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| <div class="subTitle">org.apache.commons.math3.linear</div> |
| <h2 title="Class CholeskyDecomposition" class="title">Class CholeskyDecomposition</h2> |
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| <li>org.apache.commons.math3.linear.CholeskyDecomposition</li> |
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| <pre>public class <span class="strong">CholeskyDecomposition</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 Cholesky decomposition of a matrix. |
| <p>The Cholesky decomposition of a real symmetric positive-definite |
| matrix A consists of a lower triangular matrix L with same size such |
| that: A = LL<sup>T</sup>. In a sense, this is the square root of A.</p> |
| <p>This class is based on the class with similar name from the |
| <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library, with the |
| following changes:</p> |
| <ul> |
| <li>a <a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#getLT()"><code>getLT</code></a> method has been added,</li> |
| <li>the <code>isspd</code> method has been removed, since the constructor of |
| this class throws a <a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math3.linear"><code>NonPositiveDefiniteMatrixException</code></a> when a |
| matrix cannot be decomposed,</li> |
| <li>a <a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#getDeterminant()"><code>getDeterminant</code></a> method has been added,</li> |
| <li>the <code>solve</code> method has been replaced by a <a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#getSolver()"><code>getSolver</code></a> method and the equivalent method provided by the returned |
| <a href="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html" title="interface in org.apache.commons.math3.linear"><code>DecompositionSolver</code></a>.</li> |
| </ul></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: CholeskyDecomposition.java 1566017 2014-02-08 14:13:34Z tn $</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> |
| </li> |
| </ul> |
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| <th class="colLast" scope="col">Field and Description</th> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD">DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD</a></strong></code> |
| <div class="block">Default threshold below which diagonal elements are considered null |
| and matrix not positive definite.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#DEFAULT_RELATIVE_SYMMETRY_THRESHOLD">DEFAULT_RELATIVE_SYMMETRY_THRESHOLD</a></strong></code> |
| <div class="block">Default threshold above which off-diagonal elements are considered too different |
| and matrix not symmetric.</div> |
| </td> |
| </tr> |
| </table> |
| </li> |
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| <tr> |
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| <tr class="altColor"> |
| <td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#CholeskyDecomposition(org.apache.commons.math3.linear.RealMatrix)">CholeskyDecomposition</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">Calculates the Cholesky decomposition of the given matrix.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#CholeskyDecomposition(org.apache.commons.math3.linear.RealMatrix, double, double)">CholeskyDecomposition</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> matrix, |
| double relativeSymmetryThreshold, |
| double absolutePositivityThreshold)</code> |
| <div class="block">Calculates the Cholesky decomposition of the given matrix.</div> |
| </td> |
| </tr> |
| </table> |
| </li> |
| </ul> |
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| <caption><span>Methods</span><span class="tabEnd"> </span></caption> |
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| <th class="colFirst" scope="col">Modifier and Type</th> |
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| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#getDeterminant()">getDeterminant</a></strong>()</code> |
| <div class="block">Return the determinant of the 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/CholeskyDecomposition.html#getL()">getL</a></strong>()</code> |
| <div class="block">Returns the matrix L of the decomposition.</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/linear/CholeskyDecomposition.html#getLT()">getLT</a></strong>()</code> |
| <div class="block">Returns the transpose of the matrix L of the decomposition.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html" title="interface in org.apache.commons.math3.linear">DecompositionSolver</a></code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#getSolver()">getSolver</a></strong>()</code> |
| <div class="block">Get a solver for finding the A × X = B solution in least square sense.</div> |
| </td> |
| </tr> |
| </table> |
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| <code><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</a></code></li> |
| </ul> |
| </li> |
| </ul> |
| </li> |
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| </a> |
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| <h4>DEFAULT_RELATIVE_SYMMETRY_THRESHOLD</h4> |
| <pre>public static final double DEFAULT_RELATIVE_SYMMETRY_THRESHOLD</pre> |
| <div class="block">Default threshold above which off-diagonal elements are considered too different |
| and matrix not symmetric.</div> |
| <dl><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../constant-values.html#org.apache.commons.math3.linear.CholeskyDecomposition.DEFAULT_RELATIVE_SYMMETRY_THRESHOLD">Constant Field Values</a></dd></dl> |
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| <h4>DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD</h4> |
| <pre>public static final double DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD</pre> |
| <div class="block">Default threshold below which diagonal elements are considered null |
| and matrix not positive definite.</div> |
| <dl><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../constant-values.html#org.apache.commons.math3.linear.CholeskyDecomposition.DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD">Constant Field Values</a></dd></dl> |
| </li> |
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| <h3>Constructor Detail</h3> |
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| <h4>CholeskyDecomposition</h4> |
| <pre>public CholeskyDecomposition(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> matrix)</pre> |
| <div class="block">Calculates the Cholesky decomposition of the given matrix. |
| <p> |
| Calling this constructor is equivalent to call <a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#CholeskyDecomposition(org.apache.commons.math3.linear.RealMatrix, double, double)"><code>CholeskyDecomposition(RealMatrix, double, double)</code></a> with the |
| thresholds set to the default values <a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#DEFAULT_RELATIVE_SYMMETRY_THRESHOLD"><code>DEFAULT_RELATIVE_SYMMETRY_THRESHOLD</code></a> and <a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD"><code>DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD</code></a> |
| </p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - the matrix to decompose</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</a></code> - if the matrix is not square.</dd> |
| <dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSymmetricMatrixException.html" title="class in org.apache.commons.math3.linear">NonSymmetricMatrixException</a></code> - if the matrix is not symmetric.</dd> |
| <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 |
| strictly positive definite.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#CholeskyDecomposition(org.apache.commons.math3.linear.RealMatrix, double, double)"><code>CholeskyDecomposition(RealMatrix, double, double)</code></a>, |
| <a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#DEFAULT_RELATIVE_SYMMETRY_THRESHOLD"><code>DEFAULT_RELATIVE_SYMMETRY_THRESHOLD</code></a>, |
| <a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD"><code>DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD</code></a></dd></dl> |
| </li> |
| </ul> |
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| <h4>CholeskyDecomposition</h4> |
| <pre>public CholeskyDecomposition(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> matrix, |
| double relativeSymmetryThreshold, |
| double absolutePositivityThreshold)</pre> |
| <div class="block">Calculates the Cholesky decomposition of the given matrix.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - the matrix to decompose</dd><dd><code>relativeSymmetryThreshold</code> - threshold above which off-diagonal |
| elements are considered too different and matrix not symmetric</dd><dd><code>absolutePositivityThreshold</code> - threshold below which diagonal |
| elements are considered null and matrix not positive definite</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</a></code> - if the matrix is not square.</dd> |
| <dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSymmetricMatrixException.html" title="class in org.apache.commons.math3.linear">NonSymmetricMatrixException</a></code> - if the matrix is not symmetric.</dd> |
| <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 |
| strictly positive definite.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#CholeskyDecomposition(org.apache.commons.math3.linear.RealMatrix)"><code>CholeskyDecomposition(RealMatrix)</code></a>, |
| <a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#DEFAULT_RELATIVE_SYMMETRY_THRESHOLD"><code>DEFAULT_RELATIVE_SYMMETRY_THRESHOLD</code></a>, |
| <a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD"><code>DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD</code></a></dd></dl> |
| </li> |
| </ul> |
| </li> |
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| <h3>Method Detail</h3> |
| <a name="getL()"> |
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| </a> |
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| <h4>getL</h4> |
| <pre>public <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> getL()</pre> |
| <div class="block">Returns the matrix L of the decomposition. |
| <p>L is an lower-triangular matrix</p></div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>the L matrix</dd></dl> |
| </li> |
| </ul> |
| <a name="getLT()"> |
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| <h4>getLT</h4> |
| <pre>public <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> getLT()</pre> |
| <div class="block">Returns the transpose of the matrix L of the decomposition. |
| <p>L<sup>T</sup> is an upper-triangular matrix</p></div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>the transpose of the matrix L of the decomposition</dd></dl> |
| </li> |
| </ul> |
| <a name="getDeterminant()"> |
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| </a> |
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| <h4>getDeterminant</h4> |
| <pre>public double getDeterminant()</pre> |
| <div class="block">Return the determinant of the matrix</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>determinant of the matrix</dd></dl> |
| </li> |
| </ul> |
| <a name="getSolver()"> |
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| </a> |
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| <h4>getSolver</h4> |
| <pre>public <a href="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html" title="interface in org.apache.commons.math3.linear">DecompositionSolver</a> getSolver()</pre> |
| <div class="block">Get a solver for finding the A × X = B solution in least square sense.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>a solver</dd></dl> |
| </li> |
| </ul> |
| </li> |
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