Actual source code: nrefine.c

slepc-3.7.2 2016-07-19
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  1: /*
  2:    Newton refinement for polynomial eigenproblems.

  4:    References:

  6:        [1] T. Betcke and D. Kressner, "Perturbation, extraction and refinement
  7:            of invariant pairs for matrix polynomials", Linear Algebra Appl.
  8:            435(3):514-536, 2011.

 10:        [2] C. Campos and J.E. Roman, "Parallel iterative refinement in
 11:            polynomial eigenvalue problems", submitted, 2015.

 13:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 14:    SLEPc - Scalable Library for Eigenvalue Problem Computations
 15:    Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain

 17:    This file is part of SLEPc.

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

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

 28:    You  should have received a copy of the GNU Lesser General  Public  License
 29:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
 30:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 31: */

 33: #include <slepc/private/pepimpl.h>
 34: #include <slepcblaslapack.h>

 36: typedef struct {
 37:   Mat          *A,M1;
 38:   BV           V,M2,M3,W;
 39:   PetscInt     k,nmat;
 40:   PetscScalar  *fih,*work,*M4;
 41:   PetscBLASInt *pM4;
 42:   PetscBool    compM1;
 43:   Vec          t;
 44: } FSubctx;

 46: typedef struct {
 47:   Mat          E[2],M1;
 48:   Vec          tN,ttN,t1,vseq;
 49:   VecScatter   scatterctx;
 50:   PetscBool    compM1;
 51:   PetscInt     *map0,*map1,*idxg,*idxp;
 52:   PetscSubcomm subc;
 53:   VecScatter   scatter_sub;
 54:   VecScatter   *scatter_id,*scatterp_id;
 55:   Mat          *A;
 56:   BV           V,W,M2,M3,Wt;
 57:   PetscScalar  *M4,*w,*wt,*d,*dt;
 58:   Vec          t,tg,Rv,Vi,tp,tpg;
 59:   PetscInt     idx,*cols;
 60: } MatExplicitCtx;

 64: static PetscErrorCode MatFSMult(Mat M ,Vec x,Vec y)
 65: {
 66: #if defined(PETSC_MISSING_LAPACK_GETRS)
 68:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GETRS - Lapack routine is unavailable");
 69: #else
 71:   FSubctx        *ctx;
 72:   PetscInt       k,i;
 73:   PetscScalar    *c;
 74:   PetscBLASInt   k_,one=1,info;

 77:   MatShellGetContext(M,&ctx);
 78:   VecCopy(x,ctx->t);
 79:   k    = ctx->k;
 80:   c    = ctx->work;
 81:   PetscBLASIntCast(k,&k_);
 82:   MatMult(ctx->M1,x,y);
 83:   VecConjugate(ctx->t);
 84:   BVDotVec(ctx->M3,ctx->t,c);
 85:   for (i=0;i<k;i++) c[i] = PetscConj(c[i]);
 86:   PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("N",&k_,&one,ctx->M4,&k_,ctx->pM4,c,&k_,&info));
 87:   BVMultVec(ctx->M2,-1.0,1.0,y,c);
 88:   return(0);
 89: #endif
 90: }

 94: /*
 95:   Evaluates the first d elements of the polynomial basis
 96:   on a given matrix H which is considered to be triangular
 97: */
 98: static PetscErrorCode PEPEvaluateBasisforMatrix(PEP pep,PetscInt nm,PetscInt k,PetscScalar *H,PetscInt ldh,PetscScalar *fH)
 99: {
101:   PetscInt       i,j,ldfh=nm*k,off,nmat=pep->nmat;
102:   PetscReal      *a=pep->pbc,*b=pep->pbc+nmat,*g=pep->pbc+2*nmat,t;
103:   PetscScalar    corr=0.0,alpha,beta;
104:   PetscBLASInt   k_,ldh_,ldfh_;

107:   PetscBLASIntCast(ldh,&ldh_);
108:   PetscBLASIntCast(k,&k_);
109:   PetscBLASIntCast(ldfh,&ldfh_);
110:   PetscMemzero(fH,nm*k*k*sizeof(PetscScalar));
111:   if (nm>0) for (j=0;j<k;j++) fH[j+j*ldfh] = 1.0;
112:   if (nm>1) {
113:     t = b[0]/a[0];
114:     off = k;
115:     for (j=0;j<k;j++) {
116:       for (i=0;i<k;i++) fH[off+i+j*ldfh] = H[i+j*ldh]/a[0];
117:       fH[j+j*ldfh] -= t;
118:     }
119:   }
120:   for (i=2;i<nm;i++) {
121:     off = i*k;
122:     if (i==2) {
123:       for (j=0;j<k;j++) {
124:         fH[off+j+j*ldfh] = 1.0;
125:         H[j+j*ldh] -= b[1];
126:       }
127:     } else {
128:       for (j=0;j<k;j++) {
129:         PetscMemcpy(fH+off+j*ldfh,fH+(i-2)*k+j*ldfh,k*sizeof(PetscScalar));
130:         H[j+j*ldh] += corr-b[i-1];
131:       }
132:     }
133:     corr  = b[i-1];
134:     beta  = -g[i-1]/a[i-1];
135:     alpha = 1/a[i-1];
136:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&k_,&k_,&k_,&alpha,H,&ldh_,fH+(i-1)*k,&ldfh_,&beta,fH+off,&ldfh_));
137:   }
138:   for (j=0;j<k;j++) H[j+j*ldh] += corr;
139:   return(0);
140: }

144: static PetscErrorCode NRefSysSetup_shell(PEP pep,PetscInt k,PetscScalar *fH,PetscScalar *S,PetscInt lds,PetscScalar *fh,PetscScalar h,FSubctx *ctx)
145: {
146: #if defined(PETSC_MISSING_LAPACK_GESV)
148:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GESV - Lapack routine is unavailable");
149: #else
150:   PetscErrorCode    ierr;
151:   PetscScalar       *DHii,*T12,*Tr,*Ts,*array,s,ss,sone=1.0,zero=0.0,*M4=ctx->M4,t,*v,*T;
152:   const PetscScalar *m3,*m2;
153:   PetscInt          i,d,j,nmat=pep->nmat,lda=nmat*k,deg=nmat-1,nloc;
154:   PetscReal         *a=pep->pbc,*b=pep->pbc+nmat,*g=pep->pbc+2*nmat;
155:   PetscBLASInt      k_,lda_,lds_,nloc_,one=1,info;
156:   Mat               *A=ctx->A,Mk,M1=ctx->M1,P;
157:   BV                V=ctx->V,M2=ctx->M2,M3=ctx->M3,W=ctx->W;
158:   MatStructure      str;
159:   Vec               vc;

162:   STGetMatStructure(pep->st,&str);
163:   PetscMalloc3(nmat*k*k,&T12,k*k,&Tr,PetscMax(k*k,nmat),&Ts);
164:   DHii = T12;
165:   PetscMemzero(DHii,k*k*nmat*sizeof(PetscScalar));
166:   for (i=0;i<k;i++) DHii[k+i+i*lda] = 1.0/a[0];
167:   for (d=2;d<nmat;d++) {
168:     for (j=0;j<k;j++) {
169:       for (i=0;i<k;i++) {
170:         DHii[d*k+i+j*lda] = ((h-b[d-1])*DHii[(d-1)*k+i+j*lda]+fH[(d-1)*k+i+j*lda]-g[d-1]*DHii[(d-2)*k+i+j*lda])/(a[d-1]);
171:       }
172:     }
173:   }
174:   /* T11 */
175:   if (!ctx->compM1) {
176:     MatCopy(A[0],M1,DIFFERENT_NONZERO_PATTERN);
177:     PEPEvaluateBasis(pep,h,0,Ts,NULL);
178:     for (j=1;j<nmat;j++) {
179:       MatAXPY(M1,Ts[j],A[j],str);
180:     }
181:   }

183:   /* T22 */
184:   PetscBLASIntCast(lds,&lds_);
185:   PetscBLASIntCast(k,&k_);
186:   PetscBLASIntCast(lda,&lda_);
187:   PetscStackCallBLAS("BLASgemm",BLASgemm_("C","N",&k_,&k_,&k_,&sone,S,&lds_,S,&lds_,&zero,Tr,&k_));
188:   for (i=1;i<deg;i++) {
189:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&k_,&k_,&k_,&sone,Tr,&k_,DHii+i*k,&lda_,&zero,Ts,&k_));
190:     s = (i==1)?0.0:1.0;
191:     PetscStackCallBLAS("BLASgemm",BLASgemm_("C","N",&k_,&k_,&k_,&sone,fH+i*k,&lda_,Ts,&k_,&s,M4,&k_));
192:   }
193:   for (i=0;i<k;i++) for (j=0;j<i;j++) { t=M4[i+j*k];M4[i+j*k]=M4[j+i*k];M4[j+i*k]=t; }

195:   /* T12 */
196:   MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&Mk);
197:   for (i=1;i<nmat;i++) {
198:     MatDenseGetArray(Mk,&array);
199:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&k_,&k_,&k_,&sone,S,&lds_,DHii+i*k,&lda_,&zero,array,&k_));
200:     MatDenseRestoreArray(Mk,&array);
201:     BVSetActiveColumns(W,0,k);
202:     BVMult(W,1.0,0.0,V,Mk);
203:     if (i==1) {
204:       BVMatMult(W,A[i],M2);
205:     } else {
206:       BVMatMult(W,A[i],M3); /* using M3 as work space */
207:       BVMult(M2,1.0,1.0,M3,NULL);
208:     }
209:   }

211:   /* T21 */
212:   MatDenseGetArray(Mk,&array);
213:   for (i=1;i<deg;i++) {
214:     s = (i==1)?0.0:1.0;
215:     ss = PetscConj(fh[i]);
216:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&k_,&k_,&k_,&ss,S,&lds_,fH+i*k,&lda_,&s,array,&k_));
217:   }
218:   MatDenseRestoreArray(Mk,&array);
219:   BVSetActiveColumns(M3,0,k);
220:   BVMult(M3,1.0,0.0,V,Mk);
221:   for (i=0;i<k;i++) {
222:     BVGetColumn(M3,i,&vc);
223:     VecConjugate(vc);
224:     BVRestoreColumn(M3,i,&vc);
225:   }
226:   MatDestroy(&Mk);
227:   PetscFree3(T12,Tr,Ts);

229:   VecGetLocalSize(ctx->t,&nloc);
230:   PetscBLASIntCast(nloc,&nloc_);
231:   PetscMalloc1(nloc*k,&T);
232:   KSPGetOperators(pep->refineksp,NULL,&P);
233:   if (!ctx->compM1) { MatCopy(ctx->M1,P,SAME_NONZERO_PATTERN); }
234:   BVGetArrayRead(ctx->M2,&m2);
235:   BVGetArrayRead(ctx->M3,&m3);
236:   VecGetArray(ctx->t,&v);
237:   for (i=0;i<nloc;i++) for (j=0;j<k;j++) T[j+i*k] = m3[i+j*nloc];
238:   PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&k_,&nloc_,ctx->M4,&k_,ctx->pM4,T,&k_,&info));
239:   for (i=0;i<nloc;i++) v[i] = BLASdot_(&k_,m2+i,&nloc_,T+i*k,&one);
240:   VecRestoreArray(ctx->t,&v);
241:   BVRestoreArrayRead(ctx->M2,&m2);
242:   BVRestoreArrayRead(ctx->M3,&m3);
243:   MatDiagonalSet(P,ctx->t,ADD_VALUES);
244:   PetscFree(T);
245:   KSPSetUp(pep->refineksp);
246:   return(0);
247: #endif
248: }

252: static PetscErrorCode NRefSysSolve_shell(KSP ksp,PetscInt nmat,Vec Rv,PetscScalar *Rh,PetscInt k,Vec dVi,PetscScalar *dHi)
253: {
254: #if defined(PETSC_MISSING_LAPACK_GETRS)
256:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GETRS - Lapack routine is unavailable");
257: #else
259:   PetscScalar    *t0;
260:   PetscBLASInt   k_,one=1,info,lda_;
261:   PetscInt       i,lda=nmat*k;
262:   Mat            M;
263:   FSubctx        *ctx;

266:   KSPGetOperators(ksp,&M,NULL);
267:   MatShellGetContext(M,&ctx);
268:   PetscCalloc1(k,&t0);
269:   PetscBLASIntCast(lda,&lda_);
270:   PetscBLASIntCast(k,&k_);
271:   for (i=0;i<k;i++) t0[i] = Rh[i];
272:   PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("N",&k_,&one,ctx->M4,&k_,ctx->pM4,t0,&k_,&info));
273:   BVMultVec(ctx->M2,-1.0,1.0,Rv,t0);
274:   KSPSolve(ksp,Rv,dVi);
275:   VecConjugate(dVi);
276:   BVDotVec(ctx->M3,dVi,dHi);
277:   VecConjugate(dVi);
278:   for (i=0;i<k;i++) dHi[i] = Rh[i]-PetscConj(dHi[i]);
279:   PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("N",&k_,&one,ctx->M4,&k_,ctx->pM4,dHi,&k_,&info));
280:   PetscFree(t0);
281:   return(0);
282: #endif
283: }

287: /*
288:    Computes the residual P(H,V*S)*e_j for the polynomial
289: */
290: static PetscErrorCode NRefRightSide(PetscInt nmat,PetscReal *pcf,Mat *A,PetscInt k,BV V,PetscScalar *S,PetscInt lds,PetscInt j,PetscScalar *H,PetscInt ldh,PetscScalar *fH,PetscScalar *DfH,PetscScalar *dH,BV dV,PetscScalar *dVS,PetscInt rds,Vec Rv,PetscScalar *Rh,BV W,Vec t)
291: {
293:   PetscScalar    *DS0,*DS1,*F,beta=0.0,sone=1.0,none=-1.0,tt=0.0,*h,zero=0.0,*Z,*c0;
294:   PetscReal      *a=pcf,*b=pcf+nmat,*g=b+nmat;
295:   PetscInt       i,ii,jj,lda;
296:   PetscBLASInt   lda_,k_,ldh_,lds_,nmat_,k2_,krds_,j_,one=1;
297:   Mat            M0;
298:   Vec            w;

301:   PetscMalloc4(k*nmat,&h,k*k,&DS0,k*k,&DS1,k*k,&Z);
302:   lda = k*nmat;
303:   PetscBLASIntCast(k,&k_);
304:   PetscBLASIntCast(lds,&lds_);
305:   PetscBLASIntCast(lda,&lda_);
306:   PetscBLASIntCast(nmat,&nmat_);
307:   PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&k_,&nmat_,&k_,&sone,S,&lds_,fH+j*lda,&k_,&zero,h,&k_));
308:   MatCreateSeqDense(PETSC_COMM_SELF,k,nmat,h,&M0);
309:   BVSetActiveColumns(W,0,nmat);
310:   BVMult(W,1.0,0.0,V,M0);
311:   MatDestroy(&M0);

313:   BVGetColumn(W,0,&w);
314:   MatMult(A[0],w,Rv);
315:   BVRestoreColumn(W,0,&w);
316:   for (i=1;i<nmat;i++) {
317:     BVGetColumn(W,i,&w);
318:     MatMult(A[i],w,t);
319:     BVRestoreColumn(W,i,&w);
320:     VecAXPY(Rv,1.0,t);
321:   }
322:   /* Update right-hand side */
323:   if (j) {
324:     PetscBLASIntCast(ldh,&ldh_);
325:     PetscMemzero(Z,k*k*sizeof(PetscScalar));
326:     PetscMemzero(DS0,k*k*sizeof(PetscScalar));
327:     PetscMemcpy(Z+(j-1)*k,dH+(j-1)*k,k*sizeof(PetscScalar));
328:     /* Update DfH */
329:     for (i=1;i<nmat;i++) {
330:       if (i>1) {
331:         beta = -g[i-1];
332:         PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&k_,&k_,&k_,&sone,fH+(i-1)*k,&lda_,Z,&k_,&beta,DS0,&k_));
333:         tt += -b[i-1];
334:         for (ii=0;ii<k;ii++) H[ii+ii*ldh] += tt;
335:         tt = b[i-1];
336:         beta = 1.0/a[i-1];
337:         PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&k_,&k_,&k_,&beta,DS1,&k_,H,&ldh_,&beta,DS0,&k_));
338:         F = DS0; DS0 = DS1; DS1 = F;
339:       } else {
340:         PetscMemzero(DS1,k*k*sizeof(PetscScalar));
341:         for (ii=0;ii<k;ii++) DS1[ii+(j-1)*k] = Z[ii+(j-1)*k]/a[0];
342:       }
343:       for (jj=j;jj<k;jj++) {
344:         for (ii=0;ii<k;ii++) DfH[k*i+ii+jj*lda] += DS1[ii+jj*k];
345:       }
346:     }
347:     for (ii=0;ii<k;ii++) H[ii+ii*ldh] += tt;
348:     /* Update right-hand side */
349:     PetscBLASIntCast(2*k,&k2_);
350:     PetscBLASIntCast(j,&j_);
351:     PetscBLASIntCast(k+rds,&krds_);
352:     c0 = DS0;
353:     PetscMemzero(Rh,k*sizeof(PetscScalar));
354:     for (i=0;i<nmat;i++) {
355:       PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&krds_,&j_,&sone,dVS,&k2_,fH+j*lda+i*k,&one,&zero,h,&one));
356:       PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&k_,&k_,&sone,S,&lds_,DfH+i*k+j*lda,&one,&sone,h,&one));
357:       BVMultVec(V,1.0,0.0,t,h);
358:       BVSetActiveColumns(dV,0,rds);
359:       BVMultVec(dV,1.0,1.0,t,h+k);
360:       BVGetColumn(W,i,&w);
361:       MatMult(A[i],t,w);
362:       BVRestoreColumn(W,i,&w);
363:       if (i>0 && i<nmat-1) {
364:         PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&k_,&k_,&sone,S,&lds_,h,&one,&zero,c0,&one));
365:         PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&k_,&k_,&none,fH+i*k,&lda_,c0,&one,&sone,Rh,&one));
366:       }
367:     }

369:     for (i=0;i<nmat;i++) h[i] = -1.0;
370:     BVMultVec(W,1.0,1.0,Rv,h);
371:   }
372:   PetscFree4(h,DS0,DS1,Z);
373:   return(0);
374: }

378: static PetscErrorCode NRefSysSolve_mbe(PetscInt k,PetscInt sz,BV W,PetscScalar *w,BV Wt,PetscScalar *wt,PetscScalar *d,PetscScalar *dt,KSP ksp,BV T2,BV T3 ,PetscScalar *T4,PetscBool trans,Vec x1,PetscScalar *x2,Vec sol1,PetscScalar *sol2,Vec vw)
379: {
381:   PetscInt       i,j,incf,incc;
382:   PetscScalar    *y,*g,*xx2,*ww,y2,*dd;
383:   Vec            v,t,xx1;
384:   BV             WW,T;

387:   PetscMalloc3(sz,&y,sz,&g,k,&xx2);
388:   if (trans) {
389:     WW = W; ww = w; dd = d; T = T3; incf = 0; incc = 1;
390:   } else {
391:     WW = Wt; ww = wt; dd = dt; T = T2; incf = 1; incc = 0;
392:   }
393:   xx1 = vw;
394:   VecCopy(x1,xx1);
395:   PetscMemcpy(xx2,x2,sz*sizeof(PetscScalar));
396:   PetscMemzero(sol2,k*sizeof(PetscScalar));
397:   for (i=sz-1;i>=0;i--) {
398:     BVGetColumn(WW,i,&v);
399:     VecConjugate(v);
400:     VecDot(xx1,v,y+i);
401:     VecConjugate(v);
402:     BVRestoreColumn(WW,i,&v);
403:     for (j=0;j<i;j++) y[i] += ww[j+i*k]*xx2[j];
404:     y[i] = -(y[i]-xx2[i])/dd[i];
405:     BVGetColumn(T,i,&t);
406:     VecAXPY(xx1,-y[i],t);
407:     BVRestoreColumn(T,i,&t);
408:     for(j=0;j<=i;j++) xx2[j] -= y[i]*T4[j*incf+incc*i+(i*incf+incc*j)*k];
409:     g[i] = xx2[i];
410:   }
411:   if (trans) {
412:     KSPSolveTranspose(ksp,xx1,sol1);
413:   } else {
414:     KSPSolve(ksp,xx1,sol1);
415:   }
416:   if (trans) {
417:     WW = Wt; ww = wt; dd = dt; T = T2; incf = 1; incc = 0;
418:   } else {
419:     WW = W; ww = w; dd = d; T = T3; incf = 0; incc = 1;
420:   }
421:   for (i=0;i<sz;i++) {
422:     BVGetColumn(T,i,&t);
423:     VecConjugate(t);
424:     VecDot(sol1,t,&y2);
425:     VecConjugate(t);
426:     BVRestoreColumn(T,i,&t);
427:     for (j=0;j<i;j++) y2 += sol2[j]*T4[j*incf+incc*i+(i*incf+incc*j)*k];
428:     y2 = (g[i]-y2)/dd[i];
429:     BVGetColumn(WW,i,&v);
430:     VecAXPY(sol1,-y2,v);
431:     for (j=0;j<i;j++) sol2[j] -= ww[j+i*k]*y2;
432:     sol2[i] = y[i]+y2;
433:     BVRestoreColumn(WW,i,&v);
434:   }
435:   PetscFree3(y,g,xx2);
436:   return(0);
437: }

441: static PetscErrorCode NRefSysSetup_mbe(PEP pep,PetscInt k,KSP ksp,PetscScalar *fH,PetscScalar *S,PetscInt lds,PetscScalar *fh,PetscScalar h,BV V,MatExplicitCtx *matctx)
442: {
444:   PetscInt       i,j,l,nmat=pep->nmat,lda=nmat*k,deg=nmat-1;
445:   Mat            M1=matctx->M1,*A,*At,Mk;
446:   PetscReal      *a=pep->pbc,*b=pep->pbc+nmat,*g=pep->pbc+2*nmat;
447:   PetscScalar    s,ss,*DHii,*T12,*array,*Ts,*Tr,*M4=matctx->M4,sone=1.0,zero=0.0;
448:   PetscScalar    *w=matctx->w,*wt=matctx->wt,*d=matctx->d,*dt=matctx->dt;
449:   PetscBLASInt   lds_,lda_,k_;
450:   MatStructure   str;
451:   PetscBool      flg;
452:   BV             M2=matctx->M2,M3=matctx->M3,W=matctx->W,Wt=matctx->Wt;
453:   Vec            vc,vc2;

456:   PetscMalloc3(nmat*k*k,&T12,k*k,&Tr,PetscMax(k*k,nmat),&Ts);
457:   STGetMatStructure(pep->st,&str);
458:   STGetTransform(pep->st,&flg);
459:   if (flg) {
460:     PetscMalloc1(pep->nmat,&At);
461:     for (i=0;i<pep->nmat;i++) {
462:       STGetTOperators(pep->st,i,&At[i]);
463:     }
464:   } else At = pep->A;
465:   if (matctx->subc) A = matctx->A;
466:   else A = At;
467:   /* Form the explicit system matrix */
468:   DHii = T12;
469:   PetscMemzero(DHii,k*k*nmat*sizeof(PetscScalar));
470:   for (i=0;i<k;i++) DHii[k+i+i*lda] = 1.0/a[0];
471:   for (l=2;l<nmat;l++) {
472:     for (j=0;j<k;j++) {
473:       for (i=0;i<k;i++) {
474:         DHii[l*k+i+j*lda] = ((h-b[l-1])*DHii[(l-1)*k+i+j*lda]+fH[(l-1)*k+i+j*lda]-g[l-1]*DHii[(l-2)*k+i+j*lda])/a[l-1];
475:       }
476:     }
477:   }

479:   /* T11 */
480:   if (!matctx->compM1) {
481:     MatCopy(A[0],M1,DIFFERENT_NONZERO_PATTERN);
482:     PEPEvaluateBasis(pep,h,0,Ts,NULL);
483:     for (j=1;j<nmat;j++) {
484:       MatAXPY(M1,Ts[j],A[j],str);
485:     }
486:   }

488:   /* T22 */
489:   PetscBLASIntCast(lds,&lds_);
490:   PetscBLASIntCast(k,&k_);
491:   PetscBLASIntCast(lda,&lda_);
492:   PetscStackCallBLAS("BLASgemm",BLASgemm_("C","N",&k_,&k_,&k_,&sone,S,&lds_,S,&lds_,&zero,Tr,&k_));
493:   for (i=1;i<deg;i++) {
494:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&k_,&k_,&k_,&sone,Tr,&k_,DHii+i*k,&lda_,&zero,Ts,&k_));
495:     s = (i==1)?0.0:1.0;
496:     PetscStackCallBLAS("BLASgemm",BLASgemm_("C","N",&k_,&k_,&k_,&sone,fH+i*k,&lda_,Ts,&k_,&s,M4,&k_));
497:   }

499:   /* T12 */
500:   MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&Mk);
501:   for (i=1;i<nmat;i++) {
502:     MatDenseGetArray(Mk,&array);
503:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&k_,&k_,&k_,&sone,S,&lds_,DHii+i*k,&lda_,&zero,array,&k_));
504:     MatDenseRestoreArray(Mk,&array);
505:     BVSetActiveColumns(W,0,k);
506:     BVMult(W,1.0,0.0,V,Mk);
507:     if (i==1) {
508:       BVMatMult(W,A[i],M2);
509:     } else {
510:       BVMatMult(W,A[i],M3); /* using M3 as work space */
511:       BVMult(M2,1.0,1.0,M3,NULL);
512:     }
513:   }

515:   /* T21 */
516:   MatDenseGetArray(Mk,&array);
517:   for (i=1;i<deg;i++) {
518:     s = (i==1)?0.0:1.0;
519:     ss = PetscConj(fh[i]);
520:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&k_,&k_,&k_,&ss,S,&lds_,fH+i*k,&lda_,&s,array,&k_));
521:   }
522:   MatDenseRestoreArray(Mk,&array);
523:   BVSetActiveColumns(M3,0,k);
524:   BVMult(M3,1.0,0.0,V,Mk);
525:   for (i=0;i<k;i++) {
526:     BVGetColumn(M3,i,&vc);
527:     VecConjugate(vc);
528:     BVRestoreColumn(M3,i,&vc);
529:   }

531:   KSPSetOperators(ksp,M1,M1);
532:   KSPSetUp(ksp);
533:   MatDestroy(&Mk);

535:   /* Set up for BEMW */
536:   for (i=0;i<k;i++) {
537:     BVGetColumn(M2,i,&vc);
538:     BVGetColumn(W,i,&vc2);
539:     NRefSysSolve_mbe(k,i,W,w,Wt,wt,d,dt,ksp,M2,M3,M4,PETSC_FALSE,vc,M4+i*k,vc2,w+i*k,matctx->t);
540:     BVRestoreColumn(M2,i,&vc);
541:     BVGetColumn(M3,i,&vc);
542:     VecConjugate(vc);
543:     VecDot(vc2,vc,&d[i]);
544:     VecConjugate(vc);
545:     BVRestoreColumn(M3,i,&vc);
546:     for (j=0;j<i;j++) d[i] += M4[i+j*k]*w[j+i*k];
547:     d[i] = M4[i+i*k]-d[i];
548:     BVRestoreColumn(W,i,&vc2);

550:     BVGetColumn(M3,i,&vc);
551:     BVGetColumn(Wt,i,&vc2);
552:     for (j=0;j<=i;j++) Ts[j] = M4[i+j*k];
553:     NRefSysSolve_mbe(k,i,W,w,Wt,wt,d,dt,ksp,M2,M3,M4,PETSC_TRUE,vc,Ts,vc2,wt+i*k,matctx->t);
554:     BVRestoreColumn(M3,i,&vc);
555:     BVGetColumn(M2,i,&vc);
556:     VecConjugate(vc2);
557:     VecDot(vc,vc2,&dt[i]);
558:     VecConjugate(vc2);
559:     BVRestoreColumn(M2,i,&vc);
560:     for (j=0;j<i;j++) dt[i] += M4[j+i*k]*wt[j+i*k];
561:     dt[i] = M4[i+i*k]-dt[i];
562:     BVRestoreColumn(Wt,i,&vc2);
563:   }

565:   if (flg) {
566:     PetscFree(At);
567:   }
568:   PetscFree3(T12,Tr,Ts);
569:   return(0);
570: }

574: static PetscErrorCode NRefSysSetup_explicit(PEP pep,PetscInt k,KSP ksp,PetscScalar *fH,PetscScalar *S,PetscInt lds,PetscScalar *fh,PetscScalar h,BV V,MatExplicitCtx *matctx,BV W)
575: {
576:   PetscErrorCode    ierr;
577:   PetscInt          i,j,d,n,n0,m0,n1,m1,nmat=pep->nmat,lda=nmat*k,deg=nmat-1;
578:   PetscInt          *idxg=matctx->idxg,*idxp=matctx->idxp,idx,ncols;
579:   Mat               M,*E=matctx->E,*A,*At,Mk,Md;
580:   PetscReal         *a=pep->pbc,*b=pep->pbc+nmat,*g=pep->pbc+2*nmat;
581:   PetscScalar       s,ss,*DHii,*T22,*T21,*T12,*Ts,*Tr,*array,*ts,sone=1.0,zero=0.0;
582:   PetscBLASInt      lds_,lda_,k_;
583:   const PetscInt    *idxmc;
584:   const PetscScalar *valsc,*carray;
585:   MatStructure      str;
586:   Vec               vc,vc0;
587:   PetscBool         flg;

590:   PetscMalloc5(k*k,&T22,k*k,&T21,nmat*k*k,&T12,k*k,&Tr,k*k,&Ts);
591:   STGetMatStructure(pep->st,&str);
592:   KSPGetOperators(ksp,&M,NULL);
593:   MatGetOwnershipRange(E[1],&n1,&m1);
594:   MatGetOwnershipRange(E[0],&n0,&m0);
595:   MatGetOwnershipRange(M,&n,NULL);
596:   PetscMalloc1(nmat,&ts);
597:   STGetTransform(pep->st,&flg);
598:   if (flg) {
599:     PetscMalloc1(pep->nmat,&At);
600:     for (i=0;i<pep->nmat;i++) {
601:       STGetTOperators(pep->st,i,&At[i]);
602:     }
603:   } else At = pep->A;
604:   if (matctx->subc) A = matctx->A;
605:   else A = At;
606:   /* Form the explicit system matrix */
607:   DHii = T12;
608:   PetscMemzero(DHii,k*k*nmat*sizeof(PetscScalar));
609:   for (i=0;i<k;i++) DHii[k+i+i*lda] = 1.0/a[0];
610:   for (d=2;d<nmat;d++) {
611:     for (j=0;j<k;j++) {
612:       for (i=0;i<k;i++) {
613:         DHii[d*k+i+j*lda] = ((h-b[d-1])*DHii[(d-1)*k+i+j*lda]+fH[(d-1)*k+i+j*lda]-g[d-1]*DHii[(d-2)*k+i+j*lda])/a[d-1];
614:       }
615:     }
616:   }

618:   /* T11 */
619:   if (!matctx->compM1) {
620:     MatCopy(A[0],E[0],DIFFERENT_NONZERO_PATTERN);
621:     PEPEvaluateBasis(pep,h,0,Ts,NULL);
622:     for (j=1;j<nmat;j++) {
623:       MatAXPY(E[0],Ts[j],A[j],str);
624:     }
625:   }
626:   for (i=n0;i<m0;i++) {
627:     MatGetRow(E[0],i,&ncols,&idxmc,&valsc);
628:     idx = n+i-n0;
629:     for (j=0;j<ncols;j++) {
630:       idxg[j] = matctx->map0[idxmc[j]];
631:     }
632:     MatSetValues(M,1,&idx,ncols,idxg,valsc,INSERT_VALUES);
633:     MatRestoreRow(E[0],i,&ncols,&idxmc,&valsc);
634:   }

636:   /* T22 */
637:   PetscBLASIntCast(lds,&lds_);
638:   PetscBLASIntCast(k,&k_);
639:   PetscBLASIntCast(lda,&lda_);
640:   PetscStackCallBLAS("BLASgemm",BLASgemm_("C","N",&k_,&k_,&k_,&sone,S,&lds_,S,&lds_,&zero,Tr,&k_));
641:   for (i=1;i<deg;i++) {
642:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&k_,&k_,&k_,&sone,Tr,&k_,DHii+i*k,&lda_,&zero,Ts,&k_));
643:     s = (i==1)?0.0:1.0;
644:     PetscStackCallBLAS("BLASgemm",BLASgemm_("C","N",&k_,&k_,&k_,&sone,fH+i*k,&lda_,Ts,&k_,&s,T22,&k_));
645:   }
646:   for (j=0;j<k;j++) idxp[j] = matctx->map1[j];
647:   for (i=0;i<m1-n1;i++) {
648:     idx = n+m0-n0+i;
649:     for (j=0;j<k;j++) {
650:       Tr[j] = T22[n1+i+j*k];
651:     }
652:     MatSetValues(M,1,&idx,k,idxp,Tr,INSERT_VALUES);
653:   }

655:   /* T21 */
656:   for (i=1;i<deg;i++) {
657:     s = (i==1)?0.0:1.0;
658:     ss = PetscConj(fh[i]);
659:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&k_,&k_,&k_,&ss,S,&lds_,fH+i*k,&lda_,&s,T21,&k_));
660:   }
661:   BVSetActiveColumns(W,0,k);
662:   MatCreateSeqDense(PETSC_COMM_SELF,k,k,T21,&Mk);
663:   BVMult(W,1.0,0.0,V,Mk);
664:   for (i=0;i<k;i++) {
665:     BVGetColumn(W,i,&vc);
666:     VecConjugate(vc);
667:     VecGetArrayRead(vc,&carray);
668:     idx = matctx->map1[i];
669:     MatSetValues(M,1,&idx,m0-n0,matctx->map0+n0,carray,INSERT_VALUES);
670:     VecRestoreArrayRead(vc,&carray);
671:     BVRestoreColumn(W,i,&vc);
672:   }

674:   /* T12 */
675:   for (i=1;i<nmat;i++) {
676:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&k_,&k_,&k_,&sone,S,&lds_,DHii+i*k,&lda_,&zero,Ts,&k_));
677:     for (j=0;j<k;j++) {
678:       PetscMemcpy(T12+i*k+j*lda,Ts+j*k,k*sizeof(PetscScalar));
679:     }
680:   }
681:   MatCreateSeqDense(PETSC_COMM_SELF,k,nmat-1,NULL,&Md);
682:   for (i=0;i<nmat;i++) ts[i] = 1.0;
683:   for (j=0;j<k;j++) {
684:     MatDenseGetArray(Md,&array);
685:     PetscMemcpy(array,T12+k+j*lda,(nmat-1)*k*sizeof(PetscScalar));
686:     MatDenseRestoreArray(Md,&array);
687:     BVSetActiveColumns(W,0,nmat-1);
688:     BVMult(W,1.0,0.0,V,Md);
689:     for (i=nmat-1;i>0;i--) {
690:       BVGetColumn(W,i-1,&vc0);
691:       BVGetColumn(W,i,&vc);
692:       MatMult(A[i],vc0,vc);
693:       BVRestoreColumn(W,i-1,&vc0);
694:       BVRestoreColumn(W,i,&vc);
695:     }
696:     BVSetActiveColumns(W,1,nmat);
697:     BVGetColumn(W,0,&vc0);
698:     BVMultVec(W,1.0,0.0,vc0,ts);
699:     VecGetArrayRead(vc0,&carray);
700:     idx = matctx->map1[j];
701:     MatSetValues(M,m0-n0,matctx->map0+n0,1,&idx,carray,INSERT_VALUES);
702:     VecRestoreArrayRead(vc0,&carray);
703:     BVRestoreColumn(W,0,&vc0);
704:   }
705:   MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);
706:   MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);
707:   KSPSetOperators(ksp,M,M);
708:   KSPSetUp(ksp);
709:   PetscFree(ts);
710:   MatDestroy(&Mk);
711:   MatDestroy(&Md);
712:   if (flg) {
713:     PetscFree(At);
714:   }
715:   PetscFree5(T22,T21,T12,Tr,Ts);
716:   return(0);
717: }

721: static PetscErrorCode NRefSysSolve_explicit(PetscInt k,KSP ksp,Vec Rv,PetscScalar *Rh,Vec dVi,PetscScalar *dHi,MatExplicitCtx *matctx)
722: {
723:   PetscErrorCode    ierr;
724:   PetscInt          n0,m0,n1,m1,i;
725:   PetscScalar       *arrayV;
726:   const PetscScalar *array;

729:   MatGetOwnershipRange(matctx->E[1],&n1,&m1);
730:   MatGetOwnershipRange(matctx->E[0],&n0,&m0);

732:   /* Right side */
733:   VecGetArrayRead(Rv,&array);
734:   VecSetValues(matctx->tN,m0-n0,matctx->map0+n0,array,INSERT_VALUES);
735:   VecRestoreArrayRead(Rv,&array);
736:   VecSetValues(matctx->tN,m1-n1,matctx->map1+n1,Rh+n1,INSERT_VALUES);
737:   VecAssemblyBegin(matctx->tN);
738:   VecAssemblyEnd(matctx->tN);

740:   /* Solve */
741:   KSPSolve(ksp,matctx->tN,matctx->ttN);

743:   /* Retrieve solution */
744:   VecGetArray(dVi,&arrayV);
745:   VecGetArrayRead(matctx->ttN,&array);
746:   PetscMemcpy(arrayV,array,(m0-n0)*sizeof(PetscScalar));
747:   VecRestoreArray(dVi,&arrayV);
748:   if (!matctx->subc) {
749:     VecGetArray(matctx->t1,&arrayV);
750:     for (i=0;i<m1-n1;i++) arrayV[i] =  array[m0-n0+i];
751:     VecRestoreArray(matctx->t1,&arrayV);
752:     VecRestoreArrayRead(matctx->ttN,&array);
753:     VecScatterBegin(matctx->scatterctx,matctx->t1,matctx->vseq,INSERT_VALUES,SCATTER_FORWARD);
754:     VecScatterEnd(matctx->scatterctx,matctx->t1,matctx->vseq,INSERT_VALUES,SCATTER_FORWARD);
755:     VecGetArrayRead(matctx->vseq,&array);
756:     for (i=0;i<k;i++) dHi[i] = array[i];
757:     VecRestoreArrayRead(matctx->vseq,&array);
758:   }
759:   return(0);
760: }

764: static PetscErrorCode NRefSysIter(PetscInt i,PEP pep,PetscInt k,KSP ksp,PetscScalar *fH,PetscScalar *S,PetscInt lds,PetscScalar *fh,PetscScalar *H,PetscInt ldh,Vec Rv,PetscScalar *Rh,BV V,Vec dVi,PetscScalar *dHi,MatExplicitCtx *matctx,BV W)
765: {
766:   PetscErrorCode    ierr;
767:   PetscInt          j,m,lda=pep->nmat*k,n0,m0,idx;
768:   PetscMPIInt       root,len;
769:   PetscScalar       *array2,h;
770:   const PetscScalar *array;
771:   Vec               R,Vi;
772:   FSubctx           *ctx;
773:   Mat               M;

776:   if (!matctx || !matctx->subc) {
777:     for (j=0;j<pep->nmat;j++) fh[j] = fH[j*k+i+i*lda];
778:     h   = H[i+i*ldh];
779:     idx = i;
780:     R   = Rv;
781:     Vi  = dVi;
782:     switch (pep->scheme) {
783:     case PEP_REFINE_SCHEME_EXPLICIT:
784:       NRefSysSetup_explicit(pep,k,ksp,fH,S,lds,fh,h,V,matctx,W);
785:       matctx->compM1 = PETSC_FALSE;
786:       break;
787:     case PEP_REFINE_SCHEME_MBE:
788:       NRefSysSetup_mbe(pep,k,ksp,fH,S,lds,fh,h,V,matctx);
789:       matctx->compM1 = PETSC_FALSE;
790:       break;
791:     case PEP_REFINE_SCHEME_SCHUR:
792:       KSPGetOperators(ksp,&M,NULL);
793:       MatShellGetContext(M,&ctx);
794:       NRefSysSetup_shell(pep,k,fH,S,lds,fh,h,ctx);
795:       ctx->compM1 = PETSC_FALSE;
796:       break;
797:     }
798:   } else {
799:     if (i%matctx->subc->n==0 && (idx=i+matctx->subc->color)<k) {
800:       for (j=0;j<pep->nmat;j++) fh[j] = fH[j*k+idx+idx*lda];
801:       h = H[idx+idx*ldh];
802:       matctx->idx = idx;
803:       switch (pep->scheme) {
804:       case PEP_REFINE_SCHEME_EXPLICIT:
805:         NRefSysSetup_explicit(pep,k,ksp,fH,S,lds,fh,h,matctx->V,matctx,matctx->W);
806:         matctx->compM1 = PETSC_FALSE;
807:         break;
808:       case PEP_REFINE_SCHEME_MBE:
809:         NRefSysSetup_mbe(pep,k,ksp,fH,S,lds,fh,h,matctx->V,matctx);
810:         matctx->compM1 = PETSC_FALSE;
811:         break;
812:       case PEP_REFINE_SCHEME_SCHUR:
813:         break;
814:       }
815:     } else idx = matctx->idx;
816:     VecScatterBegin(matctx->scatter_id[i%matctx->subc->n],Rv,matctx->tg,INSERT_VALUES,SCATTER_FORWARD);
817:     VecScatterEnd(matctx->scatter_id[i%matctx->subc->n],Rv,matctx->tg,INSERT_VALUES,SCATTER_FORWARD);
818:     VecGetArrayRead(matctx->tg,&array);
819:     VecPlaceArray(matctx->t,array);
820:     VecCopy(matctx->t,matctx->Rv);
821:     VecResetArray(matctx->t);
822:     VecRestoreArrayRead(matctx->tg,&array);
823:     R  = matctx->Rv;
824:     Vi = matctx->Vi;
825:   }
826:   if (idx==i && idx<k) {
827:     switch (pep->scheme) {
828:       case PEP_REFINE_SCHEME_EXPLICIT:
829:         NRefSysSolve_explicit(k,ksp,R,Rh,Vi,dHi,matctx);
830:         break;
831:       case PEP_REFINE_SCHEME_MBE:
832:         NRefSysSolve_mbe(k,k,matctx->W,matctx->w,matctx->Wt,matctx->wt,matctx->d,matctx->dt,ksp,matctx->M2,matctx->M3 ,matctx->M4,PETSC_FALSE,R,Rh,Vi,dHi,matctx->t);
833:         break;
834:       case PEP_REFINE_SCHEME_SCHUR:
835:         NRefSysSolve_shell(ksp,pep->nmat,R,Rh,k,Vi,dHi);
836:         break;
837:     }
838:   }
839:   if (matctx && matctx->subc) {
840:     VecGetLocalSize(Vi,&m);
841:     VecGetArrayRead(Vi,&array);
842:     VecGetArray(matctx->tg,&array2);
843:     PetscMemcpy(array2,array,m*sizeof(PetscScalar));
844:     VecRestoreArray(matctx->tg,&array2);
845:     VecRestoreArrayRead(Vi,&array);
846:     VecScatterBegin(matctx->scatter_id[i%matctx->subc->n],matctx->tg,dVi,INSERT_VALUES,SCATTER_REVERSE);
847:     VecScatterEnd(matctx->scatter_id[i%matctx->subc->n],matctx->tg,dVi,INSERT_VALUES,SCATTER_REVERSE);
848:     switch (pep->scheme) {
849:     case PEP_REFINE_SCHEME_EXPLICIT:
850:       MatGetOwnershipRange(matctx->E[0],&n0,&m0);
851:       VecGetArrayRead(matctx->ttN,&array);
852:       VecPlaceArray(matctx->tp,array+m0-n0);
853:       VecScatterBegin(matctx->scatterp_id[i%matctx->subc->n],matctx->tp,matctx->tpg,INSERT_VALUES,SCATTER_FORWARD);
854:       VecScatterEnd(matctx->scatterp_id[i%matctx->subc->n],matctx->tp,matctx->tpg,INSERT_VALUES,SCATTER_FORWARD);
855:       VecResetArray(matctx->tp);
856:       VecRestoreArrayRead(matctx->ttN,&array);
857:       VecGetArrayRead(matctx->tpg,&array);
858:       for (j=0;j<k;j++) dHi[j] = array[j];
859:       VecRestoreArrayRead(matctx->tpg,&array);
860:       break;
861:      case PEP_REFINE_SCHEME_MBE:
862:       root = 0;
863:       for (j=0;j<i%matctx->subc->n;j++) root += matctx->subc->subsize[j];
864:       PetscMPIIntCast(k,&len);
865:       MPI_Bcast(dHi,len,MPIU_SCALAR,root,matctx->subc->dupparent);
866:       break;
867:     case PEP_REFINE_SCHEME_SCHUR:
868:       break;
869:     }
870:   }
871:   return(0);
872: }

876: static PetscErrorCode PEPNRefForwardSubstitution(PEP pep,PetscInt k,PetscScalar *S,PetscInt lds,PetscScalar *H,PetscInt ldh,PetscScalar *fH,BV dV,PetscScalar *dVS,PetscInt *rds,PetscScalar *dH,PetscInt lddh,KSP ksp,MatExplicitCtx *matctx)
877: {
879:   PetscInt       i,nmat=pep->nmat,lda=nmat*k;
880:   PetscScalar    *fh,*Rh,*DfH;
881:   PetscReal      norm;
882:   BV             W;
883:   Vec            Rv,t,dvi;
884:   FSubctx        *ctx;
885:   Mat            M,*At;
886:   PetscBool      flg,lindep;

889:   PetscMalloc2(nmat*k*k,&DfH,k,&Rh);
890:   *rds = 0;
891:   BVCreateVec(pep->V,&Rv);
892:   switch (pep->scheme) {
893:   case PEP_REFINE_SCHEME_EXPLICIT:
894:     BVCreateVec(pep->V,&t);
895:     BVDuplicateResize(pep->V,PetscMax(k,nmat),&W);
896:     PetscMalloc1(nmat,&fh);
897:     break;
898:   case PEP_REFINE_SCHEME_MBE:
899:     if (matctx->subc) {
900:       BVCreateVec(pep->V,&t);
901:       BVDuplicateResize(pep->V,PetscMax(k,nmat),&W);
902:     } else {
903:       W = matctx->W;
904:       PetscObjectReference((PetscObject)W);
905:       t = matctx->t;
906:       PetscObjectReference((PetscObject)t);
907:     }
908:     BVScale(matctx->W,0.0);
909:     BVScale(matctx->Wt,0.0);
910:     BVScale(matctx->M2,0.0);
911:     BVScale(matctx->M3,0.0);
912:     PetscMalloc1(nmat,&fh);
913:     break;
914:   case PEP_REFINE_SCHEME_SCHUR:
915:     KSPGetOperators(ksp,&M,NULL);
916:     MatShellGetContext(M,&ctx);
917:     BVCreateVec(pep->V,&t);
918:     BVDuplicateResize(pep->V,PetscMax(k,nmat),&W);
919:     fh = ctx->fih;
920:     break;
921:   }
922:   PetscMemzero(dVS,2*k*k*sizeof(PetscScalar));
923:   PetscMemzero(DfH,lda*k*sizeof(PetscScalar));
924:   STGetTransform(pep->st,&flg);
925:   if (flg) {
926:     PetscMalloc1(pep->nmat,&At);
927:     for (i=0;i<pep->nmat;i++) {
928:       STGetTOperators(pep->st,i,&At[i]);
929:     }
930:   } else At = pep->A;

932:   /* Main loop for computing the ith columns of dX and dS */
933:   for (i=0;i<k;i++) {
934:     /* Compute and update i-th column of the right hand side */
935:     PetscMemzero(Rh,k*sizeof(PetscScalar));
936:     NRefRightSide(nmat,pep->pbc,At,k,pep->V,S,lds,i,H,ldh,fH,DfH,dH,dV,dVS,*rds,Rv,Rh,W,t);

938:     /* Update and solve system */
939:     BVGetColumn(dV,i,&dvi);
940:     NRefSysIter(i,pep,k,ksp,fH,S,lds,fh,H,ldh,Rv,Rh,pep->V,dvi,dH+i*k,matctx,W);
941:     /* Orthogonalize computed solution */
942:     BVOrthogonalizeVec(pep->V,dvi,dVS+i*2*k,&norm,&lindep);
943:     BVRestoreColumn(dV,i,&dvi);
944:     if (!lindep) {
945:       BVOrthogonalizeColumn(dV,i,dVS+k+i*2*k,&norm,&lindep);
946:       if (!lindep) {
947:         dVS[k+i+i*2*k] = norm;
948:         BVScaleColumn(dV,i,1.0/norm);
949:         (*rds)++;
950:       }
951:     }
952:   }
953:   BVSetActiveColumns(dV,0,*rds);
954:   VecDestroy(&t);
955:   VecDestroy(&Rv);
956:   BVDestroy(&W);
957:   if (flg) {
958:     PetscFree(At);
959:   }
960:   PetscFree2(DfH,Rh);
961:   if (pep->scheme!=PEP_REFINE_SCHEME_SCHUR) { PetscFree(fh); }
962:   return(0);
963: }

967: static PetscErrorCode NRefOrthogStep(PEP pep,PetscInt k,PetscScalar *H,PetscInt ldh,PetscScalar *fH,PetscScalar *S,PetscInt lds,PetscInt *prs)
968: {
969: #if defined(PETSC_MISSING_LAPACK_GEQRF) || defined(PETSC_MISSING_LAPACK_ORGQR)
971:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GEQRF/ORGQR - Lapack routine is unavailable");
972: #else
974:   PetscInt       i,j,nmat=pep->nmat,deg=nmat-1,lda=nmat*k,rs=*prs,ldg;
975:   PetscScalar    *T,*G,*tau,*array,sone=1.0,zero=0.0,*work;
976:   PetscBLASInt   rs_,lds_,k_,ldh_,info,ldg_,lda_;
977:   Mat            M0;

980:   PetscMalloc4(rs*k,&T,k,&tau,k,&work,deg*k*k,&G);
981:   PetscBLASIntCast(lds,&lds_);
982:   PetscBLASIntCast(lda,&lda_);
983:   PetscBLASIntCast(k,&k_);
984:   if (rs>k) { /* Truncate S to have k columns*/
985:     for (j=0;j<k;j++) {
986:       PetscMemcpy(T+j*rs,S+j*lds,rs*sizeof(PetscScalar));
987:     }
988:     PetscBLASIntCast(rs,&rs_);
989:     PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&rs_,&k_,T,&rs_,tau,work,&k_,&info));
990:     if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xGEQRF %d",info);
991:     /* Copy triangular matrix in S */
992:     PetscMemzero(S,lds*k*sizeof(PetscScalar));
993:     for (j=0;j<k;j++) for (i=0;i<=j;i++) S[j*lds+i] = T[j*rs+i];
994:     PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&rs_,&k_,&k_,T,&rs_,tau,work,&k_,&info));
995:     if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xORGQR %d",info);
996:     MatCreateSeqDense(PETSC_COMM_SELF,rs,k,NULL,&M0);
997:     MatDenseGetArray(M0,&array);
998:     for (j=0;j<k;j++) {
999:       PetscMemcpy(array+j*rs,T+j*rs,rs*sizeof(PetscScalar));
1000:     }
1001:     MatDenseRestoreArray(M0,&array);
1002:     BVSetActiveColumns(pep->V,0,rs);
1003:     BVMultInPlace(pep->V,M0,0,k);
1004:     BVSetActiveColumns(pep->V,0,k);
1005:     MatDestroy(&M0);
1006:     *prs = rs = k;
1007:   }
1008:   /* Form auxiliary matrix for the orthogonalization step */
1009:   ldg = deg*k;
1010:   PEPEvaluateBasisforMatrix(pep,nmat,k,H,ldh,fH);
1011:   PetscBLASIntCast(ldg,&ldg_);
1012:   PetscBLASIntCast(ldh,&ldh_);
1013:   for (j=0;j<deg;j++) {
1014:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&k_,&k_,&k_,&sone,S,&lds_,fH+j*k,&lda_,&zero,G+j*k,&ldg_));
1015:   }
1016:   /* Orthogonalize and update S */
1017:   PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&ldg_,&k_,G,&ldg_,tau,work,&k_,&info));
1018:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xGEQRF %d",info);
1019:   PetscStackCallBLAS("BLAStrsm",BLAStrsm_("R","U","N","N",&k_,&k_,&sone,G,&ldg_,S,&lds_));

1021:   /* Update H */
1022:   PetscStackCallBLAS("BLAStrmm",BLAStrmm_("L","U","N","N",&k_,&k_,&sone,G,&ldg_,H,&ldh_));
1023:   PetscStackCallBLAS("BLAStrsm",BLAStrsm_("R","U","N","N",&k_,&k_,&sone,G,&ldg_,H,&ldh_));
1024:   PetscFree4(T,tau,work,G);
1025:   return(0);
1026: #endif
1027: }

1031: static PetscErrorCode PEPNRefUpdateInvPair(PEP pep,PetscInt k,PetscScalar *H,PetscInt ldh,PetscScalar *fH,PetscScalar *dH,PetscScalar *S,PetscInt lds,BV dV,PetscScalar *dVS,PetscInt rds)
1032: {
1033: #if defined(PETSC_MISSING_LAPACK_GEQRF) || defined(PETSC_MISSING_LAPACK_ORGQR)
1035:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GEQRF/ORGQR - Lapack routine is unavailable");
1036: #else
1038:   PetscInt       i,j,nmat=pep->nmat,lda=nmat*k;
1039:   PetscScalar    *tau,*array,*work;
1040:   PetscBLASInt   lds_,k_,lda_,ldh_,kdrs_,info,k2_;
1041:   Mat            M0;

1044:   PetscMalloc2(k,&tau,k,&work);
1045:   PetscBLASIntCast(lds,&lds_);
1046:   PetscBLASIntCast(lda,&lda_);
1047:   PetscBLASIntCast(ldh,&ldh_);
1048:   PetscBLASIntCast(k,&k_);
1049:   PetscBLASIntCast(2*k,&k2_);
1050:   PetscBLASIntCast((k+rds),&kdrs_);
1051:   /* Update H */
1052:   for (j=0;j<k;j++) {
1053:     for (i=0;i<k;i++) H[i+j*ldh] -= dH[i+j*k];
1054:   }
1055:   /* Update V */
1056:   for (j=0;j<k;j++) {
1057:     for (i=0;i<k;i++) dVS[i+j*2*k] = -dVS[i+j*2*k]+S[i+j*lds];
1058:     for (i=k;i<2*k;i++) dVS[i+j*2*k] = -dVS[i+j*2*k];
1059:   }
1060:   PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&kdrs_,&k_,dVS,&k2_,tau,work,&k_,&info));
1061:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xGEQRF %d",info);
1062:   /* Copy triangular matrix in S */
1063:   for (j=0;j<k;j++) {
1064:     for (i=0;i<=j;i++) S[i+j*lds] = dVS[i+j*2*k];
1065:     for (i=j+1;i<k;i++) S[i+j*lds] = 0.0;
1066:   }
1067:   PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&k2_,&k_,&k_,dVS,&k2_,tau,work,&k_,&info));
1068:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xORGQR %d",info);
1069:   MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&M0);
1070:   MatDenseGetArray(M0,&array);
1071:   for (j=0;j<k;j++) {
1072:     PetscMemcpy(array+j*k,dVS+j*2*k,k*sizeof(PetscScalar));
1073:   }
1074:   MatDenseRestoreArray(M0,&array);
1075:   BVMultInPlace(pep->V,M0,0,k);
1076:   if (rds) {
1077:     MatDenseGetArray(M0,&array);
1078:     for (j=0;j<k;j++) {
1079:       PetscMemcpy(array+j*k,dVS+k+j*2*k,rds*sizeof(PetscScalar));
1080:     }
1081:     MatDenseRestoreArray(M0,&array);
1082:     BVMultInPlace(dV,M0,0,k);
1083:     BVMult(pep->V,1.0,1.0,dV,NULL);
1084:   }
1085:   MatDestroy(&M0);
1086:   NRefOrthogStep(pep,k,H,ldh,fH,S,lds,&k);
1087:   PetscFree2(tau,work);
1088:   return(0);
1089: #endif
1090: }

1094: static PetscErrorCode PEPNRefSetUp(PEP pep,PetscInt k,PetscScalar *H,PetscInt ldh,MatExplicitCtx *matctx,PetscBool ini)
1095: {
1096:   PetscErrorCode    ierr;
1097:   FSubctx           *ctx;
1098:   PetscScalar       t,*coef;
1099:   const PetscScalar *array;
1100:   MatStructure      str;
1101:   PetscInt          j,nmat=pep->nmat,n0,m0,n1,m1,n0_,m0_,n1_,m1_,N0,N1,p,*idx1,*idx2,count,si,i,l0;
1102:   MPI_Comm          comm;
1103:   PetscMPIInt       np;
1104:   const PetscInt    *rgs0,*rgs1;
1105:   Mat               B,C,*E,*A,*At;
1106:   IS                is1,is2;
1107:   Vec               v;
1108:   PetscBool         flg;
1109:   Mat               M,P;

1112:   PetscMalloc1(nmat,&coef);
1113:   STGetTransform(pep->st,&flg);
1114:   if (flg) {
1115:     PetscMalloc1(pep->nmat,&At);
1116:     for (i=0;i<pep->nmat;i++) {
1117:       STGetTOperators(pep->st,i,&At[i]);
1118:     }
1119:   } else At = pep->A;
1120:   switch (pep->scheme) {
1121:   case PEP_REFINE_SCHEME_EXPLICIT:
1122:     if (ini) {
1123:       if (matctx->subc) {
1124:         A = matctx->A;
1125:         comm = PetscSubcommChild(matctx->subc);
1126:       } else {
1127:         A = At;
1128:         PetscObjectGetComm((PetscObject)pep,&comm);
1129:       }
1130:       E = matctx->E;
1131:       STGetMatStructure(pep->st,&str);
1132:       MatDuplicate(A[0],MAT_COPY_VALUES,&E[0]);
1133:       j = (matctx->subc)?matctx->subc->color:0;
1134:       PEPEvaluateBasis(pep,H[j+j*ldh],0,coef,NULL);
1135:       for (j=1;j<nmat;j++) {
1136:         MatAXPY(E[0],coef[j],A[j],str);
1137:       }
1138:       MatCreateDense(comm,PETSC_DECIDE,PETSC_DECIDE,k,k,NULL,&E[1]);
1139:       MatAssemblyBegin(E[1],MAT_FINAL_ASSEMBLY);
1140:       MatAssemblyEnd(E[1],MAT_FINAL_ASSEMBLY);
1141:       MatGetOwnershipRange(E[0],&n0,&m0);
1142:       MatGetOwnershipRange(E[1],&n1,&m1);
1143:       MatGetOwnershipRangeColumn(E[0],&n0_,&m0_);
1144:       MatGetOwnershipRangeColumn(E[1],&n1_,&m1_);
1145:       /* T12 and T21 are computed from V and V*, so,
1146:          they must have the same column and row ranges */
1147:       if (m0_-n0_ != m0-n0) SETERRQ(PETSC_COMM_SELF,1,"Inconsistent dimensions");
1148:       MatCreateDense(comm,m0-n0,m1_-n1_,PETSC_DECIDE,PETSC_DECIDE,NULL,&B);
1149:       MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
1150:       MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
1151:       MatCreateDense(comm,m1-n1,m0_-n0_,PETSC_DECIDE,PETSC_DECIDE,NULL,&C);
1152:       MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1153:       MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
1154:       SlepcMatTile(1.0,E[0],1.0,B,1.0,C,1.0,E[1],&M);
1155:       MatDestroy(&B);
1156:       MatDestroy(&C);
1157:       matctx->compM1 = PETSC_TRUE;
1158:       MatGetSize(E[0],NULL,&N0);
1159:       MatGetSize(E[1],NULL,&N1);
1160:       MPI_Comm_size(PetscObjectComm((PetscObject)M),&np);
1161:       MatGetOwnershipRanges(E[0],&rgs0);
1162:       MatGetOwnershipRanges(E[1],&rgs1);
1163:       PetscMalloc4(PetscMax(k,N1),&matctx->idxp,N0,&matctx->idxg,N0,&matctx->map0,N1,&matctx->map1);
1164:       /* Create column (and row) mapping */
1165:       for (p=0;p<np;p++) {
1166:         for (j=rgs0[p];j<rgs0[p+1];j++) matctx->map0[j] = j+rgs1[p];
1167:         for (j=rgs1[p];j<rgs1[p+1];j++) matctx->map1[j] = j+rgs0[p+1];
1168:       }
1169:       MatCreateVecs(M,NULL,&matctx->tN);
1170:       MatCreateVecs(matctx->E[1],NULL,&matctx->t1);
1171:       VecDuplicate(matctx->tN,&matctx->ttN);
1172:       if (matctx->subc) {
1173:         MPI_Comm_size(PetscObjectComm((PetscObject)pep),&np);
1174:         count = np*k;
1175:         PetscMalloc2(count,&idx1,count,&idx2);
1176:         VecCreateMPI(PetscObjectComm((PetscObject)pep),m1-n1,PETSC_DECIDE,&matctx->tp);
1177:         VecGetOwnershipRange(matctx->tp,&l0,NULL);
1178:         VecCreateMPI(PetscObjectComm((PetscObject)pep),k,PETSC_DECIDE,&matctx->tpg);
1179:         for (si=0;si<matctx->subc->n;si++) {
1180:           if (matctx->subc->color==si) {
1181:             j=0;
1182:             if (matctx->subc->color==si) {
1183:               for (p=0;p<np;p++) {
1184:                 for (i=n1;i<m1;i++) {
1185:                   idx1[j] = l0+i-n1;
1186:                   idx2[j++] =p*k+i;
1187:                 }
1188:               }
1189:             }
1190:             count = np*(m1-n1);
1191:           } else count =0;
1192:           ISCreateGeneral(PetscObjectComm((PetscObject)pep),count,idx1,PETSC_COPY_VALUES,&is1);
1193:           ISCreateGeneral(PetscObjectComm((PetscObject)pep),count,idx2,PETSC_COPY_VALUES,&is2);
1194:           VecScatterCreate(matctx->tp,is1,matctx->tpg,is2,&matctx->scatterp_id[si]);
1195:           ISDestroy(&is1);
1196:           ISDestroy(&is2);
1197:         }
1198:         PetscFree2(idx1,idx2);
1199:       } else {
1200:         VecScatterCreateToAll(matctx->t1,&matctx->scatterctx,&matctx->vseq);
1201:       }
1202:       P = M;
1203:     } else {
1204:       if (matctx->subc) {
1205:         /* Scatter vectors pep->V */
1206:         for (i=0;i<k;i++) {
1207:           BVGetColumn(pep->V,i,&v);
1208:           VecScatterBegin(matctx->scatter_sub,v,matctx->tg,INSERT_VALUES,SCATTER_FORWARD);
1209:           VecScatterEnd(matctx->scatter_sub,v,matctx->tg,INSERT_VALUES,SCATTER_FORWARD);
1210:           BVRestoreColumn(pep->V,i,&v);
1211:           VecGetArrayRead(matctx->tg,&array);
1212:           VecPlaceArray(matctx->t,(const PetscScalar*)array);
1213:           BVInsertVec(matctx->V,i,matctx->t);
1214:           VecResetArray(matctx->t);
1215:           VecRestoreArrayRead(matctx->tg,&array);
1216:         }
1217:       }
1218:     }
1219:     break;
1220:   case PEP_REFINE_SCHEME_MBE:
1221:     if (ini) {
1222:       if (matctx->subc) {
1223:         A = matctx->A;
1224:         comm = PetscSubcommChild(matctx->subc);
1225:       } else {
1226:         matctx->V = pep->V;
1227:         A = At;
1228:         PetscObjectGetComm((PetscObject)pep,&comm);
1229:         MatCreateVecs(pep->A[0],&matctx->t,NULL);
1230:       }
1231:       STGetMatStructure(pep->st,&str);
1232:       MatDuplicate(A[0],MAT_COPY_VALUES,&matctx->M1);
1233:       j = (matctx->subc)?matctx->subc->color:0;
1234:       PEPEvaluateBasis(pep,H[j+j*ldh],0,coef,NULL);
1235:       for (j=1;j<nmat;j++) {
1236:         MatAXPY(matctx->M1,coef[j],A[j],str);
1237:       }
1238:       BVDuplicateResize(matctx->V,PetscMax(k,pep->nmat),&matctx->W);
1239:       BVDuplicateResize(matctx->V,k,&matctx->M2);
1240:       BVDuplicate(matctx->M2,&matctx->M3);
1241:       BVDuplicate(matctx->M2,&matctx->Wt);
1242:       PetscMalloc5(k*k,&matctx->M4,k*k,&matctx->w,k*k,&matctx->wt,k,&matctx->d,k,&matctx->dt);
1243:       matctx->compM1 = PETSC_TRUE;
1244:       M = matctx->M1;
1245:       P = M;
1246:     }
1247:     break;
1248:   case PEP_REFINE_SCHEME_SCHUR:
1249:     if (ini) {
1250:       PetscObjectGetComm((PetscObject)pep,&comm);
1251:       MatGetSize(At[0],&m0,&n0);
1252:       PetscMalloc1(1,&ctx);
1253:       STGetMatStructure(pep->st,&str);
1254:       /* Create a shell matrix to solve the linear system */
1255:       ctx->A = At;
1256:       ctx->V = pep->V;
1257:       ctx->k = k; ctx->nmat = nmat;
1258:       PetscMalloc4(k*k,&ctx->M4,k,&ctx->pM4,2*k*k,&ctx->work,nmat,&ctx->fih);
1259:       PetscMemzero(ctx->M4,k*k*sizeof(PetscScalar));
1260:       MatCreateShell(comm,PETSC_DECIDE,PETSC_DECIDE,m0,n0,ctx,&M);
1261:       MatShellSetOperation(M,MATOP_MULT,(void(*)(void))MatFSMult);
1262:       BVDuplicateResize(ctx->V,PetscMax(k,pep->nmat),&ctx->W);
1263:       BVDuplicateResize(ctx->V,k,&ctx->M2);
1264:       BVDuplicate(ctx->M2,&ctx->M3);
1265:       BVCreateVec(pep->V,&ctx->t);
1266:       MatDuplicate(At[0],MAT_COPY_VALUES,&ctx->M1);
1267:       PEPEvaluateBasis(pep,H[0],0,coef,NULL);
1268:       for (j=1;j<nmat;j++) {
1269:         MatAXPY(ctx->M1,coef[j],At[j],str);
1270:       }
1271:       MatDuplicate(At[0],MAT_COPY_VALUES,&P);
1272:       /* Compute a precond matrix for the system */
1273:       t = H[0];
1274:       PEPEvaluateBasis(pep,t,0,coef,NULL);
1275:       for (j=1;j<nmat;j++) {
1276:         MatAXPY(P,coef[j],At[j],str);
1277:       }
1278:       ctx->compM1 = PETSC_TRUE;
1279:     }
1280:     break;
1281:   }
1282:   if (ini) {
1283:     PEPRefineGetKSP(pep,&pep->refineksp);
1284:     KSPSetErrorIfNotConverged(pep->refineksp,PETSC_TRUE);
1285:     KSPSetOperators(pep->refineksp,M,P);
1286:     KSPSetFromOptions(pep->refineksp);
1287:   }

1289:   if (!ini && matctx && matctx->subc) {
1290:      /* Scatter vectors pep->V */
1291:     for (i=0;i<k;i++) {
1292:       BVGetColumn(pep->V,i,&v);
1293:       VecScatterBegin(matctx->scatter_sub,v,matctx->tg,INSERT_VALUES,SCATTER_FORWARD);
1294:       VecScatterEnd(matctx->scatter_sub,v,matctx->tg,INSERT_VALUES,SCATTER_FORWARD);
1295:       BVRestoreColumn(pep->V,i,&v);
1296:       VecGetArrayRead(matctx->tg,&array);
1297:       VecPlaceArray(matctx->t,(const PetscScalar*)array);
1298:       BVInsertVec(matctx->V,i,matctx->t);
1299:       VecResetArray(matctx->t);
1300:       VecRestoreArrayRead(matctx->tg,&array);
1301:     }
1302:    }
1303:   PetscFree(coef);
1304:   if (flg) {
1305:     PetscFree(At);
1306:   }
1307:   return(0);
1308: }

1312: static PetscErrorCode NRefSubcommSetup(PEP pep,PetscInt k,MatExplicitCtx *matctx,PetscInt nsubc)
1313: {
1314:   PetscErrorCode    ierr;
1315:   PetscInt          i,si,j,m0,n0,nloc0,nloc_sub,*idx1,*idx2;
1316:   IS                is1,is2;
1317:   BVType            type;
1318:   Vec               v;
1319:   const PetscScalar *array;
1320:   Mat               *A;
1321:   PetscBool         flg;

1324:   STGetTransform(pep->st,&flg);
1325:   if (flg) {
1326:     PetscMalloc1(pep->nmat,&A);
1327:     for (i=0;i<pep->nmat;i++) {
1328:       STGetTOperators(pep->st,i,&A[i]);
1329:     }
1330:   } else A = pep->A;

1332:   /* Duplicate pep matrices */
1333:   PetscMalloc3(pep->nmat,&matctx->A,nsubc,&matctx->scatter_id,nsubc,&matctx->scatterp_id);
1334:   for (i=0;i<pep->nmat;i++) {
1335:     MatCreateRedundantMatrix(A[i],0,PetscSubcommChild(matctx->subc),MAT_INITIAL_MATRIX,&matctx->A[i]);
1336:   }

1338:   /* Create Scatter */
1339:   MatCreateVecs(matctx->A[0],&matctx->t,NULL);
1340:   MatGetLocalSize(matctx->A[0],&nloc_sub,NULL);
1341:   VecCreateMPI(PetscSubcommContiguousParent(matctx->subc),nloc_sub,PETSC_DECIDE,&matctx->tg);
1342:   BVGetColumn(pep->V,0,&v);
1343:   VecGetOwnershipRange(v,&n0,&m0);
1344:   nloc0 = m0-n0;
1345:   PetscMalloc2(matctx->subc->n*nloc0,&idx1,matctx->subc->n*nloc0,&idx2);
1346:   j = 0;
1347:   for (si=0;si<matctx->subc->n;si++) {
1348:     for (i=n0;i<m0;i++) {
1349:       idx1[j]   = i;
1350:       idx2[j++] = i+pep->n*si;
1351:     }
1352:   }
1353:   ISCreateGeneral(PetscObjectComm((PetscObject)pep),matctx->subc->n*nloc0,idx1,PETSC_COPY_VALUES,&is1);
1354:   ISCreateGeneral(PetscObjectComm((PetscObject)pep),matctx->subc->n*nloc0,idx2,PETSC_COPY_VALUES,&is2);
1355:   VecScatterCreate(v,is1,matctx->tg,is2,&matctx->scatter_sub);
1356:   ISDestroy(&is1);
1357:   ISDestroy(&is2);
1358:   for (si=0;si<matctx->subc->n;si++) {
1359:     j=0;
1360:     for (i=n0;i<m0;i++) {
1361:       idx1[j] = i;
1362:       idx2[j++] = i+pep->n*si;
1363:     }
1364:     ISCreateGeneral(PetscObjectComm((PetscObject)pep),nloc0,idx1,PETSC_COPY_VALUES,&is1);
1365:     ISCreateGeneral(PetscObjectComm((PetscObject)pep),nloc0,idx2,PETSC_COPY_VALUES,&is2);
1366:     VecScatterCreate(v,is1,matctx->tg,is2,&matctx->scatter_id[si]);
1367:     ISDestroy(&is1);
1368:     ISDestroy(&is2);
1369:   }
1370:   BVRestoreColumn(pep->V,0,&v);
1371:   PetscFree2(idx1,idx2);

1373:   /* Duplicate pep->V vecs */
1374:   BVGetType(pep->V,&type);
1375:   BVCreate(PetscSubcommChild(matctx->subc),&matctx->V);
1376:   BVSetType(matctx->V,type);
1377:   BVSetSizesFromVec(matctx->V,matctx->t,k);
1378:   if (pep->scheme==PEP_REFINE_SCHEME_EXPLICIT) {
1379:     BVDuplicateResize(matctx->V,PetscMax(k,pep->nmat),&matctx->W);
1380:   }
1381:   for (i=0;i<k;i++) {
1382:     BVGetColumn(pep->V,i,&v);
1383:     VecScatterBegin(matctx->scatter_sub,v,matctx->tg,INSERT_VALUES,SCATTER_FORWARD);
1384:     VecScatterEnd(matctx->scatter_sub,v,matctx->tg,INSERT_VALUES,SCATTER_FORWARD);
1385:     BVRestoreColumn(pep->V,i,&v);
1386:     VecGetArrayRead(matctx->tg,&array);
1387:     VecPlaceArray(matctx->t,(const PetscScalar*)array);
1388:     BVInsertVec(matctx->V,i,matctx->t);
1389:     VecResetArray(matctx->t);
1390:     VecRestoreArrayRead(matctx->tg,&array);
1391:   }

1393:   VecDuplicate(matctx->t,&matctx->Rv);
1394:   VecDuplicate(matctx->t,&matctx->Vi);
1395:   if (flg) {
1396:     PetscFree(A);
1397:   }
1398:   return(0);
1399: }

1403: static PetscErrorCode NRefSubcommDestroy(PEP pep,MatExplicitCtx *matctx)
1404: {
1406:   PetscInt       i;

1409:   VecScatterDestroy(&matctx->scatter_sub);
1410:   for (i=0;i<matctx->subc->n;i++) {
1411:     VecScatterDestroy(&matctx->scatter_id[i]);
1412:   }
1413:   for (i=0;i<pep->nmat;i++) {
1414:     MatDestroy(&matctx->A[i]);
1415:   }
1416:   if (pep->scheme==PEP_REFINE_SCHEME_EXPLICIT) {
1417:     for (i=0;i<matctx->subc->n;i++) {
1418:       VecScatterDestroy(&matctx->scatterp_id[i]);
1419:     }
1420:     VecDestroy(&matctx->tp);
1421:     VecDestroy(&matctx->tpg);
1422:     BVDestroy(&matctx->W);
1423:   }
1424:   PetscFree3(matctx->A,matctx->scatter_id,matctx->scatterp_id);
1425:   BVDestroy(&matctx->V);
1426:   VecDestroy(&matctx->t);
1427:   VecDestroy(&matctx->tg);
1428:   VecDestroy(&matctx->Rv);
1429:   VecDestroy(&matctx->Vi);
1430:   return(0);
1431: }

1435: PetscErrorCode PEPNewtonRefinement_TOAR(PEP pep,PetscScalar sigma,PetscInt *maxits,PetscReal *tol,PetscInt k,PetscScalar *S,PetscInt lds,PetscInt *prs)
1436: {
1437: #if defined(PETSC_MISSING_LAPACK_GETRF) || defined(PETSC_MISSING_LAPACK_GETRI)
1439:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GETRF/GETRI - Lapack routine is unavailable");
1440: #else
1442:   PetscScalar    *H,*work,*dH,*fH,*dVS;
1443:   PetscInt       ldh,i,j,its=1,nmat=pep->nmat,nsubc=pep->npart,rds;
1444:   PetscBLASInt   k_,ld_,*p,info;
1445:   BV             dV;
1446:   PetscBool      sinvert,flg;
1447:   MatExplicitCtx *matctx=NULL;
1448:   Vec            v;
1449:   Mat            M,P;
1450:   FSubctx        *ctx;

1453:   PetscLogEventBegin(PEP_Refine,pep,0,0,0);
1454:   if (k > pep->n) SETERRQ1(PetscObjectComm((PetscObject)pep),1,"Multiple Refinement available only for invariant pairs of dimension smaller than n=%D",pep->n);
1455:   /* the input tolerance is not being taken into account (by the moment) */
1456:   its = *maxits;
1457:   PetscMalloc3(k*k,&dH,nmat*k*k,&fH,k,&work);
1458:   DSGetLeadingDimension(pep->ds,&ldh);
1459:   DSGetArray(pep->ds,DS_MAT_A,&H);
1460:   DSRestoreArray(pep->ds,DS_MAT_A,&H);
1461:   PetscMalloc1(2*k*k,&dVS);
1462:   STGetTransform(pep->st,&flg);
1463:   if (!flg && pep->st && pep->ops->backtransform) { /* BackTransform */
1464:     PetscBLASIntCast(k,&k_);
1465:     PetscBLASIntCast(ldh,&ld_);
1466:     PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinvert);
1467:     if (sinvert) {
1468:       DSGetArray(pep->ds,DS_MAT_A,&H);
1469:       PetscMalloc1(k,&p);
1470:       PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&k_,&k_,H,&ld_,p,&info));
1471:       PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&k_,H,&ld_,p,work,&k_,&info));
1472:       DSRestoreArray(pep->ds,DS_MAT_A,&H);
1473:       pep->ops->backtransform = NULL;
1474:     }
1475:     if (sigma!=0.0) {
1476:       DSGetArray(pep->ds,DS_MAT_A,&H);
1477:       for (i=0;i<k;i++) H[i+ldh*i] += sigma;
1478:       DSRestoreArray(pep->ds,DS_MAT_A,&H);
1479:       pep->ops->backtransform = NULL;
1480:     }
1481:   }
1482:   if ((pep->scale==PEP_SCALE_BOTH || pep->scale==PEP_SCALE_SCALAR) && pep->sfactor!=1.0) {
1483:     DSGetArray(pep->ds,DS_MAT_A,&H);
1484:     for (j=0;j<k;j++) {
1485:       for (i=0;i<k;i++) H[i+j*ldh] *= pep->sfactor;
1486:     }
1487:     DSRestoreArray(pep->ds,DS_MAT_A,&H);
1488:     if (!flg) {
1489:       /* Restore original values */
1490:       for (i=0;i<pep->nmat;i++){
1491:         pep->pbc[pep->nmat+i] *= pep->sfactor;
1492:         pep->pbc[2*pep->nmat+i] *= pep->sfactor*pep->sfactor;
1493:       }
1494:     }
1495:   }
1496:   if ((pep->scale==PEP_SCALE_DIAGONAL || pep->scale==PEP_SCALE_BOTH) && pep->Dr) {
1497:     for (i=0;i<k;i++) {
1498:       BVGetColumn(pep->V,i,&v);
1499:       VecPointwiseMult(v,v,pep->Dr);
1500:       BVRestoreColumn(pep->V,i,&v);
1501:     }
1502:   }
1503:   DSGetArray(pep->ds,DS_MAT_A,&H);

1505:   NRefOrthogStep(pep,k,H,ldh,fH,S,lds,prs);
1506:   /* check if H is in Schur form */
1507:   for (i=0;i<k-1;i++) {
1508:     if (H[i+1+i*ldh]!=0.0) {
1509: #if !defined(PETSC_USES_COMPLEX)
1510:       SETERRQ(PetscObjectComm((PetscObject)pep),1,"Iterative Refinement requires the complex Schur form of the projected matrix");
1511: #else
1512:       SETERRQ(PetscObjectComm((PetscObject)pep),1,"Iterative Refinement requires an upper triangular projected matrix");
1513: #endif
1514:     }
1515:   }
1516:   if (nsubc>k) SETERRQ(PetscObjectComm((PetscObject)pep),1,"Amount of subcommunicators should not be larger than the invariant pair dimension");
1517:   BVSetActiveColumns(pep->V,0,k);
1518:   BVDuplicateResize(pep->V,k,&dV);
1519:   PetscLogObjectParent((PetscObject)pep,(PetscObject)dV);
1520:   if (pep->scheme!=PEP_REFINE_SCHEME_SCHUR) {
1521:     PetscMalloc1(1,&matctx);
1522:     if (nsubc>1) { /* spliting in subcommunicators */
1523:       matctx->subc = pep->refinesubc;
1524:       NRefSubcommSetup(pep,k,matctx,nsubc);
1525:     } else matctx->subc=NULL;
1526:   }

1528:   /* Loop performing iterative refinements */
1529:   for (i=0;i<its;i++) {
1530:     /* Pre-compute the polynomial basis evaluated in H */
1531:     PEPEvaluateBasisforMatrix(pep,nmat,k,H,ldh,fH);
1532:     PEPNRefSetUp(pep,k,H,ldh,matctx,PetscNot(i));
1533:     /* Solve the linear system */
1534:     PEPNRefForwardSubstitution(pep,k,S,lds,H,ldh,fH,dV,dVS,&rds,dH,k,pep->refineksp,matctx);
1535:     /* Update X (=V*S) and H, and orthogonalize [X;X*fH1;...;XfH(deg-1)] */
1536:     PEPNRefUpdateInvPair(pep,k,H,ldh,fH,dH,S,lds,dV,dVS,rds);
1537:   }
1538:   DSRestoreArray(pep->ds,DS_MAT_A,&H);
1539:   if (!flg && sinvert) {
1540:     PetscFree(p);
1541:   }
1542:   PetscFree3(dH,fH,work);
1543:   PetscFree(dVS);
1544:   BVDestroy(&dV);
1545:   switch (pep->scheme) {
1546:   case PEP_REFINE_SCHEME_EXPLICIT:
1547:     for (i=0;i<2;i++) {
1548:       MatDestroy(&matctx->E[i]);
1549:     }
1550:     PetscFree4(matctx->idxp,matctx->idxg,matctx->map0,matctx->map1);
1551:     VecDestroy(&matctx->tN);
1552:     VecDestroy(&matctx->ttN);
1553:     VecDestroy(&matctx->t1);
1554:     if (nsubc>1) {
1555:       NRefSubcommDestroy(pep,matctx);
1556:     } else {
1557:       VecDestroy(&matctx->vseq);
1558:       VecScatterDestroy(&matctx->scatterctx);
1559:     }
1560:     PetscFree(matctx);
1561:     KSPGetOperators(pep->refineksp,&M,NULL);
1562:     MatDestroy(&M);
1563:     break;
1564:   case PEP_REFINE_SCHEME_MBE:
1565:     BVDestroy(&matctx->W);
1566:     BVDestroy(&matctx->Wt);
1567:     BVDestroy(&matctx->M2);
1568:     BVDestroy(&matctx->M3);
1569:     MatDestroy(&matctx->M1);
1570:     VecDestroy(&matctx->t);
1571:     PetscFree5(matctx->M4,matctx->w,matctx->wt,matctx->d,matctx->dt);
1572:     if (nsubc>1) {
1573:       NRefSubcommDestroy(pep,matctx);
1574:     }
1575:     PetscFree(matctx);
1576:     break;
1577:   case PEP_REFINE_SCHEME_SCHUR:
1578:     KSPGetOperators(pep->refineksp,&M,&P);
1579:     MatShellGetContext(M,&ctx);
1580:     PetscFree4(ctx->M4,ctx->pM4,ctx->work,ctx->fih);
1581:     MatDestroy(&ctx->M1);
1582:     BVDestroy(&ctx->M2);
1583:     BVDestroy(&ctx->M3);
1584:     BVDestroy(&ctx->W);
1585:     VecDestroy(&ctx->t);
1586:     PetscFree(ctx);
1587:     MatDestroy(&M);
1588:     MatDestroy(&P);
1589:     break;
1590:   }
1591:   PetscLogEventEnd(PEP_Refine,pep,0,0,0);
1592:   return(0);
1593: #endif
1594: }