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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> <a name="line.17"></a> <FONT color="green">018</FONT> package org.apache.commons.math.estimation;<a name="line.18"></a> <FONT color="green">019</FONT> <a name="line.19"></a> <FONT color="green">020</FONT> import java.io.Serializable;<a name="line.20"></a> <FONT color="green">021</FONT> <a name="line.21"></a> <FONT color="green">022</FONT> import org.apache.commons.math.linear.InvalidMatrixException;<a name="line.22"></a> <FONT color="green">023</FONT> import org.apache.commons.math.linear.LUDecompositionImpl;<a name="line.23"></a> <FONT color="green">024</FONT> import org.apache.commons.math.linear.MatrixUtils;<a name="line.24"></a> <FONT color="green">025</FONT> import org.apache.commons.math.linear.RealMatrix;<a name="line.25"></a> <FONT color="green">026</FONT> import org.apache.commons.math.linear.RealVector;<a name="line.26"></a> <FONT color="green">027</FONT> import org.apache.commons.math.linear.ArrayRealVector;<a name="line.27"></a> <FONT color="green">028</FONT> <a name="line.28"></a> <FONT color="green">029</FONT> /**<a name="line.29"></a> <FONT color="green">030</FONT> * This class implements a solver for estimation problems.<a name="line.30"></a> <FONT color="green">031</FONT> *<a name="line.31"></a> <FONT color="green">032</FONT> * <p>This class solves estimation problems using a weighted least<a name="line.32"></a> <FONT color="green">033</FONT> * squares criterion on the measurement residuals. It uses a<a name="line.33"></a> <FONT color="green">034</FONT> * Gauss-Newton algorithm.</p><a name="line.34"></a> <FONT color="green">035</FONT> *<a name="line.35"></a> <FONT color="green">036</FONT> * @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $<a name="line.36"></a> <FONT color="green">037</FONT> * @since 1.2<a name="line.37"></a> <FONT color="green">038</FONT> * @deprecated as of 2.0, everything in package org.apache.commons.math.estimation has<a name="line.38"></a> <FONT color="green">039</FONT> * been deprecated and replaced by package org.apache.commons.math.optimization.general<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> @Deprecated<a name="line.42"></a> <FONT color="green">043</FONT> public class GaussNewtonEstimator extends AbstractEstimator implements Serializable {<a name="line.43"></a> <FONT color="green">044</FONT> <a name="line.44"></a> <FONT color="green">045</FONT> /** Serializable version identifier */<a name="line.45"></a> <FONT color="green">046</FONT> private static final long serialVersionUID = 5485001826076289109L;<a name="line.46"></a> <FONT color="green">047</FONT> <a name="line.47"></a> <FONT color="green">048</FONT> /** Default threshold for cost steady state detection. */<a name="line.48"></a> <FONT color="green">049</FONT> private static final double DEFAULT_STEADY_STATE_THRESHOLD = 1.0e-6;<a name="line.49"></a> <FONT color="green">050</FONT> <a name="line.50"></a> <FONT color="green">051</FONT> /** Default threshold for cost convergence. */<a name="line.51"></a> <FONT color="green">052</FONT> private static final double DEFAULT_CONVERGENCE = 1.0e-6;<a name="line.52"></a> <FONT color="green">053</FONT> <a name="line.53"></a> <FONT color="green">054</FONT> /** Threshold for cost steady state detection. */<a name="line.54"></a> <FONT color="green">055</FONT> private double steadyStateThreshold;<a name="line.55"></a> <FONT color="green">056</FONT> <a name="line.56"></a> <FONT color="green">057</FONT> /** Threshold for cost convergence. */<a name="line.57"></a> <FONT color="green">058</FONT> private double convergence;<a name="line.58"></a> <FONT color="green">059</FONT> <a name="line.59"></a> <FONT color="green">060</FONT> /** Simple constructor with default settings.<a name="line.60"></a> <FONT color="green">061</FONT> * <p><a name="line.61"></a> <FONT color="green">062</FONT> * The estimator is built with default values for all settings.<a name="line.62"></a> <FONT color="green">063</FONT> * </p><a name="line.63"></a> <FONT color="green">064</FONT> * @see #DEFAULT_STEADY_STATE_THRESHOLD<a name="line.64"></a> <FONT color="green">065</FONT> * @see #DEFAULT_CONVERGENCE<a name="line.65"></a> <FONT color="green">066</FONT> * @see AbstractEstimator#DEFAULT_MAX_COST_EVALUATIONS<a name="line.66"></a> <FONT color="green">067</FONT> */<a name="line.67"></a> <FONT color="green">068</FONT> public GaussNewtonEstimator() {<a name="line.68"></a> <FONT color="green">069</FONT> this.steadyStateThreshold = DEFAULT_STEADY_STATE_THRESHOLD;<a name="line.69"></a> <FONT color="green">070</FONT> this.convergence = DEFAULT_CONVERGENCE;<a name="line.70"></a> <FONT color="green">071</FONT> }<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> * Simple constructor.<a name="line.74"></a> <FONT color="green">075</FONT> *<a name="line.75"></a> <FONT color="green">076</FONT> * <p>This constructor builds an estimator and stores its convergence<a name="line.76"></a> <FONT color="green">077</FONT> * characteristics.</p><a name="line.77"></a> <FONT color="green">078</FONT> *<a name="line.78"></a> <FONT color="green">079</FONT> * <p>An estimator is considered to have converged whenever either<a name="line.79"></a> <FONT color="green">080</FONT> * the criterion goes below a physical threshold under which<a name="line.80"></a> <FONT color="green">081</FONT> * improvements are considered useless or when the algorithm is<a name="line.81"></a> <FONT color="green">082</FONT> * unable to improve it (even if it is still high). The first<a name="line.82"></a> <FONT color="green">083</FONT> * condition that is met stops the iterations.</p><a name="line.83"></a> <FONT color="green">084</FONT> *<a name="line.84"></a> <FONT color="green">085</FONT> * <p>The fact an estimator has converged does not mean that the<a name="line.85"></a> <FONT color="green">086</FONT> * model accurately fits the measurements. It only means no better<a name="line.86"></a> <FONT color="green">087</FONT> * solution can be found, it does not mean this one is good. Such an<a name="line.87"></a> <FONT color="green">088</FONT> * analysis is left to the caller.</p><a name="line.88"></a> <FONT color="green">089</FONT> *<a name="line.89"></a> <FONT color="green">090</FONT> * <p>If neither conditions are fulfilled before a given number of<a name="line.90"></a> <FONT color="green">091</FONT> * iterations, the algorithm is considered to have failed and an<a name="line.91"></a> <FONT color="green">092</FONT> * {@link EstimationException} is thrown.</p><a name="line.92"></a> <FONT color="green">093</FONT> *<a name="line.93"></a> <FONT color="green">094</FONT> * @param maxCostEval maximal number of cost evaluations allowed<a name="line.94"></a> <FONT color="green">095</FONT> * @param convergence criterion threshold below which we do not need<a name="line.95"></a> <FONT color="green">096</FONT> * to improve the criterion anymore<a name="line.96"></a> <FONT color="green">097</FONT> * @param steadyStateThreshold steady state detection threshold, the<a name="line.97"></a> <FONT color="green">098</FONT> * problem has converged has reached a steady state if<a name="line.98"></a> <FONT color="green">099</FONT> * <code>Math.abs(J<sub>n</sub> - J<sub>n-1</sub>) &lt;<a name="line.99"></a> <FONT color="green">100</FONT> * J<sub>n</sub> &times convergence</code>, where <code>J<sub>n</sub></code><a name="line.100"></a> <FONT color="green">101</FONT> * and <code>J<sub>n-1</sub></code> are the current and preceding criterion<a name="line.101"></a> <FONT color="green">102</FONT> * values (square sum of the weighted residuals of considered measurements).<a name="line.102"></a> <FONT color="green">103</FONT> */<a name="line.103"></a> <FONT color="green">104</FONT> public GaussNewtonEstimator(final int maxCostEval, final double convergence,<a name="line.104"></a> <FONT color="green">105</FONT> final double steadyStateThreshold) {<a name="line.105"></a> <FONT color="green">106</FONT> setMaxCostEval(maxCostEval);<a name="line.106"></a> <FONT color="green">107</FONT> this.steadyStateThreshold = steadyStateThreshold;<a name="line.107"></a> <FONT color="green">108</FONT> this.convergence = convergence;<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> * Set the convergence criterion threshold.<a name="line.112"></a> <FONT color="green">113</FONT> * @param convergence criterion threshold below which we do not need<a name="line.113"></a> <FONT color="green">114</FONT> * to improve the criterion anymore<a name="line.114"></a> <FONT color="green">115</FONT> */<a name="line.115"></a> <FONT color="green">116</FONT> public void setConvergence(final double convergence) {<a name="line.116"></a> <FONT color="green">117</FONT> this.convergence = convergence;<a name="line.117"></a> <FONT color="green">118</FONT> }<a name="line.118"></a> <FONT color="green">119</FONT> <a name="line.119"></a> <FONT color="green">120</FONT> /**<a name="line.120"></a> <FONT color="green">121</FONT> * Set the steady state detection threshold.<a name="line.121"></a> <FONT color="green">122</FONT> * <p><a name="line.122"></a> <FONT color="green">123</FONT> * The problem has converged has reached a steady state if<a name="line.123"></a> <FONT color="green">124</FONT> * <code>Math.abs(J<sub>n</sub> - J<sub>n-1</sub>) &lt;<a name="line.124"></a> <FONT color="green">125</FONT> * J<sub>n</sub> &times convergence</code>, where <code>J<sub>n</sub></code><a name="line.125"></a> <FONT color="green">126</FONT> * and <code>J<sub>n-1</sub></code> are the current and preceding criterion<a name="line.126"></a> <FONT color="green">127</FONT> * values (square sum of the weighted residuals of considered measurements).<a name="line.127"></a> <FONT color="green">128</FONT> * </p><a name="line.128"></a> <FONT color="green">129</FONT> * @param steadyStateThreshold steady state detection threshold<a name="line.129"></a> <FONT color="green">130</FONT> */<a name="line.130"></a> <FONT color="green">131</FONT> public void setSteadyStateThreshold(final double steadyStateThreshold) {<a name="line.131"></a> <FONT color="green">132</FONT> this.steadyStateThreshold = steadyStateThreshold;<a name="line.132"></a> <FONT color="green">133</FONT> }<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> * Solve an estimation problem using a least squares criterion.<a name="line.136"></a> <FONT color="green">137</FONT> *<a name="line.137"></a> <FONT color="green">138</FONT> * <p>This method set the unbound parameters of the given problem<a name="line.138"></a> <FONT color="green">139</FONT> * starting from their current values through several iterations. At<a name="line.139"></a> <FONT color="green">140</FONT> * each step, the unbound parameters are changed in order to<a name="line.140"></a> <FONT color="green">141</FONT> * minimize a weighted least square criterion based on the<a name="line.141"></a> <FONT color="green">142</FONT> * measurements of the problem.</p><a name="line.142"></a> <FONT color="green">143</FONT> *<a name="line.143"></a> <FONT color="green">144</FONT> * <p>The iterations are stopped either when the criterion goes<a name="line.144"></a> <FONT color="green">145</FONT> * below a physical threshold under which improvement are considered<a name="line.145"></a> <FONT color="green">146</FONT> * useless or when the algorithm is unable to improve it (even if it<a name="line.146"></a> <FONT color="green">147</FONT> * is still high). The first condition that is met stops the<a name="line.147"></a> <FONT color="green">148</FONT> * iterations. If the convergence it not reached before the maximum<a name="line.148"></a> <FONT color="green">149</FONT> * number of iterations, an {@link EstimationException} is<a name="line.149"></a> <FONT color="green">150</FONT> * thrown.</p><a name="line.150"></a> <FONT color="green">151</FONT> *<a name="line.151"></a> <FONT color="green">152</FONT> * @param problem estimation problem to solve<a name="line.152"></a> <FONT color="green">153</FONT> * @exception EstimationException if the problem cannot be solved<a name="line.153"></a> <FONT color="green">154</FONT> *<a name="line.154"></a> <FONT color="green">155</FONT> * @see EstimationProblem<a name="line.155"></a> <FONT color="green">156</FONT> *<a name="line.156"></a> <FONT color="green">157</FONT> */<a name="line.157"></a> <FONT color="green">158</FONT> @Override<a name="line.158"></a> <FONT color="green">159</FONT> public void estimate(EstimationProblem problem)<a name="line.159"></a> <FONT color="green">160</FONT> throws EstimationException {<a name="line.160"></a> <FONT color="green">161</FONT> <a name="line.161"></a> <FONT color="green">162</FONT> initializeEstimate(problem);<a name="line.162"></a> <FONT color="green">163</FONT> <a name="line.163"></a> <FONT color="green">164</FONT> // work matrices<a name="line.164"></a> <FONT color="green">165</FONT> double[] grad = new double[parameters.length];<a name="line.165"></a> <FONT color="green">166</FONT> ArrayRealVector bDecrement = new ArrayRealVector(parameters.length);<a name="line.166"></a> <FONT color="green">167</FONT> double[] bDecrementData = bDecrement.getDataRef();<a name="line.167"></a> <FONT color="green">168</FONT> RealMatrix wGradGradT = MatrixUtils.createRealMatrix(parameters.length, parameters.length);<a name="line.168"></a> <FONT color="green">169</FONT> <a name="line.169"></a> <FONT color="green">170</FONT> // iterate until convergence is reached<a name="line.170"></a> <FONT color="green">171</FONT> double previous = Double.POSITIVE_INFINITY;<a name="line.171"></a> <FONT color="green">172</FONT> do {<a name="line.172"></a> <FONT color="green">173</FONT> <a name="line.173"></a> <FONT color="green">174</FONT> // build the linear problem<a name="line.174"></a> <FONT color="green">175</FONT> incrementJacobianEvaluationsCounter();<a name="line.175"></a> <FONT color="green">176</FONT> RealVector b = new ArrayRealVector(parameters.length);<a name="line.176"></a> <FONT color="green">177</FONT> RealMatrix a = MatrixUtils.createRealMatrix(parameters.length, parameters.length);<a name="line.177"></a> <FONT color="green">178</FONT> for (int i = 0; i < measurements.length; ++i) {<a name="line.178"></a> <FONT color="green">179</FONT> if (! measurements [i].isIgnored()) {<a name="line.179"></a> <FONT color="green">180</FONT> <a name="line.180"></a> <FONT color="green">181</FONT> double weight = measurements[i].getWeight();<a name="line.181"></a> <FONT color="green">182</FONT> double residual = measurements[i].getResidual();<a name="line.182"></a> <FONT color="green">183</FONT> <a name="line.183"></a> <FONT color="green">184</FONT> // compute the normal equation<a name="line.184"></a> <FONT color="green">185</FONT> for (int j = 0; j < parameters.length; ++j) {<a name="line.185"></a> <FONT color="green">186</FONT> grad[j] = measurements[i].getPartial(parameters[j]);<a name="line.186"></a> <FONT color="green">187</FONT> bDecrementData[j] = weight * residual * grad[j];<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> // build the contribution matrix for measurement i<a name="line.190"></a> <FONT color="green">191</FONT> for (int k = 0; k < parameters.length; ++k) {<a name="line.191"></a> <FONT color="green">192</FONT> double gk = grad[k];<a name="line.192"></a> <FONT color="green">193</FONT> for (int l = 0; l < parameters.length; ++l) {<a name="line.193"></a> <FONT color="green">194</FONT> wGradGradT.setEntry(k, l, weight * gk * grad[l]);<a name="line.194"></a> <FONT color="green">195</FONT> }<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> <FONT color="green">198</FONT> // update the matrices<a name="line.198"></a> <FONT color="green">199</FONT> a = a.add(wGradGradT);<a name="line.199"></a> <FONT color="green">200</FONT> b = b.add(bDecrement);<a name="line.200"></a> <FONT color="green">201</FONT> <a name="line.201"></a> <FONT color="green">202</FONT> }<a name="line.202"></a> <FONT color="green">203</FONT> }<a name="line.203"></a> <FONT color="green">204</FONT> <a name="line.204"></a> <FONT color="green">205</FONT> try {<a name="line.205"></a> <FONT color="green">206</FONT> <a name="line.206"></a> <FONT color="green">207</FONT> // solve the linearized least squares problem<a name="line.207"></a> <FONT color="green">208</FONT> RealVector dX = new LUDecompositionImpl(a).getSolver().solve(b);<a name="line.208"></a> <FONT color="green">209</FONT> <a name="line.209"></a> <FONT color="green">210</FONT> // update the estimated parameters<a name="line.210"></a> <FONT color="green">211</FONT> for (int i = 0; i < parameters.length; ++i) {<a name="line.211"></a> <FONT color="green">212</FONT> parameters[i].setEstimate(parameters[i].getEstimate() + dX.getEntry(i));<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> } catch(InvalidMatrixException e) {<a name="line.215"></a> <FONT color="green">216</FONT> throw new EstimationException("unable to solve: singular problem");<a name="line.216"></a> <FONT color="green">217</FONT> }<a name="line.217"></a> <FONT color="green">218</FONT> <a name="line.218"></a> <FONT color="green">219</FONT> <a name="line.219"></a> <FONT color="green">220</FONT> previous = cost;<a name="line.220"></a> <FONT color="green">221</FONT> updateResidualsAndCost();<a name="line.221"></a> <FONT color="green">222</FONT> <a name="line.222"></a> <FONT color="green">223</FONT> } while ((getCostEvaluations() < 2) ||<a name="line.223"></a> <FONT color="green">224</FONT> (Math.abs(previous - cost) > (cost * steadyStateThreshold) &&<a name="line.224"></a> <FONT color="green">225</FONT> (Math.abs(cost) > convergence)));<a name="line.225"></a> <FONT color="green">226</FONT> <a name="line.226"></a> <FONT color="green">227</FONT> }<a name="line.227"></a> <FONT color="green">228</FONT> <a name="line.228"></a> <FONT color="green">229</FONT> }<a name="line.229"></a> </PRE> </BODY> </HTML>