SQUARE_MINIMAL_RULE
Quadrature Rules for the Symmetric Square.

SQUARE_MINIMAL_RULE is a FORTRAN90 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:

SQUARE_ARBQ_RULE, a FORTRAN90 library which returns quadrature rules, with exactness up to total degree 20, over the interior of the symmetric square in 2D, by Hong Xiao and Zydrunas Gimbutas.

SQUARE_EXACTNESS, a FORTRAN90 library which investigates the polynomial exactness of quadrature rules over the interior of a cube in 3D.

SQUARE_FELIPPA_RULE, a FORTRAN90 library which returns the points and weights of a Felippa quadrature rule over the interior of a square in 2D.

SQUARE_GRID, a FORTRAN90 library which computes a grid of points over the interior of a square in 2D.

SQUARE_INTEGRALS, a FORTRAN90 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 FORTRAN90 library which uses the Monte Carlo method to estimate the integral of a function over the interior of the unit square in 2D.

SQUARE_SYMQ_RULE, a FORTRAN90 library which returns efficient symmetric quadrature rules, with exactness up to total degree 15, over the interior of a symmetric square in 2D, by Hong Xiao and Zydrunas Gimbutas.

STROUD, a FORTRAN90 library which defines quadrature rules for a variety of M-dimensional regions, including the interior of the square, cube and hypercube, the pyramid, cone and ellipse, the hexagon, the M-dimensional octahedron, the circle, sphere and hypersphere, the triangle, tetrahedron and simplex, and the surface of the circle, sphere and hypersphere.

TOMS886, a FORTRAN90 library which defines the Padua points for interpolation in a 2D region, including the rectangle, triangle, and ellipse, by Marco Caliari, Stefano de Marchi, Marco Vianello. This is a version of ACM TOMS algorithm 886.

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.f90, the source code.

Examples and Tests:

• square_minimal_rule_test.f90 a sample calling program.
• square_minimal_rule_test.txt, the output file.

List of Routines:

• SMR00 returns the SMR rule of degree 0.
• SMR01 returns the SMR rule of degree 1.
• SMR02 returns the SMR rule of degree 2.
• SMR03 returns the SMR rule of degree 3.
• SMR04 returns the SMR rule of degree 4.
• SMR05 returns the SMR rule of degree 5.
• SMR06 returns the SMR rule of degree 6.
• SMR07 returns the SMR rule of degree 7.
• SMR08 returns the SMR rule of degree 8.
• SMR09 returns the SMR rule of degree 9.
• SMR10 returns the SMR rule of degree 10.
• SMR11 returns the SMR rule of degree 11.
• SMR12 returns the SMR rule of degree 12.
• SMR13 returns the SMR rule of degree 13.
• SMR14 returns the SMR rule of degree 14.
• SMR15 returns the SMR rule of degree 15.
• SMR16 returns the SMR rule of degree 16.
• SMR17 returns the SMR rule of degree 17.
• SMR18 returns the SMR rule of degree 18.
• SMR19 returns the SMR rule of degree 19.
• SMR19S returns the rotationally invariant SMR rule of degree 19.
• SMR20 returns the SMR rule of degree 20.
• SMR21 returns the SMR rule of degree 21.
• SMR22 returns the SMR rule of degree 22.
• SMR23 returns the SMR rule of degree 23.
• SMR24 returns the SMR rule of degree 24.
• SMR25 returns the SMR rule of degree 25.
• SMR26 returns the SMR rule of degree 26.
• SMR27 returns the SMR rule of degree 27.
• SMR28 returns the SMR rule of degree 28.
• SMR29 returns the SMR rule of degree 29.
• SMR29S returns the rotatonally invariant SMR rule of degree 29.
• SMR30 returns the SMR rule of degree 30.
• SMR31 returns the SMR rule of degree 31.
• SMR31S returns the rotationally invariant SMR rule of degree 31.
• SMR32 returns the SMR rule of degree 32.
• SMR33 returns the SMR rule of degree 33.
• SMR34 returns the SMR rule of degree 34.
• SMR35 returns the SMR rule of degree 35.
• SMR35S returns the rotationally invariant SMR rule of degree 35.
• SMR36 returns the SMR rule of degree 36.
• SMR37 returns the SMR rule of degree 37.
• SMR38 returns the SMR rule of degree 38.
• SMR39 returns the SMR rule of degree 39.
• SMR40 returns the SMR rule of degree 40.
• SMR41 returns the SMR rule of degree 41.
• SMR42 returns the SMR rule of degree 42.
• SMR43 returns the SMR rule of degree 43.
• SMR44 returns the SMR rule of degree 44.
• SMR45 returns the SMR rule of degree 45.
• SMR46 returns the SMR rule of degree 46.
• SMR47 returns the SMR rule of degree 47.
• SMR48 returns the SMR rule of degree 48.
• SMR49 returns the SMR rule of degree 49.
• SMR50 returns the SMR rule of degree 50.
• SMR51 returns the SMR rule of degree 51.
• SMR52 returns the SMR rule of degree 52.
• SMR53 returns the SMR rule of degree 53.
• SMR54 returns the SMR rule of degree 54.
• SMR55 returns the SMR rule of degree 55.
• SQUARE_MINIMAL_RULE returns a minimal rule for the square.
• SQUARE_MINIMAL_RULE_DEGREE_MAX returns the maximum rule degree.
• SQUARE_MINIMAL_RULE_ERROR_MAX returns the maximum error.
• SQUARE_MINIMAL_RULE_ORDER returns the order of a minimal square rule.
• SQUARESYM_AREA: area of the symmetric unit square in 2D.
• SQUARESYM_MONOMIAL_INTEGRAL: integrals over the symmetric unit square in 2D.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.