1 #include <../src/snes/impls/ncg/snesncgimpl.h> /*I "petscsnes.h" I*/ 2 const char *const SNESNCGTypes[] = {"FR", "PRP", "HS", "DY", "CD", "SNESNCGType", "SNES_NCG_", NULL}; 3 4 static PetscErrorCode SNESDestroy_NCG(SNES snes) 5 { 6 PetscFunctionBegin; 7 PetscCall(PetscObjectComposeFunction((PetscObject)snes, "SNESNCGSetType_C", NULL)); 8 PetscCall(PetscFree(snes->data)); 9 PetscFunctionReturn(PETSC_SUCCESS); 10 } 11 12 static PetscErrorCode SNESSetUp_NCG(SNES snes) 13 { 14 PetscFunctionBegin; 15 PetscCall(SNESSetWorkVecs(snes, 2)); 16 PetscCheck(snes->npcside != PC_RIGHT, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONGSTATE, "SNESNCG only supports left preconditioning"); 17 if (snes->functype == SNES_FUNCTION_DEFAULT) snes->functype = SNES_FUNCTION_UNPRECONDITIONED; 18 PetscFunctionReturn(PETSC_SUCCESS); 19 } 20 21 static PetscErrorCode SNESLineSearchApply_NCGLinear(SNESLineSearch linesearch) 22 { 23 PetscScalar alpha, ptAp; 24 Vec X, Y, F, W; 25 SNES snes; 26 PetscReal *fnorm, *xnorm, *ynorm; 27 28 PetscFunctionBegin; 29 PetscCall(SNESLineSearchGetSNES(linesearch, &snes)); 30 X = linesearch->vec_sol; 31 W = linesearch->vec_sol_new; 32 F = linesearch->vec_func; 33 Y = linesearch->vec_update; 34 fnorm = &linesearch->fnorm; 35 xnorm = &linesearch->xnorm; 36 ynorm = &linesearch->ynorm; 37 38 if (!snes->jacobian) PetscCall(SNESSetUpMatrices(snes)); 39 40 /* 41 The exact step size for unpreconditioned linear CG is just: 42 alpha = (r, r) / (p, Ap) = (f, f) / (y, Jy) 43 */ 44 PetscCall(SNESComputeJacobian(snes, X, snes->jacobian, snes->jacobian_pre)); 45 SNESLineSearchCheckJacobianDomainError(snes, linesearch); 46 47 PetscCall(VecDot(F, F, &alpha)); 48 PetscCall(MatMult(snes->jacobian, Y, W)); 49 PetscCall(VecDot(Y, W, &ptAp)); 50 alpha = alpha / ptAp; 51 PetscCall(VecAXPY(X, -alpha, Y)); 52 PetscCall(SNESComputeFunction(snes, X, F)); 53 54 PetscCall(VecNorm(F, NORM_2, fnorm)); 55 SNESLineSearchCheckFunctionDomainError(snes, linesearch, *fnorm); 56 PetscCall(VecNorm(X, NORM_2, xnorm)); 57 PetscCall(VecNorm(Y, NORM_2, ynorm)); 58 PetscFunctionReturn(PETSC_SUCCESS); 59 } 60 61 /*MC 62 SNESLINESEARCHNCGLINEAR - Special line search only for the nonlinear CG solver `SNESNCG` 63 64 This line search uses the length "as if" the problem is linear (that is what is computed by the linear CG method) using the Jacobian of the function. 65 alpha = (r, r) / (p, Ap) = (f, f) / (y, Jy) where r (f) is the current residual (function value), p (y) is the current search direction. 66 67 Level: advanced 68 69 Notes: 70 This requires a Jacobian-vector product but does not require the solution of a linear system with the Jacobian 71 72 This is a "odd-ball" line search, we don't know if it is in the literature or used in practice by anyone. 73 74 .seealso: [](ch_snes), `SNES`, `SNESNCG`, `SNESLineSearchCreate()`, `SNESLineSearchSetType()` 75 M*/ 76 77 PETSC_EXTERN PetscErrorCode SNESLineSearchCreate_NCGLinear(SNESLineSearch linesearch) 78 { 79 PetscFunctionBegin; 80 linesearch->ops->apply = SNESLineSearchApply_NCGLinear; 81 linesearch->ops->destroy = NULL; 82 linesearch->ops->setfromoptions = NULL; 83 linesearch->ops->reset = NULL; 84 linesearch->ops->view = NULL; 85 linesearch->ops->setup = NULL; 86 PetscFunctionReturn(PETSC_SUCCESS); 87 } 88 89 static PetscErrorCode SNESSetFromOptions_NCG(SNES snes, PetscOptionItems PetscOptionsObject) 90 { 91 SNES_NCG *ncg = (SNES_NCG *)snes->data; 92 PetscBool debug = PETSC_FALSE; 93 SNESNCGType ncgtype = ncg->type; 94 SNESLineSearch linesearch; 95 96 PetscFunctionBegin; 97 PetscOptionsHeadBegin(PetscOptionsObject, "SNES NCG options"); 98 PetscCall(PetscOptionsBool("-snes_ncg_monitor", "Monitor the beta values used in the NCG iterations", "SNES", ncg->monitor ? PETSC_TRUE : PETSC_FALSE, &debug, NULL)); 99 if (debug) ncg->monitor = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)snes)); 100 PetscCall(PetscOptionsEnum("-snes_ncg_type", "NCG Beta type used", "SNESNCGSetType", SNESNCGTypes, (PetscEnum)ncg->type, (PetscEnum *)&ncgtype, NULL)); 101 PetscCall(SNESNCGSetType(snes, ncgtype)); 102 PetscOptionsHeadEnd(); 103 if (!snes->linesearch) { 104 PetscCall(SNESGetLineSearch(snes, &linesearch)); 105 if (!((PetscObject)linesearch)->type_name) { 106 if (!snes->npc) { 107 PetscCall(SNESLineSearchSetType(linesearch, SNESLINESEARCHCP)); 108 } else { 109 PetscCall(SNESLineSearchSetType(linesearch, SNESLINESEARCHSECANT)); 110 } 111 } 112 } 113 PetscFunctionReturn(PETSC_SUCCESS); 114 } 115 116 static PetscErrorCode SNESView_NCG(SNES snes, PetscViewer viewer) 117 { 118 SNES_NCG *ncg = (SNES_NCG *)snes->data; 119 PetscBool isascii; 120 121 PetscFunctionBegin; 122 PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii)); 123 if (isascii) PetscCall(PetscViewerASCIIPrintf(viewer, " type: %s\n", SNESNCGTypes[ncg->type])); 124 PetscFunctionReturn(PETSC_SUCCESS); 125 } 126 127 /*@ 128 SNESNCGSetType - Sets the conjugate update type for nonlinear CG `SNESNCG`. 129 130 Logically Collective 131 132 Input Parameters: 133 + snes - the iterative context 134 - btype - update type, see `SNESNCGType` 135 136 Options Database Key: 137 . -snes_ncg_type <prp,fr,hs,dy,cd> - strategy for selecting algorithm for computing beta 138 139 Level: intermediate 140 141 Notes: 142 `SNES_NCG_PRP` is the default, and the only one that tolerates generalized search directions. 143 144 It is not clear what "generalized search directions" means, does it mean use with a nonlinear preconditioner, 145 that is using -npc_snes_type <type>, `SNESSetNPC()`, or `SNESGetNPC()`? 146 147 .seealso: [](ch_snes), `SNES`, `SNESNCG`, `SNESNCGType`, `SNES_NCG_FR`, `SNES_NCG_PRP`, `SNES_NCG_HS`, `SNES_NCG_DY`, `SNES_NCG_CD` 148 @*/ 149 PetscErrorCode SNESNCGSetType(SNES snes, SNESNCGType btype) 150 { 151 PetscFunctionBegin; 152 PetscValidHeaderSpecific(snes, SNES_CLASSID, 1); 153 PetscTryMethod(snes, "SNESNCGSetType_C", (SNES, SNESNCGType), (snes, btype)); 154 PetscFunctionReturn(PETSC_SUCCESS); 155 } 156 157 static PetscErrorCode SNESNCGSetType_NCG(SNES snes, SNESNCGType btype) 158 { 159 SNES_NCG *ncg = (SNES_NCG *)snes->data; 160 161 PetscFunctionBegin; 162 ncg->type = btype; 163 PetscFunctionReturn(PETSC_SUCCESS); 164 } 165 166 /* 167 SNESSolve_NCG - Solves a nonlinear system with the Nonlinear Conjugate Gradient method. 168 169 Input Parameter: 170 . snes - the `SNES` context 171 172 Output Parameter: 173 . outits - number of iterations until termination 174 175 Application Interface Routine: SNESSolve() 176 */ 177 static PetscErrorCode SNESSolve_NCG(SNES snes) 178 { 179 SNES_NCG *ncg = (SNES_NCG *)snes->data; 180 Vec X, dX, lX, F, dXold; 181 PetscReal fnorm, ynorm, xnorm, beta = 0.0; 182 PetscScalar dXdotdX, dXolddotdXold, dXdotdXold, lXdotdX, lXdotdXold; 183 PetscInt maxits, i; 184 SNESLineSearch linesearch; 185 SNESConvergedReason reason; 186 187 PetscFunctionBegin; 188 PetscCheck(!snes->xl && !snes->xu && !snes->ops->computevariablebounds, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONGSTATE, "SNES solver %s does not support bounds", ((PetscObject)snes)->type_name); 189 190 PetscCall(PetscCitationsRegister(SNESCitation, &SNEScite)); 191 snes->reason = SNES_CONVERGED_ITERATING; 192 193 maxits = snes->max_its; /* maximum number of iterations */ 194 X = snes->vec_sol; /* X^n */ 195 dXold = snes->work[0]; /* The previous iterate of X */ 196 dX = snes->work[1]; /* the preconditioned direction */ 197 lX = snes->vec_sol_update; /* the conjugate direction */ 198 F = snes->vec_func; /* residual vector */ 199 200 PetscCall(SNESGetLineSearch(snes, &linesearch)); 201 202 PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes)); 203 snes->iter = 0; 204 snes->norm = 0.; 205 PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes)); 206 207 /* compute the initial function and preconditioned update dX */ 208 209 if (snes->npc && snes->functype == SNES_FUNCTION_PRECONDITIONED) { 210 PetscCall(SNESApplyNPC(snes, X, NULL, dX)); 211 PetscCall(SNESGetConvergedReason(snes->npc, &reason)); 212 if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) { 213 snes->reason = SNES_DIVERGED_INNER; 214 PetscFunctionReturn(PETSC_SUCCESS); 215 } 216 PetscCall(VecCopy(dX, F)); 217 PetscCall(VecNorm(F, NORM_2, &fnorm)); 218 } else { 219 if (!snes->vec_func_init_set) PetscCall(SNESComputeFunction(snes, X, F)); 220 else snes->vec_func_init_set = PETSC_FALSE; 221 222 /* convergence test */ 223 PetscCall(VecNorm(F, NORM_2, &fnorm)); 224 SNESCheckFunctionDomainError(snes, fnorm); 225 PetscCall(VecCopy(F, dX)); 226 } 227 if (snes->npc) { 228 if (snes->functype == SNES_FUNCTION_UNPRECONDITIONED) { 229 PetscCall(SNESApplyNPC(snes, X, F, dX)); 230 PetscCall(SNESGetConvergedReason(snes->npc, &reason)); 231 if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) { 232 snes->reason = SNES_DIVERGED_INNER; 233 PetscFunctionReturn(PETSC_SUCCESS); 234 } 235 } 236 } 237 PetscCall(VecCopy(dX, lX)); 238 PetscCall(VecDot(dX, dX, &dXdotdX)); 239 240 PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes)); 241 snes->norm = fnorm; 242 PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes)); 243 PetscCall(SNESLogConvergenceHistory(snes, fnorm, 0)); 244 245 /* test convergence */ 246 PetscCall(SNESConverged(snes, 0, 0.0, 0.0, fnorm)); 247 PetscCall(SNESMonitor(snes, 0, fnorm)); 248 if (snes->reason) PetscFunctionReturn(PETSC_SUCCESS); 249 250 /* Call general purpose update function */ 251 PetscTryTypeMethod(snes, update, snes->iter); 252 253 /* first update -- just use the (preconditioned) residual direction for the initial conjugate direction */ 254 255 for (i = 1; i < maxits + 1; i++) { 256 /* some update types require the old update direction or conjugate direction */ 257 if (ncg->type != SNES_NCG_FR) PetscCall(VecCopy(dX, dXold)); 258 PetscCall(SNESLineSearchApply(linesearch, X, F, &fnorm, lX)); 259 if (snes->reason) PetscFunctionReturn(PETSC_SUCCESS); 260 PetscCall(SNESLineSearchGetNorms(linesearch, &xnorm, &fnorm, &ynorm)); 261 SNESCheckLineSearchFailure(snes); 262 if (snes->nfuncs >= snes->max_funcs && snes->max_funcs >= 0) { 263 snes->reason = SNES_DIVERGED_FUNCTION_COUNT; 264 PetscFunctionReturn(PETSC_SUCCESS); 265 } 266 /* Monitor convergence */ 267 PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes)); 268 snes->iter = i; 269 snes->norm = fnorm; 270 snes->xnorm = xnorm; 271 snes->ynorm = ynorm; 272 PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes)); 273 PetscCall(SNESLogConvergenceHistory(snes, snes->norm, 0)); 274 275 /* Test for convergence */ 276 PetscCall(SNESConverged(snes, snes->iter, xnorm, ynorm, fnorm)); 277 PetscCall(SNESMonitor(snes, snes->iter, snes->norm)); 278 if (snes->reason) PetscFunctionReturn(PETSC_SUCCESS); 279 280 /* Call general purpose update function */ 281 PetscTryTypeMethod(snes, update, snes->iter); 282 if (snes->npc) { 283 if (snes->functype == SNES_FUNCTION_PRECONDITIONED) { 284 PetscCall(SNESApplyNPC(snes, X, NULL, dX)); 285 PetscCall(SNESGetConvergedReason(snes->npc, &reason)); 286 if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) { 287 snes->reason = SNES_DIVERGED_INNER; 288 PetscFunctionReturn(PETSC_SUCCESS); 289 } 290 PetscCall(VecCopy(dX, F)); 291 } else { 292 PetscCall(SNESApplyNPC(snes, X, F, dX)); 293 PetscCall(SNESGetConvergedReason(snes->npc, &reason)); 294 if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) { 295 snes->reason = SNES_DIVERGED_INNER; 296 PetscFunctionReturn(PETSC_SUCCESS); 297 } 298 } 299 } else { 300 PetscCall(VecCopy(F, dX)); 301 } 302 303 /* compute the conjugate direction lX = dX + beta*lX with beta = ((dX, dX) / (dX_old, dX_old) (Fletcher-Reeves update)*/ 304 switch (ncg->type) { 305 case SNES_NCG_FR: /* Fletcher-Reeves */ 306 dXolddotdXold = dXdotdX; 307 PetscCall(VecDot(dX, dX, &dXdotdX)); 308 beta = PetscRealPart(dXdotdX / dXolddotdXold); 309 break; 310 case SNES_NCG_PRP: /* Polak-Ribiere-Poylak */ 311 dXolddotdXold = dXdotdX; 312 PetscCall(VecDotBegin(dX, dX, &dXdotdX)); 313 PetscCall(VecDotBegin(dXold, dX, &dXdotdXold)); 314 PetscCall(VecDotEnd(dX, dX, &dXdotdX)); 315 PetscCall(VecDotEnd(dXold, dX, &dXdotdXold)); 316 beta = PetscRealPart((dXdotdX - dXdotdXold) / dXolddotdXold); 317 if (beta < 0.0) beta = 0.0; /* restart */ 318 break; 319 case SNES_NCG_HS: /* Hestenes-Stiefel */ 320 PetscCall(VecDotBegin(dX, dX, &dXdotdX)); 321 PetscCall(VecDotBegin(dX, dXold, &dXdotdXold)); 322 PetscCall(VecDotBegin(lX, dX, &lXdotdX)); 323 PetscCall(VecDotBegin(lX, dXold, &lXdotdXold)); 324 PetscCall(VecDotEnd(dX, dX, &dXdotdX)); 325 PetscCall(VecDotEnd(dX, dXold, &dXdotdXold)); 326 PetscCall(VecDotEnd(lX, dX, &lXdotdX)); 327 PetscCall(VecDotEnd(lX, dXold, &lXdotdXold)); 328 beta = PetscRealPart((dXdotdX - dXdotdXold) / (lXdotdX - lXdotdXold)); 329 break; 330 case SNES_NCG_DY: /* Dai-Yuan */ 331 PetscCall(VecDotBegin(dX, dX, &dXdotdX)); 332 PetscCall(VecDotBegin(lX, dX, &lXdotdX)); 333 PetscCall(VecDotBegin(lX, dXold, &lXdotdXold)); 334 PetscCall(VecDotEnd(dX, dX, &dXdotdX)); 335 PetscCall(VecDotEnd(lX, dX, &lXdotdX)); 336 PetscCall(VecDotEnd(lX, dXold, &lXdotdXold)); 337 beta = PetscRealPart(dXdotdX / (lXdotdXold - lXdotdX)); 338 break; 339 case SNES_NCG_CD: /* Conjugate Descent */ 340 PetscCall(VecDotBegin(dX, dX, &dXdotdX)); 341 PetscCall(VecDotBegin(lX, dXold, &lXdotdXold)); 342 PetscCall(VecDotEnd(dX, dX, &dXdotdX)); 343 PetscCall(VecDotEnd(lX, dXold, &lXdotdXold)); 344 beta = PetscRealPart(dXdotdX / lXdotdXold); 345 break; 346 } 347 if (ncg->monitor) PetscCall(PetscViewerASCIIPrintf(ncg->monitor, "beta = %e\n", (double)beta)); 348 PetscCall(VecAYPX(lX, beta, dX)); 349 } 350 PetscFunctionReturn(PETSC_SUCCESS); 351 } 352 353 /*MC 354 SNESNCG - Nonlinear Conjugate-Gradient method for the solution of nonlinear systems {cite}`bruneknepleysmithtu15`. 355 356 Level: beginner 357 358 Options Database Keys: 359 + -snes_ncg_type <fr, prp, dy, hs, cd> - Choice of conjugate-gradient update parameter, default is `prp`. 360 . -snes_linesearch_type <cp,l2,basic> - Line search type. 361 - -snes_ncg_monitor - Print the beta values nonlinear Conjugate-Gradient used in the iteration, . 362 363 Notes: 364 This solves the nonlinear system of equations $ F(x) = 0 $ using the nonlinear generalization of the conjugate 365 gradient method. This may be used with a nonlinear preconditioner used to pick the new search directions, but otherwise 366 chooses the initial search direction as $ F(x) $ for the initial guess $x$. 367 368 Only supports left non-linear preconditioning. 369 370 Default line search is `SNESLINESEARCHCP`, unless a nonlinear preconditioner is used with `-npc_snes_type` <type>, `SNESSetNPC()`, or `SNESGetNPC()` then 371 `SNESLINESEARCHSECANT` is used. Also supports the special-purpose line search `SNESLINESEARCHNCGLINEAR` 372 373 .seealso: [](ch_snes), `SNES`, `SNESNCG`, `SNESCreate()`, `SNES`, `SNESSetType()`, `SNESNEWTONLS`, `SNESNEWTONTR`, `SNESNGMRES`, `SNESQN`, `SNESLINESEARCHNCGLINEAR`, `SNESNCGSetType()`, `SNESLineSearchSetType()` 374 M*/ 375 PETSC_EXTERN PetscErrorCode SNESCreate_NCG(SNES snes) 376 { 377 SNES_NCG *neP; 378 379 PetscFunctionBegin; 380 snes->ops->destroy = SNESDestroy_NCG; 381 snes->ops->setup = SNESSetUp_NCG; 382 snes->ops->setfromoptions = SNESSetFromOptions_NCG; 383 snes->ops->view = SNESView_NCG; 384 snes->ops->solve = SNESSolve_NCG; 385 386 snes->usesksp = PETSC_FALSE; 387 snes->usesnpc = PETSC_TRUE; 388 snes->npcside = PC_LEFT; 389 390 snes->alwayscomputesfinalresidual = PETSC_TRUE; 391 392 PetscCall(SNESParametersInitialize(snes)); 393 PetscObjectParameterSetDefault(snes, max_funcs, 30000); 394 PetscObjectParameterSetDefault(snes, max_its, 10000); 395 PetscObjectParameterSetDefault(snes, stol, 1e-20); 396 397 PetscCall(PetscNew(&neP)); 398 snes->data = (void *)neP; 399 neP->monitor = NULL; 400 neP->type = SNES_NCG_PRP; 401 PetscCall(PetscObjectComposeFunction((PetscObject)snes, "SNESNCGSetType_C", SNESNCGSetType_NCG)); 402 PetscFunctionReturn(PETSC_SUCCESS); 403 } 404