Raymond | dee0849 | 2015-04-02 10:43:13 -0700 | [diff] [blame] | 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.math.estimation; |
| 19 | |
| 20 | import java.io.Serializable; |
| 21 | |
| 22 | import org.apache.commons.math.exception.util.LocalizedFormats; |
| 23 | import org.apache.commons.math.linear.InvalidMatrixException; |
| 24 | import org.apache.commons.math.linear.LUDecompositionImpl; |
| 25 | import org.apache.commons.math.linear.MatrixUtils; |
| 26 | import org.apache.commons.math.linear.RealMatrix; |
| 27 | import org.apache.commons.math.linear.RealVector; |
| 28 | import org.apache.commons.math.linear.ArrayRealVector; |
| 29 | import org.apache.commons.math.util.FastMath; |
| 30 | |
| 31 | /** |
| 32 | * This class implements a solver for estimation problems. |
| 33 | * |
| 34 | * <p>This class solves estimation problems using a weighted least |
| 35 | * squares criterion on the measurement residuals. It uses a |
| 36 | * Gauss-Newton algorithm.</p> |
| 37 | * |
| 38 | * @version $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $ |
| 39 | * @since 1.2 |
| 40 | * @deprecated as of 2.0, everything in package org.apache.commons.math.estimation has |
| 41 | * been deprecated and replaced by package org.apache.commons.math.optimization.general |
| 42 | * |
| 43 | */ |
| 44 | @Deprecated |
| 45 | public class GaussNewtonEstimator extends AbstractEstimator implements Serializable { |
| 46 | |
| 47 | /** Serializable version identifier */ |
| 48 | private static final long serialVersionUID = 5485001826076289109L; |
| 49 | |
| 50 | /** Default threshold for cost steady state detection. */ |
| 51 | private static final double DEFAULT_STEADY_STATE_THRESHOLD = 1.0e-6; |
| 52 | |
| 53 | /** Default threshold for cost convergence. */ |
| 54 | private static final double DEFAULT_CONVERGENCE = 1.0e-6; |
| 55 | |
| 56 | /** Threshold for cost steady state detection. */ |
| 57 | private double steadyStateThreshold; |
| 58 | |
| 59 | /** Threshold for cost convergence. */ |
| 60 | private double convergence; |
| 61 | |
| 62 | /** Simple constructor with default settings. |
| 63 | * <p> |
| 64 | * The estimator is built with default values for all settings. |
| 65 | * </p> |
| 66 | * @see #DEFAULT_STEADY_STATE_THRESHOLD |
| 67 | * @see #DEFAULT_CONVERGENCE |
| 68 | * @see AbstractEstimator#DEFAULT_MAX_COST_EVALUATIONS |
| 69 | */ |
| 70 | public GaussNewtonEstimator() { |
| 71 | this.steadyStateThreshold = DEFAULT_STEADY_STATE_THRESHOLD; |
| 72 | this.convergence = DEFAULT_CONVERGENCE; |
| 73 | } |
| 74 | |
| 75 | /** |
| 76 | * Simple constructor. |
| 77 | * |
| 78 | * <p>This constructor builds an estimator and stores its convergence |
| 79 | * characteristics.</p> |
| 80 | * |
| 81 | * <p>An estimator is considered to have converged whenever either |
| 82 | * the criterion goes below a physical threshold under which |
| 83 | * improvements are considered useless or when the algorithm is |
| 84 | * unable to improve it (even if it is still high). The first |
| 85 | * condition that is met stops the iterations.</p> |
| 86 | * |
| 87 | * <p>The fact an estimator has converged does not mean that the |
| 88 | * model accurately fits the measurements. It only means no better |
| 89 | * solution can be found, it does not mean this one is good. Such an |
| 90 | * analysis is left to the caller.</p> |
| 91 | * |
| 92 | * <p>If neither conditions are fulfilled before a given number of |
| 93 | * iterations, the algorithm is considered to have failed and an |
| 94 | * {@link EstimationException} is thrown.</p> |
| 95 | * |
| 96 | * @param maxCostEval maximal number of cost evaluations allowed |
| 97 | * @param convergence criterion threshold below which we do not need |
| 98 | * to improve the criterion anymore |
| 99 | * @param steadyStateThreshold steady state detection threshold, the |
| 100 | * problem has converged has reached a steady state if |
| 101 | * <code>FastMath.abs(J<sub>n</sub> - J<sub>n-1</sub>) < |
| 102 | * J<sub>n</sub> × convergence</code>, where <code>J<sub>n</sub></code> |
| 103 | * and <code>J<sub>n-1</sub></code> are the current and preceding criterion |
| 104 | * values (square sum of the weighted residuals of considered measurements). |
| 105 | */ |
| 106 | public GaussNewtonEstimator(final int maxCostEval, final double convergence, |
| 107 | final double steadyStateThreshold) { |
| 108 | setMaxCostEval(maxCostEval); |
| 109 | this.steadyStateThreshold = steadyStateThreshold; |
| 110 | this.convergence = convergence; |
| 111 | } |
| 112 | |
| 113 | /** |
| 114 | * Set the convergence criterion threshold. |
| 115 | * @param convergence criterion threshold below which we do not need |
| 116 | * to improve the criterion anymore |
| 117 | */ |
| 118 | public void setConvergence(final double convergence) { |
| 119 | this.convergence = convergence; |
| 120 | } |
| 121 | |
| 122 | /** |
| 123 | * Set the steady state detection threshold. |
| 124 | * <p> |
| 125 | * The problem has converged has reached a steady state if |
| 126 | * <code>FastMath.abs(J<sub>n</sub> - J<sub>n-1</sub>) < |
| 127 | * J<sub>n</sub> × convergence</code>, where <code>J<sub>n</sub></code> |
| 128 | * and <code>J<sub>n-1</sub></code> are the current and preceding criterion |
| 129 | * values (square sum of the weighted residuals of considered measurements). |
| 130 | * </p> |
| 131 | * @param steadyStateThreshold steady state detection threshold |
| 132 | */ |
| 133 | public void setSteadyStateThreshold(final double steadyStateThreshold) { |
| 134 | this.steadyStateThreshold = steadyStateThreshold; |
| 135 | } |
| 136 | |
| 137 | /** |
| 138 | * Solve an estimation problem using a least squares criterion. |
| 139 | * |
| 140 | * <p>This method set the unbound parameters of the given problem |
| 141 | * starting from their current values through several iterations. At |
| 142 | * each step, the unbound parameters are changed in order to |
| 143 | * minimize a weighted least square criterion based on the |
| 144 | * measurements of the problem.</p> |
| 145 | * |
| 146 | * <p>The iterations are stopped either when the criterion goes |
| 147 | * below a physical threshold under which improvement are considered |
| 148 | * useless or when the algorithm is unable to improve it (even if it |
| 149 | * is still high). The first condition that is met stops the |
| 150 | * iterations. If the convergence it not reached before the maximum |
| 151 | * number of iterations, an {@link EstimationException} is |
| 152 | * thrown.</p> |
| 153 | * |
| 154 | * @param problem estimation problem to solve |
| 155 | * @exception EstimationException if the problem cannot be solved |
| 156 | * |
| 157 | * @see EstimationProblem |
| 158 | * |
| 159 | */ |
| 160 | @Override |
| 161 | public void estimate(EstimationProblem problem) |
| 162 | throws EstimationException { |
| 163 | |
| 164 | initializeEstimate(problem); |
| 165 | |
| 166 | // work matrices |
| 167 | double[] grad = new double[parameters.length]; |
| 168 | ArrayRealVector bDecrement = new ArrayRealVector(parameters.length); |
| 169 | double[] bDecrementData = bDecrement.getDataRef(); |
| 170 | RealMatrix wGradGradT = MatrixUtils.createRealMatrix(parameters.length, parameters.length); |
| 171 | |
| 172 | // iterate until convergence is reached |
| 173 | double previous = Double.POSITIVE_INFINITY; |
| 174 | do { |
| 175 | |
| 176 | // build the linear problem |
| 177 | incrementJacobianEvaluationsCounter(); |
| 178 | RealVector b = new ArrayRealVector(parameters.length); |
| 179 | RealMatrix a = MatrixUtils.createRealMatrix(parameters.length, parameters.length); |
| 180 | for (int i = 0; i < measurements.length; ++i) { |
| 181 | if (! measurements [i].isIgnored()) { |
| 182 | |
| 183 | double weight = measurements[i].getWeight(); |
| 184 | double residual = measurements[i].getResidual(); |
| 185 | |
| 186 | // compute the normal equation |
| 187 | for (int j = 0; j < parameters.length; ++j) { |
| 188 | grad[j] = measurements[i].getPartial(parameters[j]); |
| 189 | bDecrementData[j] = weight * residual * grad[j]; |
| 190 | } |
| 191 | |
| 192 | // build the contribution matrix for measurement i |
| 193 | for (int k = 0; k < parameters.length; ++k) { |
| 194 | double gk = grad[k]; |
| 195 | for (int l = 0; l < parameters.length; ++l) { |
| 196 | wGradGradT.setEntry(k, l, weight * gk * grad[l]); |
| 197 | } |
| 198 | } |
| 199 | |
| 200 | // update the matrices |
| 201 | a = a.add(wGradGradT); |
| 202 | b = b.add(bDecrement); |
| 203 | |
| 204 | } |
| 205 | } |
| 206 | |
| 207 | try { |
| 208 | |
| 209 | // solve the linearized least squares problem |
| 210 | RealVector dX = new LUDecompositionImpl(a).getSolver().solve(b); |
| 211 | |
| 212 | // update the estimated parameters |
| 213 | for (int i = 0; i < parameters.length; ++i) { |
| 214 | parameters[i].setEstimate(parameters[i].getEstimate() + dX.getEntry(i)); |
| 215 | } |
| 216 | |
| 217 | } catch(InvalidMatrixException e) { |
| 218 | throw new EstimationException(LocalizedFormats.UNABLE_TO_SOLVE_SINGULAR_PROBLEM); |
| 219 | } |
| 220 | |
| 221 | |
| 222 | previous = cost; |
| 223 | updateResidualsAndCost(); |
| 224 | |
| 225 | } while ((getCostEvaluations() < 2) || |
| 226 | (FastMath.abs(previous - cost) > (cost * steadyStateThreshold) && |
| 227 | (FastMath.abs(cost) > convergence))); |
| 228 | |
| 229 | } |
| 230 | |
| 231 | } |