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.linear.RealMatrix;
025
026 /** This class converts {@link MultivariateVectorialFunction vectorial
027 * objective functions} to {@link MultivariateRealFunction scalar objective functions}
028 * when the goal is to minimize them.
029 * <p>
030 * This class is mostly used when the vectorial objective function represents
031 * a theoretical result computed from a point set applied to a model and
032 * the models point must be adjusted to fit the theoretical result to some
033 * reference observations. The observations may be obtained for example from
034 * physical measurements whether the model is built from theoretical
035 * considerations.
036 * </p>
037 * <p>
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 MultivariateRealFunction} 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 * </p>
047 * <p>
048 * This class support combination of residuals with or without weights and correlations.
049 * </p>
050 *
051 * @see MultivariateRealFunction
052 * @see MultivariateVectorialFunction
053 * @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $
054 * @since 2.0
055 */
056
057 public class LeastSquaresConverter implements MultivariateRealFunction {
058
059 /** Underlying vectorial function. */
060 private final MultivariateVectorialFunction 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 MultivariateVectorialFunction 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 FunctionEvaluationException} will be
102 * 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 IllegalArgumentException if the observations vector and the weights
108 * vector dimensions don't match (objective function dimension is checked only when
109 * the {@link #value(double[])} method is called)
110 */
111 public LeastSquaresConverter(final MultivariateVectorialFunction function,
112 final double[] observations, final double[] weights)
113 throws IllegalArgumentException {
114 if (observations.length != weights.length) {
115 throw MathRuntimeException.createIllegalArgumentException(
116 "dimension mismatch {0} != {1}",
117 observations.length, weights.length);
118 }
119 this.function = function;
120 this.observations = observations.clone();
121 this.weights = weights.clone();
122 this.scale = null;
123 }
124
125 /** Build a simple converter for correlated residuals with the specific 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 FunctionEvaluationException}
135 * will be triggered while computing the scalar objective.
136 * </p>
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 * @exception IllegalArgumentException if the observations vector and the scale
141 * matrix dimensions don't match (objective function dimension is checked only when
142 * the {@link #value(double[])} method is called)
143 */
144 public LeastSquaresConverter(final MultivariateVectorialFunction function,
145 final double[] observations, final RealMatrix scale)
146 throws IllegalArgumentException {
147 if (observations.length != scale.getColumnDimension()) {
148 throw MathRuntimeException.createIllegalArgumentException(
149 "dimension mismatch {0} != {1}",
150 observations.length, scale.getColumnDimension());
151 }
152 this.function = function;
153 this.observations = observations.clone();
154 this.weights = null;
155 this.scale = scale.copy();
156 }
157
158 /** {@inheritDoc} */
159 public double value(final double[] point) throws FunctionEvaluationException {
160
161 // compute residuals
162 final double[] residuals = function.value(point);
163 if (residuals.length != observations.length) {
164 throw new FunctionEvaluationException(point, "dimension mismatch {0} != {1}",
165 residuals.length, observations.length);
166 }
167 for (int i = 0; i < residuals.length; ++i) {
168 residuals[i] -= observations[i];
169 }
170
171 // compute sum of squares
172 double sumSquares = 0;
173 if (weights != null) {
174 for (int i = 0; i < residuals.length; ++i) {
175 final double ri = residuals[i];
176 sumSquares += weights[i] * ri * ri;
177 }
178 } else if (scale != null) {
179 for (final double yi : scale.operate(residuals)) {
180 sumSquares += yi * yi;
181 }
182 } else {
183 for (final double ri : residuals) {
184 sumSquares += ri * ri;
185 }
186 }
187
188 return sumSquares;
189
190 }
191
192 }