    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    }