Date: 2016-03-29T14:57:26+00:00

Actual source code: bvorthog.c
slepc-3.6.3 2016-03-29
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      1: /*
      2:    BV orthogonalization routines.

      4:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      5:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      6:    Copyright (c) 2002-2015, 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) {
    162:       if (nrm < bv->orthog_eta*onrm) *lindep = PETSC_TRUE;
    163:       else *lindep = PETSC_FALSE;
    164:     }
    165:     break;

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

    177:   case BV_ORTHOG_REFINE_ALWAYS:
    178:     /* first step */
    179:     BVOrthogonalizeMGS1(bv,k,w,which,bv->h);
    180:     if (lindep) {
    181:       BVNormVec(bv,w,NORM_2,&onrm);
    182:     }
    183:     /* second step */
    184:     BVOrthogonalizeMGS1(bv,k,w,which,bv->h);
    185:     if (norm || lindep) {
    186:       BVNormVec(bv,w,NORM_2,&nrm);
    187:     }
    188:     if (lindep) {
    189:       if (nrm==0.0 || nrm < bv->orthog_eta*onrm) *lindep = PETSC_TRUE;
    190:       else *lindep = PETSC_FALSE;
    191:     }
    192:     break;
    193:   }
    194:   if (bv->indef) {
    195:     BVNormVec(bv,w,NORM_2,&nrm);
    196:     bv->omega[bv->nc+j] = (nrm<0.0)? -1.0: 1.0;
    197:   }
    198:   if (!v) { BVRestoreColumn(bv,j,&w); }
    199:   if (norm) *norm = nrm;
    200:   return(0);
    201: }

    205: /*
    206:   BVOrthogonalizeCGS - Orthogonalize with classical Gram-Schmidt
    207: */
    208: static PetscErrorCode BVOrthogonalizeCGS(BV bv,PetscInt j,Vec v,PetscScalar *H,PetscReal *norm,PetscBool *lindep)
    209: {
    211:   PetscReal      onrm,nrm;
    212:   PetscInt       i,k,l;

    215:   if (v) k = bv->k;
    216:   else k = j;
    217:   switch (bv->orthog_ref) {

    219:   case BV_ORTHOG_REFINE_IFNEEDED:
    220:     BVOrthogonalizeCGS1(bv,k,v,bv->h,&onrm,&nrm);
    221:     /* ||q|| < eta ||h|| */
    222:     l = 1;
    223:     while (l<3 && nrm && nrm < bv->orthog_eta*onrm) {
    224:       l++;
    225:       BVOrthogonalizeCGS1(bv,k,v,bv->c,&onrm,&nrm);
    226:       for (i=0;i<bv->nc+k;i++) bv->h[i] += bv->c[i];
    227:     }
    228:     if (norm) *norm = nrm;
    229:     if (lindep) {
    230:       if (nrm < bv->orthog_eta*onrm) *lindep = PETSC_TRUE;
    231:       else *lindep = PETSC_FALSE;
    232:     }
    233:     break;

    235:   case BV_ORTHOG_REFINE_NEVER:
    236:     BVOrthogonalizeCGS1(bv,k,v,bv->h,NULL,NULL);
    237:     /* compute |v| */
    238:     if (norm || lindep) {
    239:       if (v) { BVNormVec(bv,v,NORM_2,&nrm); }
    240:       else { BVNormColumn(bv,k,NORM_2,&nrm); }
    241:     }
    242:     if (norm) *norm = nrm;
    243:     /* linear dependence check: just test for exactly zero norm */
    244:     if (lindep) *lindep = nrm? PETSC_FALSE: PETSC_TRUE;
    245:     break;

    247:   case BV_ORTHOG_REFINE_ALWAYS:
    248:     BVOrthogonalizeCGS1(bv,k,v,bv->h,NULL,NULL);
    249:     if (lindep) {
    250:       BVOrthogonalizeCGS1(bv,k,v,bv->c,&onrm,&nrm);
    251:       if (norm) *norm = nrm;
    252:       if (nrm==0.0 || nrm < bv->orthog_eta*onrm) *lindep = PETSC_TRUE;
    253:       else *lindep = PETSC_FALSE;
    254:     } else {
    255:       BVOrthogonalizeCGS1(bv,k,v,bv->c,NULL,norm);
    256:     }
    257:     for (i=0;i<bv->nc+k;i++) bv->h[i] += bv->c[i];
    258:     break;
    259:   }
    260:   return(0);
    261: }

    265: /*@
    266:    BVOrthogonalizeVec - Orthogonalize a given vector with respect to all
    267:    active columns.

    269:    Collective on BV

    271:    Input Parameters:
    272: +  bv     - the basis vectors context
    273: -  v      - the vector

    275:    Output Parameters:
    276: +  H      - (optional) coefficients computed during orthogonalization
    277: .  norm   - (optional) norm of the vector after being orthogonalized
    278: -  lindep - (optional) flag indicating that refinement did not improve the quality
    279:             of orthogonalization

    281:    Notes:
    282:    This function is equivalent to BVOrthogonalizeColumn() but orthogonalizes
    283:    a vector as an argument rather than taking one of the BV columns. The
    284:    vector is orthogonalized against all active columns.

    286:    Level: advanced

    288: .seealso: BVOrthogonalizeColumn(), BVSetOrthogonalization(), BVSetActiveColumns()
    289: @*/
    290: PetscErrorCode BVOrthogonalizeVec(BV bv,Vec v,PetscScalar *H,PetscReal *norm,PetscBool *lindep)
    291: {
    293:   PetscInt       i,ksave,lsave;

    299:   BVCheckSizes(bv,1);

    303:   PetscLogEventBegin(BV_Orthogonalize,bv,0,0,0);
    304:   ksave = bv->k;
    305:   lsave = bv->l;
    306:   bv->l = -bv->nc;  /* must also orthogonalize against constraints and leading columns */
    307:   BV_AllocateCoeffs(bv);
    308:   BV_AllocateSignature(bv);
    309:   switch (bv->orthog_type) {
    310:   case BV_ORTHOG_CGS:
    311:     BVOrthogonalizeCGS(bv,0,v,H,norm,lindep);
    312:     break;
    313:   case BV_ORTHOG_MGS:
    314:     BVOrthogonalizeMGS(bv,0,v,NULL,H,norm,lindep);
    315:     break;
    316:   }
    317:   bv->k = ksave;
    318:   bv->l = lsave;
    319:   if (H) for (i=bv->l;i<bv->k;i++) H[i-bv->l] = bv->h[bv->nc+i];
    320:   PetscLogEventEnd(BV_Orthogonalize,bv,0,0,0);
    321:   return(0);
    322: }

    326: /*@
    327:    BVOrthogonalizeColumn - Orthogonalize one of the column vectors with respect to
    328:    the previous ones.

    330:    Collective on BV

    332:    Input Parameters:
    333: +  bv     - the basis vectors context
    334: -  j      - index of column to be orthogonalized

    336:    Output Parameters:
    337: +  H      - (optional) coefficients computed during orthogonalization
    338: .  norm   - (optional) norm of the vector after being orthogonalized
    339: -  lindep - (optional) flag indicating that refinement did not improve the quality
    340:             of orthogonalization

    342:    Notes:
    343:    This function applies an orthogonal projector to project vector V[j] onto
    344:    the orthogonal complement of the span of the columns of V[0..j-1],
    345:    where V[.] are the vectors of BV. The columns V[0..j-1] are assumed to be
    346:    mutually orthonormal.

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

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

    354:    This routine does not normalize the resulting vector.

    356:    Level: advanced

    358: .seealso: BVSetOrthogonalization(), BVSetMatrix(), BVSetActiveColumns(), BVOrthogonalize(), BVOrthogonalizeVec()
    359: @*/
    360: PetscErrorCode BVOrthogonalizeColumn(BV bv,PetscInt j,PetscScalar *H,PetscReal *norm,PetscBool *lindep)
    361: {
    363:   PetscInt       i,ksave,lsave;

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

    373:   PetscLogEventBegin(BV_Orthogonalize,bv,0,0,0);
    374:   ksave = bv->k;
    375:   lsave = bv->l;
    376:   bv->l = -bv->nc;  /* must also orthogonalize against constraints and leading columns */
    377:   BV_AllocateCoeffs(bv);
    378:   BV_AllocateSignature(bv);
    379:   switch (bv->orthog_type) {
    380:   case BV_ORTHOG_CGS:
    381:     BVOrthogonalizeCGS(bv,j,NULL,H,norm,lindep);
    382:     break;
    383:   case BV_ORTHOG_MGS:
    384:     BVOrthogonalizeMGS(bv,j,NULL,NULL,H,norm,lindep);
    385:     break;
    386:   }
    387:   bv->k = ksave;
    388:   bv->l = lsave;
    389:   if (H) for (i=bv->l;i<j;i++) H[i-bv->l] = bv->h[bv->nc+i];
    390:   PetscLogEventEnd(BV_Orthogonalize,bv,0,0,0);
    391:   return(0);
    392: }

    396: /*@
    397:    BVOrthogonalizeSomeColumn - Orthogonalize one of the column vectors with
    398:    respect to some of the previous ones.

    400:    Collective on BV

    402:    Input Parameters:
    403: +  bv     - the basis vectors context
    404: .  j      - index of column to be orthogonalized
    405: -  which  - logical array indicating selected columns

    407:    Output Parameters:
    408: +  H      - (optional) coefficients computed during orthogonalization
    409: .  norm   - (optional) norm of the vector after being orthogonalized
    410: -  lindep - (optional) flag indicating that refinement did not improve the quality
    411:             of orthogonalization

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

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

    420:    Level: advanced

    422: .seealso: BVOrthogonalizeColumn(), BVSetOrthogonalization()
    423: @*/
    424: PetscErrorCode BVOrthogonalizeSomeColumn(BV bv,PetscInt j,PetscBool *which,PetscScalar *H,PetscReal *norm,PetscBool *lindep)
    425: {
    427:   PetscInt       i,ksave,lsave;

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

    439:   PetscLogEventBegin(BV_Orthogonalize,bv,0,0,0);
    440:   ksave = bv->k;
    441:   lsave = bv->l;
    442:   bv->l = -bv->nc;  /* must also orthogonalize against constraints and leading columns */
    443:   BV_AllocateCoeffs(bv);
    444:   BV_AllocateSignature(bv);
    445:   BVOrthogonalizeMGS(bv,j,NULL,which,H,norm,lindep);
    446:   bv->k = ksave;
    447:   bv->l = lsave;
    448:   if (H) for (i=bv->l;i<j;i++) H[i-bv->l] = bv->h[bv->nc+i];
    449:   PetscLogEventEnd(BV_Orthogonalize,bv,0,0,0);
    450:   return(0);
    451: }

    455: /*
    456:    Orthogonalize a set of vectors with Gram-Schmidt, column by column.
    457:  */
    458: static PetscErrorCode BVOrthogonalize_GS(BV V,Mat R)
    459: {
    461:   PetscScalar    *r=NULL;
    462:   PetscReal      norm;
    463:   PetscInt       j,ldr;
    464:   Vec            v;

    467:   if (R) {
    468:     MatGetSize(R,&ldr,NULL);
    469:     MatDenseGetArray(R,&r);
    470:   }
    471:   if (V->matrix) {
    472:     BV_AllocateCachedBV(V);
    473:     BVSetActiveColumns(V->cached,V->l,V->k);
    474:   }
    475:   for (j=V->l;j<V->k;j++) {
    476:     if (R) {
    477:       BVOrthogonalizeColumn(V,j,r+j*ldr+V->l,&norm,NULL);
    478:       r[j+j*ldr] = norm;
    479:     } else {
    480:       BVOrthogonalizeColumn(V,j,NULL,&norm,NULL);
    481:     }
    482:     if (V->matrix) { /* fill cached BV */
    483:       BVGetColumn(V->cached,j,&v);
    484:       VecCopy(V->Bx,v);
    485:       BVRestoreColumn(V->cached,j,&v);
    486:     }
    487:     BVScaleColumn(V,j,1.0/norm);
    488:   }
    489:   if (R) { MatDenseRestoreArray(R,&r); }
    490:   return(0);
    491: }

    495: /*
    496:    Compute the upper Cholesky factor in R and its inverse in S.
    497:  */
    498: static PetscErrorCode MatCholeskyFactorInvert(Mat R,PetscInt l,Mat *S)
    499: {
    501:   PetscInt       i,n,m,ld;
    502:   PetscScalar    *pR,*pS,done=1.0;
    503:   PetscBLASInt   info,n_,l_,m_,ld_;

    506:   MatGetSize(R,&m,NULL);
    507:   n = m-l;
    508:   PetscBLASIntCast(m,&m_);
    509:   PetscBLASIntCast(l,&l_);
    510:   PetscBLASIntCast(n,&n_);
    511:   ld  = m;
    512:   ld_ = m_;
    513:   MatCreateSeqDense(PETSC_COMM_SELF,ld,ld,NULL,S);
    514:   MatDenseGetArray(R,&pR);
    515:   MatDenseGetArray(*S,&pS);

    517:   /* compute upper Cholesky factor in R */
    518:   PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("U",&n_,pR+l*ld+l,&ld_,&info));
    519:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Error in Cholesky factorization, info=%D",(PetscInt)info);
    520:   PetscLogFlops((1.0*n*n*n)/3.0);

    522:   /* build identity and compute S = R\I */
    523:   PetscMemzero(pS,m*m*sizeof(PetscScalar));
    524:   for (i=0;i<m;i++) pS[i+i*ld] = 1.0;
    525:   PetscStackCallBLAS("BLAStrsm",BLAStrsm_("L","U","N","N",&n_,&n_,&done,pR+l*ld+l,&ld_,pS+l*ld+l,&ld_));

    527:   /* Zero out entries below the diagonal */
    528:   for (i=l;i<m-1;i++) {
    529:     PetscMemzero(pR+i*ld+i+1,(m-i-1)*sizeof(PetscScalar));
    530:     PetscMemzero(pS+i*ld+i+1,(m-i-1)*sizeof(PetscScalar));
    531:   }
    532:   MatDenseRestoreArray(R,&pR);
    533:   MatDenseRestoreArray(*S,&pS);
    534:   return(0);
    535: }

    539: /*
    540:    Orthogonalize a set of vectors with Cholesky: R=chol(V'*V), Q=V*inv(R)
    541:  */
    542: static PetscErrorCode BVOrthogonalize_Chol(BV V,Mat Rin)
    543: {
    545:   Mat            S,R=Rin,B;

    548:   if (!Rin) {
    549:     MatCreateSeqDense(PETSC_COMM_SELF,V->k,V->k,NULL,&R);
    550:   }
    551:   if (V->matrix) {
    552:     BV_IPMatMultBV(V);
    553:     B = V->matrix;
    554:     V->matrix = NULL;
    555:     BVDot(V->cached,V,R);
    556:     V->matrix = B;
    557:   } else {
    558:     BVDot(V,V,R);
    559:   }
    560:   MatCholeskyFactorInvert(R,V->l,&S);
    561:   BVMultInPlace(V,S,V->l,V->k);
    562:   MatDestroy(&S);
    563:   if (!Rin) {
    564:     MatDestroy(&R);
    565:   }
    566:   return(0);
    567: }

    571: /*@
    572:    BVOrthogonalize - Orthogonalize all columns (except leading ones), that is,
    573:    compute the QR decomposition.

    575:    Collective on BV

    577:    Input Parameter:
    578: .  V - basis vectors

    580:    Output Parameters:
    581: +  V - the modified basis vectors
    582: -  R - a sequential dense matrix (or NULL)

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

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

    592:    Can pass NULL if R is not required.

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

    598:    Level: intermediate

    600: .seealso: BVOrthogonalizeColumn(), BVOrthogonalizeVec(), BVSetActiveColumns(), BVSetOrthogonalization(), BVOrthogBlockType
    601: @*/
    602: PetscErrorCode BVOrthogonalize(BV V,Mat R)
    603: {
    605:   PetscBool      match;
    606:   PetscInt       m,n;

    611:   BVCheckSizes(V,1);
    612:   if (R) {
    615:     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");
    616:     PetscObjectTypeCompare((PetscObject)R,MATSEQDENSE,&match);
    617:     if (!match) SETERRQ(PetscObjectComm((PetscObject)V),PETSC_ERR_SUP,"Mat argument must be of type seqdense");
    618:     MatGetSize(R,&m,&n);
    619:     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);
    620:     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);
    621:   }
    622:   if (V->nc) SETERRQ(PetscObjectComm((PetscObject)V),PETSC_ERR_SUP,"Not implemented for BV with constraints, use BVOrthogonalizeColumn() instead");

    624:   PetscLogEventBegin(BV_Orthogonalize,V,R,0,0);
    625:   switch (V->orthog_block) {
    626:   case BV_ORTHOG_BLOCK_GS: /* proceed column by column with Gram-Schmidt */
    627:     BVOrthogonalize_GS(V,R);
    628:     break;
    629:   case BV_ORTHOG_BLOCK_CHOL:
    630:     BVOrthogonalize_Chol(V,R);
    631:     /*if (V->ops->orthogonalize) {
    632:       (*V->ops->orthogonalize)(V,R);
    633:     }*/
    634:     break;
    635:   }
    636:   PetscLogEventEnd(BV_Orthogonalize,V,R,0,0);
    637:   PetscObjectStateIncrease((PetscObject)V);
    638:   return(0);
    639: }