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<html>
<head>
<title>
ELLIPSOID_MONTE_CARLO - Monte Carlo Estimate of Integrals in an Ellipsoid
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
ELLIPSOID_MONTE_CARLO <br> Monte Carlo Estimate of Integrals in an Ellipsoid
</h1>
<hr>
<p>
<b>ELLIPSOID_MONTE_CARLO</b>
is a MATLAB library which
uses the Monte Carlo method to estimate the value of an integral
over the interior of an ellipsoid in M dimensions.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files 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>ELLIPSOID_MONTE_CARLO</b> is available in
<a href = "../../c_src/ellipsoid_monte_carlo/ellipsoid_monte_carlo.html">a C version</a> and
<a href = "../../cpp_src/ellipsoid_monte_carlo/ellipsoid_monte_carlo.html">a C+= version</a> and
<a href = "../../f77_src/ellipsoid_monte_carlo/ellipsoid_monte_carlo.html">a FORTRAN77 version</a> and
<a href = "../../f_src/ellipsoid_monte_carlo/ellipsoid_monte_carlo.html">a FORTRAN90 version</a> and
<a href = "../../m_src/ellipsoid_monte_carlo/ellipsoid_monte_carlo.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/ball_monte_carlo/ball_monte_carlo.html">
BALL_MONTE_CARLO</a>,
a MATLAB library which
applies a Monte Carlo method to estimate integrals of a function
over the interior of the unit ball in 3D;
</p>
<p>
<a href = "../../m_src/circle_monte_carlo/circle_monte_carlo.html">
CIRCLE_MONTE_CARLO</a>,
a MATLAB library which
applies a Monte Carlo method to estimate the integral of a function
on the circumference of the unit circle in 2D;
</p>
<p>
<a href = "../../m_src/cube_monte_carlo/cube_monte_carlo.html">
CUBE_MONTE_CARLO</a>,
a MATLAB library which
applies a Monte Carlo method to estimate the integral of a function
over the interior of the unit cube in 3D;
</p>
<p>
<a href = "../../m_src/disk_monte_carlo/disk_monte_carlo.html">
DISK_MONTE_CARLO</a>,
a MATLAB library which
applies a Monte Carlo method to estimate the integral of a function
over the interior of the unit disk in 2D;
</p>
<p>
<a href = "../../m_src/ellipse_monte_carlo/ellipse_monte_carlo.html">
ELLIPSE_MONTE_CARLO</a>,
a MATLAB library which
applies a Monte Carlo method to estimate the integral of a function
over the interior of an ellipse in 2D.
</p>
<p>
<a href = "../../m_src/hyperball_monte_carlo/hyperball_monte_carlo.html">
HYPERBALL_MONTE_CARLO</a>,
a MATLAB library which
applies a Monte Carlo method to estimate the integral of a function
over the interior of the unit ball in M dimensions;
</p>
<p>
<a href = "../../m_src/hyperball_volume_monte_carlo/hyperball_volume_monte_carlo.html">
HYPERBALL_VOLUME_MONTE_CARLO</a>,
a FORTRAN90 program which
applies a Monte Carlo method to estimate the volume of
the unit hyperball in M dimensions;
</p>
<p>
<a href = "../../m_src/hypercube_monte_carlo/hypercube_monte_carlo.html">
HYPERCUBE_MONTE_CARLO</a>,
a MATLAB library which
applies a Monte Carlo method to estimate the integral of a function
over the interior of the unit hypercube in M dimensions;
</p>
<p>
<a href = "../../m_src/hypersphere_monte_carlo/hypersphere_monte_carlo.html">
HYPERSPHERE_MONTE_CARLO</a>,
a MATLAB library which
applies a Monte Carlo method to estimate the integral of a function
on the surface of the unit sphere in M dimensions;
</p>
<p>
<a href = "../../m_src/line_monte_carlo/line_monte_carlo.html">
LINE_MONTE_CARLO</a>,
a MATLAB library which
applies a Monte Carlo method to estimate the integral of a function
over the length of the unit line in 1D;
</p>
<p>
<a href = "../../m_src/polygon_monte_carlo/polygon_monte_carlo.html">
POLYGON_MONTE_CARLO</a>,
a MATLAB library which
applies a Monte Carlo method to estimate the integral of a function
over the interior of a polygon in 2D.
</p>
<p>
<a href = "../../m_src/pyramid_monte_carlo/pyramid_monte_carlo.html">
PYRAMID_MONTE_CARLO</a>,
a MATLAB library which
applies a Monte Carlo method to estimate integrals of a function
over the interior of the unit pyramid in 3D;
</p>
<p>
<a href = "../../m_src/simplex_monte_carlo/simplex_monte_carlo.html">
SIMPLEX_MONTE_CARLO</a>,
a MATLAB library which
uses the Monte Carlo method to estimate integrals
over the interior of the unit simplex in M dimensions.
</p>
<p>
<a href = "../../m_src/sphere_monte_carlo/sphere_monte_carlo.html">
SPHERE_MONTE_CARLO</a>,
a MATLAB library which
applies a Monte Carlo method to estimate integrals of a function
over the surface of the unit sphere in 3D;
</p>
<p>
<a href = "../../m_src/sphere_triangle_monte_carlo/sphere_triangle_monte_carlo.html">
SPHERE_TRIANGLE_MONTE_CARLO</a>,
a MATLAB library which
applies a Monte Carlo method to estimate the integral of a function
over a spherical triangle
on the surface of the unit sphere in 3D;
</p>
<p>
<a href = "../../m_src/square_monte_carlo/square_monte_carlo.html">
SQUARE_MONTE_CARLO</a>,
a MATLAB library which
applies a Monte Carlo method to estimate the integral of a function
over the interior of the unit square in 2D;
</p>
<p>
<a href = "../../m_src/tetrahedron_monte_carlo/tetrahedron_monte_carlo.html">
TETRAHEDRON_MONTE_CARLO</a>,
a MATLAB library which
uses the Monte Carlo method to estimate integrals
over the interior of the unit tetrahedron in 3D.
</p>
<p>
<a href = "../../m_src/triangle_monte_carlo/triangle_monte_carlo.html">
TRIANGLE_MONTE_CARLO</a>,
a MATLAB library which
uses the Monte Carlo method to estimate integrals
over the interior of a triangle in 2D.
</p>
<p>
<a href = "../../m_src/wedge_monte_carlo/wedge_monte_carlo.html">
WEDGE_MONTE_CARLO</a>,
a MATLAB library which
uses the Monte Carlo method to estimate integrals
over the interior of the unit wedge in 3D.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "ellipsoid_sample.m">ellipsoid_sample.m</a>,
samples points uniformly from an ellipsoid.
</li>
<li>
<a href = "ellipsoid_volume.m">ellipsoid_volume.m</a>,
returns the volume of an ellipsoid.
</li>
<li>
<a href = "hypersphere_unit_volume.m">hypersphere_unit_volume.m</a>,
volume of a unit hypersphere in M dimensions.
</li>
<li>
<a href = "monomial_value.m">monomial_value.m</a>,
evaluates a monomial.
</li>
<li>
<a href = ".m">.m</a>,
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</li>
<li>
<a href = "r8mat_print.m">r8mat_print.m</a>,
prints an R8MAT.
</li>
<li>
<a href = "r8mat_print_some.m">r8mat_print_some.m</a>,
prints some of an R8MAT.
</li>
<li>
<a href = "r8mat_transpose_print.m">r8mat_transpose_print.m</a>,
prints an R8MAT, transposed.
</li>
<li>
<a href = "r8mat_transpose_print_some.m">r8mat_transpose_print_some.m</a>,
prints some of an R8MAT, transposed.
</li>
<li>
<a href = "r8po_fa.m">r8po_fa.m</a>,
factors an R8PO matrix.
</li>
<li>
<a href = "r8po_sl.m">r8po_sl.m</a>,
solves an R8PO system factored by R8PO_FA.
</li>
<li>
<a href = "r8vec_normal_01.m">r8vec_normal_01.m</a>,
returns a unit pseudonormal R8VEC.
</li>
<li>
<a href = "r8vec_print.m">r8vec_print.m</a>,
prints an R8VEC.
</li>
<li>
<a href = "r8vec_uniform_01.m">r8vec_uniform_01.m</a>,
returns a unit pseudorandom R8VEC.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>,
prints the current YMDHMS date as a time stamp.
</li>
<li>
<a href = "uniform_in_sphere01_map.m">uniform_in_sphere01_map.m</a>,
maps uniform points into the unit sphere.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "ellipsoid_monte_carlo_test.m">ellipsoid_monte_carlo_test.m</a>,
calls all the tests.
</li>
<li>
<a href = "ellipsoid_monte_carlo_test01.m">ellipsoid_monte_carlo_test01.m</a>,
tests ellipsoid_sample() on a 2D ellipse centered at (0,0).
</li>
<li>
<a href = "ellipsoid_monte_carlo_test02.m">ellipsoid_monte_carlo_test02.m</a>,
tests ellipsoid_sample() on a 2D ellipse centered at (2,3).
</li>
<li>
<a href = "ellipsoid_monte_carlo_test03.m">ellipsoid_monte_carlo_test03.m</a>,
tests ellipsoid_sample() on a 3D ellipsoid centered at (1,2,3).
</li>
<li>
<a href = "ellipsoid_monte_carlo_test_output.txt">ellipsoid_monte_carlo_test_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 13 August 2014.
</i>
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