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| <div class="subTitle">org.apache.commons.math3.linear</div> |
| <h2 title="Class SingularValueDecomposition" class="title">Class SingularValueDecomposition</h2> |
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| <li>org.apache.commons.math3.linear.SingularValueDecomposition</li> |
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| <pre>public class <span class="strong">SingularValueDecomposition</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 compact Singular Value Decomposition of a matrix. |
| <p> |
| The Singular Value Decomposition of matrix A is a set of three matrices: U, |
| Σ and V such that A = U × Σ × V<sup>T</sup>. Let A be |
| a m × n matrix, then U is a m × p orthogonal matrix, Σ is a |
| p × p diagonal matrix with positive or null elements, V is a p × |
| n orthogonal matrix (hence V<sup>T</sup> is also orthogonal) where |
| p=min(m,n). |
| </p> |
| <p>This class is similar to 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>the <code>norm2</code> method which has been renamed as <a href="../../../../../org/apache/commons/math3/linear/SingularValueDecomposition.html#getNorm()"><code>getNorm</code></a>,</li> |
| <li>the <code>cond</code> method which has been renamed as <a href="../../../../../org/apache/commons/math3/linear/SingularValueDecomposition.html#getConditionNumber()"><code>getConditionNumber</code></a>,</li> |
| <li>the <code>rank</code> method which has been renamed as <a href="../../../../../org/apache/commons/math3/linear/SingularValueDecomposition.html#getRank()"><code>getRank</code></a>,</li> |
| <li>a <a href="../../../../../org/apache/commons/math3/linear/SingularValueDecomposition.html#getUT()"><code>getUT</code></a> method has been added,</li> |
| <li>a <a href="../../../../../org/apache/commons/math3/linear/SingularValueDecomposition.html#getVT()"><code>getVT</code></a> method has been added,</li> |
| <li>a <a href="../../../../../org/apache/commons/math3/linear/SingularValueDecomposition.html#getSolver()"><code>getSolver</code></a> method has been added,</li> |
| <li>a <a href="../../../../../org/apache/commons/math3/linear/SingularValueDecomposition.html#getCovariance(double)"><code>getCovariance</code></a> method has been added.</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: SingularValueDecomposition.java 1538368 2013-11-03 13:57:37Z erans $</dd> |
| <dt><span class="strong">See Also:</span></dt><dd><a href="http://mathworld.wolfram.com/SingularValueDecomposition.html">MathWorld</a>, |
| <a href="http://en.wikipedia.org/wiki/Singular_value_decomposition">Wikipedia</a></dd></dl> |
| </li> |
| </ul> |
| </div> |
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| <caption><span>Constructors</span><span class="tabEnd"> </span></caption> |
| <tr> |
| <th class="colOne" scope="col">Constructor and Description</th> |
| </tr> |
| <tr class="altColor"> |
| <td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/linear/SingularValueDecomposition.html#SingularValueDecomposition(org.apache.commons.math3.linear.RealMatrix)">SingularValueDecomposition</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 compact Singular Value Decomposition of the given matrix.</div> |
| </td> |
| </tr> |
| </table> |
| </li> |
| </ul> |
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| <h3>Method Summary</h3> |
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| <caption><span>Methods</span><span class="tabEnd"> </span></caption> |
| <tr> |
| <th class="colFirst" scope="col">Modifier and Type</th> |
| <th class="colLast" scope="col">Method and Description</th> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/SingularValueDecomposition.html#getConditionNumber()">getConditionNumber</a></strong>()</code> |
| <div class="block">Return the condition number 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/SingularValueDecomposition.html#getCovariance(double)">getCovariance</a></strong>(double minSingularValue)</code> |
| <div class="block">Returns the n × n covariance matrix.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/SingularValueDecomposition.html#getInverseConditionNumber()">getInverseConditionNumber</a></strong>()</code> |
| <div class="block">Computes the inverse of the condition number.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/SingularValueDecomposition.html#getNorm()">getNorm</a></strong>()</code> |
| <div class="block">Returns the L<sub>2</sub> norm of the matrix.</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/SingularValueDecomposition.html#getRank()">getRank</a></strong>()</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/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/SingularValueDecomposition.html#getS()">getS</a></strong>()</code> |
| <div class="block">Returns the diagonal matrix Σ of the decomposition.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>double[]</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/SingularValueDecomposition.html#getSingularValues()">getSingularValues</a></strong>()</code> |
| <div class="block">Returns the diagonal elements of the matrix Σ 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/SingularValueDecomposition.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><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/SingularValueDecomposition.html#getU()">getU</a></strong>()</code> |
| <div class="block">Returns the matrix U of the decomposition.</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/SingularValueDecomposition.html#getUT()">getUT</a></strong>()</code> |
| <div class="block">Returns the transpose of the matrix U 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/SingularValueDecomposition.html#getV()">getV</a></strong>()</code> |
| <div class="block">Returns the matrix V of the decomposition.</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/SingularValueDecomposition.html#getVT()">getVT</a></strong>()</code> |
| <div class="block">Returns the transpose of the matrix V of the decomposition.</div> |
| </td> |
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| <h3>Methods inherited from class java.lang.<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></h3> |
| <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> |
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| <h4>SingularValueDecomposition</h4> |
| <pre>public SingularValueDecomposition(<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 compact Singular Value Decomposition of the given matrix.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - Matrix to decompose.</dd></dl> |
| </li> |
| </ul> |
| </li> |
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| <h3>Method Detail</h3> |
| <a name="getU()"> |
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| <h4>getU</h4> |
| <pre>public <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> getU()</pre> |
| <div class="block">Returns the matrix U of the decomposition. |
| <p>U is an orthogonal matrix, i.e. its transpose is also its inverse.</p></div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>the U matrix</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/linear/SingularValueDecomposition.html#getUT()"><code>getUT()</code></a></dd></dl> |
| </li> |
| </ul> |
| <a name="getUT()"> |
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| <h4>getUT</h4> |
| <pre>public <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> getUT()</pre> |
| <div class="block">Returns the transpose of the matrix U of the decomposition. |
| <p>U is an orthogonal matrix, i.e. its transpose is also its inverse.</p></div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>the U matrix (or null if decomposed matrix is singular)</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/linear/SingularValueDecomposition.html#getU()"><code>getU()</code></a></dd></dl> |
| </li> |
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| <a name="getS()"> |
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| <h4>getS</h4> |
| <pre>public <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> getS()</pre> |
| <div class="block">Returns the diagonal matrix Σ of the decomposition. |
| <p>Σ is a diagonal matrix. The singular values are provided in |
| non-increasing order, for compatibility with Jama.</p></div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>the Σ matrix</dd></dl> |
| </li> |
| </ul> |
| <a name="getSingularValues()"> |
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| </a> |
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| <h4>getSingularValues</h4> |
| <pre>public double[] getSingularValues()</pre> |
| <div class="block">Returns the diagonal elements of the matrix Σ of the decomposition. |
| <p>The singular values are provided in non-increasing order, for |
| compatibility with Jama.</p></div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>the diagonal elements of the Σ matrix</dd></dl> |
| </li> |
| </ul> |
| <a name="getV()"> |
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| <h4>getV</h4> |
| <pre>public <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> getV()</pre> |
| <div class="block">Returns the matrix V of the decomposition. |
| <p>V is an orthogonal matrix, i.e. its transpose is also its inverse.</p></div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>the V matrix (or null if decomposed matrix is singular)</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/linear/SingularValueDecomposition.html#getVT()"><code>getVT()</code></a></dd></dl> |
| </li> |
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| <a name="getVT()"> |
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| <h4>getVT</h4> |
| <pre>public <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> getVT()</pre> |
| <div class="block">Returns the transpose of the matrix V of the decomposition. |
| <p>V is an orthogonal matrix, i.e. its transpose is also its inverse.</p></div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>the V matrix (or null if decomposed matrix is singular)</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/linear/SingularValueDecomposition.html#getV()"><code>getV()</code></a></dd></dl> |
| </li> |
| </ul> |
| <a name="getCovariance(double)"> |
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| <h4>getCovariance</h4> |
| <pre>public <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> getCovariance(double minSingularValue)</pre> |
| <div class="block">Returns the n × n covariance matrix. |
| <p>The covariance matrix is V × J × V<sup>T</sup> |
| where J is the diagonal matrix of the inverse of the squares of |
| the singular values.</p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>minSingularValue</code> - value below which singular values are ignored |
| (a 0 or negative value implies all singular value will be used)</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>covariance matrix</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</a></code> - if minSingularValue is larger than |
| the largest singular value, meaning all singular values are ignored</dd></dl> |
| </li> |
| </ul> |
| <a name="getNorm()"> |
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| </a> |
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| <h4>getNorm</h4> |
| <pre>public double getNorm()</pre> |
| <div class="block">Returns the L<sub>2</sub> norm of the matrix. |
| <p>The L<sub>2</sub> norm is max(|A × u|<sub>2</sub> / |
| |u|<sub>2</sub>), where |.|<sub>2</sub> denotes the vectorial 2-norm |
| (i.e. the traditional euclidian norm).</p></div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>norm</dd></dl> |
| </li> |
| </ul> |
| <a name="getConditionNumber()"> |
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| <h4>getConditionNumber</h4> |
| <pre>public double getConditionNumber()</pre> |
| <div class="block">Return the condition number of the matrix.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>condition number of the matrix</dd></dl> |
| </li> |
| </ul> |
| <a name="getInverseConditionNumber()"> |
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| <h4>getInverseConditionNumber</h4> |
| <pre>public double getInverseConditionNumber()</pre> |
| <div class="block">Computes the inverse of the condition number. |
| In cases of rank deficiency, the <a href="../../../../../org/apache/commons/math3/linear/SingularValueDecomposition.html#getConditionNumber()"><code>condition |
| number</code></a> will become undefined.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>the inverse of the condition number.</dd></dl> |
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| <pre>public int getRank()</pre> |
| <div class="block">Return the effective numerical matrix rank. |
| <p>The effective numerical rank is the number of non-negligible |
| singular values. The threshold used to identify non-negligible |
| terms is max(m,n) × ulp(s<sub>1</sub>) where ulp(s<sub>1</sub>) |
| is the least significant bit of the largest singular value.</p></div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>effective numerical matrix rank</dd></dl> |
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| <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> |
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