Cubature
========
Github Actions status:
[](https://github.com/saullocastro/cubature/actions/workflows/pytest_and_coverage.yml)
Coverage status:
[](https://codecov.io/gh/saullocastro/cubature)
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 0.18.6, 2024.
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>`_.
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