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Project Description

Your one-stop shop for numerical integration in Python.

Hundreds of numerical integration schemes for line segments, circles, disks, triangles, quadrilaterals, spheres, tetrahedra, hexahedra, wedges, pyramids.

To numerically integrate any function over any given triangle, do

import numpy
import quadrature

def f(x):
    return numpy.sin(x[0]) * numpy.sin(x[1])

triangle = numpy.array([[0.0, 0.0], [1.0, 0.0], [0.7, 0.5]])

val = quadrature.triangle.integrate(f, triangle, quadrature.triangle.Strang(9))

This uses Strang’s rule of degree 6.

Schemes

Line segment

  • Chebyshev-Gauß (both variants, arbitrary order)
  • Clenshaw-Curtis (after Waldvogel, arbitrary order)
  • Fejér-type-1 (after Waldvogel, arbitrary order)
  • Fejér-type-2 (after Waldvogel, arbitrary order)
  • Gauß-Hermite (via NumPy, arbitrary order)
  • Gauß-Laguerre (via NumPy, arbitrary order)
  • Gauß-Legendre (via NumPy, arbitrary order)
  • Gauß-Lobatto (arbitrary order)
  • Gauß-Patterson (7 schemes up to degree 191)
  • Gauß-Radau (arbitrary order)
  • closed Newton-Cotes (arbitray order)
  • open Newton-Cotes (arbitray order)

Circle

  • equidistant points

Triangle

Apart from the classical centroid, vertex, and seven-point schemes we have

Disk

  • Peirce (1957, arbitrary degree)
  • Lether (1971, arbitrary degree)

Quadrilateral

  • Product schemes derived from line segment schemes
  • Stroud’s schemes (6 schemes up to degree 15)

Tetrahedron

Hexahedron

  • Product schemes derived from line segment schemes

Pyramid

Wedge

Sphere

Installation

Python Package Index

quadrature is available from the Python Package Index, so with

pip install -U quadrature

you can install/upgrade.

Manual installation

Download quadrature from the Python Package Index. Place the quadrature script in a directory where Python can find it (e.g., $PYTHONPATH). You can install it system-wide with

python setup.py install

Testing

To run the tests, just check out this repository and type

pytest

Distribution

To create a new release

  1. bump the __version__ number,

  2. publish to PyPi and GitHub:

    $ make publish
    

License

quadrature is published under the MIT license.

Release History

Release History

0.2.2

This version

History Node

TODO: Figure out how to actually get changelog content.

Changelog content for this version goes here.

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0.2.1

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0.2.0

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0.1.1

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0.1.0

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Download Files

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TODO: Brief introduction on what you do with files - including link to relevant help section.

File Name & Checksum SHA256 Checksum Help Version File Type Upload Date
quadrature-0.2.2.tar.gz (219.4 kB) Copy SHA256 Checksum SHA256 Source Oct 31, 2016

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