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| <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/6/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> |
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| <div class="description"> |
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| <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, org.apache.commons.math3.linear.RealVector, org.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, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.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, org.apache.commons.math3.linear.RealVector, org.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, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.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, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector, boolean, double)"><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> |
| <dt><span class="strong">Version:</span></dt> |
| <dd>$Id: SymmLQ.java 1505938 2013-07-23 08:50:10Z luc $</dd></dl> |
| </li> |
| </ul> |
| </div> |
| <div class="summary"> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <!-- ======== CONSTRUCTOR SUMMARY ======== --> |
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| <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, double, boolean)">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, double, boolean)">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, org.apache.commons.math3.linear.RealLinearOperator, org.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, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, boolean, double)">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, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.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, org.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, org.apache.commons.math3.linear.RealVector, boolean, double)">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, org.apache.commons.math3.linear.RealVector, org.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, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.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, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector, boolean, double)">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, org.apache.commons.math3.linear.RealVector, org.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> |
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| <code><a href="../../../../../org/apache/commons/math3/linear/IterativeLinearSolver.html#checkParameters(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector)">checkParameters</a>, <a href="../../../../../org/apache/commons/math3/linear/IterativeLinearSolver.html#getIterationManager()">getIterationManager</a></code></li> |
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| <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> |
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| <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> |
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| <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)"> |
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| <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, org.apache.commons.math3.linear.RealLinearOperator, org.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> |
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| <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> |
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| <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, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.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)"> |
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| </a> |
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| <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, org.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"> |
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| <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"> |
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| <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, org.apache.commons.math3.linear.RealVector, org.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, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.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, org.apache.commons.math3.linear.RealVector, org.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> |
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