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Added correlated vector generation example. 

git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/branches/MATH_2_X@1067592 13f79535-47bb-0310-9956-ffa450edef68
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Phil Steitz 2011-02-06 05:42:35 +00:00
parent e380da5bd1
commit a59bf744d0
1 changed files with 43 additions and 1 deletions
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44
src/site/xdoc/userguide/random.xml
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@ -34,6 +34,7 @@
The Commons Math random package includes utilities for
<ul>
<li>generating random numbers</li>
<li>generating random vectors</li>
<li>generating random strings</li>
<li>generating cryptographically secure sequences of random numbers or
strings</li>
@ -184,7 +185,48 @@ for (int i = 0; i &lt; 1000; i++) {
href="http://en.wikipedia.org/wiki/Multivariate_normal_distribution">
Multivariate Normal Distribution</a>.
</p>
</subsection>
<p><dl>
<dt>Generating random vectors from a bivariate normal distribution</dt><dd>
<source>
// Create and seed a RandomGenerator (could use any of the generators in the random package here)
RandomGenerator rg = new JDKRandomGenerator();
rg.setSeed(17399225432l); // Fixed seed means same results every time
// Create a GassianRandomGenerator using rg as its source of randomness
GaussianRandomGenerator rawGenerator = new GaussianRandomGenerator(rg);
// Create a CorrelatedRandomVectorGenerator using rawGenerator for the components
CorrelatedRandomVectorGenerator generator =
new CorrelatedRandomVectorGenerator(mean, covariance, 1.0e-12 * covariance.getNorm(), rawGenerator);
// Use the generator to generate correlated vectors
double[] randomVector = generator.nextVector();
... </source>
The <code>mean</code> argument is a double[] array holding the means of the random vector
components. In the bivariate case, it must have length 2. The <code>covariance</code> argument
is a RealMatrix, which needs to be 2 x 2. The main diagonal elements are the
variances of the vector components and the off-diagonal elements are the covariances.
For example, if the means are 1 and 2 respectively, and the desired standard deviations
are 3 and 4, respectively, then we need to use
<source>
double[] mean = {1, 2};
double[][] cov = {{9, c}, {c, 16}};
RealMatrix covariance = MatrixUtils.createRealMatrix(cov); </source>
where c is the desired covariance. If you are starting with a desired correlation,
you need to translate this to a covariance by multiplying it by the product of the
standard deviations. For example, if you want to generate data that will give Pearson's
R of 0.5, you would use c = 3 * 4 * .5 = 6.
</dd></dl></p>
<p>
In addition to multivariate normal distributions, correlated vectors from multivariate uniform
distributions can be generated by creating a
<a href="../apidocs/org/apache/commons/math/random/UniformRandomGenerator.html">UniformRandomGenerator</a>
in place of the
<code>GaussianRandomGenerator</code> above. More generally, any
<a href="../apidocs/org/apache/commons/math/random/NormalizedRandomGenerator.html">NormalizedRandomGenerator</a>
may be used.
</p>
</subsection>
<subsection name="2.4 Random Strings" href="strings">
<p>