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| <div class="subTitle">org.apache.mahout.math</div> |
| <h2 title="Class QRDecomposition" class="title">Class QRDecomposition</h2> |
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| <li>org.apache.mahout.math.QRDecomposition</li> |
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| <dt>All Implemented Interfaces:</dt> |
| <dd><a href="../../../../org/apache/mahout/math/QR.html" title="interface in org.apache.mahout.math">QR</a></dd> |
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| <pre>public class <span class="typeNameLabel">QRDecomposition</span> |
| extends <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a> |
| implements <a href="../../../../org/apache/mahout/math/QR.html" title="interface in org.apache.mahout.math">QR</a></pre> |
| <div class="block">For an <tt>m x n</tt> matrix <tt>A</tt> with <code>m >= n</code>, the QR decomposition is an <tt>m x n</tt> |
| orthogonal matrix <tt>Q</tt> and an <tt>n x n</tt> upper triangular matrix <tt>R</tt> so that |
| <tt>A = Q*R</tt>. |
| <P> |
| The QR decomposition always exists, even if the matrix does not have |
| full rank, so the constructor will never fail. The primary use of the |
| QR decomposition is in the least squares solution of non-square systems |
| of simultaneous linear equations. This will fail if <tt>isFullRank()</tt> |
| returns <tt>false</tt>.</div> |
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| <td class="colOne"><code><span class="memberNameLink"><a href="../../../../org/apache/mahout/math/QRDecomposition.html#QRDecomposition-org.apache.mahout.math.Matrix-">QRDecomposition</a></span>(<a href="../../../../org/apache/mahout/math/Matrix.html" title="interface in org.apache.mahout.math">Matrix</a> a)</code> |
| <div class="block">Constructs and returns a new QR decomposition object; computed by Householder reflections; The |
| decomposed matrices can be retrieved via instance methods of the returned decomposition |
| object.</div> |
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| <td class="colFirst"><code><a href="../../../../org/apache/mahout/math/Matrix.html" title="interface in org.apache.mahout.math">Matrix</a></code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/apache/mahout/math/QRDecomposition.html#getQ--">getQ</a></span>()</code> |
| <div class="block">Generates and returns the (economy-sized) orthogonal factor <tt>Q</tt>.</div> |
| </td> |
| </tr> |
| <tr id="i1" class="rowColor"> |
| <td class="colFirst"><code><a href="../../../../org/apache/mahout/math/Matrix.html" title="interface in org.apache.mahout.math">Matrix</a></code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/apache/mahout/math/QRDecomposition.html#getR--">getR</a></span>()</code> |
| <div class="block">Returns the upper triangular factor, <tt>R</tt>.</div> |
| </td> |
| </tr> |
| <tr id="i2" class="altColor"> |
| <td class="colFirst"><code>boolean</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/apache/mahout/math/QRDecomposition.html#hasFullRank--">hasFullRank</a></span>()</code> |
| <div class="block">Returns whether the matrix <tt>A</tt> has full rank.</div> |
| </td> |
| </tr> |
| <tr id="i3" class="rowColor"> |
| <td class="colFirst"><code><a href="../../../../org/apache/mahout/math/Matrix.html" title="interface in org.apache.mahout.math">Matrix</a></code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/apache/mahout/math/QRDecomposition.html#solve-org.apache.mahout.math.Matrix-">solve</a></span>(<a href="../../../../org/apache/mahout/math/Matrix.html" title="interface in org.apache.mahout.math">Matrix</a> B)</code> |
| <div class="block">Least squares solution of <tt>A*X = B</tt>; <tt>returns X</tt>.</div> |
| </td> |
| </tr> |
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| <td class="colFirst"><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</a></code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/apache/mahout/math/QRDecomposition.html#toString--">toString</a></span>()</code> |
| <div class="block">Returns a rough string rendition of a QR.</div> |
| </td> |
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| <h4>QRDecomposition</h4> |
| <pre>public QRDecomposition(<a href="../../../../org/apache/mahout/math/Matrix.html" title="interface in org.apache.mahout.math">Matrix</a> a)</pre> |
| <div class="block">Constructs and returns a new QR decomposition object; computed by Householder reflections; The |
| decomposed matrices can be retrieved via instance methods of the returned decomposition |
| object.</div> |
| <dl> |
| <dt><span class="paramLabel">Parameters:</span></dt> |
| <dd><code>a</code> - A rectangular matrix.</dd> |
| <dt><span class="throwsLabel">Throws:</span></dt> |
| <dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</a></code> - if <code>A.rows() < A.columns()</code>.</dd> |
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| <a name="getQ--"> |
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| <h4>getQ</h4> |
| <pre>public <a href="../../../../org/apache/mahout/math/Matrix.html" title="interface in org.apache.mahout.math">Matrix</a> getQ()</pre> |
| <div class="block">Generates and returns the (economy-sized) orthogonal factor <tt>Q</tt>.</div> |
| <dl> |
| <dt><span class="overrideSpecifyLabel">Specified by:</span></dt> |
| <dd><code><a href="../../../../org/apache/mahout/math/QR.html#getQ--">getQ</a></code> in interface <code><a href="../../../../org/apache/mahout/math/QR.html" title="interface in org.apache.mahout.math">QR</a></code></dd> |
| <dt><span class="returnLabel">Returns:</span></dt> |
| <dd><tt>Q</tt></dd> |
| </dl> |
| </li> |
| </ul> |
| <a name="getR--"> |
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| <h4>getR</h4> |
| <pre>public <a href="../../../../org/apache/mahout/math/Matrix.html" title="interface in org.apache.mahout.math">Matrix</a> getR()</pre> |
| <div class="block">Returns the upper triangular factor, <tt>R</tt>.</div> |
| <dl> |
| <dt><span class="overrideSpecifyLabel">Specified by:</span></dt> |
| <dd><code><a href="../../../../org/apache/mahout/math/QR.html#getR--">getR</a></code> in interface <code><a href="../../../../org/apache/mahout/math/QR.html" title="interface in org.apache.mahout.math">QR</a></code></dd> |
| <dt><span class="returnLabel">Returns:</span></dt> |
| <dd><tt>R</tt></dd> |
| </dl> |
| </li> |
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| <h4>hasFullRank</h4> |
| <pre>public boolean hasFullRank()</pre> |
| <div class="block">Returns whether the matrix <tt>A</tt> has full rank.</div> |
| <dl> |
| <dt><span class="overrideSpecifyLabel">Specified by:</span></dt> |
| <dd><code><a href="../../../../org/apache/mahout/math/QR.html#hasFullRank--">hasFullRank</a></code> in interface <code><a href="../../../../org/apache/mahout/math/QR.html" title="interface in org.apache.mahout.math">QR</a></code></dd> |
| <dt><span class="returnLabel">Returns:</span></dt> |
| <dd>true if <tt>R</tt>, and hence <tt>A</tt>, has full rank.</dd> |
| </dl> |
| </li> |
| </ul> |
| <a name="solve-org.apache.mahout.math.Matrix-"> |
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| <h4>solve</h4> |
| <pre>public <a href="../../../../org/apache/mahout/math/Matrix.html" title="interface in org.apache.mahout.math">Matrix</a> solve(<a href="../../../../org/apache/mahout/math/Matrix.html" title="interface in org.apache.mahout.math">Matrix</a> B)</pre> |
| <div class="block">Least squares solution of <tt>A*X = B</tt>; <tt>returns X</tt>.</div> |
| <dl> |
| <dt><span class="overrideSpecifyLabel">Specified by:</span></dt> |
| <dd><code><a href="../../../../org/apache/mahout/math/QR.html#solve-org.apache.mahout.math.Matrix-">solve</a></code> in interface <code><a href="../../../../org/apache/mahout/math/QR.html" title="interface in org.apache.mahout.math">QR</a></code></dd> |
| <dt><span class="paramLabel">Parameters:</span></dt> |
| <dd><code>B</code> - A matrix with as many rows as <tt>A</tt> and any number of columns.</dd> |
| <dt><span class="returnLabel">Returns:</span></dt> |
| <dd><tt>X</tt> that minimizes the two norm of <tt>Q*R*X - B</tt>.</dd> |
| <dt><span class="throwsLabel">Throws:</span></dt> |
| <dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</a></code> - if <tt>B.rows() != A.rows()</tt>.</dd> |
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| <h4>toString</h4> |
| <pre>public <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</a> toString()</pre> |
| <div class="block">Returns a rough string rendition of a QR.</div> |
| <dl> |
| <dt><span class="overrideSpecifyLabel">Overrides:</span></dt> |
| <dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#toString--" title="class or interface in java.lang">toString</a></code> in class <code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></code></dd> |
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