1 #include <petsctaolinesearch.h> 2 #include <../src/tao/matrix/lmvmmat.h> 3 #include <../src/tao/unconstrained/impls/lmvm/lmvm.h> 4 5 #define LMVM_BFGS 0 6 #define LMVM_SCALED_GRADIENT 1 7 #define LMVM_GRADIENT 2 8 9 static PetscErrorCode TaoSolve_LMVM(Tao tao) 10 { 11 TAO_LMVM *lmP = (TAO_LMVM *)tao->data; 12 PetscReal f, fold, gdx, gnorm; 13 PetscReal step = 1.0; 14 PetscReal delta; 15 PetscErrorCode ierr; 16 PetscInt stepType, nupdates; 17 PetscBool recycle; 18 TaoConvergedReason reason = TAO_CONTINUE_ITERATING; 19 TaoLineSearchConvergedReason ls_status = TAOLINESEARCH_CONTINUE_ITERATING; 20 21 PetscFunctionBegin; 22 23 if (tao->XL || tao->XU || tao->ops->computebounds) { 24 ierr = PetscPrintf(((PetscObject)tao)->comm,"WARNING: Variable bounds have been set but will be ignored by lmvm algorithm\n");CHKERRQ(ierr); 25 } 26 27 /* Check convergence criteria */ 28 ierr = TaoComputeObjectiveAndGradient(tao, tao->solution, &f, tao->gradient);CHKERRQ(ierr); 29 ierr = TaoGradientNorm(tao, tao->gradient,NORM_2,&gnorm);CHKERRQ(ierr); 30 31 if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN"); 32 33 ierr = TaoMonitor(tao, tao->niter, f, gnorm, 0.0, step, &reason);CHKERRQ(ierr); 34 if (reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0); 35 36 /* Set initial scaling for the function */ 37 if (f != 0.0) { 38 delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm); 39 } else { 40 delta = 2.0 / (gnorm*gnorm); 41 } 42 ierr = MatLMVMSetDelta(lmP->M,delta);CHKERRQ(ierr); 43 44 /* Set counter for gradient/reset steps */ 45 ierr = MatLMVMGetRecycleFlag(lmP->M, &recycle);CHKERRQ(ierr); 46 if (!recycle) { 47 lmP->bfgs = 0; 48 lmP->sgrad = 0; 49 lmP->grad = 0; 50 ierr = MatLMVMReset(lmP->M); CHKERRQ(ierr); 51 } 52 53 /* Have not converged; continue with Newton method */ 54 while (reason == TAO_CONTINUE_ITERATING) { 55 /* Compute direction */ 56 ierr = MatLMVMUpdate(lmP->M,tao->solution,tao->gradient);CHKERRQ(ierr); 57 ierr = MatLMVMSolve(lmP->M, tao->gradient, lmP->D);CHKERRQ(ierr); 58 59 /* Check for success (descent direction) */ 60 ierr = VecDot(lmP->D, tao->gradient, &gdx);CHKERRQ(ierr); 61 if ((gdx <= 0.0) || PetscIsInfOrNanReal(gdx)) { 62 /* Step is not descent or direction produced not a number 63 We can assert bfgsUpdates > 1 in this case because 64 the first solve produces the scaled gradient direction, 65 which is guaranteed to be descent 66 67 Use steepest descent direction (scaled) 68 */ 69 70 if (f != 0.0) { 71 delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm); 72 } else { 73 delta = 2.0 / (gnorm*gnorm); 74 } 75 ierr = MatLMVMSetDelta(lmP->M, delta);CHKERRQ(ierr); 76 ierr = MatLMVMReset(lmP->M);CHKERRQ(ierr); 77 ierr = MatLMVMUpdate(lmP->M, tao->solution, tao->gradient);CHKERRQ(ierr); 78 ierr = MatLMVMSolve(lmP->M,tao->gradient, lmP->D);CHKERRQ(ierr); 79 80 /* On a reset, the direction cannot be not a number; it is a 81 scaled gradient step. No need to check for this condition. */ 82 ++lmP->sgrad; 83 stepType = LMVM_SCALED_GRADIENT; 84 } else { 85 ierr = MatLMVMGetUpdates(lmP->M, &nupdates); CHKERRQ(ierr); 86 if (1 == nupdates) { 87 /* The first BFGS direction is always the scaled gradient */ 88 ++lmP->sgrad; 89 stepType = LMVM_SCALED_GRADIENT; 90 } else { 91 ++lmP->bfgs; 92 stepType = LMVM_BFGS; 93 } 94 } 95 ierr = VecScale(lmP->D, -1.0);CHKERRQ(ierr); 96 97 /* Perform the linesearch */ 98 fold = f; 99 ierr = VecCopy(tao->solution, lmP->Xold);CHKERRQ(ierr); 100 ierr = VecCopy(tao->gradient, lmP->Gold);CHKERRQ(ierr); 101 102 ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &f, tao->gradient, lmP->D, &step,&ls_status);CHKERRQ(ierr); 103 ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr); 104 105 while (ls_status != TAOLINESEARCH_SUCCESS && ls_status != TAOLINESEARCH_SUCCESS_USER && (stepType != LMVM_GRADIENT)) { 106 /* Linesearch failed */ 107 ierr = PetscInfo(lmP, "WARNING: Linesearch failed!\n"); CHKERRQ(ierr); 108 /* Reset factors and use scaled gradient step */ 109 f = fold; 110 ierr = VecCopy(lmP->Xold, tao->solution);CHKERRQ(ierr); 111 ierr = VecCopy(lmP->Gold, tao->gradient);CHKERRQ(ierr); 112 113 switch(stepType) { 114 case LMVM_BFGS: 115 /* Failed to obtain acceptable iterate with BFGS step */ 116 /* Attempt to use the scaled gradient direction */ 117 118 if (f != 0.0) { 119 delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm); 120 } else { 121 delta = 2.0 / (gnorm*gnorm); 122 } 123 ierr = MatLMVMSetDelta(lmP->M, delta);CHKERRQ(ierr); 124 ierr = MatLMVMReset(lmP->M);CHKERRQ(ierr); 125 ierr = MatLMVMUpdate(lmP->M, tao->solution, tao->gradient);CHKERRQ(ierr); 126 ierr = MatLMVMSolve(lmP->M, tao->gradient, lmP->D);CHKERRQ(ierr); 127 128 /* On a reset, the direction cannot be not a number; it is a 129 scaled gradient step. No need to check for this condition. */ 130 --lmP->bfgs; 131 ++lmP->sgrad; 132 stepType = LMVM_SCALED_GRADIENT; 133 break; 134 135 case LMVM_SCALED_GRADIENT: 136 /* The scaled gradient step did not produce a new iterate; 137 attempt to use the gradient direction. 138 Need to make sure we are not using a different diagonal scaling */ 139 ierr = MatLMVMSetDelta(lmP->M, 1.0);CHKERRQ(ierr); 140 ierr = MatLMVMReset(lmP->M);CHKERRQ(ierr); 141 ierr = MatLMVMUpdate(lmP->M, tao->solution, tao->gradient);CHKERRQ(ierr); 142 ierr = MatLMVMSolve(lmP->M, tao->gradient, lmP->D);CHKERRQ(ierr); 143 144 --lmP->sgrad; 145 ++lmP->grad; 146 stepType = LMVM_GRADIENT; 147 break; 148 } 149 ierr = VecScale(lmP->D, -1.0);CHKERRQ(ierr); 150 151 /* Perform the linesearch */ 152 ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &f, tao->gradient, lmP->D, &step, &ls_status);CHKERRQ(ierr); 153 ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr); 154 } 155 156 if (ls_status != TAOLINESEARCH_SUCCESS && ls_status != TAOLINESEARCH_SUCCESS_USER) { 157 /* Failed to find an improving point */ 158 f = fold; 159 ierr = VecCopy(lmP->Xold, tao->solution);CHKERRQ(ierr); 160 ierr = VecCopy(lmP->Gold, tao->gradient);CHKERRQ(ierr); 161 step = 0.0; 162 reason = TAO_DIVERGED_LS_FAILURE; 163 tao->reason = TAO_DIVERGED_LS_FAILURE; 164 } 165 166 /* Check for termination */ 167 ierr = TaoGradientNorm(tao, tao->gradient,NORM_2,&gnorm);CHKERRQ(ierr); 168 169 tao->niter++; 170 ierr = TaoMonitor(tao,tao->niter,f,gnorm,0.0,step,&reason);CHKERRQ(ierr); 171 } 172 PetscFunctionReturn(0); 173 } 174 175 static PetscErrorCode TaoSetUp_LMVM(Tao tao) 176 { 177 TAO_LMVM *lmP = (TAO_LMVM *)tao->data; 178 PetscInt n,N; 179 PetscErrorCode ierr; 180 KSP H0ksp; 181 182 PetscFunctionBegin; 183 /* Existence of tao->solution checked in TaoSetUp() */ 184 if (!tao->gradient) {ierr = VecDuplicate(tao->solution,&tao->gradient);CHKERRQ(ierr); } 185 if (!tao->stepdirection) {ierr = VecDuplicate(tao->solution,&tao->stepdirection);CHKERRQ(ierr); } 186 if (!lmP->D) {ierr = VecDuplicate(tao->solution,&lmP->D);CHKERRQ(ierr); } 187 if (!lmP->Xold) {ierr = VecDuplicate(tao->solution,&lmP->Xold);CHKERRQ(ierr); } 188 if (!lmP->Gold) {ierr = VecDuplicate(tao->solution,&lmP->Gold);CHKERRQ(ierr); } 189 190 /* Create matrix for the limited memory approximation */ 191 ierr = VecGetLocalSize(tao->solution,&n);CHKERRQ(ierr); 192 ierr = VecGetSize(tao->solution,&N);CHKERRQ(ierr); 193 ierr = MatCreateLMVM(((PetscObject)tao)->comm,n,N,&lmP->M);CHKERRQ(ierr); 194 ierr = MatLMVMAllocateVectors(lmP->M,tao->solution);CHKERRQ(ierr); 195 196 /* If the user has set a matrix to solve as the initial H0, set the options prefix here, and set up the KSP */ 197 if (lmP->H0) { 198 const char *prefix; 199 PC H0pc; 200 201 ierr = MatLMVMSetH0(lmP->M, lmP->H0);CHKERRQ(ierr); 202 ierr = MatLMVMGetH0KSP(lmP->M, &H0ksp);CHKERRQ(ierr); 203 204 ierr = TaoGetOptionsPrefix(tao, &prefix);CHKERRQ(ierr); 205 ierr = KSPSetOptionsPrefix(H0ksp, prefix);CHKERRQ(ierr); 206 ierr = PetscObjectAppendOptionsPrefix((PetscObject)H0ksp, "tao_h0_");CHKERRQ(ierr); 207 ierr = KSPGetPC(H0ksp, &H0pc);CHKERRQ(ierr); 208 ierr = PetscObjectAppendOptionsPrefix((PetscObject)H0pc, "tao_h0_");CHKERRQ(ierr); 209 210 ierr = KSPSetFromOptions(H0ksp);CHKERRQ(ierr); 211 ierr = KSPSetUp(H0ksp);CHKERRQ(ierr); 212 } 213 214 PetscFunctionReturn(0); 215 } 216 217 /* ---------------------------------------------------------- */ 218 static PetscErrorCode TaoDestroy_LMVM(Tao tao) 219 { 220 TAO_LMVM *lmP = (TAO_LMVM *)tao->data; 221 PetscErrorCode ierr; 222 PetscBool recycle; 223 224 PetscFunctionBegin; 225 if (lmP->M) { 226 ierr = MatLMVMGetRecycleFlag(lmP->M, &recycle); CHKERRQ(ierr); 227 if (recycle) { 228 ierr = PetscInfo(lmP->M, "WARNING: TaoDestroy() called when LMVM recycling is enabled!\n"); CHKERRQ(ierr); 229 } 230 } 231 232 if (tao->setupcalled) { 233 ierr = VecDestroy(&lmP->Xold);CHKERRQ(ierr); 234 ierr = VecDestroy(&lmP->Gold);CHKERRQ(ierr); 235 ierr = VecDestroy(&lmP->D);CHKERRQ(ierr); 236 ierr = MatDestroy(&lmP->M);CHKERRQ(ierr); 237 } 238 239 if (lmP->H0) { 240 ierr = PetscObjectDereference((PetscObject)lmP->H0);CHKERRQ(ierr); 241 } 242 243 ierr = PetscFree(tao->data);CHKERRQ(ierr); 244 245 PetscFunctionReturn(0); 246 } 247 248 /*------------------------------------------------------------*/ 249 static PetscErrorCode TaoSetFromOptions_LMVM(PetscOptionItems *PetscOptionsObject,Tao tao) 250 { 251 PetscErrorCode ierr; 252 253 PetscFunctionBegin; 254 ierr = PetscOptionsHead(PetscOptionsObject,"Limited-memory variable-metric method for unconstrained optimization");CHKERRQ(ierr); 255 ierr = TaoLineSearchSetFromOptions(tao->linesearch);CHKERRQ(ierr); 256 ierr = PetscOptionsTail();CHKERRQ(ierr); 257 PetscFunctionReturn(0); 258 } 259 260 /*------------------------------------------------------------*/ 261 static PetscErrorCode TaoView_LMVM(Tao tao, PetscViewer viewer) 262 { 263 TAO_LMVM *lm = (TAO_LMVM *)tao->data; 264 PetscBool isascii, recycle; 265 PetscInt recycled_its; 266 PetscErrorCode ierr; 267 268 PetscFunctionBegin; 269 ierr = PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii);CHKERRQ(ierr); 270 if (isascii) { 271 ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr); 272 ierr = PetscViewerASCIIPrintf(viewer, "BFGS steps: %D\n", lm->bfgs);CHKERRQ(ierr); 273 ierr = PetscViewerASCIIPrintf(viewer, "Scaled gradient steps: %D\n", lm->sgrad);CHKERRQ(ierr); 274 ierr = PetscViewerASCIIPrintf(viewer, "Gradient steps: %D\n", lm->grad);CHKERRQ(ierr); 275 ierr = MatLMVMGetRecycleFlag(lm->M, &recycle);CHKERRQ(ierr); 276 if (recycle) { 277 ierr = PetscViewerASCIIPrintf(viewer, "Recycle: on\n");CHKERRQ(ierr); 278 recycled_its = lm->bfgs + lm->sgrad + lm->grad; 279 ierr = PetscViewerASCIIPrintf(viewer, "Total recycled iterations: %D\n", recycled_its);CHKERRQ(ierr); 280 } 281 ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr); 282 } 283 PetscFunctionReturn(0); 284 } 285 286 /* ---------------------------------------------------------- */ 287 288 /*MC 289 TAOLMVM - Limited Memory Variable Metric method is a quasi-Newton 290 optimization solver for unconstrained minimization. It solves 291 the Newton step 292 Hkdk = - gk 293 294 using an approximation Bk in place of Hk, where Bk is composed using 295 the BFGS update formula. A More-Thuente line search is then used 296 to computed the steplength in the dk direction 297 Options Database Keys: 298 + -tao_lmm_vectors - number of vectors to use for approximation 299 . -tao_lmm_scale_type - "none","scalar","broyden" 300 . -tao_lmm_limit_type - "none","average","relative","absolute" 301 . -tao_lmm_rescale_type - "none","scalar","gl" 302 . -tao_lmm_limit_mu - mu limiting factor 303 . -tao_lmm_limit_nu - nu limiting factor 304 . -tao_lmm_delta_min - minimum delta value 305 . -tao_lmm_delta_max - maximum delta value 306 . -tao_lmm_broyden_phi - phi factor for Broyden scaling 307 . -tao_lmm_scalar_alpha - alpha factor for scalar scaling 308 . -tao_lmm_rescale_alpha - alpha factor for rescaling diagonal 309 . -tao_lmm_rescale_beta - beta factor for rescaling diagonal 310 . -tao_lmm_scalar_history - amount of history for scalar scaling 311 . -tao_lmm_rescale_history - amount of history for rescaling diagonal 312 . -tao_lmm_eps - rejection tolerance 313 - -tao_lmm_recycle - enable recycling LMVM updates between TaoSolve() calls 314 315 Level: beginner 316 M*/ 317 318 PETSC_EXTERN PetscErrorCode TaoCreate_LMVM(Tao tao) 319 { 320 TAO_LMVM *lmP; 321 const char *morethuente_type = TAOLINESEARCHMT; 322 PetscErrorCode ierr; 323 324 PetscFunctionBegin; 325 tao->ops->setup = TaoSetUp_LMVM; 326 tao->ops->solve = TaoSolve_LMVM; 327 tao->ops->view = TaoView_LMVM; 328 tao->ops->setfromoptions = TaoSetFromOptions_LMVM; 329 tao->ops->destroy = TaoDestroy_LMVM; 330 331 ierr = PetscNewLog(tao,&lmP);CHKERRQ(ierr); 332 lmP->D = 0; 333 lmP->M = 0; 334 lmP->Xold = 0; 335 lmP->Gold = 0; 336 lmP->H0 = NULL; 337 338 tao->data = (void*)lmP; 339 /* Override default settings (unless already changed) */ 340 if (!tao->max_it_changed) tao->max_it = 2000; 341 if (!tao->max_funcs_changed) tao->max_funcs = 4000; 342 343 ierr = TaoLineSearchCreate(((PetscObject)tao)->comm,&tao->linesearch);CHKERRQ(ierr); 344 ierr = PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1);CHKERRQ(ierr); 345 ierr = TaoLineSearchSetType(tao->linesearch,morethuente_type);CHKERRQ(ierr); 346 ierr = TaoLineSearchUseTaoRoutines(tao->linesearch,tao);CHKERRQ(ierr); 347 ierr = TaoLineSearchSetOptionsPrefix(tao->linesearch,tao->hdr.prefix);CHKERRQ(ierr); 348 PetscFunctionReturn(0); 349 } 350