SQUARE_INTEGRALS
Integrals Over the Interior of the Unit Square in 2D

SQUARE_INTEGRALS is a C library which returns the exact value of the integral of any monomial over the interior of the unit square or symmetric unit square in 2D.

The interior of the unit square in 2D is defined by

        0 <= X <= 1,
        0 <= Y <= 1.
      

The interior of the symmetric unit square in 2D is defined by

        -1 <= X <= 1,
        -1 <= Y <= 1.
      

The integrands are all of the form

        f(x,y) = x^e1 * y^e2
      

Licensing:

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

Languages:

SQUARE_INTEGRALS 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:

BALL_INTEGRALS, a C library which returns the exact value of the integral of any monomial over the interior of the unit ball in 3D.

CIRCLE_INTEGRALS, a C library which returns the exact value of the integral of any monomial over the circumference of the unit circle in 2D.

CUBE_INTEGRALS, a C library which returns the exact value of the integral of any monomial over the interior of the unit cube in 3D.

DISK01_INTEGRALS, a C library which returns the exact value of the integral of any monomial over the interior of the unit disk in 2D.

HYPERBALL_INTEGRALS, a C library which returns the exact value of the integral of any monomial over the interior of the unit hyperball in M dimensions.

HYPERCUBE_INTEGRALS, a C library which returns the exact value of the integral of any monomial over the interior of the unit hypercube in M dimensions.

HYPERSPHERE_INTEGRALS, a C library which returns the exact value of the integral of any monomial over the surface of the unit hypersphere in M dimensions.

LINE_INTEGRALS, a C library which returns the exact value of the integral of any monomial over the length of the unit line in 1D.

POLYGON_INTEGRALS, a C library which returns the exact value of the integral of any monomial over the interior of a polygon in 2D.

PYRAMID_INTEGRALS, a C library which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3D.

SIMPLEX_INTEGRALS, a C library which returns the exact value of the integral of any monomial over the interior of the unit simplex in M dimensions.

SPHERE_INTEGRALS, a C library which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3D.

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

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

TETRAHEDRON_INTEGRALS, a C library which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3D.

TRIANGLE_INTEGRALS, a C library which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2D.

WEDGE_INTEGRALS, a C library which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3D.

Source Code:

• square_integrals.c, the source code.
• square_integrals.h, the source code.

Examples and Tests:

• square_integrals_test.c, a sample calling program.
• square_integrals_test.txt, the output file.

List of Routines:

• I4VEC_UNIFORM_AB_NEW returns a scaled pseudorandom I4VEC.
• MONOMIAL_VALUE evaluates a monomial.
• R8MAT_UNIFORM_AB_NEW returns a scaled pseudorandom R8MAT.
• R8VEC_SUM returns the sum of an R8VEC.
• SQUARE01_AREA: area of the unit square in 2D.
• SQUARE01_MONOMIAL_INTEGRAL: integrals over the unit square in 2D.
• SQUARE01_SAMPLE samples points in the unit square in 2D.
• SQUARESYM_AREA: area of the symmetric unit square in 2D.
• SQUARESYM_MONOMIAL_INTEGRAL: integrals over the symmetric unit square in 2D.
• SQUARESYM_SAMPLE samples points in 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.