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 018package org.apache.commons.math3.optimization.general; 019 020import org.apache.commons.math3.exception.ConvergenceException; 021import org.apache.commons.math3.exception.NullArgumentException; 022import org.apache.commons.math3.exception.MathInternalError; 023import org.apache.commons.math3.exception.util.LocalizedFormats; 024import org.apache.commons.math3.linear.ArrayRealVector; 025import org.apache.commons.math3.linear.BlockRealMatrix; 026import org.apache.commons.math3.linear.DecompositionSolver; 027import org.apache.commons.math3.linear.LUDecomposition; 028import org.apache.commons.math3.linear.QRDecomposition; 029import org.apache.commons.math3.linear.RealMatrix; 030import org.apache.commons.math3.linear.SingularMatrixException; 031import org.apache.commons.math3.optimization.ConvergenceChecker; 032import org.apache.commons.math3.optimization.SimpleVectorValueChecker; 033import 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 * @deprecated As of 3.1 (to be removed in 4.0). 045 * @since 2.0 046 * 047 */ 048@Deprecated 049public class GaussNewtonOptimizer extends AbstractLeastSquaresOptimizer { 050 /** Indicator for using LU decomposition. */ 051 private final boolean useLU; 052 053 /** 054 * Simple constructor with default settings. 055 * The normal equations will be solved using LU decomposition and the 056 * convergence check is set to a {@link SimpleVectorValueChecker} 057 * with default tolerances. 058 * @deprecated See {@link SimpleVectorValueChecker#SimpleVectorValueChecker()} 059 */ 060 @Deprecated 061 public GaussNewtonOptimizer() { 062 this(true); 063 } 064 065 /** 066 * Simple constructor with default settings. 067 * The normal equations will be solved using LU decomposition. 068 * 069 * @param checker Convergence checker. 070 */ 071 public GaussNewtonOptimizer(ConvergenceChecker<PointVectorValuePair> checker) { 072 this(true, checker); 073 } 074 075 /** 076 * Simple constructor with default settings. 077 * The convergence check is set to a {@link SimpleVectorValueChecker} 078 * with default tolerances. 079 * 080 * @param useLU If {@code true}, the normal equations will be solved 081 * using LU decomposition, otherwise they will be solved using QR 082 * decomposition. 083 * @deprecated See {@link SimpleVectorValueChecker#SimpleVectorValueChecker()} 084 */ 085 @Deprecated 086 public GaussNewtonOptimizer(final boolean useLU) { 087 this(useLU, new SimpleVectorValueChecker()); 088 } 089 090 /** 091 * @param useLU If {@code true}, the normal equations will be solved 092 * using LU decomposition, otherwise they will be solved using QR 093 * decomposition. 094 * @param checker Convergence checker. 095 */ 096 public GaussNewtonOptimizer(final boolean useLU, 097 ConvergenceChecker<PointVectorValuePair> checker) { 098 super(checker); 099 this.useLU = useLU; 100 } 101 102 /** {@inheritDoc} */ 103 @Override 104 public PointVectorValuePair doOptimize() { 105 final ConvergenceChecker<PointVectorValuePair> checker 106 = getConvergenceChecker(); 107 108 // Computation will be useless without a checker (see "for-loop"). 109 if (checker == null) { 110 throw new NullArgumentException(); 111 } 112 113 final double[] targetValues = getTarget(); 114 final int nR = targetValues.length; // Number of observed data. 115 116 final RealMatrix weightMatrix = getWeight(); 117 // Diagonal of the weight matrix. 118 final double[] residualsWeights = new double[nR]; 119 for (int i = 0; i < nR; i++) { 120 residualsWeights[i] = weightMatrix.getEntry(i, i); 121 } 122 123 final double[] currentPoint = getStartPoint(); 124 final int nC = currentPoint.length; 125 126 // iterate until convergence is reached 127 PointVectorValuePair current = null; 128 int iter = 0; 129 for (boolean converged = false; !converged;) { 130 ++iter; 131 132 // evaluate the objective function and its jacobian 133 PointVectorValuePair previous = current; 134 // Value of the objective function at "currentPoint". 135 final double[] currentObjective = computeObjectiveValue(currentPoint); 136 final double[] currentResiduals = computeResiduals(currentObjective); 137 final RealMatrix weightedJacobian = computeWeightedJacobian(currentPoint); 138 current = new PointVectorValuePair(currentPoint, currentObjective); 139 140 // build the linear problem 141 final double[] b = new double[nC]; 142 final double[][] a = new double[nC][nC]; 143 for (int i = 0; i < nR; ++i) { 144 145 final double[] grad = weightedJacobian.getRow(i); 146 final double weight = residualsWeights[i]; 147 final double residual = currentResiduals[i]; 148 149 // compute the normal equation 150 final double wr = weight * residual; 151 for (int j = 0; j < nC; ++j) { 152 b[j] += wr * grad[j]; 153 } 154 155 // build the contribution matrix for measurement i 156 for (int k = 0; k < nC; ++k) { 157 double[] ak = a[k]; 158 double wgk = weight * grad[k]; 159 for (int l = 0; l < nC; ++l) { 160 ak[l] += wgk * grad[l]; 161 } 162 } 163 } 164 165 try { 166 // solve the linearized least squares problem 167 RealMatrix mA = new BlockRealMatrix(a); 168 DecompositionSolver solver = useLU ? 169 new LUDecomposition(mA).getSolver() : 170 new QRDecomposition(mA).getSolver(); 171 final double[] dX = solver.solve(new ArrayRealVector(b, false)).toArray(); 172 // update the estimated parameters 173 for (int i = 0; i < nC; ++i) { 174 currentPoint[i] += dX[i]; 175 } 176 } catch (SingularMatrixException e) { 177 throw new ConvergenceException(LocalizedFormats.UNABLE_TO_SOLVE_SINGULAR_PROBLEM); 178 } 179 180 // Check convergence. 181 if (previous != null) { 182 converged = checker.converged(iter, previous, current); 183 if (converged) { 184 cost = computeCost(currentResiduals); 185 // Update (deprecated) "point" field. 186 point = current.getPoint(); 187 return current; 188 } 189 } 190 } 191 // Must never happen. 192 throw new MathInternalError(); 193 } 194}