1 #include <petsctaolinesearch.h> 2 #include <../src/tao/unconstrained/impls/lmvm/lmvm.h> 3 4 #define LMVM_STEP_BFGS 0 5 #define LMVM_STEP_GRAD 1 6 7 static PetscErrorCode TaoSolve_LMVM(Tao tao) 8 { 9 TAO_LMVM *lmP = (TAO_LMVM *)tao->data; 10 PetscReal f, fold, gdx, gnorm; 11 PetscReal step = 1.0; 12 PetscInt stepType = LMVM_STEP_GRAD, nupdates; 13 TaoLineSearchConvergedReason ls_status = TAOLINESEARCH_CONTINUE_ITERATING; 14 15 PetscFunctionBegin; 16 if (tao->XL || tao->XU || tao->ops->computebounds) PetscCall(PetscInfo(tao, "WARNING: Variable bounds have been set but will be ignored by lmvm algorithm\n")); 17 18 /* Check convergence criteria */ 19 PetscCall(TaoComputeObjectiveAndGradient(tao, tao->solution, &f, tao->gradient)); 20 PetscCall(TaoGradientNorm(tao, tao->gradient, NORM_2, &gnorm)); 21 22 PetscCheck(!PetscIsInfOrNanReal(f) && !PetscIsInfOrNanReal(gnorm), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated Inf or NaN"); 23 24 tao->reason = TAO_CONTINUE_ITERATING; 25 PetscCall(TaoLogConvergenceHistory(tao, f, gnorm, 0.0, tao->ksp_its)); 26 PetscCall(TaoMonitor(tao, tao->niter, f, gnorm, 0.0, step)); 27 PetscUseTypeMethod(tao, convergencetest, tao->cnvP); 28 if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(PETSC_SUCCESS); 29 30 /* Set counter for gradient/reset steps */ 31 if (!lmP->recycle) { 32 lmP->bfgs = 0; 33 lmP->grad = 0; 34 PetscCall(MatLMVMReset(lmP->M, PETSC_FALSE)); 35 } 36 37 /* Have not converged; continue with Newton method */ 38 while (tao->reason == TAO_CONTINUE_ITERATING) { 39 /* Call general purpose update function */ 40 PetscTryTypeMethod(tao, update, tao->niter, tao->user_update); 41 42 /* Compute direction */ 43 if (lmP->H0) { 44 PetscCall(MatLMVMSetJ0(lmP->M, lmP->H0)); 45 stepType = LMVM_STEP_BFGS; 46 } 47 PetscCall(MatLMVMUpdate(lmP->M, tao->solution, tao->gradient)); 48 PetscCall(MatSolve(lmP->M, tao->gradient, lmP->D)); 49 PetscCall(MatLMVMGetUpdateCount(lmP->M, &nupdates)); 50 if (nupdates > 0) stepType = LMVM_STEP_BFGS; 51 52 /* Check for success (descent direction) */ 53 PetscCall(VecDotRealPart(lmP->D, tao->gradient, &gdx)); 54 if ((gdx <= 0.0) || PetscIsInfOrNanReal(gdx)) { 55 /* Step is not descent or direction produced not a number 56 We can assert bfgsUpdates > 1 in this case because 57 the first solve produces the scaled gradient direction, 58 which is guaranteed to be descent 59 60 Use steepest descent direction (scaled) 61 */ 62 63 PetscCall(MatLMVMReset(lmP->M, PETSC_FALSE)); 64 PetscCall(MatLMVMClearJ0(lmP->M)); 65 PetscCall(MatLMVMUpdate(lmP->M, tao->solution, tao->gradient)); 66 PetscCall(MatSolve(lmP->M, tao->gradient, lmP->D)); 67 68 /* On a reset, the direction cannot be not a number; it is a 69 scaled gradient step. No need to check for this condition. */ 70 stepType = LMVM_STEP_GRAD; 71 } 72 PetscCall(VecScale(lmP->D, -1.0)); 73 74 /* Perform the linesearch */ 75 fold = f; 76 PetscCall(VecCopy(tao->solution, lmP->Xold)); 77 PetscCall(VecCopy(tao->gradient, lmP->Gold)); 78 79 PetscCall(TaoLineSearchApply(tao->linesearch, tao->solution, &f, tao->gradient, lmP->D, &step, &ls_status)); 80 PetscCall(TaoAddLineSearchCounts(tao)); 81 82 if (ls_status != TAOLINESEARCH_SUCCESS && ls_status != TAOLINESEARCH_SUCCESS_USER && (stepType != LMVM_STEP_GRAD)) { 83 /* Reset factors and use scaled gradient step */ 84 f = fold; 85 PetscCall(VecCopy(lmP->Xold, tao->solution)); 86 PetscCall(VecCopy(lmP->Gold, tao->gradient)); 87 88 /* Failed to obtain acceptable iterate with BFGS step */ 89 /* Attempt to use the scaled gradient direction */ 90 91 PetscCall(MatLMVMReset(lmP->M, PETSC_FALSE)); 92 PetscCall(MatLMVMClearJ0(lmP->M)); 93 PetscCall(MatLMVMUpdate(lmP->M, tao->solution, tao->gradient)); 94 PetscCall(MatSolve(lmP->M, tao->solution, tao->gradient)); 95 96 /* On a reset, the direction cannot be not a number; it is a 97 scaled gradient step. No need to check for this condition. */ 98 stepType = LMVM_STEP_GRAD; 99 PetscCall(VecScale(lmP->D, -1.0)); 100 101 /* Perform the linesearch */ 102 PetscCall(TaoLineSearchApply(tao->linesearch, tao->solution, &f, tao->gradient, lmP->D, &step, &ls_status)); 103 PetscCall(TaoAddLineSearchCounts(tao)); 104 } 105 106 if (ls_status != TAOLINESEARCH_SUCCESS && ls_status != TAOLINESEARCH_SUCCESS_USER) { 107 /* Failed to find an improving point */ 108 f = fold; 109 PetscCall(VecCopy(lmP->Xold, tao->solution)); 110 PetscCall(VecCopy(lmP->Gold, tao->gradient)); 111 step = 0.0; 112 tao->reason = TAO_DIVERGED_LS_FAILURE; 113 } else { 114 /* LS found valid step, so tally up step type */ 115 switch (stepType) { 116 case LMVM_STEP_BFGS: 117 ++lmP->bfgs; 118 break; 119 case LMVM_STEP_GRAD: 120 ++lmP->grad; 121 break; 122 default: 123 break; 124 } 125 /* Compute new gradient norm */ 126 PetscCall(TaoGradientNorm(tao, tao->gradient, NORM_2, &gnorm)); 127 } 128 129 /* Check convergence */ 130 tao->niter++; 131 PetscCall(TaoLogConvergenceHistory(tao, f, gnorm, 0.0, tao->ksp_its)); 132 PetscCall(TaoMonitor(tao, tao->niter, f, gnorm, 0.0, step)); 133 PetscUseTypeMethod(tao, convergencetest, tao->cnvP); 134 } 135 PetscFunctionReturn(PETSC_SUCCESS); 136 } 137 138 static PetscErrorCode TaoSetUp_LMVM(Tao tao) 139 { 140 TAO_LMVM *lmP = (TAO_LMVM *)tao->data; 141 PetscInt n, N; 142 PetscBool is_set, is_spd; 143 144 PetscFunctionBegin; 145 /* Existence of tao->solution checked in TaoSetUp() */ 146 if (!tao->gradient) PetscCall(VecDuplicate(tao->solution, &tao->gradient)); 147 if (!tao->stepdirection) PetscCall(VecDuplicate(tao->solution, &tao->stepdirection)); 148 if (!lmP->D) PetscCall(VecDuplicate(tao->solution, &lmP->D)); 149 if (!lmP->Xold) PetscCall(VecDuplicate(tao->solution, &lmP->Xold)); 150 if (!lmP->Gold) PetscCall(VecDuplicate(tao->solution, &lmP->Gold)); 151 152 /* Create matrix for the limited memory approximation */ 153 PetscCall(VecGetLocalSize(tao->solution, &n)); 154 PetscCall(VecGetSize(tao->solution, &N)); 155 PetscCall(MatSetSizes(lmP->M, n, n, N, N)); 156 PetscCall(MatLMVMAllocate(lmP->M, tao->solution, tao->gradient)); 157 PetscCall(MatIsSPDKnown(lmP->M, &is_set, &is_spd)); 158 PetscCheck(is_set && is_spd, PetscObjectComm((PetscObject)tao), PETSC_ERR_ARG_INCOMP, "LMVM matrix is not symmetric positive-definite."); 159 160 /* If the user has set a matrix to solve as the initial H0, set the options prefix here, and set up the KSP */ 161 if (lmP->H0) PetscCall(MatLMVMSetJ0(lmP->M, lmP->H0)); 162 PetscFunctionReturn(PETSC_SUCCESS); 163 } 164 165 /* ---------------------------------------------------------- */ 166 static PetscErrorCode TaoDestroy_LMVM(Tao tao) 167 { 168 TAO_LMVM *lmP = (TAO_LMVM *)tao->data; 169 170 PetscFunctionBegin; 171 if (tao->setupcalled) { 172 PetscCall(VecDestroy(&lmP->Xold)); 173 PetscCall(VecDestroy(&lmP->Gold)); 174 PetscCall(VecDestroy(&lmP->D)); 175 } 176 PetscCall(MatDestroy(&lmP->M)); 177 if (lmP->H0) PetscCall(PetscObjectDereference((PetscObject)lmP->H0)); 178 PetscCall(PetscFree(tao->data)); 179 PetscFunctionReturn(PETSC_SUCCESS); 180 } 181 182 /*------------------------------------------------------------*/ 183 static PetscErrorCode TaoSetFromOptions_LMVM(Tao tao, PetscOptionItems *PetscOptionsObject) 184 { 185 TAO_LMVM *lm = (TAO_LMVM *)tao->data; 186 187 PetscFunctionBegin; 188 PetscOptionsHeadBegin(PetscOptionsObject, "Limited-memory variable-metric method for unconstrained optimization"); 189 PetscCall(PetscOptionsBool("-tao_lmvm_recycle", "enable recycling of the BFGS matrix between subsequent TaoSolve() calls", "", lm->recycle, &lm->recycle, NULL)); 190 PetscCall(TaoLineSearchSetFromOptions(tao->linesearch)); 191 PetscCall(MatSetFromOptions(lm->M)); 192 PetscOptionsHeadEnd(); 193 PetscFunctionReturn(PETSC_SUCCESS); 194 } 195 196 /*------------------------------------------------------------*/ 197 static PetscErrorCode TaoView_LMVM(Tao tao, PetscViewer viewer) 198 { 199 TAO_LMVM *lm = (TAO_LMVM *)tao->data; 200 PetscBool isascii; 201 PetscInt recycled_its; 202 203 PetscFunctionBegin; 204 PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii)); 205 if (isascii) { 206 PetscCall(PetscViewerASCIIPushTab(viewer)); 207 PetscCall(PetscViewerASCIIPrintf(viewer, "Gradient steps: %" PetscInt_FMT "\n", lm->grad)); 208 if (lm->recycle) { 209 PetscCall(PetscViewerASCIIPrintf(viewer, "Recycle: on\n")); 210 recycled_its = lm->bfgs + lm->grad; 211 PetscCall(PetscViewerASCIIPrintf(viewer, "Total recycled iterations: %" PetscInt_FMT "\n", recycled_its)); 212 } 213 PetscCall(PetscViewerASCIIPrintf(viewer, "LMVM Matrix:\n")); 214 PetscCall(PetscViewerASCIIPushTab(viewer)); 215 PetscCall(MatView(lm->M, viewer)); 216 PetscCall(PetscViewerASCIIPopTab(viewer)); 217 PetscCall(PetscViewerASCIIPopTab(viewer)); 218 } 219 PetscFunctionReturn(PETSC_SUCCESS); 220 } 221 222 /* ---------------------------------------------------------- */ 223 224 /*MC 225 TAOLMVM - Limited Memory Variable Metric method is a quasi-Newton 226 optimization solver for unconstrained minimization. It solves 227 the Newton step 228 Hkdk = - gk 229 230 using an approximation Bk in place of Hk, where Bk is composed using 231 the BFGS update formula. A More-Thuente line search is then used 232 to computed the steplength in the dk direction 233 234 Options Database Keys: 235 + -tao_lmvm_recycle - enable recycling LMVM updates between TaoSolve() calls 236 - -tao_lmvm_no_scale - (developer) disables diagonal Broyden scaling on the LMVM approximation 237 238 Level: beginner 239 M*/ 240 241 PETSC_EXTERN PetscErrorCode TaoCreate_LMVM(Tao tao) 242 { 243 TAO_LMVM *lmP; 244 const char *morethuente_type = TAOLINESEARCHMT; 245 246 PetscFunctionBegin; 247 tao->ops->setup = TaoSetUp_LMVM; 248 tao->ops->solve = TaoSolve_LMVM; 249 tao->ops->view = TaoView_LMVM; 250 tao->ops->setfromoptions = TaoSetFromOptions_LMVM; 251 tao->ops->destroy = TaoDestroy_LMVM; 252 253 PetscCall(PetscNew(&lmP)); 254 lmP->D = NULL; 255 lmP->M = NULL; 256 lmP->Xold = NULL; 257 lmP->Gold = NULL; 258 lmP->H0 = NULL; 259 lmP->recycle = PETSC_FALSE; 260 261 tao->data = (void *)lmP; 262 /* Override default settings (unless already changed) */ 263 if (!tao->max_it_changed) tao->max_it = 2000; 264 if (!tao->max_funcs_changed) tao->max_funcs = 4000; 265 266 PetscCall(TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch)); 267 PetscCall(PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1)); 268 PetscCall(TaoLineSearchSetType(tao->linesearch, morethuente_type)); 269 PetscCall(TaoLineSearchUseTaoRoutines(tao->linesearch, tao)); 270 PetscCall(TaoLineSearchSetOptionsPrefix(tao->linesearch, tao->hdr.prefix)); 271 272 PetscCall(KSPInitializePackage()); 273 PetscCall(MatCreate(((PetscObject)tao)->comm, &lmP->M)); 274 PetscCall(PetscObjectIncrementTabLevel((PetscObject)lmP->M, (PetscObject)tao, 1)); 275 PetscCall(MatSetType(lmP->M, MATLMVMBFGS)); 276 PetscCall(MatSetOptionsPrefix(lmP->M, "tao_lmvm_")); 277 PetscFunctionReturn(PETSC_SUCCESS); 278 } 279