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Added section about low-discrepancy sequences to user-guide.

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git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1486420 13f79535-47bb-0310-9956-ffa450edef68
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Thomas Neidhart 2013-05-26 15:43:33 +00:00
parent 5121bcfcb3
commit ba68b44abf
2 changed files with 26 additions and 1 deletions
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@ -227,6 +227,31 @@ RealMatrix covariance = MatrixUtils.createRealMatrix(cov); </source>
<a href="../apidocs/org/apache/commons/math3/random/NormalizedRandomGenerator.html">NormalizedRandomGenerator</a>
may be used.
</p>
<p><dl>
<dt>Low discrepancy sequences</dt>
<dd>
There exist several quasi-random sequences with the property that for all values of N, the subsequence
x<sub>1</sub>, ..., x<sub>N</sub> has low discrepancy, which results in equi-distributed samples.
While their quasi-randomness makes them unsuitable for most applications (i.e. the sequence of values
is completely deterministic), their unique properties give them an important advantage for quasi-Monte Carlo simulations.<br/>
Currently, the following low-discrepancy sequences are supported:
<ul>
<li><a href="../apidocs/org/apache/commons/math3/random/SobolSequenceGenerator.html">Sobol sequence</a> (pre-configured up to dimension 1000)</li>
<li><a href="../apidocs/org/apache/commons/math3/random/HaltonSequenceGenerator.html">Halton sequence</a> (pre-configured up to dimension 40)</li>
</ul>
<source>
// Create a Sobol sequence generator for 2-dimensional vectors
RandomVectorGenerator generator = new SobolSequence(2);
// Use the generator to generate vectors
double[] randomVector = generator.nextVector();
... </source>
The figure below illustrates the unique properties of low-discrepancy sequences when generating N samples in the interval [0, 1].
Roughly speaking, such sequences fill up the respective space more evenly which leads to faster convergence in quasi-Monte Carlo simulations.
<img src="../images/userguide/low_discrepancy_sequences.png" alt="Comparison of low-discrepancy sequences"/>
</dd></dl>
</p>
<p></p>
</subsection>
<subsection name="2.4 Random Strings" href="strings">
@ -448,7 +473,7 @@ RealMatrix covariance = MatrixUtils.createRealMatrix(cov); </source>
<p>
<table border="1" align="center">
<tr BGCOLOR="#CCCCFF"><td colspan="2"><font size="+2">Example of performances</font></td></tr>
<tr BGCOLOR="#CCCCFF"><td colspan="2"><font size="+1">Example of performances</font></td></tr>
<tr BGCOLOR="#EEEEFF"><font size="+1"><td>Name</td><td>generation rate (relative to MersenneTwister)</td></font></tr>
<tr><td><a href="../apidocs/org/apache/commons/math3/random/MersenneTwister.html">MersenneTwister</a></td><td>1</td></tr>
<tr><td><a href="../apidocs/org/apache/commons/math3/random/JDKRandomGenerator.html">JDKRandomGenerator</a></td><td>between 0.96 and 1.16</td></tr>