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<html>
<head>
<title>
TRIANGLE_HISTOGRAM - Histograms of Triangle Data
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TRIANGLE_HISTOGRAM <br> Histograms of Triangle Data
</h1>
<hr>
<p>
<b>TRIANGLE_HISTOGRAM</b>
is a MATLAB program which
creates a histogram of data in the unit triangle.
</p>
<p>
The unit triangle has the vertices (1,0), (0,1), (0,0).
</p>
<p>
"Data" in the unit triangle is assumed to take the form of a file,
containing a list of points that lie in the triangle.
</p>
<p>
The sides of the triangle can each be
divided into N subintervals, and by connecting them, the result is
N*N subtriangles of the same area.
</p>
<p>
The program then determines the number of points that lie within
each subtriangle, and prints this list.
</p>
<p>
This program is particularly suitable for investigating whether
a set of points in the unit triangle are close to a uniformly
sampling, or if there is some bias in the selection.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>triangle_histogram</b> ( <i>'data_file'</i>, <i>n</i> )
</blockquote>
where
<ul>
<li>
<i>'data_file'</i> is the file containing the sample points;
</li>
<li>
<i>n</i> is the number of subintervals into which each side
of the unit triangle is to be divided.
</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">
Languages:
</h3>
<p>
<b>TRIANGLE_HISTOGRAM</b> is available in
<a href = "../../cpp_src/triangle_histogram/triangle_histogram.html">a C++ version</a> and
<a href = "../../f_src/triangle_histogram/triangle_histogram.html">a FORTRAN90 version</a> and
<a href = "../../m_src/triangle_histogram/triangle_histogram.html">a MATLAB version.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/random_data/random_data.html">
RANDOM_DATA</a>,
a MATLAB program which
produces random samples from a number of regions, including triangles.
</p>
<p>
<a href = "../../m_src/triangle_monte_carlo/triangle_monte_carlo.html">
TRIANGLE_MONTE_CARLO</a>,
a MATLAB program which
uses the Monte Carlo method to estimate integrals over a triangle.
</p>
<p>
<a href = "../../datasets/triangle_samples/triangle_samples.html">
TRIANGLE_SAMPLES</a>,
a dataset directory which
contains sets of sample points drawn from the unit triangle.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<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_histogram.m">triangle_histogram.m</a>, the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>B10000</b> is a "bad" set of sample points.
<ul>
<li>
<a href = "b10000.txt">b10000.txt</a>,
the sample points.
</li>
<li>
<a href = "b10000_output.txt">b10000_output.txt</a>,
output from the command "triangle_histogram b10000.txt 4".
</li>
</ul>
</p>
<p>
<b>G10000</b> is a "good" set of sample points.
<ul>
<li>
<a href = "g10000.txt">g10000.txt</a>,
the sample points.
</li>
<li>
<a href = "g10000_output.txt">g10000_output.txt</a>,
output from the command "triangle_histogram g10000.txt 4".
</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 14 August 2009.
</i>
<!-- John Burkardt -->
</body>
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</html>