CUBE_INTEGRALS
Integrals Over the Interior of the Unit Cube in 3D

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

The interior of the unit cube in 3D is defined by

        0 <= X <= 1,
        0 <= Y <= 1,
        0 <= Z <= 1.
      

The integrands are all of the form

        f(x,y,z) = x^e1 * y^e2 * z^e3.
      

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

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

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

CUBE_ARBQ_RULE, a MATLAB library which returns quadrature rules, with exactness up to total degree 15, over the interior of the symmetric cube in 3D, by Hong Xiao and Zydrunas Gimbutas.

CUBE_EXACTNESS, a MATLAB library which investigates the polynomial exactness of quadrature rules over the interior of a cube in 3D.

CUBE_FELIPPA_RULE, a MATLAB library which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.

CUBE_GRID, a MATLAB library which computes a grid of points over the interior of a cube in 3D.

cube_integrals_test

CUBE_MONTE_CARLO, a MATLAB library which uses the Monte Carlo method to estimate the integral of a function over the interior of the unit cube in 3D.

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

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

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

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

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

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

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

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

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

Source Code:

• cube01_volume.m, returns the volume of the unit cube in 3D.
• cube01_monomial_integral.m, integrates a monomial in the unit cube in 3D.
• cube01_sample.m, samples points from the unit cube in 3D.
• i4vec_uniform_ab.m, returns a scaled pseudorandom I4VEC.
• monomial_value.m, evaluates a monomial.
• r8mat_uniform_01.m, returns a uniform pseudorandom R8MAT.
• timestamp.m, prints the current YMDHMS date as a time stamp.