.0 }} , x5 = {{ 5.0 , 5.0 }} , x6 = {{ 6.0 , 6.0 }} , x7 = {{ 7.0 , 7.0 }};
+ algebra.for_each7( x1 , x2 , x3 , x4 , x5 , x6 , x7 , default_operations::scale_sum6<>( 1.0 , 2.0 , 3.0 , 4.0 , 5.0 , 6.0 ) );
+ BOOST_CHECK_CLOSE( x1[0] , 112.0 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( x1[1] , 112.0 , 1.0e-10 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( for_each8 , algebra_type , algebra_types )
+{
+ algebra_type algebra;
+ boost::array< double , 2 > x1 = {{ 1.0 , 1.0 }} , x2 = {{ 2.0 , 2.0 }} , x3 = {{ 3.0 , 3.0 }} , x4 = {{ 4.0 , 4.0 }} , x5 = {{ 5.0 , 5.0 }} , x6 = {{ 6.0 , 6.0 }} , x7 = {{ 7.0 , 7.0 }} , x8 = {{ 8.0 , 8.0 }};
+ algebra.for_each8( x1 , x2 , x3 , x4 , x5 , x6 , x7 , x8 , default_operations::scale_sum7<>( 1.0 , 2.0 , 3.0 , 4.0 , 5.0 , 6.0 , 7.0 ) );
+ BOOST_CHECK_CLOSE( x1[0] , 168.0 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( x1[1] , 168.0 , 1.0e-10 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( norm_inf , algebra_type , algebra_types )
+{
+ algebra_type algebra;
+ boost::array< double , 2 > x = {{ 1.25 , 2.25 }};
+ double nrm = algebra.norm_inf( x );
+ BOOST_CHECK_CLOSE( nrm , 2.25 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( x[0] , 1.25 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( x[1] , 2.25 , 1.0e-10 );
+}
+
+
+BOOST_AUTO_TEST_CASE( for_each2_with_units )
+{
+ range_algebra algebra;
+ typedef units::quantity< si::time , double > time_type;
+ typedef units::quantity< si::length , double > length_type;
+ typedef units::quantity< si::velocity , double > velocity_type;
+ boost::array< length_type , 2 > x1 = {{ 1.0 * si::meter , 1.0 * si::meter }};
+ boost::array< velocity_type , 2 > x2 = {{ 2.0 * si::meter / si::seconds , 2.0 * si::meter / si::seconds }};
+ algebra.for_each2( x1 , x2 , default_operations::scale_sum1< time_type >( 0.1 * si::second ) );
+ BOOST_CHECK_CLOSE( x1[0].value() , 0.2 , 1.0e-10 );
+ BOOST_CHECK_CLOSE( x1[1].value() , 0.2 , 1.0e-10 );
+}
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/regression/Jamfile.v2 b/test/regression/Jamfile.v2
new file mode 100644
index 0000000..bb085f4
--- /dev/null
+++ b/test/regression/Jamfile.v2
@@ -0,0 +1,31 @@
+# Copyright 2012 Karsten Ahnert
+# Copyright 2012 Mario Mulansky
+# Distributed under the Boost Software License, Version 1.0.
+# (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+# bring in rules for testing
+
+
+import testing ;
+
+use-project boost : $(BOOST_ROOT) ;
+
+project
+ : requirements
+ <library>/boost/test//boost_unit_test_framework
+ <define>BOOST_ALL_NO_LIB=1
+ <include>../../include
+ <link>static
+ <toolset>clang:<cxxflags>-Wno-unused-variable
+
+# <cxxflags>-D_SCL_SECURE_NO_WARNINGS
+ ;
+
+test-suite "odeint"
+ :
+ [ run regression_147.cpp ]
+ [ compile regression_149.cpp ]
+ [ run regression_168.cpp ]
+ [ run regression_189.cpp ]
+ : <testing.launcher>valgrind
+ ;
diff --git a/test/regression/regression_147.cpp b/test/regression/regression_147.cpp
new file mode 100644
index 0000000..7373782
--- /dev/null
+++ b/test/regression/regression_147.cpp
@@ -0,0 +1,88 @@
+/*
+
+ [begin_description]
+ Test case for issue 147
+ [end_description]
+
+ Copyright 2011-2015 Karsten Ahnert
+ Copyright 2011-2015 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+// disable checked iterator warning for msvc
+
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_regression_147
+
+#include <utility>
+
+#include <boost/array.hpp>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/mpl/vector.hpp>
+
+#include <boost/numeric/odeint.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+namespace mpl = boost::mpl;
+
+typedef double state_type;
+
+void rhs( const state_type &x , state_type &dxdt , const double t )
+{
+ dxdt = 1;
+}
+
+
+template<class Stepper, class InitStepper>
+struct perform_init_test
+{
+ void operator()( void )
+ {
+ double t = 0;
+ const double dt = 0.1;
+
+ state_type x = 0;
+
+ Stepper stepper;
+ InitStepper init_stepper;
+ stepper.initialize( init_stepper, rhs, x, t, dt );
+
+ // ab-stepper needs order-1 init steps: t and x should be (order-1)*dt
+ BOOST_CHECK_CLOSE( t , (stepper.order()-1)*dt , 1E-16 );
+ BOOST_CHECK_CLOSE( x, ( stepper.order() - 1 ) * dt, 2E-14 );
+ }
+};
+
+typedef mpl::vector<
+ euler< state_type > ,
+ modified_midpoint< state_type > ,
+ runge_kutta4< state_type > ,
+ runge_kutta4_classic< state_type > ,
+ runge_kutta_cash_karp54_classic< state_type > ,
+ runge_kutta_cash_karp54< state_type > ,
+ runge_kutta_dopri5< state_type > ,
+ runge_kutta_fehlberg78< state_type >
+ > runge_kutta_steppers;
+
+
+BOOST_AUTO_TEST_SUITE( regression_147_test )
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( init_test , InitStepper,
+ runge_kutta_steppers )
+{
+ perform_init_test< adams_bashforth<4, state_type>, InitStepper > tester;
+ tester();
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/regression/regression_149.cpp b/test/regression/regression_149.cpp
new file mode 100644
index 0000000..2790d68
--- /dev/null
+++ b/test/regression/regression_149.cpp
@@ -0,0 +1,93 @@
+/*
+
+ [begin_description]
+ Test case for issue 149:
+ Error C2582 with msvc-10 when using iterator-based integration
+ [end_description]
+
+ Copyright 2011-2015 Karsten Ahnert
+ Copyright 2011-2015 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+// disable checked iterator warning for msvc
+
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_regression_147
+
+#include <utility>
+#include <iostream>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/mpl/vector.hpp>
+#include <boost/range/algorithm/find_if.hpp>
+
+#include <boost/numeric/odeint.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+namespace mpl = boost::mpl;
+
+typedef std::vector<double> state_type;
+
+void rhs( const state_type &x , state_type &dxdt , const double t )
+{
+}
+
+
+template<class Stepper>
+struct perform_test
+{
+ void operator()( void )
+ {
+ bulirsch_stoer< state_type > stepper( 1e-9, 0.0, 0.0, 0.0 );
+ state_type x( 3, 10.0 );
+
+ print( boost::find_if(
+ make_adaptive_time_range( stepper, rhs, x, 0.0, 1.0, 0.01 ),
+ pred ) );
+
+ }
+
+ static bool pred( const std::pair< const state_type &, double > &x )
+ {
+ return ( x.first[0] < 0.0 );
+ }
+
+ template<class Iterator>
+ void print( Iterator iter )
+ {
+ std::cout << iter->second << "\t" << iter->first[0] << "\t"
+ << iter->first[1] << "\t" << iter->first[2] << "\n";
+ }
+};
+
+typedef mpl::vector<
+ euler< state_type > ,
+ runge_kutta4< state_type > ,
+ runge_kutta_cash_karp54< state_type > ,
+ runge_kutta_dopri5< state_type > ,
+ runge_kutta_fehlberg78< state_type > ,
+ bulirsch_stoer< state_type >
+ > steppers;
+
+
+BOOST_AUTO_TEST_SUITE( regression_147_test )
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( regression_147_test , Stepper,
+ steppers )
+{
+ perform_test< Stepper > tester;
+ tester();
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/regression/regression_168.cpp b/test/regression/regression_168.cpp
new file mode 100644
index 0000000..8349261
--- /dev/null
+++ b/test/regression/regression_168.cpp
@@ -0,0 +1,90 @@
+/*
+
+ [begin_description]
+ Test case for issue 149:
+ Error C2582 with msvc-10 when using iterator-based integration
+ [end_description]
+
+ Copyright 2011-2015 Karsten Ahnert
+ Copyright 2011-2015 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+// disable checked iterator warning for msvc
+
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_regression_147
+
+#include <utility>
+#include <iostream>
+
+#include <boost/array.hpp>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/mpl/vector.hpp>
+#include <boost/range/algorithm/find_if.hpp>
+
+#include <boost/numeric/odeint.hpp>
+#include <boost/numeric/odeint/algebra/fusion_algebra.hpp>
+#include <boost/numeric/odeint/algebra/fusion_algebra_dispatcher.hpp>
+
+
+#include <boost/units/systems/si/length.hpp>
+#include <boost/units/systems/si/time.hpp>
+#include <boost/units/systems/si/velocity.hpp>
+#include <boost/units/systems/si/acceleration.hpp>
+#include <boost/units/systems/si/io.hpp>
+
+#include <boost/fusion/container.hpp>
+
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+namespace mpl = boost::mpl;
+
+namespace fusion = boost::fusion;
+namespace units = boost::units;
+namespace si = boost::units::si;
+
+typedef units::quantity< si::time , double > time_type;
+typedef units::quantity< si::length , double > length_type;
+typedef units::quantity< si::velocity , double > velocity_type;
+typedef units::quantity< si::acceleration , double > acceleration_type;
+typedef units::quantity< si::frequency , double > frequency_type;
+
+typedef fusion::vector< length_type , velocity_type > state_type;
+typedef fusion::vector< velocity_type , acceleration_type > deriv_type;
+
+
+struct oscillator
+{
+ frequency_type m_omega;
+
+ oscillator( const frequency_type &omega = 1.0 * si::hertz ) : m_omega( omega ) { }
+
+ void operator()( const state_type &x , deriv_type &dxdt , time_type t ) const
+ {
+ fusion::at_c< 0 >( dxdt ) = fusion::at_c< 1 >( x );
+ fusion::at_c< 1 >( dxdt ) = - m_omega * m_omega * fusion::at_c< 0 >( x );
+ }
+};
+
+
+BOOST_AUTO_TEST_CASE( regression_168 )
+{
+ typedef runge_kutta_dopri5< state_type , double , deriv_type , time_type > stepper_type;
+
+ state_type x( 1.0 * si::meter , 0.0 * si::meter_per_second );
+
+ integrate_const( make_dense_output( 1.0e-6 , 1.0e-6 , stepper_type() ) , oscillator( 2.0 * si::hertz ) ,
+ x , 0.0 * si::second , 100.0 * si::second , 0.1 * si::second);
+}
\ No newline at end of file
diff --git a/test/regression/regression_189.cpp b/test/regression/regression_189.cpp
new file mode 100644
index 0000000..5453007
--- /dev/null
+++ b/test/regression/regression_189.cpp
@@ -0,0 +1,72 @@
+/*
+
+ [begin_description]
+ Test case for issue 189:
+ Controlled Rosenbrock stepper fails to increase step size
+ [end_description]
+
+ Copyright 2016 Karsten Ahnert
+ Copyright 2016 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#define BOOST_TEST_MODULE odeint_regression_189
+
+#include <boost/numeric/odeint.hpp>
+
+#include <boost/test/unit_test.hpp>
+#include <boost/phoenix/core.hpp>
+#include <boost/phoenix/operator.hpp>
+
+using namespace boost::numeric::odeint;
+namespace phoenix = boost::phoenix;
+
+typedef boost::numeric::ublas::vector< double > vector_type;
+typedef boost::numeric::ublas::matrix< double > matrix_type;
+
+struct stiff_system
+{
+ void operator()( const vector_type &x , vector_type &dxdt , double /* t */ )
+ {
+ dxdt[ 0 ] = -101.0 * x[ 0 ] - 100.0 * x[ 1 ];
+ dxdt[ 1 ] = x[ 0 ];
+ }
+};
+
+struct stiff_system_jacobi
+{
+ void operator()( const vector_type & /* x */ , matrix_type &J , const double & /* t */ , vector_type &dfdt )
+ {
+ J( 0 , 0 ) = -101.0;
+ J( 0 , 1 ) = -100.0;
+ J( 1 , 0 ) = 1.0;
+ J( 1 , 1 ) = 0.0;
+ dfdt[0] = 0.0;
+ dfdt[1] = 0.0;
+ }
+};
+
+
+BOOST_AUTO_TEST_CASE( regression_189 )
+{
+ vector_type x( 2 , 1.0 );
+
+ size_t num_of_steps = integrate_const( make_dense_output< rosenbrock4< double > >( 1.0e-6 , 1.0e-6 ) ,
+ std::make_pair( stiff_system() , stiff_system_jacobi() ) ,
+ x , 0.0 , 50.0 , 0.01 ,
+ std::cout << phoenix::arg_names::arg2 << " " << phoenix::arg_names::arg1[0] << "\n" );
+ // regression: number of steps should be 74
+ size_t num_of_steps_expected = 74;
+ BOOST_CHECK_EQUAL( num_of_steps , num_of_steps_expected );
+
+ vector_type x2( 2 , 1.0 );
+
+ size_t num_of_steps2 = integrate_const( make_dense_output< runge_kutta_dopri5< vector_type > >( 1.0e-6 , 1.0e-6 ) ,
+ stiff_system() , x2 , 0.0 , 50.0 , 0.01 ,
+ std::cout << phoenix::arg_names::arg2 << " " << phoenix::arg_names::arg1[0] << "\n" );
+ num_of_steps_expected = 1531;
+ BOOST_CHECK_EQUAL( num_of_steps2 , num_of_steps_expected );
+}
diff --git a/test/resize.cpp b/test/resize.cpp
new file mode 100644
index 0000000..db40f4b
--- /dev/null
+++ b/test/resize.cpp
@@ -0,0 +1,98 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/resize.cpp
+
+ [begin_description]
+ This file tests the resize function of odeint.
+ [end_description]
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+// disable checked iterator warning for msvc
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_resize
+
+#include <vector>
+#include <cmath>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/numeric/odeint/util/resize.hpp>
+#include <boost/fusion/include/vector.hpp>
+#include <boost/fusion/include/at.hpp>
+#include <boost/units/systems/si/length.hpp>
+#include <boost/units/systems/si/time.hpp>
+#include <boost/units/systems/si/velocity.hpp>
+#include <boost/units/systems/si/acceleration.hpp>
+#include <boost/units/systems/si/io.hpp>
+
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+BOOST_AUTO_TEST_CASE( test_vector )
+{
+ std::vector< double > x1( 10 );
+ std::vector< double > x2;
+ resize( x2 , x1 );
+ BOOST_CHECK( x2.size() == 10 );
+}
+
+
+BOOST_AUTO_TEST_CASE( test_fusion_vector_of_vector )
+{
+ typedef boost::fusion::vector< std::vector< double > , std::vector< double > > state_type;
+ state_type x1;
+ boost::fusion::at_c< 0 >( x1 ).resize( 10 );
+ boost::fusion::at_c< 1 >( x1 ).resize( 10 );
+ state_type x2;
+ resize( x2 , x1 );
+ BOOST_CHECK( boost::fusion::at_c< 0 >( x2 ).size() == 10 );
+ BOOST_CHECK( boost::fusion::at_c< 1 >( x2 ).size() == 10 );
+}
+
+
+BOOST_AUTO_TEST_CASE( test_fusion_vector_mixed1 )
+{
+ typedef boost::fusion::vector< std::vector< double > , double > state_type;
+ state_type x1;
+ boost::fusion::at_c< 0 >( x1 ).resize( 10 );
+ state_type x2;
+ resize( x2 , x1 );
+ BOOST_CHECK( boost::fusion::at_c< 0 >( x2 ).size() == 10 );
+}
+
+BOOST_AUTO_TEST_CASE( test_fusion_vector_mixed2 )
+{
+ typedef boost::fusion::vector< double , std::vector< double > , double > state_type;
+ state_type x1;
+ boost::fusion::at_c< 1 >( x1 ).resize( 10 );
+ state_type x2;
+ resize( x2 , x1 );
+ BOOST_CHECK( boost::fusion::at_c< 1 >( x2 ).size() == 10 );
+}
+
+BOOST_AUTO_TEST_CASE( test_fusion_quantity_sequence )
+{
+ namespace units = boost::units;
+ namespace si = boost::units::si;
+
+ typedef double value_type;
+ typedef units::quantity< si::time , value_type > time_type;
+ typedef units::quantity< si::length , value_type > length_type;
+ typedef units::quantity< si::velocity , value_type > velocity_type;
+ typedef boost::fusion::vector< length_type , velocity_type > state_type;
+
+ state_type x1 , x2;
+ resize( x2 , x1 );
+}
diff --git a/test/resizing.cpp b/test/resizing.cpp
new file mode 100644
index 0000000..7517951
--- /dev/null
+++ b/test/resizing.cpp
@@ -0,0 +1,110 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/resizing.cpp
+
+ [begin_description]
+ This file tests the resizing mechanism of odeint.
+ [end_description]
+
+ Copyright 2010-2012 Karsten Ahnert
+ Copyright 2010-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+// disable checked iterator warning for msvc
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_resize
+
+#include <vector>
+#include <cmath>
+
+#include <boost/array.hpp>
+#include <boost/bind.hpp>
+#include <boost/utility.hpp>
+#include <boost/type_traits/integral_constant.hpp>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/mpl/vector.hpp>
+#include <boost/mpl/int.hpp>
+#include <boost/mpl/at.hpp>
+
+#include <boost/numeric/odeint/stepper/euler.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta4_classic.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta4.hpp>
+#include <boost/numeric/odeint/algebra/vector_space_algebra.hpp>
+
+#include <boost/numeric/odeint/util/resizer.hpp>
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+
+#include "resizing_test_state_type.hpp"
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+namespace mpl = boost::mpl;
+
+
+
+
+
+
+void constant_system( const test_array_type &x , test_array_type &dxdt , double t ) { dxdt[0] = 1.0; }
+
+
+BOOST_AUTO_TEST_SUITE( check_resize_test )
+
+
+typedef euler< test_array_type , double , test_array_type , double , range_algebra , default_operations , never_resizer > euler_manual_type;
+typedef euler< test_array_type , double , test_array_type , double , range_algebra , default_operations , initially_resizer > euler_initially_type;
+typedef euler< test_array_type , double , test_array_type , double , range_algebra , default_operations , always_resizer > euler_always_type;
+
+typedef runge_kutta4_classic< test_array_type , double , test_array_type , double , range_algebra , default_operations , never_resizer > rk4_manual_type;
+typedef runge_kutta4_classic< test_array_type , double , test_array_type , double , range_algebra , default_operations , initially_resizer > rk4_initially_type;
+typedef runge_kutta4_classic< test_array_type , double , test_array_type , double , range_algebra , default_operations , always_resizer > rk4_always_type;
+
+
+typedef runge_kutta4< test_array_type , double , test_array_type , double , range_algebra , default_operations , never_resizer > rk4_gen_manual_type;
+typedef runge_kutta4< test_array_type , double , test_array_type , double , range_algebra , default_operations , initially_resizer > rk4_gen_initially_type;
+typedef runge_kutta4< test_array_type , double , test_array_type , double , range_algebra , default_operations , always_resizer > rk4_gen_always_type;
+
+
+typedef mpl::vector<
+ mpl::vector< euler_manual_type , mpl::int_<1> , mpl::int_<0> > ,
+ mpl::vector< euler_initially_type , mpl::int_<1> , mpl::int_<1> > ,
+ mpl::vector< euler_always_type , mpl::int_<1> , mpl::int_<3> > ,
+ mpl::vector< rk4_manual_type , mpl::int_<5> , mpl::int_<0> > ,
+ mpl::vector< rk4_initially_type , mpl::int_<5> , mpl::int_<1> > ,
+ mpl::vector< rk4_always_type , mpl::int_<5> , mpl::int_<3> > ,
+ mpl::vector< rk4_gen_manual_type , mpl::int_<5> , mpl::int_<0> > ,
+ mpl::vector< rk4_gen_initially_type , mpl::int_<5> , mpl::int_<1> > ,
+ mpl::vector< rk4_gen_always_type , mpl::int_<5> , mpl::int_<3> >
+ >::type resize_check_types;
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( test_resize , T, resize_check_types )
+{
+ typedef typename mpl::at< T , mpl::int_< 0 > >::type stepper_type;
+ const size_t resize_calls = mpl::at< T , mpl::int_< 1 > >::type::value;
+ const size_t multiplicity = mpl::at< T , mpl::int_< 2 > >::type::value;
+ adjust_size_count = 0;
+
+ stepper_type stepper;
+ test_array_type x;
+ stepper.do_step( constant_system , x , 0.0 , 0.1 );
+ stepper.do_step( constant_system , x , 0.0 , 0.1 );
+ stepper.do_step( constant_system , x , 0.0 , 0.1 );
+
+ BOOST_TEST_MESSAGE( "adjust_size_count : " << adjust_size_count );
+ BOOST_CHECK_MESSAGE( adjust_size_count == resize_calls * multiplicity , "adjust_size_count : " << adjust_size_count << " expected: " << resize_calls * multiplicity );
+}
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/resizing_test_state_type.hpp b/test/resizing_test_state_type.hpp
new file mode 100644
index 0000000..af55937
--- /dev/null
+++ b/test/resizing_test_state_type.hpp
@@ -0,0 +1,69 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/resizing_test_state_type.hpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2009-2012 Karsten Ahnert
+ Copyright 2009-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+
+#ifndef LIBS_NUMERIC_ODEINT_TEST_RESIZING_TEST_STATE_TYPE_HPP_DEFINED
+#define LIBS_NUMERIC_ODEINT_TEST_RESIZING_TEST_STATE_TYPE_HPP_DEFINED
+
+#include <boost/numeric/odeint/util/is_resizeable.hpp>
+#include <boost/numeric/odeint/util/resize.hpp>
+#include <boost/numeric/odeint/util/same_size.hpp>
+
+#include <boost/array.hpp>
+
+
+
+// Mario: velocity verlet tests need arrays of size 2
+// some ugly detailed dependency, maybe this can be improved?
+class test_array_type : public boost::array< double , 2 > { };
+
+size_t adjust_size_count;
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+ template<>
+ struct is_resizeable< test_array_type >
+ {
+ typedef boost::true_type type;
+ const static bool value = type::value;
+ };
+
+ template<>
+ struct same_size_impl< test_array_type , test_array_type >
+ {
+ static bool same_size( const test_array_type &x1 , const test_array_type &x2 )
+ {
+ return false;
+ }
+ };
+
+ template<>
+ struct resize_impl< test_array_type , test_array_type >
+ {
+ static void resize( test_array_type &x1 , const test_array_type &x2 )
+ {
+ adjust_size_count++;
+ }
+ };
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // LIBS_NUMERIC_ODEINT_TEST_RESIZING_TEST_STATE_TYPE_HPP_DEFINED
diff --git a/test/rosenbrock4.cpp b/test/rosenbrock4.cpp
new file mode 100644
index 0000000..f0b79d5
--- /dev/null
+++ b/test/rosenbrock4.cpp
@@ -0,0 +1,140 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/rosenbrock4.cpp
+
+ [begin_description]
+ This file tests the Rosenbrock 4 stepper and its controller and dense output stepper.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+// disable checked iterator warning for msvc
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_rosenbrock4
+
+#include <utility>
+#include <iostream>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/numeric/odeint/stepper/rosenbrock4.hpp>
+#include <boost/numeric/odeint/stepper/rosenbrock4_controller.hpp>
+#include <boost/numeric/odeint/stepper/rosenbrock4_dense_output.hpp>
+
+#include <boost/numeric/ublas/vector.hpp>
+#include <boost/numeric/ublas/matrix.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+typedef double value_type;
+typedef boost::numeric::ublas::vector< value_type > state_type;
+typedef boost::numeric::ublas::matrix< value_type > matrix_type;
+
+
+struct sys
+{
+ void operator()( const state_type &x , state_type &dxdt , const value_type &t ) const
+ {
+ dxdt( 0 ) = x( 0 ) + 2 * x( 1 );
+ dxdt( 1 ) = x( 1 );
+ }
+};
+
+struct jacobi
+{
+ void operator()( const state_type &x , matrix_type &jacobi , const value_type &t , state_type &dfdt ) const
+ {
+ jacobi( 0 , 0 ) = 1;
+ jacobi( 0 , 1 ) = 2;
+ jacobi( 1 , 0 ) = 0;
+ jacobi( 1 , 1 ) = 1;
+ dfdt( 0 ) = 0.0;
+ dfdt( 1 ) = 0.0;
+ }
+};
+
+BOOST_AUTO_TEST_SUITE( rosenbrock4_test )
+
+BOOST_AUTO_TEST_CASE( test_rosenbrock4_stepper )
+{
+ typedef rosenbrock4< value_type > stepper_type;
+ stepper_type stepper;
+
+ typedef stepper_type::state_type state_type;
+ typedef stepper_type::value_type stepper_value_type;
+ typedef stepper_type::deriv_type deriv_type;
+ typedef stepper_type::time_type time_type;
+
+ state_type x( 2 ) , xerr( 2 );
+ x(0) = 0.0; x(1) = 1.0;
+
+ stepper.do_step( std::make_pair( sys() , jacobi() ) , x , 0.0 , 0.1 , xerr );
+
+ stepper.do_step( std::make_pair( sys() , jacobi() ) , x , 0.0 , 0.1 );
+
+// using std::abs;
+// value_type eps = 1E-12;
+//
+// // compare with analytic solution of above system
+// BOOST_CHECK_SMALL( abs( x(0) - 20.0/81.0 ) , eps );
+// BOOST_CHECK_SMALL( abs( x(1) - 10.0/9.0 ) , eps );
+
+}
+
+BOOST_AUTO_TEST_CASE( test_rosenbrock4_controller )
+{
+ typedef rosenbrock4_controller< rosenbrock4< value_type > > stepper_type;
+ stepper_type stepper;
+
+ typedef stepper_type::state_type state_type;
+ typedef stepper_type::value_type stepper_value_type;
+ typedef stepper_type::deriv_type deriv_type;
+ typedef stepper_type::time_type time_type;
+
+ state_type x( 2 );
+ x( 0 ) = 0.0 ; x(1) = 1.0;
+
+ value_type t = 0.0 , dt = 0.01;
+ stepper.try_step( std::make_pair( sys() , jacobi() ) , x , t , dt );
+}
+
+BOOST_AUTO_TEST_CASE( test_rosenbrock4_dense_output )
+{
+ typedef rosenbrock4_dense_output< rosenbrock4_controller< rosenbrock4< value_type > > > stepper_type;
+ typedef rosenbrock4_controller< rosenbrock4< value_type > > controlled_stepper_type;
+ controlled_stepper_type c_stepper;
+ stepper_type stepper( c_stepper );
+
+ typedef stepper_type::state_type state_type;
+ typedef stepper_type::value_type stepper_value_type;
+ typedef stepper_type::deriv_type deriv_type;
+ typedef stepper_type::time_type time_type;
+ state_type x( 2 );
+ x( 0 ) = 0.0 ; x(1) = 1.0;
+ stepper.initialize( x , 0.0 , 0.1 );
+ std::pair< value_type , value_type > tr = stepper.do_step( std::make_pair( sys() , jacobi() ) );
+ stepper.calc_state( 0.5 * ( tr.first + tr.second ) , x );
+}
+
+BOOST_AUTO_TEST_CASE( test_rosenbrock4_copy_dense_output )
+{
+ typedef rosenbrock4_controller< rosenbrock4< value_type > > controlled_stepper_type;
+ typedef rosenbrock4_dense_output< controlled_stepper_type > stepper_type;
+
+ controlled_stepper_type c_stepper;
+ stepper_type stepper( c_stepper );
+ stepper_type stepper2( stepper );
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/rosenbrock4_mp.cpp b/test/rosenbrock4_mp.cpp
new file mode 100644
index 0000000..dc295c4
--- /dev/null
+++ b/test/rosenbrock4_mp.cpp
@@ -0,0 +1,143 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/rosenbrock4.cpp
+
+ [begin_description]
+ This file tests the Rosenbrock 4 stepper and its controller and dense output stepper.
+ [end_description]
+
+ Copyright 2009-2012 Karsten Ahnert
+ Copyright 2009-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+// disable checked iterator warning for msvc
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_rosenbrock4
+
+#include <utility>
+#include <iostream>
+
+#include <boost/test/unit_test.hpp>
+#include <boost/multiprecision/cpp_dec_float.hpp>
+
+#include <boost/numeric/odeint/stepper/rosenbrock4.hpp>
+#include <boost/numeric/odeint/stepper/rosenbrock4_controller.hpp>
+#include <boost/numeric/odeint/stepper/rosenbrock4_dense_output.hpp>
+
+#include <boost/numeric/ublas/vector.hpp>
+#include <boost/numeric/ublas/matrix.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+typedef boost::multiprecision::cpp_dec_float_50 value_type;
+typedef boost::numeric::ublas::vector< value_type > state_type;
+typedef boost::numeric::ublas::matrix< value_type > matrix_type;
+
+
+struct sys
+{
+ void operator()( const state_type &x , state_type &dxdt , const value_type &t ) const
+ {
+ dxdt( 0 ) = x( 0 ) + 2 * x( 1 );
+ dxdt( 1 ) = x( 1 );
+ }
+};
+
+struct jacobi
+{
+ void operator()( const state_type &x , matrix_type &jacobi , const value_type &t , state_type &dfdt ) const
+ {
+ jacobi( 0 , 0 ) = 1;
+ jacobi( 0 , 1 ) = 2;
+ jacobi( 1 , 0 ) = 0;
+ jacobi( 1 , 1 ) = 1;
+ dfdt( 0 ) = 0.0;
+ dfdt( 1 ) = 0.0;
+ }
+};
+
+BOOST_AUTO_TEST_SUITE( rosenbrock4_test )
+
+BOOST_AUTO_TEST_CASE( test_rosenbrock4_stepper )
+{
+ typedef rosenbrock4< value_type > stepper_type;
+ stepper_type stepper;
+
+ typedef stepper_type::state_type state_type;
+ typedef stepper_type::value_type stepper_value_type;
+ typedef stepper_type::deriv_type deriv_type;
+ typedef stepper_type::time_type time_type;
+
+ state_type x( 2 ) , xerr( 2 );
+ x(0) = 0.0; x(1) = 1.0;
+
+ stepper.do_step( std::make_pair( sys() , jacobi() ) , x ,
+ static_cast<value_type>(0.0) , static_cast<value_type>(0.1) , xerr );
+
+ stepper.do_step( std::make_pair( sys() , jacobi() ) , x ,
+ static_cast<value_type>(0.0) , static_cast<value_type>(0.1) );
+
+// using std::abs;
+// value_type eps = 1E-12;
+//
+// // compare with analytic solution of above system
+// BOOST_CHECK_SMALL( abs( x(0) - 20.0/81.0 ) , eps );
+// BOOST_CHECK_SMALL( abs( x(1) - 10.0/9.0 ) , eps );
+
+}
+
+BOOST_AUTO_TEST_CASE( test_rosenbrock4_controller )
+{
+ typedef rosenbrock4_controller< rosenbrock4< value_type > > stepper_type;
+ stepper_type stepper;
+
+ typedef stepper_type::state_type state_type;
+ typedef stepper_type::value_type stepper_value_type;
+ typedef stepper_type::deriv_type deriv_type;
+ typedef stepper_type::time_type time_type;
+
+ state_type x( 2 );
+ x( 0 ) = 0.0 ; x(1) = 1.0;
+
+ value_type t = 0.0 , dt = 0.01;
+ stepper.try_step( std::make_pair( sys() , jacobi() ) , x , t , dt );
+}
+
+BOOST_AUTO_TEST_CASE( test_rosenbrock4_dense_output )
+{
+ typedef rosenbrock4_dense_output< rosenbrock4_controller< rosenbrock4< value_type > > > stepper_type;
+ typedef rosenbrock4_controller< rosenbrock4< value_type > > controlled_stepper_type;
+ controlled_stepper_type c_stepper;
+ stepper_type stepper( c_stepper );
+
+ typedef stepper_type::state_type state_type;
+ typedef stepper_type::value_type stepper_value_type;
+ typedef stepper_type::deriv_type deriv_type;
+ typedef stepper_type::time_type time_type;
+ state_type x( 2 );
+ x( 0 ) = 0.0 ; x(1) = 1.0;
+ stepper.initialize( x , 0.0 , 0.1 );
+ std::pair< value_type , value_type > tr = stepper.do_step( std::make_pair( sys() , jacobi() ) );
+ stepper.calc_state( 0.5 * ( tr.first + tr.second ) , x );
+}
+
+BOOST_AUTO_TEST_CASE( test_rosenbrock4_copy_dense_output )
+{
+ typedef rosenbrock4_controller< rosenbrock4< value_type > > controlled_stepper_type;
+ typedef rosenbrock4_dense_output< controlled_stepper_type > stepper_type;
+
+ controlled_stepper_type c_stepper;
+ stepper_type stepper( c_stepper );
+ stepper_type stepper2( stepper );
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/runge_kutta_concepts.cpp b/test/runge_kutta_concepts.cpp
new file mode 100644
index 0000000..42235de
--- /dev/null
+++ b/test/runge_kutta_concepts.cpp
@@ -0,0 +1,217 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/runge_kutta_concepts.cpp
+
+ [begin_description]
+ This file tests the Stepper concepts of odeint with all Runge-Kutta steppers. It's one of the main tests
+ of odeint.
+ [end_description]
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+// disable checked iterator warning for msvc
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_runge_kutta_concepts
+
+#include <vector>
+#include <cmath>
+#include <iostream>
+
+#include <boost/numeric/odeint/config.hpp>
+
+#include <boost/array.hpp>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/ref.hpp>
+#include <boost/bind.hpp>
+#include <boost/utility.hpp>
+#include <boost/type_traits/add_reference.hpp>
+
+#include <boost/mpl/vector.hpp>
+#include <boost/mpl/for_each.hpp>
+#include <boost/mpl/insert_range.hpp>
+#include <boost/mpl/end.hpp>
+#include <boost/mpl/copy.hpp>
+#include <boost/mpl/placeholders.hpp>
+#include <boost/mpl/inserter.hpp>
+
+#include <boost/numeric/odeint/stepper/euler.hpp>
+#include <boost/numeric/odeint/stepper/modified_midpoint.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta4_classic.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta4.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54_classic.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_fehlberg78.hpp>
+
+#include <boost/numeric/odeint/algebra/detail/extract_value_type.hpp>
+
+#include "prepare_stepper_testing.hpp"
+#include "dummy_odes.hpp"
+
+using std::vector;
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+namespace mpl = boost::mpl;
+
+const double result = 2.2;
+
+const double eps = 1.0e-14;
+
+template< class Stepper , class System >
+void check_stepper_concept( Stepper &stepper , System system , typename Stepper::state_type &x )
+{
+ typedef Stepper stepper_type;
+ typedef typename stepper_type::deriv_type container_type;
+ typedef typename stepper_type::order_type order_type;
+ typedef typename stepper_type::time_type time_type;
+
+ stepper.do_step( system , x , static_cast<time_type>(0.0) , static_cast<time_type>(0.1) );
+}
+
+// default case is used for vector space types like plain double
+template< class Stepper , typename T >
+struct perform_stepper_test
+{
+ typedef T vector_space_type;
+ void operator()( void ) const
+ {
+ using std::abs;
+ vector_space_type x;
+ x = 2.0;
+ Stepper stepper;
+ constant_system_functor_vector_space sys;
+#ifndef _MSC_VER
+ // dont run this for MSVC due to compiler bug 697006
+ check_stepper_concept( stepper , constant_system_vector_space< vector_space_type , vector_space_type , typename Stepper::time_type > , x );
+#else
+ check_stepper_concept( stepper , boost::cref( sys ) , x );
+#endif
+ check_stepper_concept( stepper , boost::cref( sys ) , x );
+ std::cout << x << " ?= " << result << std::endl;
+ BOOST_CHECK( (abs( x - result )) < eps );
+ }
+};
+
+template< class Stepper , typename T >
+struct perform_stepper_test< Stepper , std::vector<T> >
+{
+ typedef std::vector<T> vector_type;
+ void operator()( void )
+ {
+ using std::abs;
+ vector_type x( 1 , static_cast<T>(2.0) );
+ Stepper stepper;
+ constant_system_functor_standard sys;
+#ifndef _MSC_VER
+ // dont run this for MSVC due to compiler bug 697006
+ check_stepper_concept( stepper , constant_system_standard< vector_type , vector_type , typename Stepper::time_type > , x );
+#else
+ check_stepper_concept( stepper , boost::cref( sys ) , x );
+#endif
+ check_stepper_concept( stepper , boost::cref( sys ) , x );
+ std::cout << x[0] << " ?= " << result << std::endl;
+ BOOST_CHECK( (abs( x[0] - result )) < eps );
+ }
+};
+
+template< class Stepper , typename T >
+struct perform_stepper_test< Stepper , boost::array<T,1> >
+{
+ typedef boost::array<T,1> array_type;
+ void operator()( void )
+ {
+ using std::abs;
+ array_type x;
+ x[0] = static_cast<T>(2.0);
+ Stepper stepper;
+ constant_system_functor_standard sys;
+#ifndef _MSC_VER
+ // dont run this for MSVC due to compiler bug 697006
+ check_stepper_concept( stepper , constant_system_standard< array_type , array_type , typename Stepper::time_type > , x );
+#else
+ check_stepper_concept( stepper , boost::cref( sys ) , x );
+#endif
+ check_stepper_concept( stepper , boost::cref( sys ) , x );
+ std::cout << x[0] << " ?= " << result << std::endl;
+ BOOST_CHECK( (abs( x[0] - result )) < eps );
+ }
+};
+
+// split stepper methods to ensure the final vector has less than 30(?) elements
+// (stepper_methods*container_types) < 30(?)
+template< class State > class stepper_methods1 : public mpl::vector<
+ euler< State , typename detail::extract_value_type<State>::type > ,
+ modified_midpoint< State , typename detail::extract_value_type<State>::type > ,
+ runge_kutta4< State , typename detail::extract_value_type<State>::type > ,
+ runge_kutta4_classic< State , typename detail::extract_value_type<State>::type >
+ > { };
+
+template< class State > class stepper_methods2 : public mpl::vector<
+ runge_kutta_cash_karp54_classic< State , typename detail::extract_value_type<State>::type > ,
+ runge_kutta_cash_karp54< State , typename detail::extract_value_type<State>::type > ,
+ runge_kutta_dopri5< State , typename detail::extract_value_type<State>::type > ,
+ runge_kutta_fehlberg78< State , typename detail::extract_value_type<State>::type >
+ > { };
+
+
+
+typedef mpl::copy
+<
+ container_types ,
+ mpl::inserter
+ <
+ mpl::vector0<> ,
+ mpl::insert_range
+ <
+ mpl::_1 ,
+ mpl::end< mpl::_1 > ,
+ stepper_methods1< mpl::_2 >
+ >
+ >
+>::type stepper_combinations1;
+
+typedef mpl::copy
+<
+ container_types ,
+ mpl::inserter
+ <
+ mpl::vector0<> ,
+ mpl::insert_range
+ <
+ mpl::_1 ,
+ mpl::end< mpl::_1 > ,
+ stepper_methods2< mpl::_2 >
+ >
+ >
+>::type stepper_combinations2;
+
+
+BOOST_AUTO_TEST_SUITE( runge_kutta_concept_test )
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_test1 , Stepper, stepper_combinations1 )
+{
+ perform_stepper_test< Stepper , typename Stepper::deriv_type > tester;
+ tester();
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_test2 , Stepper, stepper_combinations2 )
+{
+ perform_stepper_test< Stepper , typename Stepper::deriv_type > tester;
+ tester();
+}
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/runge_kutta_controlled_concepts.cpp b/test/runge_kutta_controlled_concepts.cpp
new file mode 100644
index 0000000..7f70cc5
--- /dev/null
+++ b/test/runge_kutta_controlled_concepts.cpp
@@ -0,0 +1,212 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/runge_kutta_controlled_concepts.cpp
+
+ [begin_description]
+ This file tests the Stepper concepts of odeint with all Controlled Runge-Kutta steppers.
+ It's one of the main tests of odeint.
+ [end_description]
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+// disable checked iterator warning for msvc
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_runge_kutta_controlled_concepts
+
+#include <vector>
+#include <cmath>
+#include <iostream>
+
+#include <boost/numeric/odeint/config.hpp>
+
+#include <boost/array.hpp>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/ref.hpp>
+#include <boost/bind.hpp>
+#include <boost/utility.hpp>
+#include <boost/type_traits/add_reference.hpp>
+
+#include <boost/mpl/vector.hpp>
+#include <boost/mpl/for_each.hpp>
+#include <boost/mpl/insert_range.hpp>
+#include <boost/mpl/end.hpp>
+#include <boost/mpl/copy.hpp>
+#include <boost/mpl/placeholders.hpp>
+#include <boost/mpl/inserter.hpp>
+
+#include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54_classic.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_fehlberg78.hpp>
+#include <boost/numeric/odeint/stepper/controlled_runge_kutta.hpp>
+#include <boost/numeric/odeint/stepper/bulirsch_stoer.hpp>
+
+#include "prepare_stepper_testing.hpp"
+#include "dummy_odes.hpp"
+
+using std::vector;
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+namespace mpl = boost::mpl;
+
+const double result = 2.2; // two steps
+
+const double eps = 1.0e-14;
+
+template< class Stepper , class System >
+void check_controlled_stepper_concept( Stepper &stepper , System system , typename Stepper::state_type &x )
+{
+ typedef Stepper stepper_type;
+ typedef typename stepper_type::deriv_type container_type;
+ //typedef typename stepper_type::order_type order_type; controlled_error_stepper don't necessarily have a order (burlish-stoer)
+ typedef typename stepper_type::time_type time_type;
+
+ time_type t = 0.0 , dt = 0.1;
+ controlled_step_result step_result = stepper.try_step( system , x , t , dt );
+
+ BOOST_CHECK_MESSAGE( step_result == success , "step result: " << step_result ); // error = 0 for constant system -> step size is always too small
+}
+
+
+template< class ControlledStepper , typename T >
+struct perform_controlled_stepper_test
+{
+ typedef T vector_space_type;
+ void operator()( void ) const
+ {
+ using std::abs;
+ vector_space_type x;
+ x = 2.0;
+ ControlledStepper controlled_stepper;
+ constant_system_functor_vector_space sys;
+#ifndef _MSC_VER
+ // dont run this for MSVC due to compiler bug 697006
+ check_controlled_stepper_concept( controlled_stepper ,
+ constant_system_vector_space< vector_space_type , vector_space_type , typename ControlledStepper::time_type >
+ , x );
+#else
+ check_controlled_stepper_concept( controlled_stepper , boost::cref( sys ) , x );
+#endif
+ check_controlled_stepper_concept( controlled_stepper , boost::cref( sys ) , x );
+ BOOST_CHECK( (abs( x - result )) < eps );
+ }
+};
+
+template< class ControlledStepper , typename T >
+struct perform_controlled_stepper_test< ControlledStepper , std::vector<T> >
+{
+ typedef std::vector<T> vector_type;
+ void operator()( void )
+ {
+ using std::abs;
+ vector_type x( 1 , 2.0 );
+ ControlledStepper controlled_stepper;
+ constant_system_functor_standard sys;
+#ifndef _MSC_VER
+ // dont run this for MSVC due to compiler bug 697006
+
+ check_controlled_stepper_concept( controlled_stepper ,
+ constant_system_standard< vector_type , vector_type , typename ControlledStepper::time_type > ,
+ x );
+#else
+ check_controlled_stepper_concept( controlled_stepper , boost::cref( sys ) , x );
+#endif
+ check_controlled_stepper_concept( controlled_stepper , boost::cref( sys ) , x );
+ BOOST_CHECK( (abs( x[0] - result )) < eps );
+ }
+};
+
+
+template< class ControlledStepper >
+struct perform_controlled_stepper_test< ControlledStepper , vector_space_type >
+{
+ void operator()( void ) const
+ {
+ using std::abs;
+ vector_space_type x;
+ x = 2.0;
+ ControlledStepper controlled_stepper;
+ constant_system_functor_vector_space sys;
+#ifndef _MSC_VER
+ // dont run this for MSVC due to compiler bug 697006
+ check_controlled_stepper_concept( controlled_stepper ,
+ constant_system_vector_space< vector_space_type , vector_space_type , typename ControlledStepper::time_type >
+ , x );
+#else
+ check_controlled_stepper_concept( controlled_stepper , boost::cref( sys ) , x );
+#endif
+ check_controlled_stepper_concept( controlled_stepper , boost::cref( sys ) , x );
+ BOOST_CHECK( (abs( x - result )) < eps );
+ }
+};
+
+template< class ControlledStepper , typename T >
+struct perform_controlled_stepper_test< ControlledStepper , boost::array<T,1> >
+{
+ typedef boost::array<T,1> array_type;
+ void operator()( void )
+ {
+ using std::abs;
+ array_type x;
+ x[0] = 2.0;
+ ControlledStepper controlled_stepper;
+ constant_system_functor_standard sys;
+#ifndef _MSC_VER
+ // dont run this for MSVC due to compiler bug 697006
+ check_controlled_stepper_concept( controlled_stepper , constant_system_standard< array_type , array_type , typename ControlledStepper::time_type > , x );
+#else
+ check_controlled_stepper_concept( controlled_stepper , boost::cref( sys ) , x );
+#endif
+ check_controlled_stepper_concept( controlled_stepper , boost::cref( sys ) , x );
+ BOOST_CHECK( (abs( x[0] - result )) < eps );
+ }
+};
+
+
+template< class State > class controlled_stepper_methods : public mpl::vector<
+ controlled_runge_kutta< runge_kutta_cash_karp54_classic< State , typename detail::extract_value_type<State>::type > > ,
+ controlled_runge_kutta< runge_kutta_dopri5< State , typename detail::extract_value_type<State>::type > > ,
+ controlled_runge_kutta< runge_kutta_fehlberg78< State , typename detail::extract_value_type<State>::type > > ,
+ bulirsch_stoer< State , typename detail::extract_value_type<State>::type >
+ > { };
+
+typedef mpl::copy
+<
+ container_types ,
+ mpl::inserter
+ <
+ mpl::vector0<> ,
+ mpl::insert_range
+ <
+ mpl::_1 ,
+ mpl::end< mpl::_1 > ,
+ controlled_stepper_methods< mpl::_2 >
+ >
+ >
+ >::type all_controlled_stepper_methods;
+
+
+
+
+BOOST_AUTO_TEST_SUITE( controlled_runge_kutta_concept_test )
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( controlled_stepper_test , ControlledStepper , all_controlled_stepper_methods )
+{
+ perform_controlled_stepper_test< ControlledStepper , typename ControlledStepper::state_type > tester;
+ tester();
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/runge_kutta_error_concepts.cpp b/test/runge_kutta_error_concepts.cpp
new file mode 100644
index 0000000..0698077
--- /dev/null
+++ b/test/runge_kutta_error_concepts.cpp
@@ -0,0 +1,182 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/runge_kutta_error_concepts.cpp
+
+ [begin_description]
+ This file tests the Stepper concepts of odeint with all Runge-Kutta Error steppers.
+ It's one of the main tests of odeint.
+ [end_description]
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+// disable checked iterator warning for msvc
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_runge_kutta_error_concepts
+
+#include <vector>
+#include <cmath>
+#include <iostream>
+
+#include <boost/numeric/odeint/config.hpp>
+
+#include <boost/array.hpp>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/ref.hpp>
+#include <boost/bind.hpp>
+#include <boost/utility.hpp>
+#include <boost/type_traits/add_reference.hpp>
+
+#include <boost/mpl/vector.hpp>
+#include <boost/mpl/for_each.hpp>
+#include <boost/mpl/insert_range.hpp>
+#include <boost/mpl/end.hpp>
+#include <boost/mpl/copy.hpp>
+#include <boost/mpl/placeholders.hpp>
+#include <boost/mpl/inserter.hpp>
+
+#include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54_classic.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_fehlberg78.hpp>
+
+#include "prepare_stepper_testing.hpp"
+#include "dummy_odes.hpp"
+
+using std::vector;
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+namespace mpl = boost::mpl;
+
+const double result = 2.4; // four steps total...
+
+const double eps = 1.0e-14;
+
+template< class Stepper , class System >
+void check_error_stepper_concept( Stepper &stepper , System system , typename Stepper::state_type &x , typename Stepper::state_type &xerr )
+{
+ typedef Stepper stepper_type;
+ typedef typename stepper_type::deriv_type container_type;
+ typedef typename stepper_type::order_type order_type;
+ typedef typename stepper_type::time_type time_type;
+
+ stepper.do_step( system , x , static_cast<time_type>(0.0) , static_cast<time_type>(0.1) );
+ stepper.do_step( system , x , static_cast<time_type>(0.0) , static_cast<time_type>(0.1) , xerr );
+}
+
+// default case is used for vector space types like plain double
+template< class Stepper , typename T >
+struct perform_error_stepper_test
+{
+ typedef T vector_space_type;
+ void operator()( void ) const
+ {
+ using std::abs;
+ vector_space_type x , xerr;
+ x = 2.0;
+ Stepper stepper;
+ constant_system_functor_vector_space sys;
+#ifndef _MSC_VER
+ // dont run this for MSVC due to compiler bug 697006
+ check_error_stepper_concept( stepper ,
+ constant_system_vector_space< vector_space_type , vector_space_type , typename Stepper::time_type > ,
+ x ,
+ xerr );
+#else
+ check_error_stepper_concept( stepper , boost::cref( sys ) , x , xerr );
+#endif
+ check_error_stepper_concept( stepper , boost::cref( sys ) , x , xerr );
+
+ BOOST_CHECK_MESSAGE( (abs( x - result )) < eps , x );
+ }
+};
+
+template< class Stepper , typename T >
+struct perform_error_stepper_test< Stepper , std::vector<T> >
+{
+ typedef std::vector<T> vector_type;
+ void operator()( void )
+ {
+ using std::abs;
+ vector_type x( 1 , 2.0 ) , xerr( 1 );
+ Stepper stepper;
+ constant_system_functor_standard sys;
+#ifndef _MSC_VER
+ // dont run this for MSVC due to compiler bug 697006
+ check_error_stepper_concept( stepper , constant_system_standard< vector_type , vector_type , typename Stepper::time_type > , x , xerr );
+#else
+ check_error_stepper_concept( stepper , boost::cref( sys ) , x , xerr );
+#endif
+ check_error_stepper_concept( stepper , boost::cref( sys ) , x , xerr );
+ BOOST_CHECK( (abs( x[0] - result )) < eps );
+ }
+};
+
+
+template< class Stepper , typename T >
+struct perform_error_stepper_test< Stepper , boost::array<T,1> >
+{
+ typedef boost::array<T,1> array_type;
+ void operator()( void )
+ {
+ using std::abs;
+ array_type x , xerr;
+ x[0] = 2.0;
+ Stepper stepper;
+ constant_system_functor_standard sys;
+#ifndef _MSC_VER
+ // dont run this for MSVC due to compiler bug 697006
+ check_error_stepper_concept( stepper , constant_system_standard< array_type , array_type , typename Stepper::time_type > , x , xerr );
+#else
+ check_error_stepper_concept( stepper , boost::cref( sys ) , x , xerr );
+#endif
+ check_error_stepper_concept( stepper , boost::cref( sys ) , x , xerr );
+ BOOST_CHECK( (abs( x[0] - result )) < eps );
+ }
+};
+
+template< class State > class error_stepper_methods : public mpl::vector<
+ runge_kutta_cash_karp54_classic< State , typename detail::extract_value_type<State>::type > ,
+ runge_kutta_cash_karp54< State , typename detail::extract_value_type<State>::type > ,
+ runge_kutta_dopri5< State , typename detail::extract_value_type<State>::type > ,
+ runge_kutta_fehlberg78< State , typename detail::extract_value_type<State>::type >
+ > { };
+
+
+typedef mpl::copy
+<
+ container_types ,
+ mpl::inserter
+ <
+ mpl::vector0<> ,
+ mpl::insert_range
+ <
+ mpl::_1 ,
+ mpl::end< mpl::_1 > ,
+ error_stepper_methods< mpl::_2 >
+ >
+ >
+ >::type all_error_stepper_methods;
+
+
+BOOST_AUTO_TEST_SUITE( runge_kutta_error_concept_test )
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( error_stepper_test , Stepper , all_error_stepper_methods )
+{
+ perform_error_stepper_test< Stepper , typename Stepper::state_type > tester;
+ tester();
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/same_size.cpp b/test/same_size.cpp
new file mode 100644
index 0000000..09a04c1
--- /dev/null
+++ b/test/same_size.cpp
@@ -0,0 +1,65 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/same_size.cpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_dummy
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/numeric/odeint/util/same_size.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+
+BOOST_AUTO_TEST_SUITE( same_size_test )
+
+BOOST_AUTO_TEST_CASE( test_vector_true )
+{
+ std::vector< double > v1( 10 ) , v2( 10 );
+ BOOST_CHECK_EQUAL( true , same_size( v1 , v2 ) );
+}
+
+
+BOOST_AUTO_TEST_CASE( test_vector_false )
+{
+ std::vector< double > v1( 10 ) , v2( 20 );
+ BOOST_CHECK_EQUAL( false , same_size( v1 , v2 ) );
+}
+
+BOOST_AUTO_TEST_CASE( test_fusion_true )
+{
+ boost::fusion::vector< double , std::vector< double > > v1 , v2;
+ boost::fusion::at_c< 1 >( v1 ).resize( 10 );
+ boost::fusion::at_c< 1 >( v2 ).resize( 10 );
+ BOOST_CHECK_EQUAL( true , same_size( v1 , v2 ) );
+}
+
+BOOST_AUTO_TEST_CASE( test_fusion_false )
+{
+ boost::fusion::vector< double , std::vector< double > > v1 , v2;
+ boost::fusion::at_c< 1 >( v1 ).resize( 10 );
+ boost::fusion::at_c< 1 >( v2 ).resize( 20 );
+ BOOST_CHECK_EQUAL( false , same_size( v1 , v2 ) );
+}
+
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/split.cpp b/test/split.cpp
new file mode 100644
index 0000000..b8f056b
--- /dev/null
+++ b/test/split.cpp
@@ -0,0 +1,68 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/split.cpp
+
+ [begin_description]
+ Test the range split.
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+ Copyright 2013 Pascal Germroth
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#define BOOST_TEST_MODULE odeint_split
+
+#include <iostream>
+
+#include <boost/test/unit_test.hpp>
+#include <boost/numeric/odeint/util/split_adaptor.hpp>
+#include <boost/range/irange.hpp>
+
+template<class T>
+inline void dump_range(const T &r) {
+ std::cout << '[';
+ std::copy(boost::begin(r), boost::end(r), std::ostream_iterator<
+ typename std::iterator_traits<
+ typename boost::range_iterator<const T>::type
+ >::value_type >(std::cout, " ") );
+ std::cout << ']';
+}
+
+template<class A, class B>
+inline void check_equal_range(const A a, const B b) {
+ BOOST_CHECK_EQUAL_COLLECTIONS( boost::begin(a), boost::end(a), boost::begin(b), boost::end(b) );
+}
+
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint::detail;
+using namespace boost;
+
+BOOST_AUTO_TEST_CASE( test_eleven )
+{
+ // 0 1 2 3 | 4 5 6 7 | 8 9 10 11
+ check_equal_range( irange(0, 12) | split(0, 3), irange(0, 4) );
+ check_equal_range( irange(0, 12) | split(1, 3), irange(4, 8) );
+ check_equal_range( irange(0, 12) | split(2, 3), irange(8, 12) );
+}
+
+BOOST_AUTO_TEST_CASE( test_ten )
+{
+ // 0 1 2 3 | 4 5 6 7 | 8 9 10
+ check_equal_range( irange(0, 11) | split(0, 3), irange(0, 4) );
+ check_equal_range( irange(0, 11) | split(1, 3), irange(4, 8) );
+ check_equal_range( irange(0, 11) | split(2, 3), irange(8, 11) );
+}
+
+BOOST_AUTO_TEST_CASE( test_nine )
+{
+ // 0 1 2 3 | 4 5 6 | 7 8 9
+ check_equal_range( irange(0, 10) | split(0, 3), irange(0, 4) );
+ check_equal_range( irange(0, 10) | split(1, 3), irange(4, 7) );
+ check_equal_range( irange(0, 10) | split(2, 3), irange(7, 10) );
+}
diff --git a/test/std_array.cpp b/test/std_array.cpp
new file mode 100644
index 0000000..350a387
--- /dev/null
+++ b/test/std_array.cpp
@@ -0,0 +1,57 @@
+/*
+ [auto_generated]
+ test/std_array.cpp
+
+ [begin_description]
+ Checks if odeint compiles fine with the std::array using the array algebra
+ [end_description]
+
+ Copyright 2009-2014 Karsten Ahnert
+ Copyright 2009-2014 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#define BOOST_TEST_MODULE odeint_std_array
+
+#include <array>
+#include <boost/numeric/odeint.hpp>
+#include <boost/static_assert.hpp>
+#include <boost/type_traits/is_same.hpp>
+#include <boost/test/unit_test.hpp>
+
+using namespace boost::unit_test;
+
+typedef std::array<double, 3> state_type;
+
+void rhs(const state_type &x, state_type &dxdt, const double t)
+{
+}
+
+BOOST_AUTO_TEST_SUITE( unwrap_reference_test )
+
+BOOST_AUTO_TEST_CASE( test_case )
+{
+ state_type x = {0.0, 0.0, 0.0};
+
+ typedef boost::numeric::odeint::runge_kutta4<state_type> stepper_type;
+// check if array algebra is selected, but only if odeint detects c++11
+#ifdef BOOST_NUMERIC_ODEINT_CXX11
+ BOOST_STATIC_ASSERT(( boost::is_same< stepper_type::algebra_type ,
+ boost::numeric::odeint::array_algebra >::value ));
+#endif
+ stepper_type stepper1;
+ stepper1.do_step(rhs, x, 0.0, 0.1);
+
+ boost::numeric::odeint::runge_kutta4<
+ state_type, double, state_type, double,
+ boost::numeric::odeint::array_algebra > stepper;
+ stepper.do_step(rhs, x, 0.0, 0.1);
+
+}
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/step_size_limitation.cpp b/test/step_size_limitation.cpp
new file mode 100644
index 0000000..2d8e472
--- /dev/null
+++ b/test/step_size_limitation.cpp
@@ -0,0 +1,268 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/step_size_limitation.cpp
+
+ [begin_description]
+ Tests the step size limitation functionality
+ [end_description]
+
+ Copyright 2015 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#define BOOST_TEST_MODULE odeint_integrate_times
+
+#include <boost/test/unit_test.hpp>
+
+#include <utility>
+#include <iostream>
+#include <vector>
+
+#include <boost/numeric/odeint.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+typedef double value_type;
+typedef std::vector< value_type > state_type;
+
+/***********************************************
+ * first part of the tests: explicit methods
+ ***********************************************
+ */
+
+void damped_osc( const state_type &x , state_type &dxdt , const value_type t )
+{
+ const value_type gam( 0.1);
+
+ dxdt[0] = x[1];
+ dxdt[1] = -x[0] - gam*x[1];
+}
+
+
+struct push_back_time
+{
+ std::vector< double >& m_times;
+
+ push_back_time( std::vector< double > × )
+ : m_times( times ) { }
+
+ template<typename State>
+ void operator()( const State &x , double t )
+ {
+ m_times.push_back( t );
+ }
+};
+
+BOOST_AUTO_TEST_SUITE( step_size_limitation_test )
+
+BOOST_AUTO_TEST_CASE( test_step_adjuster )
+{
+ // first use adjuster without step size limitation
+ default_step_adjuster<double, double> step_adjuster;
+ const double dt = 0.1;
+ double dt_new = step_adjuster.decrease_step(dt, 1.5, 2);
+ BOOST_CHECK(dt_new < dt*2.0/3.0);
+
+ dt_new = step_adjuster.increase_step(dt, 0.8, 1);
+ // for errors > 0.5 no increase is performed
+ BOOST_CHECK(dt_new == dt);
+
+ dt_new = step_adjuster.increase_step(dt, 0.4, 1);
+ // smaller errors should lead to step size increase
+ std::cout << dt_new << std::endl;
+ BOOST_CHECK(dt_new > dt);
+
+
+ // now test with step size limitation max_dt = 0.1
+ default_step_adjuster<double, double>
+ limited_adjuster(dt);
+
+ dt_new = limited_adjuster.decrease_step(dt, 1.5, 2);
+ // decreasing works as before
+ BOOST_CHECK(dt_new < dt*2.0/3.0);
+
+ dt_new = limited_adjuster.decrease_step(2*dt, 1.1, 2);
+ // decreasing a large step size should give max_dt
+ BOOST_CHECK(dt_new == dt);
+
+ dt_new = limited_adjuster.increase_step(dt, 0.8, 1);
+ // for errors > 0.5 no increase is performed, still valid
+ BOOST_CHECK(dt_new == dt);
+
+ dt_new = limited_adjuster.increase_step(dt, 0.4, 1);
+ // but even for smaller errors, we should at most get 0.1
+ BOOST_CHECK_EQUAL(dt_new, dt);
+
+ dt_new = limited_adjuster.increase_step(0.9*dt, 0.1, 1);
+ std::cout << dt_new << std::endl;
+ // check that we don't increase beyond max_dt
+ BOOST_CHECK(dt_new == dt);
+}
+
+
+template<class Stepper>
+void test_explicit_stepper(Stepper stepper, const double max_dt)
+{
+ state_type x( 2 );
+ x[0] = x[1] = 10.0;
+ const size_t steps = 100;
+
+ std::vector<double> times;
+
+ integrate_adaptive(stepper, damped_osc, x, 0.0, steps*max_dt, max_dt, push_back_time(times));
+
+ BOOST_CHECK_EQUAL(times.size(), steps+1);
+ // check that dt remains at exactly max_dt
+ for( size_t i=0 ; i<times.size() ; ++i )
+ // check if observer was called at times 0,1,2,...
+ BOOST_CHECK_SMALL( times[i] - static_cast<double>(i)*max_dt , 1E-15);
+ times.clear();
+
+ // this should also work when we provide some bigger initial dt
+ integrate_adaptive(stepper, damped_osc, x, 0.0, steps*max_dt, 10*max_dt, push_back_time(times));
+
+ BOOST_CHECK_EQUAL(times.size(), steps+1);
+ // check that dt remains at exactly max_dt
+ for( size_t i=0 ; i<times.size() ; ++i )
+ // check if observer was called at times 0,1,2,...
+ BOOST_CHECK_SMALL( times[i] - static_cast<double>(i)*max_dt , 1E-15);
+ times.clear();
+}
+
+
+BOOST_AUTO_TEST_CASE( test_controlled )
+{
+ const double max_dt = 0.01;
+
+ test_explicit_stepper(make_controlled(1E-2, 1E-2, max_dt,
+ runge_kutta_dopri5<state_type>()),
+ max_dt);
+ test_explicit_stepper(make_controlled(1E-2, 1E-2, -max_dt,
+ runge_kutta_dopri5<state_type>()),
+ -max_dt);
+
+ test_explicit_stepper(make_controlled(1E-2, 1E-2, max_dt,
+ runge_kutta_cash_karp54<state_type>()),
+ max_dt);
+ test_explicit_stepper(make_controlled(1E-2, 1E-2, -max_dt,
+ runge_kutta_cash_karp54<state_type>()),
+ -max_dt);
+
+ test_explicit_stepper(bulirsch_stoer<state_type>(1E-2, 1E-2, 1.0, 1.0, max_dt),
+ max_dt);
+ test_explicit_stepper(bulirsch_stoer<state_type>(1E-2, 1E-2, 1.0, 1.0, -max_dt),
+ -max_dt);
+}
+
+
+BOOST_AUTO_TEST_CASE( test_dense_out )
+{
+ const double max_dt = 0.01;
+ test_explicit_stepper(make_dense_output(1E-2, 1E-2, max_dt,
+ runge_kutta_dopri5<state_type>()),
+ max_dt);
+ test_explicit_stepper(make_dense_output(1E-2, 1E-2, -max_dt,
+ runge_kutta_dopri5<state_type>()),
+ -max_dt);
+
+ test_explicit_stepper(bulirsch_stoer_dense_out<state_type>(1E-2, 1E-2, 1, 1, max_dt),
+ max_dt);
+
+ test_explicit_stepper(bulirsch_stoer_dense_out<state_type>(1E-2, 1E-2, 1, 1, -max_dt),
+ -max_dt);
+}
+
+
+/***********************************************
+ * second part of the tests: implicit Rosenbrock
+ ***********************************************
+ */
+
+typedef boost::numeric::ublas::vector< value_type > vector_type;
+typedef boost::numeric::ublas::matrix< value_type > matrix_type;
+
+
+// harmonic oscillator, analytic solution x[0] = sin( t )
+struct osc_rhs
+{
+ void operator()( const vector_type &x , vector_type &dxdt , const value_type &t ) const
+ {
+ dxdt( 0 ) = x( 1 );
+ dxdt( 1 ) = -x( 0 );
+ }
+};
+
+struct osc_jacobi
+{
+ void operator()( const vector_type &x , matrix_type &jacobi , const value_type &t , vector_type &dfdt ) const
+ {
+ jacobi( 0 , 0 ) = 0;
+ jacobi( 0 , 1 ) = 1;
+ jacobi( 1 , 0 ) = -1;
+ jacobi( 1 , 1 ) = 0;
+ dfdt( 0 ) = 0.0;
+ dfdt( 1 ) = 0.0;
+ }
+};
+
+
+template<class Stepper>
+void test_rosenbrock_stepper(Stepper stepper, const double max_dt)
+{
+ vector_type x( 2 );
+ x(0) = x(1) = 10.0;
+ const size_t steps = 100;
+
+ std::vector<double> times;
+
+ integrate_adaptive(stepper,
+ std::make_pair(osc_rhs(), osc_jacobi()),
+ x, 0.0, steps*max_dt, max_dt, push_back_time(times));
+
+ BOOST_CHECK_EQUAL(times.size(), steps+1);
+ // check that dt remains at exactly max_dt
+ for( size_t i=0 ; i<times.size() ; ++i )
+ // check if observer was called at times 0,1,2,...
+ BOOST_CHECK_SMALL( times[i] - static_cast<double>(i)*max_dt , 1E-15);
+ times.clear();
+
+ // this should also work when we provide some bigger initial dt
+ integrate_adaptive(stepper,
+ std::make_pair(osc_rhs(), osc_jacobi()),
+ x, 0.0, steps*max_dt, 10*max_dt, push_back_time(times));
+
+ BOOST_CHECK_EQUAL(times.size(), steps+1);
+ // check that dt remains at exactly max_dt
+ for( size_t i=0 ; i<times.size() ; ++i )
+ // check if observer was called at times 0,1,2,...
+ BOOST_CHECK_SMALL( times[i] - static_cast<double>(i)*max_dt , 1E-15);
+ times.clear();
+}
+
+
+BOOST_AUTO_TEST_CASE( test_controlled_rosenbrock )
+{
+ const double max_dt = 0.01;
+
+ test_rosenbrock_stepper(make_controlled(1E-2, 1E-2, max_dt, rosenbrock4<value_type>()),
+ max_dt);
+ test_rosenbrock_stepper(make_controlled(1E-2, 1E-2, -max_dt, rosenbrock4<value_type>()),
+ -max_dt);
+}
+
+
+BOOST_AUTO_TEST_CASE( test_dense_out_rosenbrock )
+{
+ const double max_dt = 0.01;
+
+ test_rosenbrock_stepper(make_dense_output(1E-2, 1E-2, max_dt, rosenbrock4<value_type>()),
+ max_dt);
+ test_rosenbrock_stepper(make_dense_output(1E-2, 1E-2, -max_dt, rosenbrock4<value_type>()),
+ -max_dt);
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/stepper_copying.cpp b/test/stepper_copying.cpp
new file mode 100644
index 0000000..c29e4de
--- /dev/null
+++ b/test/stepper_copying.cpp
@@ -0,0 +1,856 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/stepper_copying.cpp
+
+ [begin_description]
+ This file tests the copying of the steppers.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+// disable checked iterator warning for msvc
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+#pragma warning(disable:4996)
+#endif
+
+
+#define BOOST_TEST_MODULE odeint_stepper_copying
+
+#include <boost/test/unit_test.hpp>
+#include <boost/type_traits/integral_constant.hpp>
+
+//#include <boost/numeric/odeint/util/construct.hpp>
+//#include <boost/numeric/odeint/util/destruct.hpp>
+#include <boost/numeric/odeint/util/copy.hpp>
+
+#include <boost/numeric/odeint/util/state_wrapper.hpp>
+
+#include <boost/numeric/odeint/stepper/euler.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta4_classic.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta4.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54_classic.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp>
+#include <boost/numeric/odeint/stepper/controlled_runge_kutta.hpp>
+#include <boost/numeric/odeint/stepper/dense_output_runge_kutta.hpp>
+
+template< class T , size_t Dim >
+class test_array
+{
+public:
+
+ const static size_t dim = Dim;
+ typedef T value_type;
+ typedef value_type* iterator;
+ typedef const value_type* const_iterator;
+
+ value_type& operator[]( size_t i )
+ {
+ return m_data[i];
+ }
+
+ const value_type& operator[]( size_t i ) const
+ {
+ return m_data[i];
+ }
+
+ iterator begin( void )
+ {
+ return m_data;
+ }
+
+ iterator end( void )
+ {
+ return m_data + dim;
+ }
+
+ const_iterator begin( void ) const
+ {
+ return m_data;
+ }
+
+ const_iterator end( void ) const
+ {
+ return m_data + dim;
+ }
+
+
+private:
+
+ value_type m_data[dim];
+};
+
+template< class T , size_t Dim >
+class test_array2 : public test_array< T , Dim >
+{
+};
+
+
+
+/*
+ * Explicit testing if copying was successful is difficult,
+ * hence we only test if the number of copy operations is right.
+ *
+ * Otherwise one has to prepare the states.
+ */
+
+size_t construct_count = 0;
+size_t construct2_count = 0;
+size_t destruct_count = 0;
+size_t destruct2_count = 0;
+size_t copy_count = 0;
+size_t copy2_count = 0;
+
+void reset_counter( void )
+{
+ construct_count = 0;
+ construct2_count = 0;
+ destruct_count = 0;
+ destruct2_count = 0;
+ copy_count = 0;
+ copy2_count = 0;
+}
+
+
+namespace boost { namespace numeric { namespace odeint {
+
+//provide the state_wrapper
+ template< class T , size_t Dim >
+ struct state_wrapper< test_array< T , Dim > >
+ {
+ typedef state_wrapper< test_array< T , Dim > > state_wrapper_type;
+ typedef test_array< T , Dim > state_type;
+ typedef T value_type;
+
+ state_type m_v;
+
+ state_wrapper() : m_v()
+ {
+ construct_count++;
+ }
+
+ state_wrapper( const state_type &v ) : m_v( v )
+ {
+ construct_count++;
+ copy_count++;
+ }
+
+ state_wrapper( const state_wrapper_type &x ) : m_v( x.m_v )
+ {
+ construct_count++;
+ copy_count++;
+ }
+
+ state_wrapper_type& operator=( const state_wrapper_type &x )
+ {
+ copy_count++;
+ return *this;
+ }
+
+ ~state_wrapper()
+ {
+ destruct_count++;
+ }
+ };
+
+//provide the state_wrapper
+ template< class T , size_t Dim >
+ struct state_wrapper< test_array2< T , Dim > >
+ {
+ typedef state_wrapper< test_array2< T , Dim > > state_wrapper_type;
+ typedef test_array2< T , Dim > state_type;
+ typedef T value_type;
+
+ state_type m_v;
+
+ state_wrapper() : m_v()
+ {
+ construct2_count++;
+ }
+
+ state_wrapper( const state_type &v ) : m_v( v )
+ {
+ construct2_count++;
+ copy2_count++;
+ }
+
+ state_wrapper( const state_wrapper_type &x ) : m_v( x.m_v )
+ {
+ construct2_count++;
+ copy2_count++;
+ }
+
+ state_wrapper_type& operator=( const state_wrapper_type &x )
+ {
+ copy2_count++;
+ return *this;
+ }
+
+ ~state_wrapper()
+ {
+ destruct2_count++;
+ }
+ };
+
+
+ } } }
+
+
+
+typedef test_array< double , 3 > state_type;
+typedef test_array2< double , 3 > deriv_type;
+typedef boost::numeric::odeint::euler< state_type , double , deriv_type > euler_type;
+typedef boost::numeric::odeint::runge_kutta4_classic< state_type , double , deriv_type > rk4_type;
+typedef boost::numeric::odeint::runge_kutta4< state_type , double , deriv_type > rk4_generic_type;
+typedef boost::numeric::odeint::runge_kutta_cash_karp54_classic< state_type , double , deriv_type > rk54_type;
+typedef boost::numeric::odeint::runge_kutta_cash_karp54< state_type , double , deriv_type > rk54_generic_type;
+typedef boost::numeric::odeint::runge_kutta_dopri5< state_type , double , deriv_type > dopri5_type;
+typedef boost::numeric::odeint::controlled_runge_kutta< rk54_type > controlled_rk54_type;
+typedef boost::numeric::odeint::controlled_runge_kutta< rk54_generic_type > controlled_rk54_generic_type;
+typedef boost::numeric::odeint::controlled_runge_kutta< dopri5_type > controlled_dopri5_type;
+typedef boost::numeric::odeint::dense_output_runge_kutta< euler_type > dense_output_euler_type;
+typedef boost::numeric::odeint::dense_output_runge_kutta< controlled_dopri5_type > dense_output_dopri5_type;
+
+#define CHECK_COUNTERS( c1 , c2 , c3 , c4 , c5 , c6 ) \
+ BOOST_CHECK_EQUAL( construct_count , size_t( c1 ) ); \
+ BOOST_CHECK_EQUAL( construct2_count , size_t( c2 ) ); \
+ BOOST_CHECK_EQUAL( destruct_count , size_t( c3 ) ); \
+ BOOST_CHECK_EQUAL( destruct2_count , size_t( c4) ); \
+ BOOST_CHECK_EQUAL( copy_count , size_t( c5 ) ) ; \
+ BOOST_CHECK_EQUAL( copy2_count, size_t( c6 ) )
+
+BOOST_AUTO_TEST_SUITE( stepper_copying )
+
+/*
+ * Construct + Destruct
+ * 1 deriv_type in explicit_stepper_base
+ */
+BOOST_AUTO_TEST_CASE( explicit_euler_construct )
+{
+ reset_counter();
+ {
+ euler_type euler;
+ }
+ CHECK_COUNTERS( 0 , 1 , 0 , 1 , 0 , 0 );
+}
+
+
+/*
+ * Construct + Destruct
+ * 2 * 1 deriv_type in explicit_stepper_base
+ *
+ * Copying
+ * 1 deriv_type in explicit_stepper_base
+ */
+BOOST_AUTO_TEST_CASE( explicit_euler_copy_construct )
+{
+ reset_counter();
+ {
+ euler_type euler;
+ euler_type euler2( euler );
+ }
+ CHECK_COUNTERS( 0 , 1 + 1 , 0 , 1 + 1 , 0 , 1 );
+}
+
+/*
+ * Construct + Destruct
+ * 2 * 1 deriv_type in explicit_stepper_base
+ *
+ * Copying
+ * 1 deriv_type in explicit_stepper_base
+ */
+BOOST_AUTO_TEST_CASE( explicit_euler_assign )
+{
+ reset_counter();
+ {
+ euler_type euler;
+ euler_type euler2;
+ euler2 = euler;
+ }
+ CHECK_COUNTERS( 0 , 2 , 0 , 2 , 0 , 1 );
+}
+
+/*
+ * Construct + Destruct
+ * 1 deriv_type in explicit_stepper_base
+ * 3 deriv_type in explicit_rk4
+ * 1 state_type in explicit_rk4
+ */
+BOOST_AUTO_TEST_CASE( explicit_rk4_construct )
+{
+ reset_counter();
+ {
+ rk4_type rk4;
+ }
+ CHECK_COUNTERS( 1 , 4 , 1 , 4 , 0 , 0 );
+}
+
+/*
+ * Construct + Destruct
+ * 2 * 1 deriv_type in explicit_stepper_base
+ * 2 * 3 deriv_type in explicit_rk4
+ * 2 * 1 state_type in explicit_rk4
+ *
+ * Copying
+ * 1 deriv_type in explicit_stepper_base
+ * 3 deriv_type in explicit_stepper_base
+ * 1 state_type in explicit_stepper_base
+ */
+BOOST_AUTO_TEST_CASE( explicit_rk4_copy_construct )
+{
+ reset_counter();
+ {
+ rk4_type rk4;
+ rk4_type rk4_2( rk4 );
+ }
+ CHECK_COUNTERS( 2 , 8 , 2 , 8 , 1 , 4 );
+}
+
+/*
+ * Construct + Destruct
+ * 2 * 1 deriv_type in explicit_stepper_base
+ * 2 * 3 deriv_type in explicit_rk4
+ * 2 * 1 state_type in explicit_rk4
+ *
+ * Copying
+ * 1 deriv_type in explicit_stepper_base
+ * 3 deriv_type in explicit_stepper_base
+ * 1 state_type in explicit_stepper_base
+ */
+BOOST_AUTO_TEST_CASE( explicit_rk4_assign )
+{
+ reset_counter();
+ {
+ rk4_type rk4;
+ rk4_type rk4_2;
+ rk4 = rk4_2;
+ }
+ CHECK_COUNTERS( 2 , 8 , 2 , 8 , 1 , 4 );
+}
+
+
+/*
+ * Construct + Destruct
+ * 1 deriv_type in explicit_stepper_base
+ * 3 deriv_type in explicit_rk4
+ * 1 state_type in explicit_rk4
+ */
+BOOST_AUTO_TEST_CASE( explicit_rk4_generic_construct )
+{
+ reset_counter();
+ {
+ rk4_generic_type rk4;
+ }
+ CHECK_COUNTERS( 1 , 4 , 1 , 4 , 0 , 0 );
+}
+
+/*
+ * Construct + Destruct
+ * 2 * 1 deriv_type in explicit_stepper_base
+ * 2 * 3 deriv_type in explicit_rk4
+ * 2 * 1 state_type in explicit_rk4
+ *
+ * Copying
+ * 1 deriv_type in explicit_stepper_base
+ * 3 deriv_type in explicit_stepper_base
+ * 1 state_type in explicit_stepper_base
+ */
+BOOST_AUTO_TEST_CASE( explicit_rk4_generic_copy_construct )
+{
+ reset_counter();
+ {
+ rk4_generic_type rk4;
+ rk4_generic_type rk4_2( rk4 );
+ }
+ CHECK_COUNTERS( 2 , 8 , 2 , 8 , 1 , 4 );
+}
+
+/*
+ * Construct + Destruct
+ * 2 * 1 deriv_type in explicit_stepper_base
+ * 2 * 3 deriv_type in explicit_rk4
+ * 2 * 1 state_type in explicit_rk4
+ *
+ * Copying
+ * 1 deriv_type in explicit_stepper_base
+ * 3 deriv_type in explicit_stepper_base
+ * 1 state_type in explicit_stepper_base
+ */
+BOOST_AUTO_TEST_CASE( explicit_rk4_generic_assign )
+{
+ reset_counter();
+ {
+ rk4_generic_type rk4;
+ rk4_generic_type rk4_2;
+ rk4 = rk4_2;
+ }
+ CHECK_COUNTERS( 2 , 8 , 2 , 8 , 1 , 4 );
+}
+
+/*
+ * Construct + Destruct
+ * 2 explicit_rk54_ck:
+ * 2 * 1 deriv_type in explicit_error_stepper_base
+ * 2 * 5 deriv_type in explicit_error_rk54_ck
+ * 2 * 1 state_type in explicit_error_rk4
+ * 1 controlled_stepper:
+ * 1 deriv_type
+ * 2 state_type
+ *
+ * Copying
+ * 1 copy process of explicit_rk54_ck:
+ * 1 deriv_type from explicit_error_stepper_base
+ * 5 deriv_type from explicit_error_rk54_ck
+ * 1 state_type from explicit_error_rk54_ck
+ */
+BOOST_AUTO_TEST_CASE( controlled_rk54_construct )
+{
+ reset_counter();
+ {
+ controlled_rk54_type stepper;
+ }
+ CHECK_COUNTERS( 4 , 13 , 4 , 13 , 1 , 6 );
+}
+
+
+/*
+ * Construct + Destruct
+ * 3 explicit_rk54_ck:
+ * 3 * 1 deriv_type in explicit_error_stepper_base
+ * 3 * 5 deriv_type in explicit_error_rk54_ck
+ * 3 * 1 state_type in explicit_error_rk4
+ * 2 controlled_stepper:
+ * 2 * 1 deriv_type
+ * 2 * 2 state_type
+ *
+ * Copying
+ * 1 copy process of explicit_rk54_ck:
+ * 1 deriv_type from explicit_error_stepper_base
+ * 5 deriv_type from explicit_error_rk54_ck
+ * 1 state_type from explicit_error_rk54_ck
+ *
+ * 1 process of copying controlled_error_stepper
+ * 1 deriv_type from explicit_error_stepper_base
+ * 5 deriv_type from explicit_error_rk54_ck
+ * 1 state_type from explicit_error_rk54_ck
+ * 1 deriv_type from controlled_error_stepper
+ * 2 state_type from controlled_error_stepper
+ */
+BOOST_AUTO_TEST_CASE( controlled_rk54_copy_construct )
+{
+ reset_counter();
+ {
+ controlled_rk54_type stepper;
+ controlled_rk54_type stepper2( stepper );
+ }
+ CHECK_COUNTERS( 7 , 20 , 7 , 20 , 4 , 13 );
+}
+
+/*
+ * Construct + Destruct
+ * 4 explicit_rk54_ck:
+ * 4 * 1 deriv_type in explicit_error_stepper_base
+ * 4 * 5 deriv_type in explicit_error_rk54_ck
+ * 4 * 1 state_type in explicit_error_rk4
+ * 2 controlled_stepper:
+ * 2 * 1 deriv_type
+ * 2 * 2 state_type
+ *
+ * Copying
+ * 2 copy process of explicit_rk54_ck:
+ * 2 * 1 deriv_type from explicit_error_stepper_base
+ * 2 * 5 deriv_type from explicit_error_rk54_ck
+ * 2 * 1 state_type from explicit_error_rk54_ck
+ *
+ * 1 process of copying controlled_error_stepper
+ * 1 deriv_type from explicit_error_stepper_base
+ * 5 deriv_type from explicit_error_rk54_ck
+ * 1 state_type from explicit_error_rk54_ck
+ * 1 deriv_type from controlled_error_stepper
+ * 2 state_type from controlled_error_stepper
+ */
+BOOST_AUTO_TEST_CASE( controlled_rk54_assign )
+{
+ reset_counter();
+ {
+ controlled_rk54_type stepper;
+ controlled_rk54_type stepper2;
+ stepper2 = stepper;
+ }
+ CHECK_COUNTERS( 8 , 26 , 8 , 26 , 5 , 19 );
+}
+
+
+
+/*
+ * Construct + Destruct
+ * 2 explicit_rk54_ck_generic:
+ * 2 * 1 deriv_type in explicit_error_stepper_base
+ * 2 * 5 deriv_type in explicit_error_rk54_ck_generic
+ * 2 * 1 state_type in explicit_error_rk54_ck_generic
+ * 1 controlled_stepper:
+ * 1 deriv_type
+ * 2 state_type
+ *
+ * Copying
+ * 1 copy process of explicit_rk54_ck_generic:
+ * 1 deriv_type from explicit_error_stepper_base
+ * 5 deriv_type from explicit_error_rk54_ck_generic
+ * 1 state_type from explicit_error_rk54_ck_generic
+ */
+BOOST_AUTO_TEST_CASE( controlled_rk54_generic_construct )
+{
+ reset_counter();
+ {
+ controlled_rk54_generic_type stepper;
+ }
+ CHECK_COUNTERS( 4 , 13 , 4 , 13 , 1 , 6 );
+}
+
+
+/*
+ * Construct + Destruct
+ * 3 explicit_rk54_ck_generic:
+ * 3 * 1 deriv_type in explicit_error_stepper_base
+ * 3 * 5 deriv_type in explicit_error_rk54_ck_generic
+ * 3 * 1 state_type in explicit_error_rk4_generic
+ * 2 controlled_stepper:
+ * 2 * 1 deriv_type
+ * 2 * 2 state_type
+ *
+ * Copying
+ * 1 copy process of explicit_rk54_ck_generic:
+ * 1 deriv_type from explicit_error_stepper_base
+ * 5 deriv_type from explicit_error_rk54_ck_generic
+ * 1 state_type from explicit_error_rk54_ck_generic
+ *
+ * 1 process of copying controlled_error_stepper
+ * 1 deriv_type from explicit_error_stepper_base
+ * 5 deriv_type from explicit_error_rk54_ck_generic
+ * 1 state_type from explicit_error_rk54_ck_generic
+ * 1 deriv_type from controlled_error_stepper
+ * 2 state_type from controlled_error_stepper
+ */
+BOOST_AUTO_TEST_CASE( controlled_rk54_generic_copy_construct )
+{
+ reset_counter();
+ {
+ controlled_rk54_generic_type stepper;
+ controlled_rk54_generic_type stepper2( stepper );
+ }
+ CHECK_COUNTERS( 7 , 20 , 7 , 20 , 4 , 13 );
+}
+
+/*
+ * Construct + Destruct
+ * 4 explicit_rk54_ck_generic:
+ * 4 * 1 deriv_type in explicit_error_stepper_base
+ * 4 * 5 deriv_type in explicit_error_rk54_ck_generic
+ * 4 * 1 state_type in explicit_error_rk4_generic
+ * 2 controlled_stepper:
+ * 2 * 1 deriv_type
+ * 2 * 2 state_type
+ *
+ * Copying
+ * 2 copy process of explicit_rk54_ck_generic:
+ * 2 * 1 deriv_type from explicit_error_stepper_base
+ * 2 * 5 deriv_type from explicit_error_rk54_ck_generic
+ * 2 * 1 state_type from explicit_error_rk54_ck_generic
+ *
+ * 1 process of copying controlled_error_stepper
+ * 1 deriv_type from explicit_error_stepper_base
+ * 5 deriv_type from explicit_error_rk54_ck_generic
+ * 1 state_type from explicit_error_rk54_ck_generic
+ * 1 deriv_type from controlled_error_stepper
+ * 2 state_type from controlled_error_stepper
+ */
+BOOST_AUTO_TEST_CASE( controlled_rk54_generic_assign )
+{
+ reset_counter();
+ {
+ controlled_rk54_generic_type stepper;
+ controlled_rk54_generic_type stepper2;
+ stepper2 = stepper;
+ }
+ CHECK_COUNTERS( 8 , 26 , 8 , 26 , 5 , 19 );
+}
+
+
+/*
+ * Construct + Destruct
+ * 2 explicit_error_dopri5:
+ * 2 * 1 deriv_type in explicit_error_stepper_base_fsal
+ * 2 * 6 deriv_type in explicit_error_dopri5
+ * 2 * 1 state_type in explicit_error_dopri5
+ * 1 controlled_error_stepper (fsal):
+ * 2 deriv_type
+ * 2 state_type
+ *
+ * Copying
+ * 1 copy process of explicit_dopri5:
+ * 1 deriv_type from explicit_error_stepper_base_fsal
+ * 6 deriv_type from explicit_error_dopri5
+ * 1 state_type from explicit_error_dopri5
+ */
+
+BOOST_AUTO_TEST_CASE( controlled_dopri5_construct )
+{
+ reset_counter();
+ {
+ controlled_dopri5_type dopri5;
+ }
+ CHECK_COUNTERS( 2 * 1 + 2 , 2 * (6+1) + 2 , 2 * 1 + 2 , 2 * (6+1) + 2 , 1 , 1 + 6 );
+}
+
+
+/*
+ * Construct + Destruct
+ * 3 explicit_error_dopri5:
+ * 3 * 1 deriv_type in explicit_error_stepper_base_fsal
+ * 3 * 6 deriv_type in explicit_error_dopri5
+ * 3 * 1 state_type in explicit_error_dopri5
+ * 2 controlled_error_stepper (fsal):
+ * 2 * 2 deriv_type
+ * 2 * 2 state_type
+ *
+ * Copying
+ * 1 copy process of explicit_error_dopri5:
+ * 1 deriv_type from explicit_error_stepper_base_fsal
+ * 6 deriv_type from explicit_error_error_dopri5
+ * 1 state_type from explicit_error_error_dopri5
+ *
+ * 1 process of copying controlled_error_stepper
+ * 1 deriv_type from explicit_error_stepper_base_fsal
+ * 6 deriv_type from explicit_error_dopri5
+ * 1 state_type from explicit_error_dopri5
+ * 2 deriv_type from controlled_error_stepper (fsal)
+ * 2 state_type from controlled_error_stepper (fsal)
+ */
+BOOST_AUTO_TEST_CASE( controlled_dopri5_copy_construct )
+{
+ reset_counter();
+ {
+ controlled_dopri5_type dopri5;
+ controlled_dopri5_type dopri5_2( dopri5 );
+ }
+ CHECK_COUNTERS( 3 * 1 + 2 * 2 , 3 * (6+1) + 2 * 2 , 3 * 1 + 2 * 2 , 3 * (6+1) + 2 * 2 , 1 + 1 + 2 , 1 + 6 + 1 + 6 + 2 );
+}
+
+/*
+ * Construct + Destruct
+ * 4 explicit_error_dopri5:
+ * 4 * 1 deriv_type in explicit_error_stepper_base_fsal
+ * 4 * 6 deriv_type in explicit_error_dopri5
+ * 4 * 1 state_type in explicit_error_dopri5
+ * 2 controlled_error_stepper (fsal):
+ * 2 * 2 deriv_type
+ * 2 * 2 state_type
+ *
+ * Copying
+ * 2 copy process of explicit_error_dopri5:
+ * 2 * 1 deriv_type from explicit_error_stepper_base_fsal
+ * 2 * 6 deriv_type from explicit_error_dopri5
+ * 2 * 1 state_type from explicit_error_dopri5
+ *
+ * 1 process of copying controlled_error_stepper
+ * 1 deriv_type from explicit_error_stepper_base
+ * 6 deriv_type from explicit_error_dopri5
+ * 1 state_type from explicit_error_dopri5
+ * 2 deriv_type from controlled_error_stepper (fsal)
+ * 2 state_type from controlled_error_stepper (fsal)
+ */
+BOOST_AUTO_TEST_CASE( controlled_dopri5_assign )
+{
+ reset_counter();
+ {
+ controlled_dopri5_type dopri5;
+ controlled_dopri5_type dopri5_2;
+ dopri5_2 = dopri5;
+ }
+ CHECK_COUNTERS( 4 * 1 + 2 * 2 , 4 * (1+6) + 2 * 2 , 4 * 1 + 2 * 2 , 4 * (1+6) + 2 * 2 , 2 * 1 + 1 + 2 , 2 * (6+1) + 1 + 6 + 2 );
+}
+
+
+/*
+ * Construct + Destruct
+ * 2 explicit_euler:
+ * 2 * 1 deriv_type in explicit_stepper_base
+ * 1 dense_output_explicit:
+ * 2 state_type
+ *
+ * Copying
+ * 1 copy process of explicit_euler:
+ * 1 deriv_type from explicit_stepper_base
+ */
+BOOST_AUTO_TEST_CASE( dense_output_euler_construct )
+{
+ reset_counter();
+ {
+ dense_output_euler_type euler;
+ }
+ CHECK_COUNTERS( 2 , 2 * 1 , 2 , 2 * 1 , 0 , 1 );
+}
+
+/*
+ * Construct + Destruct
+ * 3 explicit_euler:
+ * 3 * 1 deriv_type in explicit_stepper_base
+ * 2 dense_output_explicit:
+ * 2 * 2 state_type
+ *
+ * Copying
+ * 1 copy process of explicit_euler:
+ * 1 deriv_type from explicit_stepper_base
+ *
+ * 1 process of copying
+ * 1 deriv_type from explicit_stepper_base
+ * 2 state_type from dense_output_explicit
+ */
+BOOST_AUTO_TEST_CASE( dense_output_euler_copy_construct )
+{
+ reset_counter();
+ {
+ dense_output_euler_type euler;
+ dense_output_euler_type euler2( euler );
+ }
+ CHECK_COUNTERS( 2 * 2 , 3 * 1 , 2 * 2 , 3 * 1 , 2 , 1 + 1 );
+}
+
+/*
+ * Construct + Destruct
+ * 4 explicit_euler:
+ * 4 * 1 deriv_type in explicit_stepper_base
+ * 2 dense_output_explicit:
+ * 2 * 2 state_type
+ *
+ * Copying
+ * 2 copy process of explicit_euler:
+ * 2 * 1 deriv_type from explicit_stepper_base
+ *
+ * 1 process of copying dense_ouput_explicit
+ * 1 deriv_type from explicit_stepper_base
+ * 2 state_type from dense_output_explicit
+ */
+BOOST_AUTO_TEST_CASE( dense_output_euler_assign )
+{
+ reset_counter();
+ {
+ dense_output_euler_type euler;
+ dense_output_euler_type euler2;
+ euler2 = euler;
+ }
+ CHECK_COUNTERS( 2 * 2 , 4 * 1 , 2 * 2 , 4 * 1 , 2 , 2 * 1 + 1 );
+}
+
+/*
+ * Construct + Destruct
+ * 3 dense_output_dopri5:
+ * 3 * 1 deriv_type in explicit_error_stepper_base_fsal
+ * 3 * 6 deriv_type in explicit_error_dopri5
+ * 3 * 1 state_type in explicit_error_dopri5
+ * 2 controlled_error_stepper (fsal):
+ * 2 * 2 state_type
+ * 2 * 2 deriv_type
+ * 1 dense_output_controlled_explicit:
+ * 2 state_type
+ * 2 deriv_type
+ *
+ * Copying
+ * 2 copy process of explicit_error_dopri5:
+ * 2 * 1 deriv_type from explicit_erro_stepper_base_fsal
+ * 2 * 6 deriv_type in explicit_error_dopri5
+ * 2 * 1 state_type in explicit_error_dopri5
+ * 1 copy process of dense_output_controlled (fsal)
+ * 2 state_type
+ * 2 deriv_type
+ */
+BOOST_AUTO_TEST_CASE( dense_output_dopri5_construct )
+{
+ reset_counter();
+ {
+ dense_output_dopri5_type dopri5;
+ }
+ CHECK_COUNTERS( 3*1 + 2*2 + 2 , 3*(1+6) + 2*2 + 2 , 3*1 + 2*2 + 2 , 3*(1+6) + 2*2 + 2 , 2*1 + 2 , 2*(1+6) + 2 );
+}
+
+/*
+ * Construct + Destruct
+ * 4 dense_output_dopri5:
+ * 4 * 1 deriv_type in explicit_error_stepper_base_fsal
+ * 4 * 5 deriv_type in explicit_error_dopri5
+ * 4 * 1 state_type in explicit_error_dopri5
+ * 3 controlled_error_stepper (fsal):
+ * 3 * 2 state_type
+ * 3 * 2 deriv_type
+ * 2 dense_output_controlled_explicit:
+ * 2 * 2 state_type
+ * 2 * 2 deriv_type
+ *
+ * Copying
+ * 3 copy process of explicit_error_dopri5:
+ * 3 * 1 deriv_type from explicit_erro_stepper_base_fsal
+ * 3 * 6 deriv_type in explicit_error_dopri5
+ * 3 * 1 state_type in explicit_error_dopri5
+ * 2 copy process of controlled_error_stepper (fsal):
+ * 2 * 2 state_type
+ * 2 * 2 deriv_type
+ * 1 copy process of dense_output_controlled_explicit:
+ * 2 state_type
+ * 2 deriv_type
+ */
+BOOST_AUTO_TEST_CASE( dense_output_dopri5_copy_construct )
+{
+ reset_counter();
+ {
+ dense_output_dopri5_type dopri5;
+ dense_output_dopri5_type dopri5_2( dopri5 );
+ }
+ CHECK_COUNTERS( 4*1 + 3*2 + 2*2 , 4*(1+6) + 3*2 + 2*2 , 4*1 + 3*2 + 2*2 , 4*(1+6) + 3*2 + 2*2 , 3*1 + 2*2 + 1*2 , 3*(6+1) + 2*2 + 2 );
+}
+
+/*
+ * Construct + Destruct
+ * 6 dense_output_dopri5:
+ * 6 * 1 deriv_type in explicit_error_stepper_base_fsal
+ * 6 * 6 deriv_type in explicit_error_dopri5
+ * 6 * 1 state_type in explicit_error_dopri5
+ * 4 controlled_error_stepper (fsal):
+ * 4 * 2 state_type
+ * 4 * 2 deriv_type
+ * 2 dense_output_controlled_explicit:
+ * 2 * 2 state_type
+ * 2 * 2 deriv_type
+ *
+ * Copying
+ * 5 copy process of explicit_error_dopri5:
+ * 5 * 1 deriv_type from explicit_erro_stepper_base_fsal
+ * 5 * 6 deriv_type in explicit_error_dopri5
+ * 5 * 1 state_type in explicit_error_dopri5
+ * 3 copy process of controlled_error_stepper (fsal):
+ * 3 * 2 state_type
+ * 3 * 2 deriv_type
+ * 1 copy process of dense_output_controlled_explicit:
+ * 2 state_type
+ * 2 deriv_type
+ */
+BOOST_AUTO_TEST_CASE( dense_output_dopri5_assign )
+{
+ reset_counter();
+ {
+ dense_output_dopri5_type dopri5;
+ dense_output_dopri5_type dopri5_2;
+ dopri5_2 = dopri5;
+ }
+ CHECK_COUNTERS( 6*1 + 4*2 + 2*2 , 6*(6+1) + 4*2 + 2*2 , 6*1 + 4*2 + 2*2 , 6*(6+1) + 4*2 + 2*2 , 5*1 + 3*2 + 2 , 5*(6+1) + 3*2 + 2 );
+}
+
+
+BOOST_AUTO_TEST_SUITE_END()
+
diff --git a/test/stepper_with_ranges.cpp b/test/stepper_with_ranges.cpp
new file mode 100644
index 0000000..59f007f
--- /dev/null
+++ b/test/stepper_with_ranges.cpp
@@ -0,0 +1,292 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/stepper_with_ranges.cpp
+
+ [begin_description]
+ This file tests if the steppers play well with Boost.Range.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+// disable checked iterator warning for msvc
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_stepper_with_ranges
+
+#include <boost/test/unit_test.hpp>
+
+#include <vector>
+#include <utility>
+#include <iostream>
+
+#include <boost/array.hpp>
+#include <boost/range.hpp>
+#include <boost/ref.hpp>
+
+#include <boost/numeric/odeint/stepper/euler.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54_classic.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp>
+#include <boost/numeric/odeint/stepper/controlled_runge_kutta.hpp>
+#include <boost/numeric/odeint/stepper/symplectic_euler.hpp>
+#include <boost/numeric/odeint/stepper/dense_output_runge_kutta.hpp>
+
+typedef std::vector< double > state_type;
+typedef boost::array< double , 3 > state_type2;
+
+/* explicitly force range algebra for this array! */
+namespace boost { namespace numeric { namespace odeint {
+
+template<>
+struct algebra_dispatcher< state_type2 >
+{ typedef range_algebra algebra_type; };
+
+} } }
+
+
+/*
+ * The two systems are needed, since for steppers with more than
+ * one internal step it is difficult to calculate the exact result
+ *
+ * system1 is suited for euler
+ */
+struct system1
+{
+ template< class State , class Deriv >
+ void operator()( const State &x_ , Deriv &dxdt_ , double t )
+ {
+ typename boost::range_iterator< const State >::type x = boost::begin( x_ );
+ typename boost::range_iterator< Deriv >::type dxdt = boost::begin( dxdt_ );
+
+ dxdt[0] = x[0];
+ dxdt[1] = 2.0;
+ dxdt[2] = 3.0;
+ }
+
+ template< class State , class Deriv >
+ void operator()( const State &x_ , const Deriv &dxdt_ , double t )
+ {
+ typename boost::range_iterator< const State >::type x = boost::begin( x_ );
+ typename boost::range_iterator< Deriv >::type dxdt = boost::begin( dxdt_ );
+
+ dxdt[0] = x[0];
+ dxdt[1] = 2.0;
+ dxdt[2] = 3.0;
+ }
+};
+
+/*
+ * system2 is suited for all steppers, it allows you to calculate the result analytically.
+ */
+struct system2
+{
+ template< class State , class Deriv >
+ void operator()( const State &x_ , Deriv &dxdt_ , double t )
+ {
+ typename boost::range_iterator< Deriv >::type dxdt = boost::begin( dxdt_ );
+
+ dxdt[0] = 1.0;
+ dxdt[1] = 2.0;
+ dxdt[2] = 3.0;
+ }
+
+ template< class State , class Deriv >
+ void operator()( const State &x_ , const Deriv &dxdt_ , double t )
+ {
+ typename boost::range_iterator< Deriv >::type dxdt = boost::begin( dxdt_ );
+
+ dxdt[0] = 1.0;
+ dxdt[1] = 2.0;
+ dxdt[2] = 3.0;
+ }
+};
+
+
+/*
+ * Useful for Hamiltonian systems
+ */
+struct ham_sys
+{
+ template< class State , class Deriv >
+ void operator()( const State &x_ , Deriv &dxdt_ )
+ {
+ typename boost::range_iterator< Deriv >::type dxdt = boost::begin( dxdt_ );
+ dxdt[0] = 1.0;
+ dxdt[1] = 2.0;
+ dxdt[2] = 3.0;
+ }
+
+ template< class State , class Deriv >
+ void operator()( const State &x_ , const Deriv &dxdt_ )
+ {
+ typename boost::range_iterator< Deriv >::type dxdt = boost::begin( dxdt_ );
+ dxdt[0] = 1.0;
+ dxdt[1] = 2.0;
+ dxdt[2] = 3.0;
+ }
+};
+
+
+struct vector_fixture
+{
+ const static size_t dim = 6;
+ boost::array< double , dim > in;
+ boost::array< double , dim > q;
+ boost::array< double , dim > p;
+ state_type err;
+
+ vector_fixture( void )
+ : in() , err( 3 )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ {
+ in[ i ] = q[i] = p[i] = double( i );
+ }
+ for( size_t i=0 ; i<3 ; ++i )
+ {
+ err[i] = double( i ) * 10.0;
+ }
+ }
+
+ ~vector_fixture( void )
+ {
+ }
+};
+
+#define CHECK_VALUES( x , x0 , x1 , x2 , x3 , x4 , x5 ) \
+ BOOST_CHECK_CLOSE( x[0] , x0 , 1.0e-8 ); \
+ BOOST_CHECK_CLOSE( x[1] , x1 , 1.0e-8 ); \
+ BOOST_CHECK_CLOSE( x[2] , x2 , 1.0e-8 ); \
+ BOOST_CHECK_CLOSE( x[3] , x3 , 1.0e-8 ); \
+ BOOST_CHECK_CLOSE( x[4] , x4 , 1.0e-8 ); \
+ BOOST_CHECK_CLOSE( x[5] , x5 , 1.0e-8 )
+
+
+
+BOOST_AUTO_TEST_SUITE( stepper_with_ranges )
+
+BOOST_AUTO_TEST_CASE( explicit_euler_with_range_v1 )
+{
+ vector_fixture f;
+ boost::numeric::odeint::euler< state_type > euler;
+ euler.do_step( system1() , std::make_pair( f.in.begin() + 1 , f.in.begin() + 4 ) , 0.1 , 0.1 );
+ CHECK_VALUES( f.in , 0.0 , 1.1 , 2.2 , 3.3 , 4.0 , 5.0 );
+}
+
+
+
+BOOST_AUTO_TEST_CASE( explicit_error_k54_with_range_v1 )
+{
+ vector_fixture f;
+ boost::numeric::odeint::runge_kutta_cash_karp54_classic< state_type > rk54;
+ rk54.do_step( system2() , std::make_pair( f.in.begin() + 1 , f.in.begin() + 4 ) , 0.1 , 0.1 );
+ CHECK_VALUES( f.in , 0.0 , 1.1 , 2.2 , 3.3 , 4.0 , 5.0 );
+}
+
+BOOST_AUTO_TEST_CASE( explicit_error_k54_with_range_v5 )
+{
+ vector_fixture f;
+ boost::numeric::odeint::runge_kutta_cash_karp54_classic< state_type > rk54;
+ rk54.do_step( system2() , std::make_pair( f.in.begin() + 1 , f.in.begin() + 4 ) , 0.1 , 0.1 , f.err );
+ CHECK_VALUES( f.in , 0.0 , 1.1 , 2.2 , 3.3 , 4.0 , 5.0 );
+}
+
+
+BOOST_AUTO_TEST_CASE( runge_kutta_dopri5_with_range_v1 )
+{
+ vector_fixture f;
+ boost::numeric::odeint::runge_kutta_dopri5< state_type > dopri5;
+ dopri5.do_step( system2() , std::make_pair( f.in.begin() + 1 , f.in.begin() + 4 ) , 0.1 , 0.1 );
+ CHECK_VALUES( f.in , 0.0 , 1.1 , 2.2 , 3.3 , 4.0 , 5.0 );
+}
+
+
+BOOST_AUTO_TEST_CASE( runge_kutta_dopri5_with_range_v5 )
+{
+ vector_fixture f;
+ boost::numeric::odeint::runge_kutta_dopri5< state_type > dopri5;
+ dopri5.do_step( system2() , std::make_pair( f.in.begin() + 1 , f.in.begin() + 4 ) , 0.1 , 0.1 , f.err );
+ CHECK_VALUES( f.in , 0.0 , 1.1 , 2.2 , 3.3 , 4.0 , 5.0 );
+}
+
+
+BOOST_AUTO_TEST_CASE( controlled_error_stepper_rk54 )
+{
+ double t = 0.0 , dt = 0.1;
+ vector_fixture f;
+ boost::numeric::odeint::controlled_runge_kutta< boost::numeric::odeint::runge_kutta_cash_karp54_classic< state_type > > stepper;
+ stepper.try_step( system2() , std::make_pair( f.in.begin() + 1 , f.in.begin() + 4 ) , t , dt );
+ CHECK_VALUES( f.in , 0.0 , 1.1 , 2.2 , 3.3 , 4.0 , 5.0 );
+}
+
+BOOST_AUTO_TEST_CASE( controlled_error_stepper_dopri5 )
+{
+ double t = 0.0 , dt = 0.1;
+ vector_fixture f;
+ boost::numeric::odeint::controlled_runge_kutta< boost::numeric::odeint::runge_kutta_dopri5< state_type > > stepper;
+ stepper.try_step( system2() , std::make_pair( f.in.begin() + 1 , f.in.begin() + 4 ) , t , dt );
+ CHECK_VALUES( f.in , 0.0 , 1.1 , 2.2 , 3.3 , 4.0 , 5.0 );
+}
+
+
+BOOST_AUTO_TEST_CASE( symplectic_euler_coor_func )
+{
+ vector_fixture f;
+ boost::numeric::odeint::symplectic_euler< state_type > euler;
+ euler.do_step( ham_sys() ,
+ std::make_pair( f.q.begin() + 1 , f.q.begin() + 4 ) ,
+ std::make_pair( f.p.begin() + 3 , f.p.begin() + 6 ) ,
+ 0.0 , 0.1 );
+ CHECK_VALUES( f.q , 0.0 , 1.3 , 2.4 , 3.5 , 4.0 , 5.0 );
+ CHECK_VALUES( f.p , 0.0 , 1.0 , 2.0 , 3.1 , 4.2 , 5.3 );
+}
+
+BOOST_AUTO_TEST_CASE( symplectic_euler_coor_and_mom_func )
+{
+ vector_fixture f;
+ boost::numeric::odeint::symplectic_euler< state_type > euler;
+ euler.do_step( std::make_pair( ham_sys() , ham_sys() ) ,
+ std::make_pair( f.q.begin() + 1 , f.q.begin() + 4 ) ,
+ std::make_pair( f.p.begin() + 3 , f.p.begin() + 6 ) ,
+ 0.0 , 0.1 );
+ CHECK_VALUES( f.q , 0.0 , 1.1 , 2.2 , 3.3 , 4.0 , 5.0 );
+ CHECK_VALUES( f.p , 0.0 , 1.0 , 2.0 , 3.1 , 4.2 , 5.3 );
+}
+
+
+BOOST_AUTO_TEST_CASE( dense_output_euler_with_ranges )
+{
+ using namespace boost::numeric::odeint;
+ vector_fixture f;
+ dense_output_runge_kutta< euler< state_type > > stepper;
+ stepper.initialize( std::make_pair( f.in.begin() + 1, f.in.begin() + 4 ) , 0.0 , 0.1 );
+ stepper.do_step( system1() );
+ stepper.calc_state( 0.05 , std::make_pair( f.in.begin() + 1 ,f.in.begin() +4 ) );
+ CHECK_VALUES( f.in , 0.0 , 1.05 , 2.1 , 3.15 , 4.0 , 5.0 );
+}
+
+BOOST_AUTO_TEST_CASE( dense_output_dopri5_with_ranges )
+{
+ using namespace boost::numeric::odeint;
+ vector_fixture f;
+ dense_output_runge_kutta<
+ controlled_runge_kutta<
+ runge_kutta_dopri5< state_type >
+ > > stepper;
+ stepper.initialize( std::make_pair( f.in.begin() + 1, f.in.begin() + 4 ) , 0.0 , 0.1 );
+ stepper.do_step( system2() );
+ stepper.calc_state( 0.05 , std::make_pair( f.in.begin() + 1 ,f.in.begin() +4 ) );
+ CHECK_VALUES( f.in , 0.0 , 1.05 , 2.1 , 3.15 , 4.0 , 5.0 );
+}
+
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/stepper_with_units.cpp b/test/stepper_with_units.cpp
new file mode 100644
index 0000000..3e3a645
--- /dev/null
+++ b/test/stepper_with_units.cpp
@@ -0,0 +1,328 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/stepper_with_units.cpp
+
+ [begin_description]
+ This file tests if the steppers play well with Boost.Units.
+ [end_description]
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#define BOOST_TEST_MODULE odeint_stepper_with_units
+
+// the runge-kutta 78 stepper invoked with boost units requires increased fusion macro variables!
+// note that by default the rk78 + units test case is disabled as it requires enormous memory when compiling (5 GB)
+#define BOOST_FUSION_INVOKE_MAX_ARITY 15
+#define BOOST_RESULT_OF_NUM_ARGS 15
+
+
+#include <boost/numeric/odeint/config.hpp>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/units/systems/si/length.hpp>
+#include <boost/units/systems/si/time.hpp>
+#include <boost/units/systems/si/velocity.hpp>
+#include <boost/units/systems/si/acceleration.hpp>
+#include <boost/units/systems/si/io.hpp>
+
+#include <boost/fusion/container.hpp>
+#include <boost/mpl/vector.hpp>
+
+#include <boost/numeric/odeint/stepper/euler.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta4.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta4_classic.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54_classic.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_fehlberg78.hpp>
+#include <boost/numeric/odeint/stepper/controlled_runge_kutta.hpp>
+#include <boost/numeric/odeint/stepper/dense_output_runge_kutta.hpp>
+#include <boost/numeric/odeint/stepper/bulirsch_stoer.hpp>
+#include <boost/numeric/odeint/stepper/bulirsch_stoer_dense_out.hpp>
+#include <boost/numeric/odeint/algebra/fusion_algebra.hpp>
+#include <boost/numeric/odeint/algebra/fusion_algebra_dispatcher.hpp>
+
+
+using namespace boost::numeric::odeint;
+using namespace boost::unit_test;
+namespace mpl = boost::mpl;
+namespace fusion = boost::fusion;
+namespace units = boost::units;
+namespace si = boost::units::si;
+
+typedef double value_type;
+typedef units::quantity< si::time , value_type > time_type;
+typedef units::quantity< si::length , value_type > length_type;
+typedef units::quantity< si::velocity , value_type > velocity_type;
+typedef units::quantity< si::acceleration , value_type > acceleration_type;
+typedef fusion::vector< length_type , velocity_type > state_type;
+typedef fusion::vector< velocity_type , acceleration_type > deriv_type;
+
+void oscillator( const state_type &x , deriv_type &dxdt , time_type t )
+{
+ const units::quantity< si::frequency , value_type > omega = 1.0 * si::hertz;
+ fusion::at_c< 0 >( dxdt ) = fusion::at_c< 1 >( x );
+ fusion::at_c< 1 >( dxdt ) = - omega * omega * fusion::at_c< 0 >( x );
+}
+
+template< class Stepper >
+void check_stepper( Stepper &stepper )
+{
+ typedef Stepper stepper_type;
+ typedef typename stepper_type::state_type state_type;
+ typedef typename stepper_type::value_type value_type;
+ typedef typename stepper_type::deriv_type deriv_type;
+ typedef typename stepper_type::time_type time_type;
+ typedef typename stepper_type::order_type order_type;
+ typedef typename stepper_type::algebra_type algebra_type;
+ typedef typename stepper_type::operations_type operations_type;
+
+ const time_type t( 0.0 * si::second );
+ time_type dt( 0.1 * si::second );
+ state_type x( 1.0 * si::meter , 0.0 * si::meter_per_second );
+
+ // test call method one
+ stepper.do_step( oscillator , x , t , dt );
+
+ // test call method two
+ stepper.do_step( oscillator , x , t , x , dt );
+
+ // test call method three
+ deriv_type dxdt;
+ oscillator( x , dxdt , t );
+ stepper.do_step( oscillator , x , dxdt , t , dt );
+
+ // test call method four
+ oscillator( x , dxdt , t );
+ stepper.do_step( oscillator , x , dxdt , t , x , dt );
+}
+
+template< class Stepper >
+void check_fsal_stepper( Stepper &stepper )
+{
+ typedef Stepper stepper_type;
+ typedef typename stepper_type::state_type state_type;
+ typedef typename stepper_type::value_type value_type;
+ typedef typename stepper_type::deriv_type deriv_type;
+ typedef typename stepper_type::time_type time_type;
+ typedef typename stepper_type::order_type order_type;
+ typedef typename stepper_type::algebra_type algebra_type;
+ typedef typename stepper_type::operations_type operations_type;
+
+ const time_type t( 0.0 * si::second );
+ time_type dt( 0.1 * si::second );
+ state_type x( 1.0 * si::meter , 0.0 * si::meter_per_second );
+
+ // test call method one
+ stepper.do_step( oscillator , x , t , dt );
+
+ // test call method two
+ stepper.do_step( oscillator , x , t , x , dt );
+
+ // test call method three
+ deriv_type dxdt;
+ oscillator( x , dxdt , t );
+ stepper.do_step( oscillator , x , dxdt , t , dt );
+
+ // test call method four
+ stepper.do_step( oscillator , x , dxdt , t , x , dxdt , dt );
+}
+
+template< class Stepper >
+void check_error_stepper( Stepper &stepper )
+{
+ typedef Stepper stepper_type;
+ typedef typename stepper_type::state_type state_type;
+ typedef typename stepper_type::value_type value_type;
+ typedef typename stepper_type::deriv_type deriv_type;
+ typedef typename stepper_type::time_type time_type;
+ typedef typename stepper_type::order_type order_type;
+ typedef typename stepper_type::algebra_type algebra_type;
+ typedef typename stepper_type::operations_type operations_type;
+
+ const time_type t( 0.0 * si::second );
+ time_type dt( 0.1 * si::second );
+ state_type x( 1.0 * si::meter , 0.0 * si::meter_per_second ) , xerr;
+
+ // test call method one
+ stepper.do_step( oscillator , x , t , dt , xerr );
+
+ // test call method two
+ stepper.do_step( oscillator , x , t , x , dt , xerr );
+
+ // test call method three
+ deriv_type dxdt;
+ oscillator( x , dxdt , t );
+ stepper.do_step( oscillator , x , dxdt , t , dt , xerr );
+
+ // test call method four
+ stepper.do_step( oscillator , x , dxdt , t , x , dt , xerr );
+}
+
+template< class Stepper >
+void check_fsal_error_stepper( Stepper &stepper )
+{
+ typedef Stepper stepper_type;
+ typedef typename stepper_type::state_type state_type;
+ typedef typename stepper_type::value_type value_type;
+ typedef typename stepper_type::deriv_type deriv_type;
+ typedef typename stepper_type::time_type time_type;
+ typedef typename stepper_type::order_type order_type;
+ typedef typename stepper_type::algebra_type algebra_type;
+ typedef typename stepper_type::operations_type operations_type;
+
+ const time_type t( 0.0 * si::second );
+ time_type dt( 0.1 * si::second );
+ state_type x( 1.0 * si::meter , 0.0 * si::meter_per_second ) , xerr;
+
+ // test call method one
+ stepper.do_step( oscillator , x , t , dt , xerr );
+
+ // test call method two
+ stepper.do_step( oscillator , x , t , x , dt , xerr );
+
+ // test call method three
+ deriv_type dxdt;
+ oscillator( x , dxdt , t );
+ stepper.do_step( oscillator , x , dxdt , t , dt , xerr );
+
+ // test call method four
+ stepper.do_step( oscillator , x , dxdt , t , x , dxdt , dt , xerr );
+}
+
+template< class Stepper >
+void check_controlled_stepper( Stepper &stepper )
+{
+ typedef Stepper stepper_type;
+ typedef typename stepper_type::state_type state_type;
+ typedef typename stepper_type::value_type value_type;
+ typedef typename stepper_type::deriv_type deriv_type;
+ typedef typename stepper_type::time_type time_type;
+
+ time_type t( 0.0 * si::second );
+ time_type dt( 0.1 * si::second );
+ state_type x( 1.0 * si::meter , 0.0 * si::meter_per_second );
+
+ // test call method one
+ stepper.try_step( oscillator , x , t , dt );
+}
+
+
+template< class Stepper >
+void check_dense_output_stepper( Stepper &stepper )
+{
+ typedef Stepper stepper_type;
+ typedef typename stepper_type::state_type state_type;
+ typedef typename stepper_type::value_type value_type;
+ typedef typename stepper_type::deriv_type deriv_type;
+ typedef typename stepper_type::time_type time_type;
+// typedef typename stepper_type::order_type order_type;
+
+ time_type t( 0.0 * si::second );
+ time_type dt( 0.1 * si::second );
+ state_type x( 1.0 * si::meter , 0.0 * si::meter_per_second ) , x2;
+
+ stepper.initialize( x , t , dt );
+ stepper.do_step( oscillator );
+ stepper.calc_state( dt / 2.0 , x2 );
+}
+
+
+
+
+
+
+class stepper_types : public mpl::vector
+<
+ euler< state_type , value_type , deriv_type , time_type >,
+ runge_kutta4< state_type , value_type , deriv_type , time_type > ,
+ runge_kutta4_classic< state_type , value_type , deriv_type , time_type > ,
+ runge_kutta_cash_karp54< state_type , value_type , deriv_type , time_type >,
+ runge_kutta_cash_karp54_classic< state_type , value_type , deriv_type , time_type >
+ // don't run rk78 test - gcc requires > 5GB RAM to compile this
+ //, runge_kutta_fehlberg78< state_type , value_type , deriv_type , time_type >
+ > { };
+
+class fsal_stepper_types : public mpl::vector
+<
+ runge_kutta_dopri5< state_type , value_type , deriv_type , time_type >
+ > { };
+
+class error_stepper_types : public mpl::vector
+<
+ runge_kutta_cash_karp54_classic< state_type , value_type , deriv_type , time_type >
+ //, runge_kutta_fehlberg78< state_type , value_type , deriv_type , time_type >
+ > { };
+
+class fsal_error_stepper_types : public mpl::vector
+<
+ runge_kutta_dopri5< state_type , value_type , deriv_type , time_type >
+ > { };
+
+class controlled_stepper_types : public mpl::vector
+<
+ controlled_runge_kutta< runge_kutta_cash_karp54_classic< state_type , value_type , deriv_type , time_type > > ,
+ controlled_runge_kutta< runge_kutta_dopri5< state_type , value_type , deriv_type , time_type > >
+ , bulirsch_stoer< state_type , value_type , deriv_type , time_type >
+ // rk78 with units needs up to 3GB memory to compile - disable testing...
+ //, controlled_runge_kutta< runge_kutta_fehlberg78< state_type , value_type , deriv_type , time_type > >
+ > { };
+
+class dense_output_stepper_types : public mpl::vector
+<
+ dense_output_runge_kutta< euler< state_type , value_type , deriv_type , time_type > > ,
+ dense_output_runge_kutta<
+ controlled_runge_kutta< runge_kutta_dopri5< state_type , value_type , deriv_type , time_type > > >
+ //, bulirsch_stoer_dense_out< state_type , value_type , deriv_type , time_type >
+ > { };
+
+
+
+
+BOOST_AUTO_TEST_SUITE( stepper_with_units )
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_test , Stepper , stepper_types )
+{
+ Stepper stepper;
+ check_stepper( stepper );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( fsl_stepper_test , Stepper , fsal_stepper_types )
+{
+ Stepper stepper;
+ check_fsal_stepper( stepper );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( error_stepper_test , Stepper , error_stepper_types )
+{
+ Stepper stepper;
+ check_error_stepper( stepper );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( fsal_error_stepper_test , Stepper , fsal_error_stepper_types )
+{
+ Stepper stepper;
+ check_fsal_error_stepper( stepper );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( controlled_stepper_test , Stepper , controlled_stepper_types )
+{
+ Stepper stepper;
+ check_controlled_stepper( stepper );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( dense_ouput_test , Stepper , dense_output_stepper_types )
+{
+ Stepper stepper;
+ check_dense_output_stepper( stepper );
+}
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/symplectic_steppers.cpp b/test/symplectic_steppers.cpp
new file mode 100644
index 0000000..498983b
--- /dev/null
+++ b/test/symplectic_steppers.cpp
@@ -0,0 +1,391 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/symplectic_steppers.cpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_symplectic_steppers
+
+#define BOOST_FUSION_INVOKE_MAX_ARITY 15
+#define BOOST_RESULT_OF_NUM_ARGS 15
+#define FUSION_MAX_VECTOR_SIZE 15
+
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/array.hpp>
+#include <boost/static_assert.hpp>
+#include <boost/type_traits/is_same.hpp>
+
+#include <boost/mpl/vector.hpp>
+#include <boost/mpl/zip_view.hpp>
+#include <boost/mpl/vector_c.hpp>
+#include <boost/mpl/insert_range.hpp>
+#include <boost/mpl/end.hpp>
+#include <boost/mpl/size.hpp>
+#include <boost/mpl/copy.hpp>
+#include <boost/mpl/placeholders.hpp>
+#include <boost/mpl/inserter.hpp>
+#include <boost/mpl/at.hpp>
+
+#include <boost/fusion/container/vector.hpp>
+#include <boost/fusion/include/make_vector.hpp>
+
+#include <boost/numeric/odeint/algebra/vector_space_algebra.hpp>
+#include <boost/numeric/odeint/algebra/fusion_algebra.hpp>
+#include <boost/numeric/odeint/stepper/symplectic_euler.hpp>
+#include <boost/numeric/odeint/stepper/symplectic_rkn_sb3a_mclachlan.hpp>
+#include <boost/numeric/odeint/stepper/symplectic_rkn_sb3a_m4_mclachlan.hpp>
+#include <boost/numeric/odeint/integrate/integrate_const.hpp>
+
+#include "diagnostic_state_type.hpp"
+#include "const_range.hpp"
+#include "dummy_odes.hpp"
+#include "boost_units_helpers.hpp"
+
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+namespace mpl = boost::mpl;
+namespace fusion = boost::fusion;
+
+class custom_range_algebra : public range_algebra { };
+class custom_default_operations : public default_operations { };
+
+
+template< class Coor , class Mom , class Value , class CoorDeriv , class MomDeriv , class Time ,
+ class Algebra , class Operations , class Resizer >
+class complete_steppers : public mpl::vector<
+ symplectic_euler< Coor , Mom , Value , CoorDeriv , MomDeriv , Time ,
+ Algebra , Operations , Resizer >
+ , symplectic_rkn_sb3a_mclachlan< Coor , Mom , Value , CoorDeriv , MomDeriv , Time ,
+ Algebra , Operations , Resizer >
+ , symplectic_rkn_sb3a_m4_mclachlan< Coor , Mom , Value , CoorDeriv , MomDeriv , Time ,
+ Algebra , Operations , Resizer >
+ > {};
+
+template< class Resizer >
+class vector_steppers : public complete_steppers<
+ diagnostic_state_type , diagnostic_state_type2 , double ,
+ diagnostic_deriv_type , diagnostic_deriv_type2 , double ,
+ custom_range_algebra , custom_default_operations , Resizer
+ > { };
+
+
+typedef mpl::vector< initially_resizer , always_resizer , never_resizer > resizers;
+typedef mpl::vector_c< int , 1 , 3 , 0 > resizer_multiplicities ;
+
+
+typedef mpl::copy<
+ resizers ,
+ mpl::inserter<
+ mpl::vector0<> ,
+ mpl::insert_range<
+ mpl::_1 ,
+ mpl::end< mpl::_1 > ,
+ vector_steppers< mpl::_2 >
+ >
+ >
+ >::type all_stepper_methods;
+
+
+typedef mpl::size< vector_steppers< initially_resizer > >::type num_steppers;
+typedef mpl::copy<
+ resizer_multiplicities ,
+ mpl::inserter<
+ mpl::vector0<> ,
+ mpl::insert_range<
+ mpl::_1 ,
+ mpl::end< mpl::_1 > ,
+ const_range< num_steppers , mpl::_2 >
+ >
+ >
+ >::type all_multiplicities;
+
+
+
+
+
+
+
+BOOST_AUTO_TEST_SUITE( symplectic_steppers_test )
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( test_assoc_types , Stepper , vector_steppers< initially_resizer > )
+{
+ BOOST_STATIC_ASSERT_MSG(
+ ( boost::is_same< typename Stepper::coor_type , diagnostic_state_type >::value ) ,
+ "Coordinate type" );
+ BOOST_STATIC_ASSERT_MSG(
+ ( boost::is_same< typename Stepper::momentum_type , diagnostic_state_type2 >::value ) ,
+ "Momentum type" );
+ BOOST_STATIC_ASSERT_MSG(
+ ( boost::is_same< typename Stepper::coor_deriv_type , diagnostic_deriv_type >::value ) ,
+ "Coordinate deriv type" );
+ BOOST_STATIC_ASSERT_MSG(
+ ( boost::is_same< typename Stepper::momentum_deriv_type , diagnostic_deriv_type2 >::value ) ,
+ "Momentum deriv type" );
+
+ BOOST_STATIC_ASSERT_MSG(
+ ( boost::is_same< typename Stepper::state_type , std::pair< diagnostic_state_type , diagnostic_state_type2 > >::value ) ,
+ "State type" );
+ BOOST_STATIC_ASSERT_MSG(
+ ( boost::is_same< typename Stepper::deriv_type , std::pair< diagnostic_deriv_type , diagnostic_deriv_type2 > >::value ) ,
+ "Deriv type" );
+
+ BOOST_STATIC_ASSERT_MSG( ( boost::is_same< typename Stepper::value_type , double >::value ) , "Value type" );
+ BOOST_STATIC_ASSERT_MSG( ( boost::is_same< typename Stepper::time_type , double >::value ) , "Time type" );
+ BOOST_STATIC_ASSERT_MSG( ( boost::is_same< typename Stepper::algebra_type , custom_range_algebra >::value ) , "Algebra type" );
+ BOOST_STATIC_ASSERT_MSG( ( boost::is_same< typename Stepper::operations_type , custom_default_operations >::value ) , "Operations type" );
+
+ BOOST_STATIC_ASSERT_MSG( ( boost::is_same< typename Stepper::resizer_type , initially_resizer >::value ) , "Resizer type" );
+ BOOST_STATIC_ASSERT_MSG( ( boost::is_same< typename Stepper::stepper_category , stepper_tag >::value ) , "Stepper category" );
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( test_adjust_size , Stepper , vector_steppers< initially_resizer > )
+{
+ counter_state::init_counter();
+ counter_deriv::init_counter();
+ counter_state2::init_counter();
+ counter_deriv2::init_counter();
+
+ {
+ Stepper stepper;
+ diagnostic_state_type x;
+ stepper.adjust_size( x );
+ }
+
+ TEST_COUNTERS( counter_state , 0 , 0 , 0 , 0 );
+ TEST_COUNTERS( counter_state2 , 0 , 0 , 0 , 0 );
+ TEST_COUNTERS( counter_deriv , 1 , 1 , 0 , 1 );
+ TEST_COUNTERS( counter_deriv2 , 1 , 1 , 0 , 1 );
+}
+
+
+typedef mpl::zip_view< mpl::vector< all_stepper_methods , all_multiplicities > >::type zipped_steppers;
+BOOST_AUTO_TEST_CASE_TEMPLATE( test_resizing , Stepper , zipped_steppers )
+{
+ typedef typename mpl::at_c< Stepper , 0 >::type stepper_type;
+ const size_t multiplicity = mpl::at_c< Stepper , 1 >::type::value;
+
+ counter_state::init_counter();
+ counter_deriv::init_counter();
+ counter_state2::init_counter();
+ counter_deriv2::init_counter();
+
+ {
+ stepper_type stepper;
+ std::pair< diagnostic_state_type , diagnostic_state_type2 > x;
+ stepper.do_step( constant_mom_func() , x , 0.0 , 0.1 );
+ stepper.do_step( constant_mom_func() , x , 0.0 , 0.1 );
+ stepper.do_step( constant_mom_func() , x , 0.0 , 0.1 );
+ }
+
+ TEST_COUNTERS( counter_state , 0 , 0 , 0 , 0 );
+ TEST_COUNTERS( counter_state2 , 0 , 0 , 0 , 0 );
+ // dqdt is not needed when called with mom func only, so no resizing
+ // TEST_COUNTERS( counter_deriv , multiplicity , 1 , 0 , 1 );
+ TEST_COUNTERS( counter_deriv2 , multiplicity , 1 , 0 , 1 );
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( test_copying1 , Stepper , vector_steppers< initially_resizer > )
+{
+ counter_state::init_counter();
+ counter_deriv::init_counter();
+ counter_state2::init_counter();
+ counter_deriv2::init_counter();
+
+ {
+ Stepper stepper;
+ Stepper stepper2( stepper );
+ }
+
+ TEST_COUNTERS( counter_state , 0 , 0 , 0 , 0 );
+ TEST_COUNTERS( counter_state2 , 0 , 0 , 0 , 0 );
+ TEST_COUNTERS( counter_deriv , 0 , 2 , 1 , 2 );
+ TEST_COUNTERS( counter_deriv2 , 0 , 2 , 1 , 2 );
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( test_copying2 , Stepper , vector_steppers< initially_resizer > )
+{
+ counter_state::init_counter();
+ counter_deriv::init_counter();
+ counter_state2::init_counter();
+ counter_deriv2::init_counter();
+
+ {
+ Stepper stepper;
+ std::pair< diagnostic_state_type , diagnostic_state_type2 > x;
+ stepper.do_step( constant_mom_func() , x , 0.0 , 0.1 );
+ Stepper stepper2( stepper );
+ }
+
+ TEST_COUNTERS( counter_state , 0 , 0 , 0 , 0 );
+ TEST_COUNTERS( counter_state2 , 0 , 0 , 0 , 0 );
+ // dqdt is not needed when called with mom func only, so no resizing
+ //TEST_COUNTERS( counter_deriv , 1 , 2 , 1 , 2 );
+ TEST_COUNTERS( counter_deriv2 , 1 , 2 , 1 , 2 );
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( test_do_step_v1 , Stepper , vector_steppers< initially_resizer > )
+{
+ Stepper s;
+ std::pair< diagnostic_state_type , diagnostic_state_type2 > x1 , x2 , x3 , x4;
+ x1.first[0] = 1.0;
+ x1.second[0] = 2.0;
+ x2 = x3 = x4 = x1;
+ diagnostic_state_type x5_coor , x5_mom;
+ x5_coor[0] = x1.first[0];
+ x5_mom[0] = x1.second[0];
+
+ s.do_step( constant_mom_func() , x1 , 0.0 , 0.1 );
+
+ s.do_step( std::make_pair( default_coor_func() , constant_mom_func() ) , x2 , 0.0 , 0.1 );
+
+ default_coor_func cf;
+ constant_mom_func mf;
+ s.do_step( std::make_pair( boost::ref( cf ) , boost::ref( mf ) ) , x3 , 0.0 , 0.1 );
+
+ std::pair< default_coor_func , constant_mom_func > pf;
+ s.do_step( boost::ref( pf ) , x4 , 0.0 , 0.1 );
+
+ s.do_step( constant_mom_func() , std::make_pair( boost::ref( x5_coor ) , boost::ref( x5_mom ) ) , 0.0 , 0.1 );
+
+ // checking for absolute values is not possible here, since the steppers are to different
+ BOOST_CHECK_CLOSE( x1.first[0] , x2.first[0] , 1.0e-14 );
+ BOOST_CHECK_CLOSE( x2.first[0] , x3.first[0] , 1.0e-14 );
+ BOOST_CHECK_CLOSE( x3.first[0] , x4.first[0] , 1.0e-14 );
+ BOOST_CHECK_CLOSE( x4.first[0] , x5_coor[0] , 1.0e-14 );
+
+ BOOST_CHECK_CLOSE( x1.second[0] , x2.second[0] , 1.0e-14 );
+ BOOST_CHECK_CLOSE( x2.second[0] , x3.second[0] , 1.0e-14 );
+ BOOST_CHECK_CLOSE( x3.second[0] , x4.second[0] , 1.0e-14 );
+ BOOST_CHECK_CLOSE( x4.second[0] , x5_mom[0] , 1.0e-14 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( test_do_step_range , Stepper , vector_steppers< initially_resizer > )
+{
+ Stepper s;
+ diagnostic_state_type q , p ;
+ q[0] = 1.0;
+ p[0] = 2.0;
+
+ std::vector< double > x;
+ x.push_back( 1.0 );
+ x.push_back( 2.0 );
+ s.do_step( constant_mom_func() ,
+ std::make_pair( x.begin() , x.begin() + 1 ) ,
+ std::make_pair( x.begin() + 1 , x.begin() + 2 ) ,
+ 0.0 , 0.1 );
+
+ s.do_step( constant_mom_func() , q , p , 0.0 , 0.1 );
+
+ BOOST_CHECK_CLOSE( q[0] , x[0] , 1.0e-14 );
+ BOOST_CHECK_CLOSE( p[0] , x[1] , 1.0e-14 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( test_do_step_v2 , Stepper , vector_steppers< initially_resizer > )
+{
+ Stepper s;
+ diagnostic_state_type q , p ;
+ q[0] = 1.0;
+ p[0] = 2.0;
+ diagnostic_state_type q2 = q , p2 = p;
+
+
+ s.do_step( constant_mom_func() , q , p , 0.0 , 0.1 );
+ s.do_step( constant_mom_func() , std::make_pair( boost::ref( q2 ) , boost::ref( p2 ) ) , 0.0 , 0.1 );
+
+ BOOST_CHECK_CLOSE( q[0] , q2[0] , 1.0e-14 );
+ BOOST_CHECK_CLOSE( p[0] , p2[0] , 1.0e-14 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( test_do_step_v3 , Stepper , vector_steppers< initially_resizer > )
+{
+ Stepper s;
+ std::pair< diagnostic_state_type , diagnostic_state_type2 > x_in , x_out;
+ x_in.first[0] = 1.0;
+ x_in.second[0] = 2.0;
+ diagnostic_state_type q2 , p2;
+ q2[0] = x_in.first[0];
+ p2[0] = x_in.second[0];
+
+
+ s.do_step( constant_mom_func() , x_in , 0.0 , x_out , 0.1 );
+ s.do_step( constant_mom_func() , std::make_pair( boost::ref( q2 ) , boost::ref( p2 ) ) , 0.0 , 0.1 );
+
+ BOOST_CHECK_CLOSE( x_in.first[0] , 1.0 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( x_in.second[0] , 2.0 , 1.0e-14 );
+ BOOST_CHECK_CLOSE( x_out.first[0] , q2[0] , 1.0e-14 );
+ BOOST_CHECK_CLOSE( x_out.second[0] , p2[0] , 1.0e-14 );
+}
+
+
+typedef double vector_space;
+typedef complete_steppers< vector_space , vector_space , double ,
+ vector_space , vector_space , double ,
+ vector_space_algebra , default_operations , initially_resizer > vector_space_steppers;
+BOOST_AUTO_TEST_CASE_TEMPLATE( test_with_vector_space_algebra , Stepper , vector_space_steppers )
+{
+ Stepper s;
+ std::pair< vector_space , vector_space > x;
+ s.do_step( constant_mom_func_vector_space_1d() , x , 0.0 , 0.1 );
+
+ s.do_step( std::make_pair( default_coor_func_vector_space_1d() , constant_mom_func_vector_space_1d() ) , x , 0.0 , 0.1 );
+}
+
+
+typedef boost::fusion::vector< length_type > coor_type;
+typedef boost::fusion::vector< velocity_type > mom_type;
+typedef boost::fusion::vector< acceleration_type > acc_type;
+typedef complete_steppers< coor_type , mom_type , double ,
+ mom_type , acc_type , time_type,
+ fusion_algebra , default_operations , initially_resizer > boost_unit_steppers;
+BOOST_AUTO_TEST_CASE_TEMPLATE( test_with_boost_units , Stepper , boost_unit_steppers )
+{
+ namespace fusion = boost::fusion;
+ namespace si = boost::units::si;
+ Stepper s;
+
+ coor_type q = fusion::make_vector( 1.0 * si::meter );
+ mom_type p = fusion::make_vector( 2.0 * si::meter_per_second );
+ time_type t = 0.0 * si::second;
+ time_type dt = 0.1 * si::second;
+
+ coor_type q1 = q , q2 = q;
+ mom_type p1 = p , p2 = p;
+
+ s.do_step( oscillator_mom_func_units() , std::make_pair( boost::ref( q ) , boost::ref( p ) ) , t , dt );
+
+ s.do_step( std::make_pair( oscillator_coor_func_units() , oscillator_mom_func_units() ) ,
+ std::make_pair( boost::ref( q1 ) , boost::ref( p1 ) ) , t , dt );
+
+ s.do_step( oscillator_mom_func_units() , q2 , p2 , t , dt );
+
+ BOOST_CHECK_CLOSE( ( fusion::at_c< 0 >( q ).value() ) , ( fusion::at_c< 0 >( q1 ).value() ) , 1.0e-14 );
+ BOOST_CHECK_CLOSE( ( fusion::at_c< 0 >( q1 ).value() ) , ( fusion::at_c< 0 >( q2 ).value() ) , 1.0e-14 );
+ BOOST_CHECK_CLOSE( ( fusion::at_c< 0 >( p ).value() ) , ( fusion::at_c< 0 >( p1 ).value() ) , 1.0e-14 );
+ BOOST_CHECK_CLOSE( ( fusion::at_c< 0 >( p1 ).value() ) , ( fusion::at_c< 0 >( p2 ).value() ) , 1.0e-14 );
+}
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/times_iterator.cpp b/test/times_iterator.cpp
new file mode 100644
index 0000000..552d5af
--- /dev/null
+++ b/test/times_iterator.cpp
@@ -0,0 +1,237 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/times_iterator.cpp
+
+ [begin_description]
+ This file tests the n-step iterator.
+ [end_description]
+
+ Copyright 2009-2013 Karsten Ahnert
+ Copyright 2009-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#define BOOST_TEST_MODULE odeint_times_iterator
+
+#include <iterator>
+#include <algorithm>
+#include <vector>
+#include <iostream>
+
+#include <boost/numeric/odeint/config.hpp>
+#include <boost/array.hpp>
+#include <boost/range/algorithm/for_each.hpp>
+#include <boost/range/algorithm/copy.hpp>
+#include <boost/mpl/vector.hpp>
+
+#include <boost/test/unit_test.hpp>
+#include <boost/test/floating_point_comparison.hpp>
+
+#include <boost/numeric/odeint/iterator/times_iterator.hpp>
+#include "dummy_steppers.hpp"
+#include "dummy_odes.hpp"
+#include "dummy_observers.hpp"
+
+namespace mpl = boost::mpl;
+using namespace boost::numeric::odeint;
+
+typedef dummy_stepper::state_type state_type;
+typedef dummy_stepper::value_type value_type;
+
+
+BOOST_AUTO_TEST_SUITE( times_iterator_test )
+
+typedef mpl::vector<
+ dummy_stepper
+ , dummy_dense_output_stepper
+ > dummy_steppers;
+
+boost::array<double,4> times = {{ 0.0 , 0.1, 0.2, 0.3 }};
+typedef boost::array<double,4>::iterator time_iterator_type;
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_stepper_iterator , Stepper , dummy_steppers )
+{
+ typedef times_iterator< Stepper , empty_system , state_type , time_iterator_type > iterator_type;
+ state_type x = {{ 1.0 }};
+ iterator_type iter1 = iterator_type( Stepper() , empty_system() , x , times.begin() , times.end() , 0.1 );
+ iterator_type iter2 = iter1;
+ BOOST_CHECK_EQUAL( &(*iter1) , &(*iter2) );
+ BOOST_CHECK_EQUAL( &(*iter1) , &x );
+ BOOST_CHECK( iter1.same( iter2 ) );
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( assignment_stepper_iterator , Stepper , dummy_steppers )
+{
+ std::cout << "assignment" << std::endl;
+ typedef times_iterator< Stepper , empty_system , state_type , time_iterator_type> iterator_type;
+ state_type x1 = {{ 1.0 }} , x2 = {{ 2.0 }};
+ iterator_type iter1 = iterator_type( Stepper() , empty_system() , x1 , times.begin() , times.end() , 0.1 );
+ iterator_type iter2 = iterator_type( Stepper() , empty_system() , x2 , times.begin() , times.end() , 0.2 );
+ BOOST_CHECK_EQUAL( &(*iter1) , &x1 );
+ BOOST_CHECK_EQUAL( &(*iter2) , &x2 );
+ BOOST_CHECK( !iter1.same( iter2 ) );
+ iter2 = iter1;
+ BOOST_CHECK_EQUAL( &(*iter1) , &x1 );
+ BOOST_CHECK_EQUAL( &(*iter2) , &x1 );
+ BOOST_CHECK( iter1.same( iter2 ) );
+}
+
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_iterator_factory , Stepper , dummy_steppers )
+{
+ std::cout << "factory" << std::endl;
+ Stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ std::for_each(
+ make_times_iterator_begin( stepper , boost::ref( system ) , x , times.begin(), times.end() , 0.1 ) ,
+ make_times_iterator_end<time_iterator_type>( stepper , boost::ref( system ) , x ) ,
+ dummy_observer() );
+
+ // dummy_steppers just add 0.25 at each step, the above for_each leads to 3 do_step calls so x should be 1.75
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_range , Stepper , dummy_steppers )
+{
+ std::cout << "range" << std::endl;
+ Stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ boost::for_each( make_times_range( stepper , boost::ref( system ) , x , times.begin() , times.end() , 0.1 ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_iterator_with_reference_wrapper_factory , Stepper , dummy_steppers )
+{
+ Stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ std::for_each(
+ make_times_iterator_begin( boost::ref( stepper ) , boost::ref( system ) , x , times.begin() , times.end() , 0.1 ) ,
+ make_times_iterator_end<time_iterator_type>( boost::ref( stepper ) , boost::ref( system ) , x ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_range_with_reference_wrapper , Stepper , dummy_steppers )
+{
+ Stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ boost::for_each( make_times_range( boost::ref( stepper ) , boost::ref( system ) , x , times.begin() , times.end(), 0.1 ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-13 );
+}
+
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( transitivity1 , Stepper , dummy_steppers )
+{
+ typedef times_iterator< Stepper , empty_system , state_type , time_iterator_type > stepper_iterator;
+ std::cout << "transitivity1" << std::endl;
+ state_type x = {{ 1.0 }};
+ stepper_iterator first1( Stepper() , empty_system() , x , times.end() , times.end() , 0.1 );
+ stepper_iterator last1( Stepper() , empty_system() , x );
+ stepper_iterator last2( Stepper() , empty_system() , x );
+
+ BOOST_CHECK( first1 == last1 );
+ BOOST_CHECK( first1 == last2 );
+ BOOST_CHECK( last1 == last2 );
+
+ first1 = stepper_iterator( Stepper() , empty_system() , x , times.end()-1 , times.end() , 0.1 );
+ last1 = stepper_iterator( Stepper() , empty_system() , x );
+ BOOST_CHECK( first1 != last1 );
+ BOOST_CHECK( ++first1 == last1 );
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm , Stepper , dummy_steppers )
+{
+ typedef times_iterator< Stepper , empty_system , state_type , time_iterator_type> stepper_iterator;
+ state_type x = {{ 1.0 }};
+ std::vector< state_type > res;
+ stepper_iterator first( Stepper() , empty_system() , x , times.begin() , times.end() , 0.1 );
+ stepper_iterator last( Stepper() , empty_system() , x );
+
+ std::copy( first , last , std::back_insert_iterator< std::vector< state_type > >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 4 ) );
+ BOOST_CHECK_CLOSE( res[0][0] , 1.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1][0] , 1.25 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2][0] , 1.5 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3][0] , 1.75 , 1.0e-13 );
+
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-13 ); // the iterator should not iterate over the end
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm_negative_time_step , Stepper , dummy_steppers )
+{
+ typedef times_iterator< Stepper , empty_system , state_type , time_iterator_type > stepper_iterator;
+ state_type x = {{ 1.0 }};
+ std::vector< state_type > res;
+ boost::array<double,4> neg_times = {{ 0.0 , -0.1, -0.2, -0.3 }};
+ stepper_iterator first( Stepper() , empty_system() , x , neg_times.begin() , neg_times.end() , -0.1 );
+ stepper_iterator last( Stepper() , empty_system() , x );
+
+ std::copy( first , last , std::back_insert_iterator< std::vector< state_type > >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 4 ) );
+ BOOST_CHECK_CLOSE( res[0][0] , 1.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1][0] , 1.25 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2][0] , 1.5 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3][0] , 1.75 , 1.0e-13 );
+
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-13 );
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm_with_factory , Stepper , dummy_steppers )
+{
+ state_type x = {{ 1.0 }};
+ std::vector< state_type > res;
+ std::copy( make_times_iterator_begin( Stepper() , empty_system() , x , times.begin() , times.end() , 0.1 ) ,
+ make_times_iterator_end<time_iterator_type>( Stepper() , empty_system() , x ) ,
+ std::back_insert_iterator< std::vector< state_type > >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 4 ) );
+ BOOST_CHECK_CLOSE( res[0][0] , 1.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1][0] , 1.25 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2][0] , 1.5 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3][0] , 1.75 , 1.0e-13 );
+
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm_with_range_factory , Stepper , dummy_steppers )
+{
+ state_type x = {{ 1.0 }};
+ std::vector< state_type > res;
+ boost::range::copy( make_times_range( Stepper() , empty_system() , x , times.begin() , times.end() , 0.1 ) ,
+ std::back_insert_iterator< std::vector< state_type > >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 4 ) );
+ BOOST_CHECK_CLOSE( res[0][0] , 1.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1][0] , 1.25 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2][0] , 1.5 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3][0] , 1.75 , 1.0e-13 );
+
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-13 );
+}
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/times_time_iterator.cpp b/test/times_time_iterator.cpp
new file mode 100644
index 0000000..274f8a6
--- /dev/null
+++ b/test/times_time_iterator.cpp
@@ -0,0 +1,250 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/times_time_iterator.cpp
+
+ [begin_description]
+ This file tests the times iterator.
+ [end_description]
+
+ Copyright 2009-2013 Karsten Ahnert
+ Copyright 2009-2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#define BOOST_TEST_MODULE odeint_times_time_iterator
+
+#include <iterator>
+#include <algorithm>
+#include <vector>
+#include <iostream>
+
+#include <boost/numeric/odeint/config.hpp>
+#include <boost/array.hpp>
+#include <boost/range/algorithm/for_each.hpp>
+#include <boost/range/algorithm/copy.hpp>
+#include <boost/mpl/vector.hpp>
+
+#include <boost/test/unit_test.hpp>
+#include <boost/test/floating_point_comparison.hpp>
+
+#include <boost/numeric/odeint/iterator/times_time_iterator.hpp>
+#include "dummy_steppers.hpp"
+#include "dummy_odes.hpp"
+#include "dummy_observers.hpp"
+
+namespace mpl = boost::mpl;
+using namespace boost::numeric::odeint;
+
+typedef dummy_stepper::state_type state_type;
+typedef dummy_stepper::value_type value_type;
+typedef dummy_stepper::time_type time_type;
+
+BOOST_AUTO_TEST_SUITE( times_time_iterator_test )
+
+typedef mpl::vector<
+ dummy_stepper
+ , dummy_dense_output_stepper
+ > dummy_steppers;
+
+boost::array<double,4> times = {{ 0.0 , 0.1, 0.2, 0.3 }};
+typedef boost::array<double,4>::iterator time_iterator_type;
+typedef std::vector< std::pair< state_type , time_type > > result_vector;
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_stepper_iterator , Stepper , dummy_steppers )
+{
+ typedef times_time_iterator< Stepper , empty_system , state_type , time_iterator_type > iterator_type;
+ state_type x = {{ 1.0 }};
+ iterator_type iter1 = iterator_type( Stepper() , empty_system() , x , times.begin() , times.end() , 0.1 );
+ iterator_type iter2 = iter1;
+ BOOST_CHECK_EQUAL( &(iter1->first) , &(iter2->first) );
+ BOOST_CHECK_EQUAL( &(iter1->first) , &x );
+ BOOST_CHECK( iter1.same( iter2 ) );
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( assignment_stepper_iterator , Stepper , dummy_steppers )
+{
+ std::cout << "assignment" << std::endl;
+ typedef times_time_iterator< Stepper , empty_system , state_type , time_iterator_type> iterator_type;
+ state_type x1 = {{ 1.0 }} , x2 = {{ 2.0 }};
+ iterator_type iter1 = iterator_type( Stepper() , empty_system() , x1 , times.begin() , times.end() , 0.1 );
+ iterator_type iter2 = iterator_type( Stepper() , empty_system() , x2 , times.begin() , times.end() , 0.2 );
+ BOOST_CHECK_EQUAL( &(iter1->first) , &x1 );
+ BOOST_CHECK_EQUAL( &(iter2->first) , &x2 );
+ BOOST_CHECK( !iter1.same( iter2 ) );
+ iter2 = iter1;
+ BOOST_CHECK_EQUAL( &(iter1->first) , &x1 );
+ BOOST_CHECK_EQUAL( &(iter2->first) , &x1 );
+ BOOST_CHECK( iter1.same( iter2 ) );
+}
+
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_iterator_factory , Stepper , dummy_steppers )
+{
+ std::cout << "factory" << std::endl;
+ Stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ std::for_each(
+ make_times_time_iterator_begin( stepper , boost::ref( system ) , x , times.begin(), times.end() , 0.1 ) ,
+ make_times_time_iterator_end<time_iterator_type>( stepper , boost::ref( system ) , x ) ,
+ dummy_observer() );
+
+ // dummy_steppers just add 0.25 at each step, the above for_each leads to 3 do_step calls so x should be 1.75
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_range , Stepper , dummy_steppers )
+{
+ std::cout << "range" << std::endl;
+ Stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ boost::for_each( make_times_time_range( stepper , boost::ref( system ) , x , times.begin() , times.end() , 0.1 ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_iterator_with_reference_wrapper_factory , Stepper , dummy_steppers )
+{
+ Stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ std::for_each(
+ make_times_time_iterator_begin( boost::ref( stepper ) , boost::ref( system ) , x , times.begin() , times.end() , 0.1 ) ,
+ make_times_time_iterator_end<time_iterator_type>( boost::ref( stepper ) , boost::ref( system ) , x ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( stepper_range_with_reference_wrapper , Stepper , dummy_steppers )
+{
+ Stepper stepper;
+ empty_system system;
+ state_type x = {{ 1.0 }};
+
+ boost::for_each( make_times_time_range( boost::ref( stepper ) , boost::ref( system ) , x , times.begin() , times.end(), 0.1 ) ,
+ dummy_observer() );
+
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-13 );
+}
+
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( transitivity1 , Stepper , dummy_steppers )
+{
+ typedef times_time_iterator< Stepper , empty_system , state_type , time_iterator_type > stepper_iterator;
+ std::cout << "transitivity1" << std::endl;
+ state_type x = {{ 1.0 }};
+ stepper_iterator first1( Stepper() , empty_system() , x , times.end() , times.end() , 0.1 );
+ stepper_iterator last1( Stepper() , empty_system() , x );
+ stepper_iterator last2( Stepper() , empty_system() , x );
+
+ BOOST_CHECK( first1 == last1 );
+ BOOST_CHECK( first1 == last2 );
+ BOOST_CHECK( last1 == last2 );
+
+ first1 = stepper_iterator( Stepper() , empty_system() , x , times.end()-1 , times.end() , 0.1 );
+ last1 = stepper_iterator( Stepper() , empty_system() , x );
+ BOOST_CHECK( first1 != last1 );
+ BOOST_CHECK( ++first1 == last1 );
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm , Stepper , dummy_steppers )
+{
+ typedef times_time_iterator< Stepper , empty_system , state_type , time_iterator_type> stepper_iterator;
+ state_type x = {{ 1.0 }};
+ result_vector res;
+ stepper_iterator first( Stepper() , empty_system() , x , times.begin() , times.end() , 0.1 );
+ stepper_iterator last( Stepper() , empty_system() , x );
+
+ std::copy( first , last , std::back_insert_iterator< result_vector >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 4 ) );
+ BOOST_CHECK_CLOSE( res[0].first[0] , 1.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1].first[0] , 1.25 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2].first[0] , 1.5 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3].first[0] , 1.75 , 1.0e-13 );
+
+ for( size_t n=0 ; n<4 ; ++n )
+ BOOST_CHECK_CLOSE( res[n].second , times[n] , 1.0e-13 );
+
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-13 ); // the iterator should not iterate over the end
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm_negative_time_step , Stepper , dummy_steppers )
+{
+ typedef times_time_iterator< Stepper , empty_system , state_type , time_iterator_type > stepper_iterator;
+ state_type x = {{ 1.0 }};
+ result_vector res;
+ boost::array<double,4> neg_times = {{ 0.0 , -0.1, -0.2, -0.3 }};
+ stepper_iterator first( Stepper() , empty_system() , x , neg_times.begin() , neg_times.end() , -0.1 );
+ stepper_iterator last( Stepper() , empty_system() , x );
+
+ std::copy( first , last , std::back_insert_iterator< result_vector >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 4 ) );
+ BOOST_CHECK_CLOSE( res[0].first[0] , 1.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1].first[0] , 1.25 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2].first[0] , 1.5 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3].first[0] , 1.75 , 1.0e-13 );
+
+ for( size_t n=0 ; n<4 ; ++n )
+ BOOST_CHECK_CLOSE( res[n].second , neg_times[n] , 1.0e-13 );
+
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-13 );
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm_with_factory , Stepper , dummy_steppers )
+{
+ state_type x = {{ 1.0 }};
+ result_vector res;
+ std::copy( make_times_time_iterator_begin( Stepper() , empty_system() , x , times.begin() , times.end() , 0.1 ) ,
+ make_times_time_iterator_end<time_iterator_type>( Stepper() , empty_system() , x ) ,
+ std::back_insert_iterator< result_vector >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 4 ) );
+ BOOST_CHECK_CLOSE( res[0].first[0] , 1.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1].first[0] , 1.25 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2].first[0] , 1.5 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3].first[0] , 1.75 , 1.0e-13 );
+
+ for( size_t n=0 ; n<4 ; ++n )
+ BOOST_CHECK_CLOSE( res[n].second , times[n] , 1.0e-13 );
+
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( copy_algorithm_with_range_factory , Stepper , dummy_steppers )
+{
+ state_type x = {{ 1.0 }};
+ result_vector res;
+ boost::range::copy( make_times_time_range( Stepper() , empty_system() , x , times.begin() , times.end() , 0.1 ) ,
+ std::back_insert_iterator< result_vector >( res ) );
+
+ BOOST_CHECK_EQUAL( res.size() , size_t( 4 ) );
+ BOOST_CHECK_CLOSE( res[0].first[0] , 1.0 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[1].first[0] , 1.25 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[2].first[0] , 1.5 , 1.0e-13 );
+ BOOST_CHECK_CLOSE( res[3].first[0] , 1.75 , 1.0e-13 );
+
+ for( size_t n=0 ; n<4 ; ++n )
+ BOOST_CHECK_CLOSE( res[n].second , times[n] , 1.0e-13 );
+
+ BOOST_CHECK_CLOSE( x[0] , 1.75 , 1.0e-13 );
+}
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/trivial_state.cpp b/test/trivial_state.cpp
new file mode 100644
index 0000000..9976db7
--- /dev/null
+++ b/test/trivial_state.cpp
@@ -0,0 +1,109 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/trivial_state.cpp
+
+ [begin_description]
+ This file tests if the steppers can integrate the trivial state consisting of a single double.
+ [end_description]
+
+ Copyright 2012-2013 Mario Mulansky
+ Copyright 2012 Karsten Ahnert
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <limits>
+
+// disable checked iterator warning for msvc
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_trivial_state
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/mpl/vector.hpp>
+#include <boost/mpl/int.hpp>
+#include <boost/mpl/at.hpp>
+
+#include <boost/numeric/odeint/stepper/euler.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta4.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp>
+#include <boost/numeric/odeint/stepper/generation.hpp>
+#include <boost/numeric/odeint/integrate/integrate_adaptive.hpp>
+#include <boost/numeric/odeint/algebra/vector_space_algebra.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+namespace mpl = boost::mpl;
+
+struct constant_system
+{
+ template< typename T >
+ void operator()( const T &x , T &dxdt , const T t ) const
+ { dxdt = 1.0; }
+};
+
+
+BOOST_AUTO_TEST_SUITE( trivial_state_test )
+
+/* test different do_step methods of simple steppers */
+
+typedef mpl::vector<
+ euler< double > ,
+ runge_kutta4< double > ,
+ // with floats all four parameters have to be given explicitly to override default double
+ euler< float , float , float , float > ,
+ runge_kutta4< float , float , float , float >
+ >::type stepper_types;
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( test_do_step , T, stepper_types )
+{
+ typedef T stepper_type;
+ stepper_type stepper;
+ typename stepper_type::state_type x = 0.0;
+ typename stepper_type::time_type t = 0.0;
+ typename stepper_type::time_type dt = 0.1;
+ stepper.do_step( constant_system() , x , t , dt );
+ BOOST_CHECK_CLOSE( x , 0.1 , 100*std::numeric_limits< typename stepper_type::state_type >::epsilon() );
+
+ // this overload is not allowed if the types of dxdt and dt are the same
+ // deriv_type dxdt = 1.0;
+ // stepper.do_step( constant_system , x , dxdt , t , dt );
+
+ typename stepper_type::state_type x_out;
+ stepper.do_step( constant_system() , x , t , x_out , dt );
+ BOOST_CHECK_CLOSE( x , 0.1 , 100*std::numeric_limits< typename stepper_type::state_type >::epsilon() );
+ BOOST_CHECK_CLOSE( x_out , 0.2 , 100*std::numeric_limits< typename stepper_type::state_type >::epsilon() );
+}
+
+
+/* test integrate_adaptive with controlled steppers */
+
+typedef mpl::vector<
+ runge_kutta_cash_karp54< double > ,
+ runge_kutta_dopri5< double > ,
+ // with floats all four parameters have to be given explicitly to override default double
+ runge_kutta_cash_karp54< float , float , float , float > ,
+ runge_kutta_dopri5< float , float , float , float >
+ > error_stepper_types;
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( test_integrate , T , error_stepper_types )
+{
+ typedef T stepper_type;
+ typename stepper_type::state_type x = 0.0;
+ typename stepper_type::time_type t0 = 0.0;
+ typename stepper_type::time_type t1 = 1.0;
+ typename stepper_type::time_type dt = 0.1;
+ integrate_adaptive( make_controlled< stepper_type >( 1e-6 , 1e-6 ) , constant_system() , x , t0 , t1 , dt );
+ BOOST_CHECK_CLOSE( x , 1.0 , 100*std::numeric_limits< typename stepper_type::state_type >::epsilon() );
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/unwrap_boost_reference.cpp b/test/unwrap_boost_reference.cpp
new file mode 100644
index 0000000..4106fdf
--- /dev/null
+++ b/test/unwrap_boost_reference.cpp
@@ -0,0 +1,40 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/unwrap_boost_reference.cpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2009-2012 Karsten Ahnert
+ Copyright 2009-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#define BOOST_TEST_MODULE odeint_unwrap_boost_reference
+
+#include <boost/numeric/odeint/util/unwrap_reference.hpp>
+#include <boost/test/unit_test.hpp>
+
+using namespace boost::unit_test;
+
+template< typename T >
+void func( T t )
+{
+ typedef typename boost::numeric::odeint::unwrap_reference< T >::type type;
+}
+
+BOOST_AUTO_TEST_SUITE( unwrap_boost_reference_test )
+
+BOOST_AUTO_TEST_CASE( test_case )
+{
+ int a;
+ func( boost::ref( a ) );
+ func( a );
+}
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/unwrap_reference.cpp b/test/unwrap_reference.cpp
new file mode 100644
index 0000000..7337ddd
--- /dev/null
+++ b/test/unwrap_reference.cpp
@@ -0,0 +1,42 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/unwrap_reference.cpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2009-2012 Karsten Ahnert
+ Copyright 2009-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#define BOOST_TEST_MODULE odeint_unwrap_reference
+
+#include <boost/numeric/odeint/util/unwrap_reference.hpp>
+
+#include <boost/test/unit_test.hpp>
+
+using namespace boost::unit_test;
+
+template< typename T >
+void func( T t )
+{
+ typedef typename boost::numeric::odeint::unwrap_reference< T >::type type;
+}
+
+BOOST_AUTO_TEST_SUITE( unwrap_reference_test )
+
+BOOST_AUTO_TEST_CASE( test_case )
+{
+ int a;
+ func( std::ref( a ) );
+ func( a );
+}
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/velocity_verlet.cpp b/test/velocity_verlet.cpp
new file mode 100644
index 0000000..93a2e97
--- /dev/null
+++ b/test/velocity_verlet.cpp
@@ -0,0 +1,298 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test/velocity_verlet.cpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2009-2012 Karsten Ahnert
+ Copyright 2009-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_velocity_verlet
+
+#define BOOST_FUSION_INVOKE_MAX_ARITY 15
+#define BOOST_RESULT_OF_NUM_ARGS 15
+
+#include <boost/numeric/odeint/config.hpp>
+
+#include "resizing_test_state_type.hpp"
+
+#include <boost/numeric/odeint/stepper/velocity_verlet.hpp>
+#include <boost/numeric/odeint/algebra/fusion_algebra.hpp>
+
+#include <boost/array.hpp>
+#include <boost/test/unit_test.hpp>
+
+#include <boost/units/systems/si/length.hpp>
+#include <boost/units/systems/si/time.hpp>
+#include <boost/units/systems/si/velocity.hpp>
+#include <boost/units/systems/si/acceleration.hpp>
+#include <boost/units/systems/si/io.hpp>
+
+#include <boost/fusion/include/vector.hpp>
+#include <boost/fusion/include/vector20.hpp>
+#include <boost/fusion/container.hpp>
+
+namespace fusion = boost::fusion;
+namespace units = boost::units;
+namespace si = boost::units::si;
+
+typedef double value_type;
+typedef units::quantity< si::time , value_type > time_type;
+typedef units::unit< units::derived_dimension< units::time_base_dimension , 2 >::type , si::system > time_2;
+typedef units::quantity< time_2 , value_type > time_2_type;
+typedef units::quantity< si::length , value_type > length_type;
+typedef units::quantity< si::velocity , value_type > velocity_type;
+typedef units::quantity< si::acceleration , value_type > acceleration_type;
+typedef fusion::vector< length_type , length_type > coor_vector;
+typedef fusion::vector< velocity_type , velocity_type > velocity_vector;
+typedef fusion::vector< acceleration_type , acceleration_type > accelartion_vector;
+
+
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+size_t ode_call_count;
+
+struct velocity_verlet_fixture
+{
+ velocity_verlet_fixture( void ) { ode_call_count = 0; adjust_size_count = 0; }
+};
+
+struct ode
+{
+ template< class CoorIn , class MomentumIn , class AccelerationOut , class Time >
+ void operator()( const CoorIn &q , const MomentumIn &p , AccelerationOut &a , Time t ) const
+ {
+ a[0] = -q[0] - p[0];
+ a[1] = -q[1] - p[1];
+ ++ode_call_count;
+ }
+};
+
+struct ode_units
+{
+ void operator()( coor_vector const &q , velocity_vector const &p , accelartion_vector &a , time_type t ) const
+ {
+ const units::quantity< si::frequency , value_type > omega = 1.0 * si::hertz;
+ const units::quantity< si::frequency , value_type > friction = 0.001 * si::hertz;
+ fusion::at_c< 0 >( a ) = omega * omega * fusion::at_c< 0 >( q ) - friction * fusion::at_c< 0 >( p );
+ fusion::at_c< 1 >( a ) = omega * omega * fusion::at_c< 1 >( q ) - friction * fusion::at_c< 0 >( p );
+ ++ode_call_count;
+ }
+};
+
+template< class Q , class P >
+void init_state( Q &q , P &p )
+{
+ q[0] = 1.0 ; q[1] = 0.5;
+ p[0] = 2.0 ; p[1] = -1.0;
+}
+
+typedef boost::array< double , 2 > array_type;
+typedef std::vector< double > vector_type;
+
+typedef velocity_verlet< array_type > array_stepper;
+typedef velocity_verlet< vector_type > vector_stepper;
+
+template< typename Resizer >
+struct get_resizer_test_stepper
+{
+ typedef velocity_verlet< test_array_type , test_array_type , double , test_array_type ,
+ double , double , range_algebra , default_operations , Resizer > type;
+};
+
+
+
+
+
+BOOST_AUTO_TEST_SUITE( velocity_verlet_test )
+
+BOOST_FIXTURE_TEST_CASE( test_with_array_ref , velocity_verlet_fixture )
+{
+ array_stepper stepper;
+ array_type q , p ;
+ init_state( q , p );
+ stepper.do_step( ode() , std::make_pair( boost::ref( q ) , boost::ref( p ) ) , 0.0 , 0.01 );
+ BOOST_CHECK_EQUAL( ode_call_count , size_t( 2 ) );
+}
+
+BOOST_FIXTURE_TEST_CASE( test_with_array_pair , velocity_verlet_fixture )
+{
+ array_stepper stepper;
+ std::pair< array_type , array_type > xxx;
+ init_state( xxx.first , xxx.second );
+ stepper.do_step( ode() , xxx , 0.0 , 0.01 );
+ BOOST_CHECK_EQUAL( ode_call_count , size_t( 2 ) );
+}
+
+BOOST_FIXTURE_TEST_CASE( test_with_vector_ref , velocity_verlet_fixture )
+{
+ vector_stepper stepper;
+ vector_type q( 2 ) , p( 2 );
+ init_state( q , p );
+ stepper.do_step( ode() , std::make_pair( boost::ref( q ) , boost::ref( p ) ) , 0.0 , 0.01 );
+ BOOST_CHECK_EQUAL( ode_call_count , size_t( 2 ) );
+}
+
+BOOST_FIXTURE_TEST_CASE( test_with_vector_pair , velocity_verlet_fixture )
+{
+ vector_stepper stepper;
+ std::pair< vector_type , vector_type > x;
+ x.first.resize( 2 ) ; x.second.resize( 2 );
+ init_state( x.first , x.second );
+ stepper.do_step( ode() , x , 0.0 , 0.01 );
+ BOOST_CHECK_EQUAL( ode_call_count , size_t( 2 ) );
+}
+
+BOOST_FIXTURE_TEST_CASE( test_initial_resizer , velocity_verlet_fixture )
+{
+ typedef get_resizer_test_stepper< initially_resizer >::type stepper_type;
+ std::pair< test_array_type , test_array_type > x;
+ init_state( x.first , x.second );
+ stepper_type stepper;
+ stepper.do_step( ode() , x , 0.0 , 0.01 );
+ stepper.do_step( ode() , x , 0.0 , 0.01 );
+ BOOST_CHECK_EQUAL( adjust_size_count , size_t( 2 ) );
+ BOOST_CHECK_EQUAL( ode_call_count , size_t( 3 ) );
+}
+
+BOOST_FIXTURE_TEST_CASE( test_always_resizer , velocity_verlet_fixture )
+{
+ typedef get_resizer_test_stepper< always_resizer >::type stepper_type;
+ std::pair< test_array_type , test_array_type > x;
+ init_state( x.first , x.second );
+ stepper_type stepper;
+ stepper.do_step( ode() , x , 0.0 , 0.01 );
+ stepper.do_step( ode() , x , 0.0 , 0.01 );
+ BOOST_CHECK_EQUAL( adjust_size_count , size_t( 4 ) );
+ BOOST_CHECK_EQUAL( ode_call_count , size_t( 4 ) ); // attention: one more system call, since the size of the state has been changed
+}
+
+BOOST_FIXTURE_TEST_CASE( test_with_never_resizer , velocity_verlet_fixture )
+{
+ typedef get_resizer_test_stepper< never_resizer >::type stepper_type;
+ std::pair< test_array_type , test_array_type > x;
+ init_state( x.first , x.second );
+ stepper_type stepper;
+ stepper.do_step( ode() , x , 0.0 , 0.01 );
+ stepper.do_step( ode() , x , 0.0 , 0.01 );
+ BOOST_CHECK_EQUAL( adjust_size_count , size_t( 0 ) );
+ BOOST_CHECK_EQUAL( ode_call_count , size_t( 3 ) );
+}
+
+BOOST_FIXTURE_TEST_CASE( test_reset , velocity_verlet_fixture )
+{
+ typedef get_resizer_test_stepper< initially_resizer >::type stepper_type;
+ std::pair< test_array_type , test_array_type > x;
+ init_state( x.first , x.second );
+ stepper_type stepper;
+ stepper.do_step( ode() , x , 0.0 , 0.01 );
+ BOOST_CHECK_EQUAL( adjust_size_count , size_t( 2 ) );
+ BOOST_CHECK_EQUAL( ode_call_count , size_t( 2 ) );
+ stepper.do_step( ode() , x , 0.0 , 0.01 );
+ BOOST_CHECK_EQUAL( adjust_size_count , size_t( 2 ) );
+ BOOST_CHECK_EQUAL( ode_call_count , size_t( 3 ) );
+ stepper.reset();
+ BOOST_CHECK_EQUAL( adjust_size_count , size_t( 2 ) );
+ BOOST_CHECK_EQUAL( ode_call_count , size_t( 3 ) );
+ stepper.do_step( ode() , x , 0.0 , 0.01 );
+ BOOST_CHECK_EQUAL( adjust_size_count , size_t( 2 ) );
+ BOOST_CHECK_EQUAL( ode_call_count , size_t( 5 ) );
+}
+
+BOOST_FIXTURE_TEST_CASE( test_initialize1 , velocity_verlet_fixture )
+{
+ typedef get_resizer_test_stepper< initially_resizer >::type stepper_type;
+ std::pair< test_array_type , test_array_type > x;
+ init_state( x.first , x.second );
+ stepper_type stepper;
+ test_array_type ain;
+ ode()( x.first , x.second , ain , 0.0 );
+ BOOST_CHECK_EQUAL( adjust_size_count , size_t( 0 ) );
+ stepper.initialize( ain );
+ BOOST_CHECK_EQUAL( adjust_size_count , size_t( 2 ) );
+ BOOST_CHECK_EQUAL( ode_call_count , size_t( 1 ) );
+ stepper.do_step( ode() , x , 0.0 , 0.01 );
+ BOOST_CHECK_EQUAL( adjust_size_count , size_t( 2 ) );
+ BOOST_CHECK_EQUAL( ode_call_count , size_t( 2 ) );
+}
+
+BOOST_FIXTURE_TEST_CASE( test_initialize2 , velocity_verlet_fixture )
+{
+ typedef get_resizer_test_stepper< initially_resizer >::type stepper_type;
+ std::pair< test_array_type , test_array_type > x;
+ init_state( x.first , x.second );
+ stepper_type stepper;
+ stepper.initialize( ode() , x.first , x.second , 0.0 );
+ BOOST_CHECK_EQUAL( adjust_size_count , size_t( 2 ) );
+ BOOST_CHECK_EQUAL( ode_call_count , size_t( 1 ) );
+ stepper.do_step( ode() , x , 0.0 , 0.01 );
+ BOOST_CHECK_EQUAL( adjust_size_count , size_t( 2 ) );
+ BOOST_CHECK_EQUAL( ode_call_count , size_t( 2 ) );
+}
+
+
+BOOST_FIXTURE_TEST_CASE( test_adjust_size , velocity_verlet_fixture )
+{
+ typedef get_resizer_test_stepper< initially_resizer >::type stepper_type;
+ std::pair< test_array_type , test_array_type > x;
+ init_state( x.first , x.second );
+ stepper_type stepper;
+ stepper.do_step( ode() , x , 0.0 , 0.01 );
+ BOOST_CHECK_EQUAL( adjust_size_count , size_t( 2 ) );
+ BOOST_CHECK_EQUAL( ode_call_count , size_t( 2 ) );
+ stepper.adjust_size( x.first );
+ BOOST_CHECK_EQUAL( adjust_size_count , size_t( 4 ) );
+ BOOST_CHECK_EQUAL( ode_call_count , size_t( 2 ) );
+ stepper.do_step( ode() , x , 0.0 , 0.01 );
+ BOOST_CHECK_EQUAL( adjust_size_count , size_t( 4 ) );
+ BOOST_CHECK_EQUAL( ode_call_count , size_t( 4 ) );
+}
+
+BOOST_FIXTURE_TEST_CASE( test_with_unit_pair , velocity_verlet_fixture )
+{
+ typedef velocity_verlet< coor_vector , velocity_vector , value_type , accelartion_vector ,
+ time_type , time_2_type , fusion_algebra , default_operations > stepper_type;
+
+ std::pair< coor_vector , velocity_vector > x;
+ fusion::at_c< 0 >( x.first ) = 1.0 * si::meter;
+ fusion::at_c< 1 >( x.first ) = 0.5 * si::meter;
+ fusion::at_c< 0 >( x.second ) = 2.0 * si::meter_per_second;
+ fusion::at_c< 1 >( x.second ) = -1.0 * si::meter_per_second;
+ stepper_type stepper;
+ stepper.do_step( ode_units() , x , 0.0 * si::second , 0.01 * si::second );
+ BOOST_CHECK_EQUAL( ode_call_count , size_t( 2 ) );
+}
+
+
+BOOST_FIXTURE_TEST_CASE( test_with_unit_ref , velocity_verlet_fixture )
+{
+ typedef velocity_verlet< coor_vector , velocity_vector , value_type , accelartion_vector ,
+ time_type , time_2_type , fusion_algebra , default_operations > stepper_type;
+
+ coor_vector q;
+ velocity_vector p;
+ fusion::at_c< 0 >( q ) = 1.0 * si::meter;
+ fusion::at_c< 1 >( q ) = 0.5 * si::meter;
+ fusion::at_c< 0 >( p ) = 2.0 * si::meter_per_second;
+ fusion::at_c< 1 >( p ) = -1.0 * si::meter_per_second;
+ stepper_type stepper;
+ stepper.do_step( ode_units() , std::make_pair( boost::ref( q ) , boost::ref( p ) ) , 0.0 * si::second , 0.01 * si::second );
+ BOOST_CHECK_EQUAL( ode_call_count , size_t( 2 ) );
+}
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test_external/eigen/Jamfile.v2 b/test_external/eigen/Jamfile.v2
new file mode 100644
index 0000000..489f67c
--- /dev/null
+++ b/test_external/eigen/Jamfile.v2
@@ -0,0 +1,36 @@
+# Copyright 2012-2013 Karsten Ahnert
+# Copyright 2012-2013 Mario Mulansky
+# Distributed under the Boost Software License, Version 1.0.
+# (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+# bring in rules for testing
+
+
+import testing ;
+import os ;
+
+use-project boost : $(BOOST_ROOT) ;
+
+local EIGEN_ROOT = [ os.environ EIGEN_ROOT ] ;
+
+project
+ : requirements
+ <library>/boost/test//boost_unit_test_framework
+ <define>BOOST_ALL_NO_LIB=1
+ <include>$(EIGEN_ROOT)
+ <include>../../test
+ <link>static
+ # <cxxflags>-D_SCL_SECURE_NO_WARNINGS
+ ;
+
+test-suite "odeint"
+ :
+ [ compile is_resizeable.cpp ]
+ [ run same_size.cpp ]
+ [ run resize.cpp ]
+ [ run runge_kutta4.cpp ]
+ [ run runge_kutta_dopri5.cpp ]
+ [ run integrate.cpp ]
+ [ compile-fail fail_integrate.cpp ]
+ : <testing.launcher>valgrind
+ ;
diff --git a/test_external/eigen/fail_integrate.cpp b/test_external/eigen/fail_integrate.cpp
new file mode 100644
index 0000000..4c71b01
--- /dev/null
+++ b/test_external/eigen/fail_integrate.cpp
@@ -0,0 +1,47 @@
+/*
+ [auto_generated]
+ fail_integrate.cpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2009-2012 Karsten Ahnert
+ Copyright 2009-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_dummy
+
+#include <boost/numeric/odeint/integrate/integrate.hpp>
+#include <boost/numeric/odeint/external/eigen/eigen.hpp>
+
+#include <boost/test/unit_test.hpp>
+
+#include "dummy_odes.hpp"
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+
+BOOST_AUTO_TEST_SUITE( eigen_fail_integrate )
+
+BOOST_AUTO_TEST_CASE( test )
+{
+ typedef Eigen::Matrix< double , 1 , 1 > state_type;
+ state_type x;
+ x[0] = 10.0;
+ double t_start = 0.0 , t_end = 1.0 , dt = 0.1;
+ integrate( constant_system_functor_standard() , x , t_start , t_end , dt );
+}
+
+BOOST_AUTO_TEST_SUITE_END()
+
diff --git a/test_external/eigen/integrate.cpp b/test_external/eigen/integrate.cpp
new file mode 100644
index 0000000..c64496a
--- /dev/null
+++ b/test_external/eigen/integrate.cpp
@@ -0,0 +1,69 @@
+/*
+ [auto_generated]
+ integrate.cpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2009-2012 Karsten Ahnert
+ Copyright 2009-2012 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_eigen_integrate
+
+#include <boost/numeric/odeint/integrate/integrate.hpp>
+#include <boost/numeric/odeint/external/eigen/eigen.hpp>
+
+#include <boost/test/unit_test.hpp>
+
+#include "dummy_odes.hpp"
+
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+
+BOOST_AUTO_TEST_SUITE( eigen_integrate )
+
+BOOST_AUTO_TEST_CASE( test_const_sys )
+{
+ typedef Eigen::Matrix< double , 1 , 1 > state_type;
+ state_type x;
+ x[0] = 10.0;
+ double t_start = 0.0 , t_end = 1.0 , dt = 0.1;
+ integrate< double >( constant_system_functor_standard() , x , t_start , t_end , dt );
+ BOOST_CHECK_CLOSE( x[0] , 11.0 , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_CASE( test_lorenz )
+{
+ typedef Eigen::Matrix< double , 3 , 1 > state_type;
+ state_type x;
+ x[0] = 10.0;
+ x[1] = 10.0;
+ x[2] = 10.0;
+ double t_start = 0.0 , t_end = 1000.0 , dt = 0.1;
+ integrate< double >( lorenz() , x , t_start , t_end , dt );
+
+ std::vector< double > x2( 3 );
+ x2[0] = 10.0;
+ x2[1] = 10.0;
+ x2[2] = 10.0;
+ integrate( lorenz() , x2 , t_start , t_end , dt );
+
+ BOOST_CHECK_CLOSE( x[0] , x2[0] , 1.0e-13 );
+ BOOST_CHECK_CLOSE( x[1] , x2[1] , 1.0e-13 );
+ BOOST_CHECK_CLOSE( x[2] , x2[2] , 1.0e-13 );
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test_external/eigen/is_resizeable.cpp b/test_external/eigen/is_resizeable.cpp
new file mode 100644
index 0000000..5f29ee5
--- /dev/null
+++ b/test_external/eigen/is_resizeable.cpp
@@ -0,0 +1,47 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test_external/eigen/is_resizeable.cpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_eigen_is_resizeable
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/numeric/odeint/external/eigen/eigen_resize.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+
+BOOST_AUTO_TEST_SUITE( is_resizeable )
+
+BOOST_AUTO_TEST_CASE( test_compile_time_matrix )
+{
+ typedef Eigen::Matrix< double , 1 , 1 > matrix_type;
+ BOOST_STATIC_ASSERT(( boost::numeric::odeint::is_resizeable< matrix_type >::value ));
+}
+
+BOOST_AUTO_TEST_CASE( test_compile_time_array )
+{
+ typedef Eigen::Array< double , 1 , 1 > array_type;
+ BOOST_STATIC_ASSERT(( boost::numeric::odeint::is_resizeable< array_type >::value ));
+}
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test_external/eigen/resize.cpp b/test_external/eigen/resize.cpp
new file mode 100644
index 0000000..4efcdd4
--- /dev/null
+++ b/test_external/eigen/resize.cpp
@@ -0,0 +1,145 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test_external/eigen/resize.cpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_eigen_resize
+
+#include <boost/test/unit_test.hpp>
+#include <boost/numeric/odeint/external/eigen/eigen_resize.hpp>
+
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+
+BOOST_AUTO_TEST_SUITE( eigen_resize )
+
+BOOST_AUTO_TEST_CASE( test_compile_time_matrix )
+{
+ typedef Eigen::Matrix< double , 1 , 1 > matrix_type;
+ matrix_type a , b;
+ boost::numeric::odeint::resize( a , b );
+ BOOST_CHECK( boost::numeric::odeint::same_size( a , b ) );
+ BOOST_CHECK_EQUAL( a.rows() , 1 );
+ BOOST_CHECK_EQUAL( a.cols() , 1 );
+}
+
+BOOST_AUTO_TEST_CASE( test_rumtime_matrix )
+{
+ typedef Eigen::Matrix< double , Eigen::Dynamic , Eigen::Dynamic > matrix_type;
+ matrix_type a( 5 , 2 ) , b;
+
+ BOOST_CHECK_EQUAL( a.rows() , 5 );
+ BOOST_CHECK_EQUAL( a.cols() , 2 );
+ BOOST_CHECK_EQUAL( b.rows() , 0 );
+ BOOST_CHECK_EQUAL( b.cols() , 0 );
+ BOOST_CHECK( !boost::numeric::odeint::same_size( a , b ) );
+
+ boost::numeric::odeint::resize( b , a );
+
+ BOOST_CHECK_EQUAL( a.rows() , 5 );
+ BOOST_CHECK_EQUAL( a.cols() , 2 );
+ BOOST_CHECK_EQUAL( b.rows() , 5 );
+ BOOST_CHECK_EQUAL( b.cols() , 2 );
+
+ BOOST_CHECK( boost::numeric::odeint::same_size( a , b ) );
+}
+
+BOOST_AUTO_TEST_CASE( test_rumtime_matrix2 )
+{
+ typedef Eigen::Matrix< double , Eigen::Dynamic , Eigen::Dynamic > matrix_type;
+ matrix_type a( 5 , 2 ) , b( 2 , 3 );
+
+ BOOST_CHECK_EQUAL( a.rows() , 5 );
+ BOOST_CHECK_EQUAL( a.cols() , 2 );
+ BOOST_CHECK_EQUAL( b.rows() , 2 );
+ BOOST_CHECK_EQUAL( b.cols() , 3 );
+ BOOST_CHECK( !boost::numeric::odeint::same_size( a , b ) );
+
+ boost::numeric::odeint::resize( b , a );
+
+ BOOST_CHECK_EQUAL( a.rows() , 5 );
+ BOOST_CHECK_EQUAL( a.cols() , 2 );
+ BOOST_CHECK_EQUAL( b.rows() , 5 );
+ BOOST_CHECK_EQUAL( b.cols() , 2 );
+
+ BOOST_CHECK( boost::numeric::odeint::same_size( a , b ) );
+}
+
+
+
+
+
+
+BOOST_AUTO_TEST_CASE( test_compile_time_array )
+{
+ typedef Eigen::Array< double , 1 , 1 > array_type;
+ array_type a , b;
+ boost::numeric::odeint::resize( a , b );
+ BOOST_CHECK( boost::numeric::odeint::same_size( a , b ) );
+ BOOST_CHECK_EQUAL( a.rows() , 1 );
+ BOOST_CHECK_EQUAL( a.cols() , 1 );
+}
+
+BOOST_AUTO_TEST_CASE( test_rumtime_array )
+{
+ typedef Eigen::Array< double , Eigen::Dynamic , Eigen::Dynamic > array_type;
+ array_type a( 5 , 2 ) , b;
+
+ BOOST_CHECK_EQUAL( a.rows() , 5 );
+ BOOST_CHECK_EQUAL( a.cols() , 2 );
+ BOOST_CHECK_EQUAL( b.rows() , 0 );
+ BOOST_CHECK_EQUAL( b.cols() , 0 );
+ BOOST_CHECK( !boost::numeric::odeint::same_size( a , b ) );
+
+ boost::numeric::odeint::resize( b , a );
+
+ BOOST_CHECK_EQUAL( a.rows() , 5 );
+ BOOST_CHECK_EQUAL( a.cols() , 2 );
+ BOOST_CHECK_EQUAL( b.rows() , 5 );
+ BOOST_CHECK_EQUAL( b.cols() , 2 );
+
+ BOOST_CHECK( boost::numeric::odeint::same_size( a , b ) );
+}
+
+BOOST_AUTO_TEST_CASE( test_rumtime_array2 )
+{
+ typedef Eigen::Array< double , Eigen::Dynamic , Eigen::Dynamic > array_type;
+ array_type a( 5 , 2 ) , b( 2 , 3 );
+
+ BOOST_CHECK_EQUAL( a.rows() , 5 );
+ BOOST_CHECK_EQUAL( a.cols() , 2 );
+ BOOST_CHECK_EQUAL( b.rows() , 2 );
+ BOOST_CHECK_EQUAL( b.cols() , 3 );
+ BOOST_CHECK( !boost::numeric::odeint::same_size( a , b ) );
+
+ boost::numeric::odeint::resize( b , a );
+
+ BOOST_CHECK_EQUAL( a.rows() , 5 );
+ BOOST_CHECK_EQUAL( a.cols() , 2 );
+ BOOST_CHECK_EQUAL( b.rows() , 5 );
+ BOOST_CHECK_EQUAL( b.cols() , 2 );
+
+ BOOST_CHECK( boost::numeric::odeint::same_size( a , b ) );
+}
+
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test_external/eigen/runge_kutta4.cpp b/test_external/eigen/runge_kutta4.cpp
new file mode 100644
index 0000000..c4054fd
--- /dev/null
+++ b/test_external/eigen/runge_kutta4.cpp
@@ -0,0 +1,94 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test_external/eigen/runge_kutta4.cpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_eigen_runge_kutta4
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/numeric/odeint/algebra/vector_space_algebra.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta4.hpp>
+#include <boost/numeric/odeint/external/eigen/eigen_resize.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+struct sys
+{
+ template< class State , class Deriv >
+ void operator()( const State &x , Deriv &dxdt , double t ) const
+ {
+ dxdt[0] = 1.0;
+ }
+};
+
+
+BOOST_AUTO_TEST_SUITE( eigen_runge_kutta4 )
+
+BOOST_AUTO_TEST_CASE( compile_time_matrix )
+{
+ typedef Eigen::Matrix< double , 1 , 1 > state_type;
+ state_type x;
+ x[0] = 10.0;
+ runge_kutta4< state_type , double , state_type , double , vector_space_algebra > rk4;
+ rk4.do_step( sys() , x , 0.0 , 0.1 );
+ BOOST_CHECK_CLOSE( x[0] , 10.1 , 1.0e-13 );
+
+}
+
+BOOST_AUTO_TEST_CASE( runtime_matrix )
+{
+ typedef Eigen::Matrix< double , Eigen::Dynamic , 1 > state_type;
+ state_type x( 1 );
+ x[0] = 10.0;
+ runge_kutta4< state_type , double , state_type , double , vector_space_algebra > rk4;
+ rk4.do_step( sys() , x , 0.0 , 0.1 );
+ BOOST_CHECK_CLOSE( x[0] , 10.1 , 1.0e-13 );
+}
+
+
+
+
+
+
+BOOST_AUTO_TEST_CASE( compile_time_array )
+{
+ typedef Eigen::Array< double , 1 , 1 > state_type;
+ state_type x;
+ x[0] = 10.0;
+ runge_kutta4< state_type , double , state_type , double , vector_space_algebra > rk4;
+ rk4.do_step( sys() , x , 0.0 , 0.1 );
+ BOOST_CHECK_CLOSE( x[0] , 10.1 , 1.0e-13 );
+
+}
+
+BOOST_AUTO_TEST_CASE( runtime_array )
+{
+ typedef Eigen::Array< double , Eigen::Dynamic , 1 > state_type;
+ state_type x( 1 );
+ x[0] = 10.0;
+ runge_kutta4< state_type , double , state_type , double , vector_space_algebra > rk4;
+ rk4.do_step( sys() , x , 0.0 , 0.1 );
+ BOOST_CHECK_CLOSE( x[0] , 10.1 , 1.0e-13 );
+}
+
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test_external/eigen/runge_kutta_dopri5.cpp b/test_external/eigen/runge_kutta_dopri5.cpp
new file mode 100644
index 0000000..516f04f
--- /dev/null
+++ b/test_external/eigen/runge_kutta_dopri5.cpp
@@ -0,0 +1,132 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test_external/eigen/runge_kutta_dopri5.cpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_eigen_runge_kutta4
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/numeric/odeint/algebra/vector_space_algebra.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta4.hpp>
+#include <boost/numeric/odeint/stepper/controlled_runge_kutta.hpp>
+#include <boost/numeric/odeint/stepper/dense_output_runge_kutta.hpp>
+
+// #include <boost/numeric/odeint/external/eigen/eigen_resize.hpp>
+#include <boost/numeric/odeint/external/eigen/eigen_algebra.hpp>
+
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+struct sys
+{
+ template< class State , class Deriv >
+ void operator()( const State &x , Deriv &dxdt , double t ) const
+ {
+ dxdt[0] = 1.0;
+ }
+};
+
+template< class State >
+struct stepper
+{
+ typedef runge_kutta_dopri5< State , double , State , double , vector_space_algebra > type;
+};
+
+template< class State >
+struct controlled_stepper
+{
+ typedef controlled_runge_kutta< typename stepper< State >::type > type;
+};
+
+template< class State >
+struct dense_output_stepper
+{
+ typedef dense_output_runge_kutta< typename controlled_stepper< State >::type > type;
+};
+
+
+
+
+BOOST_AUTO_TEST_SUITE( eigen_runge_kutta_dopri5 )
+
+BOOST_AUTO_TEST_CASE( compile_time_matrix )
+{
+ typedef Eigen::Matrix< double , 1 , 1 > state_type;
+ state_type x;
+ x[0] = 10.0;
+ double t = 0.0 , dt = 0.1 ;
+
+ // dense_output_stepper< state_type >::type s;
+ // s.initialize( x , t , dt );
+
+ // controlled_stepper< state_type >::type s;
+ // s.try_step( sys() , x , t , dt );
+
+ stepper< state_type >::type s;
+ s.do_step( sys() , x , t , dt );
+
+ // runge_kutta4< state_type , double , state_type , double , vector_space_algebra > rk4;
+ // rk4.do_step( sys() , x , 0.0 , 0.1 );
+ // BOOST_CHECK_CLOSE( x[0] , 10.1 , 1.0e-13 );
+
+}
+
+BOOST_AUTO_TEST_CASE( runtime_matrix )
+{
+ typedef Eigen::Matrix< double , Eigen::Dynamic , 1 > state_type;
+ state_type x( 1 );
+ x[0] = 10.0;
+
+ // runge_kutta4< state_type , double , state_type , double , vector_space_algebra > rk4;
+ // rk4.do_step( sys() , x , 0.0 , 0.1 );
+ // BOOST_CHECK_CLOSE( x[0] , 10.1 , 1.0e-13 );
+}
+
+
+
+
+
+
+BOOST_AUTO_TEST_CASE( compile_time_array )
+{
+ typedef Eigen::Array< double , 1 , 1 > state_type;
+ state_type x;
+ x[0] = 10.0;
+ // runge_kutta4< state_type , double , state_type , double , vector_space_algebra > rk4;
+ // rk4.do_step( sys() , x , 0.0 , 0.1 );
+ // BOOST_CHECK_CLOSE( x[0] , 10.1 , 1.0e-13 );
+
+}
+
+BOOST_AUTO_TEST_CASE( runtime_array )
+{
+ typedef Eigen::Array< double , Eigen::Dynamic , 1 > state_type;
+ state_type x( 1 );
+ x[0] = 10.0;
+ // runge_kutta4< state_type , double , state_type , double , vector_space_algebra > rk4;
+ // rk4.do_step( sys() , x , 0.0 , 0.1 );
+ // BOOST_CHECK_CLOSE( x[0] , 10.1 , 1.0e-13 );
+}
+
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test_external/eigen/same_size.cpp b/test_external/eigen/same_size.cpp
new file mode 100644
index 0000000..ea771f9
--- /dev/null
+++ b/test_external/eigen/same_size.cpp
@@ -0,0 +1,83 @@
+/*
+ [auto_generated]
+ libs/numeric/odeint/test_external/eigen/same_size.cpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_eigen_same_size
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/numeric/odeint/external/eigen/eigen_resize.hpp>
+
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+
+BOOST_AUTO_TEST_SUITE( eigen_same_size )
+
+BOOST_AUTO_TEST_CASE( compile_time_matrix )
+{
+ typedef Eigen::Matrix< double , 1 , 1 > matrix_type;
+ matrix_type a , b;
+ BOOST_CHECK( boost::numeric::odeint::same_size( a , b ) );
+}
+
+BOOST_AUTO_TEST_CASE( runtime_matrix )
+{
+ typedef Eigen::Matrix< double , Eigen::Dynamic , Eigen::Dynamic > matrix_type;
+ matrix_type a( 10 , 2 ) , b( 10 , 2 );
+ BOOST_CHECK( boost::numeric::odeint::same_size( a , b ) );
+}
+
+BOOST_AUTO_TEST_CASE( fail_runtime_matrix )
+{
+ typedef Eigen::Matrix< double , Eigen::Dynamic , Eigen::Dynamic > matrix_type;
+ matrix_type a( 11 , 2 ) , b( 10 , 2 );
+ BOOST_CHECK( !boost::numeric::odeint::same_size( a , b ) );
+
+}
+
+
+
+BOOST_AUTO_TEST_CASE( compile_time_array )
+{
+ typedef Eigen::Array< double , 1 , 1 > array_type;
+ array_type a , b;
+ BOOST_CHECK( boost::numeric::odeint::same_size( a , b ) );
+}
+
+BOOST_AUTO_TEST_CASE( runtime_array )
+{
+ typedef Eigen::Array< double , Eigen::Dynamic , Eigen::Dynamic > array_type;
+ array_type a( 10 , 2 ) , b( 10 , 2 );
+ BOOST_CHECK( boost::numeric::odeint::same_size( a , b ) );
+}
+
+BOOST_AUTO_TEST_CASE( fail_runtime_array )
+{
+ typedef Eigen::Array< double , Eigen::Dynamic , Eigen::Dynamic > array_type;
+ array_type a( 11 , 2 ) , b( 10 , 2 );
+ BOOST_CHECK( !boost::numeric::odeint::same_size( a , b ) );
+
+}
+
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test_external/gmp/Jamfile.v2 b/test_external/gmp/Jamfile.v2
new file mode 100644
index 0000000..f0e6af0
--- /dev/null
+++ b/test_external/gmp/Jamfile.v2
@@ -0,0 +1,26 @@
+# Copyright 2012 Karsten Ahnert
+# Copyright 2012 Mario Mulansky
+# Distributed under the Boost Software License, Version 1.0.
+# (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+# bring in rules for testing
+
+import testing ;
+use-project boost : $(BOOST_ROOT) ;
+
+project gmp
+ : requirements
+ <library>/boost/test//boost_unit_test_framework
+ ;
+
+
+lib libgmp : : <name>gmp <link>shared ;
+lib libgmpxx : : <name>gmpxx <link>shared ;
+
+test-suite "gmp"
+ :
+ [ run check_gmp.cpp libgmpxx libgmp : : : <link>shared:<define>BOOST_TEST_DYN_LINK=1 ]
+ [ run gmp_integrate.cpp libgmpxx libgmp : : : <link>shared:<define>BOOST_TEST_DYN_LINK=1 ]
+ ;
+
+
diff --git a/test_external/gmp/check_gmp.cpp b/test_external/gmp/check_gmp.cpp
new file mode 100644
index 0000000..04b3e10
--- /dev/null
+++ b/test_external/gmp/check_gmp.cpp
@@ -0,0 +1,165 @@
+/* Boost check_gmp.cpp test file
+
+ Copyright 2010-2012 Mario Mulansky
+ Copyright 2011-2012 Karsten Ahnert
+
+ This file tests the odeint library with the gmp arbitrary precision types
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+#define BOOST_TEST_MODULE odeint_gmp
+
+#include <iostream>
+
+#include <gmpxx.h>
+
+#include <boost/test/unit_test.hpp>
+#include <boost/array.hpp>
+
+#include <boost/mpl/vector.hpp>
+
+#include <boost/numeric/odeint.hpp>
+//#include <boost/numeric/odeint/algebra/vector_space_algebra.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+namespace mpl = boost::mpl;
+
+const int precision = 1024;
+
+typedef mpf_class value_type;
+typedef mpf_class state_type;
+
+//provide min, max and pow functions for mpf types - required for controlled steppers
+value_type min( const value_type a , const value_type b )
+{
+ if( a<b ) return a;
+ else return b;
+}
+value_type max( const value_type a , const value_type b )
+{
+ if( a>b ) return a;
+ else return b;
+}
+value_type pow( const value_type a , const value_type b )
+{
+ // do calculation in double precision
+ return value_type( std::pow( a.get_d() , b.get_d() ) );
+}
+
+
+//provide vector_space reduce:
+
+namespace boost { namespace numeric { namespace odeint {
+
+template<>
+struct vector_space_reduce< state_type >
+{
+ template< class Op >
+ state_type operator()( state_type x , Op op , state_type init ) const
+ {
+ init = op( init , x );
+ return init;
+ }
+};
+
+} } }
+
+
+void constant_system( const state_type &x , state_type &dxdt , value_type t )
+{
+ dxdt = value_type( 1.0 , precision );
+}
+
+
+/* check runge kutta stepers */
+typedef mpl::vector<
+ euler< state_type , value_type , state_type , value_type , vector_space_algebra > ,
+ modified_midpoint< state_type , value_type , state_type , value_type , vector_space_algebra > ,
+ runge_kutta4< state_type , value_type , state_type , value_type , vector_space_algebra > ,
+ runge_kutta4_classic< state_type , value_type , state_type , value_type , vector_space_algebra > ,
+ runge_kutta_cash_karp54_classic< state_type , value_type , state_type , value_type , vector_space_algebra > ,
+ runge_kutta_cash_karp54< state_type , value_type , state_type , value_type , vector_space_algebra > ,
+ runge_kutta_dopri5< state_type , value_type , state_type , value_type , vector_space_algebra > ,
+ runge_kutta_fehlberg78< state_type , value_type , state_type , value_type , vector_space_algebra >
+ > stepper_types;
+
+
+template< class Stepper >
+struct perform_runge_kutta_test {
+
+ void operator()( void )
+ {
+ /* We have to specify the desired precision in advance! */
+ mpf_set_default_prec( precision );
+
+ mpf_t eps_ , unity;
+ mpf_init( eps_ ); mpf_init( unity );
+ mpf_set_d( unity , 1.0 );
+ mpf_div_2exp( eps_ , unity , precision-1 ); // 2^(-precision+1) : smallest number that can be represented with used precision
+ value_type eps( eps_ );
+
+ Stepper stepper;
+ state_type x;
+ x = 0.0;
+
+ stepper.do_step( constant_system , x , 0.0 , 0.1 );
+
+ BOOST_MESSAGE( eps );
+ BOOST_CHECK_MESSAGE( abs( x - value_type( 0.1 , precision ) ) < eps , x - 0.1 );
+ }
+};
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( runge_kutta_stepper_test , Stepper , stepper_types )
+{
+ perform_runge_kutta_test< Stepper > tester;
+ tester();
+}
+
+
+/* check controlled steppers */
+typedef mpl::vector<
+ controlled_runge_kutta< runge_kutta_cash_karp54_classic< state_type , value_type , state_type , value_type , vector_space_algebra > > ,
+ controlled_runge_kutta< runge_kutta_dopri5< state_type , value_type , state_type , value_type , vector_space_algebra > > ,
+ controlled_runge_kutta< runge_kutta_fehlberg78< state_type , value_type , state_type , value_type , vector_space_algebra > > ,
+ bulirsch_stoer< state_type , value_type , state_type , value_type , vector_space_algebra >
+ > controlled_stepper_types;
+
+
+template< class Stepper >
+struct perform_controlled_test {
+
+ void operator()( void )
+ {
+ mpf_set_default_prec( precision );
+
+ mpf_t eps_ , unity;
+ mpf_init( eps_ ); mpf_init( unity );
+ mpf_set_d( unity , 1.0 );
+ mpf_div_2exp( eps_ , unity , precision-1 ); // 2^(-precision+1) : smallest number that can be represented with used precision
+ value_type eps( eps_ );
+
+ Stepper stepper;
+ state_type x;
+ x = 0.0;
+
+ value_type t(0.0);
+ value_type dt(0.1);
+
+ stepper.try_step( constant_system , x , t , dt );
+
+ BOOST_MESSAGE( eps );
+ BOOST_CHECK_MESSAGE( abs( x - value_type( 0.1 , precision ) ) < eps , x - 0.1 );
+ }
+};
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( controlled_stepper_test , Stepper , controlled_stepper_types )
+{
+ perform_controlled_test< Stepper > tester;
+ tester();
+}
diff --git a/test_external/gmp/gmp_integrate.cpp b/test_external/gmp/gmp_integrate.cpp
new file mode 100644
index 0000000..0a6be30
--- /dev/null
+++ b/test_external/gmp/gmp_integrate.cpp
@@ -0,0 +1,169 @@
+/* Boost check_gmp.cpp test file
+
+ Copyright 2010-2012 Mario Mulansky
+ Copyright 2011-2012 Karsten Ahnert
+
+ This file tests the odeint library with the gmp arbitrary precision types
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+#define BOOST_TEST_MODULE odeint_gmp
+
+#include <gmpxx.h>
+
+#include <boost/test/unit_test.hpp>
+#include <boost/array.hpp>
+
+#include <boost/mpl/vector.hpp>
+
+#include <boost/numeric/odeint.hpp>
+//#include <boost/numeric/odeint/algebra/vector_space_algebra.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+namespace mpl = boost::mpl;
+
+const int precision = 1024;
+
+typedef mpf_class value_type;
+typedef mpf_class state_type;
+
+//provide min, max and pow functions for mpf types - required for controlled steppers
+value_type min( const value_type a , const value_type b )
+{
+ if( a<b ) return a;
+ else return b;
+}
+value_type max( const value_type a , const value_type b )
+{
+ if( a>b ) return a;
+ else return b;
+}
+value_type pow( const value_type a , const value_type b )
+{
+ // do the calculation in double precision...
+ return value_type( std::pow( a.get_d() , b.get_d() ) );
+}
+
+
+//provide vector_space reduce:
+
+namespace boost { namespace numeric { namespace odeint {
+
+template<>
+struct vector_space_reduce< state_type >
+{
+ template< class Op >
+ state_type operator()( state_type x , Op op , state_type init ) const
+ {
+ init = op( init , x );
+ return init;
+ }
+};
+
+} } }
+
+
+void constant_system( const state_type &x , state_type &dxdt , value_type t )
+{
+ dxdt = value_type( 1.0 , precision );
+}
+
+/* check runge kutta stepers */
+typedef mpl::vector<
+ euler< state_type , value_type , state_type , value_type , vector_space_algebra > ,
+ modified_midpoint< state_type , value_type , state_type , value_type , vector_space_algebra > ,
+ runge_kutta4< state_type , value_type , state_type , value_type , vector_space_algebra > ,
+ runge_kutta4_classic< state_type , value_type , state_type , value_type , vector_space_algebra > ,
+ runge_kutta_cash_karp54_classic< state_type , value_type , state_type , value_type , vector_space_algebra > ,
+ runge_kutta_cash_karp54< state_type , value_type , state_type , value_type , vector_space_algebra > ,
+ runge_kutta_dopri5< state_type , value_type , state_type , value_type , vector_space_algebra > ,
+ runge_kutta_fehlberg78< state_type , value_type , state_type , value_type , vector_space_algebra >
+ > stepper_types;
+
+
+template< class Stepper >
+struct perform_integrate_const_test {
+
+ void operator()( void )
+ {
+ /* We have to specify the desired precision in advance! */
+ mpf_set_default_prec( precision );
+
+ mpf_t eps_ , unity;
+ mpf_init( eps_ ); mpf_init( unity );
+ mpf_set_d( unity , 1.0 );
+ mpf_div_2exp( eps_ , unity , precision-1 ); // 2^(-precision+1) : smallest number that can be represented with used precision
+ value_type eps( eps_ );
+
+ Stepper stepper;
+ state_type x;
+ x = 0.0;
+ value_type t0( 0.0 );
+ value_type tend( 1.0 );
+ value_type dt(0.1);
+
+ integrate_const( stepper , constant_system , x , t0 , tend , dt );
+
+ x = 0.0;
+ t0 = 0.0;
+ dt = 0.1;
+ size_t steps = 10;
+
+ integrate_n_steps( stepper , constant_system , x , t0 , dt , steps );
+
+ BOOST_CHECK_MESSAGE( abs( x - 10*dt ) < eps , x );
+ }
+};
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( integrate_const_test , Stepper , stepper_types )
+{
+ perform_integrate_const_test< Stepper > tester;
+ tester();
+}
+
+
+typedef mpl::vector<
+ controlled_runge_kutta< runge_kutta_cash_karp54_classic< state_type , value_type , state_type , value_type , vector_space_algebra > > ,
+ controlled_runge_kutta< runge_kutta_dopri5< state_type , value_type , state_type , value_type , vector_space_algebra > > ,
+ controlled_runge_kutta< runge_kutta_fehlberg78< state_type , value_type , state_type , value_type , vector_space_algebra > > ,
+ bulirsch_stoer< state_type , value_type , state_type , value_type , vector_space_algebra >
+ > controlled_stepper_types;
+
+
+template< class Stepper >
+struct perform_integrate_adaptive_test {
+
+ void operator()( void )
+ {
+ mpf_set_default_prec( precision );
+
+ mpf_t eps_ , unity;
+ mpf_init( eps_ ); mpf_init( unity );
+ mpf_set_d( unity , 1.0 );
+ mpf_div_2exp( eps_ , unity , precision-1 ); // 2^(-precision+1) : smallest number that can be represented with used precision
+ value_type eps( eps_ );
+
+ Stepper stepper;
+ state_type x;
+ x = 0.0;
+ value_type t0( 0.0 );
+ value_type tend( 1.0 );
+ value_type dt(0.1);
+
+ integrate_adaptive( stepper , constant_system , x , t0 , tend , dt );
+
+ BOOST_CHECK_MESSAGE( abs( x - tend ) < eps , x - 0.1 );
+ }
+};
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( integrate_adaptive__test , Stepper , controlled_stepper_types )
+{
+ perform_integrate_adaptive_test< Stepper > tester;
+ tester();
+}
diff --git a/test_external/gsl/Jamfile.v2 b/test_external/gsl/Jamfile.v2
new file mode 100644
index 0000000..086edf6
--- /dev/null
+++ b/test_external/gsl/Jamfile.v2
@@ -0,0 +1,28 @@
+# Copyright 2012 Karsten Ahnert
+# Copyright 2012 Mario Mulansky
+# Distributed under the Boost Software License, Version 1.0.
+# (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+# bring in rules for testing
+
+import testing ;
+use-project boost : $(BOOST_ROOT) ;
+
+project
+ : requirements
+ <library>/boost/test//boost_unit_test_framework
+ ;
+
+
+lib libgsl : : <name>gsl <link>shared ;
+lib libgslcblas : : <name>gslcblas <link>shared ;
+
+test-suite "gsl"
+ :
+ [ run check_gsl.cpp libgslcblas libgsl
+ :
+ :
+ : <link>shared:<define>BOOST_TEST_DYN_LINK=1
+ ]
+ ;
+
diff --git a/test_external/gsl/check_gsl.cpp b/test_external/gsl/check_gsl.cpp
new file mode 100644
index 0000000..3e7856d
--- /dev/null
+++ b/test_external/gsl/check_gsl.cpp
@@ -0,0 +1,58 @@
+/* Boost check_gmp.cpp test file
+
+ Copyright 2010-2011 Karsten Ahnert
+ Copyright 2011 Mario Mulansky
+
+ This file tests the odeint library with the gmp arbitrary precision types
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+#define BOOST_TEST_MODULE odeint_gsl
+
+#include <gsl/gsl_vector.h>
+#include <boost/numeric/odeint/stepper/euler.hpp>
+#include <boost/numeric/odeint/external/gsl/gsl_wrapper.hpp>
+
+#include <boost/test/unit_test.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+typedef gsl_vector *state_type;
+
+const double sigma = 10.0;
+const double R = 28.0;
+const double b = 8.0 / 3.0;
+
+void lorenz( const state_type x , state_type dxdt , double t )
+{
+ gsl_vector_set( dxdt , 0 , sigma * ( gsl_vector_get(x , 1 ) - gsl_vector_get( x , 0 ) ) );
+ gsl_vector_set( dxdt , 1 , R * gsl_vector_get( x , 0 ) - gsl_vector_get( x , 1 ) - gsl_vector_get( x , 0 ) * gsl_vector_get( x , 2) );
+ gsl_vector_set( dxdt , 2 , gsl_vector_get( x , 0 ) * gsl_vector_get( x , 1 ) - b * gsl_vector_get( x , 2) );
+}
+
+BOOST_AUTO_TEST_CASE( gsl )
+{
+ euler< state_type > euler;
+
+ state_type x = gsl_vector_alloc( 3 );
+
+ // check resizing
+ state_type y = 0;
+ boost::numeric::odeint::resize( y , x );
+ BOOST_CHECK( 0 != y );
+
+ gsl_vector_set( x , 0 , 1.0);
+ gsl_vector_set( x , 1 , 1.0);
+ gsl_vector_set( x , 2 , 2.0);
+
+ euler.do_step( lorenz , x , 0.0 , 0.1 );
+
+ //cout << gsl_vector_get( x , 0 ) << " " << gsl_vector_get( x , 1 ) << " " << gsl_vector_get( x , 2 ) << endl;
+
+ gsl_vector_free( x );
+
+}
diff --git a/test_external/mkl/Jamfile.v2 b/test_external/mkl/Jamfile.v2
new file mode 100644
index 0000000..f585fa8
--- /dev/null
+++ b/test_external/mkl/Jamfile.v2
@@ -0,0 +1,30 @@
+# Copyright 2012 Karsten Ahnert
+# Copyright 2012 Mario Mulansky
+# Distributed under the Boost Software License, Version 1.0.
+# (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+# bring in rules for testing
+
+import testing ;
+use-project boost : $(BOOST_ROOT) ;
+
+project
+ : requirements
+ <library>/boost/test//boost_unit_test_framework
+ ;
+
+
+lib libmkl : : <name>mkl_intel_lp64 <link>shared ;
+lib libmkl_core : : <name>mkl_core <link>shared ;
+lib libmkl_intel_thread : : <name>mkl_intel_thread ;
+lib libiomp5 : : <name>iomp5 ;
+lib libpthread : : <name>pthread ;
+
+test-suite "mkl"
+ :
+ [ run check_mkl.cpp libpthread libiomp5 libmkl_core libmkl_intel_thread libmkl
+ :
+ :
+ : <link>shared:<define>BOOST_TEST_DYN_LINK=1
+ ]
+ ;
diff --git a/test_external/mkl/check_mkl.cpp b/test_external/mkl/check_mkl.cpp
new file mode 100644
index 0000000..bedbd66
--- /dev/null
+++ b/test_external/mkl/check_mkl.cpp
@@ -0,0 +1,51 @@
+/* Boost check_mkl.cpp test file
+
+ Copyright 2010-2011 Mario Mulansky
+ Copyright 2011 Karsten Ahnert
+
+ This file tests the odeint library with the intel mkl blas1 routines
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+#define BOOST_TEST_MODULE test_mkl
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/numeric/odeint/stepper/euler.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta4.hpp>
+#include <boost/numeric/odeint/algebra/vector_space_algebra.hpp>
+#include <boost/numeric/odeint/external/mkl/mkl_operations.hpp>
+
+using namespace boost::numeric::odeint;
+
+typedef double value_type;
+typedef boost::array< value_type , 1 > state_type;
+
+
+void constant_system( state_type &x , state_type &dxdt , value_type t )
+{
+ dxdt[0] = 1.0;
+}
+
+const double eps = 1E-14;
+
+
+BOOST_AUTO_TEST_CASE( test_mkl )
+{
+
+ //to use mkl routines we have to use the vector_space_algebra and the mkl_operations
+ runge_kutta4< state_type , value_type , state_type , value_type , vector_space_algebra , mkl_operations > stepper;
+ state_type x;
+ x[0] = 0.0;
+
+ stepper.do_step( constant_system , x , 0.0 , 0.1 );
+
+ using std::abs;
+
+ std::cout << x[0] << " ?= " << 0.1 << std::endl;
+ BOOST_CHECK_SMALL( abs( x[0] - 0.1 ) , eps );
+
+}
diff --git a/test_external/mpi/Jamfile.v2 b/test_external/mpi/Jamfile.v2
new file mode 100644
index 0000000..0a02bcc
--- /dev/null
+++ b/test_external/mpi/Jamfile.v2
@@ -0,0 +1,27 @@
+# Copyright 2012 Karsten Ahnert
+# Copyright 2012-2013 Mario Mulansky
+# Copyright 2013 Pascal Germroth
+# Distributed under the Boost Software License, Version 1.0.
+# (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+import testing ;
+import mpi : mpi-test ;
+
+use-project boost : $(BOOST_ROOT) ;
+
+project
+ : requirements
+ <library>/boost/test//boost_unit_test_framework
+ <library>/boost//mpi
+ <link>static
+ <define>BOOST_ALL_NO_LIB=1
+ ;
+
+# mpi-test name : source : req : np=1 2 3 4 7 8 13 17
+test-suite "odeint-mpi"
+ :
+ [ mpi-test split_test ]
+ [ mpi-test state_test ]
+ [ mpi-test norm_test ]
+ ;
+
diff --git a/test_external/mpi/norm_test.cpp b/test_external/mpi/norm_test.cpp
new file mode 100644
index 0000000..69f1d40
--- /dev/null
+++ b/test_external/mpi/norm_test.cpp
@@ -0,0 +1,62 @@
+/*
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+ Copyright 2013 Pascal Germroth
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <iostream>
+#include <sstream>
+#include <cstdlib>
+
+#define BOOST_TEST_MODULE odeint_mpi
+#include <boost/test/unit_test.hpp>
+
+#include <boost/numeric/odeint/external/mpi/mpi.hpp>
+
+using namespace boost::numeric::odeint;
+
+boost::mpi::environment env;
+
+BOOST_AUTO_TEST_SUITE( norm_test_suite )
+
+BOOST_AUTO_TEST_CASE( norm_test )
+{
+ boost::mpi::communicator world;
+
+ int ref_value = 0;
+ std::vector<int> in_data;
+ mpi_state< std::vector<int> > state(world);
+
+ // generate data and reference value on master
+ if(world.rank() == 0) {
+ for(size_t i = 0 ; i < 400 ; i++)
+ in_data.push_back( rand() % 10000 );
+ ref_value = *std::max_element(in_data.begin(), in_data.end());
+ }
+ boost::mpi::broadcast(world, ref_value, 0);
+
+ // copy to nodes
+ split( in_data, state );
+
+ int value = mpi_nested_algebra< range_algebra >::norm_inf( state );
+
+ {
+ std::ostringstream ss;
+ ss << "state[" << world.rank() << "]"
+ << " local:" << range_algebra::norm_inf( state() )
+ << " global:" << value
+ << " ref:" << ref_value << "\n";
+ std::clog << ss.str() << std::flush;
+ }
+
+ BOOST_REQUIRE_EQUAL( value, ref_value );
+}
+
+
+BOOST_AUTO_TEST_SUITE_END()
+
+
diff --git a/test_external/mpi/split_test.cpp b/test_external/mpi/split_test.cpp
new file mode 100644
index 0000000..f78a601
--- /dev/null
+++ b/test_external/mpi/split_test.cpp
@@ -0,0 +1,61 @@
+/*
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+ Copyright 2013 Pascal Germroth
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <iostream>
+#include <sstream>
+
+#define BOOST_TEST_MODULE odeint_mpi
+#include <boost/test/unit_test.hpp>
+
+#include <boost/numeric/odeint/external/mpi/mpi.hpp>
+
+using namespace boost::numeric::odeint;
+
+boost::mpi::environment env;
+
+BOOST_AUTO_TEST_SUITE( split_test_suite )
+
+BOOST_AUTO_TEST_CASE( split_test )
+{
+ boost::mpi::communicator world;
+
+ const size_t total_size = 31;
+
+ std::vector<size_t> in_data, out_data;
+ mpi_state< std::vector<size_t> > state(world);
+
+ // generate data on master
+ if(world.rank() == 0)
+ for(size_t i = 0 ; i < total_size ; i++) in_data.push_back(i);
+
+ // copy to nodes
+ split( in_data, state );
+
+ BOOST_REQUIRE((state().size() == total_size / world.size())
+ || (state().size() == total_size / world.size() + 1));
+
+ {
+ std::ostringstream ss;
+ ss << "state[" << world.rank() << "].data = {";
+ std::copy(state().begin(), state().end(), std::ostream_iterator<size_t>(ss, ", "));
+ ss << "}\n";
+ std::clog << ss.str() << std::flush;
+ }
+
+ // copy back to master
+ if(world.rank() == 0) out_data.resize(in_data.size());
+ unsplit( state, out_data );
+
+ if(world.rank() == 0)
+ BOOST_REQUIRE_EQUAL_COLLECTIONS(in_data.begin(), in_data.end(), out_data.begin(), out_data.end());
+}
+
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test_external/mpi/state_test.cpp b/test_external/mpi/state_test.cpp
new file mode 100644
index 0000000..490b46e
--- /dev/null
+++ b/test_external/mpi/state_test.cpp
@@ -0,0 +1,78 @@
+/*
+ Copyright 2013 Karsten Ahnert
+ Copyright 2013 Mario Mulansky
+ Copyright 2013 Pascal Germroth
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <iostream>
+#include <sstream>
+
+#define BOOST_TEST_MODULE odeint_mpi
+#include <boost/test/unit_test.hpp>
+
+#include <boost/numeric/odeint/external/mpi/mpi.hpp>
+
+using namespace boost::numeric::odeint;
+
+boost::mpi::environment env;
+
+BOOST_AUTO_TEST_SUITE( state_test_suite )
+
+BOOST_AUTO_TEST_CASE( state_test )
+{
+ boost::mpi::communicator world;
+
+ std::vector<size_t> in_data1, in_data2;
+ mpi_state< std::vector<size_t> > state1(world), state2(world);
+
+ // generate data on master
+ if(world.rank() == 0) {
+ in_data1.resize(31);
+ in_data2.resize(33);
+ for(size_t i = 0 ; i < in_data2.size() ; i++)
+ in_data2[i] = i;
+ }
+
+ // copy to nodes
+ split( in_data1, state1 );
+ split( in_data2, state2 );
+
+ {
+ std::ostringstream ss;
+ ss << "state[" << world.rank() << "] {"
+ << state1().size() << ", "
+ << state2().size() << "}\n";
+ std::clog << ss.str() << std::flush;
+ }
+
+ // compare size
+ BOOST_REQUIRE( !same_size( state1, state2 ) );
+
+ // resize state1 to match state2.
+ resize( state1, state2 );
+
+ {
+ std::ostringstream ss;
+ ss << "state[" << world.rank() << "] 1:"
+ << state1().size() << " 2:"
+ << state2().size() << "\n";
+ std::clog << ss.str() << std::flush;
+ }
+
+ // compare size
+ BOOST_REQUIRE( same_size( state1, state2 ) );
+
+ // copy state2 to state1
+ copy( state2, state1 );
+
+ BOOST_REQUIRE_EQUAL_COLLECTIONS(state1().begin(), state1().end(),
+ state2().begin(), state2().end());
+}
+
+
+BOOST_AUTO_TEST_SUITE_END()
+
diff --git a/test_external/mtl4/Jamfile.v2 b/test_external/mtl4/Jamfile.v2
new file mode 100644
index 0000000..de9d87f
--- /dev/null
+++ b/test_external/mtl4/Jamfile.v2
@@ -0,0 +1,30 @@
+# Copyright 2012 Karsten Ahnert
+# Copyright 2013 Mario Mulansky
+# Distributed under the Boost Software License, Version 1.0. (See
+# accompanying file LICENSE_1_0.txt or copy at
+# http://www.boost.org/LICENSE_1_0.txt)
+
+import testing ;
+import boost ;
+
+# boost.use-project ;
+use-project boost : $(BOOST_ROOT) ;
+
+# set your MTL4 directory here
+MTL4_INCLUDE = /home/mario/MTL4/usr/include ;
+
+project
+ : requirements
+ <library>/boost/test//boost_unit_test_framework
+ <include>$(MTL4_INCLUDE)
+ <define>BOOST_ALL_NO_LIB=1
+ <link>static
+ :
+ : default-build release
+ ;
+
+test-suite "odeint-mtl4"
+ :
+ [ run mtl4_resize.cpp ]
+ : <testing.launcher>valgrind
+ ;
diff --git a/test_external/mtl4/mtl4_resize.cpp b/test_external/mtl4/mtl4_resize.cpp
new file mode 100644
index 0000000..7ef985d
--- /dev/null
+++ b/test_external/mtl4/mtl4_resize.cpp
@@ -0,0 +1,89 @@
+/* Boost mtl4_resize.cpp test file
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+
+ This file tests the odeint library with the mtl4 routines.
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+#define BOOST_TEST_MODULE test_mtl4_resize
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/numeric/odeint/external/mtl4/mtl4_resize.hpp>
+#include <boost/numeric/mtl/vector/dense_vector.hpp>
+
+namespace odeint = boost::numeric::odeint;
+
+
+BOOST_AUTO_TEST_CASE( test_dense_vector_resizeability )
+{
+ BOOST_CHECK( odeint::is_resizeable< mtl::dense_vector< double > >::value );
+}
+
+BOOST_AUTO_TEST_CASE( test_dense2D_resizeability )
+{
+ BOOST_CHECK( odeint::is_resizeable< mtl::dense2D< double > >::value );
+}
+
+BOOST_AUTO_TEST_CASE( test_compressed2D_resizeability )
+{
+ BOOST_CHECK( odeint::is_resizeable< mtl::compressed2D< double > >::value );
+}
+
+
+
+BOOST_AUTO_TEST_CASE( test_dense_vector_vector_same_size )
+{
+ mtl::dense_vector< double > v1( 10 ) , v2( 10 );
+ BOOST_CHECK( odeint::same_size( v2 , v1 ) );
+}
+
+BOOST_AUTO_TEST_CASE( test_dense_vector_dense2D_same_size )
+{
+ mtl::dense_vector< double > v( 10 );
+ mtl::dense2D< double > m( 10 , 10 );
+ BOOST_CHECK( odeint::same_size( m , v ) );
+}
+
+BOOST_AUTO_TEST_CASE( test_dense_vector_compressed2D_same_size )
+{
+ mtl::dense_vector< double > v( 10 );
+ mtl::compressed2D< double > m( 10 , 10 );
+ BOOST_CHECK( odeint::same_size( m , v ) );
+}
+
+
+
+
+BOOST_AUTO_TEST_CASE( test_dense_vector_vector_resize )
+{
+ mtl::dense_vector< double > v1( 10 );
+ mtl::dense_vector< double > v2;
+ odeint::resize( v2 , v1 );
+ BOOST_CHECK( mtl::size( v2 ) == mtl::size( v1 ) );
+}
+
+BOOST_AUTO_TEST_CASE( test_dense_vector_dense2D_resize )
+{
+ mtl::dense_vector< double > v( 10 );
+ mtl::dense2D< double > m;
+
+ odeint::resize( m , v );
+ BOOST_CHECK( m.num_cols() == mtl::size( v ) );
+ BOOST_CHECK( m.num_rows() == mtl::size( v ) );
+}
+
+BOOST_AUTO_TEST_CASE( test_dense_vector_compressed2D_resize )
+{
+ mtl::dense_vector< double > v( 10 );
+ mtl::compressed2D< double > m;
+
+ odeint::resize( m , v );
+ BOOST_CHECK( m.num_cols() == mtl::size( v ) );
+ BOOST_CHECK( m.num_rows() == mtl::size( v ) );
+}
diff --git a/test_external/nt2/Jamfile.v2 b/test_external/nt2/Jamfile.v2
new file mode 100644
index 0000000..26763da
--- /dev/null
+++ b/test_external/nt2/Jamfile.v2
@@ -0,0 +1,44 @@
+#==============================================================================
+# Copyright 2014 LRI UMR 8623 CNRS/Univ Paris Sud XI
+# Copyright 2014 NumScale SAS
+#
+# Distributed under the Boost Software License, Version 1.0.
+# See accompanying file LICENSE.txt or copy at
+# http://www.boost.org/LICENSE_1_0.txt
+#==============================================================================
+
+import testing ;
+import os ;
+
+# This must be built using an NT2 installation.
+# NT2_ROOT_PATH should point to the build directory.
+# Currently, cxxflags needs to be set to the required architecture
+# if using avx/avx2, set the environemnt variable NT2_SIMD_FLAGS to the
+# required value for your compiler (i.e. -mavx2 on g++)
+# If using sse2/3/4 in 64 bits, this is set automatically.
+
+local NT2_ROOT_PATH = [ os.environ NT2_ROOT_PATH ] ;
+local NT2_SIMD_FLAGS = [ os.environ NT2_SIMD_FLAGS ] ;
+
+use-project boost : $(BOOST_ROOT) ;
+
+project
+ : requirements
+ <library>$(BOOST_ROOT)/boost/test/included/unit_test_framework.hpp
+ <define>BOOST_ALL_NO_LIB=1
+ <include>$(NT2_ROOT_PATH)/include/
+ <link>static
+ <toolset>gcc:<cxxflags>-DBOOST_SIMD_NO_STRICT_ALIASING
+ <toolset>gcc:<cxxflags>-fno-strict-aliasing
+ <cxxflags>$(NT2_SIMD_FLAGS)
+ ;
+
+test-suite "odeint"
+ :
+ [ run copy.cpp ]
+ [ run norm_inf.cpp ]
+ [ run resize.cpp ]
+ [ run is_resizeable.cpp ]
+ [ run algebra_dispatcher.cpp ]
+ : <testing.launcher>valgrind
+ ;
diff --git a/test_external/nt2/algebra_dispatcher.cpp b/test_external/nt2/algebra_dispatcher.cpp
new file mode 100644
index 0000000..bea6349
--- /dev/null
+++ b/test_external/nt2/algebra_dispatcher.cpp
@@ -0,0 +1,55 @@
+//==============================================================================
+// Copyright 2014 LRI UMR 8623 CNRS/Univ Paris Sud XI
+// Copyright 2014 NumScale SAS
+//
+// Distributed under the Boost Software License, Version 1.0.
+// See accompanying file LICENSE.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt
+//==============================================================================
+#define BOOST_TEST_MODULE odeint_nt2_algebra_dispatcher
+
+#include <boost/test/included/unit_test.hpp>
+#include <boost/test/floating_point_comparison.hpp>
+#include <boost/numeric/odeint/external/nt2/nt2_algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+#include <boost/mpl/list.hpp>
+
+#include <boost/preprocessor/repetition.hpp>
+#include <boost/preprocessor/arithmetic/mul.hpp>
+
+#include <nt2/table.hpp>
+#include <nt2/sdk/meta/as.hpp>
+#include <nt2/include/functions/ones.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+typedef boost::mpl::list< float , double > fp_types;
+
+#define TABLE(z,n,text) nt2::table<T> y ## n = \
+ nt2::ones(1,2,nt2::meta::as_<T>() )*T(BOOST_PP_ADD(n,1));
+
+#define PARAMS(z,n,text) T(BOOST_PP_ADD(n,1)),
+
+#define SUM(z,n,text) +BOOST_PP_MUL(BOOST_PP_ADD(n,3),BOOST_PP_ADD(n,2))
+
+#define TEST(z,n,text) BOOST_CHECK_SMALL( y0(BOOST_PP_ADD(n,1)) \
+ -T( 2 BOOST_PP_REPEAT(text, SUM, text) ), T(1e-10) );
+
+#define TEST_CASE(z,n,text) BOOST_AUTO_TEST_CASE_TEMPLATE ( \
+ BOOST_PP_CAT(odeint_foreach, n), T, fp_types ) \
+{ \
+ vector_space_algebra algebra; \
+ BOOST_PP_REPEAT(BOOST_PP_ADD(n,2),TABLE,tt) \
+ BOOST_PP_CAT(algebra.for_each,BOOST_PP_ADD(n,2))( \
+ BOOST_PP_ENUM_PARAMS(BOOST_PP_ADD(n,2),y), default_operations:: \
+ BOOST_PP_CAT(scale_sum,BOOST_PP_ADD(n,1)) <T>( \
+ BOOST_PP_REPEAT(n, PARAMS, text ) T(BOOST_PP_ADD(n,1)))); \
+ BOOST_PP_REPEAT(2,TEST,n) \
+}
+
+BOOST_AUTO_TEST_SUITE( nt2_algebra )
+
+BOOST_PP_REPEAT(7,TEST_CASE,dummy)
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test_external/nt2/copy.cpp b/test_external/nt2/copy.cpp
new file mode 100644
index 0000000..841728e
--- /dev/null
+++ b/test_external/nt2/copy.cpp
@@ -0,0 +1,44 @@
+//==============================================================================
+// Copyright 2014 LRI UMR 8623 CNRS/Univ Paris Sud XI
+// Copyright 2014 NumScale SAS
+//
+// Distributed under the Boost Software License, Version 1.0.
+// See accompanying file LICENSE.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt
+//==============================================================================
+#include <boost/numeric/odeint.hpp>
+#include <nt2/table.hpp>
+#include <nt2/include/functions/linspace.hpp>
+
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_nt2_copy
+
+#include <boost/test/included/unit_test.hpp>
+#include <boost/numeric/odeint/external/nt2/nt2_copy.hpp>
+
+#include <boost/mpl/list.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+typedef boost::mpl::list< float , double > fp_types;
+
+BOOST_AUTO_TEST_SUITE( nt2_copy )
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( test_copy, T, fp_types )
+{
+ nt2::table<T> x = nt2::linspace(T(1),T(0),7);
+
+ nt2::table<T> y;
+
+ copy(y,x);
+
+ for (std::size_t ii=1; ii<=x.size();ii++)
+ BOOST_CHECK_EQUAL(x(ii),y(ii));
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test_external/nt2/is_resizeable.cpp b/test_external/nt2/is_resizeable.cpp
new file mode 100644
index 0000000..10ecdbb
--- /dev/null
+++ b/test_external/nt2/is_resizeable.cpp
@@ -0,0 +1,36 @@
+//==============================================================================
+// Copyright 2014 LRI UMR 8623 CNRS/Univ Paris Sud XI
+// Copyright 2014 NumScale SAS
+//
+// Distributed under the Boost Software License, Version 1.0.
+// See accompanying file LICENSE.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt
+//==============================================================================
+#include <boost/numeric/odeint.hpp>
+#include <nt2/table.hpp>
+
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_nt2_resize
+
+#include <boost/test/included/unit_test.hpp>
+#include <boost/numeric/odeint/external/nt2/nt2_resize.hpp>
+
+#include <boost/mpl/list.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+typedef boost::mpl::list< float , double > fp_types;
+
+BOOST_AUTO_TEST_SUITE( nt2_is_resizeable )
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( is_resizeable, T, fp_types )
+{
+ BOOST_STATIC_ASSERT(( boost::numeric::odeint::is_resizeable< nt2::table<T> >::value ));
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test_external/nt2/norm_inf.cpp b/test_external/nt2/norm_inf.cpp
new file mode 100644
index 0000000..1e12061
--- /dev/null
+++ b/test_external/nt2/norm_inf.cpp
@@ -0,0 +1,46 @@
+//==============================================================================
+// Copyright 2014 LRI UMR 8623 CNRS/Univ Paris Sud XI
+// Copyright 2014 NumScale SAS
+//
+// Distributed under the Boost Software License, Version 1.0.
+// See accompanying file LICENSE.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt
+//==============================================================================
+#include <boost/numeric/odeint.hpp>
+#include <nt2/table.hpp>
+#include <nt2/include/functions/zeros.hpp>
+#include <nt2/include/functions/ones.hpp>
+
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_nt2_copy
+
+#include <boost/test/included/unit_test.hpp>
+#include <boost/test/floating_point_comparison.hpp>
+#include <boost/numeric/odeint/external/nt2/nt2_norm_inf.hpp>
+
+#include <boost/mpl/list.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+typedef boost::mpl::list< float , double > fp_types;
+
+BOOST_AUTO_TEST_SUITE( nt2_norm_inf )
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( test_norm_inf, T, fp_types )
+{
+ nt2::table<T> x = nt2::ones(10,1, nt2::meta::as_<T>() );
+ x(4) = 55;
+
+ nt2::table<T> y = nt2::zeros(8,8, nt2::meta::as_<T>() );
+ y(6,4) = -42;
+
+ BOOST_CHECK_SMALL(vector_space_norm_inf<nt2::table<T> >()(x) - T(55), T(1e-10));
+ BOOST_CHECK_SMALL(vector_space_norm_inf<nt2::table<T> >()(y) - T(42), T(1e-10));
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test_external/nt2/resize.cpp b/test_external/nt2/resize.cpp
new file mode 100644
index 0000000..56d7ce4
--- /dev/null
+++ b/test_external/nt2/resize.cpp
@@ -0,0 +1,45 @@
+//==============================================================================
+// Copyright 2014 LRI UMR 8623 CNRS/Univ Paris Sud XI
+// Copyright 2014 NumScale SAS
+//
+// Distributed under the Boost Software License, Version 1.0.
+// See accompanying file LICENSE.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt
+//==============================================================================
+#include <boost/numeric/odeint.hpp>
+#include <nt2/table.hpp>
+
+#include <boost/config.hpp>
+#ifdef BOOST_MSVC
+ #pragma warning(disable:4996)
+#endif
+
+#define BOOST_TEST_MODULE odeint_nt2_resize
+
+#include <boost/test/included/unit_test.hpp>
+#include <boost/numeric/odeint/external/nt2/nt2_resize.hpp>
+
+#include <boost/mpl/list.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+
+typedef boost::mpl::list< float , double > fp_types;
+
+BOOST_AUTO_TEST_SUITE( nt2_resize )
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( test_resize, T, fp_types )
+{
+ nt2::table<T> x;
+ x.resize(nt2::of_size(10,10));
+
+ nt2::table<T> y;
+
+ BOOST_CHECK_EQUAL(same_size(x,y),false);
+
+ resize(y,x);
+
+ BOOST_CHECK_EQUAL(same_size(x,y),true);
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test_external/thrust/Makefile b/test_external/thrust/Makefile
new file mode 100644
index 0000000..49d9cd7
--- /dev/null
+++ b/test_external/thrust/Makefile
@@ -0,0 +1,34 @@
+# Copyright 2010-2014 Mario Mulansky
+# Copyright 2010-2012 Karsten Ahnert
+#
+# Distributed under the Boost Software License, Version 1.0.
+# (See accompanying file LICENSE_1_0.txt or
+# copy at http://www.boost.org/LICENSE_1_0.txt)
+
+# make sure BOOST_ROOT is pointing to your boost directory
+# otherwise, set it here:
+# BOOST_ROOT = /path/to/boost
+
+# path to the cuda installation
+CUDA_ROOT = /usr/local/cuda
+# target architecture
+ARCH = sm_13
+
+NVCC = $(CUDA_ROOT)/bin/nvcc
+
+INCLUDES += -I../../include/ -I$(BOOST_ROOT)
+
+NVCCFLAGS = -O3 $(INCLUDES) -arch $(ARCH)
+
+%.o : %.cu
+ $(NVCC) $(NVCCFLAGS) -c $< -o $@
+
+% : %.o
+ $(NVCC) $(NVCCFLAGS) -o $@ $<
+
+
+all : check_thrust
+
+
+clean :
+ -rm *~ *.o check_thrust
diff --git a/test_external/thrust/check_thrust.cu b/test_external/thrust/check_thrust.cu
new file mode 100644
index 0000000..3623c37
--- /dev/null
+++ b/test_external/thrust/check_thrust.cu
@@ -0,0 +1,72 @@
+/* Boost check_thrust.cu test file
+
+ Copyright 2010-2013 Mario Mulansky
+ Copyright 2010-2011 Karsten Ahnert
+
+ This file tests the use of the euler stepper
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+//#include <boost/test/unit_test.hpp>
+
+#include <boost/numeric/odeint/stepper/euler.hpp>
+#include <boost/numeric/odeint/external/thrust/thrust.hpp>
+
+#include <thrust/device_vector.h>
+#include <thrust/fill.h>
+
+using namespace boost::numeric::odeint;
+
+typedef float base_type;
+// typedef thrust::device_vector< base_type > state_type;
+typedef thrust::host_vector< base_type > state_type;
+
+void constant_system( const state_type &x , state_type &dxdt , base_type t )
+{
+ thrust::fill( dxdt.begin() , dxdt.end() , static_cast<base_type>(1.0) );
+}
+
+const base_type eps = 1.0e-7;
+
+
+template< class Stepper , class System >
+void check_stepper_concept( Stepper &stepper , System system , typename Stepper::state_type &x )
+{
+ typedef Stepper stepper_type;
+ typedef typename stepper_type::state_type container_type;
+ typedef typename stepper_type::order_type order_type;
+ typedef typename stepper_type::time_type time_type;
+
+ stepper.do_step( system , x , 0.0 , 0.1 );
+ base_type xval = *boost::begin( x );
+ if( fabs( xval - 0.1 ) < eps )
+ std::clog << "TEST PASSED" << std::endl;
+ else
+ std::clog << "TEST FAILED" << std::endl;
+}
+
+void test_euler_with_thrust( void )
+{
+ state_type x(1);
+ thrust::fill( x.begin() , x.end() , static_cast<base_type>(0.0) );
+ euler< state_type , base_type , state_type , base_type > euler;
+ check_stepper_concept( euler , constant_system , x );
+
+
+}
+
+/*test_suite* init_unit_test_suite( int argc, char* argv[] )
+{
+ test_suite *test = BOOST_TEST_SUITE("check stepper with thrust");
+
+ test->add( BOOST_TEST_CASE( &test_euler_with_thrust ) );
+
+ return test;
+}*/
+
+int main() {
+ test_euler_with_thrust();
+}
diff --git a/test_external/vexcl/Jamfile.v2 b/test_external/vexcl/Jamfile.v2
new file mode 100644
index 0000000..9b76b43
--- /dev/null
+++ b/test_external/vexcl/Jamfile.v2
@@ -0,0 +1,35 @@
+# Copyright 2012 Karsten Ahnert
+# Copyright 2013 Mario Mulansky
+# Distributed under the Boost Software License, Version 1.0.
+# (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+# bring in rules for testing
+
+
+import testing ;
+
+use-project boost : $(BOOST_ROOT) ;
+VEXCL_INCLUDE = /home/karsten/boost/testing/vexcl ;
+OPENCL_INCLUDE = /usr/local/cuda/include ;
+#OPENCL_INCLUDE = /usr/include ;
+
+project
+ : requirements
+ <library>/boost/test//boost_unit_test_framework
+ <define>BOOST_ALL_NO_LIB=1
+ <include>$(VEXCL_INCLUDE)
+ <include>$(OPENCL_INCLUDE)
+ <cxxflags>-std=c++0x
+ <library>/boost//system/
+ ;
+
+lib OpenCL : : <name>OpenCL <link>shared ;
+
+test-suite "odeint"
+ :
+ [ run lorenz.cpp OpenCL ]
+ [ run norm_inf.cpp OpenCL ]
+ : <testing.launcher>valgrind
+ :
+ : <link>shared:<define>BOOST_TEST_DYN_LINK=1
+ ;
\ No newline at end of file
diff --git a/test_external/vexcl/lorenz.cpp b/test_external/vexcl/lorenz.cpp
new file mode 100644
index 0000000..6bde91f
--- /dev/null
+++ b/test_external/vexcl/lorenz.cpp
@@ -0,0 +1,147 @@
+/* Boost lorenz.cpp test file
+
+ Copyright 2012 Karsten Ahnert
+ Copyright 2012 Mario Mulansky
+
+ This file tests the odeint library with the vexcl types
+
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+*/
+
+#define BOOST_TEST_MODULE odeint_vexcl
+
+#include <vector>
+#include <iostream>
+
+#include <vexcl/vexcl.hpp>
+
+#include <boost/numeric/odeint/stepper/runge_kutta4.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp>
+#include <boost/numeric/odeint/stepper/controlled_runge_kutta.hpp>
+#include <boost/numeric/odeint/stepper/dense_output_runge_kutta.hpp>
+#include <boost/numeric/odeint/algebra/vector_space_algebra.hpp>
+#include <boost/numeric/odeint/integrate/integrate_const.hpp>
+#include <boost/numeric/odeint/external/vexcl/vexcl.hpp>
+
+#include <boost/test/unit_test.hpp>
+
+using namespace boost::unit_test;
+namespace odeint = boost::numeric::odeint;
+
+
+typedef vex::vector< double > vector_type;
+typedef vex::multivector< double, 3 > state_type;
+
+
+
+const double sigma = 10.0;
+const double b = 8.0 / 3.0;
+
+struct sys_func
+{
+ const vector_type &R;
+
+ sys_func( const vector_type &_R ) : R( _R ) { }
+
+ void operator()( const state_type &x , state_type &dxdt , double t ) const
+ {
+ dxdt(0) = -sigma * ( x(0) - x(1) );
+ dxdt(1) = R * x(0) - x(1) - x(0) * x(2);
+ dxdt(2) = - b * x(2) + x(0) * x(1);
+ }
+};
+
+const size_t n = 1024 ;
+const double dt = 0.01;
+const double t_max = 1.0;
+
+
+BOOST_AUTO_TEST_CASE( integrate_const_rk4 )
+{
+ vex::Context ctx( vex::Filter::Type(CL_DEVICE_TYPE_GPU) );
+
+ double Rmin = 0.1 , Rmax = 50.0 , dR = ( Rmax - Rmin ) / double( n - 1 );
+ std::vector<double> x( n * 3 ) , r( n );
+ for( size_t i=0 ; i<n ; ++i ) r[i] = Rmin + dR * double( i );
+
+ state_type X( ctx.queue() , n );
+ X(0) = 10.0;
+ X(1) = 10.0;
+ X(2) = 10.0;
+
+ vector_type R( ctx.queue() , r );
+
+ odeint::runge_kutta4<
+ state_type , double , state_type , double ,
+ odeint::vector_space_algebra , odeint::default_operations
+ > stepper;
+
+ odeint::integrate_const( stepper , sys_func( R ) , X , 0.0 , t_max , dt );
+
+ std::vector< double > res( 3 * n );
+ vex::copy( X(0) , res );
+ std::cout << res[0] << std::endl;
+}
+
+BOOST_AUTO_TEST_CASE( integrate_const_controlled_rk54 )
+{
+ vex::Context ctx( vex::Filter::Type(CL_DEVICE_TYPE_GPU) );
+
+ double Rmin = 0.1 , Rmax = 50.0 , dR = ( Rmax - Rmin ) / double( n - 1 );
+ std::vector<double> x( n * 3 ) , r( n );
+ for( size_t i=0 ; i<n ; ++i ) r[i] = Rmin + dR * double( i );
+
+ state_type X( ctx.queue() , n );
+ X(0) = 10.0;
+ X(1) = 10.0;
+ X(2) = 10.0;
+
+ vector_type R( ctx.queue() , r );
+
+ typedef odeint::runge_kutta_cash_karp54<
+ state_type , double , state_type , double ,
+ odeint::vector_space_algebra , odeint::default_operations
+ > stepper_type;
+ typedef odeint::controlled_runge_kutta< stepper_type > controlled_stepper_type;
+
+ odeint::integrate_const( controlled_stepper_type() , sys_func( R ) , X , 0.0 , t_max , dt );
+
+ std::vector< double > res( 3 * n );
+ vex::copy( X(0) , res );
+ std::cout << res[0] << std::endl;
+}
+
+BOOST_AUTO_TEST_CASE( integrate_const_dense_output_dopri5 )
+{
+ vex::Context ctx( vex::Filter::Type(CL_DEVICE_TYPE_GPU) );
+
+ double Rmin = 0.1 , Rmax = 50.0 , dR = ( Rmax - Rmin ) / double( n - 1 );
+ std::vector<double> x( n * 3 ) , r( n );
+ for( size_t i=0 ; i<n ; ++i ) r[i] = Rmin + dR * double( i );
+
+ state_type X( ctx.queue() , n );
+ X(0) = 10.0;
+ X(1) = 10.0;
+ X(2) = 10.0;
+
+ vector_type R( ctx.queue() , r );
+
+ typedef odeint::runge_kutta_dopri5<
+ state_type , double , state_type , double ,
+ odeint::vector_space_algebra , odeint::default_operations
+ > stepper_type;
+ typedef odeint::controlled_runge_kutta< stepper_type > controlled_stepper_type;
+ typedef odeint::dense_output_runge_kutta< controlled_stepper_type > dense_output_stepper_type;
+
+ odeint::integrate_const( dense_output_stepper_type() , sys_func( R ) , X , 0.0 , t_max , dt );
+
+ std::vector< double > res( 3 * n );
+ vex::copy( X(0) , res );
+ std::cout << res[0] << std::endl;
+}
+
+
+
diff --git a/test_external/vexcl/norm_inf.cpp b/test_external/vexcl/norm_inf.cpp
new file mode 100644
index 0000000..71481d2
--- /dev/null
+++ b/test_external/vexcl/norm_inf.cpp
@@ -0,0 +1,25 @@
+#define BOOST_TEST_MODULE odeint_vexcl_norm_inf
+
+#include <boost/numeric/odeint/external/vexcl/vexcl_norm_inf.hpp>
+#include <boost/test/unit_test.hpp>
+
+template <class T>
+double norm(const T &x) {
+ return boost::numeric::odeint::vector_space_norm_inf<T>()(x);
+}
+
+BOOST_AUTO_TEST_CASE( norm_inf )
+{
+ vex::Context ctx(vex::Filter::Env);
+ std::cout << ctx << std::endl;
+
+ vex::vector<double> x(ctx, 1024);
+ x = 41;
+
+ vex::multivector<double, 2> y(ctx, 1024);
+ y = 42;
+
+ BOOST_CHECK_EQUAL( norm(x), 41 );
+ BOOST_CHECK_EQUAL( norm(y), 42 );
+}
+
diff --git a/toolset.jam.patch b/toolset.jam.patch
new file mode 100644
index 0000000..dca997d
--- /dev/null
+++ b/toolset.jam.patch
@@ -0,0 +1,61 @@
+diff --git a/src/build/toolset.jam b/src/build/toolset.jam
+index b5defd5..a942cd9 100644
+--- a/src/build/toolset.jam
++++ b/src/build/toolset.jam
+@@ -17,6 +17,8 @@ import regex ;
+ import sequence ;
+ import set ;
+ import property-set ;
++import order ;
++import "class" : new ;
+
+
+ .flag-no = 1 ;
+@@ -237,6 +239,7 @@ rule handle-flag-value ( value * : properties * )
+ if $(value:G)
+ {
+ local matches = [ property.select $(value) : $(properties) ] ;
++ local order ;
+ for local p in $(matches)
+ {
+ local att = [ feature.attributes $(p:G) ] ;
+@@ -263,11 +266,24 @@ rule handle-flag-value ( value * : properties * )
+ }
+ if path in $(att)
+ {
+- result += [ sequence.transform path.native : $(values) ] ;
++ values = [ sequence.transform path.native : $(values) ] ;
+ }
+- else
++ result += $(values) ;
++ if $(values[2])
+ {
+- result += $(values) ;
++ if ! $(order)
++ {
++ order = [ new order ] ;
++ }
++ local prev ;
++ for local v in $(values)
++ {
++ if $(prev)
++ {
++ $(order).add-pair $(prev) $(v) ;
++ }
++ prev = $(v) ;
++ }
+ }
+ }
+ else
+@@ -275,6 +291,11 @@ rule handle-flag-value ( value * : properties * )
+ result += $(p:G=) ;
+ }
+ }
++ if $(order)
++ {
++ result = [ $(order).order [ sequence.unique $(result) : stable ] ] ;
++ DELETE_MODULE $(order) ;
++ }
+ }
+ else
+ {
