Actual source code: bvorthog.c

slepc-3.7.0 2016-05-16
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  1: /*
  2:    BV orthogonalization routines.

  4:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  5:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  6:    Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain

  8:    This file is part of SLEPc.

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

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

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

 24: #include <slepc/private/bvimpl.h>          /*I   "slepcbv.h"   I*/
 25: #include <slepcblaslapack.h>

 29: /*
 30:    BVOrthogonalizeMGS1 - Compute one step of Modified Gram-Schmidt
 31: */
 32: static PetscErrorCode BVOrthogonalizeMGS1(BV bv,PetscInt k,Vec v,PetscBool *which,PetscScalar *H)
 33: {
 35:   PetscInt       i;
 36:   PetscScalar    dot;
 37:   Vec            vi,z;

 40:   z = v;
 41:   for (i=-bv->nc;i<k;i++) {
 42:     if (which && i>=0 && !which[i]) continue;
 43:     BVGetColumn(bv,i,&vi);
 44:     /* h_i = ( v, v_i ) */
 45:     if (bv->matrix) {
 46:       BV_IPMatMult(bv,v);
 47:       z = bv->Bx;
 48:     }
 49:     VecDot(z,vi,&dot);
 50:     /* v <- v - h_i v_i */
 51:     if (bv->indef) dot /= bv->omega[bv->nc+i];
 52:     VecAXPY(v,-dot,vi);
 53:     if (bv->indef) dot *= bv->omega[bv->nc+i];
 54:     if (H) H[bv->nc+i] += dot;
 55:     BVRestoreColumn(bv,i,&vi);
 56:   }
 57:   return(0);
 58: }

 62: /*
 63:    BVOrthogonalizeCGS1 - Compute |v'| (estimated), |v| and one step of CGS with
 64:    only one global synchronization
 65: */
 66: PetscErrorCode BVOrthogonalizeCGS1(BV bv,PetscInt j,Vec v,PetscScalar *H,PetscReal *onorm,PetscReal *norm)
 67: {
 69:   PetscInt       i;
 70:   PetscReal      sum,nrm,beta;
 71:   Vec            w=v;

 74:   /* h = W^* v ; alpha = (v, v) */
 75:   bv->k = j;
 76:   if (onorm || norm) {
 77:     if (!v) {
 78:       bv->k++;
 79:       BVGetColumn(bv,j,&w);
 80:     }
 81:     BVDotVec(bv,w,H);
 82:     if (!v) {
 83:       BVRestoreColumn(bv,j,&w);
 84:       bv->k--;
 85:       BV_SafeSqrt(bv,H[bv->nc+j],&beta);
 86:     } else {
 87:       BVNormVec(bv,w,NORM_2,&beta);
 88:     }
 89:   } else {
 90:     if (!v) { BVDotColumn(bv,j,H); }
 91:     else { BVDotVec(bv,w,H); }
 92:   }

 94:   /* q = v - V h */
 95:   if (bv->indef) {
 96:     for (i=0;i<bv->nc+j;i++) H[i] /= bv->omega[i];  /* apply inverse of signature */
 97:   }
 98:   if (!v) { BVMultColumn(bv,-1.0,1.0,j,H); }
 99:   else { BVMultVec(bv,-1.0,1.0,w,H); }
100:   if (bv->indef) {
101:     for (i=0;i<bv->nc+j;i++) H[i] *= bv->omega[i];  /* revert signature */
102:   }

104:   /* compute |v| */
105:   if (onorm) *onorm = beta;

107:   if (bv->indef) {
108:     if (!v) { BVNormColumn(bv,j,NORM_2,&nrm); }
109:     else { BVNormVec(bv,w,NORM_2,&nrm); }
110:     if (norm) *norm = nrm;
111:     bv->omega[bv->nc+j] = (nrm<0.0)? -1.0: 1.0;
112:   } else if (norm) {
113:     /* estimate |v'| from |v| */
114:     sum = 0.0;
115:     for (i=0;i<bv->nc+j;i++) sum += PetscRealPart(H[i]*PetscConj(H[i]));
116:     *norm = beta*beta-sum;
117:     if (*norm <= 0.0) {
118:       if (!v) { BVNormColumn(bv,j,NORM_2,norm); }
119:       else { BVNormVec(bv,w,NORM_2,norm); }
120:     } else *norm = PetscSqrtReal(*norm);
121:   }
122:   return(0);
123: }

127: /*
128:   BVOrthogonalizeMGS - Orthogonalize with modified Gram-Schmidt
129: */
130: static PetscErrorCode BVOrthogonalizeMGS(BV bv,PetscInt j,Vec v,PetscBool *which,PetscScalar *H,PetscReal *norm,PetscBool *lindep)
131: {
133:   PetscReal      onrm,nrm;
134:   PetscInt       k,l;
135:   Vec            w;

138:   if (v) {
139:     w = v;
140:     k = bv->k;
141:   } else {
142:     BVGetColumn(bv,j,&w);
143:     k = j;
144:   }
145:   PetscMemzero(bv->h,(bv->nc+k)*sizeof(PetscScalar));
146:   switch (bv->orthog_ref) {

148:   case BV_ORTHOG_REFINE_IFNEEDED:
149:     /* first step */
150:     BVNormVec(bv,w,NORM_2,&onrm);
151:     BVOrthogonalizeMGS1(bv,k,w,which,bv->h);
152:     BVNormVec(bv,w,NORM_2,&nrm);
153:     /* ||q|| < eta ||h|| */
154:     l = 1;
155:     while (l<3 && nrm && nrm < bv->orthog_eta*onrm) {
156:       l++;
157:       onrm = nrm;
158:       BVOrthogonalizeMGS1(bv,k,w,which,bv->c);
159:       BVNormVec(bv,w,NORM_2,&nrm);
160:     }
161:     if (lindep) *lindep = PetscNot(nrm >= bv->orthog_eta*onrm);
162:     break;

164:   case BV_ORTHOG_REFINE_NEVER:
165:     BVOrthogonalizeMGS1(bv,k,w,which,bv->h);
166:     /* compute |v| */
167:     if (norm || lindep) {
168:       BVNormVec(bv,w,NORM_2,&nrm);
169:     }
170:     /* linear dependence check: just test for exactly zero norm */
171:     if (lindep) *lindep = PetscNot(nrm);
172:     break;

174:   case BV_ORTHOG_REFINE_ALWAYS:
175:     /* first step */
176:     BVOrthogonalizeMGS1(bv,k,w,which,bv->h);
177:     if (lindep) {
178:       BVNormVec(bv,w,NORM_2,&onrm);
179:     }
180:     /* second step */
181:     BVOrthogonalizeMGS1(bv,k,w,which,bv->h);
182:     if (norm || lindep) {
183:       BVNormVec(bv,w,NORM_2,&nrm);
184:     }
185:     if (lindep) *lindep = PetscNot(nrm && nrm >= bv->orthog_eta*onrm);
186:     break;
187:   }
188:   if (bv->indef) {
189:     BVNormVec(bv,w,NORM_2,&nrm);
190:     bv->omega[bv->nc+j] = (nrm<0.0)? -1.0: 1.0;
191:   }
192:   if (!v) { BVRestoreColumn(bv,j,&w); }
193:   if (norm) *norm = nrm;
194:   return(0);
195: }

199: /*
200:   BVOrthogonalizeCGS - Orthogonalize with classical Gram-Schmidt
201: */
202: static PetscErrorCode BVOrthogonalizeCGS(BV bv,PetscInt j,Vec v,PetscScalar *H,PetscReal *norm,PetscBool *lindep)
203: {
205:   PetscReal      onrm,nrm;
206:   PetscInt       i,k,l;

209:   if (v) k = bv->k;
210:   else k = j;
211:   switch (bv->orthog_ref) {

213:   case BV_ORTHOG_REFINE_IFNEEDED:
214:     BVOrthogonalizeCGS1(bv,k,v,bv->h,&onrm,&nrm);
215:     /* ||q|| < eta ||h|| */
216:     l = 1;
217:     while (l<3 && nrm && nrm < bv->orthog_eta*onrm) {
218:       l++;
219:       BVOrthogonalizeCGS1(bv,k,v,bv->c,&onrm,&nrm);
220:       for (i=0;i<bv->nc+k;i++) bv->h[i] += bv->c[i];
221:     }
222:     if (norm) *norm = nrm;
223:     if (lindep) *lindep = PetscNot(nrm >= bv->orthog_eta*onrm);
224:     break;

226:   case BV_ORTHOG_REFINE_NEVER:
227:     BVOrthogonalizeCGS1(bv,k,v,bv->h,NULL,NULL);
228:     /* compute |v| */
229:     if (norm || lindep) {
230:       if (v) { BVNormVec(bv,v,NORM_2,&nrm); }
231:       else { BVNormColumn(bv,k,NORM_2,&nrm); }
232:     }
233:     if (norm) *norm = nrm;
234:     /* linear dependence check: just test for exactly zero norm */
235:     if (lindep) *lindep = PetscNot(nrm);
236:     break;

238:   case BV_ORTHOG_REFINE_ALWAYS:
239:     BVOrthogonalizeCGS1(bv,k,v,bv->h,NULL,NULL);
240:     if (lindep) {
241:       BVOrthogonalizeCGS1(bv,k,v,bv->c,&onrm,&nrm);
242:       if (norm) *norm = nrm;
243:       *lindep = PetscNot(nrm && nrm >= bv->orthog_eta*onrm);
244:     } else {
245:       BVOrthogonalizeCGS1(bv,k,v,bv->c,NULL,norm);
246:     }
247:     for (i=0;i<bv->nc+k;i++) bv->h[i] += bv->c[i];
248:     break;
249:   }
250:   return(0);
251: }

255: /*@
256:    BVOrthogonalizeVec - Orthogonalize a given vector with respect to all
257:    active columns.

259:    Collective on BV

261:    Input Parameters:
262: +  bv     - the basis vectors context
263: -  v      - the vector

265:    Output Parameters:
266: +  H      - (optional) coefficients computed during orthogonalization
267: .  norm   - (optional) norm of the vector after being orthogonalized
268: -  lindep - (optional) flag indicating that refinement did not improve the quality
269:             of orthogonalization

271:    Notes:
272:    This function is equivalent to BVOrthogonalizeColumn() but orthogonalizes
273:    a vector as an argument rather than taking one of the BV columns. The
274:    vector is orthogonalized against all active columns.

276:    Level: advanced

278: .seealso: BVOrthogonalizeColumn(), BVSetOrthogonalization(), BVSetActiveColumns()
279: @*/
280: PetscErrorCode BVOrthogonalizeVec(BV bv,Vec v,PetscScalar *H,PetscReal *norm,PetscBool *lindep)
281: {
283:   PetscInt       i,ksave,lsave;

289:   BVCheckSizes(bv,1);

293:   PetscLogEventBegin(BV_OrthogonalizeVec,bv,0,0,0);
294:   ksave = bv->k;
295:   lsave = bv->l;
296:   bv->l = -bv->nc;  /* must also orthogonalize against constraints and leading columns */
297:   BV_AllocateCoeffs(bv);
298:   BV_AllocateSignature(bv);
299:   switch (bv->orthog_type) {
300:   case BV_ORTHOG_CGS:
301:     BVOrthogonalizeCGS(bv,0,v,H,norm,lindep);
302:     break;
303:   case BV_ORTHOG_MGS:
304:     BVOrthogonalizeMGS(bv,0,v,NULL,H,norm,lindep);
305:     break;
306:   }
307:   bv->k = ksave;
308:   bv->l = lsave;
309:   if (H) for (i=bv->l;i<bv->k;i++) H[i-bv->l] = bv->h[bv->nc+i];
310:   PetscLogEventEnd(BV_OrthogonalizeVec,bv,0,0,0);
311:   return(0);
312: }

316: /*@
317:    BVOrthogonalizeColumn - Orthogonalize one of the column vectors with respect to
318:    the previous ones.

320:    Collective on BV

322:    Input Parameters:
323: +  bv     - the basis vectors context
324: -  j      - index of column to be orthogonalized

326:    Output Parameters:
327: +  H      - (optional) coefficients computed during orthogonalization
328: .  norm   - (optional) norm of the vector after being orthogonalized
329: -  lindep - (optional) flag indicating that refinement did not improve the quality
330:             of orthogonalization

332:    Notes:
333:    This function applies an orthogonal projector to project vector V[j] onto
334:    the orthogonal complement of the span of the columns of V[0..j-1],
335:    where V[.] are the vectors of BV. The columns V[0..j-1] are assumed to be
336:    mutually orthonormal.

338:    Leading columns V[0..l-1] also participate in the orthogonalization.

340:    If a non-standard inner product has been specified with BVSetMatrix(),
341:    then the vector is B-orthogonalized, using the non-standard inner product
342:    defined by matrix B. The output vector satisfies V[j]'*B*V[0..j-1] = 0.

344:    This routine does not normalize the resulting vector.

346:    Level: advanced

348: .seealso: BVSetOrthogonalization(), BVSetMatrix(), BVSetActiveColumns(), BVOrthogonalize(), BVOrthogonalizeVec()
349: @*/
350: PetscErrorCode BVOrthogonalizeColumn(BV bv,PetscInt j,PetscScalar *H,PetscReal *norm,PetscBool *lindep)
351: {
353:   PetscInt       i,ksave,lsave;

359:   BVCheckSizes(bv,1);
360:   if (j<0) SETERRQ(PetscObjectComm((PetscObject)bv),PETSC_ERR_ARG_OUTOFRANGE,"Index j must be non-negative");
361:   if (j>=bv->m) SETERRQ2(PetscObjectComm((PetscObject)bv),PETSC_ERR_ARG_OUTOFRANGE,"Index j=%D but BV only has %D columns",j,bv->m);

363:   PetscLogEventBegin(BV_OrthogonalizeVec,bv,0,0,0);
364:   ksave = bv->k;
365:   lsave = bv->l;
366:   bv->l = -bv->nc;  /* must also orthogonalize against constraints and leading columns */
367:   BV_AllocateCoeffs(bv);
368:   BV_AllocateSignature(bv);
369:   switch (bv->orthog_type) {
370:   case BV_ORTHOG_CGS:
371:     BVOrthogonalizeCGS(bv,j,NULL,H,norm,lindep);
372:     break;
373:   case BV_ORTHOG_MGS:
374:     BVOrthogonalizeMGS(bv,j,NULL,NULL,H,norm,lindep);
375:     break;
376:   }
377:   bv->k = ksave;
378:   bv->l = lsave;
379:   if (H) for (i=bv->l;i<j;i++) H[i-bv->l] = bv->h[bv->nc+i];
380:   PetscLogEventEnd(BV_OrthogonalizeVec,bv,0,0,0);
381:   return(0);
382: }

386: /*@
387:    BVOrthogonalizeSomeColumn - Orthogonalize one of the column vectors with
388:    respect to some of the previous ones.

390:    Collective on BV

392:    Input Parameters:
393: +  bv     - the basis vectors context
394: .  j      - index of column to be orthogonalized
395: -  which  - logical array indicating selected columns

397:    Output Parameters:
398: +  H      - (optional) coefficients computed during orthogonalization
399: .  norm   - (optional) norm of the vector after being orthogonalized
400: -  lindep - (optional) flag indicating that refinement did not improve the quality
401:             of orthogonalization

403:    Notes:
404:    This function is similar to BVOrthogonalizeColumn(), but V[j] is
405:    orthogonalized only against columns V[i] having which[i]=PETSC_TRUE.
406:    The length of array which must be j at least.

408:    The use of this operation is restricted to MGS orthogonalization type.

410:    Level: advanced

412: .seealso: BVOrthogonalizeColumn(), BVSetOrthogonalization()
413: @*/
414: PetscErrorCode BVOrthogonalizeSomeColumn(BV bv,PetscInt j,PetscBool *which,PetscScalar *H,PetscReal *norm,PetscBool *lindep)
415: {
417:   PetscInt       i,ksave,lsave;

424:   BVCheckSizes(bv,1);
425:   if (j<0) SETERRQ(PetscObjectComm((PetscObject)bv),PETSC_ERR_ARG_OUTOFRANGE,"Index j must be non-negative");
426:   if (j>=bv->m) SETERRQ2(PetscObjectComm((PetscObject)bv),PETSC_ERR_ARG_OUTOFRANGE,"Index j=%D but BV only has %D columns",j,bv->m);
427:   if (bv->orthog_type!=BV_ORTHOG_MGS) SETERRQ(PetscObjectComm((PetscObject)bv),PETSC_ERR_SUP,"Operation only available for MGS orthogonalization");

429:   PetscLogEventBegin(BV_OrthogonalizeVec,bv,0,0,0);
430:   ksave = bv->k;
431:   lsave = bv->l;
432:   bv->l = -bv->nc;  /* must also orthogonalize against constraints and leading columns */
433:   BV_AllocateCoeffs(bv);
434:   BV_AllocateSignature(bv);
435:   BVOrthogonalizeMGS(bv,j,NULL,which,H,norm,lindep);
436:   bv->k = ksave;
437:   bv->l = lsave;
438:   if (H) for (i=bv->l;i<j;i++) H[i-bv->l] = bv->h[bv->nc+i];
439:   PetscLogEventEnd(BV_OrthogonalizeVec,bv,0,0,0);
440:   return(0);
441: }

445: /*
446:    Orthogonalize a set of vectors with Gram-Schmidt, column by column.
447:  */
448: static PetscErrorCode BVOrthogonalize_GS(BV V,Mat R)
449: {
451:   PetscScalar    *r=NULL;
452:   PetscReal      norm;
453:   PetscInt       j,ldr;
454:   Vec            v;

457:   if (R) {
458:     MatGetSize(R,&ldr,NULL);
459:     MatDenseGetArray(R,&r);
460:   }
461:   if (V->matrix) {
462:     BV_AllocateCachedBV(V);
463:     BVSetActiveColumns(V->cached,V->l,V->k);
464:   }
465:   for (j=V->l;j<V->k;j++) {
466:     if (R) {
467:       BVOrthogonalizeColumn(V,j,r+j*ldr+V->l,&norm,NULL);
468:       r[j+j*ldr] = norm;
469:     } else {
470:       BVOrthogonalizeColumn(V,j,NULL,&norm,NULL);
471:     }
472:     if (!norm) SETERRQ(PETSC_COMM_SELF,1,"Breakdown in BVOrthogonalize due to a linearly dependent column");
473:     if (V->matrix) { /* fill cached BV */
474:       BVGetColumn(V->cached,j,&v);
475:       VecCopy(V->Bx,v);
476:       BVRestoreColumn(V->cached,j,&v);
477:     }
478:     BVScaleColumn(V,j,1.0/norm);
479:   }
480:   if (R) { MatDenseRestoreArray(R,&r); }
481:   return(0);
482: }

486: /*
487:    Compute the upper Cholesky factor in R and its inverse in S.
488:  */
489: static PetscErrorCode MatCholeskyFactorInvert(Mat R,PetscInt l,Mat *S)
490: {
491: #if defined(PETSC_MISSING_LAPACK_POTRF) || defined(SLEPC_MISSING_LAPACK_TRTRI)
493:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"POTRF/TRTRI - Lapack routine is unavailable");
494: #else
496:   PetscInt       i,n,m,ld;
497:   PetscScalar    *pR,*pS;
498:   PetscBLASInt   info,n_,l_,m_,ld_;

501:   MatGetSize(R,&m,NULL);
502:   n = m-l;
503:   PetscBLASIntCast(m,&m_);
504:   PetscBLASIntCast(l,&l_);
505:   PetscBLASIntCast(n,&n_);
506:   ld  = m;
507:   ld_ = m_;
508:   MatCreateSeqDense(PETSC_COMM_SELF,ld,ld,NULL,S);
509:   MatDenseGetArray(R,&pR);
510:   MatDenseGetArray(*S,&pS);

512:   /* save a copy of matrix in S */
513:   for (i=l;i<m;i++) {
514:     PetscMemcpy(pS+i*ld+l,pR+i*ld+l,n*sizeof(PetscScalar));
515:   }

517:   /* compute upper Cholesky factor in R */
518:   PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("U",&n_,pR+l*ld+l,&ld_,&info));
519:   PetscLogFlops((1.0*n*n*n)/3.0);

521:   if (info) {  /* LAPACKpotrf failed, retry on diagonally perturbed matrix */
522:     for (i=l;i<m;i++) {
523:       PetscMemcpy(pR+i*ld+l,pS+i*ld+l,n*sizeof(PetscScalar));
524:       pR[i+i*ld] += 50.0*PETSC_MACHINE_EPSILON;
525:     }
526:     PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("U",&n_,pR+l*ld+l,&ld_,&info));
527:     if (info) SETERRQ1(PETSC_COMM_SELF,1,"Error in Cholesky factorization, info=%D",(PetscInt)info);
528:     PetscLogFlops((1.0*n*n*n)/3.0);
529:   }

531:   /* compute S = inv(R) */
532:   PetscMemzero(pS,m*m*sizeof(PetscScalar));
533:   for (i=l;i<m;i++) {
534:     PetscMemcpy(pS+i*ld+l,pR+i*ld+l,n*sizeof(PetscScalar));
535:   }
536:   PetscStackCallBLAS("LAPACKtrtri",LAPACKtrtri_("U","N",&n_,pS+l*ld+l,&ld_,&info));
537:   if (info) SETERRQ1(PETSC_COMM_SELF,1,"Error in xTRTRI, info=%D",(PetscInt)info);
538:   PetscLogFlops(1.0*n*n*n);

540:   /* Zero out entries below the diagonal */
541:   for (i=l;i<m-1;i++) {
542:     PetscMemzero(pR+i*ld+i+1,(m-i-1)*sizeof(PetscScalar));
543:     PetscMemzero(pS+i*ld+i+1,(m-i-1)*sizeof(PetscScalar));
544:   }
545:   MatDenseRestoreArray(R,&pR);
546:   MatDenseRestoreArray(*S,&pS);
547:   return(0);
548: #endif
549: }

553: /*
554:    Orthogonalize a set of vectors with Cholesky: R=chol(V'*V), Q=V*inv(R)
555:  */
556: static PetscErrorCode BVOrthogonalize_Chol(BV V,Mat Rin)
557: {
559:   Mat            S,R=Rin;

562:   if (!Rin) {
563:     MatCreateSeqDense(PETSC_COMM_SELF,V->k,V->k,NULL,&R);
564:   }
565:   BVDot(V,V,R);
566:   MatCholeskyFactorInvert(R,V->l,&S);
567:   BVMultInPlace(V,S,V->l,V->k);
568:   MatDestroy(&S);
569:   if (!Rin) {
570:     MatDestroy(&R);
571:   }
572:   return(0);
573: }

577: /*@
578:    BVOrthogonalize - Orthogonalize all columns (except leading ones), that is,
579:    compute the QR decomposition.

581:    Collective on BV

583:    Input Parameter:
584: .  V - basis vectors

586:    Output Parameters:
587: +  V - the modified basis vectors
588: -  R - a sequential dense matrix (or NULL)

590:    Notes:
591:    On input, matrix R must be a sequential dense Mat, with at least as many rows
592:    and columns as the number of active columns of V. The output satisfies
593:    V0 = V*R (where V0 represent the input V) and V'*V = I.

595:    If V has leading columns, then they are not modified (are assumed to be already
596:    orthonormal) and the corresponding part of R is not referenced.

598:    Can pass NULL if R is not required.

600:    The method to be used for block orthogonalization can be set with
601:    BVSetOrthogonalization(). If set to GS, the computation is done column by
602:    column with successive calls to BVOrthogonalizeColumn().

604:    If V is rank-deficient or very ill-conditioned, that is, one or more columns are
605:    (almost) linearly dependent with respect to the rest, then the algorithm may
606:    break down or result in larger numerical error. Linearly dependent columns are
607:    essentially replaced by random directions, and the corresponding diagonal entry
608:    in R is set to (nearly) zero.

610:    Level: intermediate

612: .seealso: BVOrthogonalizeColumn(), BVOrthogonalizeVec(), BVSetActiveColumns(), BVSetOrthogonalization(), BVOrthogBlockType
613: @*/
614: PetscErrorCode BVOrthogonalize(BV V,Mat R)
615: {
617:   PetscBool      match;
618:   PetscInt       m,n;

623:   BVCheckSizes(V,1);
624:   if (R) {
627:     if (V->l>0 && V->orthog_block==BV_ORTHOG_BLOCK_GS) SETERRQ(PetscObjectComm((PetscObject)V),PETSC_ERR_SUP,"Cannot request matrix R in Gram-Schmidt orthogonalization if l>0");
628:     PetscObjectTypeCompare((PetscObject)R,MATSEQDENSE,&match);
629:     if (!match) SETERRQ(PetscObjectComm((PetscObject)V),PETSC_ERR_SUP,"Mat argument must be of type seqdense");
630:     MatGetSize(R,&m,&n);
631:     if (m!=n) SETERRQ2(PetscObjectComm((PetscObject)V),PETSC_ERR_ARG_SIZ,"Mat argument is not square, it has %D rows and %D columns",m,n);
632:     if (n<V->k) SETERRQ2(PetscObjectComm((PetscObject)V),PETSC_ERR_ARG_SIZ,"Mat size %D is smaller than the number of BV active columns %D",n,V->k);
633:   }
634:   if (V->nc) SETERRQ(PetscObjectComm((PetscObject)V),PETSC_ERR_SUP,"Not implemented for BV with constraints, use BVOrthogonalizeColumn() instead");

636:   PetscLogEventBegin(BV_Orthogonalize,V,R,0,0);
637:   switch (V->orthog_block) {
638:   case BV_ORTHOG_BLOCK_GS: /* proceed column by column with Gram-Schmidt */
639:     BVOrthogonalize_GS(V,R);
640:     break;
641:   case BV_ORTHOG_BLOCK_CHOL:
642:     BVOrthogonalize_Chol(V,R);
643:     /*if (V->ops->orthogonalize) {
644:       (*V->ops->orthogonalize)(V,R);
645:     }*/
646:     break;
647:   }
648:   PetscLogEventEnd(BV_Orthogonalize,V,R,0,0);
649:   PetscObjectStateIncrease((PetscObject)V);
650:   return(0);
651: }