It is a numerical integration technique. From MathWorld, Ueberhuber (1997, p. 71) and Krommer and Ueberhuber (1998, pp. 49 and 155-165) use the word "quadrature" to mean numerical computation of a univariate integral, and "cubature" to mean numerical computation of a multiple integral.

Please, see the module documentation here.

From the Nanostructures and Computation Wiki at MIT, Steven W. Johnson has written a simple C package for adaptive multidimensional integration (cubature) of vector-valued functions over hypercubes and this is a Python wrapper for the referred C package.

If you are changing _cubature.pyx, you must have Cython installed in order to create a new _cubature.c file (the same is valid for _test_integrands.pyx). The setup.py script will automatically try to use the Cython compiler first.

To install in the site-packages directory and make it importable from anywhere:

python setup.py install

Windows:

set prefix=anydirectory
set PYTHONPATH=%anydirectory%\Lib\site-packages;%PYTHONPATH%
mkdir %anydirectory%
python setup.py install --prefix="%anydirectory%"

Linux:

export prefix=anydirectory
export PYTHONPATH=$anydirectory/Lib/site-packages;$PYTHONPATH
mkdir $anydirectory
python setup.py install --prefix=$anydirectory

It will create an .egg file that will go to $anydirectory\Lib\site-packages. This file can be unzipped to obtain the importable module, OR, the full path to this .egg can be added to $PYTHONPATH (which can be also done inside a script through sys.path.append().

If you want to build it locally (without installing in Python's site-packages) just type:

python setup.py build_ext --inplace clean

The Python wrapper has been proven using test integrands from the C package and some additional testing functions from Genz. The integrands were implemented in Cython and verified with Mathematica.

After building cubature, run the unit tests with the `pytest` package in the package directory. Be aware that this takes several minutes:

python -m pytest test_cubature.py

Some examples are given in ./examples.

You are welcome to fork this repository and modify it in whatever way you want. It will also be nice if you could send a pull request here in case you think your modifications are valuable for another person.

This wrapper follows the GNU-GPL license terms discribed in the C Package.