001 // CHECKSTYLE: stop all 002 /* 003 * Licensed to the Apache Software Foundation (ASF) under one or more 004 * contributor license agreements. See the NOTICE file distributed with 005 * this work for additional information regarding copyright ownership. 006 * The ASF licenses this file to You under the Apache License, Version 2.0 007 * (the "License"); you may not use this file except in compliance with 008 * the License. You may obtain a copy of the License at 009 * 010 * http://www.apache.org/licenses/LICENSE-2.0 011 * 012 * Unless required by applicable law or agreed to in writing, software 013 * distributed under the License is distributed on an "AS IS" BASIS, 014 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 015 * See the License for the specific language governing permissions and 016 * limitations under the License. 017 */ 018 019 package org.apache.commons.math3.optimization.direct; 020 021 import java.util.Arrays; 022 023 import org.apache.commons.math3.analysis.MultivariateFunction; 024 import org.apache.commons.math3.exception.MathIllegalStateException; 025 import org.apache.commons.math3.exception.NumberIsTooSmallException; 026 import org.apache.commons.math3.exception.OutOfRangeException; 027 import org.apache.commons.math3.exception.util.LocalizedFormats; 028 import org.apache.commons.math3.linear.Array2DRowRealMatrix; 029 import org.apache.commons.math3.linear.ArrayRealVector; 030 import org.apache.commons.math3.linear.RealVector; 031 import org.apache.commons.math3.optimization.GoalType; 032 import org.apache.commons.math3.optimization.PointValuePair; 033 import org.apache.commons.math3.optimization.MultivariateOptimizer; 034 035 /** 036 * Powell's BOBYQA algorithm. This implementation is translated and 037 * adapted from the Fortran version available 038 * <a href="http://plato.asu.edu/ftp/other_software/bobyqa.zip">here</a>. 039 * See <a href="http://www.optimization-online.org/DB_HTML/2010/05/2616.html"> 040 * this paper</a> for an introduction. 041 * <br/> 042 * BOBYQA is particularly well suited for high dimensional problems 043 * where derivatives are not available. In most cases it outperforms the 044 * {@link PowellOptimizer} significantly. Stochastic algorithms like 045 * {@link CMAESOptimizer} succeed more often than BOBYQA, but are more 046 * expensive. BOBYQA could also be considered as a replacement of any 047 * derivative-based optimizer when the derivatives are approximated by 048 * finite differences. 049 * 050 * @version $Id: BOBYQAOptimizer.java 1422230 2012-12-15 12:11:13Z erans $ 051 * @deprecated As of 3.1 (to be removed in 4.0). 052 * @since 3.0 053 */ 054 @Deprecated 055 public class BOBYQAOptimizer 056 extends BaseAbstractMultivariateSimpleBoundsOptimizer<MultivariateFunction> 057 implements MultivariateOptimizer { 058 /** Minimum dimension of the problem: {@value} */ 059 public static final int MINIMUM_PROBLEM_DIMENSION = 2; 060 /** Default value for {@link #initialTrustRegionRadius}: {@value} . */ 061 public static final double DEFAULT_INITIAL_RADIUS = 10.0; 062 /** Default value for {@link #stoppingTrustRegionRadius}: {@value} . */ 063 public static final double DEFAULT_STOPPING_RADIUS = 1E-8; 064 065 private static final double ZERO = 0d; 066 private static final double ONE = 1d; 067 private static final double TWO = 2d; 068 private static final double TEN = 10d; 069 private static final double SIXTEEN = 16d; 070 private static final double TWO_HUNDRED_FIFTY = 250d; 071 private static final double MINUS_ONE = -ONE; 072 private static final double HALF = ONE / 2; 073 private static final double ONE_OVER_FOUR = ONE / 4; 074 private static final double ONE_OVER_EIGHT = ONE / 8; 075 private static final double ONE_OVER_TEN = ONE / 10; 076 private static final double ONE_OVER_A_THOUSAND = ONE / 1000; 077 078 /** 079 * numberOfInterpolationPoints XXX 080 */ 081 private final int numberOfInterpolationPoints; 082 /** 083 * initialTrustRegionRadius XXX 084 */ 085 private double initialTrustRegionRadius; 086 /** 087 * stoppingTrustRegionRadius XXX 088 */ 089 private final double stoppingTrustRegionRadius; 090 /** Goal type (minimize or maximize). */ 091 private boolean isMinimize; 092 /** 093 * Current best values for the variables to be optimized. 094 * The vector will be changed in-place to contain the values of the least 095 * calculated objective function values. 096 */ 097 private ArrayRealVector currentBest; 098 /** Differences between the upper and lower bounds. */ 099 private double[] boundDifference; 100 /** 101 * Index of the interpolation point at the trust region center. 102 */ 103 private int trustRegionCenterInterpolationPointIndex; 104 /** 105 * Last <em>n</em> columns of matrix H (where <em>n</em> is the dimension 106 * of the problem). 107 * XXX "bmat" in the original code. 108 */ 109 private Array2DRowRealMatrix bMatrix; 110 /** 111 * Factorization of the leading <em>npt</em> square submatrix of H, this 112 * factorization being Z Z<sup>T</sup>, which provides both the correct 113 * rank and positive semi-definiteness. 114 * XXX "zmat" in the original code. 115 */ 116 private Array2DRowRealMatrix zMatrix; 117 /** 118 * Coordinates of the interpolation points relative to {@link #originShift}. 119 * XXX "xpt" in the original code. 120 */ 121 private Array2DRowRealMatrix interpolationPoints; 122 /** 123 * Shift of origin that should reduce the contributions from rounding 124 * errors to values of the model and Lagrange functions. 125 * XXX "xbase" in the original code. 126 */ 127 private ArrayRealVector originShift; 128 /** 129 * Values of the objective function at the interpolation points. 130 * XXX "fval" in the original code. 131 */ 132 private ArrayRealVector fAtInterpolationPoints; 133 /** 134 * Displacement from {@link #originShift} of the trust region center. 135 * XXX "xopt" in the original code. 136 */ 137 private ArrayRealVector trustRegionCenterOffset; 138 /** 139 * Gradient of the quadratic model at {@link #originShift} + 140 * {@link #trustRegionCenterOffset}. 141 * XXX "gopt" in the original code. 142 */ 143 private ArrayRealVector gradientAtTrustRegionCenter; 144 /** 145 * Differences {@link #getLowerBound()} - {@link #originShift}. 146 * All the components of every {@link #trustRegionCenterOffset} are going 147 * to satisfy the bounds<br/> 148 * {@link #getLowerBound() lowerBound}<sub>i</sub> ≤ 149 * {@link #trustRegionCenterOffset}<sub>i</sub>,<br/> 150 * with appropriate equalities when {@link #trustRegionCenterOffset} is 151 * on a constraint boundary. 152 * XXX "sl" in the original code. 153 */ 154 private ArrayRealVector lowerDifference; 155 /** 156 * Differences {@link #getUpperBound()} - {@link #originShift} 157 * All the components of every {@link #trustRegionCenterOffset} are going 158 * to satisfy the bounds<br/> 159 * {@link #trustRegionCenterOffset}<sub>i</sub> ≤ 160 * {@link #getUpperBound() upperBound}<sub>i</sub>,<br/> 161 * with appropriate equalities when {@link #trustRegionCenterOffset} is 162 * on a constraint boundary. 163 * XXX "su" in the original code. 164 */ 165 private ArrayRealVector upperDifference; 166 /** 167 * Parameters of the implicit second derivatives of the quadratic model. 168 * XXX "pq" in the original code. 169 */ 170 private ArrayRealVector modelSecondDerivativesParameters; 171 /** 172 * Point chosen by function {@link #trsbox(double,ArrayRealVector, 173 * ArrayRealVector, ArrayRealVector,ArrayRealVector,ArrayRealVector) trsbox} 174 * or {@link #altmov(int,double) altmov}. 175 * Usually {@link #originShift} + {@link #newPoint} is the vector of 176 * variables for the next evaluation of the objective function. 177 * It also satisfies the constraints indicated in {@link #lowerDifference} 178 * and {@link #upperDifference}. 179 * XXX "xnew" in the original code. 180 */ 181 private ArrayRealVector newPoint; 182 /** 183 * Alternative to {@link #newPoint}, chosen by 184 * {@link #altmov(int,double) altmov}. 185 * It may replace {@link #newPoint} in order to increase the denominator 186 * in the {@link #update(double, double, int) updating procedure}. 187 * XXX "xalt" in the original code. 188 */ 189 private ArrayRealVector alternativeNewPoint; 190 /** 191 * Trial step from {@link #trustRegionCenterOffset} which is usually 192 * {@link #newPoint} - {@link #trustRegionCenterOffset}. 193 * XXX "d__" in the original code. 194 */ 195 private ArrayRealVector trialStepPoint; 196 /** 197 * Values of the Lagrange functions at a new point. 198 * XXX "vlag" in the original code. 199 */ 200 private ArrayRealVector lagrangeValuesAtNewPoint; 201 /** 202 * Explicit second derivatives of the quadratic model. 203 * XXX "hq" in the original code. 204 */ 205 private ArrayRealVector modelSecondDerivativesValues; 206 207 /** 208 * @param numberOfInterpolationPoints Number of interpolation conditions. 209 * For a problem of dimension {@code n}, its value must be in the interval 210 * {@code [n+2, (n+1)(n+2)/2]}. 211 * Choices that exceed {@code 2n+1} are not recommended. 212 */ 213 public BOBYQAOptimizer(int numberOfInterpolationPoints) { 214 this(numberOfInterpolationPoints, 215 DEFAULT_INITIAL_RADIUS, 216 DEFAULT_STOPPING_RADIUS); 217 } 218 219 /** 220 * @param numberOfInterpolationPoints Number of interpolation conditions. 221 * For a problem of dimension {@code n}, its value must be in the interval 222 * {@code [n+2, (n+1)(n+2)/2]}. 223 * Choices that exceed {@code 2n+1} are not recommended. 224 * @param initialTrustRegionRadius Initial trust region radius. 225 * @param stoppingTrustRegionRadius Stopping trust region radius. 226 */ 227 public BOBYQAOptimizer(int numberOfInterpolationPoints, 228 double initialTrustRegionRadius, 229 double stoppingTrustRegionRadius) { 230 super(null); // No custom convergence criterion. 231 this.numberOfInterpolationPoints = numberOfInterpolationPoints; 232 this.initialTrustRegionRadius = initialTrustRegionRadius; 233 this.stoppingTrustRegionRadius = stoppingTrustRegionRadius; 234 } 235 236 /** {@inheritDoc} */ 237 @Override 238 protected PointValuePair doOptimize() { 239 final double[] lowerBound = getLowerBound(); 240 final double[] upperBound = getUpperBound(); 241 242 // Validity checks. 243 setup(lowerBound, upperBound); 244 245 isMinimize = (getGoalType() == GoalType.MINIMIZE); 246 currentBest = new ArrayRealVector(getStartPoint()); 247 248 final double value = bobyqa(lowerBound, upperBound); 249 250 return new PointValuePair(currentBest.getDataRef(), 251 isMinimize ? value : -value); 252 } 253 254 /** 255 * This subroutine seeks the least value of a function of many variables, 256 * by applying a trust region method that forms quadratic models by 257 * interpolation. There is usually some freedom in the interpolation 258 * conditions, which is taken up by minimizing the Frobenius norm of 259 * the change to the second derivative of the model, beginning with the 260 * zero matrix. The values of the variables are constrained by upper and 261 * lower bounds. The arguments of the subroutine are as follows. 262 * 263 * N must be set to the number of variables and must be at least two. 264 * NPT is the number of interpolation conditions. Its value must be in 265 * the interval [N+2,(N+1)(N+2)/2]. Choices that exceed 2*N+1 are not 266 * recommended. 267 * Initial values of the variables must be set in X(1),X(2),...,X(N). They 268 * will be changed to the values that give the least calculated F. 269 * For I=1,2,...,N, XL(I) and XU(I) must provide the lower and upper 270 * bounds, respectively, on X(I). The construction of quadratic models 271 * requires XL(I) to be strictly less than XU(I) for each I. Further, 272 * the contribution to a model from changes to the I-th variable is 273 * damaged severely by rounding errors if XU(I)-XL(I) is too small. 274 * RHOBEG and RHOEND must be set to the initial and final values of a trust 275 * region radius, so both must be positive with RHOEND no greater than 276 * RHOBEG. Typically, RHOBEG should be about one tenth of the greatest 277 * expected change to a variable, while RHOEND should indicate the 278 * accuracy that is required in the final values of the variables. An 279 * error return occurs if any of the differences XU(I)-XL(I), I=1,...,N, 280 * is less than 2*RHOBEG. 281 * MAXFUN must be set to an upper bound on the number of calls of CALFUN. 282 * The array W will be used for working space. Its length must be at least 283 * (NPT+5)*(NPT+N)+3*N*(N+5)/2. 284 * 285 * @param lowerBound Lower bounds. 286 * @param upperBound Upper bounds. 287 * @return the value of the objective at the optimum. 288 */ 289 private double bobyqa(double[] lowerBound, 290 double[] upperBound) { 291 printMethod(); // XXX 292 293 final int n = currentBest.getDimension(); 294 295 // Return if there is insufficient space between the bounds. Modify the 296 // initial X if necessary in order to avoid conflicts between the bounds 297 // and the construction of the first quadratic model. The lower and upper 298 // bounds on moves from the updated X are set now, in the ISL and ISU 299 // partitions of W, in order to provide useful and exact information about 300 // components of X that become within distance RHOBEG from their bounds. 301 302 for (int j = 0; j < n; j++) { 303 final double boundDiff = boundDifference[j]; 304 lowerDifference.setEntry(j, lowerBound[j] - currentBest.getEntry(j)); 305 upperDifference.setEntry(j, upperBound[j] - currentBest.getEntry(j)); 306 if (lowerDifference.getEntry(j) >= -initialTrustRegionRadius) { 307 if (lowerDifference.getEntry(j) >= ZERO) { 308 currentBest.setEntry(j, lowerBound[j]); 309 lowerDifference.setEntry(j, ZERO); 310 upperDifference.setEntry(j, boundDiff); 311 } else { 312 currentBest.setEntry(j, lowerBound[j] + initialTrustRegionRadius); 313 lowerDifference.setEntry(j, -initialTrustRegionRadius); 314 // Computing MAX 315 final double deltaOne = upperBound[j] - currentBest.getEntry(j); 316 upperDifference.setEntry(j, Math.max(deltaOne, initialTrustRegionRadius)); 317 } 318 } else if (upperDifference.getEntry(j) <= initialTrustRegionRadius) { 319 if (upperDifference.getEntry(j) <= ZERO) { 320 currentBest.setEntry(j, upperBound[j]); 321 lowerDifference.setEntry(j, -boundDiff); 322 upperDifference.setEntry(j, ZERO); 323 } else { 324 currentBest.setEntry(j, upperBound[j] - initialTrustRegionRadius); 325 // Computing MIN 326 final double deltaOne = lowerBound[j] - currentBest.getEntry(j); 327 final double deltaTwo = -initialTrustRegionRadius; 328 lowerDifference.setEntry(j, Math.min(deltaOne, deltaTwo)); 329 upperDifference.setEntry(j, initialTrustRegionRadius); 330 } 331 } 332 } 333 334 // Make the call of BOBYQB. 335 336 return bobyqb(lowerBound, upperBound); 337 } // bobyqa 338 339 // ---------------------------------------------------------------------------------------- 340 341 /** 342 * The arguments N, NPT, X, XL, XU, RHOBEG, RHOEND, IPRINT and MAXFUN 343 * are identical to the corresponding arguments in SUBROUTINE BOBYQA. 344 * XBASE holds a shift of origin that should reduce the contributions 345 * from rounding errors to values of the model and Lagrange functions. 346 * XPT is a two-dimensional array that holds the coordinates of the 347 * interpolation points relative to XBASE. 348 * FVAL holds the values of F at the interpolation points. 349 * XOPT is set to the displacement from XBASE of the trust region centre. 350 * GOPT holds the gradient of the quadratic model at XBASE+XOPT. 351 * HQ holds the explicit second derivatives of the quadratic model. 352 * PQ contains the parameters of the implicit second derivatives of the 353 * quadratic model. 354 * BMAT holds the last N columns of H. 355 * ZMAT holds the factorization of the leading NPT by NPT submatrix of H, 356 * this factorization being ZMAT times ZMAT^T, which provides both the 357 * correct rank and positive semi-definiteness. 358 * NDIM is the first dimension of BMAT and has the value NPT+N. 359 * SL and SU hold the differences XL-XBASE and XU-XBASE, respectively. 360 * All the components of every XOPT are going to satisfy the bounds 361 * SL(I) .LEQ. XOPT(I) .LEQ. SU(I), with appropriate equalities when 362 * XOPT is on a constraint boundary. 363 * XNEW is chosen by SUBROUTINE TRSBOX or ALTMOV. Usually XBASE+XNEW is the 364 * vector of variables for the next call of CALFUN. XNEW also satisfies 365 * the SL and SU constraints in the way that has just been mentioned. 366 * XALT is an alternative to XNEW, chosen by ALTMOV, that may replace XNEW 367 * in order to increase the denominator in the updating of UPDATE. 368 * D is reserved for a trial step from XOPT, which is usually XNEW-XOPT. 369 * VLAG contains the values of the Lagrange functions at a new point X. 370 * They are part of a product that requires VLAG to be of length NDIM. 371 * W is a one-dimensional array that is used for working space. Its length 372 * must be at least 3*NDIM = 3*(NPT+N). 373 * 374 * @param lowerBound Lower bounds. 375 * @param upperBound Upper bounds. 376 * @return the value of the objective at the optimum. 377 */ 378 private double bobyqb(double[] lowerBound, 379 double[] upperBound) { 380 printMethod(); // XXX 381 382 final int n = currentBest.getDimension(); 383 final int npt = numberOfInterpolationPoints; 384 final int np = n + 1; 385 final int nptm = npt - np; 386 final int nh = n * np / 2; 387 388 final ArrayRealVector work1 = new ArrayRealVector(n); 389 final ArrayRealVector work2 = new ArrayRealVector(npt); 390 final ArrayRealVector work3 = new ArrayRealVector(npt); 391 392 double cauchy = Double.NaN; 393 double alpha = Double.NaN; 394 double dsq = Double.NaN; 395 double crvmin = Double.NaN; 396 397 // Set some constants. 398 // Parameter adjustments 399 400 // Function Body 401 402 // The call of PRELIM sets the elements of XBASE, XPT, FVAL, GOPT, HQ, PQ, 403 // BMAT and ZMAT for the first iteration, with the corresponding values of 404 // of NF and KOPT, which are the number of calls of CALFUN so far and the 405 // index of the interpolation point at the trust region centre. Then the 406 // initial XOPT is set too. The branch to label 720 occurs if MAXFUN is 407 // less than NPT. GOPT will be updated if KOPT is different from KBASE. 408 409 trustRegionCenterInterpolationPointIndex = 0; 410 411 prelim(lowerBound, upperBound); 412 double xoptsq = ZERO; 413 for (int i = 0; i < n; i++) { 414 trustRegionCenterOffset.setEntry(i, interpolationPoints.getEntry(trustRegionCenterInterpolationPointIndex, i)); 415 // Computing 2nd power 416 final double deltaOne = trustRegionCenterOffset.getEntry(i); 417 xoptsq += deltaOne * deltaOne; 418 } 419 double fsave = fAtInterpolationPoints.getEntry(0); 420 final int kbase = 0; 421 422 // Complete the settings that are required for the iterative procedure. 423 424 int ntrits = 0; 425 int itest = 0; 426 int knew = 0; 427 int nfsav = getEvaluations(); 428 double rho = initialTrustRegionRadius; 429 double delta = rho; 430 double diffa = ZERO; 431 double diffb = ZERO; 432 double diffc = ZERO; 433 double f = ZERO; 434 double beta = ZERO; 435 double adelt = ZERO; 436 double denom = ZERO; 437 double ratio = ZERO; 438 double dnorm = ZERO; 439 double scaden = ZERO; 440 double biglsq = ZERO; 441 double distsq = ZERO; 442 443 // Update GOPT if necessary before the first iteration and after each 444 // call of RESCUE that makes a call of CALFUN. 445 446 int state = 20; 447 for(;;) switch (state) { 448 case 20: { 449 printState(20); // XXX 450 if (trustRegionCenterInterpolationPointIndex != kbase) { 451 int ih = 0; 452 for (int j = 0; j < n; j++) { 453 for (int i = 0; i <= j; i++) { 454 if (i < j) { 455 gradientAtTrustRegionCenter.setEntry(j, gradientAtTrustRegionCenter.getEntry(j) + modelSecondDerivativesValues.getEntry(ih) * trustRegionCenterOffset.getEntry(i)); 456 } 457 gradientAtTrustRegionCenter.setEntry(i, gradientAtTrustRegionCenter.getEntry(i) + modelSecondDerivativesValues.getEntry(ih) * trustRegionCenterOffset.getEntry(j)); 458 ih++; 459 } 460 } 461 if (getEvaluations() > npt) { 462 for (int k = 0; k < npt; k++) { 463 double temp = ZERO; 464 for (int j = 0; j < n; j++) { 465 temp += interpolationPoints.getEntry(k, j) * trustRegionCenterOffset.getEntry(j); 466 } 467 temp *= modelSecondDerivativesParameters.getEntry(k); 468 for (int i = 0; i < n; i++) { 469 gradientAtTrustRegionCenter.setEntry(i, gradientAtTrustRegionCenter.getEntry(i) + temp * interpolationPoints.getEntry(k, i)); 470 } 471 } 472 // throw new PathIsExploredException(); // XXX 473 } 474 } 475 476 // Generate the next point in the trust region that provides a small value 477 // of the quadratic model subject to the constraints on the variables. 478 // The int NTRITS is set to the number "trust region" iterations that 479 // have occurred since the last "alternative" iteration. If the length 480 // of XNEW-XOPT is less than HALF*RHO, however, then there is a branch to 481 // label 650 or 680 with NTRITS=-1, instead of calculating F at XNEW. 482 483 } 484 case 60: { 485 printState(60); // XXX 486 final ArrayRealVector gnew = new ArrayRealVector(n); 487 final ArrayRealVector xbdi = new ArrayRealVector(n); 488 final ArrayRealVector s = new ArrayRealVector(n); 489 final ArrayRealVector hs = new ArrayRealVector(n); 490 final ArrayRealVector hred = new ArrayRealVector(n); 491 492 final double[] dsqCrvmin = trsbox(delta, gnew, xbdi, s, 493 hs, hred); 494 dsq = dsqCrvmin[0]; 495 crvmin = dsqCrvmin[1]; 496 497 // Computing MIN 498 double deltaOne = delta; 499 double deltaTwo = Math.sqrt(dsq); 500 dnorm = Math.min(deltaOne, deltaTwo); 501 if (dnorm < HALF * rho) { 502 ntrits = -1; 503 // Computing 2nd power 504 deltaOne = TEN * rho; 505 distsq = deltaOne * deltaOne; 506 if (getEvaluations() <= nfsav + 2) { 507 state = 650; break; 508 } 509 510 // The following choice between labels 650 and 680 depends on whether or 511 // not our work with the current RHO seems to be complete. Either RHO is 512 // decreased or termination occurs if the errors in the quadratic model at 513 // the last three interpolation points compare favourably with predictions 514 // of likely improvements to the model within distance HALF*RHO of XOPT. 515 516 // Computing MAX 517 deltaOne = Math.max(diffa, diffb); 518 final double errbig = Math.max(deltaOne, diffc); 519 final double frhosq = rho * ONE_OVER_EIGHT * rho; 520 if (crvmin > ZERO && 521 errbig > frhosq * crvmin) { 522 state = 650; break; 523 } 524 final double bdtol = errbig / rho; 525 for (int j = 0; j < n; j++) { 526 double bdtest = bdtol; 527 if (newPoint.getEntry(j) == lowerDifference.getEntry(j)) { 528 bdtest = work1.getEntry(j); 529 } 530 if (newPoint.getEntry(j) == upperDifference.getEntry(j)) { 531 bdtest = -work1.getEntry(j); 532 } 533 if (bdtest < bdtol) { 534 double curv = modelSecondDerivativesValues.getEntry((j + j * j) / 2); 535 for (int k = 0; k < npt; k++) { 536 // Computing 2nd power 537 final double d1 = interpolationPoints.getEntry(k, j); 538 curv += modelSecondDerivativesParameters.getEntry(k) * (d1 * d1); 539 } 540 bdtest += HALF * curv * rho; 541 if (bdtest < bdtol) { 542 state = 650; break; 543 } 544 // throw new PathIsExploredException(); // XXX 545 } 546 } 547 state = 680; break; 548 } 549 ++ntrits; 550 551 // Severe cancellation is likely to occur if XOPT is too far from XBASE. 552 // If the following test holds, then XBASE is shifted so that XOPT becomes 553 // zero. The appropriate changes are made to BMAT and to the second 554 // derivatives of the current model, beginning with the changes to BMAT 555 // that do not depend on ZMAT. VLAG is used temporarily for working space. 556 557 } 558 case 90: { 559 printState(90); // XXX 560 if (dsq <= xoptsq * ONE_OVER_A_THOUSAND) { 561 final double fracsq = xoptsq * ONE_OVER_FOUR; 562 double sumpq = ZERO; 563 // final RealVector sumVector 564 // = new ArrayRealVector(npt, -HALF * xoptsq).add(interpolationPoints.operate(trustRegionCenter)); 565 for (int k = 0; k < npt; k++) { 566 sumpq += modelSecondDerivativesParameters.getEntry(k); 567 double sum = -HALF * xoptsq; 568 for (int i = 0; i < n; i++) { 569 sum += interpolationPoints.getEntry(k, i) * trustRegionCenterOffset.getEntry(i); 570 } 571 // sum = sumVector.getEntry(k); // XXX "testAckley" and "testDiffPow" fail. 572 work2.setEntry(k, sum); 573 final double temp = fracsq - HALF * sum; 574 for (int i = 0; i < n; i++) { 575 work1.setEntry(i, bMatrix.getEntry(k, i)); 576 lagrangeValuesAtNewPoint.setEntry(i, sum * interpolationPoints.getEntry(k, i) + temp * trustRegionCenterOffset.getEntry(i)); 577 final int ip = npt + i; 578 for (int j = 0; j <= i; j++) { 579 bMatrix.setEntry(ip, j, 580 bMatrix.getEntry(ip, j) 581 + work1.getEntry(i) * lagrangeValuesAtNewPoint.getEntry(j) 582 + lagrangeValuesAtNewPoint.getEntry(i) * work1.getEntry(j)); 583 } 584 } 585 } 586 587 // Then the revisions of BMAT that depend on ZMAT are calculated. 588 589 for (int m = 0; m < nptm; m++) { 590 double sumz = ZERO; 591 double sumw = ZERO; 592 for (int k = 0; k < npt; k++) { 593 sumz += zMatrix.getEntry(k, m); 594 lagrangeValuesAtNewPoint.setEntry(k, work2.getEntry(k) * zMatrix.getEntry(k, m)); 595 sumw += lagrangeValuesAtNewPoint.getEntry(k); 596 } 597 for (int j = 0; j < n; j++) { 598 double sum = (fracsq * sumz - HALF * sumw) * trustRegionCenterOffset.getEntry(j); 599 for (int k = 0; k < npt; k++) { 600 sum += lagrangeValuesAtNewPoint.getEntry(k) * interpolationPoints.getEntry(k, j); 601 } 602 work1.setEntry(j, sum); 603 for (int k = 0; k < npt; k++) { 604 bMatrix.setEntry(k, j, 605 bMatrix.getEntry(k, j) 606 + sum * zMatrix.getEntry(k, m)); 607 } 608 } 609 for (int i = 0; i < n; i++) { 610 final int ip = i + npt; 611 final double temp = work1.getEntry(i); 612 for (int j = 0; j <= i; j++) { 613 bMatrix.setEntry(ip, j, 614 bMatrix.getEntry(ip, j) 615 + temp * work1.getEntry(j)); 616 } 617 } 618 } 619 620 // The following instructions complete the shift, including the changes 621 // to the second derivative parameters of the quadratic model. 622 623 int ih = 0; 624 for (int j = 0; j < n; j++) { 625 work1.setEntry(j, -HALF * sumpq * trustRegionCenterOffset.getEntry(j)); 626 for (int k = 0; k < npt; k++) { 627 work1.setEntry(j, work1.getEntry(j) + modelSecondDerivativesParameters.getEntry(k) * interpolationPoints.getEntry(k, j)); 628 interpolationPoints.setEntry(k, j, interpolationPoints.getEntry(k, j) - trustRegionCenterOffset.getEntry(j)); 629 } 630 for (int i = 0; i <= j; i++) { 631 modelSecondDerivativesValues.setEntry(ih, 632 modelSecondDerivativesValues.getEntry(ih) 633 + work1.getEntry(i) * trustRegionCenterOffset.getEntry(j) 634 + trustRegionCenterOffset.getEntry(i) * work1.getEntry(j)); 635 bMatrix.setEntry(npt + i, j, bMatrix.getEntry(npt + j, i)); 636 ih++; 637 } 638 } 639 for (int i = 0; i < n; i++) { 640 originShift.setEntry(i, originShift.getEntry(i) + trustRegionCenterOffset.getEntry(i)); 641 newPoint.setEntry(i, newPoint.getEntry(i) - trustRegionCenterOffset.getEntry(i)); 642 lowerDifference.setEntry(i, lowerDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i)); 643 upperDifference.setEntry(i, upperDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i)); 644 trustRegionCenterOffset.setEntry(i, ZERO); 645 } 646 xoptsq = ZERO; 647 } 648 if (ntrits == 0) { 649 state = 210; break; 650 } 651 state = 230; break; 652 653 // XBASE is also moved to XOPT by a call of RESCUE. This calculation is 654 // more expensive than the previous shift, because new matrices BMAT and 655 // ZMAT are generated from scratch, which may include the replacement of 656 // interpolation points whose positions seem to be causing near linear 657 // dependence in the interpolation conditions. Therefore RESCUE is called 658 // only if rounding errors have reduced by at least a factor of two the 659 // denominator of the formula for updating the H matrix. It provides a 660 // useful safeguard, but is not invoked in most applications of BOBYQA. 661 662 } 663 case 210: { 664 printState(210); // XXX 665 // Pick two alternative vectors of variables, relative to XBASE, that 666 // are suitable as new positions of the KNEW-th interpolation point. 667 // Firstly, XNEW is set to the point on a line through XOPT and another 668 // interpolation point that minimizes the predicted value of the next 669 // denominator, subject to ||XNEW - XOPT|| .LEQ. ADELT and to the SL 670 // and SU bounds. Secondly, XALT is set to the best feasible point on 671 // a constrained version of the Cauchy step of the KNEW-th Lagrange 672 // function, the corresponding value of the square of this function 673 // being returned in CAUCHY. The choice between these alternatives is 674 // going to be made when the denominator is calculated. 675 676 final double[] alphaCauchy = altmov(knew, adelt); 677 alpha = alphaCauchy[0]; 678 cauchy = alphaCauchy[1]; 679 680 for (int i = 0; i < n; i++) { 681 trialStepPoint.setEntry(i, newPoint.getEntry(i) - trustRegionCenterOffset.getEntry(i)); 682 } 683 684 // Calculate VLAG and BETA for the current choice of D. The scalar 685 // product of D with XPT(K,.) is going to be held in W(NPT+K) for 686 // use when VQUAD is calculated. 687 688 } 689 case 230: { 690 printState(230); // XXX 691 for (int k = 0; k < npt; k++) { 692 double suma = ZERO; 693 double sumb = ZERO; 694 double sum = ZERO; 695 for (int j = 0; j < n; j++) { 696 suma += interpolationPoints.getEntry(k, j) * trialStepPoint.getEntry(j); 697 sumb += interpolationPoints.getEntry(k, j) * trustRegionCenterOffset.getEntry(j); 698 sum += bMatrix.getEntry(k, j) * trialStepPoint.getEntry(j); 699 } 700 work3.setEntry(k, suma * (HALF * suma + sumb)); 701 lagrangeValuesAtNewPoint.setEntry(k, sum); 702 work2.setEntry(k, suma); 703 } 704 beta = ZERO; 705 for (int m = 0; m < nptm; m++) { 706 double sum = ZERO; 707 for (int k = 0; k < npt; k++) { 708 sum += zMatrix.getEntry(k, m) * work3.getEntry(k); 709 } 710 beta -= sum * sum; 711 for (int k = 0; k < npt; k++) { 712 lagrangeValuesAtNewPoint.setEntry(k, lagrangeValuesAtNewPoint.getEntry(k) + sum * zMatrix.getEntry(k, m)); 713 } 714 } 715 dsq = ZERO; 716 double bsum = ZERO; 717 double dx = ZERO; 718 for (int j = 0; j < n; j++) { 719 // Computing 2nd power 720 final double d1 = trialStepPoint.getEntry(j); 721 dsq += d1 * d1; 722 double sum = ZERO; 723 for (int k = 0; k < npt; k++) { 724 sum += work3.getEntry(k) * bMatrix.getEntry(k, j); 725 } 726 bsum += sum * trialStepPoint.getEntry(j); 727 final int jp = npt + j; 728 for (int i = 0; i < n; i++) { 729 sum += bMatrix.getEntry(jp, i) * trialStepPoint.getEntry(i); 730 } 731 lagrangeValuesAtNewPoint.setEntry(jp, sum); 732 bsum += sum * trialStepPoint.getEntry(j); 733 dx += trialStepPoint.getEntry(j) * trustRegionCenterOffset.getEntry(j); 734 } 735 736 beta = dx * dx + dsq * (xoptsq + dx + dx + HALF * dsq) + beta - bsum; // Original 737 // beta += dx * dx + dsq * (xoptsq + dx + dx + HALF * dsq) - bsum; // XXX "testAckley" and "testDiffPow" fail. 738 // beta = dx * dx + dsq * (xoptsq + 2 * dx + HALF * dsq) + beta - bsum; // XXX "testDiffPow" fails. 739 740 lagrangeValuesAtNewPoint.setEntry(trustRegionCenterInterpolationPointIndex, 741 lagrangeValuesAtNewPoint.getEntry(trustRegionCenterInterpolationPointIndex) + ONE); 742 743 // If NTRITS is zero, the denominator may be increased by replacing 744 // the step D of ALTMOV by a Cauchy step. Then RESCUE may be called if 745 // rounding errors have damaged the chosen denominator. 746 747 if (ntrits == 0) { 748 // Computing 2nd power 749 final double d1 = lagrangeValuesAtNewPoint.getEntry(knew); 750 denom = d1 * d1 + alpha * beta; 751 if (denom < cauchy && cauchy > ZERO) { 752 for (int i = 0; i < n; i++) { 753 newPoint.setEntry(i, alternativeNewPoint.getEntry(i)); 754 trialStepPoint.setEntry(i, newPoint.getEntry(i) - trustRegionCenterOffset.getEntry(i)); 755 } 756 cauchy = ZERO; // XXX Useful statement? 757 state = 230; break; 758 } 759 // Alternatively, if NTRITS is positive, then set KNEW to the index of 760 // the next interpolation point to be deleted to make room for a trust 761 // region step. Again RESCUE may be called if rounding errors have damaged_ 762 // the chosen denominator, which is the reason for attempting to select 763 // KNEW before calculating the next value of the objective function. 764 765 } else { 766 final double delsq = delta * delta; 767 scaden = ZERO; 768 biglsq = ZERO; 769 knew = 0; 770 for (int k = 0; k < npt; k++) { 771 if (k == trustRegionCenterInterpolationPointIndex) { 772 continue; 773 } 774 double hdiag = ZERO; 775 for (int m = 0; m < nptm; m++) { 776 // Computing 2nd power 777 final double d1 = zMatrix.getEntry(k, m); 778 hdiag += d1 * d1; 779 } 780 // Computing 2nd power 781 final double d2 = lagrangeValuesAtNewPoint.getEntry(k); 782 final double den = beta * hdiag + d2 * d2; 783 distsq = ZERO; 784 for (int j = 0; j < n; j++) { 785 // Computing 2nd power 786 final double d3 = interpolationPoints.getEntry(k, j) - trustRegionCenterOffset.getEntry(j); 787 distsq += d3 * d3; 788 } 789 // Computing MAX 790 // Computing 2nd power 791 final double d4 = distsq / delsq; 792 final double temp = Math.max(ONE, d4 * d4); 793 if (temp * den > scaden) { 794 scaden = temp * den; 795 knew = k; 796 denom = den; 797 } 798 // Computing MAX 799 // Computing 2nd power 800 final double d5 = lagrangeValuesAtNewPoint.getEntry(k); 801 biglsq = Math.max(biglsq, temp * (d5 * d5)); 802 } 803 } 804 805 // Put the variables for the next calculation of the objective function 806 // in XNEW, with any adjustments for the bounds. 807 808 // Calculate the value of the objective function at XBASE+XNEW, unless 809 // the limit on the number of calculations of F has been reached. 810 811 } 812 case 360: { 813 printState(360); // XXX 814 for (int i = 0; i < n; i++) { 815 // Computing MIN 816 // Computing MAX 817 final double d3 = lowerBound[i]; 818 final double d4 = originShift.getEntry(i) + newPoint.getEntry(i); 819 final double d1 = Math.max(d3, d4); 820 final double d2 = upperBound[i]; 821 currentBest.setEntry(i, Math.min(d1, d2)); 822 if (newPoint.getEntry(i) == lowerDifference.getEntry(i)) { 823 currentBest.setEntry(i, lowerBound[i]); 824 } 825 if (newPoint.getEntry(i) == upperDifference.getEntry(i)) { 826 currentBest.setEntry(i, upperBound[i]); 827 } 828 } 829 830 f = computeObjectiveValue(currentBest.toArray()); 831 832 if (!isMinimize) 833 f = -f; 834 if (ntrits == -1) { 835 fsave = f; 836 state = 720; break; 837 } 838 839 // Use the quadratic model to predict the change in F due to the step D, 840 // and set DIFF to the error of this prediction. 841 842 final double fopt = fAtInterpolationPoints.getEntry(trustRegionCenterInterpolationPointIndex); 843 double vquad = ZERO; 844 int ih = 0; 845 for (int j = 0; j < n; j++) { 846 vquad += trialStepPoint.getEntry(j) * gradientAtTrustRegionCenter.getEntry(j); 847 for (int i = 0; i <= j; i++) { 848 double temp = trialStepPoint.getEntry(i) * trialStepPoint.getEntry(j); 849 if (i == j) { 850 temp *= HALF; 851 } 852 vquad += modelSecondDerivativesValues.getEntry(ih) * temp; 853 ih++; 854 } 855 } 856 for (int k = 0; k < npt; k++) { 857 // Computing 2nd power 858 final double d1 = work2.getEntry(k); 859 final double d2 = d1 * d1; // "d1" must be squared first to prevent test failures. 860 vquad += HALF * modelSecondDerivativesParameters.getEntry(k) * d2; 861 } 862 final double diff = f - fopt - vquad; 863 diffc = diffb; 864 diffb = diffa; 865 diffa = Math.abs(diff); 866 if (dnorm > rho) { 867 nfsav = getEvaluations(); 868 } 869 870 // Pick the next value of DELTA after a trust region step. 871 872 if (ntrits > 0) { 873 if (vquad >= ZERO) { 874 throw new MathIllegalStateException(LocalizedFormats.TRUST_REGION_STEP_FAILED, vquad); 875 } 876 ratio = (f - fopt) / vquad; 877 final double hDelta = HALF * delta; 878 if (ratio <= ONE_OVER_TEN) { 879 // Computing MIN 880 delta = Math.min(hDelta, dnorm); 881 } else if (ratio <= .7) { 882 // Computing MAX 883 delta = Math.max(hDelta, dnorm); 884 } else { 885 // Computing MAX 886 delta = Math.max(hDelta, 2 * dnorm); 887 } 888 if (delta <= rho * 1.5) { 889 delta = rho; 890 } 891 892 // Recalculate KNEW and DENOM if the new F is less than FOPT. 893 894 if (f < fopt) { 895 final int ksav = knew; 896 final double densav = denom; 897 final double delsq = delta * delta; 898 scaden = ZERO; 899 biglsq = ZERO; 900 knew = 0; 901 for (int k = 0; k < npt; k++) { 902 double hdiag = ZERO; 903 for (int m = 0; m < nptm; m++) { 904 // Computing 2nd power 905 final double d1 = zMatrix.getEntry(k, m); 906 hdiag += d1 * d1; 907 } 908 // Computing 2nd power 909 final double d1 = lagrangeValuesAtNewPoint.getEntry(k); 910 final double den = beta * hdiag + d1 * d1; 911 distsq = ZERO; 912 for (int j = 0; j < n; j++) { 913 // Computing 2nd power 914 final double d2 = interpolationPoints.getEntry(k, j) - newPoint.getEntry(j); 915 distsq += d2 * d2; 916 } 917 // Computing MAX 918 // Computing 2nd power 919 final double d3 = distsq / delsq; 920 final double temp = Math.max(ONE, d3 * d3); 921 if (temp * den > scaden) { 922 scaden = temp * den; 923 knew = k; 924 denom = den; 925 } 926 // Computing MAX 927 // Computing 2nd power 928 final double d4 = lagrangeValuesAtNewPoint.getEntry(k); 929 final double d5 = temp * (d4 * d4); 930 biglsq = Math.max(biglsq, d5); 931 } 932 if (scaden <= HALF * biglsq) { 933 knew = ksav; 934 denom = densav; 935 } 936 } 937 } 938 939 // Update BMAT and ZMAT, so that the KNEW-th interpolation point can be 940 // moved. Also update the second derivative terms of the model. 941 942 update(beta, denom, knew); 943 944 ih = 0; 945 final double pqold = modelSecondDerivativesParameters.getEntry(knew); 946 modelSecondDerivativesParameters.setEntry(knew, ZERO); 947 for (int i = 0; i < n; i++) { 948 final double temp = pqold * interpolationPoints.getEntry(knew, i); 949 for (int j = 0; j <= i; j++) { 950 modelSecondDerivativesValues.setEntry(ih, modelSecondDerivativesValues.getEntry(ih) + temp * interpolationPoints.getEntry(knew, j)); 951 ih++; 952 } 953 } 954 for (int m = 0; m < nptm; m++) { 955 final double temp = diff * zMatrix.getEntry(knew, m); 956 for (int k = 0; k < npt; k++) { 957 modelSecondDerivativesParameters.setEntry(k, modelSecondDerivativesParameters.getEntry(k) + temp * zMatrix.getEntry(k, m)); 958 } 959 } 960 961 // Include the new interpolation point, and make the changes to GOPT at 962 // the old XOPT that are caused by the updating of the quadratic model. 963 964 fAtInterpolationPoints.setEntry(knew, f); 965 for (int i = 0; i < n; i++) { 966 interpolationPoints.setEntry(knew, i, newPoint.getEntry(i)); 967 work1.setEntry(i, bMatrix.getEntry(knew, i)); 968 } 969 for (int k = 0; k < npt; k++) { 970 double suma = ZERO; 971 for (int m = 0; m < nptm; m++) { 972 suma += zMatrix.getEntry(knew, m) * zMatrix.getEntry(k, m); 973 } 974 double sumb = ZERO; 975 for (int j = 0; j < n; j++) { 976 sumb += interpolationPoints.getEntry(k, j) * trustRegionCenterOffset.getEntry(j); 977 } 978 final double temp = suma * sumb; 979 for (int i = 0; i < n; i++) { 980 work1.setEntry(i, work1.getEntry(i) + temp * interpolationPoints.getEntry(k, i)); 981 } 982 } 983 for (int i = 0; i < n; i++) { 984 gradientAtTrustRegionCenter.setEntry(i, gradientAtTrustRegionCenter.getEntry(i) + diff * work1.getEntry(i)); 985 } 986 987 // Update XOPT, GOPT and KOPT if the new calculated F is less than FOPT. 988 989 if (f < fopt) { 990 trustRegionCenterInterpolationPointIndex = knew; 991 xoptsq = ZERO; 992 ih = 0; 993 for (int j = 0; j < n; j++) { 994 trustRegionCenterOffset.setEntry(j, newPoint.getEntry(j)); 995 // Computing 2nd power 996 final double d1 = trustRegionCenterOffset.getEntry(j); 997 xoptsq += d1 * d1; 998 for (int i = 0; i <= j; i++) { 999 if (i < j) { 1000 gradientAtTrustRegionCenter.setEntry(j, gradientAtTrustRegionCenter.getEntry(j) + modelSecondDerivativesValues.getEntry(ih) * trialStepPoint.getEntry(i)); 1001 } 1002 gradientAtTrustRegionCenter.setEntry(i, gradientAtTrustRegionCenter.getEntry(i) + modelSecondDerivativesValues.getEntry(ih) * trialStepPoint.getEntry(j)); 1003 ih++; 1004 } 1005 } 1006 for (int k = 0; k < npt; k++) { 1007 double temp = ZERO; 1008 for (int j = 0; j < n; j++) { 1009 temp += interpolationPoints.getEntry(k, j) * trialStepPoint.getEntry(j); 1010 } 1011 temp *= modelSecondDerivativesParameters.getEntry(k); 1012 for (int i = 0; i < n; i++) { 1013 gradientAtTrustRegionCenter.setEntry(i, gradientAtTrustRegionCenter.getEntry(i) + temp * interpolationPoints.getEntry(k, i)); 1014 } 1015 } 1016 } 1017 1018 // Calculate the parameters of the least Frobenius norm interpolant to 1019 // the current data, the gradient of this interpolant at XOPT being put 1020 // into VLAG(NPT+I), I=1,2,...,N. 1021 1022 if (ntrits > 0) { 1023 for (int k = 0; k < npt; k++) { 1024 lagrangeValuesAtNewPoint.setEntry(k, fAtInterpolationPoints.getEntry(k) - fAtInterpolationPoints.getEntry(trustRegionCenterInterpolationPointIndex)); 1025 work3.setEntry(k, ZERO); 1026 } 1027 for (int j = 0; j < nptm; j++) { 1028 double sum = ZERO; 1029 for (int k = 0; k < npt; k++) { 1030 sum += zMatrix.getEntry(k, j) * lagrangeValuesAtNewPoint.getEntry(k); 1031 } 1032 for (int k = 0; k < npt; k++) { 1033 work3.setEntry(k, work3.getEntry(k) + sum * zMatrix.getEntry(k, j)); 1034 } 1035 } 1036 for (int k = 0; k < npt; k++) { 1037 double sum = ZERO; 1038 for (int j = 0; j < n; j++) { 1039 sum += interpolationPoints.getEntry(k, j) * trustRegionCenterOffset.getEntry(j); 1040 } 1041 work2.setEntry(k, work3.getEntry(k)); 1042 work3.setEntry(k, sum * work3.getEntry(k)); 1043 } 1044 double gqsq = ZERO; 1045 double gisq = ZERO; 1046 for (int i = 0; i < n; i++) { 1047 double sum = ZERO; 1048 for (int k = 0; k < npt; k++) { 1049 sum += bMatrix.getEntry(k, i) * 1050 lagrangeValuesAtNewPoint.getEntry(k) + interpolationPoints.getEntry(k, i) * work3.getEntry(k); 1051 } 1052 if (trustRegionCenterOffset.getEntry(i) == lowerDifference.getEntry(i)) { 1053 // Computing MIN 1054 // Computing 2nd power 1055 final double d1 = Math.min(ZERO, gradientAtTrustRegionCenter.getEntry(i)); 1056 gqsq += d1 * d1; 1057 // Computing 2nd power 1058 final double d2 = Math.min(ZERO, sum); 1059 gisq += d2 * d2; 1060 } else if (trustRegionCenterOffset.getEntry(i) == upperDifference.getEntry(i)) { 1061 // Computing MAX 1062 // Computing 2nd power 1063 final double d1 = Math.max(ZERO, gradientAtTrustRegionCenter.getEntry(i)); 1064 gqsq += d1 * d1; 1065 // Computing 2nd power 1066 final double d2 = Math.max(ZERO, sum); 1067 gisq += d2 * d2; 1068 } else { 1069 // Computing 2nd power 1070 final double d1 = gradientAtTrustRegionCenter.getEntry(i); 1071 gqsq += d1 * d1; 1072 gisq += sum * sum; 1073 } 1074 lagrangeValuesAtNewPoint.setEntry(npt + i, sum); 1075 } 1076 1077 // Test whether to replace the new quadratic model by the least Frobenius 1078 // norm interpolant, making the replacement if the test is satisfied. 1079 1080 ++itest; 1081 if (gqsq < TEN * gisq) { 1082 itest = 0; 1083 } 1084 if (itest >= 3) { 1085 for (int i = 0, max = Math.max(npt, nh); i < max; i++) { 1086 if (i < n) { 1087 gradientAtTrustRegionCenter.setEntry(i, lagrangeValuesAtNewPoint.getEntry(npt + i)); 1088 } 1089 if (i < npt) { 1090 modelSecondDerivativesParameters.setEntry(i, work2.getEntry(i)); 1091 } 1092 if (i < nh) { 1093 modelSecondDerivativesValues.setEntry(i, ZERO); 1094 } 1095 itest = 0; 1096 } 1097 } 1098 } 1099 1100 // If a trust region step has provided a sufficient decrease in F, then 1101 // branch for another trust region calculation. The case NTRITS=0 occurs 1102 // when the new interpolation point was reached by an alternative step. 1103 1104 if (ntrits == 0) { 1105 state = 60; break; 1106 } 1107 if (f <= fopt + ONE_OVER_TEN * vquad) { 1108 state = 60; break; 1109 } 1110 1111 // Alternatively, find out if the interpolation points are close enough 1112 // to the best point so far. 1113 1114 // Computing MAX 1115 // Computing 2nd power 1116 final double d1 = TWO * delta; 1117 // Computing 2nd power 1118 final double d2 = TEN * rho; 1119 distsq = Math.max(d1 * d1, d2 * d2); 1120 } 1121 case 650: { 1122 printState(650); // XXX 1123 knew = -1; 1124 for (int k = 0; k < npt; k++) { 1125 double sum = ZERO; 1126 for (int j = 0; j < n; j++) { 1127 // Computing 2nd power 1128 final double d1 = interpolationPoints.getEntry(k, j) - trustRegionCenterOffset.getEntry(j); 1129 sum += d1 * d1; 1130 } 1131 if (sum > distsq) { 1132 knew = k; 1133 distsq = sum; 1134 } 1135 } 1136 1137 // If KNEW is positive, then ALTMOV finds alternative new positions for 1138 // the KNEW-th interpolation point within distance ADELT of XOPT. It is 1139 // reached via label 90. Otherwise, there is a branch to label 60 for 1140 // another trust region iteration, unless the calculations with the 1141 // current RHO are complete. 1142 1143 if (knew >= 0) { 1144 final double dist = Math.sqrt(distsq); 1145 if (ntrits == -1) { 1146 // Computing MIN 1147 delta = Math.min(ONE_OVER_TEN * delta, HALF * dist); 1148 if (delta <= rho * 1.5) { 1149 delta = rho; 1150 } 1151 } 1152 ntrits = 0; 1153 // Computing MAX 1154 // Computing MIN 1155 final double d1 = Math.min(ONE_OVER_TEN * dist, delta); 1156 adelt = Math.max(d1, rho); 1157 dsq = adelt * adelt; 1158 state = 90; break; 1159 } 1160 if (ntrits == -1) { 1161 state = 680; break; 1162 } 1163 if (ratio > ZERO) { 1164 state = 60; break; 1165 } 1166 if (Math.max(delta, dnorm) > rho) { 1167 state = 60; break; 1168 } 1169 1170 // The calculations with the current value of RHO are complete. Pick the 1171 // next values of RHO and DELTA. 1172 } 1173 case 680: { 1174 printState(680); // XXX 1175 if (rho > stoppingTrustRegionRadius) { 1176 delta = HALF * rho; 1177 ratio = rho / stoppingTrustRegionRadius; 1178 if (ratio <= SIXTEEN) { 1179 rho = stoppingTrustRegionRadius; 1180 } else if (ratio <= TWO_HUNDRED_FIFTY) { 1181 rho = Math.sqrt(ratio) * stoppingTrustRegionRadius; 1182 } else { 1183 rho *= ONE_OVER_TEN; 1184 } 1185 delta = Math.max(delta, rho); 1186 ntrits = 0; 1187 nfsav = getEvaluations(); 1188 state = 60; break; 1189 } 1190 1191 // Return from the calculation, after another Newton-Raphson step, if 1192 // it is too short to have been tried before. 1193 1194 if (ntrits == -1) { 1195 state = 360; break; 1196 } 1197 } 1198 case 720: { 1199 printState(720); // XXX 1200 if (fAtInterpolationPoints.getEntry(trustRegionCenterInterpolationPointIndex) <= fsave) { 1201 for (int i = 0; i < n; i++) { 1202 // Computing MIN 1203 // Computing MAX 1204 final double d3 = lowerBound[i]; 1205 final double d4 = originShift.getEntry(i) + trustRegionCenterOffset.getEntry(i); 1206 final double d1 = Math.max(d3, d4); 1207 final double d2 = upperBound[i]; 1208 currentBest.setEntry(i, Math.min(d1, d2)); 1209 if (trustRegionCenterOffset.getEntry(i) == lowerDifference.getEntry(i)) { 1210 currentBest.setEntry(i, lowerBound[i]); 1211 } 1212 if (trustRegionCenterOffset.getEntry(i) == upperDifference.getEntry(i)) { 1213 currentBest.setEntry(i, upperBound[i]); 1214 } 1215 } 1216 f = fAtInterpolationPoints.getEntry(trustRegionCenterInterpolationPointIndex); 1217 } 1218 return f; 1219 } 1220 default: { 1221 throw new MathIllegalStateException(LocalizedFormats.SIMPLE_MESSAGE, "bobyqb"); 1222 }} 1223 } // bobyqb 1224 1225 // ---------------------------------------------------------------------------------------- 1226 1227 /** 1228 * The arguments N, NPT, XPT, XOPT, BMAT, ZMAT, NDIM, SL and SU all have 1229 * the same meanings as the corresponding arguments of BOBYQB. 1230 * KOPT is the index of the optimal interpolation point. 1231 * KNEW is the index of the interpolation point that is going to be moved. 1232 * ADELT is the current trust region bound. 1233 * XNEW will be set to a suitable new position for the interpolation point 1234 * XPT(KNEW,.). Specifically, it satisfies the SL, SU and trust region 1235 * bounds and it should provide a large denominator in the next call of 1236 * UPDATE. The step XNEW-XOPT from XOPT is restricted to moves along the 1237 * straight lines through XOPT and another interpolation point. 1238 * XALT also provides a large value of the modulus of the KNEW-th Lagrange 1239 * function subject to the constraints that have been mentioned, its main 1240 * difference from XNEW being that XALT-XOPT is a constrained version of 1241 * the Cauchy step within the trust region. An exception is that XALT is 1242 * not calculated if all components of GLAG (see below) are zero. 1243 * ALPHA will be set to the KNEW-th diagonal element of the H matrix. 1244 * CAUCHY will be set to the square of the KNEW-th Lagrange function at 1245 * the step XALT-XOPT from XOPT for the vector XALT that is returned, 1246 * except that CAUCHY is set to zero if XALT is not calculated. 1247 * GLAG is a working space vector of length N for the gradient of the 1248 * KNEW-th Lagrange function at XOPT. 1249 * HCOL is a working space vector of length NPT for the second derivative 1250 * coefficients of the KNEW-th Lagrange function. 1251 * W is a working space vector of length 2N that is going to hold the 1252 * constrained Cauchy step from XOPT of the Lagrange function, followed 1253 * by the downhill version of XALT when the uphill step is calculated. 1254 * 1255 * Set the first NPT components of W to the leading elements of the 1256 * KNEW-th column of the H matrix. 1257 * @param knew 1258 * @param adelt 1259 */ 1260 private double[] altmov( 1261 int knew, 1262 double adelt 1263 ) { 1264 printMethod(); // XXX 1265 1266 final int n = currentBest.getDimension(); 1267 final int npt = numberOfInterpolationPoints; 1268 1269 final ArrayRealVector glag = new ArrayRealVector(n); 1270 final ArrayRealVector hcol = new ArrayRealVector(npt); 1271 1272 final ArrayRealVector work1 = new ArrayRealVector(n); 1273 final ArrayRealVector work2 = new ArrayRealVector(n); 1274 1275 for (int k = 0; k < npt; k++) { 1276 hcol.setEntry(k, ZERO); 1277 } 1278 for (int j = 0, max = npt - n - 1; j < max; j++) { 1279 final double tmp = zMatrix.getEntry(knew, j); 1280 for (int k = 0; k < npt; k++) { 1281 hcol.setEntry(k, hcol.getEntry(k) + tmp * zMatrix.getEntry(k, j)); 1282 } 1283 } 1284 final double alpha = hcol.getEntry(knew); 1285 final double ha = HALF * alpha; 1286 1287 // Calculate the gradient of the KNEW-th Lagrange function at XOPT. 1288 1289 for (int i = 0; i < n; i++) { 1290 glag.setEntry(i, bMatrix.getEntry(knew, i)); 1291 } 1292 for (int k = 0; k < npt; k++) { 1293 double tmp = ZERO; 1294 for (int j = 0; j < n; j++) { 1295 tmp += interpolationPoints.getEntry(k, j) * trustRegionCenterOffset.getEntry(j); 1296 } 1297 tmp *= hcol.getEntry(k); 1298 for (int i = 0; i < n; i++) { 1299 glag.setEntry(i, glag.getEntry(i) + tmp * interpolationPoints.getEntry(k, i)); 1300 } 1301 } 1302 1303 // Search for a large denominator along the straight lines through XOPT 1304 // and another interpolation point. SLBD and SUBD will be lower and upper 1305 // bounds on the step along each of these lines in turn. PREDSQ will be 1306 // set to the square of the predicted denominator for each line. PRESAV 1307 // will be set to the largest admissible value of PREDSQ that occurs. 1308 1309 double presav = ZERO; 1310 double step = Double.NaN; 1311 int ksav = 0; 1312 int ibdsav = 0; 1313 double stpsav = 0; 1314 for (int k = 0; k < npt; k++) { 1315 if (k == trustRegionCenterInterpolationPointIndex) { 1316 continue; 1317 } 1318 double dderiv = ZERO; 1319 double distsq = ZERO; 1320 for (int i = 0; i < n; i++) { 1321 final double tmp = interpolationPoints.getEntry(k, i) - trustRegionCenterOffset.getEntry(i); 1322 dderiv += glag.getEntry(i) * tmp; 1323 distsq += tmp * tmp; 1324 } 1325 double subd = adelt / Math.sqrt(distsq); 1326 double slbd = -subd; 1327 int ilbd = 0; 1328 int iubd = 0; 1329 final double sumin = Math.min(ONE, subd); 1330 1331 // Revise SLBD and SUBD if necessary because of the bounds in SL and SU. 1332 1333 for (int i = 0; i < n; i++) { 1334 final double tmp = interpolationPoints.getEntry(k, i) - trustRegionCenterOffset.getEntry(i); 1335 if (tmp > ZERO) { 1336 if (slbd * tmp < lowerDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i)) { 1337 slbd = (lowerDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i)) / tmp; 1338 ilbd = -i - 1; 1339 } 1340 if (subd * tmp > upperDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i)) { 1341 // Computing MAX 1342 subd = Math.max(sumin, 1343 (upperDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i)) / tmp); 1344 iubd = i + 1; 1345 } 1346 } else if (tmp < ZERO) { 1347 if (slbd * tmp > upperDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i)) { 1348 slbd = (upperDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i)) / tmp; 1349 ilbd = i + 1; 1350 } 1351 if (subd * tmp < lowerDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i)) { 1352 // Computing MAX 1353 subd = Math.max(sumin, 1354 (lowerDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i)) / tmp); 1355 iubd = -i - 1; 1356 } 1357 } 1358 } 1359 1360 // Seek a large modulus of the KNEW-th Lagrange function when the index 1361 // of the other interpolation point on the line through XOPT is KNEW. 1362 1363 step = slbd; 1364 int isbd = ilbd; 1365 double vlag = Double.NaN; 1366 if (k == knew) { 1367 final double diff = dderiv - ONE; 1368 vlag = slbd * (dderiv - slbd * diff); 1369 final double d1 = subd * (dderiv - subd * diff); 1370 if (Math.abs(d1) > Math.abs(vlag)) { 1371 step = subd; 1372 vlag = d1; 1373 isbd = iubd; 1374 } 1375 final double d2 = HALF * dderiv; 1376 final double d3 = d2 - diff * slbd; 1377 final double d4 = d2 - diff * subd; 1378 if (d3 * d4 < ZERO) { 1379 final double d5 = d2 * d2 / diff; 1380 if (Math.abs(d5) > Math.abs(vlag)) { 1381 step = d2 / diff; 1382 vlag = d5; 1383 isbd = 0; 1384 } 1385 } 1386 1387 // Search along each of the other lines through XOPT and another point. 1388 1389 } else { 1390 vlag = slbd * (ONE - slbd); 1391 final double tmp = subd * (ONE - subd); 1392 if (Math.abs(tmp) > Math.abs(vlag)) { 1393 step = subd; 1394 vlag = tmp; 1395 isbd = iubd; 1396 } 1397 if (subd > HALF) { 1398 if (Math.abs(vlag) < ONE_OVER_FOUR) { 1399 step = HALF; 1400 vlag = ONE_OVER_FOUR; 1401 isbd = 0; 1402 } 1403 } 1404 vlag *= dderiv; 1405 } 1406 1407 // Calculate PREDSQ for the current line search and maintain PRESAV. 1408 1409 final double tmp = step * (ONE - step) * distsq; 1410 final double predsq = vlag * vlag * (vlag * vlag + ha * tmp * tmp); 1411 if (predsq > presav) { 1412 presav = predsq; 1413 ksav = k; 1414 stpsav = step; 1415 ibdsav = isbd; 1416 } 1417 } 1418 1419 // Construct XNEW in a way that satisfies the bound constraints exactly. 1420 1421 for (int i = 0; i < n; i++) { 1422 final double tmp = trustRegionCenterOffset.getEntry(i) + stpsav * (interpolationPoints.getEntry(ksav, i) - trustRegionCenterOffset.getEntry(i)); 1423 newPoint.setEntry(i, Math.max(lowerDifference.getEntry(i), 1424 Math.min(upperDifference.getEntry(i), tmp))); 1425 } 1426 if (ibdsav < 0) { 1427 newPoint.setEntry(-ibdsav - 1, lowerDifference.getEntry(-ibdsav - 1)); 1428 } 1429 if (ibdsav > 0) { 1430 newPoint.setEntry(ibdsav - 1, upperDifference.getEntry(ibdsav - 1)); 1431 } 1432 1433 // Prepare for the iterative method that assembles the constrained Cauchy 1434 // step in W. The sum of squares of the fixed components of W is formed in 1435 // WFIXSQ, and the free components of W are set to BIGSTP. 1436 1437 final double bigstp = adelt + adelt; 1438 int iflag = 0; 1439 double cauchy = Double.NaN; 1440 double csave = ZERO; 1441 while (true) { 1442 double wfixsq = ZERO; 1443 double ggfree = ZERO; 1444 for (int i = 0; i < n; i++) { 1445 final double glagValue = glag.getEntry(i); 1446 work1.setEntry(i, ZERO); 1447 if (Math.min(trustRegionCenterOffset.getEntry(i) - lowerDifference.getEntry(i), glagValue) > ZERO || 1448 Math.max(trustRegionCenterOffset.getEntry(i) - upperDifference.getEntry(i), glagValue) < ZERO) { 1449 work1.setEntry(i, bigstp); 1450 // Computing 2nd power 1451 ggfree += glagValue * glagValue; 1452 } 1453 } 1454 if (ggfree == ZERO) { 1455 return new double[] { alpha, ZERO }; 1456 } 1457 1458 // Investigate whether more components of W can be fixed. 1459 final double tmp1 = adelt * adelt - wfixsq; 1460 if (tmp1 > ZERO) { 1461 step = Math.sqrt(tmp1 / ggfree); 1462 ggfree = ZERO; 1463 for (int i = 0; i < n; i++) { 1464 if (work1.getEntry(i) == bigstp) { 1465 final double tmp2 = trustRegionCenterOffset.getEntry(i) - step * glag.getEntry(i); 1466 if (tmp2 <= lowerDifference.getEntry(i)) { 1467 work1.setEntry(i, lowerDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i)); 1468 // Computing 2nd power 1469 final double d1 = work1.getEntry(i); 1470 wfixsq += d1 * d1; 1471 } else if (tmp2 >= upperDifference.getEntry(i)) { 1472 work1.setEntry(i, upperDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i)); 1473 // Computing 2nd power 1474 final double d1 = work1.getEntry(i); 1475 wfixsq += d1 * d1; 1476 } else { 1477 // Computing 2nd power 1478 final double d1 = glag.getEntry(i); 1479 ggfree += d1 * d1; 1480 } 1481 } 1482 } 1483 } 1484 1485 // Set the remaining free components of W and all components of XALT, 1486 // except that W may be scaled later. 1487 1488 double gw = ZERO; 1489 for (int i = 0; i < n; i++) { 1490 final double glagValue = glag.getEntry(i); 1491 if (work1.getEntry(i) == bigstp) { 1492 work1.setEntry(i, -step * glagValue); 1493 final double min = Math.min(upperDifference.getEntry(i), 1494 trustRegionCenterOffset.getEntry(i) + work1.getEntry(i)); 1495 alternativeNewPoint.setEntry(i, Math.max(lowerDifference.getEntry(i), min)); 1496 } else if (work1.getEntry(i) == ZERO) { 1497 alternativeNewPoint.setEntry(i, trustRegionCenterOffset.getEntry(i)); 1498 } else if (glagValue > ZERO) { 1499 alternativeNewPoint.setEntry(i, lowerDifference.getEntry(i)); 1500 } else { 1501 alternativeNewPoint.setEntry(i, upperDifference.getEntry(i)); 1502 } 1503 gw += glagValue * work1.getEntry(i); 1504 } 1505 1506 // Set CURV to the curvature of the KNEW-th Lagrange function along W. 1507 // Scale W by a factor less than one if that can reduce the modulus of 1508 // the Lagrange function at XOPT+W. Set CAUCHY to the final value of 1509 // the square of this function. 1510 1511 double curv = ZERO; 1512 for (int k = 0; k < npt; k++) { 1513 double tmp = ZERO; 1514 for (int j = 0; j < n; j++) { 1515 tmp += interpolationPoints.getEntry(k, j) * work1.getEntry(j); 1516 } 1517 curv += hcol.getEntry(k) * tmp * tmp; 1518 } 1519 if (iflag == 1) { 1520 curv = -curv; 1521 } 1522 if (curv > -gw && 1523 curv < -gw * (ONE + Math.sqrt(TWO))) { 1524 final double scale = -gw / curv; 1525 for (int i = 0; i < n; i++) { 1526 final double tmp = trustRegionCenterOffset.getEntry(i) + scale * work1.getEntry(i); 1527 alternativeNewPoint.setEntry(i, Math.max(lowerDifference.getEntry(i), 1528 Math.min(upperDifference.getEntry(i), tmp))); 1529 } 1530 // Computing 2nd power 1531 final double d1 = HALF * gw * scale; 1532 cauchy = d1 * d1; 1533 } else { 1534 // Computing 2nd power 1535 final double d1 = gw + HALF * curv; 1536 cauchy = d1 * d1; 1537 } 1538 1539 // If IFLAG is zero, then XALT is calculated as before after reversing 1540 // the sign of GLAG. Thus two XALT vectors become available. The one that 1541 // is chosen is the one that gives the larger value of CAUCHY. 1542 1543 if (iflag == 0) { 1544 for (int i = 0; i < n; i++) { 1545 glag.setEntry(i, -glag.getEntry(i)); 1546 work2.setEntry(i, alternativeNewPoint.getEntry(i)); 1547 } 1548 csave = cauchy; 1549 iflag = 1; 1550 } else { 1551 break; 1552 } 1553 } 1554 if (csave > cauchy) { 1555 for (int i = 0; i < n; i++) { 1556 alternativeNewPoint.setEntry(i, work2.getEntry(i)); 1557 } 1558 cauchy = csave; 1559 } 1560 1561 return new double[] { alpha, cauchy }; 1562 } // altmov 1563 1564 // ---------------------------------------------------------------------------------------- 1565 1566 /** 1567 * SUBROUTINE PRELIM sets the elements of XBASE, XPT, FVAL, GOPT, HQ, PQ, 1568 * BMAT and ZMAT for the first iteration, and it maintains the values of 1569 * NF and KOPT. The vector X is also changed by PRELIM. 1570 * 1571 * The arguments N, NPT, X, XL, XU, RHOBEG, IPRINT and MAXFUN are the 1572 * same as the corresponding arguments in SUBROUTINE BOBYQA. 1573 * The arguments XBASE, XPT, FVAL, HQ, PQ, BMAT, ZMAT, NDIM, SL and SU 1574 * are the same as the corresponding arguments in BOBYQB, the elements 1575 * of SL and SU being set in BOBYQA. 1576 * GOPT is usually the gradient of the quadratic model at XOPT+XBASE, but 1577 * it is set by PRELIM to the gradient of the quadratic model at XBASE. 1578 * If XOPT is nonzero, BOBYQB will change it to its usual value later. 1579 * NF is maintaned as the number of calls of CALFUN so far. 1580 * KOPT will be such that the least calculated value of F so far is at 1581 * the point XPT(KOPT,.)+XBASE in the space of the variables. 1582 * 1583 * @param lowerBound Lower bounds. 1584 * @param upperBound Upper bounds. 1585 */ 1586 private void prelim(double[] lowerBound, 1587 double[] upperBound) { 1588 printMethod(); // XXX 1589 1590 final int n = currentBest.getDimension(); 1591 final int npt = numberOfInterpolationPoints; 1592 final int ndim = bMatrix.getRowDimension(); 1593 1594 final double rhosq = initialTrustRegionRadius * initialTrustRegionRadius; 1595 final double recip = 1d / rhosq; 1596 final int np = n + 1; 1597 1598 // Set XBASE to the initial vector of variables, and set the initial 1599 // elements of XPT, BMAT, HQ, PQ and ZMAT to zero. 1600 1601 for (int j = 0; j < n; j++) { 1602 originShift.setEntry(j, currentBest.getEntry(j)); 1603 for (int k = 0; k < npt; k++) { 1604 interpolationPoints.setEntry(k, j, ZERO); 1605 } 1606 for (int i = 0; i < ndim; i++) { 1607 bMatrix.setEntry(i, j, ZERO); 1608 } 1609 } 1610 for (int i = 0, max = n * np / 2; i < max; i++) { 1611 modelSecondDerivativesValues.setEntry(i, ZERO); 1612 } 1613 for (int k = 0; k < npt; k++) { 1614 modelSecondDerivativesParameters.setEntry(k, ZERO); 1615 for (int j = 0, max = npt - np; j < max; j++) { 1616 zMatrix.setEntry(k, j, ZERO); 1617 } 1618 } 1619 1620 // Begin the initialization procedure. NF becomes one more than the number 1621 // of function values so far. The coordinates of the displacement of the 1622 // next initial interpolation point from XBASE are set in XPT(NF+1,.). 1623 1624 int ipt = 0; 1625 int jpt = 0; 1626 double fbeg = Double.NaN; 1627 do { 1628 final int nfm = getEvaluations(); 1629 final int nfx = nfm - n; 1630 final int nfmm = nfm - 1; 1631 final int nfxm = nfx - 1; 1632 double stepa = 0; 1633 double stepb = 0; 1634 if (nfm <= 2 * n) { 1635 if (nfm >= 1 && 1636 nfm <= n) { 1637 stepa = initialTrustRegionRadius; 1638 if (upperDifference.getEntry(nfmm) == ZERO) { 1639 stepa = -stepa; 1640 // throw new PathIsExploredException(); // XXX 1641 } 1642 interpolationPoints.setEntry(nfm, nfmm, stepa); 1643 } else if (nfm > n) { 1644 stepa = interpolationPoints.getEntry(nfx, nfxm); 1645 stepb = -initialTrustRegionRadius; 1646 if (lowerDifference.getEntry(nfxm) == ZERO) { 1647 stepb = Math.min(TWO * initialTrustRegionRadius, upperDifference.getEntry(nfxm)); 1648 // throw new PathIsExploredException(); // XXX 1649 } 1650 if (upperDifference.getEntry(nfxm) == ZERO) { 1651 stepb = Math.max(-TWO * initialTrustRegionRadius, lowerDifference.getEntry(nfxm)); 1652 // throw new PathIsExploredException(); // XXX 1653 } 1654 interpolationPoints.setEntry(nfm, nfxm, stepb); 1655 } 1656 } else { 1657 final int tmp1 = (nfm - np) / n; 1658 jpt = nfm - tmp1 * n - n; 1659 ipt = jpt + tmp1; 1660 if (ipt > n) { 1661 final int tmp2 = jpt; 1662 jpt = ipt - n; 1663 ipt = tmp2; 1664 // throw new PathIsExploredException(); // XXX 1665 } 1666 final int iptMinus1 = ipt - 1; 1667 final int jptMinus1 = jpt - 1; 1668 interpolationPoints.setEntry(nfm, iptMinus1, interpolationPoints.getEntry(ipt, iptMinus1)); 1669 interpolationPoints.setEntry(nfm, jptMinus1, interpolationPoints.getEntry(jpt, jptMinus1)); 1670 } 1671 1672 // Calculate the next value of F. The least function value so far and 1673 // its index are required. 1674 1675 for (int j = 0; j < n; j++) { 1676 currentBest.setEntry(j, Math.min(Math.max(lowerBound[j], 1677 originShift.getEntry(j) + interpolationPoints.getEntry(nfm, j)), 1678 upperBound[j])); 1679 if (interpolationPoints.getEntry(nfm, j) == lowerDifference.getEntry(j)) { 1680 currentBest.setEntry(j, lowerBound[j]); 1681 } 1682 if (interpolationPoints.getEntry(nfm, j) == upperDifference.getEntry(j)) { 1683 currentBest.setEntry(j, upperBound[j]); 1684 } 1685 } 1686 1687 final double objectiveValue = computeObjectiveValue(currentBest.toArray()); 1688 final double f = isMinimize ? objectiveValue : -objectiveValue; 1689 final int numEval = getEvaluations(); // nfm + 1 1690 fAtInterpolationPoints.setEntry(nfm, f); 1691 1692 if (numEval == 1) { 1693 fbeg = f; 1694 trustRegionCenterInterpolationPointIndex = 0; 1695 } else if (f < fAtInterpolationPoints.getEntry(trustRegionCenterInterpolationPointIndex)) { 1696 trustRegionCenterInterpolationPointIndex = nfm; 1697 } 1698 1699 // Set the nonzero initial elements of BMAT and the quadratic model in the 1700 // cases when NF is at most 2*N+1. If NF exceeds N+1, then the positions 1701 // of the NF-th and (NF-N)-th interpolation points may be switched, in 1702 // order that the function value at the first of them contributes to the 1703 // off-diagonal second derivative terms of the initial quadratic model. 1704 1705 if (numEval <= 2 * n + 1) { 1706 if (numEval >= 2 && 1707 numEval <= n + 1) { 1708 gradientAtTrustRegionCenter.setEntry(nfmm, (f - fbeg) / stepa); 1709 if (npt < numEval + n) { 1710 final double oneOverStepA = ONE / stepa; 1711 bMatrix.setEntry(0, nfmm, -oneOverStepA); 1712 bMatrix.setEntry(nfm, nfmm, oneOverStepA); 1713 bMatrix.setEntry(npt + nfmm, nfmm, -HALF * rhosq); 1714 // throw new PathIsExploredException(); // XXX 1715 } 1716 } else if (numEval >= n + 2) { 1717 final int ih = nfx * (nfx + 1) / 2 - 1; 1718 final double tmp = (f - fbeg) / stepb; 1719 final double diff = stepb - stepa; 1720 modelSecondDerivativesValues.setEntry(ih, TWO * (tmp - gradientAtTrustRegionCenter.getEntry(nfxm)) / diff); 1721 gradientAtTrustRegionCenter.setEntry(nfxm, (gradientAtTrustRegionCenter.getEntry(nfxm) * stepb - tmp * stepa) / diff); 1722 if (stepa * stepb < ZERO) { 1723 if (f < fAtInterpolationPoints.getEntry(nfm - n)) { 1724 fAtInterpolationPoints.setEntry(nfm, fAtInterpolationPoints.getEntry(nfm - n)); 1725 fAtInterpolationPoints.setEntry(nfm - n, f); 1726 if (trustRegionCenterInterpolationPointIndex == nfm) { 1727 trustRegionCenterInterpolationPointIndex = nfm - n; 1728 } 1729 interpolationPoints.setEntry(nfm - n, nfxm, stepb); 1730 interpolationPoints.setEntry(nfm, nfxm, stepa); 1731 } 1732 } 1733 bMatrix.setEntry(0, nfxm, -(stepa + stepb) / (stepa * stepb)); 1734 bMatrix.setEntry(nfm, nfxm, -HALF / interpolationPoints.getEntry(nfm - n, nfxm)); 1735 bMatrix.setEntry(nfm - n, nfxm, 1736 -bMatrix.getEntry(0, nfxm) - bMatrix.getEntry(nfm, nfxm)); 1737 zMatrix.setEntry(0, nfxm, Math.sqrt(TWO) / (stepa * stepb)); 1738 zMatrix.setEntry(nfm, nfxm, Math.sqrt(HALF) / rhosq); 1739 // zMatrix.setEntry(nfm, nfxm, Math.sqrt(HALF) * recip); // XXX "testAckley" and "testDiffPow" fail. 1740 zMatrix.setEntry(nfm - n, nfxm, 1741 -zMatrix.getEntry(0, nfxm) - zMatrix.getEntry(nfm, nfxm)); 1742 } 1743 1744 // Set the off-diagonal second derivatives of the Lagrange functions and 1745 // the initial quadratic model. 1746 1747 } else { 1748 zMatrix.setEntry(0, nfxm, recip); 1749 zMatrix.setEntry(nfm, nfxm, recip); 1750 zMatrix.setEntry(ipt, nfxm, -recip); 1751 zMatrix.setEntry(jpt, nfxm, -recip); 1752 1753 final int ih = ipt * (ipt - 1) / 2 + jpt - 1; 1754 final double tmp = interpolationPoints.getEntry(nfm, ipt - 1) * interpolationPoints.getEntry(nfm, jpt - 1); 1755 modelSecondDerivativesValues.setEntry(ih, (fbeg - fAtInterpolationPoints.getEntry(ipt) - fAtInterpolationPoints.getEntry(jpt) + f) / tmp); 1756 // throw new PathIsExploredException(); // XXX 1757 } 1758 } while (getEvaluations() < npt); 1759 } // prelim 1760 1761 1762 // ---------------------------------------------------------------------------------------- 1763 1764 /** 1765 * A version of the truncated conjugate gradient is applied. If a line 1766 * search is restricted by a constraint, then the procedure is restarted, 1767 * the values of the variables that are at their bounds being fixed. If 1768 * the trust region boundary is reached, then further changes may be made 1769 * to D, each one being in the two dimensional space that is spanned 1770 * by the current D and the gradient of Q at XOPT+D, staying on the trust 1771 * region boundary. Termination occurs when the reduction in Q seems to 1772 * be close to the greatest reduction that can be achieved. 1773 * The arguments N, NPT, XPT, XOPT, GOPT, HQ, PQ, SL and SU have the same 1774 * meanings as the corresponding arguments of BOBYQB. 1775 * DELTA is the trust region radius for the present calculation, which 1776 * seeks a small value of the quadratic model within distance DELTA of 1777 * XOPT subject to the bounds on the variables. 1778 * XNEW will be set to a new vector of variables that is approximately 1779 * the one that minimizes the quadratic model within the trust region 1780 * subject to the SL and SU constraints on the variables. It satisfies 1781 * as equations the bounds that become active during the calculation. 1782 * D is the calculated trial step from XOPT, generated iteratively from an 1783 * initial value of zero. Thus XNEW is XOPT+D after the final iteration. 1784 * GNEW holds the gradient of the quadratic model at XOPT+D. It is updated 1785 * when D is updated. 1786 * xbdi.get( is a working space vector. For I=1,2,...,N, the element xbdi.get((I) is 1787 * set to -1.0, 0.0, or 1.0, the value being nonzero if and only if the 1788 * I-th variable has become fixed at a bound, the bound being SL(I) or 1789 * SU(I) in the case xbdi.get((I)=-1.0 or xbdi.get((I)=1.0, respectively. This 1790 * information is accumulated during the construction of XNEW. 1791 * The arrays S, HS and HRED are also used for working space. They hold the 1792 * current search direction, and the changes in the gradient of Q along S 1793 * and the reduced D, respectively, where the reduced D is the same as D, 1794 * except that the components of the fixed variables are zero. 1795 * DSQ will be set to the square of the length of XNEW-XOPT. 1796 * CRVMIN is set to zero if D reaches the trust region boundary. Otherwise 1797 * it is set to the least curvature of H that occurs in the conjugate 1798 * gradient searches that are not restricted by any constraints. The 1799 * value CRVMIN=-1.0D0 is set, however, if all of these searches are 1800 * constrained. 1801 * @param delta 1802 * @param gnew 1803 * @param xbdi 1804 * @param s 1805 * @param hs 1806 * @param hred 1807 */ 1808 private double[] trsbox( 1809 double delta, 1810 ArrayRealVector gnew, 1811 ArrayRealVector xbdi, 1812 ArrayRealVector s, 1813 ArrayRealVector hs, 1814 ArrayRealVector hred 1815 ) { 1816 printMethod(); // XXX 1817 1818 final int n = currentBest.getDimension(); 1819 final int npt = numberOfInterpolationPoints; 1820 1821 double dsq = Double.NaN; 1822 double crvmin = Double.NaN; 1823 1824 // Local variables 1825 double ds; 1826 int iu; 1827 double dhd, dhs, cth, shs, sth, ssq, beta=0, sdec, blen; 1828 int iact = -1; 1829 int nact = 0; 1830 double angt = 0, qred; 1831 int isav; 1832 double temp = 0, xsav = 0, xsum = 0, angbd = 0, dredg = 0, sredg = 0; 1833 int iterc; 1834 double resid = 0, delsq = 0, ggsav = 0, tempa = 0, tempb = 0, 1835 redmax = 0, dredsq = 0, redsav = 0, gredsq = 0, rednew = 0; 1836 int itcsav = 0; 1837 double rdprev = 0, rdnext = 0, stplen = 0, stepsq = 0; 1838 int itermax = 0; 1839 1840 // Set some constants. 1841 1842 // Function Body 1843 1844 // The sign of GOPT(I) gives the sign of the change to the I-th variable 1845 // that will reduce Q from its value at XOPT. Thus xbdi.get((I) shows whether 1846 // or not to fix the I-th variable at one of its bounds initially, with 1847 // NACT being set to the number of fixed variables. D and GNEW are also 1848 // set for the first iteration. DELSQ is the upper bound on the sum of 1849 // squares of the free variables. QRED is the reduction in Q so far. 1850 1851 iterc = 0; 1852 nact = 0; 1853 for (int i = 0; i < n; i++) { 1854 xbdi.setEntry(i, ZERO); 1855 if (trustRegionCenterOffset.getEntry(i) <= lowerDifference.getEntry(i)) { 1856 if (gradientAtTrustRegionCenter.getEntry(i) >= ZERO) { 1857 xbdi.setEntry(i, MINUS_ONE); 1858 } 1859 } else if (trustRegionCenterOffset.getEntry(i) >= upperDifference.getEntry(i)) { 1860 if (gradientAtTrustRegionCenter.getEntry(i) <= ZERO) { 1861 xbdi.setEntry(i, ONE); 1862 } 1863 } 1864 if (xbdi.getEntry(i) != ZERO) { 1865 ++nact; 1866 } 1867 trialStepPoint.setEntry(i, ZERO); 1868 gnew.setEntry(i, gradientAtTrustRegionCenter.getEntry(i)); 1869 } 1870 delsq = delta * delta; 1871 qred = ZERO; 1872 crvmin = MINUS_ONE; 1873 1874 // Set the next search direction of the conjugate gradient method. It is 1875 // the steepest descent direction initially and when the iterations are 1876 // restarted because a variable has just been fixed by a bound, and of 1877 // course the components of the fixed variables are zero. ITERMAX is an 1878 // upper bound on the indices of the conjugate gradient iterations. 1879 1880 int state = 20; 1881 for(;;) { 1882 switch (state) { 1883 case 20: { 1884 printState(20); // XXX 1885 beta = ZERO; 1886 } 1887 case 30: { 1888 printState(30); // XXX 1889 stepsq = ZERO; 1890 for (int i = 0; i < n; i++) { 1891 if (xbdi.getEntry(i) != ZERO) { 1892 s.setEntry(i, ZERO); 1893 } else if (beta == ZERO) { 1894 s.setEntry(i, -gnew.getEntry(i)); 1895 } else { 1896 s.setEntry(i, beta * s.getEntry(i) - gnew.getEntry(i)); 1897 } 1898 // Computing 2nd power 1899 final double d1 = s.getEntry(i); 1900 stepsq += d1 * d1; 1901 } 1902 if (stepsq == ZERO) { 1903 state = 190; break; 1904 } 1905 if (beta == ZERO) { 1906 gredsq = stepsq; 1907 itermax = iterc + n - nact; 1908 } 1909 if (gredsq * delsq <= qred * 1e-4 * qred) { 1910 state = 190; break; 1911 } 1912 1913 // Multiply the search direction by the second derivative matrix of Q and 1914 // calculate some scalars for the choice of steplength. Then set BLEN to 1915 // the length of the the step to the trust region boundary and STPLEN to 1916 // the steplength, ignoring the simple bounds. 1917 1918 state = 210; break; 1919 } 1920 case 50: { 1921 printState(50); // XXX 1922 resid = delsq; 1923 ds = ZERO; 1924 shs = ZERO; 1925 for (int i = 0; i < n; i++) { 1926 if (xbdi.getEntry(i) == ZERO) { 1927 // Computing 2nd power 1928 final double d1 = trialStepPoint.getEntry(i); 1929 resid -= d1 * d1; 1930 ds += s.getEntry(i) * trialStepPoint.getEntry(i); 1931 shs += s.getEntry(i) * hs.getEntry(i); 1932 } 1933 } 1934 if (resid <= ZERO) { 1935 state = 90; break; 1936 } 1937 temp = Math.sqrt(stepsq * resid + ds * ds); 1938 if (ds < ZERO) { 1939 blen = (temp - ds) / stepsq; 1940 } else { 1941 blen = resid / (temp + ds); 1942 } 1943 stplen = blen; 1944 if (shs > ZERO) { 1945 // Computing MIN 1946 stplen = Math.min(blen, gredsq / shs); 1947 } 1948 1949 // Reduce STPLEN if necessary in order to preserve the simple bounds, 1950 // letting IACT be the index of the new constrained variable. 1951 1952 iact = -1; 1953 for (int i = 0; i < n; i++) { 1954 if (s.getEntry(i) != ZERO) { 1955 xsum = trustRegionCenterOffset.getEntry(i) + trialStepPoint.getEntry(i); 1956 if (s.getEntry(i) > ZERO) { 1957 temp = (upperDifference.getEntry(i) - xsum) / s.getEntry(i); 1958 } else { 1959 temp = (lowerDifference.getEntry(i) - xsum) / s.getEntry(i); 1960 } 1961 if (temp < stplen) { 1962 stplen = temp; 1963 iact = i; 1964 } 1965 } 1966 } 1967 1968 // Update CRVMIN, GNEW and D. Set SDEC to the decrease that occurs in Q. 1969 1970 sdec = ZERO; 1971 if (stplen > ZERO) { 1972 ++iterc; 1973 temp = shs / stepsq; 1974 if (iact == -1 && temp > ZERO) { 1975 crvmin = Math.min(crvmin,temp); 1976 if (crvmin == MINUS_ONE) { 1977 crvmin = temp; 1978 } 1979 } 1980 ggsav = gredsq; 1981 gredsq = ZERO; 1982 for (int i = 0; i < n; i++) { 1983 gnew.setEntry(i, gnew.getEntry(i) + stplen * hs.getEntry(i)); 1984 if (xbdi.getEntry(i) == ZERO) { 1985 // Computing 2nd power 1986 final double d1 = gnew.getEntry(i); 1987 gredsq += d1 * d1; 1988 } 1989 trialStepPoint.setEntry(i, trialStepPoint.getEntry(i) + stplen * s.getEntry(i)); 1990 } 1991 // Computing MAX 1992 final double d1 = stplen * (ggsav - HALF * stplen * shs); 1993 sdec = Math.max(d1, ZERO); 1994 qred += sdec; 1995 } 1996 1997 // Restart the conjugate gradient method if it has hit a new bound. 1998 1999 if (iact >= 0) { 2000 ++nact; 2001 xbdi.setEntry(iact, ONE); 2002 if (s.getEntry(iact) < ZERO) { 2003 xbdi.setEntry(iact, MINUS_ONE); 2004 } 2005 // Computing 2nd power 2006 final double d1 = trialStepPoint.getEntry(iact); 2007 delsq -= d1 * d1; 2008 if (delsq <= ZERO) { 2009 state = 190; break; 2010 } 2011 state = 20; break; 2012 } 2013 2014 // If STPLEN is less than BLEN, then either apply another conjugate 2015 // gradient iteration or RETURN. 2016 2017 if (stplen < blen) { 2018 if (iterc == itermax) { 2019 state = 190; break; 2020 } 2021 if (sdec <= qred * .01) { 2022 state = 190; break; 2023 } 2024 beta = gredsq / ggsav; 2025 state = 30; break; 2026 } 2027 } 2028 case 90: { 2029 printState(90); // XXX 2030 crvmin = ZERO; 2031 2032 // Prepare for the alternative iteration by calculating some scalars 2033 // and by multiplying the reduced D by the second derivative matrix of 2034 // Q, where S holds the reduced D in the call of GGMULT. 2035 2036 } 2037 case 100: { 2038 printState(100); // XXX 2039 if (nact >= n - 1) { 2040 state = 190; break; 2041 } 2042 dredsq = ZERO; 2043 dredg = ZERO; 2044 gredsq = ZERO; 2045 for (int i = 0; i < n; i++) { 2046 if (xbdi.getEntry(i) == ZERO) { 2047 // Computing 2nd power 2048 double d1 = trialStepPoint.getEntry(i); 2049 dredsq += d1 * d1; 2050 dredg += trialStepPoint.getEntry(i) * gnew.getEntry(i); 2051 // Computing 2nd power 2052 d1 = gnew.getEntry(i); 2053 gredsq += d1 * d1; 2054 s.setEntry(i, trialStepPoint.getEntry(i)); 2055 } else { 2056 s.setEntry(i, ZERO); 2057 } 2058 } 2059 itcsav = iterc; 2060 state = 210; break; 2061 // Let the search direction S be a linear combination of the reduced D 2062 // and the reduced G that is orthogonal to the reduced D. 2063 } 2064 case 120: { 2065 printState(120); // XXX 2066 ++iterc; 2067 temp = gredsq * dredsq - dredg * dredg; 2068 if (temp <= qred * 1e-4 * qred) { 2069 state = 190; break; 2070 } 2071 temp = Math.sqrt(temp); 2072 for (int i = 0; i < n; i++) { 2073 if (xbdi.getEntry(i) == ZERO) { 2074 s.setEntry(i, (dredg * trialStepPoint.getEntry(i) - dredsq * gnew.getEntry(i)) / temp); 2075 } else { 2076 s.setEntry(i, ZERO); 2077 } 2078 } 2079 sredg = -temp; 2080 2081 // By considering the simple bounds on the variables, calculate an upper 2082 // bound on the tangent of half the angle of the alternative iteration, 2083 // namely ANGBD, except that, if already a free variable has reached a 2084 // bound, there is a branch back to label 100 after fixing that variable. 2085 2086 angbd = ONE; 2087 iact = -1; 2088 for (int i = 0; i < n; i++) { 2089 if (xbdi.getEntry(i) == ZERO) { 2090 tempa = trustRegionCenterOffset.getEntry(i) + trialStepPoint.getEntry(i) - lowerDifference.getEntry(i); 2091 tempb = upperDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i) - trialStepPoint.getEntry(i); 2092 if (tempa <= ZERO) { 2093 ++nact; 2094 xbdi.setEntry(i, MINUS_ONE); 2095 state = 100; break; 2096 } else if (tempb <= ZERO) { 2097 ++nact; 2098 xbdi.setEntry(i, ONE); 2099 state = 100; break; 2100 } 2101 // Computing 2nd power 2102 double d1 = trialStepPoint.getEntry(i); 2103 // Computing 2nd power 2104 double d2 = s.getEntry(i); 2105 ssq = d1 * d1 + d2 * d2; 2106 // Computing 2nd power 2107 d1 = trustRegionCenterOffset.getEntry(i) - lowerDifference.getEntry(i); 2108 temp = ssq - d1 * d1; 2109 if (temp > ZERO) { 2110 temp = Math.sqrt(temp) - s.getEntry(i); 2111 if (angbd * temp > tempa) { 2112 angbd = tempa / temp; 2113 iact = i; 2114 xsav = MINUS_ONE; 2115 } 2116 } 2117 // Computing 2nd power 2118 d1 = upperDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i); 2119 temp = ssq - d1 * d1; 2120 if (temp > ZERO) { 2121 temp = Math.sqrt(temp) + s.getEntry(i); 2122 if (angbd * temp > tempb) { 2123 angbd = tempb / temp; 2124 iact = i; 2125 xsav = ONE; 2126 } 2127 } 2128 } 2129 } 2130 2131 // Calculate HHD and some curvatures for the alternative iteration. 2132 2133 state = 210; break; 2134 } 2135 case 150: { 2136 printState(150); // XXX 2137 shs = ZERO; 2138 dhs = ZERO; 2139 dhd = ZERO; 2140 for (int i = 0; i < n; i++) { 2141 if (xbdi.getEntry(i) == ZERO) { 2142 shs += s.getEntry(i) * hs.getEntry(i); 2143 dhs += trialStepPoint.getEntry(i) * hs.getEntry(i); 2144 dhd += trialStepPoint.getEntry(i) * hred.getEntry(i); 2145 } 2146 } 2147 2148 // Seek the greatest reduction in Q for a range of equally spaced values 2149 // of ANGT in [0,ANGBD], where ANGT is the tangent of half the angle of 2150 // the alternative iteration. 2151 2152 redmax = ZERO; 2153 isav = -1; 2154 redsav = ZERO; 2155 iu = (int) (angbd * 17. + 3.1); 2156 for (int i = 0; i < iu; i++) { 2157 angt = angbd * i / iu; 2158 sth = (angt + angt) / (ONE + angt * angt); 2159 temp = shs + angt * (angt * dhd - dhs - dhs); 2160 rednew = sth * (angt * dredg - sredg - HALF * sth * temp); 2161 if (rednew > redmax) { 2162 redmax = rednew; 2163 isav = i; 2164 rdprev = redsav; 2165 } else if (i == isav + 1) { 2166 rdnext = rednew; 2167 } 2168 redsav = rednew; 2169 } 2170 2171 // Return if the reduction is zero. Otherwise, set the sine and cosine 2172 // of the angle of the alternative iteration, and calculate SDEC. 2173 2174 if (isav < 0) { 2175 state = 190; break; 2176 } 2177 if (isav < iu) { 2178 temp = (rdnext - rdprev) / (redmax + redmax - rdprev - rdnext); 2179 angt = angbd * (isav + HALF * temp) / iu; 2180 } 2181 cth = (ONE - angt * angt) / (ONE + angt * angt); 2182 sth = (angt + angt) / (ONE + angt * angt); 2183 temp = shs + angt * (angt * dhd - dhs - dhs); 2184 sdec = sth * (angt * dredg - sredg - HALF * sth * temp); 2185 if (sdec <= ZERO) { 2186 state = 190; break; 2187 } 2188 2189 // Update GNEW, D and HRED. If the angle of the alternative iteration 2190 // is restricted by a bound on a free variable, that variable is fixed 2191 // at the bound. 2192 2193 dredg = ZERO; 2194 gredsq = ZERO; 2195 for (int i = 0; i < n; i++) { 2196 gnew.setEntry(i, gnew.getEntry(i) + (cth - ONE) * hred.getEntry(i) + sth * hs.getEntry(i)); 2197 if (xbdi.getEntry(i) == ZERO) { 2198 trialStepPoint.setEntry(i, cth * trialStepPoint.getEntry(i) + sth * s.getEntry(i)); 2199 dredg += trialStepPoint.getEntry(i) * gnew.getEntry(i); 2200 // Computing 2nd power 2201 final double d1 = gnew.getEntry(i); 2202 gredsq += d1 * d1; 2203 } 2204 hred.setEntry(i, cth * hred.getEntry(i) + sth * hs.getEntry(i)); 2205 } 2206 qred += sdec; 2207 if (iact >= 0 && isav == iu) { 2208 ++nact; 2209 xbdi.setEntry(iact, xsav); 2210 state = 100; break; 2211 } 2212 2213 // If SDEC is sufficiently small, then RETURN after setting XNEW to 2214 // XOPT+D, giving careful attention to the bounds. 2215 2216 if (sdec > qred * .01) { 2217 state = 120; break; 2218 } 2219 } 2220 case 190: { 2221 printState(190); // XXX 2222 dsq = ZERO; 2223 for (int i = 0; i < n; i++) { 2224 // Computing MAX 2225 // Computing MIN 2226 final double min = Math.min(trustRegionCenterOffset.getEntry(i) + trialStepPoint.getEntry(i), 2227 upperDifference.getEntry(i)); 2228 newPoint.setEntry(i, Math.max(min, lowerDifference.getEntry(i))); 2229 if (xbdi.getEntry(i) == MINUS_ONE) { 2230 newPoint.setEntry(i, lowerDifference.getEntry(i)); 2231 } 2232 if (xbdi.getEntry(i) == ONE) { 2233 newPoint.setEntry(i, upperDifference.getEntry(i)); 2234 } 2235 trialStepPoint.setEntry(i, newPoint.getEntry(i) - trustRegionCenterOffset.getEntry(i)); 2236 // Computing 2nd power 2237 final double d1 = trialStepPoint.getEntry(i); 2238 dsq += d1 * d1; 2239 } 2240 return new double[] { dsq, crvmin }; 2241 // The following instructions multiply the current S-vector by the second 2242 // derivative matrix of the quadratic model, putting the product in HS. 2243 // They are reached from three different parts of the software above and 2244 // they can be regarded as an external subroutine. 2245 } 2246 case 210: { 2247 printState(210); // XXX 2248 int ih = 0; 2249 for (int j = 0; j < n; j++) { 2250 hs.setEntry(j, ZERO); 2251 for (int i = 0; i <= j; i++) { 2252 if (i < j) { 2253 hs.setEntry(j, hs.getEntry(j) + modelSecondDerivativesValues.getEntry(ih) * s.getEntry(i)); 2254 } 2255 hs.setEntry(i, hs.getEntry(i) + modelSecondDerivativesValues.getEntry(ih) * s.getEntry(j)); 2256 ih++; 2257 } 2258 } 2259 final RealVector tmp = interpolationPoints.operate(s).ebeMultiply(modelSecondDerivativesParameters); 2260 for (int k = 0; k < npt; k++) { 2261 if (modelSecondDerivativesParameters.getEntry(k) != ZERO) { 2262 for (int i = 0; i < n; i++) { 2263 hs.setEntry(i, hs.getEntry(i) + tmp.getEntry(k) * interpolationPoints.getEntry(k, i)); 2264 } 2265 } 2266 } 2267 if (crvmin != ZERO) { 2268 state = 50; break; 2269 } 2270 if (iterc > itcsav) { 2271 state = 150; break; 2272 } 2273 for (int i = 0; i < n; i++) { 2274 hred.setEntry(i, hs.getEntry(i)); 2275 } 2276 state = 120; break; 2277 } 2278 default: { 2279 throw new MathIllegalStateException(LocalizedFormats.SIMPLE_MESSAGE, "trsbox"); 2280 }} 2281 } 2282 } // trsbox 2283 2284 // ---------------------------------------------------------------------------------------- 2285 2286 /** 2287 * The arrays BMAT and ZMAT are updated, as required by the new position 2288 * of the interpolation point that has the index KNEW. The vector VLAG has 2289 * N+NPT components, set on entry to the first NPT and last N components 2290 * of the product Hw in equation (4.11) of the Powell (2006) paper on 2291 * NEWUOA. Further, BETA is set on entry to the value of the parameter 2292 * with that name, and DENOM is set to the denominator of the updating 2293 * formula. Elements of ZMAT may be treated as zero if their moduli are 2294 * at most ZTEST. The first NDIM elements of W are used for working space. 2295 * @param beta 2296 * @param denom 2297 * @param knew 2298 */ 2299 private void update( 2300 double beta, 2301 double denom, 2302 int knew 2303 ) { 2304 printMethod(); // XXX 2305 2306 final int n = currentBest.getDimension(); 2307 final int npt = numberOfInterpolationPoints; 2308 final int nptm = npt - n - 1; 2309 2310 // XXX Should probably be split into two arrays. 2311 final ArrayRealVector work = new ArrayRealVector(npt + n); 2312 2313 double ztest = ZERO; 2314 for (int k = 0; k < npt; k++) { 2315 for (int j = 0; j < nptm; j++) { 2316 // Computing MAX 2317 ztest = Math.max(ztest, Math.abs(zMatrix.getEntry(k, j))); 2318 } 2319 } 2320 ztest *= 1e-20; 2321 2322 // Apply the rotations that put zeros in the KNEW-th row of ZMAT. 2323 2324 for (int j = 1; j < nptm; j++) { 2325 final double d1 = zMatrix.getEntry(knew, j); 2326 if (Math.abs(d1) > ztest) { 2327 // Computing 2nd power 2328 final double d2 = zMatrix.getEntry(knew, 0); 2329 // Computing 2nd power 2330 final double d3 = zMatrix.getEntry(knew, j); 2331 final double d4 = Math.sqrt(d2 * d2 + d3 * d3); 2332 final double d5 = zMatrix.getEntry(knew, 0) / d4; 2333 final double d6 = zMatrix.getEntry(knew, j) / d4; 2334 for (int i = 0; i < npt; i++) { 2335 final double d7 = d5 * zMatrix.getEntry(i, 0) + d6 * zMatrix.getEntry(i, j); 2336 zMatrix.setEntry(i, j, d5 * zMatrix.getEntry(i, j) - d6 * zMatrix.getEntry(i, 0)); 2337 zMatrix.setEntry(i, 0, d7); 2338 } 2339 } 2340 zMatrix.setEntry(knew, j, ZERO); 2341 } 2342 2343 // Put the first NPT components of the KNEW-th column of HLAG into W, 2344 // and calculate the parameters of the updating formula. 2345 2346 for (int i = 0; i < npt; i++) { 2347 work.setEntry(i, zMatrix.getEntry(knew, 0) * zMatrix.getEntry(i, 0)); 2348 } 2349 final double alpha = work.getEntry(knew); 2350 final double tau = lagrangeValuesAtNewPoint.getEntry(knew); 2351 lagrangeValuesAtNewPoint.setEntry(knew, lagrangeValuesAtNewPoint.getEntry(knew) - ONE); 2352 2353 // Complete the updating of ZMAT. 2354 2355 final double sqrtDenom = Math.sqrt(denom); 2356 final double d1 = tau / sqrtDenom; 2357 final double d2 = zMatrix.getEntry(knew, 0) / sqrtDenom; 2358 for (int i = 0; i < npt; i++) { 2359 zMatrix.setEntry(i, 0, 2360 d1 * zMatrix.getEntry(i, 0) - d2 * lagrangeValuesAtNewPoint.getEntry(i)); 2361 } 2362 2363 // Finally, update the matrix BMAT. 2364 2365 for (int j = 0; j < n; j++) { 2366 final int jp = npt + j; 2367 work.setEntry(jp, bMatrix.getEntry(knew, j)); 2368 final double d3 = (alpha * lagrangeValuesAtNewPoint.getEntry(jp) - tau * work.getEntry(jp)) / denom; 2369 final double d4 = (-beta * work.getEntry(jp) - tau * lagrangeValuesAtNewPoint.getEntry(jp)) / denom; 2370 for (int i = 0; i <= jp; i++) { 2371 bMatrix.setEntry(i, j, 2372 bMatrix.getEntry(i, j) + d3 * lagrangeValuesAtNewPoint.getEntry(i) + d4 * work.getEntry(i)); 2373 if (i >= npt) { 2374 bMatrix.setEntry(jp, (i - npt), bMatrix.getEntry(i, j)); 2375 } 2376 } 2377 } 2378 } // update 2379 2380 /** 2381 * Performs validity checks. 2382 * 2383 * @param lowerBound Lower bounds (constraints) of the objective variables. 2384 * @param upperBound Upperer bounds (constraints) of the objective variables. 2385 */ 2386 private void setup(double[] lowerBound, 2387 double[] upperBound) { 2388 printMethod(); // XXX 2389 2390 double[] init = getStartPoint(); 2391 final int dimension = init.length; 2392 2393 // Check problem dimension. 2394 if (dimension < MINIMUM_PROBLEM_DIMENSION) { 2395 throw new NumberIsTooSmallException(dimension, MINIMUM_PROBLEM_DIMENSION, true); 2396 } 2397 // Check number of interpolation points. 2398 final int[] nPointsInterval = { dimension + 2, (dimension + 2) * (dimension + 1) / 2 }; 2399 if (numberOfInterpolationPoints < nPointsInterval[0] || 2400 numberOfInterpolationPoints > nPointsInterval[1]) { 2401 throw new OutOfRangeException(LocalizedFormats.NUMBER_OF_INTERPOLATION_POINTS, 2402 numberOfInterpolationPoints, 2403 nPointsInterval[0], 2404 nPointsInterval[1]); 2405 } 2406 2407 // Initialize bound differences. 2408 boundDifference = new double[dimension]; 2409 2410 double requiredMinDiff = 2 * initialTrustRegionRadius; 2411 double minDiff = Double.POSITIVE_INFINITY; 2412 for (int i = 0; i < dimension; i++) { 2413 boundDifference[i] = upperBound[i] - lowerBound[i]; 2414 minDiff = Math.min(minDiff, boundDifference[i]); 2415 } 2416 if (minDiff < requiredMinDiff) { 2417 initialTrustRegionRadius = minDiff / 3.0; 2418 } 2419 2420 // Initialize the data structures used by the "bobyqa" method. 2421 bMatrix = new Array2DRowRealMatrix(dimension + numberOfInterpolationPoints, 2422 dimension); 2423 zMatrix = new Array2DRowRealMatrix(numberOfInterpolationPoints, 2424 numberOfInterpolationPoints - dimension - 1); 2425 interpolationPoints = new Array2DRowRealMatrix(numberOfInterpolationPoints, 2426 dimension); 2427 originShift = new ArrayRealVector(dimension); 2428 fAtInterpolationPoints = new ArrayRealVector(numberOfInterpolationPoints); 2429 trustRegionCenterOffset = new ArrayRealVector(dimension); 2430 gradientAtTrustRegionCenter = new ArrayRealVector(dimension); 2431 lowerDifference = new ArrayRealVector(dimension); 2432 upperDifference = new ArrayRealVector(dimension); 2433 modelSecondDerivativesParameters = new ArrayRealVector(numberOfInterpolationPoints); 2434 newPoint = new ArrayRealVector(dimension); 2435 alternativeNewPoint = new ArrayRealVector(dimension); 2436 trialStepPoint = new ArrayRealVector(dimension); 2437 lagrangeValuesAtNewPoint = new ArrayRealVector(dimension + numberOfInterpolationPoints); 2438 modelSecondDerivativesValues = new ArrayRealVector(dimension * (dimension + 1) / 2); 2439 } 2440 2441 /** 2442 * Creates a new array. 2443 * 2444 * @param n Dimension of the returned array. 2445 * @param value Value for each element. 2446 * @return an array containing {@code n} elements set to the given 2447 * {@code value}. 2448 */ 2449 private static double[] fillNewArray(int n, 2450 double value) { 2451 double[] ds = new double[n]; 2452 Arrays.fill(ds, value); 2453 return ds; 2454 } 2455 2456 // XXX utility for figuring out call sequence. 2457 private static String caller(int n) { 2458 final Throwable t = new Throwable(); 2459 final StackTraceElement[] elements = t.getStackTrace(); 2460 final StackTraceElement e = elements[n]; 2461 return e.getMethodName() + " (at line " + e.getLineNumber() + ")"; 2462 } 2463 // XXX utility for figuring out call sequence. 2464 private static void printState(int s) { 2465 // System.out.println(caller(2) + ": state " + s); 2466 } 2467 // XXX utility for figuring out call sequence. 2468 private static void printMethod() { 2469 // System.out.println(caller(2)); 2470 } 2471 2472 /** 2473 * Marker for code paths that are not explored with the current unit tests. 2474 * If the path becomes explored, it should just be removed from the code. 2475 */ 2476 private static class PathIsExploredException extends RuntimeException { 2477 private static final long serialVersionUID = 745350979634801853L; 2478 2479 private static final String PATH_IS_EXPLORED 2480 = "If this exception is thrown, just remove it from the code"; 2481 2482 PathIsExploredException() { 2483 super(PATH_IS_EXPLORED + " " + BOBYQAOptimizer.caller(3)); 2484 } 2485 } 2486 } 2487 //CHECKSTYLE: resume all