.. pycvodes documentation master file, created by
   sphinx-quickstart on Wed Dec 30 23:12:01 2020.
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Welcome to pycvodes's documentation!
====================================

.. toctree::
   :maxdepth: 4
   :caption: Contents:

   pycvodes


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

* :ref:`genindex`
* :ref:`modindex`
* :ref:`search`
Overview
========

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`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>`_. ``pycvodes`` 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``: Backward differentiation formula (of order 1 to 5)
- ``adams``: implicit Adams method (order 1 to 12)

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

You may also want to know that you can use ``pycvodes`` from
`pyodesys <https://github.com/bjodah/pyodesys>`_
which can e.g. derive the Jacobian analytically (using SymPy). Pyodesys also provides
plotting functions, C++ code-generation and more.

Documentation
-------------
Autogenerated API documentation for latest stable release is found here:
`<https://bjodah.github.io/pycvodes/latest>`_
(and the development version 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 conda-forge pycvodes pytest
   $ python -m pytest --pyargs pycvodes

tests should pass.

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

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

When installing from source you can choose what lapack lib to link against by setting
the environment variable ``PYCVODES_LAPACK``, your choice can later be accessed from python:

.. code:: python

   >>> from pycvodes import config
   >>> config['LAPACK']  # doctest: +SKIP
   'lapack,blas'

If you use ``pip`` to install ``pycvodes``, note that prior to installing pycvodes, you will need
to install sundials (pycvodes>=0.12.0 requires sundials>=5.1.0, pycvodes<0.12 requires sundials<5)
and its development headers, with cvodes & lapack enabled

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

See file `AUTHORS <AUTHORS>`_ in root for a list of all authors.