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.math.optimization.general; 019 020 import java.awt.geom.Point2D; 021 import java.io.Serializable; 022 import java.util.ArrayList; 023 import java.util.Arrays; 024 import java.util.List; 025 026 import junit.framework.Test; 027 import junit.framework.TestCase; 028 import junit.framework.TestSuite; 029 030 import org.apache.commons.math.FunctionEvaluationException; 031 import org.apache.commons.math.analysis.DifferentiableMultivariateVectorialFunction; 032 import org.apache.commons.math.analysis.MultivariateMatrixFunction; 033 import org.apache.commons.math.linear.BlockRealMatrix; 034 import org.apache.commons.math.linear.RealMatrix; 035 import org.apache.commons.math.optimization.OptimizationException; 036 import org.apache.commons.math.optimization.SimpleVectorialValueChecker; 037 import org.apache.commons.math.optimization.VectorialPointValuePair; 038 039 /** 040 * <p>Some of the unit tests are re-implementations of the MINPACK <a 041 * href="http://www.netlib.org/minpack/ex/file17">file17</a> and <a 042 * href="http://www.netlib.org/minpack/ex/file22">file22</a> test files. 043 * The redistribution policy for MINPACK is available <a 044 * href="http://www.netlib.org/minpack/disclaimer">here</a>, for 045 * convenience, it is reproduced below.</p> 046 047 * <table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0"> 048 * <tr><td> 049 * Minpack Copyright Notice (1999) University of Chicago. 050 * All rights reserved 051 * </td></tr> 052 * <tr><td> 053 * Redistribution and use in source and binary forms, with or without 054 * modification, are permitted provided that the following conditions 055 * are met: 056 * <ol> 057 * <li>Redistributions of source code must retain the above copyright 058 * notice, this list of conditions and the following disclaimer.</li> 059 * <li>Redistributions in binary form must reproduce the above 060 * copyright notice, this list of conditions and the following 061 * disclaimer in the documentation and/or other materials provided 062 * with the distribution.</li> 063 * <li>The end-user documentation included with the redistribution, if any, 064 * must include the following acknowledgment: 065 * <code>This product includes software developed by the University of 066 * Chicago, as Operator of Argonne National Laboratory.</code> 067 * Alternately, this acknowledgment may appear in the software itself, 068 * if and wherever such third-party acknowledgments normally appear.</li> 069 * <li><strong>WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS" 070 * WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE 071 * UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND 072 * THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR 073 * IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES 074 * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE 075 * OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY 076 * OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR 077 * USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF 078 * THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4) 079 * DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION 080 * UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL 081 * BE CORRECTED.</strong></li> 082 * <li><strong>LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT 083 * HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF 084 * ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT, 085 * INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF 086 * ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF 087 * PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER 088 * SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT 089 * (INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE, 090 * EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE 091 * POSSIBILITY OF SUCH LOSS OR DAMAGES.</strong></li> 092 * <ol></td></tr> 093 * </table> 094 095 * @author Argonne National Laboratory. MINPACK project. March 1980 (original fortran minpack tests) 096 * @author Burton S. Garbow (original fortran minpack tests) 097 * @author Kenneth E. Hillstrom (original fortran minpack tests) 098 * @author Jorge J. More (original fortran minpack tests) 099 * @author Luc Maisonobe (non-minpack tests and minpack tests Java translation) 100 */ 101 public class LevenbergMarquardtOptimizerTest 102 extends TestCase { 103 104 public LevenbergMarquardtOptimizerTest(String name) { 105 super(name); 106 } 107 108 public void testTrivial() throws FunctionEvaluationException, OptimizationException { 109 LinearProblem problem = 110 new LinearProblem(new double[][] { { 2 } }, new double[] { 3 }); 111 LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer(); 112 VectorialPointValuePair optimum = 113 optimizer.optimize(problem, problem.target, new double[] { 1 }, new double[] { 0 }); 114 assertEquals(0, optimizer.getRMS(), 1.0e-10); 115 try { 116 optimizer.guessParametersErrors(); 117 fail("an exception should have been thrown"); 118 } catch (OptimizationException ee) { 119 // expected behavior 120 } catch (Exception e) { 121 fail("wrong exception caught"); 122 } 123 assertEquals(1.5, optimum.getPoint()[0], 1.0e-10); 124 assertEquals(3.0, optimum.getValue()[0], 1.0e-10); 125 } 126 127 public void testQRColumnsPermutation() throws FunctionEvaluationException, OptimizationException { 128 129 LinearProblem problem = 130 new LinearProblem(new double[][] { { 1.0, -1.0 }, { 0.0, 2.0 }, { 1.0, -2.0 } }, 131 new double[] { 4.0, 6.0, 1.0 }); 132 133 LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer(); 134 VectorialPointValuePair optimum = 135 optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1 }, new double[] { 0, 0 }); 136 assertEquals(0, optimizer.getRMS(), 1.0e-10); 137 assertEquals(7.0, optimum.getPoint()[0], 1.0e-10); 138 assertEquals(3.0, optimum.getPoint()[1], 1.0e-10); 139 assertEquals(4.0, optimum.getValue()[0], 1.0e-10); 140 assertEquals(6.0, optimum.getValue()[1], 1.0e-10); 141 assertEquals(1.0, optimum.getValue()[2], 1.0e-10); 142 143 } 144 145 public void testNoDependency() throws FunctionEvaluationException, OptimizationException { 146 LinearProblem problem = new LinearProblem(new double[][] { 147 { 2, 0, 0, 0, 0, 0 }, 148 { 0, 2, 0, 0, 0, 0 }, 149 { 0, 0, 2, 0, 0, 0 }, 150 { 0, 0, 0, 2, 0, 0 }, 151 { 0, 0, 0, 0, 2, 0 }, 152 { 0, 0, 0, 0, 0, 2 } 153 }, new double[] { 0.0, 1.1, 2.2, 3.3, 4.4, 5.5 }); 154 LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer(); 155 VectorialPointValuePair optimum = 156 optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1, 1, 1, 1 }, 157 new double[] { 0, 0, 0, 0, 0, 0 }); 158 assertEquals(0, optimizer.getRMS(), 1.0e-10); 159 for (int i = 0; i < problem.target.length; ++i) { 160 assertEquals(0.55 * i, optimum.getPoint()[i], 1.0e-10); 161 } 162 } 163 164 public void testOneSet() throws FunctionEvaluationException, OptimizationException { 165 166 LinearProblem problem = new LinearProblem(new double[][] { 167 { 1, 0, 0 }, 168 { -1, 1, 0 }, 169 { 0, -1, 1 } 170 }, new double[] { 1, 1, 1}); 171 LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer(); 172 VectorialPointValuePair optimum = 173 optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1 }, new double[] { 0, 0, 0 }); 174 assertEquals(0, optimizer.getRMS(), 1.0e-10); 175 assertEquals(1.0, optimum.getPoint()[0], 1.0e-10); 176 assertEquals(2.0, optimum.getPoint()[1], 1.0e-10); 177 assertEquals(3.0, optimum.getPoint()[2], 1.0e-10); 178 179 } 180 181 public void testTwoSets() throws FunctionEvaluationException, OptimizationException { 182 double epsilon = 1.0e-7; 183 LinearProblem problem = new LinearProblem(new double[][] { 184 { 2, 1, 0, 4, 0, 0 }, 185 { -4, -2, 3, -7, 0, 0 }, 186 { 4, 1, -2, 8, 0, 0 }, 187 { 0, -3, -12, -1, 0, 0 }, 188 { 0, 0, 0, 0, epsilon, 1 }, 189 { 0, 0, 0, 0, 1, 1 } 190 }, new double[] { 2, -9, 2, 2, 1 + epsilon * epsilon, 2}); 191 192 LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer(); 193 VectorialPointValuePair optimum = 194 optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1, 1, 1, 1 }, 195 new double[] { 0, 0, 0, 0, 0, 0 }); 196 assertEquals(0, optimizer.getRMS(), 1.0e-10); 197 assertEquals( 3.0, optimum.getPoint()[0], 1.0e-10); 198 assertEquals( 4.0, optimum.getPoint()[1], 1.0e-10); 199 assertEquals(-1.0, optimum.getPoint()[2], 1.0e-10); 200 assertEquals(-2.0, optimum.getPoint()[3], 1.0e-10); 201 assertEquals( 1.0 + epsilon, optimum.getPoint()[4], 1.0e-10); 202 assertEquals( 1.0 - epsilon, optimum.getPoint()[5], 1.0e-10); 203 204 } 205 206 public void testNonInversible() throws FunctionEvaluationException, OptimizationException { 207 208 LinearProblem problem = new LinearProblem(new double[][] { 209 { 1, 2, -3 }, 210 { 2, 1, 3 }, 211 { -3, 0, -9 } 212 }, new double[] { 1, 1, 1 }); 213 214 LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer(); 215 optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1 }, new double[] { 0, 0, 0 }); 216 assertTrue(Math.sqrt(problem.target.length) * optimizer.getRMS() > 0.6); 217 try { 218 optimizer.getCovariances(); 219 fail("an exception should have been thrown"); 220 } catch (OptimizationException ee) { 221 // expected behavior 222 } catch (Exception e) { 223 fail("wrong exception caught"); 224 } 225 226 } 227 228 public void testIllConditioned() throws FunctionEvaluationException, OptimizationException { 229 LinearProblem problem1 = new LinearProblem(new double[][] { 230 { 10.0, 7.0, 8.0, 7.0 }, 231 { 7.0, 5.0, 6.0, 5.0 }, 232 { 8.0, 6.0, 10.0, 9.0 }, 233 { 7.0, 5.0, 9.0, 10.0 } 234 }, new double[] { 32, 23, 33, 31 }); 235 LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer(); 236 VectorialPointValuePair optimum1 = 237 optimizer.optimize(problem1, problem1.target, new double[] { 1, 1, 1, 1 }, 238 new double[] { 0, 1, 2, 3 }); 239 assertEquals(0, optimizer.getRMS(), 1.0e-10); 240 assertEquals(1.0, optimum1.getPoint()[0], 1.0e-10); 241 assertEquals(1.0, optimum1.getPoint()[1], 1.0e-10); 242 assertEquals(1.0, optimum1.getPoint()[2], 1.0e-10); 243 assertEquals(1.0, optimum1.getPoint()[3], 1.0e-10); 244 245 LinearProblem problem2 = new LinearProblem(new double[][] { 246 { 10.00, 7.00, 8.10, 7.20 }, 247 { 7.08, 5.04, 6.00, 5.00 }, 248 { 8.00, 5.98, 9.89, 9.00 }, 249 { 6.99, 4.99, 9.00, 9.98 } 250 }, new double[] { 32, 23, 33, 31 }); 251 VectorialPointValuePair optimum2 = 252 optimizer.optimize(problem2, problem2.target, new double[] { 1, 1, 1, 1 }, 253 new double[] { 0, 1, 2, 3 }); 254 assertEquals(0, optimizer.getRMS(), 1.0e-10); 255 assertEquals(-81.0, optimum2.getPoint()[0], 1.0e-8); 256 assertEquals(137.0, optimum2.getPoint()[1], 1.0e-8); 257 assertEquals(-34.0, optimum2.getPoint()[2], 1.0e-8); 258 assertEquals( 22.0, optimum2.getPoint()[3], 1.0e-8); 259 260 } 261 262 public void testMoreEstimatedParametersSimple() throws FunctionEvaluationException, OptimizationException { 263 264 LinearProblem problem = new LinearProblem(new double[][] { 265 { 3.0, 2.0, 0.0, 0.0 }, 266 { 0.0, 1.0, -1.0, 1.0 }, 267 { 2.0, 0.0, 1.0, 0.0 } 268 }, new double[] { 7.0, 3.0, 5.0 }); 269 270 LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer(); 271 optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1 }, 272 new double[] { 7, 6, 5, 4 }); 273 assertEquals(0, optimizer.getRMS(), 1.0e-10); 274 275 } 276 277 public void testMoreEstimatedParametersUnsorted() throws FunctionEvaluationException, OptimizationException { 278 LinearProblem problem = new LinearProblem(new double[][] { 279 { 1.0, 1.0, 0.0, 0.0, 0.0, 0.0 }, 280 { 0.0, 0.0, 1.0, 1.0, 1.0, 0.0 }, 281 { 0.0, 0.0, 0.0, 0.0, 1.0, -1.0 }, 282 { 0.0, 0.0, -1.0, 1.0, 0.0, 1.0 }, 283 { 0.0, 0.0, 0.0, -1.0, 1.0, 0.0 } 284 }, new double[] { 3.0, 12.0, -1.0, 7.0, 1.0 }); 285 286 LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer(); 287 VectorialPointValuePair optimum = 288 optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1, 1, 1 }, 289 new double[] { 2, 2, 2, 2, 2, 2 }); 290 assertEquals(0, optimizer.getRMS(), 1.0e-10); 291 assertEquals(3.0, optimum.getPointRef()[2], 1.0e-10); 292 assertEquals(4.0, optimum.getPointRef()[3], 1.0e-10); 293 assertEquals(5.0, optimum.getPointRef()[4], 1.0e-10); 294 assertEquals(6.0, optimum.getPointRef()[5], 1.0e-10); 295 296 } 297 298 public void testRedundantEquations() throws FunctionEvaluationException, OptimizationException { 299 LinearProblem problem = new LinearProblem(new double[][] { 300 { 1.0, 1.0 }, 301 { 1.0, -1.0 }, 302 { 1.0, 3.0 } 303 }, new double[] { 3.0, 1.0, 5.0 }); 304 305 LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer(); 306 VectorialPointValuePair optimum = 307 optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1 }, 308 new double[] { 1, 1 }); 309 assertEquals(0, optimizer.getRMS(), 1.0e-10); 310 assertEquals(2.0, optimum.getPointRef()[0], 1.0e-10); 311 assertEquals(1.0, optimum.getPointRef()[1], 1.0e-10); 312 313 } 314 315 public void testInconsistentEquations() throws FunctionEvaluationException, OptimizationException { 316 LinearProblem problem = new LinearProblem(new double[][] { 317 { 1.0, 1.0 }, 318 { 1.0, -1.0 }, 319 { 1.0, 3.0 } 320 }, new double[] { 3.0, 1.0, 4.0 }); 321 322 LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer(); 323 optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1 }, new double[] { 1, 1 }); 324 assertTrue(optimizer.getRMS() > 0.1); 325 326 } 327 328 public void testInconsistentSizes() throws FunctionEvaluationException, OptimizationException { 329 LinearProblem problem = 330 new LinearProblem(new double[][] { { 1, 0 }, { 0, 1 } }, new double[] { -1, 1 }); 331 LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer(); 332 333 VectorialPointValuePair optimum = 334 optimizer.optimize(problem, problem.target, new double[] { 1, 1 }, new double[] { 0, 0 }); 335 assertEquals(0, optimizer.getRMS(), 1.0e-10); 336 assertEquals(-1, optimum.getPoint()[0], 1.0e-10); 337 assertEquals(+1, optimum.getPoint()[1], 1.0e-10); 338 339 try { 340 optimizer.optimize(problem, problem.target, 341 new double[] { 1 }, 342 new double[] { 0, 0 }); 343 fail("an exception should have been thrown"); 344 } catch (OptimizationException oe) { 345 // expected behavior 346 } catch (Exception e) { 347 fail("wrong exception caught"); 348 } 349 350 try { 351 optimizer.optimize(problem, new double[] { 1 }, 352 new double[] { 1 }, 353 new double[] { 0, 0 }); 354 fail("an exception should have been thrown"); 355 } catch (FunctionEvaluationException oe) { 356 // expected behavior 357 } catch (Exception e) { 358 fail("wrong exception caught"); 359 } 360 361 } 362 363 public void testControlParameters() { 364 Circle circle = new Circle(); 365 circle.addPoint( 30.0, 68.0); 366 circle.addPoint( 50.0, -6.0); 367 circle.addPoint(110.0, -20.0); 368 circle.addPoint( 35.0, 15.0); 369 circle.addPoint( 45.0, 97.0); 370 checkEstimate(circle, 0.1, 10, 1.0e-14, 1.0e-16, 1.0e-10, false); 371 checkEstimate(circle, 0.1, 10, 1.0e-15, 1.0e-17, 1.0e-10, true); 372 checkEstimate(circle, 0.1, 5, 1.0e-15, 1.0e-16, 1.0e-10, true); 373 circle.addPoint(300, -300); 374 checkEstimate(circle, 0.1, 20, 1.0e-18, 1.0e-16, 1.0e-10, true); 375 } 376 377 private void checkEstimate(DifferentiableMultivariateVectorialFunction problem, 378 double initialStepBoundFactor, int maxCostEval, 379 double costRelativeTolerance, double parRelativeTolerance, 380 double orthoTolerance, boolean shouldFail) { 381 try { 382 LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer(); 383 optimizer.setInitialStepBoundFactor(initialStepBoundFactor); 384 optimizer.setMaxIterations(maxCostEval); 385 optimizer.setCostRelativeTolerance(costRelativeTolerance); 386 optimizer.setParRelativeTolerance(parRelativeTolerance); 387 optimizer.setOrthoTolerance(orthoTolerance); 388 optimizer.optimize(problem, new double[] { 0, 0, 0, 0, 0 }, new double[] { 1, 1, 1, 1, 1 }, 389 new double[] { 98.680, 47.345 }); 390 assertTrue(! shouldFail); 391 } catch (OptimizationException ee) { 392 assertTrue(shouldFail); 393 } catch (FunctionEvaluationException ee) { 394 assertTrue(shouldFail); 395 } catch (Exception e) { 396 fail("wrong exception type caught"); 397 } 398 } 399 400 public void testCircleFitting() throws FunctionEvaluationException, OptimizationException { 401 Circle circle = new Circle(); 402 circle.addPoint( 30.0, 68.0); 403 circle.addPoint( 50.0, -6.0); 404 circle.addPoint(110.0, -20.0); 405 circle.addPoint( 35.0, 15.0); 406 circle.addPoint( 45.0, 97.0); 407 LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer(); 408 VectorialPointValuePair optimum = 409 optimizer.optimize(circle, new double[] { 0, 0, 0, 0, 0 }, new double[] { 1, 1, 1, 1, 1 }, 410 new double[] { 98.680, 47.345 }); 411 assertTrue(optimizer.getEvaluations() < 10); 412 assertTrue(optimizer.getJacobianEvaluations() < 10); 413 double rms = optimizer.getRMS(); 414 assertEquals(1.768262623567235, Math.sqrt(circle.getN()) * rms, 1.0e-10); 415 Point2D.Double center = new Point2D.Double(optimum.getPointRef()[0], optimum.getPointRef()[1]); 416 assertEquals(69.96016176931406, circle.getRadius(center), 1.0e-10); 417 assertEquals(96.07590211815305, center.x, 1.0e-10); 418 assertEquals(48.13516790438953, center.y, 1.0e-10); 419 double[][] cov = optimizer.getCovariances(); 420 assertEquals(1.839, cov[0][0], 0.001); 421 assertEquals(0.731, cov[0][1], 0.001); 422 assertEquals(cov[0][1], cov[1][0], 1.0e-14); 423 assertEquals(0.786, cov[1][1], 0.001); 424 double[] errors = optimizer.guessParametersErrors(); 425 assertEquals(1.384, errors[0], 0.001); 426 assertEquals(0.905, errors[1], 0.001); 427 428 // add perfect measurements and check errors are reduced 429 double r = circle.getRadius(center); 430 for (double d= 0; d < 2 * Math.PI; d += 0.01) { 431 circle.addPoint(center.x + r * Math.cos(d), center.y + r * Math.sin(d)); 432 } 433 double[] target = new double[circle.getN()]; 434 Arrays.fill(target, 0.0); 435 double[] weights = new double[circle.getN()]; 436 Arrays.fill(weights, 2.0); 437 optimizer.optimize(circle, target, weights, new double[] { 98.680, 47.345 }); 438 cov = optimizer.getCovariances(); 439 assertEquals(0.0016, cov[0][0], 0.001); 440 assertEquals(3.2e-7, cov[0][1], 1.0e-9); 441 assertEquals(cov[0][1], cov[1][0], 1.0e-14); 442 assertEquals(0.0016, cov[1][1], 0.001); 443 errors = optimizer.guessParametersErrors(); 444 assertEquals(0.002, errors[0], 0.001); 445 assertEquals(0.002, errors[1], 0.001); 446 447 } 448 449 public void testCircleFittingBadInit() throws FunctionEvaluationException, OptimizationException { 450 Circle circle = new Circle(); 451 double[][] points = new double[][] { 452 {-0.312967, 0.072366}, {-0.339248, 0.132965}, {-0.379780, 0.202724}, 453 {-0.390426, 0.260487}, {-0.361212, 0.328325}, {-0.346039, 0.392619}, 454 {-0.280579, 0.444306}, {-0.216035, 0.470009}, {-0.149127, 0.493832}, 455 {-0.075133, 0.483271}, {-0.007759, 0.452680}, { 0.060071, 0.410235}, 456 { 0.103037, 0.341076}, { 0.118438, 0.273884}, { 0.131293, 0.192201}, 457 { 0.115869, 0.129797}, { 0.072223, 0.058396}, { 0.022884, 0.000718}, 458 {-0.053355, -0.020405}, {-0.123584, -0.032451}, {-0.216248, -0.032862}, 459 {-0.278592, -0.005008}, {-0.337655, 0.056658}, {-0.385899, 0.112526}, 460 {-0.405517, 0.186957}, {-0.415374, 0.262071}, {-0.387482, 0.343398}, 461 {-0.347322, 0.397943}, {-0.287623, 0.458425}, {-0.223502, 0.475513}, 462 {-0.135352, 0.478186}, {-0.061221, 0.483371}, { 0.003711, 0.422737}, 463 { 0.065054, 0.375830}, { 0.108108, 0.297099}, { 0.123882, 0.222850}, 464 { 0.117729, 0.134382}, { 0.085195, 0.056820}, { 0.029800, -0.019138}, 465 {-0.027520, -0.072374}, {-0.102268, -0.091555}, {-0.200299, -0.106578}, 466 {-0.292731, -0.091473}, {-0.356288, -0.051108}, {-0.420561, 0.014926}, 467 {-0.471036, 0.074716}, {-0.488638, 0.182508}, {-0.485990, 0.254068}, 468 {-0.463943, 0.338438}, {-0.406453, 0.404704}, {-0.334287, 0.466119}, 469 {-0.254244, 0.503188}, {-0.161548, 0.495769}, {-0.075733, 0.495560}, 470 { 0.001375, 0.434937}, { 0.082787, 0.385806}, { 0.115490, 0.323807}, 471 { 0.141089, 0.223450}, { 0.138693, 0.131703}, { 0.126415, 0.049174}, 472 { 0.066518, -0.010217}, {-0.005184, -0.070647}, {-0.080985, -0.103635}, 473 {-0.177377, -0.116887}, {-0.260628, -0.100258}, {-0.335756, -0.056251}, 474 {-0.405195, -0.000895}, {-0.444937, 0.085456}, {-0.484357, 0.175597}, 475 {-0.472453, 0.248681}, {-0.438580, 0.347463}, {-0.402304, 0.422428}, 476 {-0.326777, 0.479438}, {-0.247797, 0.505581}, {-0.152676, 0.519380}, 477 {-0.071754, 0.516264}, { 0.015942, 0.472802}, { 0.076608, 0.419077}, 478 { 0.127673, 0.330264}, { 0.159951, 0.262150}, { 0.153530, 0.172681}, 479 { 0.140653, 0.089229}, { 0.078666, 0.024981}, { 0.023807, -0.037022}, 480 {-0.048837, -0.077056}, {-0.127729, -0.075338}, {-0.221271, -0.067526} 481 }; 482 double[] target = new double[points.length]; 483 Arrays.fill(target, 0.0); 484 double[] weights = new double[points.length]; 485 Arrays.fill(weights, 2.0); 486 for (int i = 0; i < points.length; ++i) { 487 circle.addPoint(points[i][0], points[i][1]); 488 } 489 LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer(); 490 optimizer.setConvergenceChecker(new SimpleVectorialValueChecker(1.0e-10, 1.0e-10)); 491 VectorialPointValuePair optimum = 492 optimizer.optimize(circle, target, weights, new double[] { -12, -12 }); 493 Point2D.Double center = new Point2D.Double(optimum.getPointRef()[0], optimum.getPointRef()[1]); 494 assertTrue(optimizer.getEvaluations() < 25); 495 assertTrue(optimizer.getJacobianEvaluations() < 20); 496 assertEquals( 0.043, optimizer.getRMS(), 1.0e-3); 497 assertEquals( 0.292235, circle.getRadius(center), 1.0e-6); 498 assertEquals(-0.151738, center.x, 1.0e-6); 499 assertEquals( 0.2075001, center.y, 1.0e-6); 500 } 501 502 public void testMath199() throws FunctionEvaluationException { 503 try { 504 QuadraticProblem problem = new QuadraticProblem(); 505 problem.addPoint (0, -3.182591015485607); 506 problem.addPoint (1, -2.5581184967730577); 507 problem.addPoint (2, -2.1488478161387325); 508 problem.addPoint (3, -1.9122489313410047); 509 problem.addPoint (4, 1.7785661310051026); 510 new LevenbergMarquardtOptimizer().optimize(problem, 511 new double[] { 0, 0, 0, 0, 0 }, 512 new double[] { 0.0, 4.4e-323, 1.0, 4.4e-323, 0.0 }, 513 new double[] { 0, 0, 0 }); 514 fail("an exception should have been thrown"); 515 } catch (OptimizationException ee) { 516 // expected behavior 517 } 518 519 } 520 521 private static class LinearProblem implements DifferentiableMultivariateVectorialFunction, Serializable { 522 523 private static final long serialVersionUID = 703247177355019415L; 524 final RealMatrix factors; 525 final double[] target; 526 public LinearProblem(double[][] factors, double[] target) { 527 this.factors = new BlockRealMatrix(factors); 528 this.target = target; 529 } 530 531 public double[] value(double[] variables) { 532 return factors.operate(variables); 533 } 534 535 public MultivariateMatrixFunction jacobian() { 536 return new MultivariateMatrixFunction() { 537 private static final long serialVersionUID = 556396458721526234L; 538 public double[][] value(double[] point) { 539 return factors.getData(); 540 } 541 }; 542 } 543 544 } 545 546 private static class Circle implements DifferentiableMultivariateVectorialFunction, Serializable { 547 548 private static final long serialVersionUID = -4711170319243817874L; 549 550 private ArrayList<Point2D.Double> points; 551 552 public Circle() { 553 points = new ArrayList<Point2D.Double>(); 554 } 555 556 public void addPoint(double px, double py) { 557 points.add(new Point2D.Double(px, py)); 558 } 559 560 public int getN() { 561 return points.size(); 562 } 563 564 public double getRadius(Point2D.Double center) { 565 double r = 0; 566 for (Point2D.Double point : points) { 567 r += point.distance(center); 568 } 569 return r / points.size(); 570 } 571 572 private double[][] jacobian(double[] point) { 573 574 int n = points.size(); 575 Point2D.Double center = new Point2D.Double(point[0], point[1]); 576 577 // gradient of the optimal radius 578 double dRdX = 0; 579 double dRdY = 0; 580 for (Point2D.Double pk : points) { 581 double dk = pk.distance(center); 582 dRdX += (center.x - pk.x) / dk; 583 dRdY += (center.y - pk.y) / dk; 584 } 585 dRdX /= n; 586 dRdY /= n; 587 588 // jacobian of the radius residuals 589 double[][] jacobian = new double[n][2]; 590 for (int i = 0; i < n; ++i) { 591 Point2D.Double pi = points.get(i); 592 double di = pi.distance(center); 593 jacobian[i][0] = (center.x - pi.x) / di - dRdX; 594 jacobian[i][1] = (center.y - pi.y) / di - dRdY; 595 } 596 597 return jacobian; 598 599 } 600 601 public double[] value(double[] variables) 602 throws FunctionEvaluationException, IllegalArgumentException { 603 604 Point2D.Double center = new Point2D.Double(variables[0], variables[1]); 605 double radius = getRadius(center); 606 607 double[] residuals = new double[points.size()]; 608 for (int i = 0; i < residuals.length; ++i) { 609 residuals[i] = points.get(i).distance(center) - radius; 610 } 611 612 return residuals; 613 614 } 615 616 public MultivariateMatrixFunction jacobian() { 617 return new MultivariateMatrixFunction() { 618 private static final long serialVersionUID = -4340046230875165095L; 619 public double[][] value(double[] point) { 620 return jacobian(point); 621 } 622 }; 623 } 624 625 } 626 627 private static class QuadraticProblem implements DifferentiableMultivariateVectorialFunction, Serializable { 628 629 private static final long serialVersionUID = 7072187082052755854L; 630 private List<Double> x; 631 private List<Double> y; 632 633 public QuadraticProblem() { 634 x = new ArrayList<Double>(); 635 y = new ArrayList<Double>(); 636 } 637 638 public void addPoint(double x, double y) { 639 this.x.add(x); 640 this.y.add(y); 641 } 642 643 private double[][] jacobian(double[] variables) { 644 double[][] jacobian = new double[x.size()][3]; 645 for (int i = 0; i < jacobian.length; ++i) { 646 jacobian[i][0] = x.get(i) * x.get(i); 647 jacobian[i][1] = x.get(i); 648 jacobian[i][2] = 1.0; 649 } 650 return jacobian; 651 } 652 653 public double[] value(double[] variables) { 654 double[] values = new double[x.size()]; 655 for (int i = 0; i < values.length; ++i) { 656 values[i] = (variables[0] * x.get(i) + variables[1]) * x.get(i) + variables[2]; 657 } 658 return values; 659 } 660 661 public MultivariateMatrixFunction jacobian() { 662 return new MultivariateMatrixFunction() { 663 private static final long serialVersionUID = -8673650298627399464L; 664 public double[][] value(double[] point) { 665 return jacobian(point); 666 } 667 }; 668 } 669 670 } 671 672 public static Test suite() { 673 return new TestSuite(LevenbergMarquardtOptimizerTest.class); 674 } 675 676 }