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.math.estimation;
19
20 import java.io.Serializable;
21
22 import org.apache.commons.math.linear.InvalidMatrixException;
23 import org.apache.commons.math.linear.RealMatrix;
24 import org.apache.commons.math.linear.RealMatrixImpl;
25
26 /**
27 * This class implements a solver for estimation problems.
28 *
29 * <p>This class solves estimation problems using a weighted least
30 * squares criterion on the measurement residuals. It uses a
31 * Gauss-Newton algorithm.</p>
32 *
33 * @version $Revision: 627987 $ $Date: 2008-02-15 03:01:26 -0700 (Fri, 15 Feb 2008) $
34 * @since 1.2
35 *
36 */
37
38 public class GaussNewtonEstimator extends AbstractEstimator implements Serializable {
39
40 /**
41 * Simple constructor.
42 *
43 * <p>This constructor builds an estimator and stores its convergence
44 * characteristics.</p>
45 *
46 * <p>An estimator is considered to have converged whenever either
47 * the criterion goes below a physical threshold under which
48 * improvements are considered useless or when the algorithm is
49 * unable to improve it (even if it is still high). The first
50 * condition that is met stops the iterations.</p>
51 *
52 * <p>The fact an estimator has converged does not mean that the
53 * model accurately fits the measurements. It only means no better
54 * solution can be found, it does not mean this one is good. Such an
55 * analysis is left to the caller.</p>
56 *
57 * <p>If neither conditions are fulfilled before a given number of
58 * iterations, the algorithm is considered to have failed and an
59 * {@link EstimationException} is thrown.</p>
60 *
61 * @param maxCostEval maximal number of cost evaluations allowed
62 * @param convergence criterion threshold below which we do not need
63 * to improve the criterion anymore
64 * @param steadyStateThreshold steady state detection threshold, the
65 * problem has converged has reached a steady state if
66 * <code>Math.abs (Jn - Jn-1) < Jn * convergence</code>, where
67 * <code>Jn</code> and <code>Jn-1</code> are the current and
68 * preceding criterion value (square sum of the weighted residuals
69 * of considered measurements).
70 */
71 public GaussNewtonEstimator(int maxCostEval,
72 double convergence,
73 double steadyStateThreshold) {
74 setMaxCostEval(maxCostEval);
75 this.steadyStateThreshold = steadyStateThreshold;
76 this.convergence = convergence;
77 }
78
79 /**
80 * Solve an estimation problem using a least squares criterion.
81 *
82 * <p>This method set the unbound parameters of the given problem
83 * starting from their current values through several iterations. At
84 * each step, the unbound parameters are changed in order to
85 * minimize a weighted least square criterion based on the
86 * measurements of the problem.</p>
87 *
88 * <p>The iterations are stopped either when the criterion goes
89 * below a physical threshold under which improvement are considered
90 * useless or when the algorithm is unable to improve it (even if it
91 * is still high). The first condition that is met stops the
92 * iterations. If the convergence it nos reached before the maximum
93 * number of iterations, an {@link EstimationException} is
94 * thrown.</p>
95 *
96 * @param problem estimation problem to solve
97 * @exception EstimationException if the problem cannot be solved
98 *
99 * @see EstimationProblem
100 *
101 */
102 public void estimate(EstimationProblem problem)
103 throws EstimationException {
104
105 initializeEstimate(problem);
106
107 // work matrices
108 double[] grad = new double[parameters.length];
109 RealMatrixImpl bDecrement = new RealMatrixImpl(parameters.length, 1);
110 double[][] bDecrementData = bDecrement.getDataRef();
111 RealMatrixImpl wGradGradT = new RealMatrixImpl(parameters.length, parameters.length);
112 double[][] wggData = wGradGradT.getDataRef();
113
114 // iterate until convergence is reached
115 double previous = Double.POSITIVE_INFINITY;
116 do {
117
118 // build the linear problem
119 incrementJacobianEvaluationsCounter();
120 RealMatrix b = new RealMatrixImpl(parameters.length, 1);
121 RealMatrix a = new RealMatrixImpl(parameters.length, parameters.length);
122 for (int i = 0; i < measurements.length; ++i) {
123 if (! measurements [i].isIgnored()) {
124
125 double weight = measurements[i].getWeight();
126 double residual = measurements[i].getResidual();
127
128 // compute the normal equation
129 for (int j = 0; j < parameters.length; ++j) {
130 grad[j] = measurements[i].getPartial(parameters[j]);
131 bDecrementData[j][0] = weight * residual * grad[j];
132 }
133
134 // build the contribution matrix for measurement i
135 for (int k = 0; k < parameters.length; ++k) {
136 double[] wggRow = wggData[k];
137 double gk = grad[k];
138 for (int l = 0; l < parameters.length; ++l) {
139 wggRow[l] = weight * gk * grad[l];
140 }
141 }
142
143 // update the matrices
144 a = a.add(wGradGradT);
145 b = b.add(bDecrement);
146
147 }
148 }
149
150 try {
151
152 // solve the linearized least squares problem
153 RealMatrix dX = a.solve(b);
154
155 // update the estimated parameters
156 for (int i = 0; i < parameters.length; ++i) {
157 parameters[i].setEstimate(parameters[i].getEstimate() + dX.getEntry(i, 0));
158 }
159
160 } catch(InvalidMatrixException e) {
161 throw new EstimationException("unable to solve: singular problem", new Object[0]);
162 }
163
164
165 previous = cost;
166 updateResidualsAndCost();
167
168 } while ((getCostEvaluations() < 2) ||
169 (Math.abs(previous - cost) > (cost * steadyStateThreshold) &&
170 (Math.abs(cost) > convergence)));
171
172 }
173
174 /** Threshold for cost steady state detection. */
175 private double steadyStateThreshold;
176
177 /** Threshold for cost convergence. */
178 private double convergence;
179
180 /** Serializable version identifier */
181 private static final long serialVersionUID = 5485001826076289109L;
182
183 }