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| <div class="subTitle">org.apache.commons.math3.special</div> |
| <h2 title="Class Beta" class="title">Class Beta</h2> |
| </div> |
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| <ul class="inheritance"> |
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| <ul class="inheritance"> |
| <li>org.apache.commons.math3.special.Beta</li> |
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| <pre>public class <span class="strong">Beta</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"><p> |
| This is a utility class that provides computation methods related to the |
| Beta family of functions. |
| </p> |
| <p> |
| Implementation of <a href="../../../../../org/apache/commons/math3/special/Beta.html#logBeta(double, double)"><code>logBeta(double, double)</code></a> is based on the |
| algorithms described in |
| <ul> |
| <li><a href="http://dx.doi.org/10.1145/22721.23109">Didonato and Morris |
| (1986)</a>, <em>Computation of the Incomplete Gamma Function Ratios |
| and their Inverse</em>, TOMS 12(4), 377-393,</li> |
| <li><a href="http://dx.doi.org/10.1145/131766.131776">Didonato and Morris |
| (1992)</a>, <em>Algorithm 708: Significant Digit Computation of the |
| Incomplete Beta Function Ratios</em>, TOMS 18(3), 360-373,</li> |
| </ul> |
| and implemented in the |
| <a href="http://www.dtic.mil/docs/citations/ADA476840">NSWC Library of Mathematical Functions</a>, |
| available |
| <a href="http://www.ualberta.ca/CNS/RESEARCH/Software/NumericalNSWC/site.html">here</a>. |
| This library is "approved for public release", and the |
| <a href="http://www.dtic.mil/dtic/pdf/announcements/CopyrightGuidance.pdf">Copyright guidance</a> |
| indicates that unless otherwise stated in the code, all FORTRAN functions in |
| this library are license free. Since no such notice appears in the code these |
| functions can safely be ported to Commons-Math. |
| </p></div> |
| <dl><dt><span class="strong">Version:</span></dt> |
| <dd>$Id: Beta.java 1546350 2013-11-28 11:41:12Z erans $</dd></dl> |
| </li> |
| </ul> |
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| <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>static double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/special/Beta.html#logBeta(double, double)">logBeta</a></strong>(double p, |
| double q)</code> |
| <div class="block">Returns the value of log B(p, q) for 0 ≤ x ≤ 1 and p, q > 0.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/special/Beta.html#logBeta(double, double, double, int)">logBeta</a></strong>(double a, |
| double b, |
| double epsilon, |
| int maxIterations)</code> |
| <div class="block"><strong>Deprecated.</strong> |
| <div class="block"><i>as of version 3.1, this method is deprecated as the |
| computation of the beta function is no longer iterative; it will be |
| removed in version 4.0. Current implementation of this method |
| internally calls <a href="../../../../../org/apache/commons/math3/special/Beta.html#logBeta(double, double)"><code>logBeta(double, double)</code></a>.</i></div> |
| </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/Beta.html#regularizedBeta(double, double, double)">regularizedBeta</a></strong>(double x, |
| double a, |
| double b)</code> |
| <div class="block">Returns the |
| <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html"> |
| regularized beta function</a> I(x, a, b).</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/special/Beta.html#regularizedBeta(double, double, double, double)">regularizedBeta</a></strong>(double x, |
| double a, |
| double b, |
| double epsilon)</code> |
| <div class="block">Returns the |
| <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html"> |
| regularized beta function</a> I(x, a, b).</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/Beta.html#regularizedBeta(double, double, double, double, int)">regularizedBeta</a></strong>(double x, |
| double a, |
| double b, |
| double epsilon, |
| int maxIterations)</code> |
| <div class="block">Returns the regularized beta function I(x, a, b).</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/special/Beta.html#regularizedBeta(double, double, double, int)">regularizedBeta</a></strong>(double x, |
| double a, |
| double b, |
| int maxIterations)</code> |
| <div class="block">Returns the regularized beta function I(x, a, b).</div> |
| </td> |
| </tr> |
| </table> |
| <ul class="blockList"> |
| <li class="blockList"><a name="methods_inherited_from_class_java.lang.Object"> |
| <!-- --> |
| </a> |
| <h3>Methods inherited from class java.lang.<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></h3> |
| <code><a href="http://docs.oracle.com/javase/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> |
| </ul> |
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| <h3>Method Detail</h3> |
| <a name="regularizedBeta(double, double, double)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>regularizedBeta</h4> |
| <pre>public static double regularizedBeta(double x, |
| double a, |
| double b)</pre> |
| <div class="block">Returns the |
| <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html"> |
| regularized beta function</a> I(x, a, b).</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - Value.</dd><dd><code>a</code> - Parameter <code>a</code>.</dd><dd><code>b</code> - Parameter <code>b</code>.</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>the regularized beta function I(x, a, b).</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></dl> |
| </li> |
| </ul> |
| <a name="regularizedBeta(double, double, double, double)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>regularizedBeta</h4> |
| <pre>public static double regularizedBeta(double x, |
| double a, |
| double b, |
| double epsilon)</pre> |
| <div class="block">Returns the |
| <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html"> |
| regularized beta function</a> I(x, a, b).</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - Value.</dd><dd><code>a</code> - Parameter <code>a</code>.</dd><dd><code>b</code> - Parameter <code>b</code>.</dd><dd><code>epsilon</code> - When the absolute value of the nth item in the |
| series is less than epsilon the approximation ceases to calculate |
| further elements in the series.</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>the regularized beta function I(x, a, b)</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></dl> |
| </li> |
| </ul> |
| <a name="regularizedBeta(double, double, double, int)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>regularizedBeta</h4> |
| <pre>public static double regularizedBeta(double x, |
| double a, |
| double b, |
| int maxIterations)</pre> |
| <div class="block">Returns the regularized beta function I(x, a, b).</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the value.</dd><dd><code>a</code> - Parameter <code>a</code>.</dd><dd><code>b</code> - Parameter <code>b</code>.</dd><dd><code>maxIterations</code> - Maximum number of "iterations" to complete.</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>the regularized beta function I(x, a, b)</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></dl> |
| </li> |
| </ul> |
| <a name="regularizedBeta(double, double, double, double, int)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>regularizedBeta</h4> |
| <pre>public static double regularizedBeta(double x, |
| double a, |
| double b, |
| double epsilon, |
| int maxIterations)</pre> |
| <div class="block">Returns the regularized beta function I(x, a, b). |
| |
| The implementation of this method is based on: |
| <ul> |
| <li> |
| <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html"> |
| Regularized Beta Function</a>.</li> |
| <li> |
| <a href="http://functions.wolfram.com/06.21.10.0001.01"> |
| Regularized Beta Function</a>.</li> |
| </ul></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the value.</dd><dd><code>a</code> - Parameter <code>a</code>.</dd><dd><code>b</code> - Parameter <code>b</code>.</dd><dd><code>epsilon</code> - When the absolute value of the nth item in the |
| series is less than epsilon the approximation ceases to calculate |
| further elements in the series.</dd><dd><code>maxIterations</code> - Maximum number of "iterations" to complete.</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>the regularized beta function I(x, a, b)</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></dl> |
| </li> |
| </ul> |
| <a name="logBeta(double, double, double, int)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
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| <h4>logBeta</h4> |
| <pre><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Deprecated.html?is-external=true" title="class or interface in java.lang">@Deprecated</a> |
| public static double logBeta(double a, |
| double b, |
| double epsilon, |
| int maxIterations)</pre> |
| <div class="block"><span class="strong">Deprecated.</span> <i>as of version 3.1, this method is deprecated as the |
| computation of the beta function is no longer iterative; it will be |
| removed in version 4.0. Current implementation of this method |
| internally calls <a href="../../../../../org/apache/commons/math3/special/Beta.html#logBeta(double, double)"><code>logBeta(double, double)</code></a>.</i></div> |
| <div class="block">Returns the natural logarithm of the beta function B(a, b). |
| |
| The implementation of this method is based on: |
| <ul> |
| <li><a href="http://mathworld.wolfram.com/BetaFunction.html"> |
| Beta Function</a>, equation (1).</li> |
| </ul></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - Parameter <code>a</code>.</dd><dd><code>b</code> - Parameter <code>b</code>.</dd><dd><code>epsilon</code> - This parameter is ignored.</dd><dd><code>maxIterations</code> - This parameter is ignored.</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>log(B(a, b)).</dd></dl> |
| </li> |
| </ul> |
| <a name="logBeta(double, double)"> |
| <!-- --> |
| </a> |
| <ul class="blockListLast"> |
| <li class="blockList"> |
| <h4>logBeta</h4> |
| <pre>public static double logBeta(double p, |
| double q)</pre> |
| <div class="block">Returns the value of log B(p, q) for 0 ≤ x ≤ 1 and p, q > 0. Based on the |
| <em>NSWC Library of Mathematics Subroutines</em> implementation, |
| <code>DBETLN</code>.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>p</code> - First argument.</dd><dd><code>q</code> - Second argument.</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>the value of <code>log(Beta(p, q))</code>, <code>NaN</code> if |
| <code>p <= 0</code> or <code>q <= 0</code>.</dd></dl> |
| </li> |
| </ul> |
| </li> |
| </ul> |
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