SQUARE_MINIMAL_RULE
Quadrature Rules for the Symmetric Square.

SQUARE_MINIMAL_RULE is a Python library which returns "almost minimal" quadrature rules, with exactness up to total degree 55, over the interior of the symmetric unit square in 2D, by Mattia Festa and Alvise Sommariva.

Licensing:

The computer code and data files made available on this web page are distributed under the GNU LGPL license.

Languages:

SQUARE_MINIMAL_RULE is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

ANNULUS_RULE, a Python library which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2D.

SQUARE_GRID, a Python library which computes a grid of points over the interior of a square in 2D.

SQUARE_INTEGRALS, a Python library which returns the exact value of the integral of any monomial over the interior of the unit square in 2D.

SQUARE_MONTE_CARLO, a Python library which uses the Monte Carlo method to estimate the integral of a function over the interior of the unit square in 2D.

Reference:

1. Mattia Festa, Alvise Sommariva,
   Computing almost minimal formulas on the square,
   Journal of Computational and Applied Mathematics,
   Volume 17, Number 236, November 2012, pages 4296-4302.

Source Code:

• square_minimal_rule.py, the source code.
• square_minimal_rule.sh runs the tests.
• square_minimal_rule.txt, the output file.

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