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<html>
<head>
<title>
MONTE_CARLO_RULE - Monte Carlo Sampling Regarded as Quadrature Rule
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
MONTE_CARLO_RULE <br> Monte Carlo Sampling Regarded as Quadrature Rule
</h1>
<hr>
<p>
<b>MONTE_CARLO_RULE</b>
is a FORTRAN90 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.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>monte_carlo_rule</b> <i>m</i> <i>n</i> <i>s</i>
</blockquote>
where
<ul>
<li>
<i>m</i> is the spatial dimension;
</li>
<li>
<i>n</i> is the number of points to generate;
</li>
<li>
<i>s</i> is the initial seed value.
</li>
</ul>
</p>
<p>
The data is written to three files:
<ul>
<li>
an "R" or "region" file, which lists two points that bound the region,
which will be the unit hypercube.
</li>
<li>
a "W" or "weight" file, which lists the weight for each abscissa.
each weight will equal 1/N.
</li>
<li>
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.
</li>
</ul>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../datasets/quadrature_rules_uniform/quadrature_rules_uniform.html">
QUADRATURE_RULES_UNIFORM</a>,
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.
</p>
<p>
<a href = "../../f_src/sparse_grid_cc_dataset/sparse_grid_cc_dataset.html">
SPARSE_GRID_CC_DATASET</a>,
a FORTRAN90 program which
creates a Clenshaw-Curtis sparse grid and write the data to three files.
</p>
<p>
<a href = "../../f_src/sparse_grid_gl_dataset/sparse_grid_gl_dataset.html">
SPARSE_GRID_GL_DATASET</a>,
a FORTRAN90 program which
creates a Gauss-Legendre sparse grid and write the data to three files.
</p>
<p>
<a href = "../../f_src/sparse_grid_hermite_dataset/sparse_grid_hermite_dataset.html">
SPARSE_GRID_HERMITE_DATASET</a>,
a FORTRAN90 program which
creates a Gauss-Hermite sparse grid and write the data to three files.
</p>
<p>
<a href = "../../f_src/sparse_grid_laguerre_dataset/sparse_grid_laguerre_dataset.html">
SPARSE_GRID_LAGUERRE_DATASET</a>,
a FORTRAN90 program which
creates a Gauss-Laguerre sparse grid and write the data to three files.
</p>
<p>
<a href = "../../f_src/sparse_grid_mixed_dataset/sparse_grid_mixed_dataset.html">
SPARSE_GRID_MIXED_DATASET</a>,
a FORTRAN90 program which
creates a sparse grid dataset based on a mixture of 1D rules.
</p>
<p>
<a href = "../../f_src/sparse_grid_open_dataset/sparse_grid_open_dataset.html">
SPARSE_GRID_OPEN_DATASET</a>,
a FORTRAN90 program which
creates a sparse grid dataset based on
open rules (Fejer 2, Gauss-Patterson, Newton-Cotes-Open).
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Paul Bratley, Bennett Fox, Linus Schrage,<br>
A Guide to Simulation,<br>
Springer Verlag, pages 201-202, 1983.
</li>
<li>
Bennett Fox,<br>
Algorithm 647:
Implementation and Relative Efficiency of Quasirandom
Sequence Generators,<br>
ACM Transactions on Mathematical Software,<br>
Volume 12, Number 4, pages 362-376, 1986.
</li>
<li>
Donald Knuth, <br>
The Art of Computer Programming,<br>
Volume 2: Seminumerical Algorithms,<br>
Addison Wesley, 1969.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "monte_carlo_rule.f90">monte_carlo_rule.f90</a>,
the source code.
</li>
<li>
<a href = "monte_carlo_rule.sh">monte_carlo_rule.sh</a>,
commands to compile and load the source code.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for MONTE_CARLO_RULE.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>R8MAT_UNIFORM_01</b> returns a unit pseudorandom R8MAT.
</li>
<li>
<b>R8MAT_WRITE</b> writes an R8MAT file.
</li>
<li>
<b>S_BLANK_DELETE</b> removes blanks from a string, left justifying the remainder.
</li>
<li>
<b>S_TO_I4</b> reads an integer value from a string.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 23 December 2011.
</i>
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