    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.optimization.general;
    019
    020    import org.apache.commons.math.FunctionEvaluationException;
    021    import org.apache.commons.math.exception.util.LocalizedFormats;
    022    import org.apache.commons.math.linear.BlockRealMatrix;
    023    import org.apache.commons.math.linear.DecompositionSolver;
    024    import org.apache.commons.math.linear.InvalidMatrixException;
    025    import org.apache.commons.math.linear.LUDecompositionImpl;
    026    import org.apache.commons.math.linear.QRDecompositionImpl;
    027    import org.apache.commons.math.linear.RealMatrix;
    028    import org.apache.commons.math.optimization.OptimizationException;
    029    import org.apache.commons.math.optimization.VectorialPointValuePair;
    030
    031    /**
    032     * Gauss-Newton least-squares solver.
    033     * <p>
    034     * This class solve a least-square problem by solving the normal equations
    035     * of the linearized problem at each iteration. Either LU decomposition or
    036     * QR decomposition can be used to solve the normal equations. LU decomposition
    037     * is faster but QR decomposition is more robust for difficult problems.
    038     * </p>
    039     *
    040     * @version $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 f??vr. 2011) $
    041     * @since 2.0
    042     *
    043     */
    044
    045    public class GaussNewtonOptimizer extends AbstractLeastSquaresOptimizer {
    046
    047        /** Indicator for using LU decomposition. */
    048        private final boolean useLU;
    049
    050        /** Simple constructor with default settings.
    051         * <p>The convergence check is set to a {@link
    052         * org.apache.commons.math.optimization.SimpleVectorialValueChecker}
    053         * and the maximal number of evaluation is set to
    054         * {@link AbstractLeastSquaresOptimizer#DEFAULT_MAX_ITERATIONS}.
    055         * @param useLU if true, the normal equations will be solved using LU
    056         * decomposition, otherwise they will be solved using QR decomposition
    057         */
    058        public GaussNewtonOptimizer(final boolean useLU) {
    059            this.useLU = useLU;
    060        }
    061
    062        /** {@inheritDoc} */
    063        @Override
    064        public VectorialPointValuePair doOptimize()
    065            throws FunctionEvaluationException, OptimizationException, IllegalArgumentException {
    066
    067            // iterate until convergence is reached
    068            VectorialPointValuePair current = null;
    069            for (boolean converged = false; !converged;) {
    070
    071                incrementIterationsCounter();
    072
    073                // evaluate the objective function and its jacobian
    074                VectorialPointValuePair previous = current;
    075                updateResidualsAndCost();
    076                updateJacobian();
    077                current = new VectorialPointValuePair(point, objective);
    078
    079                // build the linear problem
    080                final double[]   b = new double[cols];
    081                final double[][] a = new double[cols][cols];
    082                for (int i = 0; i < rows; ++i) {
    083
    084                    final double[] grad   = jacobian[i];
    085                    final double weight   = residualsWeights[i];
    086                    final double residual = objective[i] - targetValues[i];
    087
    088                    // compute the normal equation
    089                    final double wr = weight * residual;
    090                    for (int j = 0; j < cols; ++j) {
    091                        b[j] += wr * grad[j];
    092                    }
    093
    094                    // build the contribution matrix for measurement i
    095                    for (int k = 0; k < cols; ++k) {
    096                        double[] ak = a[k];
    097                        double wgk = weight * grad[k];
    098                        for (int l = 0; l < cols; ++l) {
    099                            ak[l] += wgk * grad[l];
    100                        }
    101                    }
    102
    103                }
    104
    105                try {
    106
    107                    // solve the linearized least squares problem
    108                    RealMatrix mA = new BlockRealMatrix(a);
    109                    DecompositionSolver solver = useLU ?
    110                            new LUDecompositionImpl(mA).getSolver() :
    111                            new QRDecompositionImpl(mA).getSolver();
    112                    final double[] dX = solver.solve(b);
    113
    114                    // update the estimated parameters
    115                    for (int i = 0; i < cols; ++i) {
    116                        point[i] += dX[i];
    117                    }
    118
    119                } catch(InvalidMatrixException e) {
    120                    throw new OptimizationException(LocalizedFormats.UNABLE_TO_SOLVE_SINGULAR_PROBLEM);
    121                }
    122
    123                // check convergence
    124                if (previous != null) {
    125                    converged = checker.converged(getIterations(), previous, current);
    126                }
    127
    128            }
    129
    130            // we have converged
    131            return current;
    132
    133        }
    134
    135    }