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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.estimation;<a name="line.17"></a> <FONT color="green">018</FONT> <a name="line.18"></a> <FONT color="green">019</FONT> import java.io.Serializable;<a name="line.19"></a> <FONT color="green">020</FONT> import java.util.Arrays;<a name="line.20"></a> <FONT color="green">021</FONT> <a name="line.21"></a> <FONT color="green">022</FONT> <a name="line.22"></a> <FONT color="green">023</FONT> /**<a name="line.23"></a> <FONT color="green">024</FONT> * This class solves a least squares problem.<a name="line.24"></a> <FONT color="green">025</FONT> *<a name="line.25"></a> <FONT color="green">026</FONT> * <p>This implementation <em>should</em> work even for over-determined systems<a name="line.26"></a> <FONT color="green">027</FONT> * (i.e. systems having more variables than equations). Over-determined systems<a name="line.27"></a> <FONT color="green">028</FONT> * are solved by ignoring the variables which have the smallest impact according<a name="line.28"></a> <FONT color="green">029</FONT> * to their jacobian column norm. Only the rank of the matrix and some loop bounds<a name="line.29"></a> <FONT color="green">030</FONT> * are changed to implement this.</p><a name="line.30"></a> <FONT color="green">031</FONT> *<a name="line.31"></a> <FONT color="green">032</FONT> * <p>The resolution engine is a simple translation of the MINPACK <a<a name="line.32"></a> <FONT color="green">033</FONT> * href="http://www.netlib.org/minpack/lmder.f">lmder</a> routine with minor<a name="line.33"></a> <FONT color="green">034</FONT> * changes. The changes include the over-determined resolution and the Q.R.<a name="line.34"></a> <FONT color="green">035</FONT> * decomposition which has been rewritten following the algorithm described in the<a name="line.35"></a> <FONT color="green">036</FONT> * P. Lascaux and R. Theodor book <i>Analyse num&eacute;rique matricielle<a name="line.36"></a> <FONT color="green">037</FONT> * appliqu&eacute;e &agrave; l'art de l'ing&eacute;nieur</i>, Masson 1986.</p><a name="line.37"></a> <FONT color="green">038</FONT> * <p>The authors of the original fortran version are:<a name="line.38"></a> <FONT color="green">039</FONT> * <ul><a name="line.39"></a> <FONT color="green">040</FONT> * <li>Argonne National Laboratory. MINPACK project. March 1980</li><a name="line.40"></a> <FONT color="green">041</FONT> * <li>Burton S. Garbow</li><a name="line.41"></a> <FONT color="green">042</FONT> * <li>Kenneth E. Hillstrom</li><a name="line.42"></a> <FONT color="green">043</FONT> * <li>Jorge J. More</li><a name="line.43"></a> <FONT color="green">044</FONT> * </ul><a name="line.44"></a> <FONT color="green">045</FONT> * The redistribution policy for MINPACK is available <a<a name="line.45"></a> <FONT color="green">046</FONT> * href="http://www.netlib.org/minpack/disclaimer">here</a>, for convenience, it<a name="line.46"></a> <FONT color="green">047</FONT> * is reproduced below.</p><a name="line.47"></a> <FONT color="green">048</FONT> *<a name="line.48"></a> <FONT color="green">049</FONT> * <table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0"><a name="line.49"></a> <FONT color="green">050</FONT> * <tr><td><a name="line.50"></a> <FONT color="green">051</FONT> * Minpack Copyright Notice (1999) University of Chicago.<a name="line.51"></a> <FONT color="green">052</FONT> * All rights reserved<a name="line.52"></a> <FONT color="green">053</FONT> * </td></tr><a name="line.53"></a> <FONT color="green">054</FONT> * <tr><td><a name="line.54"></a> <FONT color="green">055</FONT> * Redistribution and use in source and binary forms, with or without<a name="line.55"></a> <FONT color="green">056</FONT> * modification, are permitted provided that the following conditions<a name="line.56"></a> <FONT color="green">057</FONT> * are met:<a name="line.57"></a> <FONT color="green">058</FONT> * <ol><a name="line.58"></a> <FONT color="green">059</FONT> * <li>Redistributions of source code must retain the above copyright<a name="line.59"></a> <FONT color="green">060</FONT> * notice, this list of conditions and the following disclaimer.</li><a name="line.60"></a> <FONT color="green">061</FONT> * <li>Redistributions in binary form must reproduce the above<a name="line.61"></a> <FONT color="green">062</FONT> * copyright notice, this list of conditions and the following<a name="line.62"></a> <FONT color="green">063</FONT> * disclaimer in the documentation and/or other materials provided<a name="line.63"></a> <FONT color="green">064</FONT> * with the distribution.</li><a name="line.64"></a> <FONT color="green">065</FONT> * <li>The end-user documentation included with the redistribution, if any,<a name="line.65"></a> <FONT color="green">066</FONT> * must include the following acknowledgment:<a name="line.66"></a> <FONT color="green">067</FONT> * <code>This product includes software developed by the University of<a name="line.67"></a> <FONT color="green">068</FONT> * Chicago, as Operator of Argonne National Laboratory.</code><a name="line.68"></a> <FONT color="green">069</FONT> * Alternately, this acknowledgment may appear in the software itself,<a name="line.69"></a> <FONT color="green">070</FONT> * if and wherever such third-party acknowledgments normally appear.</li><a name="line.70"></a> <FONT color="green">071</FONT> * <li><strong>WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS"<a name="line.71"></a> <FONT color="green">072</FONT> * WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE<a name="line.72"></a> <FONT color="green">073</FONT> * UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND<a name="line.73"></a> <FONT color="green">074</FONT> * THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR<a name="line.74"></a> <FONT color="green">075</FONT> * IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES<a name="line.75"></a> <FONT color="green">076</FONT> * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE<a name="line.76"></a> <FONT color="green">077</FONT> * OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY<a name="line.77"></a> <FONT color="green">078</FONT> * OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR<a name="line.78"></a> <FONT color="green">079</FONT> * USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF<a name="line.79"></a> <FONT color="green">080</FONT> * THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4)<a name="line.80"></a> <FONT color="green">081</FONT> * DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION<a name="line.81"></a> <FONT color="green">082</FONT> * UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL<a name="line.82"></a> <FONT color="green">083</FONT> * BE CORRECTED.</strong></li><a name="line.83"></a> <FONT color="green">084</FONT> * <li><strong>LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT<a name="line.84"></a> <FONT color="green">085</FONT> * HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF<a name="line.85"></a> <FONT color="green">086</FONT> * ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT,<a name="line.86"></a> <FONT color="green">087</FONT> * INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF<a name="line.87"></a> <FONT color="green">088</FONT> * ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF<a name="line.88"></a> <FONT color="green">089</FONT> * PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER<a name="line.89"></a> <FONT color="green">090</FONT> * SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT<a name="line.90"></a> <FONT color="green">091</FONT> * (INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,<a name="line.91"></a> <FONT color="green">092</FONT> * EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE<a name="line.92"></a> <FONT color="green">093</FONT> * POSSIBILITY OF SUCH LOSS OR DAMAGES.</strong></li><a name="line.93"></a> <FONT color="green">094</FONT> * <ol></td></tr><a name="line.94"></a> <FONT color="green">095</FONT> * </table><a name="line.95"></a> <FONT color="green">096</FONT> <a name="line.96"></a> <FONT color="green">097</FONT> * @version $Revision: 825919 $ $Date: 2009-10-16 10:51:55 -0400 (Fri, 16 Oct 2009) $<a name="line.97"></a> <FONT color="green">098</FONT> * @since 1.2<a name="line.98"></a> <FONT color="green">099</FONT> * @deprecated as of 2.0, everything in package org.apache.commons.math.estimation has<a name="line.99"></a> <FONT color="green">100</FONT> * been deprecated and replaced by package org.apache.commons.math.optimization.general<a name="line.100"></a> <FONT color="green">101</FONT> *<a name="line.101"></a> <FONT color="green">102</FONT> */<a name="line.102"></a> <FONT color="green">103</FONT> @Deprecated<a name="line.103"></a> <FONT color="green">104</FONT> public class LevenbergMarquardtEstimator extends AbstractEstimator implements Serializable {<a name="line.104"></a> <FONT color="green">105</FONT> <a name="line.105"></a> <FONT color="green">106</FONT> /** Serializable version identifier */<a name="line.106"></a> <FONT color="green">107</FONT> private static final long serialVersionUID = -5705952631533171019L;<a name="line.107"></a> <FONT color="green">108</FONT> <a name="line.108"></a> <FONT color="green">109</FONT> /** Number of solved variables. */<a name="line.109"></a> <FONT color="green">110</FONT> private int solvedCols;<a name="line.110"></a> <FONT color="green">111</FONT> <a name="line.111"></a> <FONT color="green">112</FONT> /** Diagonal elements of the R matrix in the Q.R. decomposition. */<a name="line.112"></a> <FONT color="green">113</FONT> private double[] diagR;<a name="line.113"></a> <FONT color="green">114</FONT> <a name="line.114"></a> <FONT color="green">115</FONT> /** Norms of the columns of the jacobian matrix. */<a name="line.115"></a> <FONT color="green">116</FONT> private double[] jacNorm;<a name="line.116"></a> <FONT color="green">117</FONT> <a name="line.117"></a> <FONT color="green">118</FONT> /** Coefficients of the Householder transforms vectors. */<a name="line.118"></a> <FONT color="green">119</FONT> private double[] beta;<a name="line.119"></a> <FONT color="green">120</FONT> <a name="line.120"></a> <FONT color="green">121</FONT> /** Columns permutation array. */<a name="line.121"></a> <FONT color="green">122</FONT> private int[] permutation;<a name="line.122"></a> <FONT color="green">123</FONT> <a name="line.123"></a> <FONT color="green">124</FONT> /** Rank of the jacobian matrix. */<a name="line.124"></a> <FONT color="green">125</FONT> private int rank;<a name="line.125"></a> <FONT color="green">126</FONT> <a name="line.126"></a> <FONT color="green">127</FONT> /** Levenberg-Marquardt parameter. */<a name="line.127"></a> <FONT color="green">128</FONT> private double lmPar;<a name="line.128"></a> <FONT color="green">129</FONT> <a name="line.129"></a> <FONT color="green">130</FONT> /** Parameters evolution direction associated with lmPar. */<a name="line.130"></a> <FONT color="green">131</FONT> private double[] lmDir;<a name="line.131"></a> <FONT color="green">132</FONT> <a name="line.132"></a> <FONT color="green">133</FONT> /** Positive input variable used in determining the initial step bound. */<a name="line.133"></a> <FONT color="green">134</FONT> private double initialStepBoundFactor;<a name="line.134"></a> <FONT color="green">135</FONT> <a name="line.135"></a> <FONT color="green">136</FONT> /** Desired relative error in the sum of squares. */<a name="line.136"></a> <FONT color="green">137</FONT> private double costRelativeTolerance;<a name="line.137"></a> <FONT color="green">138</FONT> <a name="line.138"></a> <FONT color="green">139</FONT> /** Desired relative error in the approximate solution parameters. */<a name="line.139"></a> <FONT color="green">140</FONT> private double parRelativeTolerance;<a name="line.140"></a> <FONT color="green">141</FONT> <a name="line.141"></a> <FONT color="green">142</FONT> /** Desired max cosine on the orthogonality between the function vector<a name="line.142"></a> <FONT color="green">143</FONT> * and the columns of the jacobian. */<a name="line.143"></a> <FONT color="green">144</FONT> private double orthoTolerance;<a name="line.144"></a> <FONT color="green">145</FONT> <a name="line.145"></a> <FONT color="green">146</FONT> /**<a name="line.146"></a> <FONT color="green">147</FONT> * Build an estimator for least squares problems.<a name="line.147"></a> <FONT color="green">148</FONT> * <p>The default values for the algorithm settings are:<a name="line.148"></a> <FONT color="green">149</FONT> * <ul><a name="line.149"></a> <FONT color="green">150</FONT> * <li>{@link #setInitialStepBoundFactor initial step bound factor}: 100.0</li><a name="line.150"></a> <FONT color="green">151</FONT> * <li>{@link #setMaxCostEval maximal cost evaluations}: 1000</li><a name="line.151"></a> <FONT color="green">152</FONT> * <li>{@link #setCostRelativeTolerance cost relative tolerance}: 1.0e-10</li><a name="line.152"></a> <FONT color="green">153</FONT> * <li>{@link #setParRelativeTolerance parameters relative tolerance}: 1.0e-10</li><a name="line.153"></a> <FONT color="green">154</FONT> * <li>{@link #setOrthoTolerance orthogonality tolerance}: 1.0e-10</li><a name="line.154"></a> <FONT color="green">155</FONT> * </ul><a name="line.155"></a> <FONT color="green">156</FONT> * </p><a name="line.156"></a> <FONT color="green">157</FONT> */<a name="line.157"></a> <FONT color="green">158</FONT> public LevenbergMarquardtEstimator() {<a name="line.158"></a> <FONT color="green">159</FONT> <a name="line.159"></a> <FONT color="green">160</FONT> // set up the superclass with a default max cost evaluations setting<a name="line.160"></a> <FONT color="green">161</FONT> setMaxCostEval(1000);<a name="line.161"></a> <FONT color="green">162</FONT> <a name="line.162"></a> <FONT color="green">163</FONT> // default values for the tuning parameters<a name="line.163"></a> <FONT color="green">164</FONT> setInitialStepBoundFactor(100.0);<a name="line.164"></a> <FONT color="green">165</FONT> setCostRelativeTolerance(1.0e-10);<a name="line.165"></a> <FONT color="green">166</FONT> setParRelativeTolerance(1.0e-10);<a name="line.166"></a> <FONT color="green">167</FONT> setOrthoTolerance(1.0e-10);<a name="line.167"></a> <FONT color="green">168</FONT> <a name="line.168"></a> <FONT color="green">169</FONT> }<a name="line.169"></a> <FONT color="green">170</FONT> <a name="line.170"></a> <FONT color="green">171</FONT> /**<a name="line.171"></a> <FONT color="green">172</FONT> * Set the positive input variable used in determining the initial step bound.<a name="line.172"></a> <FONT color="green">173</FONT> * This bound is set to the product of initialStepBoundFactor and the euclidean norm of diag*x if nonzero,<a name="line.173"></a> <FONT color="green">174</FONT> * or else to initialStepBoundFactor itself. In most cases factor should lie<a name="line.174"></a> <FONT color="green">175</FONT> * in the interval (0.1, 100.0). 100.0 is a generally recommended value<a name="line.175"></a> <FONT color="green">176</FONT> *<a name="line.176"></a> <FONT color="green">177</FONT> * @param initialStepBoundFactor initial step bound factor<a name="line.177"></a> <FONT color="green">178</FONT> * @see #estimate<a name="line.178"></a> <FONT color="green">179</FONT> */<a name="line.179"></a> <FONT color="green">180</FONT> public void setInitialStepBoundFactor(double initialStepBoundFactor) {<a name="line.180"></a> <FONT color="green">181</FONT> this.initialStepBoundFactor = initialStepBoundFactor;<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> /**<a name="line.184"></a> <FONT color="green">185</FONT> * Set the desired relative error in the sum of squares.<a name="line.185"></a> <FONT color="green">186</FONT> *<a name="line.186"></a> <FONT color="green">187</FONT> * @param costRelativeTolerance desired relative error in the sum of squares<a name="line.187"></a> <FONT color="green">188</FONT> * @see #estimate<a name="line.188"></a> <FONT color="green">189</FONT> */<a name="line.189"></a> <FONT color="green">190</FONT> public void setCostRelativeTolerance(double costRelativeTolerance) {<a name="line.190"></a> <FONT color="green">191</FONT> this.costRelativeTolerance = costRelativeTolerance;<a name="line.191"></a> <FONT color="green">192</FONT> }<a name="line.192"></a> <FONT color="green">193</FONT> <a name="line.193"></a> <FONT color="green">194</FONT> /**<a name="line.194"></a> <FONT color="green">195</FONT> * Set the desired relative error in the approximate solution parameters.<a name="line.195"></a> <FONT color="green">196</FONT> *<a name="line.196"></a> <FONT color="green">197</FONT> * @param parRelativeTolerance desired relative error<a name="line.197"></a> <FONT color="green">198</FONT> * in the approximate solution parameters<a name="line.198"></a> <FONT color="green">199</FONT> * @see #estimate<a name="line.199"></a> <FONT color="green">200</FONT> */<a name="line.200"></a> <FONT color="green">201</FONT> public void setParRelativeTolerance(double parRelativeTolerance) {<a name="line.201"></a> <FONT color="green">202</FONT> this.parRelativeTolerance = parRelativeTolerance;<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> /**<a name="line.205"></a> <FONT color="green">206</FONT> * Set the desired max cosine on the orthogonality.<a name="line.206"></a> <FONT color="green">207</FONT> *<a name="line.207"></a> <FONT color="green">208</FONT> * @param orthoTolerance desired max cosine on the orthogonality<a name="line.208"></a> <FONT color="green">209</FONT> * between the function vector and the columns of the jacobian<a name="line.209"></a> <FONT color="green">210</FONT> * @see #estimate<a name="line.210"></a> <FONT color="green">211</FONT> */<a name="line.211"></a> <FONT color="green">212</FONT> public void setOrthoTolerance(double orthoTolerance) {<a name="line.212"></a> <FONT color="green">213</FONT> this.orthoTolerance = orthoTolerance;<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> /**<a name="line.216"></a> <FONT color="green">217</FONT> * Solve an estimation problem using the Levenberg-Marquardt algorithm.<a name="line.217"></a> <FONT color="green">218</FONT> * <p>The algorithm used is a modified Levenberg-Marquardt one, based<a name="line.218"></a> <FONT color="green">219</FONT> * on the MINPACK <a href="http://www.netlib.org/minpack/lmder.f">lmder</a><a name="line.219"></a> <FONT color="green">220</FONT> * routine. The algorithm settings must have been set up before this method<a name="line.220"></a> <FONT color="green">221</FONT> * is called with the {@link #setInitialStepBoundFactor},<a name="line.221"></a> <FONT color="green">222</FONT> * {@link #setMaxCostEval}, {@link #setCostRelativeTolerance},<a name="line.222"></a> <FONT color="green">223</FONT> * {@link #setParRelativeTolerance} and {@link #setOrthoTolerance} methods.<a name="line.223"></a> <FONT color="green">224</FONT> * If these methods have not been called, the default values set up by the<a name="line.224"></a> <FONT color="green">225</FONT> * {@link #LevenbergMarquardtEstimator() constructor} will be used.</p><a name="line.225"></a> <FONT color="green">226</FONT> * <p>The authors of the original fortran function are:</p><a name="line.226"></a> <FONT color="green">227</FONT> * <ul><a name="line.227"></a> <FONT color="green">228</FONT> * <li>Argonne National Laboratory. MINPACK project. March 1980</li><a name="line.228"></a> <FONT color="green">229</FONT> * <li>Burton S. Garbow</li><a name="line.229"></a> <FONT color="green">230</FONT> * <li>Kenneth E. Hillstrom</li><a name="line.230"></a> <FONT color="green">231</FONT> * <li>Jorge J. More</li><a name="line.231"></a> <FONT color="green">232</FONT> * </ul><a name="line.232"></a> <FONT color="green">233</FONT> * <p>Luc Maisonobe did the Java translation.</p><a name="line.233"></a> <FONT color="green">234</FONT> *<a name="line.234"></a> <FONT color="green">235</FONT> * @param problem estimation problem to solve<a name="line.235"></a> <FONT color="green">236</FONT> * @exception EstimationException if convergence cannot be<a name="line.236"></a> <FONT color="green">237</FONT> * reached with the specified algorithm settings or if there are more variables<a name="line.237"></a> <FONT color="green">238</FONT> * than equations<a name="line.238"></a> <FONT color="green">239</FONT> * @see #setInitialStepBoundFactor<a name="line.239"></a> <FONT color="green">240</FONT> * @see #setCostRelativeTolerance<a name="line.240"></a> <FONT color="green">241</FONT> * @see #setParRelativeTolerance<a name="line.241"></a> <FONT color="green">242</FONT> * @see #setOrthoTolerance<a name="line.242"></a> <FONT color="green">243</FONT> */<a name="line.243"></a> <FONT color="green">244</FONT> @Override<a name="line.244"></a> <FONT color="green">245</FONT> public void estimate(EstimationProblem problem)<a name="line.245"></a> <FONT color="green">246</FONT> throws EstimationException {<a name="line.246"></a> <FONT color="green">247</FONT> <a name="line.247"></a> <FONT color="green">248</FONT> initializeEstimate(problem);<a name="line.248"></a> <FONT color="green">249</FONT> <a name="line.249"></a> <FONT color="green">250</FONT> // arrays shared with the other private methods<a name="line.250"></a> <FONT color="green">251</FONT> solvedCols = Math.min(rows, cols);<a name="line.251"></a> <FONT color="green">252</FONT> diagR = new double[cols];<a name="line.252"></a> <FONT color="green">253</FONT> jacNorm = new double[cols];<a name="line.253"></a> <FONT color="green">254</FONT> beta = new double[cols];<a name="line.254"></a> <FONT color="green">255</FONT> permutation = new int[cols];<a name="line.255"></a> <FONT color="green">256</FONT> lmDir = new double[cols];<a name="line.256"></a> <FONT color="green">257</FONT> <a name="line.257"></a> <FONT color="green">258</FONT> // local variables<a name="line.258"></a> <FONT color="green">259</FONT> double delta = 0;<a name="line.259"></a> <FONT color="green">260</FONT> double xNorm = 0;<a name="line.260"></a> <FONT color="green">261</FONT> double[] diag = new double[cols];<a name="line.261"></a> <FONT color="green">262</FONT> double[] oldX = new double[cols];<a name="line.262"></a> <FONT color="green">263</FONT> double[] oldRes = new double[rows];<a name="line.263"></a> <FONT color="green">264</FONT> double[] work1 = new double[cols];<a name="line.264"></a> <FONT color="green">265</FONT> double[] work2 = new double[cols];<a name="line.265"></a> <FONT color="green">266</FONT> double[] work3 = new double[cols];<a name="line.266"></a> <FONT color="green">267</FONT> <a name="line.267"></a> <FONT color="green">268</FONT> // evaluate the function at the starting point and calculate its norm<a name="line.268"></a> <FONT color="green">269</FONT> updateResidualsAndCost();<a name="line.269"></a> <FONT color="green">270</FONT> <a name="line.270"></a> <FONT color="green">271</FONT> // outer loop<a name="line.271"></a> <FONT color="green">272</FONT> lmPar = 0;<a name="line.272"></a> <FONT color="green">273</FONT> boolean firstIteration = true;<a name="line.273"></a> <FONT color="green">274</FONT> while (true) {<a name="line.274"></a> <FONT color="green">275</FONT> <a name="line.275"></a> <FONT color="green">276</FONT> // compute the Q.R. decomposition of the jacobian matrix<a name="line.276"></a> <FONT color="green">277</FONT> updateJacobian();<a name="line.277"></a> <FONT color="green">278</FONT> qrDecomposition();<a name="line.278"></a> <FONT color="green">279</FONT> <a name="line.279"></a> <FONT color="green">280</FONT> // compute Qt.res<a name="line.280"></a> <FONT color="green">281</FONT> qTy(residuals);<a name="line.281"></a> <FONT color="green">282</FONT> <a name="line.282"></a> <FONT color="green">283</FONT> // now we don't need Q anymore,<a name="line.283"></a> <FONT color="green">284</FONT> // so let jacobian contain the R matrix with its diagonal elements<a name="line.284"></a> <FONT color="green">285</FONT> for (int k = 0; k < solvedCols; ++k) {<a name="line.285"></a> <FONT color="green">286</FONT> int pk = permutation[k];<a name="line.286"></a> <FONT color="green">287</FONT> jacobian[k * cols + pk] = diagR[pk];<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> if (firstIteration) {<a name="line.290"></a> <FONT color="green">291</FONT> <a name="line.291"></a> <FONT color="green">292</FONT> // scale the variables according to the norms of the columns<a name="line.292"></a> <FONT color="green">293</FONT> // of the initial jacobian<a name="line.293"></a> <FONT color="green">294</FONT> xNorm = 0;<a name="line.294"></a> <FONT color="green">295</FONT> for (int k = 0; k < cols; ++k) {<a name="line.295"></a> <FONT color="green">296</FONT> double dk = jacNorm[k];<a name="line.296"></a> <FONT color="green">297</FONT> if (dk == 0) {<a name="line.297"></a> <FONT color="green">298</FONT> dk = 1.0;<a name="line.298"></a> <FONT color="green">299</FONT> }<a name="line.299"></a> <FONT color="green">300</FONT> double xk = dk * parameters[k].getEstimate();<a name="line.300"></a> <FONT color="green">301</FONT> xNorm += xk * xk;<a name="line.301"></a> <FONT color="green">302</FONT> diag[k] = dk;<a name="line.302"></a> <FONT color="green">303</FONT> }<a name="line.303"></a> <FONT color="green">304</FONT> xNorm = Math.sqrt(xNorm);<a name="line.304"></a> <FONT color="green">305</FONT> <a name="line.305"></a> <FONT color="green">306</FONT> // initialize the step bound delta<a name="line.306"></a> <FONT color="green">307</FONT> delta = (xNorm == 0) ? initialStepBoundFactor : (initialStepBoundFactor * xNorm);<a name="line.307"></a> <FONT color="green">308</FONT> <a name="line.308"></a> <FONT color="green">309</FONT> }<a name="line.309"></a> <FONT color="green">310</FONT> <a name="line.310"></a> <FONT color="green">311</FONT> // check orthogonality between function vector and jacobian columns<a name="line.311"></a> <FONT color="green">312</FONT> double maxCosine = 0;<a name="line.312"></a> <FONT color="green">313</FONT> if (cost != 0) {<a name="line.313"></a> <FONT color="green">314</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.314"></a> <FONT color="green">315</FONT> int pj = permutation[j];<a name="line.315"></a> <FONT color="green">316</FONT> double s = jacNorm[pj];<a name="line.316"></a> <FONT color="green">317</FONT> if (s != 0) {<a name="line.317"></a> <FONT color="green">318</FONT> double sum = 0;<a name="line.318"></a> <FONT color="green">319</FONT> int index = pj;<a name="line.319"></a> <FONT color="green">320</FONT> for (int i = 0; i <= j; ++i) {<a name="line.320"></a> <FONT color="green">321</FONT> sum += jacobian[index] * residuals[i];<a name="line.321"></a> <FONT color="green">322</FONT> index += cols;<a name="line.322"></a> <FONT color="green">323</FONT> }<a name="line.323"></a> <FONT color="green">324</FONT> maxCosine = Math.max(maxCosine, Math.abs(sum) / (s * cost));<a name="line.324"></a> <FONT color="green">325</FONT> }<a name="line.325"></a> <FONT color="green">326</FONT> }<a name="line.326"></a> <FONT color="green">327</FONT> }<a name="line.327"></a> <FONT color="green">328</FONT> if (maxCosine <= orthoTolerance) {<a name="line.328"></a> <FONT color="green">329</FONT> return;<a name="line.329"></a> <FONT color="green">330</FONT> }<a name="line.330"></a> <FONT color="green">331</FONT> <a name="line.331"></a> <FONT color="green">332</FONT> // rescale if necessary<a name="line.332"></a> <FONT color="green">333</FONT> for (int j = 0; j < cols; ++j) {<a name="line.333"></a> <FONT color="green">334</FONT> diag[j] = Math.max(diag[j], jacNorm[j]);<a name="line.334"></a> <FONT color="green">335</FONT> }<a name="line.335"></a> <FONT color="green">336</FONT> <a name="line.336"></a> <FONT color="green">337</FONT> // inner loop<a name="line.337"></a> <FONT color="green">338</FONT> for (double ratio = 0; ratio < 1.0e-4;) {<a name="line.338"></a> <FONT color="green">339</FONT> <a name="line.339"></a> <FONT color="green">340</FONT> // save the state<a name="line.340"></a> <FONT color="green">341</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.341"></a> <FONT color="green">342</FONT> int pj = permutation[j];<a name="line.342"></a> <FONT color="green">343</FONT> oldX[pj] = parameters[pj].getEstimate();<a name="line.343"></a> <FONT color="green">344</FONT> }<a name="line.344"></a> <FONT color="green">345</FONT> double previousCost = cost;<a name="line.345"></a> <FONT color="green">346</FONT> double[] tmpVec = residuals;<a name="line.346"></a> <FONT color="green">347</FONT> residuals = oldRes;<a name="line.347"></a> <FONT color="green">348</FONT> oldRes = tmpVec;<a name="line.348"></a> <FONT color="green">349</FONT> <a name="line.349"></a> <FONT color="green">350</FONT> // determine the Levenberg-Marquardt parameter<a name="line.350"></a> <FONT color="green">351</FONT> determineLMParameter(oldRes, delta, diag, work1, work2, work3);<a name="line.351"></a> <FONT color="green">352</FONT> <a name="line.352"></a> <FONT color="green">353</FONT> // compute the new point and the norm of the evolution direction<a name="line.353"></a> <FONT color="green">354</FONT> double lmNorm = 0;<a name="line.354"></a> <FONT color="green">355</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.355"></a> <FONT color="green">356</FONT> int pj = permutation[j];<a name="line.356"></a> <FONT color="green">357</FONT> lmDir[pj] = -lmDir[pj];<a name="line.357"></a> <FONT color="green">358</FONT> parameters[pj].setEstimate(oldX[pj] + lmDir[pj]);<a name="line.358"></a> <FONT color="green">359</FONT> double s = diag[pj] * lmDir[pj];<a name="line.359"></a> <FONT color="green">360</FONT> lmNorm += s * s;<a name="line.360"></a> <FONT color="green">361</FONT> }<a name="line.361"></a> <FONT color="green">362</FONT> lmNorm = Math.sqrt(lmNorm);<a name="line.362"></a> <FONT color="green">363</FONT> <a name="line.363"></a> <FONT color="green">364</FONT> // on the first iteration, adjust the initial step bound.<a name="line.364"></a> <FONT color="green">365</FONT> if (firstIteration) {<a name="line.365"></a> <FONT color="green">366</FONT> delta = Math.min(delta, lmNorm);<a name="line.366"></a> <FONT color="green">367</FONT> }<a name="line.367"></a> <FONT color="green">368</FONT> <a name="line.368"></a> <FONT color="green">369</FONT> // evaluate the function at x + p and calculate its norm<a name="line.369"></a> <FONT color="green">370</FONT> updateResidualsAndCost();<a name="line.370"></a> <FONT color="green">371</FONT> <a name="line.371"></a> <FONT color="green">372</FONT> // compute the scaled actual reduction<a name="line.372"></a> <FONT color="green">373</FONT> double actRed = -1.0;<a name="line.373"></a> <FONT color="green">374</FONT> if (0.1 * cost < previousCost) {<a name="line.374"></a> <FONT color="green">375</FONT> double r = cost / previousCost;<a name="line.375"></a> <FONT color="green">376</FONT> actRed = 1.0 - r * r;<a name="line.376"></a> <FONT color="green">377</FONT> }<a name="line.377"></a> <FONT color="green">378</FONT> <a name="line.378"></a> <FONT color="green">379</FONT> // compute the scaled predicted reduction<a name="line.379"></a> <FONT color="green">380</FONT> // and the scaled directional derivative<a name="line.380"></a> <FONT color="green">381</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.381"></a> <FONT color="green">382</FONT> int pj = permutation[j];<a name="line.382"></a> <FONT color="green">383</FONT> double dirJ = lmDir[pj];<a name="line.383"></a> <FONT color="green">384</FONT> work1[j] = 0;<a name="line.384"></a> <FONT color="green">385</FONT> int index = pj;<a name="line.385"></a> <FONT color="green">386</FONT> for (int i = 0; i <= j; ++i) {<a name="line.386"></a> <FONT color="green">387</FONT> work1[i] += jacobian[index] * dirJ;<a name="line.387"></a> <FONT color="green">388</FONT> index += cols;<a name="line.388"></a> <FONT color="green">389</FONT> }<a name="line.389"></a> <FONT color="green">390</FONT> }<a name="line.390"></a> <FONT color="green">391</FONT> double coeff1 = 0;<a name="line.391"></a> <FONT color="green">392</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.392"></a> <FONT color="green">393</FONT> coeff1 += work1[j] * work1[j];<a name="line.393"></a> <FONT color="green">394</FONT> }<a name="line.394"></a> <FONT color="green">395</FONT> double pc2 = previousCost * previousCost;<a name="line.395"></a> <FONT color="green">396</FONT> coeff1 = coeff1 / pc2;<a name="line.396"></a> <FONT color="green">397</FONT> double coeff2 = lmPar * lmNorm * lmNorm / pc2;<a name="line.397"></a> <FONT color="green">398</FONT> double preRed = coeff1 + 2 * coeff2;<a name="line.398"></a> <FONT color="green">399</FONT> double dirDer = -(coeff1 + coeff2);<a name="line.399"></a> <FONT color="green">400</FONT> <a name="line.400"></a> <FONT color="green">401</FONT> // ratio of the actual to the predicted reduction<a name="line.401"></a> <FONT color="green">402</FONT> ratio = (preRed == 0) ? 0 : (actRed / preRed);<a name="line.402"></a> <FONT color="green">403</FONT> <a name="line.403"></a> <FONT color="green">404</FONT> // update the step bound<a name="line.404"></a> <FONT color="green">405</FONT> if (ratio <= 0.25) {<a name="line.405"></a> <FONT color="green">406</FONT> double tmp =<a name="line.406"></a> <FONT color="green">407</FONT> (actRed < 0) ? (0.5 * dirDer / (dirDer + 0.5 * actRed)) : 0.5;<a name="line.407"></a> <FONT color="green">408</FONT> if ((0.1 * cost >= previousCost) || (tmp < 0.1)) {<a name="line.408"></a> <FONT color="green">409</FONT> tmp = 0.1;<a name="line.409"></a> <FONT color="green">410</FONT> }<a name="line.410"></a> <FONT color="green">411</FONT> delta = tmp * Math.min(delta, 10.0 * lmNorm);<a name="line.411"></a> <FONT color="green">412</FONT> lmPar /= tmp;<a name="line.412"></a> <FONT color="green">413</FONT> } else if ((lmPar == 0) || (ratio >= 0.75)) {<a name="line.413"></a> <FONT color="green">414</FONT> delta = 2 * lmNorm;<a name="line.414"></a> <FONT color="green">415</FONT> lmPar *= 0.5;<a name="line.415"></a> <FONT color="green">416</FONT> }<a name="line.416"></a> <FONT color="green">417</FONT> <a name="line.417"></a> <FONT color="green">418</FONT> // test for successful iteration.<a name="line.418"></a> <FONT color="green">419</FONT> if (ratio >= 1.0e-4) {<a name="line.419"></a> <FONT color="green">420</FONT> // successful iteration, update the norm<a name="line.420"></a> <FONT color="green">421</FONT> firstIteration = false;<a name="line.421"></a> <FONT color="green">422</FONT> xNorm = 0;<a name="line.422"></a> <FONT color="green">423</FONT> for (int k = 0; k < cols; ++k) {<a name="line.423"></a> <FONT color="green">424</FONT> double xK = diag[k] * parameters[k].getEstimate();<a name="line.424"></a> <FONT color="green">425</FONT> xNorm += xK * xK;<a name="line.425"></a> <FONT color="green">426</FONT> }<a name="line.426"></a> <FONT color="green">427</FONT> xNorm = Math.sqrt(xNorm);<a name="line.427"></a> <FONT color="green">428</FONT> } else {<a name="line.428"></a> <FONT color="green">429</FONT> // failed iteration, reset the previous values<a name="line.429"></a> <FONT color="green">430</FONT> cost = previousCost;<a name="line.430"></a> <FONT color="green">431</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.431"></a> <FONT color="green">432</FONT> int pj = permutation[j];<a name="line.432"></a> <FONT color="green">433</FONT> parameters[pj].setEstimate(oldX[pj]);<a name="line.433"></a> <FONT color="green">434</FONT> }<a name="line.434"></a> <FONT color="green">435</FONT> tmpVec = residuals;<a name="line.435"></a> <FONT color="green">436</FONT> residuals = oldRes;<a name="line.436"></a> <FONT color="green">437</FONT> oldRes = tmpVec;<a name="line.437"></a> <FONT color="green">438</FONT> }<a name="line.438"></a> <FONT color="green">439</FONT> <a name="line.439"></a> <FONT color="green">440</FONT> // tests for convergence.<a name="line.440"></a> <FONT color="green">441</FONT> if (((Math.abs(actRed) <= costRelativeTolerance) &&<a name="line.441"></a> <FONT color="green">442</FONT> (preRed <= costRelativeTolerance) &&<a name="line.442"></a> <FONT color="green">443</FONT> (ratio <= 2.0)) ||<a name="line.443"></a> <FONT color="green">444</FONT> (delta <= parRelativeTolerance * xNorm)) {<a name="line.444"></a> <FONT color="green">445</FONT> return;<a name="line.445"></a> <FONT color="green">446</FONT> }<a name="line.446"></a> <FONT color="green">447</FONT> <a name="line.447"></a> <FONT color="green">448</FONT> // tests for termination and stringent tolerances<a name="line.448"></a> <FONT color="green">449</FONT> // (2.2204e-16 is the machine epsilon for IEEE754)<a name="line.449"></a> <FONT color="green">450</FONT> if ((Math.abs(actRed) <= 2.2204e-16) && (preRed <= 2.2204e-16) && (ratio <= 2.0)) {<a name="line.450"></a> <FONT color="green">451</FONT> throw new EstimationException("cost relative tolerance is too small ({0})," +<a name="line.451"></a> <FONT color="green">452</FONT> " no further reduction in the" +<a name="line.452"></a> <FONT color="green">453</FONT> " sum of squares is possible",<a name="line.453"></a> <FONT color="green">454</FONT> costRelativeTolerance);<a name="line.454"></a> <FONT color="green">455</FONT> } else if (delta <= 2.2204e-16 * xNorm) {<a name="line.455"></a> <FONT color="green">456</FONT> throw new EstimationException("parameters relative tolerance is too small" +<a name="line.456"></a> <FONT color="green">457</FONT> " ({0}), no further improvement in" +<a name="line.457"></a> <FONT color="green">458</FONT> " the approximate solution is possible",<a name="line.458"></a> <FONT color="green">459</FONT> parRelativeTolerance);<a name="line.459"></a> <FONT color="green">460</FONT> } else if (maxCosine <= 2.2204e-16) {<a name="line.460"></a> <FONT color="green">461</FONT> throw new EstimationException("orthogonality tolerance is too small ({0})," +<a name="line.461"></a> <FONT color="green">462</FONT> " solution is orthogonal to the jacobian",<a name="line.462"></a> <FONT color="green">463</FONT> orthoTolerance);<a name="line.463"></a> <FONT color="green">464</FONT> }<a name="line.464"></a> <FONT color="green">465</FONT> <a name="line.465"></a> <FONT color="green">466</FONT> }<a name="line.466"></a> <FONT color="green">467</FONT> <a name="line.467"></a> <FONT color="green">468</FONT> }<a name="line.468"></a> <FONT color="green">469</FONT> <a name="line.469"></a> <FONT color="green">470</FONT> }<a name="line.470"></a> <FONT color="green">471</FONT> <a name="line.471"></a> <FONT color="green">472</FONT> /**<a name="line.472"></a> <FONT color="green">473</FONT> * Determine the Levenberg-Marquardt parameter.<a name="line.473"></a> <FONT color="green">474</FONT> * <p>This implementation is a translation in Java of the MINPACK<a name="line.474"></a> <FONT color="green">475</FONT> * <a href="http://www.netlib.org/minpack/lmpar.f">lmpar</a><a name="line.475"></a> <FONT color="green">476</FONT> * routine.</p><a name="line.476"></a> <FONT color="green">477</FONT> * <p>This method sets the lmPar and lmDir attributes.</p><a name="line.477"></a> <FONT color="green">478</FONT> * <p>The authors of the original fortran function are:</p><a name="line.478"></a> <FONT color="green">479</FONT> * <ul><a name="line.479"></a> <FONT color="green">480</FONT> * <li>Argonne National Laboratory. MINPACK project. March 1980</li><a name="line.480"></a> <FONT color="green">481</FONT> * <li>Burton S. Garbow</li><a name="line.481"></a> <FONT color="green">482</FONT> * <li>Kenneth E. Hillstrom</li><a name="line.482"></a> <FONT color="green">483</FONT> * <li>Jorge J. More</li><a name="line.483"></a> <FONT color="green">484</FONT> * </ul><a name="line.484"></a> <FONT color="green">485</FONT> * <p>Luc Maisonobe did the Java translation.</p><a name="line.485"></a> <FONT color="green">486</FONT> *<a name="line.486"></a> <FONT color="green">487</FONT> * @param qy array containing qTy<a name="line.487"></a> <FONT color="green">488</FONT> * @param delta upper bound on the euclidean norm of diagR * lmDir<a name="line.488"></a> <FONT color="green">489</FONT> * @param diag diagonal matrix<a name="line.489"></a> <FONT color="green">490</FONT> * @param work1 work array<a name="line.490"></a> <FONT color="green">491</FONT> * @param work2 work array<a name="line.491"></a> <FONT color="green">492</FONT> * @param work3 work array<a name="line.492"></a> <FONT color="green">493</FONT> */<a name="line.493"></a> <FONT color="green">494</FONT> private void determineLMParameter(double[] qy, double delta, double[] diag,<a name="line.494"></a> <FONT color="green">495</FONT> double[] work1, double[] work2, double[] work3) {<a name="line.495"></a> <FONT color="green">496</FONT> <a name="line.496"></a> <FONT color="green">497</FONT> // compute and store in x the gauss-newton direction, if the<a name="line.497"></a> <FONT color="green">498</FONT> // jacobian is rank-deficient, obtain a least squares solution<a name="line.498"></a> <FONT color="green">499</FONT> for (int j = 0; j < rank; ++j) {<a name="line.499"></a> <FONT color="green">500</FONT> lmDir[permutation[j]] = qy[j];<a name="line.500"></a> <FONT color="green">501</FONT> }<a name="line.501"></a> <FONT color="green">502</FONT> for (int j = rank; j < cols; ++j) {<a name="line.502"></a> <FONT color="green">503</FONT> lmDir[permutation[j]] = 0;<a name="line.503"></a> <FONT color="green">504</FONT> }<a name="line.504"></a> <FONT color="green">505</FONT> for (int k = rank - 1; k >= 0; --k) {<a name="line.505"></a> <FONT color="green">506</FONT> int pk = permutation[k];<a name="line.506"></a> <FONT color="green">507</FONT> double ypk = lmDir[pk] / diagR[pk];<a name="line.507"></a> <FONT color="green">508</FONT> int index = pk;<a name="line.508"></a> <FONT color="green">509</FONT> for (int i = 0; i < k; ++i) {<a name="line.509"></a> <FONT color="green">510</FONT> lmDir[permutation[i]] -= ypk * jacobian[index];<a name="line.510"></a> <FONT color="green">511</FONT> index += cols;<a name="line.511"></a> <FONT color="green">512</FONT> }<a name="line.512"></a> <FONT color="green">513</FONT> lmDir[pk] = ypk;<a name="line.513"></a> <FONT color="green">514</FONT> }<a name="line.514"></a> <FONT color="green">515</FONT> <a name="line.515"></a> <FONT color="green">516</FONT> // evaluate the function at the origin, and test<a name="line.516"></a> <FONT color="green">517</FONT> // for acceptance of the Gauss-Newton direction<a name="line.517"></a> <FONT color="green">518</FONT> double dxNorm = 0;<a name="line.518"></a> <FONT color="green">519</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.519"></a> <FONT color="green">520</FONT> int pj = permutation[j];<a name="line.520"></a> <FONT color="green">521</FONT> double s = diag[pj] * lmDir[pj];<a name="line.521"></a> <FONT color="green">522</FONT> work1[pj] = s;<a name="line.522"></a> <FONT color="green">523</FONT> dxNorm += s * s;<a name="line.523"></a> <FONT color="green">524</FONT> }<a name="line.524"></a> <FONT color="green">525</FONT> dxNorm = Math.sqrt(dxNorm);<a name="line.525"></a> <FONT color="green">526</FONT> double fp = dxNorm - delta;<a name="line.526"></a> <FONT color="green">527</FONT> if (fp <= 0.1 * delta) {<a name="line.527"></a> <FONT color="green">528</FONT> lmPar = 0;<a name="line.528"></a> <FONT color="green">529</FONT> return;<a name="line.529"></a> <FONT color="green">530</FONT> }<a name="line.530"></a> <FONT color="green">531</FONT> <a name="line.531"></a> <FONT color="green">532</FONT> // if the jacobian is not rank deficient, the Newton step provides<a name="line.532"></a> <FONT color="green">533</FONT> // a lower bound, parl, for the zero of the function,<a name="line.533"></a> <FONT color="green">534</FONT> // otherwise set this bound to zero<a name="line.534"></a> <FONT color="green">535</FONT> double sum2;<a name="line.535"></a> <FONT color="green">536</FONT> double parl = 0;<a name="line.536"></a> <FONT color="green">537</FONT> if (rank == solvedCols) {<a name="line.537"></a> <FONT color="green">538</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.538"></a> <FONT color="green">539</FONT> int pj = permutation[j];<a name="line.539"></a> <FONT color="green">540</FONT> work1[pj] *= diag[pj] / dxNorm;<a name="line.540"></a> <FONT color="green">541</FONT> }<a name="line.541"></a> <FONT color="green">542</FONT> sum2 = 0;<a name="line.542"></a> <FONT color="green">543</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.543"></a> <FONT color="green">544</FONT> int pj = permutation[j];<a name="line.544"></a> <FONT color="green">545</FONT> double sum = 0;<a name="line.545"></a> <FONT color="green">546</FONT> int index = pj;<a name="line.546"></a> <FONT color="green">547</FONT> for (int i = 0; i < j; ++i) {<a name="line.547"></a> <FONT color="green">548</FONT> sum += jacobian[index] * work1[permutation[i]];<a name="line.548"></a> <FONT color="green">549</FONT> index += cols;<a name="line.549"></a> <FONT color="green">550</FONT> }<a name="line.550"></a> <FONT color="green">551</FONT> double s = (work1[pj] - sum) / diagR[pj];<a name="line.551"></a> <FONT color="green">552</FONT> work1[pj] = s;<a name="line.552"></a> <FONT color="green">553</FONT> sum2 += s * s;<a name="line.553"></a> <FONT color="green">554</FONT> }<a name="line.554"></a> <FONT color="green">555</FONT> parl = fp / (delta * sum2);<a name="line.555"></a> <FONT color="green">556</FONT> }<a name="line.556"></a> <FONT color="green">557</FONT> <a name="line.557"></a> <FONT color="green">558</FONT> // calculate an upper bound, paru, for the zero of the function<a name="line.558"></a> <FONT color="green">559</FONT> sum2 = 0;<a name="line.559"></a> <FONT color="green">560</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.560"></a> <FONT color="green">561</FONT> int pj = permutation[j];<a name="line.561"></a> <FONT color="green">562</FONT> double sum = 0;<a name="line.562"></a> <FONT color="green">563</FONT> int index = pj;<a name="line.563"></a> <FONT color="green">564</FONT> for (int i = 0; i <= j; ++i) {<a name="line.564"></a> <FONT color="green">565</FONT> sum += jacobian[index] * qy[i];<a name="line.565"></a> <FONT color="green">566</FONT> index += cols;<a name="line.566"></a> <FONT color="green">567</FONT> }<a name="line.567"></a> <FONT color="green">568</FONT> sum /= diag[pj];<a name="line.568"></a> <FONT color="green">569</FONT> sum2 += sum * sum;<a name="line.569"></a> <FONT color="green">570</FONT> }<a name="line.570"></a> <FONT color="green">571</FONT> double gNorm = Math.sqrt(sum2);<a name="line.571"></a> <FONT color="green">572</FONT> double paru = gNorm / delta;<a name="line.572"></a> <FONT color="green">573</FONT> if (paru == 0) {<a name="line.573"></a> <FONT color="green">574</FONT> // 2.2251e-308 is the smallest positive real for IEE754<a name="line.574"></a> <FONT color="green">575</FONT> paru = 2.2251e-308 / Math.min(delta, 0.1);<a name="line.575"></a> <FONT color="green">576</FONT> }<a name="line.576"></a> <FONT color="green">577</FONT> <a name="line.577"></a> <FONT color="green">578</FONT> // if the input par lies outside of the interval (parl,paru),<a name="line.578"></a> <FONT color="green">579</FONT> // set par to the closer endpoint<a name="line.579"></a> <FONT color="green">580</FONT> lmPar = Math.min(paru, Math.max(lmPar, parl));<a name="line.580"></a> <FONT color="green">581</FONT> if (lmPar == 0) {<a name="line.581"></a> <FONT color="green">582</FONT> lmPar = gNorm / dxNorm;<a name="line.582"></a> <FONT color="green">583</FONT> }<a name="line.583"></a> <FONT color="green">584</FONT> <a name="line.584"></a> <FONT color="green">585</FONT> for (int countdown = 10; countdown >= 0; --countdown) {<a name="line.585"></a> <FONT color="green">586</FONT> <a name="line.586"></a> <FONT color="green">587</FONT> // evaluate the function at the current value of lmPar<a name="line.587"></a> <FONT color="green">588</FONT> if (lmPar == 0) {<a name="line.588"></a> <FONT color="green">589</FONT> lmPar = Math.max(2.2251e-308, 0.001 * paru);<a name="line.589"></a> <FONT color="green">590</FONT> }<a name="line.590"></a> <FONT color="green">591</FONT> double sPar = Math.sqrt(lmPar);<a name="line.591"></a> <FONT color="green">592</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.592"></a> <FONT color="green">593</FONT> int pj = permutation[j];<a name="line.593"></a> <FONT color="green">594</FONT> work1[pj] = sPar * diag[pj];<a name="line.594"></a> <FONT color="green">595</FONT> }<a name="line.595"></a> <FONT color="green">596</FONT> determineLMDirection(qy, work1, work2, work3);<a name="line.596"></a> <FONT color="green">597</FONT> <a name="line.597"></a> <FONT color="green">598</FONT> dxNorm = 0;<a name="line.598"></a> <FONT color="green">599</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.599"></a> <FONT color="green">600</FONT> int pj = permutation[j];<a name="line.600"></a> <FONT color="green">601</FONT> double s = diag[pj] * lmDir[pj];<a name="line.601"></a> <FONT color="green">602</FONT> work3[pj] = s;<a name="line.602"></a> <FONT color="green">603</FONT> dxNorm += s * s;<a name="line.603"></a> <FONT color="green">604</FONT> }<a name="line.604"></a> <FONT color="green">605</FONT> dxNorm = Math.sqrt(dxNorm);<a name="line.605"></a> <FONT color="green">606</FONT> double previousFP = fp;<a name="line.606"></a> <FONT color="green">607</FONT> fp = dxNorm - delta;<a name="line.607"></a> <FONT color="green">608</FONT> <a name="line.608"></a> <FONT color="green">609</FONT> // if the function is small enough, accept the current value<a name="line.609"></a> <FONT color="green">610</FONT> // of lmPar, also test for the exceptional cases where parl is zero<a name="line.610"></a> <FONT color="green">611</FONT> if ((Math.abs(fp) <= 0.1 * delta) ||<a name="line.611"></a> <FONT color="green">612</FONT> ((parl == 0) && (fp <= previousFP) && (previousFP < 0))) {<a name="line.612"></a> <FONT color="green">613</FONT> return;<a name="line.613"></a> <FONT color="green">614</FONT> }<a name="line.614"></a> <FONT color="green">615</FONT> <a name="line.615"></a> <FONT color="green">616</FONT> // compute the Newton correction<a name="line.616"></a> <FONT color="green">617</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.617"></a> <FONT color="green">618</FONT> int pj = permutation[j];<a name="line.618"></a> <FONT color="green">619</FONT> work1[pj] = work3[pj] * diag[pj] / dxNorm;<a name="line.619"></a> <FONT color="green">620</FONT> }<a name="line.620"></a> <FONT color="green">621</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.621"></a> <FONT color="green">622</FONT> int pj = permutation[j];<a name="line.622"></a> <FONT color="green">623</FONT> work1[pj] /= work2[j];<a name="line.623"></a> <FONT color="green">624</FONT> double tmp = work1[pj];<a name="line.624"></a> <FONT color="green">625</FONT> for (int i = j + 1; i < solvedCols; ++i) {<a name="line.625"></a> <FONT color="green">626</FONT> work1[permutation[i]] -= jacobian[i * cols + pj] * tmp;<a name="line.626"></a> <FONT color="green">627</FONT> }<a name="line.627"></a> <FONT color="green">628</FONT> }<a name="line.628"></a> <FONT color="green">629</FONT> sum2 = 0;<a name="line.629"></a> <FONT color="green">630</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.630"></a> <FONT color="green">631</FONT> double s = work1[permutation[j]];<a name="line.631"></a> <FONT color="green">632</FONT> sum2 += s * s;<a name="line.632"></a> <FONT color="green">633</FONT> }<a name="line.633"></a> <FONT color="green">634</FONT> double correction = fp / (delta * sum2);<a name="line.634"></a> <FONT color="green">635</FONT> <a name="line.635"></a> <FONT color="green">636</FONT> // depending on the sign of the function, update parl or paru.<a name="line.636"></a> <FONT color="green">637</FONT> if (fp > 0) {<a name="line.637"></a> <FONT color="green">638</FONT> parl = Math.max(parl, lmPar);<a name="line.638"></a> <FONT color="green">639</FONT> } else if (fp < 0) {<a name="line.639"></a> <FONT color="green">640</FONT> paru = Math.min(paru, lmPar);<a name="line.640"></a> <FONT color="green">641</FONT> }<a name="line.641"></a> <FONT color="green">642</FONT> <a name="line.642"></a> <FONT color="green">643</FONT> // compute an improved estimate for lmPar<a name="line.643"></a> <FONT color="green">644</FONT> lmPar = Math.max(parl, lmPar + correction);<a name="line.644"></a> <FONT color="green">645</FONT> <a name="line.645"></a> <FONT color="green">646</FONT> }<a name="line.646"></a> <FONT color="green">647</FONT> }<a name="line.647"></a> <FONT color="green">648</FONT> <a name="line.648"></a> <FONT color="green">649</FONT> /**<a name="line.649"></a> <FONT color="green">650</FONT> * Solve a*x = b and d*x = 0 in the least squares sense.<a name="line.650"></a> <FONT color="green">651</FONT> * <p>This implementation is a translation in Java of the MINPACK<a name="line.651"></a> <FONT color="green">652</FONT> * <a href="http://www.netlib.org/minpack/qrsolv.f">qrsolv</a><a name="line.652"></a> <FONT color="green">653</FONT> * routine.</p><a name="line.653"></a> <FONT color="green">654</FONT> * <p>This method sets the lmDir and lmDiag attributes.</p><a name="line.654"></a> <FONT color="green">655</FONT> * <p>The authors of the original fortran function are:</p><a name="line.655"></a> <FONT color="green">656</FONT> * <ul><a name="line.656"></a> <FONT color="green">657</FONT> * <li>Argonne National Laboratory. MINPACK project. March 1980</li><a name="line.657"></a> <FONT color="green">658</FONT> * <li>Burton S. Garbow</li><a name="line.658"></a> <FONT color="green">659</FONT> * <li>Kenneth E. Hillstrom</li><a name="line.659"></a> <FONT color="green">660</FONT> * <li>Jorge J. More</li><a name="line.660"></a> <FONT color="green">661</FONT> * </ul><a name="line.661"></a> <FONT color="green">662</FONT> * <p>Luc Maisonobe did the Java translation.</p><a name="line.662"></a> <FONT color="green">663</FONT> *<a name="line.663"></a> <FONT color="green">664</FONT> * @param qy array containing qTy<a name="line.664"></a> <FONT color="green">665</FONT> * @param diag diagonal matrix<a name="line.665"></a> <FONT color="green">666</FONT> * @param lmDiag diagonal elements associated with lmDir<a name="line.666"></a> <FONT color="green">667</FONT> * @param work work array<a name="line.667"></a> <FONT color="green">668</FONT> */<a name="line.668"></a> <FONT color="green">669</FONT> private void determineLMDirection(double[] qy, double[] diag,<a name="line.669"></a> <FONT color="green">670</FONT> double[] lmDiag, double[] work) {<a name="line.670"></a> <FONT color="green">671</FONT> <a name="line.671"></a> <FONT color="green">672</FONT> // copy R and Qty to preserve input and initialize s<a name="line.672"></a> <FONT color="green">673</FONT> // in particular, save the diagonal elements of R in lmDir<a name="line.673"></a> <FONT color="green">674</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.674"></a> <FONT color="green">675</FONT> int pj = permutation[j];<a name="line.675"></a> <FONT color="green">676</FONT> for (int i = j + 1; i < solvedCols; ++i) {<a name="line.676"></a> <FONT color="green">677</FONT> jacobian[i * cols + pj] = jacobian[j * cols + permutation[i]];<a name="line.677"></a> <FONT color="green">678</FONT> }<a name="line.678"></a> <FONT color="green">679</FONT> lmDir[j] = diagR[pj];<a name="line.679"></a> <FONT color="green">680</FONT> work[j] = qy[j];<a name="line.680"></a> <FONT color="green">681</FONT> }<a name="line.681"></a> <FONT color="green">682</FONT> <a name="line.682"></a> <FONT color="green">683</FONT> // eliminate the diagonal matrix d using a Givens rotation<a name="line.683"></a> <FONT color="green">684</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.684"></a> <FONT color="green">685</FONT> <a name="line.685"></a> <FONT color="green">686</FONT> // prepare the row of d to be eliminated, locating the<a name="line.686"></a> <FONT color="green">687</FONT> // diagonal element using p from the Q.R. factorization<a name="line.687"></a> <FONT color="green">688</FONT> int pj = permutation[j];<a name="line.688"></a> <FONT color="green">689</FONT> double dpj = diag[pj];<a name="line.689"></a> <FONT color="green">690</FONT> if (dpj != 0) {<a name="line.690"></a> <FONT color="green">691</FONT> Arrays.fill(lmDiag, j + 1, lmDiag.length, 0);<a name="line.691"></a> <FONT color="green">692</FONT> }<a name="line.692"></a> <FONT color="green">693</FONT> lmDiag[j] = dpj;<a name="line.693"></a> <FONT color="green">694</FONT> <a name="line.694"></a> <FONT color="green">695</FONT> // the transformations to eliminate the row of d<a name="line.695"></a> <FONT color="green">696</FONT> // modify only a single element of Qty<a name="line.696"></a> <FONT color="green">697</FONT> // beyond the first n, which is initially zero.<a name="line.697"></a> <FONT color="green">698</FONT> double qtbpj = 0;<a name="line.698"></a> <FONT color="green">699</FONT> for (int k = j; k < solvedCols; ++k) {<a name="line.699"></a> <FONT color="green">700</FONT> int pk = permutation[k];<a name="line.700"></a> <FONT color="green">701</FONT> <a name="line.701"></a> <FONT color="green">702</FONT> // determine a Givens rotation which eliminates the<a name="line.702"></a> <FONT color="green">703</FONT> // appropriate element in the current row of d<a name="line.703"></a> <FONT color="green">704</FONT> if (lmDiag[k] != 0) {<a name="line.704"></a> <FONT color="green">705</FONT> <a name="line.705"></a> <FONT color="green">706</FONT> final double sin;<a name="line.706"></a> <FONT color="green">707</FONT> final double cos;<a name="line.707"></a> <FONT color="green">708</FONT> double rkk = jacobian[k * cols + pk];<a name="line.708"></a> <FONT color="green">709</FONT> if (Math.abs(rkk) < Math.abs(lmDiag[k])) {<a name="line.709"></a> <FONT color="green">710</FONT> final double cotan = rkk / lmDiag[k];<a name="line.710"></a> <FONT color="green">711</FONT> sin = 1.0 / Math.sqrt(1.0 + cotan * cotan);<a name="line.711"></a> <FONT color="green">712</FONT> cos = sin * cotan;<a name="line.712"></a> <FONT color="green">713</FONT> } else {<a name="line.713"></a> <FONT color="green">714</FONT> final double tan = lmDiag[k] / rkk;<a name="line.714"></a> <FONT color="green">715</FONT> cos = 1.0 / Math.sqrt(1.0 + tan * tan);<a name="line.715"></a> <FONT color="green">716</FONT> sin = cos * tan;<a name="line.716"></a> <FONT color="green">717</FONT> }<a name="line.717"></a> <FONT color="green">718</FONT> <a name="line.718"></a> <FONT color="green">719</FONT> // compute the modified diagonal element of R and<a name="line.719"></a> <FONT color="green">720</FONT> // the modified element of (Qty,0)<a name="line.720"></a> <FONT color="green">721</FONT> jacobian[k * cols + pk] = cos * rkk + sin * lmDiag[k];<a name="line.721"></a> <FONT color="green">722</FONT> final double temp = cos * work[k] + sin * qtbpj;<a name="line.722"></a> <FONT color="green">723</FONT> qtbpj = -sin * work[k] + cos * qtbpj;<a name="line.723"></a> <FONT color="green">724</FONT> work[k] = temp;<a name="line.724"></a> <FONT color="green">725</FONT> <a name="line.725"></a> <FONT color="green">726</FONT> // accumulate the tranformation in the row of s<a name="line.726"></a> <FONT color="green">727</FONT> for (int i = k + 1; i < solvedCols; ++i) {<a name="line.727"></a> <FONT color="green">728</FONT> double rik = jacobian[i * cols + pk];<a name="line.728"></a> <FONT color="green">729</FONT> final double temp2 = cos * rik + sin * lmDiag[i];<a name="line.729"></a> <FONT color="green">730</FONT> lmDiag[i] = -sin * rik + cos * lmDiag[i];<a name="line.730"></a> <FONT color="green">731</FONT> jacobian[i * cols + pk] = temp2;<a name="line.731"></a> <FONT color="green">732</FONT> }<a name="line.732"></a> <FONT color="green">733</FONT> <a name="line.733"></a> <FONT color="green">734</FONT> }<a name="line.734"></a> <FONT color="green">735</FONT> }<a name="line.735"></a> <FONT color="green">736</FONT> <a name="line.736"></a> <FONT color="green">737</FONT> // store the diagonal element of s and restore<a name="line.737"></a> <FONT color="green">738</FONT> // the corresponding diagonal element of R<a name="line.738"></a> <FONT color="green">739</FONT> int index = j * cols + permutation[j];<a name="line.739"></a> <FONT color="green">740</FONT> lmDiag[j] = jacobian[index];<a name="line.740"></a> <FONT color="green">741</FONT> jacobian[index] = lmDir[j];<a name="line.741"></a> <FONT color="green">742</FONT> <a name="line.742"></a> <FONT color="green">743</FONT> }<a name="line.743"></a> <FONT color="green">744</FONT> <a name="line.744"></a> <FONT color="green">745</FONT> // solve the triangular system for z, if the system is<a name="line.745"></a> <FONT color="green">746</FONT> // singular, then obtain a least squares solution<a name="line.746"></a> <FONT color="green">747</FONT> int nSing = solvedCols;<a name="line.747"></a> <FONT color="green">748</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.748"></a> <FONT color="green">749</FONT> if ((lmDiag[j] == 0) && (nSing == solvedCols)) {<a name="line.749"></a> <FONT color="green">750</FONT> nSing = j;<a name="line.750"></a> <FONT color="green">751</FONT> }<a name="line.751"></a> <FONT color="green">752</FONT> if (nSing < solvedCols) {<a name="line.752"></a> <FONT color="green">753</FONT> work[j] = 0;<a name="line.753"></a> <FONT color="green">754</FONT> }<a name="line.754"></a> <FONT color="green">755</FONT> }<a name="line.755"></a> <FONT color="green">756</FONT> if (nSing > 0) {<a name="line.756"></a> <FONT color="green">757</FONT> for (int j = nSing - 1; j >= 0; --j) {<a name="line.757"></a> <FONT color="green">758</FONT> int pj = permutation[j];<a name="line.758"></a> <FONT color="green">759</FONT> double sum = 0;<a name="line.759"></a> <FONT color="green">760</FONT> for (int i = j + 1; i < nSing; ++i) {<a name="line.760"></a> <FONT color="green">761</FONT> sum += jacobian[i * cols + pj] * work[i];<a name="line.761"></a> <FONT color="green">762</FONT> }<a name="line.762"></a> <FONT color="green">763</FONT> work[j] = (work[j] - sum) / lmDiag[j];<a name="line.763"></a> <FONT color="green">764</FONT> }<a name="line.764"></a> <FONT color="green">765</FONT> }<a name="line.765"></a> <FONT color="green">766</FONT> <a name="line.766"></a> <FONT color="green">767</FONT> // permute the components of z back to components of lmDir<a name="line.767"></a> <FONT color="green">768</FONT> for (int j = 0; j < lmDir.length; ++j) {<a name="line.768"></a> <FONT color="green">769</FONT> lmDir[permutation[j]] = work[j];<a name="line.769"></a> <FONT color="green">770</FONT> }<a name="line.770"></a> <FONT color="green">771</FONT> <a name="line.771"></a> <FONT color="green">772</FONT> }<a name="line.772"></a> <FONT color="green">773</FONT> <a name="line.773"></a> <FONT color="green">774</FONT> /**<a name="line.774"></a> <FONT color="green">775</FONT> * Decompose a matrix A as A.P = Q.R using Householder transforms.<a name="line.775"></a> <FONT color="green">776</FONT> * <p>As suggested in the P. Lascaux and R. Theodor book<a name="line.776"></a> <FONT color="green">777</FONT> * <i>Analyse num&eacute;rique matricielle appliqu&eacute;e &agrave;<a name="line.777"></a> <FONT color="green">778</FONT> * l'art de l'ing&eacute;nieur</i> (Masson, 1986), instead of representing<a name="line.778"></a> <FONT color="green">779</FONT> * the Householder transforms with u<sub>k</sub> unit vectors such that:<a name="line.779"></a> <FONT color="green">780</FONT> * <pre><a name="line.780"></a> <FONT color="green">781</FONT> * H<sub>k</sub> = I - 2u<sub>k</sub>.u<sub>k</sub><sup>t</sup><a name="line.781"></a> <FONT color="green">782</FONT> * </pre><a name="line.782"></a> <FONT color="green">783</FONT> * we use <sub>k</sub> non-unit vectors such that:<a name="line.783"></a> <FONT color="green">784</FONT> * <pre><a name="line.784"></a> <FONT color="green">785</FONT> * H<sub>k</sub> = I - beta<sub>k</sub>v<sub>k</sub>.v<sub>k</sub><sup>t</sup><a name="line.785"></a> <FONT color="green">786</FONT> * </pre><a name="line.786"></a> <FONT color="green">787</FONT> * where v<sub>k</sub> = a<sub>k</sub> - alpha<sub>k</sub> e<sub>k</sub>.<a name="line.787"></a> <FONT color="green">788</FONT> * The beta<sub>k</sub> coefficients are provided upon exit as recomputing<a name="line.788"></a> <FONT color="green">789</FONT> * them from the v<sub>k</sub> vectors would be costly.</p><a name="line.789"></a> <FONT color="green">790</FONT> * <p>This decomposition handles rank deficient cases since the tranformations<a name="line.790"></a> <FONT color="green">791</FONT> * are performed in non-increasing columns norms order thanks to columns<a name="line.791"></a> <FONT color="green">792</FONT> * pivoting. The diagonal elements of the R matrix are therefore also in<a name="line.792"></a> <FONT color="green">793</FONT> * non-increasing absolute values order.</p><a name="line.793"></a> <FONT color="green">794</FONT> * @exception EstimationException if the decomposition cannot be performed<a name="line.794"></a> <FONT color="green">795</FONT> */<a name="line.795"></a> <FONT color="green">796</FONT> private void qrDecomposition() throws EstimationException {<a name="line.796"></a> <FONT color="green">797</FONT> <a name="line.797"></a> <FONT color="green">798</FONT> // initializations<a name="line.798"></a> <FONT color="green">799</FONT> for (int k = 0; k < cols; ++k) {<a name="line.799"></a> <FONT color="green">800</FONT> permutation[k] = k;<a name="line.800"></a> <FONT color="green">801</FONT> double norm2 = 0;<a name="line.801"></a> <FONT color="green">802</FONT> for (int index = k; index < jacobian.length; index += cols) {<a name="line.802"></a> <FONT color="green">803</FONT> double akk = jacobian[index];<a name="line.803"></a> <FONT color="green">804</FONT> norm2 += akk * akk;<a name="line.804"></a> <FONT color="green">805</FONT> }<a name="line.805"></a> <FONT color="green">806</FONT> jacNorm[k] = Math.sqrt(norm2);<a name="line.806"></a> <FONT color="green">807</FONT> }<a name="line.807"></a> <FONT color="green">808</FONT> <a name="line.808"></a> <FONT color="green">809</FONT> // transform the matrix column after column<a name="line.809"></a> <FONT color="green">810</FONT> for (int k = 0; k < cols; ++k) {<a name="line.810"></a> <FONT color="green">811</FONT> <a name="line.811"></a> <FONT color="green">812</FONT> // select the column with the greatest norm on active components<a name="line.812"></a> <FONT color="green">813</FONT> int nextColumn = -1;<a name="line.813"></a> <FONT color="green">814</FONT> double ak2 = Double.NEGATIVE_INFINITY;<a name="line.814"></a> <FONT color="green">815</FONT> for (int i = k; i < cols; ++i) {<a name="line.815"></a> <FONT color="green">816</FONT> double norm2 = 0;<a name="line.816"></a> <FONT color="green">817</FONT> int iDiag = k * cols + permutation[i];<a name="line.817"></a> <FONT color="green">818</FONT> for (int index = iDiag; index < jacobian.length; index += cols) {<a name="line.818"></a> <FONT color="green">819</FONT> double aki = jacobian[index];<a name="line.819"></a> <FONT color="green">820</FONT> norm2 += aki * aki;<a name="line.820"></a> <FONT color="green">821</FONT> }<a name="line.821"></a> <FONT color="green">822</FONT> if (Double.isInfinite(norm2) || Double.isNaN(norm2)) {<a name="line.822"></a> <FONT color="green">823</FONT> throw new EstimationException(<a name="line.823"></a> <FONT color="green">824</FONT> "unable to perform Q.R decomposition on the {0}x{1} jacobian matrix",<a name="line.824"></a> <FONT color="green">825</FONT> rows, cols);<a name="line.825"></a> <FONT color="green">826</FONT> }<a name="line.826"></a> <FONT color="green">827</FONT> if (norm2 > ak2) {<a name="line.827"></a> <FONT color="green">828</FONT> nextColumn = i;<a name="line.828"></a> <FONT color="green">829</FONT> ak2 = norm2;<a name="line.829"></a> <FONT color="green">830</FONT> }<a name="line.830"></a> <FONT color="green">831</FONT> }<a name="line.831"></a> <FONT color="green">832</FONT> if (ak2 == 0) {<a name="line.832"></a> <FONT color="green">833</FONT> rank = k;<a name="line.833"></a> <FONT color="green">834</FONT> return;<a name="line.834"></a> <FONT color="green">835</FONT> }<a name="line.835"></a> <FONT color="green">836</FONT> int pk = permutation[nextColumn];<a name="line.836"></a> <FONT color="green">837</FONT> permutation[nextColumn] = permutation[k];<a name="line.837"></a> <FONT color="green">838</FONT> permutation[k] = pk;<a name="line.838"></a> <FONT color="green">839</FONT> <a name="line.839"></a> <FONT color="green">840</FONT> // choose alpha such that Hk.u = alpha ek<a name="line.840"></a> <FONT color="green">841</FONT> int kDiag = k * cols + pk;<a name="line.841"></a> <FONT color="green">842</FONT> double akk = jacobian[kDiag];<a name="line.842"></a> <FONT color="green">843</FONT> double alpha = (akk > 0) ? -Math.sqrt(ak2) : Math.sqrt(ak2);<a name="line.843"></a> <FONT color="green">844</FONT> double betak = 1.0 / (ak2 - akk * alpha);<a name="line.844"></a> <FONT color="green">845</FONT> beta[pk] = betak;<a name="line.845"></a> <FONT color="green">846</FONT> <a name="line.846"></a> <FONT color="green">847</FONT> // transform the current column<a name="line.847"></a> <FONT color="green">848</FONT> diagR[pk] = alpha;<a name="line.848"></a> <FONT color="green">849</FONT> jacobian[kDiag] -= alpha;<a name="line.849"></a> <FONT color="green">850</FONT> <a name="line.850"></a> <FONT color="green">851</FONT> // transform the remaining columns<a name="line.851"></a> <FONT color="green">852</FONT> for (int dk = cols - 1 - k; dk > 0; --dk) {<a name="line.852"></a> <FONT color="green">853</FONT> int dkp = permutation[k + dk] - pk;<a name="line.853"></a> <FONT color="green">854</FONT> double gamma = 0;<a name="line.854"></a> <FONT color="green">855</FONT> for (int index = kDiag; index < jacobian.length; index += cols) {<a name="line.855"></a> <FONT color="green">856</FONT> gamma += jacobian[index] * jacobian[index + dkp];<a name="line.856"></a> <FONT color="green">857</FONT> }<a name="line.857"></a> <FONT color="green">858</FONT> gamma *= betak;<a name="line.858"></a> <FONT color="green">859</FONT> for (int index = kDiag; index < jacobian.length; index += cols) {<a name="line.859"></a> <FONT color="green">860</FONT> jacobian[index + dkp] -= gamma * jacobian[index];<a name="line.860"></a> <FONT color="green">861</FONT> }<a name="line.861"></a> <FONT color="green">862</FONT> }<a name="line.862"></a> <FONT color="green">863</FONT> <a name="line.863"></a> <FONT color="green">864</FONT> }<a name="line.864"></a> <FONT color="green">865</FONT> <a name="line.865"></a> <FONT color="green">866</FONT> rank = solvedCols;<a name="line.866"></a> <FONT color="green">867</FONT> <a name="line.867"></a> <FONT color="green">868</FONT> }<a name="line.868"></a> <FONT color="green">869</FONT> <a name="line.869"></a> <FONT color="green">870</FONT> /**<a name="line.870"></a> <FONT color="green">871</FONT> * Compute the product Qt.y for some Q.R. decomposition.<a name="line.871"></a> <FONT color="green">872</FONT> *<a name="line.872"></a> <FONT color="green">873</FONT> * @param y vector to multiply (will be overwritten with the result)<a name="line.873"></a> <FONT color="green">874</FONT> */<a name="line.874"></a> <FONT color="green">875</FONT> private void qTy(double[] y) {<a name="line.875"></a> <FONT color="green">876</FONT> for (int k = 0; k < cols; ++k) {<a name="line.876"></a> <FONT color="green">877</FONT> int pk = permutation[k];<a name="line.877"></a> <FONT color="green">878</FONT> int kDiag = k * cols + pk;<a name="line.878"></a> <FONT color="green">879</FONT> double gamma = 0;<a name="line.879"></a> <FONT color="green">880</FONT> int index = kDiag;<a name="line.880"></a> <FONT color="green">881</FONT> for (int i = k; i < rows; ++i) {<a name="line.881"></a> <FONT color="green">882</FONT> gamma += jacobian[index] * y[i];<a name="line.882"></a> <FONT color="green">883</FONT> index += cols;<a name="line.883"></a> <FONT color="green">884</FONT> }<a name="line.884"></a> <FONT color="green">885</FONT> gamma *= beta[pk];<a name="line.885"></a> <FONT color="green">886</FONT> index = kDiag;<a name="line.886"></a> <FONT color="green">887</FONT> for (int i = k; i < rows; ++i) {<a name="line.887"></a> <FONT color="green">888</FONT> y[i] -= gamma * jacobian[index];<a name="line.888"></a> <FONT color="green">889</FONT> index += cols;<a name="line.889"></a> <FONT color="green">890</FONT> }<a name="line.890"></a> <FONT color="green">891</FONT> }<a name="line.891"></a> <FONT color="green">892</FONT> }<a name="line.892"></a> <FONT color="green">893</FONT> <a name="line.893"></a> <FONT color="green">894</FONT> }<a name="line.894"></a> </PRE> </BODY> </HTML>