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.math3.optim.nonlinear.scalar; 019 020 import org.apache.commons.math3.analysis.MultivariateFunction; 021 import org.apache.commons.math3.analysis.MultivariateVectorFunction; 022 import org.apache.commons.math3.exception.DimensionMismatchException; 023 import org.apache.commons.math3.linear.RealMatrix; 024 025 /** 026 * This class converts 027 * {@link MultivariateVectorFunction vectorial objective functions} to 028 * {@link MultivariateFunction scalar objective functions} 029 * when the goal is to minimize them. 030 * <br/> 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 * <br/> 038 * This class computes a possibly weighted squared sum of the residuals, which is 039 * a scalar value. The residuals are the difference between the theoretical model 040 * (i.e. the output of the vectorial objective function) and the observations. The 041 * class implements the {@link MultivariateFunction} interface and can therefore be 042 * minimized by any optimizer supporting scalar objectives functions.This is one way 043 * to perform a least square estimation. There are other ways to do this without using 044 * this converter, as some optimization algorithms directly support vectorial objective 045 * functions. 046 * <br/> 047 * This class support combination of residuals with or without weights and correlations. 048 * 049 * @see MultivariateFunction 050 * @see MultivariateVectorFunction 051 * @version $Id: LeastSquaresConverter.java 1416643 2012-12-03 19:37:14Z tn $ 052 * @since 2.0 053 */ 054 055 public class LeastSquaresConverter implements MultivariateFunction { 056 /** Underlying vectorial function. */ 057 private final MultivariateVectorFunction function; 058 /** Observations to be compared to objective function to compute residuals. */ 059 private final double[] observations; 060 /** Optional weights for the residuals. */ 061 private final double[] weights; 062 /** Optional scaling matrix (weight and correlations) for the residuals. */ 063 private final RealMatrix scale; 064 065 /** 066 * Builds a simple converter for uncorrelated residuals with identical 067 * weights. 068 * 069 * @param function vectorial residuals function to wrap 070 * @param observations observations to be compared to objective function to compute residuals 071 */ 072 public LeastSquaresConverter(final MultivariateVectorFunction function, 073 final double[] observations) { 074 this.function = function; 075 this.observations = observations.clone(); 076 this.weights = null; 077 this.scale = null; 078 } 079 080 /** 081 * Builds a simple converter for uncorrelated residuals with the 082 * specified weights. 083 * <p> 084 * The scalar objective function value is computed as: 085 * <pre> 086 * objective = ∑weight<sub>i</sub>(observation<sub>i</sub>-objective<sub>i</sub>)<sup>2</sup> 087 * </pre> 088 * </p> 089 * <p> 090 * Weights can be used for example to combine residuals with different standard 091 * deviations. As an example, consider a residuals array in which even elements 092 * are angular measurements in degrees with a 0.01° standard deviation and 093 * odd elements are distance measurements in meters with a 15m standard deviation. 094 * In this case, the weights array should be initialized with value 095 * 1.0/(0.01<sup>2</sup>) in the even elements and 1.0/(15.0<sup>2</sup>) in the 096 * odd elements (i.e. reciprocals of variances). 097 * </p> 098 * <p> 099 * The array computed by the objective function, the observations array and the 100 * weights array must have consistent sizes or a {@link DimensionMismatchException} 101 * will be triggered while computing the scalar objective. 102 * </p> 103 * 104 * @param function vectorial residuals function to wrap 105 * @param observations observations to be compared to objective function to compute residuals 106 * @param weights weights to apply to the residuals 107 * @throws DimensionMismatchException if the observations vector and the weights 108 * vector dimensions do not match (objective function dimension is checked only when 109 * the {@link #value(double[])} method is called) 110 */ 111 public LeastSquaresConverter(final MultivariateVectorFunction function, 112 final double[] observations, 113 final double[] weights) { 114 if (observations.length != weights.length) { 115 throw new DimensionMismatchException(observations.length, weights.length); 116 } 117 this.function = function; 118 this.observations = observations.clone(); 119 this.weights = weights.clone(); 120 this.scale = null; 121 } 122 123 /** 124 * Builds a simple converter for correlated residuals with the 125 * specified weights. 126 * <p> 127 * The scalar objective function value is computed as: 128 * <pre> 129 * objective = y<sup>T</sup>y with y = scale×(observation-objective) 130 * </pre> 131 * </p> 132 * <p> 133 * The array computed by the objective function, the observations array and the 134 * the scaling matrix must have consistent sizes or a {@link DimensionMismatchException} 135 * will be triggered while computing the scalar objective. 136 * </p> 137 * 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 * @throws DimensionMismatchException if the observations vector and the scale 142 * matrix dimensions do not match (objective function dimension is checked only when 143 * the {@link #value(double[])} method is called) 144 */ 145 public LeastSquaresConverter(final MultivariateVectorFunction function, 146 final double[] observations, 147 final RealMatrix scale) { 148 if (observations.length != scale.getColumnDimension()) { 149 throw new DimensionMismatchException(observations.length, scale.getColumnDimension()); 150 } 151 this.function = function; 152 this.observations = observations.clone(); 153 this.weights = null; 154 this.scale = scale.copy(); 155 } 156 157 /** {@inheritDoc} */ 158 public double value(final double[] point) { 159 // compute residuals 160 final double[] residuals = function.value(point); 161 if (residuals.length != observations.length) { 162 throw new DimensionMismatchException(residuals.length, observations.length); 163 } 164 for (int i = 0; i < residuals.length; ++i) { 165 residuals[i] -= observations[i]; 166 } 167 168 // compute sum of squares 169 double sumSquares = 0; 170 if (weights != null) { 171 for (int i = 0; i < residuals.length; ++i) { 172 final double ri = residuals[i]; 173 sumSquares += weights[i] * ri * ri; 174 } 175 } else if (scale != null) { 176 for (final double yi : scale.operate(residuals)) { 177 sumSquares += yi * yi; 178 } 179 } else { 180 for (final double ri : residuals) { 181 sumSquares += ri * ri; 182 } 183 } 184 185 return sumSquares; 186 } 187 }