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Java example source code file (GaussNewtonOptimizer.java)

This example Java source code file (GaussNewtonOptimizer.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

abstractleastsquaresoptimizer, arrayrealvector, blockrealmatrix, convergencechecker, decompositionsolver, deprecated, gaussnewtonoptimizer, mathinternalerror, nullargumentexception, number, override, pointvectorvaluepair, realmatrix, singularmatrixexception

The GaussNewtonOptimizer.java Java example source code

 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *      http://www.apache.org/licenses/LICENSE-2.0
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * See the License for the specific language governing permissions and
 * limitations under the License.
package org.apache.commons.math3.optim.nonlinear.vector.jacobian;

import org.apache.commons.math3.exception.ConvergenceException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.MathInternalError;
import org.apache.commons.math3.exception.MathUnsupportedOperationException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.linear.ArrayRealVector;
import org.apache.commons.math3.linear.BlockRealMatrix;
import org.apache.commons.math3.linear.DecompositionSolver;
import org.apache.commons.math3.linear.LUDecomposition;
import org.apache.commons.math3.linear.QRDecomposition;
import org.apache.commons.math3.linear.RealMatrix;
import org.apache.commons.math3.linear.SingularMatrixException;
import org.apache.commons.math3.optim.ConvergenceChecker;
import org.apache.commons.math3.optim.PointVectorValuePair;

 * Gauss-Newton least-squares solver.
 * <br/>
 * Constraints are not supported: the call to
 * {@link #optimize(OptimizationData[]) optimize} will throw
 * {@link MathUnsupportedOperationException} if bounds are passed to it.
 * <p>
 * This class solve a least-square problem by solving the normal equations
 * of the linearized problem at each iteration. Either LU decomposition or
 * QR decomposition can be used to solve the normal equations. LU decomposition
 * is faster but QR decomposition is more robust for difficult problems.
 * </p>
 * @since 2.0
 * @deprecated All classes and interfaces in this package are deprecated.
 * The optimizers that were provided here were moved to the
 * {@link org.apache.commons.math3.fitting.leastsquares} package
 * (cf. MATH-1008).
public class GaussNewtonOptimizer extends AbstractLeastSquaresOptimizer {
    /** Indicator for using LU decomposition. */
    private final boolean useLU;

     * Simple constructor with default settings.
     * The normal equations will be solved using LU decomposition.
     * @param checker Convergence checker.
    public GaussNewtonOptimizer(ConvergenceChecker<PointVectorValuePair> checker) {
        this(true, checker);

     * @param useLU If {@code true}, the normal equations will be solved
     * using LU decomposition, otherwise they will be solved using QR
     * decomposition.
     * @param checker Convergence checker.
    public GaussNewtonOptimizer(final boolean useLU,
                                ConvergenceChecker<PointVectorValuePair> checker) {
        this.useLU = useLU;

    /** {@inheritDoc} */
    public PointVectorValuePair doOptimize() {

        final ConvergenceChecker<PointVectorValuePair> checker
            = getConvergenceChecker();

        // Computation will be useless without a checker (see "for-loop").
        if (checker == null) {
            throw new NullArgumentException();

        final double[] targetValues = getTarget();
        final int nR = targetValues.length; // Number of observed data.

        final RealMatrix weightMatrix = getWeight();
        // Diagonal of the weight matrix.
        final double[] residualsWeights = new double[nR];
        for (int i = 0; i < nR; i++) {
            residualsWeights[i] = weightMatrix.getEntry(i, i);

        final double[] currentPoint = getStartPoint();
        final int nC = currentPoint.length;

        // iterate until convergence is reached
        PointVectorValuePair current = null;
        for (boolean converged = false; !converged;) {

            // evaluate the objective function and its jacobian
            PointVectorValuePair previous = current;
            // Value of the objective function at "currentPoint".
            final double[] currentObjective = computeObjectiveValue(currentPoint);
            final double[] currentResiduals = computeResiduals(currentObjective);
            final RealMatrix weightedJacobian = computeWeightedJacobian(currentPoint);
            current = new PointVectorValuePair(currentPoint, currentObjective);

            // build the linear problem
            final double[]   b = new double[nC];
            final double[][] a = new double[nC][nC];
            for (int i = 0; i < nR; ++i) {

                final double[] grad   = weightedJacobian.getRow(i);
                final double weight   = residualsWeights[i];
                final double residual = currentResiduals[i];

                // compute the normal equation
                final double wr = weight * residual;
                for (int j = 0; j < nC; ++j) {
                    b[j] += wr * grad[j];

                // build the contribution matrix for measurement i
                for (int k = 0; k < nC; ++k) {
                    double[] ak = a[k];
                    double wgk = weight * grad[k];
                    for (int l = 0; l < nC; ++l) {
                        ak[l] += wgk * grad[l];

            // Check convergence.
            if (previous != null) {
                converged = checker.converged(getIterations(), previous, current);
                if (converged) {
                    return current;

            try {
                // solve the linearized least squares problem
                RealMatrix mA = new BlockRealMatrix(a);
                DecompositionSolver solver = useLU ?
                        new LUDecomposition(mA).getSolver() :
                        new QRDecomposition(mA).getSolver();
                final double[] dX = solver.solve(new ArrayRealVector(b, false)).toArray();
                // update the estimated parameters
                for (int i = 0; i < nC; ++i) {
                    currentPoint[i] += dX[i];
            } catch (SingularMatrixException e) {
                throw new ConvergenceException(LocalizedFormats.UNABLE_TO_SOLVE_SINGULAR_PROBLEM);
        // Must never happen.
        throw new MathInternalError();

     * @throws MathUnsupportedOperationException if bounds were passed to the
     * {@link #optimize(OptimizationData[]) optimize} method.
    private void checkParameters() {
        if (getLowerBound() != null ||
            getUpperBound() != null) {
            throw new MathUnsupportedOperationException(LocalizedFormats.CONSTRAINT);

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