Python binding for cvodes from the sundials library.
pycvodes provides a Python binding to the Ordinary Differential Equation integration routines from cvodes in the SUNDIALS suite. 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 which can e.g. derive the Jacobian analytically (using SymPy). Pyodesys also provides plotting functions, C++ code-generation and more.
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).
Simplest way to install is to use the conda package manager:
$ conda install -c conda-forge 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['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
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 = y ... dydt = -y + mu*y*(1 - y**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*y ... Jmat[1, 1] = mu*(1 - y**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
For more examples see examples/, and rendered jupyter notebooks here: http://hera.physchem.kth.se/~pycvodes/branches/master/examples
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