Actual source code: dvd_improvex.c

  1: /*
  2:   SLEPc eigensolver: "davidson"

  4:   Step: improve the eigenvectors X

  6:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  7:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  8:    Copyright (c) 2002-2011, Universitat Politecnica de Valencia, Spain

 10:    This file is part of SLEPc.
 11:       
 12:    SLEPc is free software: you can redistribute it and/or modify it under  the
 13:    terms of version 3 of the GNU Lesser General Public License as published by
 14:    the Free Software Foundation.

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

 21:    You  should have received a copy of the GNU Lesser General  Public  License
 22:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
 23:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 24: */

 26:  #include davidson.h
 27: #include <slepcvec.h>
 28: #include <slepcblaslapack.h>

 30: PetscErrorCode dvd_improvex_PfuncV(dvdDashboard *d, void *funcV, Vec *D,
 31:   PetscInt max_size_D, PetscInt r_s, PetscInt r_e, Vec *auxV,
 32:   PetscScalar *auxS);
 33: PetscErrorCode dvd_matmult_jd(Mat A, Vec in, Vec out);
 34: PetscErrorCode dvd_matgetvecs_jd(Mat A, Vec *right, Vec *left);
 35: PetscErrorCode dvd_improvex_jd_d(dvdDashboard *d);
 36: PetscErrorCode dvd_improvex_jd_start(dvdDashboard *d);
 37: PetscErrorCode dvd_improvex_jd_end(dvdDashboard *d);
 38: PetscErrorCode dvd_improvex_jd_gen(dvdDashboard *d, Vec *D,
 39:                                    PetscInt max_size_D, PetscInt r_s,
 40:                                    PetscInt r_e, PetscInt *size_D);
 41: PetscErrorCode dvd_improvex_jd_proj_cuv(dvdDashboard *d, PetscInt i_s,
 42:   PetscInt i_e, Vec **u, Vec **v, Vec *kr, Vec **auxV, PetscScalar **auxS,
 43:   PetscScalar *theta, PetscScalar *thetai, PetscScalar *pX, PetscScalar *pY,
 44:   PetscInt ld);
 45: PetscErrorCode dvd_improvex_jd_proj_uv_KXX(dvdDashboard *d, PetscInt i_s,
 46:   PetscInt i_e, Vec *u, Vec *v, Vec *kr, Vec *auxV, PetscScalar *theta,
 47:   PetscScalar *thetai, PetscScalar *pX, PetscScalar *pY, PetscInt ld);
 48: PetscErrorCode dvd_improvex_jd_proj_uv_KZX(dvdDashboard *d, PetscInt i_s,
 49:   PetscInt i_e, Vec *u, Vec *v, Vec *kr, Vec *auxV, PetscScalar *theta,
 50:   PetscScalar *thetai, PetscScalar *pX, PetscScalar *pY, PetscInt ld);
 51: PetscErrorCode dvd_improvex_jd_lit_const_0(dvdDashboard *d, PetscInt i,
 52:   PetscScalar* theta, PetscScalar* thetai,
 53:   PetscInt *maxits, PetscReal *tol);
 54: PetscErrorCode dvd_improvex_get_eigenvectors(dvdDashboard *d, PetscScalar *pX,
 55:   PetscScalar *pY, PetscInt ld_,
 56:   PetscScalar *auxS, PetscInt size_auxS);
 57: PetscErrorCode dvd_improvex_apply_proj(dvdDashboard *d, Vec *V, PetscInt cV, PetscScalar *auxS);

 59: #define size_Z (64*4)

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

 63: typedef struct {
 64:   PetscInt size_X;
 65:   void
 66:     *old_improveX_data;   /* old improveX_data */
 67:   improveX_type
 68:     old_improveX;         /* old improveX */
 69:   KSP ksp;                /* correction equation solver */
 70:   Vec
 71:     friends,              /* reference vector for composite vectors */
 72:     *auxV;                /* auxiliar vectors */
 73:   PetscScalar *auxS,      /* auxiliar scalars */
 74:     *theta,
 75:     *thetai;              /* the shifts used in the correction eq. */
 76:   PetscInt maxits,        /* maximum number of iterations */
 77:     r_s, r_e,             /* the selected eigenpairs to improve */
 78:     ksp_max_size;         /* the ksp maximum subvectors size */
 79:   PetscReal tol,          /* the maximum solution tolerance */
 80:     lastTol,              /* last tol for dynamic stopping criterion */
 81:     fix;                  /* tolerance for using the approx. eigenvalue */
 82:   PetscBool
 83:     dynamic;              /* if the dynamic stopping criterion is applied */
 84:   dvdDashboard
 85:     *d;                   /* the currect dvdDashboard reference */
 86:   PC old_pc;              /* old pc in ksp */
 87:   Vec
 88:     *u,                   /* new X vectors */
 89:     *real_KZ,             /* original KZ */
 90:     *KZ;                  /* KZ vecs for the projector KZ*inv(X'*KZ)*X' */
 91:   PetscScalar
 92:    *XKZ,                  /* X'*KZ */
 93:    *iXKZ;                 /* inverse of XKZ */
 94:   PetscInt
 95:     ldXKZ,                /* leading dimension of XKZ */
 96:     size_iXKZ,            /* size of iXKZ */
 97:     ldiXKZ,               /* leading dimension of iXKZ */
 98:     size_KZ,              /* size of converged KZ */
 99:     size_real_KZ,         /* original size of KZ */
100:     size_cX,              /* last value of d->size_cX */
101:     old_size_X;           /* last number of improved vectors */
102:   PetscBLASInt
103:     *iXKZPivots;          /* array of pivots */
104: } dvdImprovex_jd;

106: #define _Ceil(A,B) ((A)/(B)+((A)%(B)==0?0:1))
107: #define FromIntToScalar(S) ((PetscInt)_Ceil((S)*sizeof(PetscBLASInt),sizeof(PetscScalar)))

111: PetscErrorCode dvd_improvex_jd(dvdDashboard *d, dvdBlackboard *b, KSP ksp,
112:                                PetscInt max_bs, PetscInt cX_impr, PetscBool dynamic)
113: {
114:   PetscErrorCode  ierr;
115:   dvdImprovex_jd  *data;
116:   PetscBool       t, herm = DVD_IS(d->sEP, DVD_EP_HERMITIAN)?PETSC_TRUE:PETSC_FALSE;
117:   PC              pc;
118:   PetscInt        size_P;


122:   /* Setting configuration constrains */
123:   PetscTypeCompare((PetscObject)ksp, KSPPREONLY, &t);
124:   if (t) ksp = PETSC_NULL;

126:   /* If the arithmetic is real and the problem is not Hermitian, then
127:      the block size is incremented in one */
128: #if !defined(PETSC_USE_COMPLEX)
129:   if (!herm) {
130:     max_bs++;
131:     b->max_size_P = PetscMax(b->max_size_P, 2);
132:   } else
133: #endif
134:     b->max_size_P = PetscMax(b->max_size_P, 1);
135:   b->max_size_X = PetscMax(b->max_size_X, max_bs);
136:   size_P = b->max_size_P+cX_impr;
137:   b->max_size_auxV = PetscMax(b->max_size_auxV, b->max_size_X*(ksp?3:2));
138:                                                             /* u, kr?, auxV */
139:   b->own_scalars+= size_P*size_P; /* XKZ */
140:   b->max_size_auxS = PetscMax(b->max_size_auxS,
141:     (herm?0:1)*2*b->max_size_proj*b->max_size_proj + /* pX, pY */
142:     b->max_size_X*3 + /* theta, thetai */
143:     size_P*size_P + /* iXKZ */
144:     FromIntToScalar(size_P) + /* iXkZPivots */
145:     PetscMax(PetscMax(
146:       3*b->max_size_proj*b->max_size_X, /* dvd_improvex_apply_proj */
147:       8*cX_impr*b->max_size_X),
148:                                           /* dvd_improvex_jd_proj_cuv_KZX */
149:       (herm?0:1)*11*b->max_size_proj+4*b->max_size_proj*b->max_size_proj));
150:                                            /* dvd_improvex_get_eigenvectors */
151:   b->own_vecs+= size_P; /* KZ */

153:   /* Setup the preconditioner */
154:   if (ksp) {
155:     KSPGetPC(ksp, &pc);
156:     dvd_static_precond_PC(d, b, pc);
157:   } else {
158:     dvd_static_precond_PC(d, b, 0);
159:   }

161:   /* Setup the step */
162:   if (b->state >= DVD_STATE_CONF) {
163:     PetscMalloc(sizeof(dvdImprovex_jd), &data);
164:     data->dynamic = dynamic;
165:     data->size_real_KZ = size_P;
166:     data->real_KZ = b->free_vecs; b->free_vecs+= data->size_real_KZ;
167:     d->max_cX_in_impr = cX_impr;
168:     data->XKZ = b->free_scalars; b->free_scalars+= size_P*size_P;
169:     data->ldXKZ = size_P;
170:     data->size_X = b->max_size_X;
171:     data->old_improveX_data = d->improveX_data;
172:     d->improveX_data = data;
173:     data->old_improveX = d->improveX;
174:     data->ksp = ksp;
175:     data->d = d;
176:     d->improveX = dvd_improvex_jd_gen;
177:     data->ksp_max_size = max_bs;

179:     DVD_FL_ADD(d->startList, dvd_improvex_jd_start);
180:     DVD_FL_ADD(d->endList, dvd_improvex_jd_end);
181:     DVD_FL_ADD(d->destroyList, dvd_improvex_jd_d);
182:   }

184:   return(0);
185: }


190: PetscErrorCode dvd_improvex_jd_start(dvdDashboard *d)
191: {
192:   PetscErrorCode  ierr;
193:   dvdImprovex_jd  *data = (dvdImprovex_jd*)d->improveX_data;
194:   PetscInt        rA, cA, rlA, clA;
195:   Mat             A;
196:   PetscBool       t;
197:   PC              pc;


201:   data->KZ = data->real_KZ;
202:   data->size_KZ = data->size_cX = data->old_size_X = 0;
203:   data->lastTol = data->dynamic?0.5:0.0;

205:   /* Setup the ksp */
206:   if(data->ksp) {
207:     /* Create the reference vector */
208:     VecCreateCompWithVecs(d->V, data->ksp_max_size, PETSC_NULL,
209:                                  &data->friends);

211:     /* Save the current pc and set a PCNONE */
212:     KSPGetPC(data->ksp, &data->old_pc);
213:     PetscTypeCompare((PetscObject)data->old_pc, PCNONE, &t);
214: 
215:     data->lastTol = 0.5;
216:     if (t) {
217:       data->old_pc = 0;
218:     } else {
219:       PetscObjectReference((PetscObject)data->old_pc);
220:       PCCreate(((PetscObject)d->eps)->comm, &pc);
221:       PCSetType(pc, PCNONE);
222:       PCSetOperators(pc, d->A, d->A, SAME_PRECONDITIONER);
223:       KSPSetPC(data->ksp, pc);
224:       PCDestroy(&pc);
225:     }

227:     /* Create the (I-v*u')*K*(A-s*B) matrix */
228:     MatGetSize(d->A, &rA, &cA);
229:     MatGetLocalSize(d->A, &rlA, &clA);
230:     MatCreateShell(((PetscObject)d->A)->comm, rlA*data->ksp_max_size,
231:                           clA*data->ksp_max_size, rA*data->ksp_max_size,
232:                           cA*data->ksp_max_size, data, &A);
233:     MatShellSetOperation(A, MATOP_MULT,
234:                                 (void(*)(void))dvd_matmult_jd);
235:     MatShellSetOperation(A, MATOP_GET_VECS,
236:                                 (void(*)(void))dvd_matgetvecs_jd);
237: 

239:     /* Try to avoid KSPReset */
240:     KSPGetOperatorsSet(data->ksp,&t,PETSC_NULL);
241:     if (t) {
242:       Mat M;
243:       PetscInt rM;
244:       KSPGetOperators(data->ksp,&M,PETSC_NULL,PETSC_NULL);
245:       MatGetSize(M,&rM,PETSC_NULL);
246:       if (rM != rA*data->ksp_max_size) { KSPReset(data->ksp); }
247:     }
248:     KSPSetOperators(data->ksp, A, A, SAME_PRECONDITIONER);
249: 
250:     KSPSetUp(data->ksp);
251:     MatDestroy(&A);
252:   } else {
253:     data->old_pc = 0;
254:     data->friends = PETSC_NULL;
255:   }
256: 
257:   return(0);
258: }


263: PetscErrorCode dvd_improvex_jd_end(dvdDashboard *d)
264: {
265:   PetscErrorCode  ierr;
266:   dvdImprovex_jd  *data = (dvdImprovex_jd*)d->improveX_data;


270:   if (data->friends) { VecDestroy(&data->friends);  }

272:   /* Restore the pc of ksp */
273:   if (data->old_pc) {
274:     KSPSetPC(data->ksp, data->old_pc);
275:     PCDestroy(&data->old_pc);
276:   }

278:   return(0);
279: }


284: PetscErrorCode dvd_improvex_jd_d(dvdDashboard *d)
285: {
286:   PetscErrorCode  ierr;
287:   dvdImprovex_jd  *data = (dvdImprovex_jd*)d->improveX_data;

290: 
291:   /* Restore changes in dvdDashboard */
292:   d->improveX_data = data->old_improveX_data;

294:   /* Free local data and objects */
295:   PetscFree(data);

297:   return(0);
298: }


303: PetscErrorCode dvd_improvex_jd_gen(dvdDashboard *d, Vec *D,
304:                              PetscInt max_size_D, PetscInt r_s,
305:                              PetscInt r_e, PetscInt *size_D)
306: {
307:   dvdImprovex_jd  *data = (dvdImprovex_jd*)d->improveX_data;
308:   PetscErrorCode  ierr;
309:   PetscInt        i, j, n, maxits, maxits0, lits, s;
310:   PetscScalar     *pX, *pY, *auxS = d->auxS, *auxS0;
311:   PetscReal       tol, tol0;
312:   Vec             *u, *v, *kr, kr_comp, D_comp;


316:   /* Quick exit */
317:   if ((max_size_D == 0) || r_e-r_s <= 0) {
318:    /* Callback old improveX */
319:     if (data->old_improveX) {
320:       d->improveX_data = data->old_improveX_data;
321:       data->old_improveX(d, PETSC_NULL, 0, 0, 0, PETSC_NULL);
322:       d->improveX_data = data;
323:     }
324:     return(0);
325:   }
326: 
327:   n = PetscMin(PetscMin(data->size_X, max_size_D), r_e-r_s);
328:   if (n == 0) SETERRQ(PETSC_COMM_SELF,1, "n == 0!\n");
329:   if (data->size_X < r_e-r_s) SETERRQ(PETSC_COMM_SELF,1, "size_X < r_e-r_s!\n");

331:   /* Compute the eigenvectors of the selected pairs */
332:   if (DVD_IS(d->sEP, DVD_EP_HERMITIAN)) {
333:     pX = pY = d->pX;
334:   } else {
335:     pX = auxS; auxS+= d->size_H*d->size_H;
336:     pY = auxS; auxS+= d->size_H*d->size_H;
337:     dvd_improvex_get_eigenvectors(d, pX, pY, d->size_H, auxS,
338:                                          d->size_auxS-(auxS-d->auxS));
339: 
340:   }

342:   /* Restart lastTol if a new pair converged */
343:   if (data->dynamic && data->size_cX < d->size_cX)
344:     data->lastTol = 0.5;

346:   for(i=0, s=0, auxS0=auxS; i<n; i+=s) {
347:     /* If the selected eigenvalue is complex, but the arithmetic is real... */
348: #if !defined(PETSC_USE_COMPLEX)
349:     if (PetscAbsScalar(d->eigi[i] != 0.0)) {
350:       if (i+2 <= max_size_D) s=2; else break;
351:     } else
352: #endif
353:       s=1;

355:     data->auxV = d->auxV;
356:     data->r_s = r_s+i; data->r_e = r_s+i+s;
357:     auxS = auxS0;
358:     data->theta = auxS; auxS+= 2*s;
359:     data->thetai = auxS; auxS+= s;
360:     /* If GD, kr = D */
361:     if (!data->ksp) {
362:       kr = &D[i];

364:     /* If JD, kr = auxV */
365:     } else {
366:       kr = data->auxV; data->auxV+= s;
367:     }

369:     /* Compute theta, maximum iterations and tolerance */
370:     maxits = 0; tol = 1;
371:     for(j=0; j<s; j++) {
372:       d->improvex_jd_lit(d, r_s+i+j, &data->theta[2*j],
373:                                 &data->thetai[j], &maxits0, &tol0);
374: 
375:       maxits+= maxits0; tol*= tol0;
376:     }
377:     maxits/= s; tol = data->dynamic?data->lastTol:exp(log(tol)/s);

379:     /* Compute u, v and kr */
380:     dvd_improvex_jd_proj_cuv(d, r_s+i, r_s+i+s, &u, &v, kr,
381:              &data->auxV, &auxS, data->theta, data->thetai,
382:              &pX[d->size_H*(r_s+i+d->cX_in_H)], &pY[d->size_H*(r_s+i+d->cX_in_H)], d->size_H);
383: 
384:     data->u = u;

386:     /* Check if the first eigenpairs are converged */
387:     if (i == 0) {
388:       d->preTestConv(d, 0, s, s, PETSC_NULL, PETSC_NULL, &d->npreconv);
389: 
390:       if (d->npreconv > 0) break;
391:     }

393:     /* Compute kr <- kr - v*(u'*kr) */
394:     dvd_improvex_apply_proj(d, kr, s, auxS);

396:     /* If JD */
397:     if (data->ksp) {
398:       data->auxS = auxS;

400:       /* kr <- -kr */
401:       for(j=0; j<s; j++) {
402:         VecScale(kr[j], -1.0);
403:       }

405:       /* Compouse kr and D */
406:       VecCreateCompWithVecs(kr, data->ksp_max_size, data->friends,
407:                                    &kr_comp);
408:       VecCreateCompWithVecs(&D[i], data->ksp_max_size, data->friends,
409:                                    &D_comp);
410:       VecCompSetSubVecs(data->friends,s,PETSC_NULL);
411: 
412:       /* Solve the correction equation */
413:       KSPSetTolerances(data->ksp, tol, PETSC_DEFAULT, PETSC_DEFAULT,
414:                               maxits);
415:       KSPSolve(data->ksp, kr_comp, D_comp);
416:       KSPGetIterationNumber(data->ksp, &lits);
417:       d->eps->OP->lineariterations+= lits;
418: 
419:       /* Destroy the composed ks and D */
420:       VecDestroy(&kr_comp);
421:       VecDestroy(&D_comp);
422:     }
423:   }
424:   *size_D = i;
425:   if (data->dynamic) data->lastTol = PetscMax(data->lastTol/2.0,PETSC_MACHINE_EPSILON*10.0);
426: 
427:   /* Callback old improveX */
428:   if (data->old_improveX) {
429:     d->improveX_data = data->old_improveX_data;
430:     data->old_improveX(d, PETSC_NULL, 0, 0, 0, PETSC_NULL);
431:     d->improveX_data = data;
432:   }

434:   return(0);
435: }


440: PetscErrorCode dvd_matmult_jd(Mat A, Vec in, Vec out)
441: {
442:   PetscErrorCode  ierr;
443:   dvdImprovex_jd  *data;
444:   PetscInt        n, i;
445:   const Vec       *inx, *outx, *Bx;


449:   MatShellGetContext(A, (void**)&data);
450:   VecCompGetSubVecs(in,PETSC_NULL,&inx);
451:   VecCompGetSubVecs(out,PETSC_NULL,&outx);
452:   n = data->r_e - data->r_s;

454:   /* aux <- theta[1]A*in - theta[0]*B*in */
455:   for(i=0; i<n; i++) {
456:     MatMult(data->d->A, inx[i], data->auxV[i]);
457:   }
458:   if (data->d->B) {
459:     for(i=0; i<n; i++) {
460:       MatMult(data->d->B, inx[i], outx[i]);
461:     }
462:     Bx = outx;
463:   } else
464:     Bx = inx;

466:   for(i=0; i<n; i++) {
467: #if !defined(PETSC_USE_COMPLEX)
468:     if(data->d->eigi[data->r_s+i] != 0.0) {
469:       /* aux_i   <- [ t_2i+1*A*inx_i   - t_2i*Bx_i + ti_i*Bx_i+1;
470:          aux_i+1      t_2i+1*A*inx_i+1 - ti_i*Bx_i - t_2i*Bx_i+1  ] */
471:       VecAXPBYPCZ(data->auxV[i], -data->theta[2*i], data->thetai[i],
472:                          data->theta[2*i+1], Bx[i], Bx[i+1]);
473: 
474:       VecAXPBYPCZ(data->auxV[i+1], -data->thetai[i],
475:                          -data->theta[2*i], data->theta[2*i+1], Bx[i],
476:                          Bx[i+1]);
477:       i++;
478:     } else
479: #endif
480:     {
481:       VecAXPBY(data->auxV[i], -data->theta[i*2], data->theta[i*2+1],
482:                       Bx[i]);
483:     }
484:   }

486:   /* out <- K * aux */
487:   for(i=0; i<n; i++) {
488:     data->d->improvex_precond(data->d, data->r_s+i, data->auxV[i],
489:                                      outx[i]);
490:   }

492:   /* out <- out - v*(u'*out) */
493:   dvd_improvex_apply_proj(data->d, (Vec*)outx, n, data->auxS);

495:   return(0);
496: }


501: PetscErrorCode dvd_matgetvecs_jd(Mat A, Vec *right, Vec *left)
502: {
503:   PetscErrorCode  ierr;
504:   Vec             *r, *l;
505:   dvdImprovex_jd  *data;
506:   PetscInt        n, i;


510:   MatShellGetContext(A, (void**)&data);
511:   n = data->ksp_max_size;
512:   if (right) {
513:     PetscMalloc(sizeof(Vec)*n, &r);
514:   }
515:   if (left) {
516:     PetscMalloc(sizeof(Vec)*n, &l);
517:   }
518:   for (i=0; i<n; i++) {
519:     MatGetVecs(data->d->A, right?&r[i]:PETSC_NULL,
520:                       left?&l[i]:PETSC_NULL);
521:   }
522:   if(right) {
523:     VecCreateCompWithVecs(r, n, data->friends, right);
524:     for (i=0; i<n; i++) {
525:       VecDestroy(&r[i]);
526:     }
527:   }
528:   if(left) {
529:     VecCreateCompWithVecs(l, n, data->friends, left);
530:     for (i=0; i<n; i++) {
531:       VecDestroy(&l[i]);
532:     }
533:   }

535:   if (right) {
536:     PetscFree(r);
537:   }
538:   if (left) {
539:     PetscFree(l);
540:   }

542:   return(0);
543: }


548: PetscErrorCode dvd_improvex_jd_proj_uv(dvdDashboard *d, dvdBlackboard *b,
549:                                        ProjType_t p)
550: {

553:   /* Setup the step */
554:   if (b->state >= DVD_STATE_CONF) {
555:     switch(p) {
556:     case DVD_PROJ_KXX:
557:       d->improvex_jd_proj_uv = dvd_improvex_jd_proj_uv_KXX; break;
558:     case DVD_PROJ_KZX:
559:       d->improvex_jd_proj_uv = dvd_improvex_jd_proj_uv_KZX; break;
560:     }
561:   }

563:   return(0);
564: }

568: /* 
569:   Compute: u <- X, v <- K*(theta[0]*A+theta[1]*B)*X,
570:   kr <- K^{-1}*(A-eig*B)*X, being X <- V*pX[i_s..i_e-1], Y <- W*pY[i_s..i_e-1]
571:   where
572:   auxV, 4*(i_e-i_s) auxiliar global vectors
573:   pX,pY, the right and left eigenvectors of the projected system
574:   ld, the leading dimension of pX and pY
575:   auxS: max(8*bs*max_cX_in_proj,size_V*size_V)
576: */
577: PetscErrorCode dvd_improvex_jd_proj_cuv(dvdDashboard *d, PetscInt i_s,
578:   PetscInt i_e, Vec **u, Vec **v, Vec *kr, Vec **auxV, PetscScalar **auxS,
579:   PetscScalar *theta, PetscScalar *thetai, PetscScalar *pX, PetscScalar *pY,
580:   PetscInt ld)
581: {
582:   PetscErrorCode  ierr;
583:   PetscInt        n = i_e - i_s, size_KZ, V_new, rm, i;
584:   PetscScalar     *wS0, *wS1;
585:   dvdImprovex_jd  *data = (dvdImprovex_jd*)d->improveX_data;
586:   PetscBLASInt    s, ldXKZ, info;


590:   /* Check consistency */
591:   V_new = d->size_cX - data->size_cX;
592:   if (V_new > data->old_size_X) { SETERRQ(PETSC_COMM_SELF,1, "Consistency broken!"); }
593:   data->old_size_X = n;

595:   /* KZ <- KZ(rm:rm+max_cX-1) */
596:   rm = PetscMax(V_new+data->size_KZ-d->max_cX_in_impr, 0);
597:   for (i=0; i<d->max_cX_in_impr; i++) {
598:     VecCopy(data->KZ[i+rm], data->KZ[i]);
599:   }
600:   data->size_cX = d->size_cX;

602:   /* XKZ <- XKZ(rm:rm+max_cX-1,rm:rm+max_cX-1) */
603:   for (i=0; i<d->max_cX_in_impr; i++) {
604:     SlepcDenseCopy(&data->XKZ[i*data->ldXKZ+i], data->ldXKZ, &data->XKZ[(i+rm)*data->ldXKZ+i+rm], data->ldXKZ, data->size_KZ, 1);
605:   }
606:   data->size_KZ = PetscMin(d->max_cX_in_impr, data->size_KZ+V_new);

608:   /* Compute X, KZ and KR */
609:   *u = *auxV; *auxV+= n;
610:   *v = &data->KZ[data->size_KZ];
611:   d->improvex_jd_proj_uv(d, i_s, i_e, *u, *v, kr, *auxV, theta, thetai,
612:                                 pX, pY, ld);

614:   /* XKZ <- X'*KZ */
615:   size_KZ = data->size_KZ+n;
616:   wS0 = *auxS; wS1 = wS0+2*n*data->size_KZ+n*n;
617:   VecsMult(data->XKZ, 0, data->ldXKZ, d->V-data->size_KZ, 0, data->size_KZ, data->KZ, 0, size_KZ, wS0, wS1);
618:   VecsMult(&data->XKZ[data->size_KZ], 0, data->ldXKZ, *u, 0, n, data->KZ, 0, size_KZ, wS0, wS1);

620:   /* iXKZ <- inv(XKZ) */
621:   s = PetscBLASIntCast(size_KZ);
622:   data->ldiXKZ = data->size_iXKZ = size_KZ;
623:   data->iXKZ = *auxS; *auxS+= size_KZ*size_KZ;
624:   data->iXKZPivots = (PetscBLASInt*)*auxS;
625:   *auxS += FromIntToScalar(size_KZ);
626:   SlepcDenseCopy(data->iXKZ,data->ldiXKZ,data->XKZ,data->ldXKZ,size_KZ,size_KZ);
627:   ldXKZ = PetscBLASIntCast(data->ldiXKZ);
628:   LAPACKgetrf_(&s, &s, data->iXKZ, &ldXKZ, data->iXKZPivots, &info);
629:   if (info) SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_LIB, "Error in Lapack XGETRF %d", info);

631:   return(0);
632: }

634: #define DVD_COMPLEX_RAYLEIGH_QUOTIENT(ur,ui,Axr,Axi,Bxr,Bxi,eigr,eigi,b,ierr)\
635: { \
636:   VecDot((Axr), (ur), &(b)[0]);  /* r*A*r */ \
637:   VecDot((Axr), (ui), &(b)[1]);  /* i*A*r */ \
638:   VecDot((Axi), (ur), &(b)[2]);  /* r*A*i */ \
639:   VecDot((Axi), (ui), &(b)[3]);  /* i*A*i */ \
640:   VecDot((Bxr), (ur), &(b)[4]);  /* r*B*r */ \
641:   VecDot((Bxr), (ui), &(b)[5]);  /* i*B*r */ \
642:   VecDot((Bxi), (ur), &(b)[6]);  /* r*B*i */ \
643:   VecDot((Bxi), (ui), &(b)[7]);  /* i*B*i */ \
644:   (b)[0]  = (b)[0]+(b)[3]; /* rAr+iAi */ \
645:   (b)[2] =  (b)[2]-(b)[1]; /* rAi-iAr */ \
646:   (b)[4] = (b)[4]+(b)[7]; /* rBr+iBi */ \
647:   (b)[6] = (b)[6]-(b)[5]; /* rBi-iBr */ \
648:   (b)[7] = (b)[4]*(b)[4] + (b)[6]*(b)[6]; /* k */ \
649:   *(eigr) = ((b)[0]*(b)[4] + (b)[2]*(b)[6]) / (b)[7]; /* eig_r */ \
650:   *(eigi) = ((b)[2]*(b)[4] - (b)[0]*(b)[6]) / (b)[7]; /* eig_i */ \
651: }

653: #if !defined(PETSC_USE_COMPLEX)
654: #define DVD_COMPUTE_N_RR(eps,i,i_s,n,eigr,eigi,u,Ax,Bx,b,ierr) \
655:   for((i)=0; (i)<(n); (i)++) { \
656:     if ((eigi)[(i_s)+(i)] != 0.0) { \
657:       /* eig_r = [(rAr+iAi)*(rBr+iBi) + (rAi-iAr)*(rBi-iBr)]/k \
658:          eig_i = [(rAi-iAr)*(rBr+iBi) - (rAr+iAi)*(rBi-iBr)]/k \
659:          k     =  (rBr+iBi)*(rBr+iBi) + (rBi-iBr)*(rBi-iBr)    */ \
660:       DVD_COMPLEX_RAYLEIGH_QUOTIENT((u)[(i)], (u)[(i)+1], (Ax)[(i)], \
661:         (Ax)[(i)+1], (Bx)[(i)], (Bx)[(i)+1], &(b)[8], &(b)[9], (b), (ierr)); \
662:       if (PetscAbsScalar((eigr)[(i_s)+(i)] - (b)[8])/ \
663:             PetscAbsScalar((eigr)[(i_s)+(i)]) > 1e-10    || \
664:           PetscAbsScalar((eigi)[(i_s)+(i)] - (b)[9])/ \
665:             PetscAbsScalar((eigi)[(i_s)+(i)]) > 1e-10         ) { \
666:         (ierr) = PetscInfo4((eps), "The eigenvalue %G+%G is far from its "\
667:                             "Rayleigh quotient value %G+%G\n", \
668:                             (eigr)[(i_s)+(i)], \
669:                             (eigi)[(i_s)+1], (b)[8], (b)[9]); \
670:       } \
671:       (i)++; \
672:     } \
673:   }
674: #else
675: #define DVD_COMPUTE_N_RR(eps,i,i_s,n,eigr,eigi,u,Ax,Bx,b,ierr) \
676:   for((i)=0; (i)<(n); (i)++) { \
677:       (ierr) = VecDot((Ax)[(i)], (u)[(i)], &(b)[0]);  \
678:       (ierr) = VecDot((Bx)[(i)], (u)[(i)], &(b)[1]);  \
679:       (b)[0] = (b)[0]/(b)[1]; \
680:       if (PetscAbsScalar((eigr)[(i_s)+(i)] - (b)[0])/ \
681:             PetscAbsScalar((eigr)[(i_s)+(i)]) > 1e-10     ) { \
682:         (ierr) = PetscInfo4((eps), "The eigenvalue %G+%G is far from its " \
683:                "Rayleigh quotient value %G+%G\n", \
684:                PetscRealPart((eigr)[(i_s)+(i)]), \
685:                PetscImaginaryPart((eigr)[(i_s)+(i)]), PetscRealPart((b)[0]), \
686:                PetscImaginaryPart((b)[0])); \
687:       } \
688:     }
689: #endif

691: #if !defined(PETSC_USE_COMPLEX)
692: #define DVD_NORM_FOR_UV(x) PetscAbsScalar(x)
693: #else
694: #define DVD_NORM_FOR_UV(x) (x)
695: #endif

697: #define DVD_NORMALIZE_UV(u,v,ierr,a) { \
698:     (ierr) = VecDot((u), (v), &(a));  \
699:     if ((a) == 0.0) { \
700:       SETERRQ(((PetscObject)u)->comm,1, "Inappropriate approximate eigenvector norm"); \
701:     } \
702:     if ((u) == (v)) { \
703:       VecScale((u), 1.0/PetscSqrtScalar(DVD_NORM_FOR_UV(a))); \
704:        \
705:     } else { \
706:       VecScale((u), 1.0/(a));  \
707:     } \
708: }


713: /* 
714:   Compute: u <- X, v <- K*(theta[0]*A+theta[1]*B)*X,
715:   kr <- K^{-1}*(A-eig*B)*X, being X <- V*pX[i_s..i_e-1], Y <- W*pY[i_s..i_e-1]
716:   where
717:   auxV, 4*(i_e-i_s) auxiliar global vectors
718:   pX,pY, the right and left eigenvectors of the projected system
719:   ld, the leading dimension of pX and pY
720: */
721: PetscErrorCode dvd_improvex_jd_proj_uv_KZX(dvdDashboard *d, PetscInt i_s,
722:   PetscInt i_e, Vec *u, Vec *v, Vec *kr, Vec *auxV, PetscScalar *theta,
723:   PetscScalar *thetai, PetscScalar *pX, PetscScalar *pY, PetscInt ld)
724: {
725:   PetscErrorCode  ierr;
726:   PetscInt        n = i_e - i_s, i;
727:   PetscScalar     b[16];
728:   Vec             *Ax, *Bx, *r=auxV, X[4];
729:   /* The memory manager doen't allow to call a subroutines */
730:   PetscScalar     Z[size_Z];


734:   /* u <- X(i) */
735:   SlepcUpdateVectorsZ(u, 0.0, 1.0, d->V-d->cX_in_H, d->size_V+d->cX_in_H, pX, ld, d->size_H, n);
736:   /* nX(i) <- ||X(i)|| */
737:   if (d->correctXnorm) {
738:     for (i=0; i<n; i++) {
739:       VecNormBegin(u[i], NORM_2, &d->nX[i_s+i]);
740:     }
741:     for (i=0; i<n; i++) {
742:       VecNormEnd(u[i], NORM_2, &d->nX[i_s+i]);
743:     }
744:   } else {
745:     for (i=0; i<n; i++) d->nX[i_s+i] = 1.0;
746:   }

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

750:   /* Bx <- B*X(i) */
751:   Bx = kr;
752:   for(i=i_s; i<i_e; i++) d->nX[i] = 1.0;
753:   if (d->BV) {
754:     SlepcUpdateVectorsZ(Bx, 0.0, 1.0, d->BV-d->cX_in_H, d->size_BV+d->cX_in_H, pX, ld, d->size_H, n);
755:   } else {
756:     for(i=0; i<n; i++) {
757:       if (d->B) {
758:         MatMult(d->B, u[i], Bx[i]);
759:       } else {
760:         VecCopy(u[i], Bx[i]);
761:       }
762:     }
763:   }

765:   /* Ax <- A*X(i) */
766:   Ax = r;
767:   SlepcUpdateVectorsZ(Ax, 0.0, 1.0, d->AV-d->cX_in_H, d->size_AV+d->cX_in_H, pX, ld, d->size_H, n);

769:   /* v <- Y(i) */
770:   SlepcUpdateVectorsZ(v, 0.0, 1.0, (d->W?d->W:d->V)-d->cX_in_H, d->size_V+d->cX_in_H, pY, ld, d->size_H, n);

772:   /* Recompute the eigenvalue */
773:   DVD_COMPUTE_N_RR(d->eps, i, i_s, n, d->eigr, d->eigi, v, Ax, Bx, b, ierr);

775:   for(i=0; i<n; i++) {
776: #if !defined(PETSC_USE_COMPLEX)
777:     if(d->eigi[i_s+i] != 0.0) {
778:       /* [r_i r_i+1 kr_i kr_i+1]*= [ theta_2i'    0            1        0   
779:                                        0         theta_2i'     0        1   
780:                                      theta_2i+1 -thetai_i   -eigr_i -eigi_i 
781:                                      thetai_i    theta_2i+1  eigi_i -eigr_i ] */
782:       b[0] = b[5] = PetscConj(theta[2*i]);
783:       b[2] = b[7] = -theta[2*i+1];
784:       b[6] = -(b[3] = thetai[i]);
785:       b[1] = b[4] = 0.0;
786:       b[8] = b[13] = 1.0;
787:       b[10] = b[15] = -d->eigr[i_s+i];
788:       b[14] = -(b[11] = d->eigi[i_s+i]);
789:       b[9] = b[12] = 0.0;
790:       X[0] = Ax[i]; X[1] = Ax[i+1]; X[2] = Bx[i]; X[3] = Bx[i+1];
791:       SlepcUpdateVectorsD(X, 4, 1.0, b, 4, 4, 4, Z, size_Z);
792: 
793:       i++;
794:     } else
795: #endif
796:     {
797:       /* [Ax_i Bx_i]*= [ theta_2i'    1/nX_i
798:                         theta_2i+1  -eig_i/nX_i ] */
799:       b[0] = PetscConj(theta[i*2]);
800:       b[1] = theta[i*2+1];
801:       b[2] = 1.0/d->nX[i_s+i];
802:       b[3] = -d->eigr[i_s+i]/d->nX[i_s+i];
803:       X[0] = Ax[i]; X[1] = Bx[i];
804:       SlepcUpdateVectorsD(X, 2, 1.0, b, 2, 2, 2, Z, size_Z);
805: 
806:     }
807:   }

809:   /* v <- K^{-1} r = K^{-1}(theta_2i'*Ax + theta_2i+1*Bx) */
810:   for(i=0; i<n; i++) {
811:     d->improvex_precond(d, i_s+i, r[i], v[i]);
812:   }

814:   /* kr <- K^{-1}*kr = K^{-1}*(Ax - eig_i*Bx) */
815:   d->calcpairs_proj_res(d, i_s, i_e, Bx);
816:   for(i=0; i<n; i++) {
817:     VecCopy(Bx[i], r[i]);
818:     d->improvex_precond(d, i_s+i, r[i], kr[i]);
819:   }

821:   return(0);
822: }

826: /* 
827:   Compute: u <- K^{-1}*X, v <- X,
828:   kr <- K^{-1}*(A-eig*B)*X, being X <- V*pX[i_s..i_e-1]
829:   where
830:   auxV, 4*(i_e-i_s) auxiliar global vectors
831:   pX,pY, the right and left eigenvectors of the projected system
832:   ld, the leading dimension of pX and pY
833: */
834: PetscErrorCode dvd_improvex_jd_proj_uv_KXX(dvdDashboard *d, PetscInt i_s,
835:   PetscInt i_e, Vec *u, Vec *v, Vec *kr, Vec *auxV, PetscScalar *theta,
836:   PetscScalar *thetai, PetscScalar *pX, PetscScalar *pY, PetscInt ld)
837: {
838:   PetscErrorCode  ierr;
839:   PetscInt        n = i_e - i_s, i;
840:   PetscScalar     b[16];
841:   Vec             *Ax, *Bx, *r = auxV, X[4];
842:   /* The memory manager doen't allow to call a subroutines */
843:   PetscScalar     Z[size_Z];


847:   /* [v u] <- X(i) Y(i) */
848:   SlepcUpdateVectorsZ(v, 0.0, 1.0, d->V-d->cX_in_H, d->size_V+d->cX_in_H, pX, ld, d->size_H, n);
849:   SlepcUpdateVectorsZ(u, 0.0, 1.0, (d->W?d->W:d->V)-d->cX_in_H, d->size_V+d->cX_in_H, pY, ld, d->size_H, n);

851:   /* Bx <- B*X(i) */
852:   Bx = kr;
853:   for(i=i_s; i<i_e; i++) d->nX[i] = 1.0;
854:   if (d->BV) {
855:     SlepcUpdateVectorsZ(Bx, 0.0, 1.0, d->BV-d->cX_in_H, d->size_BV+d->cX_in_H, pX, ld, d->size_H, n);
856:   } else {
857:     if (d->B) {
858:       for(i=0; i<n; i++) {
859:         MatMult(d->B, v[i], Bx[i]);
860:       }
861:     } else
862:       Bx = v;
863:   }

865:   /* Ax <- A*X(i) */
866:   Ax = r;
867:   SlepcUpdateVectorsZ(Ax, 0.0, 1.0, d->AV-d->cX_in_H, d->size_AV+d->cX_in_H, pX, ld, d->size_H, n);

869:   /* Recompute the eigenvalue */
870:   DVD_COMPUTE_N_RR(d->eps, i, i_s, n, d->eigr, d->eigi, u, Ax, Bx, b, ierr);

872:   for(i=0; i<n; i++) {
873:     if (d->eigi[i_s+i] == 0.0) {
874:       /* r <- Ax -eig*Bx */
875:       VecAXPBY(r[i], -d->eigr[i_s+i], 1.0, Bx[i]);
876:     } else {
877:       /* [r_i r_i+1 kr_i kr_i+1]*= [   1        0 
878:                                        0        1
879:                                     -eigr_i -eigi_i
880:                                      eigi_i -eigr_i] */
881:       b[0] = b[5] = 1.0;
882:       b[2] = b[7] = -d->eigr[i_s+i];
883:       b[6] = -(b[3] = d->eigi[i_s+i]);
884:       b[1] = b[4] = 0.0;
885:       X[0] = r[i]; X[1] = r[i+1]; X[2] = kr[i]; X[3] = kr[i+1];
886:       SlepcUpdateVectorsD(X, 4, 1.0, b, 4, 4, 2, Z, size_Z);
887: 
888:       i++;
889:     }
890:   }

892:   /* kr <- K^{-1}*r */
893:   d->calcpairs_proj_res(d, i_s, i_e, r);
894:   for(i=0; i<n; i++) {
895:     d->improvex_precond(d, i_s+i, r[i], kr[i]);
896:   }

898:   /* u <- K^{-1} X(i) */
899:   for(i=0; i<n; i++) {
900:     d->improvex_precond(d, i_s+i, v[i], u[i]);
901:   }

903:   return(0);
904: }


909: PetscErrorCode dvd_improvex_jd_lit_const(dvdDashboard *d, dvdBlackboard *b,
910:                                          PetscInt maxits, PetscReal tol,
911:                                          PetscReal fix)
912: {
913:   dvdImprovex_jd  *data = (dvdImprovex_jd*)d->improveX_data;


917:   /* Setup the step */
918:   if (b->state >= DVD_STATE_CONF) {
919:     data->maxits = maxits;
920:     data->tol = tol;
921:     data->fix = fix;
922:     d->improvex_jd_lit = dvd_improvex_jd_lit_const_0;
923:   }

925:   return(0);
926: }


931: PetscErrorCode dvd_improvex_jd_lit_const_0(dvdDashboard *d, PetscInt i,
932:   PetscScalar* theta, PetscScalar* thetai, PetscInt *maxits, PetscReal *tol)
933: {
934:   dvdImprovex_jd  *data = (dvdImprovex_jd*)d->improveX_data;
935:   PetscReal       a;

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

940:   if (d->nR[i]/a < data->fix) {
941:     theta[0] = d->eigr[i];
942:     theta[1] = 1.0;
943: #if !defined(PETSC_USE_COMPLEX)
944:     *thetai = d->eigi[i];
945: #endif
946:   } else {
947:     theta[0] = d->target[0];
948:     theta[1] = d->target[1];
949: #if !defined(PETSC_USE_COMPLEX)
950:     *thetai = 0.0;
951: #endif
952: }

954: #if defined(PETSC_USE_COMPLEX)
955:   if(thetai) *thetai = 0.0;
956: #endif
957:   *maxits = data->maxits;
958:   *tol = data->tol;

960:   return(0);
961: }


964: /**** Patterns implementation *************************************************/

966: typedef PetscInt (*funcV0_t)(dvdDashboard*, PetscInt, PetscInt, Vec*);
967: typedef PetscInt (*funcV1_t)(dvdDashboard*, PetscInt, PetscInt, Vec*,
968:                              PetscScalar*, Vec);

972: /* Compute D <- K^{-1} * funcV[r_s..r_e] */
973: PetscErrorCode dvd_improvex_PfuncV(dvdDashboard *d, void *funcV, Vec *D,
974:   PetscInt max_size_D, PetscInt r_s, PetscInt r_e, Vec *auxV,
975:   PetscScalar *auxS)
976: {
977:   PetscErrorCode  ierr;
978:   PetscInt        i;


982:   if (max_size_D >= r_e-r_s+1) {
983:     /* The optimized version needs one vector extra of D */
984:     /* D(1:r.size) = R(r_s:r_e-1) */
985:     if (auxS) ((funcV1_t)funcV)(d, r_s, r_e, D+1, auxS, auxV[0]);
986:     else      ((funcV0_t)funcV)(d, r_s, r_e, D+1);

988:     /* D = K^{-1} * R */
989:     for (i=0; i<r_e-r_s; i++) {
990:       d->improvex_precond(d, i+r_s, D[i+1], D[i]);
991:     }
992:   } else if (max_size_D == r_e-r_s) {
993:     /* Non-optimized version */
994:     /* auxV <- R[r_e-1] */
995:     if (auxS) ((funcV1_t)funcV)(d, r_e-1, r_e, auxV, auxS, auxV[1]);
996:     else      ((funcV0_t)funcV)(d, r_e-1, r_e, auxV);

998:     /* D(1:r.size-1) = R(r_s:r_e-2) */
999:     if (auxS) ((funcV1_t)funcV)(d, r_s, r_e-1, D+1, auxS, auxV[1]);
1000:     else      ((funcV0_t)funcV)(d, r_s, r_e-1, D+1);

1002:     /* D = K^{-1} * R */
1003:     for (i=0; i<r_e-r_s-1; i++) {
1004:       d->improvex_precond(d, i+r_s, D[i+1], D[i]);
1005:     }
1006:     d->improvex_precond(d, r_e-1, auxV[0], D[r_e-r_s-1]);
1007:   } else {
1008:     SETERRQ(PETSC_COMM_SELF,1, "Problem: r_e-r_s > max_size_D!");
1009:   }

1011:   return(0);
1012: }


1017: /* Compute the left and right projected eigenvectors where,
1018:    pX, the returned right eigenvectors
1019:    pY, the returned left eigenvectors,
1020:    ld_, the leading dimension of pX and pY,
1021:    auxS, auxiliar vector of size length 6*d->size_H
1022: */
1023: PetscErrorCode dvd_improvex_get_eigenvectors(dvdDashboard *d, PetscScalar *pX,
1024:   PetscScalar *pY, PetscInt ld, PetscScalar *auxS, PetscInt size_auxS)
1025: {
1026:   PetscErrorCode  ierr;
1027: 

1030:   SlepcDenseCopy(pY, ld, d->T?d->pY:d->pX, d->ldpX, d->size_H,
1031:                         d->size_H);
1032:   SlepcDenseCopy(pX, ld, d->pX, d->ldpX, d->size_H, d->size_H);
1033: 
1034: 
1035:   /* [qX, qY] <- eig(S, T); pX <- d->pX * qX; pY <- d->pY * qY */
1036:   dvd_compute_eigenvectors(d->size_H, d->S, d->ldS, d->T, d->ldT, pX,
1037:                                   ld, pY, ld, auxS, size_auxS, PETSC_TRUE);
1038: 

1040:   /* 2-Normalize the columns of pX an pY */
1041:   SlepcDenseNorm(pX, ld, d->size_H, d->size_H, d->eigi);
1042:   SlepcDenseNorm(pY, ld, d->size_H, d->size_H, d->eigi);

1044:   return(0);
1045: }

1049: /* Compute (I - KZ*iXKZ*X')*V where,
1050:    V, the vectors to apply the projector,
1051:    cV, the number of vectors in V,
1052:    auxS, auxiliar vector of size length 3*size_iXKZ*cV
1053: */
1054: PetscErrorCode dvd_improvex_apply_proj(dvdDashboard *d, Vec *V, PetscInt cV, PetscScalar *auxS)
1055: {
1056:   PetscErrorCode  ierr;
1057:   dvdImprovex_jd  *data = (dvdImprovex_jd*)d->improveX_data;
1058:   PetscInt        size_in = data->size_iXKZ*cV, i, ldh;
1059:   PetscScalar     *h, *in, *out;
1060:   PetscBLASInt    cV_, n, info, ld;
1061:   DvdReduction    r;
1062:   DvdReductionChunk
1063:                   ops[4];
1064:   DvdMult_copy_func
1065:                   sr[4];
1066: 

1069:   /* Check consistency */
1070:   if (cV > 2) { SETERRQ(PETSC_COMM_SELF,1, "Consistency broken!"); }

1072:   /* h <- X'*V */
1073:   h = auxS; in = h+size_in; out = in+size_in; ldh = data->size_iXKZ;
1074:   SlepcAllReduceSumBegin(ops, 4, in, out, size_in, &r,
1075:                                 ((PetscObject)d->V[0])->comm);
1076:   for (i=0; i<cV; i++) {
1077:     VecsMultS(&h[i*ldh],0,ldh,d->V-data->size_KZ,0,data->size_KZ,V+i,0,1,&r,&sr[i*2]);
1078:     VecsMultS(&h[i*ldh+data->size_KZ],0,ldh,data->u,0,data->size_iXKZ-data->size_KZ,V+i,0,1,&r,&sr[i*2+1]);
1079:   }
1080:   SlepcAllReduceSumEnd(&r);

1082:   /* h <- iXKZ\h */
1083:   cV_ = PetscBLASIntCast(cV);
1084:   n = PetscBLASIntCast(data->size_iXKZ);
1085:   ld = PetscBLASIntCast(data->ldiXKZ);
1086:   LAPACKgetrs_("N", &n, &cV_, data->iXKZ, &ld, data->iXKZPivots, h, &n, &info);
1087:   if (info) SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_LIB, "Error in Lapack XGETRS %d", info);

1089:   /* V <- V - KZ*h */
1090:   for (i=0; i<cV; i++) {
1091:     SlepcUpdateVectorsZ(V+i,1.0,-1.0,data->KZ,data->size_iXKZ,&h[ldh*i],ldh,data->size_iXKZ,1);
1092:   }

1094:   return(0);
1095: }