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pj2/doc/edu/rit/numeric/Tridiagonal.html
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<div class="subTitle">edu.rit.numeric</div>
<h2 title="Class Tridiagonal" class="title">Class Tridiagonal</h2>
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<pre>public class <span class="strong">Tridiagonal</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></pre>
<div class="block">Class Tridiagonal provides static methods for solving tridiagonal systems of
linear equations.
<P>
The Java code was translated from routines
<TT>gsl_linalg_solve_tridiag()</TT>,
<TT>gsl_linalg_solve_symm_tridiag()</TT>,
<TT>gsl_linalg_solve_cyc_tridiag()</TT>, and
<TT>gsl_linalg_solve_symm_cyc_tridiag()</TT>
in the GNU Scientific Library Version 1.9.</div>
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<h3>Method Summary</h3>
<table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Method Summary table, listing methods, and an explanation">
<caption><span>Methods</span><span class="tabEnd">&nbsp;</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>static void</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Tridiagonal.html#solve(double[], double[], double[], double[], double[])">solve</a></strong>(double[]&nbsp;d,
double[]&nbsp;e,
double[]&nbsp;f,
double[]&nbsp;b,
double[]&nbsp;x)</code>
<div class="block">Solve the given tridiagonal system of linear equations.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Tridiagonal.html#solveCyclic(double[], double[], double[], double[], double[])">solveCyclic</a></strong>(double[]&nbsp;d,
double[]&nbsp;e,
double[]&nbsp;f,
double[]&nbsp;b,
double[]&nbsp;x)</code>
<div class="block">Solve the given cyclic tridiagonal system of linear equations.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Tridiagonal.html#solveSymmetric(double[], double[], double[], double[])">solveSymmetric</a></strong>(double[]&nbsp;d,
double[]&nbsp;e,
double[]&nbsp;b,
double[]&nbsp;x)</code>
<div class="block">Solve the given symmetric tridiagonal system of linear equations.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Tridiagonal.html#solveSymmetricCyclic(double[], double[], double[], double[])">solveSymmetricCyclic</a></strong>(double[]&nbsp;d,
double[]&nbsp;e,
double[]&nbsp;b,
double[]&nbsp;x)</code>
<div class="block">Solve the given symmetric cyclic tridiagonal system of linear equations.</div>
</td>
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<h3>Methods inherited from class&nbsp;java.lang.<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></h3>
<code><a href="http://docs.oracle.com/javase/7/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/7/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/7/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/7/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/7/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/7/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/7/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/7/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/7/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/7/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/7/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</a></code></li>
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<h3>Method Detail</h3>
<a name="solve(double[], double[], double[], double[], double[])">
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<h4>solve</h4>
<pre>public static&nbsp;void&nbsp;solve(double[]&nbsp;d,
double[]&nbsp;e,
double[]&nbsp;f,
double[]&nbsp;b,
double[]&nbsp;x)</pre>
<div class="block">Solve the given tridiagonal system of linear equations. This method
solves the general <I>N</I>-by-<I>N</I> system <I>Ax</I> = <I>b</I> where
<I>A</I> is tridiagonal (<I>N</I> &gt;= 2). The form of <I>A</I> for the
4-by-4 case is:
<PRE>
[ d0 e0 0 0 ]
A = [ f0 d1 e1 0 ]
[ 0 f1 d2 e2 ]
[ 0 0 f2 d3 ]
</PRE></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>d</code> - (input) Vector of diagonal elements. Length <I>N</I> must be
&gt;= 2.</dd><dd><code>e</code> - (input) Vector of super-diagonal elements. Length must be
<I>N</I>-1.</dd><dd><code>f</code> - (input) Vector of sub-diagonal elements. Length must be
<I>N</I>-1.</dd><dd><code>b</code> - (input) Vector of right hand side elements. Length must be
<I>N</I>.</dd><dd><code>x</code> - (output) Solution vector. Length must be <I>N</I>.</dd>
<dt><span class="strong">Throws:</span></dt>
<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 any argument is null.</dd>
<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 any argument is the wrong length.</dd>
<dd><code><a href="../../../edu/rit/numeric/DomainException.html" title="class in edu.rit.numeric">DomainException</a></code> - (unchecked exception) Thrown if the linear system cannot be solved.</dd></dl>
</li>
</ul>
<a name="solveSymmetric(double[], double[], double[], double[])">
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<h4>solveSymmetric</h4>
<pre>public static&nbsp;void&nbsp;solveSymmetric(double[]&nbsp;d,
double[]&nbsp;e,
double[]&nbsp;b,
double[]&nbsp;x)</pre>
<div class="block">Solve the given symmetric tridiagonal system of linear equations. This
method solves the general <I>N</I>-by-<I>N</I> system <I>Ax</I> =
<I>b</I> where <I>A</I> is symmetric tridiagonal (<I>N</I> &gt;= 2). The
form of <I>A</I> for the 4-by-4 case is:
<PRE>
[ d0 e0 0 0 ]
A = [ e0 d1 e1 0 ]
[ 0 e1 d2 e2 ]
[ 0 0 e2 d3 ]
</PRE></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>d</code> - (input) Vector of diagonal elements. Length <I>N</I> must be
&gt;= 2.</dd><dd><code>e</code> - (input) Vector of off-diagonal elements. Length must be
<I>N</I>-1.</dd><dd><code>b</code> - (input) Vector of right hand side elements. Length must be
<I>N</I>.</dd><dd><code>x</code> - (output) Solution vector. Length must be <I>N</I>.</dd>
<dt><span class="strong">Throws:</span></dt>
<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 any argument is null.</dd>
<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 any argument is the wrong length.</dd>
<dd><code><a href="../../../edu/rit/numeric/DomainException.html" title="class in edu.rit.numeric">DomainException</a></code> - (unchecked exception) Thrown if the linear system cannot be solved.</dd></dl>
</li>
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<a name="solveCyclic(double[], double[], double[], double[], double[])">
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<h4>solveCyclic</h4>
<pre>public static&nbsp;void&nbsp;solveCyclic(double[]&nbsp;d,
double[]&nbsp;e,
double[]&nbsp;f,
double[]&nbsp;b,
double[]&nbsp;x)</pre>
<div class="block">Solve the given cyclic tridiagonal system of linear equations. This
method solves the general <I>N</I>-by-<I>N</I> system <I>Ax</I> =
<I>b</I> where <I>A</I> is cyclic tridiagonal (<I>N</I> &gt;= 3). The
form of <I>A</I> for the 4-by-4 case is:
<PRE>
[ d0 e0 0 f3 ]
A = [ f0 d1 e1 0 ]
[ 0 f1 d2 e2 ]
[ e3 0 f2 d3 ]
</PRE></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>d</code> - (input) Vector of diagonal elements. Length <I>N</I> must be
&gt;= 3.</dd><dd><code>e</code> - (input) Vector of super-diagonal elements. Length must be
<I>N</I>.</dd><dd><code>f</code> - (input) Vector of sub-diagonal elements. Length must be
<I>N</I>.</dd><dd><code>b</code> - (input) Vector of right hand side elements. Length must be
<I>N</I>.</dd><dd><code>x</code> - (output) Solution vector. Length must be <I>N</I>.</dd>
<dt><span class="strong">Throws:</span></dt>
<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 any argument is null.</dd>
<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 any argument is the wrong length.</dd>
<dd><code><a href="../../../edu/rit/numeric/DomainException.html" title="class in edu.rit.numeric">DomainException</a></code> - (unchecked exception) Thrown if the linear system cannot be solved.</dd></dl>
</li>
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<a name="solveSymmetricCyclic(double[], double[], double[], double[])">
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<h4>solveSymmetricCyclic</h4>
<pre>public static&nbsp;void&nbsp;solveSymmetricCyclic(double[]&nbsp;d,
double[]&nbsp;e,
double[]&nbsp;b,
double[]&nbsp;x)</pre>
<div class="block">Solve the given symmetric cyclic tridiagonal system of linear equations.
This method solves the general <I>N</I>-by-<I>N</I> system <I>Ax</I> =
<I>b</I> where <I>A</I> is symmetric cyclic tridiagonal (<I>N</I> &gt;=
3). The form of <I>A</I> for the 4-by-4 case is:
<PRE>
[ d0 e0 0 e3 ]
A = [ e0 d1 e1 0 ]
[ 0 e1 d2 e2 ]
[ e3 0 e2 d3 ]
</PRE></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>d</code> - (input) Vector of diagonal elements. Length <I>N</I> must be
&gt;= 3.</dd><dd><code>e</code> - (input) Vector of off-diagonal elements. Length must be
<I>N</I>.</dd><dd><code>b</code> - (input) Vector of right hand side elements. Length must be
<I>N</I>.</dd><dd><code>x</code> - (output) Solution vector. Length must be <I>N</I>.</dd>
<dt><span class="strong">Throws:</span></dt>
<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 any argument is null.</dd>
<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 any argument is the wrong length.</dd>
<dd><code><a href="../../../edu/rit/numeric/DomainException.html" title="class in edu.rit.numeric">DomainException</a></code> - (unchecked exception) Thrown if the linear system cannot be solved.</dd></dl>
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