HYPERCUBE_INTEGRALS
Integrals Over the Interior of the Unit Hypercube in M Dimensions

HYPERCUBE_INTEGRALS is a Python 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 Python library which returns the exact value of the integral of any monomial over the interior of the unit ball in 3D.

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

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

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

HYPERBALL_INTEGRALS, a Python 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 Python library which computes a grid of points over the interior of a hypercube in M dimensions.

HYPERCUBE_MONTE_CARLO, a Python library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit hypercube in M dimensions;

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

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

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

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

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

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

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

WEDGE_INTEGRALS, a Python 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.py, returns the volume of the unit cube in M dimensions.
• hypercube01_monomial_integral.py, integrates a monomial in the unit cube in M dimensions.
• hypercube01_sample.py, samples points from the unit cube in M dimensions.
• i4vec_print.py, prints an I4VEC.
• i4vec_transpose_print.py, prints an I4VEC "transposed", that is, 5 entries to a line.
• i4vec_uniform_ab.py, returns a scaled pseudorandom I4VEC.
• monomial_value.py, evaluates a monomial.
• r8mat_print.py, prints an R8MAT.
• r8mat_print_some.py, prints some of an R8MAT.
• r8mat_transpose_print.py, prints an R8MAT, transposed.
• r8mat_transpose_print_some.py, prints some of an R8MAT, transposed.
• r8mat_uniform_01.py, returns a uniform pseudorandom R8MAT.
• r8mat_uniform_ab.py, returns a scaled pseudorandom R8MAT.
• timestamp.py, prints the current YMDHMS date as a time stamp.

Examples and Tests:

• hypercube_integrals_test.py, calls all the tests.
• hypercube_integrals_test.sh, runs all the tests.
• hypercube_integrals_test.txt, the output file.

You can go up one level to the Python source codes.