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 }