Actual source code: bcgsl.c

petsc-3.5.2 2014-09-08
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  1: /*
  2:  * Implementation of BiCGstab(L) the paper by D.R. Fokkema,
  3:  * "Enhanced implementation of BiCGStab(L) for solving linear systems
  4:  * of equations". This uses tricky delayed updating ideas to prevent
  5:  * round-off buildup.
  6:  *
  7:  * This has not been completely cleaned up into PETSc style.
  8:  *
  9:  * All the BLAS and LAPACK calls below should be removed and replaced with
 10:  * loops and the macros for block solvers converted from LINPACK; there is no way
 11:  * calls to BLAS/LAPACK make sense for size 2, 3, 4, etc.
 12:  */
 13: #include <petsc-private/kspimpl.h>              /*I   "petscksp.h" I*/
 14: #include <../src/ksp/ksp/impls/bcgsl/bcgslimpl.h>
 15: #include <petscblaslapack.h>


 20: static PetscErrorCode  KSPSolve_BCGSL(KSP ksp)
 21: {
 22:   KSP_BCGSL      *bcgsl = (KSP_BCGSL*) ksp->data;
 23:   PetscScalar    alpha, beta, omega, sigma;
 24:   PetscScalar    rho0, rho1;
 25:   PetscReal      kappa0, kappaA, kappa1;
 26:   PetscReal      ghat;
 27:   PetscReal      zeta, zeta0, rnmax_computed, rnmax_true, nrm0;
 28:   PetscBool      bUpdateX;
 29:   PetscInt       maxit;
 30:   PetscInt       h, i, j, k, vi, ell;
 31:   PetscBLASInt   ldMZ,bierr;
 32:   PetscScalar    utb;
 33:   PetscReal      max_s, pinv_tol;

 37:   /* set up temporary vectors */
 38:   vi         = 0;
 39:   ell        = bcgsl->ell;
 40:   bcgsl->vB  = ksp->work[vi]; vi++;
 41:   bcgsl->vRt = ksp->work[vi]; vi++;
 42:   bcgsl->vTm = ksp->work[vi]; vi++;
 43:   bcgsl->vvR = ksp->work+vi; vi += ell+1;
 44:   bcgsl->vvU = ksp->work+vi; vi += ell+1;
 45:   bcgsl->vXr = ksp->work[vi]; vi++;
 46:   PetscBLASIntCast(ell+1,&ldMZ);

 48:   /* Prime the iterative solver */
 49:   KSPInitialResidual(ksp, VX, VTM, VB, VVR[0], ksp->vec_rhs);
 50:   VecNorm(VVR[0], NORM_2, &zeta0);
 51:   rnmax_computed = zeta0;
 52:   rnmax_true     = zeta0;

 54:   (*ksp->converged)(ksp, 0, zeta0, &ksp->reason, ksp->cnvP);
 55:   if (ksp->reason) {
 56:     PetscObjectSAWsTakeAccess((PetscObject)ksp);
 57:     ksp->its   = 0;
 58:     ksp->rnorm = zeta0;
 59:     PetscObjectSAWsGrantAccess((PetscObject)ksp);
 60:     return(0);
 61:   }

 63:   VecSet(VVU[0],0.0);
 64:   alpha = 0.;
 65:   rho0  = omega = 1;

 67:   if (bcgsl->delta>0.0) {
 68:     VecCopy(VX, VXR);
 69:     VecSet(VX,0.0);
 70:     VecCopy(VVR[0], VB);
 71:   } else {
 72:     VecCopy(ksp->vec_rhs, VB);
 73:   }

 75:   /* Life goes on */
 76:   VecCopy(VVR[0], VRT);
 77:   zeta = zeta0;

 79:   KSPGetTolerances(ksp, NULL, NULL, NULL, &maxit);

 81:   for (k=0; k<maxit; k += bcgsl->ell) {
 82:     ksp->its   = k;
 83:     ksp->rnorm = zeta;

 85:     KSPLogResidualHistory(ksp, zeta);
 86:     KSPMonitor(ksp, ksp->its, zeta);

 88:     (*ksp->converged)(ksp, k, zeta, &ksp->reason, ksp->cnvP);
 89:     if (ksp->reason < 0) return(0);
 90:     else if (ksp->reason) break;

 92:     /* BiCG part */
 93:     rho0 = -omega*rho0;
 94:     nrm0 = zeta;
 95:     for (j=0; j<bcgsl->ell; j++) {
 96:       /* rho1 <- r_j' * r_tilde */
 97:       VecDot(VVR[j], VRT, &rho1);
 98:       if (rho1 == 0.0) {
 99:         ksp->reason = KSP_DIVERGED_BREAKDOWN_BICG;
100:         return(0);
101:       }
102:       beta = alpha*(rho1/rho0);
103:       rho0 = rho1;
104:       for (i=0; i<=j; i++) {
105:         /* u_i <- r_i - beta*u_i */
106:         VecAYPX(VVU[i], -beta, VVR[i]);
107:       }
108:       /* u_{j+1} <- inv(K)*A*u_j */
109:       KSP_PCApplyBAorAB(ksp, VVU[j], VVU[j+1], VTM);

111:       VecDot(VVU[j+1], VRT, &sigma);
112:       if (sigma == 0.0) {
113:         ksp->reason = KSP_DIVERGED_BREAKDOWN_BICG;
114:         return(0);
115:       }
116:       alpha = rho1/sigma;

118:       /* x <- x + alpha*u_0 */
119:       VecAXPY(VX, alpha, VVU[0]);

121:       for (i=0; i<=j; i++) {
122:         /* r_i <- r_i - alpha*u_{i+1} */
123:         VecAXPY(VVR[i], -alpha, VVU[i+1]);
124:       }

126:       /* r_{j+1} <- inv(K)*A*r_j */
127:       KSP_PCApplyBAorAB(ksp, VVR[j], VVR[j+1], VTM);

129:       VecNorm(VVR[0], NORM_2, &nrm0);
130:       if (bcgsl->delta>0.0) {
131:         if (rnmax_computed<nrm0) rnmax_computed = nrm0;
132:         if (rnmax_true<nrm0) rnmax_true = nrm0;
133:       }

135:       /* NEW: check for early exit */
136:       (*ksp->converged)(ksp, k+j, nrm0, &ksp->reason, ksp->cnvP);
137:       if (ksp->reason) {
138:         PetscObjectSAWsTakeAccess((PetscObject)ksp);

140:         ksp->its   = k+j;
141:         ksp->rnorm = nrm0;

143:         PetscObjectSAWsGrantAccess((PetscObject)ksp);
144:         if (ksp->reason < 0) return(0);
145:       }
146:     }

148:     /* Polynomial part */
149:     for (i = 0; i <= bcgsl->ell; ++i) {
150:       VecMDot(VVR[i], i+1, VVR, &MZa[i*ldMZ]);
151:     }
152:     /* Symmetrize MZa */
153:     for (i = 0; i <= bcgsl->ell; ++i) {
154:       for (j = i+1; j <= bcgsl->ell; ++j) {
155:         MZa[i*ldMZ+j] = MZa[j*ldMZ+i] = PetscConj(MZa[j*ldMZ+i]);
156:       }
157:     }
158:     /* Copy MZa to MZb */
159:     PetscMemcpy(MZb,MZa,ldMZ*ldMZ*sizeof(PetscScalar));

161:     if (!bcgsl->bConvex || bcgsl->ell==1) {
162:       PetscBLASInt ione = 1,bell;
163:       PetscBLASIntCast(bcgsl->ell,&bell);

165:       AY0c[0] = -1;
166:       if (bcgsl->pinv) {
167: #if defined(PETSC_MISSING_LAPACK_GESVD)
168:         SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GESVD - Lapack routine is unavailable.");
169: #else
170: #  if defined(PETSC_USE_COMPLEX)
171:         PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("A","A",&bell,&bell,&MZa[1+ldMZ],&ldMZ,bcgsl->s,bcgsl->u,&bell,bcgsl->v,&bell,bcgsl->work,&bcgsl->lwork,bcgsl->realwork,&bierr));
172: #  else
173:         PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("A","A",&bell,&bell,&MZa[1+ldMZ],&ldMZ,bcgsl->s,bcgsl->u,&bell,bcgsl->v,&bell,bcgsl->work,&bcgsl->lwork,&bierr));
174: #  endif
175: #endif
176:         if (bierr!=0) {
177:           ksp->reason = KSP_DIVERGED_BREAKDOWN;
178:           return(0);
179:         }
180:         /* Apply pseudo-inverse */
181:         max_s = bcgsl->s[0];
182:         for (i=1; i<bell; i++) {
183:           if (bcgsl->s[i] > max_s) {
184:             max_s = bcgsl->s[i];
185:           }
186:         }
187:         /* tolerance is hardwired to bell*max(s)*PETSC_MACHINE_EPSILON */
188:         pinv_tol = bell*max_s*PETSC_MACHINE_EPSILON;
189:         PetscMemzero(&AY0c[1],bell*sizeof(PetscScalar));
190:         for (i=0; i<bell; i++) {
191:           if (bcgsl->s[i] >= pinv_tol) {
192:             utb=0.;
193:             for (j=0; j<bell; j++) {
194:               utb += MZb[1+j]*bcgsl->u[i*bell+j];
195:             }

197:             for (j=0; j<bell; j++) {
198:               AY0c[1+j] += utb/bcgsl->s[i]*bcgsl->v[j*bell+i];
199:             }
200:           }
201:         }
202:       } else {
203: #if defined(PETSC_MISSING_LAPACK_POTRF)
204:         SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"POTRF - Lapack routine is unavailable.");
205: #else
206:         PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("Lower", &bell, &MZa[1+ldMZ], &ldMZ, &bierr));
207: #endif
208:         if (bierr!=0) {
209:           ksp->reason = KSP_DIVERGED_BREAKDOWN;
210:           return(0);
211:         }
212:         PetscMemcpy(&AY0c[1],&MZb[1],bcgsl->ell*sizeof(PetscScalar));
213:         PetscStackCallBLAS("LAPACKpotrs",LAPACKpotrs_("Lower", &bell, &ione, &MZa[1+ldMZ], &ldMZ, &AY0c[1], &ldMZ, &bierr));
214:       }
215:     } else {
216:       PetscBLASInt ione = 1;
217:       PetscScalar  aone = 1.0, azero = 0.0;
218:       PetscBLASInt neqs;
219:       PetscBLASIntCast(bcgsl->ell-1,&neqs);

221: #if defined(PETSC_MISSING_LAPACK_POTRF)
222:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"POTRF - Lapack routine is unavailable.");
223: #else
224:       PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("Lower", &neqs, &MZa[1+ldMZ], &ldMZ, &bierr));
225: #endif
226:       if (bierr!=0) {
227:         ksp->reason = KSP_DIVERGED_BREAKDOWN;
228:         return(0);
229:       }
230:       PetscMemcpy(&AY0c[1],&MZb[1],(bcgsl->ell-1)*sizeof(PetscScalar));
231:       PetscStackCallBLAS("LAPACKpotrs",LAPACKpotrs_("Lower", &neqs, &ione, &MZa[1+ldMZ], &ldMZ, &AY0c[1], &ldMZ, &bierr));
232:       AY0c[0]          = -1;
233:       AY0c[bcgsl->ell] = 0.;

235:       PetscMemcpy(&AYlc[1],&MZb[1+ldMZ*(bcgsl->ell)],(bcgsl->ell-1)*sizeof(PetscScalar));
236:       PetscStackCallBLAS("LAPACKpotrs",LAPACKpotrs_("Lower", &neqs, &ione, &MZa[1+ldMZ], &ldMZ, &AYlc[1], &ldMZ, &bierr));

238:       AYlc[0]          = 0.;
239:       AYlc[bcgsl->ell] = -1;

241:       PetscStackCallBLAS("BLASgemv",BLASgemv_("NoTr", &ldMZ, &ldMZ, &aone, MZb, &ldMZ, AY0c, &ione, &azero, AYtc, &ione));

243:       kappa0 = PetscRealPart(BLASdot_(&ldMZ, AY0c, &ione, AYtc, &ione));

245:       /* round-off can cause negative kappa's */
246:       if (kappa0<0) kappa0 = -kappa0;
247:       kappa0 = PetscSqrtReal(kappa0);

249:       kappaA = PetscRealPart(BLASdot_(&ldMZ, AYlc, &ione, AYtc, &ione));

251:       PetscStackCallBLAS("BLASgemv",BLASgemv_("noTr", &ldMZ, &ldMZ, &aone, MZb, &ldMZ, AYlc, &ione, &azero, AYtc, &ione));

253:       kappa1 = PetscRealPart(BLASdot_(&ldMZ, AYlc, &ione, AYtc, &ione));

255:       if (kappa1<0) kappa1 = -kappa1;
256:       kappa1 = PetscSqrtReal(kappa1);

258:       if (kappa0!=0.0 && kappa1!=0.0) {
259:         if (kappaA<0.7*kappa0*kappa1) {
260:           ghat = (kappaA<0.0) ?  -0.7*kappa0/kappa1 : 0.7*kappa0/kappa1;
261:         } else {
262:           ghat = kappaA/(kappa1*kappa1);
263:         }
264:         for (i=0; i<=bcgsl->ell; i++) {
265:           AY0c[i] = AY0c[i] - ghat* AYlc[i];
266:         }
267:       }
268:     }

270:     omega = AY0c[bcgsl->ell];
271:     for (h=bcgsl->ell; h>0 && omega==0.0; h--) omega = AY0c[h];
272:     if (omega==0.0) {
273:       ksp->reason = KSP_DIVERGED_BREAKDOWN;
274:       return(0);
275:     }


278:     VecMAXPY(VX, bcgsl->ell,AY0c+1, VVR);
279:     for (i=1; i<=bcgsl->ell; i++) AY0c[i] *= -1.0;
280:     VecMAXPY(VVU[0], bcgsl->ell,AY0c+1, VVU+1);
281:     VecMAXPY(VVR[0], bcgsl->ell,AY0c+1, VVR+1);
282:     for (i=1; i<=bcgsl->ell; i++) AY0c[i] *= -1.0;
283:     VecNorm(VVR[0], NORM_2, &zeta);

285:     /* Accurate Update */
286:     if (bcgsl->delta>0.0) {
287:       if (rnmax_computed<zeta) rnmax_computed = zeta;
288:       if (rnmax_true<zeta) rnmax_true = zeta;

290:       bUpdateX = (PetscBool) (zeta<bcgsl->delta*zeta0 && zeta0<=rnmax_computed);
291:       if ((zeta<bcgsl->delta*rnmax_true && zeta0<=rnmax_true) || bUpdateX) {
292:         /* r0 <- b-inv(K)*A*X */
293:         KSP_PCApplyBAorAB(ksp, VX, VVR[0], VTM);
294:         VecAYPX(VVR[0], -1.0, VB);
295:         rnmax_true = zeta;

297:         if (bUpdateX) {
298:           VecAXPY(VXR,1.0,VX);
299:           VecSet(VX,0.0);
300:           VecCopy(VVR[0], VB);
301:           rnmax_computed = zeta;
302:         }
303:       }
304:     }
305:   }
306:   if (bcgsl->delta>0.0) {
307:     VecAXPY(VX,1.0,VXR);
308:   }

310:   (*ksp->converged)(ksp, k, zeta, &ksp->reason, ksp->cnvP);
311:   if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
312:   return(0);
313: }

317: /*@
318:    KSPBCGSLSetXRes - Sets the parameter governing when
319:    exact residuals will be used instead of computed residuals.

321:    Logically Collective on KSP

323:    Input Parameters:
324: +  ksp - iterative context obtained from KSPCreate
325: -  delta - computed residuals are used alone when delta is not positive

327:    Options Database Keys:

329: .  -ksp_bcgsl_xres delta

331:    Level: intermediate

333: .keywords: KSP, BiCGStab(L), set, exact residuals

335: .seealso: KSPBCGSLSetEll(), KSPBCGSLSetPol()
336: @*/
337: PetscErrorCode  KSPBCGSLSetXRes(KSP ksp, PetscReal delta)
338: {
339:   KSP_BCGSL      *bcgsl = (KSP_BCGSL*)ksp->data;

344:   if (ksp->setupstage) {
345:     if ((delta<=0 && bcgsl->delta>0) || (delta>0 && bcgsl->delta<=0)) {
346:       VecDestroyVecs(ksp->nwork,&ksp->work);
347:       PetscFree5(AY0c,AYlc,AYtc,MZa,MZb);
348:       PetscFree4(bcgsl->work,bcgsl->s,bcgsl->u,bcgsl->v);
349:       ksp->setupstage = KSP_SETUP_NEW;
350:     }
351:   }
352:   bcgsl->delta = delta;
353:   return(0);
354: }

358: /*@
359:    KSPBCGSLSetUsePseudoinverse - Use pseudoinverse (via SVD) to solve polynomial part of update

361:    Logically Collective on KSP

363:    Input Parameters:
364: +  ksp - iterative context obtained from KSPCreate
365: -  use_pinv - set to PETSC_TRUE when using pseudoinverse

367:    Options Database Keys:

369: +  -ksp_bcgsl_pinv - use pseudoinverse

371:    Level: intermediate

373: .keywords: KSP, BiCGStab(L), set, polynomial

375: .seealso: KSPBCGSLSetEll()
376: @*/
377: PetscErrorCode KSPBCGSLSetUsePseudoinverse(KSP ksp,PetscBool use_pinv)
378: {
379:   KSP_BCGSL *bcgsl = (KSP_BCGSL*)ksp->data;

382:   bcgsl->pinv = use_pinv;
383:   return(0);
384: }

388: /*@
389:    KSPBCGSLSetPol - Sets the type of polynomial part will
390:    be used in the BiCGSTab(L) solver.

392:    Logically Collective on KSP

394:    Input Parameters:
395: +  ksp - iterative context obtained from KSPCreate
396: -  uMROR - set to PETSC_TRUE when the polynomial is a convex combination of an MR and an OR step.

398:    Options Database Keys:

400: +  -ksp_bcgsl_cxpoly - use enhanced polynomial
401: .  -ksp_bcgsl_mrpoly - use standard polynomial

403:    Level: intermediate

405: .keywords: KSP, BiCGStab(L), set, polynomial

407: .seealso: @()
408: @*/
409: PetscErrorCode  KSPBCGSLSetPol(KSP ksp, PetscBool uMROR)
410: {
411:   KSP_BCGSL      *bcgsl = (KSP_BCGSL*)ksp->data;


417:   if (!ksp->setupstage) bcgsl->bConvex = uMROR;
418:   else if (bcgsl->bConvex != uMROR) {
419:     /* free the data structures,
420:        then create them again
421:      */
422:     VecDestroyVecs(ksp->nwork,&ksp->work);
423:     PetscFree5(AY0c,AYlc,AYtc,MZa,MZb);
424:     PetscFree4(bcgsl->work,bcgsl->s,bcgsl->u,bcgsl->v);

426:     bcgsl->bConvex  = uMROR;
427:     ksp->setupstage = KSP_SETUP_NEW;
428:   }
429:   return(0);
430: }

434: /*@
435:    KSPBCGSLSetEll - Sets the number of search directions in BiCGStab(L).

437:    Logically Collective on KSP

439:    Input Parameters:
440: +  ksp - iterative context obtained from KSPCreate
441: -  ell - number of search directions

443:    Options Database Keys:

445: .  -ksp_bcgsl_ell ell

447:    Level: intermediate

449:    Notes:
450:    For large ell it is common for the polynomial update problem to become singular (due to happy breakdown for smallish
451:    test problems, but also for larger problems). Consequently, by default, the system is solved by pseudoinverse, which
452:    allows the iteration to complete successfully. See KSPBCGSLSetUsePseudoinverse() to switch to a conventional solve.

454: .keywords: KSP, BiCGStab(L), set, exact residuals,

456: .seealso: KSPBCGSLSetUsePseudoinverse()
457: @*/
458: PetscErrorCode  KSPBCGSLSetEll(KSP ksp, PetscInt ell)
459: {
460:   KSP_BCGSL      *bcgsl = (KSP_BCGSL*)ksp->data;

464:   if (ell < 1) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE, "KSPBCGSLSetEll: second argument must be positive");

467:   if (!ksp->setupstage) bcgsl->ell = ell;
468:   else if (bcgsl->ell != ell) {
469:     /* free the data structures, then create them again */
470:     VecDestroyVecs(ksp->nwork,&ksp->work);
471:     PetscFree5(AY0c,AYlc,AYtc,MZa,MZb);
472:     PetscFree4(bcgsl->work,bcgsl->s,bcgsl->u,bcgsl->v);

474:     bcgsl->ell      = ell;
475:     ksp->setupstage = KSP_SETUP_NEW;
476:   }
477:   return(0);
478: }

482: PetscErrorCode KSPView_BCGSL(KSP ksp, PetscViewer viewer)
483: {
484:   KSP_BCGSL      *bcgsl = (KSP_BCGSL*)ksp->data;
486:   PetscBool      isascii;

489:   PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii);

491:   if (isascii) {
492:     PetscViewerASCIIPrintf(viewer, "  BCGSL: Ell = %D\n", bcgsl->ell);
493:     PetscViewerASCIIPrintf(viewer, "  BCGSL: Delta = %lg\n", bcgsl->delta);
494:   }
495:   return(0);
496: }

500: PetscErrorCode KSPSetFromOptions_BCGSL(KSP ksp)
501: {
502:   KSP_BCGSL      *bcgsl = (KSP_BCGSL*)ksp->data;
504:   PetscInt       this_ell;
505:   PetscReal      delta;
506:   PetscBool      flga = PETSC_FALSE, flg;

509:   /* PetscOptionsBegin/End are called in KSPSetFromOptions. They
510:      don't need to be called here.
511:   */
512:   PetscOptionsHead("KSP BiCGStab(L) Options");

514:   /* Set number of search directions */
515:   PetscOptionsInt("-ksp_bcgsl_ell","Number of Krylov search directions","KSPBCGSLSetEll",bcgsl->ell,&this_ell,&flg);
516:   if (flg) {
517:     KSPBCGSLSetEll(ksp, this_ell);
518:   }

520:   /* Set polynomial type */
521:   PetscOptionsBool("-ksp_bcgsl_cxpoly", "Polynomial part of BiCGStabL is MinRes + OR", "KSPBCGSLSetPol", flga,&flga,NULL);
522:   if (flga) {
523:     KSPBCGSLSetPol(ksp, PETSC_TRUE);
524:   } else {
525:     flg  = PETSC_FALSE;
526:     PetscOptionsBool("-ksp_bcgsl_mrpoly", "Polynomial part of BiCGStabL is MinRes", "KSPBCGSLSetPol", flg,&flg,NULL);
527:     KSPBCGSLSetPol(ksp, PETSC_FALSE);
528:   }

530:   /* Will computed residual be refreshed? */
531:   PetscOptionsReal("-ksp_bcgsl_xres", "Threshold used to decide when to refresh computed residuals", "KSPBCGSLSetXRes", bcgsl->delta, &delta, &flg);
532:   if (flg) {
533:     KSPBCGSLSetXRes(ksp, delta);
534:   }

536:   /* Use pseudoinverse? */
537:   flg  = bcgsl->pinv;
538:   PetscOptionsBool("-ksp_bcgsl_pinv", "Polynomial correction via pseudoinverse", "KSPBCGSLSetUsePseudoinverse",flg,&flg,NULL);
539:   KSPBCGSLSetUsePseudoinverse(ksp,flg);
540:   PetscOptionsTail();
541:   return(0);
542: }

546: PetscErrorCode KSPSetUp_BCGSL(KSP ksp)
547: {
548:   KSP_BCGSL      *bcgsl = (KSP_BCGSL*)ksp->data;
549:   PetscInt       ell    = bcgsl->ell,ldMZ = ell+1;

553:   KSPSetWorkVecs(ksp, 6+2*ell);
554:   PetscMalloc5(ldMZ,&AY0c,ldMZ,&AYlc,ldMZ,&AYtc,ldMZ*ldMZ,&MZa,ldMZ*ldMZ,&MZb);
555:   PetscBLASIntCast(5*ell,&bcgsl->lwork);
556:   PetscMalloc5(bcgsl->lwork,&bcgsl->work,ell,&bcgsl->s,ell*ell,&bcgsl->u,ell*ell,&bcgsl->v,5*ell,&bcgsl->realwork);
557:   return(0);
558: }

562: PetscErrorCode KSPReset_BCGSL(KSP ksp)
563: {
564:   KSP_BCGSL      *bcgsl = (KSP_BCGSL*)ksp->data;

568:   VecDestroyVecs(ksp->nwork,&ksp->work);
569:   PetscFree5(AY0c,AYlc,AYtc,MZa,MZb);
570:   PetscFree5(bcgsl->work,bcgsl->s,bcgsl->u,bcgsl->v,bcgsl->realwork);
571:   return(0);
572: }

576: PetscErrorCode KSPDestroy_BCGSL(KSP ksp)
577: {

581:   KSPReset_BCGSL(ksp);
582:   KSPDestroyDefault(ksp);
583:   return(0);
584: }

586: /*MC
587:      KSPBCGSL - Implements a slight variant of the Enhanced
588:                 BiCGStab(L) algorithm in (3) and (2).  The variation
589:                 concerns cases when either kappa0**2 or kappa1**2 is
590:                 negative due to round-off. Kappa0 has also been pulled
591:                 out of the denominator in the formula for ghat.

593:     References:
594:       1. G.L.G. Sleijpen, H.A. van der Vorst, "An overview of
595:          approaches for the stable computation of hybrid BiCG
596:          methods", Applied Numerical Mathematics: Transactions
597:          f IMACS, 19(3), pp 235-54, 1996.
598:       2. G.L.G. Sleijpen, H.A. van der Vorst, D.R. Fokkema,
599:          "BiCGStab(L) and other hybrid Bi-CG methods",
600:           Numerical Algorithms, 7, pp 75-109, 1994.
601:       3. D.R. Fokkema, "Enhanced implementation of BiCGStab(L)
602:          for solving linear systems of equations", preprint
603:          from www.citeseer.com.

605:    Contributed by: Joel M. Malard, email jm.malard@pnl.gov

607:    Options Database Keys:
608: +  -ksp_bcgsl_ell <ell> Number of Krylov search directions, defaults to 2 -- KSPBCGSLSetEll()
609: .  -ksp_bcgsl_cxpol - Use a convex function of the MinRes and OR polynomials after the BiCG step instead of default MinRes -- KSPBCGSLSetPol()
610: .  -ksp_bcgsl_mrpoly - Use the default MinRes polynomial after the BiCG step  -- KSPBCGSLSetPol()
611: .  -ksp_bcgsl_xres <res> Threshold used to decide when to refresh computed residuals -- KSPBCGSLSetXRes()
612: -  -ksp_bcgsl_pinv <true/false> - (de)activate use of pseudoinverse -- KSPBCGSLSetUsePseudoinverse()

614:    Level: beginner

616: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPFGMRES, KSPBCGS, KSPSetPCSide(), KSPBCGSLSetEll(), KSPBCGSLSetXRes()

618: M*/
621: PETSC_EXTERN PetscErrorCode KSPCreate_BCGSL(KSP ksp)
622: {
624:   KSP_BCGSL      *bcgsl;

627:   /* allocate BiCGStab(L) context */
628:   PetscNewLog(ksp,&bcgsl);
629:   ksp->data = (void*)bcgsl;

631:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
632:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,2);

634:   ksp->ops->setup          = KSPSetUp_BCGSL;
635:   ksp->ops->solve          = KSPSolve_BCGSL;
636:   ksp->ops->reset          = KSPReset_BCGSL;
637:   ksp->ops->destroy        = KSPDestroy_BCGSL;
638:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
639:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
640:   ksp->ops->setfromoptions = KSPSetFromOptions_BCGSL;
641:   ksp->ops->view           = KSPView_BCGSL;

643:   /* Let the user redefine the number of directions vectors */
644:   bcgsl->ell = 2;

646:   /*Choose between a single MR step or an averaged MR/OR */
647:   bcgsl->bConvex = PETSC_FALSE;

649:   bcgsl->pinv = PETSC_TRUE;     /* Use the reliable method by default */

651:   /* Set the threshold for when exact residuals will be used */
652:   bcgsl->delta = 0.0;
653:   return(0);
654: }