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