Actual source code: pod.c

petsc-3.12.2 2019-11-22
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  1:  #include <petsc/private/kspimpl.h>
  2:  #include <petsc/private/matimpl.h>
  3:  #include <petscblaslapack.h>
  4: static PetscBool  cited = PETSC_FALSE;
  5: static const char citation[] =
  6: "@phdthesis{zampini2010non,\n"
  7: "  title={Non-overlapping Domain Decomposition Methods for Cardiac Reaction-Diffusion Models and Applications},\n"
  8: "  author={Zampini, S},\n"
  9: "  year={2010},\n"
 10: "  school={PhD thesis, Universita degli Studi di Milano}\n"
 11: "}\n";

 13: typedef struct {
 14:   PetscInt     maxn;             /* maximum number of snapshots */
 15:   PetscInt     n;                /* number of active snapshots */
 16:   PetscInt     curr;             /* current tip of snapshots set */
 17:   Vec          *xsnap;           /* snapshots */
 18:   Vec          *bsnap;           /* rhs snapshots */
 19:   PetscScalar  *dots_iallreduce;
 20:   MPI_Request  req_iallreduce;
 21:   PetscInt     ndots_iallreduce; /* if we have iallreduce we can hide the VecMDot communications */
 22:   PetscReal    tol;              /* relative tolerance to retain eigenvalues */
 23:   PetscBool    Aspd;             /* if true, uses the SPD operator as inner product */
 24:   PetscScalar  *corr;            /* correlation matrix */
 25:   PetscReal    *eigs;            /* eigenvalues */
 26:   PetscScalar  *eigv;            /* eigenvectors */
 27:   PetscBLASInt nen;              /* dimension of lower dimensional system */
 28:   PetscInt     st;               /* first eigenvector of correlation matrix to be retained */
 29:   PetscBLASInt *iwork;           /* integer work vector */
 30:   PetscScalar  *yhay;            /* Y^H * A * Y */
 31:   PetscScalar  *low;             /* lower dimensional linear system */
 32: #if defined(PETSC_USE_COMPLEX)
 33:   PetscReal    *rwork;
 34: #endif
 35:   PetscBLASInt lwork;
 36:   PetscScalar  *swork;
 37:   PetscBool    monitor;
 38: } KSPGuessPOD;

 40: static PetscErrorCode KSPGuessReset_POD(KSPGuess guess)
 41: {
 42:   KSPGuessPOD    *pod = (KSPGuessPOD*)guess->data;
 44:   PetscLayout    Alay = NULL,vlay = NULL;
 45:   PetscBool      cong;

 48:   pod->nen  = 0;
 49:   pod->n    = 0;
 50:   pod->curr = 0;
 51:   /* need to wait for completion of outstanding requests */
 52:   if (pod->ndots_iallreduce) {
 53:     MPI_Wait(&pod->req_iallreduce,MPI_STATUS_IGNORE);
 54:   }
 55:   pod->ndots_iallreduce = 0;
 56:   /* destroy vectors if the size of the linear system has changed */
 57:   if (guess->A) {
 58:     MatGetLayouts(guess->A,&Alay,NULL);
 59:   }
 60:   if (pod->xsnap) {
 61:     VecGetLayout(pod->xsnap[0],&vlay);
 62:   }
 63:   cong = PETSC_FALSE;
 64:   if (vlay && Alay) {
 65:     PetscLayoutCompare(Alay,vlay,&cong);
 66:   }
 67:   if (!cong) {
 68:     VecDestroyVecs(pod->maxn,&pod->xsnap);
 69:     VecDestroyVecs(pod->maxn,&pod->bsnap);
 70:   }
 71:   return(0);
 72: }

 74: static PetscErrorCode KSPGuessSetUp_POD(KSPGuess guess)
 75: {
 76:   KSPGuessPOD    *pod = (KSPGuessPOD*)guess->data;

 80:   if (!pod->corr) {
 81:     PetscScalar  sdummy;
 82:     PetscReal    rdummy = 0;
 83:     PetscBLASInt bN,lierr,idummy;

 85:     PetscCalloc6(pod->maxn*pod->maxn,&pod->corr,pod->maxn,&pod->eigs,pod->maxn*pod->maxn,&pod->eigv,
 86:                         6*pod->maxn,&pod->iwork,pod->maxn*pod->maxn,&pod->yhay,pod->maxn*pod->maxn,&pod->low);
 87: #if defined(PETSC_USE_COMPLEX)
 88:     PetscMalloc1(7*pod->maxn,&pod->rwork);
 89: #endif
 90: #if defined(PETSC_HAVE_MPI_IALLREDUCE)
 91:     PetscMalloc1(3*pod->maxn,&pod->dots_iallreduce);
 92: #endif
 93:     pod->lwork = -1;
 94:     PetscBLASIntCast(pod->maxn,&bN);
 95: #if !defined(PETSC_USE_COMPLEX)
 96:     PetscStackCallBLAS("LAPACKsyevx",LAPACKsyevx_("V","A","L",&bN,pod->corr,&bN,&rdummy,&rdummy,&idummy,&idummy,
 97:                                                   &rdummy,&idummy,pod->eigs,pod->eigv,&bN,&sdummy,&pod->lwork,pod->iwork,pod->iwork+5*bN,&lierr));
 98: #else
 99:     PetscStackCallBLAS("LAPACKsyevx",LAPACKsyevx_("V","A","L",&bN,pod->corr,&bN,&rdummy,&rdummy,&idummy,&idummy,
100:                                                   &rdummy,&idummy,pod->eigs,pod->eigv,&bN,&sdummy,&pod->lwork,pod->rwork,pod->iwork,pod->iwork+5*bN,&lierr));
101: #endif
102:     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYEV Lapack routine %d",(int)lierr);
103:     PetscBLASIntCast((PetscInt)PetscRealPart(sdummy),&pod->lwork);
104:     PetscMalloc1(pod->lwork+PetscMax(bN*bN,6*bN),&pod->swork);
105:   }
106:   /* work vectors are sequential, we explicitly use MPI_Allreduce */
107:   if (!pod->xsnap) {
108:     VecType   type;
109:     Vec       *v,vseq;
110:     PetscInt  n;

112:     KSPCreateVecs(guess->ksp,1,&v,0,NULL);
113:     VecCreate(PETSC_COMM_SELF,&vseq);
114:     VecGetLocalSize(v[0],&n);
115:     VecSetSizes(vseq,n,n);
116:     VecGetType(v[0],&type);
117:     VecSetType(vseq,type);
118:     VecDestroyVecs(1,&v);
119:     VecDuplicateVecs(vseq,pod->maxn,&pod->xsnap);
120:     VecDestroy(&vseq);
121:     PetscLogObjectParents(guess,pod->maxn,pod->xsnap);
122:   }
123:   if (!pod->bsnap) {
124:     VecDuplicateVecs(pod->xsnap[0],pod->maxn,&pod->bsnap);
125:     PetscLogObjectParents(guess,pod->maxn,pod->bsnap);
126:   }
127:   return(0);
128: }

130: static PetscErrorCode KSPGuessDestroy_POD(KSPGuess guess)
131: {
132:   KSPGuessPOD *pod = (KSPGuessPOD*)guess->data;
133:   PetscErrorCode  ierr;

136:   PetscFree6(pod->corr,pod->eigs,pod->eigv,pod->iwork,
137:                     pod->yhay,pod->low);
138: #if defined(PETSC_USE_COMPLEX)
139:   PetscFree(pod->rwork);
140: #endif
141:   /* need to wait for completion before destroying dots_iallreduce */
142:   if (pod->ndots_iallreduce) {
143:     MPI_Wait(&pod->req_iallreduce,MPI_STATUS_IGNORE);
144:   }
145:   PetscFree(pod->dots_iallreduce);
146:   PetscFree(pod->swork);
147:   VecDestroyVecs(pod->maxn,&pod->bsnap);
148:   VecDestroyVecs(pod->maxn,&pod->xsnap);
149:   PetscFree(pod);
150:   return(0);
151: }

153: static PetscErrorCode KSPGuessUpdate_POD(KSPGuess,Vec,Vec);

155: static PetscErrorCode KSPGuessFormGuess_POD(KSPGuess guess,Vec b,Vec x)
156: {
157:   KSPGuessPOD    *pod = (KSPGuessPOD*)guess->data;
159:   PetscScalar    one = 1, zero = 0, *array;
160:   PetscBLASInt   bN,ione = 1,bNen,lierr;
161:   PetscInt       i;

164:   PetscCitationsRegister(citation,&cited);
165:   if (pod->ndots_iallreduce) { /* complete communication and project the linear system */
166:     KSPGuessUpdate_POD(guess,NULL,NULL);
167:   }
168:   if (!pod->nen) return(0);
169:   /* b_low = S * V^T * X^T * b */
170:   VecGetArrayRead(b,(const PetscScalar**)&array);
171:   VecPlaceArray(pod->bsnap[pod->curr],array);
172:   VecRestoreArrayRead(b,(const PetscScalar**)&array);
173:   VecMDot(pod->bsnap[pod->curr],pod->n,pod->xsnap,pod->swork);
174:   VecResetArray(pod->bsnap[pod->curr]);
175:   MPIU_Allreduce(pod->swork,pod->swork + pod->n,pod->n,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)guess));
176:   PetscBLASIntCast(pod->n,&bN);
177:   PetscBLASIntCast(pod->nen,&bNen);
178:   PetscStackCallBLAS("BLASgemv",BLASgemv_("T",&bN,&bNen,&one,pod->eigv+pod->st*pod->n,&bN,pod->swork+pod->n,&ione,&zero,pod->swork,&ione));
179:   if (pod->monitor) {
180:     PetscPrintf(PetscObjectComm((PetscObject)guess),"  KSPGuessPOD alphas = ");
181:     for (i=0; i<pod->nen; i++) {
182: #if defined(PETSC_USE_COMPLEX)
183:       PetscPrintf(PetscObjectComm((PetscObject)guess),"%g + %g i",(double)PetscRealPart(pod->swork[i]),(double)PetscImaginaryPart(pod->swork[i]));
184: #else
185:       PetscPrintf(PetscObjectComm((PetscObject)guess),"%g ",(double)pod->swork[i]);
186: #endif
187:     }
188:     PetscPrintf(PetscObjectComm((PetscObject)guess),"\n");
189:   }
190:   /* A_low x_low = b_low */
191:   if (!pod->Aspd) { /* A is spd -> LOW = Identity */
192:     KSP       pksp = guess->ksp;
193:     PetscBool tsolve,symm;

195:     if (pod->monitor) {
196:       PetscMPIInt rank;
197:       Mat         L;

199:       MPI_Comm_rank(PetscObjectComm((PetscObject)guess),&rank);
200:       MatCreateSeqDense(PETSC_COMM_SELF,pod->nen,pod->nen,pod->low,&L);
201:       if (!rank) {
202:         MatView(L,NULL);
203:       }
204:       MatDestroy(&L);
205:     }
206:     MatGetOption(guess->A,MAT_SYMMETRIC,&symm);
207:     tsolve = symm ? PETSC_FALSE : pksp->transpose_solve;
208:     PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&bNen,&bNen,pod->low,&bNen,pod->iwork,&lierr));
209:     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)lierr);
210:     PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_(tsolve ? "T" : "N",&bNen,&ione,pod->low,&bNen,pod->iwork,pod->swork,&bNen,&lierr));
211:     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRS Lapack routine %d",(int)lierr);
212:   }
213:   /* x = X * V * S * x_low */
214:   PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&bN,&bNen,&one,pod->eigv+pod->st*pod->n,&bN,pod->swork,&ione,&zero,pod->swork+pod->n,&ione));
215:   if (pod->monitor) {
216:     PetscPrintf(PetscObjectComm((PetscObject)guess),"  KSPGuessPOD sol = ");
217:     for (i=0; i<pod->nen; i++) {
218: #if defined(PETSC_USE_COMPLEX)
219:       PetscPrintf(PetscObjectComm((PetscObject)guess),"%g + %g i",(double)PetscRealPart(pod->swork[i+pod->n]),(double)PetscImaginaryPart(pod->swork[i+pod->n]));
220: #else
221:       PetscPrintf(PetscObjectComm((PetscObject)guess),"%g ",(double)pod->swork[i+pod->n]);
222: #endif
223:     }
224:     PetscPrintf(PetscObjectComm((PetscObject)guess),"\n");
225:   }
226:   VecGetArray(x,&array);
227:   VecPlaceArray(pod->bsnap[pod->curr],array);
228:   VecRestoreArray(x,&array);
229:   VecSet(pod->bsnap[pod->curr],0);
230:   VecMAXPY(pod->bsnap[pod->curr],pod->n,pod->swork+pod->n,pod->xsnap);
231:   VecResetArray(pod->bsnap[pod->curr]);
232:   PetscObjectStateIncrease((PetscObject)x);
233:   return(0);
234: }

236: static PetscErrorCode KSPGuessUpdate_POD(KSPGuess guess, Vec b, Vec x)
237: {
238:   KSPGuessPOD    *pod = (KSPGuessPOD*)guess->data;
239:   PetscScalar    one = 1, zero = 0,*array;
240:   PetscReal      toten, parten, reps = 0; /* dlamch? */
241:   PetscBLASInt   bN,lierr,idummy;
242:   PetscInt       i;

246:   if (pod->ndots_iallreduce) goto complete_request;
247:   pod->n = pod->n < pod->maxn ? pod->n+1 : pod->maxn;
248:   VecCopy(x,pod->xsnap[pod->curr]);
249:   VecGetArray(pod->bsnap[pod->curr],&array);
250:   VecPlaceArray(b,array);
251:   VecRestoreArray(pod->bsnap[pod->curr],&array);
252:   KSP_MatMult(guess->ksp,guess->A,x,b);
253:   VecResetArray(b);
254:   PetscObjectStateIncrease((PetscObject)pod->bsnap[pod->curr]);
255:   if (pod->Aspd) {
256:     VecMDot(pod->xsnap[pod->curr],pod->n,pod->bsnap,pod->swork);
257: #if !defined(PETSC_HAVE_MPI_IALLREDUCE)
258:     MPIU_Allreduce(pod->swork,pod->swork + 3*pod->n,pod->n,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)guess));
259: #else
260:     MPI_Iallreduce(pod->swork,pod->dots_iallreduce,pod->n,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)guess),&pod->req_iallreduce);
261:     pod->ndots_iallreduce = 1;
262: #endif
263:   } else {
264:     PetscInt  off;
265:     PetscBool herm;

267: #if defined(PETSC_USE_COMPLEX)
268:     MatGetOption(guess->A,MAT_HERMITIAN,&herm);
269: #else
270:     MatGetOption(guess->A,MAT_SYMMETRIC,&herm);
271: #endif
272:     off = (guess->ksp->transpose_solve && !herm) ? 2*pod->n : pod->n;

274:     /* TODO: we may want to use a user-defined dot for the correlation matrix */
275:     VecMDot(pod->xsnap[pod->curr],pod->n,pod->xsnap,pod->swork);
276:     VecMDot(pod->bsnap[pod->curr],pod->n,pod->xsnap,pod->swork + off);
277:     if (!herm) {
278:       off  = (off == pod->n) ? 2*pod->n : pod->n;
279:       VecMDot(pod->xsnap[pod->curr],pod->n,pod->bsnap,pod->swork + off);
280: #if !defined(PETSC_HAVE_MPI_IALLREDUCE)
281:       MPIU_Allreduce(pod->swork,pod->swork + 3*pod->n,3*pod->n,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)guess));
282: #else
283:       MPI_Iallreduce(pod->swork,pod->dots_iallreduce,3*pod->n,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)guess),&pod->req_iallreduce);
284:       pod->ndots_iallreduce = 3;
285: #endif
286:     } else {
287: #if !defined(PETSC_HAVE_MPI_IALLREDUCE)
288:       MPIU_Allreduce(pod->swork,pod->swork + 3*pod->n,2*pod->n,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)guess));
289:       for (i=0;i<pod->n;i++) pod->swork[5*pod->n + i] = pod->swork[4*pod->n + i];
290: #else
291:       MPI_Iallreduce(pod->swork,pod->dots_iallreduce,2*pod->n,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)guess),&pod->req_iallreduce);
292:       pod->ndots_iallreduce = 2;
293: #endif
294:     }
295:   }
296:   if (pod->ndots_iallreduce) return(0);

298: complete_request:
299:   if (pod->ndots_iallreduce) {
300:     MPI_Wait(&pod->req_iallreduce,MPI_STATUS_IGNORE);
301:     switch (pod->ndots_iallreduce) {
302:     case 3:
303:       for (i=0;i<pod->n;i++) pod->swork[3*pod->n + i] = pod->dots_iallreduce[         i];
304:       for (i=0;i<pod->n;i++) pod->swork[4*pod->n + i] = pod->dots_iallreduce[  pod->n+i];
305:       for (i=0;i<pod->n;i++) pod->swork[5*pod->n + i] = pod->dots_iallreduce[2*pod->n+i];
306:       break;
307:     case 2:
308:       for (i=0;i<pod->n;i++) pod->swork[3*pod->n + i] = pod->dots_iallreduce[       i];
309:       for (i=0;i<pod->n;i++) pod->swork[4*pod->n + i] = pod->dots_iallreduce[pod->n+i];
310:       for (i=0;i<pod->n;i++) pod->swork[5*pod->n + i] = pod->dots_iallreduce[pod->n+i];
311:       break;
312:     case 1:
313:       for (i=0;i<pod->n;i++) pod->swork[3*pod->n + i] = pod->dots_iallreduce[i];
314:       break;
315:     default:
316:       SETERRQ1(PetscObjectComm((PetscObject)guess),PETSC_ERR_PLIB,"Invalid number of outstanding dots operations: %D",pod->ndots_iallreduce);
317:       break;
318:     }
319:   }
320:   pod->ndots_iallreduce = 0;

322:   /* correlation matrix and Y^H A Y (Galerkin) */
323:   for (i=0;i<pod->n;i++) {
324:     pod->corr[pod->curr*pod->maxn+i] = pod->swork[3*pod->n + i];
325:     pod->corr[i*pod->maxn+pod->curr] = PetscConj(pod->swork[3*pod->n + i]);
326:     if (!pod->Aspd) {
327:       pod->yhay[pod->curr*pod->maxn+i] = pod->swork[4*pod->n + i];
328:       pod->yhay[i*pod->maxn+pod->curr] = PetscConj(pod->swork[5*pod->n + i]);
329:     }
330:   }
331:   /* syevx change the input matrix */
332:   for (i=0;i<pod->n;i++) {
333:     PetscInt j;
334:     for (j=i;j<pod->n;j++) pod->swork[i*pod->n+j] = pod->corr[i*pod->maxn+j];
335:   }
336:   PetscBLASIntCast(pod->n,&bN);
337: #if !defined(PETSC_USE_COMPLEX)
338:   PetscStackCallBLAS("LAPACKsyevx",LAPACKsyevx_("V","A","L",&bN,pod->swork,&bN,
339:                                                 &reps,&reps,&idummy,&idummy,
340:                                                 &reps,&idummy,pod->eigs,pod->eigv,&bN,
341:                                                 pod->swork+bN*bN,&pod->lwork,pod->iwork,pod->iwork+5*bN,&lierr));
342: #else
343:   PetscStackCallBLAS("LAPACKsyevx",LAPACKsyevx_("V","A","L",&bN,pod->swork,&bN,
344:                                                 &reps,&reps,&idummy,&idummy,
345:                                                 &reps,&idummy,pod->eigs,pod->eigv,&bN,
346:                                                 pod->swork+bN*bN,&pod->lwork,pod->rwork,pod->iwork,pod->iwork+5*bN,&lierr));
347: #endif
348:   if (lierr<0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYEV Lapack routine: illegal argument %d",-(int)lierr);
349:   else if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYEV Lapack routine: %d eigenvectors failed to converge",(int)lierr);

351:   /* dimension of lower dimensional system */
352:   pod->st = -1;
353:   for (i=0,toten=0;i<pod->n;i++) {
354:     pod->eigs[i] = PetscMax(pod->eigs[i],0.0);
355:     toten += pod->eigs[i];
356:     if (!pod->eigs[i]) pod->st = i;
357:   }
358:   pod->nen = 0;
359:   for (i=pod->n-1,parten=0;i>pod->st && toten > 0;i--) {
360:     pod->nen++;
361:     parten += pod->eigs[i];
362:     if (parten + toten*pod->tol >= toten) break;
363:   }
364:   pod->st = pod->n - pod->nen;

366:   /* Compute eigv = V * S */
367:   for (i=pod->st;i<pod->n;i++) {
368:     const PetscReal v = 1.0/PetscSqrtReal(pod->eigs[i]);
369:     const PetscInt  st = pod->n*i;
370:     PetscInt        j;

372:     for (j=0;j<pod->n;j++) pod->eigv[st+j] *= v;
373:   }

375:   /* compute S * V^T * X^T * A * X * V * S if needed */
376:   if (pod->nen && !pod->Aspd) {
377:     PetscBLASInt bNen,bMaxN;
378:     PetscInt     st = pod->st*pod->n;
379:     PetscBLASIntCast(pod->nen,&bNen);
380:     PetscBLASIntCast(pod->maxn,&bMaxN);
381:     PetscStackCallBLAS("BLASgemm",BLASgemm_("T","N",&bNen,&bN,&bN,&one,pod->eigv+st,&bN,pod->yhay,&bMaxN,&zero,pod->swork,&bNen));
382:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&bNen,&bNen,&bN,&one,pod->swork,&bNen,pod->eigv+st,&bN,&zero,pod->low,&bNen));
383:   }

385:   if (pod->monitor) {
386:     PetscPrintf(PetscObjectComm((PetscObject)guess),"  KSPGuessPOD: basis %D, energy fractions = ",pod->nen);
387:     for (i=pod->n-1;i>=0;i--) {
388:       PetscPrintf(PetscObjectComm((PetscObject)guess),"%1.6e (%d) ",pod->eigs[i]/toten,i >= pod->st ? 1 : 0);
389:     }
390:     PetscPrintf(PetscObjectComm((PetscObject)guess),"\n");
391: #if defined(PETSC_USE_DEBUG)
392:     for (i=0;i<pod->n;i++) {
393:       Vec v;
394:       PetscInt j;
395:       PetscBLASInt bNen,ione = 1;

397:       VecDuplicate(pod->xsnap[i],&v);
398:       VecCopy(pod->xsnap[i],v);
399:       PetscBLASIntCast(pod->nen,&bNen);
400:       PetscStackCallBLAS("BLASgemv",BLASgemv_("T",&bN,&bNen,&one,pod->eigv+pod->st*pod->n,&bN,pod->corr+pod->maxn*i,&ione,&zero,pod->swork,&ione));
401:       PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&bN,&bNen,&one,pod->eigv+pod->st*pod->n,&bN,pod->swork,&ione,&zero,pod->swork+pod->n,&ione));
402:       for (j=0;j<pod->n;j++) pod->swork[j] = -pod->swork[pod->n+j];
403:       VecMAXPY(v,pod->n,pod->swork,pod->xsnap);
404:       VecDot(v,v,pod->swork);
405:       MPIU_Allreduce(pod->swork,pod->swork + 1,1,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)guess));
406:       PetscPrintf(PetscObjectComm((PetscObject)guess),"  Error projection %D: %g (expected lower than %g)\n",i,(double)PetscRealPart(pod->swork[1]),(double)(toten-parten));
407:       VecDestroy(&v);
408:     }
409: #endif
410:   }
411:   /* new tip */
412:   pod->curr = (pod->curr+1)%pod->maxn;
413:   return(0);
414: }

416: static PetscErrorCode KSPGuessSetFromOptions_POD(KSPGuess guess)
417: {
418:   KSPGuessPOD    *pod = (KSPGuessPOD *)guess->data;

422:   PetscOptionsBegin(PetscObjectComm((PetscObject)guess),((PetscObject)guess)->prefix,"POD initial guess options","KSPGuess");
423:   PetscOptionsInt("-ksp_guess_pod_size","Number of snapshots",NULL,pod->maxn,&pod->maxn,NULL);
424:   PetscOptionsBool("-ksp_guess_pod_monitor","Monitor initial guess generator",NULL,pod->monitor,&pod->monitor,NULL);
425:   PetscOptionsReal("-ksp_guess_pod_tol","Tolerance to retain eigenvectors",NULL,pod->tol,&pod->tol,NULL);
426:   PetscOptionsBool("-ksp_guess_pod_Ainner","Use the operator as inner product (must be SPD)",NULL,pod->Aspd,&pod->Aspd,NULL);
427:   PetscOptionsEnd();
428:   return(0);
429: }

431: static PetscErrorCode KSPGuessView_POD(KSPGuess guess,PetscViewer viewer)
432: {
433:   KSPGuessPOD    *pod = (KSPGuessPOD*)guess->data;
434:   PetscBool      isascii;

438:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
439:   if (isascii) {
440:     PetscViewerASCIIPrintf(viewer,"Max size %D, tolerance %g, Ainner %d\n",pod->maxn,pod->tol,pod->Aspd);
441:   }
442:   return(0);
443: }

445: /*
446:     KSPGUESSPOD - Implements a proper orthogonal decomposition based Galerkin scheme for repeated linear system solves.

448:   The initial guess is obtained by solving a small and dense linear system, obtained by Galerkin projection on a lower dimensional space generated by the previous solutions.
449:   The number of solutions to be retained and the energy tolerance to construct the lower dimensional basis can be specified at command line by -ksp_guess_pod_tol <real> and -ksp_guess_pod_size <int>.

451:   References:
452: .   1. - http://www.math.uni-konstanz.de/numerik/personen/volkwein/teaching/POD-Book.pdf 

454:     Level: intermediate

456: .seealso: KSPGuess, KSPGuessType, KSPGuessCreate(), KSPSetGuess(), KSPGetGuess()
457: @*/
458: PetscErrorCode KSPGuessCreate_POD(KSPGuess guess)
459: {
460:   KSPGuessPOD    *pod;

464:   PetscNewLog(guess,&pod);
465:   pod->maxn   = 10;
466:   pod->tol    = PETSC_MACHINE_EPSILON;
467:   guess->data = pod;

469:   guess->ops->setfromoptions = KSPGuessSetFromOptions_POD;
470:   guess->ops->destroy        = KSPGuessDestroy_POD;
471:   guess->ops->setup          = KSPGuessSetUp_POD;
472:   guess->ops->view           = KSPGuessView_POD;
473:   guess->ops->reset          = KSPGuessReset_POD;
474:   guess->ops->update         = KSPGuessUpdate_POD;
475:   guess->ops->formguess      = KSPGuessFormGuess_POD;
476:   return(0);
477: }