monte_carlo_rule

monte_carlo_rule, a Fortran77 code which generates a dataset of N random M-dimensional points, regards it as a quadrature rule for the unit hypercube, and writes out three files of information.

Usage:

monte_carlo_rule m n s

• m is the spatial dimension;
• n is the number of points to generate;
• s is the initial seed value.

The data is written to three files:

• an "R" or "region" file, which lists two points that bound the region, which will be the unit hypercube.
• a "W" or "weight" file, which lists the weight for each abscissa. each weight will equal 1/N.
• an "X" or "abscissa" file, which lists the abscissas of the rule. These will simply be the N random points in the M-dimensional hypercube.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

monte_carlo_rule 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:

monte_carlo_rule_test

f77_rule, a Fortran77 code which computes a quadrature rule which estimates the integral of a function f(x), which might be defined over a one dimensional region (a line) or more complex shapes such as a circle, a triangle, a quadrilateral, a polygon, or a higher dimensional region, and which might include an associated weight function w(x).

Reference:

1. Paul Bratley, Bennett Fox, Linus Schrage,
   A Guide to Simulation,
   Springer Verlag, pages 201-202, 1983.
2. Bennett Fox,
   Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators,
   ACM Transactions on Mathematical Software,
   Volume 12, Number 4, pages 362-376, 1986.
3. Donald Knuth,
   The Art of Computer Programming,
   Volume 2: Seminumerical Algorithms,
   Addison Wesley, 1969.

Source Code:

• monte_carlo_rule.f, the source code.
• monte_carlo_rule.sh, commands to compile and load the source code.

• monte_carlo_rule_test.sh, runs all the tests.
• monte_carlo_rule_test.txt, the output file.