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.optimization;
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 /** 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 * @version $Id: LeastSquaresConverter.java 1422230 2012-12-15 12:11:13Z erans $
053 * @deprecated As of 3.1 (to be removed in 4.0).
054 * @since 2.0
055 */
056
057 @Deprecated
058 public class LeastSquaresConverter implements MultivariateFunction {
059
060 /** Underlying vectorial function. */
061 private final MultivariateVectorFunction 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 MultivariateVectorFunction 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 DimensionMismatchException}
103 * will be 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 DimensionMismatchException if the observations vector and the weights
109 * vector dimensions do not match (objective function dimension is checked only when
110 * the {@link #value(double[])} method is called)
111 */
112 public LeastSquaresConverter(final MultivariateVectorFunction function,
113 final double[] observations, 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 /** Build a simple converter for correlated residuals with the specific weights.
124 * <p>
125 * The scalar objective function value is computed as:
126 * <pre>
127 * objective = y<sup>T</sup>y with y = scale×(observation-objective)
128 * </pre>
129 * </p>
130 * <p>
131 * The array computed by the objective function, the observations array and the
132 * the scaling matrix must have consistent sizes or a {@link DimensionMismatchException}
133 * will be triggered while computing the scalar objective.
134 * </p>
135 * @param function vectorial residuals function to wrap
136 * @param observations observations to be compared to objective function to compute residuals
137 * @param scale scaling matrix
138 * @throws DimensionMismatchException if the observations vector and the scale
139 * matrix dimensions do not match (objective function dimension is checked only when
140 * the {@link #value(double[])} method is called)
141 */
142 public LeastSquaresConverter(final MultivariateVectorFunction function,
143 final double[] observations, final RealMatrix scale) {
144 if (observations.length != scale.getColumnDimension()) {
145 throw new DimensionMismatchException(observations.length, scale.getColumnDimension());
146 }
147 this.function = function;
148 this.observations = observations.clone();
149 this.weights = null;
150 this.scale = scale.copy();
151 }
152
153 /** {@inheritDoc} */
154 public double value(final double[] point) {
155 // compute residuals
156 final double[] residuals = function.value(point);
157 if (residuals.length != observations.length) {
158 throw new DimensionMismatchException(residuals.length, observations.length);
159 }
160 for (int i = 0; i < residuals.length; ++i) {
161 residuals[i] -= observations[i];
162 }
163
164 // compute sum of squares
165 double sumSquares = 0;
166 if (weights != null) {
167 for (int i = 0; i < residuals.length; ++i) {
168 final double ri = residuals[i];
169 sumSquares += weights[i] * ri * ri;
170 }
171 } else if (scale != null) {
172 for (final double yi : scale.operate(residuals)) {
173 sumSquares += yi * yi;
174 }
175 } else {
176 for (final double ri : residuals) {
177 sumSquares += ri * ri;
178 }
179 }
180
181 return sumSquares;
182 }
183 }