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| <div class="subTitle">org.apache.commons.math3.linear</div> |
| <h2 title="Class ConjugateGradient" class="title">Class ConjugateGradient</h2> |
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| <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.ConjugateGradient</li> |
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| <pre>public class <span class="strong">ConjugateGradient</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> |
| This is an implementation of the conjugate gradient method for |
| <a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear"><code>RealLinearOperator</code></a>. It follows closely the template by <a |
| href="#BARR1994">Barrett et al. (1994)</a> (figure 2.5). The linear system at |
| hand is A · x = b, and the residual is r = b - A · x. |
| </p> |
| <h3><a id="stopcrit">Default stopping criterion</a></h3> |
| <p> |
| A default stopping criterion is implemented. The iterations stop when || r || |
| ≤ δ || b ||, where b is the right-hand side vector, r the current |
| estimate of the residual, and δ a user-specified tolerance. It should |
| be noted that r is the so-called <em>updated</em> residual, which might |
| differ from the true residual due to rounding-off errors (see e.g. <a |
| href="#STRA2002">Strakos and Tichy, 2002</a>). |
| </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. |
| </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/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear"><code>NonPositiveDefiniteOperatorException</code></a> if the linear operator or |
| the preconditioner are not positive definite. 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 some more information |
| <ul> |
| <li>key <code>"operator"</code> points to the offending linear operator, say L,</li> |
| <li>key <code>"vector"</code> 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="BARR1994">Barret et al. (1994)</a></dt> |
| <dd>R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. M. Donato, J. Dongarra, |
| V. Eijkhout, R. Pozo, C. Romine and H. Van der Vorst, |
| <a href="http://www.netlib.org/linalg/html_templates/Templates.html"><em> |
| Templates for the Solution of Linear Systems: Building Blocks for Iterative |
| Methods</em></a>, SIAM</dd> |
| <dt><a id="STRA2002">Strakos and Tichy (2002) |
| <dt> |
| <dd>Z. Strakos and P. Tichy, <a |
| href="http://etna.mcs.kent.edu/vol.13.2002/pp56-80.dir/pp56-80.pdf"> |
| <em>On error estimation in the conjugate gradient method and why it works |
| in finite precision computations</em></a>, Electronic Transactions on |
| Numerical Analysis 13: 56-80, 2002</dd> |
| </dl></div> |
| <dl><dt><span class="strong">Since:</span></dt> |
| <dd>3.0</dd> |
| <dt><span class="strong">Version:</span></dt> |
| <dd>$Id: ConjugateGradient.java 1562755 2014-01-30 09:37:08Z luc $</dd></dl> |
| </li> |
| </ul> |
| </div> |
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| <!-- =========== FIELD SUMMARY =========== --> |
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| <h3>Field Summary</h3> |
| <table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Field Summary table, listing fields, and an explanation"> |
| <caption><span>Fields</span><span class="tabEnd"> </span></caption> |
| <tr> |
| <th class="colFirst" scope="col">Modifier and Type</th> |
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| <tr class="altColor"> |
| <td class="colFirst"><code>static <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</a></code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/ConjugateGradient.html#OPERATOR">OPERATOR</a></strong></code> |
| <div class="block">Key for the <a href="#context">exception context</a>.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>static <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</a></code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/ConjugateGradient.html#VECTOR">VECTOR</a></strong></code> |
| <div class="block">Key for the <a href="#context">exception context</a>.</div> |
| </td> |
| </tr> |
| </table> |
| </li> |
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| <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/ConjugateGradient.html#ConjugateGradient(int, double, boolean)">ConjugateGradient</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/ConjugateGradient.html#ConjugateGradient(org.apache.commons.math3.util.IterationManager, double, boolean)">ConjugateGradient</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> |
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| <h3>Method Summary</h3> |
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| <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/ConjugateGradient.html#getCheck()">getCheck</a></strong>()</code> |
| <div class="block">Returns <code>true</code> if positive-definiteness should be checked for both |
| matrix and preconditioner.</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/ConjugateGradient.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> x0)</code> |
| <div class="block">Returns an estimate of the solution to the linear system A · x = |
| b.</div> |
| </td> |
| </tr> |
| </table> |
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| <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, 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/PreconditionedIterativeLinearSolver.html#solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector)">solve</a>, <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>, <a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html#solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector)">solve</a>, <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>, <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></li> |
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| <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, 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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| <code><a href="http://docs.oracle.com/javase/6/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/6/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/6/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/6/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/6/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/6/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/6/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/6/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/6/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/6/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/6/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</a></code></li> |
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| <h3>Field Detail</h3> |
| <a name="OPERATOR"> |
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| <h4>OPERATOR</h4> |
| <pre>public static final <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</a> OPERATOR</pre> |
| <div class="block">Key for the <a href="#context">exception context</a>.</div> |
| <dl><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../constant-values.html#org.apache.commons.math3.linear.ConjugateGradient.OPERATOR">Constant Field Values</a></dd></dl> |
| </li> |
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| <h4>VECTOR</h4> |
| <pre>public static final <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</a> VECTOR</pre> |
| <div class="block">Key for the <a href="#context">exception context</a>.</div> |
| <dl><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../constant-values.html#org.apache.commons.math3.linear.ConjugateGradient.VECTOR">Constant Field Values</a></dd></dl> |
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| <h4>ConjugateGradient</h4> |
| <pre>public ConjugateGradient(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>.</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 positive definiteness of both matrix and |
| preconditioner should be checked</dd></dl> |
| </li> |
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| <pre>public ConjugateGradient(<a href="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util">IterationManager</a> manager, |
| double delta, |
| boolean check) |
| throws <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></pre> |
| <div class="block">Creates a new instance of this class, with <a href="#stopcrit">default |
| stopping criterion</a> and custom iteration manager.</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 positive definiteness of both matrix and |
| preconditioner should be checked</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 <code>manager</code> is <code>null</code></dd></dl> |
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| <h4>getCheck</h4> |
| <pre>public final boolean getCheck()</pre> |
| <div class="block">Returns <code>true</code> if positive-definiteness should be checked for both |
| matrix and preconditioner.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd><code>true</code> if the tests are to be performed</dd></dl> |
| </li> |
| </ul> |
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| <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> x0) |
| 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/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteOperatorException</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></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>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>x0</code> - the initial guess of the solution</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/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteOperatorException</a></code> - if <code>a</code> or <code>m</code> is |
| not positive definite</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> |
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