.. pycvodes documentation master file, created by
   sphinx-quickstart on Thu Aug 18 13:18:39 2016.
   You can adapt this file completely to your liking, but it should at least
   contain the root `toctree` directive.

Welcome to pycvodes's documentation!
====================================

Contents:

.. toctree::
   :maxdepth: 4

   pycvodes


Indices and tables
==================

* :ref:`genindex`
* :ref:`modindex`
* :ref:`search`

Overview
========

.. image:: http://hera.physchem.kth.se:9090/api/badges/bjodah/pycvodes/status.svg
   :target: http://hera.physchem.kth.se:9090/bjodah/pycvodes
   :alt: Build status
.. image:: https://img.shields.io/pypi/v/pycvodes.svg
   :target: https://pypi.python.org/pypi/pycvodes
   :alt: PyPI version
.. image:: https://img.shields.io/pypi/l/pycvodes.svg
   :target: https://github.com/bjodah/pycvodes/blob/master/LICENSE
   :alt: License
.. image:: http://hera.physchem.kth.se/~pycvodes/branches/master/htmlcov/coverage.svg
   :target: http://hera.physchem.kth.se/~pycvodes/branches/master/htmlcov
   :alt: coverage


`pycvodes <https://github.com/bjodah/pycvodes>`_ provides a
`Python <http://www.python.org>`_ binding to the
`Ordinary Differential Equation <https://en.wikipedia.org/wiki/Ordinary_differential_equation>`_
integration routines from `cvodes <https://computation.llnl.gov/casc/sundials/description/description.html#descr_cvodes>`_ in the
`SUNDIALS suite <https://computation.llnl.gov/casc/sundials/main.html>`_. ``pcyvodes`` allows a user to numerically integrate
(systems of) differential equations. Note that routines for sensitivity analysis is not yet exposed in this binding (which makes
the functionality essentially the same as cvode). 

The following multistep methods are available:

- bdf
- adams

Note that bdf (as an implicit stepper) require a user supplied
callback for calculating the jacobian.

Documentation
-------------
Autogenerated API documentation for latest stable release is found here:
`<https://pythonhosted.org/pycvodes>`_
(and development docs for the current master branch are found here:
`<http://hera.physchem.kth.se/~pycvodes/branches/master/html>`_).

Installation
------------
Simplest way to install is to use the `conda package manager <http://conda.pydata.org/docs/>`_:

::

   $ conda install -c bjodah pycvodes pytest
   $ python -m pytest --pyargs pycvodes

tests should pass.

Binary distribution is available here:
`<https://anaconda.org/bjodah/pycvodes>`_

Source distribution is available here:
`<https://pypi.python.org/pypi/pycvodes>`_

Examples
--------
The classic van der Pol oscillator (see `examples/van_der_pol.py <examples/van_der_pol.py>`_)

.. code:: python

   >>> import numpy as np
   >>> from pycvodes import integrate_predefined  # also: integrate_adaptive
   >>> mu = 1.0
   >>> def f(t, y, dydt):
   ...     dydt[0] = y[1]
   ...     dydt[1] = -y[0] + mu*y[1]*(1 - y[0]**2)
   ... 
   >>> def j(t, y, Jmat, dfdt=None, fy=None):
   ...     Jmat[0, 0] = 0
   ...     Jmat[0, 1] = 1
   ...     Jmat[1, 0] = -1 - mu*2*y[1]*y[0]
   ...     Jmat[1, 1] = mu*(1 - y[0]**2)
   ...     if dfdt is not None:
   ...         dfdt[:] = 0
   ...
   >>> y0 = [1, 0]; dt0=1e-8; t0=0.0; atol=1e-8; rtol=1e-8
   >>> tout = np.linspace(0, 10.0, 200)
   >>> yout, info = integrate_predefined(f, j, y0, tout, atol, rtol, dt0,
   ...                                   method='bdf')
   >>> import matplotlib.pyplot as plt
   >>> series = plt.plot(tout, yout)
   >>> plt.show()  # doctest: +SKIP


.. image:: https://raw.githubusercontent.com/bjodah/pycvodes/master/examples/van_der_pol.png

For more examples see `examples/ <https://github.com/bjodah/pycvodes/tree/master/examples>`_, and rendered jupyter notebooks here:
`<http://hera.physchem.kth.se/~pycvodes/branches/master/examples>`_


License
-------
The source code is Open Source and is released under the simplified 2-clause BSD license. See `LICENSE <LICENSE>`_ for further details.

Contributors are welcome to suggest improvements at https://github.com/bjodah/pycvodes

Author
------
Björn I. Dahlgren, contact:

- gmail address: bjodah
- kth.se address: bda