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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> import org.apache.commons.math.FunctionEvaluationException;<a name="line.19"></a> <FONT color="green">020</FONT> import org.apache.commons.math.ConvergenceException;<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.analysis.UnivariateRealFunction;<a name="line.22"></a> <FONT color="green">023</FONT> <a name="line.23"></a> <FONT color="green">024</FONT> /**<a name="line.24"></a> <FONT color="green">025</FONT> * Utility routines for {@link UnivariateRealSolver} objects.<a name="line.25"></a> <FONT color="green">026</FONT> *<a name="line.26"></a> <FONT color="green">027</FONT> * @version $Revision: 885278 $ $Date: 2009-11-29 16:47:51 -0500 (Sun, 29 Nov 2009) $<a name="line.27"></a> <FONT color="green">028</FONT> */<a name="line.28"></a> <FONT color="green">029</FONT> public class UnivariateRealSolverUtils {<a name="line.29"></a> <FONT color="green">030</FONT> <a name="line.30"></a> <FONT color="green">031</FONT> /** Message for null function.*/<a name="line.31"></a> <FONT color="green">032</FONT> private static final String NULL_FUNCTION_MESSAGE =<a name="line.32"></a> <FONT color="green">033</FONT> "function is null";<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 constructor.<a name="line.36"></a> <FONT color="green">037</FONT> */<a name="line.37"></a> <FONT color="green">038</FONT> private UnivariateRealSolverUtils() {<a name="line.38"></a> <FONT color="green">039</FONT> super();<a name="line.39"></a> <FONT color="green">040</FONT> }<a name="line.40"></a> <FONT color="green">041</FONT> <a name="line.41"></a> <FONT color="green">042</FONT> /**<a name="line.42"></a> <FONT color="green">043</FONT> * Convenience method to find a zero of a univariate real function. A default<a name="line.43"></a> <FONT color="green">044</FONT> * solver is used.<a name="line.44"></a> <FONT color="green">045</FONT> *<a name="line.45"></a> <FONT color="green">046</FONT> * @param f the function.<a name="line.46"></a> <FONT color="green">047</FONT> * @param x0 the lower bound for the interval.<a name="line.47"></a> <FONT color="green">048</FONT> * @param x1 the upper bound for the interval.<a name="line.48"></a> <FONT color="green">049</FONT> * @return a value where the function is zero.<a name="line.49"></a> <FONT color="green">050</FONT> * @throws ConvergenceException if the iteration count was exceeded<a name="line.50"></a> <FONT color="green">051</FONT> * @throws FunctionEvaluationException if an error occurs evaluating<a name="line.51"></a> <FONT color="green">052</FONT> * the function<a name="line.52"></a> <FONT color="green">053</FONT> * @throws IllegalArgumentException if f is null or the endpoints do not<a name="line.53"></a> <FONT color="green">054</FONT> * specify a valid interval<a name="line.54"></a> <FONT color="green">055</FONT> */<a name="line.55"></a> <FONT color="green">056</FONT> public static double solve(UnivariateRealFunction f, double x0, double x1)<a name="line.56"></a> <FONT color="green">057</FONT> throws ConvergenceException, FunctionEvaluationException {<a name="line.57"></a> <FONT color="green">058</FONT> setup(f);<a name="line.58"></a> <FONT color="green">059</FONT> return LazyHolder.FACTORY.newDefaultSolver().solve(f, x0, x1);<a name="line.59"></a> <FONT color="green">060</FONT> }<a name="line.60"></a> <FONT color="green">061</FONT> <a name="line.61"></a> <FONT color="green">062</FONT> /**<a name="line.62"></a> <FONT color="green">063</FONT> * Convenience method to find a zero of a univariate real function. A default<a name="line.63"></a> <FONT color="green">064</FONT> * solver is used.<a name="line.64"></a> <FONT color="green">065</FONT> *<a name="line.65"></a> <FONT color="green">066</FONT> * @param f the function<a name="line.66"></a> <FONT color="green">067</FONT> * @param x0 the lower bound for the interval<a name="line.67"></a> <FONT color="green">068</FONT> * @param x1 the upper bound for the interval<a name="line.68"></a> <FONT color="green">069</FONT> * @param absoluteAccuracy the accuracy to be used by the solver<a name="line.69"></a> <FONT color="green">070</FONT> * @return a value where the function is zero<a name="line.70"></a> <FONT color="green">071</FONT> * @throws ConvergenceException if the iteration count is exceeded<a name="line.71"></a> <FONT color="green">072</FONT> * @throws FunctionEvaluationException if an error occurs evaluating the<a name="line.72"></a> <FONT color="green">073</FONT> * function<a name="line.73"></a> <FONT color="green">074</FONT> * @throws IllegalArgumentException if f is null, the endpoints do not<a name="line.74"></a> <FONT color="green">075</FONT> * specify a valid interval, or the absoluteAccuracy is not valid for the<a name="line.75"></a> <FONT color="green">076</FONT> * default solver<a name="line.76"></a> <FONT color="green">077</FONT> */<a name="line.77"></a> <FONT color="green">078</FONT> public static double solve(UnivariateRealFunction f, double x0, double x1,<a name="line.78"></a> <FONT color="green">079</FONT> double absoluteAccuracy) throws ConvergenceException,<a name="line.79"></a> <FONT color="green">080</FONT> FunctionEvaluationException {<a name="line.80"></a> <FONT color="green">081</FONT> <a name="line.81"></a> <FONT color="green">082</FONT> setup(f);<a name="line.82"></a> <FONT color="green">083</FONT> UnivariateRealSolver solver = LazyHolder.FACTORY.newDefaultSolver();<a name="line.83"></a> <FONT color="green">084</FONT> solver.setAbsoluteAccuracy(absoluteAccuracy);<a name="line.84"></a> <FONT color="green">085</FONT> return solver.solve(f, x0, x1);<a name="line.85"></a> <FONT color="green">086</FONT> }<a name="line.86"></a> <FONT color="green">087</FONT> <a name="line.87"></a> <FONT color="green">088</FONT> /**<a name="line.88"></a> <FONT color="green">089</FONT> * This method attempts to find two values a and b satisfying <ul><a name="line.89"></a> <FONT color="green">090</FONT> * <li> <code> lowerBound <= a < initial < b <= upperBound</code> </li><a name="line.90"></a> <FONT color="green">091</FONT> * <li> <code> f(a) * f(b) < 0 </code></li><a name="line.91"></a> <FONT color="green">092</FONT> * </ul><a name="line.92"></a> <FONT color="green">093</FONT> * If f is continuous on <code>[a,b],</code> this means that <code>a</code><a name="line.93"></a> <FONT color="green">094</FONT> * and <code>b</code> bracket a root of f.<a name="line.94"></a> <FONT color="green">095</FONT> * <p><a name="line.95"></a> <FONT color="green">096</FONT> * The algorithm starts by setting<a name="line.96"></a> <FONT color="green">097</FONT> * <code>a := initial -1; b := initial +1,</code> examines the value of the<a name="line.97"></a> <FONT color="green">098</FONT> * function at <code>a</code> and <code>b</code> and keeps moving<a name="line.98"></a> <FONT color="green">099</FONT> * the endpoints out by one unit each time through a loop that terminates<a name="line.99"></a> <FONT color="green">100</FONT> * when one of the following happens: <ul><a name="line.100"></a> <FONT color="green">101</FONT> * <li> <code> f(a) * f(b) < 0 </code> -- success!</li><a name="line.101"></a> <FONT color="green">102</FONT> * <li> <code> a = lower </code> and <code> b = upper</code><a name="line.102"></a> <FONT color="green">103</FONT> * -- ConvergenceException </li><a name="line.103"></a> <FONT color="green">104</FONT> * <li> <code> Integer.MAX_VALUE</code> iterations elapse<a name="line.104"></a> <FONT color="green">105</FONT> * -- ConvergenceException </li><a name="line.105"></a> <FONT color="green">106</FONT> * </ul></p><a name="line.106"></a> <FONT color="green">107</FONT> * <p><a name="line.107"></a> <FONT color="green">108</FONT> * <strong>Note: </strong> this method can take<a name="line.108"></a> <FONT color="green">109</FONT> * <code>Integer.MAX_VALUE</code> iterations to throw a<a name="line.109"></a> <FONT color="green">110</FONT> * <code>ConvergenceException.</code> Unless you are confident that there<a name="line.110"></a> <FONT color="green">111</FONT> * is a root between <code>lowerBound</code> and <code>upperBound</code><a name="line.111"></a> <FONT color="green">112</FONT> * near <code>initial,</code> it is better to use<a name="line.112"></a> <FONT color="green">113</FONT> * {@link #bracket(UnivariateRealFunction, double, double, double, int)},<a name="line.113"></a> <FONT color="green">114</FONT> * explicitly specifying the maximum number of iterations.</p><a name="line.114"></a> <FONT color="green">115</FONT> *<a name="line.115"></a> <FONT color="green">116</FONT> * @param function the function<a name="line.116"></a> <FONT color="green">117</FONT> * @param initial initial midpoint of interval being expanded to<a name="line.117"></a> <FONT color="green">118</FONT> * bracket a root<a name="line.118"></a> <FONT color="green">119</FONT> * @param lowerBound lower bound (a is never lower than this value)<a name="line.119"></a> <FONT color="green">120</FONT> * @param upperBound upper bound (b never is greater than this<a name="line.120"></a> <FONT color="green">121</FONT> * value)<a name="line.121"></a> <FONT color="green">122</FONT> * @return a two element array holding {a, b}<a name="line.122"></a> <FONT color="green">123</FONT> * @throws ConvergenceException if a root can not be bracketted<a name="line.123"></a> <FONT color="green">124</FONT> * @throws FunctionEvaluationException if an error occurs evaluating the<a name="line.124"></a> <FONT color="green">125</FONT> * function<a name="line.125"></a> <FONT color="green">126</FONT> * @throws IllegalArgumentException if function is null, maximumIterations<a name="line.126"></a> <FONT color="green">127</FONT> * is not positive, or initial is not between lowerBound and upperBound<a name="line.127"></a> <FONT color="green">128</FONT> */<a name="line.128"></a> <FONT color="green">129</FONT> public static double[] bracket(UnivariateRealFunction function,<a name="line.129"></a> <FONT color="green">130</FONT> double initial, double lowerBound, double upperBound)<a name="line.130"></a> <FONT color="green">131</FONT> throws ConvergenceException, FunctionEvaluationException {<a name="line.131"></a> <FONT color="green">132</FONT> return bracket( function, initial, lowerBound, upperBound,<a name="line.132"></a> <FONT color="green">133</FONT> Integer.MAX_VALUE ) ;<a name="line.133"></a> <FONT color="green">134</FONT> }<a name="line.134"></a> <FONT color="green">135</FONT> <a name="line.135"></a> <FONT color="green">136</FONT> /**<a name="line.136"></a> <FONT color="green">137</FONT> * This method attempts to find two values a and b satisfying <ul><a name="line.137"></a> <FONT color="green">138</FONT> * <li> <code> lowerBound <= a < initial < b <= upperBound</code> </li><a name="line.138"></a> <FONT color="green">139</FONT> * <li> <code> f(a) * f(b) <= 0 </code> </li><a name="line.139"></a> <FONT color="green">140</FONT> * </ul><a name="line.140"></a> <FONT color="green">141</FONT> * If f is continuous on <code>[a,b],</code> this means that <code>a</code><a name="line.141"></a> <FONT color="green">142</FONT> * and <code>b</code> bracket a root of f.<a name="line.142"></a> <FONT color="green">143</FONT> * <p><a name="line.143"></a> <FONT color="green">144</FONT> * The algorithm starts by setting<a name="line.144"></a> <FONT color="green">145</FONT> * <code>a := initial -1; b := initial +1,</code> examines the value of the<a name="line.145"></a> <FONT color="green">146</FONT> * function at <code>a</code> and <code>b</code> and keeps moving<a name="line.146"></a> <FONT color="green">147</FONT> * the endpoints out by one unit each time through a loop that terminates<a name="line.147"></a> <FONT color="green">148</FONT> * when one of the following happens: <ul><a name="line.148"></a> <FONT color="green">149</FONT> * <li> <code> f(a) * f(b) <= 0 </code> -- success!</li><a name="line.149"></a> <FONT color="green">150</FONT> * <li> <code> a = lower </code> and <code> b = upper</code><a name="line.150"></a> <FONT color="green">151</FONT> * -- ConvergenceException </li><a name="line.151"></a> <FONT color="green">152</FONT> * <li> <code> maximumIterations</code> iterations elapse<a name="line.152"></a> <FONT color="green">153</FONT> * -- ConvergenceException </li></ul></p><a name="line.153"></a> <FONT color="green">154</FONT> *<a name="line.154"></a> <FONT color="green">155</FONT> * @param function the function<a name="line.155"></a> <FONT color="green">156</FONT> * @param initial initial midpoint of interval being expanded to<a name="line.156"></a> <FONT color="green">157</FONT> * bracket a root<a name="line.157"></a> <FONT color="green">158</FONT> * @param lowerBound lower bound (a is never lower than this value)<a name="line.158"></a> <FONT color="green">159</FONT> * @param upperBound upper bound (b never is greater than this<a name="line.159"></a> <FONT color="green">160</FONT> * value)<a name="line.160"></a> <FONT color="green">161</FONT> * @param maximumIterations maximum number of iterations to perform<a name="line.161"></a> <FONT color="green">162</FONT> * @return a two element array holding {a, b}.<a name="line.162"></a> <FONT color="green">163</FONT> * @throws ConvergenceException if the algorithm fails to find a and b<a name="line.163"></a> <FONT color="green">164</FONT> * satisfying the desired conditions<a name="line.164"></a> <FONT color="green">165</FONT> * @throws FunctionEvaluationException if an error occurs evaluating the<a name="line.165"></a> <FONT color="green">166</FONT> * function<a name="line.166"></a> <FONT color="green">167</FONT> * @throws IllegalArgumentException if function is null, maximumIterations<a name="line.167"></a> <FONT color="green">168</FONT> * is not positive, or initial is not between lowerBound and upperBound<a name="line.168"></a> <FONT color="green">169</FONT> */<a name="line.169"></a> <FONT color="green">170</FONT> public static double[] bracket(UnivariateRealFunction function,<a name="line.170"></a> <FONT color="green">171</FONT> double initial, double lowerBound, double upperBound,<a name="line.171"></a> <FONT color="green">172</FONT> int maximumIterations) throws ConvergenceException,<a name="line.172"></a> <FONT color="green">173</FONT> FunctionEvaluationException {<a name="line.173"></a> <FONT color="green">174</FONT> <a name="line.174"></a> <FONT color="green">175</FONT> if (function == null) {<a name="line.175"></a> <FONT color="green">176</FONT> throw MathRuntimeException.createIllegalArgumentException(NULL_FUNCTION_MESSAGE);<a name="line.176"></a> <FONT color="green">177</FONT> }<a name="line.177"></a> <FONT color="green">178</FONT> if (maximumIterations <= 0) {<a name="line.178"></a> <FONT color="green">179</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.179"></a> <FONT color="green">180</FONT> "bad value for maximum iterations number: {0}", maximumIterations);<a name="line.180"></a> <FONT color="green">181</FONT> }<a name="line.181"></a> <FONT color="green">182</FONT> if (initial < lowerBound || initial > upperBound || lowerBound >= upperBound) {<a name="line.182"></a> <FONT color="green">183</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.183"></a> <FONT color="green">184</FONT> "invalid bracketing parameters: lower bound={0}, initial={1}, upper bound={2}",<a name="line.184"></a> <FONT color="green">185</FONT> lowerBound, initial, upperBound);<a name="line.185"></a> <FONT color="green">186</FONT> }<a name="line.186"></a> <FONT color="green">187</FONT> double a = initial;<a name="line.187"></a> <FONT color="green">188</FONT> double b = initial;<a name="line.188"></a> <FONT color="green">189</FONT> double fa;<a name="line.189"></a> <FONT color="green">190</FONT> double fb;<a name="line.190"></a> <FONT color="green">191</FONT> int numIterations = 0 ;<a name="line.191"></a> <FONT color="green">192</FONT> <a name="line.192"></a> <FONT color="green">193</FONT> do {<a name="line.193"></a> <FONT color="green">194</FONT> a = Math.max(a - 1.0, lowerBound);<a name="line.194"></a> <FONT color="green">195</FONT> b = Math.min(b + 1.0, upperBound);<a name="line.195"></a> <FONT color="green">196</FONT> fa = function.value(a);<a name="line.196"></a> <FONT color="green">197</FONT> <a name="line.197"></a> <FONT color="green">198</FONT> fb = function.value(b);<a name="line.198"></a> <FONT color="green">199</FONT> numIterations++ ;<a name="line.199"></a> <FONT color="green">200</FONT> } while ((fa * fb > 0.0) && (numIterations < maximumIterations) &&<a name="line.200"></a> <FONT color="green">201</FONT> ((a > lowerBound) || (b < upperBound)));<a name="line.201"></a> <FONT color="green">202</FONT> <a name="line.202"></a> <FONT color="green">203</FONT> if (fa * fb > 0.0 ) {<a name="line.203"></a> <FONT color="green">204</FONT> throw new ConvergenceException(<a name="line.204"></a> <FONT color="green">205</FONT> "number of iterations={0}, maximum iterations={1}, " +<a name="line.205"></a> <FONT color="green">206</FONT> "initial={2}, lower bound={3}, upper bound={4}, final a value={5}, " +<a name="line.206"></a> <FONT color="green">207</FONT> "final b value={6}, f(a)={7}, f(b)={8}",<a name="line.207"></a> <FONT color="green">208</FONT> numIterations, maximumIterations, initial,<a name="line.208"></a> <FONT color="green">209</FONT> lowerBound, upperBound, a, b, fa, fb);<a name="line.209"></a> <FONT color="green">210</FONT> }<a name="line.210"></a> <FONT color="green">211</FONT> <a name="line.211"></a> <FONT color="green">212</FONT> return new double[]{a, b};<a name="line.212"></a> <FONT color="green">213</FONT> }<a name="line.213"></a> <FONT color="green">214</FONT> <a name="line.214"></a> <FONT color="green">215</FONT> /**<a name="line.215"></a> <FONT color="green">216</FONT> * Compute the midpoint of two values.<a name="line.216"></a> <FONT color="green">217</FONT> *<a name="line.217"></a> <FONT color="green">218</FONT> * @param a first value.<a name="line.218"></a> <FONT color="green">219</FONT> * @param b second value.<a name="line.219"></a> <FONT color="green">220</FONT> * @return the midpoint.<a name="line.220"></a> <FONT color="green">221</FONT> */<a name="line.221"></a> <FONT color="green">222</FONT> public static double midpoint(double a, double b) {<a name="line.222"></a> <FONT color="green">223</FONT> return (a + b) * .5;<a name="line.223"></a> <FONT color="green">224</FONT> }<a name="line.224"></a> <FONT color="green">225</FONT> <a name="line.225"></a> <FONT color="green">226</FONT> /**<a name="line.226"></a> <FONT color="green">227</FONT> * Checks to see if f is null, throwing IllegalArgumentException if so.<a name="line.227"></a> <FONT color="green">228</FONT> * @param f input function<a name="line.228"></a> <FONT color="green">229</FONT> * @throws IllegalArgumentException if f is null<a name="line.229"></a> <FONT color="green">230</FONT> */<a name="line.230"></a> <FONT color="green">231</FONT> private static void setup(UnivariateRealFunction f) {<a name="line.231"></a> <FONT color="green">232</FONT> if (f == null) {<a name="line.232"></a> <FONT color="green">233</FONT> throw MathRuntimeException.createIllegalArgumentException(NULL_FUNCTION_MESSAGE);<a name="line.233"></a> <FONT color="green">234</FONT> }<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> // CHECKSTYLE: stop HideUtilityClassConstructor<a name="line.237"></a> <FONT color="green">238</FONT> /** Holder for the factory.<a name="line.238"></a> <FONT color="green">239</FONT> * <p>We use here the Initialization On Demand Holder Idiom.</p><a name="line.239"></a> <FONT color="green">240</FONT> */<a name="line.240"></a> <FONT color="green">241</FONT> private static class LazyHolder {<a name="line.241"></a> <FONT color="green">242</FONT> /** Cached solver factory */<a name="line.242"></a> <FONT color="green">243</FONT> private static final UnivariateRealSolverFactory FACTORY = UnivariateRealSolverFactory.newInstance();<a name="line.243"></a> <FONT color="green">244</FONT> }<a name="line.244"></a> <FONT color="green">245</FONT> // CHECKSTYLE: resume HideUtilityClassConstructor<a name="line.245"></a> <FONT color="green">246</FONT> <a name="line.246"></a> <FONT color="green">247</FONT> }<a name="line.247"></a> </PRE> </BODY> </HTML>