Mercurial > hg > de.mpg.mpiwg.itgroup.digilib.plugin
view libs/commons-math-2.1/docs/apidocs/src-html/org/apache/commons/math/optimization/general/NonLinearConjugateGradientOptimizer.html @ 13:cbf34dd4d7e6
commons-math-2.1 added
| author | dwinter |
|---|---|
| date | Tue, 04 Jan 2011 10:02:07 +0100 |
| parents | |
| children |
line wrap: on
line source
<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> <a name="line.17"></a> <FONT color="green">018</FONT> package org.apache.commons.math.optimization.general;<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.ConvergenceException;<a name="line.20"></a> <FONT color="green">021</FONT> import org.apache.commons.math.FunctionEvaluationException;<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.analysis.solvers.BrentSolver;<a name="line.23"></a> <FONT color="green">024</FONT> import org.apache.commons.math.analysis.solvers.UnivariateRealSolver;<a name="line.24"></a> <FONT color="green">025</FONT> import org.apache.commons.math.optimization.GoalType;<a name="line.25"></a> <FONT color="green">026</FONT> import org.apache.commons.math.optimization.OptimizationException;<a name="line.26"></a> <FONT color="green">027</FONT> import org.apache.commons.math.optimization.DifferentiableMultivariateRealOptimizer;<a name="line.27"></a> <FONT color="green">028</FONT> import org.apache.commons.math.optimization.RealPointValuePair;<a name="line.28"></a> <FONT color="green">029</FONT> <a name="line.29"></a> <FONT color="green">030</FONT> /**<a name="line.30"></a> <FONT color="green">031</FONT> * Non-linear conjugate gradient optimizer.<a name="line.31"></a> <FONT color="green">032</FONT> * <p><a name="line.32"></a> <FONT color="green">033</FONT> * This class supports both the Fletcher-Reeves and the Polak-Ribi&egrave;re<a name="line.33"></a> <FONT color="green">034</FONT> * update formulas for the conjugate search directions. It also supports<a name="line.34"></a> <FONT color="green">035</FONT> * optional preconditioning.<a name="line.35"></a> <FONT color="green">036</FONT> * </p><a name="line.36"></a> <FONT color="green">037</FONT> *<a name="line.37"></a> <FONT color="green">038</FONT> * @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $<a name="line.38"></a> <FONT color="green">039</FONT> * @since 2.0<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> public class NonLinearConjugateGradientOptimizer<a name="line.43"></a> <FONT color="green">044</FONT> extends AbstractScalarDifferentiableOptimizer<a name="line.44"></a> <FONT color="green">045</FONT> implements DifferentiableMultivariateRealOptimizer {<a name="line.45"></a> <FONT color="green">046</FONT> <a name="line.46"></a> <FONT color="green">047</FONT> /** Update formula for the beta parameter. */<a name="line.47"></a> <FONT color="green">048</FONT> private final ConjugateGradientFormula updateFormula;<a name="line.48"></a> <FONT color="green">049</FONT> <a name="line.49"></a> <FONT color="green">050</FONT> /** Preconditioner (may be null). */<a name="line.50"></a> <FONT color="green">051</FONT> private Preconditioner preconditioner;<a name="line.51"></a> <FONT color="green">052</FONT> <a name="line.52"></a> <FONT color="green">053</FONT> /** solver to use in the line search (may be null). */<a name="line.53"></a> <FONT color="green">054</FONT> private UnivariateRealSolver solver;<a name="line.54"></a> <FONT color="green">055</FONT> <a name="line.55"></a> <FONT color="green">056</FONT> /** Initial step used to bracket the optimum in line search. */<a name="line.56"></a> <FONT color="green">057</FONT> private double initialStep;<a name="line.57"></a> <FONT color="green">058</FONT> <a name="line.58"></a> <FONT color="green">059</FONT> /** Simple constructor with default settings.<a name="line.59"></a> <FONT color="green">060</FONT> * <p>The convergence check is set to a {@link<a name="line.60"></a> <FONT color="green">061</FONT> * org.apache.commons.math.optimization.SimpleVectorialValueChecker}<a name="line.61"></a> <FONT color="green">062</FONT> * and the maximal number of iterations is set to<a name="line.62"></a> <FONT color="green">063</FONT> * {@link AbstractScalarDifferentiableOptimizer#DEFAULT_MAX_ITERATIONS}.<a name="line.63"></a> <FONT color="green">064</FONT> * @param updateFormula formula to use for updating the &beta; parameter,<a name="line.64"></a> <FONT color="green">065</FONT> * must be one of {@link ConjugateGradientFormula#FLETCHER_REEVES} or {@link<a name="line.65"></a> <FONT color="green">066</FONT> * ConjugateGradientFormula#POLAK_RIBIERE}<a name="line.66"></a> <FONT color="green">067</FONT> */<a name="line.67"></a> <FONT color="green">068</FONT> public NonLinearConjugateGradientOptimizer(final ConjugateGradientFormula updateFormula) {<a name="line.68"></a> <FONT color="green">069</FONT> this.updateFormula = updateFormula;<a name="line.69"></a> <FONT color="green">070</FONT> preconditioner = null;<a name="line.70"></a> <FONT color="green">071</FONT> solver = null;<a name="line.71"></a> <FONT color="green">072</FONT> initialStep = 1.0;<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> * Set the preconditioner.<a name="line.76"></a> <FONT color="green">077</FONT> * @param preconditioner preconditioner to use for next optimization,<a name="line.77"></a> <FONT color="green">078</FONT> * may be null to remove an already registered preconditioner<a name="line.78"></a> <FONT color="green">079</FONT> */<a name="line.79"></a> <FONT color="green">080</FONT> public void setPreconditioner(final Preconditioner preconditioner) {<a name="line.80"></a> <FONT color="green">081</FONT> this.preconditioner = preconditioner;<a name="line.81"></a> <FONT color="green">082</FONT> }<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> * Set the solver to use during line search.<a name="line.85"></a> <FONT color="green">086</FONT> * @param lineSearchSolver solver to use during line search, may be null<a name="line.86"></a> <FONT color="green">087</FONT> * to remove an already registered solver and fall back to the<a name="line.87"></a> <FONT color="green">088</FONT> * default {@link BrentSolver Brent solver}.<a name="line.88"></a> <FONT color="green">089</FONT> */<a name="line.89"></a> <FONT color="green">090</FONT> public void setLineSearchSolver(final UnivariateRealSolver lineSearchSolver) {<a name="line.90"></a> <FONT color="green">091</FONT> this.solver = lineSearchSolver;<a name="line.91"></a> <FONT color="green">092</FONT> }<a name="line.92"></a> <FONT color="green">093</FONT> <a name="line.93"></a> <FONT color="green">094</FONT> /**<a name="line.94"></a> <FONT color="green">095</FONT> * Set the initial step used to bracket the optimum in line search.<a name="line.95"></a> <FONT color="green">096</FONT> * <p><a name="line.96"></a> <FONT color="green">097</FONT> * The initial step is a factor with respect to the search direction,<a name="line.97"></a> <FONT color="green">098</FONT> * which itself is roughly related to the gradient of the function<a name="line.98"></a> <FONT color="green">099</FONT> * </p><a name="line.99"></a> <FONT color="green">100</FONT> * @param initialStep initial step used to bracket the optimum in line search,<a name="line.100"></a> <FONT color="green">101</FONT> * if a non-positive value is used, the initial step is reset to its<a name="line.101"></a> <FONT color="green">102</FONT> * default value of 1.0<a name="line.102"></a> <FONT color="green">103</FONT> */<a name="line.103"></a> <FONT color="green">104</FONT> public void setInitialStep(final double initialStep) {<a name="line.104"></a> <FONT color="green">105</FONT> if (initialStep <= 0) {<a name="line.105"></a> <FONT color="green">106</FONT> this.initialStep = 1.0;<a name="line.106"></a> <FONT color="green">107</FONT> } else {<a name="line.107"></a> <FONT color="green">108</FONT> this.initialStep = initialStep;<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> <a name="line.111"></a> <FONT color="green">112</FONT> /** {@inheritDoc} */<a name="line.112"></a> <FONT color="green">113</FONT> @Override<a name="line.113"></a> <FONT color="green">114</FONT> protected RealPointValuePair doOptimize()<a name="line.114"></a> <FONT color="green">115</FONT> throws FunctionEvaluationException, OptimizationException, IllegalArgumentException {<a name="line.115"></a> <FONT color="green">116</FONT> try {<a name="line.116"></a> <FONT color="green">117</FONT> <a name="line.117"></a> <FONT color="green">118</FONT> // initialization<a name="line.118"></a> <FONT color="green">119</FONT> if (preconditioner == null) {<a name="line.119"></a> <FONT color="green">120</FONT> preconditioner = new IdentityPreconditioner();<a name="line.120"></a> <FONT color="green">121</FONT> }<a name="line.121"></a> <FONT color="green">122</FONT> if (solver == null) {<a name="line.122"></a> <FONT color="green">123</FONT> solver = new BrentSolver();<a name="line.123"></a> <FONT color="green">124</FONT> }<a name="line.124"></a> <FONT color="green">125</FONT> final int n = point.length;<a name="line.125"></a> <FONT color="green">126</FONT> double[] r = computeObjectiveGradient(point);<a name="line.126"></a> <FONT color="green">127</FONT> if (goal == GoalType.MINIMIZE) {<a name="line.127"></a> <FONT color="green">128</FONT> for (int i = 0; i < n; ++i) {<a name="line.128"></a> <FONT color="green">129</FONT> r[i] = -r[i];<a name="line.129"></a> <FONT color="green">130</FONT> }<a name="line.130"></a> <FONT color="green">131</FONT> }<a name="line.131"></a> <FONT color="green">132</FONT> <a name="line.132"></a> <FONT color="green">133</FONT> // initial search direction<a name="line.133"></a> <FONT color="green">134</FONT> double[] steepestDescent = preconditioner.precondition(point, r);<a name="line.134"></a> <FONT color="green">135</FONT> double[] searchDirection = steepestDescent.clone();<a name="line.135"></a> <FONT color="green">136</FONT> <a name="line.136"></a> <FONT color="green">137</FONT> double delta = 0;<a name="line.137"></a> <FONT color="green">138</FONT> for (int i = 0; i < n; ++i) {<a name="line.138"></a> <FONT color="green">139</FONT> delta += r[i] * searchDirection[i];<a name="line.139"></a> <FONT color="green">140</FONT> }<a name="line.140"></a> <FONT color="green">141</FONT> <a name="line.141"></a> <FONT color="green">142</FONT> RealPointValuePair current = null;<a name="line.142"></a> <FONT color="green">143</FONT> while (true) {<a name="line.143"></a> <FONT color="green">144</FONT> <a name="line.144"></a> <FONT color="green">145</FONT> final double objective = computeObjectiveValue(point);<a name="line.145"></a> <FONT color="green">146</FONT> RealPointValuePair previous = current;<a name="line.146"></a> <FONT color="green">147</FONT> current = new RealPointValuePair(point, objective);<a name="line.147"></a> <FONT color="green">148</FONT> if (previous != null) {<a name="line.148"></a> <FONT color="green">149</FONT> if (checker.converged(getIterations(), previous, current)) {<a name="line.149"></a> <FONT color="green">150</FONT> // we have found an optimum<a name="line.150"></a> <FONT color="green">151</FONT> return current;<a name="line.151"></a> <FONT color="green">152</FONT> }<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> incrementIterationsCounter();<a name="line.155"></a> <FONT color="green">156</FONT> <a name="line.156"></a> <FONT color="green">157</FONT> double dTd = 0;<a name="line.157"></a> <FONT color="green">158</FONT> for (final double di : searchDirection) {<a name="line.158"></a> <FONT color="green">159</FONT> dTd += di * di;<a name="line.159"></a> <FONT color="green">160</FONT> }<a name="line.160"></a> <FONT color="green">161</FONT> <a name="line.161"></a> <FONT color="green">162</FONT> // find the optimal step in the search direction<a name="line.162"></a> <FONT color="green">163</FONT> final UnivariateRealFunction lsf = new LineSearchFunction(searchDirection);<a name="line.163"></a> <FONT color="green">164</FONT> final double step = solver.solve(lsf, 0, findUpperBound(lsf, 0, initialStep));<a name="line.164"></a> <FONT color="green">165</FONT> <a name="line.165"></a> <FONT color="green">166</FONT> // validate new point<a name="line.166"></a> <FONT color="green">167</FONT> for (int i = 0; i < point.length; ++i) {<a name="line.167"></a> <FONT color="green">168</FONT> point[i] += step * searchDirection[i];<a name="line.168"></a> <FONT color="green">169</FONT> }<a name="line.169"></a> <FONT color="green">170</FONT> r = computeObjectiveGradient(point);<a name="line.170"></a> <FONT color="green">171</FONT> if (goal == GoalType.MINIMIZE) {<a name="line.171"></a> <FONT color="green">172</FONT> for (int i = 0; i < n; ++i) {<a name="line.172"></a> <FONT color="green">173</FONT> r[i] = -r[i];<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> // compute beta<a name="line.177"></a> <FONT color="green">178</FONT> final double deltaOld = delta;<a name="line.178"></a> <FONT color="green">179</FONT> final double[] newSteepestDescent = preconditioner.precondition(point, r);<a name="line.179"></a> <FONT color="green">180</FONT> delta = 0;<a name="line.180"></a> <FONT color="green">181</FONT> for (int i = 0; i < n; ++i) {<a name="line.181"></a> <FONT color="green">182</FONT> delta += r[i] * newSteepestDescent[i];<a name="line.182"></a> <FONT color="green">183</FONT> }<a name="line.183"></a> <FONT color="green">184</FONT> <a name="line.184"></a> <FONT color="green">185</FONT> final double beta;<a name="line.185"></a> <FONT color="green">186</FONT> if (updateFormula == ConjugateGradientFormula.FLETCHER_REEVES) {<a name="line.186"></a> <FONT color="green">187</FONT> beta = delta / deltaOld;<a name="line.187"></a> <FONT color="green">188</FONT> } else {<a name="line.188"></a> <FONT color="green">189</FONT> double deltaMid = 0;<a name="line.189"></a> <FONT color="green">190</FONT> for (int i = 0; i < r.length; ++i) {<a name="line.190"></a> <FONT color="green">191</FONT> deltaMid += r[i] * steepestDescent[i];<a name="line.191"></a> <FONT color="green">192</FONT> }<a name="line.192"></a> <FONT color="green">193</FONT> beta = (delta - deltaMid) / deltaOld;<a name="line.193"></a> <FONT color="green">194</FONT> }<a name="line.194"></a> <FONT color="green">195</FONT> steepestDescent = newSteepestDescent;<a name="line.195"></a> <FONT color="green">196</FONT> <a name="line.196"></a> <FONT color="green">197</FONT> // compute conjugate search direction<a name="line.197"></a> <FONT color="green">198</FONT> if ((getIterations() % n == 0) || (beta < 0)) {<a name="line.198"></a> <FONT color="green">199</FONT> // break conjugation: reset search direction<a name="line.199"></a> <FONT color="green">200</FONT> searchDirection = steepestDescent.clone();<a name="line.200"></a> <FONT color="green">201</FONT> } else {<a name="line.201"></a> <FONT color="green">202</FONT> // compute new conjugate search direction<a name="line.202"></a> <FONT color="green">203</FONT> for (int i = 0; i < n; ++i) {<a name="line.203"></a> <FONT color="green">204</FONT> searchDirection[i] = steepestDescent[i] + beta * searchDirection[i];<a name="line.204"></a> <FONT color="green">205</FONT> }<a name="line.205"></a> <FONT color="green">206</FONT> }<a name="line.206"></a> <FONT color="green">207</FONT> <a name="line.207"></a> <FONT color="green">208</FONT> }<a name="line.208"></a> <FONT color="green">209</FONT> <a name="line.209"></a> <FONT color="green">210</FONT> } catch (ConvergenceException ce) {<a name="line.210"></a> <FONT color="green">211</FONT> throw new OptimizationException(ce);<a name="line.211"></a> <FONT color="green">212</FONT> }<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> * Find the upper bound b ensuring bracketing of a root between a and b<a name="line.216"></a> <FONT color="green">217</FONT> * @param f function whose root must be bracketed<a name="line.217"></a> <FONT color="green">218</FONT> * @param a lower bound of the interval<a name="line.218"></a> <FONT color="green">219</FONT> * @param h initial step to try<a name="line.219"></a> <FONT color="green">220</FONT> * @return b such that f(a) and f(b) have opposite signs<a name="line.220"></a> <FONT color="green">221</FONT> * @exception FunctionEvaluationException if the function cannot be computed<a name="line.221"></a> <FONT color="green">222</FONT> * @exception OptimizationException if no bracket can be found<a name="line.222"></a> <FONT color="green">223</FONT> */<a name="line.223"></a> <FONT color="green">224</FONT> private double findUpperBound(final UnivariateRealFunction f,<a name="line.224"></a> <FONT color="green">225</FONT> final double a, final double h)<a name="line.225"></a> <FONT color="green">226</FONT> throws FunctionEvaluationException, OptimizationException {<a name="line.226"></a> <FONT color="green">227</FONT> final double yA = f.value(a);<a name="line.227"></a> <FONT color="green">228</FONT> double yB = yA;<a name="line.228"></a> <FONT color="green">229</FONT> for (double step = h; step < Double.MAX_VALUE; step *= Math.max(2, yA / yB)) {<a name="line.229"></a> <FONT color="green">230</FONT> final double b = a + step;<a name="line.230"></a> <FONT color="green">231</FONT> yB = f.value(b);<a name="line.231"></a> <FONT color="green">232</FONT> if (yA * yB <= 0) {<a name="line.232"></a> <FONT color="green">233</FONT> return b;<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> throw new OptimizationException("unable to bracket optimum in line search");<a name="line.236"></a> <FONT color="green">237</FONT> }<a name="line.237"></a> <FONT color="green">238</FONT> <a name="line.238"></a> <FONT color="green">239</FONT> /** Default identity preconditioner. */<a name="line.239"></a> <FONT color="green">240</FONT> private static class IdentityPreconditioner implements Preconditioner {<a name="line.240"></a> <FONT color="green">241</FONT> <a name="line.241"></a> <FONT color="green">242</FONT> /** {@inheritDoc} */<a name="line.242"></a> <FONT color="green">243</FONT> public double[] precondition(double[] variables, double[] r) {<a name="line.243"></a> <FONT color="green">244</FONT> return r.clone();<a name="line.244"></a> <FONT color="green">245</FONT> }<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> <FONT color="green">248</FONT> <a name="line.248"></a> <FONT color="green">249</FONT> /** Internal class for line search.<a name="line.249"></a> <FONT color="green">250</FONT> * <p><a name="line.250"></a> <FONT color="green">251</FONT> * The function represented by this class is the dot product of<a name="line.251"></a> <FONT color="green">252</FONT> * the objective function gradient and the search direction. Its<a name="line.252"></a> <FONT color="green">253</FONT> * value is zero when the gradient is orthogonal to the search<a name="line.253"></a> <FONT color="green">254</FONT> * direction, i.e. when the objective function value is a local<a name="line.254"></a> <FONT color="green">255</FONT> * extremum along the search direction.<a name="line.255"></a> <FONT color="green">256</FONT> * </p><a name="line.256"></a> <FONT color="green">257</FONT> */<a name="line.257"></a> <FONT color="green">258</FONT> private class LineSearchFunction implements UnivariateRealFunction {<a name="line.258"></a> <FONT color="green">259</FONT> /** Search direction. */<a name="line.259"></a> <FONT color="green">260</FONT> private final double[] searchDirection;<a name="line.260"></a> <FONT color="green">261</FONT> <a name="line.261"></a> <FONT color="green">262</FONT> /** Simple constructor.<a name="line.262"></a> <FONT color="green">263</FONT> * @param searchDirection search direction<a name="line.263"></a> <FONT color="green">264</FONT> */<a name="line.264"></a> <FONT color="green">265</FONT> public LineSearchFunction(final double[] searchDirection) {<a name="line.265"></a> <FONT color="green">266</FONT> this.searchDirection = searchDirection;<a name="line.266"></a> <FONT color="green">267</FONT> }<a name="line.267"></a> <FONT color="green">268</FONT> <a name="line.268"></a> <FONT color="green">269</FONT> /** {@inheritDoc} */<a name="line.269"></a> <FONT color="green">270</FONT> public double value(double x) throws FunctionEvaluationException {<a name="line.270"></a> <FONT color="green">271</FONT> <a name="line.271"></a> <FONT color="green">272</FONT> // current point in the search direction<a name="line.272"></a> <FONT color="green">273</FONT> final double[] shiftedPoint = point.clone();<a name="line.273"></a> <FONT color="green">274</FONT> for (int i = 0; i < shiftedPoint.length; ++i) {<a name="line.274"></a> <FONT color="green">275</FONT> shiftedPoint[i] += x * searchDirection[i];<a name="line.275"></a> <FONT color="green">276</FONT> }<a name="line.276"></a> <FONT color="green">277</FONT> <a name="line.277"></a> <FONT color="green">278</FONT> // gradient of the objective function<a name="line.278"></a> <FONT color="green">279</FONT> final double[] gradient = computeObjectiveGradient(shiftedPoint);<a name="line.279"></a> <FONT color="green">280</FONT> <a name="line.280"></a> <FONT color="green">281</FONT> // dot product with the search direction<a name="line.281"></a> <FONT color="green">282</FONT> double dotProduct = 0;<a name="line.282"></a> <FONT color="green">283</FONT> for (int i = 0; i < gradient.length; ++i) {<a name="line.283"></a> <FONT color="green">284</FONT> dotProduct += gradient[i] * searchDirection[i];<a name="line.284"></a> <FONT color="green">285</FONT> }<a name="line.285"></a> <FONT color="green">286</FONT> <a name="line.286"></a> <FONT color="green">287</FONT> return dotProduct;<a name="line.287"></a> <FONT color="green">288</FONT> <a name="line.288"></a> <FONT color="green">289</FONT> }<a name="line.289"></a> <FONT color="green">290</FONT> <a name="line.290"></a> <FONT color="green">291</FONT> }<a name="line.291"></a> <FONT color="green">292</FONT> <a name="line.292"></a> <FONT color="green">293</FONT> }<a name="line.293"></a> </PRE> </BODY> </HTML>