Actual source code: gcr.c

  1: #include <petsc/private/kspimpl.h>

  3: typedef struct {
  4:   PetscInt     restart;
  5:   PetscInt     n_restarts;
  6:   PetscScalar *val;
  7:   Vec         *VV, *SS;
  8:   Vec          R;

 10:   KSPFlexibleModifyPCFn *modifypc;         /* function to modify the preconditioner*/
 11:   PetscCtxDestroyFn     *modifypc_destroy; /* function to destroy the user context for the modifypc function */

 13:   void *modifypc_ctx; /* user defined data for the modifypc function */
 14: } KSP_GCR;

 16: static PetscErrorCode KSPSolve_GCR_cycle(KSP ksp)
 17: {
 18:   KSP_GCR    *ctx = (KSP_GCR *)ksp->data;
 19:   PetscScalar r_dot_v;
 20:   Mat         A, B;
 21:   PC          pc;
 22:   Vec         s, v, r;
 23:   /*
 24:      The residual norm will not be computed when ksp->its > ksp->chknorm hence need to initialize norm_r with some dummy value
 25:   */
 26:   PetscReal norm_r = 0.0, nrm;
 27:   PetscInt  k, i, restart;
 28:   Vec       x;

 30:   PetscFunctionBegin;
 31:   restart = ctx->restart;
 32:   PetscCall(KSPGetPC(ksp, &pc));
 33:   PetscCall(KSPGetOperators(ksp, &A, &B));

 35:   x = ksp->vec_sol;
 36:   r = ctx->R;

 38:   for (k = 0; k < restart; k++) {
 39:     v = ctx->VV[k];
 40:     s = ctx->SS[k];
 41:     if (ctx->modifypc) PetscCall((*ctx->modifypc)(ksp, ksp->its, k, ksp->rnorm, ctx->modifypc_ctx));

 43:     PetscCall(KSP_PCApply(ksp, r, s));    /* s = B^{-1} r */
 44:     PetscCall(KSP_MatMult(ksp, A, s, v)); /* v = A s */

 46:     PetscCall(VecMDot(v, k, ctx->VV, ctx->val));
 47:     for (i = 0; i < k; i++) ctx->val[i] = -ctx->val[i];
 48:     PetscCall(VecMAXPY(v, k, ctx->val, ctx->VV)); /* v = v - sum_{i=0}^{k-1} alpha_i v_i */
 49:     PetscCall(VecMAXPY(s, k, ctx->val, ctx->SS)); /* s = s - sum_{i=0}^{k-1} alpha_i s_i */

 51:     PetscCall(VecDotNorm2(r, v, &r_dot_v, &nrm));
 52:     nrm     = PetscSqrtReal(nrm);
 53:     r_dot_v = r_dot_v / nrm;
 54:     PetscCall(VecScale(v, 1.0 / nrm));
 55:     PetscCall(VecScale(s, 1.0 / nrm));
 56:     PetscCall(VecAXPY(x, r_dot_v, s));
 57:     PetscCall(VecAXPY(r, -r_dot_v, v));
 58:     if (ksp->its > ksp->chknorm && ksp->normtype != KSP_NORM_NONE) {
 59:       PetscCall(VecNorm(r, NORM_2, &norm_r));
 60:       KSPCheckNorm(ksp, norm_r);
 61:     }
 62:     /* update the local counter and the global counter */
 63:     ksp->its++;
 64:     ksp->rnorm = norm_r;

 66:     PetscCall(KSPLogResidualHistory(ksp, norm_r));
 67:     PetscCall(KSPMonitor(ksp, ksp->its, norm_r));

 69:     if (ksp->its - 1 > ksp->chknorm) {
 70:       PetscCall((*ksp->converged)(ksp, ksp->its, norm_r, &ksp->reason, ksp->cnvP));
 71:       if (ksp->reason) break;
 72:     }

 74:     if (ksp->its >= ksp->max_it) {
 75:       ksp->reason = KSP_CONVERGED_ITS;
 76:       break;
 77:     }
 78:   }
 79:   ctx->n_restarts++;
 80:   PetscFunctionReturn(PETSC_SUCCESS);
 81: }

 83: static PetscErrorCode KSPSolve_GCR(KSP ksp)
 84: {
 85:   KSP_GCR  *ctx = (KSP_GCR *)ksp->data;
 86:   Mat       A, B;
 87:   Vec       r, b, x;
 88:   PetscReal norm_r = 0.0;

 90:   PetscFunctionBegin;
 91:   PetscCall(KSPGetOperators(ksp, &A, &B));
 92:   x = ksp->vec_sol;
 93:   b = ksp->vec_rhs;
 94:   r = ctx->R;

 96:   /* compute initial residual */
 97:   PetscCall(KSP_MatMult(ksp, A, x, r));
 98:   PetscCall(VecAYPX(r, -1.0, b)); /* r = b - A x  */
 99:   if (ksp->normtype != KSP_NORM_NONE) {
100:     PetscCall(VecNorm(r, NORM_2, &norm_r));
101:     KSPCheckNorm(ksp, norm_r);
102:   }
103:   ksp->its    = 0;
104:   ksp->rnorm0 = norm_r;

106:   PetscCall(KSPLogResidualHistory(ksp, ksp->rnorm0));
107:   PetscCall(KSPMonitor(ksp, ksp->its, ksp->rnorm0));
108:   PetscCall((*ksp->converged)(ksp, ksp->its, ksp->rnorm0, &ksp->reason, ksp->cnvP));
109:   if (ksp->reason) PetscFunctionReturn(PETSC_SUCCESS);

111:   do {
112:     PetscCall(KSPSolve_GCR_cycle(ksp));
113:     if (ksp->reason) PetscFunctionReturn(PETSC_SUCCESS); /* catch case when convergence occurs inside the cycle */
114:   } while (ksp->its < ksp->max_it);

116:   if (ksp->its >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
117:   PetscFunctionReturn(PETSC_SUCCESS);
118: }

120: static PetscErrorCode KSPView_GCR(KSP ksp, PetscViewer viewer)
121: {
122:   KSP_GCR  *ctx = (KSP_GCR *)ksp->data;
123:   PetscBool isascii;

125:   PetscFunctionBegin;
126:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
127:   if (isascii) {
128:     PetscCall(PetscViewerASCIIPrintf(viewer, "  restart = %" PetscInt_FMT " \n", ctx->restart));
129:     PetscCall(PetscViewerASCIIPrintf(viewer, "  restarts performed = %" PetscInt_FMT " \n", ctx->n_restarts));
130:   }
131:   PetscFunctionReturn(PETSC_SUCCESS);
132: }

134: static PetscErrorCode KSPSetUp_GCR(KSP ksp)
135: {
136:   KSP_GCR  *ctx = (KSP_GCR *)ksp->data;
137:   Mat       A;
138:   PetscBool diagonalscale;

140:   PetscFunctionBegin;
141:   PetscCall(PCGetDiagonalScale(ksp->pc, &diagonalscale));
142:   PetscCheck(!diagonalscale, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "Krylov method %s does not support diagonal scaling", ((PetscObject)ksp)->type_name);

144:   PetscCall(KSPGetOperators(ksp, &A, NULL));
145:   PetscCall(MatCreateVecs(A, &ctx->R, NULL));
146:   PetscCall(VecDuplicateVecs(ctx->R, ctx->restart, &ctx->VV));
147:   PetscCall(VecDuplicateVecs(ctx->R, ctx->restart, &ctx->SS));

149:   PetscCall(PetscMalloc1(ctx->restart, &ctx->val));
150:   PetscFunctionReturn(PETSC_SUCCESS);
151: }

153: static PetscErrorCode KSPReset_GCR(KSP ksp)
154: {
155:   KSP_GCR *ctx = (KSP_GCR *)ksp->data;

157:   PetscFunctionBegin;
158:   PetscCall(VecDestroy(&ctx->R));
159:   PetscCall(VecDestroyVecs(ctx->restart, &ctx->VV));
160:   PetscCall(VecDestroyVecs(ctx->restart, &ctx->SS));
161:   if (ctx->modifypc_destroy) PetscCall((*ctx->modifypc_destroy)(&ctx->modifypc_ctx));
162:   PetscCall(PetscFree(ctx->val));
163:   PetscFunctionReturn(PETSC_SUCCESS);
164: }

166: static PetscErrorCode KSPDestroy_GCR(KSP ksp)
167: {
168:   PetscFunctionBegin;
169:   PetscCall(KSPReset_GCR(ksp));
170:   PetscCall(KSPDestroyDefault(ksp));
171:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGCRSetRestart_C", NULL));
172:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGCRGetRestart_C", NULL));
173:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGCRSetModifyPC_C", NULL));
174:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPFlexibleSetModifyPC_C", NULL));
175:   PetscFunctionReturn(PETSC_SUCCESS);
176: }

178: static PetscErrorCode KSPSetFromOptions_GCR(KSP ksp, PetscOptionItems PetscOptionsObject)
179: {
180:   KSP_GCR  *ctx = (KSP_GCR *)ksp->data;
181:   PetscInt  restart;
182:   PetscBool flg;

184:   PetscFunctionBegin;
185:   PetscOptionsHeadBegin(PetscOptionsObject, "KSP GCR options");
186:   PetscCall(PetscOptionsInt("-ksp_gcr_restart", "Number of Krylov search directions", "KSPGCRSetRestart", ctx->restart, &restart, &flg));
187:   if (flg) PetscCall(KSPGCRSetRestart(ksp, restart));
188:   PetscOptionsHeadEnd();
189:   PetscFunctionReturn(PETSC_SUCCESS);
190: }

192: static PetscErrorCode KSPGCRSetModifyPC_GCR(KSP ksp, KSPFlexibleModifyPCFn *function, void *ctx, PetscCtxDestroyFn *destroy)
193: {
194:   KSP_GCR *gcr = (KSP_GCR *)ksp->data;

196:   PetscFunctionBegin;
198:   gcr->modifypc         = function;
199:   gcr->modifypc_destroy = destroy;
200:   gcr->modifypc_ctx     = ctx;
201:   PetscFunctionReturn(PETSC_SUCCESS);
202: }

204: /*@C
205:   KSPGCRSetModifyPC - Sets the routine used by `KSPGCR` to modify the preconditioner for each iteration

207:   Logically Collective

209:   Input Parameters:
210: + ksp      - iterative context obtained from `KSPCreate()`
211: . function - user defined function to modify the preconditioner, see `KSPFlexibleModifyPCFn`
212: . ctx      - user provided context for the modify preconditioner function
213: - destroy  - the function to use to destroy the user provided application context.

215:   Level: intermediate

217: .seealso: [](ch_ksp), `KSP`, `KSPGCR`, `KSPFlexibleModifyPCFn`, `KSPFGMRESModifyPCFn`, [](sec_flexibleksp)
218:  @*/
219: PetscErrorCode KSPGCRSetModifyPC(KSP ksp, KSPFlexibleModifyPCFn *function, void *ctx, PetscCtxDestroyFn *destroy)
220: {
221:   PetscFunctionBegin;
222:   PetscUseMethod(ksp, "KSPGCRSetModifyPC_C", (KSP, KSPFlexibleModifyPCFn *, void *, PetscCtxDestroyFn *), (ksp, function, ctx, destroy));
223:   PetscFunctionReturn(PETSC_SUCCESS);
224: }

226: static PetscErrorCode KSPGCRSetRestart_GCR(KSP ksp, PetscInt restart)
227: {
228:   KSP_GCR *ctx;

230:   PetscFunctionBegin;
231:   ctx          = (KSP_GCR *)ksp->data;
232:   ctx->restart = restart;
233:   PetscFunctionReturn(PETSC_SUCCESS);
234: }

236: static PetscErrorCode KSPGCRGetRestart_GCR(KSP ksp, PetscInt *restart)
237: {
238:   KSP_GCR *ctx;

240:   PetscFunctionBegin;
241:   ctx      = (KSP_GCR *)ksp->data;
242:   *restart = ctx->restart;
243:   PetscFunctionReturn(PETSC_SUCCESS);
244: }

246: /*@
247:   KSPGCRSetRestart - Sets number of iterations at which `KSPGCR` restarts.

249:   Not Collective

251:   Input Parameters:
252: + ksp     - the Krylov space context
253: - restart - integer restart value

255:   Options Database Key:
256: . -ksp_gcr_restart <restart> - the number of stored vectors to orthogonalize against

258:   Level: intermediate

260:   Note:
261:   The default value is 30.

263:   Developer Note:
264:   The API could be made uniform for all `KSP` methods that have a restart.

266: .seealso: [](ch_ksp), `KSPGCR`, `KSPSetTolerances()`, `KSPGCRGetRestart()`, `KSPGMRESSetRestart()`
267: @*/
268: PetscErrorCode KSPGCRSetRestart(KSP ksp, PetscInt restart)
269: {
270:   PetscFunctionBegin;
271:   PetscTryMethod(ksp, "KSPGCRSetRestart_C", (KSP, PetscInt), (ksp, restart));
272:   PetscFunctionReturn(PETSC_SUCCESS);
273: }

275: /*@
276:   KSPGCRGetRestart - Gets number of iterations at which `KSPGCR` restarts.

278:   Not Collective

280:   Input Parameter:
281: . ksp - the Krylov space context

283:   Output Parameter:
284: . restart - integer restart value

286:   Level: intermediate

288: .seealso: [](ch_ksp), `KSPGCR`, `KSPSetTolerances()`, `KSPGCRSetRestart()`, `KSPGMRESGetRestart()`
289: @*/
290: PetscErrorCode KSPGCRGetRestart(KSP ksp, PetscInt *restart)
291: {
292:   PetscFunctionBegin;
293:   PetscTryMethod(ksp, "KSPGCRGetRestart_C", (KSP, PetscInt *), (ksp, restart));
294:   PetscFunctionReturn(PETSC_SUCCESS);
295: }

297: static PetscErrorCode KSPBuildSolution_GCR(KSP ksp, Vec v, Vec *V)
298: {
299:   Vec x;

301:   PetscFunctionBegin;
302:   x = ksp->vec_sol;
303:   if (v) {
304:     PetscCall(VecCopy(x, v));
305:     if (V) *V = v;
306:   } else if (V) {
307:     *V = ksp->vec_sol;
308:   }
309:   PetscFunctionReturn(PETSC_SUCCESS);
310: }

312: static PetscErrorCode KSPBuildResidual_GCR(KSP ksp, Vec t, Vec v, Vec *V)
313: {
314:   KSP_GCR *ctx;

316:   PetscFunctionBegin;
317:   ctx = (KSP_GCR *)ksp->data;
318:   if (v) {
319:     PetscCall(VecCopy(ctx->R, v));
320:     if (V) *V = v;
321:   } else if (V) {
322:     *V = ctx->R;
323:   }
324:   PetscFunctionReturn(PETSC_SUCCESS);
325: }

327: /*MC
328:    KSPGCR - Implements the preconditioned flexible Generalized Conjugate Residual method {cite}`eisenstat1983variational`. [](sec_flexibleksp),

330:    Options Database Key:
331: .   -ksp_gcr_restart <restart> - the number of stored vectors to orthogonalize against

333:    Level: beginner

335:     Notes:
336:     The GCR Krylov method supports non-symmetric matrices and permits the use of a preconditioner
337:     which may vary from one iteration to the next.

339:     Users can define a method to vary the preconditioner between iterates via `KSPFlexibleSetModifyPC()` or `KSPGCRSetModifyPC()`.

341:     Restarts are solves with x0 not equal to zero. When a restart occurs, the initial starting
342:     solution is given by the current estimate for x which was obtained by the last restart
343:     iterations of the GCR algorithm.

345:     Unlike `KSPGMRES` and `KSPFGMRES`, when using GCR, the solution and residual vector can be directly accessed at any iterate,
346:     with zero computational cost, via a call to `KSPBuildSolution()` and `KSPBuildResidual()` respectively.

348:     This implementation of GCR will only apply the stopping condition test whenever ksp->its > ksp->chknorm,
349:     where ksp->chknorm is specified via the command line argument `-ksp_check_norm_iteration` or via
350:     the function `KSPSetCheckNormIteration()`. Hence the residual norm reported by the monitor and stored
351:     in the residual history will be listed as 0.0 before this iteration. It is actually not 0.0; just not calculated.

353:     The method implemented requires the storage of 2 x restart + 1 vectors, twice as much as `KSPGMRES`.

355:     Support only for right preconditioning.

357:     Contributed by:
358:     Dave May

360: .seealso: [](ch_ksp), [](sec_flexibleksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPGCRSetRestart()`, `KSPGCRGetRestart()`,
361:           `KSPGCRSetRestart()`, `KSPFlexibleSetModifyPC()`, `KSPGCRSetModifyPC()`, `KSPGMRES`, `KSPFGMRES`
362: M*/
363: PETSC_EXTERN PetscErrorCode KSPCreate_GCR(KSP ksp)
364: {
365:   KSP_GCR *ctx;

367:   PetscFunctionBegin;
368:   PetscCall(PetscNew(&ctx));

370:   ctx->restart    = 30;
371:   ctx->n_restarts = 0;
372:   ksp->data       = (void *)ctx;

374:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_RIGHT, 1));
375:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 3));

377:   ksp->ops->setup          = KSPSetUp_GCR;
378:   ksp->ops->solve          = KSPSolve_GCR;
379:   ksp->ops->reset          = KSPReset_GCR;
380:   ksp->ops->destroy        = KSPDestroy_GCR;
381:   ksp->ops->view           = KSPView_GCR;
382:   ksp->ops->setfromoptions = KSPSetFromOptions_GCR;
383:   ksp->ops->buildsolution  = KSPBuildSolution_GCR;
384:   ksp->ops->buildresidual  = KSPBuildResidual_GCR;

386:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGCRSetRestart_C", KSPGCRSetRestart_GCR));
387:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGCRGetRestart_C", KSPGCRGetRestart_GCR));
388:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGCRSetModifyPC_C", KSPGCRSetModifyPC_GCR));
389:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPFlexibleSetModifyPC_C", KSPGCRSetModifyPC_GCR));
390:   PetscFunctionReturn(PETSC_SUCCESS);
391: }