Monte Carlo Estimate of Integrals in an Ellipse

**ELLIPSE_MONTE_CARLO**
is a MATLAB library which
uses the Monte Carlo method to estimate the value of integrals
over the interior of an ellipse in 2D.

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

**ELLIPSE_MONTE_CARLO** is available in
a C version and
a C++ version and
a FORTRAN77 version and
a FORTRAN90 version and
a MATLAB version and
a Python version.

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

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

ELLIPSE_GRID, a MATLAB library which computes a grid of points over the interior of an ellipse in 2D.

ELLIPSOID_MONTE_CARLO a MATLAB library which uses the Monte Carlo method to estimate the value of integrals over the interior of an ellipsoid in M dimensions.

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

HYPERBALL_VOLUME_MONTE_CARLO, a MATLAB program which applies a Monte Carlo method to estimate the volume of the unit hyperball in M dimensions;

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

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

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

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

- ellipse_area1.m, returns the area of an ellipse defined by a matrix.
- ellipse_area1_test.m
- ellipse_area2.m, returns the area of an ellipse defined by an equation.
- ellipse_area2_test.m
- ellipse_sample.m, samples points in an ellipse.
- monomial_value.m, evaluates a monomial.
- r8_uniform_01.m, returns a unit pseudorandom R8.
- r8mat_print.m, prints an R8MAT.
- r8mat_print_some.m, prints some of an R8MAT.
- r8po_fa.m, factors an R8PO matrix.
- r8po_sl.m, solves an R8PO system factored by R8PO_FA.
- r8vec_normal_01.m, returns a unit pseudonormal R8VEC.
- r8vec_uniform_01.m, returns a unit pseudorandom R8VEC.
- timestamp.m, prints the current YMDHMS date as a time stamp.
- uniform_in_sphere01_map.m, maps uniform points into the unit sphere.

- ellipse_monte_carlo_test.m, a sample calling program.
- ellipse_monte_carlo_test01.m, uses the sampling method to estimate integrals of monomials over an ellipse.
- ellipse_monte_carlo_test_output.txt, the output file.

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