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 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:

square_integrals_test

octave_integrals, an Octave 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_exactness, an Octave code which computes the polynomial exactness of quadrature rules for f(x,y) over the interior of a quadrilateral in 2D.

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.