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