HYPERCUBE_INTEGRALS
Integrals Over the Interior of the Unit Hypercube 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.

The interior of the unit hypercube in M dimensions is defined by

        0 <= X(1:M) <= 1.
      

The integrands are all of the form

        F(X) = product ( 1 <= I <= M ) X(I)^E(I)
      

Licensing:

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

Languages:

HYPERCUBE_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_INTEGRALS, a MATLAB library which returns the exact value of the integral of any monomial 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_GRID, a MATLAB library which computes a grid of points over the interior of a hypercube in M dimensions.

hypercube_integrals_test

HYPERCUBE_MONTE_CARLO, a MATLAB library which uses the Monte Carlo method to estimate the integral of a function 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:

• hypercube01_volume.m, returns the volume of the unit cube in M dimensions.
• hypercube01_monomial_integral.m, integrates a monomial in the unit cube in M dimensions.
• hypercube01_sample.m, samples points from the unit cube in M dimensions.
• 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.