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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.optimization.univariate;<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.MaxIterationsExceededException;<a name="line.20"></a> <FONT color="green">021</FONT> import org.apache.commons.math.analysis.UnivariateRealFunction;<a name="line.21"></a> <FONT color="green">022</FONT> import org.apache.commons.math.optimization.GoalType;<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> * Implements Richard Brent's algorithm (from his book "Algorithms for<a name="line.25"></a> <FONT color="green">026</FONT> * Minimization without Derivatives", p. 79) for finding minima of real<a name="line.26"></a> <FONT color="green">027</FONT> * univariate functions.<a name="line.27"></a> <FONT color="green">028</FONT> *<a name="line.28"></a> <FONT color="green">029</FONT> * @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $<a name="line.29"></a> <FONT color="green">030</FONT> * @since 2.0<a name="line.30"></a> <FONT color="green">031</FONT> */<a name="line.31"></a> <FONT color="green">032</FONT> public class BrentOptimizer extends AbstractUnivariateRealOptimizer {<a name="line.32"></a> <FONT color="green">033</FONT> <a name="line.33"></a> <FONT color="green">034</FONT> /**<a name="line.34"></a> <FONT color="green">035</FONT> * Golden section.<a name="line.35"></a> <FONT color="green">036</FONT> */<a name="line.36"></a> <FONT color="green">037</FONT> private static final double GOLDEN_SECTION = 0.5 * (3 - Math.sqrt(5));<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.<a name="line.40"></a> <FONT color="green">041</FONT> */<a name="line.41"></a> <FONT color="green">042</FONT> public BrentOptimizer() {<a name="line.42"></a> <FONT color="green">043</FONT> super(100, 1E-10);<a name="line.43"></a> <FONT color="green">044</FONT> }<a name="line.44"></a> <FONT color="green">045</FONT> <a name="line.45"></a> <FONT color="green">046</FONT> /** {@inheritDoc} */<a name="line.46"></a> <FONT color="green">047</FONT> public double optimize(final UnivariateRealFunction f, final GoalType goalType,<a name="line.47"></a> <FONT color="green">048</FONT> final double min, final double max, final double startValue)<a name="line.48"></a> <FONT color="green">049</FONT> throws MaxIterationsExceededException, FunctionEvaluationException {<a name="line.49"></a> <FONT color="green">050</FONT> return optimize(f, goalType, min, max);<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> /** {@inheritDoc} */<a name="line.53"></a> <FONT color="green">054</FONT> public double optimize(final UnivariateRealFunction f, final GoalType goalType,<a name="line.54"></a> <FONT color="green">055</FONT> final double min, final double max)<a name="line.55"></a> <FONT color="green">056</FONT> throws MaxIterationsExceededException, FunctionEvaluationException {<a name="line.56"></a> <FONT color="green">057</FONT> clearResult();<a name="line.57"></a> <FONT color="green">058</FONT> return localMin(f, goalType, min, max, relativeAccuracy, absoluteAccuracy);<a name="line.58"></a> <FONT color="green">059</FONT> }<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> * Find the minimum of the function {@code f} within the interval {@code (a, b)}.<a name="line.62"></a> <FONT color="green">063</FONT> *<a name="line.63"></a> <FONT color="green">064</FONT> * If the function {@code f} is defined on the interval {@code (a, b)}, then<a name="line.64"></a> <FONT color="green">065</FONT> * this method finds an approximation {@code x} to the point at which {@code f}<a name="line.65"></a> <FONT color="green">066</FONT> * attains its minimum.<br/><a name="line.66"></a> <FONT color="green">067</FONT> * {@code t} and {@code eps} define a tolerance {@code tol = eps |x| + t} and<a name="line.67"></a> <FONT color="green">068</FONT> * {@code f} is never evaluated at two points closer together than {@code tol}.<a name="line.68"></a> <FONT color="green">069</FONT> * {@code eps} should be no smaller than <em>2 macheps</em> and preferable not<a name="line.69"></a> <FONT color="green">070</FONT> * much less than <em>sqrt(macheps)</em>, where <em>macheps</em> is the relative<a name="line.70"></a> <FONT color="green">071</FONT> * machine precision. {@code t} should be positive.<a name="line.71"></a> <FONT color="green">072</FONT> * @param f the function to solve<a name="line.72"></a> <FONT color="green">073</FONT> * @param goalType type of optimization goal: either {@link GoalType#MAXIMIZE}<a name="line.73"></a> <FONT color="green">074</FONT> * or {@link GoalType#MINIMIZE}<a name="line.74"></a> <FONT color="green">075</FONT> * @param a Lower bound of the interval<a name="line.75"></a> <FONT color="green">076</FONT> * @param b Higher bound of the interval<a name="line.76"></a> <FONT color="green">077</FONT> * @param eps Relative accuracy<a name="line.77"></a> <FONT color="green">078</FONT> * @param t Absolute accuracy<a name="line.78"></a> <FONT color="green">079</FONT> * @return the point at which the function is minimal.<a name="line.79"></a> <FONT color="green">080</FONT> * @throws MaxIterationsExceededException if the maximum iteration count<a name="line.80"></a> <FONT color="green">081</FONT> * is exceeded.<a name="line.81"></a> <FONT color="green">082</FONT> * @throws FunctionEvaluationException if an error occurs evaluating<a name="line.82"></a> <FONT color="green">083</FONT> * the function.<a name="line.83"></a> <FONT color="green">084</FONT> */<a name="line.84"></a> <FONT color="green">085</FONT> private double localMin(final UnivariateRealFunction f, final GoalType goalType,<a name="line.85"></a> <FONT color="green">086</FONT> double a, double b, final double eps, final double t)<a name="line.86"></a> <FONT color="green">087</FONT> throws MaxIterationsExceededException, FunctionEvaluationException {<a name="line.87"></a> <FONT color="green">088</FONT> double x = a + GOLDEN_SECTION * (b - a);<a name="line.88"></a> <FONT color="green">089</FONT> double v = x;<a name="line.89"></a> <FONT color="green">090</FONT> double w = x;<a name="line.90"></a> <FONT color="green">091</FONT> double e = 0;<a name="line.91"></a> <FONT color="green">092</FONT> double fx = computeObjectiveValue(f, x);<a name="line.92"></a> <FONT color="green">093</FONT> if (goalType == GoalType.MAXIMIZE) {<a name="line.93"></a> <FONT color="green">094</FONT> fx = -fx;<a name="line.94"></a> <FONT color="green">095</FONT> }<a name="line.95"></a> <FONT color="green">096</FONT> double fv = fx;<a name="line.96"></a> <FONT color="green">097</FONT> double fw = fx;<a name="line.97"></a> <FONT color="green">098</FONT> <a name="line.98"></a> <FONT color="green">099</FONT> int count = 0;<a name="line.99"></a> <FONT color="green">100</FONT> while (count < maximalIterationCount) {<a name="line.100"></a> <FONT color="green">101</FONT> double m = 0.5 * (a + b);<a name="line.101"></a> <FONT color="green">102</FONT> double tol = eps * Math.abs(x) + t;<a name="line.102"></a> <FONT color="green">103</FONT> double t2 = 2 * tol;<a name="line.103"></a> <FONT color="green">104</FONT> <a name="line.104"></a> <FONT color="green">105</FONT> // Check stopping criterion.<a name="line.105"></a> <FONT color="green">106</FONT> if (Math.abs(x - m) > t2 - 0.5 * (b - a)) {<a name="line.106"></a> <FONT color="green">107</FONT> double p = 0;<a name="line.107"></a> <FONT color="green">108</FONT> double q = 0;<a name="line.108"></a> <FONT color="green">109</FONT> double r = 0;<a name="line.109"></a> <FONT color="green">110</FONT> double d = 0;<a name="line.110"></a> <FONT color="green">111</FONT> double u = 0;<a name="line.111"></a> <FONT color="green">112</FONT> <a name="line.112"></a> <FONT color="green">113</FONT> if (Math.abs(e) > tol) { // Fit parabola.<a name="line.113"></a> <FONT color="green">114</FONT> r = (x - w) * (fx - fv);<a name="line.114"></a> <FONT color="green">115</FONT> q = (x - v) * (fx - fw);<a name="line.115"></a> <FONT color="green">116</FONT> p = (x - v) * q - (x - w) * r;<a name="line.116"></a> <FONT color="green">117</FONT> q = 2 * (q - r);<a name="line.117"></a> <FONT color="green">118</FONT> <a name="line.118"></a> <FONT color="green">119</FONT> if (q > 0) {<a name="line.119"></a> <FONT color="green">120</FONT> p = -p;<a name="line.120"></a> <FONT color="green">121</FONT> } else {<a name="line.121"></a> <FONT color="green">122</FONT> q = -q;<a name="line.122"></a> <FONT color="green">123</FONT> }<a name="line.123"></a> <FONT color="green">124</FONT> <a name="line.124"></a> <FONT color="green">125</FONT> r = e;<a name="line.125"></a> <FONT color="green">126</FONT> e = d;<a name="line.126"></a> <FONT color="green">127</FONT> }<a name="line.127"></a> <FONT color="green">128</FONT> <a name="line.128"></a> <FONT color="green">129</FONT> if (Math.abs(p) < Math.abs(0.5 * q * r) &&<a name="line.129"></a> <FONT color="green">130</FONT> (p < q * (a - x)) && (p < q * (b - x))) { // Parabolic interpolation step.<a name="line.130"></a> <FONT color="green">131</FONT> d = p / q;<a name="line.131"></a> <FONT color="green">132</FONT> u = x + d;<a name="line.132"></a> <FONT color="green">133</FONT> <a name="line.133"></a> <FONT color="green">134</FONT> // f must not be evaluated too close to a or b.<a name="line.134"></a> <FONT color="green">135</FONT> if (((u - a) < t2) || ((b - u) < t2)) {<a name="line.135"></a> <FONT color="green">136</FONT> d = (x < m) ? tol : -tol;<a name="line.136"></a> <FONT color="green">137</FONT> }<a name="line.137"></a> <FONT color="green">138</FONT> } else { // Golden section step.<a name="line.138"></a> <FONT color="green">139</FONT> e = ((x < m) ? b : a) - x;<a name="line.139"></a> <FONT color="green">140</FONT> d = GOLDEN_SECTION * e;<a name="line.140"></a> <FONT color="green">141</FONT> }<a name="line.141"></a> <FONT color="green">142</FONT> <a name="line.142"></a> <FONT color="green">143</FONT> // f must not be evaluated too close to a or b.<a name="line.143"></a> <FONT color="green">144</FONT> u = x + ((Math.abs(d) > tol) ? d : ((d > 0) ? tol : -tol));<a name="line.144"></a> <FONT color="green">145</FONT> double fu = computeObjectiveValue(f, u);<a name="line.145"></a> <FONT color="green">146</FONT> if (goalType == GoalType.MAXIMIZE) {<a name="line.146"></a> <FONT color="green">147</FONT> fu = -fu;<a name="line.147"></a> <FONT color="green">148</FONT> }<a name="line.148"></a> <FONT color="green">149</FONT> <a name="line.149"></a> <FONT color="green">150</FONT> // Update a, b, v, w and x.<a name="line.150"></a> <FONT color="green">151</FONT> if (fu <= fx) {<a name="line.151"></a> <FONT color="green">152</FONT> if (u < x) {<a name="line.152"></a> <FONT color="green">153</FONT> b = x;<a name="line.153"></a> <FONT color="green">154</FONT> } else {<a name="line.154"></a> <FONT color="green">155</FONT> a = x;<a name="line.155"></a> <FONT color="green">156</FONT> }<a name="line.156"></a> <FONT color="green">157</FONT> v = w;<a name="line.157"></a> <FONT color="green">158</FONT> fv = fw;<a name="line.158"></a> <FONT color="green">159</FONT> w = x;<a name="line.159"></a> <FONT color="green">160</FONT> fw = fx;<a name="line.160"></a> <FONT color="green">161</FONT> x = u;<a name="line.161"></a> <FONT color="green">162</FONT> fx = fu;<a name="line.162"></a> <FONT color="green">163</FONT> } else {<a name="line.163"></a> <FONT color="green">164</FONT> if (u < x) {<a name="line.164"></a> <FONT color="green">165</FONT> a = u;<a name="line.165"></a> <FONT color="green">166</FONT> } else {<a name="line.166"></a> <FONT color="green">167</FONT> b = u;<a name="line.167"></a> <FONT color="green">168</FONT> }<a name="line.168"></a> <FONT color="green">169</FONT> if ((fu <= fw) || (w == x)) {<a name="line.169"></a> <FONT color="green">170</FONT> v = w;<a name="line.170"></a> <FONT color="green">171</FONT> fv = fw;<a name="line.171"></a> <FONT color="green">172</FONT> w = u;<a name="line.172"></a> <FONT color="green">173</FONT> fw = fu;<a name="line.173"></a> <FONT color="green">174</FONT> } else if ((fu <= fv) || (v == x) || (v == w)) {<a name="line.174"></a> <FONT color="green">175</FONT> v = u;<a name="line.175"></a> <FONT color="green">176</FONT> fv = fu;<a name="line.176"></a> <FONT color="green">177</FONT> }<a name="line.177"></a> <FONT color="green">178</FONT> }<a name="line.178"></a> <FONT color="green">179</FONT> } else { // termination<a name="line.179"></a> <FONT color="green">180</FONT> setResult(x, (goalType == GoalType.MAXIMIZE) ? -fx : fx, count);<a name="line.180"></a> <FONT color="green">181</FONT> return x;<a name="line.181"></a> <FONT color="green">182</FONT> }<a name="line.182"></a> <FONT color="green">183</FONT> <a name="line.183"></a> <FONT color="green">184</FONT> ++count;<a name="line.184"></a> <FONT color="green">185</FONT> }<a name="line.185"></a> <FONT color="green">186</FONT> <a name="line.186"></a> <FONT color="green">187</FONT> throw new MaxIterationsExceededException(maximalIterationCount);<a name="line.187"></a> <FONT color="green">188</FONT> <a name="line.188"></a> <FONT color="green">189</FONT> }<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> </PRE> </BODY> </HTML>