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
18package org.apache.commons.math.estimation;
19
20import java.io.Serializable;
21
22import org.apache.commons.math.exception.util.LocalizedFormats;
23import org.apache.commons.math.linear.InvalidMatrixException;
24import org.apache.commons.math.linear.LUDecompositionImpl;
25import org.apache.commons.math.linear.MatrixUtils;
26import org.apache.commons.math.linear.RealMatrix;
27import org.apache.commons.math.linear.RealVector;
28import org.apache.commons.math.linear.ArrayRealVector;
29import org.apache.commons.math.util.FastMath;
30
31/**
32 * This class implements a solver for estimation problems.
33 *
34 * <p>This class solves estimation problems using a weighted least
35 * squares criterion on the measurement residuals. It uses a
36 * Gauss-Newton algorithm.</p>
37 *
38 * @version $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $
39 * @since 1.2
40 * @deprecated as of 2.0, everything in package org.apache.commons.math.estimation has
41 * been deprecated and replaced by package org.apache.commons.math.optimization.general
42 *
43 */
44@Deprecated
45public class GaussNewtonEstimator extends AbstractEstimator implements Serializable {
46
47    /** Serializable version identifier */
48    private static final long serialVersionUID = 5485001826076289109L;
49
50    /** Default threshold for cost steady state detection. */
51    private static final double DEFAULT_STEADY_STATE_THRESHOLD = 1.0e-6;
52
53    /** Default threshold for cost convergence. */
54    private static final double DEFAULT_CONVERGENCE = 1.0e-6;
55
56    /** Threshold for cost steady state detection. */
57    private double steadyStateThreshold;
58
59    /** Threshold for cost convergence. */
60    private double convergence;
61
62    /** Simple constructor with default settings.
63     * <p>
64     * The estimator is built with default values for all settings.
65     * </p>
66     * @see #DEFAULT_STEADY_STATE_THRESHOLD
67     * @see #DEFAULT_CONVERGENCE
68     * @see AbstractEstimator#DEFAULT_MAX_COST_EVALUATIONS
69     */
70    public GaussNewtonEstimator() {
71        this.steadyStateThreshold = DEFAULT_STEADY_STATE_THRESHOLD;
72        this.convergence          = DEFAULT_CONVERGENCE;
73    }
74
75    /**
76     * Simple constructor.
77     *
78     * <p>This constructor builds an estimator and stores its convergence
79     * characteristics.</p>
80     *
81     * <p>An estimator is considered to have converged whenever either
82     * the criterion goes below a physical threshold under which
83     * improvements are considered useless or when the algorithm is
84     * unable to improve it (even if it is still high). The first
85     * condition that is met stops the iterations.</p>
86     *
87     * <p>The fact an estimator has converged does not mean that the
88     * model accurately fits the measurements. It only means no better
89     * solution can be found, it does not mean this one is good. Such an
90     * analysis is left to the caller.</p>
91     *
92     * <p>If neither conditions are fulfilled before a given number of
93     * iterations, the algorithm is considered to have failed and an
94     * {@link EstimationException} is thrown.</p>
95     *
96     * @param maxCostEval maximal number of cost evaluations allowed
97     * @param convergence criterion threshold below which we do not need
98     * to improve the criterion anymore
99     * @param steadyStateThreshold steady state detection threshold, the
100     * problem has converged has reached a steady state if
101     * <code>FastMath.abs(J<sub>n</sub> - J<sub>n-1</sub>) &lt;
102     * J<sub>n</sub> &times convergence</code>, where <code>J<sub>n</sub></code>
103     * and <code>J<sub>n-1</sub></code> are the current and preceding criterion
104     * values (square sum of the weighted residuals of considered measurements).
105     */
106    public GaussNewtonEstimator(final int maxCostEval, final double convergence,
107                                final double steadyStateThreshold) {
108        setMaxCostEval(maxCostEval);
109        this.steadyStateThreshold = steadyStateThreshold;
110        this.convergence          = convergence;
111    }
112
113    /**
114     * Set the convergence criterion threshold.
115     * @param convergence criterion threshold below which we do not need
116     * to improve the criterion anymore
117     */
118    public void setConvergence(final double convergence) {
119        this.convergence = convergence;
120    }
121
122    /**
123     * Set the steady state detection threshold.
124     * <p>
125     * The problem has converged has reached a steady state if
126     * <code>FastMath.abs(J<sub>n</sub> - J<sub>n-1</sub>) &lt;
127     * J<sub>n</sub> &times convergence</code>, where <code>J<sub>n</sub></code>
128     * and <code>J<sub>n-1</sub></code> are the current and preceding criterion
129     * values (square sum of the weighted residuals of considered measurements).
130     * </p>
131     * @param steadyStateThreshold steady state detection threshold
132     */
133    public void setSteadyStateThreshold(final double steadyStateThreshold) {
134        this.steadyStateThreshold = steadyStateThreshold;
135    }
136
137    /**
138     * Solve an estimation problem using a least squares criterion.
139     *
140     * <p>This method set the unbound parameters of the given problem
141     * starting from their current values through several iterations. At
142     * each step, the unbound parameters are changed in order to
143     * minimize a weighted least square criterion based on the
144     * measurements of the problem.</p>
145     *
146     * <p>The iterations are stopped either when the criterion goes
147     * below a physical threshold under which improvement are considered
148     * useless or when the algorithm is unable to improve it (even if it
149     * is still high). The first condition that is met stops the
150     * iterations. If the convergence it not reached before the maximum
151     * number of iterations, an {@link EstimationException} is
152     * thrown.</p>
153     *
154     * @param problem estimation problem to solve
155     * @exception EstimationException if the problem cannot be solved
156     *
157     * @see EstimationProblem
158     *
159     */
160    @Override
161    public void estimate(EstimationProblem problem)
162    throws EstimationException {
163
164        initializeEstimate(problem);
165
166        // work matrices
167        double[] grad             = new double[parameters.length];
168        ArrayRealVector bDecrement = new ArrayRealVector(parameters.length);
169        double[] bDecrementData   = bDecrement.getDataRef();
170        RealMatrix wGradGradT     = MatrixUtils.createRealMatrix(parameters.length, parameters.length);
171
172        // iterate until convergence is reached
173        double previous = Double.POSITIVE_INFINITY;
174        do {
175
176            // build the linear problem
177            incrementJacobianEvaluationsCounter();
178            RealVector b = new ArrayRealVector(parameters.length);
179            RealMatrix a = MatrixUtils.createRealMatrix(parameters.length, parameters.length);
180            for (int i = 0; i < measurements.length; ++i) {
181                if (! measurements [i].isIgnored()) {
182
183                    double weight   = measurements[i].getWeight();
184                    double residual = measurements[i].getResidual();
185
186                    // compute the normal equation
187                    for (int j = 0; j < parameters.length; ++j) {
188                        grad[j] = measurements[i].getPartial(parameters[j]);
189                        bDecrementData[j] = weight * residual * grad[j];
190                    }
191
192                    // build the contribution matrix for measurement i
193                    for (int k = 0; k < parameters.length; ++k) {
194                        double gk = grad[k];
195                        for (int l = 0; l < parameters.length; ++l) {
196                            wGradGradT.setEntry(k, l, weight * gk * grad[l]);
197                        }
198                    }
199
200                    // update the matrices
201                    a = a.add(wGradGradT);
202                    b = b.add(bDecrement);
203
204                }
205            }
206
207            try {
208
209                // solve the linearized least squares problem
210                RealVector dX = new LUDecompositionImpl(a).getSolver().solve(b);
211
212                // update the estimated parameters
213                for (int i = 0; i < parameters.length; ++i) {
214                    parameters[i].setEstimate(parameters[i].getEstimate() + dX.getEntry(i));
215                }
216
217            } catch(InvalidMatrixException e) {
218                throw new EstimationException(LocalizedFormats.UNABLE_TO_SOLVE_SINGULAR_PROBLEM);
219            }
220
221
222            previous = cost;
223            updateResidualsAndCost();
224
225        } while ((getCostEvaluations() < 2) ||
226                 (FastMath.abs(previous - cost) > (cost * steadyStateThreshold) &&
227                  (FastMath.abs(cost) > convergence)));
228
229    }
230
231}
232