1 /* 2 * Licensed to the Apache Software Foundation (ASF) under one or more 3 * contributor license agreements. See the NOTICE file distributed with 4 * this work for additional information regarding copyright ownership. 5 * The ASF licenses this file to You under the Apache License, Version 2.0 6 * (the "License"); you may not use this file except in compliance with 7 * the License. You may obtain a copy of the License at 8 * 9 * http://www.apache.org/licenses/LICENSE-2.0 10 * 11 * Unless required by applicable law or agreed to in writing, software 12 * distributed under the License is distributed on an "AS IS" BASIS, 13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14 * See the License for the specific language governing permissions and 15 * limitations under the License. 16 */ 17 18 package org.apache.commons.math3.optimization.general; 19 20 import org.apache.commons.math3.exception.ConvergenceException; 21 import org.apache.commons.math3.exception.NullArgumentException; 22 import org.apache.commons.math3.exception.MathInternalError; 23 import org.apache.commons.math3.exception.util.LocalizedFormats; 24 import org.apache.commons.math3.linear.ArrayRealVector; 25 import org.apache.commons.math3.linear.BlockRealMatrix; 26 import org.apache.commons.math3.linear.DecompositionSolver; 27 import org.apache.commons.math3.linear.LUDecomposition; 28 import org.apache.commons.math3.linear.QRDecomposition; 29 import org.apache.commons.math3.linear.RealMatrix; 30 import org.apache.commons.math3.linear.SingularMatrixException; 31 import org.apache.commons.math3.optimization.ConvergenceChecker; 32 import org.apache.commons.math3.optimization.SimpleVectorValueChecker; 33 import org.apache.commons.math3.optimization.PointVectorValuePair; 34 35 /** 36 * Gauss-Newton least-squares solver. 37 * <p> 38 * This class solve a least-square problem by solving the normal equations 39 * of the linearized problem at each iteration. Either LU decomposition or 40 * QR decomposition can be used to solve the normal equations. LU decomposition 41 * is faster but QR decomposition is more robust for difficult problems. 42 * </p> 43 * 44 * @deprecated As of 3.1 (to be removed in 4.0). 45 * @since 2.0 46 * 47 */ 48 @Deprecated 49 public class GaussNewtonOptimizer extends AbstractLeastSquaresOptimizer { 50 /** Indicator for using LU decomposition. */ 51 private final boolean useLU; 52 53 /** 54 * Simple constructor with default settings. 55 * The normal equations will be solved using LU decomposition and the 56 * convergence check is set to a {@link SimpleVectorValueChecker} 57 * with default tolerances. 58 * @deprecated See {@link SimpleVectorValueChecker#SimpleVectorValueChecker()} 59 */ 60 @Deprecated GaussNewtonOptimizer()61 public GaussNewtonOptimizer() { 62 this(true); 63 } 64 65 /** 66 * Simple constructor with default settings. 67 * The normal equations will be solved using LU decomposition. 68 * 69 * @param checker Convergence checker. 70 */ GaussNewtonOptimizer(ConvergenceChecker<PointVectorValuePair> checker)71 public GaussNewtonOptimizer(ConvergenceChecker<PointVectorValuePair> checker) { 72 this(true, checker); 73 } 74 75 /** 76 * Simple constructor with default settings. 77 * The convergence check is set to a {@link SimpleVectorValueChecker} 78 * with default tolerances. 79 * 80 * @param useLU If {@code true}, the normal equations will be solved 81 * using LU decomposition, otherwise they will be solved using QR 82 * decomposition. 83 * @deprecated See {@link SimpleVectorValueChecker#SimpleVectorValueChecker()} 84 */ 85 @Deprecated GaussNewtonOptimizer(final boolean useLU)86 public GaussNewtonOptimizer(final boolean useLU) { 87 this(useLU, new SimpleVectorValueChecker()); 88 } 89 90 /** 91 * @param useLU If {@code true}, the normal equations will be solved 92 * using LU decomposition, otherwise they will be solved using QR 93 * decomposition. 94 * @param checker Convergence checker. 95 */ GaussNewtonOptimizer(final boolean useLU, ConvergenceChecker<PointVectorValuePair> checker)96 public GaussNewtonOptimizer(final boolean useLU, 97 ConvergenceChecker<PointVectorValuePair> checker) { 98 super(checker); 99 this.useLU = useLU; 100 } 101 102 /** {@inheritDoc} */ 103 @Override doOptimize()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 } 195