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| author | dwinter |
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| date | Tue, 04 Jan 2011 10:02:07 +0100 |
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<HTML> <BODY BGCOLOR="white"> <PRE> <FONT color="green">001</FONT> /*<a name="line.1"></a> <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a> <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a> <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a> <FONT color="green">005</FONT> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a> <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a> <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a> <FONT color="green">008</FONT> *<a name="line.8"></a> <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a> <FONT color="green">010</FONT> *<a name="line.10"></a> <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a> <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a> <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a> <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a> <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a> <FONT color="green">016</FONT> */<a name="line.16"></a> <FONT color="green">017</FONT> <a name="line.17"></a> <FONT color="green">018</FONT> package org.apache.commons.math.optimization.general;<a name="line.18"></a> <FONT color="green">019</FONT> <a name="line.19"></a> <FONT color="green">020</FONT> import org.apache.commons.math.FunctionEvaluationException;<a name="line.20"></a> <FONT color="green">021</FONT> import org.apache.commons.math.linear.BlockRealMatrix;<a name="line.21"></a> <FONT color="green">022</FONT> import org.apache.commons.math.linear.DecompositionSolver;<a name="line.22"></a> <FONT color="green">023</FONT> import org.apache.commons.math.linear.InvalidMatrixException;<a name="line.23"></a> <FONT color="green">024</FONT> import org.apache.commons.math.linear.LUDecompositionImpl;<a name="line.24"></a> <FONT color="green">025</FONT> import org.apache.commons.math.linear.QRDecompositionImpl;<a name="line.25"></a> <FONT color="green">026</FONT> import org.apache.commons.math.linear.RealMatrix;<a name="line.26"></a> <FONT color="green">027</FONT> import org.apache.commons.math.optimization.OptimizationException;<a name="line.27"></a> <FONT color="green">028</FONT> import org.apache.commons.math.optimization.VectorialPointValuePair;<a name="line.28"></a> <FONT color="green">029</FONT> <a name="line.29"></a> <FONT color="green">030</FONT> /**<a name="line.30"></a> <FONT color="green">031</FONT> * Gauss-Newton least-squares solver.<a name="line.31"></a> <FONT color="green">032</FONT> * <p><a name="line.32"></a> <FONT color="green">033</FONT> * This class solve a least-square problem by solving the normal equations<a name="line.33"></a> <FONT color="green">034</FONT> * of the linearized problem at each iteration. Either LU decomposition or<a name="line.34"></a> <FONT color="green">035</FONT> * QR decomposition can be used to solve the normal equations. LU decomposition<a name="line.35"></a> <FONT color="green">036</FONT> * is faster but QR decomposition is more robust for difficult problems.<a name="line.36"></a> <FONT color="green">037</FONT> * </p><a name="line.37"></a> <FONT color="green">038</FONT> *<a name="line.38"></a> <FONT color="green">039</FONT> * @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $<a name="line.39"></a> <FONT color="green">040</FONT> * @since 2.0<a name="line.40"></a> <FONT color="green">041</FONT> *<a name="line.41"></a> <FONT color="green">042</FONT> */<a name="line.42"></a> <FONT color="green">043</FONT> <a name="line.43"></a> <FONT color="green">044</FONT> public class GaussNewtonOptimizer extends AbstractLeastSquaresOptimizer {<a name="line.44"></a> <FONT color="green">045</FONT> <a name="line.45"></a> <FONT color="green">046</FONT> /** Indicator for using LU decomposition. */<a name="line.46"></a> <FONT color="green">047</FONT> private final boolean useLU;<a name="line.47"></a> <FONT color="green">048</FONT> <a name="line.48"></a> <FONT color="green">049</FONT> /** Simple constructor with default settings.<a name="line.49"></a> <FONT color="green">050</FONT> * <p>The convergence check is set to a {@link<a name="line.50"></a> <FONT color="green">051</FONT> * org.apache.commons.math.optimization.SimpleVectorialValueChecker}<a name="line.51"></a> <FONT color="green">052</FONT> * and the maximal number of evaluation is set to<a name="line.52"></a> <FONT color="green">053</FONT> * {@link AbstractLeastSquaresOptimizer#DEFAULT_MAX_ITERATIONS}.<a name="line.53"></a> <FONT color="green">054</FONT> * @param useLU if true, the normal equations will be solved using LU<a name="line.54"></a> <FONT color="green">055</FONT> * decomposition, otherwise they will be solved using QR decomposition<a name="line.55"></a> <FONT color="green">056</FONT> */<a name="line.56"></a> <FONT color="green">057</FONT> public GaussNewtonOptimizer(final boolean useLU) {<a name="line.57"></a> <FONT color="green">058</FONT> this.useLU = useLU;<a name="line.58"></a> <FONT color="green">059</FONT> }<a name="line.59"></a> <FONT color="green">060</FONT> <a name="line.60"></a> <FONT color="green">061</FONT> /** {@inheritDoc} */<a name="line.61"></a> <FONT color="green">062</FONT> @Override<a name="line.62"></a> <FONT color="green">063</FONT> public VectorialPointValuePair doOptimize()<a name="line.63"></a> <FONT color="green">064</FONT> throws FunctionEvaluationException, OptimizationException, IllegalArgumentException {<a name="line.64"></a> <FONT color="green">065</FONT> <a name="line.65"></a> <FONT color="green">066</FONT> // iterate until convergence is reached<a name="line.66"></a> <FONT color="green">067</FONT> VectorialPointValuePair current = null;<a name="line.67"></a> <FONT color="green">068</FONT> for (boolean converged = false; !converged;) {<a name="line.68"></a> <FONT color="green">069</FONT> <a name="line.69"></a> <FONT color="green">070</FONT> incrementIterationsCounter();<a name="line.70"></a> <FONT color="green">071</FONT> <a name="line.71"></a> <FONT color="green">072</FONT> // evaluate the objective function and its jacobian<a name="line.72"></a> <FONT color="green">073</FONT> VectorialPointValuePair previous = current;<a name="line.73"></a> <FONT color="green">074</FONT> updateResidualsAndCost();<a name="line.74"></a> <FONT color="green">075</FONT> updateJacobian();<a name="line.75"></a> <FONT color="green">076</FONT> current = new VectorialPointValuePair(point, objective);<a name="line.76"></a> <FONT color="green">077</FONT> <a name="line.77"></a> <FONT color="green">078</FONT> // build the linear problem<a name="line.78"></a> <FONT color="green">079</FONT> final double[] b = new double[cols];<a name="line.79"></a> <FONT color="green">080</FONT> final double[][] a = new double[cols][cols];<a name="line.80"></a> <FONT color="green">081</FONT> for (int i = 0; i < rows; ++i) {<a name="line.81"></a> <FONT color="green">082</FONT> <a name="line.82"></a> <FONT color="green">083</FONT> final double[] grad = jacobian[i];<a name="line.83"></a> <FONT color="green">084</FONT> final double weight = residualsWeights[i];<a name="line.84"></a> <FONT color="green">085</FONT> final double residual = objective[i] - targetValues[i];<a name="line.85"></a> <FONT color="green">086</FONT> <a name="line.86"></a> <FONT color="green">087</FONT> // compute the normal equation<a name="line.87"></a> <FONT color="green">088</FONT> final double wr = weight * residual;<a name="line.88"></a> <FONT color="green">089</FONT> for (int j = 0; j < cols; ++j) {<a name="line.89"></a> <FONT color="green">090</FONT> b[j] += wr * grad[j];<a name="line.90"></a> <FONT color="green">091</FONT> }<a name="line.91"></a> <FONT color="green">092</FONT> <a name="line.92"></a> <FONT color="green">093</FONT> // build the contribution matrix for measurement i<a name="line.93"></a> <FONT color="green">094</FONT> for (int k = 0; k < cols; ++k) {<a name="line.94"></a> <FONT color="green">095</FONT> double[] ak = a[k];<a name="line.95"></a> <FONT color="green">096</FONT> double wgk = weight * grad[k];<a name="line.96"></a> <FONT color="green">097</FONT> for (int l = 0; l < cols; ++l) {<a name="line.97"></a> <FONT color="green">098</FONT> ak[l] += wgk * grad[l];<a name="line.98"></a> <FONT color="green">099</FONT> }<a name="line.99"></a> <FONT color="green">100</FONT> }<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> <a name="line.103"></a> <FONT color="green">104</FONT> try {<a name="line.104"></a> <FONT color="green">105</FONT> <a name="line.105"></a> <FONT color="green">106</FONT> // solve the linearized least squares problem<a name="line.106"></a> <FONT color="green">107</FONT> RealMatrix mA = new BlockRealMatrix(a);<a name="line.107"></a> <FONT color="green">108</FONT> DecompositionSolver solver = useLU ?<a name="line.108"></a> <FONT color="green">109</FONT> new LUDecompositionImpl(mA).getSolver() :<a name="line.109"></a> <FONT color="green">110</FONT> new QRDecompositionImpl(mA).getSolver();<a name="line.110"></a> <FONT color="green">111</FONT> final double[] dX = solver.solve(b);<a name="line.111"></a> <FONT color="green">112</FONT> <a name="line.112"></a> <FONT color="green">113</FONT> // update the estimated parameters<a name="line.113"></a> <FONT color="green">114</FONT> for (int i = 0; i < cols; ++i) {<a name="line.114"></a> <FONT color="green">115</FONT> point[i] += dX[i];<a name="line.115"></a> <FONT color="green">116</FONT> }<a name="line.116"></a> <FONT color="green">117</FONT> <a name="line.117"></a> <FONT color="green">118</FONT> } catch(InvalidMatrixException e) {<a name="line.118"></a> <FONT color="green">119</FONT> throw new OptimizationException("unable to solve: singular problem");<a name="line.119"></a> <FONT color="green">120</FONT> }<a name="line.120"></a> <FONT color="green">121</FONT> <a name="line.121"></a> <FONT color="green">122</FONT> // check convergence<a name="line.122"></a> <FONT color="green">123</FONT> if (previous != null) {<a name="line.123"></a> <FONT color="green">124</FONT> converged = checker.converged(getIterations(), previous, current);<a name="line.124"></a> <FONT color="green">125</FONT> }<a name="line.125"></a> <FONT color="green">126</FONT> <a name="line.126"></a> <FONT color="green">127</FONT> }<a name="line.127"></a> <FONT color="green">128</FONT> <a name="line.128"></a> <FONT color="green">129</FONT> // we have converged<a name="line.129"></a> <FONT color="green">130</FONT> return current;<a name="line.130"></a> <FONT color="green">131</FONT> <a name="line.131"></a> <FONT color="green">132</FONT> }<a name="line.132"></a> <FONT color="green">133</FONT> <a name="line.133"></a> <FONT color="green">134</FONT> }<a name="line.134"></a> </PRE> </BODY> </HTML>