Actual source code: dvdimprovex.c

slepc-3.13.4 2020-09-02
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2020, Universitat Politecnica de Valencia, Spain

  6:    This file is part of SLEPc.
  7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
  8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  9: */
 10: /*
 11:    SLEPc eigensolver: "davidson"

 13:    Step: improve the eigenvectors X
 14: */

 16: #include "davidson.h"
 17:  #include <slepcblaslapack.h>

 19: /**** JD update step (I - Kfg'/(g'Kf)) K(A - sB) (I - Kfg'/(g'Kf)) t = (I - Kfg'/(g'Kf))r  ****/

 21: typedef struct {
 22:   PetscInt     size_X;
 23:   KSP          ksp;                /* correction equation solver */
 24:   Vec          friends;            /* reference vector for composite vectors */
 25:   PetscScalar  theta[4],thetai[2]; /* the shifts used in the correction eq. */
 26:   PetscInt     maxits;             /* maximum number of iterations */
 27:   PetscInt     r_s,r_e;            /* the selected eigenpairs to improve */
 28:   PetscInt     ksp_max_size;       /* the ksp maximum subvectors size */
 29:   PetscReal    tol;                /* the maximum solution tolerance */
 30:   PetscReal    lastTol;            /* last tol for dynamic stopping criterion */
 31:   PetscReal    fix;                /* tolerance for using the approx. eigenvalue */
 32:   PetscBool    dynamic;            /* if the dynamic stopping criterion is applied */
 33:   dvdDashboard *d;                 /* the currect dvdDashboard reference */
 34:   PC           old_pc;             /* old pc in ksp */
 35:   BV           KZ;                 /* KZ vecs for the projector KZ*inv(X'*KZ)*X' */
 36:   BV           U;                  /* new X vectors */
 37:   PetscScalar  *XKZ;               /* X'*KZ */
 38:   PetscScalar  *iXKZ;              /* inverse of XKZ */
 39:   PetscInt     ldXKZ;              /* leading dimension of XKZ */
 40:   PetscInt     size_iXKZ;          /* size of iXKZ */
 41:   PetscInt     ldiXKZ;             /* leading dimension of iXKZ */
 42:   PetscInt     size_cX;            /* last value of d->size_cX */
 43:   PetscInt     old_size_X;         /* last number of improved vectors */
 44:   PetscBLASInt *iXKZPivots;        /* array of pivots */
 45: } dvdImprovex_jd;

 47: /*
 48:    Compute (I - KZ*iXKZ*X')*V where,
 49:    V, the vectors to apply the projector,
 50:    cV, the number of vectors in V,
 51: */
 52: static PetscErrorCode dvd_improvex_apply_proj(dvdDashboard *d,Vec *V,PetscInt cV)
 53: {
 55:   dvdImprovex_jd *data = (dvdImprovex_jd*)d->improveX_data;
 56:   PetscInt       i,ldh,k,l;
 57:   PetscScalar    *h;
 58:   PetscBLASInt   cV_,n,info,ld;
 59: #if defined(PETSC_USE_COMPLEX)
 60:   PetscInt       j;
 61: #endif

 64:   if (cV > 2) SETERRQ(PETSC_COMM_SELF,1,"Consistency broken");

 66:   /* h <- X'*V */
 67:   PetscMalloc1(data->size_iXKZ*cV,&h);
 68:   ldh = data->size_iXKZ;
 69:   BVGetActiveColumns(data->U,&l,&k);
 70:   if (ldh!=k) SETERRQ(PETSC_COMM_SELF,1,"Consistency broken");
 71:   BVSetActiveColumns(data->U,0,k);
 72:   for (i=0;i<cV;i++) {
 73:     BVDotVec(data->U,V[i],&h[ldh*i]);
 74: #if defined(PETSC_USE_COMPLEX)
 75:     for (j=0; j<k; j++) h[ldh*i+j] = PetscConj(h[ldh*i+j]);
 76: #endif
 77:   }
 78:   BVSetActiveColumns(data->U,l,k);

 80:   /* h <- iXKZ\h */
 81:   PetscBLASIntCast(cV,&cV_);
 82:   PetscBLASIntCast(data->size_iXKZ,&n);
 83:   PetscBLASIntCast(data->ldiXKZ,&ld);
 85:   PetscFPTrapPush(PETSC_FP_TRAP_OFF);
 86:   PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("N",&n,&cV_,data->iXKZ,&ld,data->iXKZPivots,h,&n,&info));
 87:   PetscFPTrapPop();
 88:   SlepcCheckLapackInfo("getrs",info);

 90:   /* V <- V - KZ*h */
 91:   BVSetActiveColumns(data->KZ,0,k);
 92:   for (i=0;i<cV;i++) {
 93:     BVMultVec(data->KZ,-1.0,1.0,V[i],&h[ldh*i]);
 94:   }
 95:   BVSetActiveColumns(data->KZ,l,k);
 96:   PetscFree(h);
 97:   return(0);
 98: }

100: /*
101:    Compute (I - X*iXKZ*KZ')*V where,
102:    V, the vectors to apply the projector,
103:    cV, the number of vectors in V,
104: */
105: static PetscErrorCode dvd_improvex_applytrans_proj(dvdDashboard *d,Vec *V,PetscInt cV)
106: {
108:   dvdImprovex_jd *data = (dvdImprovex_jd*)d->improveX_data;
109:   PetscInt       i,ldh,k,l;
110:   PetscScalar    *h;
111:   PetscBLASInt   cV_, n, info, ld;
112: #if defined(PETSC_USE_COMPLEX)
113:   PetscInt       j;
114: #endif

117:   if (cV > 2) SETERRQ(PETSC_COMM_SELF,1,"Consistency broken");

119:   /* h <- KZ'*V */
120:   PetscMalloc1(data->size_iXKZ*cV,&h);
121:   ldh = data->size_iXKZ;
122:   BVGetActiveColumns(data->U,&l,&k);
123:   if (ldh!=k) SETERRQ(PETSC_COMM_SELF,1,"Consistency broken");
124:   BVSetActiveColumns(data->KZ,0,k);
125:   for (i=0;i<cV;i++) {
126:     BVDotVec(data->KZ,V[i],&h[ldh*i]);
127: #if defined(PETSC_USE_COMPLEX)
128:     for (j=0;j<k;j++) h[ldh*i+j] = PetscConj(h[ldh*i+j]);
129: #endif
130:   }
131:   BVSetActiveColumns(data->KZ,l,k);

133:   /* h <- iXKZ\h */
134:   PetscBLASIntCast(cV,&cV_);
135:   PetscBLASIntCast(data->size_iXKZ,&n);
136:   PetscBLASIntCast(data->ldiXKZ,&ld);
138:   PetscFPTrapPush(PETSC_FP_TRAP_OFF);
139:   PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("C",&n,&cV_,data->iXKZ,&ld,data->iXKZPivots,h,&n,&info));
140:   PetscFPTrapPop();
141:   SlepcCheckLapackInfo("getrs",info);

143:   /* V <- V - U*h */
144:   BVSetActiveColumns(data->U,0,k);
145:   for (i=0;i<cV;i++) {
146:     BVMultVec(data->U,-1.0,1.0,V[i],&h[ldh*i]);
147:   }
148:   BVSetActiveColumns(data->U,l,k);
149:   PetscFree(h);
150:   return(0);
151: }

153: static PetscErrorCode dvd_improvex_jd_end(dvdDashboard *d)
154: {
156:   dvdImprovex_jd *data = (dvdImprovex_jd*)d->improveX_data;

159:   VecDestroy(&data->friends);

161:   /* Restore the pc of ksp */
162:   if (data->old_pc) {
163:     KSPSetPC(data->ksp, data->old_pc);
164:     PCDestroy(&data->old_pc);
165:   }
166:   return(0);
167: }

169: static PetscErrorCode dvd_improvex_jd_d(dvdDashboard *d)
170: {
172:   dvdImprovex_jd *data = (dvdImprovex_jd*)d->improveX_data;

175:   /* Free local data and objects */
176:   PetscFree(data->XKZ);
177:   PetscFree(data->iXKZ);
178:   PetscFree(data->iXKZPivots);
179:   BVDestroy(&data->KZ);
180:   BVDestroy(&data->U);
181:   PetscFree(data);
182:   return(0);
183: }

185: /*
186:    y <- theta[1]A*x - theta[0]*B*x
187:    auxV, two auxiliary vectors
188:  */
189: PETSC_STATIC_INLINE PetscErrorCode dvd_aux_matmult(dvdImprovex_jd *data,const Vec *x,const Vec *y)
190: {
192:   PetscInt       n,i;
193:   const Vec      *Bx;
194:   Vec            *auxV;

197:   n = data->r_e - data->r_s;
198:   for (i=0;i<n;i++) {
199:     MatMult(data->d->A,x[i],y[i]);
200:   }

202:   SlepcVecPoolGetVecs(data->d->auxV,2,&auxV);
203:   for (i=0;i<n;i++) {
204: #if !defined(PETSC_USE_COMPLEX)
205:     if (data->d->eigi[data->r_s+i] != 0.0) {
206:       if (data->d->B) {
207:         MatMult(data->d->B,x[i],auxV[0]);
208:         MatMult(data->d->B,x[i+1],auxV[1]);
209:         Bx = auxV;
210:       } else Bx = &x[i];

212:       /* y_i   <- [ t_2i+1*A*x_i   - t_2i*Bx_i + ti_i*Bx_i+1;
213:          y_i+1      t_2i+1*A*x_i+1 - ti_i*Bx_i - t_2i*Bx_i+1  ] */
214:       VecAXPBYPCZ(y[i],-data->theta[2*i],data->thetai[i],data->theta[2*i+1],Bx[0],Bx[1]);
215:       VecAXPBYPCZ(y[i+1],-data->thetai[i],-data->theta[2*i],data->theta[2*i+1],Bx[0],Bx[1]);
216:       i++;
217:     } else
218: #endif
219:     {
220:       if (data->d->B) {
221:         MatMult(data->d->B,x[i],auxV[0]);
222:         Bx = auxV;
223:       } else Bx = &x[i];
224:       VecAXPBY(y[i],-data->theta[i*2],data->theta[i*2+1],Bx[0]);
225:     }
226:   }
227:   SlepcVecPoolRestoreVecs(data->d->auxV,2,&auxV);
228:   return(0);
229: }

231: /*
232:    y <- theta[1]'*A'*x - theta[0]'*B'*x
233:  */
234: PETSC_STATIC_INLINE PetscErrorCode dvd_aux_matmulttrans(dvdImprovex_jd *data,const Vec *x,const Vec *y)
235: {
237:   PetscInt       n,i;
238:   const Vec      *Bx;
239:   Vec            *auxV;

242:   n = data->r_e - data->r_s;
243:   for (i=0;i<n;i++) {
244:     MatMultTranspose(data->d->A,x[i],y[i]);
245:   }

247:   SlepcVecPoolGetVecs(data->d->auxV,2,&auxV);
248:   for (i=0;i<n;i++) {
249: #if !defined(PETSC_USE_COMPLEX)
250:     if (data->d->eigi[data->r_s+i] != 0.0) {
251:       if (data->d->B) {
252:         MatMultTranspose(data->d->B,x[i],auxV[0]);
253:         MatMultTranspose(data->d->B,x[i+1],auxV[1]);
254:         Bx = auxV;
255:       } else Bx = &x[i];

257:       /* y_i   <- [ t_2i+1*A*x_i   - t_2i*Bx_i - ti_i*Bx_i+1;
258:          y_i+1      t_2i+1*A*x_i+1 + ti_i*Bx_i - t_2i*Bx_i+1  ] */
259:       VecAXPBYPCZ(y[i],-data->theta[2*i],-data->thetai[i],data->theta[2*i+1],Bx[0],Bx[1]);
260:       VecAXPBYPCZ(y[i+1],data->thetai[i],-data->theta[2*i],data->theta[2*i+1],Bx[0],Bx[1]);
261:       i++;
262:     } else
263: #endif
264:     {
265:       if (data->d->B) {
266:         MatMultTranspose(data->d->B,x[i],auxV[0]);
267:         Bx = auxV;
268:       } else Bx = &x[i];
269:       VecAXPBY(y[i],PetscConj(-data->theta[i*2]),PetscConj(data->theta[i*2+1]),Bx[0]);
270:     }
271:   }
272:   SlepcVecPoolRestoreVecs(data->d->auxV,2,&auxV);
273:   return(0);
274: }

276: static PetscErrorCode PCApplyBA_dvd(PC pc,PCSide side,Vec in,Vec out,Vec w)
277: {
279:   dvdImprovex_jd *data;
280:   PetscInt       n,i;
281:   const Vec      *inx,*outx,*wx;
282:   Vec            *auxV;
283:   Mat            A;

286:   PCGetOperators(pc,&A,NULL);
287:   MatShellGetContext(A,(void**)&data);
288:   VecCompGetSubVecs(in,NULL,&inx);
289:   VecCompGetSubVecs(out,NULL,&outx);
290:   VecCompGetSubVecs(w,NULL,&wx);
291:   n = data->r_e - data->r_s;
292:   SlepcVecPoolGetVecs(data->d->auxV,n,&auxV);
293:   switch (side) {
294:   case PC_LEFT:
295:     /* aux <- theta[1]A*in - theta[0]*B*in */
296:     dvd_aux_matmult(data,inx,auxV);

298:     /* out <- K * aux */
299:     for (i=0;i<n;i++) {
300:       data->d->improvex_precond(data->d,data->r_s+i,auxV[i],outx[i]);
301:     }
302:     break;
303:   case PC_RIGHT:
304:     /* aux <- K * in */
305:     for (i=0;i<n;i++) {
306:       data->d->improvex_precond(data->d,data->r_s+i,inx[i],auxV[i]);
307:     }

309:     /* out <- theta[1]A*auxV - theta[0]*B*auxV */
310:     dvd_aux_matmult(data,auxV,outx);
311:     break;
312:   case PC_SYMMETRIC:
313:     /* aux <- K^{1/2} * in */
314:     for (i=0;i<n;i++) {
315:       PCApplySymmetricRight(data->old_pc,inx[i],auxV[i]);
316:     }

318:     /* wx <- theta[1]A*auxV - theta[0]*B*auxV */
319:     dvd_aux_matmult(data,auxV,wx);

321:     /* aux <- K^{1/2} * in */
322:     for (i=0;i<n;i++) {
323:       PCApplySymmetricLeft(data->old_pc,wx[i],outx[i]);
324:     }
325:     break;
326:   default:
327:     SETERRQ(PETSC_COMM_SELF,1,"Unsupported KSP side");
328:   }
329:   /* out <- out - v*(u'*out) */
330:   dvd_improvex_apply_proj(data->d,(Vec*)outx,n);
331:   SlepcVecPoolRestoreVecs(data->d->auxV,n,&auxV);
332:   return(0);
333: }

335: static PetscErrorCode PCApply_dvd(PC pc,Vec in,Vec out)
336: {
338:   dvdImprovex_jd *data;
339:   PetscInt       n,i;
340:   const Vec      *inx, *outx;
341:   Mat            A;

344:   PCGetOperators(pc,&A,NULL);
345:   MatShellGetContext(A,(void**)&data);
346:   VecCompGetSubVecs(in,NULL,&inx);
347:   VecCompGetSubVecs(out,NULL,&outx);
348:   n = data->r_e - data->r_s;
349:   /* out <- K * in */
350:   for (i=0;i<n;i++) {
351:     data->d->improvex_precond(data->d,data->r_s+i,inx[i],outx[i]);
352:   }
353:   /* out <- out - v*(u'*out) */
354:   dvd_improvex_apply_proj(data->d,(Vec*)outx,n);
355:   return(0);
356: }

358: static PetscErrorCode PCApplyTranspose_dvd(PC pc,Vec in,Vec out)
359: {
361:   dvdImprovex_jd *data;
362:   PetscInt       n,i;
363:   const Vec      *inx, *outx;
364:   Vec            *auxV;
365:   Mat            A;

368:   PCGetOperators(pc,&A,NULL);
369:   MatShellGetContext(A,(void**)&data);
370:   VecCompGetSubVecs(in,NULL,&inx);
371:   VecCompGetSubVecs(out,NULL,&outx);
372:   n = data->r_e - data->r_s;
373:   SlepcVecPoolGetVecs(data->d->auxV,n,&auxV);
374:   /* auxV <- in */
375:   for (i=0;i<n;i++) {
376:     VecCopy(inx[i],auxV[i]);
377:   }
378:   /* auxV <- auxV - u*(v'*auxV) */
379:   dvd_improvex_applytrans_proj(data->d,auxV,n);
380:   /* out <- K' * aux */
381:   for (i=0;i<n;i++) {
382:     PCApplyTranspose(data->old_pc,auxV[i],outx[i]);
383:   }
384:   SlepcVecPoolRestoreVecs(data->d->auxV,n,&auxV);
385:   return(0);
386: }

388: static PetscErrorCode MatMult_dvd_jd(Mat A,Vec in,Vec out)
389: {
391:   dvdImprovex_jd *data;
392:   PetscInt       n;
393:   const Vec      *inx, *outx;
394:   PCSide         side;

397:   MatShellGetContext(A,(void**)&data);
398:   VecCompGetSubVecs(in,NULL,&inx);
399:   VecCompGetSubVecs(out,NULL,&outx);
400:   n = data->r_e - data->r_s;
401:   /* out <- theta[1]A*in - theta[0]*B*in */
402:   dvd_aux_matmult(data,inx,outx);
403:   KSPGetPCSide(data->ksp,&side);
404:   if (side == PC_RIGHT) {
405:     /* out <- out - v*(u'*out) */
406:     dvd_improvex_apply_proj(data->d,(Vec*)outx,n);
407:   }
408:   return(0);
409: }

411: static PetscErrorCode MatMultTranspose_dvd_jd(Mat A,Vec in,Vec out)
412: {
414:   dvdImprovex_jd *data;
415:   PetscInt       n,i;
416:   const Vec      *inx,*outx,*r;
417:   Vec            *auxV;
418:   PCSide         side;

421:   MatShellGetContext(A,(void**)&data);
422:   VecCompGetSubVecs(in,NULL,&inx);
423:   VecCompGetSubVecs(out,NULL,&outx);
424:   n = data->r_e - data->r_s;
425:   KSPGetPCSide(data->ksp,&side);
426:   if (side == PC_RIGHT) {
427:     /* auxV <- in */
428:     SlepcVecPoolGetVecs(data->d->auxV,n,&auxV);
429:     for (i=0;i<n;i++) {
430:       VecCopy(inx[i],auxV[i]);
431:     }
432:     /* auxV <- auxV - v*(u'*auxV) */
433:     dvd_improvex_applytrans_proj(data->d,auxV,n);
434:     r = auxV;
435:   } else r = inx;
436:   /* out <- theta[1]A*r - theta[0]*B*r */
437:   dvd_aux_matmulttrans(data,r,outx);
438:   if (side == PC_RIGHT) {
439:     SlepcVecPoolRestoreVecs(data->d->auxV,n,&auxV);
440:   }
441:   return(0);
442: }

444: static PetscErrorCode MatCreateVecs_dvd_jd(Mat A,Vec *right,Vec *left)
445: {
447:   Vec            *r,*l;
448:   dvdImprovex_jd *data;
449:   PetscInt       n,i;

452:   MatShellGetContext(A,(void**)&data);
453:   n = data->ksp_max_size;
454:   if (right) {
455:     PetscMalloc1(n,&r);
456:   }
457:   if (left) {
458:     PetscMalloc1(n,&l);
459:   }
460:   for (i=0;i<n;i++) {
461:     MatCreateVecs(data->d->A,right?&r[i]:NULL,left?&l[i]:NULL);
462:   }
463:   if (right) {
464:     VecCreateCompWithVecs(r,n,data->friends,right);
465:     for (i=0;i<n;i++) {
466:       VecDestroy(&r[i]);
467:     }
468:   }
469:   if (left) {
470:     VecCreateCompWithVecs(l,n,data->friends,left);
471:     for (i=0;i<n;i++) {
472:       VecDestroy(&l[i]);
473:     }
474:   }

476:   if (right) {
477:     PetscFree(r);
478:   }
479:   if (left) {
480:     PetscFree(l);
481:   }
482:   return(0);
483: }

485: static PetscErrorCode dvd_improvex_jd_start(dvdDashboard *d)
486: {
488:   dvdImprovex_jd *data = (dvdImprovex_jd*)d->improveX_data;
489:   PetscInt       rA, cA, rlA, clA;
490:   Mat            A;
491:   PetscBool      t;
492:   PC             pc;
493:   Vec            v0[2];

496:   data->size_cX = data->old_size_X = 0;
497:   data->lastTol = data->dynamic?0.5:0.0;

499:   /* Setup the ksp */
500:   if (data->ksp) {
501:     /* Create the reference vector */
502:     BVGetColumn(d->eps->V,0,&v0[0]);
503:     v0[1] = v0[0];
504:     VecCreateCompWithVecs(v0,data->ksp_max_size,NULL,&data->friends);
505:     BVRestoreColumn(d->eps->V,0,&v0[0]);
506:     PetscLogObjectParent((PetscObject)d->eps,(PetscObject)data->friends);

508:     /* Save the current pc and set a PCNONE */
509:     KSPGetPC(data->ksp, &data->old_pc);
510:     PetscObjectTypeCompare((PetscObject)data->old_pc,PCNONE,&t);
511:     data->lastTol = 0.5;
512:     if (t) data->old_pc = 0;
513:     else {
514:       PetscObjectReference((PetscObject)data->old_pc);
515:       PCCreate(PetscObjectComm((PetscObject)d->eps),&pc);
516:       PCSetType(pc,PCSHELL);
517:       PCSetOperators(pc,d->A,d->A);
518:       PCSetReusePreconditioner(pc,PETSC_TRUE);
519:       PCShellSetApply(pc,PCApply_dvd);
520:       PCShellSetApplyBA(pc,PCApplyBA_dvd);
521:       PCShellSetApplyTranspose(pc,PCApplyTranspose_dvd);
522:       KSPSetPC(data->ksp,pc);
523:       PCDestroy(&pc);
524:     }

526:     /* Create the (I-v*u')*K*(A-s*B) matrix */
527:     MatGetSize(d->A,&rA,&cA);
528:     MatGetLocalSize(d->A,&rlA,&clA);
529:     MatCreateShell(PetscObjectComm((PetscObject)d->A),rlA*data->ksp_max_size,clA*data->ksp_max_size,rA*data->ksp_max_size,cA*data->ksp_max_size,data,&A);
530:     MatShellSetOperation(A,MATOP_MULT,(void(*)(void))MatMult_dvd_jd);
531:     MatShellSetOperation(A,MATOP_MULT_TRANSPOSE,(void(*)(void))MatMultTranspose_dvd_jd);
532:     MatShellSetOperation(A,MATOP_CREATE_VECS,(void(*)(void))MatCreateVecs_dvd_jd);

534:     /* Try to avoid KSPReset */
535:     KSPGetOperatorsSet(data->ksp,&t,NULL);
536:     if (t) {
537:       Mat      M;
538:       PetscInt rM;
539:       KSPGetOperators(data->ksp,&M,NULL);
540:       MatGetSize(M,&rM,NULL);
541:       if (rM != rA*data->ksp_max_size) { KSPReset(data->ksp); }
542:     }
543:     KSPSetOperators(data->ksp,A,A);
544:     KSPSetReusePreconditioner(data->ksp,PETSC_TRUE);
545:     KSPSetUp(data->ksp);
546:     MatDestroy(&A);
547:   } else {
548:     data->old_pc = 0;
549:     data->friends = NULL;
550:   }
551:   BVSetActiveColumns(data->KZ,0,0);
552:   BVSetActiveColumns(data->U,0,0);
553:   return(0);
554: }

556: /*
557:   Compute: u <- X, v <- K*(theta[0]*A+theta[1]*B)*X,
558:   kr <- K^{-1}*(A-eig*B)*X, being X <- V*pX[i_s..i_e-1], Y <- W*pY[i_s..i_e-1]
559:   where
560:   pX,pY, the right and left eigenvectors of the projected system
561:   ld, the leading dimension of pX and pY
562: */
563: static PetscErrorCode dvd_improvex_jd_proj_cuv(dvdDashboard *d,PetscInt i_s,PetscInt i_e,Vec *kr,PetscScalar *theta,PetscScalar *thetai,PetscScalar *pX,PetscScalar *pY,PetscInt ld)
564: {
566:   PetscInt       n=i_e-i_s,size_KZ,V_new,rm,i,lv,kv,lKZ,kKZ;
567:   dvdImprovex_jd *data = (dvdImprovex_jd*)d->improveX_data;
568:   PetscScalar    *array;
569:   Mat            M;
570:   Vec            u[2],v[2];
571:   PetscBLASInt   s,ldXKZ,info;

574:   /* Check consistency */
575:   BVGetActiveColumns(d->eps->V,&lv,&kv);
576:   V_new = lv - data->size_cX;
577:   if (V_new > data->old_size_X) SETERRQ(PETSC_COMM_SELF,1,"Consistency broken");
578:   data->old_size_X = n;
579:   data->size_cX = lv;

581:   /* KZ <- KZ(rm:rm+max_cX-1) */
582:   BVGetActiveColumns(data->KZ,&lKZ,&kKZ);
583:   rm = PetscMax(V_new+lKZ,0);
584:   if (rm > 0) {
585:     for (i=0;i<lKZ;i++) {
586:       BVCopyColumn(data->KZ,i+rm,i);
587:       BVCopyColumn(data->U,i+rm,i);
588:     }
589:   }

591:   /* XKZ <- XKZ(rm:rm+max_cX-1,rm:rm+max_cX-1) */
592:   if (rm > 0) {
593:     for (i=0;i<lKZ;i++) {
594:       PetscArraycpy(&data->XKZ[i*data->ldXKZ+i],&data->XKZ[(i+rm)*data->ldXKZ+i+rm],lKZ);
595:     }
596:   }
597:   lKZ = PetscMin(0,lKZ+V_new);
598:   BVSetActiveColumns(data->KZ,lKZ,lKZ+n);
599:   BVSetActiveColumns(data->U,lKZ,lKZ+n);

601:   /* Compute X, KZ and KR */
602:   BVGetColumn(data->U,lKZ,u);
603:   if (n>1) { BVGetColumn(data->U,lKZ+1,&u[1]); }
604:   BVGetColumn(data->KZ,lKZ,v);
605:   if (n>1) { BVGetColumn(data->KZ,lKZ+1,&v[1]); }
606:   d->improvex_jd_proj_uv(d,i_s,i_e,u,v,kr,theta,thetai,pX,pY,ld);
607:   BVRestoreColumn(data->U,lKZ,u);
608:   if (n>1) { BVRestoreColumn(data->U,lKZ+1,&u[1]); }
609:   BVRestoreColumn(data->KZ,lKZ,v);
610:   if (n>1) { BVRestoreColumn(data->KZ,lKZ+1,&v[1]); }

612:   /* XKZ <- U'*KZ */
613:   MatCreateSeqDense(PETSC_COMM_SELF,lKZ+n,lKZ+n,NULL,&M);
614:   BVMatProject(data->KZ,NULL,data->U,M);
615:   MatDenseGetArray(M,&array);
616:   for (i=lKZ;i<lKZ+n;i++) { /* upper part */
617:     PetscArraycpy(&data->XKZ[data->ldXKZ*i],&array[i*(lKZ+n)],lKZ);
618:   }
619:   for (i=0;i<lKZ+n;i++) { /* lower part */
620:     PetscArraycpy(&data->XKZ[data->ldXKZ*i+lKZ],&array[i*(lKZ+n)+lKZ],n);
621:   }
622:   MatDenseRestoreArray(M,&array);
623:   MatDestroy(&M);

625:   /* iXKZ <- inv(XKZ) */
626:   size_KZ = lKZ+n;
627:   PetscBLASIntCast(lKZ+n,&s);
628:   data->ldiXKZ = data->size_iXKZ = size_KZ;
629:   for (i=0;i<size_KZ;i++) {
630:     PetscArraycpy(&data->iXKZ[data->ldiXKZ*i],&data->XKZ[data->ldXKZ*i],size_KZ);
631:   }
632:   PetscBLASIntCast(data->ldiXKZ,&ldXKZ);
633:   PetscFPTrapPush(PETSC_FP_TRAP_OFF);
634:   PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&s,&s,data->iXKZ,&ldXKZ,data->iXKZPivots,&info));
635:   PetscFPTrapPop();
636:   SlepcCheckLapackInfo("getrf",info);
637:   return(0);
638: }

640: static PetscErrorCode dvd_improvex_jd_gen(dvdDashboard *d,PetscInt r_s,PetscInt r_e,PetscInt *size_D)
641: {
642:   dvdImprovex_jd *data = (dvdImprovex_jd*)d->improveX_data;
644:   PetscInt       i,j,n,maxits,maxits0,lits,s,ld,k,max_size_D,lV,kV;
645:   PetscScalar    *pX,*pY;
646:   PetscReal      tol,tol0;
647:   Vec            *kr,kr_comp,D_comp,D[2],kr0[2];
648:   PetscBool      odd_situation = PETSC_FALSE;

651:   BVGetActiveColumns(d->eps->V,&lV,&kV);
652:   max_size_D = d->eps->ncv-kV;
653:   /* Quick exit */
654:   if ((max_size_D == 0) || r_e-r_s <= 0) {
655:    *size_D = 0;
656:     return(0);
657:   }

659:   n = PetscMin(PetscMin(data->size_X, max_size_D), r_e-r_s);
660:   if (n == 0) SETERRQ(PETSC_COMM_SELF,1,"n == 0");
661:   if (data->size_X < r_e-r_s) SETERRQ(PETSC_COMM_SELF,1,"size_X < r_e-r_s");

663:   DSGetLeadingDimension(d->eps->ds,&ld);

665:   /* Restart lastTol if a new pair converged */
666:   if (data->dynamic && data->size_cX < lV)
667:     data->lastTol = 0.5;

669:   for (i=0,s=0;i<n;i+=s) {
670:     /* If the selected eigenvalue is complex, but the arithmetic is real... */
671: #if !defined(PETSC_USE_COMPLEX)
672:     if (d->eigi[r_s+i] != 0.0) {
673:       if (i+2 <= max_size_D) s=2;
674:       else break;
675:     } else
676: #endif
677:       s=1;

679:     data->r_s = r_s+i;
680:     data->r_e = r_s+i+s;
681:     SlepcVecPoolGetVecs(d->auxV,s,&kr);

683:     /* Compute theta, maximum iterations and tolerance */
684:     maxits = 0;
685:     tol = 1;
686:     for (j=0;j<s;j++) {
687:       d->improvex_jd_lit(d,r_s+i+j,&data->theta[2*j],&data->thetai[j],&maxits0,&tol0);
688:       maxits += maxits0;
689:       tol *= tol0;
690:     }
691:     maxits/= s;
692:     tol = data->dynamic?data->lastTol:PetscExpReal(PetscLogReal(tol)/s);

694:     /* Compute u, v and kr */
695:     k = r_s+i;
696:     DSVectors(d->eps->ds,DS_MAT_X,&k,NULL);
697:     k = r_s+i;
698:     DSVectors(d->eps->ds,DS_MAT_Y,&k,NULL);
699:     DSGetArray(d->eps->ds,DS_MAT_X,&pX);
700:     DSGetArray(d->eps->ds,DS_MAT_Y,&pY);
701:     dvd_improvex_jd_proj_cuv(d,r_s+i,r_s+i+s,kr,data->theta,data->thetai,pX,pY,ld);
702:     DSRestoreArray(d->eps->ds,DS_MAT_X,&pX);
703:     DSRestoreArray(d->eps->ds,DS_MAT_Y,&pY);

705:     /* Check if the first eigenpairs are converged */
706:     if (i == 0) {
707:       PetscInt oldnpreconv = d->npreconv;
708:       d->preTestConv(d,0,r_s+s,r_s+s,&d->npreconv);
709:       if (d->npreconv > oldnpreconv) break;
710:     }

712:     /* Test the odd situation of solving Ax=b with A=I */
713: #if !defined(PETSC_USE_COMPLEX)
714:     odd_situation = (data->ksp && data->theta[0] == 1. && data->theta[1] == 0. && data->thetai[0] == 0. && d->B == NULL)? PETSC_TRUE: PETSC_FALSE;
715: #else
716:     odd_situation = (data->ksp && data->theta[0] == 1. && data->theta[1] == 0. && d->B == NULL)? PETSC_TRUE: PETSC_FALSE;
717: #endif
718:     /* If JD */
719:     if (data->ksp && !odd_situation) {
720:       /* kr <- -kr */
721:       for (j=0;j<s;j++) {
722:         VecScale(kr[j],-1.0);
723:       }

725:       /* Compose kr and D */
726:       kr0[0] = kr[0];
727:       kr0[1] = (s==2 ? kr[1] : NULL);
728:       VecCreateCompWithVecs(kr0,data->ksp_max_size,data->friends,&kr_comp);
729:       BVGetColumn(d->eps->V,kV+i,&D[0]);
730:       if (s==2) { BVGetColumn(d->eps->V,kV+i+1,&D[1]); }
731:       else D[1] = NULL;
732:       VecCreateCompWithVecs(D,data->ksp_max_size,data->friends,&D_comp);
733:       VecCompSetSubVecs(data->friends,s,NULL);

735:       /* Solve the correction equation */
736:       KSPSetTolerances(data->ksp,tol,PETSC_DEFAULT,PETSC_DEFAULT,maxits);
737:       KSPSolve(data->ksp,kr_comp,D_comp);
738:       KSPGetIterationNumber(data->ksp,&lits);

740:       /* Destroy the composed ks and D */
741:       VecDestroy(&kr_comp);
742:       VecDestroy(&D_comp);
743:       BVRestoreColumn(d->eps->V,kV+i,&D[0]);
744:       if (s==2) { BVRestoreColumn(d->eps->V,kV+i+1,&D[1]); }

746:     /* If GD */
747:     } else {
748:       BVGetColumn(d->eps->V,kV+i,&D[0]);
749:       if (s==2) { BVGetColumn(d->eps->V,kV+i+1,&D[1]); }
750:       for (j=0;j<s;j++) {
751:         d->improvex_precond(d,r_s+i+j,kr[j],D[j]);
752:       }
753:       dvd_improvex_apply_proj(d,D,s);
754:       BVRestoreColumn(d->eps->V,kV+i,&D[0]);
755:       if (s==2) { BVRestoreColumn(d->eps->V,kV+i+1,&D[1]); }
756:     }
757:     /* Prevent that short vectors are discarded in the orthogonalization */
758:     if (i == 0 && d->eps->errest[d->nconv+r_s] > PETSC_MACHINE_EPSILON && d->eps->errest[d->nconv+r_s] < PETSC_MAX_REAL) {
759:       for (j=0;j<s;j++) {
760:         BVScaleColumn(d->eps->V,kV+i+j,1.0/d->eps->errest[d->nconv+r_s]);
761:       }
762:     }
763:     SlepcVecPoolRestoreVecs(d->auxV,s,&kr);
764:   }
765:   *size_D = i;
766:   if (data->dynamic) data->lastTol = PetscMax(data->lastTol/2.0,PETSC_MACHINE_EPSILON*10.0);
767:   return(0);
768: }

770: PetscErrorCode dvd_improvex_jd(dvdDashboard *d,dvdBlackboard *b,KSP ksp,PetscInt max_bs,PetscBool dynamic)
771: {
773:   dvdImprovex_jd *data;
774:   PetscBool      useGD;
775:   PC             pc;
776:   PetscInt       size_P;

779:   /* Setting configuration constrains */
780:   PetscObjectTypeCompare((PetscObject)ksp,KSPPREONLY,&useGD);

782:   /* If the arithmetic is real and the problem is not Hermitian, then
783:      the block size is incremented in one */
784: #if !defined(PETSC_USE_COMPLEX)
785:   if (!DVD_IS(d->sEP,DVD_EP_HERMITIAN)) {
786:     max_bs++;
787:     b->max_size_P = PetscMax(b->max_size_P,2);
788:   } else
789: #endif
790:   {
791:     b->max_size_P = PetscMax(b->max_size_P,1);
792:   }
793:   b->max_size_X = PetscMax(b->max_size_X,max_bs);
794:   size_P = b->max_size_P;

796:   /* Setup the preconditioner */
797:   if (ksp) {
798:     KSPGetPC(ksp,&pc);
799:     dvd_static_precond_PC(d,b,pc);
800:   } else {
801:     dvd_static_precond_PC(d,b,0);
802:   }

804:   /* Setup the step */
805:   if (b->state >= DVD_STATE_CONF) {
806:     PetscNewLog(d->eps,&data);
807:     data->dynamic = dynamic;
808:     PetscMalloc1(size_P*size_P,&data->XKZ);
809:     PetscMalloc1(size_P*size_P,&data->iXKZ);
810:     PetscMalloc1(size_P,&data->iXKZPivots);
811:     data->ldXKZ = size_P;
812:     data->size_X = b->max_size_X;
813:     d->improveX_data = data;
814:     data->ksp = useGD? NULL: ksp;
815:     data->d = d;
816:     d->improveX = dvd_improvex_jd_gen;
817: #if !defined(PETSC_USE_COMPLEX)
818:     if (!DVD_IS(d->sEP,DVD_EP_HERMITIAN)) data->ksp_max_size = 2;
819:     else
820: #endif
821:       data->ksp_max_size = 1;
822:     /* Create various vector basis */
823:     BVDuplicateResize(d->eps->V,size_P,&data->KZ);
824:     BVSetMatrix(data->KZ,NULL,PETSC_FALSE);
825:     BVDuplicate(data->KZ,&data->U);

827:     EPSDavidsonFLAdd(&d->startList,dvd_improvex_jd_start);
828:     EPSDavidsonFLAdd(&d->endList,dvd_improvex_jd_end);
829:     EPSDavidsonFLAdd(&d->destroyList,dvd_improvex_jd_d);
830:   }
831:   return(0);
832: }

834: #if !defined(PETSC_USE_COMPLEX)
835: PETSC_STATIC_INLINE PetscErrorCode dvd_complex_rayleigh_quotient(Vec ur,Vec ui,Vec Axr,Vec Axi,Vec Bxr,Vec Bxi,PetscScalar *eigr,PetscScalar *eigi)
836: {
838:   PetscScalar    rAr,iAr,rAi,iAi,rBr,iBr,rBi,iBi,b0,b2,b4,b6,b7;

841:   /* eigr = [(rAr+iAi)*(rBr+iBi) + (rAi-iAr)*(rBi-iBr)]/k
842:      eigi = [(rAi-iAr)*(rBr+iBi) - (rAr+iAi)*(rBi-iBr)]/k
843:      k    =  (rBr+iBi)*(rBr+iBi) + (rBi-iBr)*(rBi-iBr)    */
844:   VecDotBegin(Axr,ur,&rAr); /* r*A*r */
845:   VecDotBegin(Axr,ui,&iAr); /* i*A*r */
846:   VecDotBegin(Axi,ur,&rAi); /* r*A*i */
847:   VecDotBegin(Axi,ui,&iAi); /* i*A*i */
848:   VecDotBegin(Bxr,ur,&rBr); /* r*B*r */
849:   VecDotBegin(Bxr,ui,&iBr); /* i*B*r */
850:   VecDotBegin(Bxi,ur,&rBi); /* r*B*i */
851:   VecDotBegin(Bxi,ui,&iBi); /* i*B*i */
852:   VecDotEnd(Axr,ur,&rAr); /* r*A*r */
853:   VecDotEnd(Axr,ui,&iAr); /* i*A*r */
854:   VecDotEnd(Axi,ur,&rAi); /* r*A*i */
855:   VecDotEnd(Axi,ui,&iAi); /* i*A*i */
856:   VecDotEnd(Bxr,ur,&rBr); /* r*B*r */
857:   VecDotEnd(Bxr,ui,&iBr); /* i*B*r */
858:   VecDotEnd(Bxi,ur,&rBi); /* r*B*i */
859:   VecDotEnd(Bxi,ui,&iBi); /* i*B*i */
860:   b0 = rAr+iAi; /* rAr+iAi */
861:   b2 = rAi-iAr; /* rAi-iAr */
862:   b4 = rBr+iBi; /* rBr+iBi */
863:   b6 = rBi-iBr; /* rBi-iBr */
864:   b7 = b4*b4 + b6*b6; /* k */
865:   *eigr = (b0*b4 + b2*b6) / b7; /* eig_r */
866:   *eigi = (b2*b4 - b0*b6) / b7; /* eig_i */
867:   return(0);
868: }
869: #endif

871: PETSC_STATIC_INLINE PetscErrorCode dvd_compute_n_rr(PetscInt i_s,PetscInt n,PetscScalar *eigr,PetscScalar *eigi,Vec *u,Vec *Ax,Vec *Bx)
872: {
874:   PetscInt       i;
875:   PetscScalar    b0,b1;

878:   for (i=0; i<n; i++) {
879: #if !defined(PETSC_USE_COMPLEX)
880:     if (eigi[i_s+i] != 0.0) {
881:       PetscScalar eigr0=0.0,eigi0=0.0;
882:       dvd_complex_rayleigh_quotient(u[i],u[i+1],Ax[i],Ax[i+1],Bx[i],Bx[i+1],&eigr0,&eigi0);
883:       if (PetscAbsScalar(eigr[i_s+i]-eigr0)/PetscAbsScalar(eigr[i_s+i]) > 1e-10 || PetscAbsScalar(eigi[i_s+i]-eigi0)/PetscAbsScalar(eigi[i_s+i]) > 1e-10) {
884:         PetscInfo4(u[0],"The eigenvalue %g%+gi is far from its Rayleigh quotient value %g%+gi\n",(double)eigr[i_s+i],(double)eigi[i_s+i],(double)eigr0,(double)eigi0);
885:       }
886:       i++;
887:     } else
888: #endif
889:     {
890:       VecDotBegin(Ax[i],u[i],&b0);
891:       VecDotBegin(Bx[i],u[i],&b1);
892:       VecDotEnd(Ax[i],u[i],&b0);
893:       VecDotEnd(Bx[i],u[i],&b1);
894:       b0 = b0/b1;
895:       if (PetscAbsScalar(eigr[i_s+i]-b0)/PetscAbsScalar(eigr[i_s+i]) > 1e-10) {
896:         PetscInfo4(u[0],"The eigenvalue %g+%g is far from its Rayleigh quotient value %g+%g\n",(double)PetscRealPart(eigr[i_s+i]),(double)PetscImaginaryPart(eigr[i_s+i]),(double)PetscRealPart(b0),(double)PetscImaginaryPart(b0));
897:       }
898:     }
899:   }
900:   return(0);
901: }

903: /*
904:   Compute: u <- X, v <- K*(theta[0]*A+theta[1]*B)*X,
905:   kr <- K^{-1}*(A-eig*B)*X, being X <- V*pX[i_s..i_e-1], Y <- W*pY[i_s..i_e-1]
906:   where
907:   pX,pY, the right and left eigenvectors of the projected system
908:   ld, the leading dimension of pX and pY
909: */
910: PetscErrorCode dvd_improvex_jd_proj_uv_KZX(dvdDashboard *d,PetscInt i_s,PetscInt i_e,Vec *u,Vec *v,Vec *kr,PetscScalar *theta,PetscScalar *thetai,PetscScalar *pX,PetscScalar *pY,PetscInt ld)
911: {
913:   PetscInt       n = i_e-i_s,i;
914:   PetscScalar    *b;
915:   Vec            *Ax,*Bx,*r;
916:   Mat            M;
917:   BV             X;

920:   BVDuplicateResize(d->eps->V,4,&X);
921:   MatCreateSeqDense(PETSC_COMM_SELF,4,4,NULL,&M);
922:   /* u <- X(i) */
923:   dvd_improvex_compute_X(d,i_s,i_e,u,pX,ld);

925:   /* v <- theta[0]A*u + theta[1]*B*u */

927:   /* Bx <- B*X(i) */
928:   Bx = kr;
929:   if (d->BX) {
930:     for (i=i_s; i<i_e; ++i) {
931:       BVMultVec(d->BX,1.0,0.0,Bx[i-i_s],&pX[ld*i]);
932:     }
933:   } else {
934:     for (i=0;i<n;i++) {
935:       if (d->B) {
936:         MatMult(d->B, u[i], Bx[i]);
937:       } else {
938:         VecCopy(u[i], Bx[i]);
939:       }
940:     }
941:   }

943:   /* Ax <- A*X(i) */
944:   SlepcVecPoolGetVecs(d->auxV,i_e-i_s,&r);
945:   Ax = r;
946:   for (i=i_s; i<i_e; ++i) {
947:     BVMultVec(d->AX,1.0,0.0,Ax[i-i_s],&pX[ld*i]);
948:   }

950:   /* v <- Y(i) */
951:   for (i=i_s; i<i_e; ++i) {
952:     BVMultVec(d->W?d->W:d->eps->V,1.0,0.0,v[i-i_s],&pY[ld*i]);
953:   }

955:   /* Recompute the eigenvalue */
956:   dvd_compute_n_rr(i_s,n,d->eigr,d->eigi,v,Ax,Bx);

958:   for (i=0;i<n;i++) {
959: #if !defined(PETSC_USE_COMPLEX)
960:     if (d->eigi[i_s+i] != 0.0) {
961:       /* [r_i r_i+1 kr_i kr_i+1]*= [ theta_2i'    0            1        0
962:                                        0         theta_2i'     0        1
963:                                      theta_2i+1 -thetai_i   -eigr_i -eigi_i
964:                                      thetai_i    theta_2i+1  eigi_i -eigr_i ] */
965:       MatDenseGetArray(M,&b);
966:       b[0] = b[5] = PetscConj(theta[2*i]);
967:       b[2] = b[7] = -theta[2*i+1];
968:       b[6] = -(b[3] = thetai[i]);
969:       b[1] = b[4] = 0.0;
970:       b[8] = b[13] = 1.0/d->nX[i_s+i];
971:       b[10] = b[15] = -d->eigr[i_s+i]/d->nX[i_s+i];
972:       b[14] = -(b[11] = d->eigi[i_s+i]/d->nX[i_s+i]);
973:       b[9] = b[12] = 0.0;
974:       MatDenseRestoreArray(M,&b);
975:       BVInsertVec(X,0,Ax[i]);
976:       BVInsertVec(X,1,Ax[i+1]);
977:       BVInsertVec(X,2,Bx[i]);
978:       BVInsertVec(X,3,Bx[i+1]);
979:       BVSetActiveColumns(X,0,4);
980:       BVMultInPlace(X,M,0,4);
981:       BVCopyVec(X,0,Ax[i]);
982:       BVCopyVec(X,1,Ax[i+1]);
983:       BVCopyVec(X,2,Bx[i]);
984:       BVCopyVec(X,3,Bx[i+1]);
985:       i++;
986:     } else
987: #endif
988:     {
989:       /* [Ax_i Bx_i]*= [ theta_2i'    1/nX_i
990:                         theta_2i+1  -eig_i/nX_i ] */
991:       MatDenseGetArray(M,&b);
992:       b[0] = PetscConj(theta[i*2]);
993:       b[1] = theta[i*2+1];
994:       b[4] = 1.0/d->nX[i_s+i];
995:       b[5] = -d->eigr[i_s+i]/d->nX[i_s+i];
996:       MatDenseRestoreArray(M,&b);
997:       BVInsertVec(X,0,Ax[i]);
998:       BVInsertVec(X,1,Bx[i]);
999:       BVSetActiveColumns(X,0,2);
1000:       BVMultInPlace(X,M,0,2);
1001:       BVCopyVec(X,0,Ax[i]);
1002:       BVCopyVec(X,1,Bx[i]);
1003:     }
1004:   }
1005:   for (i=0; i<n; i++) d->nX[i_s+i] = 1.0;

1007:   /* v <- K^{-1} r = K^{-1}(theta_2i'*Ax + theta_2i+1*Bx) */
1008:   for (i=0;i<n;i++) {
1009:     d->improvex_precond(d,i_s+i,r[i],v[i]);
1010:   }
1011:   SlepcVecPoolRestoreVecs(d->auxV,i_e-i_s,&r);

1013:   /* kr <- P*(Ax - eig_i*Bx) */
1014:   d->calcpairs_proj_res(d,i_s,i_e,kr);
1015:   BVDestroy(&X);
1016:   MatDestroy(&M);
1017:   return(0);
1018: }

1020: static PetscErrorCode dvd_improvex_jd_lit_const_0(dvdDashboard *d,PetscInt i,PetscScalar* theta,PetscScalar* thetai,PetscInt *maxits,PetscReal *tol)
1021: {
1022:   dvdImprovex_jd *data = (dvdImprovex_jd*)d->improveX_data;
1023:   PetscReal      a;

1026:   a = SlepcAbsEigenvalue(d->eigr[i],d->eigi[i]);

1028:   if (d->nR[i] < data->fix*a) {
1029:     theta[0] = d->eigr[i];
1030:     theta[1] = 1.0;
1031: #if !defined(PETSC_USE_COMPLEX)
1032:     *thetai = d->eigi[i];
1033: #endif
1034:   } else {
1035:     theta[0] = d->target[0];
1036:     theta[1] = d->target[1];
1037: #if !defined(PETSC_USE_COMPLEX)
1038:     *thetai = 0.0;
1039: #endif
1040: }

1042: #if defined(PETSC_USE_COMPLEX)
1043:   if (thetai) *thetai = 0.0;
1044: #endif
1045:   *maxits = data->maxits;
1046:   *tol = data->tol;
1047:   return(0);
1048: }

1050: PetscErrorCode dvd_improvex_jd_lit_const(dvdDashboard *d,dvdBlackboard *b,PetscInt maxits,PetscReal tol,PetscReal fix)
1051: {
1052:   dvdImprovex_jd  *data = (dvdImprovex_jd*)d->improveX_data;

1055:   /* Setup the step */
1056:   if (b->state >= DVD_STATE_CONF) {
1057:     data->maxits = maxits;
1058:     data->tol = tol;
1059:     data->fix = fix;
1060:     d->improvex_jd_lit = dvd_improvex_jd_lit_const_0;
1061:   }
1062:   return(0);
1063: }

1065: PetscErrorCode dvd_improvex_jd_proj_uv(dvdDashboard *d,dvdBlackboard *b)
1066: {
1068:   /* Setup the step */
1069:   if (b->state >= DVD_STATE_CONF) {
1070:     d->improvex_jd_proj_uv = dvd_improvex_jd_proj_uv_KZX;
1071:   }
1072:   return(0);
1073: }

1075: PetscErrorCode dvd_improvex_compute_X(dvdDashboard *d,PetscInt i_s,PetscInt i_e,Vec *u_,PetscScalar *pX,PetscInt ld)
1076: {
1078:   PetscInt       n = i_e - i_s,i;
1079:   Vec            *u;

1082:   if (u_) u = u_;
1083:   else if (d->correctXnorm) {
1084:     SlepcVecPoolGetVecs(d->auxV,i_e-i_s,&u);
1085:   }
1086:   if (u_ || d->correctXnorm) {
1087:     for (i=0; i<n; i++) {
1088:       BVMultVec(d->eps->V,1.0,0.0,u[i],&pX[ld*(i+i_s)]);
1089:     }
1090:   }
1091:   /* nX(i) <- ||X(i)|| */
1092:   if (d->correctXnorm) {
1093:     for (i=0; i<n; i++) {
1094:       VecNormBegin(u[i],NORM_2,&d->nX[i_s+i]);
1095:     }
1096:     for (i=0; i<n; i++) {
1097:       VecNormEnd(u[i],NORM_2,&d->nX[i_s+i]);
1098:     }
1099: #if !defined(PETSC_USE_COMPLEX)
1100:     for (i=0;i<n;i++) {
1101:       if (d->eigi[i_s+i] != 0.0) {
1102:         d->nX[i_s+i] = d->nX[i_s+i+1] = PetscSqrtScalar(d->nX[i_s+i]*d->nX[i_s+i]+d->nX[i_s+i+1]*d->nX[i_s+i+1]);
1103:         i++;
1104:       }
1105:     }
1106: #endif
1107:   } else {
1108:     for (i=0;i<n;i++) d->nX[i_s+i] = 1.0;
1109:   }
1110:   if (d->correctXnorm && !u_) {
1111:     SlepcVecPoolRestoreVecs(d->auxV,i_e-i_s,&u);
1112:   }
1113:   return(0);
1114: }