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 = &sum;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&deg; 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&times;(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    }