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| <h2 title="Class Erf" class="title">Class Erf</h2> |
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| <li>org.apache.commons.math3.special.Erf</li> |
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| <pre>public class <span class="strong">Erf</span> |
| extends <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre> |
| <div class="block">This is a utility class that provides computation methods related to the |
| error functions.</div> |
| <dl><dt><span class="strong">Version:</span></dt> |
| <dd>$Id: Erf.java 1538368 2013-11-03 13:57:37Z erans $</dd></dl> |
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| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/special/Erf.html#erf(double)">erf</a></strong>(double x)</code> |
| <div class="block">Returns the error function.</div> |
| </td> |
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| <tr class="rowColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/special/Erf.html#erf(double, double)">erf</a></strong>(double x1, |
| double x2)</code> |
| <div class="block">Returns the difference between erf(x1) and erf(x2).</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/special/Erf.html#erfc(double)">erfc</a></strong>(double x)</code> |
| <div class="block">Returns the complementary error function.</div> |
| </td> |
| </tr> |
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| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/special/Erf.html#erfcInv(double)">erfcInv</a></strong>(double x)</code> |
| <div class="block">Returns the inverse erfc.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/special/Erf.html#erfInv(double)">erfInv</a></strong>(double x)</code> |
| <div class="block">Returns the inverse erf.</div> |
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| <h4>erf</h4> |
| <pre>public static double erf(double x)</pre> |
| <div class="block">Returns the error function. |
| |
| <p>erf(x) = 2/√π <sub>0</sub>∫<sup>x</sup> e<sup>-t<sup>2</sup></sup>dt </p> |
| |
| <p>This implementation computes erf(x) using the |
| <a href="../../../../../org/apache/commons/math3/special/Gamma.html#regularizedGammaP(double, double, double, int)"><code>regularized gamma function</code></a>, |
| following <a href="http://mathworld.wolfram.com/Erf.html"> Erf</a>, equation (3)</p> |
| |
| <p>The value returned is always between -1 and 1 (inclusive). |
| If <code>abs(x) > 40</code>, then <code>erf(x)</code> is indistinguishable from |
| either 1 or -1 as a double, so the appropriate extreme value is returned. |
| </p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the value.</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>the error function erf(x)</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></code> - if the algorithm fails to converge.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/special/Gamma.html#regularizedGammaP(double, double, double, int)"><code>Gamma.regularizedGammaP(double, double, double, int)</code></a></dd></dl> |
| </li> |
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| <a name="erfc(double)"> |
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| <h4>erfc</h4> |
| <pre>public static double erfc(double x)</pre> |
| <div class="block">Returns the complementary error function. |
| |
| <p>erfc(x) = 2/√π <sub>x</sub>∫<sup>∞</sup> e<sup>-t<sup>2</sup></sup>dt |
| <br/> |
| = 1 - <a href="../../../../../org/apache/commons/math3/special/Erf.html#erf(double)"><code>erf(x)</code></a> </p> |
| |
| <p>This implementation computes erfc(x) using the |
| <a href="../../../../../org/apache/commons/math3/special/Gamma.html#regularizedGammaQ(double, double, double, int)"><code>regularized gamma function</code></a>, |
| following <a href="http://mathworld.wolfram.com/Erf.html"> Erf</a>, equation (3).</p> |
| |
| <p>The value returned is always between 0 and 2 (inclusive). |
| If <code>abs(x) > 40</code>, then <code>erf(x)</code> is indistinguishable from |
| either 0 or 2 as a double, so the appropriate extreme value is returned. |
| </p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the value</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>the complementary error function erfc(x)</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></code> - if the algorithm fails to converge.</dd><dt><span class="strong">Since:</span></dt> |
| <dd>2.2</dd> |
| <dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/special/Gamma.html#regularizedGammaQ(double, double, double, int)"><code>Gamma.regularizedGammaQ(double, double, double, int)</code></a></dd></dl> |
| </li> |
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| <h4>erf</h4> |
| <pre>public static double erf(double x1, |
| double x2)</pre> |
| <div class="block">Returns the difference between erf(x1) and erf(x2). |
| |
| The implementation uses either erf(double) or erfc(double) |
| depending on which provides the most precise result.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>x1</code> - the first value</dd><dd><code>x2</code> - the second value</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>erf(x2) - erf(x1)</dd></dl> |
| </li> |
| </ul> |
| <a name="erfInv(double)"> |
| <!-- --> |
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| <h4>erfInv</h4> |
| <pre>public static double erfInv(double x)</pre> |
| <div class="block">Returns the inverse erf. |
| <p> |
| This implementation is described in the paper: |
| <a href="http://people.maths.ox.ac.uk/gilesm/files/gems_erfinv.pdf">Approximating |
| the erfinv function</a> by Mike Giles, Oxford-Man Institute of Quantitative Finance, |
| which was published in GPU Computing Gems, volume 2, 2010. |
| The source code is available <a href="http://gpucomputing.net/?q=node/1828">here</a>. |
| </p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the value</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>t such that x = erf(t)</dd><dt><span class="strong">Since:</span></dt> |
| <dd>3.2</dd></dl> |
| </li> |
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| <h4>erfcInv</h4> |
| <pre>public static double erfcInv(double x)</pre> |
| <div class="block">Returns the inverse erfc.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the value</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>t such that x = erfc(t)</dd><dt><span class="strong">Since:</span></dt> |
| <dd>3.2</dd></dl> |
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