jburkardt

MONTE_CARLO_RULE\ Monte Carlo Sampling Regarded as Quadrature Rule {#monte_carlo_rule-monte-carlo-sampling-regarded-as-quadrature-rule align=”center”} ================================================

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MONTE_CARLO_RULE is a C++ program 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: {#usage align=”center”}

monte_carlo_rule m n s

where

• 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: {#licensing align=”center”}

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

Languages: {#languages align=”center”}

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: {#related-data-and-programs align=”center”}

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

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

POWER_RULE, a C++ program which constructs a power rule, that is, a product quadrature rule from identical 1D factor rules.

QUADRATURE_RULES_UNIFORM, a dataset directory which contains quadrature rules for M-dimensional unit cubes, based on a uniform pseudorandom sequence. stored as a file of abscissas, a file of weights, and a file of region limits.

SPARSE_GRID_CC_DATASET, a C++ program which creates a Clenshaw-Curtis sparse grid and write the data to three files.

SPARSE_GRID_GL_DATASET, a C++ program which creates a Gauss-Legendre sparse grid and write the data to three files.

SPARSE_GRID_HERMITE_DATASET, a C++ program which creates a Gauss-Hermite sparse grid and write the data to three files.

SPARSE_GRID_LAGUERRE_DATASET, a C++ program which creates a Gauss-Laguerre sparse grid and write the data to three files.

SPARSE_GRID_MIXED_DATASET, a C++ program which creates a sparse grid dataset based on a mixture of 1D rules.

SPARSE_GRID_OPEN_DATASET, a C++ program which creates a sparse grid dataset based on open rules (Fejer 2, Gauss-Patterson, Newton-Cotes-Open).

Reference: {#reference align=”center”}

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: {#source-code align=”center”}

• monte_carlo_rule.cpp, the source code.

List of Routines: {#list-of-routines align=”center”}

• MAIN is the main program for MONTE_CARLO_RULE.
• I4_TO_STRING converts an I4 to a C++ string.
• R8MAT_UNIFORM_01_NEW returns a unit pseudorandom R8MAT.
• R8MAT_WRITE writes an R8MAT file with no header.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C++ source codes.

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Last revised on 29 March 2013.