Actual source code: pod.c

petsc-3.9.1 2018-04-29
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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->n    = 0;
 49:   pod->curr = 0;
 50:   /* need to wait for completion of outstanding requests */
 51:   if (pod->ndots_iallreduce) {
 52:     MPI_Wait(&pod->req_iallreduce,MPI_STATUS_IGNORE);
 53:   }
 54:   pod->ndots_iallreduce = 0;
 55:   /* destroy vectors if the size of the linear system has changed */
 56:   if (guess->A) {
 57:     MatGetLayouts(guess->A,&Alay,NULL);
 58:   }
 59:   if (pod->xsnap) {
 60:     VecGetLayout(pod->xsnap[0],&vlay);
 61:   }
 62:   cong = PETSC_FALSE;
 63:   if (vlay && Alay) {
 64:     PetscLayoutCompare(Alay,vlay,&cong);
 65:   }
 66:   if (!cong) {
 67:     VecDestroyVecs(pod->maxn,&pod->xsnap);
 68:     VecDestroyVecs(pod->maxn,&pod->bsnap);
 69:   }
 70:   return(0);
 71: }

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

444: /*
445:     KSPGUESSPOD - Implements a proper orthogonal decomposition based Galerkin scheme for repeated linear system solves.

447:   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.
448:   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>.

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

453:     Level: intermediate

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

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

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