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

SQUARE_INTEGRALS is a Python 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

where the exponents are nonnegative integers.

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 Python library which returns the exact value of the integral of any monomial over the interior of the unit ball in 3D.

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

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

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

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

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

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

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

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

SQUARE_MINIMAL_RULE, a Python 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.

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

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

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

Source Code:

i4vec_print.py, prints an I4VEC.
i4vec_transpose_print.py, prints an I4VEC "transposed", that is, 5 entries to a line.
i4vec_uniform_ab.m, returns a scaled pseudorandom I4VEC.
monomial_value.m, evaluates a monomial.
r8mat_print.py, prints an R8MAT.
r8mat_print_some.py, prints some of an R8MAT.
r8mat_transpose_print.py, prints an R8MAT, transposed.
r8mat_transpose_print_some.py, prints some of an R8MAT, transposed.
r8mat_uniform_01.py, returns a uniform pseudorandom R8MAT.
r8mat_uniform_ab.py, returns a scaled pseudorandom R8MAT.
square01_area.m, returns the area of the unit square in 2D.
square01_monomial_integral.m, integrates a monomial in the unit square in 2D.
square01_sample.m, samples points from the unit square in 2D.
squaresym_area.m, returns the area of the unit square in 2D.
squaresym_monomial_integral.m, integrates a monomial in the unit square in 2D.
squaresym_sample.m, samples points from the unit square in 2D.
timestamp.m, prints the current YMDHMS date as a time stamp.

Examples and Tests:

square_integrals_test.py, calls all the tests.
square_integrals_test.sh, runs all the tests.
square_integrals_test.txt, the output file.

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