001 /* 002 * Licensed to the Apache Software Foundation (ASF) under one or more 003 * contributor license agreements. See the NOTICE file distributed with 004 * this work for additional information regarding copyright ownership. 005 * The ASF licenses this file to You under the Apache License, Version 2.0 006 * (the "License"); you may not use this file except in compliance with 007 * the License. You may obtain a copy of the License at 008 * 009 * http://www.apache.org/licenses/LICENSE-2.0 010 * 011 * Unless required by applicable law or agreed to in writing, software 012 * distributed under the License is distributed on an "AS IS" BASIS, 013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 014 * See the License for the specific language governing permissions and 015 * limitations under the License. 016 */ 017 018 package org.apache.commons.math.optimization; 019 020 import org.apache.commons.math.FunctionEvaluationException; 021 import org.apache.commons.math.MathRuntimeException; 022 import org.apache.commons.math.analysis.MultivariateRealFunction; 023 import org.apache.commons.math.analysis.MultivariateVectorialFunction; 024 import org.apache.commons.math.exception.util.LocalizedFormats; 025 import org.apache.commons.math.linear.RealMatrix; 026 027 /** This class converts {@link MultivariateVectorialFunction vectorial 028 * objective functions} to {@link MultivariateRealFunction scalar objective functions} 029 * when the goal is to minimize them. 030 * <p> 031 * This class is mostly used when the vectorial objective function represents 032 * a theoretical result computed from a point set applied to a model and 033 * the models point must be adjusted to fit the theoretical result to some 034 * reference observations. The observations may be obtained for example from 035 * physical measurements whether the model is built from theoretical 036 * considerations. 037 * </p> 038 * <p> 039 * This class computes a possibly weighted squared sum of the residuals, which is 040 * a scalar value. The residuals are the difference between the theoretical model 041 * (i.e. the output of the vectorial objective function) and the observations. The 042 * class implements the {@link MultivariateRealFunction} interface and can therefore be 043 * minimized by any optimizer supporting scalar objectives functions.This is one way 044 * to perform a least square estimation. There are other ways to do this without using 045 * this converter, as some optimization algorithms directly support vectorial objective 046 * functions. 047 * </p> 048 * <p> 049 * This class support combination of residuals with or without weights and correlations. 050 * </p> 051 * 052 * @see MultivariateRealFunction 053 * @see MultivariateVectorialFunction 054 * @version $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 f??vr. 2011) $ 055 * @since 2.0 056 */ 057 058 public class LeastSquaresConverter implements MultivariateRealFunction { 059 060 /** Underlying vectorial function. */ 061 private final MultivariateVectorialFunction function; 062 063 /** Observations to be compared to objective function to compute residuals. */ 064 private final double[] observations; 065 066 /** Optional weights for the residuals. */ 067 private final double[] weights; 068 069 /** Optional scaling matrix (weight and correlations) for the residuals. */ 070 private final RealMatrix scale; 071 072 /** Build a simple converter for uncorrelated residuals with the same weight. 073 * @param function vectorial residuals function to wrap 074 * @param observations observations to be compared to objective function to compute residuals 075 */ 076 public LeastSquaresConverter(final MultivariateVectorialFunction function, 077 final double[] observations) { 078 this.function = function; 079 this.observations = observations.clone(); 080 this.weights = null; 081 this.scale = null; 082 } 083 084 /** Build a simple converter for uncorrelated residuals with the specific weights. 085 * <p> 086 * The scalar objective function value is computed as: 087 * <pre> 088 * objective = ∑weight<sub>i</sub>(observation<sub>i</sub>-objective<sub>i</sub>)<sup>2</sup> 089 * </pre> 090 * </p> 091 * <p> 092 * Weights can be used for example to combine residuals with different standard 093 * deviations. As an example, consider a residuals array in which even elements 094 * are angular measurements in degrees with a 0.01° standard deviation and 095 * odd elements are distance measurements in meters with a 15m standard deviation. 096 * In this case, the weights array should be initialized with value 097 * 1.0/(0.01<sup>2</sup>) in the even elements and 1.0/(15.0<sup>2</sup>) in the 098 * odd elements (i.e. reciprocals of variances). 099 * </p> 100 * <p> 101 * The array computed by the objective function, the observations array and the 102 * weights array must have consistent sizes or a {@link FunctionEvaluationException} will be 103 * triggered while computing the scalar objective. 104 * </p> 105 * @param function vectorial residuals function to wrap 106 * @param observations observations to be compared to objective function to compute residuals 107 * @param weights weights to apply to the residuals 108 * @exception IllegalArgumentException if the observations vector and the weights 109 * vector dimensions don't match (objective function dimension is checked only when 110 * the {@link #value(double[])} method is called) 111 */ 112 public LeastSquaresConverter(final MultivariateVectorialFunction function, 113 final double[] observations, final double[] weights) 114 throws IllegalArgumentException { 115 if (observations.length != weights.length) { 116 throw MathRuntimeException.createIllegalArgumentException( 117 LocalizedFormats.DIMENSIONS_MISMATCH_SIMPLE, 118 observations.length, weights.length); 119 } 120 this.function = function; 121 this.observations = observations.clone(); 122 this.weights = weights.clone(); 123 this.scale = null; 124 } 125 126 /** Build a simple converter for correlated residuals with the specific weights. 127 * <p> 128 * The scalar objective function value is computed as: 129 * <pre> 130 * objective = y<sup>T</sup>y with y = scale×(observation-objective) 131 * </pre> 132 * </p> 133 * <p> 134 * The array computed by the objective function, the observations array and the 135 * the scaling matrix must have consistent sizes or a {@link FunctionEvaluationException} 136 * will be triggered while computing the scalar objective. 137 * </p> 138 * @param function vectorial residuals function to wrap 139 * @param observations observations to be compared to objective function to compute residuals 140 * @param scale scaling matrix 141 * @exception IllegalArgumentException if the observations vector and the scale 142 * matrix dimensions don't match (objective function dimension is checked only when 143 * the {@link #value(double[])} method is called) 144 */ 145 public LeastSquaresConverter(final MultivariateVectorialFunction function, 146 final double[] observations, final RealMatrix scale) 147 throws IllegalArgumentException { 148 if (observations.length != scale.getColumnDimension()) { 149 throw MathRuntimeException.createIllegalArgumentException( 150 LocalizedFormats.DIMENSIONS_MISMATCH_SIMPLE, 151 observations.length, scale.getColumnDimension()); 152 } 153 this.function = function; 154 this.observations = observations.clone(); 155 this.weights = null; 156 this.scale = scale.copy(); 157 } 158 159 /** {@inheritDoc} */ 160 public double value(final double[] point) throws FunctionEvaluationException { 161 162 // compute residuals 163 final double[] residuals = function.value(point); 164 if (residuals.length != observations.length) { 165 throw new FunctionEvaluationException(point,LocalizedFormats.DIMENSIONS_MISMATCH_SIMPLE, 166 residuals.length, observations.length); 167 } 168 for (int i = 0; i < residuals.length; ++i) { 169 residuals[i] -= observations[i]; 170 } 171 172 // compute sum of squares 173 double sumSquares = 0; 174 if (weights != null) { 175 for (int i = 0; i < residuals.length; ++i) { 176 final double ri = residuals[i]; 177 sumSquares += weights[i] * ri * ri; 178 } 179 } else if (scale != null) { 180 for (final double yi : scale.operate(residuals)) { 181 sumSquares += yi * yi; 182 } 183 } else { 184 for (final double ri : residuals) { 185 sumSquares += ri * ri; 186 } 187 } 188 189 return sumSquares; 190 191 } 192 193 }