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