square_integrals

square_integrals, a MATLAB 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 information on this web page is 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:

matlab_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the surface or interior of some geometric object, including a line, quadrilateral, box, circle, disk, sphere, ball and others.

square_arbq_rule, a MATLAB code 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 MATLAB code which returns the points and weights of a felippa quadrature rule over the interior of a square in 2d.

square_grid, a MATLAB code which computes a grid of points over the interior of a square in 2d.

square_hex_grid, a MATLAB code which computes a hexagonal grid of points over the interior of a square in 2d.

square_minimal_rule, a MATLAB code 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 MATLAB code 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 MATLAB code 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.

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.