View Javadoc

1   /*
2    * Licensed to the Apache Software Foundation (ASF) under one or more
3    * contributor license agreements.  See the NOTICE file distributed with
4    * this work for additional information regarding copyright ownership.
5    * The ASF licenses this file to You under the Apache License, Version 2.0
6    * (the "License"); you may not use this file except in compliance with
7    * the License.  You may obtain a copy of the License at
8    *
9    *      http://www.apache.org/licenses/LICENSE-2.0
10   *
11   * Unless required by applicable law or agreed to in writing, software
12   * distributed under the License is distributed on an "AS IS" BASIS,
13   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14   * See the License for the specific language governing permissions and
15   * limitations under the License.
16   */
17  
18  package org.apache.commons.math3.optim.nonlinear.scalar;
19  
20  import org.apache.commons.math3.analysis.MultivariateFunction;
21  import org.apache.commons.math3.analysis.MultivariateVectorFunction;
22  import org.apache.commons.math3.exception.DimensionMismatchException;
23  import org.apache.commons.math3.linear.RealMatrix;
24  
25  /**
26   * This class converts
27   * {@link MultivariateVectorFunction vectorial objective functions} to
28   * {@link MultivariateFunction scalar objective functions}
29   * when the goal is to minimize them.
30   * <br/>
31   * This class is mostly used when the vectorial objective function represents
32   * a theoretical result computed from a point set applied to a model and
33   * the models point must be adjusted to fit the theoretical result to some
34   * reference observations. The observations may be obtained for example from
35   * physical measurements whether the model is built from theoretical
36   * considerations.
37   * <br/>
38   * This class computes a possibly weighted squared sum of the residuals, which is
39   * a scalar value. The residuals are the difference between the theoretical model
40   * (i.e. the output of the vectorial objective function) and the observations. The
41   * class implements the {@link MultivariateFunction} interface and can therefore be
42   * minimized by any optimizer supporting scalar objectives functions.This is one way
43   * to perform a least square estimation. There are other ways to do this without using
44   * this converter, as some optimization algorithms directly support vectorial objective
45   * functions.
46   * <br/>
47   * This class support combination of residuals with or without weights and correlations.
48    *
49   * @see MultivariateFunction
50   * @see MultivariateVectorFunction
51   * @version $Id: LeastSquaresConverter.java 1435539 2013-01-19 13:27:24Z tn $
52   * @since 2.0
53   */
54  
55  public class LeastSquaresConverter implements MultivariateFunction {
56      /** Underlying vectorial function. */
57      private final MultivariateVectorFunction function;
58      /** Observations to be compared to objective function to compute residuals. */
59      private final double[] observations;
60      /** Optional weights for the residuals. */
61      private final double[] weights;
62      /** Optional scaling matrix (weight and correlations) for the residuals. */
63      private final RealMatrix scale;
64  
65      /**
66       * Builds a simple converter for uncorrelated residuals with identical
67       * weights.
68       *
69       * @param function vectorial residuals function to wrap
70       * @param observations observations to be compared to objective function to compute residuals
71       */
72      public LeastSquaresConverter(final MultivariateVectorFunction function,
73                                   final double[] observations) {
74          this.function     = function;
75          this.observations = observations.clone();
76          this.weights      = null;
77          this.scale        = null;
78      }
79  
80      /**
81       * Builds a simple converter for uncorrelated residuals with the
82       * specified weights.
83       * <p>
84       * The scalar objective function value is computed as:
85       * <pre>
86       * objective = &sum;weight<sub>i</sub>(observation<sub>i</sub>-objective<sub>i</sub>)<sup>2</sup>
87       * </pre>
88       * </p>
89       * <p>
90       * Weights can be used for example to combine residuals with different standard
91       * deviations. As an example, consider a residuals array in which even elements
92       * are angular measurements in degrees with a 0.01&deg; standard deviation and
93       * odd elements are distance measurements in meters with a 15m standard deviation.
94       * In this case, the weights array should be initialized with value
95       * 1.0/(0.01<sup>2</sup>) in the even elements and 1.0/(15.0<sup>2</sup>) in the
96       * odd elements (i.e. reciprocals of variances).
97       * </p>
98       * <p>
99       * 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 }