LINE_MONTE_CARLO
Monte Carlo Estimate of Integrals Along Unit Line in 1D.

LINE_MONTE_CARLO is a FORTRAN77 library which uses the Monte Carlo method to estimate the integral of a function F(X) over the length of the unit line in 1D.

Licensing:

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

Languages:

LINE_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.

Related Data and Programs:

BALL_MONTE_CARLO, a FORTRAN77 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 FORTRAN77 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 FORTRAN77 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 FORTRAN77 library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit disk in 2D;

ELLIPSE_MONTE_CARLO a FORTRAN77 library which uses the Monte Carlo method to estimate the value of integrals over the interior of an ellipse in 2D.

ELLIPSOID_MONTE_CARLO a FORTRAN77 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 FORTRAN77 library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit hyperball in M dimensions;

HYPERBALL_VOLUME_MONTE_CARLO, a FORTRAN77 program which applies a Monte Carlo method to estimate the volume of the unit hyperball in M dimensions;

HYPERCUBE_MONTE_CARLO, a FORTRAN77 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 FORTRAN77 library which applies a Monte Carlo method to estimate the integral of a function on the surface of the unit hypersphere in M dimensions;

LINE_FEKETE_RULE, a FORTRAN77 library which approximates the location of Fekete points in an interval [A,B]. A family of sets of Fekete points, indexed by size N, represents an excellent choice for defining a polynomial interpolant.

LINE_FELIPPA_RULE, a FORTRAN77 library which returns the points and weights of a Felippa quadrature rule over the interior of a line segment in 1D.

LINE_GRID, a FORTRAN77 library which computes a grid of points over the interior of a line segment in 1D.

LINE_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the length of the unit line in 1D.

LINE_NCO_RULE, a FORTRAN77 library which computes a Newton Cotes Open (NCO) quadrature rule, using equally spaced points, over the interior of a line segment in 1D.

POLYGON_MONTE_CARLO, a FORTRAN77 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 FORTRAN77 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 FORTRAN77 library which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in M dimensions.

SPHERE_MONTE_CARLO, a FORTRAN77 library which applies a Monte Carlo method to estimate the integral of a function on the surface of the unit sphere in 3D;

SPHERE_TRIANGLE_MONTE_CARLO, a FORTRAN77 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 FORTRAN77 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 FORTRAN77 library which uses the Monte Carlo method to estimate integrals over the interior of the unit tetrahedron in 3D.

TRIANGLE_MONTE_CARLO, a FORTRAN77 library which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2D.

WEDGE_MONTE_CARLO, a FORTRAN77 library which uses the Monte Carlo method to estimate integrals over the interior of the unit wedge in 3D.

Source Code:

• line_monte_carlo.f, the source code.
• line_monte_carlo.sh, BASH commands to compile the source code.

Examples and Tests:

• line_monte_carlo_prb.f, a sample calling program.
• line_monte_carlo_prb.sh, BASH commands to compile and run the sample program.
• line_monte_carlo_prb_output.txt, the output file.

List of Routines:

• LINE01_LENGTH: length of the unit line in 1D.
• LINE01_MONOMIAL_INTEGRAL: monomial integral over the unit line in 1D.
• LINE01_SAMPLE samples the unit line in 1D.
• MONOMIAL_VALUE_1D evaluates a monomial in 1D.
• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN77 source codes.