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comparison libs/commons-math-2.1/docs/apidocs/src-html/org/apache/commons/math/estimation/LevenbergMarquardtEstimator.html @ 13:cbf34dd4d7e6
commons-math-2.1 added
| author | dwinter |
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| date | Tue, 04 Jan 2011 10:02:07 +0100 |
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| 1 <HTML> | |
| 2 <BODY BGCOLOR="white"> | |
| 3 <PRE> | |
| 4 <FONT color="green">001</FONT> /*<a name="line.1"></a> | |
| 5 <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a> | |
| 6 <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a> | |
| 7 <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a> | |
| 8 <FONT color="green">005</FONT> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a> | |
| 9 <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a> | |
| 10 <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a> | |
| 11 <FONT color="green">008</FONT> *<a name="line.8"></a> | |
| 12 <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a> | |
| 13 <FONT color="green">010</FONT> *<a name="line.10"></a> | |
| 14 <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a> | |
| 15 <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a> | |
| 16 <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a> | |
| 17 <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a> | |
| 18 <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a> | |
| 19 <FONT color="green">016</FONT> */<a name="line.16"></a> | |
| 20 <FONT color="green">017</FONT> package org.apache.commons.math.estimation;<a name="line.17"></a> | |
| 21 <FONT color="green">018</FONT> <a name="line.18"></a> | |
| 22 <FONT color="green">019</FONT> import java.io.Serializable;<a name="line.19"></a> | |
| 23 <FONT color="green">020</FONT> import java.util.Arrays;<a name="line.20"></a> | |
| 24 <FONT color="green">021</FONT> <a name="line.21"></a> | |
| 25 <FONT color="green">022</FONT> <a name="line.22"></a> | |
| 26 <FONT color="green">023</FONT> /**<a name="line.23"></a> | |
| 27 <FONT color="green">024</FONT> * This class solves a least squares problem.<a name="line.24"></a> | |
| 28 <FONT color="green">025</FONT> *<a name="line.25"></a> | |
| 29 <FONT color="green">026</FONT> * <p>This implementation <em>should</em> work even for over-determined systems<a name="line.26"></a> | |
| 30 <FONT color="green">027</FONT> * (i.e. systems having more variables than equations). Over-determined systems<a name="line.27"></a> | |
| 31 <FONT color="green">028</FONT> * are solved by ignoring the variables which have the smallest impact according<a name="line.28"></a> | |
| 32 <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> | |
| 33 <FONT color="green">030</FONT> * are changed to implement this.</p><a name="line.30"></a> | |
| 34 <FONT color="green">031</FONT> *<a name="line.31"></a> | |
| 35 <FONT color="green">032</FONT> * <p>The resolution engine is a simple translation of the MINPACK <a<a name="line.32"></a> | |
| 36 <FONT color="green">033</FONT> * href="http://www.netlib.org/minpack/lmder.f">lmder</a> routine with minor<a name="line.33"></a> | |
| 37 <FONT color="green">034</FONT> * changes. The changes include the over-determined resolution and the Q.R.<a name="line.34"></a> | |
| 38 <FONT color="green">035</FONT> * decomposition which has been rewritten following the algorithm described in the<a name="line.35"></a> | |
| 39 <FONT color="green">036</FONT> * P. Lascaux and R. Theodor book <i>Analyse num&eacute;rique matricielle<a name="line.36"></a> | |
| 40 <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> | |
| 41 <FONT color="green">038</FONT> * <p>The authors of the original fortran version are:<a name="line.38"></a> | |
| 42 <FONT color="green">039</FONT> * <ul><a name="line.39"></a> | |
| 43 <FONT color="green">040</FONT> * <li>Argonne National Laboratory. MINPACK project. March 1980</li><a name="line.40"></a> | |
| 44 <FONT color="green">041</FONT> * <li>Burton S. Garbow</li><a name="line.41"></a> | |
| 45 <FONT color="green">042</FONT> * <li>Kenneth E. Hillstrom</li><a name="line.42"></a> | |
| 46 <FONT color="green">043</FONT> * <li>Jorge J. More</li><a name="line.43"></a> | |
| 47 <FONT color="green">044</FONT> * </ul><a name="line.44"></a> | |
| 48 <FONT color="green">045</FONT> * The redistribution policy for MINPACK is available <a<a name="line.45"></a> | |
| 49 <FONT color="green">046</FONT> * href="http://www.netlib.org/minpack/disclaimer">here</a>, for convenience, it<a name="line.46"></a> | |
| 50 <FONT color="green">047</FONT> * is reproduced below.</p><a name="line.47"></a> | |
| 51 <FONT color="green">048</FONT> *<a name="line.48"></a> | |
| 52 <FONT color="green">049</FONT> * <table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0"><a name="line.49"></a> | |
| 53 <FONT color="green">050</FONT> * <tr><td><a name="line.50"></a> | |
| 54 <FONT color="green">051</FONT> * Minpack Copyright Notice (1999) University of Chicago.<a name="line.51"></a> | |
| 55 <FONT color="green">052</FONT> * All rights reserved<a name="line.52"></a> | |
| 56 <FONT color="green">053</FONT> * </td></tr><a name="line.53"></a> | |
| 57 <FONT color="green">054</FONT> * <tr><td><a name="line.54"></a> | |
| 58 <FONT color="green">055</FONT> * Redistribution and use in source and binary forms, with or without<a name="line.55"></a> | |
| 59 <FONT color="green">056</FONT> * modification, are permitted provided that the following conditions<a name="line.56"></a> | |
| 60 <FONT color="green">057</FONT> * are met:<a name="line.57"></a> | |
| 61 <FONT color="green">058</FONT> * <ol><a name="line.58"></a> | |
| 62 <FONT color="green">059</FONT> * <li>Redistributions of source code must retain the above copyright<a name="line.59"></a> | |
| 63 <FONT color="green">060</FONT> * notice, this list of conditions and the following disclaimer.</li><a name="line.60"></a> | |
| 64 <FONT color="green">061</FONT> * <li>Redistributions in binary form must reproduce the above<a name="line.61"></a> | |
| 65 <FONT color="green">062</FONT> * copyright notice, this list of conditions and the following<a name="line.62"></a> | |
| 66 <FONT color="green">063</FONT> * disclaimer in the documentation and/or other materials provided<a name="line.63"></a> | |
| 67 <FONT color="green">064</FONT> * with the distribution.</li><a name="line.64"></a> | |
| 68 <FONT color="green">065</FONT> * <li>The end-user documentation included with the redistribution, if any,<a name="line.65"></a> | |
| 69 <FONT color="green">066</FONT> * must include the following acknowledgment:<a name="line.66"></a> | |
| 70 <FONT color="green">067</FONT> * <code>This product includes software developed by the University of<a name="line.67"></a> | |
| 71 <FONT color="green">068</FONT> * Chicago, as Operator of Argonne National Laboratory.</code><a name="line.68"></a> | |
| 72 <FONT color="green">069</FONT> * Alternately, this acknowledgment may appear in the software itself,<a name="line.69"></a> | |
| 73 <FONT color="green">070</FONT> * if and wherever such third-party acknowledgments normally appear.</li><a name="line.70"></a> | |
| 74 <FONT color="green">071</FONT> * <li><strong>WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS"<a name="line.71"></a> | |
| 75 <FONT color="green">072</FONT> * WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE<a name="line.72"></a> | |
| 76 <FONT color="green">073</FONT> * UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND<a name="line.73"></a> | |
| 77 <FONT color="green">074</FONT> * THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR<a name="line.74"></a> | |
| 78 <FONT color="green">075</FONT> * IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES<a name="line.75"></a> | |
| 79 <FONT color="green">076</FONT> * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE<a name="line.76"></a> | |
| 80 <FONT color="green">077</FONT> * OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY<a name="line.77"></a> | |
| 81 <FONT color="green">078</FONT> * OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR<a name="line.78"></a> | |
| 82 <FONT color="green">079</FONT> * USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF<a name="line.79"></a> | |
| 83 <FONT color="green">080</FONT> * THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4)<a name="line.80"></a> | |
| 84 <FONT color="green">081</FONT> * DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION<a name="line.81"></a> | |
| 85 <FONT color="green">082</FONT> * UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL<a name="line.82"></a> | |
| 86 <FONT color="green">083</FONT> * BE CORRECTED.</strong></li><a name="line.83"></a> | |
| 87 <FONT color="green">084</FONT> * <li><strong>LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT<a name="line.84"></a> | |
| 88 <FONT color="green">085</FONT> * HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF<a name="line.85"></a> | |
| 89 <FONT color="green">086</FONT> * ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT,<a name="line.86"></a> | |
| 90 <FONT color="green">087</FONT> * INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF<a name="line.87"></a> | |
| 91 <FONT color="green">088</FONT> * ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF<a name="line.88"></a> | |
| 92 <FONT color="green">089</FONT> * PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER<a name="line.89"></a> | |
| 93 <FONT color="green">090</FONT> * SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT<a name="line.90"></a> | |
| 94 <FONT color="green">091</FONT> * (INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,<a name="line.91"></a> | |
| 95 <FONT color="green">092</FONT> * EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE<a name="line.92"></a> | |
| 96 <FONT color="green">093</FONT> * POSSIBILITY OF SUCH LOSS OR DAMAGES.</strong></li><a name="line.93"></a> | |
| 97 <FONT color="green">094</FONT> * <ol></td></tr><a name="line.94"></a> | |
| 98 <FONT color="green">095</FONT> * </table><a name="line.95"></a> | |
| 99 <FONT color="green">096</FONT> <a name="line.96"></a> | |
| 100 <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> | |
| 101 <FONT color="green">098</FONT> * @since 1.2<a name="line.98"></a> | |
| 102 <FONT color="green">099</FONT> * @deprecated as of 2.0, everything in package org.apache.commons.math.estimation has<a name="line.99"></a> | |
| 103 <FONT color="green">100</FONT> * been deprecated and replaced by package org.apache.commons.math.optimization.general<a name="line.100"></a> | |
| 104 <FONT color="green">101</FONT> *<a name="line.101"></a> | |
| 105 <FONT color="green">102</FONT> */<a name="line.102"></a> | |
| 106 <FONT color="green">103</FONT> @Deprecated<a name="line.103"></a> | |
| 107 <FONT color="green">104</FONT> public class LevenbergMarquardtEstimator extends AbstractEstimator implements Serializable {<a name="line.104"></a> | |
| 108 <FONT color="green">105</FONT> <a name="line.105"></a> | |
| 109 <FONT color="green">106</FONT> /** Serializable version identifier */<a name="line.106"></a> | |
| 110 <FONT color="green">107</FONT> private static final long serialVersionUID = -5705952631533171019L;<a name="line.107"></a> | |
| 111 <FONT color="green">108</FONT> <a name="line.108"></a> | |
| 112 <FONT color="green">109</FONT> /** Number of solved variables. */<a name="line.109"></a> | |
| 113 <FONT color="green">110</FONT> private int solvedCols;<a name="line.110"></a> | |
| 114 <FONT color="green">111</FONT> <a name="line.111"></a> | |
| 115 <FONT color="green">112</FONT> /** Diagonal elements of the R matrix in the Q.R. decomposition. */<a name="line.112"></a> | |
| 116 <FONT color="green">113</FONT> private double[] diagR;<a name="line.113"></a> | |
| 117 <FONT color="green">114</FONT> <a name="line.114"></a> | |
| 118 <FONT color="green">115</FONT> /** Norms of the columns of the jacobian matrix. */<a name="line.115"></a> | |
| 119 <FONT color="green">116</FONT> private double[] jacNorm;<a name="line.116"></a> | |
| 120 <FONT color="green">117</FONT> <a name="line.117"></a> | |
| 121 <FONT color="green">118</FONT> /** Coefficients of the Householder transforms vectors. */<a name="line.118"></a> | |
| 122 <FONT color="green">119</FONT> private double[] beta;<a name="line.119"></a> | |
| 123 <FONT color="green">120</FONT> <a name="line.120"></a> | |
| 124 <FONT color="green">121</FONT> /** Columns permutation array. */<a name="line.121"></a> | |
| 125 <FONT color="green">122</FONT> private int[] permutation;<a name="line.122"></a> | |
| 126 <FONT color="green">123</FONT> <a name="line.123"></a> | |
| 127 <FONT color="green">124</FONT> /** Rank of the jacobian matrix. */<a name="line.124"></a> | |
| 128 <FONT color="green">125</FONT> private int rank;<a name="line.125"></a> | |
| 129 <FONT color="green">126</FONT> <a name="line.126"></a> | |
| 130 <FONT color="green">127</FONT> /** Levenberg-Marquardt parameter. */<a name="line.127"></a> | |
| 131 <FONT color="green">128</FONT> private double lmPar;<a name="line.128"></a> | |
| 132 <FONT color="green">129</FONT> <a name="line.129"></a> | |
| 133 <FONT color="green">130</FONT> /** Parameters evolution direction associated with lmPar. */<a name="line.130"></a> | |
| 134 <FONT color="green">131</FONT> private double[] lmDir;<a name="line.131"></a> | |
| 135 <FONT color="green">132</FONT> <a name="line.132"></a> | |
| 136 <FONT color="green">133</FONT> /** Positive input variable used in determining the initial step bound. */<a name="line.133"></a> | |
| 137 <FONT color="green">134</FONT> private double initialStepBoundFactor;<a name="line.134"></a> | |
| 138 <FONT color="green">135</FONT> <a name="line.135"></a> | |
| 139 <FONT color="green">136</FONT> /** Desired relative error in the sum of squares. */<a name="line.136"></a> | |
| 140 <FONT color="green">137</FONT> private double costRelativeTolerance;<a name="line.137"></a> | |
| 141 <FONT color="green">138</FONT> <a name="line.138"></a> | |
| 142 <FONT color="green">139</FONT> /** Desired relative error in the approximate solution parameters. */<a name="line.139"></a> | |
| 143 <FONT color="green">140</FONT> private double parRelativeTolerance;<a name="line.140"></a> | |
| 144 <FONT color="green">141</FONT> <a name="line.141"></a> | |
| 145 <FONT color="green">142</FONT> /** Desired max cosine on the orthogonality between the function vector<a name="line.142"></a> | |
| 146 <FONT color="green">143</FONT> * and the columns of the jacobian. */<a name="line.143"></a> | |
| 147 <FONT color="green">144</FONT> private double orthoTolerance;<a name="line.144"></a> | |
| 148 <FONT color="green">145</FONT> <a name="line.145"></a> | |
| 149 <FONT color="green">146</FONT> /**<a name="line.146"></a> | |
| 150 <FONT color="green">147</FONT> * Build an estimator for least squares problems.<a name="line.147"></a> | |
| 151 <FONT color="green">148</FONT> * <p>The default values for the algorithm settings are:<a name="line.148"></a> | |
| 152 <FONT color="green">149</FONT> * <ul><a name="line.149"></a> | |
| 153 <FONT color="green">150</FONT> * <li>{@link #setInitialStepBoundFactor initial step bound factor}: 100.0</li><a name="line.150"></a> | |
| 154 <FONT color="green">151</FONT> * <li>{@link #setMaxCostEval maximal cost evaluations}: 1000</li><a name="line.151"></a> | |
| 155 <FONT color="green">152</FONT> * <li>{@link #setCostRelativeTolerance cost relative tolerance}: 1.0e-10</li><a name="line.152"></a> | |
| 156 <FONT color="green">153</FONT> * <li>{@link #setParRelativeTolerance parameters relative tolerance}: 1.0e-10</li><a name="line.153"></a> | |
| 157 <FONT color="green">154</FONT> * <li>{@link #setOrthoTolerance orthogonality tolerance}: 1.0e-10</li><a name="line.154"></a> | |
| 158 <FONT color="green">155</FONT> * </ul><a name="line.155"></a> | |
| 159 <FONT color="green">156</FONT> * </p><a name="line.156"></a> | |
| 160 <FONT color="green">157</FONT> */<a name="line.157"></a> | |
| 161 <FONT color="green">158</FONT> public LevenbergMarquardtEstimator() {<a name="line.158"></a> | |
| 162 <FONT color="green">159</FONT> <a name="line.159"></a> | |
| 163 <FONT color="green">160</FONT> // set up the superclass with a default max cost evaluations setting<a name="line.160"></a> | |
| 164 <FONT color="green">161</FONT> setMaxCostEval(1000);<a name="line.161"></a> | |
| 165 <FONT color="green">162</FONT> <a name="line.162"></a> | |
| 166 <FONT color="green">163</FONT> // default values for the tuning parameters<a name="line.163"></a> | |
| 167 <FONT color="green">164</FONT> setInitialStepBoundFactor(100.0);<a name="line.164"></a> | |
| 168 <FONT color="green">165</FONT> setCostRelativeTolerance(1.0e-10);<a name="line.165"></a> | |
| 169 <FONT color="green">166</FONT> setParRelativeTolerance(1.0e-10);<a name="line.166"></a> | |
| 170 <FONT color="green">167</FONT> setOrthoTolerance(1.0e-10);<a name="line.167"></a> | |
| 171 <FONT color="green">168</FONT> <a name="line.168"></a> | |
| 172 <FONT color="green">169</FONT> }<a name="line.169"></a> | |
| 173 <FONT color="green">170</FONT> <a name="line.170"></a> | |
| 174 <FONT color="green">171</FONT> /**<a name="line.171"></a> | |
| 175 <FONT color="green">172</FONT> * Set the positive input variable used in determining the initial step bound.<a name="line.172"></a> | |
| 176 <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> | |
| 177 <FONT color="green">174</FONT> * or else to initialStepBoundFactor itself. In most cases factor should lie<a name="line.174"></a> | |
| 178 <FONT color="green">175</FONT> * in the interval (0.1, 100.0). 100.0 is a generally recommended value<a name="line.175"></a> | |
| 179 <FONT color="green">176</FONT> *<a name="line.176"></a> | |
| 180 <FONT color="green">177</FONT> * @param initialStepBoundFactor initial step bound factor<a name="line.177"></a> | |
| 181 <FONT color="green">178</FONT> * @see #estimate<a name="line.178"></a> | |
| 182 <FONT color="green">179</FONT> */<a name="line.179"></a> | |
| 183 <FONT color="green">180</FONT> public void setInitialStepBoundFactor(double initialStepBoundFactor) {<a name="line.180"></a> | |
| 184 <FONT color="green">181</FONT> this.initialStepBoundFactor = initialStepBoundFactor;<a name="line.181"></a> | |
| 185 <FONT color="green">182</FONT> }<a name="line.182"></a> | |
| 186 <FONT color="green">183</FONT> <a name="line.183"></a> | |
| 187 <FONT color="green">184</FONT> /**<a name="line.184"></a> | |
| 188 <FONT color="green">185</FONT> * Set the desired relative error in the sum of squares.<a name="line.185"></a> | |
| 189 <FONT color="green">186</FONT> *<a name="line.186"></a> | |
| 190 <FONT color="green">187</FONT> * @param costRelativeTolerance desired relative error in the sum of squares<a name="line.187"></a> | |
| 191 <FONT color="green">188</FONT> * @see #estimate<a name="line.188"></a> | |
| 192 <FONT color="green">189</FONT> */<a name="line.189"></a> | |
| 193 <FONT color="green">190</FONT> public void setCostRelativeTolerance(double costRelativeTolerance) {<a name="line.190"></a> | |
| 194 <FONT color="green">191</FONT> this.costRelativeTolerance = costRelativeTolerance;<a name="line.191"></a> | |
| 195 <FONT color="green">192</FONT> }<a name="line.192"></a> | |
| 196 <FONT color="green">193</FONT> <a name="line.193"></a> | |
| 197 <FONT color="green">194</FONT> /**<a name="line.194"></a> | |
| 198 <FONT color="green">195</FONT> * Set the desired relative error in the approximate solution parameters.<a name="line.195"></a> | |
| 199 <FONT color="green">196</FONT> *<a name="line.196"></a> | |
| 200 <FONT color="green">197</FONT> * @param parRelativeTolerance desired relative error<a name="line.197"></a> | |
| 201 <FONT color="green">198</FONT> * in the approximate solution parameters<a name="line.198"></a> | |
| 202 <FONT color="green">199</FONT> * @see #estimate<a name="line.199"></a> | |
| 203 <FONT color="green">200</FONT> */<a name="line.200"></a> | |
| 204 <FONT color="green">201</FONT> public void setParRelativeTolerance(double parRelativeTolerance) {<a name="line.201"></a> | |
| 205 <FONT color="green">202</FONT> this.parRelativeTolerance = parRelativeTolerance;<a name="line.202"></a> | |
| 206 <FONT color="green">203</FONT> }<a name="line.203"></a> | |
| 207 <FONT color="green">204</FONT> <a name="line.204"></a> | |
| 208 <FONT color="green">205</FONT> /**<a name="line.205"></a> | |
| 209 <FONT color="green">206</FONT> * Set the desired max cosine on the orthogonality.<a name="line.206"></a> | |
| 210 <FONT color="green">207</FONT> *<a name="line.207"></a> | |
| 211 <FONT color="green">208</FONT> * @param orthoTolerance desired max cosine on the orthogonality<a name="line.208"></a> | |
| 212 <FONT color="green">209</FONT> * between the function vector and the columns of the jacobian<a name="line.209"></a> | |
| 213 <FONT color="green">210</FONT> * @see #estimate<a name="line.210"></a> | |
| 214 <FONT color="green">211</FONT> */<a name="line.211"></a> | |
| 215 <FONT color="green">212</FONT> public void setOrthoTolerance(double orthoTolerance) {<a name="line.212"></a> | |
| 216 <FONT color="green">213</FONT> this.orthoTolerance = orthoTolerance;<a name="line.213"></a> | |
| 217 <FONT color="green">214</FONT> }<a name="line.214"></a> | |
| 218 <FONT color="green">215</FONT> <a name="line.215"></a> | |
| 219 <FONT color="green">216</FONT> /**<a name="line.216"></a> | |
| 220 <FONT color="green">217</FONT> * Solve an estimation problem using the Levenberg-Marquardt algorithm.<a name="line.217"></a> | |
| 221 <FONT color="green">218</FONT> * <p>The algorithm used is a modified Levenberg-Marquardt one, based<a name="line.218"></a> | |
| 222 <FONT color="green">219</FONT> * on the MINPACK <a href="http://www.netlib.org/minpack/lmder.f">lmder</a><a name="line.219"></a> | |
| 223 <FONT color="green">220</FONT> * routine. The algorithm settings must have been set up before this method<a name="line.220"></a> | |
| 224 <FONT color="green">221</FONT> * is called with the {@link #setInitialStepBoundFactor},<a name="line.221"></a> | |
| 225 <FONT color="green">222</FONT> * {@link #setMaxCostEval}, {@link #setCostRelativeTolerance},<a name="line.222"></a> | |
| 226 <FONT color="green">223</FONT> * {@link #setParRelativeTolerance} and {@link #setOrthoTolerance} methods.<a name="line.223"></a> | |
| 227 <FONT color="green">224</FONT> * If these methods have not been called, the default values set up by the<a name="line.224"></a> | |
| 228 <FONT color="green">225</FONT> * {@link #LevenbergMarquardtEstimator() constructor} will be used.</p><a name="line.225"></a> | |
| 229 <FONT color="green">226</FONT> * <p>The authors of the original fortran function are:</p><a name="line.226"></a> | |
| 230 <FONT color="green">227</FONT> * <ul><a name="line.227"></a> | |
| 231 <FONT color="green">228</FONT> * <li>Argonne National Laboratory. MINPACK project. March 1980</li><a name="line.228"></a> | |
| 232 <FONT color="green">229</FONT> * <li>Burton S. Garbow</li><a name="line.229"></a> | |
| 233 <FONT color="green">230</FONT> * <li>Kenneth E. Hillstrom</li><a name="line.230"></a> | |
| 234 <FONT color="green">231</FONT> * <li>Jorge J. More</li><a name="line.231"></a> | |
| 235 <FONT color="green">232</FONT> * </ul><a name="line.232"></a> | |
| 236 <FONT color="green">233</FONT> * <p>Luc Maisonobe did the Java translation.</p><a name="line.233"></a> | |
| 237 <FONT color="green">234</FONT> *<a name="line.234"></a> | |
| 238 <FONT color="green">235</FONT> * @param problem estimation problem to solve<a name="line.235"></a> | |
| 239 <FONT color="green">236</FONT> * @exception EstimationException if convergence cannot be<a name="line.236"></a> | |
| 240 <FONT color="green">237</FONT> * reached with the specified algorithm settings or if there are more variables<a name="line.237"></a> | |
| 241 <FONT color="green">238</FONT> * than equations<a name="line.238"></a> | |
| 242 <FONT color="green">239</FONT> * @see #setInitialStepBoundFactor<a name="line.239"></a> | |
| 243 <FONT color="green">240</FONT> * @see #setCostRelativeTolerance<a name="line.240"></a> | |
| 244 <FONT color="green">241</FONT> * @see #setParRelativeTolerance<a name="line.241"></a> | |
| 245 <FONT color="green">242</FONT> * @see #setOrthoTolerance<a name="line.242"></a> | |
| 246 <FONT color="green">243</FONT> */<a name="line.243"></a> | |
| 247 <FONT color="green">244</FONT> @Override<a name="line.244"></a> | |
| 248 <FONT color="green">245</FONT> public void estimate(EstimationProblem problem)<a name="line.245"></a> | |
| 249 <FONT color="green">246</FONT> throws EstimationException {<a name="line.246"></a> | |
| 250 <FONT color="green">247</FONT> <a name="line.247"></a> | |
| 251 <FONT color="green">248</FONT> initializeEstimate(problem);<a name="line.248"></a> | |
| 252 <FONT color="green">249</FONT> <a name="line.249"></a> | |
| 253 <FONT color="green">250</FONT> // arrays shared with the other private methods<a name="line.250"></a> | |
| 254 <FONT color="green">251</FONT> solvedCols = Math.min(rows, cols);<a name="line.251"></a> | |
| 255 <FONT color="green">252</FONT> diagR = new double[cols];<a name="line.252"></a> | |
| 256 <FONT color="green">253</FONT> jacNorm = new double[cols];<a name="line.253"></a> | |
| 257 <FONT color="green">254</FONT> beta = new double[cols];<a name="line.254"></a> | |
| 258 <FONT color="green">255</FONT> permutation = new int[cols];<a name="line.255"></a> | |
| 259 <FONT color="green">256</FONT> lmDir = new double[cols];<a name="line.256"></a> | |
| 260 <FONT color="green">257</FONT> <a name="line.257"></a> | |
| 261 <FONT color="green">258</FONT> // local variables<a name="line.258"></a> | |
| 262 <FONT color="green">259</FONT> double delta = 0;<a name="line.259"></a> | |
| 263 <FONT color="green">260</FONT> double xNorm = 0;<a name="line.260"></a> | |
| 264 <FONT color="green">261</FONT> double[] diag = new double[cols];<a name="line.261"></a> | |
| 265 <FONT color="green">262</FONT> double[] oldX = new double[cols];<a name="line.262"></a> | |
| 266 <FONT color="green">263</FONT> double[] oldRes = new double[rows];<a name="line.263"></a> | |
| 267 <FONT color="green">264</FONT> double[] work1 = new double[cols];<a name="line.264"></a> | |
| 268 <FONT color="green">265</FONT> double[] work2 = new double[cols];<a name="line.265"></a> | |
| 269 <FONT color="green">266</FONT> double[] work3 = new double[cols];<a name="line.266"></a> | |
| 270 <FONT color="green">267</FONT> <a name="line.267"></a> | |
| 271 <FONT color="green">268</FONT> // evaluate the function at the starting point and calculate its norm<a name="line.268"></a> | |
| 272 <FONT color="green">269</FONT> updateResidualsAndCost();<a name="line.269"></a> | |
| 273 <FONT color="green">270</FONT> <a name="line.270"></a> | |
| 274 <FONT color="green">271</FONT> // outer loop<a name="line.271"></a> | |
| 275 <FONT color="green">272</FONT> lmPar = 0;<a name="line.272"></a> | |
| 276 <FONT color="green">273</FONT> boolean firstIteration = true;<a name="line.273"></a> | |
| 277 <FONT color="green">274</FONT> while (true) {<a name="line.274"></a> | |
| 278 <FONT color="green">275</FONT> <a name="line.275"></a> | |
| 279 <FONT color="green">276</FONT> // compute the Q.R. decomposition of the jacobian matrix<a name="line.276"></a> | |
| 280 <FONT color="green">277</FONT> updateJacobian();<a name="line.277"></a> | |
| 281 <FONT color="green">278</FONT> qrDecomposition();<a name="line.278"></a> | |
| 282 <FONT color="green">279</FONT> <a name="line.279"></a> | |
| 283 <FONT color="green">280</FONT> // compute Qt.res<a name="line.280"></a> | |
| 284 <FONT color="green">281</FONT> qTy(residuals);<a name="line.281"></a> | |
| 285 <FONT color="green">282</FONT> <a name="line.282"></a> | |
| 286 <FONT color="green">283</FONT> // now we don't need Q anymore,<a name="line.283"></a> | |
| 287 <FONT color="green">284</FONT> // so let jacobian contain the R matrix with its diagonal elements<a name="line.284"></a> | |
| 288 <FONT color="green">285</FONT> for (int k = 0; k < solvedCols; ++k) {<a name="line.285"></a> | |
| 289 <FONT color="green">286</FONT> int pk = permutation[k];<a name="line.286"></a> | |
| 290 <FONT color="green">287</FONT> jacobian[k * cols + pk] = diagR[pk];<a name="line.287"></a> | |
| 291 <FONT color="green">288</FONT> }<a name="line.288"></a> | |
| 292 <FONT color="green">289</FONT> <a name="line.289"></a> | |
| 293 <FONT color="green">290</FONT> if (firstIteration) {<a name="line.290"></a> | |
| 294 <FONT color="green">291</FONT> <a name="line.291"></a> | |
| 295 <FONT color="green">292</FONT> // scale the variables according to the norms of the columns<a name="line.292"></a> | |
| 296 <FONT color="green">293</FONT> // of the initial jacobian<a name="line.293"></a> | |
| 297 <FONT color="green">294</FONT> xNorm = 0;<a name="line.294"></a> | |
| 298 <FONT color="green">295</FONT> for (int k = 0; k < cols; ++k) {<a name="line.295"></a> | |
| 299 <FONT color="green">296</FONT> double dk = jacNorm[k];<a name="line.296"></a> | |
| 300 <FONT color="green">297</FONT> if (dk == 0) {<a name="line.297"></a> | |
| 301 <FONT color="green">298</FONT> dk = 1.0;<a name="line.298"></a> | |
| 302 <FONT color="green">299</FONT> }<a name="line.299"></a> | |
| 303 <FONT color="green">300</FONT> double xk = dk * parameters[k].getEstimate();<a name="line.300"></a> | |
| 304 <FONT color="green">301</FONT> xNorm += xk * xk;<a name="line.301"></a> | |
| 305 <FONT color="green">302</FONT> diag[k] = dk;<a name="line.302"></a> | |
| 306 <FONT color="green">303</FONT> }<a name="line.303"></a> | |
| 307 <FONT color="green">304</FONT> xNorm = Math.sqrt(xNorm);<a name="line.304"></a> | |
| 308 <FONT color="green">305</FONT> <a name="line.305"></a> | |
| 309 <FONT color="green">306</FONT> // initialize the step bound delta<a name="line.306"></a> | |
| 310 <FONT color="green">307</FONT> delta = (xNorm == 0) ? initialStepBoundFactor : (initialStepBoundFactor * xNorm);<a name="line.307"></a> | |
| 311 <FONT color="green">308</FONT> <a name="line.308"></a> | |
| 312 <FONT color="green">309</FONT> }<a name="line.309"></a> | |
| 313 <FONT color="green">310</FONT> <a name="line.310"></a> | |
| 314 <FONT color="green">311</FONT> // check orthogonality between function vector and jacobian columns<a name="line.311"></a> | |
| 315 <FONT color="green">312</FONT> double maxCosine = 0;<a name="line.312"></a> | |
| 316 <FONT color="green">313</FONT> if (cost != 0) {<a name="line.313"></a> | |
| 317 <FONT color="green">314</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.314"></a> | |
| 318 <FONT color="green">315</FONT> int pj = permutation[j];<a name="line.315"></a> | |
| 319 <FONT color="green">316</FONT> double s = jacNorm[pj];<a name="line.316"></a> | |
| 320 <FONT color="green">317</FONT> if (s != 0) {<a name="line.317"></a> | |
| 321 <FONT color="green">318</FONT> double sum = 0;<a name="line.318"></a> | |
| 322 <FONT color="green">319</FONT> int index = pj;<a name="line.319"></a> | |
| 323 <FONT color="green">320</FONT> for (int i = 0; i <= j; ++i) {<a name="line.320"></a> | |
| 324 <FONT color="green">321</FONT> sum += jacobian[index] * residuals[i];<a name="line.321"></a> | |
| 325 <FONT color="green">322</FONT> index += cols;<a name="line.322"></a> | |
| 326 <FONT color="green">323</FONT> }<a name="line.323"></a> | |
| 327 <FONT color="green">324</FONT> maxCosine = Math.max(maxCosine, Math.abs(sum) / (s * cost));<a name="line.324"></a> | |
| 328 <FONT color="green">325</FONT> }<a name="line.325"></a> | |
| 329 <FONT color="green">326</FONT> }<a name="line.326"></a> | |
| 330 <FONT color="green">327</FONT> }<a name="line.327"></a> | |
| 331 <FONT color="green">328</FONT> if (maxCosine <= orthoTolerance) {<a name="line.328"></a> | |
| 332 <FONT color="green">329</FONT> return;<a name="line.329"></a> | |
| 333 <FONT color="green">330</FONT> }<a name="line.330"></a> | |
| 334 <FONT color="green">331</FONT> <a name="line.331"></a> | |
| 335 <FONT color="green">332</FONT> // rescale if necessary<a name="line.332"></a> | |
| 336 <FONT color="green">333</FONT> for (int j = 0; j < cols; ++j) {<a name="line.333"></a> | |
| 337 <FONT color="green">334</FONT> diag[j] = Math.max(diag[j], jacNorm[j]);<a name="line.334"></a> | |
| 338 <FONT color="green">335</FONT> }<a name="line.335"></a> | |
| 339 <FONT color="green">336</FONT> <a name="line.336"></a> | |
| 340 <FONT color="green">337</FONT> // inner loop<a name="line.337"></a> | |
| 341 <FONT color="green">338</FONT> for (double ratio = 0; ratio < 1.0e-4;) {<a name="line.338"></a> | |
| 342 <FONT color="green">339</FONT> <a name="line.339"></a> | |
| 343 <FONT color="green">340</FONT> // save the state<a name="line.340"></a> | |
| 344 <FONT color="green">341</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.341"></a> | |
| 345 <FONT color="green">342</FONT> int pj = permutation[j];<a name="line.342"></a> | |
| 346 <FONT color="green">343</FONT> oldX[pj] = parameters[pj].getEstimate();<a name="line.343"></a> | |
| 347 <FONT color="green">344</FONT> }<a name="line.344"></a> | |
| 348 <FONT color="green">345</FONT> double previousCost = cost;<a name="line.345"></a> | |
| 349 <FONT color="green">346</FONT> double[] tmpVec = residuals;<a name="line.346"></a> | |
| 350 <FONT color="green">347</FONT> residuals = oldRes;<a name="line.347"></a> | |
| 351 <FONT color="green">348</FONT> oldRes = tmpVec;<a name="line.348"></a> | |
| 352 <FONT color="green">349</FONT> <a name="line.349"></a> | |
| 353 <FONT color="green">350</FONT> // determine the Levenberg-Marquardt parameter<a name="line.350"></a> | |
| 354 <FONT color="green">351</FONT> determineLMParameter(oldRes, delta, diag, work1, work2, work3);<a name="line.351"></a> | |
| 355 <FONT color="green">352</FONT> <a name="line.352"></a> | |
| 356 <FONT color="green">353</FONT> // compute the new point and the norm of the evolution direction<a name="line.353"></a> | |
| 357 <FONT color="green">354</FONT> double lmNorm = 0;<a name="line.354"></a> | |
| 358 <FONT color="green">355</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.355"></a> | |
| 359 <FONT color="green">356</FONT> int pj = permutation[j];<a name="line.356"></a> | |
| 360 <FONT color="green">357</FONT> lmDir[pj] = -lmDir[pj];<a name="line.357"></a> | |
| 361 <FONT color="green">358</FONT> parameters[pj].setEstimate(oldX[pj] + lmDir[pj]);<a name="line.358"></a> | |
| 362 <FONT color="green">359</FONT> double s = diag[pj] * lmDir[pj];<a name="line.359"></a> | |
| 363 <FONT color="green">360</FONT> lmNorm += s * s;<a name="line.360"></a> | |
| 364 <FONT color="green">361</FONT> }<a name="line.361"></a> | |
| 365 <FONT color="green">362</FONT> lmNorm = Math.sqrt(lmNorm);<a name="line.362"></a> | |
| 366 <FONT color="green">363</FONT> <a name="line.363"></a> | |
| 367 <FONT color="green">364</FONT> // on the first iteration, adjust the initial step bound.<a name="line.364"></a> | |
| 368 <FONT color="green">365</FONT> if (firstIteration) {<a name="line.365"></a> | |
| 369 <FONT color="green">366</FONT> delta = Math.min(delta, lmNorm);<a name="line.366"></a> | |
| 370 <FONT color="green">367</FONT> }<a name="line.367"></a> | |
| 371 <FONT color="green">368</FONT> <a name="line.368"></a> | |
| 372 <FONT color="green">369</FONT> // evaluate the function at x + p and calculate its norm<a name="line.369"></a> | |
| 373 <FONT color="green">370</FONT> updateResidualsAndCost();<a name="line.370"></a> | |
| 374 <FONT color="green">371</FONT> <a name="line.371"></a> | |
| 375 <FONT color="green">372</FONT> // compute the scaled actual reduction<a name="line.372"></a> | |
| 376 <FONT color="green">373</FONT> double actRed = -1.0;<a name="line.373"></a> | |
| 377 <FONT color="green">374</FONT> if (0.1 * cost < previousCost) {<a name="line.374"></a> | |
| 378 <FONT color="green">375</FONT> double r = cost / previousCost;<a name="line.375"></a> | |
| 379 <FONT color="green">376</FONT> actRed = 1.0 - r * r;<a name="line.376"></a> | |
| 380 <FONT color="green">377</FONT> }<a name="line.377"></a> | |
| 381 <FONT color="green">378</FONT> <a name="line.378"></a> | |
| 382 <FONT color="green">379</FONT> // compute the scaled predicted reduction<a name="line.379"></a> | |
| 383 <FONT color="green">380</FONT> // and the scaled directional derivative<a name="line.380"></a> | |
| 384 <FONT color="green">381</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.381"></a> | |
| 385 <FONT color="green">382</FONT> int pj = permutation[j];<a name="line.382"></a> | |
| 386 <FONT color="green">383</FONT> double dirJ = lmDir[pj];<a name="line.383"></a> | |
| 387 <FONT color="green">384</FONT> work1[j] = 0;<a name="line.384"></a> | |
| 388 <FONT color="green">385</FONT> int index = pj;<a name="line.385"></a> | |
| 389 <FONT color="green">386</FONT> for (int i = 0; i <= j; ++i) {<a name="line.386"></a> | |
| 390 <FONT color="green">387</FONT> work1[i] += jacobian[index] * dirJ;<a name="line.387"></a> | |
| 391 <FONT color="green">388</FONT> index += cols;<a name="line.388"></a> | |
| 392 <FONT color="green">389</FONT> }<a name="line.389"></a> | |
| 393 <FONT color="green">390</FONT> }<a name="line.390"></a> | |
| 394 <FONT color="green">391</FONT> double coeff1 = 0;<a name="line.391"></a> | |
| 395 <FONT color="green">392</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.392"></a> | |
| 396 <FONT color="green">393</FONT> coeff1 += work1[j] * work1[j];<a name="line.393"></a> | |
| 397 <FONT color="green">394</FONT> }<a name="line.394"></a> | |
| 398 <FONT color="green">395</FONT> double pc2 = previousCost * previousCost;<a name="line.395"></a> | |
| 399 <FONT color="green">396</FONT> coeff1 = coeff1 / pc2;<a name="line.396"></a> | |
| 400 <FONT color="green">397</FONT> double coeff2 = lmPar * lmNorm * lmNorm / pc2;<a name="line.397"></a> | |
| 401 <FONT color="green">398</FONT> double preRed = coeff1 + 2 * coeff2;<a name="line.398"></a> | |
| 402 <FONT color="green">399</FONT> double dirDer = -(coeff1 + coeff2);<a name="line.399"></a> | |
| 403 <FONT color="green">400</FONT> <a name="line.400"></a> | |
| 404 <FONT color="green">401</FONT> // ratio of the actual to the predicted reduction<a name="line.401"></a> | |
| 405 <FONT color="green">402</FONT> ratio = (preRed == 0) ? 0 : (actRed / preRed);<a name="line.402"></a> | |
| 406 <FONT color="green">403</FONT> <a name="line.403"></a> | |
| 407 <FONT color="green">404</FONT> // update the step bound<a name="line.404"></a> | |
| 408 <FONT color="green">405</FONT> if (ratio <= 0.25) {<a name="line.405"></a> | |
| 409 <FONT color="green">406</FONT> double tmp =<a name="line.406"></a> | |
| 410 <FONT color="green">407</FONT> (actRed < 0) ? (0.5 * dirDer / (dirDer + 0.5 * actRed)) : 0.5;<a name="line.407"></a> | |
| 411 <FONT color="green">408</FONT> if ((0.1 * cost >= previousCost) || (tmp < 0.1)) {<a name="line.408"></a> | |
| 412 <FONT color="green">409</FONT> tmp = 0.1;<a name="line.409"></a> | |
| 413 <FONT color="green">410</FONT> }<a name="line.410"></a> | |
| 414 <FONT color="green">411</FONT> delta = tmp * Math.min(delta, 10.0 * lmNorm);<a name="line.411"></a> | |
| 415 <FONT color="green">412</FONT> lmPar /= tmp;<a name="line.412"></a> | |
| 416 <FONT color="green">413</FONT> } else if ((lmPar == 0) || (ratio >= 0.75)) {<a name="line.413"></a> | |
| 417 <FONT color="green">414</FONT> delta = 2 * lmNorm;<a name="line.414"></a> | |
| 418 <FONT color="green">415</FONT> lmPar *= 0.5;<a name="line.415"></a> | |
| 419 <FONT color="green">416</FONT> }<a name="line.416"></a> | |
| 420 <FONT color="green">417</FONT> <a name="line.417"></a> | |
| 421 <FONT color="green">418</FONT> // test for successful iteration.<a name="line.418"></a> | |
| 422 <FONT color="green">419</FONT> if (ratio >= 1.0e-4) {<a name="line.419"></a> | |
| 423 <FONT color="green">420</FONT> // successful iteration, update the norm<a name="line.420"></a> | |
| 424 <FONT color="green">421</FONT> firstIteration = false;<a name="line.421"></a> | |
| 425 <FONT color="green">422</FONT> xNorm = 0;<a name="line.422"></a> | |
| 426 <FONT color="green">423</FONT> for (int k = 0; k < cols; ++k) {<a name="line.423"></a> | |
| 427 <FONT color="green">424</FONT> double xK = diag[k] * parameters[k].getEstimate();<a name="line.424"></a> | |
| 428 <FONT color="green">425</FONT> xNorm += xK * xK;<a name="line.425"></a> | |
| 429 <FONT color="green">426</FONT> }<a name="line.426"></a> | |
| 430 <FONT color="green">427</FONT> xNorm = Math.sqrt(xNorm);<a name="line.427"></a> | |
| 431 <FONT color="green">428</FONT> } else {<a name="line.428"></a> | |
| 432 <FONT color="green">429</FONT> // failed iteration, reset the previous values<a name="line.429"></a> | |
| 433 <FONT color="green">430</FONT> cost = previousCost;<a name="line.430"></a> | |
| 434 <FONT color="green">431</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.431"></a> | |
| 435 <FONT color="green">432</FONT> int pj = permutation[j];<a name="line.432"></a> | |
| 436 <FONT color="green">433</FONT> parameters[pj].setEstimate(oldX[pj]);<a name="line.433"></a> | |
| 437 <FONT color="green">434</FONT> }<a name="line.434"></a> | |
| 438 <FONT color="green">435</FONT> tmpVec = residuals;<a name="line.435"></a> | |
| 439 <FONT color="green">436</FONT> residuals = oldRes;<a name="line.436"></a> | |
| 440 <FONT color="green">437</FONT> oldRes = tmpVec;<a name="line.437"></a> | |
| 441 <FONT color="green">438</FONT> }<a name="line.438"></a> | |
| 442 <FONT color="green">439</FONT> <a name="line.439"></a> | |
| 443 <FONT color="green">440</FONT> // tests for convergence.<a name="line.440"></a> | |
| 444 <FONT color="green">441</FONT> if (((Math.abs(actRed) <= costRelativeTolerance) &&<a name="line.441"></a> | |
| 445 <FONT color="green">442</FONT> (preRed <= costRelativeTolerance) &&<a name="line.442"></a> | |
| 446 <FONT color="green">443</FONT> (ratio <= 2.0)) ||<a name="line.443"></a> | |
| 447 <FONT color="green">444</FONT> (delta <= parRelativeTolerance * xNorm)) {<a name="line.444"></a> | |
| 448 <FONT color="green">445</FONT> return;<a name="line.445"></a> | |
| 449 <FONT color="green">446</FONT> }<a name="line.446"></a> | |
| 450 <FONT color="green">447</FONT> <a name="line.447"></a> | |
| 451 <FONT color="green">448</FONT> // tests for termination and stringent tolerances<a name="line.448"></a> | |
| 452 <FONT color="green">449</FONT> // (2.2204e-16 is the machine epsilon for IEEE754)<a name="line.449"></a> | |
| 453 <FONT color="green">450</FONT> if ((Math.abs(actRed) <= 2.2204e-16) && (preRed <= 2.2204e-16) && (ratio <= 2.0)) {<a name="line.450"></a> | |
| 454 <FONT color="green">451</FONT> throw new EstimationException("cost relative tolerance is too small ({0})," +<a name="line.451"></a> | |
| 455 <FONT color="green">452</FONT> " no further reduction in the" +<a name="line.452"></a> | |
| 456 <FONT color="green">453</FONT> " sum of squares is possible",<a name="line.453"></a> | |
| 457 <FONT color="green">454</FONT> costRelativeTolerance);<a name="line.454"></a> | |
| 458 <FONT color="green">455</FONT> } else if (delta <= 2.2204e-16 * xNorm) {<a name="line.455"></a> | |
| 459 <FONT color="green">456</FONT> throw new EstimationException("parameters relative tolerance is too small" +<a name="line.456"></a> | |
| 460 <FONT color="green">457</FONT> " ({0}), no further improvement in" +<a name="line.457"></a> | |
| 461 <FONT color="green">458</FONT> " the approximate solution is possible",<a name="line.458"></a> | |
| 462 <FONT color="green">459</FONT> parRelativeTolerance);<a name="line.459"></a> | |
| 463 <FONT color="green">460</FONT> } else if (maxCosine <= 2.2204e-16) {<a name="line.460"></a> | |
| 464 <FONT color="green">461</FONT> throw new EstimationException("orthogonality tolerance is too small ({0})," +<a name="line.461"></a> | |
| 465 <FONT color="green">462</FONT> " solution is orthogonal to the jacobian",<a name="line.462"></a> | |
| 466 <FONT color="green">463</FONT> orthoTolerance);<a name="line.463"></a> | |
| 467 <FONT color="green">464</FONT> }<a name="line.464"></a> | |
| 468 <FONT color="green">465</FONT> <a name="line.465"></a> | |
| 469 <FONT color="green">466</FONT> }<a name="line.466"></a> | |
| 470 <FONT color="green">467</FONT> <a name="line.467"></a> | |
| 471 <FONT color="green">468</FONT> }<a name="line.468"></a> | |
| 472 <FONT color="green">469</FONT> <a name="line.469"></a> | |
| 473 <FONT color="green">470</FONT> }<a name="line.470"></a> | |
| 474 <FONT color="green">471</FONT> <a name="line.471"></a> | |
| 475 <FONT color="green">472</FONT> /**<a name="line.472"></a> | |
| 476 <FONT color="green">473</FONT> * Determine the Levenberg-Marquardt parameter.<a name="line.473"></a> | |
| 477 <FONT color="green">474</FONT> * <p>This implementation is a translation in Java of the MINPACK<a name="line.474"></a> | |
| 478 <FONT color="green">475</FONT> * <a href="http://www.netlib.org/minpack/lmpar.f">lmpar</a><a name="line.475"></a> | |
| 479 <FONT color="green">476</FONT> * routine.</p><a name="line.476"></a> | |
| 480 <FONT color="green">477</FONT> * <p>This method sets the lmPar and lmDir attributes.</p><a name="line.477"></a> | |
| 481 <FONT color="green">478</FONT> * <p>The authors of the original fortran function are:</p><a name="line.478"></a> | |
| 482 <FONT color="green">479</FONT> * <ul><a name="line.479"></a> | |
| 483 <FONT color="green">480</FONT> * <li>Argonne National Laboratory. MINPACK project. March 1980</li><a name="line.480"></a> | |
| 484 <FONT color="green">481</FONT> * <li>Burton S. Garbow</li><a name="line.481"></a> | |
| 485 <FONT color="green">482</FONT> * <li>Kenneth E. Hillstrom</li><a name="line.482"></a> | |
| 486 <FONT color="green">483</FONT> * <li>Jorge J. More</li><a name="line.483"></a> | |
| 487 <FONT color="green">484</FONT> * </ul><a name="line.484"></a> | |
| 488 <FONT color="green">485</FONT> * <p>Luc Maisonobe did the Java translation.</p><a name="line.485"></a> | |
| 489 <FONT color="green">486</FONT> *<a name="line.486"></a> | |
| 490 <FONT color="green">487</FONT> * @param qy array containing qTy<a name="line.487"></a> | |
| 491 <FONT color="green">488</FONT> * @param delta upper bound on the euclidean norm of diagR * lmDir<a name="line.488"></a> | |
| 492 <FONT color="green">489</FONT> * @param diag diagonal matrix<a name="line.489"></a> | |
| 493 <FONT color="green">490</FONT> * @param work1 work array<a name="line.490"></a> | |
| 494 <FONT color="green">491</FONT> * @param work2 work array<a name="line.491"></a> | |
| 495 <FONT color="green">492</FONT> * @param work3 work array<a name="line.492"></a> | |
| 496 <FONT color="green">493</FONT> */<a name="line.493"></a> | |
| 497 <FONT color="green">494</FONT> private void determineLMParameter(double[] qy, double delta, double[] diag,<a name="line.494"></a> | |
| 498 <FONT color="green">495</FONT> double[] work1, double[] work2, double[] work3) {<a name="line.495"></a> | |
| 499 <FONT color="green">496</FONT> <a name="line.496"></a> | |
| 500 <FONT color="green">497</FONT> // compute and store in x the gauss-newton direction, if the<a name="line.497"></a> | |
| 501 <FONT color="green">498</FONT> // jacobian is rank-deficient, obtain a least squares solution<a name="line.498"></a> | |
| 502 <FONT color="green">499</FONT> for (int j = 0; j < rank; ++j) {<a name="line.499"></a> | |
| 503 <FONT color="green">500</FONT> lmDir[permutation[j]] = qy[j];<a name="line.500"></a> | |
| 504 <FONT color="green">501</FONT> }<a name="line.501"></a> | |
| 505 <FONT color="green">502</FONT> for (int j = rank; j < cols; ++j) {<a name="line.502"></a> | |
| 506 <FONT color="green">503</FONT> lmDir[permutation[j]] = 0;<a name="line.503"></a> | |
| 507 <FONT color="green">504</FONT> }<a name="line.504"></a> | |
| 508 <FONT color="green">505</FONT> for (int k = rank - 1; k >= 0; --k) {<a name="line.505"></a> | |
| 509 <FONT color="green">506</FONT> int pk = permutation[k];<a name="line.506"></a> | |
| 510 <FONT color="green">507</FONT> double ypk = lmDir[pk] / diagR[pk];<a name="line.507"></a> | |
| 511 <FONT color="green">508</FONT> int index = pk;<a name="line.508"></a> | |
| 512 <FONT color="green">509</FONT> for (int i = 0; i < k; ++i) {<a name="line.509"></a> | |
| 513 <FONT color="green">510</FONT> lmDir[permutation[i]] -= ypk * jacobian[index];<a name="line.510"></a> | |
| 514 <FONT color="green">511</FONT> index += cols;<a name="line.511"></a> | |
| 515 <FONT color="green">512</FONT> }<a name="line.512"></a> | |
| 516 <FONT color="green">513</FONT> lmDir[pk] = ypk;<a name="line.513"></a> | |
| 517 <FONT color="green">514</FONT> }<a name="line.514"></a> | |
| 518 <FONT color="green">515</FONT> <a name="line.515"></a> | |
| 519 <FONT color="green">516</FONT> // evaluate the function at the origin, and test<a name="line.516"></a> | |
| 520 <FONT color="green">517</FONT> // for acceptance of the Gauss-Newton direction<a name="line.517"></a> | |
| 521 <FONT color="green">518</FONT> double dxNorm = 0;<a name="line.518"></a> | |
| 522 <FONT color="green">519</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.519"></a> | |
| 523 <FONT color="green">520</FONT> int pj = permutation[j];<a name="line.520"></a> | |
| 524 <FONT color="green">521</FONT> double s = diag[pj] * lmDir[pj];<a name="line.521"></a> | |
| 525 <FONT color="green">522</FONT> work1[pj] = s;<a name="line.522"></a> | |
| 526 <FONT color="green">523</FONT> dxNorm += s * s;<a name="line.523"></a> | |
| 527 <FONT color="green">524</FONT> }<a name="line.524"></a> | |
| 528 <FONT color="green">525</FONT> dxNorm = Math.sqrt(dxNorm);<a name="line.525"></a> | |
| 529 <FONT color="green">526</FONT> double fp = dxNorm - delta;<a name="line.526"></a> | |
| 530 <FONT color="green">527</FONT> if (fp <= 0.1 * delta) {<a name="line.527"></a> | |
| 531 <FONT color="green">528</FONT> lmPar = 0;<a name="line.528"></a> | |
| 532 <FONT color="green">529</FONT> return;<a name="line.529"></a> | |
| 533 <FONT color="green">530</FONT> }<a name="line.530"></a> | |
| 534 <FONT color="green">531</FONT> <a name="line.531"></a> | |
| 535 <FONT color="green">532</FONT> // if the jacobian is not rank deficient, the Newton step provides<a name="line.532"></a> | |
| 536 <FONT color="green">533</FONT> // a lower bound, parl, for the zero of the function,<a name="line.533"></a> | |
| 537 <FONT color="green">534</FONT> // otherwise set this bound to zero<a name="line.534"></a> | |
| 538 <FONT color="green">535</FONT> double sum2;<a name="line.535"></a> | |
| 539 <FONT color="green">536</FONT> double parl = 0;<a name="line.536"></a> | |
| 540 <FONT color="green">537</FONT> if (rank == solvedCols) {<a name="line.537"></a> | |
| 541 <FONT color="green">538</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.538"></a> | |
| 542 <FONT color="green">539</FONT> int pj = permutation[j];<a name="line.539"></a> | |
| 543 <FONT color="green">540</FONT> work1[pj] *= diag[pj] / dxNorm;<a name="line.540"></a> | |
| 544 <FONT color="green">541</FONT> }<a name="line.541"></a> | |
| 545 <FONT color="green">542</FONT> sum2 = 0;<a name="line.542"></a> | |
| 546 <FONT color="green">543</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.543"></a> | |
| 547 <FONT color="green">544</FONT> int pj = permutation[j];<a name="line.544"></a> | |
| 548 <FONT color="green">545</FONT> double sum = 0;<a name="line.545"></a> | |
| 549 <FONT color="green">546</FONT> int index = pj;<a name="line.546"></a> | |
| 550 <FONT color="green">547</FONT> for (int i = 0; i < j; ++i) {<a name="line.547"></a> | |
| 551 <FONT color="green">548</FONT> sum += jacobian[index] * work1[permutation[i]];<a name="line.548"></a> | |
| 552 <FONT color="green">549</FONT> index += cols;<a name="line.549"></a> | |
| 553 <FONT color="green">550</FONT> }<a name="line.550"></a> | |
| 554 <FONT color="green">551</FONT> double s = (work1[pj] - sum) / diagR[pj];<a name="line.551"></a> | |
| 555 <FONT color="green">552</FONT> work1[pj] = s;<a name="line.552"></a> | |
| 556 <FONT color="green">553</FONT> sum2 += s * s;<a name="line.553"></a> | |
| 557 <FONT color="green">554</FONT> }<a name="line.554"></a> | |
| 558 <FONT color="green">555</FONT> parl = fp / (delta * sum2);<a name="line.555"></a> | |
| 559 <FONT color="green">556</FONT> }<a name="line.556"></a> | |
| 560 <FONT color="green">557</FONT> <a name="line.557"></a> | |
| 561 <FONT color="green">558</FONT> // calculate an upper bound, paru, for the zero of the function<a name="line.558"></a> | |
| 562 <FONT color="green">559</FONT> sum2 = 0;<a name="line.559"></a> | |
| 563 <FONT color="green">560</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.560"></a> | |
| 564 <FONT color="green">561</FONT> int pj = permutation[j];<a name="line.561"></a> | |
| 565 <FONT color="green">562</FONT> double sum = 0;<a name="line.562"></a> | |
| 566 <FONT color="green">563</FONT> int index = pj;<a name="line.563"></a> | |
| 567 <FONT color="green">564</FONT> for (int i = 0; i <= j; ++i) {<a name="line.564"></a> | |
| 568 <FONT color="green">565</FONT> sum += jacobian[index] * qy[i];<a name="line.565"></a> | |
| 569 <FONT color="green">566</FONT> index += cols;<a name="line.566"></a> | |
| 570 <FONT color="green">567</FONT> }<a name="line.567"></a> | |
| 571 <FONT color="green">568</FONT> sum /= diag[pj];<a name="line.568"></a> | |
| 572 <FONT color="green">569</FONT> sum2 += sum * sum;<a name="line.569"></a> | |
| 573 <FONT color="green">570</FONT> }<a name="line.570"></a> | |
| 574 <FONT color="green">571</FONT> double gNorm = Math.sqrt(sum2);<a name="line.571"></a> | |
| 575 <FONT color="green">572</FONT> double paru = gNorm / delta;<a name="line.572"></a> | |
| 576 <FONT color="green">573</FONT> if (paru == 0) {<a name="line.573"></a> | |
| 577 <FONT color="green">574</FONT> // 2.2251e-308 is the smallest positive real for IEE754<a name="line.574"></a> | |
| 578 <FONT color="green">575</FONT> paru = 2.2251e-308 / Math.min(delta, 0.1);<a name="line.575"></a> | |
| 579 <FONT color="green">576</FONT> }<a name="line.576"></a> | |
| 580 <FONT color="green">577</FONT> <a name="line.577"></a> | |
| 581 <FONT color="green">578</FONT> // if the input par lies outside of the interval (parl,paru),<a name="line.578"></a> | |
| 582 <FONT color="green">579</FONT> // set par to the closer endpoint<a name="line.579"></a> | |
| 583 <FONT color="green">580</FONT> lmPar = Math.min(paru, Math.max(lmPar, parl));<a name="line.580"></a> | |
| 584 <FONT color="green">581</FONT> if (lmPar == 0) {<a name="line.581"></a> | |
| 585 <FONT color="green">582</FONT> lmPar = gNorm / dxNorm;<a name="line.582"></a> | |
| 586 <FONT color="green">583</FONT> }<a name="line.583"></a> | |
| 587 <FONT color="green">584</FONT> <a name="line.584"></a> | |
| 588 <FONT color="green">585</FONT> for (int countdown = 10; countdown >= 0; --countdown) {<a name="line.585"></a> | |
| 589 <FONT color="green">586</FONT> <a name="line.586"></a> | |
| 590 <FONT color="green">587</FONT> // evaluate the function at the current value of lmPar<a name="line.587"></a> | |
| 591 <FONT color="green">588</FONT> if (lmPar == 0) {<a name="line.588"></a> | |
| 592 <FONT color="green">589</FONT> lmPar = Math.max(2.2251e-308, 0.001 * paru);<a name="line.589"></a> | |
| 593 <FONT color="green">590</FONT> }<a name="line.590"></a> | |
| 594 <FONT color="green">591</FONT> double sPar = Math.sqrt(lmPar);<a name="line.591"></a> | |
| 595 <FONT color="green">592</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.592"></a> | |
| 596 <FONT color="green">593</FONT> int pj = permutation[j];<a name="line.593"></a> | |
| 597 <FONT color="green">594</FONT> work1[pj] = sPar * diag[pj];<a name="line.594"></a> | |
| 598 <FONT color="green">595</FONT> }<a name="line.595"></a> | |
| 599 <FONT color="green">596</FONT> determineLMDirection(qy, work1, work2, work3);<a name="line.596"></a> | |
| 600 <FONT color="green">597</FONT> <a name="line.597"></a> | |
| 601 <FONT color="green">598</FONT> dxNorm = 0;<a name="line.598"></a> | |
| 602 <FONT color="green">599</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.599"></a> | |
| 603 <FONT color="green">600</FONT> int pj = permutation[j];<a name="line.600"></a> | |
| 604 <FONT color="green">601</FONT> double s = diag[pj] * lmDir[pj];<a name="line.601"></a> | |
| 605 <FONT color="green">602</FONT> work3[pj] = s;<a name="line.602"></a> | |
| 606 <FONT color="green">603</FONT> dxNorm += s * s;<a name="line.603"></a> | |
| 607 <FONT color="green">604</FONT> }<a name="line.604"></a> | |
| 608 <FONT color="green">605</FONT> dxNorm = Math.sqrt(dxNorm);<a name="line.605"></a> | |
| 609 <FONT color="green">606</FONT> double previousFP = fp;<a name="line.606"></a> | |
| 610 <FONT color="green">607</FONT> fp = dxNorm - delta;<a name="line.607"></a> | |
| 611 <FONT color="green">608</FONT> <a name="line.608"></a> | |
| 612 <FONT color="green">609</FONT> // if the function is small enough, accept the current value<a name="line.609"></a> | |
| 613 <FONT color="green">610</FONT> // of lmPar, also test for the exceptional cases where parl is zero<a name="line.610"></a> | |
| 614 <FONT color="green">611</FONT> if ((Math.abs(fp) <= 0.1 * delta) ||<a name="line.611"></a> | |
| 615 <FONT color="green">612</FONT> ((parl == 0) && (fp <= previousFP) && (previousFP < 0))) {<a name="line.612"></a> | |
| 616 <FONT color="green">613</FONT> return;<a name="line.613"></a> | |
| 617 <FONT color="green">614</FONT> }<a name="line.614"></a> | |
| 618 <FONT color="green">615</FONT> <a name="line.615"></a> | |
| 619 <FONT color="green">616</FONT> // compute the Newton correction<a name="line.616"></a> | |
| 620 <FONT color="green">617</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.617"></a> | |
| 621 <FONT color="green">618</FONT> int pj = permutation[j];<a name="line.618"></a> | |
| 622 <FONT color="green">619</FONT> work1[pj] = work3[pj] * diag[pj] / dxNorm;<a name="line.619"></a> | |
| 623 <FONT color="green">620</FONT> }<a name="line.620"></a> | |
| 624 <FONT color="green">621</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.621"></a> | |
| 625 <FONT color="green">622</FONT> int pj = permutation[j];<a name="line.622"></a> | |
| 626 <FONT color="green">623</FONT> work1[pj] /= work2[j];<a name="line.623"></a> | |
| 627 <FONT color="green">624</FONT> double tmp = work1[pj];<a name="line.624"></a> | |
| 628 <FONT color="green">625</FONT> for (int i = j + 1; i < solvedCols; ++i) {<a name="line.625"></a> | |
| 629 <FONT color="green">626</FONT> work1[permutation[i]] -= jacobian[i * cols + pj] * tmp;<a name="line.626"></a> | |
| 630 <FONT color="green">627</FONT> }<a name="line.627"></a> | |
| 631 <FONT color="green">628</FONT> }<a name="line.628"></a> | |
| 632 <FONT color="green">629</FONT> sum2 = 0;<a name="line.629"></a> | |
| 633 <FONT color="green">630</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.630"></a> | |
| 634 <FONT color="green">631</FONT> double s = work1[permutation[j]];<a name="line.631"></a> | |
| 635 <FONT color="green">632</FONT> sum2 += s * s;<a name="line.632"></a> | |
| 636 <FONT color="green">633</FONT> }<a name="line.633"></a> | |
| 637 <FONT color="green">634</FONT> double correction = fp / (delta * sum2);<a name="line.634"></a> | |
| 638 <FONT color="green">635</FONT> <a name="line.635"></a> | |
| 639 <FONT color="green">636</FONT> // depending on the sign of the function, update parl or paru.<a name="line.636"></a> | |
| 640 <FONT color="green">637</FONT> if (fp > 0) {<a name="line.637"></a> | |
| 641 <FONT color="green">638</FONT> parl = Math.max(parl, lmPar);<a name="line.638"></a> | |
| 642 <FONT color="green">639</FONT> } else if (fp < 0) {<a name="line.639"></a> | |
| 643 <FONT color="green">640</FONT> paru = Math.min(paru, lmPar);<a name="line.640"></a> | |
| 644 <FONT color="green">641</FONT> }<a name="line.641"></a> | |
| 645 <FONT color="green">642</FONT> <a name="line.642"></a> | |
| 646 <FONT color="green">643</FONT> // compute an improved estimate for lmPar<a name="line.643"></a> | |
| 647 <FONT color="green">644</FONT> lmPar = Math.max(parl, lmPar + correction);<a name="line.644"></a> | |
| 648 <FONT color="green">645</FONT> <a name="line.645"></a> | |
| 649 <FONT color="green">646</FONT> }<a name="line.646"></a> | |
| 650 <FONT color="green">647</FONT> }<a name="line.647"></a> | |
| 651 <FONT color="green">648</FONT> <a name="line.648"></a> | |
| 652 <FONT color="green">649</FONT> /**<a name="line.649"></a> | |
| 653 <FONT color="green">650</FONT> * Solve a*x = b and d*x = 0 in the least squares sense.<a name="line.650"></a> | |
| 654 <FONT color="green">651</FONT> * <p>This implementation is a translation in Java of the MINPACK<a name="line.651"></a> | |
| 655 <FONT color="green">652</FONT> * <a href="http://www.netlib.org/minpack/qrsolv.f">qrsolv</a><a name="line.652"></a> | |
| 656 <FONT color="green">653</FONT> * routine.</p><a name="line.653"></a> | |
| 657 <FONT color="green">654</FONT> * <p>This method sets the lmDir and lmDiag attributes.</p><a name="line.654"></a> | |
| 658 <FONT color="green">655</FONT> * <p>The authors of the original fortran function are:</p><a name="line.655"></a> | |
| 659 <FONT color="green">656</FONT> * <ul><a name="line.656"></a> | |
| 660 <FONT color="green">657</FONT> * <li>Argonne National Laboratory. MINPACK project. March 1980</li><a name="line.657"></a> | |
| 661 <FONT color="green">658</FONT> * <li>Burton S. Garbow</li><a name="line.658"></a> | |
| 662 <FONT color="green">659</FONT> * <li>Kenneth E. Hillstrom</li><a name="line.659"></a> | |
| 663 <FONT color="green">660</FONT> * <li>Jorge J. More</li><a name="line.660"></a> | |
| 664 <FONT color="green">661</FONT> * </ul><a name="line.661"></a> | |
| 665 <FONT color="green">662</FONT> * <p>Luc Maisonobe did the Java translation.</p><a name="line.662"></a> | |
| 666 <FONT color="green">663</FONT> *<a name="line.663"></a> | |
| 667 <FONT color="green">664</FONT> * @param qy array containing qTy<a name="line.664"></a> | |
| 668 <FONT color="green">665</FONT> * @param diag diagonal matrix<a name="line.665"></a> | |
| 669 <FONT color="green">666</FONT> * @param lmDiag diagonal elements associated with lmDir<a name="line.666"></a> | |
| 670 <FONT color="green">667</FONT> * @param work work array<a name="line.667"></a> | |
| 671 <FONT color="green">668</FONT> */<a name="line.668"></a> | |
| 672 <FONT color="green">669</FONT> private void determineLMDirection(double[] qy, double[] diag,<a name="line.669"></a> | |
| 673 <FONT color="green">670</FONT> double[] lmDiag, double[] work) {<a name="line.670"></a> | |
| 674 <FONT color="green">671</FONT> <a name="line.671"></a> | |
| 675 <FONT color="green">672</FONT> // copy R and Qty to preserve input and initialize s<a name="line.672"></a> | |
| 676 <FONT color="green">673</FONT> // in particular, save the diagonal elements of R in lmDir<a name="line.673"></a> | |
| 677 <FONT color="green">674</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.674"></a> | |
| 678 <FONT color="green">675</FONT> int pj = permutation[j];<a name="line.675"></a> | |
| 679 <FONT color="green">676</FONT> for (int i = j + 1; i < solvedCols; ++i) {<a name="line.676"></a> | |
| 680 <FONT color="green">677</FONT> jacobian[i * cols + pj] = jacobian[j * cols + permutation[i]];<a name="line.677"></a> | |
| 681 <FONT color="green">678</FONT> }<a name="line.678"></a> | |
| 682 <FONT color="green">679</FONT> lmDir[j] = diagR[pj];<a name="line.679"></a> | |
| 683 <FONT color="green">680</FONT> work[j] = qy[j];<a name="line.680"></a> | |
| 684 <FONT color="green">681</FONT> }<a name="line.681"></a> | |
| 685 <FONT color="green">682</FONT> <a name="line.682"></a> | |
| 686 <FONT color="green">683</FONT> // eliminate the diagonal matrix d using a Givens rotation<a name="line.683"></a> | |
| 687 <FONT color="green">684</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.684"></a> | |
| 688 <FONT color="green">685</FONT> <a name="line.685"></a> | |
| 689 <FONT color="green">686</FONT> // prepare the row of d to be eliminated, locating the<a name="line.686"></a> | |
| 690 <FONT color="green">687</FONT> // diagonal element using p from the Q.R. factorization<a name="line.687"></a> | |
| 691 <FONT color="green">688</FONT> int pj = permutation[j];<a name="line.688"></a> | |
| 692 <FONT color="green">689</FONT> double dpj = diag[pj];<a name="line.689"></a> | |
| 693 <FONT color="green">690</FONT> if (dpj != 0) {<a name="line.690"></a> | |
| 694 <FONT color="green">691</FONT> Arrays.fill(lmDiag, j + 1, lmDiag.length, 0);<a name="line.691"></a> | |
| 695 <FONT color="green">692</FONT> }<a name="line.692"></a> | |
| 696 <FONT color="green">693</FONT> lmDiag[j] = dpj;<a name="line.693"></a> | |
| 697 <FONT color="green">694</FONT> <a name="line.694"></a> | |
| 698 <FONT color="green">695</FONT> // the transformations to eliminate the row of d<a name="line.695"></a> | |
| 699 <FONT color="green">696</FONT> // modify only a single element of Qty<a name="line.696"></a> | |
| 700 <FONT color="green">697</FONT> // beyond the first n, which is initially zero.<a name="line.697"></a> | |
| 701 <FONT color="green">698</FONT> double qtbpj = 0;<a name="line.698"></a> | |
| 702 <FONT color="green">699</FONT> for (int k = j; k < solvedCols; ++k) {<a name="line.699"></a> | |
| 703 <FONT color="green">700</FONT> int pk = permutation[k];<a name="line.700"></a> | |
| 704 <FONT color="green">701</FONT> <a name="line.701"></a> | |
| 705 <FONT color="green">702</FONT> // determine a Givens rotation which eliminates the<a name="line.702"></a> | |
| 706 <FONT color="green">703</FONT> // appropriate element in the current row of d<a name="line.703"></a> | |
| 707 <FONT color="green">704</FONT> if (lmDiag[k] != 0) {<a name="line.704"></a> | |
| 708 <FONT color="green">705</FONT> <a name="line.705"></a> | |
| 709 <FONT color="green">706</FONT> final double sin;<a name="line.706"></a> | |
| 710 <FONT color="green">707</FONT> final double cos;<a name="line.707"></a> | |
| 711 <FONT color="green">708</FONT> double rkk = jacobian[k * cols + pk];<a name="line.708"></a> | |
| 712 <FONT color="green">709</FONT> if (Math.abs(rkk) < Math.abs(lmDiag[k])) {<a name="line.709"></a> | |
| 713 <FONT color="green">710</FONT> final double cotan = rkk / lmDiag[k];<a name="line.710"></a> | |
| 714 <FONT color="green">711</FONT> sin = 1.0 / Math.sqrt(1.0 + cotan * cotan);<a name="line.711"></a> | |
| 715 <FONT color="green">712</FONT> cos = sin * cotan;<a name="line.712"></a> | |
| 716 <FONT color="green">713</FONT> } else {<a name="line.713"></a> | |
| 717 <FONT color="green">714</FONT> final double tan = lmDiag[k] / rkk;<a name="line.714"></a> | |
| 718 <FONT color="green">715</FONT> cos = 1.0 / Math.sqrt(1.0 + tan * tan);<a name="line.715"></a> | |
| 719 <FONT color="green">716</FONT> sin = cos * tan;<a name="line.716"></a> | |
| 720 <FONT color="green">717</FONT> }<a name="line.717"></a> | |
| 721 <FONT color="green">718</FONT> <a name="line.718"></a> | |
| 722 <FONT color="green">719</FONT> // compute the modified diagonal element of R and<a name="line.719"></a> | |
| 723 <FONT color="green">720</FONT> // the modified element of (Qty,0)<a name="line.720"></a> | |
| 724 <FONT color="green">721</FONT> jacobian[k * cols + pk] = cos * rkk + sin * lmDiag[k];<a name="line.721"></a> | |
| 725 <FONT color="green">722</FONT> final double temp = cos * work[k] + sin * qtbpj;<a name="line.722"></a> | |
| 726 <FONT color="green">723</FONT> qtbpj = -sin * work[k] + cos * qtbpj;<a name="line.723"></a> | |
| 727 <FONT color="green">724</FONT> work[k] = temp;<a name="line.724"></a> | |
| 728 <FONT color="green">725</FONT> <a name="line.725"></a> | |
| 729 <FONT color="green">726</FONT> // accumulate the tranformation in the row of s<a name="line.726"></a> | |
| 730 <FONT color="green">727</FONT> for (int i = k + 1; i < solvedCols; ++i) {<a name="line.727"></a> | |
| 731 <FONT color="green">728</FONT> double rik = jacobian[i * cols + pk];<a name="line.728"></a> | |
| 732 <FONT color="green">729</FONT> final double temp2 = cos * rik + sin * lmDiag[i];<a name="line.729"></a> | |
| 733 <FONT color="green">730</FONT> lmDiag[i] = -sin * rik + cos * lmDiag[i];<a name="line.730"></a> | |
| 734 <FONT color="green">731</FONT> jacobian[i * cols + pk] = temp2;<a name="line.731"></a> | |
| 735 <FONT color="green">732</FONT> }<a name="line.732"></a> | |
| 736 <FONT color="green">733</FONT> <a name="line.733"></a> | |
| 737 <FONT color="green">734</FONT> }<a name="line.734"></a> | |
| 738 <FONT color="green">735</FONT> }<a name="line.735"></a> | |
| 739 <FONT color="green">736</FONT> <a name="line.736"></a> | |
| 740 <FONT color="green">737</FONT> // store the diagonal element of s and restore<a name="line.737"></a> | |
| 741 <FONT color="green">738</FONT> // the corresponding diagonal element of R<a name="line.738"></a> | |
| 742 <FONT color="green">739</FONT> int index = j * cols + permutation[j];<a name="line.739"></a> | |
| 743 <FONT color="green">740</FONT> lmDiag[j] = jacobian[index];<a name="line.740"></a> | |
| 744 <FONT color="green">741</FONT> jacobian[index] = lmDir[j];<a name="line.741"></a> | |
| 745 <FONT color="green">742</FONT> <a name="line.742"></a> | |
| 746 <FONT color="green">743</FONT> }<a name="line.743"></a> | |
| 747 <FONT color="green">744</FONT> <a name="line.744"></a> | |
| 748 <FONT color="green">745</FONT> // solve the triangular system for z, if the system is<a name="line.745"></a> | |
| 749 <FONT color="green">746</FONT> // singular, then obtain a least squares solution<a name="line.746"></a> | |
| 750 <FONT color="green">747</FONT> int nSing = solvedCols;<a name="line.747"></a> | |
| 751 <FONT color="green">748</FONT> for (int j = 0; j < solvedCols; ++j) {<a name="line.748"></a> | |
| 752 <FONT color="green">749</FONT> if ((lmDiag[j] == 0) && (nSing == solvedCols)) {<a name="line.749"></a> | |
| 753 <FONT color="green">750</FONT> nSing = j;<a name="line.750"></a> | |
| 754 <FONT color="green">751</FONT> }<a name="line.751"></a> | |
| 755 <FONT color="green">752</FONT> if (nSing < solvedCols) {<a name="line.752"></a> | |
| 756 <FONT color="green">753</FONT> work[j] = 0;<a name="line.753"></a> | |
| 757 <FONT color="green">754</FONT> }<a name="line.754"></a> | |
| 758 <FONT color="green">755</FONT> }<a name="line.755"></a> | |
| 759 <FONT color="green">756</FONT> if (nSing > 0) {<a name="line.756"></a> | |
| 760 <FONT color="green">757</FONT> for (int j = nSing - 1; j >= 0; --j) {<a name="line.757"></a> | |
| 761 <FONT color="green">758</FONT> int pj = permutation[j];<a name="line.758"></a> | |
| 762 <FONT color="green">759</FONT> double sum = 0;<a name="line.759"></a> | |
| 763 <FONT color="green">760</FONT> for (int i = j + 1; i < nSing; ++i) {<a name="line.760"></a> | |
| 764 <FONT color="green">761</FONT> sum += jacobian[i * cols + pj] * work[i];<a name="line.761"></a> | |
| 765 <FONT color="green">762</FONT> }<a name="line.762"></a> | |
| 766 <FONT color="green">763</FONT> work[j] = (work[j] - sum) / lmDiag[j];<a name="line.763"></a> | |
| 767 <FONT color="green">764</FONT> }<a name="line.764"></a> | |
| 768 <FONT color="green">765</FONT> }<a name="line.765"></a> | |
| 769 <FONT color="green">766</FONT> <a name="line.766"></a> | |
| 770 <FONT color="green">767</FONT> // permute the components of z back to components of lmDir<a name="line.767"></a> | |
| 771 <FONT color="green">768</FONT> for (int j = 0; j < lmDir.length; ++j) {<a name="line.768"></a> | |
| 772 <FONT color="green">769</FONT> lmDir[permutation[j]] = work[j];<a name="line.769"></a> | |
| 773 <FONT color="green">770</FONT> }<a name="line.770"></a> | |
| 774 <FONT color="green">771</FONT> <a name="line.771"></a> | |
| 775 <FONT color="green">772</FONT> }<a name="line.772"></a> | |
| 776 <FONT color="green">773</FONT> <a name="line.773"></a> | |
| 777 <FONT color="green">774</FONT> /**<a name="line.774"></a> | |
| 778 <FONT color="green">775</FONT> * Decompose a matrix A as A.P = Q.R using Householder transforms.<a name="line.775"></a> | |
| 779 <FONT color="green">776</FONT> * <p>As suggested in the P. Lascaux and R. Theodor book<a name="line.776"></a> | |
| 780 <FONT color="green">777</FONT> * <i>Analyse num&eacute;rique matricielle appliqu&eacute;e &agrave;<a name="line.777"></a> | |
| 781 <FONT color="green">778</FONT> * l'art de l'ing&eacute;nieur</i> (Masson, 1986), instead of representing<a name="line.778"></a> | |
| 782 <FONT color="green">779</FONT> * the Householder transforms with u<sub>k</sub> unit vectors such that:<a name="line.779"></a> | |
| 783 <FONT color="green">780</FONT> * <pre><a name="line.780"></a> | |
| 784 <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> | |
| 785 <FONT color="green">782</FONT> * </pre><a name="line.782"></a> | |
| 786 <FONT color="green">783</FONT> * we use <sub>k</sub> non-unit vectors such that:<a name="line.783"></a> | |
| 787 <FONT color="green">784</FONT> * <pre><a name="line.784"></a> | |
| 788 <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> | |
| 789 <FONT color="green">786</FONT> * </pre><a name="line.786"></a> | |
| 790 <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> | |
| 791 <FONT color="green">788</FONT> * The beta<sub>k</sub> coefficients are provided upon exit as recomputing<a name="line.788"></a> | |
| 792 <FONT color="green">789</FONT> * them from the v<sub>k</sub> vectors would be costly.</p><a name="line.789"></a> | |
| 793 <FONT color="green">790</FONT> * <p>This decomposition handles rank deficient cases since the tranformations<a name="line.790"></a> | |
| 794 <FONT color="green">791</FONT> * are performed in non-increasing columns norms order thanks to columns<a name="line.791"></a> | |
| 795 <FONT color="green">792</FONT> * pivoting. The diagonal elements of the R matrix are therefore also in<a name="line.792"></a> | |
| 796 <FONT color="green">793</FONT> * non-increasing absolute values order.</p><a name="line.793"></a> | |
| 797 <FONT color="green">794</FONT> * @exception EstimationException if the decomposition cannot be performed<a name="line.794"></a> | |
| 798 <FONT color="green">795</FONT> */<a name="line.795"></a> | |
| 799 <FONT color="green">796</FONT> private void qrDecomposition() throws EstimationException {<a name="line.796"></a> | |
| 800 <FONT color="green">797</FONT> <a name="line.797"></a> | |
| 801 <FONT color="green">798</FONT> // initializations<a name="line.798"></a> | |
| 802 <FONT color="green">799</FONT> for (int k = 0; k < cols; ++k) {<a name="line.799"></a> | |
| 803 <FONT color="green">800</FONT> permutation[k] = k;<a name="line.800"></a> | |
| 804 <FONT color="green">801</FONT> double norm2 = 0;<a name="line.801"></a> | |
| 805 <FONT color="green">802</FONT> for (int index = k; index < jacobian.length; index += cols) {<a name="line.802"></a> | |
| 806 <FONT color="green">803</FONT> double akk = jacobian[index];<a name="line.803"></a> | |
| 807 <FONT color="green">804</FONT> norm2 += akk * akk;<a name="line.804"></a> | |
| 808 <FONT color="green">805</FONT> }<a name="line.805"></a> | |
| 809 <FONT color="green">806</FONT> jacNorm[k] = Math.sqrt(norm2);<a name="line.806"></a> | |
| 810 <FONT color="green">807</FONT> }<a name="line.807"></a> | |
| 811 <FONT color="green">808</FONT> <a name="line.808"></a> | |
| 812 <FONT color="green">809</FONT> // transform the matrix column after column<a name="line.809"></a> | |
| 813 <FONT color="green">810</FONT> for (int k = 0; k < cols; ++k) {<a name="line.810"></a> | |
| 814 <FONT color="green">811</FONT> <a name="line.811"></a> | |
| 815 <FONT color="green">812</FONT> // select the column with the greatest norm on active components<a name="line.812"></a> | |
| 816 <FONT color="green">813</FONT> int nextColumn = -1;<a name="line.813"></a> | |
| 817 <FONT color="green">814</FONT> double ak2 = Double.NEGATIVE_INFINITY;<a name="line.814"></a> | |
| 818 <FONT color="green">815</FONT> for (int i = k; i < cols; ++i) {<a name="line.815"></a> | |
| 819 <FONT color="green">816</FONT> double norm2 = 0;<a name="line.816"></a> | |
| 820 <FONT color="green">817</FONT> int iDiag = k * cols + permutation[i];<a name="line.817"></a> | |
| 821 <FONT color="green">818</FONT> for (int index = iDiag; index < jacobian.length; index += cols) {<a name="line.818"></a> | |
| 822 <FONT color="green">819</FONT> double aki = jacobian[index];<a name="line.819"></a> | |
| 823 <FONT color="green">820</FONT> norm2 += aki * aki;<a name="line.820"></a> | |
| 824 <FONT color="green">821</FONT> }<a name="line.821"></a> | |
| 825 <FONT color="green">822</FONT> if (Double.isInfinite(norm2) || Double.isNaN(norm2)) {<a name="line.822"></a> | |
| 826 <FONT color="green">823</FONT> throw new EstimationException(<a name="line.823"></a> | |
| 827 <FONT color="green">824</FONT> "unable to perform Q.R decomposition on the {0}x{1} jacobian matrix",<a name="line.824"></a> | |
| 828 <FONT color="green">825</FONT> rows, cols);<a name="line.825"></a> | |
| 829 <FONT color="green">826</FONT> }<a name="line.826"></a> | |
| 830 <FONT color="green">827</FONT> if (norm2 > ak2) {<a name="line.827"></a> | |
| 831 <FONT color="green">828</FONT> nextColumn = i;<a name="line.828"></a> | |
| 832 <FONT color="green">829</FONT> ak2 = norm2;<a name="line.829"></a> | |
| 833 <FONT color="green">830</FONT> }<a name="line.830"></a> | |
| 834 <FONT color="green">831</FONT> }<a name="line.831"></a> | |
| 835 <FONT color="green">832</FONT> if (ak2 == 0) {<a name="line.832"></a> | |
| 836 <FONT color="green">833</FONT> rank = k;<a name="line.833"></a> | |
| 837 <FONT color="green">834</FONT> return;<a name="line.834"></a> | |
| 838 <FONT color="green">835</FONT> }<a name="line.835"></a> | |
| 839 <FONT color="green">836</FONT> int pk = permutation[nextColumn];<a name="line.836"></a> | |
| 840 <FONT color="green">837</FONT> permutation[nextColumn] = permutation[k];<a name="line.837"></a> | |
| 841 <FONT color="green">838</FONT> permutation[k] = pk;<a name="line.838"></a> | |
| 842 <FONT color="green">839</FONT> <a name="line.839"></a> | |
| 843 <FONT color="green">840</FONT> // choose alpha such that Hk.u = alpha ek<a name="line.840"></a> | |
| 844 <FONT color="green">841</FONT> int kDiag = k * cols + pk;<a name="line.841"></a> | |
| 845 <FONT color="green">842</FONT> double akk = jacobian[kDiag];<a name="line.842"></a> | |
| 846 <FONT color="green">843</FONT> double alpha = (akk > 0) ? -Math.sqrt(ak2) : Math.sqrt(ak2);<a name="line.843"></a> | |
| 847 <FONT color="green">844</FONT> double betak = 1.0 / (ak2 - akk * alpha);<a name="line.844"></a> | |
| 848 <FONT color="green">845</FONT> beta[pk] = betak;<a name="line.845"></a> | |
| 849 <FONT color="green">846</FONT> <a name="line.846"></a> | |
| 850 <FONT color="green">847</FONT> // transform the current column<a name="line.847"></a> | |
| 851 <FONT color="green">848</FONT> diagR[pk] = alpha;<a name="line.848"></a> | |
| 852 <FONT color="green">849</FONT> jacobian[kDiag] -= alpha;<a name="line.849"></a> | |
| 853 <FONT color="green">850</FONT> <a name="line.850"></a> | |
| 854 <FONT color="green">851</FONT> // transform the remaining columns<a name="line.851"></a> | |
| 855 <FONT color="green">852</FONT> for (int dk = cols - 1 - k; dk > 0; --dk) {<a name="line.852"></a> | |
| 856 <FONT color="green">853</FONT> int dkp = permutation[k + dk] - pk;<a name="line.853"></a> | |
| 857 <FONT color="green">854</FONT> double gamma = 0;<a name="line.854"></a> | |
| 858 <FONT color="green">855</FONT> for (int index = kDiag; index < jacobian.length; index += cols) {<a name="line.855"></a> | |
| 859 <FONT color="green">856</FONT> gamma += jacobian[index] * jacobian[index + dkp];<a name="line.856"></a> | |
| 860 <FONT color="green">857</FONT> }<a name="line.857"></a> | |
| 861 <FONT color="green">858</FONT> gamma *= betak;<a name="line.858"></a> | |
| 862 <FONT color="green">859</FONT> for (int index = kDiag; index < jacobian.length; index += cols) {<a name="line.859"></a> | |
| 863 <FONT color="green">860</FONT> jacobian[index + dkp] -= gamma * jacobian[index];<a name="line.860"></a> | |
| 864 <FONT color="green">861</FONT> }<a name="line.861"></a> | |
| 865 <FONT color="green">862</FONT> }<a name="line.862"></a> | |
| 866 <FONT color="green">863</FONT> <a name="line.863"></a> | |
| 867 <FONT color="green">864</FONT> }<a name="line.864"></a> | |
| 868 <FONT color="green">865</FONT> <a name="line.865"></a> | |
| 869 <FONT color="green">866</FONT> rank = solvedCols;<a name="line.866"></a> | |
| 870 <FONT color="green">867</FONT> <a name="line.867"></a> | |
| 871 <FONT color="green">868</FONT> }<a name="line.868"></a> | |
| 872 <FONT color="green">869</FONT> <a name="line.869"></a> | |
| 873 <FONT color="green">870</FONT> /**<a name="line.870"></a> | |
| 874 <FONT color="green">871</FONT> * Compute the product Qt.y for some Q.R. decomposition.<a name="line.871"></a> | |
| 875 <FONT color="green">872</FONT> *<a name="line.872"></a> | |
| 876 <FONT color="green">873</FONT> * @param y vector to multiply (will be overwritten with the result)<a name="line.873"></a> | |
| 877 <FONT color="green">874</FONT> */<a name="line.874"></a> | |
| 878 <FONT color="green">875</FONT> private void qTy(double[] y) {<a name="line.875"></a> | |
| 879 <FONT color="green">876</FONT> for (int k = 0; k < cols; ++k) {<a name="line.876"></a> | |
| 880 <FONT color="green">877</FONT> int pk = permutation[k];<a name="line.877"></a> | |
| 881 <FONT color="green">878</FONT> int kDiag = k * cols + pk;<a name="line.878"></a> | |
| 882 <FONT color="green">879</FONT> double gamma = 0;<a name="line.879"></a> | |
| 883 <FONT color="green">880</FONT> int index = kDiag;<a name="line.880"></a> | |
| 884 <FONT color="green">881</FONT> for (int i = k; i < rows; ++i) {<a name="line.881"></a> | |
| 885 <FONT color="green">882</FONT> gamma += jacobian[index] * y[i];<a name="line.882"></a> | |
| 886 <FONT color="green">883</FONT> index += cols;<a name="line.883"></a> | |
| 887 <FONT color="green">884</FONT> }<a name="line.884"></a> | |
| 888 <FONT color="green">885</FONT> gamma *= beta[pk];<a name="line.885"></a> | |
| 889 <FONT color="green">886</FONT> index = kDiag;<a name="line.886"></a> | |
| 890 <FONT color="green">887</FONT> for (int i = k; i < rows; ++i) {<a name="line.887"></a> | |
| 891 <FONT color="green">888</FONT> y[i] -= gamma * jacobian[index];<a name="line.888"></a> | |
| 892 <FONT color="green">889</FONT> index += cols;<a name="line.889"></a> | |
| 893 <FONT color="green">890</FONT> }<a name="line.890"></a> | |
| 894 <FONT color="green">891</FONT> }<a name="line.891"></a> | |
| 895 <FONT color="green">892</FONT> }<a name="line.892"></a> | |
| 896 <FONT color="green">893</FONT> <a name="line.893"></a> | |
| 897 <FONT color="green">894</FONT> }<a name="line.894"></a> | |
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| 958 </PRE> | |
| 959 </BODY> | |
| 960 </HTML> |