square_integrals

square_integrals, an Octave code 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 MIT license

Languages:

square_integrals is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

square_integrals_test

ball_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit ball in 3d.

circle_integrals, an Octave code which returns the exact value of the integral of any monomial over the circumference of the unit circle in 2d.

cube_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit cube in 3d.

disk01_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit disk in 2d.

hexagon_integrals, an Octave code which returns the exact value of the integral of a monomial over the interior of a hexagon in 2d.

hyperball_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit hyperball in m dimensions.

hypercube_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit hypercube in m dimensions.

hypersphere_integrals, an Octave code which returns the exact value of the integral of any monomial over the surface of the unit hypersphere in m dimensions.

line_integrals, an Octave code which returns the exact value of the integral of any monomial over the length of the unit line in 1d.

polygon_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of a polygon in 2d.

pyramid_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3d.

simplex_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit simplex in m dimensions.

sphere_integrals, an Octave code which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3d.

Source Code:

• i4vec_uniform_ab.m, returns a scaled pseudorandom I4VEC.
• monomial_value.m, evaluates a monomial.
• r8mat_uniform_ab.m, returns a scaled uniform 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 symmetric unit square in 2D.
• squaresym_monomial_integral.m, integrates a monomial in the symmetric square in 2D.
• squaresym_sample.m, samples points from the symmetric unit square in 2D.