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.optimization; 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/** This class converts {@link MultivariateVectorFunction vectorial 026 * objective functions} to {@link MultivariateFunction scalar objective functions} 027 * when the goal is to minimize them. 028 * <p> 029 * This class is mostly used when the vectorial objective function represents 030 * a theoretical result computed from a point set applied to a model and 031 * the models point must be adjusted to fit the theoretical result to some 032 * reference observations. The observations may be obtained for example from 033 * physical measurements whether the model is built from theoretical 034 * considerations. 035 * </p> 036 * <p> 037 * This class computes a possibly weighted squared sum of the residuals, which is 038 * a scalar value. The residuals are the difference between the theoretical model 039 * (i.e. the output of the vectorial objective function) and the observations. The 040 * class implements the {@link MultivariateFunction} interface and can therefore be 041 * minimized by any optimizer supporting scalar objectives functions.This is one way 042 * to perform a least square estimation. There are other ways to do this without using 043 * this converter, as some optimization algorithms directly support vectorial objective 044 * functions. 045 * </p> 046 * <p> 047 * This class support combination of residuals with or without weights and correlations. 048 * </p> 049 * 050 * @see MultivariateFunction 051 * @see MultivariateVectorFunction 052 * @deprecated As of 3.1 (to be removed in 4.0). 053 * @since 2.0 054 */ 055 056@Deprecated 057public class LeastSquaresConverter implements MultivariateFunction { 058 059 /** Underlying vectorial function. */ 060 private final MultivariateVectorFunction function; 061 062 /** Observations to be compared to objective function to compute residuals. */ 063 private final double[] observations; 064 065 /** Optional weights for the residuals. */ 066 private final double[] weights; 067 068 /** Optional scaling matrix (weight and correlations) for the residuals. */ 069 private final RealMatrix scale; 070 071 /** Build a simple converter for uncorrelated residuals with the same weight. 072 * @param function vectorial residuals function to wrap 073 * @param observations observations to be compared to objective function to compute residuals 074 */ 075 public LeastSquaresConverter(final MultivariateVectorFunction function, 076 final double[] observations) { 077 this.function = function; 078 this.observations = observations.clone(); 079 this.weights = null; 080 this.scale = null; 081 } 082 083 /** Build a simple converter for uncorrelated residuals with the specific weights. 084 * <p> 085 * The scalar objective function value is computed as: 086 * <pre> 087 * objective = ∑weight<sub>i</sub>(observation<sub>i</sub>-objective<sub>i</sub>)<sup>2</sup> 088 * </pre> 089 * </p> 090 * <p> 091 * Weights can be used for example to combine residuals with different standard 092 * deviations. As an example, consider a residuals array in which even elements 093 * are angular measurements in degrees with a 0.01° standard deviation and 094 * odd elements are distance measurements in meters with a 15m standard deviation. 095 * In this case, the weights array should be initialized with value 096 * 1.0/(0.01<sup>2</sup>) in the even elements and 1.0/(15.0<sup>2</sup>) in the 097 * odd elements (i.e. reciprocals of variances). 098 * </p> 099 * <p> 100 * The array computed by the objective function, the observations array and the 101 * weights array must have consistent sizes or a {@link DimensionMismatchException} 102 * will be triggered while computing the scalar objective. 103 * </p> 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 * @exception 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, 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 /** Build a simple converter for correlated residuals with the specific weights. 123 * <p> 124 * The scalar objective function value is computed as: 125 * <pre> 126 * objective = y<sup>T</sup>y with y = scale×(observation-objective) 127 * </pre> 128 * </p> 129 * <p> 130 * The array computed by the objective function, the observations array and the 131 * the scaling matrix must have consistent sizes or a {@link DimensionMismatchException} 132 * will be triggered while computing the scalar objective. 133 * </p> 134 * @param function vectorial residuals function to wrap 135 * @param observations observations to be compared to objective function to compute residuals 136 * @param scale scaling matrix 137 * @throws DimensionMismatchException if the observations vector and the scale 138 * matrix dimensions do not match (objective function dimension is checked only when 139 * the {@link #value(double[])} method is called) 140 */ 141 public LeastSquaresConverter(final MultivariateVectorFunction function, 142 final double[] observations, final RealMatrix scale) { 143 if (observations.length != scale.getColumnDimension()) { 144 throw new DimensionMismatchException(observations.length, scale.getColumnDimension()); 145 } 146 this.function = function; 147 this.observations = observations.clone(); 148 this.weights = null; 149 this.scale = scale.copy(); 150 } 151 152 /** {@inheritDoc} */ 153 public double value(final double[] point) { 154 // compute residuals 155 final double[] residuals = function.value(point); 156 if (residuals.length != observations.length) { 157 throw new DimensionMismatchException(residuals.length, observations.length); 158 } 159 for (int i = 0; i < residuals.length; ++i) { 160 residuals[i] -= observations[i]; 161 } 162 163 // compute sum of squares 164 double sumSquares = 0; 165 if (weights != null) { 166 for (int i = 0; i < residuals.length; ++i) { 167 final double ri = residuals[i]; 168 sumSquares += weights[i] * ri * ri; 169 } 170 } else if (scale != null) { 171 for (final double yi : scale.operate(residuals)) { 172 sumSquares += yi * yi; 173 } 174 } else { 175 for (final double ri : residuals) { 176 sumSquares += ri * ri; 177 } 178 } 179 180 return sumSquares; 181 } 182}