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/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
index 0000000..7819940
--- /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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index 0000000..42e8996
--- /dev/null
+++ b/doc/html/boostbook.css
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+/*=============================================================================
+ 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;
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+
+/*=============================================================================
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+=============================================================================*/
+
+ /* 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;
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+
+ /* Program listings in tables don't get borders */
+ td .programlisting,
+ td .screen
+ {
+ margin: 0pc 0pc 0pc 0pc;
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+ }
+
+/*=============================================================================
+ Headings
+=============================================================================*/
+
+ h1, h2, h3, h4, h5, h6
+ {
+ text-align: left;
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+ font-weight: bold;
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+
+ /* Top page titles */
+ title,
+ h1.title,
+ h2.title
+ h3.title,
+ h4.title,
+ h5.title,
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+ {
+ font-weight: bold;
+ margin-bottom: 1pc;
+ }
+
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+ .section h1
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+ font-size: 140%;
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+ .section h2 { font-size: 140% }
+ .section h3 { font-size: 130% }
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+
+
+/*=============================================================================
+ Author
+=============================================================================*/
+
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+ {
+ font-size: 100%
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+ Lists
+=============================================================================*/
+
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+ {
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+ {
+ text-align: left;
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+=============================================================================*/
+
+ a
+ {
+ text-decoration: none; /* no underline */
+ }
+
+ a:hover
+ {
+ text-decoration: underline;
+ }
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+/*=============================================================================
+ Spirit style navigation
+=============================================================================*/
+
+ .spirit-nav
+ {
+ text-align: right;
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+ {
+ color: white;
+ padding-left: 0.5em;
+ }
+
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+ {
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+ }
+
+/*=============================================================================
+ 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
+=============================================================================*/
+
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+ {
+ margin: 1em 0;
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+ /* 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;
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+
+ div.variablelist dl dt
+ {
+ margin-bottom: 0.2em;
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+
+ div.variablelist dl dd
+ {
+ margin: 0em 0em 0.5em 2em;
+ font-size: 10pt;
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+
+ div.variablelist table tbody tr td p,
+ div.variablelist dl dd p
+ {
+ margin: 0em 0em 0.5em 0em;
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+ {
+ text-decoration: underline;
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+ span.strikethrough
+ {
+ text-decoration: line-through;
+ }
+
+ /* Copyright, Legal Notice */
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+ {
+ text-align: left
+ }
+
+/*=============================================================================
+ Colors
+=============================================================================*/
+
+ @media screen
+ {
+ body {
+ background-color: #FFFFFF;
+ color: #000000;
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+ .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,
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+ 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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diff --git a/doc/literature.qbk b/doc/literature.qbk
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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]
