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 package org.apache.commons.math3.optim.nonlinear.vector.jacobian; 018 019 import org.apache.commons.math3.exception.ConvergenceException; 020 import org.apache.commons.math3.exception.NullArgumentException; 021 import org.apache.commons.math3.exception.MathInternalError; 022 import org.apache.commons.math3.exception.util.LocalizedFormats; 023 import org.apache.commons.math3.linear.ArrayRealVector; 024 import org.apache.commons.math3.linear.BlockRealMatrix; 025 import org.apache.commons.math3.linear.DecompositionSolver; 026 import org.apache.commons.math3.linear.LUDecomposition; 027 import org.apache.commons.math3.linear.QRDecomposition; 028 import org.apache.commons.math3.linear.RealMatrix; 029 import org.apache.commons.math3.linear.SingularMatrixException; 030 import org.apache.commons.math3.optim.ConvergenceChecker; 031 import org.apache.commons.math3.optim.PointVectorValuePair; 032 033 /** 034 * Gauss-Newton least-squares solver. 035 * <p> 036 * This class solve a least-square problem by solving the normal equations 037 * of the linearized problem at each iteration. Either LU decomposition or 038 * QR decomposition can be used to solve the normal equations. LU decomposition 039 * is faster but QR decomposition is more robust for difficult problems. 040 * </p> 041 * 042 * @version $Id: GaussNewtonOptimizer.java 1416643 2012-12-03 19:37:14Z tn $ 043 * @since 2.0 044 * 045 */ 046 public class GaussNewtonOptimizer extends AbstractLeastSquaresOptimizer { 047 /** Indicator for using LU decomposition. */ 048 private final boolean useLU; 049 050 /** 051 * Simple constructor with default settings. 052 * The normal equations will be solved using LU decomposition. 053 * 054 * @param checker Convergence checker. 055 */ 056 public GaussNewtonOptimizer(ConvergenceChecker<PointVectorValuePair> checker) { 057 this(true, checker); 058 } 059 060 /** 061 * @param useLU If {@code true}, the normal equations will be solved 062 * using LU decomposition, otherwise they will be solved using QR 063 * decomposition. 064 * @param checker Convergence checker. 065 */ 066 public GaussNewtonOptimizer(final boolean useLU, 067 ConvergenceChecker<PointVectorValuePair> checker) { 068 super(checker); 069 this.useLU = useLU; 070 } 071 072 /** {@inheritDoc} */ 073 @Override 074 public PointVectorValuePair doOptimize() { 075 final ConvergenceChecker<PointVectorValuePair> checker 076 = getConvergenceChecker(); 077 078 // Computation will be useless without a checker (see "for-loop"). 079 if (checker == null) { 080 throw new NullArgumentException(); 081 } 082 083 final double[] targetValues = getTarget(); 084 final int nR = targetValues.length; // Number of observed data. 085 086 final RealMatrix weightMatrix = getWeight(); 087 // Diagonal of the weight matrix. 088 final double[] residualsWeights = new double[nR]; 089 for (int i = 0; i < nR; i++) { 090 residualsWeights[i] = weightMatrix.getEntry(i, i); 091 } 092 093 final double[] currentPoint = getStartPoint(); 094 final int nC = currentPoint.length; 095 096 // iterate until convergence is reached 097 PointVectorValuePair current = null; 098 int iter = 0; 099 for (boolean converged = false; !converged;) { 100 ++iter; 101 102 // evaluate the objective function and its jacobian 103 PointVectorValuePair previous = current; 104 // Value of the objective function at "currentPoint". 105 final double[] currentObjective = computeObjectiveValue(currentPoint); 106 final double[] currentResiduals = computeResiduals(currentObjective); 107 final RealMatrix weightedJacobian = computeWeightedJacobian(currentPoint); 108 current = new PointVectorValuePair(currentPoint, currentObjective); 109 110 // build the linear problem 111 final double[] b = new double[nC]; 112 final double[][] a = new double[nC][nC]; 113 for (int i = 0; i < nR; ++i) { 114 115 final double[] grad = weightedJacobian.getRow(i); 116 final double weight = residualsWeights[i]; 117 final double residual = currentResiduals[i]; 118 119 // compute the normal equation 120 final double wr = weight * residual; 121 for (int j = 0; j < nC; ++j) { 122 b[j] += wr * grad[j]; 123 } 124 125 // build the contribution matrix for measurement i 126 for (int k = 0; k < nC; ++k) { 127 double[] ak = a[k]; 128 double wgk = weight * grad[k]; 129 for (int l = 0; l < nC; ++l) { 130 ak[l] += wgk * grad[l]; 131 } 132 } 133 } 134 135 try { 136 // solve the linearized least squares problem 137 RealMatrix mA = new BlockRealMatrix(a); 138 DecompositionSolver solver = useLU ? 139 new LUDecomposition(mA).getSolver() : 140 new QRDecomposition(mA).getSolver(); 141 final double[] dX = solver.solve(new ArrayRealVector(b, false)).toArray(); 142 // update the estimated parameters 143 for (int i = 0; i < nC; ++i) { 144 currentPoint[i] += dX[i]; 145 } 146 } catch (SingularMatrixException e) { 147 throw new ConvergenceException(LocalizedFormats.UNABLE_TO_SOLVE_SINGULAR_PROBLEM); 148 } 149 150 // Check convergence. 151 if (previous != null) { 152 converged = checker.converged(iter, previous, current); 153 if (converged) { 154 setCost(computeCost(currentResiduals)); 155 return current; 156 } 157 } 158 } 159 // Must never happen. 160 throw new MathInternalError(); 161 } 162 }