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| <h2 title="Class HermiteRuleFactory" class="title">Class HermiteRuleFactory</h2> |
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| <li><a href="../../../../../../../org/apache/commons/math3/analysis/integration/gauss/BaseRuleFactory.html" title="class in org.apache.commons.math3.analysis.integration.gauss">org.apache.commons.math3.analysis.integration.gauss.BaseRuleFactory</a><<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Double.html?is-external=true" title="class or interface in java.lang">Double</a>></li> |
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| <li>org.apache.commons.math3.analysis.integration.gauss.HermiteRuleFactory</li> |
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| <pre>public class <span class="strong">HermiteRuleFactory</span> |
| extends <a href="../../../../../../../org/apache/commons/math3/analysis/integration/gauss/BaseRuleFactory.html" title="class in org.apache.commons.math3.analysis.integration.gauss">BaseRuleFactory</a><<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Double.html?is-external=true" title="class or interface in java.lang">Double</a>></pre> |
| <div class="block">Factory that creates a |
| <a href="http://en.wikipedia.org/wiki/Gauss-Hermite_quadrature"> |
| Gauss-type quadrature rule using Hermite polynomials</a> |
| of the first kind. |
| Such a quadrature rule allows the calculation of improper integrals |
| of a function |
| <code> |
| f(x) e<sup>-x<sup>2</sup></sup> |
| </code> |
| <br/> |
| Recurrence relation and weights computation follow |
| <a href="http://en.wikipedia.org/wiki/Abramowitz_and_Stegun" |
| Abramowitz and Stegun, 1964</a>. |
| <br/> |
| The coefficients of the standard Hermite polynomials grow very rapidly; |
| in order to avoid overflows, each Hermite polynomial is normalized with |
| respect to the underlying scalar product. |
| The initial interval for the application of the bisection method is |
| based on the roots of the previous Hermite polynomial (interlacing). |
| Upper and lower bounds of these roots are provided by |
| <quote> |
| I. Krasikov, |
| <em>Nonnegative quadratic forms and bounds on orthogonal polynomials</em>, |
| Journal of Approximation theory <b>111</b>, 31-49 |
| </quote></div> |
| <dl><dt><span class="strong">Since:</span></dt> |
| <dd>3.3</dd> |
| <dt><span class="strong">Version:</span></dt> |
| <dd>$Id: HermiteRuleFactory.java 1500018 2013-07-05 14:20:19Z erans $</dd></dl> |
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| <td class="colOne"><code><strong><a href="../../../../../../../org/apache/commons/math3/analysis/integration/gauss/HermiteRuleFactory.html#HermiteRuleFactory()">HermiteRuleFactory</a></strong>()</code> </td> |
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| <td class="colFirst"><code>protected <a href="../../../../../../../org/apache/commons/math3/util/Pair.html" title="class in org.apache.commons.math3.util">Pair</a><<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Double.html?is-external=true" title="class or interface in java.lang">Double</a>[],<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Double.html?is-external=true" title="class or interface in java.lang">Double</a>[]></code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../../org/apache/commons/math3/analysis/integration/gauss/HermiteRuleFactory.html#computeRule(int)">computeRule</a></strong>(int numberOfPoints)</code> |
| <div class="block">Computes the rule for the given order.</div> |
| </td> |
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| <h3>Methods inherited from class org.apache.commons.math3.analysis.integration.gauss.<a href="../../../../../../../org/apache/commons/math3/analysis/integration/gauss/BaseRuleFactory.html" title="class in org.apache.commons.math3.analysis.integration.gauss">BaseRuleFactory</a></h3> |
| <code><a href="../../../../../../../org/apache/commons/math3/analysis/integration/gauss/BaseRuleFactory.html#addRule(org.apache.commons.math3.util.Pair)">addRule</a>, <a href="../../../../../../../org/apache/commons/math3/analysis/integration/gauss/BaseRuleFactory.html#getRule(int)">getRule</a>, <a href="../../../../../../../org/apache/commons/math3/analysis/integration/gauss/BaseRuleFactory.html#getRuleInternal(int)">getRuleInternal</a></code></li> |
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| <h4>HermiteRuleFactory</h4> |
| <pre>public HermiteRuleFactory()</pre> |
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| <h4>computeRule</h4> |
| <pre>protected <a href="../../../../../../../org/apache/commons/math3/util/Pair.html" title="class in org.apache.commons.math3.util">Pair</a><<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Double.html?is-external=true" title="class or interface in java.lang">Double</a>[],<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Double.html?is-external=true" title="class or interface in java.lang">Double</a>[]> computeRule(int numberOfPoints) |
| throws <a href="../../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></pre> |
| <div class="block">Computes the rule for the given order.</div> |
| <dl> |
| <dt><strong>Specified by:</strong></dt> |
| <dd><code><a href="../../../../../../../org/apache/commons/math3/analysis/integration/gauss/BaseRuleFactory.html#computeRule(int)">computeRule</a></code> in class <code><a href="../../../../../../../org/apache/commons/math3/analysis/integration/gauss/BaseRuleFactory.html" title="class in org.apache.commons.math3.analysis.integration.gauss">BaseRuleFactory</a><<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Double.html?is-external=true" title="class or interface in java.lang">Double</a>></code></dd> |
| <dt><span class="strong">Parameters:</span></dt><dd><code>numberOfPoints</code> - Order of the rule to be computed.</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>the computed rule.</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the elements of the pair do not |
| have the same length.</dd></dl> |
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