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Python binding for cvodes from the sundials library.

Project description

Build status PyPI version License coverage

pycvodes provides a Python binding to the Ordinary Differential Equation integration routines from cvodes in the SUNDIALS suite. 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: 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.

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:

$ conda install -c conda-forge -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

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:

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

Examples

The classic van der Pol oscillator (see examples/van_der_pol.py)

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

For more examples see 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 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

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