Actual source code: eisen.c

  1: /*
  2:    Defines a  Eisenstat trick SSOR  preconditioner. This uses about
  3:  %50 of the usual amount of floating point ops used for SSOR + Krylov
  4:  method. But it requires actually solving the preconditioned problem
  5:  with both left and right preconditioning.
  6: */
  7: #include <petsc/private/pcimpl.h>

  9: typedef struct {
 10:   Mat       shell, A;
 11:   Vec       b[2], diag; /* temporary storage for true right-hand side */
 12:   PetscReal omega;
 13:   PetscBool usediag; /* indicates preconditioner should include diagonal scaling*/
 14: } PC_Eisenstat;

 16: static PetscErrorCode PCMult_Eisenstat(Mat mat, Vec b, Vec x)
 17: {
 18:   PC            pc;
 19:   PC_Eisenstat *eis;

 21:   PetscFunctionBegin;
 22:   PetscCall(MatShellGetContext(mat, &pc));
 23:   eis = (PC_Eisenstat *)pc->data;
 24:   PetscCall(MatSOR(eis->A, b, eis->omega, SOR_EISENSTAT, 0.0, 1, 1, x));
 25:   PetscCall(MatFactorGetError(eis->A, (MatFactorError *)&pc->failedreason));
 26:   PetscFunctionReturn(PETSC_SUCCESS);
 27: }

 29: static PetscErrorCode PCNorm_Eisenstat(Mat mat, NormType type, PetscReal *nrm)
 30: {
 31:   PC            pc;
 32:   PC_Eisenstat *eis;

 34:   PetscFunctionBegin;
 35:   PetscCall(MatShellGetContext(mat, &pc));
 36:   eis = (PC_Eisenstat *)pc->data;
 37:   PetscCall(MatNorm(eis->A, type, nrm));
 38:   PetscFunctionReturn(PETSC_SUCCESS);
 39: }

 41: static PetscErrorCode PCApply_Eisenstat(PC pc, Vec x, Vec y)
 42: {
 43:   PC_Eisenstat *eis = (PC_Eisenstat *)pc->data;
 44:   PetscBool     hasop;

 46:   PetscFunctionBegin;
 47:   if (eis->usediag) {
 48:     PetscCall(MatHasOperation(pc->pmat, MATOP_MULT_DIAGONAL_BLOCK, &hasop));
 49:     if (hasop) {
 50:       PetscCall(MatMultDiagonalBlock(pc->pmat, x, y));
 51:     } else {
 52:       PetscCall(VecPointwiseMult(y, x, eis->diag));
 53:     }
 54:   } else PetscCall(VecCopy(x, y));
 55:   PetscFunctionReturn(PETSC_SUCCESS);
 56: }

 58: static PetscErrorCode PCApplyTranspose_Eisenstat(PC pc, Vec x, Vec y)
 59: {
 60:   PC_Eisenstat *eis = (PC_Eisenstat *)pc->data;
 61:   PetscBool     hasop, set, sym;

 63:   PetscFunctionBegin;
 64:   PetscCall(MatIsSymmetricKnown(eis->A, &set, &sym));
 65:   PetscCheck(set && sym, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Can only apply transpose of Eisenstat if matrix is symmetric");
 66:   if (eis->usediag) {
 67:     PetscCall(MatHasOperation(pc->pmat, MATOP_MULT_DIAGONAL_BLOCK, &hasop));
 68:     if (hasop) {
 69:       PetscCall(MatMultDiagonalBlock(pc->pmat, x, y));
 70:     } else {
 71:       PetscCall(VecPointwiseMult(y, x, eis->diag));
 72:     }
 73:   } else PetscCall(VecCopy(x, y));
 74:   PetscFunctionReturn(PETSC_SUCCESS);
 75: }

 77: static PetscErrorCode PCPreSolve_Eisenstat(PC pc, KSP ksp, Vec b, Vec x)
 78: {
 79:   PC_Eisenstat *eis = (PC_Eisenstat *)pc->data;
 80:   PetscBool     nonzero;

 82:   PetscFunctionBegin;
 83:   if (pc->presolvedone < 2) {
 84:     PetscCheck(pc->mat == pc->pmat, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Cannot have different mat and pmat");
 85:     /* swap shell matrix and true matrix */
 86:     eis->A  = pc->mat;
 87:     pc->mat = eis->shell;
 88:   }

 90:   if (!eis->b[pc->presolvedone - 1]) PetscCall(VecDuplicate(b, &eis->b[pc->presolvedone - 1]));

 92:   /* if nonzero initial guess, modify x */
 93:   PetscCall(KSPGetInitialGuessNonzero(ksp, &nonzero));
 94:   if (nonzero) {
 95:     PetscCall(VecCopy(x, eis->b[pc->presolvedone - 1]));
 96:     PetscCall(MatSOR(eis->A, eis->b[pc->presolvedone - 1], eis->omega, SOR_APPLY_UPPER, 0.0, 1, 1, x));
 97:     PetscCall(MatFactorGetError(eis->A, (MatFactorError *)&pc->failedreason));
 98:   }

100:   /* save true b, other option is to swap pointers */
101:   PetscCall(VecCopy(b, eis->b[pc->presolvedone - 1]));

103:   /* modify b by (L + D/omega)^{-1} */
104:   PetscCall(MatSOR(eis->A, eis->b[pc->presolvedone - 1], eis->omega, (MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_FORWARD_SWEEP), 0.0, 1, 1, b));
105:   PetscCall(MatFactorGetError(eis->A, (MatFactorError *)&pc->failedreason));
106:   PetscFunctionReturn(PETSC_SUCCESS);
107: }

109: static PetscErrorCode PCPostSolve_Eisenstat(PC pc, KSP ksp, Vec b, Vec x)
110: {
111:   PC_Eisenstat *eis = (PC_Eisenstat *)pc->data;

113:   PetscFunctionBegin;
114:   /* get back true b */
115:   PetscCall(VecCopy(eis->b[pc->presolvedone], b));

117:   /* modify x by (U + D/omega)^{-1} */
118:   PetscCall(VecCopy(x, eis->b[pc->presolvedone]));
119:   PetscCall(MatSOR(eis->A, eis->b[pc->presolvedone], eis->omega, (MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_BACKWARD_SWEEP), 0.0, 1, 1, x));
120:   PetscCall(MatFactorGetError(eis->A, (MatFactorError *)&pc->failedreason));
121:   if (!pc->presolvedone) pc->mat = eis->A;
122:   PetscFunctionReturn(PETSC_SUCCESS);
123: }

125: static PetscErrorCode PCReset_Eisenstat(PC pc)
126: {
127:   PC_Eisenstat *eis = (PC_Eisenstat *)pc->data;

129:   PetscFunctionBegin;
130:   PetscCall(VecDestroy(&eis->b[0]));
131:   PetscCall(VecDestroy(&eis->b[1]));
132:   PetscCall(MatDestroy(&eis->shell));
133:   PetscCall(VecDestroy(&eis->diag));
134:   PetscFunctionReturn(PETSC_SUCCESS);
135: }

137: static PetscErrorCode PCDestroy_Eisenstat(PC pc)
138: {
139:   PetscFunctionBegin;
140:   PetscCall(PCReset_Eisenstat(pc));
141:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCEisenstatSetOmega_C", NULL));
142:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCEisenstatSetNoDiagonalScaling_C", NULL));
143:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCEisenstatGetOmega_C", NULL));
144:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCEisenstatGetNoDiagonalScaling_C", NULL));
145:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCPreSolveChangeRHS_C", NULL));
146:   PetscCall(PetscFree(pc->data));
147:   PetscFunctionReturn(PETSC_SUCCESS);
148: }

150: static PetscErrorCode PCSetFromOptions_Eisenstat(PC pc, PetscOptionItems PetscOptionsObject)
151: {
152:   PC_Eisenstat *eis = (PC_Eisenstat *)pc->data;
153:   PetscBool     set, flg;
154:   PetscReal     omega;

156:   PetscFunctionBegin;
157:   PetscOptionsHeadBegin(PetscOptionsObject, "Eisenstat SSOR options");
158:   PetscCall(PetscOptionsReal("-pc_eisenstat_omega", "Relaxation factor 0 < omega < 2", "PCEisenstatSetOmega", eis->omega, &omega, &flg));
159:   if (flg) PetscCall(PCEisenstatSetOmega(pc, omega));
160:   PetscCall(PetscOptionsBool("-pc_eisenstat_no_diagonal_scaling", "Do not use standard diagonal scaling", "PCEisenstatSetNoDiagonalScaling", eis->usediag ? PETSC_FALSE : PETSC_TRUE, &flg, &set));
161:   if (set) PetscCall(PCEisenstatSetNoDiagonalScaling(pc, flg));
162:   PetscOptionsHeadEnd();
163:   PetscFunctionReturn(PETSC_SUCCESS);
164: }

166: static PetscErrorCode PCView_Eisenstat(PC pc, PetscViewer viewer)
167: {
168:   PC_Eisenstat *eis = (PC_Eisenstat *)pc->data;
169:   PetscBool     isascii;

171:   PetscFunctionBegin;
172:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
173:   if (isascii) {
174:     PetscCall(PetscViewerASCIIPrintf(viewer, "  omega = %g\n", (double)eis->omega));
175:     if (eis->usediag) {
176:       PetscCall(PetscViewerASCIIPrintf(viewer, "  Using diagonal scaling (default)\n"));
177:     } else {
178:       PetscCall(PetscViewerASCIIPrintf(viewer, "  Not using diagonal scaling\n"));
179:     }
180:   }
181:   PetscFunctionReturn(PETSC_SUCCESS);
182: }

184: static PetscErrorCode PCSetUp_Eisenstat(PC pc)
185: {
186:   PetscInt      M, N, m, n;
187:   PetscBool     set, sym;
188:   PC_Eisenstat *eis = (PC_Eisenstat *)pc->data;

190:   PetscFunctionBegin;
191:   if (!pc->setupcalled) {
192:     PetscCall(MatGetSize(pc->mat, &M, &N));
193:     PetscCall(MatGetLocalSize(pc->mat, &m, &n));
194:     PetscCall(MatIsSymmetricKnown(pc->mat, &set, &sym));
195:     PetscCall(MatCreate(PetscObjectComm((PetscObject)pc), &eis->shell));
196:     PetscCall(MatSetSizes(eis->shell, m, n, M, N));
197:     PetscCall(MatSetType(eis->shell, MATSHELL));
198:     PetscCall(MatSetUp(eis->shell));
199:     PetscCall(MatShellSetContext(eis->shell, pc));
200:     PetscCall(MatShellSetOperation(eis->shell, MATOP_MULT, (PetscErrorCodeFn *)PCMult_Eisenstat));
201:     if (set && sym) PetscCall(MatShellSetOperation(eis->shell, MATOP_MULT_TRANSPOSE, (PetscErrorCodeFn *)PCMult_Eisenstat));
202:     PetscCall(MatShellSetOperation(eis->shell, MATOP_NORM, (PetscErrorCodeFn *)PCNorm_Eisenstat));
203:   }
204:   if (!eis->usediag) PetscFunctionReturn(PETSC_SUCCESS);
205:   if (!pc->setupcalled) PetscCall(MatCreateVecs(pc->pmat, &eis->diag, NULL));
206:   PetscCall(MatGetDiagonal(pc->pmat, eis->diag));
207:   PetscFunctionReturn(PETSC_SUCCESS);
208: }

210: static PetscErrorCode PCEisenstatSetOmega_Eisenstat(PC pc, PetscReal omega)
211: {
212:   PC_Eisenstat *eis = (PC_Eisenstat *)pc->data;

214:   PetscFunctionBegin;
215:   PetscCheck(omega > 0.0 && omega < 2.0, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Relaxation out of range");
216:   eis->omega = omega;
217:   PetscFunctionReturn(PETSC_SUCCESS);
218: }

220: static PetscErrorCode PCEisenstatSetNoDiagonalScaling_Eisenstat(PC pc, PetscBool flg)
221: {
222:   PC_Eisenstat *eis = (PC_Eisenstat *)pc->data;

224:   PetscFunctionBegin;
225:   eis->usediag = flg;
226:   PetscFunctionReturn(PETSC_SUCCESS);
227: }

229: static PetscErrorCode PCEisenstatGetOmega_Eisenstat(PC pc, PetscReal *omega)
230: {
231:   PC_Eisenstat *eis = (PC_Eisenstat *)pc->data;

233:   PetscFunctionBegin;
234:   *omega = eis->omega;
235:   PetscFunctionReturn(PETSC_SUCCESS);
236: }

238: static PetscErrorCode PCEisenstatGetNoDiagonalScaling_Eisenstat(PC pc, PetscBool *flg)
239: {
240:   PC_Eisenstat *eis = (PC_Eisenstat *)pc->data;

242:   PetscFunctionBegin;
243:   *flg = eis->usediag;
244:   PetscFunctionReturn(PETSC_SUCCESS);
245: }

247: /*@
248:   PCEisenstatSetOmega - Sets the SSOR relaxation coefficient, omega,
249:   to use with Eisenstat's trick (where omega = 1.0 by default)

251:   Logically Collective

253:   Input Parameters:
254: + pc    - the preconditioner context
255: - omega - relaxation coefficient (0 < omega < 2)

257:   Options Database Key:
258: . -pc_eisenstat_omega <omega> - Sets omega

260:   Level: intermediate

262:   Notes:
263:   The Eisenstat trick implementation of SSOR requires about 50% of the
264:   usual amount of floating point operations used for SSOR + Krylov method;
265:   however, the preconditioned problem must be solved with both left
266:   and right preconditioning.

268:   To use SSOR without the Eisenstat trick, employ the `PCSOR` preconditioner,
269:   which can be chosen with the database options `-pc_type sor -pc_sor_symmetric`

271: .seealso: [](ch_ksp), `PCSORSetOmega()`, `PCEISENSTAT`
272: @*/
273: PetscErrorCode PCEisenstatSetOmega(PC pc, PetscReal omega)
274: {
275:   PetscFunctionBegin;
278:   PetscTryMethod(pc, "PCEisenstatSetOmega_C", (PC, PetscReal), (pc, omega));
279:   PetscFunctionReturn(PETSC_SUCCESS);
280: }

282: /*@
283:   PCEisenstatSetNoDiagonalScaling - Causes the Eisenstat preconditioner, `PCEISENSTAT`
284:   not to do additional diagonal preconditioning. For matrices with a constant
285:   along the diagonal, this may save a small amount of work.

287:   Logically Collective

289:   Input Parameters:
290: + pc  - the preconditioner context
291: - flg - `PETSC_TRUE` turns off diagonal scaling inside the algorithm

293:   Options Database Key:
294: . -pc_eisenstat_no_diagonal_scaling - Activates `PCEisenstatSetNoDiagonalScaling()`

296:   Level: intermediate

298:   Note:
299:   If you use the `KSPSetDiagonalScaling()` or -ksp_diagonal_scale option then you will
300:   likely want to use this routine since it will save you some unneeded flops.

302: .seealso: [](ch_ksp), `PCEisenstatSetOmega()`, `PCEISENSTAT`
303: @*/
304: PetscErrorCode PCEisenstatSetNoDiagonalScaling(PC pc, PetscBool flg)
305: {
306:   PetscFunctionBegin;
308:   PetscTryMethod(pc, "PCEisenstatSetNoDiagonalScaling_C", (PC, PetscBool), (pc, flg));
309:   PetscFunctionReturn(PETSC_SUCCESS);
310: }

312: /*@
313:   PCEisenstatGetOmega - Gets the SSOR relaxation coefficient, omega,
314:   to use with Eisenstat's trick (where omega = 1.0 by default).

316:   Logically Collective

318:   Input Parameter:
319: . pc - the preconditioner context

321:   Output Parameter:
322: . omega - relaxation coefficient (0 < omega < 2)

324:   Options Database Key:
325: . -pc_eisenstat_omega <omega> - Sets omega

327:   Notes:
328:   The Eisenstat trick implementation of SSOR requires about 50% of the
329:   usual amount of floating point operations used for SSOR + Krylov method;
330:   however, the preconditioned problem must be solved with both left
331:   and right preconditioning.

333:   To use SSOR without the Eisenstat trick, employ the PCSOR preconditioner,
334:   which can be chosen with the database options `-pc_type sor -pc_sor_symmetric`

336:   Level: intermediate

338: .seealso: [](ch_ksp), `PCEISENSTAT`, `PCSORGetOmega()`, `PCEisenstatSetOmega()`
339: @*/
340: PetscErrorCode PCEisenstatGetOmega(PC pc, PetscReal *omega)
341: {
342:   PetscFunctionBegin;
344:   PetscUseMethod(pc, "PCEisenstatGetOmega_C", (PC, PetscReal *), (pc, omega));
345:   PetscFunctionReturn(PETSC_SUCCESS);
346: }

348: /*@
349:   PCEisenstatGetNoDiagonalScaling - Tells if the Eisenstat preconditioner
350:   not to do additional diagonal preconditioning. For matrices with a constant
351:   along the diagonal, this may save a small amount of work.

353:   Logically Collective

355:   Input Parameter:
356: . pc - the preconditioner context

358:   Output Parameter:
359: . flg - `PETSC_TRUE` means there is no diagonal scaling applied

361:   Options Database Key:
362: . -pc_eisenstat_no_diagonal_scaling - Activates `PCEisenstatSetNoDiagonalScaling()`

364:   Level: intermediate

366:   Note:
367:   If you use the KSPSetDiagonalScaling() or -ksp_diagonal_scale option then you will
368:   likely want to use this routine since it will save you some unneeded flops.

370: .seealso: , `PCEISENSTAT`, `PCEisenstatGetOmega()`
371: @*/
372: PetscErrorCode PCEisenstatGetNoDiagonalScaling(PC pc, PetscBool *flg)
373: {
374:   PetscFunctionBegin;
376:   PetscUseMethod(pc, "PCEisenstatGetNoDiagonalScaling_C", (PC, PetscBool *), (pc, flg));
377:   PetscFunctionReturn(PETSC_SUCCESS);
378: }

380: static PetscErrorCode PCPreSolveChangeRHS_Eisenstat(PC pc, PetscBool *change)
381: {
382:   PetscFunctionBegin;
383:   *change = PETSC_TRUE;
384:   PetscFunctionReturn(PETSC_SUCCESS);
385: }

387: /*MC
388:      PCEISENSTAT - An implementation of SSOR (symmetric successive over relaxation, symmetric Gauss-Seidel)
389:                    preconditioning that incorporates Eisenstat's trick to reduce the amount of computation needed.

391:    Options Database Keys:
392: +  -pc_eisenstat_omega <omega> - Sets omega
393: -  -pc_eisenstat_no_diagonal_scaling - Activates `PCEisenstatSetNoDiagonalScaling()`

395:    Level: beginner

397:    Notes:
398:    Only implemented for the `MATAIJ` matrix format.

400:    Not a true parallel SOR, in parallel this implementation corresponds to block Jacobi with SOR on each block.

402:    Developer Note:
403:    Since this algorithm runs the Krylov method on a transformed linear system the implementation provides `PCPreSolve()` and `PCPostSolve()`
404:    routines that `KSP` uses to set up the transformed linear system.

406: .seealso: [](ch_ksp), `PCCreate()`, `PCSetType()`, `PCType`, `PC`, `PCEisenstatGetOmega()`,
407:           `PCEisenstatSetNoDiagonalScaling()`, `PCEisenstatSetOmega()`, `PCSOR`
408: M*/

410: PETSC_EXTERN PetscErrorCode PCCreate_Eisenstat(PC pc)
411: {
412:   PC_Eisenstat *eis;

414:   PetscFunctionBegin;
415:   PetscCall(PetscNew(&eis));

417:   pc->ops->apply           = PCApply_Eisenstat;
418:   pc->ops->applytranspose  = PCApplyTranspose_Eisenstat;
419:   pc->ops->presolve        = PCPreSolve_Eisenstat;
420:   pc->ops->postsolve       = PCPostSolve_Eisenstat;
421:   pc->ops->applyrichardson = NULL;
422:   pc->ops->setfromoptions  = PCSetFromOptions_Eisenstat;
423:   pc->ops->destroy         = PCDestroy_Eisenstat;
424:   pc->ops->reset           = PCReset_Eisenstat;
425:   pc->ops->view            = PCView_Eisenstat;
426:   pc->ops->setup           = PCSetUp_Eisenstat;

428:   pc->data     = eis;
429:   eis->omega   = 1.0;
430:   eis->b[0]    = NULL;
431:   eis->b[1]    = NULL;
432:   eis->diag    = NULL;
433:   eis->usediag = PETSC_TRUE;

435:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCEisenstatSetOmega_C", PCEisenstatSetOmega_Eisenstat));
436:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCEisenstatSetNoDiagonalScaling_C", PCEisenstatSetNoDiagonalScaling_Eisenstat));
437:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCEisenstatGetOmega_C", PCEisenstatGetOmega_Eisenstat));
438:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCEisenstatGetNoDiagonalScaling_C", PCEisenstatGetNoDiagonalScaling_Eisenstat));
439:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCPreSolveChangeRHS_C", PCPreSolveChangeRHS_Eisenstat));
440:   PetscFunctionReturn(PETSC_SUCCESS);
441: }