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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
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<title> TemplateJAMA::LU class Reference</title>
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<!-- Generated by Doxygen 1.2.5 on Mon Jan 20 07:47:18 2003 -->
<center>
<a class="qindex" href="index.html">Main Page</a> <a class="qindex" href="namespaces.html">Namespace List</a> <a class="qindex" href="annotated.html">Compound List</a> <a class="qindex" href="files.html">File List</a> <a class="qindex" href="functions.html">Compound Members</a> </center>
<hr><h1>JAMA::LU Class Template Reference</h1><code>#include <<a class="el" href="jama_lu_h-source.html">jama_lu.h</a>></code>
<p>
<a href="class_JAMA__LU-members.html">List of all members.</a><table border=0 cellpadding=0 cellspacing=0>
<tr><td colspan=2><br><h2>Public Methods</h2></td></tr>
<tr><td nowrap align=right valign=top> </td><td valign=bottom><a class="el" href="class_JAMA__LU.html#a0">LU</a> (const Array2D< Real > &A)</td></tr>
<tr><td nowrap align=right valign=top>int </td><td valign=bottom><a class="el" href="class_JAMA__LU.html#a1">isNonsingular</a> ()</td></tr>
<tr><td nowrap align=right valign=top>Array2D<Real> </td><td valign=bottom><a class="el" href="class_JAMA__LU.html#a2">getL</a> ()</td></tr>
<tr><td nowrap align=right valign=top>Array2D<Real> </td><td valign=bottom><a class="el" href="class_JAMA__LU.html#a3">getU</a> ()</td></tr>
<tr><td nowrap align=right valign=top>Array1D<int> </td><td valign=bottom><a class="el" href="class_JAMA__LU.html#a4">getPivot</a> ()</td></tr>
<tr><td nowrap align=right valign=top>Real </td><td valign=bottom><a class="el" href="class_JAMA__LU.html#a5">det</a> ()</td></tr>
<tr><td nowrap align=right valign=top>Array2D<Real> </td><td valign=bottom><a class="el" href="class_JAMA__LU.html#a6">solve</a> (const Array2D< Real > &B)</td></tr>
<tr><td nowrap align=right valign=top>Array1D<Real> </td><td valign=bottom><a class="el" href="class_JAMA__LU.html#a7">solve</a> (const Array1D< Real > &b)</td></tr>
</table>
<hr><a name="_details"></a><h2>Detailed Description</h2>
<h3>template<class Real> class JAMA::LU</h3>
<a class="el" href="class_JAMA__LU.html">LU</a> Decomposition.
<p>
For an m-by-n matrix A with m >= n, the <a class="el" href="class_JAMA__LU.html">LU</a> decomposition is an m-by-n unit lower triangular matrix L, an n-by-n upper triangular matrix U, and a permutation vector piv of length m so that A(piv,:) = L*U. If m < n, then L is m-by-m and U is m-by-n.
<p>
The <a class="el" href="class_JAMA__LU.html">LU</a> decompostion with pivoting always exists, even if the matrix is singular, so the constructor will never fail. The primary use of the <a class="el" href="class_JAMA__LU.html">LU</a> decomposition is in the solution of square systems of simultaneous linear equations. This will fail if <a class="el" href="class_JAMA__LU.html#a1">isNonsingular</a>() returns false.
<p>
<hr><h2>Constructor & Destructor Documentation</h2>
<a name="a0" doxytag="JAMA::LU::LU"></a><p>
<table width="100%" cellpadding="2" cellspacing="0" border="0">
<tr>
<td class="md">
<table cellpadding="0" cellspacing="0" border="0">
<tr>
<td colspan="2"><b>
template<class Real> </b></td>
</tr>
<tr>
<td nowrap valign="top"><b>
JAMA::LU<Real>::LU<Real> (
</b></td>
<td valign="bottom"><b>
const Array2D< Real > & <em>A</em> )<code> [inline]</code>
</b></td>
</tr>
</table>
</td>
</tr>
</table>
<table cellspacing=5 cellpadding=0 border=0>
<tr>
<td>
</td>
<td>
<p>
<a class="el" href="class_JAMA__LU.html">LU</a> Decomposition <dl compact><dt>
<b>Parameters: </b><dd>
<table border=0 cellspacing=2 cellpadding=0>
<tr><td valign=top><em>A</em>
</td><td>
Rectangular matrix </td></tr>
</table>
</dl><dl compact><dt>
<b>Returns: </b><dd>
<a class="el" href="class_JAMA__LU.html">LU</a> Decomposition object to access L, U and piv. </dl> </td>
</tr>
</table>
<hr><h2>Member Function Documentation</h2>
<a name="a5" doxytag="JAMA::LU::det"></a><p>
<table width="100%" cellpadding="2" cellspacing="0" border="0">
<tr>
<td class="md">
<table cellpadding="0" cellspacing="0" border="0">
<tr>
<td colspan="2"><b>
template<class Real> </b></td>
</tr>
<tr>
<td nowrap valign="top"><b>
Real JAMA::LU<Real>::det (
</b></td>
<td valign="bottom"><b>
)<code> [inline]</code>
</b></td>
</tr>
</table>
</td>
</tr>
</table>
<table cellspacing=5 cellpadding=0 border=0>
<tr>
<td>
</td>
<td>
<p>
Compute determinant using <a class="el" href="class_JAMA__LU.html">LU</a> factors. <dl compact><dt>
<b>Returns: </b><dd>
determinant of A, or 0 if A is not square. </dl> </td>
</tr>
</table>
<a name="a2" doxytag="JAMA::LU::getL"></a><p>
<table width="100%" cellpadding="2" cellspacing="0" border="0">
<tr>
<td class="md">
<table cellpadding="0" cellspacing="0" border="0">
<tr>
<td colspan="2"><b>
template<class Real> </b></td>
</tr>
<tr>
<td nowrap valign="top"><b>
Array2D< Real > JAMA::LU<Real>::getL (
</b></td>
<td valign="bottom"><b>
)<code> [inline]</code>
</b></td>
</tr>
</table>
</td>
</tr>
</table>
<table cellspacing=5 cellpadding=0 border=0>
<tr>
<td>
</td>
<td>
<p>
Return lower triangular factor <dl compact><dt>
<b>Returns: </b><dd>
L </dl> </td>
</tr>
</table>
<a name="a4" doxytag="JAMA::LU::getPivot"></a><p>
<table width="100%" cellpadding="2" cellspacing="0" border="0">
<tr>
<td class="md">
<table cellpadding="0" cellspacing="0" border="0">
<tr>
<td colspan="2"><b>
template<class Real> </b></td>
</tr>
<tr>
<td nowrap valign="top"><b>
Array1D< int > JAMA::LU<Real>::getPivot (
</b></td>
<td valign="bottom"><b>
)<code> [inline]</code>
</b></td>
</tr>
</table>
</td>
</tr>
</table>
<table cellspacing=5 cellpadding=0 border=0>
<tr>
<td>
</td>
<td>
<p>
Return pivot permutation vector <dl compact><dt>
<b>Returns: </b><dd>
piv </dl> </td>
</tr>
</table>
<a name="a3" doxytag="JAMA::LU::getU"></a><p>
<table width="100%" cellpadding="2" cellspacing="0" border="0">
<tr>
<td class="md">
<table cellpadding="0" cellspacing="0" border="0">
<tr>
<td colspan="2"><b>
template<class Real> </b></td>
</tr>
<tr>
<td nowrap valign="top"><b>
Array2D< Real > JAMA::LU<Real>::getU (
</b></td>
<td valign="bottom"><b>
)<code> [inline]</code>
</b></td>
</tr>
</table>
</td>
</tr>
</table>
<table cellspacing=5 cellpadding=0 border=0>
<tr>
<td>
</td>
<td>
<p>
Return upper triangular factor <dl compact><dt>
<b>Returns: </b><dd>
U portion of <a class="el" href="class_JAMA__LU.html">LU</a> factorization. </dl> </td>
</tr>
</table>
<a name="a1" doxytag="JAMA::LU::isNonsingular"></a><p>
<table width="100%" cellpadding="2" cellspacing="0" border="0">
<tr>
<td class="md">
<table cellpadding="0" cellspacing="0" border="0">
<tr>
<td colspan="2"><b>
template<class Real> </b></td>
</tr>
<tr>
<td nowrap valign="top"><b>
int JAMA::LU<Real>::isNonsingular (
</b></td>
<td valign="bottom"><b>
)<code> [inline]</code>
</b></td>
</tr>
</table>
</td>
</tr>
</table>
<table cellspacing=5 cellpadding=0 border=0>
<tr>
<td>
</td>
<td>
<p>
Is the matrix nonsingular? <dl compact><dt>
<b>Returns: </b><dd>
1 (true) if upper triangular factor U (and hence A) is nonsingular, 0 otherwise. </dl> </td>
</tr>
</table>
<a name="a7" doxytag="JAMA::LU::solve"></a><p>
<table width="100%" cellpadding="2" cellspacing="0" border="0">
<tr>
<td class="md">
<table cellpadding="0" cellspacing="0" border="0">
<tr>
<td colspan="2"><b>
template<class Real> </b></td>
</tr>
<tr>
<td nowrap valign="top"><b>
Array1D< Real > JAMA::LU<Real>::solve (
</b></td>
<td valign="bottom"><b>
const Array1D< Real > & <em>b</em> )<code> [inline]</code>
</b></td>
</tr>
</table>
</td>
</tr>
</table>
<table cellspacing=5 cellpadding=0 border=0>
<tr>
<td>
</td>
<td>
<p>
Solve A*x = b, where x and b are vectors of length equal to the number of rows in A.<dl compact><dt>
<b>Parameters: </b><dd>
<table border=0 cellspacing=2 cellpadding=0>
<tr><td valign=top><em>b</em>
</td><td>
a vector (Array1D> of length equal to the first dimension of A. </td></tr>
</table>
</dl><dl compact><dt>
<b>Returns: </b><dd>
x a vector (Array1D> so that L*U*x = b(piv), if B is nonconformant, returns 0x0 (null) array. </dl> </td>
</tr>
</table>
<a name="a6" doxytag="JAMA::LU::solve"></a><p>
<table width="100%" cellpadding="2" cellspacing="0" border="0">
<tr>
<td class="md">
<table cellpadding="0" cellspacing="0" border="0">
<tr>
<td colspan="2"><b>
template<class Real> </b></td>
</tr>
<tr>
<td nowrap valign="top"><b>
Array2D< Real > JAMA::LU<Real>::solve (
</b></td>
<td valign="bottom"><b>
const Array2D< Real > & <em>B</em> )<code> [inline]</code>
</b></td>
</tr>
</table>
</td>
</tr>
</table>
<table cellspacing=5 cellpadding=0 border=0>
<tr>
<td>
</td>
<td>
<p>
Solve A*X = B <dl compact><dt>
<b>Parameters: </b><dd>
<table border=0 cellspacing=2 cellpadding=0>
<tr><td valign=top><em>B</em>
</td><td>
A Matrix with as many rows as A and any number of columns. </td></tr>
</table>
</dl><dl compact><dt>
<b>Returns: </b><dd>
X so that L*U*X = B(piv,:), if B is nonconformant, returns 0x0 (null) array. </dl> </td>
</tr>
</table>
<hr>The documentation for this class was generated from the following file:<ul>
<li><a class="el" href="jama_lu_h-source.html">jama_lu.h</a></ul>
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