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| author | dwinter |
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| date | Tue, 04 Jan 2011 10:02:07 +0100 |
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<HTML> <BODY BGCOLOR="white"> <PRE> <FONT color="green">001</FONT> /*<a name="line.1"></a> <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a> <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a> <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a> <FONT color="green">005</FONT> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a> <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a> <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a> <FONT color="green">008</FONT> *<a name="line.8"></a> <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a> <FONT color="green">010</FONT> *<a name="line.10"></a> <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a> <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a> <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a> <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a> <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a> <FONT color="green">016</FONT> */<a name="line.16"></a> <FONT color="green">017</FONT> package org.apache.commons.math.special;<a name="line.17"></a> <FONT color="green">018</FONT> <a name="line.18"></a> <FONT color="green">019</FONT> import org.apache.commons.math.MathException;<a name="line.19"></a> <FONT color="green">020</FONT> import org.apache.commons.math.util.ContinuedFraction;<a name="line.20"></a> <FONT color="green">021</FONT> <a name="line.21"></a> <FONT color="green">022</FONT> /**<a name="line.22"></a> <FONT color="green">023</FONT> * This is a utility class that provides computation methods related to the<a name="line.23"></a> <FONT color="green">024</FONT> * Beta family of functions.<a name="line.24"></a> <FONT color="green">025</FONT> *<a name="line.25"></a> <FONT color="green">026</FONT> * @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $<a name="line.26"></a> <FONT color="green">027</FONT> */<a name="line.27"></a> <FONT color="green">028</FONT> public class Beta {<a name="line.28"></a> <FONT color="green">029</FONT> <a name="line.29"></a> <FONT color="green">030</FONT> /** Maximum allowed numerical error. */<a name="line.30"></a> <FONT color="green">031</FONT> private static final double DEFAULT_EPSILON = 10e-15;<a name="line.31"></a> <FONT color="green">032</FONT> <a name="line.32"></a> <FONT color="green">033</FONT> /**<a name="line.33"></a> <FONT color="green">034</FONT> * Default constructor. Prohibit instantiation.<a name="line.34"></a> <FONT color="green">035</FONT> */<a name="line.35"></a> <FONT color="green">036</FONT> private Beta() {<a name="line.36"></a> <FONT color="green">037</FONT> super();<a name="line.37"></a> <FONT color="green">038</FONT> }<a name="line.38"></a> <FONT color="green">039</FONT> <a name="line.39"></a> <FONT color="green">040</FONT> /**<a name="line.40"></a> <FONT color="green">041</FONT> * Returns the<a name="line.41"></a> <FONT color="green">042</FONT> * <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html"><a name="line.42"></a> <FONT color="green">043</FONT> * regularized beta function</a> I(x, a, b).<a name="line.43"></a> <FONT color="green">044</FONT> *<a name="line.44"></a> <FONT color="green">045</FONT> * @param x the value.<a name="line.45"></a> <FONT color="green">046</FONT> * @param a the a parameter.<a name="line.46"></a> <FONT color="green">047</FONT> * @param b the b parameter.<a name="line.47"></a> <FONT color="green">048</FONT> * @return the regularized beta function I(x, a, b)<a name="line.48"></a> <FONT color="green">049</FONT> * @throws MathException if the algorithm fails to converge.<a name="line.49"></a> <FONT color="green">050</FONT> */<a name="line.50"></a> <FONT color="green">051</FONT> public static double regularizedBeta(double x, double a, double b)<a name="line.51"></a> <FONT color="green">052</FONT> throws MathException<a name="line.52"></a> <FONT color="green">053</FONT> {<a name="line.53"></a> <FONT color="green">054</FONT> return regularizedBeta(x, a, b, DEFAULT_EPSILON, Integer.MAX_VALUE);<a name="line.54"></a> <FONT color="green">055</FONT> }<a name="line.55"></a> <FONT color="green">056</FONT> <a name="line.56"></a> <FONT color="green">057</FONT> /**<a name="line.57"></a> <FONT color="green">058</FONT> * Returns the<a name="line.58"></a> <FONT color="green">059</FONT> * <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html"><a name="line.59"></a> <FONT color="green">060</FONT> * regularized beta function</a> I(x, a, b).<a name="line.60"></a> <FONT color="green">061</FONT> *<a name="line.61"></a> <FONT color="green">062</FONT> * @param x the value.<a name="line.62"></a> <FONT color="green">063</FONT> * @param a the a parameter.<a name="line.63"></a> <FONT color="green">064</FONT> * @param b the b parameter.<a name="line.64"></a> <FONT color="green">065</FONT> * @param epsilon When the absolute value of the nth item in the<a name="line.65"></a> <FONT color="green">066</FONT> * series is less than epsilon the approximation ceases<a name="line.66"></a> <FONT color="green">067</FONT> * to calculate further elements in the series.<a name="line.67"></a> <FONT color="green">068</FONT> * @return the regularized beta function I(x, a, b)<a name="line.68"></a> <FONT color="green">069</FONT> * @throws MathException if the algorithm fails to converge.<a name="line.69"></a> <FONT color="green">070</FONT> */<a name="line.70"></a> <FONT color="green">071</FONT> public static double regularizedBeta(double x, double a, double b,<a name="line.71"></a> <FONT color="green">072</FONT> double epsilon) throws MathException<a name="line.72"></a> <FONT color="green">073</FONT> {<a name="line.73"></a> <FONT color="green">074</FONT> return regularizedBeta(x, a, b, epsilon, Integer.MAX_VALUE);<a name="line.74"></a> <FONT color="green">075</FONT> }<a name="line.75"></a> <FONT color="green">076</FONT> <a name="line.76"></a> <FONT color="green">077</FONT> /**<a name="line.77"></a> <FONT color="green">078</FONT> * Returns the regularized beta function I(x, a, b).<a name="line.78"></a> <FONT color="green">079</FONT> *<a name="line.79"></a> <FONT color="green">080</FONT> * @param x the value.<a name="line.80"></a> <FONT color="green">081</FONT> * @param a the a parameter.<a name="line.81"></a> <FONT color="green">082</FONT> * @param b the b parameter.<a name="line.82"></a> <FONT color="green">083</FONT> * @param maxIterations Maximum number of "iterations" to complete.<a name="line.83"></a> <FONT color="green">084</FONT> * @return the regularized beta function I(x, a, b)<a name="line.84"></a> <FONT color="green">085</FONT> * @throws MathException if the algorithm fails to converge.<a name="line.85"></a> <FONT color="green">086</FONT> */<a name="line.86"></a> <FONT color="green">087</FONT> public static double regularizedBeta(double x, double a, double b,<a name="line.87"></a> <FONT color="green">088</FONT> int maxIterations) throws MathException<a name="line.88"></a> <FONT color="green">089</FONT> {<a name="line.89"></a> <FONT color="green">090</FONT> return regularizedBeta(x, a, b, DEFAULT_EPSILON, maxIterations);<a name="line.90"></a> <FONT color="green">091</FONT> }<a name="line.91"></a> <FONT color="green">092</FONT> <a name="line.92"></a> <FONT color="green">093</FONT> /**<a name="line.93"></a> <FONT color="green">094</FONT> * Returns the regularized beta function I(x, a, b).<a name="line.94"></a> <FONT color="green">095</FONT> *<a name="line.95"></a> <FONT color="green">096</FONT> * The implementation of this method is based on:<a name="line.96"></a> <FONT color="green">097</FONT> * <ul><a name="line.97"></a> <FONT color="green">098</FONT> * <li><a name="line.98"></a> <FONT color="green">099</FONT> * <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html"><a name="line.99"></a> <FONT color="green">100</FONT> * Regularized Beta Function</a>.</li><a name="line.100"></a> <FONT color="green">101</FONT> * <li><a name="line.101"></a> <FONT color="green">102</FONT> * <a href="http://functions.wolfram.com/06.21.10.0001.01"><a name="line.102"></a> <FONT color="green">103</FONT> * Regularized Beta Function</a>.</li><a name="line.103"></a> <FONT color="green">104</FONT> * </ul><a name="line.104"></a> <FONT color="green">105</FONT> *<a name="line.105"></a> <FONT color="green">106</FONT> * @param x the value.<a name="line.106"></a> <FONT color="green">107</FONT> * @param a the a parameter.<a name="line.107"></a> <FONT color="green">108</FONT> * @param b the b parameter.<a name="line.108"></a> <FONT color="green">109</FONT> * @param epsilon When the absolute value of the nth item in the<a name="line.109"></a> <FONT color="green">110</FONT> * series is less than epsilon the approximation ceases<a name="line.110"></a> <FONT color="green">111</FONT> * to calculate further elements in the series.<a name="line.111"></a> <FONT color="green">112</FONT> * @param maxIterations Maximum number of "iterations" to complete.<a name="line.112"></a> <FONT color="green">113</FONT> * @return the regularized beta function I(x, a, b)<a name="line.113"></a> <FONT color="green">114</FONT> * @throws MathException if the algorithm fails to converge.<a name="line.114"></a> <FONT color="green">115</FONT> */<a name="line.115"></a> <FONT color="green">116</FONT> public static double regularizedBeta(double x, final double a,<a name="line.116"></a> <FONT color="green">117</FONT> final double b, double epsilon, int maxIterations) throws MathException<a name="line.117"></a> <FONT color="green">118</FONT> {<a name="line.118"></a> <FONT color="green">119</FONT> double ret;<a name="line.119"></a> <FONT color="green">120</FONT> <a name="line.120"></a> <FONT color="green">121</FONT> if (Double.isNaN(x) || Double.isNaN(a) || Double.isNaN(b) || (x < 0) ||<a name="line.121"></a> <FONT color="green">122</FONT> (x > 1) || (a <= 0.0) || (b <= 0.0))<a name="line.122"></a> <FONT color="green">123</FONT> {<a name="line.123"></a> <FONT color="green">124</FONT> ret = Double.NaN;<a name="line.124"></a> <FONT color="green">125</FONT> } else if (x > (a + 1.0) / (a + b + 2.0)) {<a name="line.125"></a> <FONT color="green">126</FONT> ret = 1.0 - regularizedBeta(1.0 - x, b, a, epsilon, maxIterations);<a name="line.126"></a> <FONT color="green">127</FONT> } else {<a name="line.127"></a> <FONT color="green">128</FONT> ContinuedFraction fraction = new ContinuedFraction() {<a name="line.128"></a> <FONT color="green">129</FONT> <a name="line.129"></a> <FONT color="green">130</FONT> @Override<a name="line.130"></a> <FONT color="green">131</FONT> protected double getB(int n, double x) {<a name="line.131"></a> <FONT color="green">132</FONT> double ret;<a name="line.132"></a> <FONT color="green">133</FONT> double m;<a name="line.133"></a> <FONT color="green">134</FONT> if (n % 2 == 0) { // even<a name="line.134"></a> <FONT color="green">135</FONT> m = n / 2.0;<a name="line.135"></a> <FONT color="green">136</FONT> ret = (m * (b - m) * x) /<a name="line.136"></a> <FONT color="green">137</FONT> ((a + (2 * m) - 1) * (a + (2 * m)));<a name="line.137"></a> <FONT color="green">138</FONT> } else {<a name="line.138"></a> <FONT color="green">139</FONT> m = (n - 1.0) / 2.0;<a name="line.139"></a> <FONT color="green">140</FONT> ret = -((a + m) * (a + b + m) * x) /<a name="line.140"></a> <FONT color="green">141</FONT> ((a + (2 * m)) * (a + (2 * m) + 1.0));<a name="line.141"></a> <FONT color="green">142</FONT> }<a name="line.142"></a> <FONT color="green">143</FONT> return ret;<a name="line.143"></a> <FONT color="green">144</FONT> }<a name="line.144"></a> <FONT color="green">145</FONT> <a name="line.145"></a> <FONT color="green">146</FONT> @Override<a name="line.146"></a> <FONT color="green">147</FONT> protected double getA(int n, double x) {<a name="line.147"></a> <FONT color="green">148</FONT> return 1.0;<a name="line.148"></a> <FONT color="green">149</FONT> }<a name="line.149"></a> <FONT color="green">150</FONT> };<a name="line.150"></a> <FONT color="green">151</FONT> ret = Math.exp((a * Math.log(x)) + (b * Math.log(1.0 - x)) -<a name="line.151"></a> <FONT color="green">152</FONT> Math.log(a) - logBeta(a, b, epsilon, maxIterations)) *<a name="line.152"></a> <FONT color="green">153</FONT> 1.0 / fraction.evaluate(x, epsilon, maxIterations);<a name="line.153"></a> <FONT color="green">154</FONT> }<a name="line.154"></a> <FONT color="green">155</FONT> <a name="line.155"></a> <FONT color="green">156</FONT> return ret;<a name="line.156"></a> <FONT color="green">157</FONT> }<a name="line.157"></a> <FONT color="green">158</FONT> <a name="line.158"></a> <FONT color="green">159</FONT> /**<a name="line.159"></a> <FONT color="green">160</FONT> * Returns the natural logarithm of the beta function B(a, b).<a name="line.160"></a> <FONT color="green">161</FONT> *<a name="line.161"></a> <FONT color="green">162</FONT> * @param a the a parameter.<a name="line.162"></a> <FONT color="green">163</FONT> * @param b the b parameter.<a name="line.163"></a> <FONT color="green">164</FONT> * @return log(B(a, b))<a name="line.164"></a> <FONT color="green">165</FONT> */<a name="line.165"></a> <FONT color="green">166</FONT> public static double logBeta(double a, double b) {<a name="line.166"></a> <FONT color="green">167</FONT> return logBeta(a, b, DEFAULT_EPSILON, Integer.MAX_VALUE);<a name="line.167"></a> <FONT color="green">168</FONT> }<a name="line.168"></a> <FONT color="green">169</FONT> <a name="line.169"></a> <FONT color="green">170</FONT> /**<a name="line.170"></a> <FONT color="green">171</FONT> * Returns the natural logarithm of the beta function B(a, b).<a name="line.171"></a> <FONT color="green">172</FONT> *<a name="line.172"></a> <FONT color="green">173</FONT> * The implementation of this method is based on:<a name="line.173"></a> <FONT color="green">174</FONT> * <ul><a name="line.174"></a> <FONT color="green">175</FONT> * <li><a href="http://mathworld.wolfram.com/BetaFunction.html"><a name="line.175"></a> <FONT color="green">176</FONT> * Beta Function</a>, equation (1).</li><a name="line.176"></a> <FONT color="green">177</FONT> * </ul><a name="line.177"></a> <FONT color="green">178</FONT> *<a name="line.178"></a> <FONT color="green">179</FONT> * @param a the a parameter.<a name="line.179"></a> <FONT color="green">180</FONT> * @param b the b parameter.<a name="line.180"></a> <FONT color="green">181</FONT> * @param epsilon When the absolute value of the nth item in the<a name="line.181"></a> <FONT color="green">182</FONT> * series is less than epsilon the approximation ceases<a name="line.182"></a> <FONT color="green">183</FONT> * to calculate further elements in the series.<a name="line.183"></a> <FONT color="green">184</FONT> * @param maxIterations Maximum number of "iterations" to complete.<a name="line.184"></a> <FONT color="green">185</FONT> * @return log(B(a, b))<a name="line.185"></a> <FONT color="green">186</FONT> */<a name="line.186"></a> <FONT color="green">187</FONT> public static double logBeta(double a, double b, double epsilon,<a name="line.187"></a> <FONT color="green">188</FONT> int maxIterations) {<a name="line.188"></a> <FONT color="green">189</FONT> <a name="line.189"></a> <FONT color="green">190</FONT> double ret;<a name="line.190"></a> <FONT color="green">191</FONT> <a name="line.191"></a> <FONT color="green">192</FONT> if (Double.isNaN(a) || Double.isNaN(b) || (a <= 0.0) || (b <= 0.0)) {<a name="line.192"></a> <FONT color="green">193</FONT> ret = Double.NaN;<a name="line.193"></a> <FONT color="green">194</FONT> } else {<a name="line.194"></a> <FONT color="green">195</FONT> ret = Gamma.logGamma(a) + Gamma.logGamma(b) -<a name="line.195"></a> <FONT color="green">196</FONT> Gamma.logGamma(a + b);<a name="line.196"></a> <FONT color="green">197</FONT> }<a name="line.197"></a> <FONT color="green">198</FONT> <a name="line.198"></a> <FONT color="green">199</FONT> return ret;<a name="line.199"></a> <FONT color="green">200</FONT> }<a name="line.200"></a> <FONT color="green">201</FONT> }<a name="line.201"></a> </PRE> </BODY> </HTML>