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Posted to commits@commons.apache.org by er...@apache.org on 2014/12/30 18:15:37 UTC
svn commit: r934426 [10/10] - in
/websites/production/commons/content/proper/commons-math/apidocs:
org/apache/commons/math3/analysis/interpolation/
org/apache/commons/math3/analysis/interpolation/class-use/
org/apache/commons/math3/fitting/ org/apache/...
Added: websites/production/commons/content/proper/commons-math/apidocs/src-html/org/apache/commons/math3/special/BesselJ.html
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--- websites/production/commons/content/proper/commons-math/apidocs/src-html/org/apache/commons/math3/special/BesselJ.html (added)
+++ websites/production/commons/content/proper/commons-math/apidocs/src-html/org/apache/commons/math3/special/BesselJ.html Tue Dec 30 17:15:36 2014
@@ -0,0 +1,722 @@
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
+<html lang="en">
+<head>
+<title>Source code</title>
+<link rel="stylesheet" type="text/css" href="../../../../../../stylesheet.css" title="Style">
+</head>
+<body>
+<div class="sourceContainer">
+<pre><span class="sourceLineNo">001</span>/*<a name="line.1"></a>
+<span class="sourceLineNo">002</span> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
+<span class="sourceLineNo">003</span> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a>
+<span class="sourceLineNo">004</span> * this work for additional information regarding copyright ownership.<a name="line.4"></a>
+<span class="sourceLineNo">005</span> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
+<span class="sourceLineNo">006</span> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
+<span class="sourceLineNo">007</span> * the License. You may obtain a copy of the License at<a name="line.7"></a>
+<span class="sourceLineNo">008</span> *<a name="line.8"></a>
+<span class="sourceLineNo">009</span> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
+<span class="sourceLineNo">010</span> *<a name="line.10"></a>
+<span class="sourceLineNo">011</span> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
+<span class="sourceLineNo">012</span> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
+<span class="sourceLineNo">013</span> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
+<span class="sourceLineNo">014</span> * See the License for the specific language governing permissions and<a name="line.14"></a>
+<span class="sourceLineNo">015</span> * limitations under the License.<a name="line.15"></a>
+<span class="sourceLineNo">016</span> */<a name="line.16"></a>
+<span class="sourceLineNo">017</span><a name="line.17"></a>
+<span class="sourceLineNo">018</span>package org.apache.commons.math3.special;<a name="line.18"></a>
+<span class="sourceLineNo">019</span><a name="line.19"></a>
+<span class="sourceLineNo">020</span>import java.util.Arrays;<a name="line.20"></a>
+<span class="sourceLineNo">021</span><a name="line.21"></a>
+<span class="sourceLineNo">022</span>import org.apache.commons.math3.analysis.UnivariateFunction;<a name="line.22"></a>
+<span class="sourceLineNo">023</span>import org.apache.commons.math3.exception.ConvergenceException;<a name="line.23"></a>
+<span class="sourceLineNo">024</span>import org.apache.commons.math3.exception.MathIllegalArgumentException;<a name="line.24"></a>
+<span class="sourceLineNo">025</span>import org.apache.commons.math3.exception.util.LocalizedFormats;<a name="line.25"></a>
+<span class="sourceLineNo">026</span>import org.apache.commons.math3.special.Gamma;<a name="line.26"></a>
+<span class="sourceLineNo">027</span>import org.apache.commons.math3.util.FastMath;<a name="line.27"></a>
+<span class="sourceLineNo">028</span><a name="line.28"></a>
+<span class="sourceLineNo">029</span>/**<a name="line.29"></a>
+<span class="sourceLineNo">030</span> * This class provides computation methods related to Bessel<a name="line.30"></a>
+<span class="sourceLineNo">031</span> * functions of the first kind. Detailed descriptions of these functions are<a name="line.31"></a>
+<span class="sourceLineNo">032</span> * available in <a<a name="line.32"></a>
+<span class="sourceLineNo">033</span> * href="http://en.wikipedia.org/wiki/Bessel_function">Wikipedia</a>, <a<a name="line.33"></a>
+<span class="sourceLineNo">034</span> * href="http://en.wikipedia.org/wiki/Abramowitz_and_Stegun">Abrabowitz and<a name="line.34"></a>
+<span class="sourceLineNo">035</span> * Stegun</a> (Ch. 9-11), and <a href="http://dlmf.nist.gov/">DLMF</a> (Ch. 10).<a name="line.35"></a>
+<span class="sourceLineNo">036</span> * <p><a name="line.36"></a>
+<span class="sourceLineNo">037</span> * This implementation is based on the rjbesl Fortran routine at<a name="line.37"></a>
+<span class="sourceLineNo">038</span> * <a href="http://www.netlib.org/specfun/rjbesl">Netlib</a>.</p><a name="line.38"></a>
+<span class="sourceLineNo">039</span> * <p><a name="line.39"></a>
+<span class="sourceLineNo">040</span> * From the Fortran code: </p><a name="line.40"></a>
+<span class="sourceLineNo">041</span> * <p><a name="line.41"></a>
+<span class="sourceLineNo">042</span> * This program is based on a program written by David J. Sookne (2) that<a name="line.42"></a>
+<span class="sourceLineNo">043</span> * computes values of the Bessel functions J or I of real argument and integer<a name="line.43"></a>
+<span class="sourceLineNo">044</span> * order. Modifications include the restriction of the computation to the J<a name="line.44"></a>
+<span class="sourceLineNo">045</span> * Bessel function of non-negative real argument, the extension of the<a name="line.45"></a>
+<span class="sourceLineNo">046</span> * computation to arbitrary positive order, and the elimination of most<a name="line.46"></a>
+<span class="sourceLineNo">047</span> * underflow.</p><a name="line.47"></a>
+<span class="sourceLineNo">048</span> * <p><a name="line.48"></a>
+<span class="sourceLineNo">049</span> * References:</p><a name="line.49"></a>
+<span class="sourceLineNo">050</span> * <ul><a name="line.50"></a>
+<span class="sourceLineNo">051</span> * <li>"A Note on Backward Recurrence Algorithms," Olver, F. W. J., and Sookne,<a name="line.51"></a>
+<span class="sourceLineNo">052</span> * D. J., Math. Comp. 26, 1972, pp 941-947.</li><a name="line.52"></a>
+<span class="sourceLineNo">053</span> * <li>"Bessel Functions of Real Argument and Integer Order," Sookne, D. J., NBS<a name="line.53"></a>
+<span class="sourceLineNo">054</span> * Jour. of Res. B. 77B, 1973, pp 125-132.</li><a name="line.54"></a>
+<span class="sourceLineNo">055</span> * </ul> </p><a name="line.55"></a>
+<span class="sourceLineNo">056</span> * @since 3.4<a name="line.56"></a>
+<span class="sourceLineNo">057</span> */<a name="line.57"></a>
+<span class="sourceLineNo">058</span>public class BesselJ<a name="line.58"></a>
+<span class="sourceLineNo">059</span> implements UnivariateFunction {<a name="line.59"></a>
+<span class="sourceLineNo">060</span><a name="line.60"></a>
+<span class="sourceLineNo">061</span> // ---------------------------------------------------------------------<a name="line.61"></a>
+<span class="sourceLineNo">062</span> // Mathematical constants<a name="line.62"></a>
+<span class="sourceLineNo">063</span> // ---------------------------------------------------------------------<a name="line.63"></a>
+<span class="sourceLineNo">064</span><a name="line.64"></a>
+<span class="sourceLineNo">065</span> /** -2 / pi */<a name="line.65"></a>
+<span class="sourceLineNo">066</span> private static final double PI2 = 0.636619772367581343075535;<a name="line.66"></a>
+<span class="sourceLineNo">067</span><a name="line.67"></a>
+<span class="sourceLineNo">068</span> /** first few significant digits of 2pi */<a name="line.68"></a>
+<span class="sourceLineNo">069</span> private static final double TOWPI1 = 6.28125;<a name="line.69"></a>
+<span class="sourceLineNo">070</span><a name="line.70"></a>
+<span class="sourceLineNo">071</span> /** 2pi - TWOPI1 to working precision */<a name="line.71"></a>
+<span class="sourceLineNo">072</span> private static final double TWOPI2 = 1.935307179586476925286767e-3;<a name="line.72"></a>
+<span class="sourceLineNo">073</span><a name="line.73"></a>
+<span class="sourceLineNo">074</span> /** TOWPI1 + TWOPI2 */<a name="line.74"></a>
+<span class="sourceLineNo">075</span> private static final double TWOPI = TOWPI1 + TWOPI2;<a name="line.75"></a>
+<span class="sourceLineNo">076</span><a name="line.76"></a>
+<span class="sourceLineNo">077</span> // ---------------------------------------------------------------------<a name="line.77"></a>
+<span class="sourceLineNo">078</span> // Machine-dependent parameters<a name="line.78"></a>
+<span class="sourceLineNo">079</span> // ---------------------------------------------------------------------<a name="line.79"></a>
+<span class="sourceLineNo">080</span><a name="line.80"></a>
+<span class="sourceLineNo">081</span> /**<a name="line.81"></a>
+<span class="sourceLineNo">082</span> * 10.0^K, where K is the largest integer such that ENTEN is<a name="line.82"></a>
+<span class="sourceLineNo">083</span> * machine-representable in working precision<a name="line.83"></a>
+<span class="sourceLineNo">084</span> */<a name="line.84"></a>
+<span class="sourceLineNo">085</span> private static final double ENTEN = 1.0e308;<a name="line.85"></a>
+<span class="sourceLineNo">086</span><a name="line.86"></a>
+<span class="sourceLineNo">087</span> /**<a name="line.87"></a>
+<span class="sourceLineNo">088</span> * Decimal significance desired. Should be set to (INT(log_{10}(2) * (it)+1)).<a name="line.88"></a>
+<span class="sourceLineNo">089</span> * Setting NSIG lower will result in decreased accuracy while setting<a name="line.89"></a>
+<span class="sourceLineNo">090</span> * NSIG higher will increase CPU time without increasing accuracy.<a name="line.90"></a>
+<span class="sourceLineNo">091</span> * The truncation error is limited to a relative error of<a name="line.91"></a>
+<span class="sourceLineNo">092</span> * T=.5(10^(-NSIG)).<a name="line.92"></a>
+<span class="sourceLineNo">093</span> */<a name="line.93"></a>
+<span class="sourceLineNo">094</span> private static final double ENSIG = 1.0e16;<a name="line.94"></a>
+<span class="sourceLineNo">095</span><a name="line.95"></a>
+<span class="sourceLineNo">096</span> /** 10.0 ** (-K) for the smallest integer K such that K >= NSIG/4 */<a name="line.96"></a>
+<span class="sourceLineNo">097</span> private static final double RTNSIG = 1.0e-4;<a name="line.97"></a>
+<span class="sourceLineNo">098</span><a name="line.98"></a>
+<span class="sourceLineNo">099</span> /** Smallest ABS(X) such that X/4 does not underflow */<a name="line.99"></a>
+<span class="sourceLineNo">100</span> private static final double ENMTEN = 8.90e-308;<a name="line.100"></a>
+<span class="sourceLineNo">101</span><a name="line.101"></a>
+<span class="sourceLineNo">102</span> /** Minimum acceptable value for x */<a name="line.102"></a>
+<span class="sourceLineNo">103</span> private static final double X_MIN = 0.0;<a name="line.103"></a>
+<span class="sourceLineNo">104</span><a name="line.104"></a>
+<span class="sourceLineNo">105</span> /**<a name="line.105"></a>
+<span class="sourceLineNo">106</span> * Upper limit on the magnitude of x. If abs(x) = n, then at least<a name="line.106"></a>
+<span class="sourceLineNo">107</span> * n iterations of the backward recursion will be executed. The value of<a name="line.107"></a>
+<span class="sourceLineNo">108</span> * 10.0 ** 4 is used on every machine.<a name="line.108"></a>
+<span class="sourceLineNo">109</span> */<a name="line.109"></a>
+<span class="sourceLineNo">110</span> private static final double X_MAX = 1.0e4;<a name="line.110"></a>
+<span class="sourceLineNo">111</span><a name="line.111"></a>
+<span class="sourceLineNo">112</span> /** First 25 factorials as doubles */<a name="line.112"></a>
+<span class="sourceLineNo">113</span> private static final double[] FACT = {<a name="line.113"></a>
+<span class="sourceLineNo">114</span> 1.0, 1.0, 2.0, 6.0, 24.0, 120.0, 720.0, 5040.0, 40320.0, 362880.0,<a name="line.114"></a>
+<span class="sourceLineNo">115</span> 3628800.0, 39916800.0, 479001600.0, 6227020800.0, 87178291200.0,<a name="line.115"></a>
+<span class="sourceLineNo">116</span> 1.307674368e12, 2.0922789888e13, 3.55687428096e14, 6.402373705728e15,<a name="line.116"></a>
+<span class="sourceLineNo">117</span> 1.21645100408832e17, 2.43290200817664e18, 5.109094217170944e19,<a name="line.117"></a>
+<span class="sourceLineNo">118</span> 1.12400072777760768e21, 2.585201673888497664e22,<a name="line.118"></a>
+<span class="sourceLineNo">119</span> 6.2044840173323943936e23<a name="line.119"></a>
+<span class="sourceLineNo">120</span> };<a name="line.120"></a>
+<span class="sourceLineNo">121</span><a name="line.121"></a>
+<span class="sourceLineNo">122</span> /** Order of the function computed when {@link #value(double)} is used */<a name="line.122"></a>
+<span class="sourceLineNo">123</span> private final double order;<a name="line.123"></a>
+<span class="sourceLineNo">124</span><a name="line.124"></a>
+<span class="sourceLineNo">125</span> /**<a name="line.125"></a>
+<span class="sourceLineNo">126</span> * Create a new BesselJ with the given order.<a name="line.126"></a>
+<span class="sourceLineNo">127</span> *<a name="line.127"></a>
+<span class="sourceLineNo">128</span> * @param order order of the function computed when using {@link #value(double)}.<a name="line.128"></a>
+<span class="sourceLineNo">129</span> */<a name="line.129"></a>
+<span class="sourceLineNo">130</span> public BesselJ(double order) {<a name="line.130"></a>
+<span class="sourceLineNo">131</span> this.order = order;<a name="line.131"></a>
+<span class="sourceLineNo">132</span> }<a name="line.132"></a>
+<span class="sourceLineNo">133</span><a name="line.133"></a>
+<span class="sourceLineNo">134</span> /**<a name="line.134"></a>
+<span class="sourceLineNo">135</span> * Returns the value of the constructed Bessel function of the first kind,<a name="line.135"></a>
+<span class="sourceLineNo">136</span> * for the passed argument.<a name="line.136"></a>
+<span class="sourceLineNo">137</span> *<a name="line.137"></a>
+<span class="sourceLineNo">138</span> * @param x Argument<a name="line.138"></a>
+<span class="sourceLineNo">139</span> * @return Value of the Bessel function at x<a name="line.139"></a>
+<span class="sourceLineNo">140</span> * @throws MathIllegalArgumentException if {@code x} is too large relative to {@code order}<a name="line.140"></a>
+<span class="sourceLineNo">141</span> * @throws ConvergenceException if the algorithm fails to converge<a name="line.141"></a>
+<span class="sourceLineNo">142</span> */<a name="line.142"></a>
+<span class="sourceLineNo">143</span> public double value(double x)<a name="line.143"></a>
+<span class="sourceLineNo">144</span> throws MathIllegalArgumentException, ConvergenceException {<a name="line.144"></a>
+<span class="sourceLineNo">145</span> return BesselJ.value(order, x);<a name="line.145"></a>
+<span class="sourceLineNo">146</span> }<a name="line.146"></a>
+<span class="sourceLineNo">147</span><a name="line.147"></a>
+<span class="sourceLineNo">148</span> /**<a name="line.148"></a>
+<span class="sourceLineNo">149</span> * Returns the first Bessel function, \(J_{order}(x)\).<a name="line.149"></a>
+<span class="sourceLineNo">150</span> *<a name="line.150"></a>
+<span class="sourceLineNo">151</span> * @param order Order of the Bessel function<a name="line.151"></a>
+<span class="sourceLineNo">152</span> * @param x Argument<a name="line.152"></a>
+<span class="sourceLineNo">153</span> * @return Value of the Bessel function of the first kind, \(J_{order}(x)\)<a name="line.153"></a>
+<span class="sourceLineNo">154</span> * @throws MathIllegalArgumentException if {@code x} is too large relative to {@code order}<a name="line.154"></a>
+<span class="sourceLineNo">155</span> * @throws ConvergenceException if the algorithm fails to converge<a name="line.155"></a>
+<span class="sourceLineNo">156</span> */<a name="line.156"></a>
+<span class="sourceLineNo">157</span> public static double value(double order, double x)<a name="line.157"></a>
+<span class="sourceLineNo">158</span> throws MathIllegalArgumentException, ConvergenceException {<a name="line.158"></a>
+<span class="sourceLineNo">159</span> final int n = (int) order;<a name="line.159"></a>
+<span class="sourceLineNo">160</span> final double alpha = order - n;<a name="line.160"></a>
+<span class="sourceLineNo">161</span> final int nb = n + 1;<a name="line.161"></a>
+<span class="sourceLineNo">162</span> final BesselJResult res = rjBesl(x, alpha, nb);<a name="line.162"></a>
+<span class="sourceLineNo">163</span><a name="line.163"></a>
+<span class="sourceLineNo">164</span> if (res.nVals >= nb) {<a name="line.164"></a>
+<span class="sourceLineNo">165</span> return res.vals[n];<a name="line.165"></a>
+<span class="sourceLineNo">166</span> } else if (res.nVals < 0) {<a name="line.166"></a>
+<span class="sourceLineNo">167</span> throw new MathIllegalArgumentException(LocalizedFormats.BESSEL_FUNCTION_BAD_ARGUMENT,order, x);<a name="line.167"></a>
+<span class="sourceLineNo">168</span> } else if (FastMath.abs(res.vals[res.nVals - 1]) < 1e-100) {<a name="line.168"></a>
+<span class="sourceLineNo">169</span> return res.vals[n]; // underflow; return value (will be zero)<a name="line.169"></a>
+<span class="sourceLineNo">170</span> }<a name="line.170"></a>
+<span class="sourceLineNo">171</span> throw new ConvergenceException(LocalizedFormats.BESSEL_FUNCTION_FAILED_CONVERGENCE, order, x);<a name="line.171"></a>
+<span class="sourceLineNo">172</span> }<a name="line.172"></a>
+<span class="sourceLineNo">173</span><a name="line.173"></a>
+<span class="sourceLineNo">174</span> /**<a name="line.174"></a>
+<span class="sourceLineNo">175</span> * Encapsulates the results returned by {@link BesselJ#rjBesl(double, double, int)}.<a name="line.175"></a>
+<span class="sourceLineNo">176</span> * <p><a name="line.176"></a>
+<span class="sourceLineNo">177</span> * {@link #getVals()} returns the computed function values.<a name="line.177"></a>
+<span class="sourceLineNo">178</span> * {@link #getnVals()} is the number of values among those returned by {@link #getnVals()}<a name="line.178"></a>
+<span class="sourceLineNo">179</span> * that can be considered accurate.<a name="line.179"></a>
+<span class="sourceLineNo">180</span> * </p><p><a name="line.180"></a>
+<span class="sourceLineNo">181</span> * <ul><a name="line.181"></a>
+<span class="sourceLineNo">182</span> * <li>nVals < 0: An argument is out of range. For example, nb <= 0, alpha<a name="line.182"></a>
+<span class="sourceLineNo">183</span> * < 0 or > 1, or x is too large. In this case, b(0) is set to zero, the<a name="line.183"></a>
+<span class="sourceLineNo">184</span> * remainder of the b-vector is not calculated, and nVals is set to<a name="line.184"></a>
+<span class="sourceLineNo">185</span> * MIN(nb,0) - 1 so that nVals != nb.</li><a name="line.185"></a>
+<span class="sourceLineNo">186</span> * <li>nb > nVals > 0: Not all requested function values could be calculated<a name="line.186"></a>
+<span class="sourceLineNo">187</span> * accurately. This usually occurs because nb is much larger than abs(x). In<a name="line.187"></a>
+<span class="sourceLineNo">188</span> * this case, b(n) is calculated to the desired accuracy for n < nVals, but<a name="line.188"></a>
+<span class="sourceLineNo">189</span> * precision is lost for nVals < n <= nb. If b(n) does not vanish for n ><a name="line.189"></a>
+<span class="sourceLineNo">190</span> * nVals (because it is too small to be represented), and b(n)/b(nVals) =<a name="line.190"></a>
+<span class="sourceLineNo">191</span> * \(10^{-k}\), then only the first NSIG-k significant figures of b(n) can be<a name="line.191"></a>
+<span class="sourceLineNo">192</span> * trusted.</li></ul></p><a name="line.192"></a>
+<span class="sourceLineNo">193</span> */<a name="line.193"></a>
+<span class="sourceLineNo">194</span> public static class BesselJResult {<a name="line.194"></a>
+<span class="sourceLineNo">195</span><a name="line.195"></a>
+<span class="sourceLineNo">196</span> /** Bessel function values */<a name="line.196"></a>
+<span class="sourceLineNo">197</span> private final double[] vals;<a name="line.197"></a>
+<span class="sourceLineNo">198</span><a name="line.198"></a>
+<span class="sourceLineNo">199</span> /** Valid value count */<a name="line.199"></a>
+<span class="sourceLineNo">200</span> private final int nVals;<a name="line.200"></a>
+<span class="sourceLineNo">201</span><a name="line.201"></a>
+<span class="sourceLineNo">202</span> /**<a name="line.202"></a>
+<span class="sourceLineNo">203</span> * Create a new BesselJResult with the given values and valid value count.<a name="line.203"></a>
+<span class="sourceLineNo">204</span> *<a name="line.204"></a>
+<span class="sourceLineNo">205</span> * @param b values<a name="line.205"></a>
+<span class="sourceLineNo">206</span> * @param n count of valid values<a name="line.206"></a>
+<span class="sourceLineNo">207</span> */<a name="line.207"></a>
+<span class="sourceLineNo">208</span> public BesselJResult(double[] b, int n) {<a name="line.208"></a>
+<span class="sourceLineNo">209</span> vals = Arrays.copyOf(b, b.length);<a name="line.209"></a>
+<span class="sourceLineNo">210</span> nVals = n;<a name="line.210"></a>
+<span class="sourceLineNo">211</span> }<a name="line.211"></a>
+<span class="sourceLineNo">212</span><a name="line.212"></a>
+<span class="sourceLineNo">213</span> /**<a name="line.213"></a>
+<span class="sourceLineNo">214</span> * @return the computed function values<a name="line.214"></a>
+<span class="sourceLineNo">215</span> */<a name="line.215"></a>
+<span class="sourceLineNo">216</span> public double[] getVals() {<a name="line.216"></a>
+<span class="sourceLineNo">217</span> return Arrays.copyOf(vals, vals.length);<a name="line.217"></a>
+<span class="sourceLineNo">218</span> }<a name="line.218"></a>
+<span class="sourceLineNo">219</span><a name="line.219"></a>
+<span class="sourceLineNo">220</span> /**<a name="line.220"></a>
+<span class="sourceLineNo">221</span> * @return the number of valid function values (normally the same as the<a name="line.221"></a>
+<span class="sourceLineNo">222</span> * length of the array returned by {@link #getnVals()})<a name="line.222"></a>
+<span class="sourceLineNo">223</span> */<a name="line.223"></a>
+<span class="sourceLineNo">224</span> public int getnVals() {<a name="line.224"></a>
+<span class="sourceLineNo">225</span> return nVals;<a name="line.225"></a>
+<span class="sourceLineNo">226</span> }<a name="line.226"></a>
+<span class="sourceLineNo">227</span> }<a name="line.227"></a>
+<span class="sourceLineNo">228</span><a name="line.228"></a>
+<span class="sourceLineNo">229</span> /**<a name="line.229"></a>
+<span class="sourceLineNo">230</span> * Calculates Bessel functions \(J_{n+alpha}(x)\) for<a name="line.230"></a>
+<span class="sourceLineNo">231</span> * non-negative argument x, and non-negative order n + alpha.<a name="line.231"></a>
+<span class="sourceLineNo">232</span> * <p><a name="line.232"></a>
+<span class="sourceLineNo">233</span> * Before using the output vector, the user should check that<a name="line.233"></a>
+<span class="sourceLineNo">234</span> * nVals = nb, i.e., all orders have been calculated to the desired accuracy.<a name="line.234"></a>
+<span class="sourceLineNo">235</span> * See BesselResult class javadoc for details on return values.<a name="line.235"></a>
+<span class="sourceLineNo">236</span> * </p><a name="line.236"></a>
+<span class="sourceLineNo">237</span> * @param x non-negative real argument for which J's are to be calculated<a name="line.237"></a>
+<span class="sourceLineNo">238</span> * @param alpha fractional part of order for which J's or exponentially<a name="line.238"></a>
+<span class="sourceLineNo">239</span> * scaled J's (\(J\cdot e^{x}\)) are to be calculated. 0 <= alpha < 1.0.<a name="line.239"></a>
+<span class="sourceLineNo">240</span> * @param nb integer number of functions to be calculated, nb > 0. The first<a name="line.240"></a>
+<span class="sourceLineNo">241</span> * function calculated is of order alpha, and the last is of order<a name="line.241"></a>
+<span class="sourceLineNo">242</span> * nb - 1 + alpha.<a name="line.242"></a>
+<span class="sourceLineNo">243</span> * @return BesselJResult a vector of the functions<a name="line.243"></a>
+<span class="sourceLineNo">244</span> * \(J_{alpha}(x)\) through \(J_{nb-1+alpha}(x)\), or the corresponding exponentially<a name="line.244"></a>
+<span class="sourceLineNo">245</span> * scaled functions and an integer output variable indicating possible errors<a name="line.245"></a>
+<span class="sourceLineNo">246</span> */<a name="line.246"></a>
+<span class="sourceLineNo">247</span> public static BesselJResult rjBesl(double x, double alpha, int nb) {<a name="line.247"></a>
+<span class="sourceLineNo">248</span> final double[] b = new double[nb];<a name="line.248"></a>
+<span class="sourceLineNo">249</span><a name="line.249"></a>
+<span class="sourceLineNo">250</span> int ncalc = 0;<a name="line.250"></a>
+<span class="sourceLineNo">251</span> double alpem = 0;<a name="line.251"></a>
+<span class="sourceLineNo">252</span> double alp2em = 0;<a name="line.252"></a>
+<span class="sourceLineNo">253</span><a name="line.253"></a>
+<span class="sourceLineNo">254</span> // ---------------------------------------------------------------------<a name="line.254"></a>
+<span class="sourceLineNo">255</span> // Check for out of range arguments.<a name="line.255"></a>
+<span class="sourceLineNo">256</span> // ---------------------------------------------------------------------<a name="line.256"></a>
+<span class="sourceLineNo">257</span> final int magx = (int) x;<a name="line.257"></a>
+<span class="sourceLineNo">258</span> if ((nb > 0) && (x >= X_MIN) && (x <= X_MAX) && (alpha >= 0) &&<a name="line.258"></a>
+<span class="sourceLineNo">259</span> (alpha < 1)) {<a name="line.259"></a>
+<span class="sourceLineNo">260</span> // ---------------------------------------------------------------------<a name="line.260"></a>
+<span class="sourceLineNo">261</span> // Initialize result array to zero.<a name="line.261"></a>
+<span class="sourceLineNo">262</span> // ---------------------------------------------------------------------<a name="line.262"></a>
+<span class="sourceLineNo">263</span> ncalc = nb;<a name="line.263"></a>
+<span class="sourceLineNo">264</span> for (int i = 0; i < nb; ++i) {<a name="line.264"></a>
+<span class="sourceLineNo">265</span> b[i] = 0;<a name="line.265"></a>
+<span class="sourceLineNo">266</span> }<a name="line.266"></a>
+<span class="sourceLineNo">267</span><a name="line.267"></a>
+<span class="sourceLineNo">268</span> // ---------------------------------------------------------------------<a name="line.268"></a>
+<span class="sourceLineNo">269</span> // Branch to use 2-term ascending series for small X and asymptotic<a name="line.269"></a>
+<span class="sourceLineNo">270</span> // form for large X when NB is not too large.<a name="line.270"></a>
+<span class="sourceLineNo">271</span> // ---------------------------------------------------------------------<a name="line.271"></a>
+<span class="sourceLineNo">272</span> double tempa;<a name="line.272"></a>
+<span class="sourceLineNo">273</span> double tempb;<a name="line.273"></a>
+<span class="sourceLineNo">274</span> double tempc;<a name="line.274"></a>
+<span class="sourceLineNo">275</span> double tover;<a name="line.275"></a>
+<span class="sourceLineNo">276</span> if (x < RTNSIG) {<a name="line.276"></a>
+<span class="sourceLineNo">277</span> // ---------------------------------------------------------------------<a name="line.277"></a>
+<span class="sourceLineNo">278</span> // Two-term ascending series for small X.<a name="line.278"></a>
+<span class="sourceLineNo">279</span> // ---------------------------------------------------------------------<a name="line.279"></a>
+<span class="sourceLineNo">280</span> tempa = 1;<a name="line.280"></a>
+<span class="sourceLineNo">281</span> alpem = 1 + alpha;<a name="line.281"></a>
+<span class="sourceLineNo">282</span> double halfx = 0;<a name="line.282"></a>
+<span class="sourceLineNo">283</span> if (x > ENMTEN) {<a name="line.283"></a>
+<span class="sourceLineNo">284</span> halfx = 0.5 * x;<a name="line.284"></a>
+<span class="sourceLineNo">285</span> }<a name="line.285"></a>
+<span class="sourceLineNo">286</span> if (alpha != 0) {<a name="line.286"></a>
+<span class="sourceLineNo">287</span> tempa = FastMath.pow(halfx, alpha) /<a name="line.287"></a>
+<span class="sourceLineNo">288</span> (alpha * Gamma.gamma(alpha));<a name="line.288"></a>
+<span class="sourceLineNo">289</span> }<a name="line.289"></a>
+<span class="sourceLineNo">290</span> tempb = 0;<a name="line.290"></a>
+<span class="sourceLineNo">291</span> if (x + 1 > 1) {<a name="line.291"></a>
+<span class="sourceLineNo">292</span> tempb = -halfx * halfx;<a name="line.292"></a>
+<span class="sourceLineNo">293</span> }<a name="line.293"></a>
+<span class="sourceLineNo">294</span> b[0] = tempa + (tempa * tempb / alpem);<a name="line.294"></a>
+<span class="sourceLineNo">295</span> if ((x != 0) && (b[0] == 0)) {<a name="line.295"></a>
+<span class="sourceLineNo">296</span> ncalc = 0;<a name="line.296"></a>
+<span class="sourceLineNo">297</span> }<a name="line.297"></a>
+<span class="sourceLineNo">298</span> if (nb != 1) {<a name="line.298"></a>
+<span class="sourceLineNo">299</span> if (x <= 0) {<a name="line.299"></a>
+<span class="sourceLineNo">300</span> for (int n = 1; n < nb; ++n) {<a name="line.300"></a>
+<span class="sourceLineNo">301</span> b[n] = 0;<a name="line.301"></a>
+<span class="sourceLineNo">302</span> }<a name="line.302"></a>
+<span class="sourceLineNo">303</span> } else {<a name="line.303"></a>
+<span class="sourceLineNo">304</span> // ---------------------------------------------------------------------<a name="line.304"></a>
+<span class="sourceLineNo">305</span> // Calculate higher order functions.<a name="line.305"></a>
+<span class="sourceLineNo">306</span> // ---------------------------------------------------------------------<a name="line.306"></a>
+<span class="sourceLineNo">307</span> tempc = halfx;<a name="line.307"></a>
+<span class="sourceLineNo">308</span> tover = tempb != 0 ? ENMTEN / tempb : 2 * ENMTEN / x;<a name="line.308"></a>
+<span class="sourceLineNo">309</span> for (int n = 1; n < nb; ++n) {<a name="line.309"></a>
+<span class="sourceLineNo">310</span> tempa /= alpem;<a name="line.310"></a>
+<span class="sourceLineNo">311</span> alpem += 1;<a name="line.311"></a>
+<span class="sourceLineNo">312</span> tempa *= tempc;<a name="line.312"></a>
+<span class="sourceLineNo">313</span> if (tempa <= tover * alpem) {<a name="line.313"></a>
+<span class="sourceLineNo">314</span> tempa = 0;<a name="line.314"></a>
+<span class="sourceLineNo">315</span> }<a name="line.315"></a>
+<span class="sourceLineNo">316</span> b[n] = tempa + (tempa * tempb / alpem);<a name="line.316"></a>
+<span class="sourceLineNo">317</span> if ((b[n] == 0) && (ncalc > n)) {<a name="line.317"></a>
+<span class="sourceLineNo">318</span> ncalc = n;<a name="line.318"></a>
+<span class="sourceLineNo">319</span> }<a name="line.319"></a>
+<span class="sourceLineNo">320</span> }<a name="line.320"></a>
+<span class="sourceLineNo">321</span> }<a name="line.321"></a>
+<span class="sourceLineNo">322</span> }<a name="line.322"></a>
+<span class="sourceLineNo">323</span> } else if ((x > 25.0) && (nb <= magx + 1)) {<a name="line.323"></a>
+<span class="sourceLineNo">324</span> // ---------------------------------------------------------------------<a name="line.324"></a>
+<span class="sourceLineNo">325</span> // Asymptotic series for X > 25<a name="line.325"></a>
+<span class="sourceLineNo">326</span> // ---------------------------------------------------------------------<a name="line.326"></a>
+<span class="sourceLineNo">327</span> final double xc = FastMath.sqrt(PI2 / x);<a name="line.327"></a>
+<span class="sourceLineNo">328</span> final double mul = 0.125 / x;<a name="line.328"></a>
+<span class="sourceLineNo">329</span> final double xin = mul * mul;<a name="line.329"></a>
+<span class="sourceLineNo">330</span> int m = 0;<a name="line.330"></a>
+<span class="sourceLineNo">331</span> if (x >= 130.0) {<a name="line.331"></a>
+<span class="sourceLineNo">332</span> m = 4;<a name="line.332"></a>
+<span class="sourceLineNo">333</span> } else if (x >= 35.0) {<a name="line.333"></a>
+<span class="sourceLineNo">334</span> m = 8;<a name="line.334"></a>
+<span class="sourceLineNo">335</span> } else {<a name="line.335"></a>
+<span class="sourceLineNo">336</span> m = 11;<a name="line.336"></a>
+<span class="sourceLineNo">337</span> }<a name="line.337"></a>
+<span class="sourceLineNo">338</span><a name="line.338"></a>
+<span class="sourceLineNo">339</span> final double xm = 4.0 * m;<a name="line.339"></a>
+<span class="sourceLineNo">340</span> // ---------------------------------------------------------------------<a name="line.340"></a>
+<span class="sourceLineNo">341</span> // Argument reduction for SIN and COS routines.<a name="line.341"></a>
+<span class="sourceLineNo">342</span> // ---------------------------------------------------------------------<a name="line.342"></a>
+<span class="sourceLineNo">343</span> double t = (double) ((int) ((x / TWOPI) + 0.5));<a name="line.343"></a>
+<span class="sourceLineNo">344</span> final double z = x - t * TOWPI1 - t * TWOPI2 - (alpha + 0.5) / PI2;<a name="line.344"></a>
+<span class="sourceLineNo">345</span> double vsin = FastMath.sin(z);<a name="line.345"></a>
+<span class="sourceLineNo">346</span> double vcos = FastMath.cos(z);<a name="line.346"></a>
+<span class="sourceLineNo">347</span> double gnu = 2 * alpha;<a name="line.347"></a>
+<span class="sourceLineNo">348</span> double capq;<a name="line.348"></a>
+<span class="sourceLineNo">349</span> double capp;<a name="line.349"></a>
+<span class="sourceLineNo">350</span> double s;<a name="line.350"></a>
+<span class="sourceLineNo">351</span> double t1;<a name="line.351"></a>
+<span class="sourceLineNo">352</span> double xk;<a name="line.352"></a>
+<span class="sourceLineNo">353</span> for (int i = 1; i <= 2; i++) {<a name="line.353"></a>
+<span class="sourceLineNo">354</span> s = (xm - 1 - gnu) * (xm - 1 + gnu) * xin * 0.5;<a name="line.354"></a>
+<span class="sourceLineNo">355</span> t = (gnu - (xm - 3.0)) * (gnu + (xm - 3.0));<a name="line.355"></a>
+<span class="sourceLineNo">356</span> capp = (s * t) / FACT[2 * m];<a name="line.356"></a>
+<span class="sourceLineNo">357</span> t1 = (gnu - (xm + 1)) * (gnu + (xm + 1));<a name="line.357"></a>
+<span class="sourceLineNo">358</span> capq = (s * t1) / FACT[2 * m + 1];<a name="line.358"></a>
+<span class="sourceLineNo">359</span> xk = xm;<a name="line.359"></a>
+<span class="sourceLineNo">360</span> int k = 2 * m;<a name="line.360"></a>
+<span class="sourceLineNo">361</span> t1 = t;<a name="line.361"></a>
+<span class="sourceLineNo">362</span><a name="line.362"></a>
+<span class="sourceLineNo">363</span> for (int j = 2; j <= m; j++) {<a name="line.363"></a>
+<span class="sourceLineNo">364</span> xk -= 4.0;<a name="line.364"></a>
+<span class="sourceLineNo">365</span> s = (xk - 1 - gnu) * (xk - 1 + gnu);<a name="line.365"></a>
+<span class="sourceLineNo">366</span> t = (gnu - (xk - 3.0)) * (gnu + (xk - 3.0));<a name="line.366"></a>
+<span class="sourceLineNo">367</span> capp = (capp + 1 / FACT[k - 2]) * s * t * xin;<a name="line.367"></a>
+<span class="sourceLineNo">368</span> capq = (capq + 1 / FACT[k - 1]) * s * t1 * xin;<a name="line.368"></a>
+<span class="sourceLineNo">369</span> k -= 2;<a name="line.369"></a>
+<span class="sourceLineNo">370</span> t1 = t;<a name="line.370"></a>
+<span class="sourceLineNo">371</span> }<a name="line.371"></a>
+<span class="sourceLineNo">372</span><a name="line.372"></a>
+<span class="sourceLineNo">373</span> capp += 1;<a name="line.373"></a>
+<span class="sourceLineNo">374</span> capq = (capq + 1) * ((gnu * gnu) - 1) * (0.125 / x);<a name="line.374"></a>
+<span class="sourceLineNo">375</span> b[i - 1] = xc * (capp * vcos - capq * vsin);<a name="line.375"></a>
+<span class="sourceLineNo">376</span> if (nb == 1) {<a name="line.376"></a>
+<span class="sourceLineNo">377</span> return new BesselJResult(Arrays.copyOf(b, b.length),<a name="line.377"></a>
+<span class="sourceLineNo">378</span> ncalc);<a name="line.378"></a>
+<span class="sourceLineNo">379</span> }<a name="line.379"></a>
+<span class="sourceLineNo">380</span> t = vsin;<a name="line.380"></a>
+<span class="sourceLineNo">381</span> vsin = -vcos;<a name="line.381"></a>
+<span class="sourceLineNo">382</span> vcos = t;<a name="line.382"></a>
+<span class="sourceLineNo">383</span> gnu += 2.0;<a name="line.383"></a>
+<span class="sourceLineNo">384</span> }<a name="line.384"></a>
+<span class="sourceLineNo">385</span><a name="line.385"></a>
+<span class="sourceLineNo">386</span> // ---------------------------------------------------------------------<a name="line.386"></a>
+<span class="sourceLineNo">387</span> // If NB > 2, compute J(X,ORDER+I) I = 2, NB-1<a name="line.387"></a>
+<span class="sourceLineNo">388</span> // ---------------------------------------------------------------------<a name="line.388"></a>
+<span class="sourceLineNo">389</span> if (nb > 2) {<a name="line.389"></a>
+<span class="sourceLineNo">390</span> gnu = 2 * alpha + 2.0;<a name="line.390"></a>
+<span class="sourceLineNo">391</span> for (int j = 2; j < nb; ++j) {<a name="line.391"></a>
+<span class="sourceLineNo">392</span> b[j] = gnu * b[j - 1] / x - b[j - 2];<a name="line.392"></a>
+<span class="sourceLineNo">393</span> gnu += 2.0;<a name="line.393"></a>
+<span class="sourceLineNo">394</span> }<a name="line.394"></a>
+<span class="sourceLineNo">395</span> }<a name="line.395"></a>
+<span class="sourceLineNo">396</span> } else {<a name="line.396"></a>
+<span class="sourceLineNo">397</span> // ---------------------------------------------------------------------<a name="line.397"></a>
+<span class="sourceLineNo">398</span> // Use recurrence to generate results. First initialize the<a name="line.398"></a>
+<span class="sourceLineNo">399</span> // calculation of P*S.<a name="line.399"></a>
+<span class="sourceLineNo">400</span> // ---------------------------------------------------------------------<a name="line.400"></a>
+<span class="sourceLineNo">401</span> final int nbmx = nb - magx;<a name="line.401"></a>
+<span class="sourceLineNo">402</span> int n = magx + 1;<a name="line.402"></a>
+<span class="sourceLineNo">403</span> int nstart = 0;<a name="line.403"></a>
+<span class="sourceLineNo">404</span> int nend = 0;<a name="line.404"></a>
+<span class="sourceLineNo">405</span> double en = 2 * (n + alpha);<a name="line.405"></a>
+<span class="sourceLineNo">406</span> double plast = 1;<a name="line.406"></a>
+<span class="sourceLineNo">407</span> double p = en / x;<a name="line.407"></a>
+<span class="sourceLineNo">408</span> double pold;<a name="line.408"></a>
+<span class="sourceLineNo">409</span> // ---------------------------------------------------------------------<a name="line.409"></a>
+<span class="sourceLineNo">410</span> // Calculate general significance test.<a name="line.410"></a>
+<span class="sourceLineNo">411</span> // ---------------------------------------------------------------------<a name="line.411"></a>
+<span class="sourceLineNo">412</span> double test = 2 * ENSIG;<a name="line.412"></a>
+<span class="sourceLineNo">413</span> boolean readyToInitialize = false;<a name="line.413"></a>
+<span class="sourceLineNo">414</span> if (nbmx >= 3) {<a name="line.414"></a>
+<span class="sourceLineNo">415</span> // ---------------------------------------------------------------------<a name="line.415"></a>
+<span class="sourceLineNo">416</span> // Calculate P*S until N = NB-1. Check for possible<a name="line.416"></a>
+<span class="sourceLineNo">417</span> // overflow.<a name="line.417"></a>
+<span class="sourceLineNo">418</span> // ---------------------------------------------------------------------<a name="line.418"></a>
+<span class="sourceLineNo">419</span> tover = ENTEN / ENSIG;<a name="line.419"></a>
+<span class="sourceLineNo">420</span> nstart = magx + 2;<a name="line.420"></a>
+<span class="sourceLineNo">421</span> nend = nb - 1;<a name="line.421"></a>
+<span class="sourceLineNo">422</span> en = 2 * (nstart - 1 + alpha);<a name="line.422"></a>
+<span class="sourceLineNo">423</span> double psave;<a name="line.423"></a>
+<span class="sourceLineNo">424</span> double psavel;<a name="line.424"></a>
+<span class="sourceLineNo">425</span> for (int k = nstart; k <= nend; k++) {<a name="line.425"></a>
+<span class="sourceLineNo">426</span> n = k;<a name="line.426"></a>
+<span class="sourceLineNo">427</span> en += 2.0;<a name="line.427"></a>
+<span class="sourceLineNo">428</span> pold = plast;<a name="line.428"></a>
+<span class="sourceLineNo">429</span> plast = p;<a name="line.429"></a>
+<span class="sourceLineNo">430</span> p = (en * plast / x) - pold;<a name="line.430"></a>
+<span class="sourceLineNo">431</span> if (p > tover) {<a name="line.431"></a>
+<span class="sourceLineNo">432</span> // ---------------------------------------------------------------------<a name="line.432"></a>
+<span class="sourceLineNo">433</span> // To avoid overflow, divide P*S by TOVER. Calculate<a name="line.433"></a>
+<span class="sourceLineNo">434</span> // P*S until<a name="line.434"></a>
+<span class="sourceLineNo">435</span> // ABS(P) > 1.<a name="line.435"></a>
+<span class="sourceLineNo">436</span> // ---------------------------------------------------------------------<a name="line.436"></a>
+<span class="sourceLineNo">437</span> tover = ENTEN;<a name="line.437"></a>
+<span class="sourceLineNo">438</span> p /= tover;<a name="line.438"></a>
+<span class="sourceLineNo">439</span> plast /= tover;<a name="line.439"></a>
+<span class="sourceLineNo">440</span> psave = p;<a name="line.440"></a>
+<span class="sourceLineNo">441</span> psavel = plast;<a name="line.441"></a>
+<span class="sourceLineNo">442</span> nstart = n + 1;<a name="line.442"></a>
+<span class="sourceLineNo">443</span> do {<a name="line.443"></a>
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+<span class="sourceLineNo">445</span> en += 2.0;<a name="line.445"></a>
+<span class="sourceLineNo">446</span> pold = plast;<a name="line.446"></a>
+<span class="sourceLineNo">447</span> plast = p;<a name="line.447"></a>
+<span class="sourceLineNo">448</span> p = (en * plast / x) - pold;<a name="line.448"></a>
+<span class="sourceLineNo">449</span> } while (p <= 1);<a name="line.449"></a>
+<span class="sourceLineNo">450</span> tempb = en / x;<a name="line.450"></a>
+<span class="sourceLineNo">451</span> // ---------------------------------------------------------------------<a name="line.451"></a>
+<span class="sourceLineNo">452</span> // Calculate backward test and find NCALC, the<a name="line.452"></a>
+<span class="sourceLineNo">453</span> // highest N such that<a name="line.453"></a>
+<span class="sourceLineNo">454</span> // the test is passed.<a name="line.454"></a>
+<span class="sourceLineNo">455</span> // ---------------------------------------------------------------------<a name="line.455"></a>
+<span class="sourceLineNo">456</span> test = pold * plast * (0.5 - 0.5 / (tempb * tempb));<a name="line.456"></a>
+<span class="sourceLineNo">457</span> test /= ENSIG;<a name="line.457"></a>
+<span class="sourceLineNo">458</span> p = plast * tover;<a name="line.458"></a>
+<span class="sourceLineNo">459</span> n -= 1;<a name="line.459"></a>
+<span class="sourceLineNo">460</span> en -= 2.0;<a name="line.460"></a>
+<span class="sourceLineNo">461</span> nend = FastMath.min(nb, n);<a name="line.461"></a>
+<span class="sourceLineNo">462</span> for (int l = nstart; l <= nend; l++) {<a name="line.462"></a>
+<span class="sourceLineNo">463</span> pold = psavel;<a name="line.463"></a>
+<span class="sourceLineNo">464</span> psavel = psave;<a name="line.464"></a>
+<span class="sourceLineNo">465</span> psave = (en * psavel / x) - pold;<a name="line.465"></a>
+<span class="sourceLineNo">466</span> if (psave * psavel > test) {<a name="line.466"></a>
+<span class="sourceLineNo">467</span> ncalc = l - 1;<a name="line.467"></a>
+<span class="sourceLineNo">468</span> readyToInitialize = true;<a name="line.468"></a>
+<span class="sourceLineNo">469</span> break;<a name="line.469"></a>
+<span class="sourceLineNo">470</span> }<a name="line.470"></a>
+<span class="sourceLineNo">471</span> }<a name="line.471"></a>
+<span class="sourceLineNo">472</span> ncalc = nend;<a name="line.472"></a>
+<span class="sourceLineNo">473</span> readyToInitialize = true;<a name="line.473"></a>
+<span class="sourceLineNo">474</span> break;<a name="line.474"></a>
+<span class="sourceLineNo">475</span> }<a name="line.475"></a>
+<span class="sourceLineNo">476</span> }<a name="line.476"></a>
+<span class="sourceLineNo">477</span> if (!readyToInitialize) {<a name="line.477"></a>
+<span class="sourceLineNo">478</span> n = nend;<a name="line.478"></a>
+<span class="sourceLineNo">479</span> en = 2 * (n + alpha);<a name="line.479"></a>
+<span class="sourceLineNo">480</span> // ---------------------------------------------------------------------<a name="line.480"></a>
+<span class="sourceLineNo">481</span> // Calculate special significance test for NBMX > 2.<a name="line.481"></a>
+<span class="sourceLineNo">482</span> // ---------------------------------------------------------------------<a name="line.482"></a>
+<span class="sourceLineNo">483</span> test = FastMath.max(test, FastMath.sqrt(plast * ENSIG) *<a name="line.483"></a>
+<span class="sourceLineNo">484</span> FastMath.sqrt(2 * p));<a name="line.484"></a>
+<span class="sourceLineNo">485</span> }<a name="line.485"></a>
+<span class="sourceLineNo">486</span> }<a name="line.486"></a>
+<span class="sourceLineNo">487</span> // ---------------------------------------------------------------------<a name="line.487"></a>
+<span class="sourceLineNo">488</span> // Calculate P*S until significance test passes.<a name="line.488"></a>
+<span class="sourceLineNo">489</span> // ---------------------------------------------------------------------<a name="line.489"></a>
+<span class="sourceLineNo">490</span> if (!readyToInitialize) {<a name="line.490"></a>
+<span class="sourceLineNo">491</span> do {<a name="line.491"></a>
+<span class="sourceLineNo">492</span> n += 1;<a name="line.492"></a>
+<span class="sourceLineNo">493</span> en += 2.0;<a name="line.493"></a>
+<span class="sourceLineNo">494</span> pold = plast;<a name="line.494"></a>
+<span class="sourceLineNo">495</span> plast = p;<a name="line.495"></a>
+<span class="sourceLineNo">496</span> p = (en * plast / x) - pold;<a name="line.496"></a>
+<span class="sourceLineNo">497</span> } while (p < test);<a name="line.497"></a>
+<span class="sourceLineNo">498</span> }<a name="line.498"></a>
+<span class="sourceLineNo">499</span> // ---------------------------------------------------------------------<a name="line.499"></a>
+<span class="sourceLineNo">500</span> // Initialize the backward recursion and the normalization sum.<a name="line.500"></a>
+<span class="sourceLineNo">501</span> // ---------------------------------------------------------------------<a name="line.501"></a>
+<span class="sourceLineNo">502</span> n += 1;<a name="line.502"></a>
+<span class="sourceLineNo">503</span> en += 2.0;<a name="line.503"></a>
+<span class="sourceLineNo">504</span> tempb = 0;<a name="line.504"></a>
+<span class="sourceLineNo">505</span> tempa = 1 / p;<a name="line.505"></a>
+<span class="sourceLineNo">506</span> int m = (2 * n) - 4 * (n / 2);<a name="line.506"></a>
+<span class="sourceLineNo">507</span> double sum = 0;<a name="line.507"></a>
+<span class="sourceLineNo">508</span> double em = (double) (n / 2);<a name="line.508"></a>
+<span class="sourceLineNo">509</span> alpem = em - 1 + alpha;<a name="line.509"></a>
+<span class="sourceLineNo">510</span> alp2em = 2 * em + alpha;<a name="line.510"></a>
+<span class="sourceLineNo">511</span> if (m != 0) {<a name="line.511"></a>
+<span class="sourceLineNo">512</span> sum = tempa * alpem * alp2em / em;<a name="line.512"></a>
+<span class="sourceLineNo">513</span> }<a name="line.513"></a>
+<span class="sourceLineNo">514</span> nend = n - nb;<a name="line.514"></a>
+<span class="sourceLineNo">515</span><a name="line.515"></a>
+<span class="sourceLineNo">516</span> boolean readyToNormalize = false;<a name="line.516"></a>
+<span class="sourceLineNo">517</span> boolean calculatedB0 = false;<a name="line.517"></a>
+<span class="sourceLineNo">518</span><a name="line.518"></a>
+<span class="sourceLineNo">519</span> // ---------------------------------------------------------------------<a name="line.519"></a>
+<span class="sourceLineNo">520</span> // Recur backward via difference equation, calculating (but not<a name="line.520"></a>
+<span class="sourceLineNo">521</span> // storing) B(N), until N = NB.<a name="line.521"></a>
+<span class="sourceLineNo">522</span> // ---------------------------------------------------------------------<a name="line.522"></a>
+<span class="sourceLineNo">523</span> for (int l = 1; l <= nend; l++) {<a name="line.523"></a>
+<span class="sourceLineNo">524</span> n -= 1;<a name="line.524"></a>
+<span class="sourceLineNo">525</span> en -= 2.0;<a name="line.525"></a>
+<span class="sourceLineNo">526</span> tempc = tempb;<a name="line.526"></a>
+<span class="sourceLineNo">527</span> tempb = tempa;<a name="line.527"></a>
+<span class="sourceLineNo">528</span> tempa = (en * tempb / x) - tempc;<a name="line.528"></a>
+<span class="sourceLineNo">529</span> m = 2 - m;<a name="line.529"></a>
+<span class="sourceLineNo">530</span> if (m != 0) {<a name="line.530"></a>
+<span class="sourceLineNo">531</span> em -= 1;<a name="line.531"></a>
+<span class="sourceLineNo">532</span> alp2em = 2 * em + alpha;<a name="line.532"></a>
+<span class="sourceLineNo">533</span> if (n == 1) {<a name="line.533"></a>
+<span class="sourceLineNo">534</span> break;<a name="line.534"></a>
+<span class="sourceLineNo">535</span> }<a name="line.535"></a>
+<span class="sourceLineNo">536</span> alpem = em - 1 + alpha;<a name="line.536"></a>
+<span class="sourceLineNo">537</span> if (alpem == 0) {<a name="line.537"></a>
+<span class="sourceLineNo">538</span> alpem = 1;<a name="line.538"></a>
+<span class="sourceLineNo">539</span> }<a name="line.539"></a>
+<span class="sourceLineNo">540</span> sum = (sum + tempa * alp2em) * alpem / em;<a name="line.540"></a>
+<span class="sourceLineNo">541</span> }<a name="line.541"></a>
+<span class="sourceLineNo">542</span> }<a name="line.542"></a>
+<span class="sourceLineNo">543</span><a name="line.543"></a>
+<span class="sourceLineNo">544</span> // ---------------------------------------------------------------------<a name="line.544"></a>
+<span class="sourceLineNo">545</span> // Store B(NB).<a name="line.545"></a>
+<span class="sourceLineNo">546</span> // ---------------------------------------------------------------------<a name="line.546"></a>
+<span class="sourceLineNo">547</span> b[n - 1] = tempa;<a name="line.547"></a>
+<span class="sourceLineNo">548</span> if (nend >= 0) {<a name="line.548"></a>
+<span class="sourceLineNo">549</span> if (nb <= 1) {<a name="line.549"></a>
+<span class="sourceLineNo">550</span> alp2em = alpha;<a name="line.550"></a>
+<span class="sourceLineNo">551</span> if (alpha + 1 == 1) {<a name="line.551"></a>
+<span class="sourceLineNo">552</span> alp2em = 1;<a name="line.552"></a>
+<span class="sourceLineNo">553</span> }<a name="line.553"></a>
+<span class="sourceLineNo">554</span> sum += b[0] * alp2em;<a name="line.554"></a>
+<span class="sourceLineNo">555</span> readyToNormalize = true;<a name="line.555"></a>
+<span class="sourceLineNo">556</span> } else {<a name="line.556"></a>
+<span class="sourceLineNo">557</span> // ---------------------------------------------------------------------<a name="line.557"></a>
+<span class="sourceLineNo">558</span> // Calculate and store B(NB-1).<a name="line.558"></a>
+<span class="sourceLineNo">559</span> // ---------------------------------------------------------------------<a name="line.559"></a>
+<span class="sourceLineNo">560</span> n -= 1;<a name="line.560"></a>
+<span class="sourceLineNo">561</span> en -= 2.0;<a name="line.561"></a>
+<span class="sourceLineNo">562</span> b[n - 1] = (en * tempa / x) - tempb;<a name="line.562"></a>
+<span class="sourceLineNo">563</span> if (n == 1) {<a name="line.563"></a>
+<span class="sourceLineNo">564</span> calculatedB0 = true;<a name="line.564"></a>
+<span class="sourceLineNo">565</span> } else {<a name="line.565"></a>
+<span class="sourceLineNo">566</span> m = 2 - m;<a name="line.566"></a>
+<span class="sourceLineNo">567</span> if (m != 0) {<a name="line.567"></a>
+<span class="sourceLineNo">568</span> em -= 1;<a name="line.568"></a>
+<span class="sourceLineNo">569</span> alp2em = 2 * em + alpha;<a name="line.569"></a>
+<span class="sourceLineNo">570</span> alpem = em - 1 + alpha;<a name="line.570"></a>
+<span class="sourceLineNo">571</span> if (alpem == 0) {<a name="line.571"></a>
+<span class="sourceLineNo">572</span> alpem = 1;<a name="line.572"></a>
+<span class="sourceLineNo">573</span> }<a name="line.573"></a>
+<span class="sourceLineNo">574</span><a name="line.574"></a>
+<span class="sourceLineNo">575</span> sum = (sum + (b[n - 1] * alp2em)) * alpem / em;<a name="line.575"></a>
+<span class="sourceLineNo">576</span> }<a name="line.576"></a>
+<span class="sourceLineNo">577</span> }<a name="line.577"></a>
+<span class="sourceLineNo">578</span> }<a name="line.578"></a>
+<span class="sourceLineNo">579</span> }<a name="line.579"></a>
+<span class="sourceLineNo">580</span> if (!readyToNormalize && !calculatedB0) {<a name="line.580"></a>
+<span class="sourceLineNo">581</span> nend = n - 2;<a name="line.581"></a>
+<span class="sourceLineNo">582</span> if (nend != 0) {<a name="line.582"></a>
+<span class="sourceLineNo">583</span> // ---------------------------------------------------------------------<a name="line.583"></a>
+<span class="sourceLineNo">584</span> // Calculate via difference equation and store B(N),<a name="line.584"></a>
+<span class="sourceLineNo">585</span> // until N = 2.<a name="line.585"></a>
+<span class="sourceLineNo">586</span> // ---------------------------------------------------------------------<a name="line.586"></a>
+<span class="sourceLineNo">587</span><a name="line.587"></a>
+<span class="sourceLineNo">588</span> for (int l = 1; l <= nend; l++) {<a name="line.588"></a>
+<span class="sourceLineNo">589</span> n -= 1;<a name="line.589"></a>
+<span class="sourceLineNo">590</span> en -= 2.0;<a name="line.590"></a>
+<span class="sourceLineNo">591</span> b[n - 1] = (en * b[n] / x) - b[n + 1];<a name="line.591"></a>
+<span class="sourceLineNo">592</span> m = 2 - m;<a name="line.592"></a>
+<span class="sourceLineNo">593</span> if (m != 0) {<a name="line.593"></a>
+<span class="sourceLineNo">594</span> em -= 1;<a name="line.594"></a>
+<span class="sourceLineNo">595</span> alp2em = 2 * em + alpha;<a name="line.595"></a>
+<span class="sourceLineNo">596</span> alpem = em - 1 + alpha;<a name="line.596"></a>
+<span class="sourceLineNo">597</span> if (alpem == 0) {<a name="line.597"></a>
+<span class="sourceLineNo">598</span> alpem = 1;<a name="line.598"></a>
+<span class="sourceLineNo">599</span> }<a name="line.599"></a>
+<span class="sourceLineNo">600</span><a name="line.600"></a>
+<span class="sourceLineNo">601</span> sum = (sum + b[n - 1] * alp2em) * alpem / em;<a name="line.601"></a>
+<span class="sourceLineNo">602</span> }<a name="line.602"></a>
+<span class="sourceLineNo">603</span> }<a name="line.603"></a>
+<span class="sourceLineNo">604</span> }<a name="line.604"></a>
+<span class="sourceLineNo">605</span> }<a name="line.605"></a>
+<span class="sourceLineNo">606</span> // ---------------------------------------------------------------------<a name="line.606"></a>
+<span class="sourceLineNo">607</span> // Calculate b[0]<a name="line.607"></a>
+<span class="sourceLineNo">608</span> // ---------------------------------------------------------------------<a name="line.608"></a>
+<span class="sourceLineNo">609</span> if (!readyToNormalize) {<a name="line.609"></a>
+<span class="sourceLineNo">610</span> if (!calculatedB0) {<a name="line.610"></a>
+<span class="sourceLineNo">611</span> b[0] = 2.0 * (alpha + 1) * b[1] / x - b[2];<a name="line.611"></a>
+<span class="sourceLineNo">612</span> }<a name="line.612"></a>
+<span class="sourceLineNo">613</span> em -= 1;<a name="line.613"></a>
+<span class="sourceLineNo">614</span> alp2em = 2 * em + alpha;<a name="line.614"></a>
+<span class="sourceLineNo">615</span> if (alp2em == 0) {<a name="line.615"></a>
+<span class="sourceLineNo">616</span> alp2em = 1;<a name="line.616"></a>
+<span class="sourceLineNo">617</span> }<a name="line.617"></a>
+<span class="sourceLineNo">618</span> sum += b[0] * alp2em;<a name="line.618"></a>
+<span class="sourceLineNo">619</span> }<a name="line.619"></a>
+<span class="sourceLineNo">620</span> // ---------------------------------------------------------------------<a name="line.620"></a>
+<span class="sourceLineNo">621</span> // Normalize. Divide all B(N) by sum.<a name="line.621"></a>
+<span class="sourceLineNo">622</span> // ---------------------------------------------------------------------<a name="line.622"></a>
+<span class="sourceLineNo">623</span><a name="line.623"></a>
+<span class="sourceLineNo">624</span> if (FastMath.abs(alpha) > 1e-16) {<a name="line.624"></a>
+<span class="sourceLineNo">625</span> sum *= Gamma.gamma(alpha) * FastMath.pow(x * 0.5, -alpha);<a name="line.625"></a>
+<span class="sourceLineNo">626</span> }<a name="line.626"></a>
+<span class="sourceLineNo">627</span> tempa = ENMTEN;<a name="line.627"></a>
+<span class="sourceLineNo">628</span> if (sum > 1) {<a name="line.628"></a>
+<span class="sourceLineNo">629</span> tempa *= sum;<a name="line.629"></a>
+<span class="sourceLineNo">630</span> }<a name="line.630"></a>
+<span class="sourceLineNo">631</span><a name="line.631"></a>
+<span class="sourceLineNo">632</span> for (n = 0; n < nb; n++) {<a name="line.632"></a>
+<span class="sourceLineNo">633</span> if (FastMath.abs(b[n]) < tempa) {<a name="line.633"></a>
+<span class="sourceLineNo">634</span> b[n] = 0;<a name="line.634"></a>
+<span class="sourceLineNo">635</span> }<a name="line.635"></a>
+<span class="sourceLineNo">636</span> b[n] /= sum;<a name="line.636"></a>
+<span class="sourceLineNo">637</span> }<a name="line.637"></a>
+<span class="sourceLineNo">638</span> }<a name="line.638"></a>
+<span class="sourceLineNo">639</span> // ---------------------------------------------------------------------<a name="line.639"></a>
+<span class="sourceLineNo">640</span> // Error return -- X, NB, or ALPHA is out of range.<a name="line.640"></a>
+<span class="sourceLineNo">641</span> // ---------------------------------------------------------------------<a name="line.641"></a>
+<span class="sourceLineNo">642</span> } else {<a name="line.642"></a>
+<span class="sourceLineNo">643</span> if (b.length > 0) {<a name="line.643"></a>
+<span class="sourceLineNo">644</span> b[0] = 0;<a name="line.644"></a>
+<span class="sourceLineNo">645</span> }<a name="line.645"></a>
+<span class="sourceLineNo">646</span> ncalc = FastMath.min(nb, 0) - 1;<a name="line.646"></a>
+<span class="sourceLineNo">647</span> }<a name="line.647"></a>
+<span class="sourceLineNo">648</span> return new BesselJResult(Arrays.copyOf(b, b.length), ncalc);<a name="line.648"></a>
+<span class="sourceLineNo">649</span> }<a name="line.649"></a>
+<span class="sourceLineNo">650</span>}<a name="line.650"></a>
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+</pre>
+</div>
+</body>
+</html>
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