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.optimization.general; |
| 19 | |
| 20 | import org.apache.commons.math.FunctionEvaluationException; |
| 21 | import org.apache.commons.math.MaxEvaluationsExceededException; |
| 22 | import org.apache.commons.math.MaxIterationsExceededException; |
| 23 | import org.apache.commons.math.analysis.DifferentiableMultivariateVectorialFunction; |
| 24 | import org.apache.commons.math.analysis.MultivariateMatrixFunction; |
| 25 | import org.apache.commons.math.exception.util.LocalizedFormats; |
| 26 | import org.apache.commons.math.linear.InvalidMatrixException; |
| 27 | import org.apache.commons.math.linear.LUDecompositionImpl; |
| 28 | import org.apache.commons.math.linear.MatrixUtils; |
| 29 | import org.apache.commons.math.linear.RealMatrix; |
| 30 | import org.apache.commons.math.optimization.OptimizationException; |
| 31 | import org.apache.commons.math.optimization.SimpleVectorialValueChecker; |
| 32 | import org.apache.commons.math.optimization.VectorialConvergenceChecker; |
| 33 | import org.apache.commons.math.optimization.DifferentiableMultivariateVectorialOptimizer; |
| 34 | import org.apache.commons.math.optimization.VectorialPointValuePair; |
| 35 | import org.apache.commons.math.util.FastMath; |
| 36 | |
| 37 | /** |
| 38 | * Base class for implementing least squares optimizers. |
| 39 | * <p>This base class handles the boilerplate methods associated to thresholds |
| 40 | * settings, jacobian and error estimation.</p> |
| 41 | * @version $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 févr. 2011) $ |
| 42 | * @since 1.2 |
| 43 | * |
| 44 | */ |
| 45 | public abstract class AbstractLeastSquaresOptimizer implements DifferentiableMultivariateVectorialOptimizer { |
| 46 | |
| 47 | /** Default maximal number of iterations allowed. */ |
| 48 | public static final int DEFAULT_MAX_ITERATIONS = 100; |
| 49 | |
| 50 | /** Convergence checker. */ |
| 51 | protected VectorialConvergenceChecker checker; |
| 52 | |
| 53 | /** |
| 54 | * Jacobian matrix. |
| 55 | * <p>This matrix is in canonical form just after the calls to |
| 56 | * {@link #updateJacobian()}, but may be modified by the solver |
| 57 | * in the derived class (the {@link LevenbergMarquardtOptimizer |
| 58 | * Levenberg-Marquardt optimizer} does this).</p> |
| 59 | */ |
| 60 | protected double[][] jacobian; |
| 61 | |
| 62 | /** Number of columns of the jacobian matrix. */ |
| 63 | protected int cols; |
| 64 | |
| 65 | /** Number of rows of the jacobian matrix. */ |
| 66 | protected int rows; |
| 67 | |
| 68 | /** |
| 69 | * Target value for the objective functions at optimum. |
| 70 | * @since 2.1 |
| 71 | */ |
| 72 | protected double[] targetValues; |
| 73 | |
| 74 | /** |
| 75 | * Weight for the least squares cost computation. |
| 76 | * @since 2.1 |
| 77 | */ |
| 78 | protected double[] residualsWeights; |
| 79 | |
| 80 | /** Current point. */ |
| 81 | protected double[] point; |
| 82 | |
| 83 | /** Current objective function value. */ |
| 84 | protected double[] objective; |
| 85 | |
| 86 | /** Current residuals. */ |
| 87 | protected double[] residuals; |
| 88 | |
| 89 | /** Weighted Jacobian */ |
| 90 | protected double[][] wjacobian; |
| 91 | |
| 92 | /** Weighted residuals */ |
| 93 | protected double[] wresiduals; |
| 94 | |
| 95 | /** Cost value (square root of the sum of the residuals). */ |
| 96 | protected double cost; |
| 97 | |
| 98 | /** Maximal number of iterations allowed. */ |
| 99 | private int maxIterations; |
| 100 | |
| 101 | /** Number of iterations already performed. */ |
| 102 | private int iterations; |
| 103 | |
| 104 | /** Maximal number of evaluations allowed. */ |
| 105 | private int maxEvaluations; |
| 106 | |
| 107 | /** Number of evaluations already performed. */ |
| 108 | private int objectiveEvaluations; |
| 109 | |
| 110 | /** Number of jacobian evaluations. */ |
| 111 | private int jacobianEvaluations; |
| 112 | |
| 113 | /** Objective function. */ |
| 114 | private DifferentiableMultivariateVectorialFunction function; |
| 115 | |
| 116 | /** Objective function derivatives. */ |
| 117 | private MultivariateMatrixFunction jF; |
| 118 | |
| 119 | /** Simple constructor with default settings. |
| 120 | * <p>The convergence check is set to a {@link SimpleVectorialValueChecker} |
| 121 | * and the maximal number of evaluation is set to its default value.</p> |
| 122 | */ |
| 123 | protected AbstractLeastSquaresOptimizer() { |
| 124 | setConvergenceChecker(new SimpleVectorialValueChecker()); |
| 125 | setMaxIterations(DEFAULT_MAX_ITERATIONS); |
| 126 | setMaxEvaluations(Integer.MAX_VALUE); |
| 127 | } |
| 128 | |
| 129 | /** {@inheritDoc} */ |
| 130 | public void setMaxIterations(int maxIterations) { |
| 131 | this.maxIterations = maxIterations; |
| 132 | } |
| 133 | |
| 134 | /** {@inheritDoc} */ |
| 135 | public int getMaxIterations() { |
| 136 | return maxIterations; |
| 137 | } |
| 138 | |
| 139 | /** {@inheritDoc} */ |
| 140 | public int getIterations() { |
| 141 | return iterations; |
| 142 | } |
| 143 | |
| 144 | /** {@inheritDoc} */ |
| 145 | public void setMaxEvaluations(int maxEvaluations) { |
| 146 | this.maxEvaluations = maxEvaluations; |
| 147 | } |
| 148 | |
| 149 | /** {@inheritDoc} */ |
| 150 | public int getMaxEvaluations() { |
| 151 | return maxEvaluations; |
| 152 | } |
| 153 | |
| 154 | /** {@inheritDoc} */ |
| 155 | public int getEvaluations() { |
| 156 | return objectiveEvaluations; |
| 157 | } |
| 158 | |
| 159 | /** {@inheritDoc} */ |
| 160 | public int getJacobianEvaluations() { |
| 161 | return jacobianEvaluations; |
| 162 | } |
| 163 | |
| 164 | /** {@inheritDoc} */ |
| 165 | public void setConvergenceChecker(VectorialConvergenceChecker convergenceChecker) { |
| 166 | this.checker = convergenceChecker; |
| 167 | } |
| 168 | |
| 169 | /** {@inheritDoc} */ |
| 170 | public VectorialConvergenceChecker getConvergenceChecker() { |
| 171 | return checker; |
| 172 | } |
| 173 | |
| 174 | /** Increment the iterations counter by 1. |
| 175 | * @exception OptimizationException if the maximal number |
| 176 | * of iterations is exceeded |
| 177 | */ |
| 178 | protected void incrementIterationsCounter() |
| 179 | throws OptimizationException { |
| 180 | if (++iterations > maxIterations) { |
| 181 | throw new OptimizationException(new MaxIterationsExceededException(maxIterations)); |
| 182 | } |
| 183 | } |
| 184 | |
| 185 | /** |
| 186 | * Update the jacobian matrix. |
| 187 | * @exception FunctionEvaluationException if the function jacobian |
| 188 | * cannot be evaluated or its dimension doesn't match problem dimension |
| 189 | */ |
| 190 | protected void updateJacobian() throws FunctionEvaluationException { |
| 191 | ++jacobianEvaluations; |
| 192 | jacobian = jF.value(point); |
| 193 | if (jacobian.length != rows) { |
| 194 | throw new FunctionEvaluationException(point, LocalizedFormats.DIMENSIONS_MISMATCH_SIMPLE, |
| 195 | jacobian.length, rows); |
| 196 | } |
| 197 | for (int i = 0; i < rows; i++) { |
| 198 | final double[] ji = jacobian[i]; |
| 199 | double wi = FastMath.sqrt(residualsWeights[i]); |
| 200 | for (int j = 0; j < cols; ++j) { |
| 201 | ji[j] *= -1.0; |
| 202 | wjacobian[i][j] = ji[j]*wi; |
| 203 | } |
| 204 | } |
| 205 | } |
| 206 | |
| 207 | /** |
| 208 | * Update the residuals array and cost function value. |
| 209 | * @exception FunctionEvaluationException if the function cannot be evaluated |
| 210 | * or its dimension doesn't match problem dimension or maximal number of |
| 211 | * of evaluations is exceeded |
| 212 | */ |
| 213 | protected void updateResidualsAndCost() |
| 214 | throws FunctionEvaluationException { |
| 215 | |
| 216 | if (++objectiveEvaluations > maxEvaluations) { |
| 217 | throw new FunctionEvaluationException(new MaxEvaluationsExceededException(maxEvaluations), |
| 218 | point); |
| 219 | } |
| 220 | objective = function.value(point); |
| 221 | if (objective.length != rows) { |
| 222 | throw new FunctionEvaluationException(point, LocalizedFormats.DIMENSIONS_MISMATCH_SIMPLE, |
| 223 | objective.length, rows); |
| 224 | } |
| 225 | cost = 0; |
| 226 | int index = 0; |
| 227 | for (int i = 0; i < rows; i++) { |
| 228 | final double residual = targetValues[i] - objective[i]; |
| 229 | residuals[i] = residual; |
| 230 | wresiduals[i]= residual*FastMath.sqrt(residualsWeights[i]); |
| 231 | cost += residualsWeights[i] * residual * residual; |
| 232 | index += cols; |
| 233 | } |
| 234 | cost = FastMath.sqrt(cost); |
| 235 | |
| 236 | } |
| 237 | |
| 238 | /** |
| 239 | * Get the Root Mean Square value. |
| 240 | * Get the Root Mean Square value, i.e. the root of the arithmetic |
| 241 | * mean of the square of all weighted residuals. This is related to the |
| 242 | * criterion that is minimized by the optimizer as follows: if |
| 243 | * <em>c</em> if the criterion, and <em>n</em> is the number of |
| 244 | * measurements, then the RMS is <em>sqrt (c/n)</em>. |
| 245 | * |
| 246 | * @return RMS value |
| 247 | */ |
| 248 | public double getRMS() { |
| 249 | return FastMath.sqrt(getChiSquare() / rows); |
| 250 | } |
| 251 | |
| 252 | /** |
| 253 | * Get a Chi-Square-like value assuming the N residuals follow N |
| 254 | * distinct normal distributions centered on 0 and whose variances are |
| 255 | * the reciprocal of the weights. |
| 256 | * @return chi-square value |
| 257 | */ |
| 258 | public double getChiSquare() { |
| 259 | return cost*cost; |
| 260 | } |
| 261 | |
| 262 | /** |
| 263 | * Get the covariance matrix of optimized parameters. |
| 264 | * @return covariance matrix |
| 265 | * @exception FunctionEvaluationException if the function jacobian cannot |
| 266 | * be evaluated |
| 267 | * @exception OptimizationException if the covariance matrix |
| 268 | * cannot be computed (singular problem) |
| 269 | */ |
| 270 | public double[][] getCovariances() |
| 271 | throws FunctionEvaluationException, OptimizationException { |
| 272 | |
| 273 | // set up the jacobian |
| 274 | updateJacobian(); |
| 275 | |
| 276 | // compute transpose(J).J, avoiding building big intermediate matrices |
| 277 | double[][] jTj = new double[cols][cols]; |
| 278 | for (int i = 0; i < cols; ++i) { |
| 279 | for (int j = i; j < cols; ++j) { |
| 280 | double sum = 0; |
| 281 | for (int k = 0; k < rows; ++k) { |
| 282 | sum += wjacobian[k][i] * wjacobian[k][j]; |
| 283 | } |
| 284 | jTj[i][j] = sum; |
| 285 | jTj[j][i] = sum; |
| 286 | } |
| 287 | } |
| 288 | |
| 289 | try { |
| 290 | // compute the covariance matrix |
| 291 | RealMatrix inverse = |
| 292 | new LUDecompositionImpl(MatrixUtils.createRealMatrix(jTj)).getSolver().getInverse(); |
| 293 | return inverse.getData(); |
| 294 | } catch (InvalidMatrixException ime) { |
| 295 | throw new OptimizationException(LocalizedFormats.UNABLE_TO_COMPUTE_COVARIANCE_SINGULAR_PROBLEM); |
| 296 | } |
| 297 | |
| 298 | } |
| 299 | |
| 300 | /** |
| 301 | * Guess the errors in optimized parameters. |
| 302 | * <p>Guessing is covariance-based, it only gives rough order of magnitude.</p> |
| 303 | * @return errors in optimized parameters |
| 304 | * @exception FunctionEvaluationException if the function jacobian cannot b evaluated |
| 305 | * @exception OptimizationException if the covariances matrix cannot be computed |
| 306 | * or the number of degrees of freedom is not positive (number of measurements |
| 307 | * lesser or equal to number of parameters) |
| 308 | */ |
| 309 | public double[] guessParametersErrors() |
| 310 | throws FunctionEvaluationException, OptimizationException { |
| 311 | if (rows <= cols) { |
| 312 | throw new OptimizationException( |
| 313 | LocalizedFormats.NO_DEGREES_OF_FREEDOM, |
| 314 | rows, cols); |
| 315 | } |
| 316 | double[] errors = new double[cols]; |
| 317 | final double c = FastMath.sqrt(getChiSquare() / (rows - cols)); |
| 318 | double[][] covar = getCovariances(); |
| 319 | for (int i = 0; i < errors.length; ++i) { |
| 320 | errors[i] = FastMath.sqrt(covar[i][i]) * c; |
| 321 | } |
| 322 | return errors; |
| 323 | } |
| 324 | |
| 325 | /** {@inheritDoc} */ |
| 326 | public VectorialPointValuePair optimize(final DifferentiableMultivariateVectorialFunction f, |
| 327 | final double[] target, final double[] weights, |
| 328 | final double[] startPoint) |
| 329 | throws FunctionEvaluationException, OptimizationException, IllegalArgumentException { |
| 330 | |
| 331 | if (target.length != weights.length) { |
| 332 | throw new OptimizationException(LocalizedFormats.DIMENSIONS_MISMATCH_SIMPLE, |
| 333 | target.length, weights.length); |
| 334 | } |
| 335 | |
| 336 | // reset counters |
| 337 | iterations = 0; |
| 338 | objectiveEvaluations = 0; |
| 339 | jacobianEvaluations = 0; |
| 340 | |
| 341 | // store least squares problem characteristics |
| 342 | function = f; |
| 343 | jF = f.jacobian(); |
| 344 | targetValues = target.clone(); |
| 345 | residualsWeights = weights.clone(); |
| 346 | this.point = startPoint.clone(); |
| 347 | this.residuals = new double[target.length]; |
| 348 | |
| 349 | // arrays shared with the other private methods |
| 350 | rows = target.length; |
| 351 | cols = point.length; |
| 352 | jacobian = new double[rows][cols]; |
| 353 | |
| 354 | wjacobian = new double[rows][cols]; |
| 355 | wresiduals = new double[rows]; |
| 356 | |
| 357 | cost = Double.POSITIVE_INFINITY; |
| 358 | |
| 359 | return doOptimize(); |
| 360 | |
| 361 | } |
| 362 | |
| 363 | /** Perform the bulk of optimization algorithm. |
| 364 | * @return the point/value pair giving the optimal value for objective function |
| 365 | * @exception FunctionEvaluationException if the objective function throws one during |
| 366 | * the search |
| 367 | * @exception OptimizationException if the algorithm failed to converge |
| 368 | * @exception IllegalArgumentException if the start point dimension is wrong |
| 369 | */ |
| 370 | protected abstract VectorialPointValuePair doOptimize() |
| 371 | throws FunctionEvaluationException, OptimizationException, IllegalArgumentException; |
| 372 | |
| 373 | |
| 374 | } |