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| <h2 title="Class RRQRDecomposition" class="title">Class RRQRDecomposition</h2> |
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| <li><a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html" title="class in org.apache.commons.math3.linear">org.apache.commons.math3.linear.QRDecomposition</a></li> |
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| <li>org.apache.commons.math3.linear.RRQRDecomposition</li> |
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| <pre>public class <span class="strong">RRQRDecomposition</span> |
| extends <a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html" title="class in org.apache.commons.math3.linear">QRDecomposition</a></pre> |
| <div class="block">Calculates the rank-revealing QR-decomposition of a matrix, with column pivoting. |
| <p>The rank-revealing QR-decomposition of a matrix A consists of three matrices Q, |
| R and P such that AP=QR. Q is orthogonal (Q<sup>T</sup>Q = I), and R is upper triangular. |
| If A is m×n, Q is m×m and R is m×n and P is n×n.</p> |
| <p>QR decomposition with column pivoting produces a rank-revealing QR |
| decomposition and the <a href="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#getRank(double)"><code>getRank(double)</code></a> method may be used to return the rank of the |
| input matrix A.</p> |
| <p>This class compute the decomposition using Householder reflectors.</p> |
| <p>For efficiency purposes, the decomposition in packed form is transposed. |
| This allows inner loop to iterate inside rows, which is much more cache-efficient |
| in Java.</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/QRDecomposition.html#getQT()"><code>getQT</code></a> method has been added,</li> |
| <li>the <code>solve</code> and <code>isFullRank</code> methods have been replaced |
| by a <a href="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#getSolver()"><code>getSolver</code></a> method and the equivalent methods |
| 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>3.2</dd> |
| <dt><span class="strong">Version:</span></dt> |
| <dd>$Id: RRQRDecomposition.java 1570994 2014-02-23 11:10:41Z luc $</dd> |
| <dt><span class="strong">See Also:</span></dt><dd><a href="http://mathworld.wolfram.com/QRDecomposition.html">MathWorld</a>, |
| <a href="http://en.wikipedia.org/wiki/QR_decomposition">Wikipedia</a></dd></dl> |
| </li> |
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| <tr class="altColor"> |
| <td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#RRQRDecomposition(org.apache.commons.math3.linear.RealMatrix)">RRQRDecomposition</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 QR-decomposition of the given matrix.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#RRQRDecomposition(org.apache.commons.math3.linear.RealMatrix, double)">RRQRDecomposition</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> matrix, |
| double threshold)</code> |
| <div class="block">Calculates the QR-decomposition of the given matrix.</div> |
| </td> |
| </tr> |
| </table> |
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| <td class="colFirst"><code>protected void</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#decompose(double[][])">decompose</a></strong>(double[][] qrt)</code> |
| <div class="block">Decompose 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/RRQRDecomposition.html#getP()">getP</a></strong>()</code> |
| <div class="block">Returns the pivot matrix, P, used in the QR Decomposition of matrix A such that AP = QR.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>int</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#getRank(double)">getRank</a></strong>(double dropThreshold)</code> |
| <div class="block">Return the effective numerical matrix rank.</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/RRQRDecomposition.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> |
| <tr class="altColor"> |
| <td class="colFirst"><code>protected void</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#performHouseholderReflection(int, double[][])">performHouseholderReflection</a></strong>(int minor, |
| double[][] qrt)</code> |
| <div class="block">Perform Householder reflection for a minor A(minor, minor) of A.</div> |
| </td> |
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| <h3>Methods inherited from class org.apache.commons.math3.linear.<a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html" title="class in org.apache.commons.math3.linear">QRDecomposition</a></h3> |
| <code><a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html#getH()">getH</a>, <a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html#getQ()">getQ</a>, <a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html#getQT()">getQT</a>, <a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html#getR()">getR</a></code></li> |
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| <h4>RRQRDecomposition</h4> |
| <pre>public RRQRDecomposition(<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 QR-decomposition of the given matrix. |
| The singularity threshold defaults to zero.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - The matrix to decompose.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#RRQRDecomposition(org.apache.commons.math3.linear.RealMatrix, double)"><code>RRQRDecomposition(RealMatrix, double)</code></a></dd></dl> |
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| <h4>RRQRDecomposition</h4> |
| <pre>public RRQRDecomposition(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> matrix, |
| double threshold)</pre> |
| <div class="block">Calculates the QR-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>threshold</code> - Singularity threshold.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#RRQRDecomposition(org.apache.commons.math3.linear.RealMatrix)"><code>RRQRDecomposition(RealMatrix)</code></a></dd></dl> |
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| <a name="decompose(double[][])"> |
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| <h4>decompose</h4> |
| <pre>protected void decompose(double[][] qrt)</pre> |
| <div class="block">Decompose matrix.</div> |
| <dl> |
| <dt><strong>Overrides:</strong></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html#decompose(double[][])">decompose</a></code> in class <code><a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html" title="class in org.apache.commons.math3.linear">QRDecomposition</a></code></dd> |
| <dt><span class="strong">Parameters:</span></dt><dd><code>qrt</code> - transposed matrix</dd></dl> |
| </li> |
| </ul> |
| <a name="performHouseholderReflection(int, double[][])"> |
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| <h4>performHouseholderReflection</h4> |
| <pre>protected void performHouseholderReflection(int minor, |
| double[][] qrt)</pre> |
| <div class="block">Perform Householder reflection for a minor A(minor, minor) of A.</div> |
| <dl> |
| <dt><strong>Overrides:</strong></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html#performHouseholderReflection(int, double[][])">performHouseholderReflection</a></code> in class <code><a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html" title="class in org.apache.commons.math3.linear">QRDecomposition</a></code></dd> |
| <dt><span class="strong">Parameters:</span></dt><dd><code>minor</code> - minor index</dd><dd><code>qrt</code> - transposed matrix</dd></dl> |
| </li> |
| </ul> |
| <a name="getP()"> |
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| <h4>getP</h4> |
| <pre>public <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> getP()</pre> |
| <div class="block">Returns the pivot matrix, P, used in the QR Decomposition of matrix A such that AP = QR. |
| |
| If no pivoting is used in this decomposition then P is equal to the identity matrix.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>a permutation matrix.</dd></dl> |
| </li> |
| </ul> |
| <a name="getRank(double)"> |
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| </a> |
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| <h4>getRank</h4> |
| <pre>public int getRank(double dropThreshold)</pre> |
| <div class="block">Return the effective numerical matrix rank. |
| <p>The effective numerical rank is the number of non-negligible |
| singular values.</p> |
| <p>This implementation looks at Frobenius norms of the sequence of |
| bottom right submatrices. When a large fall in norm is seen, |
| the rank is returned. The drop is computed as:</p> |
| <pre> |
| (thisNorm/lastNorm) * rNorm < dropThreshold |
| </pre> |
| <p> |
| where thisNorm is the Frobenius norm of the current submatrix, |
| lastNorm is the Frobenius norm of the previous submatrix, |
| rNorm is is the Frobenius norm of the complete matrix |
| </p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>dropThreshold</code> - threshold triggering rank computation</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>effective numerical matrix rank</dd></dl> |
| </li> |
| </ul> |
| <a name="getSolver()"> |
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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. |
| <p> |
| Least Square sense means a solver can be computed for an overdetermined system, |
| (i.e. a system with more equations than unknowns, which corresponds to a tall A |
| matrix with more rows than columns). In any case, if the matrix is singular |
| within the tolerance set at <a href="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#RRQRDecomposition(org.apache.commons.math3.linear.RealMatrix, double)"><code>construction</code></a>, an error will be triggered when |
| the <a href="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html#solve(org.apache.commons.math3.linear.RealVector)"><code>solve</code></a> method will be called. |
| </p></div> |
| <dl> |
| <dt><strong>Overrides:</strong></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html#getSolver()">getSolver</a></code> in class <code><a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html" title="class in org.apache.commons.math3.linear">QRDecomposition</a></code></dd> |
| <dt><span class="strong">Returns:</span></dt><dd>a solver</dd></dl> |
| </li> |
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