Squashed 'third_party/osqp/' content from commit 33454b3e23
Change-Id: I056df0582ca06664e86554c341a94c47ab932001
git-subtree-dir: third_party/osqp
git-subtree-split: 33454b3e236f1f44193bfbbb6b8c8e71f8f04e9a
Signed-off-by: Austin Schuh <austin.linux@gmail.com>
diff --git a/docs/Makefile b/docs/Makefile
new file mode 100644
index 0000000..61564e9
--- /dev/null
+++ b/docs/Makefile
@@ -0,0 +1,24 @@
+# Minimal makefile for Sphinx documentation
+#
+
+# You can set these variables from the command line.
+SPHINXOPTS =
+SPHINXBUILD = sphinx-build
+SPHINXPROJ = osqp
+SOURCEDIR = .
+BUILDDIR = _build
+HTMLCOPYDIR = _build/html
+
+# Put it first so that "make" without argument is like "make help".
+help:
+ @$(SPHINXBUILD) -M help "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)
+
+.PHONY: help Makefile
+
+# Catch-all target: route all unknown targets to Sphinx using the new
+# "make mode" option. $(O) is meant as a shortcut for $(SPHINXOPTS).
+%: Makefile
+ @$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)
+ifneq ("$(HTMLCOPYDIR)", "$(BUILDDIR)/html")
+ cp -rT $(BUILDDIR)/html $(HTMLCOPYDIR)
+endif
\ No newline at end of file
diff --git a/docs/_static/css/osqp_theme.css b/docs/_static/css/osqp_theme.css
new file mode 100644
index 0000000..161e526
--- /dev/null
+++ b/docs/_static/css/osqp_theme.css
@@ -0,0 +1,198 @@
+/* Default header fonts are ugly */
+@import url(https://fonts.googleapis.com/css?family=Open+Sans:400,400i,600,600i,700,700i);
+@import url(https://fonts.googleapis.com/css?family=Inconsolata);
+
+h1, h2, h3, h4, h5, h6 {
+ font-family: "Open Sans", "Helvetica Neue",Helvetica,Arial,sans-serif;
+ font-weight: 600;
+}
+body {
+ font-family: 'Open Sans', sans-serif;
+}
+
+.wy-nav-top a {
+ font-size: 175%;
+ font-weight: 600;
+}
+
+/* Remove rounded navigation bar */
+.wy-side-nav-search input[type=text] {
+ border-radius: 2px;
+}
+
+div[class^='highlight'] pre {
+ font-family: 'Inconsolata', monospace;
+ font-size: 16px;
+ background: #f3f6f6;
+}
+
+/* Make glossary entries bolder to stand out */
+dl.glossary>dt{
+ font-weight: 700;
+}
+
+/* Make bold things less bold */
+b, strong {
+ font-weight: 600;
+}
+
+/* Less bold table head */
+.wy-table thead th, .rst-content table.docutils thead th, .rst-content table.field-list thead th {
+ font-weight: 600;
+}
+
+/* Less bold current active element */
+.wy-menu-vertical li.on a, .wy-menu-vertical li.current>a {
+ font-weight: 600;
+}
+
+
+/* Types link refs less bold */
+.rst-content tt.xref, a .rst-content tt, .rst-content tt.xref, .rst-content code.xref, a .rst-content tt, a .rst-content code {
+ font-weight: normal;
+}
+
+/* Make types in C docs less bold */
+.rst-content dl dt {
+ font-weight: 600;
+}
+
+
+/* Link Styling */
+a,a:visited, a:focus {
+ color: rgb(46, 118, 176); /* Light blue*/
+ text-decoration: none;
+}
+a:hover, a:active {
+ color: rgb(0, 32, 72); /* blue*/
+ text-decoration: none;
+}
+
+
+
+/* Make bar oxford blue*/
+.wy-side-nav-search {
+ background-color: rgb(0, 32, 72); /* Oxford blue */
+}
+
+.wy-nav-side {
+ background: rgb(0, 32, 72); /* Oxford blue */
+}
+
+
+.wy-nav-content-wrap, .wy-menu li.current > a {
+ background-color: #fff;
+ /* font-weight: 600; */
+}
+
+@media screen and (min-width: 1400px) {
+ .wy-nav-content-wrap {
+ /*background-color: rgba(0, 0, 0, 0.0470588);*/
+ background-color: rgb(245, 245, 245); /* Light grey */
+ }
+
+ .wy-nav-content {
+ background-color: #fff;
+ }
+}
+
+.wy-nav-top {
+ background-color: rgb(0, 32, 72); /* Oxford blue */
+}
+
+
+/* Change color of the line at the top of Read the Docs box at the bottom left
+ corner */
+.rst-versions{
+ border-top:solid 10px rgb(0, 32, 72); /* Oxford blue */
+}
+
+
+/* Change color of top left name */
+.wy-side-nav-search>a{
+ color: rgb(255, 255, 255); /* White text*/
+}
+.wy-side-nav-search>div.version{
+ color: rgb(245, 245, 245); /* Light grey text*/
+}
+.wy-nav-top a{
+ color: rgb(255, 255, 255); /* White text*/
+}
+
+
+
+/* Navigation bar text */
+.wy-menu-vertical header, .wy-menu-vertical p.caption {
+ color: rgb(255, 255, 255); /* White text*/
+ font-weight: 600;
+}
+
+.wy-menu-vertical a{
+ color: rgb(178, 188, 200); /* Grey */
+}
+
+.wy-menu-vertical a:hover{
+ background: rgb(46, 118, 176);
+ color: rgb(255, 255, 255); /* White text*/
+}
+
+
+
+
+
+
+/* Change text color for tt literal */
+.rst-content tt.literal, .rst-content tt.literal, .rst-content code.literal{
+ color: rgb(46, 118, 176); /* Light blue*/
+ font-size: 14px;
+}
+
+tr td code span{
+ font-size: 13px;
+}
+
+.s1, .s2{
+ color: rgb(46, 118, 176); /* Light blue*/
+}
+
+
+/* Rubric bigger (initial page) */
+.rst-content p.rubric {
+ font-family: "Open Sans", "Helvetica Neue",Helvetica,Arial,sans-serif;
+ font-weight: 600;
+ font-size: 150%;
+ margin-bottom: 20px;
+}
+
+/* Smaller rubric in C description */
+p.breathe-sectiondef-title.rubric {
+ font-size: 100%;
+}
+
+
+
+
+/* Remove box shadow from buttons */
+.btn {
+ font-weight: normal;
+ font-family: "Open Sans", "Helvetica Neue",Helvetica,Arial,sans-serif;
+ box-shadow: none;
+}
+/* Force breathe display inline parameters */
+/*.wy-plain-list-disc li p:last-child, .rst-content .section ul li p:last-child, .rst-content .toctree-wrapper ul li p:last-child, article ul li p:last-child{
+ display: inline;
+}*/
+
+
+/* Remove line block indentation */
+.rst-content .line-block {
+ margin-bottom: 0px !important;
+ margin-left: 0px !important;
+}
+
+
+/* Margin below tables */
+table p {
+ margin-bottom: 0px;
+}
+
diff --git a/docs/_static/img/favicon.ico b/docs/_static/img/favicon.ico
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+++ b/docs/_static/img/favicon.ico
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diff --git a/docs/_static/img/logo.pdf b/docs/_static/img/logo.pdf
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diff --git a/docs/_templates/layout.html b/docs/_templates/layout.html
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+++ b/docs/_templates/layout.html
@@ -0,0 +1,20 @@
+{% extends '!layout.html' %}
+
+{% block extrahead %}
+<meta name="twitter:card" content="summary_large_image" >
+<meta name="twitter:creator" content="@bstellato" >
+<meta name="twitter:image"
+ content="https://osqp.org/docs/_static/img/logo.png">
+<meta name="twitter:description" content="The OSQP (Operator Splitting
+Quadratic Program) solver is a numerical optimization package for solving
+convex quadratic programs." >
+<meta property="og:url" content="https://osqp.org" >
+<meta property="og:title" content="OSQP solver documentation" >
+<meta property="og:description" content="The OSQP (Operator Splitting Quadratic
+Program) solver is a numerical optimization package for solving convex
+quadratic programs." >
+<meta property="og:image"
+content="https://osqp.org/docs/_static/img/logo.png">
+<meta property="fb:app_id" content="129555174389689">
+<meta property="og:type" content="website" >
+{% endblock %}
diff --git a/docs/citing/index.rst b/docs/citing/index.rst
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+++ b/docs/citing/index.rst
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+.. _citing :
+
+Citing OSQP
+===========
+
+If you use OSQP for published work, we encourage you to put a star on `GitHub <https://github.com/osqp/osqp>`_ and cite the accompanying papers:
+
+
+.. glossary::
+
+ Main paper
+ Main algorithm description, derivation and benchmark available in this `paper <https://web.stanford.edu/~boyd/papers/pdf/osqp.pdf>`__.
+
+ .. code:: latex
+
+ @article{osqp,
+ author = {Stellato, B. and Banjac, G. and Goulart, P. and Bemporad, A. and Boyd, S.},
+ title = {{OSQP}: an operator splitting solver for quadratic programs},
+ journal = {Mathematical Programming Computation},
+ volume = {12},
+ number = {4},
+ pages = {637--672},
+ year = {2020},
+ doi = {10.1007/s12532-020-00179-2},
+ url = {https://doi.org/10.1007/s12532-020-00179-2},
+ }
+
+ Infeasibility detection
+ Infeasibility detection proofs using ADMM (also for general conic programs) in this `paper <https://stanford.edu/~boyd/papers/pdf/admm_infeas.pdf>`__.
+
+ .. code:: latex
+
+ @article{osqp-infeasibility,
+ author = {Banjac, G. and Goulart, P. and Stellato, B. and Boyd, S.},
+ title = {Infeasibility detection in the alternating direction method of multipliers for convex optimization},
+ journal = {Journal of Optimization Theory and Applications},
+ year = {2019},
+ volume = {183},
+ number = {2},
+ pages = {490--519},
+ doi = {10.1007/s10957-019-01575-y},
+ url = {https://doi.org/10.1007/s10957-019-01575-y},
+ }
+
+ GPU implementation
+ GPU implementation and PCG method for solving linear systems in this `paper <https://doi.org/10.1016/j.jpdc.2020.05.021>`__.
+
+ .. code:: latex
+
+ @article{osqp-gpu,
+ author = {Schubiger, M. and Banjac, G. and Lygeros, J.},
+ title = {{GPU} acceleration of {ADMM} for large-scale quadratic programming},
+ journal = {Journal of Parallel and Distributed Computing},
+ year = {2020},
+ volume = {144},
+ pages = {55--67},
+ doi = {10.1016/j.jpdc.2020.05.021},
+ url = {https://doi.org/10.1016/j.jpdc.2020.05.021},
+ }
+
+ Code generation
+ Code generation functionality and example in this `paper <https://stanford.edu/~boyd/papers/pdf/osqp_embedded.pdf>`__.
+
+ .. code:: latex
+
+ @inproceedings{osqp-codegen,
+ author = {Banjac, G. and Stellato, B. and Moehle, N. and Goulart, P. and Bemporad, A. and Boyd, S.},
+ title = {Embedded code generation using the {OSQP} solver},
+ booktitle = {IEEE Conference on Decision and Control (CDC)},
+ year = {2017},
+ doi = {10.1109/CDC.2017.8263928},
+ url = {https://doi.org/10.1109/CDC.2017.8263928},
+ }
+
+ Mixed-integer optimization
+ A branch-and-bound solver for mixed-integer quadratic optimization in this `paper <https://stellato.io/downloads/publications/2018/miosqp_ecc.pdf>`__.
+
+ .. code:: latex
+
+ @inproceedings{miosqp,
+ author = {Stellato, B. and Naik, V. V. and Bemporad, A. and Goulart, P. and Boyd, S.},
+ title = {Embedded mixed-integer quadratic optimization using the {OSQP} solver},
+ booktitle = {European Control Conference (ECC)},
+ year = {2018},
+ doi = {10.23919/ECC.2018.8550136},
+ url = {https://doi.org/10.23919/ECC.2018.8550136},
+ }
diff --git a/docs/codegen/index.rst b/docs/codegen/index.rst
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+++ b/docs/codegen/index.rst
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+Code generation
+===============
+
+OSQP can generate tailored C code that compiles into a fast and reliable solver
+for the given family of QP problems in which the problem data, but not its
+dimensions, change between problem instances.
+
+
+The generated code is:
+
+.. glossary::
+
+ Malloc-free
+ It does not perform any dynamic memory allocation.
+
+ Library-free
+ It is not linked to any external library.
+
+ Division-free
+ There are no division required in the ADMM algorithm
+
+
+We make a distinction between two cases depending on which of the data are to be
+treated as parameters.
+
+.. glossary::
+
+ Vectors as parameters
+ Vectors :math:`q`, :math:`l` and :math:`u` can change between problem instances.
+ This corresponds to the compiler flag :code:`EMBEDDED=1`.
+ :math:`\rho` adaptation is not enabled.
+ The generated code is division-free and has a very small footprint.
+
+ Matrices as parameters
+ Both vectors :math:`q`, :math:`l`, :math:`u` and values in matrices
+ :math:`P` and :math:`A` can change between problem instances.
+ This corresponds to the compiler flag :code:`EMBEDDED=2`.
+ :math:`\rho` adaptation is enabled but the frequency does not rely on any timing.
+ We assume that the sparsity patterns of :math:`P` and :math:`A` are fixed.
+
+
+.. toctree::
+ :maxdepth: 1
+ :glob:
+
+ *
diff --git a/docs/codegen/matlab.rst b/docs/codegen/matlab.rst
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+++ b/docs/codegen/matlab.rst
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+Matlab
+======
+
+Before generating code for a parametric problem, the problem should be first
+specified in the setup phase. See :ref:`matlab_setup` for more details.
+
+
+Codegen
+-------
+The code is generated by running
+
+.. code:: matlab
+
+ m.codegen(dir_name, varargin)
+
+The argument :code:`dir_name` is the name of a directory where the generated
+code is stored.
+The second argument :code:`varargin` specifies additional codegen options
+shown in the following table
+
+
++-----------------------+---------------------------------------------------+--------------------------------+
+| Option | Description | Allowed values |
++=======================+===================================================+================================+
+| :code:`project_type` | Build environment | | :code:`''` (default) |
+| | | | :code:`'Makefile'` |
+| | | | :code:`'MinGW Makefiles'` |
+| | | | :code:`'Unix Makefiles'` |
+| | | | :code:`'CodeBlocks'` |
+| | | | :code:`'Xcode'` |
++-----------------------+---------------------------------------------------+--------------------------------+
+| :code:`parameters` | Problem parameters | | :code:`'vectors'` (default) |
+| | | | :code:`'matrices'` |
++-----------------------+---------------------------------------------------+--------------------------------+
+| :code:`mexname` | Name of the compiled mex interface | | :code:`'emosqp'` (default) |
+| | | | Nonempty string |
++-----------------------+---------------------------------------------------+--------------------------------+
+| :code:`force_rewrite` | Rewrite existing directory | | :code:`false` (default) |
+| | | | :code:`true` |
++-----------------------+---------------------------------------------------+--------------------------------+
+| :code:`FLOAT` | Use :code:`float` type instead of :code:`double` | | :code:`false` (default) |
+| | | | :code:`true` |
++-----------------------+---------------------------------------------------+--------------------------------+
+| :code:`LONG` | Use :code:`long long` type instead of :code:`int` | | :code:`true` (default) |
+| | | | :code:`false` |
++-----------------------+---------------------------------------------------+--------------------------------+
+
+You can pass the options as field-value pairs, e.g.,
+
+.. code:: matlab
+
+ m.codegen('code', 'parameters', 'matrices', 'mexname', 'emosqp');
+
+If the :code:`project_type` argument is not passed or is set to :code:`''`,
+then no build files are generated.
+
+
+
+Mex interface
+-------------
+Once the code is generated the following functions are provided through its mex interface. Each function is called as
+
+.. code:: matlab
+
+ emosqp('function_name');
+
+
+where :code:`emosqp` is the name of the mex interface specified in the previous section
+
+.. function:: emosqp('solve')
+ :noindex:
+
+ Solve the problem.
+
+ :returns: multiple variables [x, y, status_val, iter, run_time]
+
+ - **x** (*ndarray*) - Primal solution
+ - **y** (*ndarray*) - Dual solution
+ - **status_val** (*int*) - Status value as in :ref:`status_values`
+ - **iter** (*int*) - Number of iterations
+ - **run_time** (*double*) - Run time
+
+
+.. function:: emosqp('update_lin_cost', q_new)
+ :noindex:
+
+ Update linear cost.
+
+ :param ndarray q_new: New linear cost vector
+
+
+.. function:: emosqp('update_lower_bound', l_new)
+ :noindex:
+
+ Update lower bound in the constraints.
+
+ :param ndarray l_new: New lower bound vector
+
+
+.. function:: emosqp('update_upper_bound', u_new)
+ :noindex:
+
+ Update upper bound in the constraints.
+
+ :param ndarray u_new: New upper bound vector
+
+
+.. function:: emosqp('update_bounds', l_new, u_new)
+ :noindex:
+
+ Update lower and upper bounds in the constraints.
+
+ :param ndarray l_new: New lower bound vector
+ :param ndarray u_new: New upper bound vector
+
+
+If the code is generated with the option :code:`parameters` set to
+:code:`'matrices'`, then the following functions are also provided
+
+
+.. function:: emosqp('update_P', Px, Px_idx, Px_n)
+ :noindex:
+
+ Update nonzero entries of the quadratic cost matrix (only upper triangular) without changing sparsity structure.
+
+ :param ndarray Px: Values of entries to be updated
+ :param ndarray Px_idx: Indices of entries to be updated. Pass :code:`[]` if
+ all the indices are to be updated
+ :param int Px_n: Number of entries to be updated. Used only if Px_idx is not
+ :code:`[]`.
+
+
+.. function:: emosqp('update_A', Ax, Ax_idx, Ax_n)
+ :noindex:
+
+ Update nonzero entries of the constraint matrix.
+
+ :param ndarray Ax: Values of entries to be updated
+ :param ndarray Ax_idx: Indices of entries to be updated. Pass :code:`[]` if
+ all the indices are to be updated
+ :param int Ax_n: Number of entries to be updated. Used only if Ax_idx is not
+ :code:`[]`.
+
+
+.. function:: emosqp('update_P_A', Px, Px_idx, Px_n, Ax, Ax_idx, Ax_n)
+ :noindex:
+
+ Update nonzero entries of the quadratic cost and constraint matrices. It considers only the upper-triangular part of P.
+
+ :param ndarray Px: Values of entries to be updated
+ :param ndarray Px_idx: Indices of entries to be updated. Pass :code:`[]` if
+ all the indices are to be updated
+ :param int Px_n: Number of entries to be updated. Used only if Px_idx is not
+ :code:`[]`.
+ :param ndarray Ax: Values of entries to be updated
+ :param ndarray Ax_idx: Indices of entries to be updated. Pass :code:`[]` if
+ all the indices are to be updated
+ :param int Ax_n: Number of entries to be updated. Used only if Ax_idx is not
+ :code:`[]`.
+
+
+You can update all the nonzero entries in matrix :math:`A` by running
+
+.. code:: matlab
+
+ emosqp('update_A', Ax_new, [], 0);
+
+See C :ref:`C_sublevel_API` for more details on the input arguments.
diff --git a/docs/codegen/python.rst b/docs/codegen/python.rst
new file mode 100644
index 0000000..512ddc3
--- /dev/null
+++ b/docs/codegen/python.rst
@@ -0,0 +1,168 @@
+Python
+======
+
+Before generating code for a parametric problem, the problem should be first
+specified in the setup phase. See :ref:`python_setup` for more details.
+
+
+Codegen
+-------
+The code is generated by running
+
+.. code:: python
+
+ m.codegen(dir_name, **opts)
+
+The argument :code:`dir_name` is the name of a directory where the generated
+code is stored.
+Additional codegen options are shown in the following table
+
++-------------------------+---------------------------------------------------+--------------------------------+
+| Option | Description | Allowed values |
++=========================+===================================================+================================+
+| :code:`project_type` | Build environment | | :code:`''` (default) |
+| | | | :code:`'Makefile'` |
+| | | | :code:`'MinGW Makefiles'` |
+| | | | :code:`'Unix Makefiles'` |
+| | | | :code:`'CodeBlocks'` |
+| | | | :code:`'Xcode'` |
++-------------------------+---------------------------------------------------+--------------------------------+
+| :code:`parameters` | Problem parameters | | :code:`'vectors'` (default) |
+| | | | :code:`'matrices'` |
++-------------------------+---------------------------------------------------+--------------------------------+
+| :code:`python_ext_name` | Name of the generated Python module | | :code:`'emosqp'` (default) |
+| | | | Nonempty string |
++-------------------------+---------------------------------------------------+--------------------------------+
+| :code:`force_rewrite` | Rewrite existing directory | | :code:`False` (default) |
+| | | | :code:`True` |
++-------------------------+---------------------------------------------------+--------------------------------+
+| :code:`FLOAT` | Use :code:`float` type instead of :code:`double` | | :code:`False` (default) |
+| | | | :code:`True` |
++-------------------------+---------------------------------------------------+--------------------------------+
+| :code:`LONG` | Use :code:`long long` type instead of :code:`int` | | :code:`True` (default) |
+| | | | :code:`False` |
++-------------------------+---------------------------------------------------+--------------------------------+
+
+The options are passed using named arguments, e.g.,
+
+.. code:: python
+
+ m.codegen('code', parameters='matrices', python_ext_name='emosqp')
+
+If the :code:`project_type` argument is not passed or is set to :code:`''`,
+then no build files are generated.
+
+
+
+Extension module API
+--------------------
+Once the code is generated, you can import a light python wrapper with
+
+.. code:: python
+
+ import emosqp
+
+where :code:`emosqp` is the extension name given in the previous section. The module imports the following functions
+
+.. py:function:: solve()
+ :noindex:
+
+ Solve the problem.
+
+ :returns: tuple (x, y, status_val, iter, run_time)
+
+ - **x** (*ndarray*) - Primal solution
+ - **y** (*ndarray*) - Dual solution
+ - **status_val** (*int*) - Status value as in :ref:`status_values`
+ - **iter** (*int*) - Number of iterations
+ - **run_time** (*double*) - Run time
+
+
+
+
+
+.. py:function:: update_lin_cost(q_new)
+ :noindex:
+
+ Update linear cost.
+
+ :param ndarray q_new: New linear cost vector
+
+
+.. py:function:: update_lower_bound(l_new)
+ :noindex:
+
+ Update lower bound in the constraints.
+
+ :param ndarray l_new: New lower bound vector
+
+
+.. py:function:: update_upper_bound(u_new)
+ :noindex:
+
+ Update upper bound in the constraints.
+
+ :param ndarray u_new: New upper bound vector
+
+
+.. py:function:: update_bounds(l_new, u_new)
+ :noindex:
+
+ Update lower and upper bounds in the constraints.
+
+ :param ndarray l_new: New lower bound vector
+ :param ndarray u_new: New upper bound vector
+
+
+If the code is generated with the option :code:`parameters` set to
+:code:`'matrices'`, the following functions are also provided
+
+
+.. py:function:: update_P(Px, Px_idx, Px_n)
+ :noindex:
+
+ Update nonzero entries of the quadratic cost matrix (only upper triangular) without changing sparsity structure.
+
+ :param ndarray Px: Values of entries to be updated
+ :param ndarray Px_idx: Indices of entries to be updated. Pass :code:`None` if
+ all the indices are to be updated
+ :param int Px_n: Number of entries to be updated. Used only if Px_idx is not
+ :code:`None`.
+
+
+.. py:function:: update_A(Ax, Ax_idx, Ax_n)
+ :noindex:
+
+ Update nonzero entries of the constraint matrix.
+
+ :param ndarray Ax: Values of entries to be updated
+ :param ndarray Ax_idx: Indices of entries to be updated. Pass :code:`None` if
+ all the indices are to be updated
+ :param int Ax_n: Number of entries to be updated. Used only if Ax_idx is not
+ :code:`None`.
+
+
+.. py:function:: update_P_A(Px, Px_idx, Px_n, Ax, Ax_idx, Ax_n)
+ :noindex:
+
+ Update nonzero entries of the quadratic cost and constraint matrices. It considers only the upper-triangular part of P.
+
+ :param ndarray Px: Values of entries to be updated
+ :param ndarray Px_idx: Indices of entries to be updated. Pass :code:`None` if
+ all the indices are to be updated
+ :param int Px_n: Number of entries to be updated. Used only if Px_idx is not
+ :code:`None`.
+ :param ndarray Ax: Values of entries to be updated
+ :param ndarray Ax_idx: Indices of entries to be updated. Pass :code:`None` if
+ all the indices are to be updated
+ :param int Ax_n: Number of entries to be updated. Used only if Ax_idx is not
+ :code:`None`.
+
+
+You can update all the nonzero entries in matrix :math:`A` by running
+
+.. code:: python
+
+ emosqp.update_A(Ax_new, None, 0);
+
+See C :ref:`C_sublevel_API` for more details on the input arguments.
diff --git a/docs/conf.py b/docs/conf.py
new file mode 100644
index 0000000..baac394
--- /dev/null
+++ b/docs/conf.py
@@ -0,0 +1,200 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+#
+# OSQP documentation build configuration file, created by
+# sphinx-quickstart on Sat Feb 18 15:49:00 2017.
+#
+# This file is execfile()d with the current directory set to its
+# containing dir.
+#
+# Note that not all possible configuration values are present in this
+# autogenerated file.
+#
+# All configuration values have a default; values that are commented out
+# serve to show the default.
+
+# If extensions (or modules to document with autodoc) are in another directory,
+# add these directories to sys.path here. If the directory is relative to the
+# documentation root, use os.path.abspath to make it absolute, like shown here.
+
+import sphinx_rtd_theme
+import os
+import subprocess
+# import sys
+# sys.path.insert(0, os.path.abspath('.'))
+
+__version__ = os.environ.get('OSQP_VERSION', '0.0.0')
+
+# An incoming version number of '0.0.0' is a placeholder for missing version information.
+# In such cases, use a <blank> version to effectively avoid mentioning the version number
+# in the built documentation at all.
+__version__ = '' if __version__ == '0.0.0' else __version__
+
+# Set OSQP_VERSION envvar in case subprocesses (like doxygen) need it too
+os.environ['OSQP_VERSION'] = __version__
+
+# -- General configuration ------------------------------------------------
+
+# If your documentation needs a minimal Sphinx version, state it here.
+#
+# needs_sphinx = '1.0'
+
+# Add any Sphinx extension module names here, as strings. They can be
+# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom
+# ones.
+extensions = ['sphinx.ext.todo', 'sphinx.ext.mathjax', 'breathe']
+
+# Add any paths that contain templates here, relative to this directory.
+templates_path = ['_templates']
+
+# The suffix(es) of source filenames.
+# You can specify multiple suffix as a list of string:
+#
+# source_suffix = ['.rst', '.md']
+source_suffix = '.rst'
+
+# The master toctree document.
+master_doc = 'index'
+
+# General information about the project.
+project = 'OSQP'
+copyright = '2021, Bartolomeo Stellato, Goran Banjac'
+author = 'Bartolomeo Stellato, Goran Banjac'
+
+# The version info for the project you're documenting, acts as replacement for
+# |version| and |release|, also used in various other places throughout the
+# built documents.
+#
+
+version = '.'.join(__version__.split('.')[:4])
+
+# The full version, including alpha/beta/rc tags.
+release = __version__
+
+# The language for content autogenerated by Sphinx. Refer to documentation
+# for a list of supported languages.
+#
+# This is also used if you do content translation via gettext catalogs.
+# Usually you set "language" from the command line for these cases.
+language = None
+
+# List of patterns, relative to source directory, that match files and
+# directories to ignore when looking for source files.
+# This patterns also effect to html_static_path and html_extra_path
+exclude_patterns = ['_build', 'Thumbs.db', '.DS_Store']
+
+# The name of the Pygments (syntax highlighting) style to use.
+pygments_style = 'sphinx'
+
+# If true, `todo` and `todoList` produce output, else they produce nothing.
+todo_include_todos = False
+
+
+# -- Options for HTML output ----------------------------------------------
+
+# The theme to use for HTML and HTML Help pages. See the documentation for
+# a list of builtin themes.
+#
+html_theme = 'sphinx_rtd_theme'
+html_theme_path = [sphinx_rtd_theme.get_html_theme_path()]
+
+# Theme options are theme-specific and customize the look and feel of a theme
+# further. For a list of options available for each theme, see the
+# documentation.
+#
+
+html_theme_options = {
+ 'logo_only': True,
+}
+
+
+html_logo = '_static/img/logo.png'
+html_favicon = "_static/img/favicon.ico"
+
+# Add any paths that contain custom static files (such as style sheets) here,
+# relative to this directory. They are copied after the builtin static files,
+# so a file named "default.css" will overwrite the builtin "default.css".
+html_static_path = ['_static']
+
+# on_rtd is whether we are on readthedocs.org, this line of code grabbed from docs.readthedocs.org
+on_rtd = os.environ.get('READTHEDOCS', None) == 'True'
+
+if not on_rtd: # only import and set the theme if we're building docs locally
+ # Override default css to get a larger width for local build
+ def setup(app):
+ app.add_css_file('css/osqp_theme.css')
+else:
+ html_context = {
+ 'css_files': [
+ 'https://media.readthedocs.org/css/sphinx_rtd_theme.css',
+ 'https://media.readthedocs.org/css/readthedocs-doc-embed.css',
+ '_static/css/osqp_theme.css'],
+ }
+
+
+
+# -- Options for HTMLHelp output ------------------------------------------
+
+# Output file base name for HTML help builder.
+htmlhelp_basename = 'OSQPdoc'
+
+
+# -- Options for LaTeX output ---------------------------------------------
+
+latex_elements = {
+ # The paper size ('letterpaper' or 'a4paper').
+ #
+ # 'papersize': 'letterpaper',
+
+ # The font size ('10pt', '11pt' or '12pt').
+ #
+ # 'pointsize': '10pt',
+
+ # Additional stuff for the LaTeX preamble.
+ #
+ # 'preamble': '',
+
+ # Latex figure (float) alignment
+ #
+ # 'figure_align': 'htbp',
+ 'sphinxsetup': 'hmargin={1.5cm,1.5cm}',
+}
+
+# Grouping the document tree into LaTeX files. List of tuples
+# (source start file, target name, title,
+# author, documentclass [howto, manual, or own class]).
+latex_documents = [
+ (master_doc, 'OSQP.tex', 'OSQP Documentation',
+ 'Bartolomeo Stellato, Goran Banjac', 'manual'),
+]
+
+
+# -- Options for manual page output ---------------------------------------
+
+# One entry per manual page. List of tuples
+# (source start file, name, description, authors, manual section).
+man_pages = [
+ (master_doc, 'OSQP', 'OSQP Documentation',
+ [author], 1)
+]
+
+# -- Options for breathe ---------------------------------------
+
+# Generate doxygen documentation
+subprocess.call('doxygen doxygen.conf', shell=True)
+
+breathe_projects = {"osqp": "doxygen_out/xml/"}
+breathe_default_project = "osqp"
+
+
+
+# -- Options for Texinfo output -------------------------------------------
+
+# Grouping the document tree into Texinfo files. List of tuples
+# (source start file, target name, title, author,
+# dir menu entry, description, category)
+texinfo_documents = [
+ (master_doc, 'OSQP', 'OSQP Documentation',
+ author, 'OSQP', 'One line description of project.',
+ 'Miscellaneous'),
+]
diff --git a/docs/contributing/index.rst b/docs/contributing/index.rst
new file mode 100644
index 0000000..a3a235d
--- /dev/null
+++ b/docs/contributing/index.rst
@@ -0,0 +1,93 @@
+Contributing
+=============
+
+OSQP is an open-source project open to any academic or commercial applications.
+Contributions are welcome as `GitHub pull requests <https://help.github.com/articles/creating-a-pull-request/>`_ in any part of the project such as
+
+* algorithm developments
+* interfaces to other languages
+* compatibility with new architectures
+* linear system solvers interfaces
+
+
+.. _interfacing_new_linear_system_solvers :
+
+Interfacing new linear system solvers
+-------------------------------------
+OSQP is designed to be easily interfaced to new linear system solvers via dynamic library loading.
+To add a linear system solver interface you need to edit the :code:`lin_sys/` directory subfolder :code:`direct/` or :code:`indirect/` depending on the type of solver.
+Create a subdirectory with your solver name with four files:
+
+* Dynamic library loading: :code:`mysolver_loader.c` and :code:`mysolver_loader.h`.
+* Linear system solution: :code:`mysolver.c` and :code:`mysolver.h`.
+
+We suggest you to have a look at the `MKL Pardiso solver interface <https://github.com/osqp/osqp/tree/master/lin_sys/direct/pardiso>`_ for more details.
+
+Dynamic library loading
+^^^^^^^^^^^^^^^^^^^^^^^
+In this part define the methods to load the shared library and obtain the functions required to solve the linear system.
+The main functions to be exported are :code:`lh_load_mysolver(const char* libname)` and :code:`lh_unload_mysolver()`.
+In addition, the file :code:`mysolver_loader.c` must define static function pointers to the shared library functions to be loaded.
+
+Linear system solution
+^^^^^^^^^^^^^^^^^^^^^^
+In this part we define the core of the interface: **linear system solver object**.
+The main functions are the external method
+
+* :code:`init_linsys_solver_mysolver`: create the instance and perform the setup
+
+and the internal methods of the object
+
+* :code:`free_linsys_solver_mysolver`: free the instance
+* :code:`solve_linsys_mysolver`: solve the linear system
+* :code:`update_matrices`: update problem matrices
+* :code:`update_rho_vec`: update :math:`\rho` as a diagonal vector.
+
+After the initializations these functions are assigned to the internal pointers so that, for an instance :code:`s` they can be called as :code:`s->free`, :code:`s->solve`, :code:`s->update_matrices` and :code:`s->update_rho_vec`.
+
+The linear system solver object is defined in :code:`mysolver.h` as follows
+
+.. code:: c
+
+ typedef struct mysolver mysolver_solver;
+
+ struct mysolver {
+ // Methods
+ enum linsys_solver_type type; // Linear system solver defined in constants.h
+
+ c_int (*solve)(struct mysolver * self, c_float * b);
+ void (*free)(struct mysolver * self);
+ c_int (*update_matrices)(struct mysolver * self, const csc *P, const csc *A);
+ c_int (*update_rho_vec)(struct mysolver * self, const c_float * rho_vec);
+
+ // Attributes
+ c_int nthreads; // Number of threads used (required!)
+
+ // Internal attributes of the solver
+ ...
+
+ // Internal attributes required for matrix updates
+ c_int * Pdiag_idx, Pdiag_n; ///< index and number of diagonal elements in P
+ c_int * PtoKKT, * AtoKKT; ///< Index of elements from P and A to KKT matrix
+ c_int * rhotoKKT; ///< Index of rho places in KKT matrix
+ ...
+
+ };
+
+ // Initialize mysolver solver
+ c_int init_linsys_solver_mysolver(mysolver_solver ** s, const csc * P, const csc * A, c_float sigma, c_float * rho_vec, c_int polish);
+
+ // Solve linear system and store result in b
+ c_int solve_linsys_mysolver(mysolver_solver * s, c_float * b);
+
+ // Update linear system solver matrices
+ c_int update_linsys_solver_matrices_mysolver(mysolver_solver * s, const csc *P, const csc *A);
+
+ // Update rho_vec parameter in linear system solver structure
+ c_int update_linsys_solver_rho_vec_mysolver(mysolver_solver * s, const c_float * rho_vec);
+
+ // Free linear system solver
+ void free_linsys_solver_mysolver(mysolver_solver * s);
+
+
+The function details are coded in the :code:`mysolver.c` file.
diff --git a/docs/doxygen.conf b/docs/doxygen.conf
new file mode 100644
index 0000000..09626ad
--- /dev/null
+++ b/docs/doxygen.conf
@@ -0,0 +1,2473 @@
+# Doxyfile 1.8.13
+
+# This file describes the settings to be used by the documentation system
+# doxygen (www.doxygen.org) for a project.
+#
+# All text after a double hash (##) is considered a comment and is placed in
+# front of the TAG it is preceding.
+#
+# All text after a single hash (#) is considered a comment and will be ignored.
+# The format is:
+# TAG = value [value, ...]
+# For lists, items can also be appended using:
+# TAG += value [value, ...]
+# Values that contain spaces should be placed between quotes (\" \").
+
+#---------------------------------------------------------------------------
+# Project related configuration options
+#---------------------------------------------------------------------------
+
+# This tag specifies the encoding used for all characters in the config file
+# that follow. The default is UTF-8 which is also the encoding used for all text
+# before the first occurrence of this tag. Doxygen uses libiconv (or the iconv
+# built into libc) for the transcoding. See http://www.gnu.org/software/libiconv
+# for the list of possible encodings.
+# The default value is: UTF-8.
+
+DOXYFILE_ENCODING = UTF-8
+
+# The PROJECT_NAME tag is a single word (or a sequence of words surrounded by
+# double-quotes, unless you are using Doxywizard) that should identify the
+# project for which the documentation is generated. This name is used in the
+# title of most generated pages and in a few other places.
+# The default value is: My Project.
+
+PROJECT_NAME = "OSQP"
+
+# The PROJECT_NUMBER tag can be used to enter a project or revision number. This
+# could be handy for archiving the generated documentation or if some version
+# control system is used.
+
+PROJECT_NUMBER = $(OSQP_VERSION)
+
+# Using the PROJECT_BRIEF tag one can provide an optional one line description
+# for a project that appears at the top of each page and should give viewer a
+# quick idea about the purpose of the project. Keep the description short.
+
+PROJECT_BRIEF = "The Operator Splitting QP Solver"
+
+# With the PROJECT_LOGO tag one can specify a logo or an icon that is included
+# in the documentation. The maximum height of the logo should not exceed 55
+# pixels and the maximum width should not exceed 200 pixels. Doxygen will copy
+# the logo to the output directory.
+
+PROJECT_LOGO =
+
+# The OUTPUT_DIRECTORY tag is used to specify the (relative or absolute) path
+# into which the generated documentation will be written. If a relative path is
+# entered, it will be relative to the location where doxygen was started. If
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+
+OUTPUT_DIRECTORY = ./doxygen_out
+
+# If the CREATE_SUBDIRS tag is set to YES then doxygen will create 4096 sub-
+# directories (in 2 levels) under the output directory of each output format and
+# will distribute the generated files over these directories. Enabling this
+# option can be useful when feeding doxygen a huge amount of source files, where
+# putting all generated files in the same directory would otherwise causes
+# performance problems for the file system.
+# The default value is: NO.
+
+CREATE_SUBDIRS = YES
+
+# If the ALLOW_UNICODE_NAMES tag is set to YES, doxygen will allow non-ASCII
+# characters to appear in the names of generated files. If set to NO, non-ASCII
+# characters will be escaped, for example _xE3_x81_x84 will be used for Unicode
+# U+3044.
+# The default value is: NO.
+
+ALLOW_UNICODE_NAMES = NO
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+OUTPUT_LANGUAGE = English
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+# descriptions after the members that are listed in the file and class
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+BRIEF_MEMBER_DESC = YES
+
+# If the REPEAT_BRIEF tag is set to YES, doxygen will prepend the brief
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+INLINE_INHERITED_MEMB = NO
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+FULL_PATH_NAMES = YES
+
+# The STRIP_FROM_PATH tag can be used to strip a user-defined part of the path.
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+
+# If the MARKDOWN_SUPPORT tag is enabled then doxygen pre-processes all comments
+# according to the Markdown format, which allows for more readable
+# documentation. See http://daringfireball.net/projects/markdown/ for details.
+# The output of markdown processing is further processed by doxygen, so you can
+# mix doxygen, HTML, and XML commands with Markdown formatting. Disable only in
+# case of backward compatibilities issues.
+# The default value is: YES.
+
+MARKDOWN_SUPPORT = YES
+
+# When the TOC_INCLUDE_HEADINGS tag is set to a non-zero value, all headings up
+# to that level are automatically included in the table of contents, even if
+# they do not have an id attribute.
+# Note: This feature currently applies only to Markdown headings.
+# Minimum value: 0, maximum value: 99, default value: 0.
+# This tag requires that the tag MARKDOWN_SUPPORT is set to YES.
+
+TOC_INCLUDE_HEADINGS = 0
+
+# When enabled doxygen tries to link words that correspond to documented
+# classes, or namespaces to their corresponding documentation. Such a link can
+# be prevented in individual cases by putting a % sign in front of the word or
+# globally by setting AUTOLINK_SUPPORT to NO.
+# The default value is: YES.
+
+AUTOLINK_SUPPORT = YES
+
+# If you use STL classes (i.e. std::string, std::vector, etc.) but do not want
+# to include (a tag file for) the STL sources as input, then you should set this
+# tag to YES in order to let doxygen match functions declarations and
+# definitions whose arguments contain STL classes (e.g. func(std::string);
+# versus func(std::string) {}). This also make the inheritance and collaboration
+# diagrams that involve STL classes more complete and accurate.
+# The default value is: NO.
+
+BUILTIN_STL_SUPPORT = NO
+
+# If you use Microsoft's C++/CLI language, you should set this option to YES to
+# enable parsing support.
+# The default value is: NO.
+
+CPP_CLI_SUPPORT = NO
+
+# Set the SIP_SUPPORT tag to YES if your project consists of sip (see:
+# http://www.riverbankcomputing.co.uk/software/sip/intro) sources only. Doxygen
+# will parse them like normal C++ but will assume all classes use public instead
+# of private inheritance when no explicit protection keyword is present.
+# The default value is: NO.
+
+SIP_SUPPORT = NO
+
+# For Microsoft's IDL there are propget and propput attributes to indicate
+# getter and setter methods for a property. Setting this option to YES will make
+# doxygen to replace the get and set methods by a property in the documentation.
+# This will only work if the methods are indeed getting or setting a simple
+# type. If this is not the case, or you want to show the methods anyway, you
+# should set this option to NO.
+# The default value is: YES.
+
+IDL_PROPERTY_SUPPORT = YES
+
+# If member grouping is used in the documentation and the DISTRIBUTE_GROUP_DOC
+# tag is set to YES then doxygen will reuse the documentation of the first
+# member in the group (if any) for the other members of the group. By default
+# all members of a group must be documented explicitly.
+# The default value is: NO.
+
+DISTRIBUTE_GROUP_DOC = NO
+
+# If one adds a struct or class to a group and this option is enabled, then also
+# any nested class or struct is added to the same group. By default this option
+# is disabled and one has to add nested compounds explicitly via \ingroup.
+# The default value is: NO.
+
+GROUP_NESTED_COMPOUNDS = NO
+
+# Set the SUBGROUPING tag to YES to allow class member groups of the same type
+# (for instance a group of public functions) to be put as a subgroup of that
+# type (e.g. under the Public Functions section). Set it to NO to prevent
+# subgrouping. Alternatively, this can be done per class using the
+# \nosubgrouping command.
+# The default value is: YES.
+
+SUBGROUPING = YES
+
+# When the INLINE_GROUPED_CLASSES tag is set to YES, classes, structs and unions
+# are shown inside the group in which they are included (e.g. using \ingroup)
+# instead of on a separate page (for HTML and Man pages) or section (for LaTeX
+# and RTF).
+#
+# Note that this feature does not work in combination with
+# SEPARATE_MEMBER_PAGES.
+# The default value is: NO.
+
+INLINE_GROUPED_CLASSES = NO
+
+# When the INLINE_SIMPLE_STRUCTS tag is set to YES, structs, classes, and unions
+# with only public data fields or simple typedef fields will be shown inline in
+# the documentation of the scope in which they are defined (i.e. file,
+# namespace, or group documentation), provided this scope is documented. If set
+# to NO, structs, classes, and unions are shown on a separate page (for HTML and
+# Man pages) or section (for LaTeX and RTF).
+# The default value is: NO.
+
+INLINE_SIMPLE_STRUCTS = NO
+
+# When TYPEDEF_HIDES_STRUCT tag is enabled, a typedef of a struct, union, or
+# enum is documented as struct, union, or enum with the name of the typedef. So
+# typedef struct TypeS {} TypeT, will appear in the documentation as a struct
+# with name TypeT. When disabled the typedef will appear as a member of a file,
+# namespace, or class. And the struct will be named TypeS. This can typically be
+# useful for C code in case the coding convention dictates that all compound
+# types are typedef'ed and only the typedef is referenced, never the tag name.
+# The default value is: NO.
+
+TYPEDEF_HIDES_STRUCT = NO
+
+# The size of the symbol lookup cache can be set using LOOKUP_CACHE_SIZE. This
+# cache is used to resolve symbols given their name and scope. Since this can be
+# an expensive process and often the same symbol appears multiple times in the
+# code, doxygen keeps a cache of pre-resolved symbols. If the cache is too small
+# doxygen will become slower. If the cache is too large, memory is wasted. The
+# cache size is given by this formula: 2^(16+LOOKUP_CACHE_SIZE). The valid range
+# is 0..9, the default is 0, corresponding to a cache size of 2^16=65536
+# symbols. At the end of a run doxygen will report the cache usage and suggest
+# the optimal cache size from a speed point of view.
+# Minimum value: 0, maximum value: 9, default value: 0.
+
+LOOKUP_CACHE_SIZE = 0
+
+#---------------------------------------------------------------------------
+# Build related configuration options
+#---------------------------------------------------------------------------
+
+# If the EXTRACT_ALL tag is set to YES, doxygen will assume all entities in
+# documentation are documented, even if no documentation was available. Private
+# class members and static file members will be hidden unless the
+# EXTRACT_PRIVATE respectively EXTRACT_STATIC tags are set to YES.
+# Note: This will also disable the warnings about undocumented members that are
+# normally produced when WARNINGS is set to YES.
+# The default value is: NO.
+
+EXTRACT_ALL = YES
+
+# If the EXTRACT_PRIVATE tag is set to YES, all private members of a class will
+# be included in the documentation.
+# The default value is: NO.
+
+EXTRACT_PRIVATE = NO
+
+# If the EXTRACT_PACKAGE tag is set to YES, all members with package or internal
+# scope will be included in the documentation.
+# The default value is: NO.
+
+EXTRACT_PACKAGE = NO
+
+# If the EXTRACT_STATIC tag is set to YES, all static members of a file will be
+# included in the documentation.
+# The default value is: NO.
+
+EXTRACT_STATIC = NO
+
+# If the EXTRACT_LOCAL_CLASSES tag is set to YES, classes (and structs) defined
+# locally in source files will be included in the documentation. If set to NO,
+# only classes defined in header files are included. Does not have any effect
+# for Java sources.
+# The default value is: YES.
+
+EXTRACT_LOCAL_CLASSES = YES
+
+# This flag is only useful for Objective-C code. If set to YES, local methods,
+# which are defined in the implementation section but not in the interface are
+# included in the documentation. If set to NO, only methods in the interface are
+# included.
+# The default value is: NO.
+
+EXTRACT_LOCAL_METHODS = NO
+
+# If this flag is set to YES, the members of anonymous namespaces will be
+# extracted and appear in the documentation as a namespace called
+# 'anonymous_namespace{file}', where file will be replaced with the base name of
+# the file that contains the anonymous namespace. By default anonymous namespace
+# are hidden.
+# The default value is: NO.
+
+EXTRACT_ANON_NSPACES = NO
+
+# If the HIDE_UNDOC_MEMBERS tag is set to YES, doxygen will hide all
+# undocumented members inside documented classes or files. If set to NO these
+# members will be included in the various overviews, but no documentation
+# section is generated. This option has no effect if EXTRACT_ALL is enabled.
+# The default value is: NO.
+
+HIDE_UNDOC_MEMBERS = NO
+
+# If the HIDE_UNDOC_CLASSES tag is set to YES, doxygen will hide all
+# undocumented classes that are normally visible in the class hierarchy. If set
+# to NO, these classes will be included in the various overviews. This option
+# has no effect if EXTRACT_ALL is enabled.
+# The default value is: NO.
+
+HIDE_UNDOC_CLASSES = NO
+
+# If the HIDE_FRIEND_COMPOUNDS tag is set to YES, doxygen will hide all friend
+# (class|struct|union) declarations. If set to NO, these declarations will be
+# included in the documentation.
+# The default value is: NO.
+
+HIDE_FRIEND_COMPOUNDS = NO
+
+# If the HIDE_IN_BODY_DOCS tag is set to YES, doxygen will hide any
+# documentation blocks found inside the body of a function. If set to NO, these
+# blocks will be appended to the function's detailed documentation block.
+# The default value is: NO.
+
+HIDE_IN_BODY_DOCS = NO
+
+# The INTERNAL_DOCS tag determines if documentation that is typed after a
+# \internal command is included. If the tag is set to NO then the documentation
+# will be excluded. Set it to YES to include the internal documentation.
+# The default value is: NO.
+
+INTERNAL_DOCS = NO
+
+# If the CASE_SENSE_NAMES tag is set to NO then doxygen will only generate file
+# names in lower-case letters. If set to YES, upper-case letters are also
+# allowed. This is useful if you have classes or files whose names only differ
+# in case and if your file system supports case sensitive file names. Windows
+# and Mac users are advised to set this option to NO.
+# The default value is: system dependent.
+
+CASE_SENSE_NAMES = NO
+
+# If the HIDE_SCOPE_NAMES tag is set to NO then doxygen will show members with
+# their full class and namespace scopes in the documentation. If set to YES, the
+# scope will be hidden.
+# The default value is: NO.
+
+HIDE_SCOPE_NAMES = NO
+
+# If the HIDE_COMPOUND_REFERENCE tag is set to NO (default) then doxygen will
+# append additional text to a page's title, such as Class Reference. If set to
+# YES the compound reference will be hidden.
+# The default value is: NO.
+
+HIDE_COMPOUND_REFERENCE= NO
+
+# If the SHOW_INCLUDE_FILES tag is set to YES then doxygen will put a list of
+# the files that are included by a file in the documentation of that file.
+# The default value is: YES.
+
+SHOW_INCLUDE_FILES = YES
+
+# If the SHOW_GROUPED_MEMB_INC tag is set to YES then Doxygen will add for each
+# grouped member an include statement to the documentation, telling the reader
+# which file to include in order to use the member.
+# The default value is: NO.
+
+SHOW_GROUPED_MEMB_INC = NO
+
+# If the FORCE_LOCAL_INCLUDES tag is set to YES then doxygen will list include
+# files with double quotes in the documentation rather than with sharp brackets.
+# The default value is: NO.
+
+FORCE_LOCAL_INCLUDES = NO
+
+# If the INLINE_INFO tag is set to YES then a tag [inline] is inserted in the
+# documentation for inline members.
+# The default value is: YES.
+
+INLINE_INFO = YES
+
+# If the SORT_MEMBER_DOCS tag is set to YES then doxygen will sort the
+# (detailed) documentation of file and class members alphabetically by member
+# name. If set to NO, the members will appear in declaration order.
+# The default value is: YES.
+
+SORT_MEMBER_DOCS = YES
+
+# If the SORT_BRIEF_DOCS tag is set to YES then doxygen will sort the brief
+# descriptions of file, namespace and class members alphabetically by member
+# name. If set to NO, the members will appear in declaration order. Note that
+# this will also influence the order of the classes in the class list.
+# The default value is: NO.
+
+SORT_BRIEF_DOCS = NO
+
+# If the SORT_MEMBERS_CTORS_1ST tag is set to YES then doxygen will sort the
+# (brief and detailed) documentation of class members so that constructors and
+# destructors are listed first. If set to NO the constructors will appear in the
+# respective orders defined by SORT_BRIEF_DOCS and SORT_MEMBER_DOCS.
+# Note: If SORT_BRIEF_DOCS is set to NO this option is ignored for sorting brief
+# member documentation.
+# Note: If SORT_MEMBER_DOCS is set to NO this option is ignored for sorting
+# detailed member documentation.
+# The default value is: NO.
+
+SORT_MEMBERS_CTORS_1ST = NO
+
+# If the SORT_GROUP_NAMES tag is set to YES then doxygen will sort the hierarchy
+# of group names into alphabetical order. If set to NO the group names will
+# appear in their defined order.
+# The default value is: NO.
+
+SORT_GROUP_NAMES = NO
+
+# If the SORT_BY_SCOPE_NAME tag is set to YES, the class list will be sorted by
+# fully-qualified names, including namespaces. If set to NO, the class list will
+# be sorted only by class name, not including the namespace part.
+# Note: This option is not very useful if HIDE_SCOPE_NAMES is set to YES.
+# Note: This option applies only to the class list, not to the alphabetical
+# list.
+# The default value is: NO.
+
+SORT_BY_SCOPE_NAME = NO
+
+# If the STRICT_PROTO_MATCHING option is enabled and doxygen fails to do proper
+# type resolution of all parameters of a function it will reject a match between
+# the prototype and the implementation of a member function even if there is
+# only one candidate or it is obvious which candidate to choose by doing a
+# simple string match. By disabling STRICT_PROTO_MATCHING doxygen will still
+# accept a match between prototype and implementation in such cases.
+# The default value is: NO.
+
+STRICT_PROTO_MATCHING = NO
+
+# The GENERATE_TODOLIST tag can be used to enable (YES) or disable (NO) the todo
+# list. This list is created by putting \todo commands in the documentation.
+# The default value is: YES.
+
+GENERATE_TODOLIST = YES
+
+# The GENERATE_TESTLIST tag can be used to enable (YES) or disable (NO) the test
+# list. This list is created by putting \test commands in the documentation.
+# The default value is: YES.
+
+GENERATE_TESTLIST = YES
+
+# The GENERATE_BUGLIST tag can be used to enable (YES) or disable (NO) the bug
+# list. This list is created by putting \bug commands in the documentation.
+# The default value is: YES.
+
+GENERATE_BUGLIST = YES
+
+# The GENERATE_DEPRECATEDLIST tag can be used to enable (YES) or disable (NO)
+# the deprecated list. This list is created by putting \deprecated commands in
+# the documentation.
+# The default value is: YES.
+
+GENERATE_DEPRECATEDLIST= YES
+
+# The ENABLED_SECTIONS tag can be used to enable conditional documentation
+# sections, marked by \if <section_label> ... \endif and \cond <section_label>
+# ... \endcond blocks.
+
+ENABLED_SECTIONS =
+
+# The MAX_INITIALIZER_LINES tag determines the maximum number of lines that the
+# initial value of a variable or macro / define can have for it to appear in the
+# documentation. If the initializer consists of more lines than specified here
+# it will be hidden. Use a value of 0 to hide initializers completely. The
+# appearance of the value of individual variables and macros / defines can be
+# controlled using \showinitializer or \hideinitializer command in the
+# documentation regardless of this setting.
+# Minimum value: 0, maximum value: 10000, default value: 30.
+
+MAX_INITIALIZER_LINES = 30
+
+# Set the SHOW_USED_FILES tag to NO to disable the list of files generated at
+# the bottom of the documentation of classes and structs. If set to YES, the
+# list will mention the files that were used to generate the documentation.
+# The default value is: YES.
+
+SHOW_USED_FILES = YES
+
+# Set the SHOW_FILES tag to NO to disable the generation of the Files page. This
+# will remove the Files entry from the Quick Index and from the Folder Tree View
+# (if specified).
+# The default value is: YES.
+
+SHOW_FILES = YES
+
+# Set the SHOW_NAMESPACES tag to NO to disable the generation of the Namespaces
+# page. This will remove the Namespaces entry from the Quick Index and from the
+# Folder Tree View (if specified).
+# The default value is: YES.
+
+SHOW_NAMESPACES = YES
+
+# The FILE_VERSION_FILTER tag can be used to specify a program or script that
+# doxygen should invoke to get the current version for each file (typically from
+# the version control system). Doxygen will invoke the program by executing (via
+# popen()) the command command input-file, where command is the value of the
+# FILE_VERSION_FILTER tag, and input-file is the name of an input file provided
+# by doxygen. Whatever the program writes to standard output is used as the file
+# version. For an example see the documentation.
+
+FILE_VERSION_FILTER =
+
+# The LAYOUT_FILE tag can be used to specify a layout file which will be parsed
+# by doxygen. The layout file controls the global structure of the generated
+# output files in an output format independent way. To create the layout file
+# that represents doxygen's defaults, run doxygen with the -l option. You can
+# optionally specify a file name after the option, if omitted DoxygenLayout.xml
+# will be used as the name of the layout file.
+#
+# Note that if you run doxygen from a directory containing a file called
+# DoxygenLayout.xml, doxygen will parse it automatically even if the LAYOUT_FILE
+# tag is left empty.
+
+LAYOUT_FILE =
+
+# The CITE_BIB_FILES tag can be used to specify one or more bib files containing
+# the reference definitions. This must be a list of .bib files. The .bib
+# extension is automatically appended if omitted. This requires the bibtex tool
+# to be installed. See also http://en.wikipedia.org/wiki/BibTeX for more info.
+# For LaTeX the style of the bibliography can be controlled using
+# LATEX_BIB_STYLE. To use this feature you need bibtex and perl available in the
+# search path. See also \cite for info how to create references.
+
+CITE_BIB_FILES =
+
+#---------------------------------------------------------------------------
+# Configuration options related to warning and progress messages
+#---------------------------------------------------------------------------
+
+# The QUIET tag can be used to turn on/off the messages that are generated to
+# standard output by doxygen. If QUIET is set to YES this implies that the
+# messages are off.
+# The default value is: NO.
+
+QUIET = NO
+
+# The WARNINGS tag can be used to turn on/off the warning messages that are
+# generated to standard error (stderr) by doxygen. If WARNINGS is set to YES
+# this implies that the warnings are on.
+#
+# Tip: Turn warnings on while writing the documentation.
+# The default value is: YES.
+
+WARNINGS = YES
+
+# If the WARN_IF_UNDOCUMENTED tag is set to YES then doxygen will generate
+# warnings for undocumented members. If EXTRACT_ALL is set to YES then this flag
+# will automatically be disabled.
+# The default value is: YES.
+
+WARN_IF_UNDOCUMENTED = YES
+
+# If the WARN_IF_DOC_ERROR tag is set to YES, doxygen will generate warnings for
+# potential errors in the documentation, such as not documenting some parameters
+# in a documented function, or documenting parameters that don't exist or using
+# markup commands wrongly.
+# The default value is: YES.
+
+WARN_IF_DOC_ERROR = YES
+
+# This WARN_NO_PARAMDOC option can be enabled to get warnings for functions that
+# are documented, but have no documentation for their parameters or return
+# value. If set to NO, doxygen will only warn about wrong or incomplete
+# parameter documentation, but not about the absence of documentation.
+# The default value is: NO.
+
+WARN_NO_PARAMDOC = NO
+
+# If the WARN_AS_ERROR tag is set to YES then doxygen will immediately stop when
+# a warning is encountered.
+# The default value is: NO.
+
+WARN_AS_ERROR = NO
+
+# The WARN_FORMAT tag determines the format of the warning messages that doxygen
+# can produce. The string should contain the $file, $line, and $text tags, which
+# will be replaced by the file and line number from which the warning originated
+# and the warning text. Optionally the format may contain $version, which will
+# be replaced by the version of the file (if it could be obtained via
+# FILE_VERSION_FILTER)
+# The default value is: $file:$line: $text.
+
+WARN_FORMAT = "$file:$line: $text"
+
+# The WARN_LOGFILE tag can be used to specify a file to which warning and error
+# messages should be written. If left blank the output is written to standard
+# error (stderr).
+
+WARN_LOGFILE =
+
+#---------------------------------------------------------------------------
+# Configuration options related to the input files
+#---------------------------------------------------------------------------
+
+# The INPUT tag is used to specify the files and/or directories that contain
+# documented source files. You may enter file names like myfile.cpp or
+# directories like /usr/src/myproject. Separate the files or directories with
+# spaces. See also FILE_PATTERNS and EXTENSION_MAPPING
+# Note: If this tag is empty the current directory is searched.
+
+INPUT = ./../include ./../src
+
+# This tag can be used to specify the character encoding of the source files
+# that doxygen parses. Internally doxygen uses the UTF-8 encoding. Doxygen uses
+# libiconv (or the iconv built into libc) for the transcoding. See the libiconv
+# documentation (see: http://www.gnu.org/software/libiconv) for the list of
+# possible encodings.
+# The default value is: UTF-8.
+
+INPUT_ENCODING = UTF-8
+
+# If the value of the INPUT tag contains directories, you can use the
+# FILE_PATTERNS tag to specify one or more wildcard patterns (like *.cpp and
+# *.h) to filter out the source-files in the directories.
+#
+# Note that for custom extensions or not directly supported extensions you also
+# need to set EXTENSION_MAPPING for the extension otherwise the files are not
+# read by doxygen.
+#
+# If left blank the following patterns are tested:*.c, *.cc, *.cxx, *.cpp,
+# *.c++, *.java, *.ii, *.ixx, *.ipp, *.i++, *.inl, *.idl, *.ddl, *.odl, *.h,
+# *.hh, *.hxx, *.hpp, *.h++, *.cs, *.d, *.php, *.php4, *.php5, *.phtml, *.inc,
+# *.m, *.markdown, *.md, *.mm, *.dox, *.py, *.pyw, *.f90, *.f95, *.f03, *.f08,
+# *.f, *.for, *.tcl, *.vhd, *.vhdl, *.ucf and *.qsf.
+
+FILE_PATTERNS = *.c \
+ *.cc \
+ *.cxx \
+ *.cpp \
+ *.c++ \
+ *.java \
+ *.ii \
+ *.ixx \
+ *.ipp \
+ *.i++ \
+ *.inl \
+ *.idl \
+ *.ddl \
+ *.odl \
+ *.h \
+ *.hh \
+ *.hxx \
+ *.hpp \
+ *.h++ \
+ *.cs \
+ *.d \
+ *.php \
+ *.php4 \
+ *.php5 \
+ *.phtml \
+ *.inc \
+ *.m \
+ *.markdown \
+ *.md \
+ *.mm \
+ *.dox \
+ *.py \
+ *.pyw \
+ *.f90 \
+ *.f95 \
+ *.f03 \
+ *.f08 \
+ *.f \
+ *.for \
+ *.tcl \
+ *.vhd \
+ *.vhdl \
+ *.ucf \
+ *.qsf
+
+# The RECURSIVE tag can be used to specify whether or not subdirectories should
+# be searched for input files as well.
+# The default value is: NO.
+
+RECURSIVE = NO
+
+# The EXCLUDE tag can be used to specify files and/or directories that should be
+# excluded from the INPUT source files. This way you can easily exclude a
+# subdirectory from a directory tree whose root is specified with the INPUT tag.
+#
+# Note that relative paths are relative to the directory from which doxygen is
+# run.
+
+EXCLUDE =
+
+# The EXCLUDE_SYMLINKS tag can be used to select whether or not files or
+# directories that are symbolic links (a Unix file system feature) are excluded
+# from the input.
+# The default value is: NO.
+
+EXCLUDE_SYMLINKS = NO
+
+# If the value of the INPUT tag contains directories, you can use the
+# EXCLUDE_PATTERNS tag to specify one or more wildcard patterns to exclude
+# certain files from those directories.
+#
+# Note that the wildcards are matched against the file with absolute path, so to
+# exclude all test directories for example use the pattern */test/*
+
+EXCLUDE_PATTERNS =
+
+# The EXCLUDE_SYMBOLS tag can be used to specify one or more symbol names
+# (namespaces, classes, functions, etc.) that should be excluded from the
+# output. The symbol name can be a fully qualified name, a word, or if the
+# wildcard * is used, a substring. Examples: ANamespace, AClass,
+# AClass::ANamespace, ANamespace::*Test
+#
+# Note that the wildcards are matched against the file with absolute path, so to
+# exclude all test directories use the pattern */test/*
+
+EXCLUDE_SYMBOLS =
+
+# The EXAMPLE_PATH tag can be used to specify one or more files or directories
+# that contain example code fragments that are included (see the \include
+# command).
+
+EXAMPLE_PATH =
+
+# If the value of the EXAMPLE_PATH tag contains directories, you can use the
+# EXAMPLE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp and
+# *.h) to filter out the source-files in the directories. If left blank all
+# files are included.
+
+EXAMPLE_PATTERNS = *
+
+# If the EXAMPLE_RECURSIVE tag is set to YES then subdirectories will be
+# searched for input files to be used with the \include or \dontinclude commands
+# irrespective of the value of the RECURSIVE tag.
+# The default value is: NO.
+
+EXAMPLE_RECURSIVE = NO
+
+# The IMAGE_PATH tag can be used to specify one or more files or directories
+# that contain images that are to be included in the documentation (see the
+# \image command).
+
+IMAGE_PATH =
+
+# The INPUT_FILTER tag can be used to specify a program that doxygen should
+# invoke to filter for each input file. Doxygen will invoke the filter program
+# by executing (via popen()) the command:
+#
+# <filter> <input-file>
+#
+# where <filter> is the value of the INPUT_FILTER tag, and <input-file> is the
+# name of an input file. Doxygen will then use the output that the filter
+# program writes to standard output. If FILTER_PATTERNS is specified, this tag
+# will be ignored.
+#
+# Note that the filter must not add or remove lines; it is applied before the
+# code is scanned, but not when the output code is generated. If lines are added
+# or removed, the anchors will not be placed correctly.
+#
+# Note that for custom extensions or not directly supported extensions you also
+# need to set EXTENSION_MAPPING for the extension otherwise the files are not
+# properly processed by doxygen.
+
+INPUT_FILTER =
+
+# The FILTER_PATTERNS tag can be used to specify filters on a per file pattern
+# basis. Doxygen will compare the file name with each pattern and apply the
+# filter if there is a match. The filters are a list of the form: pattern=filter
+# (like *.cpp=my_cpp_filter). See INPUT_FILTER for further information on how
+# filters are used. If the FILTER_PATTERNS tag is empty or if none of the
+# patterns match the file name, INPUT_FILTER is applied.
+#
+# Note that for custom extensions or not directly supported extensions you also
+# need to set EXTENSION_MAPPING for the extension otherwise the files are not
+# properly processed by doxygen.
+
+FILTER_PATTERNS =
+
+# If the FILTER_SOURCE_FILES tag is set to YES, the input filter (if set using
+# INPUT_FILTER) will also be used to filter the input files that are used for
+# producing the source files to browse (i.e. when SOURCE_BROWSER is set to YES).
+# The default value is: NO.
+
+FILTER_SOURCE_FILES = NO
+
+# The FILTER_SOURCE_PATTERNS tag can be used to specify source filters per file
+# pattern. A pattern will override the setting for FILTER_PATTERN (if any) and
+# it is also possible to disable source filtering for a specific pattern using
+# *.ext= (so without naming a filter).
+# This tag requires that the tag FILTER_SOURCE_FILES is set to YES.
+
+FILTER_SOURCE_PATTERNS =
+
+# If the USE_MDFILE_AS_MAINPAGE tag refers to the name of a markdown file that
+# is part of the input, its contents will be placed on the main page
+# (index.html). This can be useful if you have a project on for instance GitHub
+# and want to reuse the introduction page also for the doxygen output.
+
+USE_MDFILE_AS_MAINPAGE =
+
+#---------------------------------------------------------------------------
+# Configuration options related to source browsing
+#---------------------------------------------------------------------------
+
+# If the SOURCE_BROWSER tag is set to YES then a list of source files will be
+# generated. Documented entities will be cross-referenced with these sources.
+#
+# Note: To get rid of all source code in the generated output, make sure that
+# also VERBATIM_HEADERS is set to NO.
+# The default value is: NO.
+
+SOURCE_BROWSER = NO
+
+# Setting the INLINE_SOURCES tag to YES will include the body of functions,
+# classes and enums directly into the documentation.
+# The default value is: NO.
+
+INLINE_SOURCES = NO
+
+# Setting the STRIP_CODE_COMMENTS tag to YES will instruct doxygen to hide any
+# special comment blocks from generated source code fragments. Normal C, C++ and
+# Fortran comments will always remain visible.
+# The default value is: YES.
+
+STRIP_CODE_COMMENTS = YES
+
+# If the REFERENCED_BY_RELATION tag is set to YES then for each documented
+# function all documented functions referencing it will be listed.
+# The default value is: NO.
+
+REFERENCED_BY_RELATION = NO
+
+# If the REFERENCES_RELATION tag is set to YES then for each documented function
+# all documented entities called/used by that function will be listed.
+# The default value is: NO.
+
+REFERENCES_RELATION = NO
+
+# If the REFERENCES_LINK_SOURCE tag is set to YES and SOURCE_BROWSER tag is set
+# to YES then the hyperlinks from functions in REFERENCES_RELATION and
+# REFERENCED_BY_RELATION lists will link to the source code. Otherwise they will
+# link to the documentation.
+# The default value is: YES.
+
+REFERENCES_LINK_SOURCE = YES
+
+# If SOURCE_TOOLTIPS is enabled (the default) then hovering a hyperlink in the
+# source code will show a tooltip with additional information such as prototype,
+# brief description and links to the definition and documentation. Since this
+# will make the HTML file larger and loading of large files a bit slower, you
+# can opt to disable this feature.
+# The default value is: YES.
+# This tag requires that the tag SOURCE_BROWSER is set to YES.
+
+SOURCE_TOOLTIPS = YES
+
+# If the USE_HTAGS tag is set to YES then the references to source code will
+# point to the HTML generated by the htags(1) tool instead of doxygen built-in
+# source browser. The htags tool is part of GNU's global source tagging system
+# (see http://www.gnu.org/software/global/global.html). You will need version
+# 4.8.6 or higher.
+#
+# To use it do the following:
+# - Install the latest version of global
+# - Enable SOURCE_BROWSER and USE_HTAGS in the config file
+# - Make sure the INPUT points to the root of the source tree
+# - Run doxygen as normal
+#
+# Doxygen will invoke htags (and that will in turn invoke gtags), so these
+# tools must be available from the command line (i.e. in the search path).
+#
+# The result: instead of the source browser generated by doxygen, the links to
+# source code will now point to the output of htags.
+# The default value is: NO.
+# This tag requires that the tag SOURCE_BROWSER is set to YES.
+
+USE_HTAGS = NO
+
+# If the VERBATIM_HEADERS tag is set the YES then doxygen will generate a
+# verbatim copy of the header file for each class for which an include is
+# specified. Set to NO to disable this.
+# See also: Section \class.
+# The default value is: YES.
+
+VERBATIM_HEADERS = YES
+
+#---------------------------------------------------------------------------
+# Configuration options related to the alphabetical class index
+#---------------------------------------------------------------------------
+
+# If the ALPHABETICAL_INDEX tag is set to YES, an alphabetical index of all
+# compounds will be generated. Enable this if the project contains a lot of
+# classes, structs, unions or interfaces.
+# The default value is: YES.
+
+ALPHABETICAL_INDEX = YES
+
+# The COLS_IN_ALPHA_INDEX tag can be used to specify the number of columns in
+# which the alphabetical index list will be split.
+# Minimum value: 1, maximum value: 20, default value: 5.
+# This tag requires that the tag ALPHABETICAL_INDEX is set to YES.
+
+COLS_IN_ALPHA_INDEX = 5
+
+# In case all classes in a project start with a common prefix, all classes will
+# be put under the same header in the alphabetical index. The IGNORE_PREFIX tag
+# can be used to specify a prefix (or a list of prefixes) that should be ignored
+# while generating the index headers.
+# This tag requires that the tag ALPHABETICAL_INDEX is set to YES.
+
+IGNORE_PREFIX =
+
+#---------------------------------------------------------------------------
+# Configuration options related to the HTML output
+#---------------------------------------------------------------------------
+
+# If the GENERATE_HTML tag is set to YES, doxygen will generate HTML output
+# The default value is: YES.
+
+GENERATE_HTML = NO
+
+# The HTML_OUTPUT tag is used to specify where the HTML docs will be put. If a
+# relative path is entered the value of OUTPUT_DIRECTORY will be put in front of
+# it.
+# The default directory is: html.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+HTML_OUTPUT = html
+
+# The HTML_FILE_EXTENSION tag can be used to specify the file extension for each
+# generated HTML page (for example: .htm, .php, .asp).
+# The default value is: .html.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+HTML_FILE_EXTENSION = .html
+
+# The HTML_HEADER tag can be used to specify a user-defined HTML header file for
+# each generated HTML page. If the tag is left blank doxygen will generate a
+# standard header.
+#
+# To get valid HTML the header file that includes any scripts and style sheets
+# that doxygen needs, which is dependent on the configuration options used (e.g.
+# the setting GENERATE_TREEVIEW). It is highly recommended to start with a
+# default header using
+# doxygen -w html new_header.html new_footer.html new_stylesheet.css
+# YourConfigFile
+# and then modify the file new_header.html. See also section "Doxygen usage"
+# for information on how to generate the default header that doxygen normally
+# uses.
+# Note: The header is subject to change so you typically have to regenerate the
+# default header when upgrading to a newer version of doxygen. For a description
+# of the possible markers and block names see the documentation.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+HTML_HEADER =
+
+# The HTML_FOOTER tag can be used to specify a user-defined HTML footer for each
+# generated HTML page. If the tag is left blank doxygen will generate a standard
+# footer. See HTML_HEADER for more information on how to generate a default
+# footer and what special commands can be used inside the footer. See also
+# section "Doxygen usage" for information on how to generate the default footer
+# that doxygen normally uses.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+HTML_FOOTER =
+
+# The HTML_STYLESHEET tag can be used to specify a user-defined cascading style
+# sheet that is used by each HTML page. It can be used to fine-tune the look of
+# the HTML output. If left blank doxygen will generate a default style sheet.
+# See also section "Doxygen usage" for information on how to generate the style
+# sheet that doxygen normally uses.
+# Note: It is recommended to use HTML_EXTRA_STYLESHEET instead of this tag, as
+# it is more robust and this tag (HTML_STYLESHEET) will in the future become
+# obsolete.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+HTML_STYLESHEET =
+
+# The HTML_EXTRA_STYLESHEET tag can be used to specify additional user-defined
+# cascading style sheets that are included after the standard style sheets
+# created by doxygen. Using this option one can overrule certain style aspects.
+# This is preferred over using HTML_STYLESHEET since it does not replace the
+# standard style sheet and is therefore more robust against future updates.
+# Doxygen will copy the style sheet files to the output directory.
+# Note: The order of the extra style sheet files is of importance (e.g. the last
+# style sheet in the list overrules the setting of the previous ones in the
+# list). For an example see the documentation.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+HTML_EXTRA_STYLESHEET =
+
+# The HTML_EXTRA_FILES tag can be used to specify one or more extra images or
+# other source files which should be copied to the HTML output directory. Note
+# that these files will be copied to the base HTML output directory. Use the
+# $relpath^ marker in the HTML_HEADER and/or HTML_FOOTER files to load these
+# files. In the HTML_STYLESHEET file, use the file name only. Also note that the
+# files will be copied as-is; there are no commands or markers available.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+HTML_EXTRA_FILES =
+
+# The HTML_COLORSTYLE_HUE tag controls the color of the HTML output. Doxygen
+# will adjust the colors in the style sheet and background images according to
+# this color. Hue is specified as an angle on a colorwheel, see
+# http://en.wikipedia.org/wiki/Hue for more information. For instance the value
+# 0 represents red, 60 is yellow, 120 is green, 180 is cyan, 240 is blue, 300
+# purple, and 360 is red again.
+# Minimum value: 0, maximum value: 359, default value: 220.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+HTML_COLORSTYLE_HUE = 220
+
+# The HTML_COLORSTYLE_SAT tag controls the purity (or saturation) of the colors
+# in the HTML output. For a value of 0 the output will use grayscales only. A
+# value of 255 will produce the most vivid colors.
+# Minimum value: 0, maximum value: 255, default value: 100.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+HTML_COLORSTYLE_SAT = 100
+
+# The HTML_COLORSTYLE_GAMMA tag controls the gamma correction applied to the
+# luminance component of the colors in the HTML output. Values below 100
+# gradually make the output lighter, whereas values above 100 make the output
+# darker. The value divided by 100 is the actual gamma applied, so 80 represents
+# a gamma of 0.8, The value 220 represents a gamma of 2.2, and 100 does not
+# change the gamma.
+# Minimum value: 40, maximum value: 240, default value: 80.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+HTML_COLORSTYLE_GAMMA = 80
+
+# If the HTML_TIMESTAMP tag is set to YES then the footer of each generated HTML
+# page will contain the date and time when the page was generated. Setting this
+# to YES can help to show when doxygen was last run and thus if the
+# documentation is up to date.
+# The default value is: NO.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+HTML_TIMESTAMP = NO
+
+# If the HTML_DYNAMIC_SECTIONS tag is set to YES then the generated HTML
+# documentation will contain sections that can be hidden and shown after the
+# page has loaded.
+# The default value is: NO.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+HTML_DYNAMIC_SECTIONS = NO
+
+# With HTML_INDEX_NUM_ENTRIES one can control the preferred number of entries
+# shown in the various tree structured indices initially; the user can expand
+# and collapse entries dynamically later on. Doxygen will expand the tree to
+# such a level that at most the specified number of entries are visible (unless
+# a fully collapsed tree already exceeds this amount). So setting the number of
+# entries 1 will produce a full collapsed tree by default. 0 is a special value
+# representing an infinite number of entries and will result in a full expanded
+# tree by default.
+# Minimum value: 0, maximum value: 9999, default value: 100.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+HTML_INDEX_NUM_ENTRIES = 100
+
+# If the GENERATE_DOCSET tag is set to YES, additional index files will be
+# generated that can be used as input for Apple's Xcode 3 integrated development
+# environment (see: http://developer.apple.com/tools/xcode/), introduced with
+# OSX 10.5 (Leopard). To create a documentation set, doxygen will generate a
+# Makefile in the HTML output directory. Running make will produce the docset in
+# that directory and running make install will install the docset in
+# ~/Library/Developer/Shared/Documentation/DocSets so that Xcode will find it at
+# startup. See http://developer.apple.com/tools/creatingdocsetswithdoxygen.html
+# for more information.
+# The default value is: NO.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+GENERATE_DOCSET = NO
+
+# This tag determines the name of the docset feed. A documentation feed provides
+# an umbrella under which multiple documentation sets from a single provider
+# (such as a company or product suite) can be grouped.
+# The default value is: Doxygen generated docs.
+# This tag requires that the tag GENERATE_DOCSET is set to YES.
+
+DOCSET_FEEDNAME = "Doxygen generated docs"
+
+# This tag specifies a string that should uniquely identify the documentation
+# set bundle. This should be a reverse domain-name style string, e.g.
+# com.mycompany.MyDocSet. Doxygen will append .docset to the name.
+# The default value is: org.doxygen.Project.
+# This tag requires that the tag GENERATE_DOCSET is set to YES.
+
+DOCSET_BUNDLE_ID = org.doxygen.Project
+
+# The DOCSET_PUBLISHER_ID tag specifies a string that should uniquely identify
+# the documentation publisher. This should be a reverse domain-name style
+# string, e.g. com.mycompany.MyDocSet.documentation.
+# The default value is: org.doxygen.Publisher.
+# This tag requires that the tag GENERATE_DOCSET is set to YES.
+
+DOCSET_PUBLISHER_ID = org.doxygen.Publisher
+
+# The DOCSET_PUBLISHER_NAME tag identifies the documentation publisher.
+# The default value is: Publisher.
+# This tag requires that the tag GENERATE_DOCSET is set to YES.
+
+DOCSET_PUBLISHER_NAME = Publisher
+
+# If the GENERATE_HTMLHELP tag is set to YES then doxygen generates three
+# additional HTML index files: index.hhp, index.hhc, and index.hhk. The
+# index.hhp is a project file that can be read by Microsoft's HTML Help Workshop
+# (see: http://www.microsoft.com/en-us/download/details.aspx?id=21138) on
+# Windows.
+#
+# The HTML Help Workshop contains a compiler that can convert all HTML output
+# generated by doxygen into a single compiled HTML file (.chm). Compiled HTML
+# files are now used as the Windows 98 help format, and will replace the old
+# Windows help format (.hlp) on all Windows platforms in the future. Compressed
+# HTML files also contain an index, a table of contents, and you can search for
+# words in the documentation. The HTML workshop also contains a viewer for
+# compressed HTML files.
+# The default value is: NO.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+GENERATE_HTMLHELP = NO
+
+# The CHM_FILE tag can be used to specify the file name of the resulting .chm
+# file. You can add a path in front of the file if the result should not be
+# written to the html output directory.
+# This tag requires that the tag GENERATE_HTMLHELP is set to YES.
+
+CHM_FILE =
+
+# The HHC_LOCATION tag can be used to specify the location (absolute path
+# including file name) of the HTML help compiler (hhc.exe). If non-empty,
+# doxygen will try to run the HTML help compiler on the generated index.hhp.
+# The file has to be specified with full path.
+# This tag requires that the tag GENERATE_HTMLHELP is set to YES.
+
+HHC_LOCATION =
+
+# The GENERATE_CHI flag controls if a separate .chi index file is generated
+# (YES) or that it should be included in the master .chm file (NO).
+# The default value is: NO.
+# This tag requires that the tag GENERATE_HTMLHELP is set to YES.
+
+GENERATE_CHI = NO
+
+# The CHM_INDEX_ENCODING is used to encode HtmlHelp index (hhk), content (hhc)
+# and project file content.
+# This tag requires that the tag GENERATE_HTMLHELP is set to YES.
+
+CHM_INDEX_ENCODING =
+
+# The BINARY_TOC flag controls whether a binary table of contents is generated
+# (YES) or a normal table of contents (NO) in the .chm file. Furthermore it
+# enables the Previous and Next buttons.
+# The default value is: NO.
+# This tag requires that the tag GENERATE_HTMLHELP is set to YES.
+
+BINARY_TOC = NO
+
+# The TOC_EXPAND flag can be set to YES to add extra items for group members to
+# the table of contents of the HTML help documentation and to the tree view.
+# The default value is: NO.
+# This tag requires that the tag GENERATE_HTMLHELP is set to YES.
+
+TOC_EXPAND = NO
+
+# If the GENERATE_QHP tag is set to YES and both QHP_NAMESPACE and
+# QHP_VIRTUAL_FOLDER are set, an additional index file will be generated that
+# can be used as input for Qt's qhelpgenerator to generate a Qt Compressed Help
+# (.qch) of the generated HTML documentation.
+# The default value is: NO.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+GENERATE_QHP = NO
+
+# If the QHG_LOCATION tag is specified, the QCH_FILE tag can be used to specify
+# the file name of the resulting .qch file. The path specified is relative to
+# the HTML output folder.
+# This tag requires that the tag GENERATE_QHP is set to YES.
+
+QCH_FILE =
+
+# The QHP_NAMESPACE tag specifies the namespace to use when generating Qt Help
+# Project output. For more information please see Qt Help Project / Namespace
+# (see: http://qt-project.org/doc/qt-4.8/qthelpproject.html#namespace).
+# The default value is: org.doxygen.Project.
+# This tag requires that the tag GENERATE_QHP is set to YES.
+
+QHP_NAMESPACE = org.doxygen.Project
+
+# The QHP_VIRTUAL_FOLDER tag specifies the namespace to use when generating Qt
+# Help Project output. For more information please see Qt Help Project / Virtual
+# Folders (see: http://qt-project.org/doc/qt-4.8/qthelpproject.html#virtual-
+# folders).
+# The default value is: doc.
+# This tag requires that the tag GENERATE_QHP is set to YES.
+
+QHP_VIRTUAL_FOLDER = doc
+
+# If the QHP_CUST_FILTER_NAME tag is set, it specifies the name of a custom
+# filter to add. For more information please see Qt Help Project / Custom
+# Filters (see: http://qt-project.org/doc/qt-4.8/qthelpproject.html#custom-
+# filters).
+# This tag requires that the tag GENERATE_QHP is set to YES.
+
+QHP_CUST_FILTER_NAME =
+
+# The QHP_CUST_FILTER_ATTRS tag specifies the list of the attributes of the
+# custom filter to add. For more information please see Qt Help Project / Custom
+# Filters (see: http://qt-project.org/doc/qt-4.8/qthelpproject.html#custom-
+# filters).
+# This tag requires that the tag GENERATE_QHP is set to YES.
+
+QHP_CUST_FILTER_ATTRS =
+
+# The QHP_SECT_FILTER_ATTRS tag specifies the list of the attributes this
+# project's filter section matches. Qt Help Project / Filter Attributes (see:
+# http://qt-project.org/doc/qt-4.8/qthelpproject.html#filter-attributes).
+# This tag requires that the tag GENERATE_QHP is set to YES.
+
+QHP_SECT_FILTER_ATTRS =
+
+# The QHG_LOCATION tag can be used to specify the location of Qt's
+# qhelpgenerator. If non-empty doxygen will try to run qhelpgenerator on the
+# generated .qhp file.
+# This tag requires that the tag GENERATE_QHP is set to YES.
+
+QHG_LOCATION =
+
+# If the GENERATE_ECLIPSEHELP tag is set to YES, additional index files will be
+# generated, together with the HTML files, they form an Eclipse help plugin. To
+# install this plugin and make it available under the help contents menu in
+# Eclipse, the contents of the directory containing the HTML and XML files needs
+# to be copied into the plugins directory of eclipse. The name of the directory
+# within the plugins directory should be the same as the ECLIPSE_DOC_ID value.
+# After copying Eclipse needs to be restarted before the help appears.
+# The default value is: NO.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+GENERATE_ECLIPSEHELP = NO
+
+# A unique identifier for the Eclipse help plugin. When installing the plugin
+# the directory name containing the HTML and XML files should also have this
+# name. Each documentation set should have its own identifier.
+# The default value is: org.doxygen.Project.
+# This tag requires that the tag GENERATE_ECLIPSEHELP is set to YES.
+
+ECLIPSE_DOC_ID = org.doxygen.Project
+
+# If you want full control over the layout of the generated HTML pages it might
+# be necessary to disable the index and replace it with your own. The
+# DISABLE_INDEX tag can be used to turn on/off the condensed index (tabs) at top
+# of each HTML page. A value of NO enables the index and the value YES disables
+# it. Since the tabs in the index contain the same information as the navigation
+# tree, you can set this option to YES if you also set GENERATE_TREEVIEW to YES.
+# The default value is: NO.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+DISABLE_INDEX = NO
+
+# The GENERATE_TREEVIEW tag is used to specify whether a tree-like index
+# structure should be generated to display hierarchical information. If the tag
+# value is set to YES, a side panel will be generated containing a tree-like
+# index structure (just like the one that is generated for HTML Help). For this
+# to work a browser that supports JavaScript, DHTML, CSS and frames is required
+# (i.e. any modern browser). Windows users are probably better off using the
+# HTML help feature. Via custom style sheets (see HTML_EXTRA_STYLESHEET) one can
+# further fine-tune the look of the index. As an example, the default style
+# sheet generated by doxygen has an example that shows how to put an image at
+# the root of the tree instead of the PROJECT_NAME. Since the tree basically has
+# the same information as the tab index, you could consider setting
+# DISABLE_INDEX to YES when enabling this option.
+# The default value is: NO.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+GENERATE_TREEVIEW = NO
+
+# The ENUM_VALUES_PER_LINE tag can be used to set the number of enum values that
+# doxygen will group on one line in the generated HTML documentation.
+#
+# Note that a value of 0 will completely suppress the enum values from appearing
+# in the overview section.
+# Minimum value: 0, maximum value: 20, default value: 4.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+ENUM_VALUES_PER_LINE = 4
+
+# If the treeview is enabled (see GENERATE_TREEVIEW) then this tag can be used
+# to set the initial width (in pixels) of the frame in which the tree is shown.
+# Minimum value: 0, maximum value: 1500, default value: 250.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+TREEVIEW_WIDTH = 250
+
+# If the EXT_LINKS_IN_WINDOW option is set to YES, doxygen will open links to
+# external symbols imported via tag files in a separate window.
+# The default value is: NO.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+EXT_LINKS_IN_WINDOW = NO
+
+# Use this tag to change the font size of LaTeX formulas included as images in
+# the HTML documentation. When you change the font size after a successful
+# doxygen run you need to manually remove any form_*.png images from the HTML
+# output directory to force them to be regenerated.
+# Minimum value: 8, maximum value: 50, default value: 10.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+FORMULA_FONTSIZE = 10
+
+# Use the FORMULA_TRANPARENT tag to determine whether or not the images
+# generated for formulas are transparent PNGs. Transparent PNGs are not
+# supported properly for IE 6.0, but are supported on all modern browsers.
+#
+# Note that when changing this option you need to delete any form_*.png files in
+# the HTML output directory before the changes have effect.
+# The default value is: YES.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+FORMULA_TRANSPARENT = YES
+
+# Enable the USE_MATHJAX option to render LaTeX formulas using MathJax (see
+# http://www.mathjax.org) which uses client side Javascript for the rendering
+# instead of using pre-rendered bitmaps. Use this if you do not have LaTeX
+# installed or if you want to formulas look prettier in the HTML output. When
+# enabled you may also need to install MathJax separately and configure the path
+# to it using the MATHJAX_RELPATH option.
+# The default value is: NO.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+USE_MATHJAX = YES
+
+# When MathJax is enabled you can set the default output format to be used for
+# the MathJax output. See the MathJax site (see:
+# http://docs.mathjax.org/en/latest/output.html) for more details.
+# Possible values are: HTML-CSS (which is slower, but has the best
+# compatibility), NativeMML (i.e. MathML) and SVG.
+# The default value is: HTML-CSS.
+# This tag requires that the tag USE_MATHJAX is set to YES.
+
+MATHJAX_FORMAT = HTML-CSS
+
+# When MathJax is enabled you need to specify the location relative to the HTML
+# output directory using the MATHJAX_RELPATH option. The destination directory
+# should contain the MathJax.js script. For instance, if the mathjax directory
+# is located at the same level as the HTML output directory, then
+# MATHJAX_RELPATH should be ../mathjax. The default value points to the MathJax
+# Content Delivery Network so you can quickly see the result without installing
+# MathJax. However, it is strongly recommended to install a local copy of
+# MathJax from http://www.mathjax.org before deployment.
+# The default value is: http://cdn.mathjax.org/mathjax/latest.
+# This tag requires that the tag USE_MATHJAX is set to YES.
+
+MATHJAX_RELPATH = http://cdn.mathjax.org/mathjax/latest
+
+# The MATHJAX_EXTENSIONS tag can be used to specify one or more MathJax
+# extension names that should be enabled during MathJax rendering. For example
+# MATHJAX_EXTENSIONS = TeX/AMSmath TeX/AMSsymbols
+# This tag requires that the tag USE_MATHJAX is set to YES.
+
+MATHJAX_EXTENSIONS =
+
+# The MATHJAX_CODEFILE tag can be used to specify a file with javascript pieces
+# of code that will be used on startup of the MathJax code. See the MathJax site
+# (see: http://docs.mathjax.org/en/latest/output.html) for more details. For an
+# example see the documentation.
+# This tag requires that the tag USE_MATHJAX is set to YES.
+
+MATHJAX_CODEFILE =
+
+# When the SEARCHENGINE tag is enabled doxygen will generate a search box for
+# the HTML output. The underlying search engine uses javascript and DHTML and
+# should work on any modern browser. Note that when using HTML help
+# (GENERATE_HTMLHELP), Qt help (GENERATE_QHP), or docsets (GENERATE_DOCSET)
+# there is already a search function so this one should typically be disabled.
+# For large projects the javascript based search engine can be slow, then
+# enabling SERVER_BASED_SEARCH may provide a better solution. It is possible to
+# search using the keyboard; to jump to the search box use <access key> + S
+# (what the <access key> is depends on the OS and browser, but it is typically
+# <CTRL>, <ALT>/<option>, or both). Inside the search box use the <cursor down
+# key> to jump into the search results window, the results can be navigated
+# using the <cursor keys>. Press <Enter> to select an item or <escape> to cancel
+# the search. The filter options can be selected when the cursor is inside the
+# search box by pressing <Shift>+<cursor down>. Also here use the <cursor keys>
+# to select a filter and <Enter> or <escape> to activate or cancel the filter
+# option.
+# The default value is: YES.
+# This tag requires that the tag GENERATE_HTML is set to YES.
+
+SEARCHENGINE = YES
+
+# When the SERVER_BASED_SEARCH tag is enabled the search engine will be
+# implemented using a web server instead of a web client using Javascript. There
+# are two flavors of web server based searching depending on the EXTERNAL_SEARCH
+# setting. When disabled, doxygen will generate a PHP script for searching and
+# an index file used by the script. When EXTERNAL_SEARCH is enabled the indexing
+# and searching needs to be provided by external tools. See the section
+# "External Indexing and Searching" for details.
+# The default value is: NO.
+# This tag requires that the tag SEARCHENGINE is set to YES.
+
+SERVER_BASED_SEARCH = NO
+
+# When EXTERNAL_SEARCH tag is enabled doxygen will no longer generate the PHP
+# script for searching. Instead the search results are written to an XML file
+# which needs to be processed by an external indexer. Doxygen will invoke an
+# external search engine pointed to by the SEARCHENGINE_URL option to obtain the
+# search results.
+#
+# Doxygen ships with an example indexer (doxyindexer) and search engine
+# (doxysearch.cgi) which are based on the open source search engine library
+# Xapian (see: http://xapian.org/).
+#
+# See the section "External Indexing and Searching" for details.
+# The default value is: NO.
+# This tag requires that the tag SEARCHENGINE is set to YES.
+
+EXTERNAL_SEARCH = NO
+
+# The SEARCHENGINE_URL should point to a search engine hosted by a web server
+# which will return the search results when EXTERNAL_SEARCH is enabled.
+#
+# Doxygen ships with an example indexer (doxyindexer) and search engine
+# (doxysearch.cgi) which are based on the open source search engine library
+# Xapian (see: http://xapian.org/). See the section "External Indexing and
+# Searching" for details.
+# This tag requires that the tag SEARCHENGINE is set to YES.
+
+SEARCHENGINE_URL =
+
+# When SERVER_BASED_SEARCH and EXTERNAL_SEARCH are both enabled the unindexed
+# search data is written to a file for indexing by an external tool. With the
+# SEARCHDATA_FILE tag the name of this file can be specified.
+# The default file is: searchdata.xml.
+# This tag requires that the tag SEARCHENGINE is set to YES.
+
+SEARCHDATA_FILE = searchdata.xml
+
+# When SERVER_BASED_SEARCH and EXTERNAL_SEARCH are both enabled the
+# EXTERNAL_SEARCH_ID tag can be used as an identifier for the project. This is
+# useful in combination with EXTRA_SEARCH_MAPPINGS to search through multiple
+# projects and redirect the results back to the right project.
+# This tag requires that the tag SEARCHENGINE is set to YES.
+
+EXTERNAL_SEARCH_ID =
+
+# The EXTRA_SEARCH_MAPPINGS tag can be used to enable searching through doxygen
+# projects other than the one defined by this configuration file, but that are
+# all added to the same external search index. Each project needs to have a
+# unique id set via EXTERNAL_SEARCH_ID. The search mapping then maps the id of
+# to a relative location where the documentation can be found. The format is:
+# EXTRA_SEARCH_MAPPINGS = tagname1=loc1 tagname2=loc2 ...
+# This tag requires that the tag SEARCHENGINE is set to YES.
+
+EXTRA_SEARCH_MAPPINGS =
+
+#---------------------------------------------------------------------------
+# Configuration options related to the LaTeX output
+#---------------------------------------------------------------------------
+
+# If the GENERATE_LATEX tag is set to YES, doxygen will generate LaTeX output.
+# The default value is: YES.
+
+GENERATE_LATEX = NO
+
+# The LATEX_OUTPUT tag is used to specify where the LaTeX docs will be put. If a
+# relative path is entered the value of OUTPUT_DIRECTORY will be put in front of
+# it.
+# The default directory is: latex.
+# This tag requires that the tag GENERATE_LATEX is set to YES.
+
+LATEX_OUTPUT = latex
+
+# The LATEX_CMD_NAME tag can be used to specify the LaTeX command name to be
+# invoked.
+#
+# Note that when enabling USE_PDFLATEX this option is only used for generating
+# bitmaps for formulas in the HTML output, but not in the Makefile that is
+# written to the output directory.
+# The default file is: latex.
+# This tag requires that the tag GENERATE_LATEX is set to YES.
+
+LATEX_CMD_NAME = latex
+
+# The MAKEINDEX_CMD_NAME tag can be used to specify the command name to generate
+# index for LaTeX.
+# The default file is: makeindex.
+# This tag requires that the tag GENERATE_LATEX is set to YES.
+
+MAKEINDEX_CMD_NAME = makeindex
+
+# If the COMPACT_LATEX tag is set to YES, doxygen generates more compact LaTeX
+# documents. This may be useful for small projects and may help to save some
+# trees in general.
+# The default value is: NO.
+# This tag requires that the tag GENERATE_LATEX is set to YES.
+
+COMPACT_LATEX = NO
+
+# The PAPER_TYPE tag can be used to set the paper type that is used by the
+# printer.
+# Possible values are: a4 (210 x 297 mm), letter (8.5 x 11 inches), legal (8.5 x
+# 14 inches) and executive (7.25 x 10.5 inches).
+# The default value is: a4.
+# This tag requires that the tag GENERATE_LATEX is set to YES.
+
+PAPER_TYPE = a4
+
+# The EXTRA_PACKAGES tag can be used to specify one or more LaTeX package names
+# that should be included in the LaTeX output. The package can be specified just
+# by its name or with the correct syntax as to be used with the LaTeX
+# \usepackage command. To get the times font for instance you can specify :
+# EXTRA_PACKAGES=times or EXTRA_PACKAGES={times}
+# To use the option intlimits with the amsmath package you can specify:
+# EXTRA_PACKAGES=[intlimits]{amsmath}
+# If left blank no extra packages will be included.
+# This tag requires that the tag GENERATE_LATEX is set to YES.
+
+EXTRA_PACKAGES =
+
+# The LATEX_HEADER tag can be used to specify a personal LaTeX header for the
+# generated LaTeX document. The header should contain everything until the first
+# chapter. If it is left blank doxygen will generate a standard header. See
+# section "Doxygen usage" for information on how to let doxygen write the
+# default header to a separate file.
+#
+# Note: Only use a user-defined header if you know what you are doing! The
+# following commands have a special meaning inside the header: $title,
+# $datetime, $date, $doxygenversion, $projectname, $projectnumber,
+# $projectbrief, $projectlogo. Doxygen will replace $title with the empty
+# string, for the replacement values of the other commands the user is referred
+# to HTML_HEADER.
+# This tag requires that the tag GENERATE_LATEX is set to YES.
+
+LATEX_HEADER =
+
+# The LATEX_FOOTER tag can be used to specify a personal LaTeX footer for the
+# generated LaTeX document. The footer should contain everything after the last
+# chapter. If it is left blank doxygen will generate a standard footer. See
+# LATEX_HEADER for more information on how to generate a default footer and what
+# special commands can be used inside the footer.
+#
+# Note: Only use a user-defined footer if you know what you are doing!
+# This tag requires that the tag GENERATE_LATEX is set to YES.
+
+LATEX_FOOTER =
+
+# The LATEX_EXTRA_STYLESHEET tag can be used to specify additional user-defined
+# LaTeX style sheets that are included after the standard style sheets created
+# by doxygen. Using this option one can overrule certain style aspects. Doxygen
+# will copy the style sheet files to the output directory.
+# Note: The order of the extra style sheet files is of importance (e.g. the last
+# style sheet in the list overrules the setting of the previous ones in the
+# list).
+# This tag requires that the tag GENERATE_LATEX is set to YES.
+
+LATEX_EXTRA_STYLESHEET =
+
+# The LATEX_EXTRA_FILES tag can be used to specify one or more extra images or
+# other source files which should be copied to the LATEX_OUTPUT output
+# directory. Note that the files will be copied as-is; there are no commands or
+# markers available.
+# This tag requires that the tag GENERATE_LATEX is set to YES.
+
+LATEX_EXTRA_FILES =
+
+# If the PDF_HYPERLINKS tag is set to YES, the LaTeX that is generated is
+# prepared for conversion to PDF (using ps2pdf or pdflatex). The PDF file will
+# contain links (just like the HTML output) instead of page references. This
+# makes the output suitable for online browsing using a PDF viewer.
+# The default value is: YES.
+# This tag requires that the tag GENERATE_LATEX is set to YES.
+
+PDF_HYPERLINKS = YES
+
+# If the USE_PDFLATEX tag is set to YES, doxygen will use pdflatex to generate
+# the PDF file directly from the LaTeX files. Set this option to YES, to get a
+# higher quality PDF documentation.
+# The default value is: YES.
+# This tag requires that the tag GENERATE_LATEX is set to YES.
+
+USE_PDFLATEX = YES
+
+# If the LATEX_BATCHMODE tag is set to YES, doxygen will add the \batchmode
+# command to the generated LaTeX files. This will instruct LaTeX to keep running
+# if errors occur, instead of asking the user for help. This option is also used
+# when generating formulas in HTML.
+# The default value is: NO.
+# This tag requires that the tag GENERATE_LATEX is set to YES.
+
+LATEX_BATCHMODE = NO
+
+# If the LATEX_HIDE_INDICES tag is set to YES then doxygen will not include the
+# index chapters (such as File Index, Compound Index, etc.) in the output.
+# The default value is: NO.
+# This tag requires that the tag GENERATE_LATEX is set to YES.
+
+LATEX_HIDE_INDICES = NO
+
+# If the LATEX_SOURCE_CODE tag is set to YES then doxygen will include source
+# code with syntax highlighting in the LaTeX output.
+#
+# Note that which sources are shown also depends on other settings such as
+# SOURCE_BROWSER.
+# The default value is: NO.
+# This tag requires that the tag GENERATE_LATEX is set to YES.
+
+LATEX_SOURCE_CODE = NO
+
+# The LATEX_BIB_STYLE tag can be used to specify the style to use for the
+# bibliography, e.g. plainnat, or ieeetr. See
+# http://en.wikipedia.org/wiki/BibTeX and \cite for more info.
+# The default value is: plain.
+# This tag requires that the tag GENERATE_LATEX is set to YES.
+
+LATEX_BIB_STYLE = plain
+
+# If the LATEX_TIMESTAMP tag is set to YES then the footer of each generated
+# page will contain the date and time when the page was generated. Setting this
+# to NO can help when comparing the output of multiple runs.
+# The default value is: NO.
+# This tag requires that the tag GENERATE_LATEX is set to YES.
+
+LATEX_TIMESTAMP = NO
+
+#---------------------------------------------------------------------------
+# Configuration options related to the RTF output
+#---------------------------------------------------------------------------
+
+# If the GENERATE_RTF tag is set to YES, doxygen will generate RTF output. The
+# RTF output is optimized for Word 97 and may not look too pretty with other RTF
+# readers/editors.
+# The default value is: NO.
+
+GENERATE_RTF = NO
+
+# The RTF_OUTPUT tag is used to specify where the RTF docs will be put. If a
+# relative path is entered the value of OUTPUT_DIRECTORY will be put in front of
+# it.
+# The default directory is: rtf.
+# This tag requires that the tag GENERATE_RTF is set to YES.
+
+RTF_OUTPUT = rtf
+
+# If the COMPACT_RTF tag is set to YES, doxygen generates more compact RTF
+# documents. This may be useful for small projects and may help to save some
+# trees in general.
+# The default value is: NO.
+# This tag requires that the tag GENERATE_RTF is set to YES.
+
+COMPACT_RTF = NO
+
+# If the RTF_HYPERLINKS tag is set to YES, the RTF that is generated will
+# contain hyperlink fields. The RTF file will contain links (just like the HTML
+# output) instead of page references. This makes the output suitable for online
+# browsing using Word or some other Word compatible readers that support those
+# fields.
+#
+# Note: WordPad (write) and others do not support links.
+# The default value is: NO.
+# This tag requires that the tag GENERATE_RTF is set to YES.
+
+RTF_HYPERLINKS = NO
+
+# Load stylesheet definitions from file. Syntax is similar to doxygen's config
+# file, i.e. a series of assignments. You only have to provide replacements,
+# missing definitions are set to their default value.
+#
+# See also section "Doxygen usage" for information on how to generate the
+# default style sheet that doxygen normally uses.
+# This tag requires that the tag GENERATE_RTF is set to YES.
+
+RTF_STYLESHEET_FILE =
+
+# Set optional variables used in the generation of an RTF document. Syntax is
+# similar to doxygen's config file. A template extensions file can be generated
+# using doxygen -e rtf extensionFile.
+# This tag requires that the tag GENERATE_RTF is set to YES.
+
+RTF_EXTENSIONS_FILE =
+
+# If the RTF_SOURCE_CODE tag is set to YES then doxygen will include source code
+# with syntax highlighting in the RTF output.
+#
+# Note that which sources are shown also depends on other settings such as
+# SOURCE_BROWSER.
+# The default value is: NO.
+# This tag requires that the tag GENERATE_RTF is set to YES.
+
+RTF_SOURCE_CODE = NO
+
+#---------------------------------------------------------------------------
+# Configuration options related to the man page output
+#---------------------------------------------------------------------------
+
+# If the GENERATE_MAN tag is set to YES, doxygen will generate man pages for
+# classes and files.
+# The default value is: NO.
+
+GENERATE_MAN = NO
+
+# The MAN_OUTPUT tag is used to specify where the man pages will be put. If a
+# relative path is entered the value of OUTPUT_DIRECTORY will be put in front of
+# it. A directory man3 will be created inside the directory specified by
+# MAN_OUTPUT.
+# The default directory is: man.
+# This tag requires that the tag GENERATE_MAN is set to YES.
+
+MAN_OUTPUT = man
+
+# The MAN_EXTENSION tag determines the extension that is added to the generated
+# man pages. In case the manual section does not start with a number, the number
+# 3 is prepended. The dot (.) at the beginning of the MAN_EXTENSION tag is
+# optional.
+# The default value is: .3.
+# This tag requires that the tag GENERATE_MAN is set to YES.
+
+MAN_EXTENSION = .3
+
+# The MAN_SUBDIR tag determines the name of the directory created within
+# MAN_OUTPUT in which the man pages are placed. If defaults to man followed by
+# MAN_EXTENSION with the initial . removed.
+# This tag requires that the tag GENERATE_MAN is set to YES.
+
+MAN_SUBDIR =
+
+# If the MAN_LINKS tag is set to YES and doxygen generates man output, then it
+# will generate one additional man file for each entity documented in the real
+# man page(s). These additional files only source the real man page, but without
+# them the man command would be unable to find the correct page.
+# The default value is: NO.
+# This tag requires that the tag GENERATE_MAN is set to YES.
+
+MAN_LINKS = NO
+
+#---------------------------------------------------------------------------
+# Configuration options related to the XML output
+#---------------------------------------------------------------------------
+
+# If the GENERATE_XML tag is set to YES, doxygen will generate an XML file that
+# captures the structure of the code including all documentation.
+# The default value is: NO.
+
+GENERATE_XML = YES
+
+# The XML_OUTPUT tag is used to specify where the XML pages will be put. If a
+# relative path is entered the value of OUTPUT_DIRECTORY will be put in front of
+# it.
+# The default directory is: xml.
+# This tag requires that the tag GENERATE_XML is set to YES.
+
+XML_OUTPUT = xml
+
+# If the XML_PROGRAMLISTING tag is set to YES, doxygen will dump the program
+# listings (including syntax highlighting and cross-referencing information) to
+# the XML output. Note that enabling this will significantly increase the size
+# of the XML output.
+# The default value is: YES.
+# This tag requires that the tag GENERATE_XML is set to YES.
+
+XML_PROGRAMLISTING = YES
+
+#---------------------------------------------------------------------------
+# Configuration options related to the DOCBOOK output
+#---------------------------------------------------------------------------
+
+# If the GENERATE_DOCBOOK tag is set to YES, doxygen will generate Docbook files
+# that can be used to generate PDF.
+# The default value is: NO.
+
+GENERATE_DOCBOOK = NO
+
+# The DOCBOOK_OUTPUT tag is used to specify where the Docbook pages will be put.
+# If a relative path is entered the value of OUTPUT_DIRECTORY will be put in
+# front of it.
+# The default directory is: docbook.
+# This tag requires that the tag GENERATE_DOCBOOK is set to YES.
+
+DOCBOOK_OUTPUT = docbook
+
+# If the DOCBOOK_PROGRAMLISTING tag is set to YES, doxygen will include the
+# program listings (including syntax highlighting and cross-referencing
+# information) to the DOCBOOK output. Note that enabling this will significantly
+# increase the size of the DOCBOOK output.
+# The default value is: NO.
+# This tag requires that the tag GENERATE_DOCBOOK is set to YES.
+
+DOCBOOK_PROGRAMLISTING = NO
+
+#---------------------------------------------------------------------------
+# Configuration options for the AutoGen Definitions output
+#---------------------------------------------------------------------------
+
+# If the GENERATE_AUTOGEN_DEF tag is set to YES, doxygen will generate an
+# AutoGen Definitions (see http://autogen.sf.net) file that captures the
+# structure of the code including all documentation. Note that this feature is
+# still experimental and incomplete at the moment.
+# The default value is: NO.
+
+GENERATE_AUTOGEN_DEF = NO
+
+#---------------------------------------------------------------------------
+# Configuration options related to the Perl module output
+#---------------------------------------------------------------------------
+
+# If the GENERATE_PERLMOD tag is set to YES, doxygen will generate a Perl module
+# file that captures the structure of the code including all documentation.
+#
+# Note that this feature is still experimental and incomplete at the moment.
+# The default value is: NO.
+
+GENERATE_PERLMOD = NO
+
+# If the PERLMOD_LATEX tag is set to YES, doxygen will generate the necessary
+# Makefile rules, Perl scripts and LaTeX code to be able to generate PDF and DVI
+# output from the Perl module output.
+# The default value is: NO.
+# This tag requires that the tag GENERATE_PERLMOD is set to YES.
+
+PERLMOD_LATEX = NO
+
+# If the PERLMOD_PRETTY tag is set to YES, the Perl module output will be nicely
+# formatted so it can be parsed by a human reader. This is useful if you want to
+# understand what is going on. On the other hand, if this tag is set to NO, the
+# size of the Perl module output will be much smaller and Perl will parse it
+# just the same.
+# The default value is: YES.
+# This tag requires that the tag GENERATE_PERLMOD is set to YES.
+
+PERLMOD_PRETTY = YES
+
+# The names of the make variables in the generated doxyrules.make file are
+# prefixed with the string contained in PERLMOD_MAKEVAR_PREFIX. This is useful
+# so different doxyrules.make files included by the same Makefile don't
+# overwrite each other's variables.
+# This tag requires that the tag GENERATE_PERLMOD is set to YES.
+
+PERLMOD_MAKEVAR_PREFIX =
+
+#---------------------------------------------------------------------------
+# Configuration options related to the preprocessor
+#---------------------------------------------------------------------------
+
+# If the ENABLE_PREPROCESSING tag is set to YES, doxygen will evaluate all
+# C-preprocessor directives found in the sources and include files.
+# The default value is: YES.
+
+ENABLE_PREPROCESSING = NO
+
+# If the MACRO_EXPANSION tag is set to YES, doxygen will expand all macro names
+# in the source code. If set to NO, only conditional compilation will be
+# performed. Macro expansion can be done in a controlled way by setting
+# EXPAND_ONLY_PREDEF to YES.
+# The default value is: NO.
+# This tag requires that the tag ENABLE_PREPROCESSING is set to YES.
+
+MACRO_EXPANSION = NO
+
+# If the EXPAND_ONLY_PREDEF and MACRO_EXPANSION tags are both set to YES then
+# the macro expansion is limited to the macros specified with the PREDEFINED and
+# EXPAND_AS_DEFINED tags.
+# The default value is: NO.
+# This tag requires that the tag ENABLE_PREPROCESSING is set to YES.
+
+EXPAND_ONLY_PREDEF = NO
+
+# If the SEARCH_INCLUDES tag is set to YES, the include files in the
+# INCLUDE_PATH will be searched if a #include is found.
+# The default value is: YES.
+# This tag requires that the tag ENABLE_PREPROCESSING is set to YES.
+
+SEARCH_INCLUDES = YES
+
+# The INCLUDE_PATH tag can be used to specify one or more directories that
+# contain include files that are not input files but should be processed by the
+# preprocessor.
+# This tag requires that the tag SEARCH_INCLUDES is set to YES.
+
+INCLUDE_PATH =
+
+# You can use the INCLUDE_FILE_PATTERNS tag to specify one or more wildcard
+# patterns (like *.h and *.hpp) to filter out the header-files in the
+# directories. If left blank, the patterns specified with FILE_PATTERNS will be
+# used.
+# This tag requires that the tag ENABLE_PREPROCESSING is set to YES.
+
+INCLUDE_FILE_PATTERNS =
+
+# The PREDEFINED tag can be used to specify one or more macro names that are
+# defined before the preprocessor is started (similar to the -D option of e.g.
+# gcc). The argument of the tag is a list of macros of the form: name or
+# name=definition (no spaces). If the definition and the "=" are omitted, "=1"
+# is assumed. To prevent a macro definition from being undefined via #undef or
+# recursively expanded use the := operator instead of the = operator.
+# This tag requires that the tag ENABLE_PREPROCESSING is set to YES.
+
+PREDEFINED =
+
+# If the MACRO_EXPANSION and EXPAND_ONLY_PREDEF tags are set to YES then this
+# tag can be used to specify a list of macro names that should be expanded. The
+# macro definition that is found in the sources will be used. Use the PREDEFINED
+# tag if you want to use a different macro definition that overrules the
+# definition found in the source code.
+# This tag requires that the tag ENABLE_PREPROCESSING is set to YES.
+
+EXPAND_AS_DEFINED =
+
+# If the SKIP_FUNCTION_MACROS tag is set to YES then doxygen's preprocessor will
+# remove all references to function-like macros that are alone on a line, have
+# an all uppercase name, and do not end with a semicolon. Such function macros
+# are typically used for boiler-plate code, and will confuse the parser if not
+# removed.
+# The default value is: YES.
+# This tag requires that the tag ENABLE_PREPROCESSING is set to YES.
+
+SKIP_FUNCTION_MACROS = YES
+
+#---------------------------------------------------------------------------
+# Configuration options related to external references
+#---------------------------------------------------------------------------
+
+# The TAGFILES tag can be used to specify one or more tag files. For each tag
+# file the location of the external documentation should be added. The format of
+# a tag file without this location is as follows:
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diff --git a/docs/examples/huber.rst b/docs/examples/huber.rst
new file mode 100644
index 0000000..b21c50a
--- /dev/null
+++ b/docs/examples/huber.rst
@@ -0,0 +1,162 @@
+Huber fitting
+=============
+
+*Huber fitting* or the *robust least-squares problem* performs linear regression under the assumption that there are outliers in the data.
+The fitting problem is written as
+
+.. math::
+ \begin{array}{ll}
+ \mbox{minimize} & \sum_{i=1}^{m} \phi_{\rm hub}(a_i^T x - b_i),
+ \end{array}
+
+with the Huber penalty function :math:`\phi_{\rm hub}:\mathbf{R}\to\mathbf{R}` defined as
+
+.. math::
+ \phi_{\rm hub}(u) =
+ \begin{cases}
+ u^2 & |u| \le 1 \\
+ (2|u| - 1) & |u| > 1
+ \end{cases}
+
+The problem has the following equivalent form (see `here <https://doi.org/10.1109/34.877518>`_ for more details)
+
+.. math::
+ \begin{array}{ll}
+ \mbox{minimize} & u^T u + 2\,\boldsymbol{1}^T (r+s) \\
+ \mbox{subject to} & Ax - b - u = r - s \\
+ & r \ge 0 \\
+ & s \ge 0
+ \end{array}
+
+
+
+Python
+------
+
+.. code:: python
+
+ import osqp
+ import numpy as np
+ import scipy as sp
+ from scipy import sparse
+
+ # Generate problem data
+ sp.random.seed(1)
+ n = 10
+ m = 100
+ Ad = sparse.random(m, n, density=0.5, format='csc')
+ x_true = np.random.randn(n) / np.sqrt(n)
+ ind95 = (np.random.rand(m) < 0.95).astype(float)
+ b = Ad.dot(x_true) + np.multiply(0.5*np.random.randn(m), ind95) \
+ + np.multiply(10.*np.random.rand(m), 1. - ind95)
+
+ # OSQP data
+ Im = sparse.eye(m)
+ P = sparse.block_diag([sparse.csc_matrix((n, n)), 2*Im,
+ sparse.csc_matrix((2*m, 2*m))],
+ format='csc')
+ q = np.append(np.zeros(m+n), 2*np.ones(2*m))
+ A = sparse.bmat([[Ad, -Im, -Im, Im],
+ [None, None, Im, None],
+ [None, None, None, Im]], format='csc')
+ l = np.hstack([b, np.zeros(2*m)])
+ u = np.hstack([b, np.inf*np.ones(2*m)])
+
+ # Create an OSQP object
+ prob = osqp.OSQP()
+
+ # Setup workspace
+ prob.setup(P, q, A, l, u)
+
+ # Solve problem
+ res = prob.solve()
+
+
+
+Matlab
+------
+
+.. code:: matlab
+
+ % Generate problem data
+ rng(1)
+ n = 10;
+ m = 100;
+ Ad = sprandn(m, n, 0.5);
+ x_true = randn(n, 1) / sqrt(n);
+ ind95 = rand(m, 1) > 0.95;
+ b = Ad*x_true + 10*rand(m, 1).*ind95 + 0.5*randn(m, 1).*(1-ind95);
+
+ % OSQP data
+ Im = speye(m);
+ Om = sparse(m, m);
+ Omn = sparse(m, n);
+ P = blkdiag(sparse(n, n), 2*Im, sparse(2*m, 2*m));
+ q = [zeros(m + n, 1); 2*ones(2*m, 1)];
+ A = [Ad, -Im, -Im, Im;
+ Omn, Om, Im, Om;
+ Omn, Om, Om, Im];
+ l = [b; zeros(2*m, 1)];
+ u = [b; inf*ones(2*m, 1)];
+
+ % Create an OSQP object
+ prob = osqp;
+
+ % Setup workspace
+ prob.setup(P, q, A, l, u);
+
+ % Solve problem
+ res = prob.solve();
+
+
+
+CVXPY
+-----
+
+.. code:: python
+
+ from cvxpy import *
+ import numpy as np
+ import scipy as sp
+ from scipy import sparse
+
+ # Generate problem data
+ sp.random.seed(1)
+ n = 10
+ m = 100
+ A = sparse.random(m, n, density=0.5, format='csc')
+ x_true = np.random.randn(n) / np.sqrt(n)
+ ind95 = (np.random.rand(m) < 0.95).astype(float)
+ b = A.dot(x_true) + np.multiply(0.5*np.random.randn(m), ind95) \
+ + np.multiply(10.*np.random.rand(m), 1. - ind95)
+
+ # Define problem
+ x = Variable(n)
+ objective = sum(huber(A*x - b))
+
+ # Solve with OSQP
+ Problem(Minimize(objective)).solve(solver=OSQP)
+
+
+
+YALMIP
+------
+
+.. code:: matlab
+
+ % Generate problem data
+ rng(1)
+ n = 10;
+ m = 100;
+ A = sprandn(m, n, 0.5);
+ x_true = randn(n, 1) / sqrt(n);
+ ind95 = rand(m, 1) > 0.95;
+ b = A*x_true + 10*rand(m, 1).*ind95 + 0.5*randn(m, 1).*(1-ind95);
+
+ % Define problem
+ x = sdpvar(n, 1);
+ objective = huber(A*x - b);
+
+ % Solve with OSQP
+ options = sdpsettings('solver', 'osqp');
+ optimize([], objective, options);
diff --git a/docs/examples/index.rst b/docs/examples/index.rst
new file mode 100644
index 0000000..86cd66e
--- /dev/null
+++ b/docs/examples/index.rst
@@ -0,0 +1,27 @@
+Examples
+========
+
+
+Demo
+----
+
+.. toctree::
+ :maxdepth: 1
+
+ setup-and-solve.rst
+ update-vectors.rst
+ update-matrices.rst
+
+
+Applications
+------------
+
+.. toctree::
+ :maxdepth: 1
+
+ huber.rst
+ lasso.rst
+ least-squares.rst
+ mpc.rst
+ portfolio.rst
+ svm.rst
diff --git a/docs/examples/lasso.rst b/docs/examples/lasso.rst
new file mode 100644
index 0000000..cbb566b
--- /dev/null
+++ b/docs/examples/lasso.rst
@@ -0,0 +1,181 @@
+Lasso
+=====
+
+
+Lasso is a well known technique for sparse linear regression.
+It is obtained by adding an :math:`\ell_1` regularization term in the objective,
+
+.. math::
+ \begin{array}{ll}
+ \mbox{minimize} & \frac{1}{2} \| Ax - b \|_2^2 + \gamma \| x \|_1
+ \end{array}
+
+
+where :math:`x \in \mathbf{R}^{n}` is the vector of parameters, :math:`A \in \mathbf{R}^{m \times n}` is the data matrix, and :math:`\gamma > 0` is the weighting parameter.
+The problem has the following equivalent form,
+
+.. math::
+ \begin{array}{ll}
+ \mbox{minimize} & \frac{1}{2} y^T y + \gamma \boldsymbol{1}^T t \\
+ \mbox{subject to} & y = Ax - b \\
+ & -t \le x \le t
+ \end{array}
+
+
+In order to get a good trade-off between sparsity of the solution and quality of the linear fit, we solve the problem for varying weighting parameter :math:`\gamma`.
+Since :math:`\gamma` enters only in the linear part of the objective function, we can reuse the matrix factorization and enable warm starting to reduce the computation time.
+
+
+
+Python
+------
+
+.. code:: python
+
+ import osqp
+ import numpy as np
+ import scipy as sp
+ from scipy import sparse
+
+ # Generate problem data
+ sp.random.seed(1)
+ n = 10
+ m = 1000
+ Ad = sparse.random(m, n, density=0.5)
+ x_true = np.multiply((np.random.rand(n) > 0.8).astype(float),
+ np.random.randn(n)) / np.sqrt(n)
+ b = Ad.dot(x_true) + 0.5*np.random.randn(m)
+ gammas = np.linspace(1, 10, 11)
+
+ # Auxiliary data
+ In = sparse.eye(n)
+ Im = sparse.eye(m)
+ On = sparse.csc_matrix((n, n))
+ Onm = sparse.csc_matrix((n, m))
+
+ # OSQP data
+ P = sparse.block_diag([On, sparse.eye(m), On], format='csc')
+ q = np.zeros(2*n + m)
+ A = sparse.vstack([sparse.hstack([Ad, -Im, Onm.T]),
+ sparse.hstack([In, Onm, -In]),
+ sparse.hstack([In, Onm, In])], format='csc')
+ l = np.hstack([b, -np.inf * np.ones(n), np.zeros(n)])
+ u = np.hstack([b, np.zeros(n), np.inf * np.ones(n)])
+
+ # Create an OSQP object
+ prob = osqp.OSQP()
+
+ # Setup workspace
+ prob.setup(P, q, A, l, u, warm_start=True)
+
+ # Solve problem for different values of gamma parameter
+ for gamma in gammas:
+ # Update linear cost
+ q_new = np.hstack([np.zeros(n+m), gamma*np.ones(n)])
+ prob.update(q=q_new)
+
+ # Solve
+ res = prob.solve()
+
+
+Matlab
+------
+
+.. code:: matlab
+
+ % Generate problem data
+ rng(1)
+ n = 10;
+ m = 1000;
+ Ad = sprandn(m, n, 0.5);
+ x_true = (randn(n, 1) > 0.8) .* randn(n, 1) / sqrt(n);
+ b = Ad * x_true + 0.5 * randn(m, 1);
+ gammas = linspace(1, 10, 11);
+
+ % OSQP data
+ P = blkdiag(sparse(n, n), speye(m), sparse(n, n));
+ q = zeros(2*n+m, 1);
+ A = [Ad, -speye(m), sparse(m,n);
+ speye(n), sparse(n, m), -speye(n);
+ speye(n), sparse(n, m), speye(n);];
+ l = [b; -inf*ones(n, 1); zeros(n, 1)];
+ u = [b; zeros(n, 1); inf*ones(n, 1)];
+
+ % Create an OSQP object
+ prob = osqp;
+
+ % Setup workspace
+ prob.setup(P, q, A, l, u, 'warm_start', true);
+
+ % Solve problem for different values of gamma parameter
+ for i = 1 : length(gammas)
+ % Update linear cost
+ gamma = gammas(i);
+ q_new = [zeros(n+m,1); gamma*ones(n,1)];
+ prob.update('q', q_new);
+
+ % Solve
+ res = prob.solve();
+ end
+
+
+
+CVXPY
+-----
+
+.. code:: python
+
+ from cvxpy import *
+ import numpy as np
+ import scipy as sp
+ from scipy import sparse
+
+ # Generate problem data
+ sp.random.seed(1)
+ n = 10
+ m = 1000
+ A = sparse.random(m, n, density=0.5)
+ x_true = np.multiply((np.random.rand(n) > 0.8).astype(float),
+ np.random.randn(n)) / np.sqrt(n)
+ b = A.dot(x_true) + 0.5*np.random.randn(m)
+ gammas = np.linspace(1, 10, 11)
+
+ # Define problem
+ x = Variable(n)
+ gamma = Parameter(nonneg=True)
+ objective = 0.5*sum_squares(A*x - b) + gamma*norm1(x)
+ prob = Problem(Minimize(objective))
+
+ # Solve problem for different values of gamma parameter
+ for gamma_val in gammas:
+ gamma.value = gamma_val
+ prob.solve(solver=OSQP, warm_start=True)
+
+
+YALMIP
+------
+
+.. code:: matlab
+
+ % Generate problem data
+ rng(1)
+ n = 10;
+ m = 1000;
+ A = sprandn(m, n, 0.5);
+ x_true = (randn(n, 1) > 0.8) .* randn(n, 1) / sqrt(n);
+ b = A * x_true + 0.5 * randn(m, 1);
+ gammas = linspace(1, 10, 11);
+
+ % Define problem
+ x = sdpvar(n, 1);
+ gamma = sdpvar;
+ objective = 0.5*norm(A*x - b)^2 + gamma*norm(x,1);
+
+ % Solve with OSQP
+ options = sdpsettings('solver', 'osqp');
+ x_opt = optimizer([], objective, options, gamma, x);
+
+ % Solve problem for different values of gamma parameter
+ for i = 1 : length(gammas)
+ x_opt(gammas(i));
+ end
diff --git a/docs/examples/least-squares.rst b/docs/examples/least-squares.rst
new file mode 100644
index 0000000..56adb7e
--- /dev/null
+++ b/docs/examples/least-squares.rst
@@ -0,0 +1,138 @@
+Least-squares
+=============
+
+Consider the following constrained least-squares problem
+
+.. math::
+ \begin{array}{ll}
+ \mbox{minimize} & \frac{1}{2} \|Ax - b\|_2^2 \\
+ \mbox{subject to} & 0 \leq x \leq 1
+ \end{array}
+
+The problem has the following equivalent form
+
+.. math::
+ \begin{array}{ll}
+ \mbox{minimize} & \frac{1}{2} y^T y \\
+ \mbox{subject to} & y = A x - b \\
+ & 0 \le x \le 1
+ \end{array}
+
+
+
+Python
+------
+
+.. code:: python
+
+ import osqp
+ import numpy as np
+ import scipy as sp
+ from scipy import sparse
+
+ # Generate problem data
+ sp.random.seed(1)
+ m = 30
+ n = 20
+ Ad = sparse.random(m, n, density=0.7, format='csc')
+ b = np.random.randn(m)
+
+ # OSQP data
+ P = sparse.block_diag([sparse.csc_matrix((n, n)), sparse.eye(m)], format='csc')
+ q = np.zeros(n+m)
+ A = sparse.vstack([
+ sparse.hstack([Ad, -sparse.eye(m)]),
+ sparse.hstack([sparse.eye(n), sparse.csc_matrix((n, m))])], format='csc')
+ l = np.hstack([b, np.zeros(n)])
+ u = np.hstack([b, np.ones(n)])
+
+ # Create an OSQP object
+ prob = osqp.OSQP()
+
+ # Setup workspace
+ prob.setup(P, q, A, l, u)
+
+ # Solve problem
+ res = prob.solve()
+
+
+
+Matlab
+------
+
+.. code:: matlab
+
+ % Generate problem data
+ rng(1)
+ m = 30;
+ n = 20;
+ Ad = sprandn(m, n, 0.7);
+ b = randn(m, 1);
+
+ % OSQP data
+ P = blkdiag(sparse(n, n), speye(m));
+ q = zeros(n+m, 1);
+ A = [Ad, -speye(m);
+ speye(n), sparse(n, m)];
+ l = [b; zeros(n, 1)];
+ u = [b; ones(n, 1)];
+
+ % Create an OSQP object
+ prob = osqp;
+
+ % Setup workspace
+ prob.setup(P, q, A, l, u);
+
+ % Solve problem
+ res = prob.solve();
+
+
+
+CVXPY
+-----
+
+.. code:: python
+
+ from cvxpy import *
+ import numpy as np
+ import scipy as sp
+ from scipy import sparse
+
+ # Generate problem data
+ sp.random.seed(1)
+ m = 30
+ n = 20
+ A = sparse.random(m, n, density=0.7, format='csc')
+ b = np.random.randn(m)
+
+ # Define problem
+ x = Variable(n)
+ objective = 0.5*sum_squares(A*x - b)
+ constraints = [x >= 0, x <= 1]
+
+ # Solve with OSQP
+ Problem(Minimize(objective), constraints).solve(solver=OSQP)
+
+
+
+YALMIP
+------
+
+.. code:: matlab
+
+ % Generate data
+ rng(1)
+ m = 30;
+ n = 20;
+ A = sprandn(m, n, 0.7);
+ b = randn(m, 1);
+
+ % Define problem
+ x = sdpvar(n, 1);
+ objective = 0.5*norm(A*x - b)^2;
+ constraints = [ 0 <= x <= 1];
+
+ % Solve with OSQP
+ options = sdpsettings('solver','osqp');
+ optimize(constraints, objective, options);
+
diff --git a/docs/examples/mpc.rst b/docs/examples/mpc.rst
new file mode 100644
index 0000000..f5da713
--- /dev/null
+++ b/docs/examples/mpc.rst
@@ -0,0 +1,489 @@
+Model predictive control (MPC)
+==============================
+
+We consider the problem of controlling a linear time-invariant dynamical system to some reference state :math:`x_r \in \mathbf{R}^{n_x}`.
+To achieve this we use *constrained linear-quadratic MPC*, which solves at each time step the following finite-horizon optimal control problem
+
+.. math::
+ \begin{array}{ll}
+ \mbox{minimize} & (x_N-x_r)^T Q_N (x_N-x_r) + \sum_{k=0}^{N-1} (x_k-x_r)^T Q (x_k-x_r) + u_k^T R u_k \\
+ \mbox{subject to} & x_{k+1} = A x_k + B u_k \\
+ & x_{\rm min} \le x_k \le x_{\rm max} \\
+ & u_{\rm min} \le u_k \le u_{\rm max} \\
+ & x_0 = \bar{x}
+ \end{array}
+
+The states :math:`x_k \in \mathbf{R}^{n_x}` and the inputs :math:`u_k \in \mathbf{R}^{n_u}` are constrained to be between some lower and upper bounds.
+The problem is solved repeatedly for varying initial state :math:`\bar{x} \in \mathbf{R}^{n_x}`.
+
+
+Python
+------
+
+.. code:: python
+
+ import osqp
+ import numpy as np
+ import scipy as sp
+ from scipy import sparse
+
+ # Discrete time model of a quadcopter
+ Ad = sparse.csc_matrix([
+ [1., 0., 0., 0., 0., 0., 0.1, 0., 0., 0., 0., 0. ],
+ [0., 1., 0., 0., 0., 0., 0., 0.1, 0., 0., 0., 0. ],
+ [0., 0., 1., 0., 0., 0., 0., 0., 0.1, 0., 0., 0. ],
+ [0.0488, 0., 0., 1., 0., 0., 0.0016, 0., 0., 0.0992, 0., 0. ],
+ [0., -0.0488, 0., 0., 1., 0., 0., -0.0016, 0., 0., 0.0992, 0. ],
+ [0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0.0992],
+ [0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0. ],
+ [0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0. ],
+ [0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0. ],
+ [0.9734, 0., 0., 0., 0., 0., 0.0488, 0., 0., 0.9846, 0., 0. ],
+ [0., -0.9734, 0., 0., 0., 0., 0., -0.0488, 0., 0., 0.9846, 0. ],
+ [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.9846]
+ ])
+ Bd = sparse.csc_matrix([
+ [0., -0.0726, 0., 0.0726],
+ [-0.0726, 0., 0.0726, 0. ],
+ [-0.0152, 0.0152, -0.0152, 0.0152],
+ [-0., -0.0006, -0., 0.0006],
+ [0.0006, 0., -0.0006, 0.0000],
+ [0.0106, 0.0106, 0.0106, 0.0106],
+ [0, -1.4512, 0., 1.4512],
+ [-1.4512, 0., 1.4512, 0. ],
+ [-0.3049, 0.3049, -0.3049, 0.3049],
+ [-0., -0.0236, 0., 0.0236],
+ [0.0236, 0., -0.0236, 0. ],
+ [0.2107, 0.2107, 0.2107, 0.2107]])
+ [nx, nu] = Bd.shape
+
+ # Constraints
+ u0 = 10.5916
+ umin = np.array([9.6, 9.6, 9.6, 9.6]) - u0
+ umax = np.array([13., 13., 13., 13.]) - u0
+ xmin = np.array([-np.pi/6,-np.pi/6,-np.inf,-np.inf,-np.inf,-1.,
+ -np.inf,-np.inf,-np.inf,-np.inf,-np.inf,-np.inf])
+ xmax = np.array([ np.pi/6, np.pi/6, np.inf, np.inf, np.inf, np.inf,
+ np.inf, np.inf, np.inf, np.inf, np.inf, np.inf])
+
+ # Objective function
+ Q = sparse.diags([0., 0., 10., 10., 10., 10., 0., 0., 0., 5., 5., 5.])
+ QN = Q
+ R = 0.1*sparse.eye(4)
+
+ # Initial and reference states
+ x0 = np.zeros(12)
+ xr = np.array([0.,0.,1.,0.,0.,0.,0.,0.,0.,0.,0.,0.])
+
+ # Prediction horizon
+ N = 10
+
+ # Cast MPC problem to a QP: x = (x(0),x(1),...,x(N),u(0),...,u(N-1))
+ # - quadratic objective
+ P = sparse.block_diag([sparse.kron(sparse.eye(N), Q), QN,
+ sparse.kron(sparse.eye(N), R)], format='csc')
+ # - linear objective
+ q = np.hstack([np.kron(np.ones(N), -Q.dot(xr)), -QN.dot(xr),
+ np.zeros(N*nu)])
+ # - linear dynamics
+ Ax = sparse.kron(sparse.eye(N+1),-sparse.eye(nx)) + sparse.kron(sparse.eye(N+1, k=-1), Ad)
+ Bu = sparse.kron(sparse.vstack([sparse.csc_matrix((1, N)), sparse.eye(N)]), Bd)
+ Aeq = sparse.hstack([Ax, Bu])
+ leq = np.hstack([-x0, np.zeros(N*nx)])
+ ueq = leq
+ # - input and state constraints
+ Aineq = sparse.eye((N+1)*nx + N*nu)
+ lineq = np.hstack([np.kron(np.ones(N+1), xmin), np.kron(np.ones(N), umin)])
+ uineq = np.hstack([np.kron(np.ones(N+1), xmax), np.kron(np.ones(N), umax)])
+ # - OSQP constraints
+ A = sparse.vstack([Aeq, Aineq], format='csc')
+ l = np.hstack([leq, lineq])
+ u = np.hstack([ueq, uineq])
+
+ # Create an OSQP object
+ prob = osqp.OSQP()
+
+ # Setup workspace
+ prob.setup(P, q, A, l, u, warm_start=True)
+
+ # Simulate in closed loop
+ nsim = 15
+ for i in range(nsim):
+ # Solve
+ res = prob.solve()
+
+ # Check solver status
+ if res.info.status != 'solved':
+ raise ValueError('OSQP did not solve the problem!')
+
+ # Apply first control input to the plant
+ ctrl = res.x[-N*nu:-(N-1)*nu]
+ x0 = Ad.dot(x0) + Bd.dot(ctrl)
+
+ # Update initial state
+ l[:nx] = -x0
+ u[:nx] = -x0
+ prob.update(l=l, u=u)
+
+
+
+Matlab
+------
+
+.. code:: matlab
+
+ % Discrete time model of a quadcopter
+ Ad = [1 0 0 0 0 0 0.1 0 0 0 0 0;
+ 0 1 0 0 0 0 0 0.1 0 0 0 0;
+ 0 0 1 0 0 0 0 0 0.1 0 0 0;
+ 0.0488 0 0 1 0 0 0.0016 0 0 0.0992 0 0;
+ 0 -0.0488 0 0 1 0 0 -0.0016 0 0 0.0992 0;
+ 0 0 0 0 0 1 0 0 0 0 0 0.0992;
+ 0 0 0 0 0 0 1 0 0 0 0 0;
+ 0 0 0 0 0 0 0 1 0 0 0 0;
+ 0 0 0 0 0 0 0 0 1 0 0 0;
+ 0.9734 0 0 0 0 0 0.0488 0 0 0.9846 0 0;
+ 0 -0.9734 0 0 0 0 0 -0.0488 0 0 0.9846 0;
+ 0 0 0 0 0 0 0 0 0 0 0 0.9846];
+ Bd = [0 -0.0726 0 0.0726;
+ -0.0726 0 0.0726 0;
+ -0.0152 0.0152 -0.0152 0.0152;
+ 0 -0.0006 -0.0000 0.0006;
+ 0.0006 0 -0.0006 0;
+ 0.0106 0.0106 0.0106 0.0106;
+ 0 -1.4512 0 1.4512;
+ -1.4512 0 1.4512 0;
+ -0.3049 0.3049 -0.3049 0.3049;
+ 0 -0.0236 0 0.0236;
+ 0.0236 0 -0.0236 0;
+ 0.2107 0.2107 0.2107 0.2107];
+ [nx, nu] = size(Bd);
+
+ % Constraints
+ u0 = 10.5916;
+ umin = [9.6; 9.6; 9.6; 9.6] - u0;
+ umax = [13; 13; 13; 13] - u0;
+ xmin = [-pi/6; -pi/6; -Inf; -Inf; -Inf; -1; -Inf(6,1)];
+ xmax = [ pi/6; pi/6; Inf; Inf; Inf; Inf; Inf(6,1)];
+
+ % Objective function
+ Q = diag([0 0 10 10 10 10 0 0 0 5 5 5]);
+ QN = Q;
+ R = 0.1*eye(4);
+
+ % Initial and reference states
+ x0 = zeros(12,1);
+ xr = [0; 0; 1; 0; 0; 0; 0; 0; 0; 0; 0; 0];
+
+ % Prediction horizon
+ N = 10;
+
+ % Cast MPC problem to a QP: x = (x(0),x(1),...,x(N),u(0),...,u(N-1))
+ % - quadratic objective
+ P = blkdiag( kron(speye(N), Q), QN, kron(speye(N), R) );
+ % - linear objective
+ q = [repmat(-Q*xr, N, 1); -QN*xr; zeros(N*nu, 1)];
+ % - linear dynamics
+ Ax = kron(speye(N+1), -speye(nx)) + kron(sparse(diag(ones(N, 1), -1)), Ad);
+ Bu = kron([sparse(1, N); speye(N)], Bd);
+ Aeq = [Ax, Bu];
+ leq = [-x0; zeros(N*nx, 1)];
+ ueq = leq;
+ % - input and state constraints
+ Aineq = speye((N+1)*nx + N*nu);
+ lineq = [repmat(xmin, N+1, 1); repmat(umin, N, 1)];
+ uineq = [repmat(xmax, N+1, 1); repmat(umax, N, 1)];
+ % - OSQP constraints
+ A = [Aeq; Aineq];
+ l = [leq; lineq];
+ u = [ueq; uineq];
+
+ % Create an OSQP object
+ prob = osqp;
+
+ % Setup workspace
+ prob.setup(P, q, A, l, u, 'warm_start', true);
+
+ % Simulate in closed loop
+ nsim = 15;
+ for i = 1 : nsim
+ % Solve
+ res = prob.solve();
+
+ % Check solver status
+ if ~strcmp(res.info.status, 'solved')
+ error('OSQP did not solve the problem!')
+ end
+
+ % Apply first control input to the plant
+ ctrl = res.x((N+1)*nx+1:(N+1)*nx+nu);
+ x0 = Ad*x0 + Bd*ctrl;
+
+ % Update initial state
+ l(1:nx) = -x0;
+ u(1:nx) = -x0;
+ prob.update('l', l, 'u', u);
+ end
+
+
+
+CVXPY
+-----
+
+.. code:: python
+
+ from cvxpy import *
+ import numpy as np
+ import scipy as sp
+ from scipy import sparse
+
+ # Discrete time model of a quadcopter
+ Ad = sparse.csc_matrix([
+ [1., 0., 0., 0., 0., 0., 0.1, 0., 0., 0., 0., 0. ],
+ [0., 1., 0., 0., 0., 0., 0., 0.1, 0., 0., 0., 0. ],
+ [0., 0., 1., 0., 0., 0., 0., 0., 0.1, 0., 0., 0. ],
+ [0.0488, 0., 0., 1., 0., 0., 0.0016, 0., 0., 0.0992, 0., 0. ],
+ [0., -0.0488, 0., 0., 1., 0., 0., -0.0016, 0., 0., 0.0992, 0. ],
+ [0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0.0992],
+ [0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0. ],
+ [0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0. ],
+ [0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0. ],
+ [0.9734, 0., 0., 0., 0., 0., 0.0488, 0., 0., 0.9846, 0., 0. ],
+ [0., -0.9734, 0., 0., 0., 0., 0., -0.0488, 0., 0., 0.9846, 0. ],
+ [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.9846]
+ ])
+ Bd = sparse.csc_matrix([
+ [0., -0.0726, 0., 0.0726],
+ [-0.0726, 0., 0.0726, 0. ],
+ [-0.0152, 0.0152, -0.0152, 0.0152],
+ [-0., -0.0006, -0., 0.0006],
+ [0.0006, 0., -0.0006, 0.0000],
+ [0.0106, 0.0106, 0.0106, 0.0106],
+ [0, -1.4512, 0., 1.4512],
+ [-1.4512, 0., 1.4512, 0. ],
+ [-0.3049, 0.3049, -0.3049, 0.3049],
+ [-0., -0.0236, 0., 0.0236],
+ [0.0236, 0., -0.0236, 0. ],
+ [0.2107, 0.2107, 0.2107, 0.2107]])
+ [nx, nu] = Bd.shape
+
+ # Constraints
+ u0 = 10.5916
+ umin = np.array([9.6, 9.6, 9.6, 9.6]) - u0
+ umax = np.array([13., 13., 13., 13.]) - u0
+ xmin = np.array([-np.pi/6,-np.pi/6,-np.inf,-np.inf,-np.inf,-1.,
+ -np.inf,-np.inf,-np.inf,-np.inf,-np.inf,-np.inf])
+ xmax = np.array([ np.pi/6, np.pi/6, np.inf, np.inf, np.inf, np.inf,
+ np.inf, np.inf, np.inf, np.inf, np.inf, np.inf])
+
+ # Objective function
+ Q = sparse.diags([0., 0., 10., 10., 10., 10., 0., 0., 0., 5., 5., 5.])
+ QN = Q
+ R = 0.1*sparse.eye(4)
+
+ # Initial and reference states
+ x0 = np.zeros(12)
+ xr = np.array([0.,0.,1.,0.,0.,0.,0.,0.,0.,0.,0.,0.])
+
+ # Prediction horizon
+ N = 10
+
+ # Define problem
+ u = Variable((nu, N))
+ x = Variable((nx, N+1))
+ x_init = Parameter(nx)
+ objective = 0
+ constraints = [x[:,0] == x_init]
+ for k in range(N):
+ objective += quad_form(x[:,k] - xr, Q) + quad_form(u[:,k], R)
+ constraints += [x[:,k+1] == Ad*x[:,k] + Bd*u[:,k]]
+ constraints += [xmin <= x[:,k], x[:,k] <= xmax]
+ constraints += [umin <= u[:,k], u[:,k] <= umax]
+ objective += quad_form(x[:,N] - xr, QN)
+ prob = Problem(Minimize(objective), constraints)
+
+ # Simulate in closed loop
+ nsim = 15
+ for i in range(nsim):
+ x_init.value = x0
+ prob.solve(solver=OSQP, warm_start=True)
+ x0 = Ad.dot(x0) + Bd.dot(u[:,0].value)
+
+
+
+YALMIP
+------
+
+.. code:: matlab
+
+ % Discrete time model of a quadcopter
+ Ad = [1 0 0 0 0 0 0.1 0 0 0 0 0;
+ 0 1 0 0 0 0 0 0.1 0 0 0 0;
+ 0 0 1 0 0 0 0 0 0.1 0 0 0;
+ 0.0488 0 0 1 0 0 0.0016 0 0 0.0992 0 0;
+ 0 -0.0488 0 0 1 0 0 -0.0016 0 0 0.0992 0;
+ 0 0 0 0 0 1 0 0 0 0 0 0.0992;
+ 0 0 0 0 0 0 1 0 0 0 0 0;
+ 0 0 0 0 0 0 0 1 0 0 0 0;
+ 0 0 0 0 0 0 0 0 1 0 0 0;
+ 0.9734 0 0 0 0 0 0.0488 0 0 0.9846 0 0;
+ 0 -0.9734 0 0 0 0 0 -0.0488 0 0 0.9846 0;
+ 0 0 0 0 0 0 0 0 0 0 0 0.9846];
+ Bd = [0 -0.0726 0 0.0726;
+ -0.0726 0 0.0726 0;
+ -0.0152 0.0152 -0.0152 0.0152;
+ 0 -0.0006 -0.0000 0.0006;
+ 0.0006 0 -0.0006 0;
+ 0.0106 0.0106 0.0106 0.0106;
+ 0 -1.4512 0 1.4512;
+ -1.4512 0 1.4512 0;
+ -0.3049 0.3049 -0.3049 0.3049;
+ 0 -0.0236 0 0.0236;
+ 0.0236 0 -0.0236 0;
+ 0.2107 0.2107 0.2107 0.2107];
+ [nx, nu] = size(Bd);
+
+ % Constraints
+ u0 = 10.5916;
+ umin = [9.6; 9.6; 9.6; 9.6] - u0;
+ umax = [13; 13; 13; 13] - u0;
+ xmin = [-pi/6; -pi/6; -Inf; -Inf; -Inf; -1; -Inf(6,1)];
+ xmax = [ pi/6; pi/6; Inf; Inf; Inf; Inf; Inf(6,1)];
+
+ % Objective function
+ Q = diag([0 0 10 10 10 10 0 0 0 5 5 5]);
+ QN = Q;
+ R = 0.1*eye(4);
+
+ % Initial and reference states
+ x0 = zeros(12,1);
+ xr = [0; 0; 1; 0; 0; 0; 0; 0; 0; 0; 0; 0];
+
+ % Prediction horizon
+ N = 10;
+
+ % Define problem
+ u = sdpvar(repmat(nu,1,N), repmat(1,1,N));
+ x = sdpvar(repmat(nx,1,N+1), repmat(1,1,N+1));
+ constraints = [xmin <= x{1} <= xmax];
+ objective = 0;
+ for k = 1 : N
+ objective = objective + (x{k}-xr)'*Q*(x{k}-xr) + u{k}'*R*u{k};
+ constraints = [constraints, x{k+1} == Ad*x{k} + Bd*u{k}];
+ constraints = [constraints, umin <= u{k}<= umax, xmin <= x{k+1} <= xmax];
+ end
+ objective = objective + (x{N+1}-xr)'*QN*(x{N+1}-xr);
+ options = sdpsettings('solver', 'osqp');
+ controller = optimizer(constraints, objective, options, x{1}, [u{:}]);
+
+ % Simulate in closed loop
+ nsim = 15;
+ for i = 1 : nsim
+ U = controller{x0};
+ x0 = Ad*x0 + Bd*U(:,1);
+ end
+
+
+
+Julia
+------
+
+.. code:: julia
+
+ # Add packages - uncomment for first-time setup
+ # using Pkg; Pkg.add(["SparseArrays", "OSQP"])
+
+ using SparseArrays, OSQP
+
+ # Utility function
+ speye(N) = spdiagm(ones(N))
+
+ # Discrete time model of a quadcopter
+ Ad = [1 0 0 0 0 0 0.1 0 0 0 0 0;
+ 0 1 0 0 0 0 0 0.1 0 0 0 0;
+ 0 0 1 0 0 0 0 0 0.1 0 0 0;
+ 0.0488 0 0 1 0 0 0.0016 0 0 0.0992 0 0;
+ 0 -0.0488 0 0 1 0 0 -0.0016 0 0 0.0992 0;
+ 0 0 0 0 0 1 0 0 0 0 0 0.0992;
+ 0 0 0 0 0 0 1 0 0 0 0 0;
+ 0 0 0 0 0 0 0 1 0 0 0 0;
+ 0 0 0 0 0 0 0 0 1 0 0 0;
+ 0.9734 0 0 0 0 0 0.0488 0 0 0.9846 0 0;
+ 0 -0.9734 0 0 0 0 0 -0.0488 0 0 0.9846 0;
+ 0 0 0 0 0 0 0 0 0 0 0 0.9846] |> sparse
+ Bd = [0 -0.0726 0 0.0726;
+ -0.0726 0 0.0726 0;
+ -0.0152 0.0152 -0.0152 0.0152;
+ 0 -0.0006 -0.0000 0.0006;
+ 0.0006 0 -0.0006 0;
+ 0.0106 0.0106 0.0106 0.0106;
+ 0 -1.4512 0 1.4512;
+ -1.4512 0 1.4512 0;
+ -0.3049 0.3049 -0.3049 0.3049;
+ 0 -0.0236 0 0.0236;
+ 0.0236 0 -0.0236 0;
+ 0.2107 0.2107 0.2107 0.2107] |> sparse
+ (nx, nu) = size(Bd)
+
+ # Constraints
+ u0 = 10.5916
+ umin = [9.6, 9.6, 9.6, 9.6] .- u0
+ umax = [13, 13, 13, 13] .- u0
+ xmin = [[-pi/6, -pi/6, -Inf, -Inf, -Inf, -1]; -Inf .* ones(6)]
+ xmax = [[pi/6, pi/6, Inf, Inf, Inf, Inf]; Inf .* ones(6)]
+
+ # Objective function
+ Q = spdiagm([0, 0, 10, 10, 10, 10, 0, 0, 0, 5, 5, 5])
+ QN = Q
+ R = 0.1 * speye(nu)
+
+ # Initial and reference states
+ x0 = zeros(12)
+ xr = [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
+
+ # Prediction horizon
+ N = 10
+
+ # Cast MPC problem to a QP: x = (x(0),x(1),...,x(N),u(0),...,u(N-1))
+ # - quadratic objective
+ P = blockdiag(kron(speye(N), Q), QN, kron(speye(N), R))
+ # - linear objective
+ q = [repeat(-Q * xr, N); -QN * xr; zeros(N*nu)]
+ # - linear dynamics
+ Ax = kron(speye(N + 1), -speye(nx)) + kron(spdiagm(-1 => ones(N)), Ad)
+ Bu = kron([spzeros(1, N); speye(N)], Bd)
+ Aeq = [Ax Bu]
+ leq = [-x0; zeros(N * nx)]
+ ueq = leq
+ # - input and state constraints
+ Aineq = speye((N + 1) * nx + N * nu)
+ lineq = [repeat(xmin, N + 1); repeat(umin, N)]
+ uineq = [repeat(xmax, N + 1); repeat(umax, N)]
+ # - OSQP constraints
+ A, l, u = [Aeq; Aineq], [leq; lineq], [ueq; uineq]
+
+ # Create an OSQP model
+ m = OSQP.Model()
+
+ # Setup workspace
+ OSQP.setup!(m; P=P, q=q, A=A, l=l, u=u, warm_start=true)
+
+ # Simulate in closed loop
+ nsim = 15;
+ @time for _ in 1 : nsim
+ # Solve
+ res = OSQP.solve!(m)
+
+ # Check solver status
+ if res.info.status != :Solved
+ error("OSQP did not solve the problem!")
+ end
+
+ # Apply first control input to the plant
+ ctrl = res.x[(N+1)*nx+1:(N+1)*nx+nu]
+ global x0 = Ad * x0 + Bd * ctrl
+
+ # Update initial state
+ l[1:nx], u[1:nx] = -x0, -x0
+ OSQP.update!(m; l=l, u=u)
+ end
diff --git a/docs/examples/portfolio.rst b/docs/examples/portfolio.rst
new file mode 100644
index 0000000..60649b6
--- /dev/null
+++ b/docs/examples/portfolio.rst
@@ -0,0 +1,165 @@
+Portfolio optimization
+======================
+
+
+Portfolio optimization seeks to allocate assets in a way that maximizes the risk adjusted return,
+
+
+.. math::
+ \begin{array}{ll}
+ \mbox{maximize} & \mu^T x - \gamma \left( x^T \Sigma x \right) \\
+ \mbox{subject to} & \boldsymbol{1}^T x = 1 \\
+ & x \ge 0
+ \end{array}
+
+
+where :math:`x \in \mathbf{R}^{n}` represents the portfolio, :math:`\mu \in \mathbf{R}^{n}` the vector of expected returns, :math:`\gamma > 0` the risk aversion parameter, and :math:`\Sigma \in \mathbf{S}^{n}_{+}` the risk model covariance matrix.
+The risk model is usually assumed to be the sum of a diagonal and a rank :math:`k < n` matrix,
+
+
+.. math::
+ \Sigma = F F^T + D,
+
+
+where :math:`F \in \mathbf{R}^{n \times k}` is the factor loading matrix and :math:`D \in \mathbf{S}^{n}_{+}` is a diagonal matrix describing the asset-specific risk.
+The resulting problem has the following equivalent form,
+
+.. math::
+ \begin{array}{ll}
+ \mbox{minimize} & \frac{1}{2} x^T D x + \frac{1}{2} y^T y - \frac{1}{2\gamma}\mu^T x \\
+ \mbox{subject to} & y = F^T x \\
+ & \boldsymbol{1}^T x = 1 \\
+ & x \ge 0
+ \end{array}
+
+
+
+Python
+------
+
+.. code:: python
+
+ import osqp
+ import numpy as np
+ import scipy as sp
+ from scipy import sparse
+
+ # Generate problem data
+ sp.random.seed(1)
+ n = 100
+ k = 10
+ F = sparse.random(n, k, density=0.7, format='csc')
+ D = sparse.diags(np.random.rand(n) * np.sqrt(k), format='csc')
+ mu = np.random.randn(n)
+ gamma = 1
+
+ # OSQP data
+ P = sparse.block_diag([D, sparse.eye(k)], format='csc')
+ q = np.hstack([-mu / (2*gamma), np.zeros(k)])
+ A = sparse.vstack([
+ sparse.hstack([F.T, -sparse.eye(k)]),
+ sparse.hstack([sparse.csc_matrix(np.ones((1, n))), sparse.csc_matrix((1, k))]),
+ sparse.hstack((sparse.eye(n), sparse.csc_matrix((n, k))))
+ ], format='csc')
+ l = np.hstack([np.zeros(k), 1., np.zeros(n)])
+ u = np.hstack([np.zeros(k), 1., np.ones(n)])
+
+ # Create an OSQP object
+ prob = osqp.OSQP()
+
+ # Setup workspace
+ prob.setup(P, q, A, l, u)
+
+ # Solve problem
+ res = prob.solve()
+
+
+
+Matlab
+------
+
+.. code:: matlab
+
+ % Generate problem data
+ rng(1)
+ n = 100;
+ k = 10;
+ F = sprandn(n, k, 0.7);
+ D = sparse(diag( sqrt(k)*rand(n,1) ));
+ mu = randn(n, 1);
+ gamma = 1;
+
+ % OSQP data
+ P = blkdiag(D, speye(k));
+ q = [-mu/(2*gamma); zeros(k, 1)];
+ A = [F', -speye(k);
+ ones(1, n), zeros(1, k);
+ speye(n), sparse(n, k)];
+ l = [zeros(k, 1); 1; zeros(n, 1)];
+ u = [zeros(k, 1); 1; ones(n, 1)];
+
+ % Create an OSQP object
+ prob = osqp;
+
+ % Setup workspace
+ prob.setup(P, q, A, l, u);
+
+ % Solve problem
+ res = prob.solve();
+
+
+
+CVXPY
+-----
+
+.. code:: python
+
+ from cvxpy import *
+ import numpy as np
+ import scipy as sp
+ from scipy import sparse
+
+ # Generate problem data
+ sp.random.seed(1)
+ n = 100
+ k = 10
+ F = sparse.random(n, k, density=0.7, format='csc')
+ D = sparse.diags(np.random.rand(n) * np.sqrt(k), format='csc')
+ mu = np.random.randn(n)
+ gamma = 1
+ Sigma = F*F.T + D
+
+ # Define problem
+ x = Variable(n)
+ objective = mu.T*x - gamma*quad_form(x, Sigma)
+ constraints = [sum(x) == 1, x >= 0]
+
+ # Solve with OSQP
+ Problem(Maximize(objective), constraints).solve(solver=OSQP)
+
+
+
+YALMIP
+------
+
+.. code:: matlab
+
+ % Generate problem data
+ rng(1)
+ n = 100;
+ k = 10;
+ F = sprandn(n, k, 0.7);
+ D = sparse(diag( sqrt(k)*rand(n,1) ));
+ mu = randn(n, 1);
+ gamma = 1;
+ Sigma = F*F' + D;
+
+ % Define problem
+ x = sdpvar(n, 1);
+ objective = gamma * (x'*Sigma*x) - mu'*x;
+ constraints = [sum(x) == 1, x >= 0];
+
+ % Solve with OSQP
+ options = sdpsettings('solver', 'osqp');
+ optimize(constraints, objective, options);
+
diff --git a/docs/examples/setup-and-solve.rst b/docs/examples/setup-and-solve.rst
new file mode 100644
index 0000000..8e6ea72
--- /dev/null
+++ b/docs/examples/setup-and-solve.rst
@@ -0,0 +1,186 @@
+Setup and solve
+===============
+
+
+Consider the following QP
+
+
+.. math::
+ \begin{array}{ll}
+ \mbox{minimize} & \frac{1}{2} x^T \begin{bmatrix}4 & 1\\ 1 & 2 \end{bmatrix} x + \begin{bmatrix}1 \\ 1\end{bmatrix}^T x \\
+ \mbox{subject to} & \begin{bmatrix}1 \\ 0 \\ 0\end{bmatrix} \leq \begin{bmatrix} 1 & 1\\ 1 & 0\\ 0 & 1\end{bmatrix} x \leq \begin{bmatrix}1 \\ 0.7 \\ 0.7\end{bmatrix}
+ \end{array}
+
+
+
+We show below how to solve the problem in Python, Matlab, Julia and C.
+
+
+
+Python
+------
+
+.. code:: python
+
+ import osqp
+ import numpy as np
+ from scipy import sparse
+
+ # Define problem data
+ P = sparse.csc_matrix([[4, 1], [1, 2]])
+ q = np.array([1, 1])
+ A = sparse.csc_matrix([[1, 1], [1, 0], [0, 1]])
+ l = np.array([1, 0, 0])
+ u = np.array([1, 0.7, 0.7])
+
+ # Create an OSQP object
+ prob = osqp.OSQP()
+
+ # Setup workspace and change alpha parameter
+ prob.setup(P, q, A, l, u, alpha=1.0)
+
+ # Solve problem
+ res = prob.solve()
+
+
+
+Matlab
+------
+
+.. code:: matlab
+
+ % Define problem data
+ P = sparse([4, 1; 1, 2]);
+ q = [1; 1];
+ A = sparse([1, 1; 1, 0; 0, 1]);
+ l = [1; 0; 0];
+ u = [1; 0.7; 0.7];
+
+ % Create an OSQP object
+ prob = osqp;
+
+ % Setup workspace and change alpha parameter
+ prob.setup(P, q, A, l, u, 'alpha', 1);
+
+ % Solve problem
+ res = prob.solve();
+
+
+
+Julia
+------
+
+.. code:: julia
+
+ using OSQP
+ using Compat.SparseArrays
+
+ # Define problem data
+ P = sparse([4. 1.; 1. 2.])
+ q = [1.; 1.]
+ A = sparse([1. 1.; 1. 0.; 0. 1.])
+ l = [1.; 0.; 0.]
+ u = [1.; 0.7; 0.7]
+
+ # Crate OSQP object
+ prob = OSQP.Model()
+
+ # Setup workspace and change alpha parameter
+ OSQP.setup!(prob; P=P, q=q, A=A, l=l, u=u, alpha=1)
+
+ # Solve problem
+ results = OSQP.solve!(prob)
+
+
+
+R
+-
+
+.. code:: r
+
+ library(osqp)
+ library(Matrix)
+
+ # Define problem data
+ P <- Matrix(c(4., 1.,
+ 1., 2.), 2, 2, sparse = TRUE)
+ q <- c(1., 1.)
+ A <- Matrix(c(1., 1., 0.,
+ 1., 0., 1.), 3, 2, sparse = TRUE)
+ l <- c(1., 0., 0.)
+ u <- c(1., 0.7, 0.7)
+
+ # Change alpha parameter and setup workspace
+ settings <- osqpSettings(alpha = 1.0)
+ model <- osqp(P, q, A, l, u, settings)
+
+ # Solve problem
+ res <- model$Solve()
+
+
+
+C
+-
+
+.. code:: c
+
+ #include "osqp.h"
+
+ int main(int argc, char **argv) {
+ // Load problem data
+ c_float P_x[3] = {4.0, 1.0, 2.0, };
+ c_int P_nnz = 3;
+ c_int P_i[3] = {0, 0, 1, };
+ c_int P_p[3] = {0, 1, 3, };
+ c_float q[2] = {1.0, 1.0, };
+ c_float A_x[4] = {1.0, 1.0, 1.0, 1.0, };
+ c_int A_nnz = 4;
+ c_int A_i[4] = {0, 1, 0, 2, };
+ c_int A_p[3] = {0, 2, 4, };
+ c_float l[3] = {1.0, 0.0, 0.0, };
+ c_float u[3] = {1.0, 0.7, 0.7, };
+ c_int n = 2;
+ c_int m = 3;
+
+ // Exitflag
+ c_int exitflag = 0;
+
+ // Workspace structures
+ OSQPWorkspace *work;
+ OSQPSettings *settings = (OSQPSettings *)c_malloc(sizeof(OSQPSettings));
+ OSQPData *data = (OSQPData *)c_malloc(sizeof(OSQPData));
+
+ // Populate data
+ if (data) {
+ data->n = n;
+ data->m = m;
+ data->P = csc_matrix(data->n, data->n, P_nnz, P_x, P_i, P_p);
+ data->q = q;
+ data->A = csc_matrix(data->m, data->n, A_nnz, A_x, A_i, A_p);
+ data->l = l;
+ data->u = u;
+ }
+
+ // Define solver settings as default
+ if (settings) {
+ osqp_set_default_settings(settings);
+ settings->alpha = 1.0; // Change alpha parameter
+ }
+
+ // Setup workspace
+ exitflag = osqp_setup(&work, data, settings);
+
+ // Solve Problem
+ osqp_solve(work);
+
+ // Cleanup
+ osqp_cleanup(work);
+ if (data) {
+ if (data->A) c_free(data->A);
+ if (data->P) c_free(data->P);
+ c_free(data);
+ }
+ if (settings) c_free(settings);
+
+ return exitflag;
+ };
diff --git a/docs/examples/svm.rst b/docs/examples/svm.rst
new file mode 100644
index 0000000..d9ecfb5
--- /dev/null
+++ b/docs/examples/svm.rst
@@ -0,0 +1,165 @@
+Support vector machine (SVM)
+============================
+
+*Support vector machine* seeks an affine function that approximately classifies the two sets of points.
+The problem can be stated as
+
+.. math::
+ \begin{array}{ll}
+ \mbox{minimize} & \frac{1}{2} x^T x + \gamma \sum_{i=1}^{m} \max(0, b_i a_i^T x + 1),
+ \end{array}
+
+where :math:`b_i \in \{ -1, +1 \}` is a set label, and :math:`a_i` is a vector of features for the :math:`i`-th point.
+The problem has the following equivalent form
+
+.. math::
+ \begin{array}{ll}
+ \mbox{minimize} & \frac{1}{2} x^T x + \gamma \boldsymbol{1}^T t \\
+ \mbox{subject to} & t \ge {\rm diag}(b) Ax + 1 \\
+ & t \ge 0,
+ \end{array}
+
+where :math:`{\rm diag}(b)` denotes the diagonal matrix with elements of :math:`b` on its diagonal.
+
+
+
+Python
+------
+
+.. code:: python
+
+ import osqp
+ import numpy as np
+ import scipy as sp
+ from scipy import sparse
+
+ # Generate problem data
+ sp.random.seed(1)
+ n = 10
+ m = 1000
+ N = int(m / 2)
+ gamma = 1.0
+ b = np.hstack([np.ones(N), -np.ones(N)])
+ A_upp = sparse.random(N, n, density=0.5)
+ A_low = sparse.random(N, n, density=0.5)
+ Ad = sparse.vstack([
+ A_upp / np.sqrt(n) + (A_upp != 0.).astype(float) / n,
+ A_low / np.sqrt(n) - (A_low != 0.).astype(float) / n
+ ], format='csc')
+
+ # OSQP data
+ Im = sparse.eye(m)
+ P = sparse.block_diag([sparse.eye(n), sparse.csc_matrix((m, m))], format='csc')
+ q = np.hstack([np.zeros(n), gamma*np.ones(m)])
+ A = sparse.vstack([
+ sparse.hstack([sparse.diags(b).dot(Ad), -Im]),
+ sparse.hstack([sparse.csc_matrix((m, n)), Im])
+ ], format='csc')
+ l = np.hstack([-np.inf*np.ones(m), np.zeros(m)])
+ u = np.hstack([-np.ones(m), np.inf*np.ones(m)])
+
+ # Create an OSQP object
+ prob = osqp.OSQP()
+
+ # Setup workspace
+ prob.setup(P, q, A, l, u)
+
+ # Solve problem
+ res = prob.solve()
+
+
+Matlab
+------
+
+.. code:: matlab
+
+ % Generate problem data
+ rng(1)
+ n = 10;
+ m = 1000;
+ N = ceil(m/2);
+ gamma = 1;
+ A_upp = sprandn(N, n, 0.5);
+ A_low = sprandn(N, n, 0.5);
+ Ad = [A_upp / sqrt(n) + (A_upp ~= 0) / n;
+ A_low / sqrt(n) - (A_low ~= 0) / n];
+ b = [ones(N, 1); -ones(N,1)];
+
+ % OSQP data
+ P = blkdiag(speye(n), sparse(m, m));
+ q = [zeros(n,1); gamma*ones(m,1)];
+ A = [diag(b)*Ad, -speye(m);
+ sparse(m, n), speye(m)];
+ l = [-inf*ones(m, 1); zeros(m, 1)];
+ u = [-ones(m, 1); inf*ones(m, 1)];
+
+ % Create an OSQP object
+ prob = osqp;
+
+ % Setup workspace
+ prob.setup(P, q, A, l, u);
+
+ % Solve problem
+ res = prob.solve();
+
+
+
+CVXPY
+-----
+
+.. code:: python
+
+ from cvxpy import *
+ import numpy as np
+ import scipy as sp
+ from scipy import sparse
+
+ # Generate problem data
+ sp.random.seed(1)
+ n = 10
+ m = 1000
+ N = int(m / 2)
+ gamma = 1.0
+ b = np.hstack([np.ones(N), -np.ones(N)])
+ A_upp = sparse.random(N, n, density=0.5)
+ A_low = sparse.random(N, n, density=0.5)
+ A = sparse.vstack([
+ A_upp / np.sqrt(n) + (A_upp != 0.).astype(float) / n,
+ A_low / np.sqrt(n) - (A_low != 0.).astype(float) / n
+ ], format='csc')
+
+ # Define problem
+ x = Variable(n)
+ objective = 0.5*sum_squares(x) + gamma*sum(pos(diag(b)*A*x + 1))
+
+ # Solve with OSQP
+ Problem(Minimize(objective)).solve(solver=OSQP)
+
+
+
+
+YALMIP
+------
+
+.. code:: matlab
+
+ % Generate problem data
+ rng(1)
+ n = 10;
+ m = 1000;
+ N = ceil(m/2);
+ gamma = 1;
+ A_upp = sprandn(N, n, 0.5);
+ A_low = sprandn(N, n, 0.5);
+ A = [A_upp / sqrt(n) + (A_upp ~= 0) / n;
+ A_low / sqrt(n) - (A_low ~= 0) / n];
+ b = [ones(N, 1); -ones(N,1)];
+
+ % Define problem
+ x = sdpvar(n, 1);
+ objective = 0.5*norm(x)^2 + gamma*sum(max(diag(b)*A*x + 1, 0));
+
+ % Solve with OSQP
+ options = sdpsettings('solver','osqp');
+ optimize([],objective,options);
+
diff --git a/docs/examples/update-matrices.rst b/docs/examples/update-matrices.rst
new file mode 100644
index 0000000..b96e304
--- /dev/null
+++ b/docs/examples/update-matrices.rst
@@ -0,0 +1,242 @@
+Update matrices
+===============
+
+
+Consider the following QP
+
+
+.. math::
+ \begin{array}{ll}
+ \mbox{minimize} & \frac{1}{2} x^T \begin{bmatrix}4 & 1\\ 1 & 2 \end{bmatrix} x + \begin{bmatrix}1 \\ 1\end{bmatrix}^T x \\
+ \mbox{subject to} & \begin{bmatrix}1 \\ 0 \\ 0\end{bmatrix} \leq \begin{bmatrix} 1 & 1\\ 1 & 0\\ 0 & 1\end{bmatrix} x \leq \begin{bmatrix}1 \\ 0.7 \\ 0.7\end{bmatrix}
+ \end{array}
+
+
+
+We show below how to setup and solve the problem.
+Then we update the matrices :math:`P` and :math:`A` and solve the updated problem
+
+
+.. math::
+ \begin{array}{ll}
+ \mbox{minimize} & \frac{1}{2} x^T \begin{bmatrix}5 & 1.5\\ 1.5 & 1 \end{bmatrix} x + \begin{bmatrix}1 \\ 1\end{bmatrix}^T x \\
+ \mbox{subject to} & \begin{bmatrix}1 \\ 0 \\ 0\end{bmatrix} \leq \begin{bmatrix} 1.2 & 1.1\\ 1.5 & 0\\ 0 & 0.8\end{bmatrix} x \leq \begin{bmatrix}1 \\ 0.7 \\ 0.7\end{bmatrix}
+ \end{array}
+
+
+
+Python
+------
+
+.. code:: python
+
+ import osqp
+ import numpy as np
+ from scipy import sparse
+
+ # Define problem data
+ P = sparse.csc_matrix([[4, 1], [1, 2]])
+ q = np.array([1, 1])
+ A = sparse.csc_matrix([[1, 1], [1, 0], [0, 1]])
+ l = np.array([1, 0, 0])
+ u = np.array([1, 0.7, 0.7])
+
+ # Create an OSQP object
+ prob = osqp.OSQP()
+
+ # Setup workspace
+ prob.setup(P, q, A, l, u)
+
+ # Solve problem
+ res = prob.solve()
+
+ # Update problem
+ # NB: Update only upper triangular part of P
+ P_new = sparse.csc_matrix([[5, 1.5], [1.5, 1]])
+ A_new = sparse.csc_matrix([[1.2, 1.1], [1.5, 0], [0, 0.8]])
+ prob.update(Px=sparse.triu(P_new).data, Ax=A_new.data)
+
+ # Solve updated problem
+ res = prob.solve()
+
+
+
+Matlab
+------
+
+.. code:: matlab
+
+ % Define problem data
+ P = sparse([4, 1; 1, 2]);
+ q = [1; 1];
+ A = sparse([1, 1; 1, 0; 0, 1]);
+ l = [1; 0; 0];
+ u = [1; 0.7; 0.7];
+
+ % Create an OSQP object
+ prob = osqp;
+
+ % Setup workspace
+ prob.setup(P, q, A, l, u);
+
+ % Solve problem
+ res = prob.solve();
+
+ % Update problem
+ % NB: Update only upper triangular part of P
+ P_new = sparse([5, 1.5; 1.5, 1]);
+ A_new = sparse([1.2, 1.1; 1.5, 0; 0, 0.8]);
+ prob.update('Px', nonzeros(triu(P_new)), 'Ax', nonzeros(A_new));
+
+ % Solve updated problem
+ res = prob.solve();
+
+
+
+Julia
+------
+
+.. code:: julia
+
+ using OSQP
+ using Compat.SparseArrays, Compat.LinearAlgebra
+
+ # Define problem data
+ P = sparse([4. 1.; 1. 2.])
+ q = [1.; 1.]
+ A = sparse([1. 1.; 1. 0.; 0. 1.])
+ l = [1.; 0.; 0.]
+ u = [1.; 0.7; 0.7]
+
+ # Crate OSQP object
+ prob = OSQP.Model()
+
+ # Setup workspace
+ OSQP.setup!(prob; P=P, q=q, A=A, l=l, u=u)
+
+ # Solve problem
+ results = OSQP.solve!(prob)
+
+ # Update problem
+ # NB: Update only upper triangular part of P
+ P_new = sparse([5. 1.5; 1.5 1.])
+ A_new = sparse([1.2 1.1; 1.5 0.; 0. 0.8])
+ OSQP.update!(prob, Px=triu(P_new).nzval, Ax=A_new.nzval)
+
+ # Solve updated problem
+ results = OSQP.solve!(prob)
+
+
+
+R
+-
+
+.. code:: r
+
+ library(osqp)
+ library(Matrix)
+
+ # Define problem data
+ P <- Matrix(c(4., 1.,
+ 1., 2.), 2, 2, sparse = TRUE)
+ q <- c(1., 1.)
+ A <- Matrix(c(1., 1., 0.,
+ 1., 0., 1.), 3, 2, sparse = TRUE)
+ l <- c(1., 0., 0.)
+ u <- c(1., 0.7, 0.7)
+
+ # Setup workspace
+ model <- osqp(P, q, A, l, u)
+
+ # Solve problem
+ res <- model$Solve()
+
+ # Update problem
+ # NB: Update only upper triangular part of P
+ P_new <- Matrix(c(5., 1.5,
+ 1.5, 1.), 2, 2, sparse = TRUE)
+ A_new <- Matrix(c(1.2, 1.5, 0.,
+ 1.1, 0., 0.8), 3, 2, sparse = TRUE)
+ model$Update(Px = P_new@x, Ax = A_new@x)
+
+ # Solve updated problem
+ res <- model$Solve()
+
+
+
+C
+-
+
+.. code:: c
+
+ #include "osqp.h"
+
+ int main(int argc, char **argv) {
+ // Load problem data
+ c_float P_x[3] = {4.0, 1.0, 2.0, };
+ c_float P_x_new[3] = {5.0, 1.5, 1.0, };
+ c_int P_nnz = 3;
+ c_int P_i[3] = {0, 0, 1, };
+ c_int P_p[3] = {0, 1, 3, };
+ c_float q[2] = {1.0, 1.0, };
+ c_float q_new[2] = {2.0, 3.0, };
+ c_float A_x[4] = {1.0, 1.0, 1.0, 1.0, };
+ c_float A_x_new[4] = {1.2, 1.5, 1.1, 0.8, };
+ c_int A_nnz = 4;
+ c_int A_i[4] = {0, 1, 0, 2, };
+ c_int A_p[3] = {0, 2, 4, };
+ c_float l[3] = {1.0, 0.0, 0.0, };
+ c_float l_new[3] = {2.0, -1.0, -1.0, };
+ c_float u[3] = {1.0, 0.7, 0.7, };
+ c_float u_new[3] = {2.0, 2.5, 2.5, };
+ c_int n = 2;
+ c_int m = 3;
+
+ // Exitflag
+ c_int exitflag = 0;
+
+ // Workspace structures
+ OSQPWorkspace *work;
+ OSQPSettings *settings = (OSQPSettings *)c_malloc(sizeof(OSQPSettings));
+ OSQPData *data = (OSQPData *)c_malloc(sizeof(OSQPData));
+
+ // Populate data
+ if (data) {
+ data = (OSQPData *)c_malloc(sizeof(OSQPData));
+ data->n = n;
+ data->m = m;
+ data->P = csc_matrix(data->n, data->n, P_nnz, P_x, P_i, P_p);
+ data->q = q;
+ data->A = csc_matrix(data->m, data->n, A_nnz, A_x, A_i, A_p);
+ data->l = l;
+ data->u = u;
+ }
+
+ // Define Solver settings as default
+ if (settings) osqp_set_default_settings(settings);
+
+ // Setup workspace
+ exitflag = osqp_setup(&work, data, settings);
+
+ // Solve problem
+ osqp_solve(work);
+
+ // Update problem
+ // NB: Update only upper triangular part of P
+ osqp_update_P(work, P_x_new, OSQP_NULL, 3);
+ osqp_update_A(work, A_x_new, OSQP_NULL, 4);
+
+ // Solve updated problem
+ osqp_solve(work);
+
+ // Cleanup
+ osqp_cleanup(work);
+ if (data) {
+ if (data->A) c_free(data->A);
+ if (data->P) c_free(data->P);
+ c_free(data);
+ }
+ if (settings) c_free(settings);
+
+ return exitflag;
+ };
diff --git a/docs/examples/update-vectors.rst b/docs/examples/update-vectors.rst
new file mode 100644
index 0000000..2b7a8ae
--- /dev/null
+++ b/docs/examples/update-vectors.rst
@@ -0,0 +1,236 @@
+Update vectors
+==============
+
+
+Consider the following QP
+
+
+.. math::
+ \begin{array}{ll}
+ \mbox{minimize} & \frac{1}{2} x^T \begin{bmatrix}4 & 1\\ 1 & 2 \end{bmatrix} x + \begin{bmatrix}1 \\ 1\end{bmatrix}^T x \\
+ \mbox{subject to} & \begin{bmatrix}1 \\ 0 \\ 0\end{bmatrix} \leq \begin{bmatrix} 1 & 1\\ 1 & 0\\ 0 & 1\end{bmatrix} x \leq \begin{bmatrix}1 \\ 0.7 \\ 0.7\end{bmatrix}
+ \end{array}
+
+
+
+We show below how to setup and solve the problem.
+Then we update the vectors :math:`q`, :math:`l`, and :math:`u` and solve the updated problem
+
+
+.. math::
+ \begin{array}{ll}
+ \mbox{minimize} & \frac{1}{2} x^T \begin{bmatrix}4 & 1\\ 1 & 2 \end{bmatrix} x + \begin{bmatrix}2 \\ 3\end{bmatrix}^T x \\
+ \mbox{subject to} & \begin{bmatrix}2 \\ -1 \\ -1\end{bmatrix} \leq \begin{bmatrix} 1 & 1\\ 1 & 0\\ 0 & 1\end{bmatrix} x \leq \begin{bmatrix}2 \\ 2.5 \\ 2.5\end{bmatrix}
+ \end{array}
+
+
+
+Python
+------
+
+.. code:: python
+
+ import osqp
+ import numpy as np
+ from scipy import sparse
+
+ # Define problem data
+ P = sparse.csc_matrix([[4, 1], [1, 2]])
+ q = np.array([1, 1])
+ A = sparse.csc_matrix([[1, 1], [1, 0], [0, 1]])
+ l = np.array([1, 0, 0])
+ u = np.array([1, 0.7, 0.7])
+
+ # Create an OSQP object
+ prob = osqp.OSQP()
+
+ # Setup workspace
+ prob.setup(P, q, A, l, u)
+
+ # Solve problem
+ res = prob.solve()
+
+ # Update problem
+ q_new = np.array([2, 3])
+ l_new = np.array([2, -1, -1])
+ u_new = np.array([2, 2.5, 2.5])
+ prob.update(q=q_new, l=l_new, u=u_new)
+
+ # Solve updated problem
+ res = prob.solve()
+
+
+
+Matlab
+------
+
+.. code:: matlab
+
+ % Define problem data
+ P = sparse([4, 1; 1, 2]);
+ q = [1; 1];
+ A = sparse([1, 1; 1, 0; 0, 1]);
+ l = [1; 0; 0];
+ u = [1; 0.7; 0.7];
+
+ % Create an OSQP object
+ prob = osqp;
+
+ % Setup workspace
+ prob.setup(P, q, A, l, u);
+
+ % Solve problem
+ res = prob.solve();
+
+ % Update problem
+ q_new = [2; 3];
+ l_new = [2; -1; -1];
+ u_new = [2; 2.5; 2.5];
+ prob.update('q', q_new, 'l', l_new, 'u', u_new);
+
+ % Solve updated problem
+ res = prob.solve();
+
+
+
+Julia
+------
+
+.. code:: julia
+
+ using OSQP
+ using Compat.SparseArrays
+
+ # Define problem data
+ P = sparse([4. 1.; 1. 2.])
+ q = [1.; 1.]
+ A = sparse([1. 1.; 1. 0.; 0. 1.])
+ l = [1.; 0.; 0.]
+ u = [1.; 0.7; 0.7]
+
+ # Crate OSQP object
+ prob = OSQP.Model()
+
+ # Setup workspace
+ OSQP.setup!(prob; P=P, q=q, A=A, l=l, u=u)
+
+ # Solve problem
+ results = OSQP.solve!(prob)
+
+ # Update problem
+ q_new = [2.; 3.]
+ l_new = [2.; -1.; -1.]
+ u_new = [2.; 2.5; 2.5]
+ OSQP.update!(prob, q=q_new, l=l_new, u=u_new)
+
+ # Solve updated problem
+ results = OSQP.solve!(prob)
+
+
+
+R
+-
+
+.. code:: r
+
+ library(osqp)
+ library(Matrix)
+
+ # Define problem data
+ P <- Matrix(c(4., 1.,
+ 1., 2.), 2, 2, sparse = TRUE)
+ q <- c(1., 1.)
+ A <- Matrix(c(1., 1., 0.,
+ 1., 0., 1.), 3, 2, sparse = TRUE)
+ l <- c(1., 0., 0.)
+ u <- c(1., 0.7, 0.7)
+
+ # Setup workspace
+ model <- osqp(P, q, A, l, u)
+
+ # Solve problem
+ res <- model$Solve()
+
+ # Update problem
+ q_new <- c(2., 3.)
+ l_new <- c(2., -1., -1.)
+ u_new <- c(2., 2.5, 2.5)
+ model$Update(q = q_new, l = l_new, u = u_new)
+
+ # Solve updated problem
+ res <- model$Solve()
+
+
+
+C
+-
+
+.. code:: c
+
+ #include "osqp.h"
+
+ int main(int argc, char **argv) {
+ // Load problem data
+ c_float P_x[3] = {4.0, 1.0, 2.0, };
+ c_int P_nnz = 3;
+ c_int P_i[3] = {0, 0, 1, };
+ c_int P_p[3] = {0, 1, 3, };
+ c_float q[2] = {1.0, 1.0, };
+ c_float q_new[2] = {2.0, 3.0, };
+ c_float A_x[4] = {1.0, 1.0, 1.0, 1.0, };
+ c_int A_nnz = 4;
+ c_int A_i[4] = {0, 1, 0, 2, };
+ c_int A_p[3] = {0, 2, 4, };
+ c_float l[3] = {1.0, 0.0, 0.0, };
+ c_float l_new[3] = {2.0, -1.0, -1.0, };
+ c_float u[3] = {1.0, 0.7, 0.7, };
+ c_float u_new[3] = {2.0, 2.5, 2.5, };
+ c_int n = 2;
+ c_int m = 3;
+
+ // Exitflag
+ c_int exitflag = 0;
+
+ // Workspace structures
+ OSQPWorkspace *work;
+ OSQPSettings *settings = (OSQPSettings *)c_malloc(sizeof(OSQPSettings));
+ OSQPData *data = (OSQPData *)c_malloc(sizeof(OSQPData));
+
+ // Populate data
+ if (data) {
+ data->n = n;
+ data->m = m;
+ data->P = csc_matrix(data->n, data->n, P_nnz, P_x, P_i, P_p);
+ data->q = q;
+ data->A = csc_matrix(data->m, data->n, A_nnz, A_x, A_i, A_p);
+ data->l = l;
+ data->u = u;
+ }
+
+ // Define solver settings as default
+ if (settings) osqp_set_default_settings(settings);
+
+ // Setup workspace
+ exitflag = osqp_setup(&work, data, settings);
+
+ // Solve problem
+ osqp_solve(work);
+
+ // Update problem
+ osqp_update_lin_cost(work, q_new);
+ osqp_update_bounds(work, l_new, u_new);
+
+ // Solve updated problem
+ osqp_solve(work);
+
+ // Cleanup
+ osqp_cleanup(work);
+ if (data) {
+ if (data->A) c_free(data->A);
+ if (data->P) c_free(data->P);
+ c_free(data);
+ }
+ if (settings) c_free(settings);
+
+ return exitflag;
+ };
diff --git a/docs/get_started/C.rst b/docs/get_started/C.rst
new file mode 100644
index 0000000..18afa57
--- /dev/null
+++ b/docs/get_started/C.rst
@@ -0,0 +1,43 @@
+.. _install_osqp_libs:
+
+CC++
+=====
+
+Binaries
+--------
+
+Precompiled platform-dependent shared and static libraries are available on `GitHub <https://github.com/osqp/osqp/releases>`_.
+We here assume that the user uncompressed each archive to :code:`OSQP_FOLDER`.
+
+Each archive contains static :code:`OSQP_FOLDER/lib/libosqp.a` and shared :code:`OSQP_FOLDER/lib/libosqp.ext` libraries to be used to interface OSQP to any C/C++ software.
+The extension :code:`.ext` is platform dependent and is :code:`.so` for Linux, :code:`.dylib` for Mac and :code:`.dll` for Windows.
+The required include files can be found in :code:`OSQP_FOLDER/include`.
+
+Simply compile with the linker option with :code:`-LOSQP_FOLDER/lib` and :code:`-losqp`.
+
+If you are interested in development builds, you can find them on `GitHub <https://github.com/osqp/osqp/releases>`__.
+
+Sources
+-------
+
+The OSQP libraries can also be compiled from sources. For more details see :ref:`build_from_sources`.
+
+
+Including OSQP in CMake projects
+--------------------------------
+If you compiled OSQP from sources and followed the CMake installation instructions in :ref:`install_the_binaries` section, you can include the package in another CMake project with the following lines depending on whether you need a shared or a static library
+
+.. code::
+
+ # Find OSQP library and headers
+ find_package(osqp REQUIRED)
+
+ # Link the OSQP shared library
+ target_link_libraries(yourTarget PRIVATE osqp::osqp)
+
+ # or...
+
+ # Link the OSQP static library
+ target_link_libraries(yourTarget PRIVATE osqp::osqpstatic)
+
+
diff --git a/docs/get_started/cutest.rst b/docs/get_started/cutest.rst
new file mode 100644
index 0000000..c3de773
--- /dev/null
+++ b/docs/get_started/cutest.rst
@@ -0,0 +1,12 @@
+CUTEst
+=======
+
+To be able to use OSQP and `CUTEst <https://github.com/ralna/CUTEst/wiki>`_ you need to
+
+* Install `CUTEst <https://github.com/ralna/CUTEst/wiki>`_
+* Compile :ref:`OSQP from sources <build_from_sources>`
+* Set the environment variable :code:`OSQP` to the main OSQP directory containing source code for which the compiled binary libraries lie in :code:`$OSQP/build/out`.
+
+For more details, see the `README.osqp <https://github.com/ralna/CUTEst/blob/master/src/osqp/README.osqp>`_ file in the CUTEst repository.
+
+
diff --git a/docs/get_started/index.rst b/docs/get_started/index.rst
new file mode 100644
index 0000000..266222a
--- /dev/null
+++ b/docs/get_started/index.rst
@@ -0,0 +1,17 @@
+Get started
+===============
+
+To get started simply choose your language interface and follow the easy installation instructions below:
+
+.. toctree::
+ :maxdepth: 1
+ :glob:
+
+ sources.rst
+ C.rst
+ python.rst
+ julia.rst
+ matlab.rst
+ r.rst
+ cutest.rst
+ linear_system_solvers.rst
diff --git a/docs/get_started/julia.rst b/docs/get_started/julia.rst
new file mode 100644
index 0000000..0acea0d
--- /dev/null
+++ b/docs/get_started/julia.rst
@@ -0,0 +1,12 @@
+Julia
+======
+
+Julia interface can be directly installed from Julia package manager by running
+
+.. code:: julia
+
+ ] add OSQP
+
+
+The interface code is available on `GitHub <https://github.com/osqp/OSQP.jl>`_.
+
diff --git a/docs/get_started/linear_system_solvers.rst b/docs/get_started/linear_system_solvers.rst
new file mode 100644
index 0000000..0cbb1c9
--- /dev/null
+++ b/docs/get_started/linear_system_solvers.rst
@@ -0,0 +1,72 @@
+.. _linear_system_solvers_installation :
+
+Linear System Solvers
+======================
+
+The linear system solver is a core part of the OSQP algorithm.
+Depending on the problem instance, different linear system solvers can greatly speedup or reduce the computation time of OSQP.
+To set the preferred linear system solver, see :ref:`linear_system_solvers_setting`.
+
+Dynamic shared library loading
+------------------------------
+OSQP dynamically loads the shared libraries related to the selected external solver. Thus, there is no need to link it at compile time.
+The only requirement is that the shared library related to the solver is in the library path of the operating system
+
++------------------+---------------------------+----------------+
+| Operating system | Path variable | Extension |
++==================+===========================+================+
+| Linux | :code:`LD_LIBRARY_PATH` | :code:`.so` |
++------------------+---------------------------+----------------+
+| Mac | :code:`DYLD_LIBRARY_PATH` | :code:`.dylib` |
++------------------+---------------------------+----------------+
+| Windows | :code:`PATH` | :code:`.dll` |
++------------------+---------------------------+----------------+
+
+
+
+
+
+QDLDL
+---------------
+OSQP comes with `QDLDL <https://github.com/osqp/qdldl>`_ internally installed.
+It does not require any external shared library.
+QDLDL is a sparse direct solver that works well for most small to medium sized problems.
+However, it becomes not really efficient for large scale problems since it is not multi-threaded.
+
+
+MKL Pardiso
+-----------
+`MKL Pardiso <https://software.intel.com/en-us/mkl-developer-reference-fortran-intel-mkl-pardiso-parallel-direct-sparse-solver-interface>`_ is an efficient multi-threaded linear system solver that works well for large scale problems part of the Intel Math Kernel Library.
+Intel offers `free lincenses <https://software.intel.com/en-us/articles/free-mkl>`_ for MKL for most non-commercial applications.
+
+Install with MKL
+^^^^^^^^^^^^^^^^
+We can install MKL Pardiso by using the standard `MKL installer <https://software.intel.com/en-us/mkl>`_.
+The main library to be loaded is called :code:`libmkl_rt`.
+To add it, together with its dependencies, to your path, just execute the automatic MKL script.
+
++------------------+------------------------------------------------+
+| Operating system | Script |
++==================+================================================+
+| Linux | :code:`source $MKLROOT/bin/mklvars.sh intel64` |
++------------------+------------------------------------------------+
+| Mac | :code:`source $MKLROOT/bin/mklvars.sh intel64` |
++------------------+------------------------------------------------+
+| Windows | :code:`%MKLROOT%\mklvars.bat intel64` |
++------------------+------------------------------------------------+
+
+where :code:`MKLROOT` is the MKL installation directory.
+
+Install with Anaconda
+^^^^^^^^^^^^^^^^^^^^^
+`Anaconda Python distribution <https://www.anaconda.com/download/>`_ comes with the intel MKL libraries preinstalled including MKL Pardiso.
+To use this version, the Anaconda libraries folders have to be in your system path.
+Anaconda environments should add them automatically so in most cases you do not have to do anything. If you get an error where OSQP cannot find MKL, you can add the right path by adding the output from the following command to your path variable:
+
+.. code::
+
+ echo "`ls -rd ${CONDA_ROOT}/pkgs/*/ | grep mkl-2 | head -n 1`lib:`ls -rd ${CONDA_ROOT}/pkgs/*/ | grep intel-openmp- | head -n 1`lib"
+
+
+where :code:`ANACONDA_ROOT` is the root of your anaconda installation.
+
diff --git a/docs/get_started/matlab.rst b/docs/get_started/matlab.rst
new file mode 100644
index 0000000..e8e58ea
--- /dev/null
+++ b/docs/get_started/matlab.rst
@@ -0,0 +1,60 @@
+Matlab
+======
+OSQP Matlab interface requires Matlab 2015b or newer.
+
+
+Binaries
+--------
+
+Precompiled platform-dependent Matlab binaries are available on `GitHub <https://github.com/osqp/osqp-matlab/releases>`_.
+
+To install the interface, just run the following commands:
+
+.. code:: matlab
+
+ websave('install_osqp.m','https://raw.githubusercontent.com/osqp/osqp-matlab/master/package/install_osqp.m');
+ install_osqp
+
+
+Sources
+-------
+
+You need to install the following (see :ref:`build_from_sources` for more details):
+
+- A supported 64bit `C/C++ compiler <https://www.mathworks.com/support/compilers.html>`_
+- `CMake <https://cmake.org/>`_
+
+
+
+After you install both, check that your compiler is selected by executing
+
+.. code:: matlab
+
+ mex -setup
+
+.. note::
+
+ **Windows**: If Matlab does not find TDM-GCC, you need to set the environment variable :code:`MW_MINGW64_LOC` as follows
+
+ .. code:: matlab
+
+ setenv('MW_MINGW64_LOC', 'C:\TDM-GCC-64')
+
+
+ where :code:`C:\TDM-GCC-64` is the installation folder for TDM-GCC.
+
+You can now build the interface by running inside Matlab
+
+.. code:: matlab
+
+ !git clone --recurse-submodules https://github.com/osqp/osqp-matlab
+ cd osqp-matlab
+ make_osqp
+
+
+Then you can add the interface to the search path by executing from the same directory
+
+.. code:: matlab
+
+ addpath(pwd)
+ savepath
diff --git a/docs/get_started/python.rst b/docs/get_started/python.rst
new file mode 100644
index 0000000..a29e0eb
--- /dev/null
+++ b/docs/get_started/python.rst
@@ -0,0 +1,44 @@
+Python
+======
+
+Python interface supports Python 2.7 and 3.5 or newer.
+
+Pip
+----
+
+.. code:: bash
+
+ pip install osqp
+
+
+Anaconda
+--------
+
+.. code:: bash
+
+ conda install -c conda-forge osqp
+
+
+Sources
+---------
+You need to install the following (see :ref:`build_from_sources` for more details):
+
+- `GCC compiler <https://gcc.gnu.org/>`_
+- `CMake <https://cmake.org/>`_
+
+.. note::
+
+ **Windows**: You need to install **also** the Visual Studio C++ compiler:
+
+ * Python 2: `Visual C++ 9.0 for Python (VC 9.0) <https://www.microsoft.com/en-us/download/details.aspx?id=44266>`_
+
+ * Python 3: `Build Tools for Visual Studio 2017 <https://visualstudio.microsoft.com/downloads/#build-tools-for-visual-studio-2017>`_
+
+
+Now you are ready to build OSQP python interface from sources. Run the following in your terminal
+
+.. code:: bash
+
+ git clone --recurse-submodules https://github.com/osqp/osqp-python
+ cd osqp-python
+ python setup.py install
diff --git a/docs/get_started/r.rst b/docs/get_started/r.rst
new file mode 100644
index 0000000..a8fb63f
--- /dev/null
+++ b/docs/get_started/r.rst
@@ -0,0 +1,40 @@
+R
+======
+
+Binaries
+--------
+
+A pre-compiled version of the OSQP R interface can be installed directly from within R. Note that this will install the OSQP interface from the current CRAN repository, which may not be the most up-to-date version:
+
+.. code:: r
+
+ install.packages("osqp")
+
+
+
+The pre-compiled binaries can also be downloaded `directly from the CRAN server
+<https://cran.r-project.org/web/packages/osqp/>`_.
+
+From Sources
+------------
+
+If you would like to use the most recent version of OSQP-R and have access to git on your machine along with a suitable compiler, then you can do the following from within a terminal:
+
+.. code:: r
+
+ git clone --recursive https://github.com/osqp/osqp-r.git
+ cd osqp-r
+ R CMD install .
+
+From Sources (within R)
+-----------------------
+
+If you would like to install the latest version directly from with R (e.g.\ because you do not have ``git`` installed) and have a suitable compiler, then you can do the following from within R:
+
+.. code:: r
+
+ install.packages("remotes")
+ remotes::install_github("r-lib/remotes#103")
+ remotes::install_git("git://github.com/OxfordControl/osqp-r",submodules = TRUE)
+
+Note that the second line above is necessary because the "remotes" package in R does not currently support recursive cloning of git submodules.
diff --git a/docs/get_started/sources.rst b/docs/get_started/sources.rst
new file mode 100644
index 0000000..760ae3b
--- /dev/null
+++ b/docs/get_started/sources.rst
@@ -0,0 +1,137 @@
+.. _build_from_sources:
+
+
+Build from sources
+==================
+
+Install GCC and CMake
+----------------------
+
+The main compilation directives are specified using
+
+- `GCC compiler <https://gcc.gnu.org/>`_ to build the binaries
+- `CMake <https://cmake.org/>`__ to create the Makefiles
+
+
+Linux
+^^^^^
+Both :code:`gcc` and :code:`cmake` commands are already installed by default.
+
+Mac OS
+^^^^^^
+
+Install Xcode and command line tools
+""""""""""""""""""""""""""""""""""""
+
+#. Install the latest release of `Xcode <https://developer.apple.com/download/>`_.
+
+#. Install the command line tools by executing from the terminal
+
+ .. code:: bash
+
+ xcode-select --install
+
+Install CMake via Homebrew
+"""""""""""""""""""""""""""
+
+#. Install `Homebrew <https://brew.sh/>`_ and update its packages to the latest version.
+
+#. Install cmake by executing
+
+ .. code:: bash
+
+ brew install cmake
+
+
+Windows
+^^^^^^^
+
+#. Install `TDM-GCC <http://tdm-gcc.tdragon.net/download>`_ 32bit or 64bit depending on your platform.
+
+#. Install the latest binaries of `CMake <https://cmake.org/download/#latest>`__.
+
+
+Build the binaries
+------------------
+
+Run the following commands from the terminal
+
+#. You first need to get the sources from one of these two options:
+
+ * Download the compressed source file from the latest OSQP release `at GitHub <https://github.com/osqp/osqp/releases>`_.
+
+ * Clone the repository
+
+ .. code:: bash
+
+ git clone --recursive https://github.com/osqp/osqp
+
+#. Create :code:`build` directory and change directory
+
+ .. code:: bash
+
+ cd osqp
+ mkdir build
+ cd build
+
+#. Create Makefiles
+
+ - In Linux and Mac OS run
+
+ .. code:: bash
+
+ cmake -G "Unix Makefiles" ..
+
+ - In Windows run
+
+ .. code:: bash
+
+ cmake -G "MinGW Makefiles" ..
+
+
+#. Compile OSQP
+
+ .. code:: bash
+
+ cmake --build .
+
+
+Thanks to CMake, it is possible to create projects for a wide variety of IDEs; see `here <https://cmake.org/cmake/help/latest/manual/cmake-generators.7.html>`_ for more details. For example, to create a project for Visual Studio 14 2015, it is just necessary to run
+
+.. code:: bash
+
+ cmake -G "Visual Studio 14 2015" ..
+
+
+The compilation will generate the demo :code:`osqp_demo` and the unittests :code:`osqp_tester` executables. In the case of :code:`Unix` or :code:`MinGW` :code:`Makefiles` option they are located in the :code:`build/out/` directory. Run them to check that the compilation was correct.
+
+
+Once the sources are built, the generated static :code:`build/out/libosqp.a` and shared :code:`build/out/libosqp.ext` libraries can be used to interface any C/C++ software to OSQP (see :ref:`install_osqp_libs` installation).
+
+.. _install_the_binaries:
+
+Install the binaries
+--------------------
+
+
+
+To install the generated libraries and headers to a system-wide location compatible with `GNU standards <http://www.gnu.org/prep/standards/html_node/Directory-Variables.html>`_ it is just necessary to run
+
+.. code:: bash
+
+ cmake --build . --target install
+
+This code installs the libraries in :code:`libdir` and the headers into :code:`includedir/osqp`. For mode details see the defaults folders on the `GNU standards <http://www.gnu.org/prep/standards/html_node/Directory-Variables.html>`_ website.
+To change the installation prefix, in the "Create Makefiles" step above, you need to specify the destination folder as :code:`cmake -DCMAKE_INSTALL_PREFIX:PATH=myfolder ..`.
+
+.. note:: This step requires write permissions in the destination
+ folders. You might be able to gain access using the
+ :code:`sudo` command.
+
+We provided also an uninstall routine to remove the copied files by running
+
+.. code:: bash
+
+ cmake --build . --target uninstall
+
+Note that this corresponds to running :code:`make install` and :code:`make uninstall` on unix machines.
diff --git a/docs/index.rst b/docs/index.rst
new file mode 100644
index 0000000..ce9bb01
--- /dev/null
+++ b/docs/index.rst
@@ -0,0 +1,110 @@
+OSQP solver documentation
+==========================
+**Join our** `forum <https://osqp.discourse.group/>`_ **for any
+questions related to the solver!**
+
+The OSQP (Operator Splitting Quadratic Program) solver is a numerical
+optimization package for solving convex quadratic programs in the form
+
+.. math::
+ \begin{array}{ll}
+ \mbox{minimize} & \frac{1}{2} x^T P x + q^T x \\
+ \mbox{subject to} & l \leq A x \leq u
+ \end{array}
+
+where :math:`x` is the optimization variable and
+:math:`P \in \mathbf{S}^{n}_{+}` a positive semidefinite matrix.
+
+**Code available on** `GitHub <https://github.com/osqp/osqp>`_.
+
+.. rubric:: Citing OSQP
+
+If you are using OSQP for your work, we encourage you to
+
+* :ref:`Cite the related papers <citing>`
+* Put a star on GitHub |github-star|
+
+
+.. |github-star| image:: https://img.shields.io/github/stars/osqp/osqp.svg?style=social&label=Star
+ :target: https://github.com/osqp/osqp
+
+
+**We are looking forward to hearing your success stories with OSQP!** Please `share them with us <bartolomeo.stellato@gmail.com>`_.
+
+.. rubric:: Features
+
+
+.. glossary::
+
+ Efficient
+ It uses a custom ADMM-based first-order method requiring only a single matrix factorization in the setup phase. All the other operations are extremely cheap. It also implements custom sparse linear algebra routines exploiting structures in the problem data.
+
+ Robust
+ The algorithm is absolutely division free after the setup and it requires no assumptions on problem data (the problem only needs to be convex). It just works!
+
+ Detects primal / dual infeasible problems
+ When the problem is primal or dual infeasible, OSQP detects it. It is the first available QP solver based on first-order methods able to do so.
+
+ Embeddable
+ It has an easy interface to generate customized embeddable C code with no memory manager required.
+
+ Library-free
+ It requires no external library to run.
+
+ Efficiently warm started
+ It can be easily warm-started and the matrix factorization can be cached to solve parametrized problems extremely efficiently.
+
+ Interfaces
+ It can be interfaced to C, C++, Fortran (soon!), Python, Julia and Matlab.
+
+
+
+.. rubric:: License
+
+OSQP is distributed under the `Apache 2.0 License <https://www.apache.org/licenses/LICENSE-2.0>`_
+
+
+
+.. rubric:: Credits
+
+The following people have been involved in the development of OSQP:
+
+* `Bartolomeo Stellato <https://stellato.io/>`_ (Princeton University): main development
+* `Goran Banjac <https://people.ee.ethz.ch/~gbanjac/>`_ (ETH Zürich): main development
+* `Nicholas Moehle <https://www.nicholasmoehle.com/>`_ (Stanford University): methods, maths, and code generation
+* `Paul Goulart <http://users.ox.ac.uk/~engs1373/>`_ (University of Oxford): methods, maths, and Matlab interface
+* `Alberto Bemporad <http://cse.lab.imtlucca.it/~bemporad/>`_ (IMT Lucca): methods and maths
+* `Stephen Boyd <https://web.stanford.edu/~boyd/>`_ (Stanford University): methods and maths
+* `Ian McInerney <mailto:i.mcinerney17@imperial.ac.uk>`_ (Imperial College London): code generation, software development
+* `Michel Schubiger <mailto:michel.schubiger@bluewin.ch>`_ (Schindler R&D): GPU implementation
+* `John Lygeros <https://control.ee.ethz.ch/people/profile.john-lygeros.html>`_ (ETH Zurich): methods and maths
+
+Interfaces development
+
+* `Nick Gould <http://www.numerical.rl.ac.uk/people/nimg/nimg.html>`_ (Rutherford Appleton Laboratory): Fortran and CUTEst interfaces
+* `Ed Barnard <eabarnard@gmail.com>`_ (University of Oxford): Rust interface
+
+
+.. rubric:: Bug reports and support
+
+Please report any issues via the `Github issue tracker <https://github.com/osqp/osqp/issues>`_. All types of issues are welcome including bug reports, documentation typos, feature requests and so on.
+
+
+.. rubric:: Numerical benchmarks
+
+Numerical benchmarks against other solvers are available `here <https://github.com/osqp/osqp_benchmarks>`_.
+
+
+.. toctree::
+ :hidden:
+ :maxdepth: 2
+ :caption: User Documentation
+
+ solver/index
+ get_started/index
+ interfaces/index
+ parsers/index
+ codegen/index
+ examples/index
+ contributing/index
+ citing/index
diff --git a/docs/interfaces/C.rst b/docs/interfaces/C.rst
new file mode 100644
index 0000000..ef574fe
--- /dev/null
+++ b/docs/interfaces/C.rst
@@ -0,0 +1,127 @@
+.. _c_interface:
+
+C
+=====
+
+
+
+
+.. _C_main_API:
+
+Main solver API
+---------------
+
+The main C API is imported from the header :code:`osqp.h` and provides the following functions
+
+
+.. doxygenfunction:: osqp_setup
+
+.. doxygenfunction:: osqp_solve
+
+.. doxygenfunction:: osqp_cleanup
+
+
+.. _C_sublevel_API:
+
+Sublevel API
+------------
+Sublevel C API is also imported from the header :code:`osqp.h` and provides the following functions
+
+Warm start
+^^^^^^^^^^
+OSQP automatically warm starts primal and dual variables from the previous QP solution. If you would like to warm start their values manually, you can use
+
+.. doxygenfunction:: osqp_warm_start
+
+.. doxygenfunction:: osqp_warm_start_x
+
+.. doxygenfunction:: osqp_warm_start_y
+
+
+.. _c_cpp_update_data :
+
+Update problem data
+^^^^^^^^^^^^^^^^^^^
+Problem data can be updated without executing the setup again using the following functions.
+
+.. doxygenfunction:: osqp_update_lin_cost
+
+.. doxygenfunction:: osqp_update_lower_bound
+
+.. doxygenfunction:: osqp_update_upper_bound
+
+.. doxygenfunction:: osqp_update_bounds
+
+.. doxygenfunction:: osqp_update_P
+
+.. doxygenfunction:: osqp_update_A
+
+.. doxygenfunction:: osqp_update_P_A
+
+
+
+.. _c_cpp_data_types :
+
+Data types
+----------
+
+The most basic used datatypes are
+
+* :code:`c_int`: can be :code:`long` or :code:`int` if the compiler flag :code:`DLONG` is set or not
+* :code:`c_float`: can be a :code:`float` or a :code:`double` if the compiler flag :code:`DFLOAT` is set or not.
+
+
+
+The relevant structures used in the API are
+
+Data
+^^^^
+
+.. doxygenstruct:: OSQPData
+ :members:
+
+The matrices are defined in `Compressed Sparse Column (CSC) format <https://people.sc.fsu.edu/~jburkardt/data/cc/cc.html>`_ using zero-based indexing.
+
+.. doxygenstruct:: csc
+ :members:
+
+Settings
+^^^^^^^^
+
+.. doxygenstruct:: OSQPSettings
+ :members:
+
+Solution
+^^^^^^^^
+
+.. doxygenstruct:: OSQPSolution
+ :members:
+
+Info
+^^^^^
+
+.. doxygenstruct:: OSQPInfo
+ :members:
+
+Workspace
+^^^^^^^^^
+
+.. doxygenstruct:: OSQPWorkspace
+ :members:
+
+
+Scaling
+^^^^^^^
+
+.. doxygenstruct:: OSQPScaling
+ :members:
+
+Polish
+^^^^^^
+.. doxygenstruct:: OSQPPolish
+ :members:
+
+
+
+.. TODO: Add sublevel API
+.. TODO: Add using your own linear system solver
diff --git a/docs/interfaces/cutest.rst b/docs/interfaces/cutest.rst
new file mode 100644
index 0000000..3b6ce63
--- /dev/null
+++ b/docs/interfaces/cutest.rst
@@ -0,0 +1,22 @@
+.. _cutest_interface:
+
+CUTEst
+======
+
+The command to solve a problem in SIF format contained in the file
+probname.SIF is
+
+.. code::
+
+ runcutest -p osqp -D probname.SIF
+
+See the man page for runcutest for more details or other options.
+
+The default OSQP settings used in CUTEst appear in the `OSQP.SPC <https://github.com/ralna/CUTEst/blob/master/src/osqp/OSQP.SPC>`_ file.
+Optionally, new parameter values to overwrite the default values can be stored in a file :code:`OSQP.SPC` in the directory where the :code:`runcutest` command is executed.
+The format of the file :code:`OSQP.SPC` is the parameter name starting in the first column followed by one or more spaces and then the parameter value.
+The parameter names are case sensitive.
+If the parameter value is :code:`true` or :code:`false`, then use :code:`1` for true and :code:`0` for :code:`false`.
+
+For more details see the `README.osqp <https://github.com/ralna/CUTEst/blob/master/src/osqp/README.osqp>`_ file in the CUTEst repository.
+
diff --git a/docs/interfaces/eigen_google.rst b/docs/interfaces/eigen_google.rst
new file mode 100644
index 0000000..73f466d
--- /dev/null
+++ b/docs/interfaces/eigen_google.rst
@@ -0,0 +1,6 @@
+.. _eigen_google:
+
+C++ Eigen interface (osqp-cpp)
+================================
+
+The Eigen interface developed at Google is documented `here <https://github.com/google/osqp-cpp>`_.
diff --git a/docs/interfaces/eigen_robotology.rst b/docs/interfaces/eigen_robotology.rst
new file mode 100644
index 0000000..876f201
--- /dev/null
+++ b/docs/interfaces/eigen_robotology.rst
@@ -0,0 +1,6 @@
+.. _eigen_robotology:
+
+C++ Eigen interface (osqp-eigen)
+================================
+
+The Eigen interface by Robotology group is documented `here <https://robotology.github.io/osqp-eigen/doxygen/doc/html/index.html>`_.
diff --git a/docs/interfaces/fortran.rst b/docs/interfaces/fortran.rst
new file mode 100644
index 0000000..7d2c465
--- /dev/null
+++ b/docs/interfaces/fortran.rst
@@ -0,0 +1,8 @@
+.. _fortran_interface:
+
+
+Fortran
+========
+
+The interface is still experimental.
+You can find a demo of how it works in the `osqp/osqp-fortran <https://github.com/osqp/osqp-fortran/blob/master/demo/osqp_demo_fortran.F90>`_ repository.
diff --git a/docs/interfaces/index.rst b/docs/interfaces/index.rst
new file mode 100644
index 0000000..800d422
--- /dev/null
+++ b/docs/interfaces/index.rst
@@ -0,0 +1,104 @@
+Interfaces
+============
+
+OSQP has several interfaces. The information about settings, status values and how to assign different linear system solvers appear in the following links
+
+* :ref:`Solver settings <solver_settings>`
+* :ref:`Linear system solvers <linear_system_solvers_setting>`
+* :ref:`Status values <status_values>`
+
+
+
+.. toctree::
+ :maxdepth: 1
+ :glob:
+ :hidden:
+
+ solver_settings.rst
+ linear_systems_solvers.rst
+ status_values.rst
+
+
+Official
+----------
+
++------------------------------------+----------------------------------------------------------+------------------------------------------------------------------------------------------+
+| Language | Maintainers | Repository |
++====================================+==========================================================+==========================================================================================+
+| :ref:`C <c_interface>` | | `Bartolomeo Stellato <bartolomeo.stellato@gmail.com>`_ | `github.com/osqp/osqp <https://github.com/osqp/osqp>`_ |
+| | | `Goran Banjac <gbanjac@control.ee.ethz.ch>`_ | |
+| | | `Paul Goulart <paul.goulart@eng.ox.ac.uk>`_ | |
++------------------------------------+----------------------------------------------------------+------------------------------------------------------------------------------------------+
+| :ref:`Python <python_interface>` | | `Bartolomeo Stellato <bartolomeo.stellato@gmail.com>`_ | `github.com/osqp/osqp-python <https://github.com/osqp/osqp-python>`_ |
+| | | `Goran Banjac <gbanjac@control.ee.ethz.ch>`_ | |
++------------------------------------+----------------------------------------------------------+------------------------------------------------------------------------------------------+
+| :ref:`Matlab <matlab_interface>` | | `Bartolomeo Stellato <bartolomeo.stellato@gmail.com>`_ | `github.com/osqp/osqp-matlab <https://github.com/osqp/osqp-matlab>`_ |
+| | | `Goran Banjac <gbanjac@control.ee.ethz.ch>`_ | |
+| | | `Paul Goulart <paul.goulart@eng.ox.ac.uk>`_ | |
++------------------------------------+----------------------------------------------------------+------------------------------------------------------------------------------------------+
+| :ref:`Julia <julia_interface>` | | `Twan Koolen <tkoolen@mit.edu>`_ | `github.com/osqp/OSQP.jl <https://github.com/osqp/OSQP.jl>`_ |
+| | | `Benoît Legat <benoit.legat@uclouvain.be>`_ | |
+| | | `Bartolomeo Stellato <bartolomeo.stellato@gmail.com>`_ | |
++------------------------------------+----------------------------------------------------------+------------------------------------------------------------------------------------------+
+| :ref:`R <rlang_interface>` | | `Bartolomeo Stellato <bartolomeo.stellato@gmail.com>`_ | `github.com/osqp/osqp-r <https://github.com/osqp/osqp-r>`_ |
+| | | `Paul Goulart <paul.goulart@eng.ox.ac.uk>`_ | |
++------------------------------------+----------------------------------------------------------+------------------------------------------------------------------------------------------+
+
+
+
+.. toctree::
+ :maxdepth: 1
+ :glob:
+ :hidden:
+
+ C.rst
+ python.rst
+ matlab.rst
+ julia.rst
+ rlang.rst
+
+
+
+
+
+
+
+
+
+Community Maintained
+--------------------
+
+
++------------------------------------------------+----------------------------------------------------------+------------------------------------------------------------------------------------------+
+| Language | Maintainers | Repository |
++================================================+==========================================================+==========================================================================================+
+| :ref:`C++/Eigen Google <eigen_google>` | | `Miles Lubin <miles.lubin@gmail.com>`_ | `github.com/google/osqp-cpp <https://github.com/google/osqp-cpp>`_ |
++------------------------------------------------+----------------------------------------------------------+------------------------------------------------------------------------------------------+
+| :ref:`C++/Eigen Robotology <eigen_robotology>` | | `Giulio Romualdi <giulio.romualdi@gmail.com>`_ | `github.com/robotology/osqp-eigen <https://github.com/robotology/osqp-eigen>`_ |
++------------------------------------------------+----------------------------------------------------------+------------------------------------------------------------------------------------------+
+| :ref:`Rust <rust_interface>` | | `Ed Barnard <eabarnard@gmail.com>`_ | `github.com/osqp/osqp.rs <https://github.com/osqp/osqp.rs>`_ |
++------------------------------------------------+----------------------------------------------------------+------------------------------------------------------------------------------------------+
+| :ref:`Ruby <ruby_interface>` | | `Andrew Kane <andrew@chartkick.com>`_ | `https://github.com/ankane/osqp <https://github.com/ankane/osqp>`_ |
++------------------------------------------------+----------------------------------------------------------+------------------------------------------------------------------------------------------+
+| :ref:`Fortran <fortran_interface>` | | `Nick Gould <nick.gould@stfc.ac.uk>`_ | `github.com/osqp/osqp-fortran <https://github.com/osqp/osqp-fortran>`_ |
+| | | `Bartolomeo Stellato <bartolomeo.stellato@gmail.com>`_ | |
+| | | `Paul Goulart <paul.goulart@eng.ox.ac.uk>`_ | |
++------------------------------------------------+----------------------------------------------------------+------------------------------------------------------------------------------------------+
+| :ref:`Cutest <cutest_interface>` | | `Nick Gould <nick.gould@stfc.ac.uk>`_ | `github.com/ralna/CUTEst <https://github.com/ralna/CUTEst/tree/master/src/osqp>`_ |
++------------------------------------------------+----------------------------------------------------------+------------------------------------------------------------------------------------------+
+
+
+
+.. toctree::
+ :maxdepth: 1
+ :glob:
+ :hidden:
+
+ eigen_google.rst
+ eigen_robotology.rst
+ rust.rst
+ ruby.rst
+ fortran.rst
+ cutest.rst
+
+
diff --git a/docs/interfaces/julia.rst b/docs/interfaces/julia.rst
new file mode 100644
index 0000000..37d08e1
--- /dev/null
+++ b/docs/interfaces/julia.rst
@@ -0,0 +1,167 @@
+.. _julia_interface:
+
+Julia
+======
+
+Load the module
+---------------
+The OSQP module can be load with
+
+.. code:: julia
+
+ using OSQP
+
+
+.. _julia_setup:
+
+Setup
+-----
+
+The solver is initialized by creating an OSQP Model
+
+.. code:: julia
+
+ m = OSQP.Model()
+
+The problem is specified in the setup phase by running
+
+.. code:: julia
+
+ OSQP.setup!(m; P=P, q=q, A=A, l=l, u=u, settings...)
+
+
+The arguments :code:`q`, :code:`l` and :code:`u` are :code:`Vector{Float64}`.
+The elements of :code:`l` and :code:`u` can be :math:`\pm \infty` ( using :code:`Inf`).
+
+The arguments :code:`P` and :code:`A` are sparse matrices of type :code:`SparseMatrixCSC`.
+Matrix :code:`P` can be either complete or just the upper triangular
+part. OSQP will make use of only the upper triangular part.
+If they are sparse matrices are in another format, the interface will attempt to convert them.
+There is no need to specify all the arguments.
+
+The argument :code:`settings` specifies the solver settings.
+Settings can also be passed as indipendent keyword arguments such as :code:`max_iter=1000`.
+The allowed parameters are defined in :ref:`solver_settings`.
+
+Solve
+-----
+
+The problem can be solved by
+
+.. code:: julia
+
+ results = OSQP.solve!(m)
+
+
+The output :code:`results` contains the primal solution :code:`x`, the dual solution :code:`y`, certificate of primal infeasibility :code:`prim_inf_cert`, certificate of dual infeasibility :code:`dual_inf_cert` and the :code:`info` object containing the solver statistics defined in the following table
+
+
++-----------------------+------------------------------------------------+
+| Member | Description |
++=======================+================================================+
+| :code:`iter` | Number of iterations |
++-----------------------+------------------------------------------------+
+| :code:`status` | Solver status |
++-----------------------+------------------------------------------------+
+| :code:`status_val` | Solver status value as in :ref:`status_values` |
++-----------------------+------------------------------------------------+
+| :code:`status_polish` | Polishing status |
++-----------------------+------------------------------------------------+
+| :code:`obj_val` | Objective value |
++-----------------------+------------------------------------------------+
+| :code:`pri_res` | Primal residual |
++-----------------------+------------------------------------------------+
+| :code:`dua_res` | Dual residual |
++-----------------------+------------------------------------------------+
+| :code:`setup_time` | Setup time |
++-----------------------+------------------------------------------------+
+| :code:`solve_time` | Solve time |
++-----------------------+------------------------------------------------+
+| :code:`update_time` | Update time |
++-----------------------+------------------------------------------------+
+| :code:`polish_time` | Polish time |
++-----------------------+------------------------------------------------+
+| :code:`run_time` | Total run time: setup/update + solve + polish |
++-----------------------+------------------------------------------------+
+| :code:`rho_estimate` | Optimal rho estimate |
++-----------------------+------------------------------------------------+
+| :code:`rho_updates` | Number of rho updates |
++-----------------------+------------------------------------------------+
+
+Note that if multiple solves are executed from single setup, then after the
+first one :code:`run_time` includes :code:`update_time` + :code:`solve_time`
++ :code:`polish_time`.
+
+
+Update
+------
+Part of problem data and settings can be updated without requiring a new problem setup.
+
+Update problem vectors
+^^^^^^^^^^^^^^^^^^^^^^
+Vectors :code:`q`, :code:`l` and :code:`u` can be updated with new values :code:`q_new`, :code:`l_new` and :code:`u_new` by just running
+
+.. code:: julia
+
+ OSQP.update!(m; q=q_new, l=l_new, u=u_new)
+
+
+The user does not have to specify all the keyword arguments.
+
+
+Update problem matrices
+^^^^^^^^^^^^^^^^^^^^^^^^
+Matrices :code:`A` and :code:`P` can be updated by changing the value of their elements but not their sparsity pattern. The interface is designed to mimic the :ref:`C/C++ counterpart <c_cpp_update_data>` with the Julia 1-based indexing. Note that the new values of :code:`P` represent only the upper triangular part while :code:`A` is always represented as a full matrix.
+
+You can update the values of all the elements of :code:`P` by executing
+
+.. code:: julia
+
+ OSQP.update!(m, Px=Px_new)
+
+
+If you want to update only some elements, you can pass
+
+.. code:: julia
+
+ OSQP.update!(m, Px=Px_new, Px_idx=Px_new_idx)
+
+where :code:`Px_new_idx` is the vector of indices of mapping the elements of :code:`Px_new` to the original vector :code:`Px` representing the data of the sparse matrix :code:`P`.
+
+Matrix :code:`A` can be changed in the same way. You can also change both matrices at the same time by running, for example
+
+
+.. code:: julia
+
+ OSQP.update!(m, Px=Px_new, Px_idx=Px_new_idx, Ax=Ax_new, Ax=Ax_new_idx)
+
+
+
+
+
+.. _julia_update_settings:
+
+Update settings
+^^^^^^^^^^^^^^^
+
+Settings can be updated by running
+
+.. code:: julia
+
+ OSQP.update_settings!(m; new_settings)
+
+
+where :code:`new_settings` are the new settings specified as keyword arguments that can be updated which are marked with an * in :ref:`solver_settings`.
+
+
+Warm start
+----------
+
+OSQP automatically warm starts primal and dual variables from the previous QP solution. If you would like to warm start their values manually, you can use
+
+.. code:: julia
+
+ OSQP.warm_start!(m; x=x0, y=y0)
+
+
+where :code:`x0` and :code:`y0` are the new primal and dual variables.
diff --git a/docs/interfaces/linear_systems_solvers.rst b/docs/interfaces/linear_systems_solvers.rst
new file mode 100644
index 0000000..1aa8475
--- /dev/null
+++ b/docs/interfaces/linear_systems_solvers.rst
@@ -0,0 +1,22 @@
+.. _linear_system_solvers_setting :
+
+Linear Systems Solvers
+-----------------------
+The settings parameter :code:`linsys_solver` defines the solver for the linear system.
+In C it corresponds to an integer :code:`c_int` (see :ref:`c_cpp_data_types`) and in the other high level languages to a string.
+
+
++-----------------+-------------------+--------------------------------+---------------+
+| Solver | String option | C Constant | Integer value |
++=================+===================+================================+===============+
+| QDLDL | "qdldl" | :code:`QDLDL_SOLVER` | :code:`0` |
++-----------------+-------------------+--------------------------------+---------------+
+| MKL Pardiso | "mkl pardiso" | :code:`MKL_PARDISO_SOLVER` | :code:`1` |
++-----------------+-------------------+--------------------------------+---------------+
+
+
+
+To add new linear system solvers see :ref:`interfacing_new_linear_system_solvers`.
+
+
+
diff --git a/docs/interfaces/matlab.rst b/docs/interfaces/matlab.rst
new file mode 100644
index 0000000..81e7027
--- /dev/null
+++ b/docs/interfaces/matlab.rst
@@ -0,0 +1,168 @@
+.. _matlab_interface:
+
+Matlab
+======
+
+.. _matlab_setup:
+
+Setup
+-----
+The solver is initialized by creating an OSQP object
+
+.. code:: matlab
+
+ m = osqp;
+
+The problem is specified in the setup phase by running
+
+.. code:: matlab
+
+ m.setup(P, q, A, l, u, varargin)
+
+
+The arguments :code:`q`, :code:`l` and :code:`u` are arrays. The elements of :code:`l` and :code:`u` can be :math:`\pm \infty` ( using :code:`Inf`). The arguments :code:`P` and :code:`A` are sparse matrices.
+Matrix :code:`P` can be either complete or just the upper triangular
+part. OSQP will make use of only the upper triangular part.
+
+There is no need to specify all the problem data. They can be omitted by writing :code:`[]`.
+
+The last argument :code:`varargin` specifies the solver options. You can pass the options in two ways. You can either set the individual parameters as field-value pairs, e.g.,
+
+.. code:: matlab
+
+ m.setup(P, q, A, l, u, 'eps_abs', 1e-04, 'eps_rel', 1e-04);
+
+
+Alternatively, you can create a structure containing all the settings, change some of the fields and then pass it as the last argument
+
+.. code:: matlab
+
+ settings = m.default_settings();
+ settings.eps_abs = 1e-04;
+ settings.eps_rel = 1e-04;
+ m.setup(P, q, A, l, u, settings);
+
+The allowed settings are defined in :ref:`solver_settings`.
+
+
+Solve
+-----
+
+The problem can be solved by
+
+.. code:: matlab
+
+ results = m.solve();
+
+The :code:`results` structure contains the primal solution :code:`x`, the dual solution :code:`y`, certificate of primal infeasibility :code:`prim_inf_cert`, certificate of dual infeasibility :code:`dual_inf_cert` and the :code:`info` structure containing the solver statistics defined in the following table
+
+
++-----------------------+------------------------------------------------+
+| Member | Description |
++=======================+================================================+
+| :code:`iter` | Number of iterations |
++-----------------------+------------------------------------------------+
+| :code:`status` | Solver status |
++-----------------------+------------------------------------------------+
+| :code:`status_val` | Solver status value as in :ref:`status_values` |
++-----------------------+------------------------------------------------+
+| :code:`status_polish` | Polishing status |
++-----------------------+------------------------------------------------+
+| :code:`obj_val` | Objective value |
++-----------------------+------------------------------------------------+
+| :code:`pri_res` | Primal residual |
++-----------------------+------------------------------------------------+
+| :code:`dua_res` | Dual residual |
++-----------------------+------------------------------------------------+
+| :code:`setup_time` | Setup time |
++-----------------------+------------------------------------------------+
+| :code:`solve_time` | Solve time |
++-----------------------+------------------------------------------------+
+| :code:`update_time` | Update time |
++-----------------------+------------------------------------------------+
+| :code:`polish_time` | Polish time |
++-----------------------+------------------------------------------------+
+| :code:`run_time` | Total run time: setup/update + solve + polish |
++-----------------------+------------------------------------------------+
+| :code:`rho_estimate` | Optimal rho estimate |
++-----------------------+------------------------------------------------+
+| :code:`rho_updates` | Number of rho updates |
++-----------------------+------------------------------------------------+
+
+Note that if multiple solves are executed from single setup, then after the
+first one :code:`run_time` includes :code:`update_time` + :code:`solve_time`
++ :code:`polish_time`.
+
+
+Update
+------
+Part of problem data and settings can be updated without requiring a new problem setup.
+
+
+
+Update problem vectors
+^^^^^^^^^^^^^^^^^^^^^^^^
+
+Vectors :code:`q`, :code:`l` and :code:`u` can be updated with new values :code:`q_new`, :code:`l_new` and :code:`u_new` by just running
+
+.. code:: python
+
+ m.update('q', q_new, 'l', l_new, 'u', u_new);
+
+
+The user does not have to specify all the arguments.
+
+
+Update problem matrices
+^^^^^^^^^^^^^^^^^^^^^^^^
+Matrices :code:`A` and :code:`P` can be updated by changing the value of their elements but not their sparsity pattern.
+The interface is designed to mimic the :ref:`C counterpart <c_cpp_update_data>` with the Matlab 1-based indexing.
+Note that the new values of :code:`P` represent only the upper triangular part while :code:`A` is always represented as a full matrix.
+
+You can update the values of all the elements of :code:`P` by executing
+
+.. code:: matlab
+
+ m.update('Px', Px_new)
+
+
+If you want to update only some elements, you can pass
+
+.. code:: matlab
+
+ m.update('Px', Px_new, 'Px_idx', Px_new_idx)
+
+where :code:`Px_new_idx` is the vector of indices of mapping the elements of :code:`Px_new` to the original vector :code:`Px` representing the data of the sparse matrix :code:`P`.
+
+Matrix :code:`A` can be changed in the same way. You can also change both matrices at the same time by running, for example
+
+
+.. code:: matlab
+
+ m.update('Px', Px_new, 'Px_idx', Px_new_idx, 'Ax' Ax_new, 'Ax', Ax_new_idx)
+
+
+Update settings
+^^^^^^^^^^^^^^^
+
+Settings can be updated by running
+
+.. code:: python
+
+ m.update_settings(varargin);
+
+
+where :code:`varargin` argument is described in :ref:`matlab_setup`. The allowed settings that can be updated are marked with an * in :ref:`solver_settings`.
+
+
+
+
+Warm start
+----------
+OSQP automatically warm starts primal and dual variables from the previous QP solution. If you would like to warm start their values manually, you can use
+
+.. code:: matlab
+
+ m.warm_start('x', x0, 'y', y0)
+
+where :code:`x0` and :code:`y0` are the new primal and dual variables.
diff --git a/docs/interfaces/python.rst b/docs/interfaces/python.rst
new file mode 100644
index 0000000..86b228e
--- /dev/null
+++ b/docs/interfaces/python.rst
@@ -0,0 +1,175 @@
+.. _python_interface:
+
+Python
+======
+
+Import
+------
+The OSQP module can be imported with
+
+.. code:: python
+
+ import osqp
+
+
+.. _python_setup:
+
+Setup
+-----
+
+The solver is initialized by creating an OSQP object
+
+.. code:: python
+
+ m = osqp.OSQP()
+
+The problem is specified in the setup phase by running
+
+.. code:: python
+
+ m.setup(P=P, q=q, A=A, l=l, u=u, **settings)
+
+
+The arguments :code:`q`, :code:`l` and :code:`u` are numpy arrays. The elements of :code:`l` and :code:`u` can be :math:`\pm \infty` ( using :code:`numpy.inf`).
+
+The arguments :code:`P` and :code:`A` are scipy sparse matrices in CSC format.
+Matrix :code:`P` can be either complete or just the upper triangular
+part. OSQP will make use of only the upper triangular part.
+If they are sparse matrices are in another format, the interface will attempt to convert them. There is no need to specify all the arguments.
+
+
+The keyword arguments :code:`**settings` specify the solver settings. The allowed parameters are defined in :ref:`solver_settings`.
+
+Solve
+-----
+
+The problem can be solved by
+
+.. code:: python
+
+ results = m.solve()
+
+
+The :code:`results` object contains the primal solution :code:`x`, the dual solution :code:`y`, certificate of primal infeasibility :code:`prim_inf_cert`, certificate of dual infeasibility :code:`dual_inf_cert` and the :code:`info` object containing the solver statistics defined in the following table
+
+
++-----------------------+------------------------------------------------+
+| Member | Description |
++=======================+================================================+
+| :code:`iter` | Number of iterations |
++-----------------------+------------------------------------------------+
+| :code:`status` | Solver status |
++-----------------------+------------------------------------------------+
+| :code:`status_val` | Solver status value as in :ref:`status_values` |
++-----------------------+------------------------------------------------+
+| :code:`status_polish` | Polishing status |
++-----------------------+------------------------------------------------+
+| :code:`obj_val` | Objective value |
++-----------------------+------------------------------------------------+
+| :code:`pri_res` | Primal residual |
++-----------------------+------------------------------------------------+
+| :code:`dua_res` | Dual residual |
++-----------------------+------------------------------------------------+
+| :code:`setup_time` | Setup time |
++-----------------------+------------------------------------------------+
+| :code:`solve_time` | Solve time |
++-----------------------+------------------------------------------------+
+| :code:`update_time` | Update time |
++-----------------------+------------------------------------------------+
+| :code:`polish_time` | Polish time |
++-----------------------+------------------------------------------------+
+| :code:`run_time` | Total run time: setup/update + solve + polish |
++-----------------------+------------------------------------------------+
+| :code:`rho_estimate` | Optimal rho estimate |
++-----------------------+------------------------------------------------+
+| :code:`rho_updates` | Number of rho updates |
++-----------------------+------------------------------------------------+
+
+Note that if multiple solves are executed from single setup, then after the
+first one :code:`run_time` includes :code:`update_time` + :code:`solve_time`
++ :code:`polish_time`.
+
+
+Solve in just one function (with GIL disabled)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+We have a dedicated solve function that performs :code:`setup` and :code:`solve` operations for you. It also disables the GIL in case you
+need it. Just run it from the main module without creating the object as follows
+
+
+.. code:: python
+
+ results = osqp.solve(P=P, q=q, A=A, l=l, u=u, **settings)
+
+
+Update
+------
+Part of problem data and settings can be updated without requiring a new problem setup.
+
+Update problem vectors
+^^^^^^^^^^^^^^^^^^^^^^
+Vectors :code:`q`, :code:`l` and :code:`u` can be updated with new values :code:`q_new`, :code:`l_new` and :code:`u_new` by just running
+
+.. code:: python
+
+ m.update(q=q_new, l=l_new, u=u_new)
+
+
+The user does not have to specify all the keyword arguments.
+
+
+.. _python_update_settings:
+
+Update problem matrices
+^^^^^^^^^^^^^^^^^^^^^^^^
+Matrices :code:`A` and :code:`P` can be updated by changing the value of their elements but not their sparsity pattern.
+The interface is designed to mimic the :ref:`C counterpart <c_cpp_update_data>`.
+Note that the new values of :code:`P` represent only the upper triangular part while :code:`A` is always represented as a full matrix.
+
+You can update the values of all the elements of :code:`P` by executing
+
+.. code:: python
+
+ m.update(Px=Px_new)
+
+
+If you want to update only some elements, you can pass
+
+.. code:: python
+
+ m.update(Px=Px_new, Px_idx=Px_new_idx)
+
+where :code:`Px_new_idx` is the vector of indices of mapping the elements of :code:`Px_new` to the original vector :code:`Px` representing the data of the sparse matrix :code:`P`.
+
+Matrix :code:`A` can be changed in the same way. You can also change both matrices at the same time by running, for example
+
+
+.. code:: python
+
+ m.update(Px=Px_new, Px_idx=Px_new_idx, Ax=Ax_new, Ax=Ax_new_idx)
+
+
+Update settings
+^^^^^^^^^^^^^^^
+
+Settings can be updated by running
+
+.. code:: python
+
+ m.update_settings(**kwargs)
+
+
+where :code:`kwargs` are the settings that can be updated which are marked with an * in :ref:`solver_settings`.
+
+
+Warm start
+----------
+
+OSQP automatically warm starts primal and dual variables from the previous QP solution. If you would like to warm start their values manually, you can use
+
+.. code:: python
+
+ m.warm_start(x=x0, y=y0)
+
+
+where :code:`x0` and :code:`y0` are the new primal and dual variables.
diff --git a/docs/interfaces/rlang.rst b/docs/interfaces/rlang.rst
new file mode 100644
index 0000000..50ddf74
--- /dev/null
+++ b/docs/interfaces/rlang.rst
@@ -0,0 +1,7 @@
+.. _rlang_interface:
+
+
+R
+==
+
+The R interface is officially on CRAN and documented `here <https://cran.r-project.org/web/packages/osqp/>`_.
diff --git a/docs/interfaces/ruby.rst b/docs/interfaces/ruby.rst
new file mode 100644
index 0000000..195cf19
--- /dev/null
+++ b/docs/interfaces/ruby.rst
@@ -0,0 +1,7 @@
+.. _ruby_interface:
+
+
+Ruby
+========
+
+The ruby interface can be installed as a Ruby gem and is documented `here <https://www.rubydoc.info/gems/osqp/>`_.
diff --git a/docs/interfaces/rust.rst b/docs/interfaces/rust.rst
new file mode 100644
index 0000000..52956a3
--- /dev/null
+++ b/docs/interfaces/rust.rst
@@ -0,0 +1,6 @@
+.. _rust_interface:
+
+Rust
+======
+
+The Rust interface is documented `here <https://docs.rs/osqp/>`_.
diff --git a/docs/interfaces/solver_settings.rst b/docs/interfaces/solver_settings.rst
new file mode 100644
index 0000000..ba3abc8
--- /dev/null
+++ b/docs/interfaces/solver_settings.rst
@@ -0,0 +1,73 @@
+.. _solver_settings :
+
+Solver settings
+---------------
+
+The solver settings are displayed in the following table. The settings marked with * can be changed without running the setup method again.
+
+.. tabularcolumns:: |p{4.5cm}|p{3.5cm}|p{6.5cm}|L|
+
++--------------------------------+-------------------------------------------------------------+--------------------------------------------------------------+-----------------+
+| Argument | Description | Allowed values | Default value |
++================================+=============================================================+==============================================================+=================+
+| :code:`rho` * | ADMM rho step | 0 < :code:`rho` | 0.1 |
++--------------------------------+-------------------------------------------------------------+--------------------------------------------------------------+-----------------+
+| :code:`sigma` | ADMM sigma step | 0 < :code:`sigma` | 1e-06 |
++--------------------------------+-------------------------------------------------------------+--------------------------------------------------------------+-----------------+
+| :code:`max_iter` * | Maximum number of iterations | 0 < :code:`max_iter` (integer) | 4000 |
++--------------------------------+-------------------------------------------------------------+--------------------------------------------------------------+-----------------+
+| :code:`eps_abs` * | Absolute tolerance | 0 <= :code:`eps_abs` | 1e-03 |
++--------------------------------+-------------------------------------------------------------+--------------------------------------------------------------+-----------------+
+| :code:`eps_rel` * | Relative tolerance | 0 <= :code:`eps_rel` | 1e-03 |
++--------------------------------+-------------------------------------------------------------+--------------------------------------------------------------+-----------------+
+| :code:`eps_prim_inf` * | Primal infeasibility tolerance | 0 <= :code:`eps_prim_inf` | 1e-04 |
++--------------------------------+-------------------------------------------------------------+--------------------------------------------------------------+-----------------+
+| :code:`eps_dual_inf` * | Dual infeasibility tolerance | 0 <= :code:`eps_dual_inf` | 1e-04 |
++--------------------------------+-------------------------------------------------------------+--------------------------------------------------------------+-----------------+
+| :code:`alpha` * | ADMM overrelaxation parameter | 0 < :code:`alpha` < 2 | 1.6 |
++--------------------------------+-------------------------------------------------------------+--------------------------------------------------------------+-----------------+
+| :code:`linsys_solver` | Linear systems solver type | See :ref:`linear_system_solvers_setting` | qdldl |
++--------------------------------+-------------------------------------------------------------+--------------------------------------------------------------+-----------------+
+| :code:`delta` * | Polishing regularization parameter | 0 < :code:`delta` | 1e-06 |
++--------------------------------+-------------------------------------------------------------+--------------------------------------------------------------+-----------------+
+| :code:`polish` * | Perform polishing | True/False | False |
++--------------------------------+-------------------------------------------------------------+--------------------------------------------------------------+-----------------+
+| :code:`polish_refine_iter` * | Refinement iterations in polish | 0 < :code:`polish_refine_iter` (integer) | 3 |
++--------------------------------+-------------------------------------------------------------+--------------------------------------------------------------+-----------------+
+| :code:`verbose` * | Print output | True/False | True |
++--------------------------------+-------------------------------------------------------------+--------------------------------------------------------------+-----------------+
+| :code:`scaled_termination` * | Scaled termination conditions | True/False | False |
++--------------------------------+-------------------------------------------------------------+--------------------------------------------------------------+-----------------+
+| :code:`check_termination` * | Check termination interval | 0 (disabled) or 0 < :code:`check_termination` (integer) | 25 |
++--------------------------------+-------------------------------------------------------------+--------------------------------------------------------------+-----------------+
+| :code:`warm_start` * | Perform warm starting | True/False | True |
++--------------------------------+-------------------------------------------------------------+--------------------------------------------------------------+-----------------+
+| :code:`scaling` | Number of scaling iterations | 0 (disabled) or 0 < :code:`scaling` (integer) | 10 |
++--------------------------------+-------------------------------------------------------------+--------------------------------------------------------------+-----------------+
+| :code:`adaptive_rho` | Adaptive rho | True/False | True |
++--------------------------------+-------------------------------------------------------------+--------------------------------------------------------------+-----------------+
+| :code:`adaptive_rho_interval` | Adaptive rho interval | 0 (automatic) or 0 < :code:`adaptive_rho_interval` (integer) | 0 |
++--------------------------------+-------------------------------------------------------------+--------------------------------------------------------------+-----------------+
+| :code:`adaptive_rho_tolerance` | Tolerance for adapting rho | 1 <= :code:`adaptive_rho_tolerance` | 5 |
++--------------------------------+-------------------------------------------------------------+--------------------------------------------------------------+-----------------+
+| :code:`adaptive_rho_fraction` | Adaptive rho interval as fraction of setup time (auto mode) | 0 < :code:`adaptive_rho_fraction` | 0.4 |
++--------------------------------+-------------------------------------------------------------+--------------------------------------------------------------+-----------------+
+| :code:`time_limit` * | Run time limit in seconds | 0 (disabled) or 0 <= :code:`time_limit` | 0 |
++--------------------------------+-------------------------------------------------------------+--------------------------------------------------------------+-----------------+
+
+The boolean values :code:`True/False` are defined as :code:`1/0` in the C interfaces.
+
+
+.. The infinity values correspond to:
+..
+.. +----------+--------------------+
+.. | Language | Value |
+.. +==========+====================+
+.. | C | :code:`OSQP_INFTY` |
+.. +----------+--------------------+
+.. | Python | :code:`numpy.inf` |
+.. +----------+--------------------+
+.. | Matlab | :code:`Inf` |
+.. +----------+--------------------+
+.. | Julia | :code:`Inf` |
+.. +----------+--------------------+
diff --git a/docs/interfaces/status_values.rst b/docs/interfaces/status_values.rst
new file mode 100644
index 0000000..3dd53fa
--- /dev/null
+++ b/docs/interfaces/status_values.rst
@@ -0,0 +1,85 @@
+.. _status_values :
+
+
+
+Status values and errors
+========================
+
+Status values
+-------------
+
+These are the exit statuses, their respective constants and values returned by the solver as defined in `constants.h <https://github.com/osqp/osqp/blob/master/include/constants.h>`_.
+The *inaccurate* statuses define when the optimality, primal infeasibility or dual infeasibility conditions are satisfied with tolerances 10 times larger than the ones set.
+
++------------------------------+-----------------------------------+-------+
+| Status | Constant | Value |
++==============================+===================================+=======+
+| solved | OSQP_SOLVED | 1 |
++------------------------------+-----------------------------------+-------+
+| solved inaccurate | OSQP_SOLVED_INACCURATE | 2 |
++------------------------------+-----------------------------------+-------+
+| maximum iterations reached | OSQP_MAX_ITER_REACHED | -2 |
++------------------------------+-----------------------------------+-------+
+| primal infeasible | OSQP_PRIMAL_INFEASIBLE | -3 |
++------------------------------+-----------------------------------+-------+
+| primal infeasible inaccurate | OSQP_PRIMAL_INFEASIBLE_INACCURATE | 3 |
++------------------------------+-----------------------------------+-------+
+| dual infeasible | OSQP_DUAL_INFEASIBLE | -4 |
++------------------------------+-----------------------------------+-------+
+| dual infeasible inaccurate | OSQP_DUAL_INFEASIBLE_INACCURATE | 4 |
++------------------------------+-----------------------------------+-------+
+| interrupted by user | OSQP_SIGINT | -5 |
++------------------------------+-----------------------------------+-------+
+| run time limit reached | OSQP_TIME_LIMIT_REACHED | -6 |
++------------------------------+-----------------------------------+-------+
+| unsolved | OSQP_UNSOLVED | -10 |
++------------------------------+-----------------------------------+-------+
+| problem non convex | OSQP_NON_CVX | -7 |
++------------------------------+-----------------------------------+-------+
+
+.. note::
+
+ We recommend the user to **check the convexity of their problem before
+ passing it to OSQP**! If the user passes a non-convex problem we do not
+ assure the solver will be able to detect it.
+
+ OSQP will try to detect **non-convex** problems by checking if the residuals
+ diverge or if there are any issues in the initial factorization (if a direct
+ method is used). It will detect non-convex problems when one or more of the
+ eigenvalues of :code:`P` are "clearly" negative, i.e., when :code:`P + sigma
+ * I` is not positive semidefinite. However, it might fail to detect
+ non-convexity when :code:`P` has slightly negative eigenvalues, i.e., when
+ :code:`P + sigma * I` is positive semidefinite and :code:`P` is not.
+
+
+
+
+Solver Errors
+-------------
+
+OSQP can return errors during the setup and solve steps. Here is a table of the meaning
+and their constant values.
+
+
++------------------------------------------------+-----------------------------------+-------+
+| Errors | Constant | Value |
++================================================+===================================+=======+
+| Data validation | OSQP_DATA_VALIDATION_ERROR | 1 |
++------------------------------------------------+-----------------------------------+-------+
+| Settings validation | OSQP_SETTINGS_VALIDATION_ERROR | 2 |
++------------------------------------------------+-----------------------------------+-------+
+| Linear system solver loading | OSQP_LINSYS_SOLVER_LOAD_ERROR | 3 |
++------------------------------------------------+-----------------------------------+-------+
+| Linear system solver initialization | OSQP_LINSYS_SOLVER_INIT_ERROR | 4 |
++------------------------------------------------+-----------------------------------+-------+
+| Non convex problem | OSQP_NONCVX_ERROR | 5 |
++------------------------------------------------+-----------------------------------+-------+
+| Memory allocation | OSQP_MEM_ALLOC_ERROR | 6 |
++------------------------------------------------+-----------------------------------+-------+
+| Workspace not initialized | OSQP_WORKSPACE_NOT_INIT | 7 |
++------------------------------------------------+-----------------------------------+-------+
+
+
+
+
+
diff --git a/docs/make.bat b/docs/make.bat
new file mode 100644
index 0000000..1d7c66c
--- /dev/null
+++ b/docs/make.bat
@@ -0,0 +1,36 @@
+@ECHO OFF
+
+pushd %~dp0
+
+REM Command file for Sphinx documentation
+
+if "%SPHINXBUILD%" == "" (
+ set SPHINXBUILD=sphinx-build
+)
+set SOURCEDIR=.
+set BUILDDIR=_build
+set SPHINXPROJ=osqp
+
+if "%1" == "" goto help
+
+%SPHINXBUILD% >NUL 2>NUL
+if errorlevel 9009 (
+ echo.
+ echo.The 'sphinx-build' command was not found. Make sure you have Sphinx
+ echo.installed, then set the SPHINXBUILD environment variable to point
+ echo.to the full path of the 'sphinx-build' executable. Alternatively you
+ echo.may add the Sphinx directory to PATH.
+ echo.
+ echo.If you don't have Sphinx installed, grab it from
+ echo.http://sphinx-doc.org/
+ exit /b 1
+)
+
+%SPHINXBUILD% -M %1 %SOURCEDIR% %BUILDDIR% %SPHINXOPTS%
+goto end
+
+:help
+%SPHINXBUILD% -M help %SOURCEDIR% %BUILDDIR% %SPHINXOPTS%
+
+:end
+popd
diff --git a/docs/parsers/cvxpy.rst b/docs/parsers/cvxpy.rst
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+CVXPY
+=====
+
+`CVXPY <http://www.cvxpy.org/>`_ 1.0 supports the OSQP solver by default. After defining your problem, you can solve it with OSQP by just calling
+
+.. code:: python
+
+ problem.solve()
+
+
+OSQP is the default QP solver used. To specify it explicitly together with some options you can execute
+
+.. code:: python
+
+ problem.solve(solver=OSQP, max_iter=2000)
+
+where we set the :code:`max_iter` option to :code:`2000`.
diff --git a/docs/parsers/index.rst b/docs/parsers/index.rst
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+++ b/docs/parsers/index.rst
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+Parsers
+=======
+
+.. toctree::
+ :maxdepth: 1
+ :glob:
+
+ yalmip.rst
+ cvxpy.rst
+ jump.rst
diff --git a/docs/parsers/jump.rst b/docs/parsers/jump.rst
new file mode 100644
index 0000000..2d8c93e
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+++ b/docs/parsers/jump.rst
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+JuMP
+=====
+
+`JuMP <https://github.com/JuliaOpt/JuMP.jl>`_ supports the OSQP solver using the `MathOptInterface interface <https://github.com/JuliaOpt/MathOptInterface.jl>`_.
+You can define a JuMP model to be solved via OSQP as follows
+
+
+.. code:: julia
+
+ # Load JuMP and OSQP
+ using JuMP, OSQP
+
+ # Create OSQP Solver instance
+ s = OSQPMathProgBaseInterface.OSQPSolver(verbose=false)
+
+ # Create JuMP model
+ model = Model(solver=s)
+
+ ...
+
+Note that here we set the verbosity to :code:`false`.
+After defining your model, you can solve it by just calling
+
+.. code:: julia
+
+ solve(model)
+
+
+For more details on how to create and modify the models, see the `JuMP Documentation <https://www.juliaopt.org/JuMP.jl/stable/>`_.
\ No newline at end of file
diff --git a/docs/parsers/yalmip.rst b/docs/parsers/yalmip.rst
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+++ b/docs/parsers/yalmip.rst
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+YALMIP
+======
+
+`YALMIP <https://yalmip.github.io/>`_ supports the OSQP solver. You can easily define problems in high-level format and then specify OSQP by simply setting
+
+.. code:: matlab
+
+ options = sdpsettings('solver', 'osqp', 'osqp.max_iter', 2000);
+
+
+where we set the :code:`max_iter` option to :code:`2000`.
diff --git a/docs/requirements.txt b/docs/requirements.txt
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+++ b/docs/requirements.txt
@@ -0,0 +1 @@
+breathe
diff --git a/docs/solver/index.rst b/docs/solver/index.rst
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+The solver
+==========
+
+Problem statement
+-----------------
+
+OSQP solves convex quadratic programs (QPs) of the form
+
+.. math::
+ \begin{array}{ll}
+ \mbox{minimize} & \frac{1}{2} x^T P x + q^T x \\
+ \mbox{subject to} & l \leq A x \leq u
+ \end{array}
+
+where :math:`x\in\mathbf{R}^{n}` is the optimization variable.
+The objective function is defined by a positive semidefinite matrix
+:math:`P \in \mathbf{S}^{n}_{+}` and vector :math:`q\in \mathbf{R}^{n}`.
+The linear constraints are defined by matrix :math:`A\in\mathbf{R}^{m \times n}`
+and vectors :math:`l` and :math:`u` so that :math:`l_i \in \mathbf{R} \cup \{-\infty\}` and :math:`u_i \in \mathbf{R} \cup \{+\infty\}` for all :math:`i \in \{1,\ldots,m\}`.
+
+
+Algorithm
+---------
+
+The solver runs the following `ADMM algorithm <http://web.stanford.edu/~boyd/papers/admm_distr_stats.html>`_ (for more details see the related papers at the :ref:`citing` section):
+
+
+.. math::
+
+ (x^{k+1}, \nu^{k+1}) & \gets \text{solve linear system}\\
+ \tilde{z}^{k+1} & \gets z^{k} + \rho^{-1}(\nu^{k+1} - y^{k})\\
+ z^{k+1} &\gets \Pi(\tilde{z}^{k} + \rho^{-1}y^{k})\\
+ y^{k+1} &\gets y^{k} + \rho (\tilde{z}^{k+1} - z^{k+1})
+
+where :math:`\Pi` is the projection onto the hyperbox :math:`[l,u]`.
+:math:`\rho` is the ADMM step-size.
+
+
+Linear system solution
+^^^^^^^^^^^^^^^^^^^^^^
+The linear system solution is the core part of the algorithm.
+It can be done using a **direct** or **indirect** method.
+
+With a **direct linear system solver** we solve the following linear system with a quasi-definite matrix
+
+.. math::
+
+ \begin{bmatrix} P + \sigma I & A^T \\ A & -\rho^{-1}I \end{bmatrix} \begin{bmatrix} x^{k+1} \\ \nu^{k+1} \end{bmatrix}= \begin{bmatrix}\sigma x^{k} - q \\ z^{k} - \rho^{-1} y^k \end{bmatrix}.
+
+With an **indirect linear system solver** we solve the following linear system with a positive definite matrix
+
+
+.. math::
+
+ \left(P + \sigma I + \rho A^T A \right)x^{k+1} = \sigma x^{k} - q + A^T (\rho z^{k} - y^{k}).
+
+
+OSQP core is designed to support different linear system solvers.
+For their installation see :ref:`this section <linear_system_solvers_installation>`.
+To specify your favorite linear system solver see :ref:`this section <linear_system_solvers_setting>`.
+
+Convergence
+^^^^^^^^^^^
+At each iteration :math:`k` OSQP produces a tuple :math:`(x^{k}, z^{k}, y^{k})` with :math:`x^{k} \in \mathbf{R}^{n}` and :math:`z^{k}, y^{k} \in \mathbf{R}^{m}`.
+
+The primal and and dual residuals associated to :math:`(x^{k}, z^{k}, y^{k})` are
+
+.. math::
+
+ \begin{aligned}
+ r_{\rm prim}^{k} &= Ax^{k} - z^{k}\\
+ r_{\rm dual}^{k} &= Px^{k} + q + A^{T} y^{k}.
+ \end{aligned}
+
+Complementary slackness is satisfied by construction at machine precision. If the problem is feasible, the residuals converge to zero as :math:`k\to\infty`. The algorithm stops when the norms of :math:`r_{\rm prim}^{k}` and :math:`r_{\rm dual}^{k}` are within the specified tolerance levels :math:`\epsilon_{\rm prim}>0` and :math:`\epsilon_{\rm dual}>0`
+
+.. math::
+
+ \| r_{\rm prim}^{k} \|_{\infty} \le
+ \epsilon_{\rm prim},
+ \quad
+ \| r_{\rm dual}^{k} \|_{\infty} \le
+ \epsilon_{\rm dual}.
+
+We set the tolerance levels as
+
+.. math::
+
+ \epsilon_{\rm prim} &= \epsilon_{\rm abs} + \epsilon_{\rm rel} \max\lbrace \|Ax^{k}\|_{\infty}, \| z^{k} \|_{\infty} \rbrace \\
+ \epsilon_{\rm dual} &= \epsilon_{\rm abs} + \epsilon_{\rm rel} \max\lbrace \| P x^{k} \|_{\infty}, \| A^T y^{k} \|_{\infty}, \| q \|_{\infty} \rbrace.
+
+
+.. _rho_step_size :
+
+:math:`\rho` step-size
+^^^^^^^^^^^^^^^^^^^^^^
+To ensure quick convergence of the algorithm we adapt :math:`\rho` by balancing the residuals.
+In default mode, the inteval (*i.e.*, number of iterations) at which we update :math:`\rho` is defined by a time measurement.
+When the iterations time becomes greater than a certain fraction of the setup time, *i.e.* :code:`adaptive_rho_fraction`, we set the current number of iterations as the interval to update :math:`\rho`.
+The update happens as follows
+
+.. math::
+
+ \rho^{k+1} \gets \rho^{k} \sqrt{\frac{\|r_{\rm prim}\|_{\infty}}{\|r_{\rm dual}\|_{\infty}}}.
+
+
+Note that :math:`\rho` is updated only if it is sufficiently different than the current one.
+In particular if it is :code:`adaptive_rho_tolerance` times larger or smaller than the current one.
+
+
+
+Infeasible problems
+-------------------------------
+
+OSQP is able to detect if the problem is primal or dual infeasible.
+
+
+Primal infeasibility
+^^^^^^^^^^^^^^^^^^^^
+
+When the problem is primal infeasible, the algorithm generates a certificate of infeasibility, *i.e.*, a vector :math:`v\in\mathbf{R}^{m}` such that
+
+.. math::
+
+ A^T v = 0, \quad u^T v_{+} + l^T v_{-} < 0,
+
+where :math:`v_+=\max(v,0)` and :math:`v_-=\min(v,0)`.
+
+The primal infeasibility check is then
+
+.. math::
+
+ \left\|A^T v \right\|_{\infty} \le \epsilon_{\rm prim\_inf}, \quad u^T v_{+} + l^T v_{-} \le \epsilon_{\rm prim\_inf}.
+
+
+
+Dual infeasibility
+^^^^^^^^^^^^^^^^^^^^
+
+When the problem is dual infeasible, OSQP generates a vector :math:`s\in\mathbf{R}^{n}` being a certificate of dual infeasibility, *i.e.*,
+
+.. math::
+
+ P s = 0, \quad q^T s < 0, \quad (As)_i = \begin{cases} 0 & l_i \in \mathbf{R}, u_i\in\mathbf{R} \\ \ge 0 & l_i\in\mathbf{R}, u_i=+\infty \\ \le 0 & u_i\in\mathbf{R}, l_i=-\infty. \end{cases}
+
+
+The dual infeasibility check is then
+
+.. math::
+
+ \| P s \|_{\infty} \le \epsilon_{\rm dual\_inf} , \quad
+ q^T s \le \epsilon_{\rm dual\_inf}, \\
+ (A s)_i \begin{cases} \in \left[-\epsilon_{\rm dual\_inf}, \epsilon_{\rm dual\_inf}\right] & u_i, l_i \in \mathbf{R}\\
+ \ge -\epsilon_{\rm dual\_inf} &u_i = +\infty\\
+ \le \epsilon_{\rm dual\_inf} &l_i = -\infty.\end{cases}
+
+
+
+
+Polishing
+^^^^^^^^^^^
+
+Polishing is an additional algorithm step where OSQP tries to compute a high-accuracy solution.
+We can enable it by turning the setting :code:`polish` to 1.
+
+Polishing works by guessing the active constraints at the optimum and solving an additional linear system.
+If the guess is correct, OSQP returns a high accuracy solution.
+Otherwise OSQP returns the ADMM solution.
+The status of the polishing phase appears in the information :code:`status_polish`.
+
+Note that polishing requires the solution of an additional linear system and thereby, an additional factorization if the linear system solver is direct.
+However, the linear system is usually much smaller than the one solved during the ADMM iterations.
+
+The chances to have a successful polishing increase if the tolerances :code:`eps_abs` and :code:`eps_rel` are small.
+However, low tolerances might require a very large number of iterations.
+
+
