Quickstart guide

What is this package?

Combining a comprehenseive collection of quadrature methods in one single interface, OpenQuad helps you to efficiently compute integrals over various domains with ease, including 1d intervals, spherical surfaces, Euler angles and more. The object-oriented interface provides Python classes for each geometry, for example the openquad.S2 class for integration over the 2d unit sphere. Python functions and array data can be integrated directly using the integrate() method. Alternatively, sample points and quadrature weights can be exported with the savetxt() method for easy integration with other software.

The best part: combine individual quadrature methods to create custom multi-dimensional quadratures.

How do I use it?

Want to integrate a Python function over the interval \([-10,5]\) with Gauss-Legendre quadrature?

>>> from openquad import Rn
>>> quad = Rn([
...     ('GaussLegendre', dict(degree=21, a=-10, b=5)),
... ])
>>> quad.integrate(your_awesome_function)

Have a Python function that you need to evaluate on a uniform grid over the surface of the unit sphere?

>>> from openquad import S2
>>> quad = S2([
...     ('S2-Covering-Fibonacci', dict(size=142)),
... ])
>>> grid = your_awesome_function(*quad.angles)

Need quadrature points and weights for performing an efficient orientation average in your molecular dynamics simulation?

>>> from openquad import SO3
>>> quad = SO3([
...     ('LebedevLaikov', dict(degree=15)),
...     ('Trapezoid', dict(size=16)),
... ])
>>> quad.savetxt('points_and_weights.dat')

How do I get it?

Install the latest stable release with

pip install openquad

Tell me more!

Have a look at the user guide and the example gallery.

Tip

Don’t know, which method to choose? Read our paper.