quadraturerules 0.9.1

quadrature rules library

Quadrature rules

The online encylopedia of quadrature rules is a reference website that lists a number of quadrature rules.

Quadrature rules are sets of points and weights that are used to approximate integrals. If ${p_0,\dots,p_{n-1}}\subset\mathbb{R}^d$ and ${w_0,\dots,w_{n-1}}\subset\mathbb{R}$ are the points and weights (repectively) of the quadrature rule for a single integral, then:

$$\int f(x),\mathrm{d}x \approx \sum_{i=0}^{n-1}f(p_i)w_i$$

Website

Before building the online encylopedia of quadrature rules, you must first install qrtools from the python directory:

cd python
python3 -m pip install .

The online encylopedia of quadrature rules website can then be built by running:

cd website
python3 build.py

Libraries

All of the quadrature rules included in the online encylopedia of quadrature rules are included in the quadraturerules library, which is available in the following languages:

Language	Badges
C
C++
Fortran
FORTRAN 77
Julia
Python
Rust

Before building any of the libraries, you must first install qrtools from the python directory:

cd python
python3 -m pip install .

You can then build the libraries using the build.py script in the library directory. For example, to build the python library, you can run:

cd library
python build.py python

and to build the rust library, you can run:

cd library
python build.py rust

Python library

The quadraturerules Python library is available on PyPI. It can be installed by running:

python -m pip install quadraturerules

Usage

The library's function single_integral_quadrature can be used to get the points and weights of quadrature rules for a single integral. For example the following snippet will create an order 3 Xiao--Gimbutas rule on a triangle:

from quadraturerules import Domain, QuadratureRule, single_integral_quadrature

points, weights = single_integral_quadrature(
    QuadratureRule.XiaoGimbutas,
    Domain.Triangle,
    3,
)

Note that the points returned by the library are represented using barycentric coordinates.

Generating the library

The Python quadraturerules library can be generated from the templates in the online encyclopedia of quadrature rules GitHub repo. First clone the repo and move into the library directory:

git clone https://github.com/quadraturerules/quadraturerules.git
cd quadraturerules/library

The Python library can then be generated by running:

python build.py python

This will create a directory called python.build containing the Python source code.

Tests can then be run by moving into this folder and using pytest:

cd python.build
python -m pytest test/