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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> import org.apache.commons.math.ConvergenceException;<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.MaxIterationsExceededException;<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> import org.apache.commons.math.util.MathUtils;<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/RiddersMethod.html"><a name="line.26"></a> <FONT color="green">027</FONT> * Ridders' Method</a> for root finding of real univariate functions. For<a name="line.27"></a> <FONT color="green">028</FONT> * reference, see C. Ridders, <i>A new algorithm for computing a single root<a name="line.28"></a> <FONT color="green">029</FONT> * of a real continuous function </i>, IEEE Transactions on Circuits and<a name="line.29"></a> <FONT color="green">030</FONT> * Systems, 26 (1979), 979 - 980.<a name="line.30"></a> <FONT color="green">031</FONT> * <p><a name="line.31"></a> <FONT color="green">032</FONT> * The function should be continuous but not necessarily smooth.</p><a name="line.32"></a> <FONT color="green">033</FONT> *<a name="line.33"></a> <FONT color="green">034</FONT> * @version $Revision: 825919 $ $Date: 2009-10-16 10:51:55 -0400 (Fri, 16 Oct 2009) $<a name="line.34"></a> <FONT color="green">035</FONT> * @since 1.2<a name="line.35"></a> <FONT color="green">036</FONT> */<a name="line.36"></a> <FONT color="green">037</FONT> public class RiddersSolver extends UnivariateRealSolverImpl {<a name="line.37"></a> <FONT color="green">038</FONT> <a name="line.38"></a> <FONT color="green">039</FONT> /**<a name="line.39"></a> <FONT color="green">040</FONT> * Construct a solver for the given function.<a name="line.40"></a> <FONT color="green">041</FONT> *<a name="line.41"></a> <FONT color="green">042</FONT> * @param f function to solve<a name="line.42"></a> <FONT color="green">043</FONT> * @deprecated as of 2.0 the function to solve is passed as an argument<a name="line.43"></a> <FONT color="green">044</FONT> * to the {@link #solve(UnivariateRealFunction, double, double)} or<a name="line.44"></a> <FONT color="green">045</FONT> * {@link UnivariateRealSolverImpl#solve(UnivariateRealFunction, double, double, double)}<a name="line.45"></a> <FONT color="green">046</FONT> * method.<a name="line.46"></a> <FONT color="green">047</FONT> */<a name="line.47"></a> <FONT color="green">048</FONT> @Deprecated<a name="line.48"></a> <FONT color="green">049</FONT> public RiddersSolver(UnivariateRealFunction f) {<a name="line.49"></a> <FONT color="green">050</FONT> super(f, 100, 1E-6);<a name="line.50"></a> <FONT color="green">051</FONT> }<a name="line.51"></a> <FONT color="green">052</FONT> <a name="line.52"></a> <FONT color="green">053</FONT> /**<a name="line.53"></a> <FONT color="green">054</FONT> * Construct a solver.<a name="line.54"></a> <FONT color="green">055</FONT> */<a name="line.55"></a> <FONT color="green">056</FONT> public RiddersSolver() {<a name="line.56"></a> <FONT color="green">057</FONT> super(100, 1E-6);<a name="line.57"></a> <FONT color="green">058</FONT> }<a name="line.58"></a> <FONT color="green">059</FONT> <a name="line.59"></a> <FONT color="green">060</FONT> /** {@inheritDoc} */<a name="line.60"></a> <FONT color="green">061</FONT> @Deprecated<a name="line.61"></a> <FONT color="green">062</FONT> public double solve(final double min, final double max)<a name="line.62"></a> <FONT color="green">063</FONT> throws ConvergenceException, FunctionEvaluationException {<a name="line.63"></a> <FONT color="green">064</FONT> return solve(f, min, max);<a name="line.64"></a> <FONT color="green">065</FONT> }<a name="line.65"></a> <FONT color="green">066</FONT> <a name="line.66"></a> <FONT color="green">067</FONT> /** {@inheritDoc} */<a name="line.67"></a> <FONT color="green">068</FONT> @Deprecated<a name="line.68"></a> <FONT color="green">069</FONT> public double solve(final double min, final double max, final double initial)<a name="line.69"></a> <FONT color="green">070</FONT> throws ConvergenceException, FunctionEvaluationException {<a name="line.70"></a> <FONT color="green">071</FONT> return solve(f, min, max, initial);<a name="line.71"></a> <FONT color="green">072</FONT> }<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> * Find a root in the given interval with initial value.<a name="line.75"></a> <FONT color="green">076</FONT> * <p><a name="line.76"></a> <FONT color="green">077</FONT> * Requires bracketing condition.</p><a name="line.77"></a> <FONT color="green">078</FONT> *<a name="line.78"></a> <FONT color="green">079</FONT> * @param f the function to solve<a name="line.79"></a> <FONT color="green">080</FONT> * @param min the lower bound for the interval<a name="line.80"></a> <FONT color="green">081</FONT> * @param max the upper bound for the interval<a name="line.81"></a> <FONT color="green">082</FONT> * @param initial the start value to use<a name="line.82"></a> <FONT color="green">083</FONT> * @return the point at which the function value is zero<a name="line.83"></a> <FONT color="green">084</FONT> * @throws MaxIterationsExceededException if the maximum iteration count is exceeded<a name="line.84"></a> <FONT color="green">085</FONT> * @throws FunctionEvaluationException if an error occurs evaluating the<a name="line.85"></a> <FONT color="green">086</FONT> * function<a name="line.86"></a> <FONT color="green">087</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.87"></a> <FONT color="green">088</FONT> */<a name="line.88"></a> <FONT color="green">089</FONT> public double solve(final UnivariateRealFunction f,<a name="line.89"></a> <FONT color="green">090</FONT> final double min, final double max, final double initial)<a name="line.90"></a> <FONT color="green">091</FONT> throws MaxIterationsExceededException, FunctionEvaluationException {<a name="line.91"></a> <FONT color="green">092</FONT> <a name="line.92"></a> <FONT color="green">093</FONT> // check for zeros before verifying bracketing<a name="line.93"></a> <FONT color="green">094</FONT> if (f.value(min) == 0.0) { return min; }<a name="line.94"></a> <FONT color="green">095</FONT> if (f.value(max) == 0.0) { return max; }<a name="line.95"></a> <FONT color="green">096</FONT> if (f.value(initial) == 0.0) { return initial; }<a name="line.96"></a> <FONT color="green">097</FONT> <a name="line.97"></a> <FONT color="green">098</FONT> verifyBracketing(min, max, f);<a name="line.98"></a> <FONT color="green">099</FONT> verifySequence(min, initial, max);<a name="line.99"></a> <FONT color="green">100</FONT> if (isBracketing(min, initial, f)) {<a name="line.100"></a> <FONT color="green">101</FONT> return solve(f, min, initial);<a name="line.101"></a> <FONT color="green">102</FONT> } else {<a name="line.102"></a> <FONT color="green">103</FONT> return solve(f, initial, max);<a name="line.103"></a> <FONT color="green">104</FONT> }<a name="line.104"></a> <FONT color="green">105</FONT> }<a name="line.105"></a> <FONT color="green">106</FONT> <a name="line.106"></a> <FONT color="green">107</FONT> /**<a name="line.107"></a> <FONT color="green">108</FONT> * Find a root in the given interval.<a name="line.108"></a> <FONT color="green">109</FONT> * <p><a name="line.109"></a> <FONT color="green">110</FONT> * Requires bracketing condition.</p><a name="line.110"></a> <FONT color="green">111</FONT> *<a name="line.111"></a> <FONT color="green">112</FONT> * @param f the function to solve<a name="line.112"></a> <FONT color="green">113</FONT> * @param min the lower bound for the interval<a name="line.113"></a> <FONT color="green">114</FONT> * @param max the upper bound for the interval<a name="line.114"></a> <FONT color="green">115</FONT> * @return the point at which the function value is zero<a name="line.115"></a> <FONT color="green">116</FONT> * @throws MaxIterationsExceededException if the maximum iteration count is exceeded<a name="line.116"></a> <FONT color="green">117</FONT> * @throws FunctionEvaluationException if an error occurs evaluating the<a name="line.117"></a> <FONT color="green">118</FONT> * function<a name="line.118"></a> <FONT color="green">119</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.119"></a> <FONT color="green">120</FONT> */<a name="line.120"></a> <FONT color="green">121</FONT> public double solve(final UnivariateRealFunction f,<a name="line.121"></a> <FONT color="green">122</FONT> final double min, final double max)<a name="line.122"></a> <FONT color="green">123</FONT> throws MaxIterationsExceededException, FunctionEvaluationException {<a name="line.123"></a> <FONT color="green">124</FONT> <a name="line.124"></a> <FONT color="green">125</FONT> // [x1, x2] is the bracketing interval in each iteration<a name="line.125"></a> <FONT color="green">126</FONT> // x3 is the midpoint of [x1, x2]<a name="line.126"></a> <FONT color="green">127</FONT> // x is the new root approximation and an endpoint of the new interval<a name="line.127"></a> <FONT color="green">128</FONT> double x1 = min;<a name="line.128"></a> <FONT color="green">129</FONT> double y1 = f.value(x1);<a name="line.129"></a> <FONT color="green">130</FONT> double x2 = max;<a name="line.130"></a> <FONT color="green">131</FONT> double y2 = f.value(x2);<a name="line.131"></a> <FONT color="green">132</FONT> <a name="line.132"></a> <FONT color="green">133</FONT> // check for zeros before verifying bracketing<a name="line.133"></a> <FONT color="green">134</FONT> if (y1 == 0.0) {<a name="line.134"></a> <FONT color="green">135</FONT> return min;<a name="line.135"></a> <FONT color="green">136</FONT> }<a name="line.136"></a> <FONT color="green">137</FONT> if (y2 == 0.0) {<a name="line.137"></a> <FONT color="green">138</FONT> return max;<a name="line.138"></a> <FONT color="green">139</FONT> }<a name="line.139"></a> <FONT color="green">140</FONT> verifyBracketing(min, max, f);<a name="line.140"></a> <FONT color="green">141</FONT> <a name="line.141"></a> <FONT color="green">142</FONT> int i = 1;<a name="line.142"></a> <FONT color="green">143</FONT> double oldx = Double.POSITIVE_INFINITY;<a name="line.143"></a> <FONT color="green">144</FONT> while (i <= maximalIterationCount) {<a name="line.144"></a> <FONT color="green">145</FONT> // calculate the new root approximation<a name="line.145"></a> <FONT color="green">146</FONT> final double x3 = 0.5 * (x1 + x2);<a name="line.146"></a> <FONT color="green">147</FONT> final double y3 = f.value(x3);<a name="line.147"></a> <FONT color="green">148</FONT> if (Math.abs(y3) <= functionValueAccuracy) {<a name="line.148"></a> <FONT color="green">149</FONT> setResult(x3, i);<a name="line.149"></a> <FONT color="green">150</FONT> return result;<a name="line.150"></a> <FONT color="green">151</FONT> }<a name="line.151"></a> <FONT color="green">152</FONT> final double delta = 1 - (y1 * y2) / (y3 * y3); // delta > 1 due to bracketing<a name="line.152"></a> <FONT color="green">153</FONT> final double correction = (MathUtils.sign(y2) * MathUtils.sign(y3)) *<a name="line.153"></a> <FONT color="green">154</FONT> (x3 - x1) / Math.sqrt(delta);<a name="line.154"></a> <FONT color="green">155</FONT> final double x = x3 - correction; // correction != 0<a name="line.155"></a> <FONT color="green">156</FONT> final double y = f.value(x);<a name="line.156"></a> <FONT color="green">157</FONT> <a name="line.157"></a> <FONT color="green">158</FONT> // check for convergence<a name="line.158"></a> <FONT color="green">159</FONT> final double tolerance = Math.max(relativeAccuracy * Math.abs(x), absoluteAccuracy);<a name="line.159"></a> <FONT color="green">160</FONT> if (Math.abs(x - oldx) <= tolerance) {<a name="line.160"></a> <FONT color="green">161</FONT> setResult(x, i);<a name="line.161"></a> <FONT color="green">162</FONT> return result;<a name="line.162"></a> <FONT color="green">163</FONT> }<a name="line.163"></a> <FONT color="green">164</FONT> if (Math.abs(y) <= functionValueAccuracy) {<a name="line.164"></a> <FONT color="green">165</FONT> setResult(x, i);<a name="line.165"></a> <FONT color="green">166</FONT> return result;<a name="line.166"></a> <FONT color="green">167</FONT> }<a name="line.167"></a> <FONT color="green">168</FONT> <a name="line.168"></a> <FONT color="green">169</FONT> // prepare the new interval for next iteration<a name="line.169"></a> <FONT color="green">170</FONT> // Ridders' method guarantees x1 < x < x2<a name="line.170"></a> <FONT color="green">171</FONT> if (correction > 0.0) { // x1 < x < x3<a name="line.171"></a> <FONT color="green">172</FONT> if (MathUtils.sign(y1) + MathUtils.sign(y) == 0.0) {<a name="line.172"></a> <FONT color="green">173</FONT> x2 = x;<a name="line.173"></a> <FONT color="green">174</FONT> y2 = y;<a name="line.174"></a> <FONT color="green">175</FONT> } else {<a name="line.175"></a> <FONT color="green">176</FONT> x1 = x;<a name="line.176"></a> <FONT color="green">177</FONT> x2 = x3;<a name="line.177"></a> <FONT color="green">178</FONT> y1 = y;<a name="line.178"></a> <FONT color="green">179</FONT> y2 = y3;<a name="line.179"></a> <FONT color="green">180</FONT> }<a name="line.180"></a> <FONT color="green">181</FONT> } else { // x3 < x < x2<a name="line.181"></a> <FONT color="green">182</FONT> if (MathUtils.sign(y2) + MathUtils.sign(y) == 0.0) {<a name="line.182"></a> <FONT color="green">183</FONT> x1 = x;<a name="line.183"></a> <FONT color="green">184</FONT> y1 = y;<a name="line.184"></a> <FONT color="green">185</FONT> } else {<a name="line.185"></a> <FONT color="green">186</FONT> x1 = x3;<a name="line.186"></a> <FONT color="green">187</FONT> x2 = x;<a name="line.187"></a> <FONT color="green">188</FONT> y1 = y3;<a name="line.188"></a> <FONT color="green">189</FONT> y2 = y;<a name="line.189"></a> <FONT color="green">190</FONT> }<a name="line.190"></a> <FONT color="green">191</FONT> }<a name="line.191"></a> <FONT color="green">192</FONT> oldx = x;<a name="line.192"></a> <FONT color="green">193</FONT> i++;<a name="line.193"></a> <FONT color="green">194</FONT> }<a name="line.194"></a> <FONT color="green">195</FONT> throw new MaxIterationsExceededException(maximalIterationCount);<a name="line.195"></a> <FONT color="green">196</FONT> }<a name="line.196"></a> <FONT color="green">197</FONT> }<a name="line.197"></a> </PRE> </BODY> </HTML>