Welcome to pyodeint’s documentation!¶

Contents:

pyodeint package

Indices and tables¶

Overview¶

pyodeint provides a Python binding to odeint. Currently, the following steppers are exposed:

rosenbrock4: 4th order Rosenbrock (implicit multistep) stepper
dopri5: 5th order DOPRI5 (explicit runge-kutta)
bs: Bulirsch-Stoer stepper (modified midpoint rule).

The Rosenbrock4 stepper requires that the user provides a routine for calculating the Jacobian.

You may also want to know that you can use pyodeint from pyodesys which can e.g. derive the Jacobian analytically for you (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/pyodeint/latest (and the development version for the current master branch are found here: http://hera.physchem.kth.se/~pyodeint/branches/master/html).

Installation¶

Simplest way to install is to use the conda package manager:

$ conda install -c conda-forge pyodeint pytest
$ python -m pytest --pyargs pyodeint

tests should pass.

Binary distribution is available here: https://anaconda.org/bjodah/pyodeint

Source distribution is available here: https://pypi.python.org/pypi/pyodeint

here is an example of how to build from source:

$ CPATH=/opt/boost_1_65_0/include python3 setup.py build_ext -i

Examples¶

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

>>> from pyodeint import integrate_adaptive  # also: integrate_predefined
>>> 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, 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)
...     dfdt[0] = 0
...     dfdt[1] = 0
...
>>> y0 = [1, 0]; tend=10.0; dt0=1e-8; t0=0.0; atol=1e-8; rtol=1e-8
>>> tout, yout, info = integrate_adaptive(f, j, y0, t0, tend, dt0, atol, rtol,
...                                       method='rosenbrock4', nsteps=1000)
>>> import matplotlib.pyplot as plt
>>> series = plt.plot(tout, yout)
>>> plt.show()  

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

For more examples see examples/, and rendered jupyter notebooks here: http://hera.physchem.kth.se/~pyodeint/branches/master/examples

License¶

The source code is Open Source and is released under the very permissive “simplified (2-clause) BSD license”. See LICENSE for further details. Contributors are welcome to suggest improvements at https://github.com/bjodah/pyodeint

Author¶

Björn I. Dahlgren, contact:

gmail address: bjodah