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/*
 * 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
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package org.apache.commons.math3.optimization.general;

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.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.optimization.ConvergenceChecker;
import org.apache.commons.math3.optimization.SimpleVectorValueChecker;
import org.apache.commons.math3.optimization.PointVectorValuePair;

/**
 * Gauss-Newton least-squares solver.
 * 

* 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. *

* * @deprecated As of 3.1 (to be removed in 4.0). * @since 2.0 * */ @Deprecated 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 and the * convergence check is set to a {@link SimpleVectorValueChecker} * with default tolerances. * @deprecated See {@link SimpleVectorValueChecker#SimpleVectorValueChecker()} */ @Deprecated public GaussNewtonOptimizer() { this(true); } /** * Simple constructor with default settings. * The normal equations will be solved using LU decomposition. * * @param checker Convergence checker. */ public GaussNewtonOptimizer(ConvergenceChecker checker) { this(true, checker); } /** * Simple constructor with default settings. * The convergence check is set to a {@link SimpleVectorValueChecker} * with default tolerances. * * @param useLU If {@code true}, the normal equations will be solved * using LU decomposition, otherwise they will be solved using QR * decomposition. * @deprecated See {@link SimpleVectorValueChecker#SimpleVectorValueChecker()} */ @Deprecated public GaussNewtonOptimizer(final boolean useLU) { this(useLU, new SimpleVectorValueChecker()); } /** * @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 checker) { super(checker); this.useLU = useLU; } /** {@inheritDoc} */ @Override public PointVectorValuePair doOptimize() { final ConvergenceChecker 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; int iter = 0; for (boolean converged = false; !converged;) { ++iter; // 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]; } } } 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); } // Check convergence. if (previous != null) { converged = checker.converged(iter, previous, current); if (converged) { cost = computeCost(currentResiduals); // Update (deprecated) "point" field. point = current.getPoint(); return current; } } } // Must never happen. throw new MathInternalError(); } }




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