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.linear.InvalidMatrixException;
023    import org.apache.commons.math.linear.LUDecompositionImpl;
024    import org.apache.commons.math.linear.MatrixUtils;
025    import org.apache.commons.math.linear.RealMatrix;
026    import org.apache.commons.math.linear.RealVector;
027    import org.apache.commons.math.linear.ArrayRealVector;
028    
029    /** 
030     * This class implements a solver for estimation problems.
031     *
032     * <p>This class solves estimation problems using a weighted least
033     * squares criterion on the measurement residuals. It uses a
034     * Gauss-Newton algorithm.</p>
035     *
036     * @version $Revision: 783702 $ $Date: 2009-06-11 04:54:02 -0400 (Thu, 11 Jun 2009) $
037     * @since 1.2
038     * @deprecated as of 2.0, everything in package org.apache.commons.math.estimation has
039     * been deprecated and replaced by package org.apache.commons.math.optimization.general
040     *
041     */
042    @Deprecated
043    public class GaussNewtonEstimator extends AbstractEstimator implements Serializable {
044    
045        /** Serializable version identifier */
046        private static final long serialVersionUID = 5485001826076289109L;
047    
048        /** Default threshold for cost steady state detection. */
049        private static final double DEFAULT_STEADY_STATE_THRESHOLD = 1.0e-6;
050    
051        /** Default threshold for cost convergence. */
052        private static final double DEFAULT_CONVERGENCE = 1.0e-6;
053    
054        /** Threshold for cost steady state detection. */
055        private double steadyStateThreshold;
056    
057        /** Threshold for cost convergence. */
058        private double convergence;
059    
060        /** Simple constructor with default settings.
061         * <p>
062         * The estimator is built with default values for all settings.
063         * </p>
064         * @see #DEFAULT_STEADY_STATE_THRESHOLD
065         * @see #DEFAULT_CONVERGENCE
066         * @see AbstractEstimator#DEFAULT_MAX_COST_EVALUATIONS
067         */
068        public GaussNewtonEstimator() {
069            this.steadyStateThreshold = DEFAULT_STEADY_STATE_THRESHOLD;
070            this.convergence          = DEFAULT_CONVERGENCE;        
071        }
072    
073        /** 
074         * Simple constructor.
075         *
076         * <p>This constructor builds an estimator and stores its convergence
077         * characteristics.</p>
078         *
079         * <p>An estimator is considered to have converged whenever either
080         * the criterion goes below a physical threshold under which
081         * improvements are considered useless or when the algorithm is
082         * unable to improve it (even if it is still high). The first
083         * condition that is met stops the iterations.</p>
084         *
085         * <p>The fact an estimator has converged does not mean that the
086         * model accurately fits the measurements. It only means no better
087         * solution can be found, it does not mean this one is good. Such an
088         * analysis is left to the caller.</p>
089         *
090         * <p>If neither conditions are fulfilled before a given number of
091         * iterations, the algorithm is considered to have failed and an
092         * {@link EstimationException} is thrown.</p>
093         *
094         * @param maxCostEval maximal number of cost evaluations allowed
095         * @param convergence criterion threshold below which we do not need
096         * to improve the criterion anymore
097         * @param steadyStateThreshold steady state detection threshold, the
098         * problem has converged has reached a steady state if
099         * <code>Math.abs(J<sub>n</sub> - J<sub>n-1</sub>) &lt;
100         * J<sub>n</sub> &times convergence</code>, where <code>J<sub>n</sub></code>
101         * and <code>J<sub>n-1</sub></code> are the current and preceding criterion
102         * values (square sum of the weighted residuals of considered measurements).
103         */
104        public GaussNewtonEstimator(final int maxCostEval, final double convergence,
105                                    final double steadyStateThreshold) {
106            setMaxCostEval(maxCostEval);
107            this.steadyStateThreshold = steadyStateThreshold;
108            this.convergence          = convergence;
109        }
110    
111        /**
112         * Set the convergence criterion threshold.
113         * @param convergence criterion threshold below which we do not need
114         * to improve the criterion anymore
115         */
116        public void setConvergence(final double convergence) {
117            this.convergence = convergence;
118        }
119    
120        /**
121         * Set the steady state detection threshold.
122         * <p>
123         * The problem has converged has reached a steady state if
124         * <code>Math.abs(J<sub>n</sub> - J<sub>n-1</sub>) &lt;
125         * J<sub>n</sub> &times convergence</code>, where <code>J<sub>n</sub></code>
126         * and <code>J<sub>n-1</sub></code> are the current and preceding criterion
127         * values (square sum of the weighted residuals of considered measurements).
128         * </p>
129         * @param steadyStateThreshold steady state detection threshold
130         */
131        public void setSteadyStateThreshold(final double steadyStateThreshold) {
132            this.steadyStateThreshold = steadyStateThreshold;
133        }
134    
135        /** 
136         * Solve an estimation problem using a least squares criterion.
137         *
138         * <p>This method set the unbound parameters of the given problem
139         * starting from their current values through several iterations. At
140         * each step, the unbound parameters are changed in order to
141         * minimize a weighted least square criterion based on the
142         * measurements of the problem.</p>
143         *
144         * <p>The iterations are stopped either when the criterion goes
145         * below a physical threshold under which improvement are considered
146         * useless or when the algorithm is unable to improve it (even if it
147         * is still high). The first condition that is met stops the
148         * iterations. If the convergence it not reached before the maximum
149         * number of iterations, an {@link EstimationException} is
150         * thrown.</p>
151         *
152         * @param problem estimation problem to solve
153         * @exception EstimationException if the problem cannot be solved
154         *
155         * @see EstimationProblem
156         *
157         */
158        @Override
159        public void estimate(EstimationProblem problem)
160        throws EstimationException {
161    
162            initializeEstimate(problem);
163    
164            // work matrices
165            double[] grad             = new double[parameters.length];
166            ArrayRealVector bDecrement = new ArrayRealVector(parameters.length);
167            double[] bDecrementData   = bDecrement.getDataRef();
168            RealMatrix wGradGradT     = MatrixUtils.createRealMatrix(parameters.length, parameters.length);
169    
170            // iterate until convergence is reached
171            double previous = Double.POSITIVE_INFINITY;
172            do {
173    
174                // build the linear problem
175                incrementJacobianEvaluationsCounter();
176                RealVector b = new ArrayRealVector(parameters.length);
177                RealMatrix a = MatrixUtils.createRealMatrix(parameters.length, parameters.length);
178                for (int i = 0; i < measurements.length; ++i) {
179                    if (! measurements [i].isIgnored()) {
180    
181                        double weight   = measurements[i].getWeight();
182                        double residual = measurements[i].getResidual();
183    
184                        // compute the normal equation
185                        for (int j = 0; j < parameters.length; ++j) {
186                            grad[j] = measurements[i].getPartial(parameters[j]);
187                            bDecrementData[j] = weight * residual * grad[j];
188                        }
189    
190                        // build the contribution matrix for measurement i
191                        for (int k = 0; k < parameters.length; ++k) {
192                            double gk = grad[k];
193                            for (int l = 0; l < parameters.length; ++l) {
194                                wGradGradT.setEntry(k, l, weight * gk * grad[l]);
195                            }
196                        }
197    
198                        // update the matrices
199                        a = a.add(wGradGradT);
200                        b = b.add(bDecrement);
201    
202                    }
203                }
204    
205                try {
206    
207                    // solve the linearized least squares problem
208                    RealVector dX = new LUDecompositionImpl(a).getSolver().solve(b);
209    
210                    // update the estimated parameters
211                    for (int i = 0; i < parameters.length; ++i) {
212                        parameters[i].setEstimate(parameters[i].getEstimate() + dX.getEntry(i));
213                    }
214    
215                } catch(InvalidMatrixException e) {
216                    throw new EstimationException("unable to solve: singular problem");
217                }
218    
219    
220                previous = cost;
221                updateResidualsAndCost();
222    
223            } while ((getCostEvaluations() < 2) ||
224                     (Math.abs(previous - cost) > (cost * steadyStateThreshold) &&
225                      (Math.abs(cost) > convergence)));
226    
227        }
228    
229    }