Actual source code: stoar.c

slepc-3.7.0 2016-05-16
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  1: /*

  3:    SLEPc polynomial eigensolver: "stoar"

  5:    Method: S-TOAR

  7:    Algorithm:

  9:        Symmetric Two-Level Orthogonal Arnoldi.

 11:    References:

 13:        [1] C. Campos and J.E. Roman, "Restarted Q-Arnoldi-type methods
 14:            exploiting symmetry in quadratic eigenvalue problems", BIT
 15:            Numer. Math. (in press), 2016.

 17:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 18:    SLEPc - Scalable Library for Eigenvalue Problem Computations
 19:    Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain

 21:    This file is part of SLEPc.

 23:    SLEPc is free software: you can redistribute it and/or modify it under  the
 24:    terms of version 3 of the GNU Lesser General Public License as published by
 25:    the Free Software Foundation.

 27:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
 28:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
 29:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
 30:    more details.

 32:    You  should have received a copy of the GNU Lesser General  Public  License
 33:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
 34:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 35: */

 37: #include <slepc/private/pepimpl.h>         /*I "slepcpep.h" I*/
 38:  #include ../src/pep/impls/krylov/pepkrylov.h
 39: #include <slepcblaslapack.h>

 41: static PetscBool  cited = PETSC_FALSE;
 42: static const char citation[] =
 43:   "@Article{slepc-stoar,\n"
 44:   "   author = \"C. Campos and J. E. Roman\",\n"
 45:   "   title = \"Restarted {Q-Arnoldi-type} methods exploiting symmetry in quadratic eigenvalue problems\",\n"
 46:   "   journal = \"{BIT} Numer. Math.\",\n"
 47:   "   volume = \"to appear\",\n"
 48:   "   number = \"\",\n"
 49:   "   pages = \"\",\n"
 50:   "   year = \"2016,\"\n"
 51:   "   doi = \"http://dx.doi.org/10.1007/s10543-016-0601-5\"\n"
 52:   "}\n";

 56: /*
 57:   Compute B-norm of v=[v1;v2] whith  B=diag(-pep->T[0],pep->T[2])
 58: */
 59: static PetscErrorCode PEPSTOARNorm(PEP pep,PetscInt j,PetscReal *norm)
 60: {
 62:   PEP_TOAR       *ctx = (PEP_TOAR*)pep->data;
 63:   PetscBLASInt   n_,one=1,ld_;
 64:   PetscScalar    sone=1.0,szero=0.0,*sp,*sq,*w1,*w2,*qK,*qM;
 65:   PetscInt       n,i,lds=ctx->d*ctx->ld;

 68:   qK = ctx->qB;
 69:   qM = ctx->qB+ctx->ld*ctx->ld;
 70:   n = j+2;
 71:   PetscMalloc2(n,&w1,n,&w2);
 72:   sp = ctx->S+lds*j;
 73:   sq = sp+ctx->ld;
 74:   PetscBLASIntCast(n,&n_);
 75:   PetscBLASIntCast(ctx->ld,&ld_);
 76:   PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&n_,&sone,qK,&ld_,sp,&one,&szero,w1,&one));
 77:   PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&n_,&sone,qM,&ld_,sq,&one,&szero,w2,&one));
 78:   *norm = 0.0;
 79:   for (i=0;i<n;i++) *norm += PetscRealPart(w1[i]*PetscConj(sp[i])+w2[i]*PetscConj(sq[i]));
 80:   *norm = (*norm>0.0)?PetscSqrtReal(*norm):-PetscSqrtReal(-*norm);
 81:   PetscFree2(w1,w2);
 82:   return(0);
 83: }

 87: static PetscErrorCode PEPSTOARqKqMupdates(PEP pep,PetscInt j,Vec *wv)
 88: {
 90:   PEP_TOAR       *ctx = (PEP_TOAR*)pep->data;
 91:   PetscInt       i,ld=ctx->ld;
 92:   PetscScalar    *qK,*qM;
 93:   Vec            vj,v1,v2;

 96:   qK = ctx->qB;
 97:   qM = ctx->qB+ctx->ld*ctx->ld;
 98:   v1 = wv[0];
 99:   v2 = wv[1];
100:   BVGetColumn(pep->V,j,&vj);
101:   STMatMult(pep->st,0,vj,v1);
102:   STMatMult(pep->st,2,vj,v2);
103:   BVRestoreColumn(pep->V,j,&vj);
104:   for (i=0;i<=j;i++) {
105:     BVGetColumn(pep->V,i,&vj);
106:     VecDot(v1,vj,qK+j*ld+i);
107:     VecDot(v2,vj,qM+j*ld+i);
108:     *(qM+j*ld+i) *= pep->sfactor*pep->sfactor;
109:     BVRestoreColumn(pep->V,i,&vj);
110:   }
111:   for (i=0;i<j;i++) {
112:     qK[i+j*ld] = -qK[i+ld*j];
113:     qK[j+i*ld] = PetscConj(qK[i+j*ld]);
114:     qM[j+i*ld] = PetscConj(qM[i+j*ld]);
115:   }
116:   qK[j+j*ld] = -PetscRealPart(qK[j+ld*j]);
117:   qM[j+j*ld] = PetscRealPart(qM[j+ld*j]);
118:   return(0);
119: }

123: PetscErrorCode PEPSetUp_STOAR(PEP pep)
124: {
126:   PetscBool      sinv,flg,lindep;
127:   PEP_TOAR       *ctx = (PEP_TOAR*)pep->data;
128:   PetscInt       ld,i;
129:   PetscReal      norm,*omega;

132:   PEPSetDimensions_Default(pep,pep->nev,&pep->ncv,&pep->mpd);
133:   if (!ctx->lock && pep->mpd<pep->ncv) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Should not use mpd parameter in non-locking variant");
134:   if (!pep->max_it) pep->max_it = PetscMax(100,2*pep->n/pep->ncv);
135:   if (!pep->which) {
136:     PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
137:     if (sinv) pep->which = PEP_TARGET_MAGNITUDE;
138:     else pep->which = PEP_LARGEST_MAGNITUDE;
139:   }
140:   if (pep->problem_type!=PEP_HERMITIAN) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Requested method is only available for Hermitian problems");

142:   if (pep->nmat!=3) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Solver only available for quadratic problems");
143:   if (pep->basis!=PEP_BASIS_MONOMIAL) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Solver not implemented for non-monomial bases");
144:   STGetTransform(pep->st,&flg);
145:   if (!flg) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Solver requires the ST transformation flag set, see STSetTransform()");

147:   PEPAllocateSolution(pep,2);
148:   PEPSetWorkVecs(pep,4);
149:   ld = pep->ncv+2;
150:   DSSetType(pep->ds,DSGHIEP);
151:   DSSetCompact(pep->ds,PETSC_TRUE);
152:   DSAllocate(pep->ds,ld);
153:   STGetNumMatrices(pep->st,&ctx->d);
154:   ctx->d--;
155:   ctx->ld = ld;
156:   PetscCalloc1(ctx->d*ld*ld,&ctx->S);
157:   PetscCalloc1(2*ld*ld,&ctx->qB);

159:   /* process starting vector */
160:   if (pep->nini>-2) {
161:     BVSetRandomColumn(pep->V,0);
162:     BVSetRandomColumn(pep->V,1);
163:   } else {
164:     BVInsertVec(pep->V,0,pep->IS[0]);
165:     BVInsertVec(pep->V,1,pep->IS[1]);
166:   }
167:   BVOrthogonalizeColumn(pep->V,0,NULL,&norm,&lindep);
168:   if (!lindep) {
169:     BVScaleColumn(pep->V,0,1.0/norm);
170:     ctx->S[0] = norm;
171:     PEPSTOARqKqMupdates(pep,0,pep->work);
172:   } else SETERRQ(PetscObjectComm((PetscObject)pep),1,"Problem with initial vector");
173:   BVOrthogonalizeColumn(pep->V,1,ctx->S+ld,&norm,&lindep);
174:   if (!lindep) {
175:     BVScaleColumn(pep->V,1,1.0/norm);
176:     ctx->S[1] = norm;
177:     PEPSTOARqKqMupdates(pep,1,pep->work);
178:   } else SETERRQ(PetscObjectComm((PetscObject)pep),1,"Problem with initial vector");

180:   PEPSTOARNorm(pep,0,&norm);
181:   for (i=0;i<2;i++) { ctx->S[i+ld] /= norm; ctx->S[i] /= norm; }
182:   DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
183:   omega[0] = (norm>0)?1.0:-1.0;
184:   DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
185:   if (pep->nini<0) {
186:     SlepcBasisDestroy_Private(&pep->nini,&pep->IS);
187:   }
188:   return(0);
189: }

193: /*
194:   Computes GS orthogonalization  x = [z;x] - [Sp;Sq]*y,
195:   where y = Omega\([Sp;Sq]'*[qK zeros(size(qK,1)) ;zeros(size(qK,1)) qM]*[z;x]).
196:   n: Column from S to be orthogonalized against previous columns.
197: */
198: static PetscErrorCode PEPSTOAROrth2(PEP pep,PetscInt k,PetscReal *Omega,PetscScalar *y)
199: {
201:   PEP_TOAR       *ctx = (PEP_TOAR*)pep->data;
202:   PetscBLASInt   n_,lds_,k_,one=1,ld_;
203:   PetscScalar    *S=ctx->S,sonem=-1.0,sone=1.0,szero=0.0,*tp,*tq,*xp,*xq,*c,*qK,*qM;
204:   PetscInt       i,lds=ctx->d*ctx->ld,n,j;

207:   qK = ctx->qB;
208:   qM = ctx->qB+ctx->ld*ctx->ld;
209:   n = k+2;
210:   PetscMalloc3(n,&tp,n,&tq,k,&c);
211:   PetscBLASIntCast(n,&n_); /* Size of qK and qM */
212:   PetscBLASIntCast(ctx->ld,&ld_);
213:   PetscBLASIntCast(lds,&lds_);
214:   PetscBLASIntCast(k,&k_); /* Number of vectors to orthogonalize against */
215:   xp = S+k*lds;
216:   xq = S+ctx->ld+k*lds;
217:   PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&n_,&sone,qK,&ld_,xp,&one,&szero,tp,&one));
218:   PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&n_,&sone,qM,&ld_,xq,&one,&szero,tq,&one));
219:   PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n_,&k_,&sone,ctx->S,&lds_,tp,&one,&szero,y,&one));
220:   PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n_,&k_,&sone,S+ctx->ld,&lds_,tq,&one,&sone,y,&one));
221:   for (i=0;i<k;i++) y[i] /= Omega[i];
222:   PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&k_,&sonem,S,&lds_,y,&one,&sone,xp,&one));
223:   PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&k_,&sonem,S+ctx->ld,&lds_,y,&one,&sone,xq,&one));
224:   /* three times */
225:   for (j=0;j<2;j++) {
226:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&n_,&sone,qK,&ld_,xp,&one,&szero,tp,&one));
227:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&n_,&sone,qM,&ld_,xq,&one,&szero,tq,&one));
228:     PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n_,&k_,&sone,ctx->S,&lds_,tp,&one,&szero,c,&one));
229:     PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n_,&k_,&sone,S+ctx->ld,&lds_,tq,&one,&sone,c,&one));
230:     for (i=0;i<k;i++) c[i] /= Omega[i];
231:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&k_,&sonem,S,&lds_,c,&one,&sone,xp,&one));
232:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&k_,&sonem,S+ctx->ld,&lds_,c,&one,&sone,xq,&one));
233:     for (i=0;i<k;i++) y[i] += c[i];
234:   }
235:   PetscFree3(tp,tq,c);
236:   return(0);
237: }

241: /*
242:   Compute a run of Lanczos iterations. dim(work)=(ctx->ld)*4
243: */
244: static PetscErrorCode PEPSTOARrun(PEP pep,PetscReal *a,PetscReal *b,PetscReal *omega,PetscInt k,PetscInt *M,PetscBool *breakdown,PetscBool *symmlost,PetscScalar *work,Vec *t_)
245: {
247:   PEP_TOAR       *ctx = (PEP_TOAR*)pep->data;
248:   PetscInt       i,j,m=*M,l;
249:   PetscInt       lds=ctx->d*ctx->ld,offq=ctx->ld;
250:   Vec            v=t_[0],t=t_[1],q=t_[2];
251:   PetscReal      norm,sym=0.0,fro=0.0,*f;
252:   PetscScalar    *y,*S=ctx->S;
253:   PetscBLASInt   j_,one=1;
254:   PetscBool      lindep;

257:   *breakdown = PETSC_FALSE; /* ----- */
258:   DSGetDimensions(pep->ds,NULL,NULL,&l,NULL,NULL);
259:   y = work;
260:   for (j=k;j<m;j++) {
261:     /* apply operator */
262:     BVSetActiveColumns(pep->V,0,j+2);
263:     BVMultVec(pep->V,1.0,0.0,v,S+j*lds);
264:     STMatMult(pep->st,0,v,t);
265:     BVMultVec(pep->V,1.0,0.0,v,S+offq+j*lds);
266:     STMatMult(pep->st,1,v,q);
267:     VecAXPY(t,pep->sfactor,q);
268:     STMatSolve(pep->st,t,q);
269:     VecScale(q,-1.0/(pep->sfactor*pep->sfactor));

271:     /* orthogonalize */
272:     BVOrthogonalizeVec(pep->V,q,S+offq+(j+1)*lds,&norm,&lindep);
273:     if (lindep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"STOAR does not support detection of linearly dependent TOAR vectors");
274:     *(S+offq+(j+1)*lds+j+2) = norm;
275:     VecScale(q,1.0/norm);
276:     BVInsertVec(pep->V,j+2,q);
277:     for (i=0;i<=j+1;i++) *(S+(j+1)*lds+i) = *(S+offq+j*lds+i);

279:     /* update qK and qM */
280:     PEPSTOARqKqMupdates(pep,j+2,t_);

282:     /* level-2 orthogonalization */
283:     PEPSTOAROrth2(pep,j+1,omega,y);
284:     a[j] = PetscRealPart(y[j])/omega[j];
285:     PEPSTOARNorm(pep,j+1,&norm);
286:     omega[j+1] = (norm > 0)?1.0:-1.0;
287:     for (i=0;i<=j+2;i++) {
288:       S[i+(j+1)*lds] /= norm;
289:       S[i+offq+(j+1)*lds] /= norm;
290:     }
291:     b[j] = PetscAbsReal(norm);

293:     /* check symmetry */
294:     DSGetArrayReal(pep->ds,DS_MAT_T,&f);
295:     if (j==k) {
296:       for (i=l;i<j-1;i++) y[i] = PetscAbsScalar(y[i])-PetscAbsReal(f[2*ctx->ld+i]);
297:       for (i=0;i<l;i++) y[i] = 0.0;
298:     }
299:     DSRestoreArrayReal(pep->ds,DS_MAT_T,&f);
300:     if (j>0) y[j-1] = PetscAbsScalar(y[j-1])-PetscAbsReal(b[j-1]);
301:     PetscBLASIntCast(j,&j_);
302:     sym = SlepcAbs(BLASnrm2_(&j_,y,&one),sym);
303:     fro = SlepcAbs(fro,SlepcAbs(a[j],b[j]));
304:     if (j>0) fro = SlepcAbs(fro,b[j-1]);
305:     if (sym/fro>PetscMax(PETSC_SQRT_MACHINE_EPSILON,10*pep->tol)) {
306:       *symmlost = PETSC_TRUE;
307:       *M=j+1;
308:       break;
309:     }
310:   }
311:   return(0);
312: }

316: static PetscErrorCode PEPSTOARTrunc(PEP pep,PetscInt rs1,PetscInt cs1,PetscScalar *work,PetscReal *rwork)
317: {
318: #if defined(PETSC_MISSING_LAPACK_GESVD)
320:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GESVD - Lapack routine is unavailable");
321: #else
323:   PEP_TOAR       *ctx = (PEP_TOAR*)pep->data;
324:   Mat            G;
325:   PetscInt       lwa,nwu=0,nrwu=0;
326:   PetscInt       i,n,lds=2*ctx->ld;
327:   PetscScalar    *M,*V,*U,*S=ctx->S,sone=1.0,zero=0.0,t,*qK,*qM;
328:   PetscReal      *sg;
329:   PetscBLASInt   cs1_,rs1_,cs1t2,cs1p1,n_,info,lw_,lds_,ld_;

332:   qK = ctx->qB;
333:   qM = ctx->qB+ctx->ld*ctx->ld;
334:   n = (rs1>2*cs1)?2*cs1:rs1;
335:   lwa = cs1*rs1*4+n*(rs1+2*cs1)+(cs1+1)*(cs1+2);
336:   M = work+nwu;
337:   nwu += rs1*cs1*2;
338:   U = work+nwu;
339:   nwu += rs1*n;
340:   V = work+nwu;
341:   nwu += 2*cs1*n;
342:   sg = rwork+nrwu;
343:   nrwu += n;
344:   for (i=0;i<cs1;i++) {
345:     PetscMemcpy(M+i*rs1,S+i*lds,rs1*sizeof(PetscScalar));
346:     PetscMemcpy(M+(i+cs1)*rs1,S+i*lds+ctx->ld,rs1*sizeof(PetscScalar));
347:   }
348:   PetscBLASIntCast(n,&n_);
349:   PetscBLASIntCast(cs1,&cs1_);
350:   PetscBLASIntCast(rs1,&rs1_);
351:   PetscBLASIntCast(cs1*2,&cs1t2);
352:   PetscBLASIntCast(cs1+1,&cs1p1);
353:   PetscBLASIntCast(lds,&lds_);
354:   PetscBLASIntCast(ctx->ld,&ld_);
355:   PetscBLASIntCast(lwa-nwu,&lw_);
356: #if !defined(PETSC_USE_COMPLEX)
357:   PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("S","S",&rs1_,&cs1t2,M,&rs1_,sg,U,&rs1_,V,&n_,work+nwu,&lw_,&info));
358: #else
359:   PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("S","S",&rs1_,&cs1t2,M,&rs1_,sg,U,&rs1_,V,&n_,work+nwu,&lw_,rwork+nrwu,&info));
360: #endif
361:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xGESVD %d",info);

363:   /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
364:   MatCreateSeqDense(PETSC_COMM_SELF,rs1,2*cs1,U,&G);
365:   BVSetActiveColumns(pep->V,0,rs1);
366:   BVMultInPlace(pep->V,G,0,cs1+1);
367:   MatDestroy(&G);

369:   /* Update S */
370:   PetscMemzero(S,lds*ctx->ld*sizeof(PetscScalar));

372:   for (i=0;i<cs1+1;i++) {
373:     t = sg[i];
374:     PetscStackCallBLAS("BLASscal",BLASscal_(&cs1t2,&t,V+i,&n_));
375:   }
376:   for (i=0;i<cs1;i++) {
377:     PetscMemcpy(S+i*lds,V+i*n,(cs1+1)*sizeof(PetscScalar));
378:     PetscMemcpy(S+ctx->ld+i*lds,V+(cs1+i)*n,(cs1+1)*sizeof(PetscScalar));
379:   }

381:   /* Update qM and qK */
382:   PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&rs1_,&cs1p1,&rs1_,&sone,qK,&ld_,U,&rs1_,&zero,work+nwu,&rs1_));
383:   PetscStackCallBLAS("BLASgemm",BLASgemm_("C","N",&cs1p1,&cs1p1,&rs1_,&sone,U,&rs1_,work+nwu,&rs1_,&zero,qK,&ld_));
384:   PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&rs1_,&cs1p1,&rs1_,&sone,qM,&ld_,U,&rs1_,&zero,work+nwu,&rs1_));
385:   PetscStackCallBLAS("BLASgemm",BLASgemm_("C","N",&cs1p1,&cs1p1,&rs1_,&sone,U,&rs1_,work+nwu,&rs1_,&zero,qM,&ld_));
386:   return(0);
387: #endif
388: }

392: /*
393:   S <- S*Q
394:   columns s-s+ncu of S
395:   rows 0-sr of S
396:   size(Q) qr x ncu
397:   dim(work)=sr*ncu;
398: */
399: static PetscErrorCode PEPSTOARSupdate(PetscScalar *S,PetscInt ld,PetscInt sr,PetscInt s,PetscInt ncu,PetscInt qr,PetscScalar *Q,PetscInt ldq,PetscScalar *work)
400: {
402:   PetscScalar    a=1.0,b=0.0;
403:   PetscBLASInt   sr_,ncu_,ldq_,lds_,qr_;
404:   PetscInt       j,lds=2*ld;

407:   PetscBLASIntCast(sr,&sr_);
408:   PetscBLASIntCast(qr,&qr_);
409:   PetscBLASIntCast(ncu,&ncu_);
410:   PetscBLASIntCast(lds,&lds_);
411:   PetscBLASIntCast(ldq,&ldq_);
412:   PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&sr_,&ncu_,&qr_,&a,S,&lds_,Q,&ldq_,&b,work,&sr_));
413:   for (j=0;j<ncu;j++) {
414:     PetscMemcpy(S+lds*(s+j),work+j*sr,sr*sizeof(PetscScalar));
415:   }
416:   PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&sr_,&ncu_,&qr_,&a,S+ld,&lds_,Q,&ldq_,&b,work,&sr_));
417:   for (j=0;j<ncu;j++) {
418:     PetscMemcpy(S+lds*(s+j)+ld,work+j*sr,sr*sizeof(PetscScalar));
419:   }
420:   return(0);
421: }

423: #if 0
426: static PetscErrorCode PEPSTOARpreKConvergence(PEP pep,PetscInt nv,PetscReal *norm,Vec *w)
427: {
429:   PEP_TOAR      *ctx = (PEP_TOAR*)pep->data;
430:   PetscBLASInt   n_,one=1;
431:   PetscInt       lds=2*ctx->ld;
432:   PetscReal      t1,t2;
433:   PetscScalar    *S=ctx->S;

436:   PetscBLASIntCast(nv+2,&n_);
437:   t1 = BLASnrm2_(&n_,S+nv*2*ctx->ld,&one);
438:   t2 = BLASnrm2_(&n_,S+(nv*2+1)*ctx->ld,&one);
439:   *norm = SlepcAbs(t1,t2);
440:   BVSetActiveColumns(pep->V,0,nv+2);
441:   BVMultVec(pep->V,1.0,0.0,w[1],S+nv*lds);
442:   STMatMult(pep->st,0,w[1],w[2]);
443:   VecNorm(w[2],NORM_2,&t1);
444:   BVMultVec(pep->V,1.0,0.0,w[1],S+ctx->ld+nv*lds);
445:   STMatMult(pep->st,2,w[1],w[2]);
446:   VecNorm(w[2],NORM_2,&t2);
447:   t2 *= pep->sfactor*pep->sfactor;
448:   *norm = PetscMax(*norm,SlepcAbs(t1,t2));
449:   return(0);
450: }
451: #endif

455: PetscErrorCode PEPSolve_STOAR(PEP pep)
456: {
458:   PEP_TOAR       *ctx = (PEP_TOAR*)pep->data;
459:   PetscInt       j,k,l,nv=0,ld=ctx->ld,lds=ctx->d*ctx->ld,off,ldds,t;
460:   PetscInt       lwa,lrwa,nwu=0,nrwu=0,nconv=0;
461:   PetscScalar    *S=ctx->S,*Q,*work;
462:   PetscReal      beta,norm=1.0,*omega,*a,*b,*r,*rwork;
463:   PetscBool      breakdown,symmlost=PETSC_FALSE,sinv;

466:   PetscCitationsRegister(citation,&cited);
467:   BVSetMatrix(pep->V,NULL,PETSC_FALSE);
468:   lwa = 9*ld*ld+5*ld;
469:   lrwa = 8*ld;
470:   PetscMalloc2(lwa,&work,lrwa,&rwork); /* REVIEW */
471:   PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
472:   RGPushScale(pep->rg,sinv?pep->sfactor:1.0/pep->sfactor);
473:   STScaleShift(pep->st,sinv?pep->sfactor:1.0/pep->sfactor);

475:   /* Restart loop */
476:   l = 0;
477:   DSGetLeadingDimension(pep->ds,&ldds);
478:   while (pep->reason == PEP_CONVERGED_ITERATING) {
479:     pep->its++;
480:     DSGetArrayReal(pep->ds,DS_MAT_T,&a);
481:     b = a+ldds;
482:     DSGetArrayReal(pep->ds,DS_MAT_D,&omega);

484:     /* Compute an nv-step Lanczos factorization */
485:     nv = PetscMin(pep->nconv+pep->mpd,pep->ncv);
486:     PEPSTOARrun(pep,a,b,omega,pep->nconv+l,&nv,&breakdown,&symmlost,work+nwu,pep->work);
487:     beta = b[nv-1];
488:     if (symmlost) {
489:       pep->reason = PEP_DIVERGED_SYMMETRY_LOST;
490:       if (nv==pep->nconv+l+1) { pep->nconv = nconv; break; }
491:     }
492:     DSRestoreArrayReal(pep->ds,DS_MAT_T,&a);
493:     DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
494:     DSSetDimensions(pep->ds,nv,0,pep->nconv,pep->nconv+l);
495:     if (l==0) {
496:       DSSetState(pep->ds,DS_STATE_INTERMEDIATE);
497:     } else {
498:       DSSetState(pep->ds,DS_STATE_RAW);
499:     }

501:     /* Solve projected problem */
502:     DSSolve(pep->ds,pep->eigr,pep->eigi);
503:     DSSort(pep->ds,pep->eigr,pep->eigi,NULL,NULL,NULL);

505:     /* Check convergence */
506:     /* PEPSTOARpreKConvergence(pep,nv,&norm,pep->work);*/
507:     norm = 1.0;
508:     DSGetDimensions(pep->ds,NULL,NULL,NULL,NULL,&t);
509:     PEPKrylovConvergence(pep,PETSC_FALSE,pep->nconv,t-pep->nconv,PetscAbsReal(beta)*norm,&k);
510:     nconv = k;
511:     (*pep->stopping)(pep,pep->its,pep->max_it,k,pep->nev,&pep->reason,pep->stoppingctx);

513:     /* Update l */
514:     if (pep->reason != PEP_CONVERGED_ITERATING || breakdown) l = 0;
515:     else {
516:       l = PetscMax(1,(PetscInt)((nv-k)/2));
517:       l = PetscMin(l,t);
518:       DSGetArrayReal(pep->ds,DS_MAT_T,&a);
519:       if (*(a+ldds+k+l-1)!=0) {
520:         if (k+l<nv-1) l = l+1;
521:         else l = l-1;
522:       }
523:       DSRestoreArrayReal(pep->ds,DS_MAT_T,&a);
524:     }
525:     if (!ctx->lock && l>0) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */

527:     /* Update S */
528:     off = pep->nconv*ldds;
529:     DSGetArray(pep->ds,DS_MAT_Q,&Q);
530:     PEPSTOARSupdate(S,ld,nv+2,pep->nconv,k+l-pep->nconv,nv,Q+off,ldds,work+nwu);
531:     DSRestoreArray(pep->ds,DS_MAT_Q,&Q);

533:     /* Copy last column of S */
534:     PetscMemcpy(S+lds*(k+l),S+lds*nv,lds*sizeof(PetscScalar));

536:     if (pep->reason == PEP_CONVERGED_ITERATING) {
537:       if (breakdown) {
538:         /* Stop if breakdown */
539:         PetscInfo2(pep,"Breakdown STOAR method (it=%D norm=%g)\n",pep->its,(double)beta);
540:         pep->reason = PEP_DIVERGED_BREAKDOWN;
541:       } else {
542:         /* Prepare the Rayleigh quotient for restart */
543:         DSGetArray(pep->ds,DS_MAT_Q,&Q);
544:         DSGetArrayReal(pep->ds,DS_MAT_T,&a);
545:         DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
546:         r = a + 2*ldds;
547:         for (j=k;j<k+l;j++) {
548:           r[j] = PetscRealPart(Q[nv-1+j*ldds]*beta);
549:         }
550:         b = a+ldds;
551:         b[k+l-1] = r[k+l-1];
552:         omega[k+l] = omega[nv];
553:         DSRestoreArray(pep->ds,DS_MAT_Q,&Q);
554:         DSRestoreArrayReal(pep->ds,DS_MAT_T,&a);
555:         DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
556:         /* Truncate S */
557:         DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
558:         PEPSTOARTrunc(pep,nv+2,k+l+1,work+nwu,rwork+nrwu);
559:         DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
560:       }
561:     }


564:     pep->nconv = k;
565:     PEPMonitor(pep,pep->its,pep->nconv,pep->eigr,pep->eigi,pep->errest,nv);
566:   }

568:   if (pep->nconv>0) {
569:     /* Truncate S */
570:     DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
571:     PEPSTOARTrunc(pep,nv+2,pep->nconv,work+nwu,rwork+nrwu);
572:     DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);

574:     /* Extraction */
575:     DSSetDimensions(pep->ds,pep->nconv,0,0,0);
576:     DSSetState(pep->ds,DS_STATE_RAW);

578:     for (j=0;j<pep->nconv;j++) {
579:       pep->eigr[j] *= pep->sfactor;
580:       pep->eigi[j] *= pep->sfactor;
581:     }
582:   }
583:   STScaleShift(pep->st,sinv?1.0/pep->sfactor:pep->sfactor);
584:   RGPopScale(pep->rg);

586:   /* truncate Schur decomposition and change the state to raw so that
587:      DSVectors() computes eigenvectors from scratch */
588:   DSSetDimensions(pep->ds,pep->nconv,0,0,0);
589:   DSSetState(pep->ds,DS_STATE_RAW);
590:   PetscFree2(work,rwork);
591:   return(0);
592: }

596: PetscErrorCode PEPSetFromOptions_STOAR(PetscOptionItems *PetscOptionsObject,PEP pep)
597: {
599:   PetscBool      flg,lock;

602:   PetscOptionsHead(PetscOptionsObject,"PEP STOAR Options");
603:   PetscOptionsBool("-pep_stoar_locking","Choose between locking and non-locking variants","PEPSTOARSetLocking",PETSC_FALSE,&lock,&flg);
604:   if (flg) {
605:     PEPSTOARSetLocking(pep,lock);
606:   }
607:   PetscOptionsTail();
608:   return(0);
609: }

613: static PetscErrorCode PEPSTOARSetLocking_STOAR(PEP pep,PetscBool lock)
614: {
615:   PEP_TOAR *ctx = (PEP_TOAR*)pep->data;

618:   ctx->lock = lock;
619:   return(0);
620: }

624: /*@
625:    PEPSTOARSetLocking - Choose between locking and non-locking variants of
626:    the STOAR method.

628:    Logically Collective on PEP

630:    Input Parameters:
631: +  pep  - the eigenproblem solver context
632: -  lock - true if the locking variant must be selected

634:    Options Database Key:
635: .  -pep_stoar_locking - Sets the locking flag

637:    Notes:
638:    The default is to lock converged eigenpairs when the method restarts.
639:    This behaviour can be changed so that all directions are kept in the
640:    working subspace even if already converged to working accuracy (the
641:    non-locking variant).

643:    Level: advanced

645: .seealso: PEPSTOARGetLocking()
646: @*/
647: PetscErrorCode PEPSTOARSetLocking(PEP pep,PetscBool lock)
648: {

654:   PetscTryMethod(pep,"PEPSTOARSetLocking_C",(PEP,PetscBool),(pep,lock));
655:   return(0);
656: }

660: static PetscErrorCode PEPSTOARGetLocking_STOAR(PEP pep,PetscBool *lock)
661: {
662:   PEP_TOAR *ctx = (PEP_TOAR*)pep->data;

665:   *lock = ctx->lock;
666:   return(0);
667: }

671: /*@
672:    PEPSTOARGetLocking - Gets the locking flag used in the STOAR method.

674:    Not Collective

676:    Input Parameter:
677: .  pep - the eigenproblem solver context

679:    Output Parameter:
680: .  lock - the locking flag

682:    Level: advanced

684: .seealso: PEPSTOARSetLocking()
685: @*/
686: PetscErrorCode PEPSTOARGetLocking(PEP pep,PetscBool *lock)
687: {

693:   PetscUseMethod(pep,"PEPSTOARGetLocking_C",(PEP,PetscBool*),(pep,lock));
694:   return(0);
695: }

699: PetscErrorCode PEPView_STOAR(PEP pep,PetscViewer viewer)
700: {
702:   PEP_TOAR      *ctx = (PEP_TOAR*)pep->data;
703:   PetscBool      isascii;

706:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
707:   if (isascii) {
708:     PetscViewerASCIIPrintf(viewer,"  STOAR: using the %slocking variant\n",ctx->lock?"":"non-");
709:   }
710:   return(0);
711: }

715: PetscErrorCode PEPDestroy_STOAR(PEP pep)
716: {

720:   PetscFree(pep->data);
721:   PetscObjectComposeFunction((PetscObject)pep,"PEPSTOARSetLocking_C",NULL);
722:   PetscObjectComposeFunction((PetscObject)pep,"PEPSTOARGetLocking_C",NULL);
723:   return(0);
724: }

728: PETSC_EXTERN PetscErrorCode PEPCreate_STOAR(PEP pep)
729: {
731:   PEP_TOAR      *ctx;

734:   PetscNewLog(pep,&ctx);
735:   pep->data = (void*)ctx;
736:   ctx->lock = PETSC_TRUE;

738:   pep->ops->solve          = PEPSolve_STOAR;
739:   pep->ops->setup          = PEPSetUp_STOAR;
740:   pep->ops->setfromoptions = PEPSetFromOptions_STOAR;
741:   pep->ops->view           = PEPView_STOAR;
742:   pep->ops->destroy        = PEPDestroy_STOAR;
743:   pep->ops->backtransform  = PEPBackTransform_Default;
744:   pep->ops->computevectors = PEPComputeVectors_Default;
745:   pep->ops->extractvectors = PEPExtractVectors_TOAR;
746:   pep->ops->reset          = PEPReset_TOAR;
747:   PetscObjectComposeFunction((PetscObject)pep,"PEPSTOARSetLocking_C",PEPSTOARSetLocking_STOAR);
748:   PetscObjectComposeFunction((PetscObject)pep,"PEPSTOARGetLocking_C",PEPSTOARGetLocking_STOAR);
749:   return(0);
750: }