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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;<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.MathRuntimeException;<a name="line.21"></a> <FONT color="green">022</FONT> import org.apache.commons.math.analysis.MultivariateRealFunction;<a name="line.22"></a> <FONT color="green">023</FONT> import org.apache.commons.math.analysis.MultivariateVectorialFunction;<a name="line.23"></a> <FONT color="green">024</FONT> import org.apache.commons.math.linear.RealMatrix;<a name="line.24"></a> <FONT color="green">025</FONT> <a name="line.25"></a> <FONT color="green">026</FONT> /** This class converts {@link MultivariateVectorialFunction vectorial<a name="line.26"></a> <FONT color="green">027</FONT> * objective functions} to {@link MultivariateRealFunction scalar objective functions}<a name="line.27"></a> <FONT color="green">028</FONT> * when the goal is to minimize them.<a name="line.28"></a> <FONT color="green">029</FONT> * <p><a name="line.29"></a> <FONT color="green">030</FONT> * This class is mostly used when the vectorial objective function represents<a name="line.30"></a> <FONT color="green">031</FONT> * a theoretical result computed from a point set applied to a model and<a name="line.31"></a> <FONT color="green">032</FONT> * the models point must be adjusted to fit the theoretical result to some<a name="line.32"></a> <FONT color="green">033</FONT> * reference observations. The observations may be obtained for example from<a name="line.33"></a> <FONT color="green">034</FONT> * physical measurements whether the model is built from theoretical<a name="line.34"></a> <FONT color="green">035</FONT> * considerations.<a name="line.35"></a> <FONT color="green">036</FONT> * </p><a name="line.36"></a> <FONT color="green">037</FONT> * <p><a name="line.37"></a> <FONT color="green">038</FONT> * This class computes a possibly weighted squared sum of the residuals, which is<a name="line.38"></a> <FONT color="green">039</FONT> * a scalar value. The residuals are the difference between the theoretical model<a name="line.39"></a> <FONT color="green">040</FONT> * (i.e. the output of the vectorial objective function) and the observations. The<a name="line.40"></a> <FONT color="green">041</FONT> * class implements the {@link MultivariateRealFunction} interface and can therefore be<a name="line.41"></a> <FONT color="green">042</FONT> * minimized by any optimizer supporting scalar objectives functions.This is one way<a name="line.42"></a> <FONT color="green">043</FONT> * to perform a least square estimation. There are other ways to do this without using<a name="line.43"></a> <FONT color="green">044</FONT> * this converter, as some optimization algorithms directly support vectorial objective<a name="line.44"></a> <FONT color="green">045</FONT> * functions.<a name="line.45"></a> <FONT color="green">046</FONT> * </p><a name="line.46"></a> <FONT color="green">047</FONT> * <p><a name="line.47"></a> <FONT color="green">048</FONT> * This class support combination of residuals with or without weights and correlations.<a name="line.48"></a> <FONT color="green">049</FONT> * </p><a name="line.49"></a> <FONT color="green">050</FONT> *<a name="line.50"></a> <FONT color="green">051</FONT> * @see MultivariateRealFunction<a name="line.51"></a> <FONT color="green">052</FONT> * @see MultivariateVectorialFunction<a name="line.52"></a> <FONT color="green">053</FONT> * @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $<a name="line.53"></a> <FONT color="green">054</FONT> * @since 2.0<a name="line.54"></a> <FONT color="green">055</FONT> */<a name="line.55"></a> <FONT color="green">056</FONT> <a name="line.56"></a> <FONT color="green">057</FONT> public class LeastSquaresConverter implements MultivariateRealFunction {<a name="line.57"></a> <FONT color="green">058</FONT> <a name="line.58"></a> <FONT color="green">059</FONT> /** Underlying vectorial function. */<a name="line.59"></a> <FONT color="green">060</FONT> private final MultivariateVectorialFunction function;<a name="line.60"></a> <FONT color="green">061</FONT> <a name="line.61"></a> <FONT color="green">062</FONT> /** Observations to be compared to objective function to compute residuals. */<a name="line.62"></a> <FONT color="green">063</FONT> private final double[] observations;<a name="line.63"></a> <FONT color="green">064</FONT> <a name="line.64"></a> <FONT color="green">065</FONT> /** Optional weights for the residuals. */<a name="line.65"></a> <FONT color="green">066</FONT> private final double[] weights;<a name="line.66"></a> <FONT color="green">067</FONT> <a name="line.67"></a> <FONT color="green">068</FONT> /** Optional scaling matrix (weight and correlations) for the residuals. */<a name="line.68"></a> <FONT color="green">069</FONT> private final RealMatrix scale;<a name="line.69"></a> <FONT color="green">070</FONT> <a name="line.70"></a> <FONT color="green">071</FONT> /** Build a simple converter for uncorrelated residuals with the same weight.<a name="line.71"></a> <FONT color="green">072</FONT> * @param function vectorial residuals function to wrap<a name="line.72"></a> <FONT color="green">073</FONT> * @param observations observations to be compared to objective function to compute residuals<a name="line.73"></a> <FONT color="green">074</FONT> */<a name="line.74"></a> <FONT color="green">075</FONT> public LeastSquaresConverter(final MultivariateVectorialFunction function,<a name="line.75"></a> <FONT color="green">076</FONT> final double[] observations) {<a name="line.76"></a> <FONT color="green">077</FONT> this.function = function;<a name="line.77"></a> <FONT color="green">078</FONT> this.observations = observations.clone();<a name="line.78"></a> <FONT color="green">079</FONT> this.weights = null;<a name="line.79"></a> <FONT color="green">080</FONT> this.scale = null;<a name="line.80"></a> <FONT color="green">081</FONT> }<a name="line.81"></a> <FONT color="green">082</FONT> <a name="line.82"></a> <FONT color="green">083</FONT> /** Build a simple converter for uncorrelated residuals with the specific weights.<a name="line.83"></a> <FONT color="green">084</FONT> * <p><a name="line.84"></a> <FONT color="green">085</FONT> * The scalar objective function value is computed as:<a name="line.85"></a> <FONT color="green">086</FONT> * <pre><a name="line.86"></a> <FONT color="green">087</FONT> * objective = &sum;weight<sub>i</sub>(observation<sub>i</sub>-objective<sub>i</sub>)<sup>2</sup><a name="line.87"></a> <FONT color="green">088</FONT> * </pre><a name="line.88"></a> <FONT color="green">089</FONT> * </p><a name="line.89"></a> <FONT color="green">090</FONT> * <p><a name="line.90"></a> <FONT color="green">091</FONT> * Weights can be used for example to combine residuals with different standard<a name="line.91"></a> <FONT color="green">092</FONT> * deviations. As an example, consider a residuals array in which even elements<a name="line.92"></a> <FONT color="green">093</FONT> * are angular measurements in degrees with a 0.01&deg; standard deviation and<a name="line.93"></a> <FONT color="green">094</FONT> * odd elements are distance measurements in meters with a 15m standard deviation.<a name="line.94"></a> <FONT color="green">095</FONT> * In this case, the weights array should be initialized with value<a name="line.95"></a> <FONT color="green">096</FONT> * 1.0/(0.01<sup>2</sup>) in the even elements and 1.0/(15.0<sup>2</sup>) in the<a name="line.96"></a> <FONT color="green">097</FONT> * odd elements (i.e. reciprocals of variances).<a name="line.97"></a> <FONT color="green">098</FONT> * </p><a name="line.98"></a> <FONT color="green">099</FONT> * <p><a name="line.99"></a> <FONT color="green">100</FONT> * The array computed by the objective function, the observations array and the<a name="line.100"></a> <FONT color="green">101</FONT> * weights array must have consistent sizes or a {@link FunctionEvaluationException} will be<a name="line.101"></a> <FONT color="green">102</FONT> * triggered while computing the scalar objective.<a name="line.102"></a> <FONT color="green">103</FONT> * </p><a name="line.103"></a> <FONT color="green">104</FONT> * @param function vectorial residuals function to wrap<a name="line.104"></a> <FONT color="green">105</FONT> * @param observations observations to be compared to objective function to compute residuals<a name="line.105"></a> <FONT color="green">106</FONT> * @param weights weights to apply to the residuals<a name="line.106"></a> <FONT color="green">107</FONT> * @exception IllegalArgumentException if the observations vector and the weights<a name="line.107"></a> <FONT color="green">108</FONT> * vector dimensions don't match (objective function dimension is checked only when<a name="line.108"></a> <FONT color="green">109</FONT> * the {@link #value(double[])} method is called)<a name="line.109"></a> <FONT color="green">110</FONT> */<a name="line.110"></a> <FONT color="green">111</FONT> public LeastSquaresConverter(final MultivariateVectorialFunction function,<a name="line.111"></a> <FONT color="green">112</FONT> final double[] observations, final double[] weights)<a name="line.112"></a> <FONT color="green">113</FONT> throws IllegalArgumentException {<a name="line.113"></a> <FONT color="green">114</FONT> if (observations.length != weights.length) {<a name="line.114"></a> <FONT color="green">115</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.115"></a> <FONT color="green">116</FONT> "dimension mismatch {0} != {1}",<a name="line.116"></a> <FONT color="green">117</FONT> observations.length, weights.length);<a name="line.117"></a> <FONT color="green">118</FONT> }<a name="line.118"></a> <FONT color="green">119</FONT> this.function = function;<a name="line.119"></a> <FONT color="green">120</FONT> this.observations = observations.clone();<a name="line.120"></a> <FONT color="green">121</FONT> this.weights = weights.clone();<a name="line.121"></a> <FONT color="green">122</FONT> this.scale = null;<a name="line.122"></a> <FONT color="green">123</FONT> }<a name="line.123"></a> <FONT color="green">124</FONT> <a name="line.124"></a> <FONT color="green">125</FONT> /** Build a simple converter for correlated residuals with the specific weights.<a name="line.125"></a> <FONT color="green">126</FONT> * <p><a name="line.126"></a> <FONT color="green">127</FONT> * The scalar objective function value is computed as:<a name="line.127"></a> <FONT color="green">128</FONT> * <pre><a name="line.128"></a> <FONT color="green">129</FONT> * objective = y<sup>T</sup>y with y = scale&times;(observation-objective)<a name="line.129"></a> <FONT color="green">130</FONT> * </pre><a name="line.130"></a> <FONT color="green">131</FONT> * </p><a name="line.131"></a> <FONT color="green">132</FONT> * <p><a name="line.132"></a> <FONT color="green">133</FONT> * The array computed by the objective function, the observations array and the<a name="line.133"></a> <FONT color="green">134</FONT> * the scaling matrix must have consistent sizes or a {@link FunctionEvaluationException}<a name="line.134"></a> <FONT color="green">135</FONT> * will be triggered while computing the scalar objective.<a name="line.135"></a> <FONT color="green">136</FONT> * </p><a name="line.136"></a> <FONT color="green">137</FONT> * @param function vectorial residuals function to wrap<a name="line.137"></a> <FONT color="green">138</FONT> * @param observations observations to be compared to objective function to compute residuals<a name="line.138"></a> <FONT color="green">139</FONT> * @param scale scaling matrix<a name="line.139"></a> <FONT color="green">140</FONT> * @exception IllegalArgumentException if the observations vector and the scale<a name="line.140"></a> <FONT color="green">141</FONT> * matrix dimensions don't match (objective function dimension is checked only when<a name="line.141"></a> <FONT color="green">142</FONT> * the {@link #value(double[])} method is called)<a name="line.142"></a> <FONT color="green">143</FONT> */<a name="line.143"></a> <FONT color="green">144</FONT> public LeastSquaresConverter(final MultivariateVectorialFunction function,<a name="line.144"></a> <FONT color="green">145</FONT> final double[] observations, final RealMatrix scale)<a name="line.145"></a> <FONT color="green">146</FONT> throws IllegalArgumentException {<a name="line.146"></a> <FONT color="green">147</FONT> if (observations.length != scale.getColumnDimension()) {<a name="line.147"></a> <FONT color="green">148</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.148"></a> <FONT color="green">149</FONT> "dimension mismatch {0} != {1}",<a name="line.149"></a> <FONT color="green">150</FONT> observations.length, scale.getColumnDimension());<a name="line.150"></a> <FONT color="green">151</FONT> }<a name="line.151"></a> <FONT color="green">152</FONT> this.function = function;<a name="line.152"></a> <FONT color="green">153</FONT> this.observations = observations.clone();<a name="line.153"></a> <FONT color="green">154</FONT> this.weights = null;<a name="line.154"></a> <FONT color="green">155</FONT> this.scale = scale.copy();<a name="line.155"></a> <FONT color="green">156</FONT> }<a name="line.156"></a> <FONT color="green">157</FONT> <a name="line.157"></a> <FONT color="green">158</FONT> /** {@inheritDoc} */<a name="line.158"></a> <FONT color="green">159</FONT> public double value(final double[] point) throws FunctionEvaluationException {<a name="line.159"></a> <FONT color="green">160</FONT> <a name="line.160"></a> <FONT color="green">161</FONT> // compute residuals<a name="line.161"></a> <FONT color="green">162</FONT> final double[] residuals = function.value(point);<a name="line.162"></a> <FONT color="green">163</FONT> if (residuals.length != observations.length) {<a name="line.163"></a> <FONT color="green">164</FONT> throw new FunctionEvaluationException(point, "dimension mismatch {0} != {1}",<a name="line.164"></a> <FONT color="green">165</FONT> residuals.length, observations.length);<a name="line.165"></a> <FONT color="green">166</FONT> }<a name="line.166"></a> <FONT color="green">167</FONT> for (int i = 0; i < residuals.length; ++i) {<a name="line.167"></a> <FONT color="green">168</FONT> residuals[i] -= observations[i];<a name="line.168"></a> <FONT color="green">169</FONT> }<a name="line.169"></a> <FONT color="green">170</FONT> <a name="line.170"></a> <FONT color="green">171</FONT> // compute sum of squares<a name="line.171"></a> <FONT color="green">172</FONT> double sumSquares = 0;<a name="line.172"></a> <FONT color="green">173</FONT> if (weights != null) {<a name="line.173"></a> <FONT color="green">174</FONT> for (int i = 0; i < residuals.length; ++i) {<a name="line.174"></a> <FONT color="green">175</FONT> final double ri = residuals[i];<a name="line.175"></a> <FONT color="green">176</FONT> sumSquares += weights[i] * ri * ri;<a name="line.176"></a> <FONT color="green">177</FONT> }<a name="line.177"></a> <FONT color="green">178</FONT> } else if (scale != null) {<a name="line.178"></a> <FONT color="green">179</FONT> for (final double yi : scale.operate(residuals)) {<a name="line.179"></a> <FONT color="green">180</FONT> sumSquares += yi * yi;<a name="line.180"></a> <FONT color="green">181</FONT> }<a name="line.181"></a> <FONT color="green">182</FONT> } else {<a name="line.182"></a> <FONT color="green">183</FONT> for (final double ri : residuals) {<a name="line.183"></a> <FONT color="green">184</FONT> sumSquares += ri * ri;<a name="line.184"></a> <FONT color="green">185</FONT> }<a name="line.185"></a> <FONT color="green">186</FONT> }<a name="line.186"></a> <FONT color="green">187</FONT> <a name="line.187"></a> <FONT color="green">188</FONT> return sumSquares;<a name="line.188"></a> <FONT color="green">189</FONT> <a name="line.189"></a> <FONT color="green">190</FONT> }<a name="line.190"></a> <FONT color="green">191</FONT> <a name="line.191"></a> <FONT color="green">192</FONT> }<a name="line.192"></a> </PRE> </BODY> </HTML>