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.math3.optimization.general; 019 020 import org.apache.commons.math3.exception.ConvergenceException; 021 import org.apache.commons.math3.exception.NullArgumentException; 022 import org.apache.commons.math3.exception.MathInternalError; 023 import org.apache.commons.math3.exception.util.LocalizedFormats; 024 import org.apache.commons.math3.linear.ArrayRealVector; 025 import org.apache.commons.math3.linear.BlockRealMatrix; 026 import org.apache.commons.math3.linear.DecompositionSolver; 027 import org.apache.commons.math3.linear.LUDecomposition; 028 import org.apache.commons.math3.linear.QRDecomposition; 029 import org.apache.commons.math3.linear.RealMatrix; 030 import org.apache.commons.math3.linear.SingularMatrixException; 031 import org.apache.commons.math3.optimization.ConvergenceChecker; 032 import org.apache.commons.math3.optimization.SimpleVectorValueChecker; 033 import org.apache.commons.math3.optimization.PointVectorValuePair; 034 035 /** 036 * Gauss-Newton least-squares solver. 037 * <p> 038 * This class solve a least-square problem by solving the normal equations 039 * of the linearized problem at each iteration. Either LU decomposition or 040 * QR decomposition can be used to solve the normal equations. LU decomposition 041 * is faster but QR decomposition is more robust for difficult problems. 042 * </p> 043 * 044 * @version $Id: GaussNewtonOptimizer.java 1423687 2012-12-18 21:56:18Z erans $ 045 * @deprecated As of 3.1 (to be removed in 4.0). 046 * @since 2.0 047 * 048 */ 049 @Deprecated 050 public class GaussNewtonOptimizer extends AbstractLeastSquaresOptimizer { 051 /** Indicator for using LU decomposition. */ 052 private final boolean useLU; 053 054 /** 055 * Simple constructor with default settings. 056 * The normal equations will be solved using LU decomposition and the 057 * convergence check is set to a {@link SimpleVectorValueChecker} 058 * with default tolerances. 059 * @deprecated See {@link SimpleVectorValueChecker#SimpleVectorValueChecker()} 060 */ 061 @Deprecated 062 public GaussNewtonOptimizer() { 063 this(true); 064 } 065 066 /** 067 * Simple constructor with default settings. 068 * The normal equations will be solved using LU decomposition. 069 * 070 * @param checker Convergence checker. 071 */ 072 public GaussNewtonOptimizer(ConvergenceChecker<PointVectorValuePair> checker) { 073 this(true, checker); 074 } 075 076 /** 077 * Simple constructor with default settings. 078 * The convergence check is set to a {@link SimpleVectorValueChecker} 079 * with default tolerances. 080 * 081 * @param useLU If {@code true}, the normal equations will be solved 082 * using LU decomposition, otherwise they will be solved using QR 083 * decomposition. 084 * @deprecated See {@link SimpleVectorValueChecker#SimpleVectorValueChecker()} 085 */ 086 @Deprecated 087 public GaussNewtonOptimizer(final boolean useLU) { 088 this(useLU, new SimpleVectorValueChecker()); 089 } 090 091 /** 092 * @param useLU If {@code true}, the normal equations will be solved 093 * using LU decomposition, otherwise they will be solved using QR 094 * decomposition. 095 * @param checker Convergence checker. 096 */ 097 public GaussNewtonOptimizer(final boolean useLU, 098 ConvergenceChecker<PointVectorValuePair> checker) { 099 super(checker); 100 this.useLU = useLU; 101 } 102 103 /** {@inheritDoc} */ 104 @Override 105 public PointVectorValuePair doOptimize() { 106 final ConvergenceChecker<PointVectorValuePair> checker 107 = getConvergenceChecker(); 108 109 // Computation will be useless without a checker (see "for-loop"). 110 if (checker == null) { 111 throw new NullArgumentException(); 112 } 113 114 final double[] targetValues = getTarget(); 115 final int nR = targetValues.length; // Number of observed data. 116 117 final RealMatrix weightMatrix = getWeight(); 118 // Diagonal of the weight matrix. 119 final double[] residualsWeights = new double[nR]; 120 for (int i = 0; i < nR; i++) { 121 residualsWeights[i] = weightMatrix.getEntry(i, i); 122 } 123 124 final double[] currentPoint = getStartPoint(); 125 final int nC = currentPoint.length; 126 127 // iterate until convergence is reached 128 PointVectorValuePair current = null; 129 int iter = 0; 130 for (boolean converged = false; !converged;) { 131 ++iter; 132 133 // evaluate the objective function and its jacobian 134 PointVectorValuePair previous = current; 135 // Value of the objective function at "currentPoint". 136 final double[] currentObjective = computeObjectiveValue(currentPoint); 137 final double[] currentResiduals = computeResiduals(currentObjective); 138 final RealMatrix weightedJacobian = computeWeightedJacobian(currentPoint); 139 current = new PointVectorValuePair(currentPoint, currentObjective); 140 141 // build the linear problem 142 final double[] b = new double[nC]; 143 final double[][] a = new double[nC][nC]; 144 for (int i = 0; i < nR; ++i) { 145 146 final double[] grad = weightedJacobian.getRow(i); 147 final double weight = residualsWeights[i]; 148 final double residual = currentResiduals[i]; 149 150 // compute the normal equation 151 final double wr = weight * residual; 152 for (int j = 0; j < nC; ++j) { 153 b[j] += wr * grad[j]; 154 } 155 156 // build the contribution matrix for measurement i 157 for (int k = 0; k < nC; ++k) { 158 double[] ak = a[k]; 159 double wgk = weight * grad[k]; 160 for (int l = 0; l < nC; ++l) { 161 ak[l] += wgk * grad[l]; 162 } 163 } 164 } 165 166 try { 167 // solve the linearized least squares problem 168 RealMatrix mA = new BlockRealMatrix(a); 169 DecompositionSolver solver = useLU ? 170 new LUDecomposition(mA).getSolver() : 171 new QRDecomposition(mA).getSolver(); 172 final double[] dX = solver.solve(new ArrayRealVector(b, false)).toArray(); 173 // update the estimated parameters 174 for (int i = 0; i < nC; ++i) { 175 currentPoint[i] += dX[i]; 176 } 177 } catch (SingularMatrixException e) { 178 throw new ConvergenceException(LocalizedFormats.UNABLE_TO_SOLVE_SINGULAR_PROBLEM); 179 } 180 181 // Check convergence. 182 if (previous != null) { 183 converged = checker.converged(iter, previous, current); 184 if (converged) { 185 cost = computeCost(currentResiduals); 186 // Update (deprecated) "point" field. 187 point = current.getPoint(); 188 return current; 189 } 190 } 191 } 192 // Must never happen. 193 throw new MathInternalError(); 194 } 195 }