Actual source code: dvdcalcpairs.c

slepc-3.15.0 2021-03-31
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2021, 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 eigensolver: "davidson"

 13:    Step: calculate the best eigenpairs in the subspace V

 15:    For that, performs these steps:
 16:      1) Update W <- A * V
 17:      2) Update H <- V' * W
 18:      3) Obtain eigenpairs of H
 19:      4) Select some eigenpairs
 20:      5) Compute the Ritz pairs of the selected ones
 21: */

 23: #include "davidson.h"
 24: #include <slepcblaslapack.h>

 26: static PetscErrorCode dvd_calcpairs_qz_start(dvdDashboard *d)
 27: {

 31:   BVSetActiveColumns(d->eps->V,0,0);
 32:   if (d->W) { BVSetActiveColumns(d->W,0,0); }
 33:   BVSetActiveColumns(d->AX,0,0);
 34:   if (d->BX) { BVSetActiveColumns(d->BX,0,0); }
 35:   return(0);
 36: }

 38: static PetscErrorCode dvd_calcpairs_qz_d(dvdDashboard *d)
 39: {
 40:   PetscErrorCode  ierr;

 43:   BVDestroy(&d->W);
 44:   BVDestroy(&d->AX);
 45:   BVDestroy(&d->BX);
 46:   BVDestroy(&d->auxBV);
 47:   MatDestroy(&d->H);
 48:   MatDestroy(&d->G);
 49:   MatDestroy(&d->auxM);
 50:   SlepcVecPoolDestroy(&d->auxV);
 51:   PetscFree(d->nBds);
 52:   return(0);
 53: }

 55: /* in complex, d->size_H real auxiliary values are needed */
 56: static PetscErrorCode dvd_calcpairs_projeig_solve(dvdDashboard *d)
 57: {
 58:   PetscErrorCode    ierr;
 59:   Vec               v;
 60:   PetscScalar       *pA;
 61:   const PetscScalar *pv;
 62:   PetscInt          i,lV,kV,n,ld;

 65:   BVGetActiveColumns(d->eps->V,&lV,&kV);
 66:   n = kV-lV;
 67:   DSSetDimensions(d->eps->ds,n,0,0,0);
 68:   DSCopyMat(d->eps->ds,DS_MAT_A,0,0,d->H,lV,lV,n,n,PETSC_FALSE);
 69:   if (d->G) {
 70:     DSCopyMat(d->eps->ds,DS_MAT_B,0,0,d->G,lV,lV,n,n,PETSC_FALSE);
 71:   }
 72:   /* Set the signature on projected matrix B */
 73:   if (DVD_IS(d->sEP,DVD_EP_INDEFINITE)) {
 74:     DSGetLeadingDimension(d->eps->ds,&ld);
 75:     DSGetArray(d->eps->ds,DS_MAT_B,&pA);
 76:     PetscArrayzero(pA,n*ld);
 77:     VecCreateSeq(PETSC_COMM_SELF,kV,&v);
 78:     BVGetSignature(d->eps->V,v);
 79:     VecGetArrayRead(v,&pv);
 80:     for (i=0;i<n;i++) {
 81:       pA[i+ld*i] = d->nBds[i] = PetscRealPart(pv[lV+i]);
 82:     }
 83:     VecRestoreArrayRead(v,&pv);
 84:     VecDestroy(&v);
 85:     DSRestoreArray(d->eps->ds,DS_MAT_B,&pA);
 86:   }
 87:   DSSetState(d->eps->ds,DS_STATE_RAW);
 88:   DSSolve(d->eps->ds,d->eigr,d->eigi);
 89:   return(0);
 90: }

 92: /*
 93:    A(lA:kA-1,lA:kA-1) <- Z(l:k-1)'*A(l:k-1,l:k-1)*Q(l,k-1), where k=l+kA-lA
 94:  */
 95: static PetscErrorCode EPSXDUpdateProj(Mat Q,Mat Z,PetscInt l,Mat A,PetscInt lA,PetscInt kA,Mat aux)
 96: {
 97:   PetscErrorCode    ierr;
 98:   PetscScalar       one=1.0,zero=0.0;
 99:   PetscInt          i,j,dA_=kA-lA,m0,n0,ldA_,ldQ_,ldZ_,nQ_;
100:   PetscBLASInt      dA,nQ,ldA,ldQ,ldZ;
101:   PetscScalar       *pA,*pW;
102:   const PetscScalar *pQ,*pZ;
103:   PetscBool         symm=PETSC_FALSE,set,flg;

106:   MatGetSize(A,&m0,&n0); ldA_=m0;
107:   if (m0!=n0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"A should be square");
108:   if (lA<0 || lA>m0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid initial row, column in A");
109:   if (kA<0 || kA<lA || kA>m0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid final row, column in A");
110:   MatIsHermitianKnown(A,&set,&flg);
111:   symm = set? flg: PETSC_FALSE;
112:   MatGetSize(Q,&m0,&n0); ldQ_=nQ_=m0;
113:   if (l<0 || l>n0 || l+dA_>n0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid initial column in Q");
114:   MatGetSize(Z,&m0,&n0); ldZ_=m0;
115:   if (l<0 || l>n0 || l+dA_>n0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid initial column in Z");
116:   MatGetSize(aux,&m0,&n0);
117:   if (m0*n0<nQ_*dA_) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"aux should be larger");
118:   PetscBLASIntCast(dA_,&dA);
119:   PetscBLASIntCast(nQ_,&nQ);
120:   PetscBLASIntCast(ldA_,&ldA);
121:   PetscBLASIntCast(ldQ_,&ldQ);
122:   PetscBLASIntCast(ldZ_,&ldZ);
123:   MatDenseGetArray(A,&pA);
124:   MatDenseGetArrayRead(Q,&pQ);
125:   if (Q!=Z) { MatDenseGetArrayRead(Z,&pZ); }
126:   else pZ = pQ;
127:   MatDenseGetArrayWrite(aux,&pW);
128:   /* W = A*Q */
129:   if (symm) {
130:     /* symmetrize before multiplying */
131:     for (i=lA+1;i<lA+nQ;i++) {
132:       for (j=lA;j<i;j++) pA[i+j*ldA] = PetscConj(pA[j+i*ldA]);
133:     }
134:   }
135:   PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&nQ,&dA,&nQ,&one,&pA[ldA*lA+lA],&ldA,&pQ[ldQ*l+l],&ldQ,&zero,pW,&nQ));
136:   /* A = Q'*W */
137:   PetscStackCallBLAS("BLASgemm",BLASgemm_("C","N",&dA,&dA,&nQ,&one,&pZ[ldZ*l+l],&ldZ,pW,&nQ,&zero,&pA[ldA*lA+lA],&ldA));
138:   MatDenseRestoreArray(A,&pA);
139:   MatDenseRestoreArrayRead(Q,&pQ);
140:   if (Q!=Z) { MatDenseRestoreArrayRead(Z,&pZ); }
141:   MatDenseRestoreArrayWrite(aux,&pW);
142:   return(0);
143: }

145: static PetscErrorCode dvd_calcpairs_updateproj(dvdDashboard *d)
146: {
148:   Mat            Q,Z;
149:   PetscInt       lV,kV;
150:   PetscBool      symm;

153:   DSGetMat(d->eps->ds,DS_MAT_Q,&Q);
154:   if (d->W) { DSGetMat(d->eps->ds,DS_MAT_Z,&Z); }
155:   else Z = Q;
156:   BVGetActiveColumns(d->eps->V,&lV,&kV);
157:   EPSXDUpdateProj(Q,Z,0,d->H,lV,lV+d->V_tra_e,d->auxM);
158:   if (d->G) { EPSXDUpdateProj(Q,Z,0,d->G,lV,lV+d->V_tra_e,d->auxM); }
159:   MatDestroy(&Q);
160:   if (d->W) { MatDestroy(&Z); }

162:   PetscObjectTypeCompareAny((PetscObject)d->eps->ds,&symm,DSHEP,DSGHIEP,DSGHEP,"");
163:   if (d->V_tra_s==0 || symm) return(0);
164:   /* Compute upper part of H (and G): H(0:l-1,l:k-1) <- W(0:l-1)' * AV(l:k-1), where
165:      k=l+d->V_tra_s */
166:   BVSetActiveColumns(d->W?d->W:d->eps->V,0,lV);
167:   BVSetActiveColumns(d->AX,lV,lV+d->V_tra_s);
168:   BVDot(d->AX,d->W?d->W:d->eps->V,d->H);
169:   if (d->G) {
170:     BVSetActiveColumns(d->BX?d->BX:d->eps->V,lV,lV+d->V_tra_s);
171:     BVDot(d->BX?d->BX:d->eps->V,d->W?d->W:d->eps->V,d->G);
172:   }
173:   PetscObjectTypeCompare((PetscObject)d->eps->ds,DSGHEP,&symm);
174:   if (!symm) {
175:     BVSetActiveColumns(d->W?d->W:d->eps->V,lV,lV+d->V_tra_s);
176:     BVSetActiveColumns(d->AX,0,lV);
177:     BVDot(d->AX,d->W?d->W:d->eps->V,d->H);
178:     if (d->G) {
179:       BVSetActiveColumns(d->BX?d->BX:d->eps->V,0,lV);
180:       BVDot(d->BX?d->BX:d->eps->V,d->W?d->W:d->eps->V,d->G);
181:     }
182:   }
183:   BVSetActiveColumns(d->eps->V,lV,kV);
184:   BVSetActiveColumns(d->AX,lV,kV);
185:   if (d->BX) { BVSetActiveColumns(d->BX,lV,kV); }
186:   if (d->W) { BVSetActiveColumns(d->W,lV,kV); }
187:   if (d->W) { dvd_harm_updateproj(d); }
188:   return(0);
189: }

191: /*
192:    BV <- BV*MT
193:  */
194: PETSC_STATIC_INLINE PetscErrorCode dvd_calcpairs_updateBV0_gen(dvdDashboard *d,BV bv,DSMatType mat)
195: {
197:   PetscInt       l,k,n;
198:   Mat            auxM;

201:   BVGetActiveColumns(d->eps->V,&l,&k);
202:   MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&auxM);
203:   MatZeroEntries(auxM);
204:   DSGetDimensions(d->eps->ds,&n,NULL,NULL,NULL,NULL);
205:   if (k-l!=n) SETERRQ(PETSC_COMM_SELF,1,"Consistency broken");
206:   DSCopyMat(d->eps->ds,mat,0,0,auxM,l,l,n,d->V_tra_e,PETSC_TRUE);
207:   BVMultInPlace(bv,auxM,l,l+d->V_tra_e);
208:   MatDestroy(&auxM);
209:   return(0);
210: }

212: static PetscErrorCode dvd_calcpairs_proj(dvdDashboard *d)
213: {
215:   PetscInt       i,l,k;
216:   Vec            v1,v2;
217:   PetscScalar    *pv;

220:   BVGetActiveColumns(d->eps->V,&l,&k);
221:   /* Update AV, BV, W and the projected matrices */
222:   /* 1. S <- S*MT */
223:   if (d->V_tra_s != d->V_tra_e || d->V_tra_e > 0) {
224:     dvd_calcpairs_updateBV0_gen(d,d->eps->V,DS_MAT_Q);
225:     if (d->W) { dvd_calcpairs_updateBV0_gen(d,d->W,DS_MAT_Z); }
226:     dvd_calcpairs_updateBV0_gen(d,d->AX,DS_MAT_Q);
227:     if (d->BX) { dvd_calcpairs_updateBV0_gen(d,d->BX,DS_MAT_Q); }
228:     dvd_calcpairs_updateproj(d);
229:     /* Update signature */
230:     if (d->nBds) {
231:       VecCreateSeq(PETSC_COMM_SELF,l+d->V_tra_e,&v1);
232:       BVSetActiveColumns(d->eps->V,0,l+d->V_tra_e);
233:       BVGetSignature(d->eps->V,v1);
234:       VecGetArray(v1,&pv);
235:       for (i=0;i<d->V_tra_e;i++) pv[l+i] = d->nBds[i];
236:       VecRestoreArray(v1,&pv);
237:       BVSetSignature(d->eps->V,v1);
238:       BVSetActiveColumns(d->eps->V,l,k);
239:       VecDestroy(&v1);
240:     }
241:     k = l+d->V_tra_e;
242:     l+= d->V_tra_s;
243:   } else {
244:     /* 2. V <- orth(V, V_new) */
245:     dvd_orthV(d->eps->V,l+d->V_new_s,l+d->V_new_e);
246:     /* 3. AV <- [AV A * V(V_new_s:V_new_e-1)] */
247:     /* Check consistency */
248:     if (k-l != d->V_new_s) SETERRQ(PETSC_COMM_SELF,1,"Consistency broken");
249:     for (i=l+d->V_new_s;i<l+d->V_new_e;i++) {
250:       BVGetColumn(d->eps->V,i,&v1);
251:       BVGetColumn(d->AX,i,&v2);
252:       MatMult(d->A,v1,v2);
253:       BVRestoreColumn(d->eps->V,i,&v1);
254:       BVRestoreColumn(d->AX,i,&v2);
255:     }
256:     /* 4. BV <- [BV B * V(V_new_s:V_new_e-1)] */
257:     if (d->BX) {
258:       /* Check consistency */
259:       if (k-l != d->V_new_s) SETERRQ(PETSC_COMM_SELF,1,"Consistency broken");
260:       for (i=l+d->V_new_s;i<l+d->V_new_e;i++) {
261:         BVGetColumn(d->eps->V,i,&v1);
262:         BVGetColumn(d->BX,i,&v2);
263:         MatMult(d->B,v1,v2);
264:         BVRestoreColumn(d->eps->V,i,&v1);
265:         BVRestoreColumn(d->BX,i,&v2);
266:       }
267:     }
268:     /* 5. W <- [W f(AV,BV)] */
269:     if (d->W) {
270:       d->calcpairs_W(d);
271:       dvd_orthV(d->W,l+d->V_new_s,l+d->V_new_e);
272:     }
273:     /* 6. H <- W' * AX; G <- W' * BX */
274:     BVSetActiveColumns(d->eps->V,l+d->V_new_s,l+d->V_new_e);
275:     BVSetActiveColumns(d->AX,l+d->V_new_s,l+d->V_new_e);
276:     if (d->BX) { BVSetActiveColumns(d->BX,l+d->V_new_s,l+d->V_new_e); }
277:     if (d->W) { BVSetActiveColumns(d->W,l+d->V_new_s,l+d->V_new_e); }
278:     BVMatProject(d->AX,NULL,d->W?d->W:d->eps->V,d->H);
279:     if (d->G) { BVMatProject(d->BX?d->BX:d->eps->V,NULL,d->W?d->W:d->eps->V,d->G); }
280:     BVSetActiveColumns(d->eps->V,l,k);
281:     BVSetActiveColumns(d->AX,l,k);
282:     if (d->BX) { BVSetActiveColumns(d->BX,l,k); }
283:     if (d->W) { BVSetActiveColumns(d->W,l,k); }

285:     /* Perform the transformation on the projected problem */
286:     if (d->W) {
287:       d->calcpairs_proj_trans(d);
288:     }
289:     k = l+d->V_new_e;
290:   }
291:   BVSetActiveColumns(d->eps->V,l,k);
292:   BVSetActiveColumns(d->AX,l,k);
293:   if (d->BX) { BVSetActiveColumns(d->BX,l,k); }
294:   if (d->W) { BVSetActiveColumns(d->W,l,k); }

296:   /* Solve the projected problem */
297:   dvd_calcpairs_projeig_solve(d);

299:   d->V_tra_s = d->V_tra_e = 0;
300:   d->V_new_s = d->V_new_e;
301:   return(0);
302: }

304: static PetscErrorCode dvd_calcpairs_apply_arbitrary(dvdDashboard *d,PetscInt r_s,PetscInt r_e,PetscScalar *rr,PetscScalar *ri)
305: {
306:   PetscInt       i,k,ld;
307:   PetscScalar    *pX;
308:   Vec            *X,xr,xi;
310: #if defined(PETSC_USE_COMPLEX)
311:   PetscInt       N=1;
312: #else
313:   PetscInt       N=2,j;
314: #endif

317:   /* Quick exit without neither arbitrary selection nor harmonic extraction */
318:   if (!d->eps->arbitrary && !d->calcpairs_eig_backtrans) return(0);

320:   /* Quick exit without arbitrary selection, but with harmonic extraction */
321:   if (d->calcpairs_eig_backtrans) {
322:     for (i=r_s; i<r_e; i++) {
323:       d->calcpairs_eig_backtrans(d,d->eigr[i],d->eigi[i],&rr[i-r_s],&ri[i-r_s]);
324:     }
325:   }
326:   if (!d->eps->arbitrary) return(0);

328:   SlepcVecPoolGetVecs(d->auxV,N,&X);
329:   DSGetLeadingDimension(d->eps->ds,&ld);
330:   for (i=r_s;i<r_e;i++) {
331:     k = i;
332:     DSVectors(d->eps->ds,DS_MAT_X,&k,NULL);
333:     DSGetArray(d->eps->ds,DS_MAT_X,&pX);
334:     dvd_improvex_compute_X(d,i,k+1,X,pX,ld);
335:     DSRestoreArray(d->eps->ds,DS_MAT_X,&pX);
336: #if !defined(PETSC_USE_COMPLEX)
337:     if (d->nX[i] != 1.0) {
338:       for (j=i;j<k+1;j++) {
339:         VecScale(X[j-i],1.0/d->nX[i]);
340:       }
341:     }
342:     xr = X[0];
343:     xi = X[1];
344:     if (i == k) {
345:       VecSet(xi,0.0);
346:     }
347: #else
348:     xr = X[0];
349:     xi = NULL;
350:     if (d->nX[i] != 1.0) {
351:       VecScale(xr,1.0/d->nX[i]);
352:     }
353: #endif
354:     (d->eps->arbitrary)(rr[i-r_s],ri[i-r_s],xr,xi,&rr[i-r_s],&ri[i-r_s],d->eps->arbitraryctx);
355: #if !defined(PETSC_USE_COMPLEX)
356:     if (i != k) {
357:       rr[i+1-r_s] = rr[i-r_s];
358:       ri[i+1-r_s] = ri[i-r_s];
359:       i++;
360:     }
361: #endif
362:   }
363:   SlepcVecPoolRestoreVecs(d->auxV,N,&X);
364:   return(0);
365: }

367: static PetscErrorCode dvd_calcpairs_selectPairs(dvdDashboard *d,PetscInt n)
368: {
369:   PetscInt       k,lV,kV,nV;
370:   PetscScalar    *rr,*ri;

374:   BVGetActiveColumns(d->eps->V,&lV,&kV);
375:   nV = kV - lV;
376:   n = PetscMin(n,nV);
377:   if (n <= 0) return(0);
378:   /* Put the best n pairs at the beginning. Useful for restarting */
379:   if (d->eps->arbitrary || d->calcpairs_eig_backtrans) {
380:     PetscMalloc1(nV,&rr);
381:     PetscMalloc1(nV,&ri);
382:     dvd_calcpairs_apply_arbitrary(d,0,nV,rr,ri);
383:   } else {
384:     rr = d->eigr;
385:     ri = d->eigi;
386:   }
387:   k = n;
388:   DSSort(d->eps->ds,d->eigr,d->eigi,rr,ri,&k);
389:   /* Put the best pair at the beginning. Useful to check its residual */
390: #if !defined(PETSC_USE_COMPLEX)
391:   if (n != 1 && (n != 2 || d->eigi[0] == 0.0))
392: #else
393:   if (n != 1)
394: #endif
395:   {
396:     dvd_calcpairs_apply_arbitrary(d,0,nV,rr,ri);
397:     k = 1;
398:     DSSort(d->eps->ds,d->eigr,d->eigi,rr,ri,&k);
399:   }
400:   DSSynchronize(d->eps->ds,d->eigr,d->eigi);

402:   if (d->calcpairs_eigs_trans) {
403:     d->calcpairs_eigs_trans(d);
404:   }
405:   if (d->eps->arbitrary || d->calcpairs_eig_backtrans) {
406:     PetscFree(rr);
407:     PetscFree(ri);
408:   }
409:   return(0);
410: }

412: static PetscErrorCode EPSXDComputeDSConv(dvdDashboard *d)
413: {
414:   PetscErrorCode    ierr;
415:   PetscInt          i,ld;
416:   Vec               v;
417:   PetscScalar       *pA;
418:   const PetscScalar *pv;
419:   PetscBool         symm;

422:   BVSetActiveColumns(d->eps->V,0,d->eps->nconv);
423:   PetscObjectTypeCompare((PetscObject)d->eps->ds,DSHEP,&symm);
424:   if (symm) return(0);
425:   DSSetDimensions(d->eps->ds,d->eps->nconv,0,0,0);
426:   DSCopyMat(d->eps->ds,DS_MAT_A,0,0,d->H,0,0,d->eps->nconv,d->eps->nconv,PETSC_FALSE);
427:   if (d->G) {
428:     DSCopyMat(d->eps->ds,DS_MAT_B,0,0,d->G,0,0,d->eps->nconv,d->eps->nconv,PETSC_FALSE);
429:   }
430:   /* Set the signature on projected matrix B */
431:   if (DVD_IS(d->sEP,DVD_EP_INDEFINITE)) {
432:     DSGetLeadingDimension(d->eps->ds,&ld);
433:     DSGetArray(d->eps->ds,DS_MAT_B,&pA);
434:     PetscArrayzero(pA,d->eps->nconv*ld);
435:     VecCreateSeq(PETSC_COMM_SELF,d->eps->nconv,&v);
436:     BVGetSignature(d->eps->V,v);
437:     VecGetArrayRead(v,&pv);
438:     for (i=0;i<d->eps->nconv;i++) pA[i+ld*i] = pv[i];
439:     VecRestoreArrayRead(v,&pv);
440:     VecDestroy(&v);
441:     DSRestoreArray(d->eps->ds,DS_MAT_B,&pA);
442:   }
443:   DSSetState(d->eps->ds,DS_STATE_RAW);
444:   DSSolve(d->eps->ds,d->eps->eigr,d->eps->eigi);
445:   DSSynchronize(d->eps->ds,d->eps->eigr,d->eps->eigi);
446:   if (d->W) {
447:     for (i=0; i<d->eps->nconv; i++) {
448:       d->calcpairs_eig_backtrans(d,d->eps->eigr[i],d->eps->eigi[i],&d->eps->eigr[i],&d->eps->eigi[i]);
449:     }
450:   }
451:   return(0);
452: }

454: /*
455:    Compute the residual vectors R(i) <- (AV - BV*eigr(i))*pX(i), and also
456:    the norm associated to the Schur pair, where i = r_s..r_e
457: */
458: static PetscErrorCode dvd_calcpairs_res_0(dvdDashboard *d,PetscInt r_s,PetscInt r_e)
459: {
460:   PetscInt       i,ldpX;
461:   PetscScalar    *pX;
463:   BV             BX = d->BX?d->BX:d->eps->V;
464:   Vec            *R;

467:   DSGetLeadingDimension(d->eps->ds,&ldpX);
468:   DSGetArray(d->eps->ds,DS_MAT_Q,&pX);
469:   /* nX(i) <- ||X(i)|| */
470:   dvd_improvex_compute_X(d,r_s,r_e,NULL,pX,ldpX);
471:   SlepcVecPoolGetVecs(d->auxV,r_e-r_s,&R);
472:   for (i=r_s;i<r_e;i++) {
473:     /* R(i-r_s) <- AV*pX(i) */
474:     BVMultVec(d->AX,1.0,0.0,R[i-r_s],&pX[ldpX*i]);
475:     /* R(i-r_s) <- R(i-r_s) - eigr(i)*BX*pX(i) */
476:     BVMultVec(BX,-d->eigr[i],1.0,R[i-r_s],&pX[ldpX*i]);
477:   }
478:   DSRestoreArray(d->eps->ds,DS_MAT_Q,&pX);
479:   d->calcpairs_proj_res(d,r_s,r_e,R);
480:   SlepcVecPoolRestoreVecs(d->auxV,r_e-r_s,&R);
481:   return(0);
482: }

484: static PetscErrorCode dvd_calcpairs_proj_res(dvdDashboard *d,PetscInt r_s,PetscInt r_e,Vec *R)
485: {
486:   PetscInt       i,l,k;
488:   PetscBool      lindep=PETSC_FALSE;
489:   BV             cX;

492:   if (d->W) cX = d->W; /* If left subspace exists, R <- orth(cY, R), nR[i] <- ||R[i]|| */
493:   else if (!(DVD_IS(d->sEP, DVD_EP_STD) && DVD_IS(d->sEP, DVD_EP_HERMITIAN))) cX = d->eps->V; /* If not HEP, R <- orth(cX, R), nR[i] <- ||R[i]|| */
494:   else cX = NULL; /* Otherwise, nR[i] <- ||R[i]|| */

496:   if (cX) {
497:     BVGetActiveColumns(cX,&l,&k);
498:     BVSetActiveColumns(cX,0,l);
499:     for (i=0;i<r_e-r_s;i++) {
500:       BVOrthogonalizeVec(cX,R[i],NULL,&d->nR[r_s+i],&lindep);
501:     }
502:     BVSetActiveColumns(cX,l,k);
503:     if (lindep || (PetscAbs(d->nR[r_s+i]) < PETSC_MACHINE_EPSILON)) {
504:       PetscInfo2(d->eps,"The computed eigenvector residual %D is too low, %g!\n",r_s+i,(double)(d->nR[r_s+i]));
505:     }
506:   } else {
507:     for (i=0;i<r_e-r_s;i++) {
508:       VecNormBegin(R[i],NORM_2,&d->nR[r_s+i]);
509:     }
510:     for (i=0;i<r_e-r_s;i++) {
511:       VecNormEnd(R[i],NORM_2,&d->nR[r_s+i]);
512:     }
513:   }
514:   return(0);
515: }

517: PetscErrorCode dvd_calcpairs_qz(dvdDashboard *d,dvdBlackboard *b,PetscBool borth,PetscBool harm)
518: {
520:   PetscBool      std_probl,her_probl,ind_probl;
521:   DSType         dstype;
522:   Vec            v1;

525:   std_probl = DVD_IS(d->sEP,DVD_EP_STD)? PETSC_TRUE: PETSC_FALSE;
526:   her_probl = DVD_IS(d->sEP,DVD_EP_HERMITIAN)? PETSC_TRUE: PETSC_FALSE;
527:   ind_probl = DVD_IS(d->sEP,DVD_EP_INDEFINITE)? PETSC_TRUE: PETSC_FALSE;

529:   /* Setting configuration constrains */
530:   b->max_size_proj = PetscMax(b->max_size_proj,b->max_size_V);
531:   d->W_shift = d->B? PETSC_TRUE: PETSC_FALSE;

533:   /* Setup the step */
534:   if (b->state >= DVD_STATE_CONF) {
535:     d->max_size_P = b->max_size_P;
536:     d->max_size_proj = b->max_size_proj;
537:     /* Create a DS if the method works with Schur decompositions */
538:     d->calcPairs = dvd_calcpairs_proj;
539:     d->calcpairs_residual = dvd_calcpairs_res_0;
540:     d->calcpairs_proj_res = dvd_calcpairs_proj_res;
541:     d->calcpairs_selectPairs = dvd_calcpairs_selectPairs;
542:     /* Create and configure a DS for solving the projected problems */
543:     if (d->W) dstype = DSGNHEP;    /* If we use harmonics */
544:     else {
545:       if (ind_probl) dstype = DSGHIEP;
546:       else if (std_probl) dstype = her_probl? DSHEP : DSNHEP;
547:       else dstype = her_probl? DSGHEP : DSGNHEP;
548:     }
549:     DSSetType(d->eps->ds,dstype);
550:     DSAllocate(d->eps->ds,d->eps->ncv);
551:     /* Create various vector basis */
552:     if (harm) {
553:       BVDuplicateResize(d->eps->V,d->eps->ncv,&d->W);
554:       BVSetMatrix(d->W,NULL,PETSC_FALSE);
555:     } else d->W = NULL;
556:     BVDuplicateResize(d->eps->V,d->eps->ncv,&d->AX);
557:     BVSetMatrix(d->AX,NULL,PETSC_FALSE);
558:     BVDuplicateResize(d->eps->V,d->eps->ncv,&d->auxBV);
559:     BVSetMatrix(d->auxBV,NULL,PETSC_FALSE);
560:     if (d->B) {
561:       BVDuplicateResize(d->eps->V,d->eps->ncv,&d->BX);
562:       BVSetMatrix(d->BX,NULL,PETSC_FALSE);
563:     } else d->BX = NULL;
564:     MatCreateVecsEmpty(d->A,&v1,NULL);
565:     SlepcVecPoolCreate(v1,0,&d->auxV);
566:     VecDestroy(&v1);
567:     /* Create projected problem matrices */
568:     MatCreateSeqDense(PETSC_COMM_SELF,d->eps->ncv,d->eps->ncv,NULL,&d->H);
569:     if (!std_probl) {
570:       MatCreateSeqDense(PETSC_COMM_SELF,d->eps->ncv,d->eps->ncv,NULL,&d->G);
571:     } else d->G = NULL;
572:     if (her_probl) {
573:       MatSetOption(d->H,MAT_HERMITIAN,PETSC_TRUE);
574:       if (d->G) { MatSetOption(d->G,MAT_HERMITIAN,PETSC_TRUE); }
575:     }

577:     if (ind_probl) {
578:       PetscMalloc1(d->eps->ncv,&d->nBds);
579:     } else d->nBds = NULL;
580:     MatCreateSeqDense(PETSC_COMM_SELF,d->eps->ncv,d->eps->ncv,NULL,&d->auxM);

582:     EPSDavidsonFLAdd(&d->startList,dvd_calcpairs_qz_start);
583:     EPSDavidsonFLAdd(&d->endList,EPSXDComputeDSConv);
584:     EPSDavidsonFLAdd(&d->destroyList,dvd_calcpairs_qz_d);
585:   }
586:   return(0);
587: }