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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.analysis.solvers;<a name="line.17"></a> <FONT color="green">018</FONT> <a name="line.18"></a> <FONT color="green">019</FONT> <a name="line.19"></a> <FONT color="green">020</FONT> import org.apache.commons.math.FunctionEvaluationException;<a name="line.20"></a> <FONT color="green">021</FONT> import org.apache.commons.math.MathRuntimeException;<a name="line.21"></a> <FONT color="green">022</FONT> import org.apache.commons.math.MaxIterationsExceededException;<a name="line.22"></a> <FONT color="green">023</FONT> import org.apache.commons.math.analysis.UnivariateRealFunction;<a name="line.23"></a> <FONT color="green">024</FONT> <a name="line.24"></a> <FONT color="green">025</FONT> /**<a name="line.25"></a> <FONT color="green">026</FONT> * Implements the <a href="http://mathworld.wolfram.com/BrentsMethod.html"><a name="line.26"></a> <FONT color="green">027</FONT> * Brent algorithm</a> for finding zeros of real univariate functions.<a name="line.27"></a> <FONT color="green">028</FONT> * <p><a name="line.28"></a> <FONT color="green">029</FONT> * The function should be continuous but not necessarily smooth.</p><a name="line.29"></a> <FONT color="green">030</FONT> *<a name="line.30"></a> <FONT color="green">031</FONT> * @version $Revision:670469 $ $Date:2008-06-23 10:01:38 +0200 (lun., 23 juin 2008) $<a name="line.31"></a> <FONT color="green">032</FONT> */<a name="line.32"></a> <FONT color="green">033</FONT> public class BrentSolver extends UnivariateRealSolverImpl {<a name="line.33"></a> <FONT color="green">034</FONT> <a name="line.34"></a> <FONT color="green">035</FONT> /**<a name="line.35"></a> <FONT color="green">036</FONT> * Default absolute accuracy<a name="line.36"></a> <FONT color="green">037</FONT> * @since 2.1<a name="line.37"></a> <FONT color="green">038</FONT> */<a name="line.38"></a> <FONT color="green">039</FONT> public static final double DEFAULT_ABSOLUTE_ACCURACY = 1E-6;<a name="line.39"></a> <FONT color="green">040</FONT> <a name="line.40"></a> <FONT color="green">041</FONT> /** Default maximum number of iterations<a name="line.41"></a> <FONT color="green">042</FONT> * @since 2.1<a name="line.42"></a> <FONT color="green">043</FONT> */<a name="line.43"></a> <FONT color="green">044</FONT> public static final int DEFAULT_MAXIMUM_ITERATIONS = 100;<a name="line.44"></a> <FONT color="green">045</FONT> <a name="line.45"></a> <FONT color="green">046</FONT> /** Error message for non-bracketing interval. */<a name="line.46"></a> <FONT color="green">047</FONT> private static final String NON_BRACKETING_MESSAGE =<a name="line.47"></a> <FONT color="green">048</FONT> "function values at endpoints do not have different signs. " +<a name="line.48"></a> <FONT color="green">049</FONT> "Endpoints: [{0}, {1}], Values: [{2}, {3}]";<a name="line.49"></a> <FONT color="green">050</FONT> <a name="line.50"></a> <FONT color="green">051</FONT> /** Serializable version identifier */<a name="line.51"></a> <FONT color="green">052</FONT> private static final long serialVersionUID = 7694577816772532779L;<a name="line.52"></a> <FONT color="green">053</FONT> <a name="line.53"></a> <FONT color="green">054</FONT> /**<a name="line.54"></a> <FONT color="green">055</FONT> * Construct a solver for the given function.<a name="line.55"></a> <FONT color="green">056</FONT> *<a name="line.56"></a> <FONT color="green">057</FONT> * @param f function to solve.<a name="line.57"></a> <FONT color="green">058</FONT> * @deprecated as of 2.0 the function to solve is passed as an argument<a name="line.58"></a> <FONT color="green">059</FONT> * to the {@link #solve(UnivariateRealFunction, double, double)} or<a name="line.59"></a> <FONT color="green">060</FONT> * {@link UnivariateRealSolverImpl#solve(UnivariateRealFunction, double, double, double)}<a name="line.60"></a> <FONT color="green">061</FONT> * method.<a name="line.61"></a> <FONT color="green">062</FONT> */<a name="line.62"></a> <FONT color="green">063</FONT> @Deprecated<a name="line.63"></a> <FONT color="green">064</FONT> public BrentSolver(UnivariateRealFunction f) {<a name="line.64"></a> <FONT color="green">065</FONT> super(f, DEFAULT_MAXIMUM_ITERATIONS, DEFAULT_ABSOLUTE_ACCURACY);<a name="line.65"></a> <FONT color="green">066</FONT> }<a name="line.66"></a> <FONT color="green">067</FONT> <a name="line.67"></a> <FONT color="green">068</FONT> /**<a name="line.68"></a> <FONT color="green">069</FONT> * Construct a solver with default properties.<a name="line.69"></a> <FONT color="green">070</FONT> */<a name="line.70"></a> <FONT color="green">071</FONT> public BrentSolver() {<a name="line.71"></a> <FONT color="green">072</FONT> super(DEFAULT_MAXIMUM_ITERATIONS, DEFAULT_ABSOLUTE_ACCURACY);<a name="line.72"></a> <FONT color="green">073</FONT> }<a name="line.73"></a> <FONT color="green">074</FONT> <a name="line.74"></a> <FONT color="green">075</FONT> /**<a name="line.75"></a> <FONT color="green">076</FONT> * Construct a solver with the given absolute accuracy.<a name="line.76"></a> <FONT color="green">077</FONT> *<a name="line.77"></a> <FONT color="green">078</FONT> * @param absoluteAccuracy lower bound for absolute accuracy of solutions returned by the solver<a name="line.78"></a> <FONT color="green">079</FONT> * @since 2.1<a name="line.79"></a> <FONT color="green">080</FONT> */<a name="line.80"></a> <FONT color="green">081</FONT> public BrentSolver(double absoluteAccuracy) {<a name="line.81"></a> <FONT color="green">082</FONT> super(DEFAULT_MAXIMUM_ITERATIONS, absoluteAccuracy);<a name="line.82"></a> <FONT color="green">083</FONT> }<a name="line.83"></a> <FONT color="green">084</FONT> <a name="line.84"></a> <FONT color="green">085</FONT> /**<a name="line.85"></a> <FONT color="green">086</FONT> * Contstruct a solver with the given maximum iterations and absolute accuracy.<a name="line.86"></a> <FONT color="green">087</FONT> *<a name="line.87"></a> <FONT color="green">088</FONT> * @param maximumIterations maximum number of iterations<a name="line.88"></a> <FONT color="green">089</FONT> * @param absoluteAccuracy lower bound for absolute accuracy of solutions returned by the solver<a name="line.89"></a> <FONT color="green">090</FONT> * @since 2.1<a name="line.90"></a> <FONT color="green">091</FONT> */<a name="line.91"></a> <FONT color="green">092</FONT> public BrentSolver(int maximumIterations, double absoluteAccuracy) {<a name="line.92"></a> <FONT color="green">093</FONT> super(maximumIterations, absoluteAccuracy);<a name="line.93"></a> <FONT color="green">094</FONT> }<a name="line.94"></a> <FONT color="green">095</FONT> <a name="line.95"></a> <FONT color="green">096</FONT> /** {@inheritDoc} */<a name="line.96"></a> <FONT color="green">097</FONT> @Deprecated<a name="line.97"></a> <FONT color="green">098</FONT> public double solve(double min, double max)<a name="line.98"></a> <FONT color="green">099</FONT> throws MaxIterationsExceededException, FunctionEvaluationException {<a name="line.99"></a> <FONT color="green">100</FONT> return solve(f, min, max);<a name="line.100"></a> <FONT color="green">101</FONT> }<a name="line.101"></a> <FONT color="green">102</FONT> <a name="line.102"></a> <FONT color="green">103</FONT> /** {@inheritDoc} */<a name="line.103"></a> <FONT color="green">104</FONT> @Deprecated<a name="line.104"></a> <FONT color="green">105</FONT> public double solve(double min, double max, double initial)<a name="line.105"></a> <FONT color="green">106</FONT> throws MaxIterationsExceededException, FunctionEvaluationException {<a name="line.106"></a> <FONT color="green">107</FONT> return solve(f, min, max, initial);<a name="line.107"></a> <FONT color="green">108</FONT> }<a name="line.108"></a> <FONT color="green">109</FONT> <a name="line.109"></a> <FONT color="green">110</FONT> /**<a name="line.110"></a> <FONT color="green">111</FONT> * Find a zero in the given interval with an initial guess.<a name="line.111"></a> <FONT color="green">112</FONT> * <p>Throws <code>IllegalArgumentException</code> if the values of the<a name="line.112"></a> <FONT color="green">113</FONT> * function at the three points have the same sign (note that it is<a name="line.113"></a> <FONT color="green">114</FONT> * allowed to have endpoints with the same sign if the initial point has<a name="line.114"></a> <FONT color="green">115</FONT> * opposite sign function-wise).</p><a name="line.115"></a> <FONT color="green">116</FONT> *<a name="line.116"></a> <FONT color="green">117</FONT> * @param f function to solve.<a name="line.117"></a> <FONT color="green">118</FONT> * @param min the lower bound for the interval.<a name="line.118"></a> <FONT color="green">119</FONT> * @param max the upper bound for the interval.<a name="line.119"></a> <FONT color="green">120</FONT> * @param initial the start value to use (must be set to min if no<a name="line.120"></a> <FONT color="green">121</FONT> * initial point is known).<a name="line.121"></a> <FONT color="green">122</FONT> * @return the value where the function is zero<a name="line.122"></a> <FONT color="green">123</FONT> * @throws MaxIterationsExceededException the maximum iteration count<a name="line.123"></a> <FONT color="green">124</FONT> * is exceeded<a name="line.124"></a> <FONT color="green">125</FONT> * @throws FunctionEvaluationException if an error occurs evaluating<a name="line.125"></a> <FONT color="green">126</FONT> * the function<a name="line.126"></a> <FONT color="green">127</FONT> * @throws IllegalArgumentException if initial is not between min and max<a name="line.127"></a> <FONT color="green">128</FONT> * (even if it <em>is</em> a root)<a name="line.128"></a> <FONT color="green">129</FONT> */<a name="line.129"></a> <FONT color="green">130</FONT> public double solve(final UnivariateRealFunction f,<a name="line.130"></a> <FONT color="green">131</FONT> final double min, final double max, final double initial)<a name="line.131"></a> <FONT color="green">132</FONT> throws MaxIterationsExceededException, FunctionEvaluationException {<a name="line.132"></a> <FONT color="green">133</FONT> <a name="line.133"></a> <FONT color="green">134</FONT> clearResult();<a name="line.134"></a> <FONT color="green">135</FONT> if ((initial < min) || (initial > max)) {<a name="line.135"></a> <FONT color="green">136</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.136"></a> <FONT color="green">137</FONT> "invalid interval, initial value parameters: lower={0}, initial={1}, upper={2}",<a name="line.137"></a> <FONT color="green">138</FONT> min, initial, max);<a name="line.138"></a> <FONT color="green">139</FONT> }<a name="line.139"></a> <FONT color="green">140</FONT> <a name="line.140"></a> <FONT color="green">141</FONT> // return the initial guess if it is good enough<a name="line.141"></a> <FONT color="green">142</FONT> double yInitial = f.value(initial);<a name="line.142"></a> <FONT color="green">143</FONT> if (Math.abs(yInitial) <= functionValueAccuracy) {<a name="line.143"></a> <FONT color="green">144</FONT> setResult(initial, 0);<a name="line.144"></a> <FONT color="green">145</FONT> return result;<a name="line.145"></a> <FONT color="green">146</FONT> }<a name="line.146"></a> <FONT color="green">147</FONT> <a name="line.147"></a> <FONT color="green">148</FONT> // return the first endpoint if it is good enough<a name="line.148"></a> <FONT color="green">149</FONT> double yMin = f.value(min);<a name="line.149"></a> <FONT color="green">150</FONT> if (Math.abs(yMin) <= functionValueAccuracy) {<a name="line.150"></a> <FONT color="green">151</FONT> setResult(min, 0);<a name="line.151"></a> <FONT color="green">152</FONT> return result;<a name="line.152"></a> <FONT color="green">153</FONT> }<a name="line.153"></a> <FONT color="green">154</FONT> <a name="line.154"></a> <FONT color="green">155</FONT> // reduce interval if min and initial bracket the root<a name="line.155"></a> <FONT color="green">156</FONT> if (yInitial * yMin < 0) {<a name="line.156"></a> <FONT color="green">157</FONT> return solve(f, min, yMin, initial, yInitial, min, yMin);<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> // return the second endpoint if it is good enough<a name="line.160"></a> <FONT color="green">161</FONT> double yMax = f.value(max);<a name="line.161"></a> <FONT color="green">162</FONT> if (Math.abs(yMax) <= functionValueAccuracy) {<a name="line.162"></a> <FONT color="green">163</FONT> setResult(max, 0);<a name="line.163"></a> <FONT color="green">164</FONT> return result;<a name="line.164"></a> <FONT color="green">165</FONT> }<a name="line.165"></a> <FONT color="green">166</FONT> <a name="line.166"></a> <FONT color="green">167</FONT> // reduce interval if initial and max bracket the root<a name="line.167"></a> <FONT color="green">168</FONT> if (yInitial * yMax < 0) {<a name="line.168"></a> <FONT color="green">169</FONT> return solve(f, initial, yInitial, max, yMax, initial, yInitial);<a name="line.169"></a> <FONT color="green">170</FONT> }<a name="line.170"></a> <FONT color="green">171</FONT> <a name="line.171"></a> <FONT color="green">172</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.172"></a> <FONT color="green">173</FONT> NON_BRACKETING_MESSAGE, min, max, yMin, yMax);<a name="line.173"></a> <FONT color="green">174</FONT> <a name="line.174"></a> <FONT color="green">175</FONT> }<a name="line.175"></a> <FONT color="green">176</FONT> <a name="line.176"></a> <FONT color="green">177</FONT> /**<a name="line.177"></a> <FONT color="green">178</FONT> * Find a zero in the given interval.<a name="line.178"></a> <FONT color="green">179</FONT> * <p><a name="line.179"></a> <FONT color="green">180</FONT> * Requires that the values of the function at the endpoints have opposite<a name="line.180"></a> <FONT color="green">181</FONT> * signs. An <code>IllegalArgumentException</code> is thrown if this is not<a name="line.181"></a> <FONT color="green">182</FONT> * the case.</p><a name="line.182"></a> <FONT color="green">183</FONT> *<a name="line.183"></a> <FONT color="green">184</FONT> * @param f the function to solve<a name="line.184"></a> <FONT color="green">185</FONT> * @param min the lower bound for the interval.<a name="line.185"></a> <FONT color="green">186</FONT> * @param max the upper bound for the interval.<a name="line.186"></a> <FONT color="green">187</FONT> * @return the value where the function is zero<a name="line.187"></a> <FONT color="green">188</FONT> * @throws MaxIterationsExceededException if the maximum iteration count is exceeded<a name="line.188"></a> <FONT color="green">189</FONT> * @throws FunctionEvaluationException if an error occurs evaluating the<a name="line.189"></a> <FONT color="green">190</FONT> * function<a name="line.190"></a> <FONT color="green">191</FONT> * @throws IllegalArgumentException if min is not less than max or the<a name="line.191"></a> <FONT color="green">192</FONT> * signs of the values of the function at the endpoints are not opposites<a name="line.192"></a> <FONT color="green">193</FONT> */<a name="line.193"></a> <FONT color="green">194</FONT> public double solve(final UnivariateRealFunction f,<a name="line.194"></a> <FONT color="green">195</FONT> final double min, final double max)<a name="line.195"></a> <FONT color="green">196</FONT> throws MaxIterationsExceededException,<a name="line.196"></a> <FONT color="green">197</FONT> FunctionEvaluationException {<a name="line.197"></a> <FONT color="green">198</FONT> <a name="line.198"></a> <FONT color="green">199</FONT> clearResult();<a name="line.199"></a> <FONT color="green">200</FONT> verifyInterval(min, max);<a name="line.200"></a> <FONT color="green">201</FONT> <a name="line.201"></a> <FONT color="green">202</FONT> double ret = Double.NaN;<a name="line.202"></a> <FONT color="green">203</FONT> <a name="line.203"></a> <FONT color="green">204</FONT> double yMin = f.value(min);<a name="line.204"></a> <FONT color="green">205</FONT> double yMax = f.value(max);<a name="line.205"></a> <FONT color="green">206</FONT> <a name="line.206"></a> <FONT color="green">207</FONT> // Verify bracketing<a name="line.207"></a> <FONT color="green">208</FONT> double sign = yMin * yMax;<a name="line.208"></a> <FONT color="green">209</FONT> if (sign > 0) {<a name="line.209"></a> <FONT color="green">210</FONT> // check if either value is close to a zero<a name="line.210"></a> <FONT color="green">211</FONT> if (Math.abs(yMin) <= functionValueAccuracy) {<a name="line.211"></a> <FONT color="green">212</FONT> setResult(min, 0);<a name="line.212"></a> <FONT color="green">213</FONT> ret = min;<a name="line.213"></a> <FONT color="green">214</FONT> } else if (Math.abs(yMax) <= functionValueAccuracy) {<a name="line.214"></a> <FONT color="green">215</FONT> setResult(max, 0);<a name="line.215"></a> <FONT color="green">216</FONT> ret = max;<a name="line.216"></a> <FONT color="green">217</FONT> } else {<a name="line.217"></a> <FONT color="green">218</FONT> // neither value is close to zero and min and max do not bracket root.<a name="line.218"></a> <FONT color="green">219</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.219"></a> <FONT color="green">220</FONT> NON_BRACKETING_MESSAGE, min, max, yMin, yMax);<a name="line.220"></a> <FONT color="green">221</FONT> }<a name="line.221"></a> <FONT color="green">222</FONT> } else if (sign < 0){<a name="line.222"></a> <FONT color="green">223</FONT> // solve using only the first endpoint as initial guess<a name="line.223"></a> <FONT color="green">224</FONT> ret = solve(f, min, yMin, max, yMax, min, yMin);<a name="line.224"></a> <FONT color="green">225</FONT> } else {<a name="line.225"></a> <FONT color="green">226</FONT> // either min or max is a root<a name="line.226"></a> <FONT color="green">227</FONT> if (yMin == 0.0) {<a name="line.227"></a> <FONT color="green">228</FONT> ret = min;<a name="line.228"></a> <FONT color="green">229</FONT> } else {<a name="line.229"></a> <FONT color="green">230</FONT> ret = max;<a name="line.230"></a> <FONT color="green">231</FONT> }<a name="line.231"></a> <FONT color="green">232</FONT> }<a name="line.232"></a> <FONT color="green">233</FONT> <a name="line.233"></a> <FONT color="green">234</FONT> return ret;<a name="line.234"></a> <FONT color="green">235</FONT> }<a name="line.235"></a> <FONT color="green">236</FONT> <a name="line.236"></a> <FONT color="green">237</FONT> /**<a name="line.237"></a> <FONT color="green">238</FONT> * Find a zero starting search according to the three provided points.<a name="line.238"></a> <FONT color="green">239</FONT> * @param f the function to solve<a name="line.239"></a> <FONT color="green">240</FONT> * @param x0 old approximation for the root<a name="line.240"></a> <FONT color="green">241</FONT> * @param y0 function value at the approximation for the root<a name="line.241"></a> <FONT color="green">242</FONT> * @param x1 last calculated approximation for the root<a name="line.242"></a> <FONT color="green">243</FONT> * @param y1 function value at the last calculated approximation<a name="line.243"></a> <FONT color="green">244</FONT> * for the root<a name="line.244"></a> <FONT color="green">245</FONT> * @param x2 bracket point (must be set to x0 if no bracket point is<a name="line.245"></a> <FONT color="green">246</FONT> * known, this will force starting with linear interpolation)<a name="line.246"></a> <FONT color="green">247</FONT> * @param y2 function value at the bracket point.<a name="line.247"></a> <FONT color="green">248</FONT> * @return the value where the function is zero<a name="line.248"></a> <FONT color="green">249</FONT> * @throws MaxIterationsExceededException if the maximum iteration count<a name="line.249"></a> <FONT color="green">250</FONT> * is exceeded<a name="line.250"></a> <FONT color="green">251</FONT> * @throws FunctionEvaluationException if an error occurs evaluating<a name="line.251"></a> <FONT color="green">252</FONT> * the function<a name="line.252"></a> <FONT color="green">253</FONT> */<a name="line.253"></a> <FONT color="green">254</FONT> private double solve(final UnivariateRealFunction f,<a name="line.254"></a> <FONT color="green">255</FONT> double x0, double y0,<a name="line.255"></a> <FONT color="green">256</FONT> double x1, double y1,<a name="line.256"></a> <FONT color="green">257</FONT> double x2, double y2)<a name="line.257"></a> <FONT color="green">258</FONT> throws MaxIterationsExceededException, FunctionEvaluationException {<a name="line.258"></a> <FONT color="green">259</FONT> <a name="line.259"></a> <FONT color="green">260</FONT> double delta = x1 - x0;<a name="line.260"></a> <FONT color="green">261</FONT> double oldDelta = delta;<a name="line.261"></a> <FONT color="green">262</FONT> <a name="line.262"></a> <FONT color="green">263</FONT> int i = 0;<a name="line.263"></a> <FONT color="green">264</FONT> while (i < maximalIterationCount) {<a name="line.264"></a> <FONT color="green">265</FONT> if (Math.abs(y2) < Math.abs(y1)) {<a name="line.265"></a> <FONT color="green">266</FONT> // use the bracket point if is better than last approximation<a name="line.266"></a> <FONT color="green">267</FONT> x0 = x1;<a name="line.267"></a> <FONT color="green">268</FONT> x1 = x2;<a name="line.268"></a> <FONT color="green">269</FONT> x2 = x0;<a name="line.269"></a> <FONT color="green">270</FONT> y0 = y1;<a name="line.270"></a> <FONT color="green">271</FONT> y1 = y2;<a name="line.271"></a> <FONT color="green">272</FONT> y2 = y0;<a name="line.272"></a> <FONT color="green">273</FONT> }<a name="line.273"></a> <FONT color="green">274</FONT> if (Math.abs(y1) <= functionValueAccuracy) {<a name="line.274"></a> <FONT color="green">275</FONT> // Avoid division by very small values. Assume<a name="line.275"></a> <FONT color="green">276</FONT> // the iteration has converged (the problem may<a name="line.276"></a> <FONT color="green">277</FONT> // still be ill conditioned)<a name="line.277"></a> <FONT color="green">278</FONT> setResult(x1, i);<a name="line.278"></a> <FONT color="green">279</FONT> return result;<a name="line.279"></a> <FONT color="green">280</FONT> }<a name="line.280"></a> <FONT color="green">281</FONT> double dx = x2 - x1;<a name="line.281"></a> <FONT color="green">282</FONT> double tolerance =<a name="line.282"></a> <FONT color="green">283</FONT> Math.max(relativeAccuracy * Math.abs(x1), absoluteAccuracy);<a name="line.283"></a> <FONT color="green">284</FONT> if (Math.abs(dx) <= tolerance) {<a name="line.284"></a> <FONT color="green">285</FONT> setResult(x1, i);<a name="line.285"></a> <FONT color="green">286</FONT> return result;<a name="line.286"></a> <FONT color="green">287</FONT> }<a name="line.287"></a> <FONT color="green">288</FONT> if ((Math.abs(oldDelta) < tolerance) ||<a name="line.288"></a> <FONT color="green">289</FONT> (Math.abs(y0) <= Math.abs(y1))) {<a name="line.289"></a> <FONT color="green">290</FONT> // Force bisection.<a name="line.290"></a> <FONT color="green">291</FONT> delta = 0.5 * dx;<a name="line.291"></a> <FONT color="green">292</FONT> oldDelta = delta;<a name="line.292"></a> <FONT color="green">293</FONT> } else {<a name="line.293"></a> <FONT color="green">294</FONT> double r3 = y1 / y0;<a name="line.294"></a> <FONT color="green">295</FONT> double p;<a name="line.295"></a> <FONT color="green">296</FONT> double p1;<a name="line.296"></a> <FONT color="green">297</FONT> // the equality test (x0 == x2) is intentional,<a name="line.297"></a> <FONT color="green">298</FONT> // it is part of the original Brent's method,<a name="line.298"></a> <FONT color="green">299</FONT> // it should NOT be replaced by proximity test<a name="line.299"></a> <FONT color="green">300</FONT> if (x0 == x2) {<a name="line.300"></a> <FONT color="green">301</FONT> // Linear interpolation.<a name="line.301"></a> <FONT color="green">302</FONT> p = dx * r3;<a name="line.302"></a> <FONT color="green">303</FONT> p1 = 1.0 - r3;<a name="line.303"></a> <FONT color="green">304</FONT> } else {<a name="line.304"></a> <FONT color="green">305</FONT> // Inverse quadratic interpolation.<a name="line.305"></a> <FONT color="green">306</FONT> double r1 = y0 / y2;<a name="line.306"></a> <FONT color="green">307</FONT> double r2 = y1 / y2;<a name="line.307"></a> <FONT color="green">308</FONT> p = r3 * (dx * r1 * (r1 - r2) - (x1 - x0) * (r2 - 1.0));<a name="line.308"></a> <FONT color="green">309</FONT> p1 = (r1 - 1.0) * (r2 - 1.0) * (r3 - 1.0);<a name="line.309"></a> <FONT color="green">310</FONT> }<a name="line.310"></a> <FONT color="green">311</FONT> if (p > 0.0) {<a name="line.311"></a> <FONT color="green">312</FONT> p1 = -p1;<a name="line.312"></a> <FONT color="green">313</FONT> } else {<a name="line.313"></a> <FONT color="green">314</FONT> p = -p;<a name="line.314"></a> <FONT color="green">315</FONT> }<a name="line.315"></a> <FONT color="green">316</FONT> if (2.0 * p >= 1.5 * dx * p1 - Math.abs(tolerance * p1) ||<a name="line.316"></a> <FONT color="green">317</FONT> p >= Math.abs(0.5 * oldDelta * p1)) {<a name="line.317"></a> <FONT color="green">318</FONT> // Inverse quadratic interpolation gives a value<a name="line.318"></a> <FONT color="green">319</FONT> // in the wrong direction, or progress is slow.<a name="line.319"></a> <FONT color="green">320</FONT> // Fall back to bisection.<a name="line.320"></a> <FONT color="green">321</FONT> delta = 0.5 * dx;<a name="line.321"></a> <FONT color="green">322</FONT> oldDelta = delta;<a name="line.322"></a> <FONT color="green">323</FONT> } else {<a name="line.323"></a> <FONT color="green">324</FONT> oldDelta = delta;<a name="line.324"></a> <FONT color="green">325</FONT> delta = p / p1;<a name="line.325"></a> <FONT color="green">326</FONT> }<a name="line.326"></a> <FONT color="green">327</FONT> }<a name="line.327"></a> <FONT color="green">328</FONT> // Save old X1, Y1<a name="line.328"></a> <FONT color="green">329</FONT> x0 = x1;<a name="line.329"></a> <FONT color="green">330</FONT> y0 = y1;<a name="line.330"></a> <FONT color="green">331</FONT> // Compute new X1, Y1<a name="line.331"></a> <FONT color="green">332</FONT> if (Math.abs(delta) > tolerance) {<a name="line.332"></a> <FONT color="green">333</FONT> x1 = x1 + delta;<a name="line.333"></a> <FONT color="green">334</FONT> } else if (dx > 0.0) {<a name="line.334"></a> <FONT color="green">335</FONT> x1 = x1 + 0.5 * tolerance;<a name="line.335"></a> <FONT color="green">336</FONT> } else if (dx <= 0.0) {<a name="line.336"></a> <FONT color="green">337</FONT> x1 = x1 - 0.5 * tolerance;<a name="line.337"></a> <FONT color="green">338</FONT> }<a name="line.338"></a> <FONT color="green">339</FONT> y1 = f.value(x1);<a name="line.339"></a> <FONT color="green">340</FONT> if ((y1 > 0) == (y2 > 0)) {<a name="line.340"></a> <FONT color="green">341</FONT> x2 = x0;<a name="line.341"></a> <FONT color="green">342</FONT> y2 = y0;<a name="line.342"></a> <FONT color="green">343</FONT> delta = x1 - x0;<a name="line.343"></a> <FONT color="green">344</FONT> oldDelta = delta;<a name="line.344"></a> <FONT color="green">345</FONT> }<a name="line.345"></a> <FONT color="green">346</FONT> i++;<a name="line.346"></a> <FONT color="green">347</FONT> }<a name="line.347"></a> <FONT color="green">348</FONT> throw new MaxIterationsExceededException(maximalIterationCount);<a name="line.348"></a> <FONT color="green">349</FONT> }<a name="line.349"></a> <FONT color="green">350</FONT> }<a name="line.350"></a> </PRE> </BODY> </HTML>