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<div class="subTitle">edu.rit.numeric</div>
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<h2 title="Class LinearSolve" class="title">Class LinearSolve</h2>
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<pre>public class <span class="strong">LinearSolve</span>
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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></pre>
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<div class="block">Class LinearSolve provides an object for solving a system of linear equations
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using LU decomposition. The <TT>solve()</TT> method finds a solution to the
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system of linear equations <B>Ax</B> = <B>b</B>, where <B>A</B> is a square
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matrix supplied to the constructor and <B>b</B> is a vector supplied to the
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<TT>solve()</TT> method. Thus, an instance of class LinearSolve can be used
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to solve many linear systems with the same left-hand-side matrix and
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different right-hand-side vectors.
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<P>
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The Java code for LU decomposition was translated from routine
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<TT>gsl_linalg_LU_decomp()</TT> in the GNU Scientific Library.</div>
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<td class="colOne"><code><strong><a href="../../../edu/rit/numeric/LinearSolve.html#LinearSolve(double[][])">LinearSolve</a></strong>(double[][] A)</code>
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<div class="block">Construct a new LinearSolve object.</div>
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<td class="colFirst"><code>double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/LinearSolve.html#determinant()">determinant</a></strong>()</code>
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<div class="block">Compute det <B>A</B>, the determinant of <B>A</B>.</div>
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</td>
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<tr class="rowColor">
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<td class="colFirst"><code>void</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/LinearSolve.html#invert(double[][])">invert</a></strong>(double[][] Ainv)</code>
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<div class="block">Compute <B>A</B><SUP>-1</SUP>, the inverse of <B>A</B>.</div>
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<td class="colFirst"><code>void</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/LinearSolve.html#invertMultiply(double[][], double[][])">invertMultiply</a></strong>(double[][] AinvB,
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double[][] B)</code>
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<div class="block">Compute <B>A</B><SUP>-1</SUP><B>B</B>.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code>void</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/LinearSolve.html#solve(double[], double[])">solve</a></strong>(double[] x,
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double[] b)</code>
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<div class="block">Solve the linear system <B>Ax</B> = <B>b</B>.</div>
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<h4>LinearSolve</h4>
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<pre>public LinearSolve(double[][] A)</pre>
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<div class="block">Construct a new LinearSolve object. <TT>A</TT> must be an
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<I>N</I>-by-<I>N</I> matrix with <I>N</I> > 0. This constructor
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calculates the LU decomposition of <TT>A</TT> and stores the result
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internally; <TT>A</TT> is unchanged.</div>
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>A</code> - Left-hand-side matrix.</dd>
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<dt><span class="strong">Throws:</span></dt>
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<dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/NullPointerException.html?is-external=true" title="class or interface in java.lang">NullPointerException</a></code> - (unchecked exception) Thrown if <TT>A</TT> or any row thereof is
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null.</dd>
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<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> - (unchecked exception) Thrown if <TT>A</TT> is zero length or is not a
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square matrix.</dd>
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<dd><code><a href="../../../edu/rit/numeric/DomainException.html" title="class in edu.rit.numeric">DomainException</a></code> - (unchecked exception) Thrown if a zero pivot was encountered during
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the LU decomposition.</dd></dl>
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<a name="solve(double[], double[])">
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<h4>solve</h4>
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<pre>public void solve(double[] x,
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double[] b)</pre>
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<div class="block">Solve the linear system <B>Ax</B> = <B>b</B>. <B>A</B> is the
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<I>N</I>-by-<I>N</I> matrix supplied to the constructor. <B>b</B> must be
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an <I>N</I>-element array initialized to the right-hand-side vector. The
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solution vector is stored in the <I>N</I>-element array <B>x</B>.
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<B>b</B> and <B>x</B> must be different arrays.</div>
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - Solution vector (output).</dd><dd><code>b</code> - Right-hand-side vector (input).</dd>
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<dt><span class="strong">Throws:</span></dt>
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<dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/NullPointerException.html?is-external=true" title="class or interface in java.lang">NullPointerException</a></code> - (unchecked exception) Thrown if <TT>x</TT> or <TT>b</TT> is null.</dd>
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<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> - (unchecked exception) Thrown if <TT>x</TT>'s length or <TT>b</TT>'s
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length is not <I>N</I>.</dd></dl>
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<h4>invert</h4>
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<pre>public void invert(double[][] Ainv)</pre>
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<div class="block">Compute <B>A</B><SUP>-1</SUP>, the inverse of <B>A</B>. <B>A</B> is the
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<I>N</I>-by-<I>N</I> matrix supplied to the constructor. The inverse of
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<B>A</B> is stored in the <I>N</I>-by-<I>N</I> matrix <TT>Ainv</TT>.</div>
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>Ainv</code> - Inverse matrix (output).</dd>
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<dt><span class="strong">Throws:</span></dt>
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<dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/NullPointerException.html?is-external=true" title="class or interface in java.lang">NullPointerException</a></code> - (unchecked exception) Thrown if <TT>Ainv</TT> or any row thereof is
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null.</dd>
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<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> - (unchecked exception) Thrown if <TT>Ainv</TT> is not an
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<I>N</I>-by-<I>N</I> matrix.</dd></dl>
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<a name="invertMultiply(double[][], double[][])">
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<h4>invertMultiply</h4>
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<pre>public void invertMultiply(double[][] AinvB,
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double[][] B)</pre>
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<div class="block">Compute <B>A</B><SUP>-1</SUP><B>B</B>. <B>A</B> is the
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<I>N</I>-by-<I>N</I> matrix supplied to the constructor. <B>B</B> must be
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an <I>N</I>-by-<I>N</I> matrix. The matrix product of
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<B>A</B><SUP>-1</SUP> and <B>B</B> is stored in the <I>N</I>-by-<I>N</I>
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matrix <TT>AinvB</TT>.</div>
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>AinvB</code> - Product matrix (output).</dd><dd><code>B</code> - Matrix (input).</dd>
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<dt><span class="strong">Throws:</span></dt>
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<dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/NullPointerException.html?is-external=true" title="class or interface in java.lang">NullPointerException</a></code> - (unchecked exception) Thrown if <TT>AinvB</TT>, <TT>B</TT>, or any
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row thereof is null.</dd>
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<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> - (unchecked exception) Thrown if <TT>AinvB</TT> or <TT>B</TT> is not
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an <I>N</I>-by-<I>N</I> matrix.</dd></dl>
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<h4>determinant</h4>
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<pre>public double determinant()</pre>
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<div class="block">Compute det <B>A</B>, the determinant of <B>A</B>. <B>A</B> is the
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<I>N</I>-by-<I>N</I> matrix supplied to the constructor. Note that for
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larger matrices, det <B>A</B> may overflow or underflow the dynamic range
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of type <TT>double</TT>.</div>
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<dl><dt><span class="strong">Returns:</span></dt><dd>The determinant of <B>A</B>.</dd></dl>
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<li>Summary: </li>
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<li>Nested | </li>
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<li>Field | </li>
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<li><a href="#method_detail">Method</a></li>
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<p class="legalCopy"><small><FONT SIZE="-2">Copyright © 2013–2016 by Alan Kaminsky. All rights reserved. Send comments to ark</FONT><FONT SIZE="1" COLOR="#FFFFFF">­</FONT><FONT SIZE="-2">@</FONT><FONT SIZE="1" COLOR="#FFFFFF">­</FONT><FONT SIZE="-2">cs.rit.edu.</FONT></small></p>
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