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<html>
<head>
<title>
SPHERE_MONTE_CARLO - Monte Carlo Estimate of Sphere Surface Integrals
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
SPHERE_MONTE_CARLO <br> Monte Carlo Estimate of Sphere Surface Integrals
</h1>
<hr>
<p>
<b>SPHERE_MONTE_CARLO</b>
is a FORTRAN90 library which
estimates the integral over the surface of the unit sphere of
a function F(X,Y,Z).
</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>SPHERE_MONTE_CARLO</b> is available in
<a href = "../../cpp_src/sphere_monte_carlo/sphere_monte_carlo.html">a C++ version</a> and
<a href = "../../f_src/sphere_monte_carlo/sphere_monte_carlo.html">a FORTRAN90 version</a> and
<a href = "../../m_src/sphere_monte_carlo/sphere_monte_carlo.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/ball_volume_monte_carlo/ball_volume_monte_carlo.html">
BALL_VOLUME_MONTE_CARLO</a>,
a FORTRAN90 program which
applies a Monte Carlo method to estimate the volume of the unit ball in 6D;
</p>
<p>
<a href = "../../f_src/sphere_cvt/sphere_cvt.html">
SPHERE_CVT</a>,
a FORTRAN90 library which
creates a mesh of well-separated points on a unit sphere using Centroidal Voronoi
Tessellations.
</p>
<p>
<a href = "../../m_src/sphere_delaunay/sphere_delaunay.html">
SPHERE_DELAUNAY</a>,
a MATLAB program which
computes the Delaunay triangulation of points on a sphere.
</p>
<p>
<a href = "../../f_src/sphere_design_rule/sphere_design_rule.html">
SPHERE_DESIGN_RULE</a>,
a FORTRAN90 library which
returns point sets on the surface of the unit sphere, known as "designs",
which can be useful for estimating integrals on the surface, among other uses.
</p>
<p>
<a href = "../../f_src/sphere_exactness/sphere_exactness.html">
SPHERE_EXACTNESS</a>,
a FORTRAN90 program which
tests the polynomial exactness of a quadrature rule for the unit sphere;
</p>
<p>
<a href = "../../datasets/sphere_grid/sphere_grid.html">
SPHERE_GRID</a>,
a dataset directory which
contains grids of points, lines, triangles or quadrilaterals on a sphere;
</p>
<p>
<a href = "../../f_src/sphere_lebedev_rule/sphere_lebedev_rule.html">
SPHERE_LEBEDEV_RULE</a>,
a FORTRAN90 library which
computes Lebedev quadrature rules for the unit sphere;
</p>
<p>
<a href = "../../f_src/sphere_quad/sphere_quad.html">
SPHERE_QUAD</a>,
a FORTRAN90 library which
estimates the integral of a function over a sphere.
</p>
<p>
<a href = "../../f_src/stroud/stroud.html">
STROUD</a>,
a FORTRAN90 library which
defines quadrature rules for
various geometric shapes.
</p>
<p>
<a href = "../../f_src/tetrahedron_monte_carlo/tetrahedron_monte_carlo.html">
TETRAHEDRON_MONTE_CARLO</a>,
a FORTRAN90 program which
uses the Monte Carlo method to estimate integrals over a tetrahedron.
</p>
<p>
<a href = "../../f_src/triangle_monte_carlo/triangle_monte_carlo.html">
TRIANGLE_MONTE_CARLO</a>,
a FORTRAN90 program which
uses the Monte Carlo method to estimate integrals over a triangle.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "sphere_monte_carlo.f90">sphere_monte_carlo.f90</a>, the source code.
</li>
<li>
<a href = "sphere_monte_carlo.sh">sphere_monte_carlo.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "sphere_monte_carlo_prb.f90">sphere_monte_carlo_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "sphere_monte_carlo_prb.sh">sphere_monte_carlo_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "sphere_monte_carlo_prb_output.txt">sphere_monte_carlo_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MONOMIAL_VALUE</b> evaluates a monomial.
</li>
<li>
<b>R8_GAMMA</b> evaluates Gamma(X) for a real argument.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</li>
<li>
<b>R8VEC_NORMAL_01</b> returns a unit pseudonormal R8VEC.
</li>
<li>
<b>R8VEC_UNIFORM_01</b> returns a unit pseudorandom R8VEC.
</li>
<li>
<b>SPHERE01_MONOMIAL_INTEGRAL</b> returns monomial integrals on the unit sphere.
</li>
<li>
<b>SPHERE01_SAMPLE</b> maps uniform points onto the unit sphere.
</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 09 September 2010.
</i>
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