diff options
Diffstat (limited to 'commons-math3-3.6.1/docs/apidocs/org/apache/commons/math3/linear/SymmLQ.html')
| -rw-r--r-- | commons-math3-3.6.1/docs/apidocs/org/apache/commons/math3/linear/SymmLQ.html | 929 |
1 files changed, 929 insertions, 0 deletions
diff --git a/commons-math3-3.6.1/docs/apidocs/org/apache/commons/math3/linear/SymmLQ.html b/commons-math3-3.6.1/docs/apidocs/org/apache/commons/math3/linear/SymmLQ.html new file mode 100644 index 0000000..ded8307 --- /dev/null +++ b/commons-math3-3.6.1/docs/apidocs/org/apache/commons/math3/linear/SymmLQ.html @@ -0,0 +1,929 @@ +<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> +<!-- NewPage --> +<html lang="en"> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> +<title>SymmLQ (Apache Commons Math 3.6.1 API)</title> +<link rel="stylesheet" type="text/css" href="../../../../../stylesheet.css" title="Style"> +</head> +<body> +<script type="text/javascript"><!-- + if (location.href.indexOf('is-external=true') == -1) { + parent.document.title="SymmLQ (Apache Commons Math 3.6.1 API)"; + } +//--> +</script> +<noscript> +<div>JavaScript is disabled on your browser.</div> +</noscript> +<!-- ========= START OF TOP NAVBAR ======= --> +<div class="topNav"><a name="navbar_top"> +<!-- --> +</a><a href="#skip-navbar_top" title="Skip navigation links"></a><a name="navbar_top_firstrow"> +<!-- --> +</a> +<ul class="navList" title="Navigation"> +<li><a href="../../../../../overview-summary.html">Overview</a></li> +<li><a href="package-summary.html">Package</a></li> +<li class="navBarCell1Rev">Class</li> +<li><a href="class-use/SymmLQ.html">Use</a></li> +<li><a href="package-tree.html">Tree</a></li> +<li><a href="../../../../../deprecated-list.html">Deprecated</a></li> +<li><a href="../../../../../index-all.html">Index</a></li> +<li><a href="../../../../../help-doc.html">Help</a></li> +</ul> +<div class="aboutLanguage"><em><script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script></em></div> +</div> +<div class="subNav"> +<ul class="navList"> +<li><a href="../../../../../org/apache/commons/math3/linear/SparseRealVector.html" title="class in org.apache.commons.math3.linear"><span class="strong">Prev Class</span></a></li> +<li>Next Class</li> +</ul> +<ul class="navList"> +<li><a href="../../../../../index.html?org/apache/commons/math3/linear/SymmLQ.html" target="_top">Frames</a></li> +<li><a href="SymmLQ.html" target="_top">No Frames</a></li> +</ul> +<ul class="navList" id="allclasses_navbar_top"> +<li><a href="../../../../../allclasses-noframe.html">All Classes</a></li> +</ul> +<div> +<script type="text/javascript"><!-- + allClassesLink = document.getElementById("allclasses_navbar_top"); + if(window==top) { + allClassesLink.style.display = "block"; + } + else { + allClassesLink.style.display = "none"; + } + //--> +</script> +</div> +<div> +<ul class="subNavList"> +<li>Summary: </li> +<li>Nested | </li> +<li>Field | </li> +<li><a href="#constructor_summary">Constr</a> | </li> +<li><a href="#method_summary">Method</a></li> +</ul> +<ul class="subNavList"> +<li>Detail: </li> +<li>Field | </li> +<li><a href="#constructor_detail">Constr</a> | </li> +<li><a href="#method_detail">Method</a></li> +</ul> +</div> +<a name="skip-navbar_top"> +<!-- --> +</a></div> +<!-- ========= END OF TOP NAVBAR ========= --> +<!-- ======== START OF CLASS DATA ======== --> +<div class="header"> +<div class="subTitle">org.apache.commons.math3.linear</div> +<h2 title="Class SymmLQ" class="title">Class SymmLQ</h2> +</div> +<div class="contentContainer"> +<ul class="inheritance"> +<li><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</a></li> +<li> +<ul class="inheritance"> +<li><a href="../../../../../org/apache/commons/math3/linear/IterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">org.apache.commons.math3.linear.IterativeLinearSolver</a></li> +<li> +<ul class="inheritance"> +<li><a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">org.apache.commons.math3.linear.PreconditionedIterativeLinearSolver</a></li> +<li> +<ul class="inheritance"> +<li>org.apache.commons.math3.linear.SymmLQ</li> +</ul> +</li> +</ul> +</li> +</ul> +</li> +</ul> +<div class="description"> +<ul class="blockList"> +<li class="blockList"> +<hr> +<br> +<pre>public class <span class="strong">SymmLQ</span> +extends <a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">PreconditionedIterativeLinearSolver</a></pre> +<div class="block"><p> + Implementation of the SYMMLQ iterative linear solver proposed by <a + href="#PAIG1975">Paige and Saunders (1975)</a>. This implementation is + largely based on the FORTRAN code by Pr. Michael A. Saunders, available <a + href="http://www.stanford.edu/group/SOL/software/symmlq/f77/">here</a>. + </p> + <p> + SYMMLQ is designed to solve the system of linear equations A · x = b + where A is an n × n self-adjoint linear operator (defined as a + <a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear"><code>RealLinearOperator</code></a>), and b is a given vector. The operator A is not + required to be positive definite. If A is known to be definite, the method of + conjugate gradients might be preferred, since it will require about the same + number of iterations as SYMMLQ but slightly less work per iteration. + </p> + <p> + SYMMLQ is designed to solve the system (A - shift · I) · x = b, + where shift is a specified scalar value. If shift and b are suitably chosen, + the computed vector x may approximate an (unnormalized) eigenvector of A, as + in the methods of inverse iteration and/or Rayleigh-quotient iteration. + Again, the linear operator (A - shift · I) need not be positive + definite (but <em>must</em> be self-adjoint). The work per iteration is very + slightly less if shift = 0. + </p> + <h3>Preconditioning</h3> + <p> + Preconditioning may reduce the number of iterations required. The solver may + be provided with a positive definite preconditioner + M = P<sup>T</sup> · P + that is known to approximate + (A - shift · I)<sup>-1</sup> in some sense, where matrix-vector + products of the form M · y = x can be computed efficiently. Then + SYMMLQ will implicitly solve the system of equations + P · (A - shift · I) · P<sup>T</sup> · + x<sub>hat</sub> = P · b, i.e. + A<sub>hat</sub> · x<sub>hat</sub> = b<sub>hat</sub>, + where + A<sub>hat</sub> = P · (A - shift · I) · P<sup>T</sup>, + b<sub>hat</sub> = P · b, + and return the solution + x = P<sup>T</sup> · x<sub>hat</sub>. + The associated residual is + r<sub>hat</sub> = b<sub>hat</sub> - A<sub>hat</sub> · x<sub>hat</sub> + = P · [b - (A - shift · I) · x] + = P · r. + </p> + <p> + In the case of preconditioning, the <a href="../../../../../org/apache/commons/math3/linear/IterativeLinearSolverEvent.html" title="class in org.apache.commons.math3.linear"><code>IterativeLinearSolverEvent</code></a>s that + this solver fires are such that + <a href="../../../../../org/apache/commons/math3/linear/IterativeLinearSolverEvent.html#getNormOfResidual()"><code>IterativeLinearSolverEvent.getNormOfResidual()</code></a> returns the norm of + the <em>preconditioned</em>, updated residual, ||P · r||, not the norm + of the <em>true</em> residual ||r||. + </p> + <h3><a id="stopcrit">Default stopping criterion</a></h3> + <p> + A default stopping criterion is implemented. The iterations stop when || rhat + || ≤ δ || Ahat || || xhat ||, where xhat is the current estimate of + the solution of the transformed system, rhat the current estimate of the + corresponding residual, and δ a user-specified tolerance. + </p> + <h3>Iteration count</h3> + <p> + In the present context, an iteration should be understood as one evaluation + of the matrix-vector product A · x. The initialization phase therefore + counts as one iteration. If the user requires checks on the symmetry of A, + this entails one further matrix-vector product in the initial phase. This + further product is <em>not</em> accounted for in the iteration count. In + other words, the number of iterations required to reach convergence will be + identical, whether checks have been required or not. + </p> + <p> + The present definition of the iteration count differs from that adopted in + the original FOTRAN code, where the initialization phase was <em>not</em> + taken into account. + </p> + <h3><a id="initguess">Initial guess of the solution</a></h3> + <p> + The <code>x</code> parameter in + <ul> + <li><a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solve(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector,%20org.apache.commons.math3.linear.RealVector)"><code>solve(RealLinearOperator, RealVector, RealVector)</code></a>,</li> + <li><a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solve(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector,%20org.apache.commons.math3.linear.RealVector)"><code>solve(RealLinearOperator, RealLinearOperator, RealVector, RealVector)</code></a>},</li> + <li><a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solveInPlace(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector,%20org.apache.commons.math3.linear.RealVector)"><code>solveInPlace(RealLinearOperator, RealVector, RealVector)</code></a>,</li> + <li><a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solveInPlace(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector,%20org.apache.commons.math3.linear.RealVector)"><code>solveInPlace(RealLinearOperator, RealLinearOperator, RealVector, RealVector)</code></a>,</li> + <li><a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solveInPlace(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector,%20org.apache.commons.math3.linear.RealVector,%20boolean,%20double)"><code>solveInPlace(RealLinearOperator, RealLinearOperator, RealVector, RealVector, boolean, double)</code></a>,</li> + </ul> + should not be considered as an initial guess, as it is set to zero in the + initial phase. If x<sub>0</sub> is known to be a good approximation to x, one + should compute r<sub>0</sub> = b - A · x, solve A · dx = r0, + and set x = x<sub>0</sub> + dx. + </p> + <h3><a id="context">Exception context</a></h3> + <p> + Besides standard <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception"><code>DimensionMismatchException</code></a>, this class might throw + <a href="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear"><code>NonSelfAdjointOperatorException</code></a> if the linear operator or the + preconditioner are not symmetric. In this case, the <a href="../../../../../org/apache/commons/math3/exception/util/ExceptionContext.html" title="class in org.apache.commons.math3.exception.util"><code>ExceptionContext</code></a> + provides more information + <ul> + <li>key <code>"operator"</code> points to the offending linear operator, say L,</li> + <li>key <code>"vector1"</code> points to the first offending vector, say x, + <li>key <code>"vector2"</code> points to the second offending vector, say y, such + that x<sup>T</sup> · L · y ≠ y<sup>T</sup> · L + · x (within a certain accuracy).</li> + </ul> + </p> + <p> + <a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear"><code>NonPositiveDefiniteOperatorException</code></a> might also be thrown in case the + preconditioner is not positive definite. The relevant keys to the + <a href="../../../../../org/apache/commons/math3/exception/util/ExceptionContext.html" title="class in org.apache.commons.math3.exception.util"><code>ExceptionContext</code></a> are + <ul> + <li>key <code>"operator"</code>, which points to the offending linear operator, + say L,</li> + <li>key <code>"vector"</code>, which points to the offending vector, say x, such + that x<sup>T</sup> · L · x < 0.</li> + </ul> + </p> + <h3>References</h3> + <dl> + <dt><a id="PAIG1975">Paige and Saunders (1975)</a></dt> + <dd>C. C. Paige and M. A. Saunders, <a + href="http://www.stanford.edu/group/SOL/software/symmlq/PS75.pdf"><em> + Solution of Sparse Indefinite Systems of Linear Equations</em></a>, SIAM + Journal on Numerical Analysis 12(4): 617-629, 1975</dd> + </dl></div> +<dl><dt><span class="strong">Since:</span></dt> + <dd>3.0</dd></dl> +</li> +</ul> +</div> +<div class="summary"> +<ul class="blockList"> +<li class="blockList"> +<!-- ======== CONSTRUCTOR SUMMARY ======== --> +<ul class="blockList"> +<li class="blockList"><a name="constructor_summary"> +<!-- --> +</a> +<h3>Constructor Summary</h3> +<table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Constructor Summary table, listing constructors, and an explanation"> +<caption><span>Constructors</span><span class="tabEnd"> </span></caption> +<tr> +<th class="colOne" scope="col">Constructor and Description</th> +</tr> +<tr class="altColor"> +<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#SymmLQ(int,%20double,%20boolean)">SymmLQ</a></strong>(int maxIterations, + double delta, + boolean check)</code> +<div class="block">Creates a new instance of this class, with <a href="#stopcrit">default + stopping criterion</a>.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#SymmLQ(org.apache.commons.math3.util.IterationManager,%20double,%20boolean)">SymmLQ</a></strong>(<a href="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util">IterationManager</a> manager, + double delta, + boolean check)</code> +<div class="block">Creates a new instance of this class, with <a href="#stopcrit">default + stopping criterion</a> and custom iteration manager.</div> +</td> +</tr> +</table> +</li> +</ul> +<!-- ========== METHOD SUMMARY =========== --> +<ul class="blockList"> +<li class="blockList"><a name="method_summary"> +<!-- --> +</a> +<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"> </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>boolean</code></td> +<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#getCheck()">getCheck</a></strong>()</code> +<div class="block">Returns <code>true</code> if symmetry of the matrix, and symmetry as well as + positive definiteness of the preconditioner should be checked.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a></code></td> +<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solve(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector)">solve</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> a, + <a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> m, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> b)</code> +<div class="block">Returns an estimate of the solution to the linear system A · x = + b.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a></code></td> +<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solve(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector,%20boolean,%20double)">solve</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> a, + <a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> m, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> b, + boolean goodb, + double shift)</code> +<div class="block">Returns an estimate of the solution to the linear system (A - shift + · I) · x = b.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a></code></td> +<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solve(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector,%20org.apache.commons.math3.linear.RealVector)">solve</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> a, + <a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> m, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> b, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> x)</code> +<div class="block">Returns an estimate of the solution to the linear system A · x = + b.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a></code></td> +<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solve(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector)">solve</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> a, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> b)</code> +<div class="block">Returns an estimate of the solution to the linear system A · x = + b.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a></code></td> +<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solve(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector,%20boolean,%20double)">solve</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> a, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> b, + boolean goodb, + double shift)</code> +<div class="block">Returns the solution to the system (A - shift · I) · x = b.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a></code></td> +<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solve(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector,%20org.apache.commons.math3.linear.RealVector)">solve</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> a, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> b, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> x)</code> +<div class="block">Returns an estimate of the solution to the linear system A · x = + b.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a></code></td> +<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solveInPlace(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector,%20org.apache.commons.math3.linear.RealVector)">solveInPlace</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> a, + <a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> m, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> b, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> x)</code> +<div class="block">Returns an estimate of the solution to the linear system A · x = + b.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a></code></td> +<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solveInPlace(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector,%20org.apache.commons.math3.linear.RealVector,%20boolean,%20double)">solveInPlace</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> a, + <a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> m, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> b, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> x, + boolean goodb, + double shift)</code> +<div class="block">Returns an estimate of the solution to the linear system (A - shift + · I) · x = b.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a></code></td> +<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solveInPlace(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector,%20org.apache.commons.math3.linear.RealVector)">solveInPlace</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> a, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> b, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> x)</code> +<div class="block">Returns an estimate of the solution to the linear system A · x = + b.</div> +</td> +</tr> +</table> +<ul class="blockList"> +<li class="blockList"><a name="methods_inherited_from_class_org.apache.commons.math3.linear.PreconditionedIterativeLinearSolver"> +<!-- --> +</a> +<h3>Methods inherited from class org.apache.commons.math3.linear.<a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">PreconditionedIterativeLinearSolver</a></h3> +<code><a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html#checkParameters(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector,%20org.apache.commons.math3.linear.RealVector)">checkParameters</a></code></li> +</ul> +<ul class="blockList"> +<li class="blockList"><a name="methods_inherited_from_class_org.apache.commons.math3.linear.IterativeLinearSolver"> +<!-- --> +</a> +<h3>Methods inherited from class org.apache.commons.math3.linear.<a href="../../../../../org/apache/commons/math3/linear/IterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">IterativeLinearSolver</a></h3> +<code><a href="../../../../../org/apache/commons/math3/linear/IterativeLinearSolver.html#checkParameters(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector,%20org.apache.commons.math3.linear.RealVector)">checkParameters</a>, <a href="../../../../../org/apache/commons/math3/linear/IterativeLinearSolver.html#getIterationManager()">getIterationManager</a></code></li> +</ul> +<ul class="blockList"> +<li class="blockList"><a name="methods_inherited_from_class_java.lang.Object"> +<!-- --> +</a> +<h3>Methods inherited from class 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,%20int)" title="class or interface in java.lang">wait</a></code></li> +</ul> +</li> +</ul> +</li> +</ul> +</div> +<div class="details"> +<ul class="blockList"> +<li class="blockList"> +<!-- ========= CONSTRUCTOR DETAIL ======== --> +<ul class="blockList"> +<li class="blockList"><a name="constructor_detail"> +<!-- --> +</a> +<h3>Constructor Detail</h3> +<a name="SymmLQ(int, double, boolean)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>SymmLQ</h4> +<pre>public SymmLQ(int maxIterations, + double delta, + boolean check)</pre> +<div class="block">Creates a new instance of this class, with <a href="#stopcrit">default + stopping criterion</a>. Note that setting <code>check</code> to <code>true</code> + entails an extra matrix-vector product in the initial phase.</div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>maxIterations</code> - the maximum number of iterations</dd><dd><code>delta</code> - the δ parameter for the default stopping criterion</dd><dd><code>check</code> - <code>true</code> if self-adjointedness of both matrix and + preconditioner should be checked</dd></dl> +</li> +</ul> +<a name="SymmLQ(org.apache.commons.math3.util.IterationManager, double, boolean)"> +<!-- --> +</a> +<ul class="blockListLast"> +<li class="blockList"> +<h4>SymmLQ</h4> +<pre>public SymmLQ(<a href="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util">IterationManager</a> manager, + double delta, + boolean check)</pre> +<div class="block">Creates a new instance of this class, with <a href="#stopcrit">default + stopping criterion</a> and custom iteration manager. Note that setting + <code>check</code> to <code>true</code> entails an extra matrix-vector product in + the initial phase.</div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>manager</code> - the custom iteration manager</dd><dd><code>delta</code> - the δ parameter for the default stopping criterion</dd><dd><code>check</code> - <code>true</code> if self-adjointedness of both matrix and + preconditioner should be checked</dd></dl> +</li> +</ul> +</li> +</ul> +<!-- ============ METHOD DETAIL ========== --> +<ul class="blockList"> +<li class="blockList"><a name="method_detail"> +<!-- --> +</a> +<h3>Method Detail</h3> +<a name="getCheck()"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>getCheck</h4> +<pre>public final boolean getCheck()</pre> +<div class="block">Returns <code>true</code> if symmetry of the matrix, and symmetry as well as + positive definiteness of the preconditioner should be checked.</div> +<dl><dt><span class="strong">Returns:</span></dt><dd><code>true</code> if the tests are to be performed</dd></dl> +</li> +</ul> +<a name="solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>solve</h4> +<pre>public <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> solve(<a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> a, + <a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> m, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> b) + throws <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>, + <a href="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>, + <a href="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a>, + <a href="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</a></pre> +<div class="block">Returns an estimate of the solution to the linear system A · x = + b.</div> +<dl> +<dt><strong>Overrides:</strong></dt> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html#solve(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector)">solve</a></code> in class <code><a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">PreconditionedIterativeLinearSolver</a></code></dd> +<dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - the linear operator A of the system</dd><dd><code>m</code> - the preconditioner, M (can be <code>null</code>)</dd><dd><code>b</code> - the right-hand side vector</dd> +<dt><span class="strong">Returns:</span></dt><dd>a new vector containing the solution</dd> +<dt><span class="strong">Throws:</span></dt> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</a></code> - if <a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#getCheck()"><code>getCheck()</code></a> is + <code>true</code>, and <code>a</code> or <code>m</code> is not self-adjoint</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteOperatorException</a></code> - if <code>m</code> is not + positive definite</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</a></code> - if <code>a</code> is ill-conditioned</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if one of the parameters is <code>null</code></dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</a></code> - if <code>a</code> or <code>m</code> is not + square</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if <code>m</code> or <code>b</code> have + dimensions inconsistent with <code>a</code></dd> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></code> - at exhaustion of the iteration count, + unless a custom + <a href="../../../../../org/apache/commons/math3/util/Incrementor.MaxCountExceededCallback.html" title="interface in org.apache.commons.math3.util"><code>callback</code></a> + has been set at construction of the <a href="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util"><code>IterationManager</code></a></dd></dl> +</li> +</ul> +<a name="solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, boolean, double)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>solve</h4> +<pre>public <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> solve(<a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> a, + <a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> m, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> b, + boolean goodb, + double shift) + throws <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>, + <a href="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>, + <a href="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a>, + <a href="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</a></pre> +<div class="block">Returns an estimate of the solution to the linear system (A - shift + · I) · x = b. + <p> + If the solution x is expected to contain a large multiple of <code>b</code> + (as in Rayleigh-quotient iteration), then better precision may be + achieved with <code>goodb</code> set to <code>true</code>; this however requires an + extra call to the preconditioner. + </p> + <p> + <code>shift</code> should be zero if the system A · x = b is to be + solved. Otherwise, it could be an approximation to an eigenvalue of A, + such as the Rayleigh quotient b<sup>T</sup> · A · b / + (b<sup>T</sup> · b) corresponding to the vector b. If b is + sufficiently like an eigenvector corresponding to an eigenvalue near + shift, then the computed x may have very large components. When + normalized, x may be closer to an eigenvector than b. + </p></div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - the linear operator A of the system</dd><dd><code>m</code> - the preconditioner, M (can be <code>null</code>)</dd><dd><code>b</code> - the right-hand side vector</dd><dd><code>goodb</code> - usually <code>false</code>, except if <code>x</code> is expected to + contain a large multiple of <code>b</code></dd><dd><code>shift</code> - the amount to be subtracted to all diagonal elements of A</dd> +<dt><span class="strong">Returns:</span></dt><dd>a reference to <code>x</code> (shallow copy)</dd> +<dt><span class="strong">Throws:</span></dt> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if one of the parameters is <code>null</code></dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</a></code> - if <code>a</code> or <code>m</code> is not square</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if <code>m</code> or <code>b</code> have dimensions + inconsistent with <code>a</code></dd> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></code> - at exhaustion of the iteration count, + unless a custom + <a href="../../../../../org/apache/commons/math3/util/Incrementor.MaxCountExceededCallback.html" title="interface in org.apache.commons.math3.util"><code>callback</code></a> + has been set at construction of the <a href="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util"><code>IterationManager</code></a></dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</a></code> - if <a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#getCheck()"><code>getCheck()</code></a> is + <code>true</code>, and <code>a</code> or <code>m</code> is not self-adjoint</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteOperatorException</a></code> - if <code>m</code> is not + positive definite</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</a></code> - if <code>a</code> is ill-conditioned</dd></dl> +</li> +</ul> +<a name="solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>solve</h4> +<pre>public <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> solve(<a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> a, + <a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> m, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> b, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> x) + throws <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>, + <a href="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>, + <a href="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></pre> +<div class="block">Returns an estimate of the solution to the linear system A · x = + b.</div> +<dl> +<dt><strong>Overrides:</strong></dt> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html#solve(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector,%20org.apache.commons.math3.linear.RealVector)">solve</a></code> in class <code><a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">PreconditionedIterativeLinearSolver</a></code></dd> +<dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - not meaningful in this implementation; should not be considered + as an initial guess (<a href="#initguess">more</a>)</dd><dd><code>a</code> - the linear operator A of the system</dd><dd><code>m</code> - the preconditioner, M (can be <code>null</code>)</dd><dd><code>b</code> - the right-hand side vector</dd> +<dt><span class="strong">Returns:</span></dt><dd>a new vector containing the solution</dd> +<dt><span class="strong">Throws:</span></dt> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</a></code> - if <a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#getCheck()"><code>getCheck()</code></a> is + <code>true</code>, and <code>a</code> or <code>m</code> is not self-adjoint</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteOperatorException</a></code> - if <code>m</code> is not positive + definite</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</a></code> - if <code>a</code> is ill-conditioned</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if one of the parameters is <code>null</code></dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</a></code> - if <code>a</code> or <code>m</code> is not + square</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if <code>m</code>, <code>b</code> or + <code>x0</code> have dimensions inconsistent with <code>a</code></dd> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></code> - at exhaustion of the iteration count, + unless a custom + <a href="../../../../../org/apache/commons/math3/util/Incrementor.MaxCountExceededCallback.html" title="interface in org.apache.commons.math3.util"><code>callback</code></a> + has been set at construction of the <a href="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util"><code>IterationManager</code></a></dd></dl> +</li> +</ul> +<a name="solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>solve</h4> +<pre>public <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> solve(<a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> a, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> b) + throws <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>, + <a href="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>, + <a href="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></pre> +<div class="block">Returns an estimate of the solution to the linear system A · x = + b.</div> +<dl> +<dt><strong>Overrides:</strong></dt> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html#solve(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector)">solve</a></code> in class <code><a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">PreconditionedIterativeLinearSolver</a></code></dd> +<dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - the linear operator A of the system</dd><dd><code>b</code> - the right-hand side vector</dd> +<dt><span class="strong">Returns:</span></dt><dd>a new vector containing the solution</dd> +<dt><span class="strong">Throws:</span></dt> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</a></code> - if <a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#getCheck()"><code>getCheck()</code></a> is + <code>true</code>, and <code>a</code> is not self-adjoint</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</a></code> - if <code>a</code> is ill-conditioned</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if one of the parameters is <code>null</code></dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</a></code> - if <code>a</code> is not square</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if <code>b</code> has dimensions + inconsistent with <code>a</code></dd> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></code> - at exhaustion of the iteration count, + unless a custom + <a href="../../../../../org/apache/commons/math3/util/Incrementor.MaxCountExceededCallback.html" title="interface in org.apache.commons.math3.util"><code>callback</code></a> + has been set at construction of the <a href="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util"><code>IterationManager</code></a></dd></dl> +</li> +</ul> +<a name="solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, boolean, double)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>solve</h4> +<pre>public <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> solve(<a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> a, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> b, + boolean goodb, + double shift) + throws <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>, + <a href="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>, + <a href="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></pre> +<div class="block">Returns the solution to the system (A - shift · I) · x = b. + <p> + If the solution x is expected to contain a large multiple of <code>b</code> + (as in Rayleigh-quotient iteration), then better precision may be + achieved with <code>goodb</code> set to <code>true</code>. + </p> + <p> + <code>shift</code> should be zero if the system A · x = b is to be + solved. Otherwise, it could be an approximation to an eigenvalue of A, + such as the Rayleigh quotient b<sup>T</sup> · A · b / + (b<sup>T</sup> · b) corresponding to the vector b. If b is + sufficiently like an eigenvector corresponding to an eigenvalue near + shift, then the computed x may have very large components. When + normalized, x may be closer to an eigenvector than b. + </p></div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - the linear operator A of the system</dd><dd><code>b</code> - the right-hand side vector</dd><dd><code>goodb</code> - usually <code>false</code>, except if <code>x</code> is expected to + contain a large multiple of <code>b</code></dd><dd><code>shift</code> - the amount to be subtracted to all diagonal elements of A</dd> +<dt><span class="strong">Returns:</span></dt><dd>a reference to <code>x</code></dd> +<dt><span class="strong">Throws:</span></dt> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if one of the parameters is <code>null</code></dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</a></code> - if <code>a</code> is not square</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if <code>b</code> has dimensions + inconsistent with <code>a</code></dd> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></code> - at exhaustion of the iteration count, + unless a custom + <a href="../../../../../org/apache/commons/math3/util/Incrementor.MaxCountExceededCallback.html" title="interface in org.apache.commons.math3.util"><code>callback</code></a> + has been set at construction of the <a href="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util"><code>IterationManager</code></a></dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</a></code> - if <a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#getCheck()"><code>getCheck()</code></a> is + <code>true</code>, and <code>a</code> is not self-adjoint</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</a></code> - if <code>a</code> is ill-conditioned</dd></dl> +</li> +</ul> +<a name="solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>solve</h4> +<pre>public <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> solve(<a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> a, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> b, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> x) + throws <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>, + <a href="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>, + <a href="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></pre> +<div class="block">Returns an estimate of the solution to the linear system A · x = + b.</div> +<dl> +<dt><strong>Overrides:</strong></dt> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html#solve(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector,%20org.apache.commons.math3.linear.RealVector)">solve</a></code> in class <code><a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">PreconditionedIterativeLinearSolver</a></code></dd> +<dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - not meaningful in this implementation; should not be considered + as an initial guess (<a href="#initguess">more</a>)</dd><dd><code>a</code> - the linear operator A of the system</dd><dd><code>b</code> - the right-hand side vector</dd> +<dt><span class="strong">Returns:</span></dt><dd>a new vector containing the solution</dd> +<dt><span class="strong">Throws:</span></dt> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</a></code> - if <a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#getCheck()"><code>getCheck()</code></a> is + <code>true</code>, and <code>a</code> is not self-adjoint</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</a></code> - if <code>a</code> is ill-conditioned</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if one of the parameters is <code>null</code></dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</a></code> - if <code>a</code> is not square</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if <code>b</code> or <code>x0</code> have + dimensions inconsistent with <code>a</code></dd> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></code> - at exhaustion of the iteration count, + unless a custom + <a href="../../../../../org/apache/commons/math3/util/Incrementor.MaxCountExceededCallback.html" title="interface in org.apache.commons.math3.util"><code>callback</code></a> + has been set at construction of the <a href="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util"><code>IterationManager</code></a></dd></dl> +</li> +</ul> +<a name="solveInPlace(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>solveInPlace</h4> +<pre>public <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> solveInPlace(<a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> a, + <a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> m, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> b, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> x) + throws <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>, + <a href="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>, + <a href="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></pre> +<div class="block">Returns an estimate of the solution to the linear system A · x = + b. The solution is computed in-place (initial guess is modified).</div> +<dl> +<dt><strong>Specified by:</strong></dt> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html#solveInPlace(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector,%20org.apache.commons.math3.linear.RealVector)">solveInPlace</a></code> in class <code><a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">PreconditionedIterativeLinearSolver</a></code></dd> +<dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the vector to be updated with the solution; <code>x</code> should + not be considered as an initial guess (<a href="#initguess">more</a>)</dd><dd><code>a</code> - the linear operator A of the system</dd><dd><code>m</code> - the preconditioner, M (can be <code>null</code>)</dd><dd><code>b</code> - the right-hand side vector</dd> +<dt><span class="strong">Returns:</span></dt><dd>a reference to <code>x0</code> (shallow copy) updated with the + solution</dd> +<dt><span class="strong">Throws:</span></dt> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</a></code> - if <a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#getCheck()"><code>getCheck()</code></a> is + <code>true</code>, and <code>a</code> or <code>m</code> is not self-adjoint</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteOperatorException</a></code> - if <code>m</code> is not + positive definite</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</a></code> - if <code>a</code> is ill-conditioned</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if one of the parameters is <code>null</code></dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</a></code> - if <code>a</code> or <code>m</code> is not + square</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if <code>m</code>, <code>b</code> or + <code>x0</code> have dimensions inconsistent with <code>a</code></dd> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></code> - at exhaustion of the iteration count, + unless a custom + <a href="../../../../../org/apache/commons/math3/util/Incrementor.MaxCountExceededCallback.html" title="interface in org.apache.commons.math3.util"><code>callback</code></a> + has been set at construction of the <a href="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util"><code>IterationManager</code></a></dd></dl> +</li> +</ul> +<a name="solveInPlace(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector, boolean, double)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>solveInPlace</h4> +<pre>public <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> solveInPlace(<a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> a, + <a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> m, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> b, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> x, + boolean goodb, + double shift) + throws <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>, + <a href="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>, + <a href="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></pre> +<div class="block">Returns an estimate of the solution to the linear system (A - shift + · I) · x = b. The solution is computed in-place. + <p> + If the solution x is expected to contain a large multiple of <code>b</code> + (as in Rayleigh-quotient iteration), then better precision may be + achieved with <code>goodb</code> set to <code>true</code>; this however requires an + extra call to the preconditioner. + </p> + <p> + <code>shift</code> should be zero if the system A · x = b is to be + solved. Otherwise, it could be an approximation to an eigenvalue of A, + such as the Rayleigh quotient b<sup>T</sup> · A · b / + (b<sup>T</sup> · b) corresponding to the vector b. If b is + sufficiently like an eigenvector corresponding to an eigenvalue near + shift, then the computed x may have very large components. When + normalized, x may be closer to an eigenvector than b. + </p></div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - the linear operator A of the system</dd><dd><code>m</code> - the preconditioner, M (can be <code>null</code>)</dd><dd><code>b</code> - the right-hand side vector</dd><dd><code>x</code> - the vector to be updated with the solution; <code>x</code> should + not be considered as an initial guess (<a href="#initguess">more</a>)</dd><dd><code>goodb</code> - usually <code>false</code>, except if <code>x</code> is expected to + contain a large multiple of <code>b</code></dd><dd><code>shift</code> - the amount to be subtracted to all diagonal elements of A</dd> +<dt><span class="strong">Returns:</span></dt><dd>a reference to <code>x</code> (shallow copy).</dd> +<dt><span class="strong">Throws:</span></dt> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if one of the parameters is <code>null</code></dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</a></code> - if <code>a</code> or <code>m</code> is not square</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if <code>m</code>, <code>b</code> or <code>x</code> + have dimensions inconsistent with <code>a</code>.</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></code> - at exhaustion of the iteration count, + unless a custom + <a href="../../../../../org/apache/commons/math3/util/Incrementor.MaxCountExceededCallback.html" title="interface in org.apache.commons.math3.util"><code>callback</code></a> + has been set at construction of the <a href="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util"><code>IterationManager</code></a></dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</a></code> - if <a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#getCheck()"><code>getCheck()</code></a> is + <code>true</code>, and <code>a</code> or <code>m</code> is not self-adjoint</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteOperatorException</a></code> - if <code>m</code> is not positive + definite</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</a></code> - if <code>a</code> is ill-conditioned</dd></dl> +</li> +</ul> +<a name="solveInPlace(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector)"> +<!-- --> +</a> +<ul class="blockListLast"> +<li class="blockList"> +<h4>solveInPlace</h4> +<pre>public <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> solveInPlace(<a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a> a, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> b, + <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> x) + throws <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>, + <a href="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>, + <a href="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</a>, + <a href="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></pre> +<div class="block">Returns an estimate of the solution to the linear system A · x = + b. The solution is computed in-place (initial guess is modified).</div> +<dl> +<dt><strong>Overrides:</strong></dt> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html#solveInPlace(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector,%20org.apache.commons.math3.linear.RealVector)">solveInPlace</a></code> in class <code><a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">PreconditionedIterativeLinearSolver</a></code></dd> +<dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the vector to be updated with the solution; <code>x</code> should + not be considered as an initial guess (<a href="#initguess">more</a>)</dd><dd><code>a</code> - the linear operator A of the system</dd><dd><code>b</code> - the right-hand side vector</dd> +<dt><span class="strong">Returns:</span></dt><dd>a reference to <code>x0</code> (shallow copy) updated with the + solution</dd> +<dt><span class="strong">Throws:</span></dt> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</a></code> - if <a href="../../../../../org/apache/commons/math3/linear/SymmLQ.html#getCheck()"><code>getCheck()</code></a> is + <code>true</code>, and <code>a</code> is not self-adjoint</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</a></code> - if <code>a</code> is ill-conditioned</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if one of the parameters is <code>null</code></dd> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</a></code> - if <code>a</code> is not square</dd> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if <code>b</code> or <code>x0</code> have + dimensions inconsistent with <code>a</code></dd> +<dd><code><a href="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></code> - at exhaustion of the iteration count, + unless a custom + <a href="../../../../../org/apache/commons/math3/util/Incrementor.MaxCountExceededCallback.html" title="interface in org.apache.commons.math3.util"><code>callback</code></a> + has been set at construction of the <a href="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util"><code>IterationManager</code></a></dd></dl> +</li> +</ul> +</li> +</ul> +</li> +</ul> +</div> +</div> +<!-- ========= END OF CLASS DATA ========= --> +<!-- ======= START OF BOTTOM NAVBAR ====== --> +<div class="bottomNav"><a name="navbar_bottom"> +<!-- --> +</a><a href="#skip-navbar_bottom" title="Skip navigation links"></a><a name="navbar_bottom_firstrow"> +<!-- --> +</a> +<ul class="navList" title="Navigation"> +<li><a href="../../../../../overview-summary.html">Overview</a></li> +<li><a href="package-summary.html">Package</a></li> +<li class="navBarCell1Rev">Class</li> +<li><a href="class-use/SymmLQ.html">Use</a></li> +<li><a href="package-tree.html">Tree</a></li> +<li><a href="../../../../../deprecated-list.html">Deprecated</a></li> +<li><a href="../../../../../index-all.html">Index</a></li> +<li><a href="../../../../../help-doc.html">Help</a></li> +</ul> +<div class="aboutLanguage"><em><script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script></em></div> +</div> +<div class="subNav"> +<ul class="navList"> +<li><a href="../../../../../org/apache/commons/math3/linear/SparseRealVector.html" title="class in org.apache.commons.math3.linear"><span class="strong">Prev Class</span></a></li> +<li>Next Class</li> +</ul> +<ul class="navList"> +<li><a href="../../../../../index.html?org/apache/commons/math3/linear/SymmLQ.html" target="_top">Frames</a></li> +<li><a href="SymmLQ.html" target="_top">No Frames</a></li> +</ul> +<ul class="navList" id="allclasses_navbar_bottom"> +<li><a href="../../../../../allclasses-noframe.html">All Classes</a></li> +</ul> +<div> +<script type="text/javascript"><!-- + allClassesLink = document.getElementById("allclasses_navbar_bottom"); + if(window==top) { + allClassesLink.style.display = "block"; + } + else { + allClassesLink.style.display = "none"; + } + //--> +</script> +</div> +<div> +<ul class="subNavList"> +<li>Summary: </li> +<li>Nested | </li> +<li>Field | </li> +<li><a href="#constructor_summary">Constr</a> | </li> +<li><a href="#method_summary">Method</a></li> +</ul> +<ul class="subNavList"> +<li>Detail: </li> +<li>Field | </li> +<li><a href="#constructor_detail">Constr</a> | </li> +<li><a href="#method_detail">Method</a></li> +</ul> +</div> +<a name="skip-navbar_bottom"> +<!-- --> +</a></div> +<!-- ======== END OF BOTTOM NAVBAR ======= --> +<p class="legalCopy"><small>Copyright © 2003–2016 <a href="http://www.apache.org/">The Apache Software Foundation</a>. All rights reserved.</small></p> +</body> +</html> |