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<h2 title="Class QRDecomposition" class="title">Class QRDecomposition</h2>
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<pre>public class <span class="strong">QRDecomposition</span>
extends <a href="/usr/share/doc/default-jdk-doc/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a>
implements <a href="/usr/share/doc/default-jdk-doc/api/java/io/Serializable.html?is-external=true" title="class or interface in java.io">Serializable</a></pre>
<div class="block">QR Decomposition.
<P>
For an m-by-n matrix A with m >= n, the QR decomposition is an m-by-n
orthogonal matrix Q and an n-by-n upper triangular matrix R so that
A = Q*R.
<P>
The QR decompostion 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 nonsquare systems
of simultaneous linear equations. This will fail if isFullRank()
returns false.</div>
<dl><dt><span class="strong">See Also:</span></dt><dd><a href="../serialized-form.html#Jama.QRDecomposition">Serialized Form</a></dd></dl>
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<td class="colOne"><code><strong><a href="../Jama/QRDecomposition.html#QRDecomposition(Jama.Matrix)">QRDecomposition</a></strong>(<a href="../Jama/Matrix.html" title="class in Jama">Matrix</a> A)</code>
<div class="block">QR Decomposition, computed by Householder reflections.</div>
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<td class="colFirst"><code><a href="../Jama/Matrix.html" title="class in Jama">Matrix</a></code></td>
<td class="colLast"><code><strong><a href="../Jama/QRDecomposition.html#getH()">getH</a></strong>()</code>
<div class="block">Return the Householder vectors</div>
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<td class="colFirst"><code><a href="../Jama/Matrix.html" title="class in Jama">Matrix</a></code></td>
<td class="colLast"><code><strong><a href="../Jama/QRDecomposition.html#getQ()">getQ</a></strong>()</code>
<div class="block">Generate and return the (economy-sized) orthogonal factor</div>
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<td class="colFirst"><code><a href="../Jama/Matrix.html" title="class in Jama">Matrix</a></code></td>
<td class="colLast"><code><strong><a href="../Jama/QRDecomposition.html#getR()">getR</a></strong>()</code>
<div class="block">Return the upper triangular factor</div>
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<td class="colFirst"><code>boolean</code></td>
<td class="colLast"><code><strong><a href="../Jama/QRDecomposition.html#isFullRank()">isFullRank</a></strong>()</code>
<div class="block">Is the matrix full rank?</div>
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<td class="colFirst"><code><a href="../Jama/Matrix.html" title="class in Jama">Matrix</a></code></td>
<td class="colLast"><code><strong><a href="../Jama/QRDecomposition.html#solve(Jama.Matrix)">solve</a></strong>(<a href="../Jama/Matrix.html" title="class in Jama">Matrix</a> B)</code>
<div class="block">Least squares solution of A*X = B</div>
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<h4>QRDecomposition</h4>
<pre>public QRDecomposition(<a href="../Jama/Matrix.html" title="class in Jama">Matrix</a> A)</pre>
<div class="block">QR Decomposition, computed by Householder reflections.
Structure to access R and the Householder vectors and compute Q.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>A</code> - Rectangular matrix</dd></dl>
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<pre>public boolean isFullRank()</pre>
<div class="block">Is the matrix full rank?</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>true if R, and hence A, has full rank.</dd></dl>
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<pre>public <a href="../Jama/Matrix.html" title="class in Jama">Matrix</a> getH()</pre>
<div class="block">Return the Householder vectors</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>Lower trapezoidal matrix whose columns define the reflections</dd></dl>
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<pre>public <a href="../Jama/Matrix.html" title="class in Jama">Matrix</a> getR()</pre>
<div class="block">Return the upper triangular factor</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>R</dd></dl>
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<h4>getQ</h4>
<pre>public <a href="../Jama/Matrix.html" title="class in Jama">Matrix</a> getQ()</pre>
<div class="block">Generate and return the (economy-sized) orthogonal factor</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>Q</dd></dl>
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<pre>public <a href="../Jama/Matrix.html" title="class in Jama">Matrix</a> solve(<a href="../Jama/Matrix.html" title="class in Jama">Matrix</a> B)</pre>
<div class="block">Least squares solution of A*X = B</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>B</code> - A Matrix with as many rows as A and any number of columns.</dd>
<dt><span class="strong">Returns:</span></dt><dd>X that minimizes the two norm of Q*R*X-B.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="/usr/share/doc/default-jdk-doc/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</a></code> - Matrix row dimensions must agree.</dd>
<dd><code><a href="/usr/share/doc/default-jdk-doc/api/java/lang/RuntimeException.html?is-external=true" title="class or interface in java.lang">RuntimeException</a></code> - Matrix is rank deficient.</dd></dl>
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