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; 024 025 import junit.framework.Test; 026 import junit.framework.TestCase; 027 import junit.framework.TestSuite; 028 029 import org.apache.commons.math.FunctionEvaluationException; 030 import org.apache.commons.math.analysis.DifferentiableMultivariateVectorialFunction; 031 import org.apache.commons.math.analysis.MultivariateMatrixFunction; 032 import org.apache.commons.math.linear.BlockRealMatrix; 033 import org.apache.commons.math.linear.RealMatrix; 034 import org.apache.commons.math.optimization.OptimizationException; 035 import org.apache.commons.math.optimization.SimpleVectorialPointChecker; 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 GaussNewtonOptimizerTest 102 extends TestCase { 103 104 public GaussNewtonOptimizerTest(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 GaussNewtonOptimizer optimizer = new GaussNewtonOptimizer(true); 112 optimizer.setMaxIterations(100); 113 optimizer.setConvergenceChecker(new SimpleVectorialValueChecker(1.0e-6, 1.0e-6)); 114 VectorialPointValuePair optimum = 115 optimizer.optimize(problem, problem.target, new double[] { 1 }, new double[] { 0 }); 116 assertEquals(0, optimizer.getRMS(), 1.0e-10); 117 assertEquals(1.5, optimum.getPoint()[0], 1.0e-10); 118 assertEquals(3.0, optimum.getValue()[0], 1.0e-10); 119 } 120 121 public void testColumnsPermutation() throws FunctionEvaluationException, OptimizationException { 122 123 LinearProblem problem = 124 new LinearProblem(new double[][] { { 1.0, -1.0 }, { 0.0, 2.0 }, { 1.0, -2.0 } }, 125 new double[] { 4.0, 6.0, 1.0 }); 126 127 GaussNewtonOptimizer optimizer = new GaussNewtonOptimizer(true); 128 optimizer.setMaxIterations(100); 129 optimizer.setConvergenceChecker(new SimpleVectorialValueChecker(1.0e-6, 1.0e-6)); 130 VectorialPointValuePair optimum = 131 optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1 }, new double[] { 0, 0 }); 132 assertEquals(0, optimizer.getRMS(), 1.0e-10); 133 assertEquals(7.0, optimum.getPoint()[0], 1.0e-10); 134 assertEquals(3.0, optimum.getPoint()[1], 1.0e-10); 135 assertEquals(4.0, optimum.getValue()[0], 1.0e-10); 136 assertEquals(6.0, optimum.getValue()[1], 1.0e-10); 137 assertEquals(1.0, optimum.getValue()[2], 1.0e-10); 138 139 } 140 141 public void testNoDependency() throws FunctionEvaluationException, OptimizationException { 142 LinearProblem problem = new LinearProblem(new double[][] { 143 { 2, 0, 0, 0, 0, 0 }, 144 { 0, 2, 0, 0, 0, 0 }, 145 { 0, 0, 2, 0, 0, 0 }, 146 { 0, 0, 0, 2, 0, 0 }, 147 { 0, 0, 0, 0, 2, 0 }, 148 { 0, 0, 0, 0, 0, 2 } 149 }, new double[] { 0.0, 1.1, 2.2, 3.3, 4.4, 5.5 }); 150 GaussNewtonOptimizer optimizer = new GaussNewtonOptimizer(true); 151 optimizer.setMaxIterations(100); 152 optimizer.setConvergenceChecker(new SimpleVectorialValueChecker(1.0e-6, 1.0e-6)); 153 VectorialPointValuePair optimum = 154 optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1, 1, 1, 1 }, 155 new double[] { 0, 0, 0, 0, 0, 0 }); 156 assertEquals(0, optimizer.getRMS(), 1.0e-10); 157 for (int i = 0; i < problem.target.length; ++i) { 158 assertEquals(0.55 * i, optimum.getPoint()[i], 1.0e-10); 159 } 160 } 161 162 public void testOneSet() throws FunctionEvaluationException, OptimizationException { 163 164 LinearProblem problem = new LinearProblem(new double[][] { 165 { 1, 0, 0 }, 166 { -1, 1, 0 }, 167 { 0, -1, 1 } 168 }, new double[] { 1, 1, 1}); 169 GaussNewtonOptimizer optimizer = new GaussNewtonOptimizer(true); 170 optimizer.setMaxIterations(100); 171 optimizer.setConvergenceChecker(new SimpleVectorialValueChecker(1.0e-6, 1.0e-6)); 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 GaussNewtonOptimizer optimizer = new GaussNewtonOptimizer(true); 193 optimizer.setMaxIterations(100); 194 optimizer.setConvergenceChecker(new SimpleVectorialValueChecker(1.0e-6, 1.0e-6)); 195 VectorialPointValuePair optimum = 196 optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1, 1, 1, 1 }, 197 new double[] { 0, 0, 0, 0, 0, 0 }); 198 assertEquals(0, optimizer.getRMS(), 1.0e-10); 199 assertEquals( 3.0, optimum.getPoint()[0], 1.0e-10); 200 assertEquals( 4.0, optimum.getPoint()[1], 1.0e-10); 201 assertEquals(-1.0, optimum.getPoint()[2], 1.0e-10); 202 assertEquals(-2.0, optimum.getPoint()[3], 1.0e-10); 203 assertEquals( 1.0 + epsilon, optimum.getPoint()[4], 1.0e-10); 204 assertEquals( 1.0 - epsilon, optimum.getPoint()[5], 1.0e-10); 205 206 } 207 208 public void testNonInversible() { 209 210 LinearProblem problem = new LinearProblem(new double[][] { 211 { 1, 2, -3 }, 212 { 2, 1, 3 }, 213 { -3, 0, -9 } 214 }, new double[] { 1, 1, 1 }); 215 GaussNewtonOptimizer optimizer = new GaussNewtonOptimizer(true); 216 optimizer.setMaxIterations(100); 217 optimizer.setConvergenceChecker(new SimpleVectorialValueChecker(1.0e-6, 1.0e-6)); 218 try { 219 optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1 }, new double[] { 0, 0, 0 }); 220 fail("an exception should have been caught"); 221 } catch (OptimizationException ee) { 222 // expected behavior 223 } catch (Exception e) { 224 fail("wrong exception type caught"); 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 GaussNewtonOptimizer optimizer = new GaussNewtonOptimizer(true); 236 optimizer.setMaxIterations(100); 237 optimizer.setConvergenceChecker(new SimpleVectorialValueChecker(1.0e-6, 1.0e-6)); 238 VectorialPointValuePair optimum1 = 239 optimizer.optimize(problem1, problem1.target, new double[] { 1, 1, 1, 1 }, 240 new double[] { 0, 1, 2, 3 }); 241 assertEquals(0, optimizer.getRMS(), 1.0e-10); 242 assertEquals(1.0, optimum1.getPoint()[0], 1.0e-10); 243 assertEquals(1.0, optimum1.getPoint()[1], 1.0e-10); 244 assertEquals(1.0, optimum1.getPoint()[2], 1.0e-10); 245 assertEquals(1.0, optimum1.getPoint()[3], 1.0e-10); 246 247 LinearProblem problem2 = new LinearProblem(new double[][] { 248 { 10.00, 7.00, 8.10, 7.20 }, 249 { 7.08, 5.04, 6.00, 5.00 }, 250 { 8.00, 5.98, 9.89, 9.00 }, 251 { 6.99, 4.99, 9.00, 9.98 } 252 }, new double[] { 32, 23, 33, 31 }); 253 VectorialPointValuePair optimum2 = 254 optimizer.optimize(problem2, problem2.target, new double[] { 1, 1, 1, 1 }, 255 new double[] { 0, 1, 2, 3 }); 256 assertEquals(0, optimizer.getRMS(), 1.0e-10); 257 assertEquals(-81.0, optimum2.getPoint()[0], 1.0e-8); 258 assertEquals(137.0, optimum2.getPoint()[1], 1.0e-8); 259 assertEquals(-34.0, optimum2.getPoint()[2], 1.0e-8); 260 assertEquals( 22.0, optimum2.getPoint()[3], 1.0e-8); 261 262 } 263 264 public void testMoreEstimatedParametersSimple() { 265 266 LinearProblem problem = new LinearProblem(new double[][] { 267 { 3.0, 2.0, 0.0, 0.0 }, 268 { 0.0, 1.0, -1.0, 1.0 }, 269 { 2.0, 0.0, 1.0, 0.0 } 270 }, new double[] { 7.0, 3.0, 5.0 }); 271 272 GaussNewtonOptimizer optimizer = new GaussNewtonOptimizer(true); 273 optimizer.setMaxIterations(100); 274 optimizer.setConvergenceChecker(new SimpleVectorialValueChecker(1.0e-6, 1.0e-6)); 275 try { 276 optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1 }, 277 new double[] { 7, 6, 5, 4 }); 278 fail("an exception should have been caught"); 279 } catch (OptimizationException ee) { 280 // expected behavior 281 } catch (Exception e) { 282 fail("wrong exception type caught"); 283 } 284 285 } 286 287 public void testMoreEstimatedParametersUnsorted() { 288 LinearProblem problem = new LinearProblem(new double[][] { 289 { 1.0, 1.0, 0.0, 0.0, 0.0, 0.0 }, 290 { 0.0, 0.0, 1.0, 1.0, 1.0, 0.0 }, 291 { 0.0, 0.0, 0.0, 0.0, 1.0, -1.0 }, 292 { 0.0, 0.0, -1.0, 1.0, 0.0, 1.0 }, 293 { 0.0, 0.0, 0.0, -1.0, 1.0, 0.0 } 294 }, new double[] { 3.0, 12.0, -1.0, 7.0, 1.0 }); 295 GaussNewtonOptimizer optimizer = new GaussNewtonOptimizer(true); 296 optimizer.setMaxIterations(100); 297 optimizer.setConvergenceChecker(new SimpleVectorialValueChecker(1.0e-6, 1.0e-6)); 298 try { 299 optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1, 1, 1 }, 300 new double[] { 2, 2, 2, 2, 2, 2 }); 301 fail("an exception should have been caught"); 302 } catch (OptimizationException ee) { 303 // expected behavior 304 } catch (Exception e) { 305 fail("wrong exception type caught"); 306 } 307 } 308 309 public void testRedundantEquations() throws FunctionEvaluationException, OptimizationException { 310 LinearProblem problem = new LinearProblem(new double[][] { 311 { 1.0, 1.0 }, 312 { 1.0, -1.0 }, 313 { 1.0, 3.0 } 314 }, new double[] { 3.0, 1.0, 5.0 }); 315 316 GaussNewtonOptimizer optimizer = new GaussNewtonOptimizer(true); 317 optimizer.setMaxIterations(100); 318 optimizer.setConvergenceChecker(new SimpleVectorialValueChecker(1.0e-6, 1.0e-6)); 319 VectorialPointValuePair optimum = 320 optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1 }, 321 new double[] { 1, 1 }); 322 assertEquals(0, optimizer.getRMS(), 1.0e-10); 323 assertEquals(2.0, optimum.getPoint()[0], 1.0e-8); 324 assertEquals(1.0, optimum.getPoint()[1], 1.0e-8); 325 326 } 327 328 public void testInconsistentEquations() throws FunctionEvaluationException, OptimizationException { 329 LinearProblem problem = new LinearProblem(new double[][] { 330 { 1.0, 1.0 }, 331 { 1.0, -1.0 }, 332 { 1.0, 3.0 } 333 }, new double[] { 3.0, 1.0, 4.0 }); 334 335 GaussNewtonOptimizer optimizer = new GaussNewtonOptimizer(true); 336 optimizer.setMaxIterations(100); 337 optimizer.setConvergenceChecker(new SimpleVectorialValueChecker(1.0e-6, 1.0e-6)); 338 optimizer.optimize(problem, problem.target, new double[] { 1, 1, 1 }, new double[] { 1, 1 }); 339 assertTrue(optimizer.getRMS() > 0.1); 340 341 } 342 343 public void testInconsistentSizes() throws FunctionEvaluationException, OptimizationException { 344 LinearProblem problem = 345 new LinearProblem(new double[][] { { 1, 0 }, { 0, 1 } }, new double[] { -1, 1 }); 346 GaussNewtonOptimizer optimizer = new GaussNewtonOptimizer(true); 347 optimizer.setMaxIterations(100); 348 optimizer.setConvergenceChecker(new SimpleVectorialValueChecker(1.0e-6, 1.0e-6)); 349 350 VectorialPointValuePair optimum = 351 optimizer.optimize(problem, problem.target, new double[] { 1, 1 }, new double[] { 0, 0 }); 352 assertEquals(0, optimizer.getRMS(), 1.0e-10); 353 assertEquals(-1, optimum.getPoint()[0], 1.0e-10); 354 assertEquals(+1, optimum.getPoint()[1], 1.0e-10); 355 356 try { 357 optimizer.optimize(problem, problem.target, 358 new double[] { 1 }, 359 new double[] { 0, 0 }); 360 fail("an exception should have been thrown"); 361 } catch (OptimizationException oe) { 362 // expected behavior 363 } catch (Exception e) { 364 fail("wrong exception caught"); 365 } 366 367 try { 368 optimizer.optimize(problem, new double[] { 1 }, 369 new double[] { 1 }, 370 new double[] { 0, 0 }); 371 fail("an exception should have been thrown"); 372 } catch (FunctionEvaluationException oe) { 373 // expected behavior 374 } catch (Exception e) { 375 fail("wrong exception caught"); 376 } 377 378 } 379 380 public void testMaxIterations() { 381 Circle circle = new Circle(); 382 circle.addPoint( 30.0, 68.0); 383 circle.addPoint( 50.0, -6.0); 384 circle.addPoint(110.0, -20.0); 385 circle.addPoint( 35.0, 15.0); 386 circle.addPoint( 45.0, 97.0); 387 GaussNewtonOptimizer optimizer = new GaussNewtonOptimizer(true); 388 optimizer.setMaxIterations(100); 389 optimizer.setConvergenceChecker(new SimpleVectorialPointChecker(1.0e-30, 1.0e-30)); 390 try { 391 optimizer.optimize(circle, new double[] { 0, 0, 0, 0, 0 }, 392 new double[] { 1, 1, 1, 1, 1 }, 393 new double[] { 98.680, 47.345 }); 394 fail("an exception should have been caught"); 395 } catch (OptimizationException ee) { 396 // expected behavior 397 } catch (Exception e) { 398 fail("wrong exception type caught"); 399 } 400 } 401 402 public void testCircleFitting() throws FunctionEvaluationException, OptimizationException { 403 Circle circle = new Circle(); 404 circle.addPoint( 30.0, 68.0); 405 circle.addPoint( 50.0, -6.0); 406 circle.addPoint(110.0, -20.0); 407 circle.addPoint( 35.0, 15.0); 408 circle.addPoint( 45.0, 97.0); 409 GaussNewtonOptimizer optimizer = new GaussNewtonOptimizer(true); 410 optimizer.setMaxIterations(100); 411 optimizer.setConvergenceChecker(new SimpleVectorialValueChecker(1.0e-13, 1.0e-13)); 412 VectorialPointValuePair optimum = 413 optimizer.optimize(circle, new double[] { 0, 0, 0, 0, 0 }, 414 new double[] { 1, 1, 1, 1, 1 }, 415 new double[] { 98.680, 47.345 }); 416 assertEquals(1.768262623567235, Math.sqrt(circle.getN()) * optimizer.getRMS(), 1.0e-10); 417 Point2D.Double center = new Point2D.Double(optimum.getPointRef()[0], optimum.getPointRef()[1]); 418 assertEquals(69.96016175359975, circle.getRadius(center), 1.0e-10); 419 assertEquals(96.07590209601095, center.x, 1.0e-10); 420 assertEquals(48.135167894714, center.y, 1.0e-10); 421 } 422 423 public void testCircleFittingBadInit() throws FunctionEvaluationException, OptimizationException { 424 Circle circle = new Circle(); 425 double[][] points = new double[][] { 426 {-0.312967, 0.072366}, {-0.339248, 0.132965}, {-0.379780, 0.202724}, 427 {-0.390426, 0.260487}, {-0.361212, 0.328325}, {-0.346039, 0.392619}, 428 {-0.280579, 0.444306}, {-0.216035, 0.470009}, {-0.149127, 0.493832}, 429 {-0.075133, 0.483271}, {-0.007759, 0.452680}, { 0.060071, 0.410235}, 430 { 0.103037, 0.341076}, { 0.118438, 0.273884}, { 0.131293, 0.192201}, 431 { 0.115869, 0.129797}, { 0.072223, 0.058396}, { 0.022884, 0.000718}, 432 {-0.053355, -0.020405}, {-0.123584, -0.032451}, {-0.216248, -0.032862}, 433 {-0.278592, -0.005008}, {-0.337655, 0.056658}, {-0.385899, 0.112526}, 434 {-0.405517, 0.186957}, {-0.415374, 0.262071}, {-0.387482, 0.343398}, 435 {-0.347322, 0.397943}, {-0.287623, 0.458425}, {-0.223502, 0.475513}, 436 {-0.135352, 0.478186}, {-0.061221, 0.483371}, { 0.003711, 0.422737}, 437 { 0.065054, 0.375830}, { 0.108108, 0.297099}, { 0.123882, 0.222850}, 438 { 0.117729, 0.134382}, { 0.085195, 0.056820}, { 0.029800, -0.019138}, 439 {-0.027520, -0.072374}, {-0.102268, -0.091555}, {-0.200299, -0.106578}, 440 {-0.292731, -0.091473}, {-0.356288, -0.051108}, {-0.420561, 0.014926}, 441 {-0.471036, 0.074716}, {-0.488638, 0.182508}, {-0.485990, 0.254068}, 442 {-0.463943, 0.338438}, {-0.406453, 0.404704}, {-0.334287, 0.466119}, 443 {-0.254244, 0.503188}, {-0.161548, 0.495769}, {-0.075733, 0.495560}, 444 { 0.001375, 0.434937}, { 0.082787, 0.385806}, { 0.115490, 0.323807}, 445 { 0.141089, 0.223450}, { 0.138693, 0.131703}, { 0.126415, 0.049174}, 446 { 0.066518, -0.010217}, {-0.005184, -0.070647}, {-0.080985, -0.103635}, 447 {-0.177377, -0.116887}, {-0.260628, -0.100258}, {-0.335756, -0.056251}, 448 {-0.405195, -0.000895}, {-0.444937, 0.085456}, {-0.484357, 0.175597}, 449 {-0.472453, 0.248681}, {-0.438580, 0.347463}, {-0.402304, 0.422428}, 450 {-0.326777, 0.479438}, {-0.247797, 0.505581}, {-0.152676, 0.519380}, 451 {-0.071754, 0.516264}, { 0.015942, 0.472802}, { 0.076608, 0.419077}, 452 { 0.127673, 0.330264}, { 0.159951, 0.262150}, { 0.153530, 0.172681}, 453 { 0.140653, 0.089229}, { 0.078666, 0.024981}, { 0.023807, -0.037022}, 454 {-0.048837, -0.077056}, {-0.127729, -0.075338}, {-0.221271, -0.067526} 455 }; 456 double[] target = new double[points.length]; 457 Arrays.fill(target, 0.0); 458 double[] weights = new double[points.length]; 459 Arrays.fill(weights, 2.0); 460 for (int i = 0; i < points.length; ++i) { 461 circle.addPoint(points[i][0], points[i][1]); 462 } 463 GaussNewtonOptimizer optimizer = new GaussNewtonOptimizer(true); 464 optimizer.setMaxIterations(100); 465 optimizer.setConvergenceChecker(new SimpleVectorialValueChecker(1.0e-6, 1.0e-6)); 466 try { 467 optimizer.optimize(circle, target, weights, new double[] { -12, -12 }); 468 fail("an exception should have been caught"); 469 } catch (OptimizationException ee) { 470 // expected behavior 471 } catch (Exception e) { 472 fail("wrong exception type caught"); 473 } 474 475 VectorialPointValuePair optimum = 476 optimizer.optimize(circle, target, weights, new double[] { 0, 0 }); 477 assertEquals(-0.1517383071957963, optimum.getPointRef()[0], 1.0e-8); 478 assertEquals(0.2074999736353867, optimum.getPointRef()[1], 1.0e-8); 479 assertEquals(0.04268731682389561, optimizer.getRMS(), 1.0e-8); 480 481 } 482 483 private static class LinearProblem implements DifferentiableMultivariateVectorialFunction, Serializable { 484 485 private static final long serialVersionUID = -8804268799379350190L; 486 final RealMatrix factors; 487 final double[] target; 488 public LinearProblem(double[][] factors, double[] target) { 489 this.factors = new BlockRealMatrix(factors); 490 this.target = target; 491 } 492 493 public double[] value(double[] variables) { 494 return factors.operate(variables); 495 } 496 497 public MultivariateMatrixFunction jacobian() { 498 return new MultivariateMatrixFunction() { 499 private static final long serialVersionUID = -8387467946663627585L; 500 public double[][] value(double[] point) { 501 return factors.getData(); 502 } 503 }; 504 } 505 506 } 507 508 private static class Circle implements DifferentiableMultivariateVectorialFunction, Serializable { 509 510 private static final long serialVersionUID = -7165774454925027042L; 511 private ArrayList<Point2D.Double> points; 512 513 public Circle() { 514 points = new ArrayList<Point2D.Double>(); 515 } 516 517 public void addPoint(double px, double py) { 518 points.add(new Point2D.Double(px, py)); 519 } 520 521 public int getN() { 522 return points.size(); 523 } 524 525 public double getRadius(Point2D.Double center) { 526 double r = 0; 527 for (Point2D.Double point : points) { 528 r += point.distance(center); 529 } 530 return r / points.size(); 531 } 532 533 private double[][] jacobian(double[] variables) { 534 535 int n = points.size(); 536 Point2D.Double center = new Point2D.Double(variables[0], variables[1]); 537 538 // gradient of the optimal radius 539 double dRdX = 0; 540 double dRdY = 0; 541 for (Point2D.Double pk : points) { 542 double dk = pk.distance(center); 543 dRdX += (center.x - pk.x) / dk; 544 dRdY += (center.y - pk.y) / dk; 545 } 546 dRdX /= n; 547 dRdY /= n; 548 549 // jacobian of the radius residuals 550 double[][] jacobian = new double[n][2]; 551 for (int i = 0; i < n; ++i) { 552 Point2D.Double pi = points.get(i); 553 double di = pi.distance(center); 554 jacobian[i][0] = (center.x - pi.x) / di - dRdX; 555 jacobian[i][1] = (center.y - pi.y) / di - dRdY; 556 } 557 558 return jacobian; 559 560 } 561 562 public double[] value(double[] variables) { 563 564 Point2D.Double center = new Point2D.Double(variables[0], variables[1]); 565 double radius = getRadius(center); 566 567 double[] residuals = new double[points.size()]; 568 for (int i = 0; i < residuals.length; ++i) { 569 residuals[i] = points.get(i).distance(center) - radius; 570 } 571 572 return residuals; 573 574 } 575 576 public MultivariateMatrixFunction jacobian() { 577 return new MultivariateMatrixFunction() { 578 private static final long serialVersionUID = -4340046230875165095L; 579 public double[][] value(double[] point) { 580 return jacobian(point); 581 } 582 }; 583 } 584 585 } 586 587 public static Test suite() { 588 return new TestSuite(GaussNewtonOptimizerTest.class); 589 } 590 591 }