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 infinity 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 if (tao->ops->update) { 41 PetscUseTypeMethod(tao, update, tao->niter, tao->user_update); 42 PetscCall(TaoComputeObjective(tao, tao->solution, &f)); 43 } 44 45 /* Compute direction */ 46 if (lmP->H0) { 47 PetscCall(MatLMVMSetJ0(lmP->M, lmP->H0)); 48 stepType = LMVM_STEP_BFGS; 49 } 50 PetscCall(MatLMVMUpdate(lmP->M, tao->solution, tao->gradient)); 51 PetscCall(MatSolve(lmP->M, tao->gradient, lmP->D)); 52 PetscCall(MatLMVMGetUpdateCount(lmP->M, &nupdates)); 53 if (nupdates > 0) stepType = LMVM_STEP_BFGS; 54 55 /* Check for success (descent direction) */ 56 PetscCall(VecDotRealPart(lmP->D, tao->gradient, &gdx)); 57 if ((gdx <= 0.0) || PetscIsInfOrNanReal(gdx)) { 58 /* Step is not descent or direction produced not a number 59 We can assert bfgsUpdates > 1 in this case because 60 the first solve produces the scaled gradient direction, 61 which is guaranteed to be descent 62 63 Use steepest descent direction (scaled) 64 */ 65 66 PetscCall(MatLMVMReset(lmP->M, PETSC_FALSE)); 67 PetscCall(MatLMVMClearJ0(lmP->M)); 68 PetscCall(MatLMVMUpdate(lmP->M, tao->solution, tao->gradient)); 69 PetscCall(MatSolve(lmP->M, tao->gradient, lmP->D)); 70 71 /* On a reset, the direction cannot be not a number; it is a 72 scaled gradient step. No need to check for this condition. */ 73 stepType = LMVM_STEP_GRAD; 74 } 75 PetscCall(VecScale(lmP->D, -1.0)); 76 77 /* Perform the linesearch */ 78 fold = f; 79 PetscCall(VecCopy(tao->solution, lmP->Xold)); 80 PetscCall(VecCopy(tao->gradient, lmP->Gold)); 81 82 PetscCall(TaoLineSearchApply(tao->linesearch, tao->solution, &f, tao->gradient, lmP->D, &step, &ls_status)); 83 PetscCall(TaoAddLineSearchCounts(tao)); 84 85 if (ls_status != TAOLINESEARCH_SUCCESS && ls_status != TAOLINESEARCH_SUCCESS_USER && (stepType != LMVM_STEP_GRAD)) { 86 /* Reset factors and use scaled gradient step */ 87 f = fold; 88 PetscCall(VecCopy(lmP->Xold, tao->solution)); 89 PetscCall(VecCopy(lmP->Gold, tao->gradient)); 90 91 /* Failed to obtain acceptable iterate with BFGS step */ 92 /* Attempt to use the scaled gradient direction */ 93 94 PetscCall(MatLMVMReset(lmP->M, PETSC_FALSE)); 95 PetscCall(MatLMVMClearJ0(lmP->M)); 96 PetscCall(MatLMVMUpdate(lmP->M, tao->solution, tao->gradient)); 97 PetscCall(MatSolve(lmP->M, tao->solution, tao->gradient)); 98 99 /* On a reset, the direction cannot be not a number; it is a 100 scaled gradient step. No need to check for this condition. */ 101 stepType = LMVM_STEP_GRAD; 102 PetscCall(VecScale(lmP->D, -1.0)); 103 104 /* Perform the linesearch */ 105 PetscCall(TaoLineSearchApply(tao->linesearch, tao->solution, &f, tao->gradient, lmP->D, &step, &ls_status)); 106 PetscCall(TaoAddLineSearchCounts(tao)); 107 } 108 109 if (ls_status != TAOLINESEARCH_SUCCESS && ls_status != TAOLINESEARCH_SUCCESS_USER) { 110 /* Failed to find an improving point */ 111 f = fold; 112 PetscCall(VecCopy(lmP->Xold, tao->solution)); 113 PetscCall(VecCopy(lmP->Gold, tao->gradient)); 114 step = 0.0; 115 tao->reason = TAO_DIVERGED_LS_FAILURE; 116 } else { 117 /* LS found valid step, so tally up step type */ 118 switch (stepType) { 119 case LMVM_STEP_BFGS: 120 ++lmP->bfgs; 121 break; 122 case LMVM_STEP_GRAD: 123 ++lmP->grad; 124 break; 125 default: 126 break; 127 } 128 /* Compute new gradient norm */ 129 PetscCall(TaoGradientNorm(tao, tao->gradient, NORM_2, &gnorm)); 130 } 131 132 /* Check convergence */ 133 tao->niter++; 134 PetscCall(TaoLogConvergenceHistory(tao, f, gnorm, 0.0, tao->ksp_its)); 135 PetscCall(TaoMonitor(tao, tao->niter, f, gnorm, 0.0, step)); 136 PetscUseTypeMethod(tao, convergencetest, tao->cnvP); 137 } 138 PetscFunctionReturn(PETSC_SUCCESS); 139 } 140 141 static PetscErrorCode TaoSetUp_LMVM(Tao tao) 142 { 143 TAO_LMVM *lmP = (TAO_LMVM *)tao->data; 144 PetscInt n, N; 145 PetscBool is_set, is_spd; 146 147 PetscFunctionBegin; 148 /* Existence of tao->solution checked in TaoSetUp() */ 149 if (!tao->gradient) PetscCall(VecDuplicate(tao->solution, &tao->gradient)); 150 if (!tao->stepdirection) PetscCall(VecDuplicate(tao->solution, &tao->stepdirection)); 151 if (!lmP->D) PetscCall(VecDuplicate(tao->solution, &lmP->D)); 152 if (!lmP->Xold) PetscCall(VecDuplicate(tao->solution, &lmP->Xold)); 153 if (!lmP->Gold) PetscCall(VecDuplicate(tao->solution, &lmP->Gold)); 154 155 /* Create matrix for the limited memory approximation */ 156 PetscCall(VecGetLocalSize(tao->solution, &n)); 157 PetscCall(VecGetSize(tao->solution, &N)); 158 PetscCall(MatSetSizes(lmP->M, n, n, N, N)); 159 PetscCall(MatLMVMAllocate(lmP->M, tao->solution, tao->gradient)); 160 PetscCall(MatIsSPDKnown(lmP->M, &is_set, &is_spd)); 161 PetscCheck(is_set && is_spd, PetscObjectComm((PetscObject)tao), PETSC_ERR_ARG_INCOMP, "LMVM matrix is not symmetric positive-definite."); 162 163 /* If the user has set a matrix to solve as the initial H0, set the options prefix here, and set up the KSP */ 164 if (lmP->H0) PetscCall(MatLMVMSetJ0(lmP->M, lmP->H0)); 165 PetscFunctionReturn(PETSC_SUCCESS); 166 } 167 168 static PetscErrorCode TaoDestroy_LMVM(Tao tao) 169 { 170 TAO_LMVM *lmP = (TAO_LMVM *)tao->data; 171 172 PetscFunctionBegin; 173 if (tao->setupcalled) { 174 PetscCall(VecDestroy(&lmP->Xold)); 175 PetscCall(VecDestroy(&lmP->Gold)); 176 PetscCall(VecDestroy(&lmP->D)); 177 } 178 PetscCall(MatDestroy(&lmP->M)); 179 if (lmP->H0) PetscCall(PetscObjectDereference((PetscObject)lmP->H0)); 180 PetscCall(PetscFree(tao->data)); 181 PetscFunctionReturn(PETSC_SUCCESS); 182 } 183 184 static PetscErrorCode TaoSetFromOptions_LMVM(Tao tao, PetscOptionItems PetscOptionsObject) 185 { 186 TAO_LMVM *lm = (TAO_LMVM *)tao->data; 187 188 PetscFunctionBegin; 189 PetscOptionsHeadBegin(PetscOptionsObject, "Limited-memory variable-metric method for unconstrained optimization"); 190 PetscCall(PetscOptionsBool("-tao_lmvm_recycle", "enable recycling of the BFGS matrix between subsequent TaoSolve() calls", "", lm->recycle, &lm->recycle, NULL)); 191 PetscCall(TaoLineSearchSetFromOptions(tao->linesearch)); 192 PetscCall(MatSetFromOptions(lm->M)); 193 PetscOptionsHeadEnd(); 194 PetscFunctionReturn(PETSC_SUCCESS); 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 /*MC 223 TAOLMVM - Limited Memory Variable Metric method is a quasi-Newton 224 optimization solver for unconstrained minimization. It solves 225 the Newton step 226 Hkdk = - gk 227 228 using an approximation Bk in place of Hk, where Bk is composed using 229 the BFGS update formula. A More-Thuente line search is then used 230 to computed the steplength in the dk direction 231 232 Options Database Keys: 233 + -tao_lmvm_recycle - enable recycling LMVM updates between TaoSolve() calls 234 - -tao_lmvm_no_scale - (developer) disables diagonal Broyden scaling on the LMVM approximation 235 236 Level: beginner 237 M*/ 238 239 PETSC_EXTERN PetscErrorCode TaoCreate_LMVM(Tao tao) 240 { 241 TAO_LMVM *lmP; 242 const char *morethuente_type = TAOLINESEARCHMT; 243 244 PetscFunctionBegin; 245 tao->ops->setup = TaoSetUp_LMVM; 246 tao->ops->solve = TaoSolve_LMVM; 247 tao->ops->view = TaoView_LMVM; 248 tao->ops->setfromoptions = TaoSetFromOptions_LMVM; 249 tao->ops->destroy = TaoDestroy_LMVM; 250 251 PetscCall(PetscNew(&lmP)); 252 lmP->D = NULL; 253 lmP->M = NULL; 254 lmP->Xold = NULL; 255 lmP->Gold = NULL; 256 lmP->H0 = NULL; 257 lmP->recycle = PETSC_FALSE; 258 259 tao->data = (void *)lmP; 260 /* Override default settings (unless already changed) */ 261 PetscCall(TaoParametersInitialize(tao)); 262 PetscObjectParameterSetDefault(tao, max_it, 2000); 263 PetscObjectParameterSetDefault(tao, max_funcs, 4000); 264 265 PetscCall(TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch)); 266 PetscCall(PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1)); 267 PetscCall(TaoLineSearchSetType(tao->linesearch, morethuente_type)); 268 PetscCall(TaoLineSearchUseTaoRoutines(tao->linesearch, tao)); 269 PetscCall(TaoLineSearchSetOptionsPrefix(tao->linesearch, tao->hdr.prefix)); 270 271 PetscCall(KSPInitializePackage()); 272 PetscCall(MatCreate(((PetscObject)tao)->comm, &lmP->M)); 273 PetscCall(PetscObjectIncrementTabLevel((PetscObject)lmP->M, (PetscObject)tao, 1)); 274 PetscCall(MatSetType(lmP->M, MATLMVMBFGS)); 275 PetscCall(MatSetOptionsPrefix(lmP->M, "tao_lmvm_")); 276 PetscFunctionReturn(PETSC_SUCCESS); 277 } 278