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 018package org.apache.commons.math3.optim.nonlinear.scalar; 019 020import org.apache.commons.math3.analysis.MultivariateFunction; 021import org.apache.commons.math3.analysis.MultivariateVectorFunction; 022import org.apache.commons.math3.exception.DimensionMismatchException; 023import 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 * @since 2.0 052 */ 053 054public class LeastSquaresConverter implements MultivariateFunction { 055 /** Underlying vectorial function. */ 056 private final MultivariateVectorFunction function; 057 /** Observations to be compared to objective function to compute residuals. */ 058 private final double[] observations; 059 /** Optional weights for the residuals. */ 060 private final double[] weights; 061 /** Optional scaling matrix (weight and correlations) for the residuals. */ 062 private final RealMatrix scale; 063 064 /** 065 * Builds a simple converter for uncorrelated residuals with identical 066 * weights. 067 * 068 * @param function vectorial residuals function to wrap 069 * @param observations observations to be compared to objective function to compute residuals 070 */ 071 public LeastSquaresConverter(final MultivariateVectorFunction function, 072 final double[] observations) { 073 this.function = function; 074 this.observations = observations.clone(); 075 this.weights = null; 076 this.scale = null; 077 } 078 079 /** 080 * Builds a simple converter for uncorrelated residuals with the 081 * specified weights. 082 * <p> 083 * The scalar objective function value is computed as: 084 * <pre> 085 * objective = ∑weight<sub>i</sub>(observation<sub>i</sub>-objective<sub>i</sub>)<sup>2</sup> 086 * </pre> 087 * </p> 088 * <p> 089 * Weights can be used for example to combine residuals with different standard 090 * deviations. As an example, consider a residuals array in which even elements 091 * are angular measurements in degrees with a 0.01° standard deviation and 092 * odd elements are distance measurements in meters with a 15m standard deviation. 093 * In this case, the weights array should be initialized with value 094 * 1.0/(0.01<sup>2</sup>) in the even elements and 1.0/(15.0<sup>2</sup>) in the 095 * odd elements (i.e. reciprocals of variances). 096 * </p> 097 * <p> 098 * The array computed by the objective function, the observations array and the 099 * weights array must have consistent sizes or a {@link DimensionMismatchException} 100 * will be triggered while computing the scalar objective. 101 * </p> 102 * 103 * @param function vectorial residuals function to wrap 104 * @param observations observations to be compared to objective function to compute residuals 105 * @param weights weights to apply to the residuals 106 * @throws DimensionMismatchException if the observations vector and the weights 107 * vector dimensions do not match (objective function dimension is checked only when 108 * the {@link #value(double[])} method is called) 109 */ 110 public LeastSquaresConverter(final MultivariateVectorFunction function, 111 final double[] observations, 112 final double[] weights) { 113 if (observations.length != weights.length) { 114 throw new DimensionMismatchException(observations.length, weights.length); 115 } 116 this.function = function; 117 this.observations = observations.clone(); 118 this.weights = weights.clone(); 119 this.scale = null; 120 } 121 122 /** 123 * Builds a simple converter for correlated residuals with the 124 * specified weights. 125 * <p> 126 * The scalar objective function value is computed as: 127 * <pre> 128 * objective = y<sup>T</sup>y with y = scale×(observation-objective) 129 * </pre> 130 * </p> 131 * <p> 132 * The array computed by the objective function, the observations array and the 133 * the scaling matrix must have consistent sizes or a {@link DimensionMismatchException} 134 * will be triggered while computing the scalar objective. 135 * </p> 136 * 137 * @param function vectorial residuals function to wrap 138 * @param observations observations to be compared to objective function to compute residuals 139 * @param scale scaling matrix 140 * @throws DimensionMismatchException if the observations vector and the scale 141 * matrix dimensions do not match (objective function dimension is checked only when 142 * the {@link #value(double[])} method is called) 143 */ 144 public LeastSquaresConverter(final MultivariateVectorFunction function, 145 final double[] observations, 146 final RealMatrix scale) { 147 if (observations.length != scale.getColumnDimension()) { 148 throw new DimensionMismatchException(observations.length, scale.getColumnDimension()); 149 } 150 this.function = function; 151 this.observations = observations.clone(); 152 this.weights = null; 153 this.scale = scale.copy(); 154 } 155 156 /** {@inheritDoc} */ 157 public double value(final double[] point) { 158 // compute residuals 159 final double[] residuals = function.value(point); 160 if (residuals.length != observations.length) { 161 throw new DimensionMismatchException(residuals.length, observations.length); 162 } 163 for (int i = 0; i < residuals.length; ++i) { 164 residuals[i] -= observations[i]; 165 } 166 167 // compute sum of squares 168 double sumSquares = 0; 169 if (weights != null) { 170 for (int i = 0; i < residuals.length; ++i) { 171 final double ri = residuals[i]; 172 sumSquares += weights[i] * ri * ri; 173 } 174 } else if (scale != null) { 175 for (final double yi : scale.operate(residuals)) { 176 sumSquares += yi * yi; 177 } 178 } else { 179 for (final double ri : residuals) { 180 sumSquares += ri * ri; 181 } 182 } 183 184 return sumSquares; 185 } 186}