1 #include <petsctaolinesearch.h> 2 #include <../src/tao/bound/impls/bnk/bnk.h> 3 4 #include <petscksp.h> 5 6 static const char *BNK_PC[64] = {"none", "ahess", "bfgs", "petsc"}; 7 static const char *BFGS_SCALE[64] = {"ahess", "phess", "bfgs"}; 8 static const char *BNK_INIT[64] = {"constant", "direction", "interpolation"}; 9 static const char *BNK_UPDATE[64] = {"step", "reduction", "interpolation"}; 10 static const char *BNK_AS[64] = {"none", "bertsekas"}; 11 12 /*------------------------------------------------------------*/ 13 14 /* Routine for BFGS preconditioner */ 15 16 PetscErrorCode MatLMVMSolveShell(PC pc, Vec b, Vec x) 17 { 18 PetscErrorCode ierr; 19 Mat M; 20 21 PetscFunctionBegin; 22 PetscValidHeaderSpecific(pc,PC_CLASSID,1); 23 PetscValidHeaderSpecific(b,VEC_CLASSID,2); 24 PetscValidHeaderSpecific(x,VEC_CLASSID,3); 25 ierr = PCShellGetContext(pc,(void**)&M);CHKERRQ(ierr); 26 ierr = MatLMVMSolve(M, b, x);CHKERRQ(ierr); 27 PetscFunctionReturn(0); 28 } 29 30 /*------------------------------------------------------------*/ 31 32 /* Routine for initializing the KSP solver, the BFGS preconditioner, and the initial trust radius estimation */ 33 34 PetscErrorCode TaoBNKInitialize(Tao tao, PetscInt initType, PetscBool *needH) 35 { 36 PetscErrorCode ierr; 37 TAO_BNK *bnk = (TAO_BNK *)tao->data; 38 PC pc; 39 40 PetscReal f_min, ftrial, prered, actred, kappa, sigma, resnorm; 41 PetscReal tau, tau_1, tau_2, tau_max, tau_min, max_radius; 42 PetscReal delta; 43 44 PetscInt n,N,nDiff; 45 46 PetscInt i_max = 5; 47 PetscInt j_max = 1; 48 PetscInt i, j; 49 50 PetscFunctionBegin; 51 /* Project the current point onto the feasible set */ 52 ierr = TaoComputeVariableBounds(tao);CHKERRQ(ierr); 53 ierr = TaoSetVariableBounds(bnk->bncg, tao->XL, tao->XU);CHKERRQ(ierr); 54 ierr = TaoLineSearchSetVariableBounds(tao->linesearch,tao->XL,tao->XU);CHKERRQ(ierr); 55 56 /* Project the initial point onto the feasible region */ 57 ierr = TaoBoundSolution(tao->XL, tao->XU, tao->solution, 0.0, &nDiff);CHKERRQ(ierr); 58 59 /* Check convergence criteria */ 60 ierr = TaoComputeObjectiveAndGradient(tao, tao->solution, &bnk->f, bnk->unprojected_gradient);CHKERRQ(ierr); 61 ierr = TaoBNKEstimateActiveSet(tao, bnk->as_type);CHKERRQ(ierr); 62 ierr = VecCopy(bnk->unprojected_gradient, tao->gradient);CHKERRQ(ierr); 63 ierr = VecISSet(tao->gradient, bnk->active_idx, 0.0);CHKERRQ(ierr); 64 ierr = VecNorm(tao->gradient,NORM_2,&bnk->gnorm);CHKERRQ(ierr); 65 if (PetscIsInfOrNanReal(bnk->f) || PetscIsInfOrNanReal(bnk->gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN"); 66 67 /* Test the initial point for convergence */ 68 ierr = VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W);CHKERRQ(ierr); 69 ierr = VecNorm(bnk->W, NORM_2, &resnorm);CHKERRQ(ierr); 70 ierr = TaoLogConvergenceHistory(tao,bnk->f,resnorm,0.0,tao->ksp_its);CHKERRQ(ierr); 71 ierr = TaoMonitor(tao,tao->niter,bnk->f,resnorm,0.0,1.0);CHKERRQ(ierr); 72 ierr = (*tao->ops->convergencetest)(tao,tao->cnvP);CHKERRQ(ierr); 73 if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0); 74 75 /* Reset KSP stopping reason counters */ 76 bnk->ksp_atol = 0; 77 bnk->ksp_rtol = 0; 78 bnk->ksp_dtol = 0; 79 bnk->ksp_ctol = 0; 80 bnk->ksp_negc = 0; 81 bnk->ksp_iter = 0; 82 bnk->ksp_othr = 0; 83 84 /* Reset accepted step type counters */ 85 bnk->tot_cg_its = 0; 86 bnk->newt = 0; 87 bnk->bfgs = 0; 88 bnk->sgrad = 0; 89 bnk->grad = 0; 90 91 /* Initialize the Hessian perturbation */ 92 bnk->pert = bnk->sval; 93 94 /* Reset initial steplength to zero (this helps BNCG reset its direction internally) */ 95 ierr = VecSet(tao->stepdirection, 0.0);CHKERRQ(ierr); 96 97 /* Allocate the vectors needed for the BFGS approximation */ 98 if (BNK_PC_BFGS == bnk->pc_type) { 99 if (!bnk->M) { 100 ierr = VecGetLocalSize(tao->solution,&n);CHKERRQ(ierr); 101 ierr = VecGetSize(tao->solution,&N);CHKERRQ(ierr); 102 ierr = MatCreateLMVM(((PetscObject)tao)->comm,n,N,&bnk->M);CHKERRQ(ierr); 103 ierr = MatLMVMAllocateVectors(bnk->M,tao->solution);CHKERRQ(ierr); 104 } 105 if (bnk->bfgs_scale_type != BFGS_SCALE_BFGS && !bnk->Diag) { 106 ierr = VecDuplicate(tao->solution,&bnk->Diag);CHKERRQ(ierr); 107 } 108 } 109 110 /* Prepare the min/max vectors for safeguarding diagonal scales */ 111 ierr = VecSet(bnk->Diag_min, bnk->dmin);CHKERRQ(ierr); 112 ierr = VecSet(bnk->Diag_max, bnk->dmax);CHKERRQ(ierr); 113 114 /* Modify the preconditioner to use the bfgs approximation */ 115 ierr = KSPGetPC(tao->ksp, &pc);CHKERRQ(ierr); 116 switch(bnk->pc_type) { 117 case BNK_PC_NONE: 118 ierr = PCSetType(pc, PCNONE);CHKERRQ(ierr); 119 ierr = PCSetFromOptions(pc);CHKERRQ(ierr); 120 break; 121 122 case BNK_PC_AHESS: 123 ierr = PCSetType(pc, PCJACOBI);CHKERRQ(ierr); 124 ierr = PCSetFromOptions(pc);CHKERRQ(ierr); 125 ierr = PCJacobiSetUseAbs(pc,PETSC_TRUE);CHKERRQ(ierr); 126 break; 127 128 case BNK_PC_BFGS: 129 ierr = PCSetType(pc, PCSHELL);CHKERRQ(ierr); 130 ierr = PCSetFromOptions(pc);CHKERRQ(ierr); 131 ierr = PCShellSetName(pc, "bfgs");CHKERRQ(ierr); 132 ierr = PCShellSetContext(pc, bnk->M);CHKERRQ(ierr); 133 ierr = PCShellSetApply(pc, MatLMVMSolveShell);CHKERRQ(ierr); 134 break; 135 136 default: 137 /* Use the pc method set by pc_type */ 138 break; 139 } 140 141 /* Initialize trust-region radius. The initialization is only performed 142 when we are using Nash, Steihaug-Toint or the Generalized Lanczos method. */ 143 *needH = PETSC_TRUE; 144 if (bnk->is_nash || bnk->is_stcg || bnk->is_gltr) { 145 switch(initType) { 146 case BNK_INIT_CONSTANT: 147 /* Use the initial radius specified */ 148 tao->trust = tao->trust0; 149 break; 150 151 case BNK_INIT_INTERPOLATION: 152 /* Use interpolation based on the initial Hessian */ 153 max_radius = 0.0; 154 tao->trust = tao->trust0; 155 for (j = 0; j < j_max; ++j) { 156 f_min = bnk->f; 157 sigma = 0.0; 158 159 if (*needH) { 160 /* Compute the Hessian at the new step, and extract the inactive subsystem */ 161 ierr = TaoBNKComputeHessian(tao);CHKERRQ(ierr); 162 ierr = TaoBNKEstimateActiveSet(tao, BNK_AS_NONE);CHKERRQ(ierr); 163 ierr = MatDestroy(&bnk->H_inactive);CHKERRQ(ierr); 164 if (bnk->active_idx) { 165 ierr = MatCreateSubMatrix(tao->hessian, bnk->inactive_idx, bnk->inactive_idx, MAT_INITIAL_MATRIX, &bnk->H_inactive);CHKERRQ(ierr); 166 } else { 167 ierr = MatDuplicate(tao->hessian, MAT_COPY_VALUES, &bnk->H_inactive);CHKERRQ(ierr); 168 } 169 *needH = PETSC_FALSE; 170 } 171 172 for (i = 0; i < i_max; ++i) { 173 /* Take a steepest descent step and snap it to bounds */ 174 ierr = VecCopy(tao->solution, bnk->Xold);CHKERRQ(ierr); 175 ierr = VecAXPY(tao->solution, -tao->trust/bnk->gnorm, tao->gradient);CHKERRQ(ierr); 176 ierr = TaoBoundSolution(tao->XL, tao->XU, tao->solution, 0.0, &nDiff);CHKERRQ(ierr); 177 /* Compute the step we actually accepted */ 178 ierr = VecCopy(tao->solution, bnk->W);CHKERRQ(ierr); 179 ierr = VecAXPY(bnk->W, -1.0, bnk->Xold);CHKERRQ(ierr); 180 /* Compute the objective at the trial */ 181 ierr = TaoComputeObjective(tao, tao->solution, &ftrial);CHKERRQ(ierr); 182 ierr = VecCopy(bnk->Xold, tao->solution);CHKERRQ(ierr); 183 if (PetscIsInfOrNanReal(ftrial)) { 184 tau = bnk->gamma1_i; 185 } else { 186 if (ftrial < f_min) { 187 f_min = ftrial; 188 sigma = -tao->trust / bnk->gnorm; 189 } 190 191 /* Compute the predicted and actual reduction */ 192 if (bnk->active_idx) { 193 ierr = VecGetSubVector(bnk->W, bnk->inactive_idx, &bnk->X_inactive);CHKERRQ(ierr); 194 ierr = VecGetSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work);CHKERRQ(ierr); 195 } else { 196 bnk->X_inactive = bnk->W; 197 bnk->inactive_work = bnk->Xwork; 198 } 199 ierr = MatMult(bnk->H_inactive, bnk->X_inactive, bnk->inactive_work);CHKERRQ(ierr); 200 ierr = VecDot(bnk->X_inactive, bnk->inactive_work, &prered);CHKERRQ(ierr); 201 if (bnk->active_idx) { 202 ierr = VecRestoreSubVector(bnk->W, bnk->inactive_idx, &bnk->X_inactive);CHKERRQ(ierr); 203 ierr = VecRestoreSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work);CHKERRQ(ierr); 204 } 205 prered = tao->trust * (bnk->gnorm - 0.5 * tao->trust * prered / (bnk->gnorm * bnk->gnorm)); 206 actred = bnk->f - ftrial; 207 if ((PetscAbsScalar(actred) <= bnk->epsilon) && (PetscAbsScalar(prered) <= bnk->epsilon)) { 208 kappa = 1.0; 209 } else { 210 kappa = actred / prered; 211 } 212 213 tau_1 = bnk->theta_i * bnk->gnorm * tao->trust / (bnk->theta_i * bnk->gnorm * tao->trust + (1.0 - bnk->theta_i) * prered - actred); 214 tau_2 = bnk->theta_i * bnk->gnorm * tao->trust / (bnk->theta_i * bnk->gnorm * tao->trust - (1.0 + bnk->theta_i) * prered + actred); 215 tau_min = PetscMin(tau_1, tau_2); 216 tau_max = PetscMax(tau_1, tau_2); 217 218 if (PetscAbsScalar(kappa - 1.0) <= bnk->mu1_i) { 219 /* Great agreement */ 220 max_radius = PetscMax(max_radius, tao->trust); 221 222 if (tau_max < 1.0) { 223 tau = bnk->gamma3_i; 224 } else if (tau_max > bnk->gamma4_i) { 225 tau = bnk->gamma4_i; 226 } else { 227 tau = tau_max; 228 } 229 } 230 else if (PetscAbsScalar(kappa - 1.0) <= bnk->mu2_i) { 231 /* Good agreement */ 232 max_radius = PetscMax(max_radius, tao->trust); 233 234 if (tau_max < bnk->gamma2_i) { 235 tau = bnk->gamma2_i; 236 } else if (tau_max > bnk->gamma3_i) { 237 tau = bnk->gamma3_i; 238 } else { 239 tau = tau_max; 240 } 241 } 242 else { 243 /* Not good agreement */ 244 if (tau_min > 1.0) { 245 tau = bnk->gamma2_i; 246 } else if (tau_max < bnk->gamma1_i) { 247 tau = bnk->gamma1_i; 248 } else if ((tau_min < bnk->gamma1_i) && (tau_max >= 1.0)) { 249 tau = bnk->gamma1_i; 250 } else if ((tau_1 >= bnk->gamma1_i) && (tau_1 < 1.0) && ((tau_2 < bnk->gamma1_i) || (tau_2 >= 1.0))) { 251 tau = tau_1; 252 } else if ((tau_2 >= bnk->gamma1_i) && (tau_2 < 1.0) && ((tau_1 < bnk->gamma1_i) || (tau_2 >= 1.0))) { 253 tau = tau_2; 254 } else { 255 tau = tau_max; 256 } 257 } 258 } 259 tao->trust = tau * tao->trust; 260 } 261 262 if (f_min < bnk->f) { 263 /* We accidentally found a solution better than the initial, so accept it */ 264 bnk->f = f_min; 265 ierr = VecCopy(tao->solution, bnk->Xold);CHKERRQ(ierr); 266 ierr = VecAXPY(tao->solution,sigma,tao->gradient);CHKERRQ(ierr); 267 ierr = TaoBoundSolution(tao->XL, tao->XU, tao->solution, 0.0, &nDiff);CHKERRQ(ierr); 268 ierr = VecCopy(tao->solution, tao->stepdirection);CHKERRQ(ierr); 269 ierr = VecAXPY(tao->stepdirection, -1.0, bnk->Xold);CHKERRQ(ierr); 270 ierr = TaoComputeGradient(tao,tao->solution,bnk->unprojected_gradient);CHKERRQ(ierr); 271 ierr = TaoBNKEstimateActiveSet(tao, bnk->as_type);CHKERRQ(ierr); 272 ierr = VecCopy(bnk->unprojected_gradient, tao->gradient);CHKERRQ(ierr); 273 ierr = VecISSet(tao->gradient, bnk->active_idx, 0.0);CHKERRQ(ierr); 274 /* Compute gradient at the new iterate and flip switch to compute the Hessian later */ 275 ierr = VecNorm(tao->gradient, NORM_2, &bnk->gnorm);CHKERRQ(ierr); 276 if (PetscIsInfOrNanReal(bnk->gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute gradient generated Inf or NaN"); 277 *needH = PETSC_TRUE; 278 /* Test the new step for convergence */ 279 ierr = VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W);CHKERRQ(ierr); 280 ierr = VecNorm(bnk->W, NORM_2, &resnorm);CHKERRQ(ierr); 281 ierr = TaoLogConvergenceHistory(tao,bnk->f,resnorm,0.0,tao->ksp_its);CHKERRQ(ierr); 282 ierr = TaoMonitor(tao,tao->niter,bnk->f,resnorm,0.0,1.0);CHKERRQ(ierr); 283 ierr = (*tao->ops->convergencetest)(tao,tao->cnvP);CHKERRQ(ierr); 284 if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0); 285 /* active BNCG recycling early because we have a stepdirection computed */ 286 ierr = TaoBNCGSetRecycleFlag(bnk->bncg, PETSC_TRUE);CHKERRQ(ierr); 287 } 288 } 289 tao->trust = PetscMax(tao->trust, max_radius); 290 291 /* Ensure that the trust radius is within the limits */ 292 tao->trust = PetscMax(tao->trust, bnk->min_radius); 293 tao->trust = PetscMin(tao->trust, bnk->max_radius); 294 break; 295 296 default: 297 /* Norm of the first direction will initialize radius */ 298 tao->trust = 0.0; 299 break; 300 } 301 } 302 303 /* Set initial scaling for the BFGS preconditioner 304 This step is done after computing the initial trust-region radius 305 since the function value may have decreased */ 306 if (BNK_PC_BFGS == bnk->pc_type) { 307 delta = 2.0 * PetscMax(1.0, PetscAbsScalar(bnk->f)) / (bnk->gnorm*bnk->gnorm); 308 ierr = MatLMVMSetDelta(bnk->M,delta);CHKERRQ(ierr); 309 } 310 PetscFunctionReturn(0); 311 } 312 313 /*------------------------------------------------------------*/ 314 315 /* Routine for computing the Hessian and preparing the preconditioner at the new iterate */ 316 317 PetscErrorCode TaoBNKComputeHessian(Tao tao) 318 { 319 PetscErrorCode ierr; 320 TAO_BNK *bnk = (TAO_BNK *)tao->data; 321 PetscBool diagExists; 322 PetscReal delta; 323 324 PetscFunctionBegin; 325 /* Compute the Hessian */ 326 ierr = TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);CHKERRQ(ierr); 327 /* Add a correction to the BFGS preconditioner */ 328 if (BNK_PC_BFGS == bnk->pc_type) { 329 ierr = MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr); 330 /* Update the BFGS diagonal scaling */ 331 ierr = MatHasOperation(tao->hessian, MATOP_GET_DIAGONAL, &diagExists);CHKERRQ(ierr); 332 if (BFGS_SCALE_AHESS == bnk->bfgs_scale_type && diagExists) { 333 ierr = MatGetDiagonal(tao->hessian, bnk->Diag);CHKERRQ(ierr); 334 ierr = VecAbs(bnk->Diag);CHKERRQ(ierr); 335 ierr = VecMedian(bnk->Diag_min, bnk->Diag, bnk->Diag_max, bnk->Diag);CHKERRQ(ierr); 336 ierr = VecReciprocal(bnk->Diag);CHKERRQ(ierr); 337 ierr = MatLMVMSetScale(bnk->M,bnk->Diag);CHKERRQ(ierr); 338 } else { 339 /* Fall back onto stand-alone BFGS scaling */ 340 delta = 2.0 * PetscMax(1.0, PetscAbsScalar(bnk->f)) / (bnk->gnorm*bnk->gnorm); 341 ierr = MatLMVMSetDelta(bnk->M,delta);CHKERRQ(ierr); 342 } 343 } 344 PetscFunctionReturn(0); 345 } 346 347 /*------------------------------------------------------------*/ 348 349 /* Routine for estimating the active set */ 350 351 PetscErrorCode TaoBNKEstimateActiveSet(Tao tao, PetscInt asType) 352 { 353 PetscErrorCode ierr; 354 TAO_BNK *bnk = (TAO_BNK *)tao->data; 355 PetscBool hessComputed, diagExists; 356 357 PetscFunctionBegin; 358 switch (asType) { 359 case BNK_AS_NONE: 360 ierr = ISDestroy(&bnk->inactive_idx);CHKERRQ(ierr); 361 ierr = VecWhichInactive(tao->XL, tao->solution, bnk->unprojected_gradient, tao->XU, PETSC_TRUE, &bnk->inactive_idx);CHKERRQ(ierr); 362 ierr = ISDestroy(&bnk->active_idx);CHKERRQ(ierr); 363 ierr = ISComplementVec(bnk->inactive_idx, tao->solution, &bnk->active_idx);CHKERRQ(ierr); 364 break; 365 366 case BNK_AS_BERTSEKAS: 367 /* Compute the trial step vector with which we will estimate the active set at the next iteration */ 368 if (BNK_PC_BFGS == bnk->pc_type) { 369 /* If the BFGS preconditioner matrix is available, we will construct a trial step with it */ 370 ierr = MatLMVMSetInactive(bnk->M, NULL);CHKERRQ(ierr); 371 ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, bnk->W);CHKERRQ(ierr); 372 } else { 373 ierr = MatAssembled(tao->hessian, &hessComputed);CHKERRQ(ierr); 374 ierr = MatHasOperation(tao->hessian, MATOP_GET_DIAGONAL, &diagExists);CHKERRQ(ierr); 375 if (hessComputed && diagExists) { 376 /* BFGS preconditioner doesn't exist so let's invert the absolute diagonal of the Hessian instead onto the gradient */ 377 ierr = MatGetDiagonal(tao->hessian, bnk->Xwork);CHKERRQ(ierr); 378 ierr = VecAbs(bnk->Xwork);CHKERRQ(ierr); 379 ierr = VecMedian(bnk->Diag_min, bnk->Xwork, bnk->Diag_max, bnk->Xwork);CHKERRQ(ierr); 380 ierr = VecReciprocal(bnk->Xwork);CHKERRQ(ierr);CHKERRQ(ierr); 381 ierr = VecPointwiseMult(bnk->W, bnk->Xwork, bnk->unprojected_gradient);CHKERRQ(ierr); 382 } else { 383 /* If the Hessian or its diagonal does not exist, we will simply use gradient step */ 384 ierr = VecCopy(bnk->unprojected_gradient, bnk->W);CHKERRQ(ierr); 385 } 386 } 387 ierr = VecScale(bnk->W, -1.0);CHKERRQ(ierr); 388 ierr = TaoEstimateActiveBounds(tao->solution, tao->XL, tao->XU, bnk->unprojected_gradient, bnk->W, bnk->Xwork, bnk->as_step, &bnk->as_tol, 389 &bnk->active_lower, &bnk->active_upper, &bnk->active_fixed, &bnk->active_idx, &bnk->inactive_idx);CHKERRQ(ierr); 390 break; 391 392 default: 393 break; 394 } 395 PetscFunctionReturn(0); 396 } 397 398 /*------------------------------------------------------------*/ 399 400 /* Routine for bounding the step direction */ 401 402 PetscErrorCode TaoBNKBoundStep(Tao tao, Vec step) 403 { 404 PetscErrorCode ierr; 405 TAO_BNK *bnk = (TAO_BNK *)tao->data; 406 407 PetscFunctionBegin; 408 switch (bnk->as_type) { 409 case BNK_AS_NONE: 410 ierr = VecISSet(step, bnk->active_idx, 0.0);CHKERRQ(ierr); 411 break; 412 413 case BNK_AS_BERTSEKAS: 414 ierr = TaoBoundStep(tao->solution, tao->XL, tao->XU, bnk->active_lower, bnk->active_upper, bnk->active_fixed, 1.0, step);CHKERRQ(ierr); 415 break; 416 417 default: 418 break; 419 } 420 PetscFunctionReturn(0); 421 } 422 423 /*------------------------------------------------------------*/ 424 425 /* Routine for taking a finite number of BNCG iterations to 426 accelerate Newton convergence. 427 428 In practice, this approach simply trades off Hessian evaluations 429 for more gradient evaluations. 430 */ 431 432 PetscErrorCode TaoBNKTakeCGSteps(Tao tao, PetscBool *terminate) 433 { 434 TAO_BNK *bnk = (TAO_BNK *)tao->data; 435 PetscErrorCode ierr; 436 437 PetscFunctionBegin; 438 *terminate = PETSC_FALSE; 439 if (bnk->max_cg_its > 0) { 440 /* Copy the current function value (important vectors are already shared) */ 441 bnk->bncg_ctx->f = bnk->f; 442 /* Take some small finite number of BNCG iterations */ 443 ierr = TaoSolve(bnk->bncg);CHKERRQ(ierr); 444 /* Add the number of gradient and function evaluations to the total */ 445 tao->nfuncs += bnk->bncg->nfuncs; 446 tao->nfuncgrads += bnk->bncg->nfuncgrads; 447 tao->ngrads += bnk->bncg->ngrads; 448 tao->nhess += bnk->bncg->nhess; 449 bnk->tot_cg_its += bnk->bncg->niter; 450 /* Extract the BNCG function value out and save it into BNK */ 451 bnk->f = bnk->bncg_ctx->f; 452 if (bnk->bncg->reason == TAO_CONVERGED_GATOL || bnk->bncg->reason == TAO_CONVERGED_GRTOL || bnk->bncg->reason == TAO_CONVERGED_GTTOL || bnk->bncg->reason == TAO_CONVERGED_MINF) { 453 *terminate = PETSC_TRUE; 454 } else { 455 ierr = TaoBNKEstimateActiveSet(tao, bnk->as_type); 456 } 457 } 458 PetscFunctionReturn(0); 459 } 460 461 /*------------------------------------------------------------*/ 462 463 /* Routine for computing the Newton step. */ 464 465 PetscErrorCode TaoBNKComputeStep(Tao tao, PetscBool shift, KSPConvergedReason *ksp_reason) 466 { 467 PetscErrorCode ierr; 468 TAO_BNK *bnk = (TAO_BNK *)tao->data; 469 470 PetscReal delta; 471 PetscInt bfgsUpdates = 0; 472 PetscInt kspits; 473 PetscBool diagExists; 474 475 PetscFunctionBegin; 476 /* If there are no inactive variables left, save some computation and return an adjusted zero step 477 that has (l-x) and (u-x) for lower and upper bounded variables. */ 478 if (!bnk->inactive_idx) { 479 ierr = VecSet(tao->stepdirection, 0.0);CHKERRQ(ierr); 480 ierr = TaoBNKBoundStep(tao, tao->stepdirection);CHKERRQ(ierr); 481 PetscFunctionReturn(0); 482 } 483 484 /* Prepare the reduced sub-matrices for the inactive set */ 485 if (BNK_PC_BFGS == bnk->pc_type) { 486 ierr = MatLMVMSetInactive(bnk->M, bnk->inactive_idx);CHKERRQ(ierr); 487 } 488 if (bnk->active_idx) { 489 ierr = MatDestroy(&bnk->H_inactive); 490 ierr = MatCreateSubMatrix(tao->hessian, bnk->inactive_idx, bnk->inactive_idx, MAT_INITIAL_MATRIX, &bnk->H_inactive);CHKERRQ(ierr); 491 if (tao->hessian == tao->hessian_pre) { 492 bnk->Hpre_inactive = bnk->H_inactive; 493 } else { 494 ierr = MatDestroy(&bnk->Hpre_inactive); 495 ierr = MatCreateSubMatrix(tao->hessian_pre, bnk->inactive_idx, bnk->inactive_idx, MAT_INITIAL_MATRIX, &bnk->Hpre_inactive);CHKERRQ(ierr); 496 } 497 } else { 498 ierr = MatDestroy(&bnk->H_inactive); 499 ierr = MatDuplicate(tao->hessian, MAT_COPY_VALUES, &bnk->H_inactive); 500 if (tao->hessian == tao->hessian_pre) { 501 bnk->Hpre_inactive = bnk->H_inactive; 502 } else { 503 ierr = MatDestroy(&bnk->Hpre_inactive); 504 ierr = MatDuplicate(tao->hessian_pre, MAT_COPY_VALUES, &bnk->Hpre_inactive); 505 } 506 } 507 508 /* Shift the reduced Hessian matrix */ 509 if ((shift) && (bnk->pert > 0)) { 510 ierr = MatShift(bnk->H_inactive, bnk->pert);CHKERRQ(ierr); 511 if (bnk->H_inactive != bnk->Hpre_inactive) { 512 ierr = MatShift(bnk->Hpre_inactive, bnk->pert);CHKERRQ(ierr); 513 } 514 } 515 516 /* Update the diagonal scaling for the BFGS preconditioner, this time with the Hessian perturbation */ 517 if ((BNK_PC_BFGS == bnk->pc_type) && (BFGS_SCALE_PHESS == bnk->bfgs_scale_type)) { 518 ierr = MatHasOperation(bnk->H_inactive, MATOP_GET_DIAGONAL, &diagExists);CHKERRQ(ierr); 519 if (diagExists) { 520 /* Obtain diagonal for the bfgs preconditioner */ 521 ierr = VecSet(bnk->Diag, 1.0);CHKERRQ(ierr); 522 if (bnk->active_idx) { 523 ierr = VecGetSubVector(bnk->Diag, bnk->inactive_idx, &bnk->Diag_red);CHKERRQ(ierr); 524 } else { 525 bnk->Diag_red = bnk->Diag; 526 } 527 ierr = MatGetDiagonal(bnk->H_inactive, bnk->Diag_red);CHKERRQ(ierr); 528 if (bnk->active_idx) { 529 ierr = VecRestoreSubVector(bnk->Diag, bnk->inactive_idx, &bnk->Diag_red);CHKERRQ(ierr); 530 } 531 ierr = VecAbs(bnk->Diag);CHKERRQ(ierr); 532 ierr = VecMedian(bnk->Diag_min, bnk->Diag, bnk->Diag_max, bnk->Diag);CHKERRQ(ierr); 533 ierr = VecReciprocal(bnk->Diag);CHKERRQ(ierr); 534 ierr = MatLMVMSetScale(bnk->M,bnk->Diag);CHKERRQ(ierr); 535 } else { 536 /* Fall back onto stand-alone BFGS scaling */ 537 delta = 2.0 * PetscMax(1.0, PetscAbsScalar(bnk->f)) / (bnk->gnorm*bnk->gnorm); 538 ierr = MatLMVMSetDelta(bnk->M,delta);CHKERRQ(ierr); 539 } 540 } 541 542 /* Solve the Newton system of equations */ 543 tao->ksp_its = 0; 544 ierr = VecSet(tao->stepdirection, 0.0);CHKERRQ(ierr); 545 ierr = KSPReset(tao->ksp);CHKERRQ(ierr); 546 ierr = KSPSetOperators(tao->ksp,bnk->H_inactive,bnk->Hpre_inactive);CHKERRQ(ierr); 547 ierr = VecCopy(bnk->unprojected_gradient, bnk->Gwork);CHKERRQ(ierr); 548 if (bnk->active_idx) { 549 ierr = VecGetSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive);CHKERRQ(ierr); 550 ierr = VecGetSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive);CHKERRQ(ierr); 551 } else { 552 bnk->G_inactive = bnk->unprojected_gradient; 553 bnk->X_inactive = tao->stepdirection; 554 } 555 if (bnk->is_nash || bnk->is_stcg || bnk->is_gltr) { 556 ierr = KSPCGSetRadius(tao->ksp,tao->trust);CHKERRQ(ierr); 557 ierr = KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive);CHKERRQ(ierr); 558 ierr = KSPGetIterationNumber(tao->ksp,&kspits);CHKERRQ(ierr); 559 tao->ksp_its+=kspits; 560 tao->ksp_tot_its+=kspits; 561 ierr = KSPCGGetNormD(tao->ksp,&bnk->dnorm);CHKERRQ(ierr); 562 563 if (0.0 == tao->trust) { 564 /* Radius was uninitialized; use the norm of the direction */ 565 if (bnk->dnorm > 0.0) { 566 tao->trust = bnk->dnorm; 567 568 /* Modify the radius if it is too large or small */ 569 tao->trust = PetscMax(tao->trust, bnk->min_radius); 570 tao->trust = PetscMin(tao->trust, bnk->max_radius); 571 } else { 572 /* The direction was bad; set radius to default value and re-solve 573 the trust-region subproblem to get a direction */ 574 tao->trust = tao->trust0; 575 576 /* Modify the radius if it is too large or small */ 577 tao->trust = PetscMax(tao->trust, bnk->min_radius); 578 tao->trust = PetscMin(tao->trust, bnk->max_radius); 579 580 ierr = KSPCGSetRadius(tao->ksp,tao->trust);CHKERRQ(ierr); 581 ierr = KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive);CHKERRQ(ierr); 582 ierr = KSPGetIterationNumber(tao->ksp,&kspits);CHKERRQ(ierr); 583 tao->ksp_its+=kspits; 584 tao->ksp_tot_its+=kspits; 585 ierr = KSPCGGetNormD(tao->ksp,&bnk->dnorm);CHKERRQ(ierr); 586 587 if (bnk->dnorm == 0.0) SETERRQ(PETSC_COMM_SELF,1, "Initial direction zero"); 588 } 589 } 590 } else { 591 ierr = KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive);CHKERRQ(ierr); 592 ierr = KSPGetIterationNumber(tao->ksp, &kspits);CHKERRQ(ierr); 593 tao->ksp_its += kspits; 594 tao->ksp_tot_its+=kspits; 595 } 596 /* Restore sub vectors back */ 597 if (bnk->active_idx) { 598 ierr = VecRestoreSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive);CHKERRQ(ierr); 599 ierr = VecRestoreSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive);CHKERRQ(ierr); 600 } 601 /* Make sure the safeguarded fall-back step is zero for actively bounded variables */ 602 ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr); 603 ierr = TaoBNKBoundStep(tao, tao->stepdirection);CHKERRQ(ierr); 604 605 /* Record convergence reasons */ 606 ierr = KSPGetConvergedReason(tao->ksp, ksp_reason);CHKERRQ(ierr); 607 if (KSP_CONVERGED_ATOL == *ksp_reason) { 608 ++bnk->ksp_atol; 609 } else if (KSP_CONVERGED_RTOL == *ksp_reason) { 610 ++bnk->ksp_rtol; 611 } else if (KSP_CONVERGED_CG_CONSTRAINED == *ksp_reason) { 612 ++bnk->ksp_ctol; 613 } else if (KSP_CONVERGED_CG_NEG_CURVE == *ksp_reason) { 614 ++bnk->ksp_negc; 615 } else if (KSP_DIVERGED_DTOL == *ksp_reason) { 616 ++bnk->ksp_dtol; 617 } else if (KSP_DIVERGED_ITS == *ksp_reason) { 618 ++bnk->ksp_iter; 619 } else { 620 ++bnk->ksp_othr; 621 } 622 623 /* Make sure the BFGS preconditioner is healthy */ 624 if (bnk->pc_type == BNK_PC_BFGS) { 625 ierr = MatLMVMGetUpdates(bnk->M, &bfgsUpdates);CHKERRQ(ierr); 626 if ((KSP_DIVERGED_INDEFINITE_PC == *ksp_reason) && (bfgsUpdates > 1)) { 627 /* Preconditioner is numerically indefinite; reset the approximation. */ 628 delta = 2.0 * PetscMax(1.0, PetscAbsScalar(bnk->f)) / (bnk->gnorm*bnk->gnorm); 629 ierr = MatLMVMSetDelta(bnk->M,delta);CHKERRQ(ierr); 630 ierr = MatLMVMReset(bnk->M);CHKERRQ(ierr); 631 ierr = MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr); 632 } 633 } 634 PetscFunctionReturn(0); 635 } 636 637 /*------------------------------------------------------------*/ 638 639 /* Routine for recomputing the predicted reduction for a given step vector */ 640 641 PetscErrorCode TaoBNKRecomputePred(Tao tao, Vec S, PetscReal *prered) 642 { 643 PetscErrorCode ierr; 644 TAO_BNK *bnk = (TAO_BNK *)tao->data; 645 646 PetscFunctionBegin; 647 /* Extract subvectors associated with the inactive set */ 648 if (bnk->active_idx){ 649 ierr = VecGetSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive);CHKERRQ(ierr); 650 ierr = VecGetSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work);CHKERRQ(ierr); 651 ierr = VecGetSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive);CHKERRQ(ierr); 652 } else { 653 bnk->X_inactive = tao->stepdirection; 654 bnk->inactive_work = bnk->Xwork; 655 bnk->G_inactive = bnk->Gwork; 656 } 657 /* Recompute the predicted decrease based on the quadratic model */ 658 ierr = MatMult(bnk->H_inactive, bnk->X_inactive, bnk->inactive_work);CHKERRQ(ierr); 659 ierr = VecAYPX(bnk->inactive_work, -0.5, bnk->G_inactive);CHKERRQ(ierr); 660 ierr = VecDot(bnk->inactive_work, bnk->X_inactive, prered); 661 /* Restore the sub vectors */ 662 if (bnk->active_idx){ 663 ierr = VecRestoreSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive);CHKERRQ(ierr); 664 ierr = VecRestoreSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work);CHKERRQ(ierr); 665 ierr = VecRestoreSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive);CHKERRQ(ierr); 666 } 667 PetscFunctionReturn(0); 668 } 669 670 /*------------------------------------------------------------*/ 671 672 /* Routine for ensuring that the Newton step is a descent direction. 673 674 The step direction falls back onto BFGS, scaled gradient and gradient steps 675 in the event that the Newton step fails the test. 676 */ 677 678 PetscErrorCode TaoBNKSafeguardStep(Tao tao, KSPConvergedReason ksp_reason, PetscInt *stepType) 679 { 680 PetscErrorCode ierr; 681 TAO_BNK *bnk = (TAO_BNK *)tao->data; 682 683 PetscReal gdx, delta, e_min; 684 PetscInt bfgsUpdates; 685 686 PetscFunctionBegin; 687 ierr = VecDot(tao->stepdirection, tao->gradient, &gdx);CHKERRQ(ierr); 688 if ((gdx >= 0.0) || PetscIsInfOrNanReal(gdx)) { 689 /* Newton step is not descent or direction produced Inf or NaN 690 Update the perturbation for next time */ 691 if (bnk->pert <= 0.0) { 692 /* Initialize the perturbation */ 693 bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm)); 694 if (bnk->is_gltr) { 695 ierr = KSPCGGLTRGetMinEig(tao->ksp,&e_min);CHKERRQ(ierr); 696 bnk->pert = PetscMax(bnk->pert, -e_min); 697 } 698 } else { 699 /* Increase the perturbation */ 700 bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm)); 701 } 702 703 if (BNK_PC_BFGS != bnk->pc_type) { 704 /* We don't have the bfgs matrix around and updated 705 Must use gradient direction in this case */ 706 ierr = VecCopy(tao->gradient, tao->stepdirection);CHKERRQ(ierr); 707 *stepType = BNK_GRADIENT; 708 } else { 709 /* Attempt to use the BFGS direction */ 710 ierr = MatLMVMSetInactive(bnk->M, NULL);CHKERRQ(ierr); 711 ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr); 712 713 /* Check for success (descent direction) 714 NOTE: Negative gdx here means not a descent direction because 715 the fall-back step is missing a negative sign. */ 716 ierr = VecDot(tao->gradient, tao->stepdirection, &gdx);CHKERRQ(ierr); 717 if ((gdx <= 0.0) || PetscIsInfOrNanReal(gdx)) { 718 /* BFGS direction is not descent or direction produced not a number 719 We can assert bfgsUpdates > 1 in this case because 720 the first solve produces the scaled gradient direction, 721 which is guaranteed to be descent */ 722 723 /* Use steepest descent direction (scaled) */ 724 delta = 2.0 * PetscMax(1.0, PetscAbsScalar(bnk->f)) / (bnk->gnorm*bnk->gnorm); 725 ierr = MatLMVMSetDelta(bnk->M, delta);CHKERRQ(ierr); 726 ierr = MatLMVMReset(bnk->M);CHKERRQ(ierr); 727 ierr = MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr); 728 ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr); 729 730 *stepType = BNK_SCALED_GRADIENT; 731 } else { 732 ierr = MatLMVMGetUpdates(bnk->M, &bfgsUpdates);CHKERRQ(ierr); 733 if (1 == bfgsUpdates) { 734 /* The first BFGS direction is always the scaled gradient */ 735 *stepType = BNK_SCALED_GRADIENT; 736 } else { 737 *stepType = BNK_BFGS; 738 } 739 } 740 } 741 /* Make sure the safeguarded fall-back step is zero for actively bounded variables */ 742 ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr); 743 ierr = TaoBNKBoundStep(tao, tao->stepdirection);CHKERRQ(ierr); 744 } else { 745 /* Computed Newton step is descent */ 746 switch (ksp_reason) { 747 case KSP_DIVERGED_NANORINF: 748 case KSP_DIVERGED_BREAKDOWN: 749 case KSP_DIVERGED_INDEFINITE_MAT: 750 case KSP_DIVERGED_INDEFINITE_PC: 751 case KSP_CONVERGED_CG_NEG_CURVE: 752 /* Matrix or preconditioner is indefinite; increase perturbation */ 753 if (bnk->pert <= 0.0) { 754 /* Initialize the perturbation */ 755 bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm)); 756 if (bnk->is_gltr) { 757 ierr = KSPCGGLTRGetMinEig(tao->ksp, &e_min);CHKERRQ(ierr); 758 bnk->pert = PetscMax(bnk->pert, -e_min); 759 } 760 } else { 761 /* Increase the perturbation */ 762 bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm)); 763 } 764 break; 765 766 default: 767 /* Newton step computation is good; decrease perturbation */ 768 bnk->pert = PetscMin(bnk->psfac * bnk->pert, bnk->pmsfac * bnk->gnorm); 769 if (bnk->pert < bnk->pmin) { 770 bnk->pert = 0.0; 771 } 772 break; 773 } 774 *stepType = BNK_NEWTON; 775 } 776 PetscFunctionReturn(0); 777 } 778 779 /*------------------------------------------------------------*/ 780 781 /* Routine for performing a bound-projected More-Thuente line search. 782 783 Includes fallbacks to BFGS, scaled gradient, and unscaled gradient steps if the 784 Newton step does not produce a valid step length. 785 */ 786 787 PetscErrorCode TaoBNKPerformLineSearch(Tao tao, PetscInt *stepType, PetscReal *steplen, TaoLineSearchConvergedReason *reason) 788 { 789 TAO_BNK *bnk = (TAO_BNK *)tao->data; 790 PetscErrorCode ierr; 791 TaoLineSearchConvergedReason ls_reason; 792 793 PetscReal e_min, gdx, delta; 794 PetscInt bfgsUpdates; 795 796 PetscFunctionBegin; 797 /* Perform the linesearch */ 798 ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &bnk->f, bnk->unprojected_gradient, tao->stepdirection, steplen, &ls_reason);CHKERRQ(ierr); 799 ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr); 800 801 while (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER && *stepType != BNK_GRADIENT) { 802 /* Linesearch failed, revert solution */ 803 bnk->f = bnk->fold; 804 ierr = VecCopy(bnk->Xold, tao->solution);CHKERRQ(ierr); 805 ierr = VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient);CHKERRQ(ierr); 806 807 switch(*stepType) { 808 case BNK_NEWTON: 809 /* Failed to obtain acceptable iterate with Newton step 810 Update the perturbation for next time */ 811 if (bnk->pert <= 0.0) { 812 /* Initialize the perturbation */ 813 bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm)); 814 if (bnk->is_gltr) { 815 ierr = KSPCGGLTRGetMinEig(tao->ksp,&e_min);CHKERRQ(ierr); 816 bnk->pert = PetscMax(bnk->pert, -e_min); 817 } 818 } else { 819 /* Increase the perturbation */ 820 bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm)); 821 } 822 823 if (BNK_PC_BFGS != bnk->pc_type) { 824 /* We don't have the bfgs matrix around and being updated 825 Must use gradient direction in this case */ 826 ierr = VecCopy(bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr); 827 *stepType = BNK_GRADIENT; 828 } else { 829 /* Attempt to use the BFGS direction */ 830 ierr = MatLMVMSetInactive(bnk->M, NULL);CHKERRQ(ierr); 831 ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr); 832 /* Check for success (descent direction) 833 NOTE: Negative gdx means not a descent direction because the step here is missing a negative sign. */ 834 ierr = VecDot(tao->gradient, tao->stepdirection, &gdx);CHKERRQ(ierr); 835 if ((gdx <= 0.0) || PetscIsInfOrNanReal(gdx)) { 836 /* BFGS direction is not descent or direction produced not a number 837 We can assert bfgsUpdates > 1 in this case 838 Use steepest descent direction (scaled) */ 839 delta = 2.0 * PetscMax(1.0, PetscAbsScalar(bnk->f)) / (bnk->gnorm*bnk->gnorm); 840 ierr = MatLMVMSetDelta(bnk->M, delta);CHKERRQ(ierr); 841 ierr = MatLMVMReset(bnk->M);CHKERRQ(ierr); 842 ierr = MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr); 843 ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr); 844 845 bfgsUpdates = 1; 846 *stepType = BNK_SCALED_GRADIENT; 847 } else { 848 ierr = MatLMVMGetUpdates(bnk->M, &bfgsUpdates);CHKERRQ(ierr); 849 if (1 == bfgsUpdates) { 850 /* The first BFGS direction is always the scaled gradient */ 851 *stepType = BNK_SCALED_GRADIENT; 852 } else { 853 *stepType = BNK_BFGS; 854 } 855 } 856 } 857 break; 858 859 case BNK_BFGS: 860 /* Can only enter if pc_type == BNK_PC_BFGS 861 Failed to obtain acceptable iterate with BFGS step 862 Attempt to use the scaled gradient direction */ 863 delta = 2.0 * PetscMax(1.0, PetscAbsScalar(bnk->f)) / (bnk->gnorm*bnk->gnorm); 864 ierr = MatLMVMSetDelta(bnk->M, delta);CHKERRQ(ierr); 865 ierr = MatLMVMReset(bnk->M);CHKERRQ(ierr); 866 ierr = MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr); 867 ierr = MatLMVMSetInactive(bnk->M, NULL);CHKERRQ(ierr); 868 ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr); 869 870 bfgsUpdates = 1; 871 *stepType = BNK_SCALED_GRADIENT; 872 break; 873 874 case BNK_SCALED_GRADIENT: 875 /* Can only enter if pc_type == BNK_PC_BFGS 876 The scaled gradient step did not produce a new iterate; 877 reset the BFGS matrix and attemp to use the gradient direction. */ 878 ierr = MatLMVMSetScale(bnk->M,0);CHKERRQ(ierr); 879 ierr = MatLMVMSetDelta(bnk->M,1.0);CHKERRQ(ierr); 880 ierr = MatLMVMReset(bnk->M);CHKERRQ(ierr); 881 ierr = MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr); 882 ierr = VecCopy(bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr); 883 884 bfgsUpdates = 1; 885 *stepType = BNK_GRADIENT; 886 break; 887 } 888 /* Make sure the safeguarded fall-back step is zero for actively bounded variables */ 889 ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr); 890 ierr = TaoBNKBoundStep(tao, tao->stepdirection);CHKERRQ(ierr); 891 892 /* Perform one last line search with the fall-back step */ 893 ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &bnk->f, bnk->unprojected_gradient, tao->stepdirection, steplen, &ls_reason);CHKERRQ(ierr); 894 ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr); 895 } 896 *reason = ls_reason; 897 PetscFunctionReturn(0); 898 } 899 900 /*------------------------------------------------------------*/ 901 902 /* Routine for updating the trust radius. 903 904 Function features three different update methods: 905 1) Line-search step length based 906 2) Predicted decrease on the CG quadratic model 907 3) Interpolation 908 */ 909 910 PetscErrorCode TaoBNKUpdateTrustRadius(Tao tao, PetscReal prered, PetscReal actred, PetscInt updateType, PetscInt stepType, PetscBool *accept) 911 { 912 TAO_BNK *bnk = (TAO_BNK *)tao->data; 913 PetscErrorCode ierr; 914 915 PetscReal step, kappa; 916 PetscReal gdx, tau_1, tau_2, tau_min, tau_max; 917 918 PetscFunctionBegin; 919 /* Update trust region radius */ 920 *accept = PETSC_FALSE; 921 switch(updateType) { 922 case BNK_UPDATE_STEP: 923 *accept = PETSC_TRUE; /* always accept here because line search succeeded */ 924 if (stepType == BNK_NEWTON) { 925 ierr = TaoLineSearchGetStepLength(tao->linesearch, &step);CHKERRQ(ierr); 926 if (step < bnk->nu1) { 927 /* Very bad step taken; reduce radius */ 928 tao->trust = bnk->omega1 * PetscMin(bnk->dnorm, tao->trust); 929 } else if (step < bnk->nu2) { 930 /* Reasonably bad step taken; reduce radius */ 931 tao->trust = bnk->omega2 * PetscMin(bnk->dnorm, tao->trust); 932 } else if (step < bnk->nu3) { 933 /* Reasonable step was taken; leave radius alone */ 934 if (bnk->omega3 < 1.0) { 935 tao->trust = bnk->omega3 * PetscMin(bnk->dnorm, tao->trust); 936 } else if (bnk->omega3 > 1.0) { 937 tao->trust = PetscMax(bnk->omega3 * bnk->dnorm, tao->trust); 938 } 939 } else if (step < bnk->nu4) { 940 /* Full step taken; increase the radius */ 941 tao->trust = PetscMax(bnk->omega4 * bnk->dnorm, tao->trust); 942 } else { 943 /* More than full step taken; increase the radius */ 944 tao->trust = PetscMax(bnk->omega5 * bnk->dnorm, tao->trust); 945 } 946 } else { 947 /* Newton step was not good; reduce the radius */ 948 tao->trust = bnk->omega1 * PetscMin(bnk->dnorm, tao->trust); 949 } 950 break; 951 952 case BNK_UPDATE_REDUCTION: 953 if (stepType == BNK_NEWTON) { 954 if (prered < 0.0) { 955 /* The predicted reduction has the wrong sign. This cannot 956 happen in infinite precision arithmetic. Step should 957 be rejected! */ 958 tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm); 959 } else { 960 if (PetscIsInfOrNanReal(actred)) { 961 tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm); 962 } else { 963 if ((PetscAbsScalar(actred) <= PetscMax(1.0, PetscAbsScalar(bnk->f))*bnk->epsilon) && (PetscAbsScalar(prered) <= PetscMax(1.0, PetscAbsScalar(bnk->f))*bnk->epsilon)) { 964 kappa = 1.0; 965 } else { 966 kappa = actred / prered; 967 } 968 969 /* Accept or reject the step and update radius */ 970 if (kappa < bnk->eta1) { 971 /* Reject the step */ 972 tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm); 973 } else { 974 /* Accept the step */ 975 *accept = PETSC_TRUE; 976 /* Update the trust region radius only if the computed step is at the trust radius boundary */ 977 if (bnk->dnorm == tao->trust) { 978 if (kappa < bnk->eta2) { 979 /* Marginal bad step */ 980 tao->trust = bnk->alpha2 * tao->trust; 981 } else if (kappa < bnk->eta3) { 982 /* Reasonable step */ 983 tao->trust = bnk->alpha3 * tao->trust; 984 } else if (kappa < bnk->eta4) { 985 /* Good step */ 986 tao->trust = bnk->alpha4 * tao->trust; 987 } else { 988 /* Very good step */ 989 tao->trust = bnk->alpha5 * tao->trust; 990 } 991 } 992 } 993 } 994 } 995 } else { 996 /* Newton step was not good; reduce the radius */ 997 tao->trust = bnk->alpha1 * PetscMin(bnk->dnorm, tao->trust); 998 } 999 break; 1000 1001 default: 1002 if (stepType == BNK_NEWTON) { 1003 if (prered < 0.0) { 1004 /* The predicted reduction has the wrong sign. This cannot */ 1005 /* happen in infinite precision arithmetic. Step should */ 1006 /* be rejected! */ 1007 tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm); 1008 } else { 1009 if (PetscIsInfOrNanReal(actred)) { 1010 tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm); 1011 } else { 1012 if ((PetscAbsScalar(actred) <= bnk->epsilon) && (PetscAbsScalar(prered) <= bnk->epsilon)) { 1013 kappa = 1.0; 1014 } else { 1015 kappa = actred / prered; 1016 } 1017 1018 ierr = VecDot(tao->gradient, tao->stepdirection, &gdx);CHKERRQ(ierr); 1019 tau_1 = bnk->theta * gdx / (bnk->theta * gdx - (1.0 - bnk->theta) * prered + actred); 1020 tau_2 = bnk->theta * gdx / (bnk->theta * gdx + (1.0 + bnk->theta) * prered - actred); 1021 tau_min = PetscMin(tau_1, tau_2); 1022 tau_max = PetscMax(tau_1, tau_2); 1023 1024 if (kappa >= 1.0 - bnk->mu1) { 1025 /* Great agreement */ 1026 *accept = PETSC_TRUE; 1027 if (tau_max < 1.0) { 1028 tao->trust = PetscMax(tao->trust, bnk->gamma3 * bnk->dnorm); 1029 } else if (tau_max > bnk->gamma4) { 1030 tao->trust = PetscMax(tao->trust, bnk->gamma4 * bnk->dnorm); 1031 } else { 1032 tao->trust = PetscMax(tao->trust, tau_max * bnk->dnorm); 1033 } 1034 } else if (kappa >= 1.0 - bnk->mu2) { 1035 /* Good agreement */ 1036 *accept = PETSC_TRUE; 1037 if (tau_max < bnk->gamma2) { 1038 tao->trust = bnk->gamma2 * PetscMin(tao->trust, bnk->dnorm); 1039 } else if (tau_max > bnk->gamma3) { 1040 tao->trust = PetscMax(tao->trust, bnk->gamma3 * bnk->dnorm); 1041 } else if (tau_max < 1.0) { 1042 tao->trust = tau_max * PetscMin(tao->trust, bnk->dnorm); 1043 } else { 1044 tao->trust = PetscMax(tao->trust, tau_max * bnk->dnorm); 1045 } 1046 } else { 1047 /* Not good agreement */ 1048 if (tau_min > 1.0) { 1049 tao->trust = bnk->gamma2 * PetscMin(tao->trust, bnk->dnorm); 1050 } else if (tau_max < bnk->gamma1) { 1051 tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm); 1052 } else if ((tau_min < bnk->gamma1) && (tau_max >= 1.0)) { 1053 tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm); 1054 } else if ((tau_1 >= bnk->gamma1) && (tau_1 < 1.0) && ((tau_2 < bnk->gamma1) || (tau_2 >= 1.0))) { 1055 tao->trust = tau_1 * PetscMin(tao->trust, bnk->dnorm); 1056 } else if ((tau_2 >= bnk->gamma1) && (tau_2 < 1.0) && ((tau_1 < bnk->gamma1) || (tau_2 >= 1.0))) { 1057 tao->trust = tau_2 * PetscMin(tao->trust, bnk->dnorm); 1058 } else { 1059 tao->trust = tau_max * PetscMin(tao->trust, bnk->dnorm); 1060 } 1061 } 1062 } 1063 } 1064 } else { 1065 /* Newton step was not good; reduce the radius */ 1066 tao->trust = bnk->gamma1 * PetscMin(bnk->dnorm, tao->trust); 1067 } 1068 break; 1069 } 1070 /* Make sure the radius does not violate min and max settings */ 1071 tao->trust = PetscMin(tao->trust, bnk->max_radius); 1072 tao->trust = PetscMax(tao->trust, bnk->min_radius); 1073 PetscFunctionReturn(0); 1074 } 1075 1076 /* ---------------------------------------------------------- */ 1077 1078 PetscErrorCode TaoBNKAddStepCounts(Tao tao, PetscInt stepType) 1079 { 1080 TAO_BNK *bnk = (TAO_BNK *)tao->data; 1081 1082 PetscFunctionBegin; 1083 switch (stepType) { 1084 case BNK_NEWTON: 1085 ++bnk->newt; 1086 break; 1087 case BNK_BFGS: 1088 ++bnk->bfgs; 1089 break; 1090 case BNK_SCALED_GRADIENT: 1091 ++bnk->sgrad; 1092 break; 1093 case BNK_GRADIENT: 1094 ++bnk->grad; 1095 break; 1096 default: 1097 break; 1098 } 1099 PetscFunctionReturn(0); 1100 } 1101 1102 /* ---------------------------------------------------------- */ 1103 1104 PetscErrorCode TaoSetUp_BNK(Tao tao) 1105 { 1106 TAO_BNK *bnk = (TAO_BNK *)tao->data; 1107 PetscErrorCode ierr; 1108 KSPType ksp_type; 1109 PetscInt i; 1110 1111 PetscFunctionBegin; 1112 if (!tao->gradient) { 1113 ierr = VecDuplicate(tao->solution,&tao->gradient);CHKERRQ(ierr); 1114 } 1115 if (!tao->stepdirection) { 1116 ierr = VecDuplicate(tao->solution,&tao->stepdirection);CHKERRQ(ierr); 1117 } 1118 if (!bnk->W) { 1119 ierr = VecDuplicate(tao->solution,&bnk->W);CHKERRQ(ierr); 1120 } 1121 if (!bnk->Xold) { 1122 ierr = VecDuplicate(tao->solution,&bnk->Xold);CHKERRQ(ierr); 1123 } 1124 if (!bnk->Gold) { 1125 ierr = VecDuplicate(tao->solution,&bnk->Gold);CHKERRQ(ierr); 1126 } 1127 if (!bnk->Xwork) { 1128 ierr = VecDuplicate(tao->solution,&bnk->Xwork);CHKERRQ(ierr); 1129 } 1130 if (!bnk->Gwork) { 1131 ierr = VecDuplicate(tao->solution,&bnk->Gwork);CHKERRQ(ierr); 1132 } 1133 if (!bnk->unprojected_gradient) { 1134 ierr = VecDuplicate(tao->solution,&bnk->unprojected_gradient);CHKERRQ(ierr); 1135 } 1136 if (!bnk->unprojected_gradient_old) { 1137 ierr = VecDuplicate(tao->solution,&bnk->unprojected_gradient_old);CHKERRQ(ierr); 1138 } 1139 if (!bnk->Diag_min) { 1140 ierr = VecDuplicate(tao->solution,&bnk->Diag_min);CHKERRQ(ierr); 1141 } 1142 if (!bnk->Diag_max) { 1143 ierr = VecDuplicate(tao->solution,&bnk->Diag_max);CHKERRQ(ierr); 1144 } 1145 if (bnk->max_cg_its > 0) { 1146 /* Ensure that the important common vectors are shared between BNK and embedded BNCG */ 1147 bnk->bncg_ctx = (TAO_BNCG *)bnk->bncg->data; 1148 ierr = PetscObjectReference((PetscObject)(bnk->unprojected_gradient_old));CHKERRQ(ierr); 1149 ierr = VecDestroy(&bnk->bncg_ctx->unprojected_gradient_old);CHKERRQ(ierr); 1150 bnk->bncg_ctx->unprojected_gradient_old = bnk->unprojected_gradient_old; 1151 ierr = PetscObjectReference((PetscObject)(bnk->unprojected_gradient));CHKERRQ(ierr); 1152 ierr = VecDestroy(&bnk->bncg_ctx->unprojected_gradient);CHKERRQ(ierr); 1153 bnk->bncg_ctx->unprojected_gradient = bnk->unprojected_gradient; 1154 ierr = PetscObjectReference((PetscObject)(bnk->Gold));CHKERRQ(ierr); 1155 ierr = VecDestroy(&bnk->bncg_ctx->G_old);CHKERRQ(ierr); 1156 bnk->bncg_ctx->G_old = bnk->Gold; 1157 ierr = PetscObjectReference((PetscObject)(tao->gradient));CHKERRQ(ierr); 1158 ierr = VecDestroy(&bnk->bncg->gradient);CHKERRQ(ierr); 1159 bnk->bncg->gradient = tao->gradient; 1160 ierr = PetscObjectReference((PetscObject)(tao->stepdirection));CHKERRQ(ierr); 1161 ierr = VecDestroy(&bnk->bncg->stepdirection);CHKERRQ(ierr); 1162 bnk->bncg->stepdirection = tao->stepdirection; 1163 ierr = TaoSetInitialVector(bnk->bncg, tao->solution);CHKERRQ(ierr); 1164 /* Copy over some settings from BNK into BNCG */ 1165 ierr = TaoSetMaximumIterations(bnk->bncg, bnk->max_cg_its);CHKERRQ(ierr); 1166 ierr = TaoSetTolerances(bnk->bncg, tao->gatol, tao->grtol, tao->gttol);CHKERRQ(ierr); 1167 ierr = TaoSetFunctionLowerBound(bnk->bncg, tao->fmin);CHKERRQ(ierr); 1168 ierr = TaoSetConvergenceTest(bnk->bncg, tao->ops->convergencetest, tao->cnvP);CHKERRQ(ierr); 1169 ierr = TaoSetObjectiveRoutine(bnk->bncg, tao->ops->computeobjective, tao->user_objP);CHKERRQ(ierr); 1170 ierr = TaoSetGradientRoutine(bnk->bncg, tao->ops->computegradient, tao->user_gradP);CHKERRQ(ierr); 1171 ierr = TaoSetObjectiveAndGradientRoutine(bnk->bncg, tao->ops->computeobjectiveandgradient, tao->user_objgradP);CHKERRQ(ierr); 1172 ierr = PetscObjectCopyFortranFunctionPointers((PetscObject)tao, (PetscObject)(bnk->bncg));CHKERRQ(ierr); 1173 for (i=0; i<tao->numbermonitors; ++i) { 1174 ierr = TaoSetMonitor(bnk->bncg, tao->monitor[i], tao->monitorcontext[i], tao->monitordestroy[i]);CHKERRQ(ierr); 1175 ierr = PetscObjectReference((PetscObject)(tao->monitorcontext[i]));CHKERRQ(ierr); 1176 } 1177 } 1178 bnk->Diag = 0; 1179 bnk->Diag_red = 0; 1180 bnk->X_inactive = 0; 1181 bnk->G_inactive = 0; 1182 bnk->inactive_work = 0; 1183 bnk->active_work = 0; 1184 bnk->inactive_idx = 0; 1185 bnk->active_idx = 0; 1186 bnk->active_lower = 0; 1187 bnk->active_upper = 0; 1188 bnk->active_fixed = 0; 1189 bnk->M = 0; 1190 bnk->H_inactive = 0; 1191 bnk->Hpre_inactive = 0; 1192 ierr = KSPGetType(tao->ksp,&ksp_type);CHKERRQ(ierr); 1193 ierr = PetscStrcmp(ksp_type,KSPCGNASH,&bnk->is_nash);CHKERRQ(ierr); 1194 ierr = PetscStrcmp(ksp_type,KSPCGSTCG,&bnk->is_stcg);CHKERRQ(ierr); 1195 ierr = PetscStrcmp(ksp_type,KSPCGGLTR,&bnk->is_gltr);CHKERRQ(ierr); 1196 PetscFunctionReturn(0); 1197 } 1198 1199 /*------------------------------------------------------------*/ 1200 1201 static PetscErrorCode TaoDestroy_BNK(Tao tao) 1202 { 1203 TAO_BNK *bnk = (TAO_BNK *)tao->data; 1204 PetscErrorCode ierr; 1205 1206 PetscFunctionBegin; 1207 if (tao->setupcalled) { 1208 ierr = VecDestroy(&bnk->W);CHKERRQ(ierr); 1209 ierr = VecDestroy(&bnk->Xold);CHKERRQ(ierr); 1210 ierr = VecDestroy(&bnk->Gold);CHKERRQ(ierr); 1211 ierr = VecDestroy(&bnk->Xwork);CHKERRQ(ierr); 1212 ierr = VecDestroy(&bnk->Gwork);CHKERRQ(ierr); 1213 ierr = VecDestroy(&bnk->unprojected_gradient);CHKERRQ(ierr); 1214 ierr = VecDestroy(&bnk->unprojected_gradient_old);CHKERRQ(ierr); 1215 ierr = VecDestroy(&bnk->Diag_min);CHKERRQ(ierr); 1216 ierr = VecDestroy(&bnk->Diag_max);CHKERRQ(ierr); 1217 } 1218 if (bnk->max_cg_its > 0) { 1219 ierr = TaoDestroy(&bnk->bncg);CHKERRQ(ierr); 1220 } 1221 ierr = VecDestroy(&bnk->Diag);CHKERRQ(ierr); 1222 ierr = MatDestroy(&bnk->M);CHKERRQ(ierr); 1223 if (bnk->Hpre_inactive != tao->hessian_pre && bnk->Hpre_inactive != bnk->H_inactive) { 1224 ierr = MatDestroy(&bnk->Hpre_inactive);CHKERRQ(ierr); 1225 } 1226 if (bnk->H_inactive != tao->hessian) { 1227 ierr = MatDestroy(&bnk->H_inactive);CHKERRQ(ierr); 1228 } 1229 ierr = PetscFree(tao->data);CHKERRQ(ierr); 1230 PetscFunctionReturn(0); 1231 } 1232 1233 /*------------------------------------------------------------*/ 1234 1235 static PetscErrorCode TaoSetFromOptions_BNK(PetscOptionItems *PetscOptionsObject,Tao tao) 1236 { 1237 TAO_BNK *bnk = (TAO_BNK *)tao->data; 1238 PetscErrorCode ierr; 1239 1240 PetscFunctionBegin; 1241 ierr = PetscOptionsHead(PetscOptionsObject,"Newton line search method for unconstrained optimization");CHKERRQ(ierr); 1242 ierr = PetscOptionsEList("-tao_bnk_pc_type", "pc type", "", BNK_PC, BNK_PC_TYPES, BNK_PC[bnk->pc_type], &bnk->pc_type, 0);CHKERRQ(ierr); 1243 ierr = PetscOptionsEList("-tao_bnk_bfgs_scale_type", "bfgs scale type", "", BFGS_SCALE, BFGS_SCALE_TYPES, BFGS_SCALE[bnk->bfgs_scale_type], &bnk->bfgs_scale_type, 0);CHKERRQ(ierr); 1244 ierr = PetscOptionsEList("-tao_bnk_init_type", "radius initialization type", "", BNK_INIT, BNK_INIT_TYPES, BNK_INIT[bnk->init_type], &bnk->init_type, 0);CHKERRQ(ierr); 1245 ierr = PetscOptionsEList("-tao_bnk_update_type", "radius update type", "", BNK_UPDATE, BNK_UPDATE_TYPES, BNK_UPDATE[bnk->update_type], &bnk->update_type, 0);CHKERRQ(ierr); 1246 ierr = PetscOptionsEList("-tao_bnk_as_type", "active set estimation method", "", BNK_AS, BNK_AS_TYPES, BNK_AS[bnk->as_type], &bnk->as_type, 0);CHKERRQ(ierr); 1247 ierr = PetscOptionsReal("-tao_bnk_sval", "perturbation starting value", "", bnk->sval, &bnk->sval,NULL);CHKERRQ(ierr); 1248 ierr = PetscOptionsReal("-tao_bnk_imin", "minimum initial perturbation", "", bnk->imin, &bnk->imin,NULL);CHKERRQ(ierr); 1249 ierr = PetscOptionsReal("-tao_bnk_imax", "maximum initial perturbation", "", bnk->imax, &bnk->imax,NULL);CHKERRQ(ierr); 1250 ierr = PetscOptionsReal("-tao_bnk_imfac", "initial merit factor", "", bnk->imfac, &bnk->imfac,NULL);CHKERRQ(ierr); 1251 ierr = PetscOptionsReal("-tao_bnk_pmin", "minimum perturbation", "", bnk->pmin, &bnk->pmin,NULL);CHKERRQ(ierr); 1252 ierr = PetscOptionsReal("-tao_bnk_pmax", "maximum perturbation", "", bnk->pmax, &bnk->pmax,NULL);CHKERRQ(ierr); 1253 ierr = PetscOptionsReal("-tao_bnk_pgfac", "growth factor", "", bnk->pgfac, &bnk->pgfac,NULL);CHKERRQ(ierr); 1254 ierr = PetscOptionsReal("-tao_bnk_psfac", "shrink factor", "", bnk->psfac, &bnk->psfac,NULL);CHKERRQ(ierr); 1255 ierr = PetscOptionsReal("-tao_bnk_pmgfac", "merit growth factor", "", bnk->pmgfac, &bnk->pmgfac,NULL);CHKERRQ(ierr); 1256 ierr = PetscOptionsReal("-tao_bnk_pmsfac", "merit shrink factor", "", bnk->pmsfac, &bnk->pmsfac,NULL);CHKERRQ(ierr); 1257 ierr = PetscOptionsReal("-tao_bnk_eta1", "poor steplength; reduce radius", "", bnk->eta1, &bnk->eta1,NULL);CHKERRQ(ierr); 1258 ierr = PetscOptionsReal("-tao_bnk_eta2", "reasonable steplength; leave radius alone", "", bnk->eta2, &bnk->eta2,NULL);CHKERRQ(ierr); 1259 ierr = PetscOptionsReal("-tao_bnk_eta3", "good steplength; increase radius", "", bnk->eta3, &bnk->eta3,NULL);CHKERRQ(ierr); 1260 ierr = PetscOptionsReal("-tao_bnk_eta4", "excellent steplength; greatly increase radius", "", bnk->eta4, &bnk->eta4,NULL);CHKERRQ(ierr); 1261 ierr = PetscOptionsReal("-tao_bnk_alpha1", "", "", bnk->alpha1, &bnk->alpha1,NULL);CHKERRQ(ierr); 1262 ierr = PetscOptionsReal("-tao_bnk_alpha2", "", "", bnk->alpha2, &bnk->alpha2,NULL);CHKERRQ(ierr); 1263 ierr = PetscOptionsReal("-tao_bnk_alpha3", "", "", bnk->alpha3, &bnk->alpha3,NULL);CHKERRQ(ierr); 1264 ierr = PetscOptionsReal("-tao_bnk_alpha4", "", "", bnk->alpha4, &bnk->alpha4,NULL);CHKERRQ(ierr); 1265 ierr = PetscOptionsReal("-tao_bnk_alpha5", "", "", bnk->alpha5, &bnk->alpha5,NULL);CHKERRQ(ierr); 1266 ierr = PetscOptionsReal("-tao_bnk_nu1", "poor steplength; reduce radius", "", bnk->nu1, &bnk->nu1,NULL);CHKERRQ(ierr); 1267 ierr = PetscOptionsReal("-tao_bnk_nu2", "reasonable steplength; leave radius alone", "", bnk->nu2, &bnk->nu2,NULL);CHKERRQ(ierr); 1268 ierr = PetscOptionsReal("-tao_bnk_nu3", "good steplength; increase radius", "", bnk->nu3, &bnk->nu3,NULL);CHKERRQ(ierr); 1269 ierr = PetscOptionsReal("-tao_bnk_nu4", "excellent steplength; greatly increase radius", "", bnk->nu4, &bnk->nu4,NULL);CHKERRQ(ierr); 1270 ierr = PetscOptionsReal("-tao_bnk_omega1", "", "", bnk->omega1, &bnk->omega1,NULL);CHKERRQ(ierr); 1271 ierr = PetscOptionsReal("-tao_bnk_omega2", "", "", bnk->omega2, &bnk->omega2,NULL);CHKERRQ(ierr); 1272 ierr = PetscOptionsReal("-tao_bnk_omega3", "", "", bnk->omega3, &bnk->omega3,NULL);CHKERRQ(ierr); 1273 ierr = PetscOptionsReal("-tao_bnk_omega4", "", "", bnk->omega4, &bnk->omega4,NULL);CHKERRQ(ierr); 1274 ierr = PetscOptionsReal("-tao_bnk_omega5", "", "", bnk->omega5, &bnk->omega5,NULL);CHKERRQ(ierr); 1275 ierr = PetscOptionsReal("-tao_bnk_mu1_i", "", "", bnk->mu1_i, &bnk->mu1_i,NULL);CHKERRQ(ierr); 1276 ierr = PetscOptionsReal("-tao_bnk_mu2_i", "", "", bnk->mu2_i, &bnk->mu2_i,NULL);CHKERRQ(ierr); 1277 ierr = PetscOptionsReal("-tao_bnk_gamma1_i", "", "", bnk->gamma1_i, &bnk->gamma1_i,NULL);CHKERRQ(ierr); 1278 ierr = PetscOptionsReal("-tao_bnk_gamma2_i", "", "", bnk->gamma2_i, &bnk->gamma2_i,NULL);CHKERRQ(ierr); 1279 ierr = PetscOptionsReal("-tao_bnk_gamma3_i", "", "", bnk->gamma3_i, &bnk->gamma3_i,NULL);CHKERRQ(ierr); 1280 ierr = PetscOptionsReal("-tao_bnk_gamma4_i", "", "", bnk->gamma4_i, &bnk->gamma4_i,NULL);CHKERRQ(ierr); 1281 ierr = PetscOptionsReal("-tao_bnk_theta_i", "", "", bnk->theta_i, &bnk->theta_i,NULL);CHKERRQ(ierr); 1282 ierr = PetscOptionsReal("-tao_bnk_mu1", "", "", bnk->mu1, &bnk->mu1,NULL);CHKERRQ(ierr); 1283 ierr = PetscOptionsReal("-tao_bnk_mu2", "", "", bnk->mu2, &bnk->mu2,NULL);CHKERRQ(ierr); 1284 ierr = PetscOptionsReal("-tao_bnk_gamma1", "", "", bnk->gamma1, &bnk->gamma1,NULL);CHKERRQ(ierr); 1285 ierr = PetscOptionsReal("-tao_bnk_gamma2", "", "", bnk->gamma2, &bnk->gamma2,NULL);CHKERRQ(ierr); 1286 ierr = PetscOptionsReal("-tao_bnk_gamma3", "", "", bnk->gamma3, &bnk->gamma3,NULL);CHKERRQ(ierr); 1287 ierr = PetscOptionsReal("-tao_bnk_gamma4", "", "", bnk->gamma4, &bnk->gamma4,NULL);CHKERRQ(ierr); 1288 ierr = PetscOptionsReal("-tao_bnk_theta", "", "", bnk->theta, &bnk->theta,NULL);CHKERRQ(ierr); 1289 ierr = PetscOptionsReal("-tao_bnk_min_radius", "lower bound on initial radius", "", bnk->min_radius, &bnk->min_radius,NULL);CHKERRQ(ierr); 1290 ierr = PetscOptionsReal("-tao_bnk_max_radius", "upper bound on radius", "", bnk->max_radius, &bnk->max_radius,NULL);CHKERRQ(ierr); 1291 ierr = PetscOptionsReal("-tao_bnk_epsilon", "tolerance used when computing actual and predicted reduction", "", bnk->epsilon, &bnk->epsilon,NULL);CHKERRQ(ierr); 1292 ierr = PetscOptionsReal("-tao_bnk_as_tol", "initial tolerance used when estimating actively bounded variables", "", bnk->as_tol, &bnk->as_tol,NULL);CHKERRQ(ierr); 1293 ierr = PetscOptionsReal("-tao_bnk_as_step", "step length used when estimating actively bounded variables", "", bnk->as_step, &bnk->as_step,NULL);CHKERRQ(ierr); 1294 ierr = PetscOptionsInt("-tao_bnk_max_cg_its", "number of BNCG iterations to take for each Newton step", "", bnk->max_cg_its, &bnk->max_cg_its,NULL);CHKERRQ(ierr); 1295 ierr = PetscOptionsTail();CHKERRQ(ierr); 1296 ierr = TaoSetFromOptions(bnk->bncg); 1297 ierr = TaoLineSearchSetFromOptions(tao->linesearch);CHKERRQ(ierr); 1298 ierr = KSPSetFromOptions(tao->ksp);CHKERRQ(ierr); 1299 PetscFunctionReturn(0); 1300 } 1301 1302 /*------------------------------------------------------------*/ 1303 1304 static PetscErrorCode TaoView_BNK(Tao tao, PetscViewer viewer) 1305 { 1306 TAO_BNK *bnk = (TAO_BNK *)tao->data; 1307 PetscInt nrejects; 1308 PetscBool isascii; 1309 PetscErrorCode ierr; 1310 1311 PetscFunctionBegin; 1312 ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);CHKERRQ(ierr); 1313 if (isascii) { 1314 ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr); 1315 if (BNK_PC_BFGS == bnk->pc_type && bnk->M) { 1316 ierr = MatLMVMGetRejects(bnk->M,&nrejects);CHKERRQ(ierr); 1317 ierr = PetscViewerASCIIPrintf(viewer, "Rejected matrix updates: %D\n",nrejects);CHKERRQ(ierr); 1318 } 1319 ierr = PetscViewerASCIIPrintf(viewer, "CG steps: %D\n", bnk->tot_cg_its);CHKERRQ(ierr); 1320 ierr = PetscViewerASCIIPrintf(viewer, "Newton steps: %D\n", bnk->newt);CHKERRQ(ierr); 1321 ierr = PetscViewerASCIIPrintf(viewer, "BFGS steps: %D\n", bnk->bfgs);CHKERRQ(ierr); 1322 ierr = PetscViewerASCIIPrintf(viewer, "Scaled gradient steps: %D\n", bnk->sgrad);CHKERRQ(ierr); 1323 ierr = PetscViewerASCIIPrintf(viewer, "Gradient steps: %D\n", bnk->grad);CHKERRQ(ierr); 1324 ierr = PetscViewerASCIIPrintf(viewer, "KSP termination reasons:\n");CHKERRQ(ierr); 1325 ierr = PetscViewerASCIIPrintf(viewer, " atol: %D\n", bnk->ksp_atol);CHKERRQ(ierr); 1326 ierr = PetscViewerASCIIPrintf(viewer, " rtol: %D\n", bnk->ksp_rtol);CHKERRQ(ierr); 1327 ierr = PetscViewerASCIIPrintf(viewer, " ctol: %D\n", bnk->ksp_ctol);CHKERRQ(ierr); 1328 ierr = PetscViewerASCIIPrintf(viewer, " negc: %D\n", bnk->ksp_negc);CHKERRQ(ierr); 1329 ierr = PetscViewerASCIIPrintf(viewer, " dtol: %D\n", bnk->ksp_dtol);CHKERRQ(ierr); 1330 ierr = PetscViewerASCIIPrintf(viewer, " iter: %D\n", bnk->ksp_iter);CHKERRQ(ierr); 1331 ierr = PetscViewerASCIIPrintf(viewer, " othr: %D\n", bnk->ksp_othr);CHKERRQ(ierr); 1332 ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr); 1333 } 1334 PetscFunctionReturn(0); 1335 } 1336 1337 /* ---------------------------------------------------------- */ 1338 1339 /*MC 1340 TAOBNK - Shared base-type for Bounded Newton-Krylov type algorithms. 1341 At each iteration, the BNK methods solve the symmetric 1342 system of equations to obtain the step diretion dk: 1343 Hk dk = -gk 1344 for free variables only. The step can be globalized either through 1345 trust-region methods, or a line search, or a heuristic mixture of both. 1346 1347 Options Database Keys: 1348 + -tao_bnk_pc_type - "none","ahess","bfgs","petsc" 1349 . -tao_bnk_bfgs_scale_type - "ahess","phess","bfgs" 1350 . -tao_bnk_init_type - "constant","direction","interpolation" 1351 . -tao_bnk_update_type - "step","direction","interpolation" 1352 . -tao_bnk_as_type - "none","bertsekas" 1353 . -tao_bnk_sval - perturbation starting value 1354 . -tao_bnk_imin - minimum initial perturbation 1355 . -tao_bnk_imax - maximum initial perturbation 1356 . -tao_bnk_pmin - minimum perturbation 1357 . -tao_bnk_pmax - maximum perturbation 1358 . -tao_bnk_pgfac - growth factor 1359 . -tao_bnk_psfac - shrink factor 1360 . -tao_bnk_imfac - initial merit factor 1361 . -tao_bnk_pmgfac - merit growth factor 1362 . -tao_bnk_pmsfac - merit shrink factor 1363 . -tao_bnk_eta1 - poor steplength; reduce radius 1364 . -tao_bnk_eta2 - reasonable steplength; leave radius 1365 . -tao_bnk_eta3 - good steplength; increase readius 1366 . -tao_bnk_eta4 - excellent steplength; greatly increase radius 1367 . -tao_bnk_alpha1 - alpha1 reduction 1368 . -tao_bnk_alpha2 - alpha2 reduction 1369 . -tao_bnk_alpha3 - alpha3 reduction 1370 . -tao_bnk_alpha4 - alpha4 reduction 1371 . -tao_bnk_alpha - alpha5 reduction 1372 . -tao_bnk_mu1 - mu1 interpolation update 1373 . -tao_bnk_mu2 - mu2 interpolation update 1374 . -tao_bnk_gamma1 - gamma1 interpolation update 1375 . -tao_bnk_gamma2 - gamma2 interpolation update 1376 . -tao_bnk_gamma3 - gamma3 interpolation update 1377 . -tao_bnk_gamma4 - gamma4 interpolation update 1378 . -tao_bnk_theta - theta interpolation update 1379 . -tao_bnk_omega1 - omega1 step update 1380 . -tao_bnk_omega2 - omega2 step update 1381 . -tao_bnk_omega3 - omega3 step update 1382 . -tao_bnk_omega4 - omega4 step update 1383 . -tao_bnk_omega5 - omega5 step update 1384 . -tao_bnk_mu1_i - mu1 interpolation init factor 1385 . -tao_bnk_mu2_i - mu2 interpolation init factor 1386 . -tao_bnk_gamma1_i - gamma1 interpolation init factor 1387 . -tao_bnk_gamma2_i - gamma2 interpolation init factor 1388 . -tao_bnk_gamma3_i - gamma3 interpolation init factor 1389 . -tao_bnk_gamma4_i - gamma4 interpolation init factor 1390 . -tao_bnk_theta_i - theta interpolation init factor 1391 - -tao_bnk_bound_tol - initial tolerance used in estimating bounded active variables 1392 1393 Level: beginner 1394 M*/ 1395 1396 PetscErrorCode TaoCreate_BNK(Tao tao) 1397 { 1398 TAO_BNK *bnk; 1399 const char *morethuente_type = TAOLINESEARCHMT; 1400 PetscErrorCode ierr; 1401 1402 PetscFunctionBegin; 1403 ierr = PetscNewLog(tao,&bnk);CHKERRQ(ierr); 1404 1405 tao->ops->setup = TaoSetUp_BNK; 1406 tao->ops->view = TaoView_BNK; 1407 tao->ops->setfromoptions = TaoSetFromOptions_BNK; 1408 tao->ops->destroy = TaoDestroy_BNK; 1409 1410 /* Override default settings (unless already changed) */ 1411 if (!tao->max_it_changed) tao->max_it = 50; 1412 if (!tao->trust0_changed) tao->trust0 = 100.0; 1413 1414 tao->data = (void*)bnk; 1415 1416 /* Hessian shifting parameters */ 1417 bnk->sval = 0.0; 1418 bnk->imin = 1.0e-4; 1419 bnk->imax = 1.0e+2; 1420 bnk->imfac = 1.0e-1; 1421 1422 bnk->pmin = 1.0e-12; 1423 bnk->pmax = 1.0e+2; 1424 bnk->pgfac = 1.0e+1; 1425 bnk->psfac = 4.0e-1; 1426 bnk->pmgfac = 1.0e-1; 1427 bnk->pmsfac = 1.0e-1; 1428 1429 /* Default values for trust-region radius update based on steplength */ 1430 bnk->nu1 = 0.25; 1431 bnk->nu2 = 0.50; 1432 bnk->nu3 = 1.00; 1433 bnk->nu4 = 1.25; 1434 1435 bnk->omega1 = 0.25; 1436 bnk->omega2 = 0.50; 1437 bnk->omega3 = 1.00; 1438 bnk->omega4 = 2.00; 1439 bnk->omega5 = 4.00; 1440 1441 /* Default values for trust-region radius update based on reduction */ 1442 bnk->eta1 = 1.0e-4; 1443 bnk->eta2 = 0.25; 1444 bnk->eta3 = 0.50; 1445 bnk->eta4 = 0.90; 1446 1447 bnk->alpha1 = 0.25; 1448 bnk->alpha2 = 0.50; 1449 bnk->alpha3 = 1.00; 1450 bnk->alpha4 = 2.00; 1451 bnk->alpha5 = 4.00; 1452 1453 /* Default values for trust-region radius update based on interpolation */ 1454 bnk->mu1 = 0.10; 1455 bnk->mu2 = 0.50; 1456 1457 bnk->gamma1 = 0.25; 1458 bnk->gamma2 = 0.50; 1459 bnk->gamma3 = 2.00; 1460 bnk->gamma4 = 4.00; 1461 1462 bnk->theta = 0.05; 1463 1464 /* Default values for trust region initialization based on interpolation */ 1465 bnk->mu1_i = 0.35; 1466 bnk->mu2_i = 0.50; 1467 1468 bnk->gamma1_i = 0.0625; 1469 bnk->gamma2_i = 0.5; 1470 bnk->gamma3_i = 2.0; 1471 bnk->gamma4_i = 5.0; 1472 1473 bnk->theta_i = 0.25; 1474 1475 /* Remaining parameters */ 1476 bnk->max_cg_its = 0; 1477 bnk->min_radius = 1.0e-10; 1478 bnk->max_radius = 1.0e10; 1479 bnk->epsilon = PetscPowReal(PETSC_MACHINE_EPSILON, 2.0/3.0); 1480 bnk->as_tol = 1.0e-3; 1481 bnk->as_step = 1.0e-3; 1482 bnk->dmin = 1.0e-6; 1483 bnk->dmax = 1.0e6; 1484 1485 bnk->pc_type = BNK_PC_AHESS; 1486 bnk->bfgs_scale_type = BFGS_SCALE_PHESS; 1487 bnk->init_type = BNK_INIT_INTERPOLATION; 1488 bnk->update_type = BNK_UPDATE_INTERPOLATION; 1489 bnk->as_type = BNK_AS_BERTSEKAS; 1490 1491 /* Create the embedded BNCG solver */ 1492 ierr = TaoCreate(PetscObjectComm((PetscObject)tao), &bnk->bncg);CHKERRQ(ierr); 1493 ierr = PetscObjectIncrementTabLevel((PetscObject)bnk->bncg, (PetscObject)tao, 1);CHKERRQ(ierr); 1494 ierr = TaoSetOptionsPrefix(bnk->bncg, "tao_bnk_");CHKERRQ(ierr); 1495 ierr = TaoSetType(bnk->bncg, TAOBNCG);CHKERRQ(ierr); 1496 1497 /* Create the line search */ 1498 ierr = TaoLineSearchCreate(((PetscObject)tao)->comm,&tao->linesearch);CHKERRQ(ierr); 1499 ierr = PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1);CHKERRQ(ierr); 1500 ierr = TaoLineSearchSetOptionsPrefix(tao->linesearch,tao->hdr.prefix);CHKERRQ(ierr); 1501 ierr = TaoLineSearchSetType(tao->linesearch,morethuente_type);CHKERRQ(ierr); 1502 ierr = TaoLineSearchUseTaoRoutines(tao->linesearch,tao);CHKERRQ(ierr); 1503 1504 /* Set linear solver to default for symmetric matrices */ 1505 ierr = KSPCreate(((PetscObject)tao)->comm,&tao->ksp);CHKERRQ(ierr); 1506 ierr = PetscObjectIncrementTabLevel((PetscObject)tao->ksp, (PetscObject)tao, 1);CHKERRQ(ierr); 1507 ierr = KSPSetOptionsPrefix(tao->ksp,tao->hdr.prefix);CHKERRQ(ierr); 1508 ierr = KSPSetType(tao->ksp,KSPCGSTCG);CHKERRQ(ierr); 1509 PetscFunctionReturn(0); 1510 } 1511