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| <h2 title="Class CorrelatedRandomVectorGenerator" class="title">Class CorrelatedRandomVectorGenerator</h2> |
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| <pre>public class <span class="strong">CorrelatedRandomVectorGenerator</span> |
| extends <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a> |
| implements <a href="../../../../../org/apache/commons/math3/random/RandomVectorGenerator.html" title="interface in org.apache.commons.math3.random">RandomVectorGenerator</a></pre> |
| <div class="block">A <a href="../../../../../org/apache/commons/math3/random/RandomVectorGenerator.html" title="interface in org.apache.commons.math3.random"><code>RandomVectorGenerator</code></a> that generates vectors with with |
| correlated components. |
| <p>Random vectors with correlated components are built by combining |
| the uncorrelated components of another random vector in such a way that |
| the resulting correlations are the ones specified by a positive |
| definite covariance matrix.</p> |
| <p>The main use for correlated random vector generation is for Monte-Carlo |
| simulation of physical problems with several variables, for example to |
| generate error vectors to be added to a nominal vector. A particularly |
| interesting case is when the generated vector should be drawn from a <a |
| href="http://en.wikipedia.org/wiki/Multivariate_normal_distribution"> |
| Multivariate Normal Distribution</a>. The approach using a Cholesky |
| decomposition is quite usual in this case. However, it can be extended |
| to other cases as long as the underlying random generator provides |
| <a href="../../../../../org/apache/commons/math3/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math3.random"><code>normalized values</code></a> like <a href="../../../../../org/apache/commons/math3/random/GaussianRandomGenerator.html" title="class in org.apache.commons.math3.random"><code>GaussianRandomGenerator</code></a> or <a href="../../../../../org/apache/commons/math3/random/UniformRandomGenerator.html" title="class in org.apache.commons.math3.random"><code>UniformRandomGenerator</code></a>.</p> |
| <p>Sometimes, the covariance matrix for a given simulation is not |
| strictly positive definite. This means that the correlations are |
| not all independent from each other. In this case, however, the non |
| strictly positive elements found during the Cholesky decomposition |
| of the covariance matrix should not be negative either, they |
| should be null. Another non-conventional extension handling this case |
| is used here. Rather than computing <code>C = U<sup>T</sup>.U</code> |
| where <code>C</code> is the covariance matrix and <code>U</code> |
| is an upper-triangular matrix, we compute <code>C = B.B<sup>T</sup></code> |
| where <code>B</code> is a rectangular matrix having |
| more rows than columns. The number of columns of <code>B</code> is |
| the rank of the covariance matrix, and it is the dimension of the |
| uncorrelated random vector that is needed to compute the component |
| of the correlated vector. This class handles this situation |
| automatically.</p></div> |
| <dl><dt><span class="strong">Since:</span></dt> |
| <dd>1.2</dd> |
| <dt><span class="strong">Version:</span></dt> |
| <dd>$Id: CorrelatedRandomVectorGenerator.java 1416643 2012-12-03 19:37:14Z tn $</dd></dl> |
| </li> |
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| <td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/random/CorrelatedRandomVectorGenerator.html#CorrelatedRandomVectorGenerator(double[], org.apache.commons.math3.linear.RealMatrix, double, org.apache.commons.math3.random.NormalizedRandomGenerator)">CorrelatedRandomVectorGenerator</a></strong>(double[] mean, |
| <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> covariance, |
| double small, |
| <a href="../../../../../org/apache/commons/math3/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math3.random">NormalizedRandomGenerator</a> generator)</code> |
| <div class="block">Builds a correlated random vector generator from its mean |
| vector and covariance matrix.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/random/CorrelatedRandomVectorGenerator.html#CorrelatedRandomVectorGenerator(org.apache.commons.math3.linear.RealMatrix, double, org.apache.commons.math3.random.NormalizedRandomGenerator)">CorrelatedRandomVectorGenerator</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> covariance, |
| double small, |
| <a href="../../../../../org/apache/commons/math3/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math3.random">NormalizedRandomGenerator</a> generator)</code> |
| <div class="block">Builds a null mean random correlated vector generator from its |
| covariance matrix.</div> |
| </td> |
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| <td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math3.random">NormalizedRandomGenerator</a></code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/random/CorrelatedRandomVectorGenerator.html#getGenerator()">getGenerator</a></strong>()</code> |
| <div class="block">Get the underlying normalized components generator.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>int</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/random/CorrelatedRandomVectorGenerator.html#getRank()">getRank</a></strong>()</code> |
| <div class="block">Get the rank of the covariance matrix.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/random/CorrelatedRandomVectorGenerator.html#getRootMatrix()">getRootMatrix</a></strong>()</code> |
| <div class="block">Get the root of the covariance matrix.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>double[]</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/random/CorrelatedRandomVectorGenerator.html#nextVector()">nextVector</a></strong>()</code> |
| <div class="block">Generate a correlated random vector.</div> |
| </td> |
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| <h3>Constructor Detail</h3> |
| <a name="CorrelatedRandomVectorGenerator(double[], org.apache.commons.math3.linear.RealMatrix, double, org.apache.commons.math3.random.NormalizedRandomGenerator)"> |
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| <h4>CorrelatedRandomVectorGenerator</h4> |
| <pre>public CorrelatedRandomVectorGenerator(double[] mean, |
| <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> covariance, |
| double small, |
| <a href="../../../../../org/apache/commons/math3/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math3.random">NormalizedRandomGenerator</a> generator)</pre> |
| <div class="block">Builds a correlated random vector generator from its mean |
| vector and covariance matrix.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>mean</code> - Expected mean values for all components.</dd><dd><code>covariance</code> - Covariance matrix.</dd><dd><code>small</code> - Diagonal elements threshold under which column are |
| considered to be dependent on previous ones and are discarded</dd><dd><code>generator</code> - underlying generator for uncorrelated normalized |
| components.</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteMatrixException</a></code> - if the covariance matrix is not strictly positive definite.</dd> |
| <dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the mean and covariance |
| arrays dimensions do not match.</dd></dl> |
| </li> |
| </ul> |
| <a name="CorrelatedRandomVectorGenerator(org.apache.commons.math3.linear.RealMatrix, double, org.apache.commons.math3.random.NormalizedRandomGenerator)"> |
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| <h4>CorrelatedRandomVectorGenerator</h4> |
| <pre>public CorrelatedRandomVectorGenerator(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> covariance, |
| double small, |
| <a href="../../../../../org/apache/commons/math3/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math3.random">NormalizedRandomGenerator</a> generator)</pre> |
| <div class="block">Builds a null mean random correlated vector generator from its |
| covariance matrix.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>covariance</code> - Covariance matrix.</dd><dd><code>small</code> - Diagonal elements threshold under which column are |
| considered to be dependent on previous ones and are discarded.</dd><dd><code>generator</code> - Underlying generator for uncorrelated normalized |
| components.</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteMatrixException</a></code> - if the covariance matrix is not strictly positive definite.</dd></dl> |
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| <a name="getGenerator()"> |
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| <h4>getGenerator</h4> |
| <pre>public <a href="../../../../../org/apache/commons/math3/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math3.random">NormalizedRandomGenerator</a> getGenerator()</pre> |
| <div class="block">Get the underlying normalized components generator.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>underlying uncorrelated components generator</dd></dl> |
| </li> |
| </ul> |
| <a name="getRank()"> |
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| <h4>getRank</h4> |
| <pre>public int getRank()</pre> |
| <div class="block">Get the rank of the covariance matrix. |
| The rank is the number of independent rows in the covariance |
| matrix, it is also the number of columns of the root matrix.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>rank of the square matrix.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/random/CorrelatedRandomVectorGenerator.html#getRootMatrix()"><code>getRootMatrix()</code></a></dd></dl> |
| </li> |
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| <a name="getRootMatrix()"> |
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| <h4>getRootMatrix</h4> |
| <pre>public <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> getRootMatrix()</pre> |
| <div class="block">Get the root of the covariance matrix. |
| The root is the rectangular matrix <code>B</code> such that |
| the covariance matrix is equal to <code>B.B<sup>T</sup></code></div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>root of the square matrix</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/random/CorrelatedRandomVectorGenerator.html#getRank()"><code>getRank()</code></a></dd></dl> |
| </li> |
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| <a name="nextVector()"> |
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| <h4>nextVector</h4> |
| <pre>public double[] nextVector()</pre> |
| <div class="block">Generate a correlated random vector.</div> |
| <dl> |
| <dt><strong>Specified by:</strong></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/random/RandomVectorGenerator.html#nextVector()">nextVector</a></code> in interface <code><a href="../../../../../org/apache/commons/math3/random/RandomVectorGenerator.html" title="interface in org.apache.commons.math3.random">RandomVectorGenerator</a></code></dd> |
| <dt><span class="strong">Returns:</span></dt><dd>a random vector as an array of double. The returned array |
| is created at each call, the caller can do what it wants with it.</dd></dl> |
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