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

SQUARE_INTEGRALS is a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit square in 2D.

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

        0 <= X <= 1,
        0 <= 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 FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

BALL_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit ball in 3D.

CIRCLE_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the circumference of the unit circle in 2D.

CUBE_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit cube in 3D.

DISK_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit disk in 2D.

HYPERBALL_INTEGRALS, a FORTRAN77 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 FORTRAN77 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 FORTRAN77 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 FORTRAN77 library which returns the exact value of the integral of any monomial over the length of the unit line in 1D.

POLYGON_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of a polygon in 2D.

PYRAMID_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3D.

SIMPLEX_INTEGRALS, a FORTRAN77 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 FORTRAN77 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 FORTRAN77 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 FORTRAN77 library which returns the points and weights of a Felippa quadrature rule over the interior of a square in 2D.

SQUARE_GRID, a FORTRAN77 library which computes a grid of points over the interior of a square in 2D.

SQUARE_MONTE_CARLO, a FORTRAN77 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 FORTRAN77 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 FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3D.

TRIANGLE_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2D.

WEDGE_INTEGRALS, a FORTRAN77 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.f, the source code.
• square_integrals.sh, BASH commands to compile the source code.

Examples and Tests:

• square_integrals_prb.f, a sample calling program.
• square_integrals_prb.sh, BASH commands to compile and run the sample program.
• square_integrals_prb_output.txt, the output file.

List of Routines:

• MONOMIAL_VALUE evaluates a monomial.
• R8MAT_UNIFORM_01 fills an R8MAT with unit pseudorandom numbers.
• SQUARE01_AREA: area of the unit square in 2D.
• SQUARE01_MONOMIAL_INTEGRAL: integral over interior of unit square in 2D.
• SQUARE01_SAMPLE samples the interior of the unit square in 2D.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN77 source codes.