# SQUARE_MINIMAL_RULE Quadrature Rules for the Symmetric Square.

SQUARE_MINIMAL_RULE is a C 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 MATLAB version.

### Related Data and Programs:

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

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

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

SQUARE_INTEGRALS, a C 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 C 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 C 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 C 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 C 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.

### List of Routines:

• R8MAT_COPY_NEW copies one R8MAT to a "new" R8MAT.
• R8VEC_SUM returns the sum of an R8VEC.
• 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 C source codes.

Last revised on 22 February 2018.