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cubature

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Python wrapper for the Cubature algorithm explained in: http://ab-initio.mit.edu/wiki/index.php/Cubature

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![Cubature](https://raw.github.com/saullocastro/cubature/master/cubature_logo.png "Cubature")

Cubature
========

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What is Cubature?
-----------------

It is a numerical integration technique.  From MathWorld
http://mathworld.wolfram.com/Cubature.html, 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.

Cubature for Python
-------------------

This is a wrapper to Prof. Steven Johnson's C package, available at https://github.com/stevengj/cubature.
The current version is a wrapper to version 1.0.4 of Prof. Johnson's package.

Documentation
-------------

Please, see the module documentation here http://saullocastro.github.io/cubature.

Python wrapper for the Cubature package
---------------------------------------

From the Nanostructures and Computation Wiki at MIT
http://ab-initio.mit.edu/wiki/index.php/Cubature, Steven W. Johnson
http://math.mit.edu/~stevenj 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.

Installation from source code
-----------------------------

You must have Cython installed. Then do:

```
python setup.py install 
```

or (usually in Linux):

```
python3 setup.py install
```

Installation from pip repository
--------------------------------

Just do:

```
python -m pip install cubature
```

or (usually in Linux):

```
python3 -m pip install cubature
```

Running the tests
-----------------

To run the tests you will have to download the source code. After installing as
explained above, go to the source code root folder and run:

```
py.test .
```

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.

Citing this Python wrapper for Cubature
---------------------------------------

We kindly ask you to cite this Python library properly. Also, it would be
helpful if you could cite the papers where this methods has been applied as
well.

Castro, S.G.P.; Loukianov, A.; et al. "Python wrapper for Cubature: adaptive multidimensional integration". DOI:10.5281/zenodo.2541552. Version 0.18.8, 2025.

Citing Papers using this Python wrapper for Cubature
----------------------------------------------------

Used to integrate tangent stiffness matrices in computational solid mechanics

Castro, S.G.P. et al. "Evaluation of non-linear buckling loads of geometrically imperfect composite cylinders and cones with the Ritz method". Composite Structures, Vol. 122, 284-299, 2015.

Castro, S.G.P. et al. "A semi-analytical approach for linear and non-linear analysis of unstiffened laminated composite cylinders and cones under axial, torsion and pressure loads". Thin-Walled Structures, Vol. 90, 61-73, 2015.

Examples
--------

Some examples are given in "./examples" https://github.com/saullocastro/cubature/tree/master/examples.

Fork me!
--------

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.

License
-------

This wrapper follows the GNU-GPL license terms of Steven G. Johnson described in the `C Package <https://github.com/saullocastro/cubature/tree/master/cubature/cpackage/COPYING>`_.

cubature

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