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.estimation;
019    
020    import java.io.Serializable;
021    
022    import org.apache.commons.math.exception.util.LocalizedFormats;
023    import org.apache.commons.math.linear.InvalidMatrixException;
024    import org.apache.commons.math.linear.LUDecompositionImpl;
025    import org.apache.commons.math.linear.MatrixUtils;
026    import org.apache.commons.math.linear.RealMatrix;
027    import org.apache.commons.math.linear.RealVector;
028    import org.apache.commons.math.linear.ArrayRealVector;
029    import org.apache.commons.math.util.FastMath;
030    
031    /**
032     * This class implements a solver for estimation problems.
033     *
034     * <p>This class solves estimation problems using a weighted least
035     * squares criterion on the measurement residuals. It uses a
036     * Gauss-Newton algorithm.</p>
037     *
038     * @version $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 ao??t 2010) $
039     * @since 1.2
040     * @deprecated as of 2.0, everything in package org.apache.commons.math.estimation has
041     * been deprecated and replaced by package org.apache.commons.math.optimization.general
042     *
043     */
044    @Deprecated
045    public class GaussNewtonEstimator extends AbstractEstimator implements Serializable {
046    
047        /** Serializable version identifier */
048        private static final long serialVersionUID = 5485001826076289109L;
049    
050        /** Default threshold for cost steady state detection. */
051        private static final double DEFAULT_STEADY_STATE_THRESHOLD = 1.0e-6;
052    
053        /** Default threshold for cost convergence. */
054        private static final double DEFAULT_CONVERGENCE = 1.0e-6;
055    
056        /** Threshold for cost steady state detection. */
057        private double steadyStateThreshold;
058    
059        /** Threshold for cost convergence. */
060        private double convergence;
061    
062        /** Simple constructor with default settings.
063         * <p>
064         * The estimator is built with default values for all settings.
065         * </p>
066         * @see #DEFAULT_STEADY_STATE_THRESHOLD
067         * @see #DEFAULT_CONVERGENCE
068         * @see AbstractEstimator#DEFAULT_MAX_COST_EVALUATIONS
069         */
070        public GaussNewtonEstimator() {
071            this.steadyStateThreshold = DEFAULT_STEADY_STATE_THRESHOLD;
072            this.convergence          = DEFAULT_CONVERGENCE;
073        }
074    
075        /**
076         * Simple constructor.
077         *
078         * <p>This constructor builds an estimator and stores its convergence
079         * characteristics.</p>
080         *
081         * <p>An estimator is considered to have converged whenever either
082         * the criterion goes below a physical threshold under which
083         * improvements are considered useless or when the algorithm is
084         * unable to improve it (even if it is still high). The first
085         * condition that is met stops the iterations.</p>
086         *
087         * <p>The fact an estimator has converged does not mean that the
088         * model accurately fits the measurements. It only means no better
089         * solution can be found, it does not mean this one is good. Such an
090         * analysis is left to the caller.</p>
091         *
092         * <p>If neither conditions are fulfilled before a given number of
093         * iterations, the algorithm is considered to have failed and an
094         * {@link EstimationException} is thrown.</p>
095         *
096         * @param maxCostEval maximal number of cost evaluations allowed
097         * @param convergence criterion threshold below which we do not need
098         * to improve the criterion anymore
099         * @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    }