Actual source code: dvd_calcpairs.c

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

  4:   Step: calc the best eigenpairs in the subspace V.

  6:   For that, performs these steps:
  7:     1) Update W <- A * V
  8:     2) Update H <- V' * W
  9:     3) Obtain eigenpairs of H
 10:     4) Select some eigenpairs
 11:     5) Compute the Ritz pairs of the selected ones

 13:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 14:    SLEPc - Scalable Library for Eigenvalue Problem Computations
 15:    Copyright (c) 2002-2011, Universitat Politecnica de Valencia, Spain

 17:    This file is part of SLEPc.
 18:       
 19:    SLEPc is free software: you can redistribute it and/or modify it under  the
 20:    terms of version 3 of the GNU Lesser General Public License as published by
 21:    the Free Software Foundation.

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

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

 33:  #include davidson.h
 34: #include <slepcblaslapack.h>

 36: PetscErrorCode dvd_calcpairs_proj(dvdDashboard *d);
 37: PetscErrorCode dvd_calcpairs_qz_start(dvdDashboard *d);
 38: PetscErrorCode dvd_calcpairs_projeig_eig(dvdDashboard *d);
 39: PetscErrorCode dvd_calcpairs_projeig_qz_std(dvdDashboard *d);
 40: PetscErrorCode dvd_calcpairs_projeig_qz_gen(dvdDashboard *d);
 41: PetscErrorCode dvd_calcpairs_selectPairs_qz(dvdDashboard *d, PetscInt n);
 42: PetscErrorCode dvd_calcpairs_selectPairs_eig(dvdDashboard *d, PetscInt n);
 43: PetscErrorCode dvd_calcpairs_X(dvdDashboard *d, PetscInt r_s, PetscInt r_e,
 44:                                Vec *X);
 45: PetscErrorCode dvd_calcpairs_Y(dvdDashboard *d, PetscInt r_s, PetscInt r_e,
 46:                                Vec *Y);
 47: PetscErrorCode dvd_calcpairs_res_0(dvdDashboard *d, PetscInt r_s, PetscInt r_e,
 48:                                    Vec *R);
 49: PetscErrorCode dvd_calcpairs_eig_res_0(dvdDashboard *d,PetscInt r_s,PetscInt r_e,Vec *R);
 50: PetscErrorCode dvd_calcpairs_proj_res(dvdDashboard *d, PetscInt r_s,
 51:                                       PetscInt r_e, Vec *R);
 52: PetscErrorCode dvd_calcpairs_updateV0(dvdDashboard *d, DvdReduction *r,
 53:                                       DvdMult_copy_func **sr);
 54: PetscErrorCode dvd_calcpairs_updateV1(dvdDashboard *d);
 55: PetscErrorCode dvd_calcpairs_updateW0(dvdDashboard *d, DvdReduction *r,
 56:                                       DvdMult_copy_func **sr);
 57: PetscErrorCode dvd_calcpairs_updateW1(dvdDashboard *d);
 58: PetscErrorCode dvd_calcpairs_updateAV0(dvdDashboard *d);
 59: PetscErrorCode dvd_calcpairs_updateAV1(dvdDashboard *d, DvdReduction *r,
 60:                                        DvdMult_copy_func **sr);
 61: PetscErrorCode dvd_calcpairs_updateBV0(dvdDashboard *d);
 62: PetscErrorCode dvd_calcpairs_updateBV1(dvdDashboard *d, DvdReduction *r,
 63:                                        DvdMult_copy_func **sr);
 64: PETSC_STATIC_INLINE PetscErrorCode dvd_calcpairs_updateBV0_gen(dvdDashboard *d,Vec *real_BV,PetscInt *size_cX,Vec **BV,PetscInt *size_BV,PetscInt *max_size_BV,PetscBool BV_shift,PetscInt *cX_in_proj,PetscScalar *MTX);

 66: /**** Control routines ********************************************************/
 69: PetscErrorCode dvd_calcpairs_qz(dvdDashboard *d, dvdBlackboard *b,
 70:                                 orthoV_type_t orth, IP ipI,
 71:                                 PetscInt cX_proj, PetscBool harm)
 72: {
 73:   PetscErrorCode  ierr;
 74:   PetscInt        i,max_cS;
 75:   PetscBool       std_probl,her_probl;


 79:   std_probl = DVD_IS(d->sEP, DVD_EP_STD)?PETSC_TRUE:PETSC_FALSE;
 80:   her_probl = DVD_IS(d->sEP, DVD_EP_HERMITIAN)?PETSC_TRUE:PETSC_FALSE;

 82:   /* Setting configuration constrains */
 83: #if !defined(PETSC_USE_COMPLEX)
 84:   /* if the last converged eigenvalue is complex its conjugate pair is also
 85:      converged */
 86:   b->max_nev = PetscMax(b->max_nev, d->nev+(her_probl && !d->B?0:1));
 87: #else
 88:   b->max_nev = PetscMax(b->max_nev, d->nev);
 89: #endif
 90:   b->max_size_proj = PetscMax(b->max_size_proj, b->max_size_V+cX_proj);
 91:   d->size_real_V = b->max_size_V+b->max_nev;
 92:   d->W_shift = d->B?PETSC_TRUE:PETSC_FALSE;
 93:   d->size_real_W = harm?(b->max_size_V+(d->W_shift?b->max_nev:b->max_size_cP)):0;
 94:   d->size_real_AV = b->max_size_V+b->max_size_cP;
 95:   d->size_BDS = 0;
 96:   if (d->B && her_probl && (orth == DVD_ORTHOV_I || orth == DVD_ORTHOV_BOneMV)) {
 97:     d->size_real_BV = b->size_V; d->BV_shift = PETSC_TRUE;
 98:     if (orth == DVD_ORTHOV_BOneMV) d->size_BDS = d->eps->nds;
 99:   } else if (d->B) {
100:     d->size_real_BV = b->max_size_V + b->max_size_P; d->BV_shift = PETSC_FALSE;
101:   } else {
102:     d->size_real_BV = 0; d->BV_shift = PETSC_FALSE;
103:   }
104:   b->own_vecs+= d->size_real_V + d->size_real_W + d->size_real_AV +
105:                 d->size_real_BV + d->size_BDS;
106:   b->own_scalars+= b->max_size_proj*b->max_size_proj*2*(std_probl?1:2) +
107:                                               /* H, G?, S, T? */
108:                    b->max_size_proj*b->max_size_proj*(std_probl?1:2) +
109:                                               /* pX, pY? */
110:                    b->max_nev*b->max_nev*(her_probl?0:(!d->B?1:2));
111:                                                 /* cS?, cT? */
112:   b->max_size_auxV = PetscMax(b->max_size_auxV, b->max_size_X);
113:                                                 /* updateV0 */
114:   max_cS = PetscMax(b->max_size_X,cX_proj);
115:   b->max_size_auxS = PetscMax(PetscMax(
116:     b->max_size_auxS,
117:     b->max_size_X*b->max_size_proj*2*(std_probl?1:2) + /* updateAV1,BV1 */
118:       max_cS*b->max_nev*(her_probl?0:(!d->B?1:2)) + /* updateV0,W0 */
119:                                                      /* SlepcReduction: in */
120:       PetscMax(
121:         b->max_size_X*b->max_size_proj*2*(std_probl?1:2) + /* updateAV1,BV1 */
122:           max_cS*b->max_nev*(her_probl?0:(!d->B?1:2)), /* updateV0,W0 */
123:                                                     /* SlepcReduction: out */
124:         PetscMax(
125:           b->max_size_proj*b->max_size_proj, /* updateAV0,BV0 */
126:           b->max_size_proj+b->max_nev))), /* dvd_orth */
127:     std_probl?0:(b->max_size_proj*11+16) /* projeig */);
128: #if defined(PETSC_USE_COMPLEX)
129:   b->max_size_auxS = PetscMax(b->max_size_auxS, b->max_size_V);
130:                                            /* dvd_calcpairs_projeig_eig */
131: #endif

133:   /* Setup the step */
134:   if (b->state >= DVD_STATE_CONF) {
135:     d->max_cX_in_proj = cX_proj;
136:     d->max_size_P = b->max_size_P;
137:     d->real_V = b->free_vecs; b->free_vecs+= d->size_real_V;
138:     if (harm) {
139:       d->real_W = b->free_vecs; b->free_vecs+= d->size_real_W;
140:     } else {
141:       d->real_W = PETSC_NULL;
142:     }
143:     d->real_AV = d->AV = b->free_vecs; b->free_vecs+= d->size_real_AV;
144:     d->max_size_proj = b->max_size_proj;
145:     d->real_H = b->free_scalars; b->free_scalars+= b->max_size_proj*b->max_size_proj;
146:     d->ldH = b->max_size_proj;
147:     d->pX = b->free_scalars; b->free_scalars+= b->max_size_proj*b->max_size_proj;
148:     d->S = b->free_scalars; b->free_scalars+= b->max_size_proj*b->max_size_proj;
149:     if (!her_probl) {
150:       d->cS = b->free_scalars; b->free_scalars+= b->max_nev*b->max_nev;
151:       d->max_size_cS = d->ldcS = b->max_nev;
152:     } else {
153:       d->cS = PETSC_NULL;
154:       d->max_size_cS = d->ldcS = 0;
155:     }
156:     d->ipV = ipI;
157:     d->ipW = ipI;
158:     if (orth == DVD_ORTHOV_BOneMV) {
159:       d->BDS = b->free_vecs; b->free_vecs+= d->eps->nds;
160:       for (i=0; i<d->eps->nds; i++) {
161:         MatMult(d->B, d->eps->DS[i], d->BDS[i]);
162:       }
163:     } else
164:       d->BDS = PETSC_NULL;
165:     if (d->B) {
166:       d->real_BV = b->free_vecs; b->free_vecs+= d->size_real_BV;
167:     } else {
168:       d->size_real_BV = 0;
169:       d->real_BV = PETSC_NULL;
170:       d->BV_shift = PETSC_FALSE;
171:     }
172:     if (!std_probl) {
173:       d->real_G = b->free_scalars; b->free_scalars+= b->max_size_proj*b->max_size_proj;
174:       d->T = b->free_scalars; b->free_scalars+= b->max_size_proj*b->max_size_proj;
175:       d->pY = b->free_scalars; b->free_scalars+= b->max_size_proj*b->max_size_proj;
176:     } else {
177:       d->real_G = PETSC_NULL;
178:       d->T = PETSC_NULL;
179:       d->pY = PETSC_NULL;
180:     }
181:     if (d->B && !her_probl) {
182:       d->cT = b->free_scalars; b->free_scalars+= b->max_nev*b->max_nev;
183:       d->ldcT = b->max_nev;
184:     } else {
185:       d->cT = PETSC_NULL;
186:       d->ldcT = 0;
187:     }

189:     d->calcPairs = dvd_calcpairs_proj;
190:     d->calcpairs_residual = dvd_calcpairs_res_0;
191:     d->calcpairs_residual_eig = dvd_calcpairs_eig_res_0;
192:     d->calcpairs_proj_res = dvd_calcpairs_proj_res;
193:     d->calcpairs_selectPairs = PETSC_NULL;
194:     d->ipI = ipI;
195:     DVD_FL_ADD(d->startList, dvd_calcpairs_qz_start);
196:   }

198:   return(0);
199: }


204: PetscErrorCode dvd_calcpairs_qz_start(dvdDashboard *d)
205: {
206:   PetscBool her_probl;
207:   PetscInt  i;

210:   her_probl = DVD_IS(d->sEP, DVD_EP_HERMITIAN)?PETSC_TRUE:PETSC_FALSE;

212:   d->size_V = 0;
213:   d->V = d->real_V;
214:   d->cX = d->real_V;
215:   d->size_cX = 0;
216:   d->max_size_V = d->size_real_V;
217:   d->W = d->real_W;
218:   d->max_size_W = d->size_real_W;
219:   d->size_W = 0;
220:   d->size_AV = 0;
221:   d->AV = d->real_AV;
222:   d->max_size_AV = d->size_real_AV;
223:   d->size_H = 0;
224:   d->H = d->real_H;
225:   if (d->cS) for (i=0; i<d->max_size_cS*d->max_size_cS; i++) d->cS[i] = 0.0;
226:   d->size_BV = 0;
227:   d->BV = d->real_BV;
228:   d->max_size_BV = d->size_real_BV;
229:   d->size_G = 0;
230:   d->G = d->real_G;
231:   if (d->cT) for (i=0; i<d->max_size_cS*d->max_size_cS; i++) d->cT[i] = 0.0;
232:   d->cY = d->B && !her_probl ? d->W : PETSC_NULL;
233:   d->BcX = d->orthoV_type == DVD_ORTHOV_I && d->B && her_probl ? d->BcX : PETSC_NULL;
234:   d->size_cY = 0;
235:   d->size_BcX = 0;
236:   d->cX_in_V = d->cX_in_H = d->cX_in_G = d->cX_in_W = d->cX_in_AV = d->cX_in_BV = 0;
237:   return(0);
238: }


243: PetscErrorCode dvd_calcpairs_proj(dvdDashboard *d)
244: {
245:   PetscErrorCode  ierr;
246:   DvdReduction    r;
247: #define MAX_OPS 7
248:   DvdReductionChunk
249:                   ops[MAX_OPS];
250:   DvdMult_copy_func
251:                   sr[MAX_OPS], *sr0 = sr;
252:   PetscInt        size_in, i;
253:   PetscScalar     *in = d->auxS, *out;
254:   PetscBool       stdp;


258:   stdp = DVD_IS(d->sEP, DVD_EP_STD)?PETSC_TRUE:PETSC_FALSE;
259:   size_in =
260:     (d->size_cX+d->V_tra_s-d->cX_in_H)*d->V_tra_s*(d->cT?2:(d->cS?1:0)) + /* updateV0,W0 */
261:     (d->size_H*(d->V_new_e-d->V_new_s)*2+
262:       (d->V_new_e-d->V_new_s)*(d->V_new_e-d->V_new_s))*(!stdp?2:1); /* updateAV1,BV1 */
263: 
264:   out = in+size_in;

266:   /* Check consistency */
267:   if (2*size_in > d->size_auxS) { SETERRQ(PETSC_COMM_SELF,1, "Consistency broken!"); }

269:   /* Prepare reductions */
270:   SlepcAllReduceSumBegin(ops, MAX_OPS, in, out, size_in, &r,
271:                                 ((PetscObject)d->V[0])->comm);
272:   /* Allocate size_in */
273:   d->auxS+= size_in;
274:   d->size_auxS-= size_in;

276:   /* Update AV, BV, W and the projected matrices */
277:   /* 1. S <- S*MT */
278:   dvd_calcpairs_updateV0(d, &r, &sr0);
279:   dvd_calcpairs_updateW0(d, &r, &sr0);
280:   dvd_calcpairs_updateAV0(d);
281:   dvd_calcpairs_updateBV0(d);
282:   /* 2. V <- orth(V, V_new) */
283:   dvd_calcpairs_updateV1(d);
284:   /* 3. AV <- [AV A * V(V_new_s:V_new_e-1)] */
285:   /* Check consistency */
286:   if (d->size_AV != d->V_new_s) { SETERRQ(PETSC_COMM_SELF,1, "Consistency broken!"); }
287:   for (i=d->V_new_s; i<d->V_new_e; i++) {
288:     MatMult(d->A, d->V[i], d->AV[i]);
289:   }
290:   d->size_AV = d->V_new_e;
291:   /* 4. BV <- [BV B * V(V_new_s:V_new_e-1)] */
292:   if (d->B && d->orthoV_type != DVD_ORTHOV_BOneMV) {
293:     /* Check consistency */
294:     if (d->size_BV != d->V_new_s) { SETERRQ(PETSC_COMM_SELF,1, "Consistency broken!"); }
295:     for (i=d->V_new_s; i<d->V_new_e; i++) {
296:       MatMult(d->B, d->V[i], d->BV[i]);
297:     }
298:     d->size_BV = d->V_new_e;
299:   }
300:   /* 5 <- W <- [W f(AV,BV)] */
301:   dvd_calcpairs_updateW1(d);
302:   dvd_calcpairs_updateAV1(d, &r, &sr0);
303:   dvd_calcpairs_updateBV1(d, &r, &sr0);

305:   /* Deallocate size_in */
306:   d->auxS-= size_in;
307:   d->size_auxS+= size_in;

309:   /* Do reductions */
310:   SlepcAllReduceSumEnd(&r);

312:   /* Perform the transformation on the projected problem */
313:   if (d->calcpairs_proj_trans) {
314:     d->calcpairs_proj_trans(d);
315:   }

317:   d->V_tra_s = d->V_tra_e = 0;
318:   d->V_new_s = d->V_new_e;

320:   /* Solve the projected problem */
321:   if (d->size_H>0) {
322:     if (DVD_IS(d->sEP, DVD_EP_STD)) {
323:       if (DVD_IS(d->sEP, DVD_EP_HERMITIAN)) {
324:         dvd_calcpairs_projeig_eig(d);
325:       } else {
326:         dvd_calcpairs_projeig_qz_std(d);
327:       }
328:     } else {
329:       dvd_calcpairs_projeig_qz_gen(d);
330:     }
331:   }

333:   /* Check consistency */
334:   if (d->size_V != d->V_new_e || d->size_V+d->cX_in_H != d->size_H || d->cX_in_V != d->cX_in_H ||
335:       d->size_V != d->size_AV || d->cX_in_H != d->cX_in_AV ||
336:         (DVD_ISNOT(d->sEP, DVD_EP_STD) && (
337:           d->size_V+d->cX_in_G != d->size_G || d->cX_in_H != d->cX_in_G ||
338:           d->size_H != d->size_G || (d->BV && (
339:             d->size_V != d->size_BV || d->cX_in_H != d->cX_in_BV)))) ||
340:       (d->W && d->size_W != d->size_V)) {
341:     SETERRQ(PETSC_COMM_SELF,1, "Consistency broken!");
342:   }

344:   return(0);
345: #undef MAX_OPS
346: }

348: /**** Basic routines **********************************************************/

352: /* auxV: V_tra_s, DvdMult_copy_func: 1 */
353: PetscErrorCode dvd_calcpairs_updateV0(dvdDashboard *d, DvdReduction *r,
354:                                       DvdMult_copy_func **sr)
355: {
356:   PetscErrorCode  ierr;
357:   PetscInt        rm;


361:   if (d->V_tra_s == 0 && d->V_tra_e == 0) { return(0); }

363:   /* cX <- [cX V*MT(0:V_tra_s-1)], V <- V*MT(V_tra_s:V_tra_e) */
364:   dvd_calcpairs_updateBV0_gen(d,d->real_V,&d->size_cX,&d->V,&d->size_V,&d->max_size_V,PETSC_TRUE,&d->cX_in_V,d->MTX);

366:   /* Udpate cS for standard problems */
367:   if (d->cS && !d->cT && !d->cY && (d->V_tra_s > d->max_cX_in_proj || d->size_cX >= d->nev)) {
368:     /* Check consistency */
369:     if (d->size_cS+d->V_tra_s != d->size_cX) { SETERRQ(PETSC_COMM_SELF,1, "Consistency broken!"); }

371:     /* auxV <- AV * MTX(0:V_tra_e-1) */
372:     rm = d->size_cX>=d->nev?0:d->max_cX_in_proj;
373:     SlepcUpdateVectorsZ(d->auxV, 0.0, 1.0, d->AV-d->cX_in_AV, d->size_AV+d->cX_in_AV, d->MTX, d->ldMTX, d->size_MT, d->V_tra_s-rm);

375:     /* cS(:, size_cS:) <- cX' * auxV */
376:     VecsMultS(&d->cS[d->ldcS*d->size_cS], 0, d->ldcS, d->cX, 0, d->size_cX-rm, d->auxV, 0, d->V_tra_s-rm, r, (*sr)++);
377:     d->size_cS+= d->V_tra_s-rm;
378:   }
379: 
380:   return(0);
381: }


386: /* auxS: size_cX+V_new_e+1 */
387: PetscErrorCode dvd_calcpairs_updateV1(dvdDashboard *d)
388: {
389:   PetscErrorCode  ierr;
390:   Vec             *cX = d->BcX? d->BcX : ( (d->cY && !d->W)? d->cY : d->cX );


394:   if (d->V_new_s == d->V_new_e) { return(0); }

396:   /* Check consistency */
397:   if (d->size_V != d->V_new_s) { SETERRQ(PETSC_COMM_SELF,1, "Consistency broken!"); }

399:   /* V <- gs([cX V(0:V_new_s-1)], V(V_new_s:V_new_e-1)) */
400:   if (d->orthoV_type == DVD_ORTHOV_BOneMV) {
401:     dvd_BorthV(d->ipV, d->eps->DS, d->BDS, d->eps->nds, d->cX, d->real_BV,
402:                       d->size_cX, d->V, d->BV, d->V_new_s, d->V_new_e,
403:                       d->auxS, d->eps->rand);
404:     d->size_BV = d->V_new_e;
405:   } else {
406:     dvd_orthV(d->ipV, d->eps->DS, d->eps->nds, cX, d->size_cX, d->V,
407:                    d->V_new_s, d->V_new_e, d->auxS, d->eps->rand);
408: 
409:   }
410:   d->size_V = d->V_new_e;

412:   return(0);
413: }

417: /* auxV: V_tra_s, DvdMult_copy_func: 2 */
418: PetscErrorCode dvd_calcpairs_updateW0(dvdDashboard *d, DvdReduction *r,
419:                                       DvdMult_copy_func **sr)
420: {
421:   PetscErrorCode  ierr;
422:   PetscInt        rm;


426:   if (d->V_tra_s == 0 && d->V_tra_e == 0) { return(0); }

428:   /* cY <- [cY W*MTY(0:V_tra_s-1)], W <- W*MTY(V_tra_s:V_tra_e) */
429:   dvd_calcpairs_updateBV0_gen(d,d->real_W,&d->size_cY,&d->W,&d->size_W,&d->max_size_W,d->W_shift,&d->cX_in_W,d->MTY);

431:   /* Udpate cS and cT */
432:   if (d->cT && (d->V_tra_s > d->max_cX_in_proj || d->size_cX >= d->nev)) {
433:     /* Check consistency */
434:     if (d->size_cS+d->V_tra_s != d->size_cX || (d->W && d->size_cY != d->size_cX)) { SETERRQ(PETSC_COMM_SELF,1, "Consistency broken!"); }

436:     /* auxV <- AV * MTX(0:V_tra_e-1) */
437:     rm = d->size_cX>=d->nev?0:d->max_cX_in_proj;
438:     SlepcUpdateVectorsZ(d->auxV, 0.0, 1.0, d->AV-d->cX_in_H, d->size_AV-d->cX_in_H, d->MTX, d->ldMTX, d->size_MT, d->V_tra_s-rm);

440:     /* cS(:, size_cS:) <- cY' * auxV */
441:     VecsMultS(&d->cS[d->ldcS*d->size_cS], 0, d->ldcS, d->cY?d->cY:d->cX, 0, d->size_cX-rm, d->auxV, 0, d->V_tra_s-rm, r, (*sr)++);

443:     /* auxV <- BV * MTX(0:V_tra_e-1) */
444:     SlepcUpdateVectorsZ(d->auxV, 0.0, 1.0, d->BV-d->cX_in_H, d->size_BV-d->cX_in_H, d->MTX, d->ldMTX, d->size_MT, d->V_tra_s-rm);

446:     /* cT(:, size_cS:) <- cY' * auxV */
447:     VecsMultS(&d->cT[d->ldcS*d->size_cS], 0, d->ldcS, d->cY?d->cY:d->cX, 0, d->size_cX-rm, d->auxV, 0, d->V_tra_s-rm, r, (*sr)++);
448: 
449:     d->size_cS+= d->V_tra_s-rm;
450:     d->size_cT+= d->V_tra_s-rm;
451:   }

453:   return(0);
454: }


459: /* auxS: size_cX+V_new_e+1 */
460: PetscErrorCode dvd_calcpairs_updateW1(dvdDashboard *d)
461: {
462:   PetscErrorCode  ierr;
463:   Vec             *cY = d->cY?d->cY:d->cX;


467:   if (!d->W || d->V_new_s == d->V_new_e) { return(0); }

469:   /* Check consistency */
470:   if (d->size_W != d->V_new_s) { SETERRQ(PETSC_COMM_SELF,1, "Consistency broken!"); }

472:   /* Update W */
473:   d->calcpairs_W(d);

475:   /* W <- gs([cY W(0:V_new_s-1)], W(V_new_s:V_new_e-1)) */
476:   dvd_orthV(d->ipW, PETSC_NULL, 0, cY, d->size_cX, d->W-d->cX_in_W, d->V_new_s+d->cX_in_W, d->V_new_e+d->cX_in_W, d->auxS, d->eps->rand);
477:   d->size_W = d->V_new_e;

479:   return(0);
480: }

484: /* auxS: size_H*(V_tra_e-V_tra_s) */
485: PetscErrorCode dvd_calcpairs_updateAV0(dvdDashboard *d)
486: {
487:   PetscErrorCode  ierr;
488:   PetscScalar     *MTY = d->W?d->MTY:d->MTX;
489:   PetscInt        cMT, tra_s;


493:   if (d->V_tra_s == 0 && d->V_tra_e == 0) { return(0); }

495:   /* AV(V_tra_s-cp-1:) = cAV*MTX(V_tra_s:) */
496:   dvd_calcpairs_updateBV0_gen(d,d->real_AV,PETSC_NULL,&d->AV,&d->size_AV,&d->max_size_AV,PETSC_FALSE,&d->cX_in_AV,d->MTX);
497:   tra_s = PetscMax(d->V_tra_s-d->max_cX_in_proj, 0);
498:   cMT = d->V_tra_e - tra_s;

500:   /* Update H <- MTY(tra_s)' * (H * MTX(tra_s:)) */
501:   SlepcDenseMatProdTriang(d->auxS, 0, d->ldH, d->H, d->sH, d->ldH, d->size_H, d->size_H, PETSC_FALSE, &d->MTX[d->ldMTX*tra_s], 0, d->ldMTX, d->size_MT, cMT, PETSC_FALSE);
502:   SlepcDenseMatProdTriang(d->H, d->sH, d->ldH, &MTY[d->ldMTX*tra_s], 0, d->ldMTX, d->size_MT, cMT, PETSC_TRUE, d->auxS, 0, d->ldH, d->size_H, cMT, PETSC_FALSE);
503:   d->size_H = cMT;
504:   d->cX_in_H = d->cX_in_AV;

506:   return(0);
507: }


512: /* DvdMult_copy_func: 2 */
513: PetscErrorCode dvd_calcpairs_updateAV1(dvdDashboard *d, DvdReduction *r,
514:                                        DvdMult_copy_func **sr)
515: {
516:   PetscErrorCode  ierr;
517:   Vec             *W = d->W?d->W:d->V;


521:   if (d->V_new_s == d->V_new_e) { return(0); }

523:   /* Check consistency */
524:   if (d->size_H != d->V_new_s+d->cX_in_H || d->size_V != d->V_new_e) {
525:     SETERRQ(PETSC_COMM_SELF,1, "Consistency broken!");
526:   }

528:   /* H = [H               W(old)'*AV(new);
529:           W(new)'*AV(old) W(new)'*AV(new) ],
530:      being old=0:V_new_s-1, new=V_new_s:V_new_e-1 */
531:   VecsMultS(d->H,d->sH,d->ldH,W-d->cX_in_H,d->V_new_s+d->cX_in_H, d->V_new_e+d->cX_in_H, d->AV-d->cX_in_H,d->V_new_s+d->cX_in_H,d->V_new_e+d->cX_in_H, r, (*sr)++);
532:   d->size_H = d->V_new_e+d->cX_in_H;

534:   return(0);
535: }

539: /* auxS: max(BcX*(size_cX+V_new_e+1), size_G*(V_tra_e-V_tra_s)) */
540: PetscErrorCode dvd_calcpairs_updateBV0(dvdDashboard *d)
541: {
542:   PetscErrorCode  ierr;
543:   PetscScalar     *MTY = d->W?d->MTY:d->MTX;
544:   PetscInt        cMT, tra_s, i;
545:   PetscBool       lindep;
546:   PetscReal       norm;


550:   if (d->V_tra_s == 0 && d->V_tra_e == 0) { return(0); }

552:   /* BV <- BV*MTX */
553:   dvd_calcpairs_updateBV0_gen(d,d->real_BV,PETSC_NULL,&d->BV,&d->size_BV,&d->max_size_BV,d->BV_shift,&d->cX_in_BV,d->MTX);

555:   /* If BcX, BcX <- orth(BcX) */
556:   if (d->BcX) {
557:     for (i=0; i<d->V_tra_s; i++) {
558:       IPOrthogonalize(d->ipI, 0, PETSC_NULL, d->size_BcX+i, PETSC_NULL,
559:                              d->BcX, d->BcX[d->size_BcX+i], PETSC_NULL,
560:                              &norm, &lindep);
561:       if(lindep) SETERRQ(((PetscObject)d->ipI)->comm,1, "Error during orth(BcX, B*cX(new))");
562:       VecScale(d->BcX[d->size_BcX+i], 1.0/norm);
563:     }
564:     d->size_BcX+= d->V_tra_s;
565:   }

567:   /* Update G <- MTY' * (G * MTX) */
568:   if (d->G) {
569:     tra_s = PetscMax(d->V_tra_s-d->max_cX_in_proj, 0);
570:     cMT = d->V_tra_e - tra_s;
571:     SlepcDenseMatProdTriang(d->auxS, 0, d->ldH, d->G, d->sG, d->ldH, d->size_G, d->size_G, PETSC_FALSE, &d->MTX[d->ldMTX*tra_s], 0, d->ldMTX, d->size_MT, cMT, PETSC_FALSE);
572:     SlepcDenseMatProdTriang(d->G, d->sG, d->ldH, &MTY[d->ldMTX*tra_s], 0, d->ldMTX, d->size_MT, cMT, PETSC_TRUE, d->auxS, 0, d->ldH, d->size_G, cMT, PETSC_FALSE);
573:     d->size_G = cMT;
574:     d->cX_in_G = d->cX_in_V;
575:   }

577:   return(0);
578: }


583: /* DvdMult_copy_func: 2 */
584: PetscErrorCode dvd_calcpairs_updateBV1(dvdDashboard *d, DvdReduction *r,
585:                                        DvdMult_copy_func **sr)
586: {
587:   PetscErrorCode  ierr;
588:   Vec             *W = d->W?d->W:d->V, *BV = d->BV?d->BV:d->V;


592:   if (!d->G || d->V_new_s == d->V_new_e) { return(0); }

594:   /* G = [G               W(old)'*BV(new);
595:           W(new)'*BV(old) W(new)'*BV(new) ],
596:      being old=0:V_new_s-1, new=V_new_s:V_new_e-1 */
597:   VecsMultS(d->G,d->sG,d->ldH,W-d->cX_in_G,d->V_new_s+d->cX_in_G,d->V_new_e+d->cX_in_G,BV-d->cX_in_G,d->V_new_s+d->cX_in_G,d->V_new_e+d->cX_in_G,r,(*sr)++);
598:   d->size_G = d->V_new_e+d->cX_in_G;

600:   return(0);
601: }

603: /* in complex, d->size_H real auxiliar values are needed */
606: PetscErrorCode dvd_calcpairs_projeig_eig(dvdDashboard *d)
607: {
608:   PetscErrorCode  ierr;
609:   PetscReal       *w;
610: #if defined(PETSC_USE_COMPLEX)
611:   PetscInt        i;
612: #endif


616:   /* S <- H */
617:   d->ldS = d->ldpX = d->size_H;
618:   SlepcDenseCopyTriang(d->S, DVD_MAT_LTRIANG, d->size_H, d->H, d->sH, d->ldH,
619:                               d->size_H, d->size_H);

621:   /* S = pX' * L * pX */
622: #if !defined(PETSC_USE_COMPLEX)
623:   w = d->eigr-d->cX_in_H;
624: #else
625:   w = (PetscReal*)d->auxS;
626: #endif
627:   EPSDenseHEP(d->size_H, d->S, d->ldS, w, d->pX);
628: #if defined(PETSC_USE_COMPLEX)
629:   for (i=0; i<d->size_H; i++) d->eigr[i-d->cX_in_H] = w[i];
630: #endif

632:   d->calcpairs_selectPairs = dvd_calcpairs_selectPairs_eig;

634:   return(0);
635: }


640: PetscErrorCode dvd_calcpairs_projeig_qz_std(dvdDashboard *d)
641: {
642:   PetscErrorCode  ierr;


646:   /* S <- H */
647:   d->ldS = d->ldpX = d->size_H;
648:   SlepcDenseCopyTriang(d->S, 0, d->size_H, d->H, d->sH, d->ldH,
649:                               d->size_H, d->size_H);

651:   /* S = pX' * H * pX */
652:   EPSDenseHessenberg(d->size_H, 0, d->S, d->ldS, d->pX);
653:   EPSDenseSchur(d->size_H, 0, d->S, d->ldS, d->pX, d->eigr-d->cX_in_H, d->eigi-d->cX_in_H);
654: 

656:   d->calcpairs_selectPairs = dvd_calcpairs_selectPairs_qz;

658:   return(0);
659: }

663: /*
664:   auxS(dgges) = size_H (beta) + 8*size_H+16 (work)
665:   auxS(zgges) = size_H (beta) + 1+2*size_H (work) + 8*size_H (rwork)
666: */
667: PetscErrorCode dvd_calcpairs_projeig_qz_gen(dvdDashboard *d)
668: {
669: #if defined(SLEPC_MISSING_LAPACK_GGES)
671:   SETERRQ(((PetscObject)(d->eps))->comm,PETSC_ERR_SUP,"GGES - Lapack routine is unavailable.");
672: #else
673:   PetscErrorCode  ierr;
674:   PetscScalar     *beta = d->auxS;
675: #if !defined(PETSC_USE_COMPLEX)
676:   PetscScalar     *auxS = beta + d->size_H;
677:   PetscBLASInt    n_auxS = d->size_auxS - d->size_H;
678: #else
679:   PetscReal       *auxR = (PetscReal*)(beta + d->size_H);
680:   PetscScalar     *auxS = (PetscScalar*)(auxR+8*d->size_H);
681:   PetscBLASInt    n_auxS = d->size_auxS - 9*d->size_H;
682: #endif
683:   PetscInt        i;
684:   PetscBLASInt    info,n,a;


694:   /* S <- H, T <- G */
695:   d->ldS = d->ldT = d->ldpX = d->ldpY = d->size_H;
696:   SlepcDenseCopyTriang(d->S, 0, d->size_H, d->H, d->sH, d->ldH,
697:                               d->size_H, d->size_H);
698:   SlepcDenseCopyTriang(d->T, 0, d->size_H, d->G, d->sG, d->ldH,
699:                               d->size_H, d->size_H);

701:   /* S = Z'*H*Q, T = Z'*G*Q */
702:   n = d->size_H;
703: #if !defined(PETSC_USE_COMPLEX)
704:   LAPACKgges_(d->pY?"V":"N", "V", "N", PETSC_NULL, &n, d->S, &n, d->T, &n,
705:               &a, d->eigr-d->cX_in_H, d->eigi-d->cX_in_H, beta, d->pY, &n, d->pX, &n,
706:               auxS, &n_auxS, PETSC_NULL, &info);
707: #else
708:   LAPACKgges_(d->pY?"V":"N", "V", "N", PETSC_NULL, &n, d->S, &n, d->T, &n,
709:               &a, d->eigr-d->cX_in_H, beta, d->pY, &n, d->pX, &n,
710:               auxS, &n_auxS, auxR, PETSC_NULL, &info);
711: #endif
712:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB, "Error in Lapack GGES %d", info);

714:   /* eigr[i] <- eigr[i] / beta[i] */
715:   for (i=0; i<d->size_H; i++)
716:     d->eigr[i-d->cX_in_H] /= beta[i],
717:     d->eigi[i-d->cX_in_H] /= beta[i];

719:   d->calcpairs_selectPairs = dvd_calcpairs_selectPairs_qz;

721:   return(0);
722: #endif
723: }

727: PetscErrorCode dvd_calcpairs_selectPairs_eig(dvdDashboard *d, PetscInt n)
728: {
729:   PetscErrorCode  ierr;


733:   EPSSortDenseHEP(d->eps, d->size_H, 0, d->eigr-d->cX_in_H, d->pX, d->ldpX);
734: 

736:   if (d->calcpairs_eigs_trans) {
737:     d->calcpairs_eigs_trans(d);
738:   }

740:   return(0);
741: }


746: PetscErrorCode dvd_calcpairs_selectPairs_qz(dvdDashboard *d, PetscInt n)
747: {
748:   PetscErrorCode  ierr;

751:   if ((d->ldpX != d->size_H) ||
752:       ( d->T &&
753:         ((d->ldS != d->ldT) || (d->ldpX != d->ldpY) ||
754:          (d->ldpX != d->size_H)) ) ) {
755:      SETERRQ(PETSC_COMM_SELF,1, "Error before ordering eigenpairs");
756:   }

758:   if (d->T) {
759:     EPSSortDenseSchurGeneralized(d->eps, d->size_H, 0, n, d->S, d->T,
760:                                         d->ldS, d->pY, d->pX, d->eigr-d->cX_in_H,
761:                                         d->eigi-d->cX_in_H);
762:   } else {
763:     EPSSortDenseSchur(d->eps, d->size_H, 0, d->S, d->ldS, d->pX,
764:                              d->eigr-d->cX_in_H, d->eigi-d->cX_in_H);
765:   }

767:   if (d->calcpairs_eigs_trans) {
768:     d->calcpairs_eigs_trans(d);
769:   }

771: #if defined(PETSC_USE_COMPLEX)
772:   if (d->T) {
773:     EPSCleanDenseSchur(d->size_H,0,d->S,d->ldS,d->T,d->ldT,d->eigi-d->cX_in_H,d->pX,d->ldpX,PETSC_TRUE);
774:   }
775: #endif

777:   return(0);
778: }


783: /* Compute the residual vectors R(i) <- (AV - BV*eigr(i))*pX(i), and also
784:    the norm associated to the Schur pair, where i = r_s..r_e
785: */
786: PetscErrorCode dvd_calcpairs_res_0(dvdDashboard *d, PetscInt r_s, PetscInt r_e,
787:                              Vec *R)
788: {
789:   PetscInt        i;
790:   PetscErrorCode  ierr;
791:   Vec             *BV = d->BV?d->BV:d->V;


795:   for (i=r_s; i<r_e; i++) {
796:     /* nX(i) <- ||X(i)|| */
797:     if (d->correctXnorm) {
798:       /* R(i) <- V*pX(i) */
799:       SlepcUpdateVectorsZ(&R[i-r_s], 0.0, 1.0,
800:         &d->V[-d->cX_in_H], d->size_V+d->cX_in_H,
801:         &d->pX[d->ldpX*(i+d->cX_in_H)], d->ldpX, d->size_H, 1);
802:       VecNorm(R[i-r_s], NORM_2, &d->nX[i]);
803:     } else
804:       d->nX[i] = 1.0;

806:     /* R(i-r_s) <- AV*pX(i) */
807:     SlepcUpdateVectorsZ(&R[i-r_s], 0.0, 1.0,
808:       &d->AV[-d->cX_in_H], d->size_AV+d->cX_in_H,
809:       &d->pX[d->ldpX*(i+d->cX_in_H)], d->ldpX, d->size_H, 1);

811:     /* R(i-r_s) <- R(i-r_s) - eigr(i)*BV*pX(i) */
812:     SlepcUpdateVectorsZ(&R[i-r_s], 1.0, -d->eigr[i+d->cX_in_H],
813:       &BV[-d->cX_in_H], d->size_V+d->cX_in_H,
814:       &d->pX[d->ldpX*(i+d->cX_in_H)], d->ldpX, d->size_H, 1);
815:   }

817:   d->calcpairs_proj_res(d, r_s, r_e, R);

819:   return(0);
820: }

824: PetscErrorCode dvd_calcpairs_proj_res(dvdDashboard *d, PetscInt r_s,
825:                                       PetscInt r_e, Vec *R)
826: {
827:   PetscInt        i;
828:   PetscErrorCode  ierr;
829:   PetscBool       lindep;
830:   Vec             *cX;


834:   /* If exists the BcX, R <- orth(BcX, R), nR[i] <- ||R[i]|| */
835:   if (d->BcX)
836:     cX = d->BcX;

838:   /* If exists left subspace, R <- orth(cY, R), nR[i] <- ||R[i]|| */
839:   else if (d->cY)
840:     cX = d->cY;

842:   /* If fany configurations, R <- orth(cX, R), nR[i] <- ||R[i]|| */
843:   else if (!(DVD_IS(d->sEP, DVD_EP_STD) && DVD_IS(d->sEP, DVD_EP_HERMITIAN)))
844:     cX = d->cX;

846:   /* Otherwise, nR[i] <- ||R[i]|| */
847:   else
848:     cX = PETSC_NULL;

850:   if (cX) for (i=0; i<r_e-r_s; i++) {
851:     IPOrthogonalize(d->ipI, 0, PETSC_NULL, d->size_cX, PETSC_NULL,
852:                            cX, R[i], PETSC_NULL, &d->nR[r_s+i], &lindep);
853: 
854:     if(lindep || (d->nR[r_s+i] < PETSC_MACHINE_EPSILON)) {
855:       PetscInfo2(d->eps,"The computed eigenvector residual %D is too low, %G!\n",r_s+i,d->nR[r_s+i]);
856:     }

858:   } else {
859:     for(i=0; i<r_e-r_s; i++) {
860:       VecNormBegin(R[i],NORM_2,&d->nR[r_s+i]);
861:     }
862:     for(i=0; i<r_e-r_s; i++) {
863:       VecNormEnd(R[i],NORM_2,&d->nR[r_s+i]);
864:     }
865:   }

867:   return(0);
868: }

872: /* Compute the residual vectors R(i) <- (AV - BV*eigr(i))*pX(i), and also
873:    the norm associated to the eigenpair, where i = r_s..r_e
874:    R, vectors of Vec of size r_e-r_s,
875:    auxV, PetscMax(r_e+cX_in_H, 2*(r_e-r_s)) vectors,
876:    auxS, auxiliar vector of size (d->size_cX+r_e)^2+6(d->size_cX+r_e)+(r_e-r_s)*d->size_H
877: */
878: PetscErrorCode dvd_calcpairs_eig_res_0(dvdDashboard *d,PetscInt r_s,PetscInt r_e,Vec *R)
879: {
880:   PetscInt        i,ldpX,size_in;
881:   PetscErrorCode  ierr;
882:   Vec             *Bx;
883:   PetscScalar     *pX,*pX0;
884:   DvdReduction    r;
885:   DvdReductionChunk
886:                   ops[2];
887:   DvdMult_copy_func
888:                   sr[2];
889: #if !defined(PETSC_USE_COMPLEX)
890:   PetscScalar     b[8];
891:   Vec             X[4];
892: #endif


896:   /* Quick return */
897:   if (!d->cS) { return(0); }

899:   size_in = (d->size_cX+r_e)*(d->cX_in_AV+r_e)*(d->cT?2:1);
900:   /* Check consistency */
901:   if (d->size_auxV < PetscMax(2*(r_e-r_s),d->cX_in_AV+r_e) || d->size_auxS <
902:       (d->size_cX+r_e)*(d->size_cX+r_e) /* pX */ + PetscMax(PetscMax(
903:         (d->size_cX+r_e)*6 /* dvd_compute_eigenvectors */,
904:         d->size_H*(r_e-r_s) /* pX0 */),
905:         2*size_in /* SlepcAllReduceSum */ )) { SETERRQ(PETSC_COMM_SELF,1, "Consistency broken!"); }

907:   /* Prepare reductions */
908:   SlepcAllReduceSumBegin(ops,2,d->auxS,d->auxS+size_in,size_in,&r,((PetscObject)d->V[0])->comm);

910:   /* auxV <- AV * pX(0:r_e+cX_in_H) */
911:   SlepcUpdateVectorsZ(d->auxV,0.0,1.0,d->AV-d->cX_in_AV,d->size_AV+d->cX_in_AV,d->pX,d->ldpX,d->size_H,d->cX_in_AV+r_e);

913:   /* cS(:, size_cS:) <- cX' * auxV */
914:   VecsMultS(&d->cS[d->ldcS*d->size_cS],0,d->ldcS,d->cY?d->cY:d->cX,0,d->size_cX+r_e,d->auxV,0,d->cX_in_AV+r_e,&r,&sr[0]);

916:   if (d->cT) {
917:     /* R <- BV * pX(0:r_e+cX_in_H) */
918:     SlepcUpdateVectorsZ(d->auxV,0.0,1.0,d->BV-d->cX_in_BV,d->size_BV+d->cX_in_BV,d->pX,d->ldpX,d->size_G,d->cX_in_BV+r_e);
919: 
920:     /* cS(:, size_cS:) <- cX' * auxV */
921:     VecsMultS(&d->cT[d->ldcT*d->size_cT],0,d->ldcT,d->cY?d->cY:d->cX,0,d->size_cY+r_e,d->auxV,0,d->cX_in_BV+r_e,&r,&sr[1]);
922:   }

924:   /* Do reductions */
925:   SlepcAllReduceSumEnd(&r);

927:   /* qX <- eig(S,T) */
928:   pX = d->auxS; d->auxS+= (d->size_cX+r_e)*(d->size_cX+r_e); d->size_auxS -= (d->size_cX+r_e)*(d->size_cX+r_e);
929:   ldpX = d->size_cX+r_e;
930:   pX0 = d->auxS;
931:   EPSCleanDenseSchur(d->size_cX+r_e,0,d->cS,d->ldcS,d->cT,d->ldcT,d->ceigi,pX,ldpX,PETSC_FALSE);
932:   dvd_compute_eigenvectors(d->size_cX+r_e,d->cS,d->ldcS,d->cT,d->ldcT,pX,ldpX,PETSC_NULL,0,d->auxS,d->size_auxS,PETSC_TRUE);

934:   /* pX[i] <- pX[i] / ||pX[i]|| */
935:   pX = &pX[ldpX*d->size_cX+r_s];
936:   SlepcDenseNorm(pX,ldpX,d->size_cX+r_e,r_e-r_s,d->eigi+r_s);

938:   /* pX0 <- d->pX(0:d->cX_in_AV+r_e-1) * pX(size_cX-cX_in_H:) */
939:   SlepcDenseMatProd(pX0,d->size_H,0.0,1.0,d->pX,d->ldpX,d->size_H,d->cX_in_AV+r_e,PETSC_FALSE,&pX[d->size_cX-d->cX_in_H],ldpX,d->cX_in_AV+r_e,r_e-r_s,PETSC_FALSE);

941:   /* auxV <- cX(0:size_cX-cX_in_AV)*pX + V*pX0 */
942:   SlepcUpdateVectorsZ(d->auxV,0.0,1.0,d->cX,d->size_cX-d->cX_in_AV,pX,ldpX,d->size_cX-d->cX_in_AV,r_e-r_s);
943:   SlepcUpdateVectorsZ(d->auxV,d->size_cX-d->cX_in_AV==0?0.0:1.0,1.0,d->V-d->cX_in_AV,d->size_V+d->cX_in_AV,pX0,d->size_H,d->size_H,r_e-r_s);
944:   d->auxS-= (d->size_cX+r_e)*(d->size_cX+r_e); d->size_auxS += (d->size_cX+r_e)*(d->size_cX+r_e);
945:   /* R <- A*auxV */
946:   for (i=0; i<r_e-r_s; i++) {
947:     MatMult(d->A,d->auxV[i],R[i]);
948:   }
949:   /* Bx <- B*auxV */
950:   if (d->B) {
951:     Bx = &d->auxV[r_e-r_s];
952:     for (i=0; i<r_e-r_s; i++) {
953:       MatMult(d->B,d->auxV[i],Bx[i]);
954:     }
955:   } else {
956:     Bx = d->auxV;
957:   }
958:   /* R <- (A - eig*B)*V*pX */
959:   for(i=0; i<r_e-r_s; i++) {
960: #if !defined(PETSC_USE_COMPLEX)
961:     if (d->eigi[r_s+i] != 0.0) {
962:       /* [Ax_i Ax_i+1 Bx_i Bx_i+1]*= [   1        0 
963:                                          0        1
964:                                       -eigr_i -eigi_i
965:                                        eigi_i -eigr_i] */
966:       b[0] = b[5] = 1.0;
967:       b[2] = b[7] = -d->eigr[r_s+i];
968:       b[6] = -(b[3] = d->eigi[r_s+i]);
969:       b[1] = b[4] = 0.0;
970:       X[0] = R[i]; X[1] = R[i+1]; X[2] = Bx[i]; X[3] = Bx[i+1];
971:       SlepcUpdateVectorsD(X,4,1.0,b,4,4,2,d->auxS,d->size_auxS);
972:       i++;
973:     } else
974: #endif
975:     {
976:       /* R <- Ax -eig*Bx */
977:       VecAXPBY(R[i], -d->eigr[r_s+i], 1.0, Bx[i]);
978:     }
979:   }

981:   /* nR <- ||R|| */
982:   for(i=0; i<r_e-r_s; i++) {
983:     VecNormBegin(R[i],NORM_2,&d->nR[r_s+i]);
984:   }
985:   for(i=0; i<r_e-r_s; i++) {
986:     VecNormEnd(R[i],NORM_2,&d->nR[r_s+i]);
987:   }

989:   return(0);
990: }


993: /**** Pattern routines ********************************************************/

995: /* BV <- BV*MTX */
998: PETSC_STATIC_INLINE PetscErrorCode dvd_calcpairs_updateBV0_gen(dvdDashboard *d,Vec *real_BV,PetscInt *size_cBV,Vec **BV,PetscInt *size_BV,PetscInt *max_size_BV,PetscBool BV_shift,PetscInt *cX_in_proj,PetscScalar *MTX)
999: {
1000:   PetscErrorCode  ierr;
1001:   PetscInt        cMT, rm, cp, tra_s, i;
1002:   Vec             *nBV;


1006:   if (!real_BV || !*BV || (d->V_tra_s == 0 && d->V_tra_e == 0)) { return(0); }

1008:   if (d->V_tra_s > d->max_cX_in_proj && !BV_shift) {
1009:     tra_s = PetscMax(d->V_tra_s-d->max_cX_in_proj, 0);
1010:     cMT = d->V_tra_e - tra_s;
1011:     rm = d->V_tra_s - tra_s;
1012:     cp = PetscMin(d->max_cX_in_proj - rm, *cX_in_proj);
1013:     nBV = real_BV+d->max_cX_in_proj;
1014:     /* BV(-cp-rm:-1-rm) <- BV(-cp:-1) */
1015:     for (i=-cp; i<0; i++) {
1016:       VecCopy((*BV)[i], nBV[i-rm]);
1017:     }
1018:     /* BV(-rm:) <- BV*MTX(tra_s:V_tra_e-1) */
1019:     SlepcUpdateVectorsZ(&nBV[-rm], 0.0, 1.0, *BV-*cX_in_proj, *size_BV+*cX_in_proj, &MTX[d->ldMTX*tra_s], d->ldMTX, d->size_MT, cMT);
1020:     *size_BV = d->V_tra_e  - d->V_tra_s;
1021:     *max_size_BV-= nBV - *BV;
1022:     *BV = nBV;
1023:     if (cX_in_proj && d->max_cX_in_proj>0) *cX_in_proj = cp+rm;
1024:   } else if (d->V_tra_s <= d->max_cX_in_proj || BV_shift) {
1025:     /* [BcX BV] <- [BcX BV*MTX] */
1026:     SlepcUpdateVectorsZ(*BV-*cX_in_proj, 0.0, 1.0, *BV-*cX_in_proj, *size_BV+*cX_in_proj, MTX, d->ldMTX, d->size_MT, d->V_tra_e);
1027:     *BV+= d->V_tra_s-*cX_in_proj;
1028:     *max_size_BV-= d->V_tra_s-*cX_in_proj;
1029:     *size_BV = d->V_tra_e  - d->V_tra_s;
1030:     if (size_cBV && BV_shift) *size_cBV = *BV - real_BV;
1031:     if (d->max_cX_in_proj>0) *cX_in_proj = PetscMin(*BV - real_BV, d->max_cX_in_proj);
1032:   } else { /* !BV_shift */
1033:     /* BV <- BV*MTX(V_tra_s:) */
1034:     SlepcUpdateVectorsZ(*BV, 0.0, 1.0, *BV, *size_BV,
1035:       &MTX[d->V_tra_s*d->ldMTX], d->ldMTX, d->size_MT, d->V_tra_e-d->V_tra_s);
1036: 
1037:     *size_BV = d->V_tra_e - d->V_tra_s;
1038:   }

1040:   return(0);
1041: }