ellipsoid_monte_carlo

ellipsoid_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate the value of an integral over the interior of an ellipsoid in M dimensions.

Licensing:

The computer code and data files made available on this web page are distributed under the MIT license

Languages:

ellipsoid_monte_carlo 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:

annulus_monte_carlo a MATLAB code which uses the Monte Carlo method to estimate the integral of a function over the interior of a circular annulus in 2D.

ball_monte_carlo, a MATLAB code which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit ball in 3D;

circle_monte_carlo, a MATLAB code which applies a Monte Carlo method to estimate the integral of a function on the circumference of the unit circle in 2D;

cube_monte_carlo, a MATLAB code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit cube in 3D;

disk_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of the general disk in 2D.

disk01_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of the unit disk in 2D.

disk01_quarter_monte_carlo, a MATLAB code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit quarter disk in 2D;

ellipse_monte_carlo, a MATLAB code which applies a Monte Carlo method to estimate the integral of a function over the interior of an ellipse in 2D.

ellipsoid_monte_carlo_test

hyperball_monte_carlo, a MATLAB code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit ball in M dimensions;

hypercube_monte_carlo, a MATLAB code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit hypercube in M dimensions;

hypersphere_monte_carlo, a MATLAB code which applies a Monte Carlo method to estimate the integral of a function on the surface of the unit sphere in M dimensions;

line_monte_carlo, a MATLAB code which applies a Monte Carlo method to estimate the integral of a function over the length of the unit line in 1D;

polygon_monte_carlo, a MATLAB code which applies a Monte Carlo method to estimate the integral of a function over the interior of a polygon in 2D.

pyramid_monte_carlo, a MATLAB code which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit pyramid in 3D;

simplex_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in M dimensions.

sphere_monte_carlo, a MATLAB code which applies a Monte Carlo method to estimate integrals of a function over the surface of the unit sphere in 3D;

sphere_triangle_monte_carlo, a MATLAB code which applies a Monte Carlo method to estimate the integral of a function over a spherical triangle on the surface of the unit sphere in 3D;

square_monte_carlo, a MATLAB code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit square in 2D;

tetrahedron_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of the unit tetrahedron in 3D.

triangle_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of a triangle in 2D.

triangle01_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2D.

wedge_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of the unit wedge in 3D.

Source Code:

• ellipsoid_sample.m, samples points uniformly from an ellipsoid.
• ellipsoid_volume.m, returns the volume of an ellipsoid.
• hypersphere_unit_volume.m, volume of a unit hypersphere in M dimensions.
• monomial_value.m, evaluates a monomial.
• r8mat_print.m, prints an R8MAT.
• r8mat_print_some.m, prints some of an R8MAT.
• r8mat_transpose_print.m, prints an R8MAT, transposed.
• r8mat_transpose_print_some.m, prints some of an R8MAT, transposed.
• r8po_fa.m, factors an R8PO matrix.
• r8po_sl.m, solves an R8PO system factored by R8PO_FA.
• r8vec_print.m, prints an R8VEC.
• uniform_in_sphere01_map.m, maps uniform points into the unit sphere.