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_proj_res(dvdDashboard *d, PetscInt r_s,
 50:                                       PetscInt r_e, Vec *R);
 51: PetscErrorCode dvd_calcpairs_updateV0(dvdDashboard *d, DvdReduction *r,
 52:                                       DvdMult_copy_func **sr);
 53: PetscErrorCode dvd_calcpairs_updateV1(dvdDashboard *d);
 54: PetscErrorCode dvd_calcpairs_updateW0(dvdDashboard *d, DvdReduction *r,
 55:                                       DvdMult_copy_func **sr);
 56: PetscErrorCode dvd_calcpairs_updateW1(dvdDashboard *d);
 57: PetscErrorCode dvd_calcpairs_updateAV0(dvdDashboard *d);
 58: PetscErrorCode dvd_calcpairs_updateAV1(dvdDashboard *d, DvdReduction *r,
 59:                                        DvdMult_copy_func **sr);
 60: PetscErrorCode dvd_calcpairs_updateBV0(dvdDashboard *d);
 61: PetscErrorCode dvd_calcpairs_updateBV1(dvdDashboard *d, DvdReduction *r,
 62:                                        DvdMult_copy_func **sr);
 63: 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);

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


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

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

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

187:     d->calcPairs = dvd_calcpairs_proj;
188:     d->calcpairs_residual = dvd_calcpairs_res_0;
189:     d->calcpairs_proj_res = dvd_calcpairs_proj_res;
190:     d->calcpairs_selectPairs = PETSC_NULL;
191:     d->ipI = ipI;
192:     DVD_FL_ADD(d->startList, dvd_calcpairs_qz_start);
193:   }

195:   return(0);
196: }


201: PetscErrorCode dvd_calcpairs_qz_start(dvdDashboard *d)
202: {
203:   PetscBool       std_probl, her_probl;
204:   PetscInt        i;


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

211:   d->size_V = 0;
212:   d->V = d->real_V;
213:   d->cX = d->real_V;
214:   d->size_cX = 0;
215:   d->max_size_V = d->size_real_V;
216:   d->W = d->real_W;
217:   d->max_size_W = d->size_real_W;
218:   d->size_W = 0;
219:   d->size_AV = 0;
220:   d->AV = d->real_AV;
221:   d->max_size_AV = d->size_real_AV;
222:   d->size_H = 0;
223:   d->H = d->real_H;
224:   if (d->cS) for (i=0; i<d->max_size_cS*d->max_size_cS; i++) d->cS[i] = 0.0;
225:   d->size_BV = 0;
226:   d->BV = d->real_BV;
227:   d->max_size_BV = d->size_real_BV;
228:   d->size_G = 0;
229:   d->G = d->real_G;
230:   if (d->cT) for (i=0; i<d->max_size_cS*d->max_size_cS; i++) d->cT[i] = 0.0;
231:   d->cY = d->B && !her_probl ? d->W : PETSC_NULL;
232:   d->BcX = d->orthoV_type == DVD_ORTHOV_I && d->B && her_probl ? d->BcX : PETSC_NULL;
233:   d->size_cY = 0;
234:   d->size_BcX = 0;
235:   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:   static const PetscInt 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->V_tra_s*(d->cT?2:(d->cS?1:0)) + /* updateV0,W0 */
261:     d->size_H*d->V_tra_e*(!stdp?2:1) + /* updateAV1,BV1 */
262:     (d->size_H*(d->V_new_e-d->V_new_s)*2+
263:       (d->V_new_e-d->V_new_s)*(d->V_new_e-d->V_new_s))*(!stdp?2:1); /* updateAV0,BV0 */
264: 
265:   out = in+size_in;

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

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

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

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

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

313:   /* Perform the transformation on the projected problem */
314:   if (d->calcpairs_proj_trans) {
315:     d->calcpairs_proj_trans(d);
316:   }

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

321:   /* Solve the projected problem */
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:   }

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

343:   return(0);
344: }

346: /**** Basic routines **********************************************************/

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


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

361:   /* cX <- [cX V*MT(0:V_tra_s-1)], V <- V*MT(V_tra_s:V_tra_e) */
362:   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);

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

369:     /* auxV <- AV * MTX(0:V_tra_e-1) */
370:     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-d->max_cX_in_proj);

372:     /* cS(:, size_cS:) <- cX' * auxV */
373:     rm = d->size_cX>=d->nev?0:d->max_cX_in_proj;
374:     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)++);
375:     d->size_cS+= d->V_tra_s-rm;
376:   }
377: 
378:   return(0);
379: }


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


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

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

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

410:   return(0);
411: }

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


424:   if (!d->W || (d->V_tra_s == 0 && d->V_tra_e == 0)) { return(0); }

426:   /* cY <- [cY W*MTY(0:V_tra_s-1)], W <- W*MTY(V_tra_s:V_tra_e) */
427:   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);

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

434:     /* auxV <- AV * MTX(0:V_tra_e-1) */
435:     rm = d->size_cX>=d->nev?0:d->max_cX_in_proj;
436:     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-d->max_cX_in_proj);

438:     /* cS(:, size_cS:) <- cY' * auxV */
439:     VecsMultS(&d->cS[d->ldcS*d->size_cS], 0, d->ldcS, d->cY, 0, d->size_cY-rm, d->auxV, 0, d->V_tra_s-rm, r, (*sr)++);

441:     /* auxV <- BV * MTX(0:V_tra_e-1) */
442:     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-d->max_cX_in_proj);

444:     /* cT(:, size_cS:) <- cY' * auxV */
445:     VecsMultS(&d->cT[d->ldcS*d->size_cS], 0, d->ldcS, d->cY, 0, d->size_cY-rm, d->auxV, 0, d->V_tra_s-rm, r, (*sr)++);
446:     d->size_cS+= d->V_tra_s-rm;
447:     d->size_cT+= d->V_tra_s-rm;
448:   }

450:   return(0);
451: }


456: /* auxS: size_cX+V_new_e+1 */
457: PetscErrorCode dvd_calcpairs_updateW1(dvdDashboard *d)
458: {
459:   PetscErrorCode  ierr;


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

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

468:   /* Update W */
469:   d->calcpairs_W(d);

471:   /* W <- gs([cY W(0:V_new_s-1)], W(V_new_s:V_new_e-1)) */
472:   dvd_orthV(d->ipW, PETSC_NULL, 0, d->cY, d->size_cY, d->W, d->V_new_s,
473:                    d->V_new_e, d->auxS, d->eps->rand);
474: 
475:   d->size_W = d->V_new_e;

477:   return(0);
478: }

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


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

493:   /* AV(V_tra_s-cp-1:) = cAV*MTX(V_tra_s:) */
494:   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);
495:   tra_s = PetscMax(d->V_tra_s-d->max_cX_in_proj, 0);
496:   cMT = d->V_tra_e - tra_s;
497:   rm = d->V_tra_s - tra_s;
498:   cp = PetscMin(d->max_cX_in_proj - rm, d->cX_in_H);

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 = cp+rm;

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, rm, cp, 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:     rm = d->V_tra_s - tra_s;
572:     cp = PetscMin(d->max_cX_in_proj - rm, d->cX_in_G);
573:     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);
574:     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);
575:     d->size_G = cMT;
576:     d->cX_in_G = cp+rm;
577:   }

579:   return(0);
580: }


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


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

596:   /* G = [G               W(old)'*BV(new);
597:           W(new)'*BV(old) W(new)'*BV(new) ],
598:      being old=0:V_new_s-1, new=V_new_s:V_new_e-1 */
599:   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)++);
600:   d->size_G = d->V_new_e+d->cX_in_G;

602:   return(0);
603: }

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


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

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

634:   d->calcpairs_selectPairs = dvd_calcpairs_selectPairs_eig;

636:   return(0);
637: }


642: PetscErrorCode dvd_calcpairs_projeig_qz_std(dvdDashboard *d)
643: {
644:   PetscErrorCode  ierr;


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

653:   /* S = pX' * H * pX */
654:   EPSDenseHessenberg(d->size_H, 0, d->S, d->ldS, d->pX);
655:   EPSDenseSchur(d->size_H, 0, d->S, d->ldS, d->pX, d->eigr-d->cX_in_H, d->eigi-d->cX_in_H);
656: 

658:   d->calcpairs_selectPairs = dvd_calcpairs_selectPairs_qz;

660:   return(0);
661: }

665: /*
666:   auxS(dgges) = size_H (beta) + 8*size_H+16 (work)
667:   auxS(zgges) = size_H (beta) + 1+2*size_H (work) + 8*size_H (rwork)
668: */
669: PetscErrorCode dvd_calcpairs_projeig_qz_gen(dvdDashboard *d)
670: {
671: #if defined(SLEPC_MISSING_LAPACK_GGES)
673:   SETERRQ(((PetscObject)(d->eps))->comm,PETSC_ERR_SUP,"GGES - Lapack routine is unavailable.");
674: #else
675:   PetscErrorCode  ierr;
676:   PetscScalar     *beta = d->auxS;
677: #if !defined(PETSC_USE_COMPLEX)
678:   PetscScalar     *auxS = beta + d->size_H;
679:   PetscBLASInt    n_auxS = d->size_auxS - d->size_H;
680: #else
681:   PetscReal       *auxR = (PetscReal*)(beta + d->size_H);
682:   PetscScalar     *auxS = (PetscScalar*)(auxR+8*d->size_H);
683:   PetscBLASInt    n_auxS = d->size_auxS - 9*d->size_H;
684: #endif
685:   PetscInt        i;
686:   PetscBLASInt    info,n,a;

689:   /* S <- H, T <- G */
690:   d->ldS = d->ldT = d->ldpX = d->ldpY = d->size_H;
691:   SlepcDenseCopyTriang(d->S, 0, d->size_H, d->H, d->sH, d->ldH,
692:                               d->size_H, d->size_H);
693:   SlepcDenseCopyTriang(d->T, 0, d->size_H, d->G, d->sG, d->ldH,
694:                               d->size_H, d->size_H);

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

709:   /* eigr[i] <- eigr[i] / beta[i] */
710:   for (i=0; i<d->size_H; i++)
711:     d->eigr[i-d->cX_in_H] /= beta[i],
712:     d->eigi[i-d->cX_in_H] /= beta[i];

714:   d->calcpairs_selectPairs = dvd_calcpairs_selectPairs_qz;

716:   return(0);
717: #endif
718: }

722: PetscErrorCode dvd_calcpairs_selectPairs_eig(dvdDashboard *d, PetscInt n)
723: {
724:   PetscErrorCode  ierr;


728:   EPSSortDenseHEP(d->eps, d->size_H, 0, d->eigr-d->cX_in_H, d->pX, d->ldpX);
729: 

731:   if (d->calcpairs_eigs_trans) {
732:     d->calcpairs_eigs_trans(d);
733:   }

735:   return(0);
736: }


741: PetscErrorCode dvd_calcpairs_selectPairs_qz(dvdDashboard *d, PetscInt n)
742: {
743:   PetscErrorCode  ierr;
744: #if defined(PETSC_USE_COMPLEX)
745:   PetscScalar     s;
746:   PetscInt        i, j;
747: #endif

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

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

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

770:   /* Some functions need the diagonal elements in T be real */
771: #if defined(PETSC_USE_COMPLEX)
772:   if (d->T) for(i=0; i<d->size_H; i++)
773:     if (PetscImaginaryPart(d->T[d->ldT*i+i]) != 0.0) {
774:       s = PetscConj(d->T[d->ldT*i+i])/PetscAbsScalar(d->T[d->ldT*i+i]);
775:       for(j=0; j<=i; j++)
776:         d->T[d->ldT*i+j] = PetscRealPart(d->T[d->ldT*i+j]*s),
777:         d->S[d->ldS*i+j]*= s;
778:       for(j=0; j<d->size_H; j++) d->pX[d->ldpX*i+j]*= s;
779:     }
780: #endif

782:   return(0);
783: }


788: /* Compute the residual vectors R(i) <- (AV - BV*eigr(i))*pX(i), and also
789:    the norm, where i = r_s..r_e
790: */
791: PetscErrorCode dvd_calcpairs_res_0(dvdDashboard *d, PetscInt r_s, PetscInt r_e,
792:                              Vec *R)
793: {
794:   PetscInt        i;
795:   PetscErrorCode  ierr;
796:   Vec             *BV = d->BV?d->BV:d->V;


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

811:     /* R(i-r_s) <- AV*pX(i) */
812:     SlepcUpdateVectorsZ(&R[i-r_s], 0.0, 1.0,
813:       &d->AV[-d->cX_in_H], d->size_AV+d->cX_in_H,
814:       &d->pX[d->ldpX*(i+d->cX_in_H)], d->ldpX, d->size_H, 1);

816:     /* R(i-r_s) <- R(i-r_s) - eigr(i)*BV*pX(i) */
817:     SlepcUpdateVectorsZ(&R[i-r_s], 1.0, -d->eigr[i+d->cX_in_H],
818:       &BV[-d->cX_in_H], d->size_V+d->cX_in_H,
819:       &d->pX[d->ldpX*(i+d->cX_in_H)], d->ldpX, d->size_H, 1);
820:   }

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

824:   return(0);
825: }

829: PetscErrorCode dvd_calcpairs_proj_res(dvdDashboard *d, PetscInt r_s,
830:                                       PetscInt r_e, Vec *R)
831: {
832:   PetscInt        i;
833:   PetscErrorCode  ierr;
834:   PetscBool       lindep;
835:   Vec             *cX;


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

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

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

851:   /* Otherwise, nR[i] <- ||R[i]|| */
852:   else
853:     cX = PETSC_NULL;

855:   if (cX) for (i=0; i<r_e-r_s; i++) {
856:     IPOrthogonalize(d->ipI, 0, PETSC_NULL, d->size_cX, PETSC_NULL,
857:                            cX, R[i], PETSC_NULL, &d->nR[r_s+i], &lindep);
858: 
859:     if(lindep || (d->nR[r_s+i] < PETSC_MACHINE_EPSILON)) {
860:       PetscInfo2(d->eps,"The computed eigenvector residual %D is too low, %G!\n",r_s+i,d->nR[r_s+i]);
861:     }

863:   } else for(i=0; i<r_e-r_s; i++) {
864:     VecNorm(R[i], NORM_2, &d->nR[r_s+i]);
865:   }

867:   return(0);
868: }

870: /**** Pattern routines ********************************************************/

872: /* BV <- BV*MTX */
875: 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)
876: {
877:   PetscErrorCode  ierr;
878:   PetscInt        cMT, rm, cp, tra_s, i;
879:   Vec             *nBV;


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

885:   if (d->V_tra_s > d->max_cX_in_proj && !BV_shift) {
886:     tra_s = PetscMax(d->V_tra_s-d->max_cX_in_proj, 0);
887:     cMT = d->V_tra_e - tra_s;
888:     rm = d->V_tra_s - tra_s;
889:     cp = PetscMin(d->max_cX_in_proj - rm, *cX_in_proj);
890:     nBV = real_BV+d->max_cX_in_proj;
891:     /* BV(-cp-rm:-1-rm) <- BV(-cp:-1) */
892:     for (i=-cp; i<0; i++) {
893:       VecCopy((*BV)[i], nBV[i-rm]);
894:     }
895:     /* BV(-rm:) <- BV*MTX(tra_s:V_tra_e-1) */
896:     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);
897:     *size_BV = d->V_tra_e  - d->V_tra_s;
898:     *max_size_BV-= nBV - *BV;
899:     *BV = nBV;
900:     if (cX_in_proj && d->max_cX_in_proj>0) *cX_in_proj = cp+rm;
901:   } else if (d->V_tra_s <= d->max_cX_in_proj || BV_shift) {
902:     /* [BcX BV] <- [BcX BV*MTX] */
903:     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);
904:     *BV+= d->V_tra_s-*cX_in_proj;
905:     *max_size_BV-= d->V_tra_s-*cX_in_proj;
906:     *size_BV = d->V_tra_e  - d->V_tra_s;
907:     if (size_cBV && BV_shift) *size_cBV = *BV - real_BV;
908:     if (d->max_cX_in_proj>0) *cX_in_proj = PetscMin(*BV - real_BV, d->max_cX_in_proj);
909:   } else { /* !BV_shift */
910:     /* BV <- BV*MTX(V_tra_s:) */
911:     SlepcUpdateVectorsZ(*BV, 0.0, 1.0, *BV, *size_BV,
912:       &MTX[d->V_tra_s*d->ldMTX], d->ldMTX, d->size_MT, d->V_tra_e-d->V_tra_s);
913: 
914:     *size_BV = d->V_tra_e - d->V_tra_s;
915:   }

917:   return(0);
918: }