Actual source code: neprefine.c

slepc-3.17.2 2022-08-09
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

  6:    This file is part of SLEPc.
  7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
  8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  9: */
 10: /*
 11:    Newton refinement for NEP, simple version
 12: */

 14: #include <slepc/private/nepimpl.h>
 15: #include <slepcblaslapack.h>

 17: #define NREF_MAXIT 10

 19: typedef struct {
 20:   VecScatter    *scatter_id,nst;
 21:   Mat           *A;
 22:   Vec           nv,vg,v,w;
 23:   FN            *fn;
 24: } NEPSimpNRefctx;

 26: typedef struct {
 27:   Mat          M1;
 28:   Vec          M2,M3;
 29:   PetscScalar  M4,m3;
 30: } NEP_REFINE_MATSHELL;

 32: static PetscErrorCode MatMult_FS(Mat M ,Vec x,Vec y)
 33: {
 34:   NEP_REFINE_MATSHELL *ctx;
 35:   PetscScalar         t;

 37:   MatShellGetContext(M,&ctx);
 38:   VecDot(x,ctx->M3,&t);
 39:   t *= ctx->m3/ctx->M4;
 40:   MatMult(ctx->M1,x,y);
 41:   VecAXPY(y,-t,ctx->M2);
 42:   PetscFunctionReturn(0);
 43: }

 45: static PetscErrorCode NEPSimpleNRefSetUp(NEP nep,NEPSimpNRefctx **ctx_)
 46: {
 47:   PetscInt       i,si,j,n0,m0,nloc,*idx1,*idx2,ne;
 48:   IS             is1,is2;
 49:   NEPSimpNRefctx *ctx;
 50:   Vec            v;
 51:   PetscMPIInt    rank,size;
 52:   MPI_Comm       child;

 54:   PetscCalloc1(1,ctx_);
 55:   ctx = *ctx_;
 56:   if (nep->npart==1) {
 57:     ctx->A  = nep->A;
 58:     ctx->fn = nep->f;
 59:     nep->refinesubc = NULL;
 60:     ctx->scatter_id = NULL;
 61:   } else {
 62:     PetscSubcommGetChild(nep->refinesubc,&child);
 63:     PetscMalloc2(nep->nt,&ctx->A,nep->npart,&ctx->scatter_id);

 65:     /* Duplicate matrices */
 66:     for (i=0;i<nep->nt;i++) {
 67:       MatCreateRedundantMatrix(nep->A[i],0,child,MAT_INITIAL_MATRIX,&ctx->A[i]);
 68:       PetscLogObjectParent((PetscObject)nep,(PetscObject)ctx->A[i]);
 69:     }
 70:     MatCreateVecs(ctx->A[0],&ctx->v,NULL);
 71:     PetscLogObjectParent((PetscObject)nep,(PetscObject)ctx->v);

 73:     /* Duplicate FNs */
 74:     PetscMalloc1(nep->nt,&ctx->fn);
 75:     for (i=0;i<nep->nt;i++) FNDuplicate(nep->f[i],child,&ctx->fn[i]);

 77:     /* Create scatters for sending vectors to each subcommucator */
 78:     BVGetColumn(nep->V,0,&v);
 79:     VecGetOwnershipRange(v,&n0,&m0);
 80:     BVRestoreColumn(nep->V,0,&v);
 81:     VecGetLocalSize(ctx->v,&nloc);
 82:     PetscMalloc2(m0-n0,&idx1,m0-n0,&idx2);
 83:     VecCreateMPI(PetscObjectComm((PetscObject)nep),nloc,PETSC_DECIDE,&ctx->vg);
 84:     for (si=0;si<nep->npart;si++) {
 85:       j = 0;
 86:       for (i=n0;i<m0;i++) {
 87:         idx1[j]   = i;
 88:         idx2[j++] = i+nep->n*si;
 89:       }
 90:       ISCreateGeneral(PetscObjectComm((PetscObject)nep),(m0-n0),idx1,PETSC_COPY_VALUES,&is1);
 91:       ISCreateGeneral(PetscObjectComm((PetscObject)nep),(m0-n0),idx2,PETSC_COPY_VALUES,&is2);
 92:       BVGetColumn(nep->V,0,&v);
 93:       VecScatterCreate(v,is1,ctx->vg,is2,&ctx->scatter_id[si]);
 94:       BVRestoreColumn(nep->V,0,&v);
 95:       ISDestroy(&is1);
 96:       ISDestroy(&is2);
 97:     }
 98:     PetscFree2(idx1,idx2);
 99:   }
100:   if (nep->scheme==NEP_REFINE_SCHEME_EXPLICIT) {
101:     MPI_Comm_rank(PetscObjectComm((PetscObject)ctx->A[0]),&rank);
102:     MPI_Comm_size(PetscObjectComm((PetscObject)ctx->A[0]),&size);
103:     if (size>1) {
104:       if (nep->npart==1) BVGetColumn(nep->V,0,&v);
105:       else v = ctx->v;
106:       VecGetOwnershipRange(v,&n0,&m0);
107:       ne = (rank == size-1)?nep->n:0;
108:       VecCreateMPI(PetscObjectComm((PetscObject)ctx->A[0]),ne,PETSC_DECIDE,&ctx->nv);
109:       PetscMalloc1(m0-n0,&idx1);
110:       for (i=n0;i<m0;i++) {
111:         idx1[i-n0] = i;
112:       }
113:       ISCreateGeneral(PetscObjectComm((PetscObject)ctx->A[0]),(m0-n0),idx1,PETSC_COPY_VALUES,&is1);
114:       VecScatterCreate(v,is1,ctx->nv,is1,&ctx->nst);
115:       if (nep->npart==1) BVRestoreColumn(nep->V,0,&v);
116:       PetscFree(idx1);
117:       ISDestroy(&is1);
118:     }
119:   }  PetscFunctionReturn(0);
120: }

122: /*
123:   Gather Eigenpair idx from subcommunicator with color sc
124: */
125: static PetscErrorCode NEPSimpleNRefGatherEigenpair(NEP nep,NEPSimpNRefctx *ctx,PetscInt sc,PetscInt idx,PetscInt *fail)
126: {
127:   PetscMPIInt    nproc,p;
128:   MPI_Comm       comm=((PetscObject)nep)->comm;
129:   Vec            v;
130:   PetscScalar    *array;

132:   MPI_Comm_size(comm,&nproc);
133:   p = (nproc/nep->npart)*(sc+1)+PetscMin(sc+1,nproc%nep->npart)-1;
134:   if (nep->npart>1) {
135:     /* Communicate convergence successful */
136:     MPI_Bcast(fail,1,MPIU_INT,p,comm);
137:     if (!(*fail)) {
138:       /* Process 0 of subcommunicator sc broadcasts the eigenvalue */
139:       MPI_Bcast(&nep->eigr[idx],1,MPIU_SCALAR,p,comm);
140:       /* Gather nep->V[idx] from the subcommuniator sc */
141:       BVGetColumn(nep->V,idx,&v);
142:       if (nep->refinesubc->color==sc) {
143:         VecGetArray(ctx->v,&array);
144:         VecPlaceArray(ctx->vg,array);
145:       }
146:       VecScatterBegin(ctx->scatter_id[sc],ctx->vg,v,INSERT_VALUES,SCATTER_REVERSE);
147:       VecScatterEnd(ctx->scatter_id[sc],ctx->vg,v,INSERT_VALUES,SCATTER_REVERSE);
148:       if (nep->refinesubc->color==sc) {
149:         VecResetArray(ctx->vg);
150:         VecRestoreArray(ctx->v,&array);
151:       }
152:       BVRestoreColumn(nep->V,idx,&v);
153:     }
154:   } else {
155:     if (nep->scheme==NEP_REFINE_SCHEME_EXPLICIT && !(*fail)) MPI_Bcast(&nep->eigr[idx],1,MPIU_SCALAR,p,comm);
156:   }
157:   PetscFunctionReturn(0);
158: }

160: static PetscErrorCode NEPSimpleNRefScatterEigenvector(NEP nep,NEPSimpNRefctx *ctx,PetscInt sc,PetscInt idx)
161: {
162:   Vec            v;
163:   PetscScalar    *array;

165:   if (nep->npart>1) {
166:     BVGetColumn(nep->V,idx,&v);
167:     if (nep->refinesubc->color==sc) {
168:       VecGetArray(ctx->v,&array);
169:       VecPlaceArray(ctx->vg,array);
170:     }
171:     VecScatterBegin(ctx->scatter_id[sc],v,ctx->vg,INSERT_VALUES,SCATTER_FORWARD);
172:     VecScatterEnd(ctx->scatter_id[sc],v,ctx->vg,INSERT_VALUES,SCATTER_FORWARD);
173:     if (nep->refinesubc->color==sc) {
174:       VecResetArray(ctx->vg);
175:       VecRestoreArray(ctx->v,&array);
176:     }
177:     BVRestoreColumn(nep->V,idx,&v);
178:   }
179:   PetscFunctionReturn(0);
180: }

182: static PetscErrorCode NEPSimpleNRefSetUpSystem(NEP nep,NEPSimpNRefctx *ctx,Mat *A,PetscInt idx,Mat *Mt,Mat *T,Mat *P,PetscBool ini,Vec t,Vec v)
183: {
184:   PetscErrorCode      ierr;
185:   PetscInt            i,st,ml,m0,n0,m1,mg;
186:   PetscInt            *dnz,*onz,ncols,*cols2=NULL,*nnz,nt=nep->nt;
187:   PetscScalar         zero=0.0,*coeffs,*coeffs2;
188:   PetscMPIInt         rank,size;
189:   MPI_Comm            comm;
190:   const PetscInt      *cols;
191:   const PetscScalar   *vals,*array;
192:   NEP_REFINE_MATSHELL *fctx;
193:   Vec                 w=ctx->w;
194:   Mat                 M;

196:   PetscMalloc2(nt,&coeffs,nt,&coeffs2);
197:   switch (nep->scheme) {
198:   case NEP_REFINE_SCHEME_SCHUR:
199:     if (ini) {
200:       PetscCalloc1(1,&fctx);
201:       MatGetSize(A[0],&m0,&n0);
202:       MatCreateShell(PetscObjectComm((PetscObject)A[0]),PETSC_DECIDE,PETSC_DECIDE,m0,n0,fctx,T);
203:       MatShellSetOperation(*T,MATOP_MULT,(void(*)(void))MatMult_FS);
204:     } else MatShellGetContext(*T,&fctx);
205:     M=fctx->M1;
206:     break;
207:   case NEP_REFINE_SCHEME_MBE:
208:     M=*T;
209:     break;
210:   case NEP_REFINE_SCHEME_EXPLICIT:
211:     M=*Mt;
212:     break;
213:   }
214:   if (ini) MatDuplicate(A[0],MAT_COPY_VALUES,&M);
215:   else MatCopy(A[0],M,DIFFERENT_NONZERO_PATTERN);
216:   for (i=0;i<nt;i++) FNEvaluateFunction(ctx->fn[i],nep->eigr[idx],coeffs+i);
217:   if (coeffs[0]!=1.0) MatScale(M,coeffs[0]);
218:   for (i=1;i<nt;i++) MatAXPY(M,coeffs[i],A[i],(ini)?nep->mstr:SUBSET_NONZERO_PATTERN);
219:   for (i=0;i<nt;i++) FNEvaluateDerivative(ctx->fn[i],nep->eigr[idx],coeffs2+i);
220:   st = 0;
221:   for (i=0;i<nt && PetscAbsScalar(coeffs2[i])==0.0;i++) st++;
222:   MatMult(A[st],v,w);
223:   if (coeffs2[st]!=1.0) VecScale(w,coeffs2[st]);
224:   for (i=st+1;i<nt;i++) {
225:     MatMult(A[i],v,t);
226:     VecAXPY(w,coeffs2[i],t);
227:   }

229:   switch (nep->scheme) {
230:   case NEP_REFINE_SCHEME_EXPLICIT:
231:     comm = PetscObjectComm((PetscObject)A[0]);
232:     MPI_Comm_rank(comm,&rank);
233:     MPI_Comm_size(comm,&size);
234:     MatGetSize(M,&mg,NULL);
235:     MatGetOwnershipRange(M,&m0,&m1);
236:     if (ini) {
237:       MatCreate(comm,T);
238:       MatGetLocalSize(M,&ml,NULL);
239:       if (rank==size-1) ml++;
240:       MatSetSizes(*T,ml,ml,mg+1,mg+1);
241:       MatSetFromOptions(*T);
242:       MatSetUp(*T);
243:       /* Preallocate M */
244:       if (size>1) {
245:         ierr = MatPreallocateInitialize(comm,ml,ml,dnz,onz);
246:         for (i=m0;i<m1;i++) {
247:           MatGetRow(M,i,&ncols,&cols,NULL);
248:           MatPreallocateSet(i,ncols,cols,dnz,onz);
249:           MatPreallocateSet(i,1,&mg,dnz,onz);
250:           MatRestoreRow(M,i,&ncols,&cols,NULL);
251:         }
252:         if (rank==size-1) {
253:           PetscCalloc1(mg+1,&cols2);
254:           for (i=0;i<mg+1;i++) cols2[i]=i;
255:           MatPreallocateSet(m1,mg+1,cols2,dnz,onz);
256:           PetscFree(cols2);
257:         }
258:         MatMPIAIJSetPreallocation(*T,0,dnz,0,onz);
259:         ierr = MatPreallocateFinalize(dnz,onz);
260:       } else {
261:         PetscCalloc1(mg+1,&nnz);
262:         for (i=0;i<mg;i++) {
263:           MatGetRow(M,i,&ncols,NULL,NULL);
264:           nnz[i] = ncols+1;
265:           MatRestoreRow(M,i,&ncols,NULL,NULL);
266:         }
267:         nnz[mg] = mg+1;
268:         MatSeqAIJSetPreallocation(*T,0,nnz);
269:         PetscFree(nnz);
270:       }
271:       *Mt = M;
272:       *P  = *T;
273:     }

275:     /* Set values */
276:     VecGetArrayRead(w,&array);
277:     for (i=m0;i<m1;i++) {
278:       MatGetRow(M,i,&ncols,&cols,&vals);
279:       MatSetValues(*T,1,&i,ncols,cols,vals,INSERT_VALUES);
280:       MatRestoreRow(M,i,&ncols,&cols,&vals);
281:       MatSetValues(*T,1,&i,1,&mg,array+i-m0,INSERT_VALUES);
282:     }
283:     VecRestoreArrayRead(w,&array);
284:     VecConjugate(v);
285:     MPI_Comm_size(PetscObjectComm((PetscObject)A[0]),&size);
286:     MPI_Comm_rank(PetscObjectComm((PetscObject)A[0]),&rank);
287:     if (size>1) {
288:       if (rank==size-1) {
289:         PetscMalloc1(nep->n,&cols2);
290:         for (i=0;i<nep->n;i++) cols2[i]=i;
291:       }
292:       VecScatterBegin(ctx->nst,v,ctx->nv,INSERT_VALUES,SCATTER_FORWARD);
293:       VecScatterEnd(ctx->nst,v,ctx->nv,INSERT_VALUES,SCATTER_FORWARD);
294:       VecGetArrayRead(ctx->nv,&array);
295:       if (rank==size-1) {
296:         MatSetValues(*T,1,&mg,nep->n,cols2,array,INSERT_VALUES);
297:         MatSetValues(*T,1,&mg,1,&mg,&zero,INSERT_VALUES);
298:       }
299:       VecRestoreArrayRead(ctx->nv,&array);
300:     } else {
301:       PetscMalloc1(m1-m0,&cols2);
302:       for (i=0;i<m1-m0;i++) cols2[i]=m0+i;
303:       VecGetArrayRead(v,&array);
304:       MatSetValues(*T,1,&mg,m1-m0,cols2,array,INSERT_VALUES);
305:       MatSetValues(*T,1,&mg,1,&mg,&zero,INSERT_VALUES);
306:       VecRestoreArrayRead(v,&array);
307:     }
308:     VecConjugate(v);
309:     MatAssemblyBegin(*T,MAT_FINAL_ASSEMBLY);
310:     MatAssemblyEnd(*T,MAT_FINAL_ASSEMBLY);
311:     PetscFree(cols2);
312:     break;
313:   case NEP_REFINE_SCHEME_SCHUR:
314:     fctx->M2 = ctx->w;
315:     fctx->M3 = v;
316:     fctx->m3 = 1.0+PetscConj(nep->eigr[idx])*nep->eigr[idx];
317:     fctx->M4 = PetscConj(nep->eigr[idx]);
318:     fctx->M1 = M;
319:     if (ini) MatDuplicate(M,MAT_COPY_VALUES,P);
320:     else MatCopy(M,*P,SAME_NONZERO_PATTERN);
321:     if (fctx->M4!=0.0) {
322:       VecConjugate(v);
323:       VecPointwiseMult(t,v,w);
324:       VecConjugate(v);
325:       VecScale(t,-fctx->m3/fctx->M4);
326:       MatDiagonalSet(*P,t,ADD_VALUES);
327:     }
328:     break;
329:   case NEP_REFINE_SCHEME_MBE:
330:     *T = M;
331:     *P = M;
332:     break;
333:   }
334:   PetscFree2(coeffs,coeffs2);
335:   PetscFunctionReturn(0);
336: }

338: PetscErrorCode NEPNewtonRefinementSimple(NEP nep,PetscInt *maxits,PetscReal tol,PetscInt k)
339: {
340:   PetscInt            i,n,its,idx=0,*idx_sc,*its_sc,color,*fail_sc;
341:   PetscMPIInt         rank,size;
342:   Mat                 Mt=NULL,T=NULL,P=NULL;
343:   MPI_Comm            comm;
344:   Vec                 r,v,dv,rr=NULL,dvv=NULL,t[2];
345:   const PetscScalar   *array;
346:   PetscScalar         *array2,deig=0.0,tt[2],ttt;
347:   PetscReal           norm,error;
348:   PetscBool           ini=PETSC_TRUE,sc_pend,solved=PETSC_FALSE;
349:   NEPSimpNRefctx      *ctx;
350:   NEP_REFINE_MATSHELL *fctx=NULL;
351:   KSPConvergedReason  reason;

353:   PetscLogEventBegin(NEP_Refine,nep,0,0,0);
354:   NEPSimpleNRefSetUp(nep,&ctx);
355:   its = (maxits)?*maxits:NREF_MAXIT;
356:   if (!nep->refineksp) NEPRefineGetKSP(nep,&nep->refineksp);
357:   if (nep->npart==1) BVGetColumn(nep->V,0,&v);
358:   else v = ctx->v;
359:   VecDuplicate(v,&ctx->w);
360:   VecDuplicate(v,&r);
361:   VecDuplicate(v,&dv);
362:   VecDuplicate(v,&t[0]);
363:   VecDuplicate(v,&t[1]);
364:   if (nep->npart==1) {
365:     BVRestoreColumn(nep->V,0,&v);
366:     PetscObjectGetComm((PetscObject)nep,&comm);
367:   } else PetscSubcommGetChild(nep->refinesubc,&comm);
368:   MPI_Comm_size(comm,&size);
369:   MPI_Comm_rank(comm,&rank);
370:   VecGetLocalSize(r,&n);
371:   PetscMalloc3(nep->npart,&idx_sc,nep->npart,&its_sc,nep->npart,&fail_sc);
372:   for (i=0;i<nep->npart;i++) fail_sc[i] = 0;
373:   for (i=0;i<nep->npart;i++) its_sc[i] = 0;
374:   color = (nep->npart==1)?0:nep->refinesubc->color;

376:   /* Loop performing iterative refinements */
377:   while (!solved) {
378:     for (i=0;i<nep->npart;i++) {
379:       sc_pend = PETSC_TRUE;
380:       if (its_sc[i]==0) {
381:         idx_sc[i] = idx++;
382:         if (idx_sc[i]>=k) {
383:           sc_pend = PETSC_FALSE;
384:         } else NEPSimpleNRefScatterEigenvector(nep,ctx,i,idx_sc[i]);
385:       }  else { /* Gather Eigenpair from subcommunicator i */
386:         NEPSimpleNRefGatherEigenpair(nep,ctx,i,idx_sc[i],&fail_sc[i]);
387:       }
388:       while (sc_pend) {
389:         if (!fail_sc[i]) NEPComputeError(nep,idx_sc[i],NEP_ERROR_RELATIVE,&error);
390:         if (error<=tol || its_sc[i]>=its || fail_sc[i]) {
391:           idx_sc[i] = idx++;
392:           its_sc[i] = 0;
393:           fail_sc[i] = 0;
394:           if (idx_sc[i]<k) NEPSimpleNRefScatterEigenvector(nep,ctx,i,idx_sc[i]);
395:         } else {
396:           sc_pend = PETSC_FALSE;
397:           its_sc[i]++;
398:         }
399:         if (idx_sc[i]>=k) sc_pend = PETSC_FALSE;
400:       }
401:     }
402:     solved = PETSC_TRUE;
403:     for (i=0;i<nep->npart&&solved;i++) solved = PetscNot(idx_sc[i]<k);
404:     if (idx_sc[color]<k) {
405: #if !defined(PETSC_USE_COMPLEX)
407: #endif
408:       if (nep->npart==1) BVGetColumn(nep->V,idx_sc[color],&v);
409:       else v = ctx->v;
410:       NEPSimpleNRefSetUpSystem(nep,ctx,ctx->A,idx_sc[color],&Mt,&T,&P,ini,t[0],v);
411:       NEP_KSPSetOperators(nep->refineksp,T,P);
412:       if (ini) {
413:         KSPSetFromOptions(nep->refineksp);
414:         if (nep->scheme==NEP_REFINE_SCHEME_EXPLICIT) {
415:           MatCreateVecs(T,&dvv,NULL);
416:           VecDuplicate(dvv,&rr);
417:         }
418:         ini = PETSC_FALSE;
419:       }
420:       switch (nep->scheme) {
421:       case NEP_REFINE_SCHEME_EXPLICIT:
422:         MatMult(Mt,v,r);
423:         VecGetArrayRead(r,&array);
424:         if (rank==size-1) {
425:           VecGetArray(rr,&array2);
426:           PetscArraycpy(array2,array,n);
427:           array2[n] = 0.0;
428:           VecRestoreArray(rr,&array2);
429:         } else VecPlaceArray(rr,array);
430:         KSPSolve(nep->refineksp,rr,dvv);
431:         KSPGetConvergedReason(nep->refineksp,&reason);
432:         if (reason>0) {
433:           if (rank != size-1) VecResetArray(rr);
434:           VecRestoreArrayRead(r,&array);
435:           VecGetArrayRead(dvv,&array);
436:           VecPlaceArray(dv,array);
437:           VecAXPY(v,-1.0,dv);
438:           VecNorm(v,NORM_2,&norm);
439:           VecScale(v,1.0/norm);
440:           VecResetArray(dv);
441:           if (rank==size-1) nep->eigr[idx_sc[color]] -= array[n];
442:           VecRestoreArrayRead(dvv,&array);
443:         } else fail_sc[color] = 1;
444:         break;
445:       case NEP_REFINE_SCHEME_MBE:
446:         MatMult(T,v,r);
447:         /* Mixed block elimination */
448:         VecConjugate(v);
449:         KSPSolveTranspose(nep->refineksp,v,t[0]);
450:         KSPGetConvergedReason(nep->refineksp,&reason);
451:         if (reason>0) {
452:           VecConjugate(t[0]);
453:           VecDot(ctx->w,t[0],&tt[0]);
454:           KSPSolve(nep->refineksp,ctx->w,t[1]);
455:           KSPGetConvergedReason(nep->refineksp,&reason);
456:           if (reason>0) {
457:             VecDot(t[1],v,&tt[1]);
458:             VecDot(r,t[0],&ttt);
459:             tt[0] = ttt/tt[0];
460:             VecAXPY(r,-tt[0],ctx->w);
461:             KSPSolve(nep->refineksp,r,dv);
462:             KSPGetConvergedReason(nep->refineksp,&reason);
463:             if (reason>0) {
464:               VecDot(dv,v,&ttt);
465:               tt[1] = ttt/tt[1];
466:               VecAXPY(dv,-tt[1],t[1]);
467:               deig = tt[0]+tt[1];
468:             }
469:           }
470:           VecConjugate(v);
471:           VecAXPY(v,-1.0,dv);
472:           VecNorm(v,NORM_2,&norm);
473:           VecScale(v,1.0/norm);
474:           nep->eigr[idx_sc[color]] -= deig;
475:           fail_sc[color] = 0;
476:         } else {
477:           VecConjugate(v);
478:           fail_sc[color] = 1;
479:         }
480:         break;
481:       case NEP_REFINE_SCHEME_SCHUR:
482:         fail_sc[color] = 1;
483:         MatShellGetContext(T,&fctx);
484:         if (fctx->M4!=0.0) {
485:           MatMult(fctx->M1,v,r);
486:           KSPSolve(nep->refineksp,r,dv);
487:           KSPGetConvergedReason(nep->refineksp,&reason);
488:           if (reason>0) {
489:             VecDot(dv,v,&deig);
490:             deig *= -fctx->m3/fctx->M4;
491:             VecAXPY(v,-1.0,dv);
492:             VecNorm(v,NORM_2,&norm);
493:             VecScale(v,1.0/norm);
494:             nep->eigr[idx_sc[color]] -= deig;
495:             fail_sc[color] = 0;
496:           }
497:         }
498:         break;
499:       }
500:       if (nep->npart==1) BVRestoreColumn(nep->V,idx_sc[color],&v);
501:     }
502:   }
503:   VecDestroy(&t[0]);
504:   VecDestroy(&t[1]);
505:   VecDestroy(&dv);
506:   VecDestroy(&ctx->w);
507:   VecDestroy(&r);
508:   PetscFree3(idx_sc,its_sc,fail_sc);
509:   VecScatterDestroy(&ctx->nst);
510:   if (nep->npart>1) {
511:     VecDestroy(&ctx->vg);
512:     VecDestroy(&ctx->v);
513:     for (i=0;i<nep->nt;i++) MatDestroy(&ctx->A[i]);
514:     for (i=0;i<nep->npart;i++) VecScatterDestroy(&ctx->scatter_id[i]);
515:     PetscFree2(ctx->A,ctx->scatter_id);
516:   }
517:   if (fctx && nep->scheme==NEP_REFINE_SCHEME_SCHUR) {
518:     MatDestroy(&P);
519:     MatDestroy(&fctx->M1);
520:     PetscFree(fctx);
521:   }
522:   if (nep->scheme==NEP_REFINE_SCHEME_EXPLICIT) {
523:     MatDestroy(&Mt);
524:     VecDestroy(&dvv);
525:     VecDestroy(&rr);
526:     VecDestroy(&ctx->nv);
527:     if (nep->npart>1) {
528:       for (i=0;i<nep->nt;i++) FNDestroy(&ctx->fn[i]);
529:       PetscFree(ctx->fn);
530:     }
531:   }
532:   if (nep->scheme==NEP_REFINE_SCHEME_MBE) {
533:     if (nep->npart>1) {
534:       for (i=0;i<nep->nt;i++) FNDestroy(&ctx->fn[i]);
535:       PetscFree(ctx->fn);
536:     }
537:   }
538:   MatDestroy(&T);
539:   PetscFree(ctx);
540:   PetscLogEventEnd(NEP_Refine,nep,0,0,0);
541:   PetscFunctionReturn(0);
542: }