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<html>
<head>
<title>
TRIANGLE_MONTE_CARLO - Monte Carlo Integral Estimates over a Triangle
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TRIANGLE_MONTE_CARLO <br> Monte Carlo Integral Estimates over a Triangle
</h1>
<hr>
<p>
<b>TRIANGLE_MONTE_CARLO</b>
is a FORTRAN90 library which
estimates the integral of a function over a triangle using the Monte Carlo method.
</p>
<p>
The library makes it relatively easy to compare different methods of
producing sample points in the triangle, and to vary the triangle over
which integration is carried out.
</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">
Languages:
</h3>
<p>
<b>TRIANGLE_MONTE_CARLO</b> is available in
<a href = "../../cpp_src/triangle_monte_carlo/triangle_monte_carlo.html">a C++ version</a> and
<a href = "../../f_src/triangle_monte_carlo/triangle_monte_carlo.html">a FORTRAN90 version</a> and
<a href = "../../m_src/triangle_monte_carlo/triangle_monte_carlo.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/dunavant/dunavant.html">
DUNAVANT</a>
is a FORTRAN90 library which
defines Dunavant rules for quadrature on a triangle.
</p>
<p>
<a href = "../../f_src/fekete/fekete.html">
FEKETE</a>
is a FORTRAN90 library which
defines Fekete rules for interpolation or quadrature on a triangle.
</p>
<p>
<a href = "../../f_src/felippa/felippa.html">
FELIPPA</a>,
a FORTRAN90 library which
defines quadrature rules for lines, triangles, quadrilaterals,
pyramids, wedges, tetrahedrons and hexahedrons.
</p>
<p>
<a href = "../../f_src/gm_rule/gm_rule.html">
GM_RULE</a>,
a FORTRAN90 library which
defines Grundmann-Moeller rules for quadrature over a triangle, tetrahedron,
or general M-dimensional simplex.
</p>
<p>
<a href = "../../f_src/ncc_triangle/ncc_triangle.html">
NCC_TRIANGLE</a>,
a FORTRAN90 library which
defines Newton-Cotes Closed quadrature rules on a triangle.
</p>
<p>
<a href = "../../f_src/nco_triangle/nco_triangle.html">
NCO_TRIANGLE</a>,
a FORTRAN90 library which
defines Newton-Cotes Open quadrature rules on a triangle.
</p>
<p>
<a href = "../../f_src/random_data/random_data.html">
RANDOM_DATA</a>,
a FORTRAN90 library which
generates sample points for
various probability distributions, spatial dimensions, and geometries;
</p>
<p>
<a href = "../../f77_src/simpack/simpack.html">
SIMPACK</a>,
a FORTRAN77 library which
approximates the integral of a function over a multidimensional simplex.
</p>
<p>
<a href = "../../f_src/stroud/stroud.html">
STROUD</a>,
a FORTRAN90 library which
defines quadrature rules for a variety of multidimensional reqions.
</p>
<p>
<a href = "../../f_src/test_tri_int/test_tri_int.html">
TEST_TRI_INT</a>,
a FORTRAN90 library which
defines test functions for quadrature over the triangle.
</p>
<p>
<a href = "../../m_src/tetrahedron_monte_carlo/tetrahedron_monte_carlo.html">
TETRAHEDRON_MONTE_CARLO</a>,
a MATLAB program which
uses the Monte Carlo method to estimate integrals over a tetrahedron.
</p>
<p>
<a href = "../../f77_src/toms612/toms612.html">
TOMS612</a>,
a FORTRAN77 library which
estimates the integral of a function over a triangle.
</p>
<p>
<a href = "../../f77_src/toms706/toms706.html">
TOMS706</a>,
a FORTRAN77 library which
estimates the integral of a function over a triangulated region.
</p>
<p>
<a href = "../../f_src/triangle_exactness/triangle_exactness.html">
TRIANGLE_EXACTNESS</a>,
a FORTRAN90 program which
investigates the polynomial exactness of a quadrature rule for the triangle.
</p>
<p>
<a href = "../../f_src/wandzura/wandzura.html">
WANDZURA</a>,
a FORTRAN90 library which
defines Wandzura rules for quadrature on a triangle.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Claudio Rocchini, Paolo Cignoni,<br>
Generating Random Points in a Tetrahedron,<br>
Journal of Graphics Tools,<br>
Volume 5, Number 4, 2000, pages 9-12.
</li>
<li>
Reuven Rubinstein,<br>
Monte Carlo Optimization, Simulation and Sensitivity of
Queueing Networks,<br>
Krieger, 1992,<br>
ISBN: 0894647644,<br>
LC: QA298.R79.
</li>
<li>
Greg Turk,<br>
Generating Random Points in a Triangle,<br>
in Graphics Gems I,<br>
edited by Andrew Glassner,<br>
AP Professional, 1990,<br>
ISBN: 0122861663,<br>
LC: T385.G697
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "triangle_monte_carlo.f90">triangle_monte_carlo.f90</a>, the source code.
</li>
<li>
<a href = "triangle_monte_carlo.sh">triangle_monte_carlo.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "triangle_monte_carlo_prb.f90">triangle_monte_carlo_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "triangle_monte_carlo_prb.sh">triangle_monte_carlo_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "triangle_monte_carlo_prb_output.txt">triangle_monte_carlo_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>R8MAT_TRANSPOSE_PRINT</b> prints an R8MAT, transposed.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT_SOME</b> prints some of an R8MAT, transposed.
</li>
<li>
<b>R8VEC_UNIFORM_01</b> returns a unit pseudorandom R8VEC.
</li>
<li>
<b>REFERENCE_TO_PHYSICAL_T3</b> maps T3 reference points to physical points.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TRIANGLE_AREA</b> computes the area of a triangle.
</li>
<li>
<b>TRIANGLE_MONTE_CARLO</b> applies the Monte Carlo rule to integrate a function.
</li>
<li>
<b>TRIANGLE_INTEGRAND_01</b> evaluates 1 integrand function.
</li>
<li>
<b>TRIANGLE_INTEGRAND_02</b> evaluates 2 integrand functions.
</li>
<li>
<b>TRIANGLE_INTEGRAND_03</b> evaluates 3 integrand functions.
</li>
<li>
<b>TRIANGLE_INTEGRAND_04</b> evaluates 4 integrand functions.
</li>
<li>
<b>TRIANGLE_INTEGRAND_05</b> evaluates 5 integrand functions.
</li>
<li>
<b>TRIANGLE_UNIT_SAMPLE_01</b> selects points from the unit triangle.
</li>
<li>
<b>TRIANGLE_UNIT_SAMPLE_02</b> selects points from the unit triangle.
</li>
<li>
<b>TRIANGLE_UNIT_SAMPLE_03</b> selects points from the unit triangle.
</li>
<li>
<b>TRIANGLE_UNIT_SAMPLE_04</b> selects points from the unit triangle.
</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 15 August 2009.
</i>
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