ELLIPSE_MONTE_CARLO
Monte Carlo Estimate of Integrals in an Ellipse

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

Licensing:

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

Languages:

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.

Related Data and Programs:

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

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

ELLIPSOID_MONTE_CARLO a C++ 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 C++ 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 C program which applies a Monte Carlo method to estimate the volume of the unit hyperball in M dimensions;

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

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

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

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

Source Code:

• ellipse_monte_carlo.cpp, the source code.
• ellipse_monte_carlo.hpp, the include file.
• ellipse_monte_carlo.sh, BASH commands to compile the source code.

Examples and Tests:

• ellipse_monte_carlo_prb.c, a sample calling program.
• ellipse_monte_carlo_prb.sh, BASH commands to compile and run the sample program.
• ellipse_monte_carlo_prb_output.txt, the output file.

List of Routines:

• DAXPY computes constant times a vector plus a vector.
• DDOT forms the dot product of two vectors.
• ELLIPSE_AREA1 returns the area of an ellipse defined by a matrix.
• ELLIPSE_AREA2 returns the area of an ellipse defined by an equation.
• ELLIPSE_SAMPLE samples points in an ellipse.
• MONOMIAL_VALUE evaluates a monomial.
• R8_UNIFORM_01 returns a pseudorandom R8 scaled to [0,1].
• R8PO_FA factors a real symmetric positive definite matrix.
• R8PO_SL solves a linear system factored by R8PO_FA.
• R8VEC_NORMAL_01 returns a unit pseudonormal R8VEC.
• R8VEC_SUM returns the sum of an R8VEC.
• R8VEC_UNIFORM_01_NEW returns a unit pseudorandom R8VEC.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• UNIFORM_IN_SPHERE01_MAP maps uniform points into the unit sphere.

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