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<html>
<head>
<title>
ELLIPSE_MONTE_CARLO - Monte Carlo Estimate of Integrals in an Ellipse
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
ELLIPSE_MONTE_CARLO <br> Monte Carlo Estimate of Integrals in an Ellipse
</h1>
<hr>
<p>
<b>ELLIPSE_MONTE_CARLO</b>
is a C++ library which
uses the Monte Carlo method to estimate the value of integrals
over the interior of an ellipse in 2D.
</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>ELLIPSE_MONTE_CARLO</b> is available in
<a href = "../../c_src/ellipse_monte_carlo/ellipse_monte_carlo.html">a C version</a> and
<a href = "../../cpp_src/ellipse_monte_carlo/ellipse_monte_carlo.html">a C++ version</a> and
<a href = "../../f77_src/ellipse_monte_carlo/ellipse_monte_carlo.html">a FORTRAN77 version</a> and
<a href = "../../f_src/ellipse_monte_carlo/ellipse_monte_carlo.html">a FORTRAN90 version</a> and
<a href = "../../m_src/ellipse_monte_carlo/ellipse_monte_carlo.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/ball_monte_carlo/ball_monte_carlo.html">
BALL_MONTE_CARLO</a>,
a C++ 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 = "../../cpp_src/circle_monte_carlo/circle_monte_carlo.html">
CIRCLE_MONTE_CARLO</a>,
a C++ 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 = "../../cpp_src/cube_monte_carlo/cube_monte_carlo.html">
CUBE_MONTE_CARLO</a>,
a C++ 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 = "../../cpp_src/disk_monte_carlo/disk_monte_carlo.html">
DISK_MONTE_CARLO</a>,
a C++ 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 = "../../cpp_src/ellipse_grid/ellipse_grid.html">
ELLIPSE_GRID</a>,
a C++ library which
computes a grid of points
over the interior of an ellipse in 2D.
</p>
<p>
<a href = "../../cpp_src/ellipsoid_monte_carlo/ellipsoid_monte_carlo.html">
ELLIPSOID_MONTE_CARLO</a>
a C++ library which
uses the Monte Carlo method to estimate the value of integrals
over the interior of an ellipsoid in M dimensions.
</p>
<p>
<a href = "../../cpp_src/hyperball_monte_carlo/hyperball_monte_carlo.html">
HYPERBALL_MONTE_CARLO</a>,
a C++ 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 = "../../cpp_src/hyperball_volume_monte_carlo/hyperball_volume_monte_carlo.html">
HYPERBALL_VOLUME_MONTE_CARLO</a>,
a C program which
applies a Monte Carlo method to estimate the volume of
the unit hyperball in M dimensions;
</p>
<p>
<a href = "../../cpp_src/hypercube_monte_carlo/hypercube_monte_carlo.html">
HYPERCUBE_MONTE_CARLO</a>,
a C++ 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 = "../../cpp_src/hypersphere_monte_carlo/hypersphere_monte_carlo.html">
HYPERSPHERE_MONTE_CARLO</a>,
a C++ 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 = "../../cpp_src/line_monte_carlo/line_monte_carlo.html">
LINE_MONTE_CARLO</a>,
a C++ 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 = "../../cpp_src/polygon_monte_carlo/polygon_monte_carlo.html">
POLYGON_MONTE_CARLO</a>,
a C++ 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 = "../../cpp_src/pyramid_monte_carlo/pyramid_monte_carlo.html">
PYRAMID_MONTE_CARLO</a>,
a C++ 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 = "../../cpp_src/simplex_monte_carlo/simplex_monte_carlo.html">
SIMPLEX_MONTE_CARLO</a>,
a C++ library which
uses the Monte Carlo method to estimate integrals
over the interior of the unit simplex in M dimensions.
</p>
<p>
<a href = "../../cpp_src/sphere_monte_carlo/sphere_monte_carlo.html">
SPHERE_MONTE_CARLO</a>,
a C++ 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 = "../../cpp_src/sphere_triangle_monte_carlo/sphere_triangle_monte_carlo.html">
SPHERE_TRIANGLE_MONTE_CARLO</a>,
a C++ 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 = "../../cpp_src/square_monte_carlo/square_monte_carlo.html">
SQUARE_MONTE_CARLO</a>,
a C++ 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 = "../../cpp_src/tetrahedron_monte_carlo/tetrahedron_monte_carlo.html">
TETRAHEDRON_MONTE_CARLO</a>,
a C++ library which
uses the Monte Carlo method to estimate integrals
over the interior of the unit tetrahedron in 3D.
</p>
<p>
<a href = "../../cpp_src/triangle_monte_carlo/triangle_monte_carlo.html">
TRIANGLE_MONTE_CARLO</a>,
a C++ library which
uses the Monte Carlo method to estimate integrals
over the interior of a triangle in 2D.
</p>
<p>
<a href = "../../cpp_src/wedge_monte_carlo/wedge_monte_carlo.html">
WEDGE_MONTE_CARLO</a>,
a C++ 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 = "ellipse_monte_carlo.cpp">ellipse_monte_carlo.cpp</a>, the source code.
</li>
<li>
<a href = "ellipse_monte_carlo.hpp">ellipse_monte_carlo.hpp</a>,
the include file.
</li>
<li>
<a href = "ellipse_monte_carlo.sh">ellipse_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 = "ellipse_monte_carlo_prb.c">ellipse_monte_carlo_prb.c</a>,
a sample calling program.
</li>
<li>
<a href = "ellipse_monte_carlo_prb.sh">ellipse_monte_carlo_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "ellipse_monte_carlo_prb_output.txt">ellipse_monte_carlo_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>DAXPY</b> computes constant times a vector plus a vector.
</li>
<li>
<b>DDOT</b> forms the dot product of two vectors.
</li>
<li>
<b>ELLIPSE_AREA1</b> returns the area of an ellipse defined by a matrix.
</li>
<li>
<b>ELLIPSE_AREA2</b> returns the area of an ellipse defined by an equation.
</li>
<li>
<b>ELLIPSE_SAMPLE</b> samples points in an ellipse.
</li>
<li>
<b>MONOMIAL_VALUE</b> evaluates a monomial.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a pseudorandom R8 scaled to [0,1].
</li>
<li>
<b>R8PO_FA</b> factors a real symmetric positive definite matrix.
</li>
<li>
<b>R8PO_SL</b> solves a linear system factored by R8PO_FA.
</li>
<li>
<b>R8VEC_NORMAL_01</b> returns a unit pseudonormal R8VEC.
</li>
<li>
<b>R8VEC_SUM</b> returns the sum of an R8VEC.
</li>
<li>
<b>R8VEC_UNIFORM_01_NEW</b> returns a unit pseudorandom R8VEC.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>UNIFORM_IN_SPHERE01_MAP</b> maps uniform points into the unit sphere.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 20 April 2014.
</i>
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