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| <h2 title="Class RectangularCholeskyDecomposition" class="title">Class RectangularCholeskyDecomposition</h2> |
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| <li>org.apache.commons.math3.linear.RectangularCholeskyDecomposition</li> |
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| <pre>public class <span class="strong">RectangularCholeskyDecomposition</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></pre> |
| <div class="block">Calculates the rectangular Cholesky decomposition of a matrix. |
| <p>The rectangular Cholesky decomposition of a real symmetric positive |
| semidefinite matrix A consists of a rectangular matrix B with the same |
| number of rows such that: A is almost equal to BB<sup>T</sup>, depending |
| on a user-defined tolerance. In a sense, this is the square root of A.</p> |
| <p>The difference with respect to the regular <a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html" title="class in org.apache.commons.math3.linear"><code>CholeskyDecomposition</code></a> |
| is that rows/columns may be permuted (hence the rectangular shape instead |
| of the traditional triangular shape) and there is a threshold to ignore |
| small diagonal elements. This is used for example to generate <a href="../../../../../org/apache/commons/math3/random/CorrelatedRandomVectorGenerator.html" title="class in org.apache.commons.math3.random"><code>correlated |
| random n-dimensions vectors</code></a> in a p-dimension subspace (p < n). |
| In other words, it allows generating random vectors from a covariance |
| matrix that is only positive semidefinite, and not positive definite.</p> |
| <p>Rectangular Cholesky decomposition is <em>not</em> suited for solving |
| linear systems, so it does not provide any <a href="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html" title="interface in org.apache.commons.math3.linear"><code>decomposition solver</code></a>.</p></div> |
| <dl><dt><span class="strong">Since:</span></dt> |
| <dd>2.0 (changed to concrete class in 3.0)</dd> |
| <dt><span class="strong">Version:</span></dt> |
| <dd>$Id: RectangularCholeskyDecomposition.java 1422313 2012-12-15 18:53:41Z psteitz $</dd> |
| <dt><span class="strong">See Also:</span></dt><dd><a href="http://mathworld.wolfram.com/CholeskyDecomposition.html">MathWorld</a>, |
| <a href="http://en.wikipedia.org/wiki/Cholesky_decomposition">Wikipedia</a></dd></dl> |
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| <td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/linear/RectangularCholeskyDecomposition.html#RectangularCholeskyDecomposition(org.apache.commons.math3.linear.RealMatrix)">RectangularCholeskyDecomposition</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> matrix)</code> |
| <div class="block">Decompose a symmetric positive semidefinite matrix.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/linear/RectangularCholeskyDecomposition.html#RectangularCholeskyDecomposition(org.apache.commons.math3.linear.RealMatrix, double)">RectangularCholeskyDecomposition</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> matrix, |
| double small)</code> |
| <div class="block">Decompose a symmetric positive semidefinite matrix.</div> |
| </td> |
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| <td class="colFirst"><code>int</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/RectangularCholeskyDecomposition.html#getRank()">getRank</a></strong>()</code> |
| <div class="block">Get the rank of the symmetric positive semidefinite matrix.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <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/linear/RectangularCholeskyDecomposition.html#getRootMatrix()">getRootMatrix</a></strong>()</code> |
| <div class="block">Get the root of the covariance matrix.</div> |
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| <h4>RectangularCholeskyDecomposition</h4> |
| <pre>public RectangularCholeskyDecomposition(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> matrix) |
| throws <a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteMatrixException</a></pre> |
| <div class="block">Decompose a symmetric positive semidefinite matrix. |
| <p> |
| <b>Note:</b> this constructor follows the linpack method to detect dependent |
| columns by proceeding with the Cholesky algorithm until a nonpositive diagonal |
| element is encountered.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - Symmetric positive semidefinite matrix.</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 matrix is not |
| positive semidefinite.</dd><dt><span class="strong">Since:</span></dt> |
| <dd>3.1</dd> |
| <dt><span class="strong">See Also:</span></dt><dd><a href="http://eprints.ma.man.ac.uk/1193/01/covered/MIMS_ep2008_56.pdf"> |
| Analysis of the Cholesky Decomposition of a Semi-definite Matrix</a></dd></dl> |
| </li> |
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| <!-- --> |
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| <h4>RectangularCholeskyDecomposition</h4> |
| <pre>public RectangularCholeskyDecomposition(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> matrix, |
| double small) |
| throws <a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteMatrixException</a></pre> |
| <div class="block">Decompose a symmetric positive semidefinite matrix.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - Symmetric positive semidefinite matrix.</dd><dd><code>small</code> - Diagonal elements threshold under which columns are |
| considered to be dependent on previous ones and are discarded.</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 matrix is not |
| positive semidefinite.</dd></dl> |
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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/linear/RectangularCholeskyDecomposition.html#getRank()"><code>getRank()</code></a></dd></dl> |
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| <h4>getRank</h4> |
| <pre>public int getRank()</pre> |
| <div class="block">Get the rank of the symmetric positive semidefinite matrix. |
| The r is the number of independent rows in the symmetric positive semidefinite |
| matrix, it is also the number of columns of the rectangular |
| matrix of the decomposition.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>r of the square matrix.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/linear/RectangularCholeskyDecomposition.html#getRootMatrix()"><code>getRootMatrix()</code></a></dd></dl> |
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