Actual source code: ptoar.c

slepc-3.14.0 2020-09-30
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2020, 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:    SLEPc polynomial eigensolver: "toar"

 13:    Method: TOAR

 15:    Algorithm:

 17:        Two-Level Orthogonal Arnoldi.

 19:    References:

 21:        [1] Y. Su, J. Zhang and Z. Bai, "A compact Arnoldi algorithm for
 22:            polynomial eigenvalue problems", talk presented at RANMEP 2008.

 24:        [2] C. Campos and J.E. Roman, "Parallel Krylov solvers for the
 25:            polynomial eigenvalue problem in SLEPc", SIAM J. Sci. Comput.
 26:            38(5):S385-S411, 2016.

 28:        [3] D. Lu, Y. Su and Z. Bai, "Stability analysis of the two-level
 29:            orthogonal Arnoldi procedure", SIAM J. Matrix Anal. App.
 30:            37(1):195-214, 2016.
 31: */

 33: #include <slepc/private/pepimpl.h>
 34: #include "../src/pep/impls/krylov/pepkrylov.h"
 35: #include <slepcblaslapack.h>

 37: static PetscBool  cited = PETSC_FALSE;
 38: static const char citation[] =
 39:   "@Article{slepc-pep,\n"
 40:   "   author = \"C. Campos and J. E. Roman\",\n"
 41:   "   title = \"Parallel {Krylov} solvers for the polynomial eigenvalue problem in {SLEPc}\",\n"
 42:   "   journal = \"{SIAM} J. Sci. Comput.\",\n"
 43:   "   volume = \"38\",\n"
 44:   "   number = \"5\",\n"
 45:   "   pages = \"S385--S411\",\n"
 46:   "   year = \"2016,\"\n"
 47:   "   doi = \"https://doi.org/10.1137/15M1022458\"\n"
 48:   "}\n";

 50: PetscErrorCode PEPSetUp_TOAR(PEP pep)
 51: {
 53:   PEP_TOAR       *ctx = (PEP_TOAR*)pep->data;
 54:   PetscBool      sinv,flg;
 55:   PetscInt       i;

 58:   PEPCheckShiftSinvert(pep);
 59:   PEPSetDimensions_Default(pep,pep->nev,&pep->ncv,&pep->mpd);
 60:   if (!ctx->lock && pep->mpd<pep->ncv) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Should not use mpd parameter in non-locking variant");
 61:   if (pep->max_it==PETSC_DEFAULT) pep->max_it = PetscMax(100,2*(pep->nmat-1)*pep->n/pep->ncv);
 62:   if (!pep->which) { PEPSetWhichEigenpairs_Default(pep); }
 63:   if (pep->which==PEP_ALL) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"This solver does not support computing all eigenvalues");
 64:   if (pep->problem_type!=PEP_GENERAL) {
 65:     PetscInfo(pep,"Problem type ignored, performing a non-symmetric linearization\n");
 66:   }

 68:   if (!ctx->keep) ctx->keep = 0.5;

 70:   PEPAllocateSolution(pep,pep->nmat-1);
 71:   PEPSetWorkVecs(pep,3);
 72:   DSSetType(pep->ds,DSNHEP);
 73:   DSSetExtraRow(pep->ds,PETSC_TRUE);
 74:   DSAllocate(pep->ds,pep->ncv+1);

 76:   PEPBasisCoefficients(pep,pep->pbc);
 77:   STGetTransform(pep->st,&flg);
 78:   if (!flg) {
 79:     PetscMalloc1(pep->nmat,&pep->solvematcoeffs);
 80:     PetscLogObjectMemory((PetscObject)pep,pep->nmat*sizeof(PetscScalar));
 81:     PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
 82:     if (sinv) {
 83:       PEPEvaluateBasis(pep,pep->target,0,pep->solvematcoeffs,NULL);
 84:     } else {
 85:       for (i=0;i<pep->nmat-1;i++) pep->solvematcoeffs[i] = 0.0;
 86:       pep->solvematcoeffs[pep->nmat-1] = 1.0;
 87:     }
 88:   }
 89:   BVDestroy(&ctx->V);
 90:   BVCreateTensor(pep->V,pep->nmat-1,&ctx->V);
 91:   return(0);
 92: }

 94: /*
 95:   Extend the TOAR basis by applying the the matrix operator
 96:   over a vector which is decomposed in the TOAR way
 97:   Input:
 98:     - pbc: array containing the polynomial basis coefficients
 99:     - S,V: define the latest Arnoldi vector (nv vectors in V)
100:   Output:
101:     - t: new vector extending the TOAR basis
102:     - r: temporary coefficients to compute the TOAR coefficients
103:          for the new Arnoldi vector
104:   Workspace: t_ (two vectors)
105: */
106: static PetscErrorCode PEPTOARExtendBasis(PEP pep,PetscBool sinvert,PetscScalar sigma,PetscScalar *S,PetscInt ls,PetscInt nv,BV V,Vec t,PetscScalar *r,PetscInt lr,Vec *t_)
107: {
109:   PetscInt       nmat=pep->nmat,deg=nmat-1,k,j,off=0,lss;
110:   Vec            v=t_[0],ve=t_[1],q=t_[2];
111:   PetscScalar    alpha=1.0,*ss,a;
112:   PetscReal      *ca=pep->pbc,*cb=pep->pbc+nmat,*cg=pep->pbc+2*nmat;
113:   PetscBool      flg;

116:   BVSetActiveColumns(pep->V,0,nv);
117:   STGetTransform(pep->st,&flg);
118:   if (sinvert) {
119:     for (j=0;j<nv;j++) {
120:       if (deg>1) r[lr+j] = S[j]/ca[0];
121:       if (deg>2) r[2*lr+j] = (S[ls+j]+(sigma-cb[1])*r[lr+j])/ca[1];
122:     }
123:     for (k=2;k<deg-1;k++) {
124:       for (j=0;j<nv;j++) r[(k+1)*lr+j] = (S[k*ls+j]+(sigma-cb[k])*r[k*lr+j]-cg[k]*r[(k-1)*lr+j])/ca[k];
125:     }
126:     k = deg-1;
127:     for (j=0;j<nv;j++) r[j] = (S[k*ls+j]+(sigma-cb[k])*r[k*lr+j]-cg[k]*r[(k-1)*lr+j])/ca[k];
128:     ss = r; lss = lr; off = 1; alpha = -1.0; a = pep->sfactor;
129:   } else {
130:     ss = S; lss = ls; off = 0; alpha = -ca[deg-1]; a = 1.0;
131:   }
132:   BVMultVec(V,1.0,0.0,v,ss+off*lss);
133:   if (pep->Dr) { /* balancing */
134:     VecPointwiseMult(v,v,pep->Dr);
135:   }
136:   STMatMult(pep->st,off,v,q);
137:   VecScale(q,a);
138:   for (j=1+off;j<deg+off-1;j++) {
139:     BVMultVec(V,1.0,0.0,v,ss+j*lss);
140:     if (pep->Dr) {
141:       VecPointwiseMult(v,v,pep->Dr);
142:     }
143:     STMatMult(pep->st,j,v,t);
144:     a *= pep->sfactor;
145:     VecAXPY(q,a,t);
146:   }
147:   if (sinvert) {
148:     BVMultVec(V,1.0,0.0,v,ss);
149:     if (pep->Dr) {
150:       VecPointwiseMult(v,v,pep->Dr);
151:     }
152:     STMatMult(pep->st,deg,v,t);
153:     a *= pep->sfactor;
154:     VecAXPY(q,a,t);
155:   } else {
156:     BVMultVec(V,1.0,0.0,ve,ss+(deg-1)*lss);
157:     if (pep->Dr) {
158:       VecPointwiseMult(ve,ve,pep->Dr);
159:     }
160:     a *= pep->sfactor;
161:     STMatMult(pep->st,deg-1,ve,t);
162:     VecAXPY(q,a,t);
163:     a *= pep->sfactor;
164:   }
165:   if (flg || !sinvert) alpha /= a;
166:   STMatSolve(pep->st,q,t);
167:   VecScale(t,alpha);
168:   if (!sinvert) {
169:     if (cg[deg-1]!=0) { VecAXPY(t,cg[deg-1],v); }
170:     if (cb[deg-1]!=0) { VecAXPY(t,cb[deg-1],ve); }
171:   }
172:   if (pep->Dr) {
173:     VecPointwiseDivide(t,t,pep->Dr);
174:   }
175:   return(0);
176: }

178: /*
179:   Compute TOAR coefficients of the blocks of the new Arnoldi vector computed
180: */
181: static PetscErrorCode PEPTOARCoefficients(PEP pep,PetscBool sinvert,PetscScalar sigma,PetscInt nv,PetscScalar *S,PetscInt ls,PetscScalar *r,PetscInt lr,PetscScalar *x)
182: {
183:   PetscInt    k,j,nmat=pep->nmat,d=nmat-1;
184:   PetscReal   *ca=pep->pbc,*cb=pep->pbc+nmat,*cg=pep->pbc+2*nmat;
185:   PetscScalar t=1.0,tp=0.0,tt;

188:   if (sinvert) {
189:     for (k=1;k<d;k++) {
190:       tt = t;
191:       t = ((sigma-cb[k-1])*t-cg[k-1]*tp)/ca[k-1]; /* k-th basis polynomial */
192:       tp = tt;
193:       for (j=0;j<=nv;j++) r[k*lr+j] += t*x[j];
194:     }
195:   } else {
196:     for (j=0;j<=nv;j++) r[j] = (cb[0]-sigma)*S[j]+ca[0]*S[ls+j];
197:     for (k=1;k<d-1;k++) {
198:       for (j=0;j<=nv;j++) r[k*lr+j] = (cb[k]-sigma)*S[k*ls+j]+ca[k]*S[(k+1)*ls+j]+cg[k]*S[(k-1)*ls+j];
199:     }
200:     if (sigma!=0.0) for (j=0;j<=nv;j++) r[(d-1)*lr+j] -= sigma*S[(d-1)*ls+j];
201:   }
202:   return(0);
203: }

205: /*
206:   Compute a run of Arnoldi iterations dim(work)=ld
207: */
208: static PetscErrorCode PEPTOARrun(PEP pep,PetscScalar sigma,PetscScalar *H,PetscInt ldh,PetscInt k,PetscInt *M,PetscBool *breakdown,Vec *t_)
209: {
211:   PEP_TOAR       *ctx = (PEP_TOAR*)pep->data;
212:   PetscInt       j,m=*M,deg=pep->nmat-1,ld;
213:   PetscInt       lds,nqt,l;
214:   Vec            t;
215:   PetscReal      norm;
216:   PetscBool      flg,sinvert=PETSC_FALSE,lindep;
217:   PetscScalar    *x,*S;
218:   Mat            MS;

221:   BVTensorGetFactors(ctx->V,NULL,&MS);
222:   MatDenseGetArray(MS,&S);
223:   BVGetSizes(pep->V,NULL,NULL,&ld);
224:   lds = ld*deg;
225:   BVGetActiveColumns(pep->V,&l,&nqt);
226:   STGetTransform(pep->st,&flg);
227:   if (!flg) {
228:     /* spectral transformation handled by the solver */
229:     PetscObjectTypeCompareAny((PetscObject)pep->st,&flg,STSINVERT,STSHIFT,"");
230:     if (!flg) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"ST type not supported for TOAR without transforming matrices");
231:     PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinvert);
232:   }
233:   BVSetActiveColumns(ctx->V,0,m);
234:   for (j=k;j<m;j++) {
235:     /* apply operator */
236:     BVGetColumn(pep->V,nqt,&t);
237:     PEPTOARExtendBasis(pep,sinvert,sigma,S+j*lds,ld,nqt,pep->V,t,S+(j+1)*lds,ld,t_);
238:     BVRestoreColumn(pep->V,nqt,&t);

240:     /* orthogonalize */
241:     if (sinvert) x = S+(j+1)*lds;
242:     else x = S+(deg-1)*ld+(j+1)*lds;
243:     BVOrthogonalizeColumn(pep->V,nqt,x,&norm,&lindep);
244:     if (!lindep) {
245:       x[nqt] = norm;
246:       BVScaleColumn(pep->V,nqt,1.0/norm);
247:       nqt++;
248:     }

250:     PEPTOARCoefficients(pep,sinvert,sigma,nqt-1,S+j*lds,ld,S+(j+1)*lds,ld,x);

252:     /* level-2 orthogonalization */
253:     BVOrthogonalizeColumn(ctx->V,j+1,H+j*ldh,&norm,breakdown);
254:     H[j+1+ldh*j] = norm;
255:     if (*breakdown) {
256:       *M = j+1;
257:       break;
258:     }
259:     BVScaleColumn(ctx->V,j+1,1.0/norm);
260:     BVSetActiveColumns(pep->V,l,nqt);
261:   }
262:   BVSetActiveColumns(ctx->V,0,*M);
263:   MatDenseRestoreArray(MS,&S);
264:   BVTensorRestoreFactors(ctx->V,NULL,&MS);
265:   return(0);
266: }

268: /*
269:   Computes T_j = phi_idx(T). In T_j and T_p are phi_{idx-1}(T)
270:    and phi_{idx-2}(T) respectively or null if idx=0,1.
271:    Tp and Tj are input/output arguments
272: */
273: static PetscErrorCode PEPEvaluateBasisM(PEP pep,PetscInt k,PetscScalar *T,PetscInt ldt,PetscInt idx,PetscScalar **Tp,PetscScalar **Tj)
274: {
276:   PetscInt       i;
277:   PetscReal      *ca,*cb,*cg;
278:   PetscScalar    *pt,g,a;
279:   PetscBLASInt   k_,ldt_;

282:   if (idx==0) {
283:     PetscArrayzero(*Tj,k*k);
284:     PetscArrayzero(*Tp,k*k);
285:     for (i=0;i<k;i++) (*Tj)[i+i*k] = 1.0;
286:   } else {
287:     PetscBLASIntCast(ldt,&ldt_);
288:     PetscBLASIntCast(k,&k_);
289:     ca = pep->pbc; cb = pep->pbc+pep->nmat; cg = pep->pbc+2*pep->nmat;
290:     for (i=0;i<k;i++) T[i*ldt+i] -= cb[idx-1];
291:     a = 1/ca[idx-1];
292:     g = (idx==1)?0.0:-cg[idx-1]/ca[idx-1];
293:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&k_,&k_,&k_,&a,T,&ldt_,*Tj,&k_,&g,*Tp,&k_));
294:     pt = *Tj; *Tj = *Tp; *Tp = pt;
295:     for (i=0;i<k;i++) T[i*ldt+i] += cb[idx-1];
296:   }
297:   return(0);
298: }

300: static PetscErrorCode PEPExtractInvariantPair(PEP pep,PetscScalar sigma,PetscInt sr,PetscInt k,PetscScalar *S,PetscInt ld,PetscInt deg,PetscScalar *H,PetscInt ldh)
301: {
303:   PetscInt       i,j,jj,lds,ldt,d=pep->nmat-1,idxcpy=0;
304:   PetscScalar    *At,*Bt,*Hj,*Hp,*T,sone=1.0,g,a,*pM,*work;
305:   PetscBLASInt   k_,sr_,lds_,ldh_,info,*p,lwork,ldt_;
306:   PetscBool      transf=PETSC_FALSE,flg;
307:   PetscReal      norm,maxnrm,*rwork;
308:   BV             *R,Y;
309:   Mat            M,*A;

312:   if (k==0) return(0);
313:   lds = deg*ld;
314:   PetscCalloc6(k,&p,sr*k,&At,k*k,&Bt,k*k,&Hj,k*k,&Hp,sr*k,&work);
315:   PetscBLASIntCast(sr,&sr_);
316:   PetscBLASIntCast(k,&k_);
317:   PetscBLASIntCast(lds,&lds_);
318:   PetscBLASIntCast(ldh,&ldh_);
319:   STGetTransform(pep->st,&flg);
320:   if (!flg) {
321:      PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&flg);
322:     if (flg || sigma!=0.0) transf=PETSC_TRUE;
323:   }
324:   if (transf) {
325:     PetscMalloc1(k*k,&T);
326:     ldt = k;
327:     for (i=0;i<k;i++) {
328:       PetscArraycpy(T+k*i,H+i*ldh,k);
329:     }
330:     if (flg) {
331:       PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&k_,&k_,T,&k_,p,&info));
332:       SlepcCheckLapackInfo("getrf",info);
333:       PetscBLASIntCast(sr*k,&lwork);
334:       PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&k_,T,&k_,p,work,&lwork,&info));
335:       SlepcCheckLapackInfo("getri",info);
336:     }
337:     if (sigma!=0.0) for (i=0;i<k;i++) T[i+k*i] += sigma;
338:   } else {
339:     T = H; ldt = ldh;
340:   }
341:   PetscBLASIntCast(ldt,&ldt_);
342:   switch (pep->extract) {
343:   case PEP_EXTRACT_NONE:
344:     break;
345:   case PEP_EXTRACT_NORM:
346:     if (pep->basis == PEP_BASIS_MONOMIAL) {
347:       PetscBLASIntCast(ldt,&ldt_);
348:       PetscMalloc1(k,&rwork);
349:       norm = LAPACKlange_("F",&k_,&k_,T,&ldt_,rwork);
350:       PetscFree(rwork);
351:       if (norm>1.0) idxcpy = d-1;
352:     } else {
353:       PetscBLASIntCast(ldt,&ldt_);
354:       PetscMalloc1(k,&rwork);
355:       maxnrm = 0.0;
356:       for (i=0;i<pep->nmat-1;i++) {
357:         PEPEvaluateBasisM(pep,k,T,ldt,i,&Hp,&Hj);
358:         norm = LAPACKlange_("F",&k_,&k_,Hj,&k_,rwork);
359:         if (norm > maxnrm) {
360:           idxcpy = i;
361:           maxnrm = norm;
362:         }
363:       }
364:       PetscFree(rwork);
365:     }
366:     if (idxcpy>0) {
367:       /* copy block idxcpy of S to the first one */
368:       for (j=0;j<k;j++) {
369:         PetscArraycpy(S+j*lds,S+idxcpy*ld+j*lds,sr);
370:       }
371:     }
372:     break;
373:   case PEP_EXTRACT_RESIDUAL:
374:     STGetTransform(pep->st,&flg);
375:     if (flg) {
376:       PetscMalloc1(pep->nmat,&A);
377:       for (i=0;i<pep->nmat;i++) {
378:         STGetMatrixTransformed(pep->st,i,A+i);
379:       }
380:     } else A = pep->A;
381:     PetscMalloc1(pep->nmat-1,&R);
382:     for (i=0;i<pep->nmat-1;i++) {
383:       BVDuplicateResize(pep->V,k,R+i);
384:     }
385:     BVDuplicateResize(pep->V,sr,&Y);
386:     MatCreateSeqDense(PETSC_COMM_SELF,sr,k,NULL,&M);
387:     g = 0.0; a = 1.0;
388:     BVSetActiveColumns(pep->V,0,sr);
389:     for (j=0;j<pep->nmat;j++) {
390:       BVMatMult(pep->V,A[j],Y);
391:       PEPEvaluateBasisM(pep,k,T,ldt,i,&Hp,&Hj);
392:       for (i=0;i<pep->nmat-1;i++) {
393:         PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&sr_,&k_,&k_,&a,S+i*ld,&lds_,Hj,&k_,&g,At,&sr_));
394:         MatDenseGetArray(M,&pM);
395:         for (jj=0;jj<k;jj++) {
396:           PetscArraycpy(pM+jj*sr,At+jj*sr,sr);
397:         }
398:         MatDenseRestoreArray(M,&pM);
399:         BVMult(R[i],1.0,(i==0)?0.0:1.0,Y,M);
400:       }
401:     }

403:     /* frobenius norm */
404:     maxnrm = 0.0;
405:     for (i=0;i<pep->nmat-1;i++) {
406:       BVNorm(R[i],NORM_FROBENIUS,&norm);
407:       if (maxnrm > norm) {
408:         maxnrm = norm;
409:         idxcpy = i;
410:       }
411:     }
412:     if (idxcpy>0) {
413:       /* copy block idxcpy of S to the first one */
414:       for (j=0;j<k;j++) {
415:         PetscArraycpy(S+j*lds,S+idxcpy*ld+j*lds,sr);
416:       }
417:     }
418:     if (flg) PetscFree(A);
419:     for (i=0;i<pep->nmat-1;i++) {
420:       BVDestroy(&R[i]);
421:     }
422:     PetscFree(R);
423:     BVDestroy(&Y);
424:     MatDestroy(&M);
425:     break;
426:   case PEP_EXTRACT_STRUCTURED:
427:     for (j=0;j<k;j++) Bt[j+j*k] = 1.0;
428:     for (j=0;j<sr;j++) {
429:       for (i=0;i<k;i++) At[j*k+i] = PetscConj(S[i*lds+j]);
430:     }
431:     PEPEvaluateBasisM(pep,k,T,ldt,0,&Hp,&Hj);
432:     for (i=1;i<deg;i++) {
433:       PEPEvaluateBasisM(pep,k,T,ldt,i,&Hp,&Hj);
434:       PetscStackCallBLAS("BLASgemm",BLASgemm_("N","C",&k_,&sr_,&k_,&sone,Hj,&k_,S+i*ld,&lds_,&sone,At,&k_));
435:       PetscStackCallBLAS("BLASgemm",BLASgemm_("N","C",&k_,&k_,&k_,&sone,Hj,&k_,Hj,&k_,&sone,Bt,&k_));
436:     }
437:     PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&k_,&sr_,Bt,&k_,p,At,&k_,&info));
438:     SlepcCheckLapackInfo("gesv",info);
439:     for (j=0;j<sr;j++) {
440:       for (i=0;i<k;i++) S[i*lds+j] = PetscConj(At[j*k+i]);
441:     }
442:     break;
443:   }
444:   if (transf) { PetscFree(T); }
445:   PetscFree6(p,At,Bt,Hj,Hp,work);
446:   return(0);
447: }

449: PetscErrorCode PEPSolve_TOAR(PEP pep)
450: {
452:   PEP_TOAR       *ctx = (PEP_TOAR*)pep->data;
453:   PetscInt       i,j,k,l,nv=0,ld,lds,ldds,newn,nq=0,nconv=0;
454:   PetscInt       nmat=pep->nmat,deg=nmat-1;
455:   PetscScalar    *S,*H,sigma;
456:   PetscReal      beta;
457:   PetscBool      breakdown=PETSC_FALSE,flg,falselock=PETSC_FALSE,sinv=PETSC_FALSE;
458:   Mat            MS,MQ;

461:   PetscCitationsRegister(citation,&cited);
462:   if (ctx->lock) {
463:     /* undocumented option to use a cheaper locking instead of the true locking */
464:     PetscOptionsGetBool(NULL,NULL,"-pep_toar_falselocking",&falselock,NULL);
465:   }
466:   DSGetLeadingDimension(pep->ds,&ldds);
467:   STGetShift(pep->st,&sigma);

469:   /* update polynomial basis coefficients */
470:   STGetTransform(pep->st,&flg);
471:   if (pep->sfactor!=1.0) {
472:     for (i=0;i<nmat;i++) {
473:       pep->pbc[nmat+i] /= pep->sfactor;
474:       pep->pbc[2*nmat+i] /= pep->sfactor*pep->sfactor;
475:     }
476:     if (!flg) {
477:       pep->target /= pep->sfactor;
478:       RGPushScale(pep->rg,1.0/pep->sfactor);
479:       STScaleShift(pep->st,1.0/pep->sfactor);
480:       sigma /= pep->sfactor;
481:     } else {
482:       PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
483:       pep->target = sinv?pep->target*pep->sfactor:pep->target/pep->sfactor;
484:       RGPushScale(pep->rg,sinv?pep->sfactor:1.0/pep->sfactor);
485:       STScaleShift(pep->st,sinv?pep->sfactor:1.0/pep->sfactor);
486:     }
487:   }

489:   if (flg) sigma = 0.0;

491:   /* clean projected matrix (including the extra-arrow) */
492:   DSGetArray(pep->ds,DS_MAT_A,&H);
493:   PetscArrayzero(H,ldds*ldds);
494:   DSRestoreArray(pep->ds,DS_MAT_A,&H);

496:   /* Get the starting Arnoldi vector */
497:   BVTensorBuildFirstColumn(ctx->V,pep->nini);

499:   /* restart loop */
500:   l = 0;
501:   while (pep->reason == PEP_CONVERGED_ITERATING) {
502:     pep->its++;

504:     /* compute an nv-step Lanczos factorization */
505:     nv = PetscMax(PetscMin(nconv+pep->mpd,pep->ncv),nv);
506:     DSGetArray(pep->ds,DS_MAT_A,&H);
507:     PEPTOARrun(pep,sigma,H,ldds,pep->nconv+l,&nv,&breakdown,pep->work);
508:     beta = PetscAbsScalar(H[(nv-1)*ldds+nv]);
509:     DSRestoreArray(pep->ds,DS_MAT_A,&H);
510:     DSSetDimensions(pep->ds,nv,0,pep->nconv,pep->nconv+l);
511:     if (l==0) {
512:       DSSetState(pep->ds,DS_STATE_INTERMEDIATE);
513:     } else {
514:       DSSetState(pep->ds,DS_STATE_RAW);
515:     }
516:     BVSetActiveColumns(ctx->V,pep->nconv,nv);

518:     /* solve projected problem */
519:     DSSolve(pep->ds,pep->eigr,pep->eigi);
520:     DSSort(pep->ds,pep->eigr,pep->eigi,NULL,NULL,NULL);
521:     DSUpdateExtraRow(pep->ds);
522:     DSSynchronize(pep->ds,pep->eigr,pep->eigi);

524:     /* check convergence */
525:     PEPKrylovConvergence(pep,PETSC_FALSE,pep->nconv,nv-pep->nconv,beta,&k);
526:     (*pep->stopping)(pep,pep->its,pep->max_it,k,pep->nev,&pep->reason,pep->stoppingctx);

528:     /* update l */
529:     if (pep->reason != PEP_CONVERGED_ITERATING || breakdown) l = 0;
530:     else {
531:       l = (nv==k)?0:PetscMax(1,(PetscInt)((nv-k)*ctx->keep));
532:       if (!breakdown) {
533:         /* prepare the Rayleigh quotient for restart */
534:         DSTruncate(pep->ds,k+l);
535:         DSGetDimensions(pep->ds,&newn,NULL,NULL,NULL,NULL);
536:         l = newn-k;
537:       }
538:     }
539:     nconv = k;
540:     if (!ctx->lock && pep->reason == PEP_CONVERGED_ITERATING && !breakdown) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */

542:     /* update S */
543:     DSGetMat(pep->ds,DS_MAT_Q,&MQ);
544:     BVMultInPlace(ctx->V,MQ,pep->nconv,k+l);
545:     MatDestroy(&MQ);

547:     /* copy last column of S */
548:     BVCopyColumn(ctx->V,nv,k+l);

550:     if (breakdown && pep->reason == PEP_CONVERGED_ITERATING) {
551:       /* stop if breakdown */
552:       PetscInfo2(pep,"Breakdown TOAR method (it=%D norm=%g)\n",pep->its,(double)beta);
553:       pep->reason = PEP_DIVERGED_BREAKDOWN;
554:     }
555:     if (pep->reason != PEP_CONVERGED_ITERATING) l--;
556:     /* truncate S */
557:     BVGetActiveColumns(pep->V,NULL,&nq);
558:     if (k+l+deg<=nq) {
559:       BVSetActiveColumns(ctx->V,pep->nconv,k+l+1);
560:       if (!falselock && ctx->lock) {
561:         BVTensorCompress(ctx->V,k-pep->nconv);
562:       } else {
563:         BVTensorCompress(ctx->V,0);
564:       }
565:     }
566:     pep->nconv = k;
567:     PEPMonitor(pep,pep->its,nconv,pep->eigr,pep->eigi,pep->errest,nv);
568:   }
569:   if (pep->nconv>0) {
570:     /* {V*S_nconv^i}_{i=0}^{d-1} has rank nconv instead of nconv+d-1. Force zeros in each S_nconv^i block */
571:     BVSetActiveColumns(ctx->V,0,pep->nconv);
572:     BVGetActiveColumns(pep->V,NULL,&nq);
573:     BVSetActiveColumns(pep->V,0,nq);
574:     if (nq>pep->nconv) {
575:       BVTensorCompress(ctx->V,pep->nconv);
576:       BVSetActiveColumns(pep->V,0,pep->nconv);
577:       nq = pep->nconv;
578:     }

580:     /* perform Newton refinement if required */
581:     if (pep->refine==PEP_REFINE_MULTIPLE && pep->rits>0) {
582:       /* extract invariant pair */
583:       BVTensorGetFactors(ctx->V,NULL,&MS);
584:       MatDenseGetArray(MS,&S);
585:       DSGetArray(pep->ds,DS_MAT_A,&H);
586:       BVGetSizes(pep->V,NULL,NULL,&ld);
587:       lds = deg*ld;
588:       PEPExtractInvariantPair(pep,sigma,nq,pep->nconv,S,ld,deg,H,ldds);
589:       DSRestoreArray(pep->ds,DS_MAT_A,&H);
590:       DSSetDimensions(pep->ds,pep->nconv,0,0,0);
591:       DSSetState(pep->ds,DS_STATE_RAW);
592:       PEPNewtonRefinement_TOAR(pep,sigma,&pep->rits,NULL,pep->nconv,S,lds);
593:       DSSolve(pep->ds,pep->eigr,pep->eigi);
594:       DSSort(pep->ds,pep->eigr,pep->eigi,NULL,NULL,NULL);
595:       DSSynchronize(pep->ds,pep->eigr,pep->eigi);
596:       DSGetMat(pep->ds,DS_MAT_Q,&MQ);
597:       BVMultInPlace(ctx->V,MQ,0,pep->nconv);
598:       MatDestroy(&MQ);
599:       MatDenseRestoreArray(MS,&S);
600:       BVTensorRestoreFactors(ctx->V,NULL,&MS);
601:     }
602:   }
603:   STGetTransform(pep->st,&flg);
604:   if (pep->refine!=PEP_REFINE_MULTIPLE || pep->rits==0) {
605:     if (!flg && pep->ops->backtransform) {
606:         (*pep->ops->backtransform)(pep);
607:     }
608:     if (pep->sfactor!=1.0) {
609:       for (j=0;j<pep->nconv;j++) {
610:         pep->eigr[j] *= pep->sfactor;
611:         pep->eigi[j] *= pep->sfactor;
612:       }
613:       /* restore original values */
614:       for (i=0;i<pep->nmat;i++){
615:         pep->pbc[pep->nmat+i] *= pep->sfactor;
616:         pep->pbc[2*pep->nmat+i] *= pep->sfactor*pep->sfactor;
617:       }
618:     }
619:   }
620:   /* restore original values */
621:   if (!flg) {
622:     pep->target *= pep->sfactor;
623:     STScaleShift(pep->st,pep->sfactor);
624:   } else {
625:     STScaleShift(pep->st,sinv?1.0/pep->sfactor:pep->sfactor);
626:     pep->target = (sinv)?pep->target/pep->sfactor:pep->target*pep->sfactor;
627:   }
628:   if (pep->sfactor!=1.0) { RGPopScale(pep->rg); }

630:   /* change the state to raw so that DSVectors() computes eigenvectors from scratch */
631:   DSSetDimensions(pep->ds,pep->nconv,0,0,0);
632:   DSSetState(pep->ds,DS_STATE_RAW);
633:   return(0);
634: }

636: static PetscErrorCode PEPTOARSetRestart_TOAR(PEP pep,PetscReal keep)
637: {
638:   PEP_TOAR *ctx = (PEP_TOAR*)pep->data;

641:   if (keep==PETSC_DEFAULT) ctx->keep = 0.5;
642:   else {
643:     if (keep<0.1 || keep>0.9) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The keep argument must be in the range [0.1,0.9]");
644:     ctx->keep = keep;
645:   }
646:   return(0);
647: }

649: /*@
650:    PEPTOARSetRestart - Sets the restart parameter for the TOAR
651:    method, in particular the proportion of basis vectors that must be kept
652:    after restart.

654:    Logically Collective on pep

656:    Input Parameters:
657: +  pep  - the eigenproblem solver context
658: -  keep - the number of vectors to be kept at restart

660:    Options Database Key:
661: .  -pep_toar_restart - Sets the restart parameter

663:    Notes:
664:    Allowed values are in the range [0.1,0.9]. The default is 0.5.

666:    Level: advanced

668: .seealso: PEPTOARGetRestart()
669: @*/
670: PetscErrorCode PEPTOARSetRestart(PEP pep,PetscReal keep)
671: {

677:   PetscTryMethod(pep,"PEPTOARSetRestart_C",(PEP,PetscReal),(pep,keep));
678:   return(0);
679: }

681: static PetscErrorCode PEPTOARGetRestart_TOAR(PEP pep,PetscReal *keep)
682: {
683:   PEP_TOAR *ctx = (PEP_TOAR*)pep->data;

686:   *keep = ctx->keep;
687:   return(0);
688: }

690: /*@
691:    PEPTOARGetRestart - Gets the restart parameter used in the TOAR method.

693:    Not Collective

695:    Input Parameter:
696: .  pep - the eigenproblem solver context

698:    Output Parameter:
699: .  keep - the restart parameter

701:    Level: advanced

703: .seealso: PEPTOARSetRestart()
704: @*/
705: PetscErrorCode PEPTOARGetRestart(PEP pep,PetscReal *keep)
706: {

712:   PetscUseMethod(pep,"PEPTOARGetRestart_C",(PEP,PetscReal*),(pep,keep));
713:   return(0);
714: }

716: static PetscErrorCode PEPTOARSetLocking_TOAR(PEP pep,PetscBool lock)
717: {
718:   PEP_TOAR *ctx = (PEP_TOAR*)pep->data;

721:   ctx->lock = lock;
722:   return(0);
723: }

725: /*@
726:    PEPTOARSetLocking - Choose between locking and non-locking variants of
727:    the TOAR method.

729:    Logically Collective on pep

731:    Input Parameters:
732: +  pep  - the eigenproblem solver context
733: -  lock - true if the locking variant must be selected

735:    Options Database Key:
736: .  -pep_toar_locking - Sets the locking flag

738:    Notes:
739:    The default is to lock converged eigenpairs when the method restarts.
740:    This behaviour can be changed so that all directions are kept in the
741:    working subspace even if already converged to working accuracy (the
742:    non-locking variant).

744:    Level: advanced

746: .seealso: PEPTOARGetLocking()
747: @*/
748: PetscErrorCode PEPTOARSetLocking(PEP pep,PetscBool lock)
749: {

755:   PetscTryMethod(pep,"PEPTOARSetLocking_C",(PEP,PetscBool),(pep,lock));
756:   return(0);
757: }

759: static PetscErrorCode PEPTOARGetLocking_TOAR(PEP pep,PetscBool *lock)
760: {
761:   PEP_TOAR *ctx = (PEP_TOAR*)pep->data;

764:   *lock = ctx->lock;
765:   return(0);
766: }

768: /*@
769:    PEPTOARGetLocking - Gets the locking flag used in the TOAR method.

771:    Not Collective

773:    Input Parameter:
774: .  pep - the eigenproblem solver context

776:    Output Parameter:
777: .  lock - the locking flag

779:    Level: advanced

781: .seealso: PEPTOARSetLocking()
782: @*/
783: PetscErrorCode PEPTOARGetLocking(PEP pep,PetscBool *lock)
784: {

790:   PetscUseMethod(pep,"PEPTOARGetLocking_C",(PEP,PetscBool*),(pep,lock));
791:   return(0);
792: }

794: PetscErrorCode PEPSetFromOptions_TOAR(PetscOptionItems *PetscOptionsObject,PEP pep)
795: {
797:   PetscBool      flg,lock;
798:   PetscReal      keep;

801:   PetscOptionsHead(PetscOptionsObject,"PEP TOAR Options");

803:     PetscOptionsReal("-pep_toar_restart","Proportion of vectors kept after restart","PEPTOARSetRestart",0.5,&keep,&flg);
804:     if (flg) { PEPTOARSetRestart(pep,keep); }

806:     PetscOptionsBool("-pep_toar_locking","Choose between locking and non-locking variants","PEPTOARSetLocking",PETSC_FALSE,&lock,&flg);
807:     if (flg) { PEPTOARSetLocking(pep,lock); }

809:   PetscOptionsTail();
810:   return(0);
811: }

813: PetscErrorCode PEPView_TOAR(PEP pep,PetscViewer viewer)
814: {
816:   PEP_TOAR       *ctx = (PEP_TOAR*)pep->data;
817:   PetscBool      isascii;

820:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
821:   if (isascii) {
822:     PetscViewerASCIIPrintf(viewer,"  %d%% of basis vectors kept after restart\n",(int)(100*ctx->keep));
823:     PetscViewerASCIIPrintf(viewer,"  using the %slocking variant\n",ctx->lock?"":"non-");
824:   }
825:   return(0);
826: }

828: PetscErrorCode PEPDestroy_TOAR(PEP pep)
829: {
831:   PEP_TOAR       *ctx = (PEP_TOAR*)pep->data;

834:   BVDestroy(&ctx->V);
835:   PetscFree(pep->data);
836:   PetscObjectComposeFunction((PetscObject)pep,"PEPTOARSetRestart_C",NULL);
837:   PetscObjectComposeFunction((PetscObject)pep,"PEPTOARGetRestart_C",NULL);
838:   PetscObjectComposeFunction((PetscObject)pep,"PEPTOARSetLocking_C",NULL);
839:   PetscObjectComposeFunction((PetscObject)pep,"PEPTOARGetLocking_C",NULL);
840:   return(0);
841: }

843: SLEPC_EXTERN PetscErrorCode PEPCreate_TOAR(PEP pep)
844: {
845:   PEP_TOAR       *ctx;

849:   PetscNewLog(pep,&ctx);
850:   pep->data = (void*)ctx;

852:   pep->lineariz = PETSC_TRUE;
853:   ctx->lock     = PETSC_TRUE;

855:   pep->ops->solve          = PEPSolve_TOAR;
856:   pep->ops->setup          = PEPSetUp_TOAR;
857:   pep->ops->setfromoptions = PEPSetFromOptions_TOAR;
858:   pep->ops->destroy        = PEPDestroy_TOAR;
859:   pep->ops->view           = PEPView_TOAR;
860:   pep->ops->backtransform  = PEPBackTransform_Default;
861:   pep->ops->computevectors = PEPComputeVectors_Default;
862:   pep->ops->extractvectors = PEPExtractVectors_TOAR;

864:   PetscObjectComposeFunction((PetscObject)pep,"PEPTOARSetRestart_C",PEPTOARSetRestart_TOAR);
865:   PetscObjectComposeFunction((PetscObject)pep,"PEPTOARGetRestart_C",PEPTOARGetRestart_TOAR);
866:   PetscObjectComposeFunction((PetscObject)pep,"PEPTOARSetLocking_C",PEPTOARSetLocking_TOAR);
867:   PetscObjectComposeFunction((PetscObject)pep,"PEPTOARGetLocking_C",PEPTOARGetLocking_TOAR);
868:   return(0);
869: }