Date: 2022-03-04T17:37:52+00:00

Actual source code: sbaijfact.c

      2: #include <../src/mat/impls/baij/seq/baij.h>
      3: #include <../src/mat/impls/sbaij/seq/sbaij.h>
      4: #include <petsc/private/kernels/blockinvert.h>
      5: #include <petscis.h>

      7: PetscErrorCode MatGetInertia_SeqSBAIJ(Mat F,PetscInt *nneg,PetscInt *nzero,PetscInt *npos)
      8: {
      9:   Mat_SeqSBAIJ *fact=(Mat_SeqSBAIJ*)F->data;
     10:   MatScalar    *dd=fact->a;
     11:   PetscInt     mbs=fact->mbs,bs=F->rmap->bs,i,nneg_tmp,npos_tmp,*fi=fact->diag;

     14:   if (bs != 1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for bs: %D >1 yet",bs);

     16:   nneg_tmp = 0; npos_tmp = 0;
     17:   for (i=0; i<mbs; i++) {
     18:     if (PetscRealPart(dd[*fi]) > 0.0) npos_tmp++;
     19:     else if (PetscRealPart(dd[*fi]) < 0.0) nneg_tmp++;
     20:     fi++;
     21:   }
     22:   if (nneg)  *nneg  = nneg_tmp;
     23:   if (npos)  *npos  = npos_tmp;
     24:   if (nzero) *nzero = mbs - nneg_tmp - npos_tmp;
     25:   return(0);
     26: }

     28: /*
     29:   Symbolic U^T*D*U factorization for SBAIJ format. Modified from SSF of YSMP.
     30:   Use Modified Sparse Row (MSR) storage for u and ju. See page 85, "Iterative Methods ..." by Saad.
     31: */
     32: PetscErrorCode MatCholeskyFactorSymbolic_SeqSBAIJ_MSR(Mat F,Mat A,IS perm,const MatFactorInfo *info)
     33: {
     34:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data,*b;
     36:   const PetscInt *rip,*ai,*aj;
     37:   PetscInt       i,mbs = a->mbs,*jutmp,bs = A->rmap->bs,bs2=a->bs2;
     38:   PetscInt       m,reallocs = 0,prow;
     39:   PetscInt       *jl,*q,jmin,jmax,juidx,nzk,qm,*iu,*ju,k,j,vj,umax,maxadd;
     40:   PetscReal      f = info->fill;
     41:   PetscBool      perm_identity;

     44:   /* check whether perm is the identity mapping */
     45:   ISIdentity(perm,&perm_identity);
     46:   ISGetIndices(perm,&rip);

     48:   if (perm_identity) { /* without permutation */
     49:     a->permute = PETSC_FALSE;

     51:     ai = a->i; aj = a->j;
     52:   } else {            /* non-trivial permutation */
     53:     a->permute = PETSC_TRUE;

     55:     MatReorderingSeqSBAIJ(A,perm);

     57:     ai = a->inew; aj = a->jnew;
     58:   }

     60:   /* initialization */
     61:   PetscMalloc1(mbs+1,&iu);
     62:   umax  = (PetscInt)(f*ai[mbs] + 1); umax += mbs + 1;
     63:   PetscMalloc1(umax,&ju);
     64:   iu[0] = mbs+1;
     65:   juidx = mbs + 1; /* index for ju */
     66:   /* jl linked list for pivot row -- linked list for col index */
     67:   PetscMalloc2(mbs,&jl,mbs,&q);
     68:   for (i=0; i<mbs; i++) {
     69:     jl[i] = mbs;
     70:     q[i]  = 0;
     71:   }

     73:   /* for each row k */
     74:   for (k=0; k<mbs; k++) {
     75:     for (i=0; i<mbs; i++) q[i] = 0;  /* to be removed! */
     76:     nzk  = 0; /* num. of nz blocks in k-th block row with diagonal block excluded */
     77:     q[k] = mbs;
     78:     /* initialize nonzero structure of k-th row to row rip[k] of A */
     79:     jmin = ai[rip[k]] +1; /* exclude diag[k] */
     80:     jmax = ai[rip[k]+1];
     81:     for (j=jmin; j<jmax; j++) {
     82:       vj = rip[aj[j]]; /* col. value */
     83:       if (vj > k) {
     84:         qm = k;
     85:         do {
     86:           m = qm; qm = q[m];
     87:         } while (qm < vj);
     88:         if (qm == vj) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Duplicate entry in A\n");
     89:         nzk++;
     90:         q[m]  = vj;
     91:         q[vj] = qm;
     92:       } /* if (vj > k) */
     93:     } /* for (j=jmin; j<jmax; j++) */

     95:     /* modify nonzero structure of k-th row by computing fill-in
     96:        for each row i to be merged in */
     97:     prow = k;
     98:     prow = jl[prow]; /* next pivot row (== mbs for symbolic factorization) */

    100:     while (prow < k) {
    101:       /* merge row prow into k-th row */
    102:       jmin = iu[prow] + 1; jmax = iu[prow+1];
    103:       qm   = k;
    104:       for (j=jmin; j<jmax; j++) {
    105:         vj = ju[j];
    106:         do {
    107:           m = qm; qm = q[m];
    108:         } while (qm < vj);
    109:         if (qm != vj) {
    110:           nzk++; q[m] = vj; q[vj] = qm; qm = vj;
    111:         }
    112:       }
    113:       prow = jl[prow]; /* next pivot row */
    114:     }

    116:     /* add k to row list for first nonzero element in k-th row */
    117:     if (nzk > 0) {
    118:       i     = q[k]; /* col value of first nonzero element in U(k, k+1:mbs-1) */
    119:       jl[k] = jl[i]; jl[i] = k;
    120:     }
    121:     iu[k+1] = iu[k] + nzk;

    123:     /* allocate more space to ju if needed */
    124:     if (iu[k+1] > umax) {
    125:       /* estimate how much additional space we will need */
    126:       /* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */
    127:       /* just double the memory each time */
    128:       maxadd = umax;
    129:       if (maxadd < nzk) maxadd = (mbs-k)*(nzk+1)/2;
    130:       umax += maxadd;

    132:       /* allocate a longer ju */
    133:       PetscMalloc1(umax,&jutmp);
    134:       PetscArraycpy(jutmp,ju,iu[k]);
    135:       PetscFree(ju);
    136:       ju   = jutmp;
    137:       reallocs++; /* count how many times we realloc */
    138:     }

    140:     /* save nonzero structure of k-th row in ju */
    141:     i=k;
    142:     while (nzk--) {
    143:       i           = q[i];
    144:       ju[juidx++] = i;
    145:     }
    146:   }

    148: #if defined(PETSC_USE_INFO)
    149:   if (ai[mbs] != 0) {
    150:     PetscReal af = ((PetscReal)iu[mbs])/((PetscReal)ai[mbs]);
    151:     PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);
    152:     PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
    153:     PetscInfo1(A,"PCFactorSetFill(pc,%g);\n",(double)af);
    154:     PetscInfo(A,"for best performance.\n");
    155:   } else {
    156:     PetscInfo(A,"Empty matrix\n");
    157:   }
    158: #endif

    160:   ISRestoreIndices(perm,&rip);
    161:   PetscFree2(jl,q);

    163:   /* put together the new matrix */
    164:   MatSeqSBAIJSetPreallocation(F,bs,MAT_SKIP_ALLOCATION,NULL);

    166:   /* PetscLogObjectParent((PetscObject)B,(PetscObject)iperm); */
    167:   b                = (Mat_SeqSBAIJ*)(F)->data;
    168:   b->singlemalloc  = PETSC_FALSE;
    169:   b->free_a        = PETSC_TRUE;
    170:   b->free_ij       = PETSC_TRUE;

    172:   PetscMalloc1((iu[mbs]+1)*bs2,&b->a);
    173:   b->j    = ju;
    174:   b->i    = iu;
    175:   b->diag = NULL;
    176:   b->ilen = NULL;
    177:   b->imax = NULL;
    178:   b->row  = perm;

    180:   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */

    182:   PetscObjectReference((PetscObject)perm);

    184:   b->icol = perm;
    185:   PetscObjectReference((PetscObject)perm);
    186:   PetscMalloc1(bs*mbs+bs,&b->solve_work);
    187:   /* In b structure:  Free imax, ilen, old a, old j.
    188:      Allocate idnew, solve_work, new a, new j */
    189:   PetscLogObjectMemory((PetscObject)F,(iu[mbs]-mbs)*(sizeof(PetscInt)+sizeof(MatScalar)));
    190:   b->maxnz = b->nz = iu[mbs];

    192:   (F)->info.factor_mallocs   = reallocs;
    193:   (F)->info.fill_ratio_given = f;
    194:   if (ai[mbs] != 0) {
    195:     (F)->info.fill_ratio_needed = ((PetscReal)iu[mbs])/((PetscReal)ai[mbs]);
    196:   } else {
    197:     (F)->info.fill_ratio_needed = 0.0;
    198:   }
    199:   MatSeqSBAIJSetNumericFactorization_inplace(F,perm_identity);
    200:   return(0);
    201: }
    202: /*
    203:     Symbolic U^T*D*U factorization for SBAIJ format.
    204:     See MatICCFactorSymbolic_SeqAIJ() for description of its data structure.
    205: */
    206: #include <petscbt.h>
    207: #include <../src/mat/utils/freespace.h>
    208: PetscErrorCode MatCholeskyFactorSymbolic_SeqSBAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
    209: {
    210:   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data;
    211:   Mat_SeqSBAIJ       *b;
    212:   PetscErrorCode     ierr;
    213:   PetscBool          perm_identity,missing;
    214:   PetscReal          fill = info->fill;
    215:   const PetscInt     *rip,*ai=a->i,*aj=a->j;
    216:   PetscInt           i,mbs=a->mbs,bs=A->rmap->bs,reallocs=0,prow;
    217:   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
    218:   PetscInt           nlnk,*lnk,ncols,*cols,*uj,**ui_ptr,*uj_ptr,*udiag;
    219:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
    220:   PetscBT            lnkbt;

    223:   if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
    224:   MatMissingDiagonal(A,&missing,&i);
    225:   if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
    226:   if (bs > 1) {
    227:     MatCholeskyFactorSymbolic_SeqSBAIJ_inplace(fact,A,perm,info);
    228:     return(0);
    229:   }

    231:   /* check whether perm is the identity mapping */
    232:   ISIdentity(perm,&perm_identity);
    233:   if (!perm_identity) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix reordering is not supported for sbaij matrix. Use aij format");
    234:   a->permute = PETSC_FALSE;
    235:   ISGetIndices(perm,&rip);

    237:   /* initialization */
    238:   PetscMalloc1(mbs+1,&ui);
    239:   PetscMalloc1(mbs+1,&udiag);
    240:   ui[0] = 0;

    242:   /* jl: linked list for storing indices of the pivot rows
    243:      il: il[i] points to the 1st nonzero entry of U(i,k:mbs-1) */
    244:   PetscMalloc4(mbs,&ui_ptr,mbs,&il,mbs,&jl,mbs,&cols);
    245:   for (i=0; i<mbs; i++) {
    246:     jl[i] = mbs; il[i] = 0;
    247:   }

    249:   /* create and initialize a linked list for storing column indices of the active row k */
    250:   nlnk = mbs + 1;
    251:   PetscLLCreate(mbs,mbs,nlnk,lnk,lnkbt);

    253:   /* initial FreeSpace size is fill*(ai[mbs]+1) */
    254:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,ai[mbs]+1),&free_space);
    255:   current_space = free_space;

    257:   for (k=0; k<mbs; k++) {  /* for each active row k */
    258:     /* initialize lnk by the column indices of row rip[k] of A */
    259:     nzk   = 0;
    260:     ncols = ai[k+1] - ai[k];
    261:     if (!ncols) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Empty row %D in matrix ",k);
    262:     for (j=0; j<ncols; j++) {
    263:       i       = *(aj + ai[k] + j);
    264:       cols[j] = i;
    265:     }
    266:     PetscLLAdd(ncols,cols,mbs,nlnk,lnk,lnkbt);
    267:     nzk += nlnk;

    269:     /* update lnk by computing fill-in for each pivot row to be merged in */
    270:     prow = jl[k]; /* 1st pivot row */

    272:     while (prow < k) {
    273:       nextprow = jl[prow];
    274:       /* merge prow into k-th row */
    275:       jmin   = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:mbs-1) */
    276:       jmax   = ui[prow+1];
    277:       ncols  = jmax-jmin;
    278:       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:mbs-1) */
    279:       PetscLLAddSorted(ncols,uj_ptr,mbs,nlnk,lnk,lnkbt);
    280:       nzk   += nlnk;

    282:       /* update il and jl for prow */
    283:       if (jmin < jmax) {
    284:         il[prow] = jmin;
    285:         j        = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
    286:       }
    287:       prow = nextprow;
    288:     }

    290:     /* if free space is not available, make more free space */
    291:     if (current_space->local_remaining<nzk) {
    292:       i    = mbs - k + 1; /* num of unfactored rows */
    293:       i    = PetscIntMultTruncate(i,PetscMin(nzk, i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
    294:       PetscFreeSpaceGet(i,&current_space);
    295:       reallocs++;
    296:     }

    298:     /* copy data into free space, then initialize lnk */
    299:     PetscLLClean(mbs,mbs,nzk,lnk,current_space->array,lnkbt);

    301:     /* add the k-th row into il and jl */
    302:     if (nzk > 1) {
    303:       i     = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:mbs-1) */
    304:       jl[k] = jl[i]; jl[i] = k;
    305:       il[k] = ui[k] + 1;
    306:     }
    307:     ui_ptr[k] = current_space->array;

    309:     current_space->array           += nzk;
    310:     current_space->local_used      += nzk;
    311:     current_space->local_remaining -= nzk;

    313:     ui[k+1] = ui[k] + nzk;
    314:   }

    316:   ISRestoreIndices(perm,&rip);
    317:   PetscFree4(ui_ptr,il,jl,cols);

    319:   /* destroy list of free space and other temporary array(s) */
    320:   PetscMalloc1(ui[mbs]+1,&uj);
    321:   PetscFreeSpaceContiguous_Cholesky(&free_space,uj,mbs,ui,udiag); /* store matrix factor */
    322:   PetscLLDestroy(lnk,lnkbt);

    324:   /* put together the new matrix in MATSEQSBAIJ format */
    325:   MatSeqSBAIJSetPreallocation(fact,bs,MAT_SKIP_ALLOCATION,NULL);

    327:   b               = (Mat_SeqSBAIJ*)fact->data;
    328:   b->singlemalloc = PETSC_FALSE;
    329:   b->free_a       = PETSC_TRUE;
    330:   b->free_ij      = PETSC_TRUE;

    332:   PetscMalloc1(ui[mbs]+1,&b->a);

    334:   b->j         = uj;
    335:   b->i         = ui;
    336:   b->diag      = udiag;
    337:   b->free_diag = PETSC_TRUE;
    338:   b->ilen      = NULL;
    339:   b->imax      = NULL;
    340:   b->row       = perm;
    341:   b->icol      = perm;

    343:   PetscObjectReference((PetscObject)perm);
    344:   PetscObjectReference((PetscObject)perm);

    346:   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */

    348:   PetscMalloc1(mbs+1,&b->solve_work);
    349:   PetscLogObjectMemory((PetscObject)fact,ui[mbs]*(sizeof(PetscInt)+sizeof(MatScalar)));

    351:   b->maxnz = b->nz = ui[mbs];

    353:   fact->info.factor_mallocs   = reallocs;
    354:   fact->info.fill_ratio_given = fill;
    355:   if (ai[mbs] != 0) {
    356:     fact->info.fill_ratio_needed = ((PetscReal)ui[mbs])/ai[mbs];
    357:   } else {
    358:     fact->info.fill_ratio_needed = 0.0;
    359:   }
    360: #if defined(PETSC_USE_INFO)
    361:   if (ai[mbs] != 0) {
    362:     PetscReal af = fact->info.fill_ratio_needed;
    363:     PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);
    364:     PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
    365:     PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);
    366:   } else {
    367:     PetscInfo(A,"Empty matrix\n");
    368:   }
    369: #endif
    370:   fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqSBAIJ_1_NaturalOrdering;
    371:   return(0);
    372: }

    374: PetscErrorCode MatCholeskyFactorSymbolic_SeqSBAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
    375: {
    376:   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data;
    377:   Mat_SeqSBAIJ       *b;
    378:   PetscErrorCode     ierr;
    379:   PetscBool          perm_identity,missing;
    380:   PetscReal          fill = info->fill;
    381:   const PetscInt     *rip,*ai,*aj;
    382:   PetscInt           i,mbs=a->mbs,bs=A->rmap->bs,reallocs=0,prow,d;
    383:   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
    384:   PetscInt           nlnk,*lnk,ncols,*cols,*uj,**ui_ptr,*uj_ptr;
    385:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
    386:   PetscBT            lnkbt;

    389:   MatMissingDiagonal(A,&missing,&d);
    390:   if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);

    392:   /*
    393:    This code originally uses Modified Sparse Row (MSR) storage
    394:    (see page 85, "Iterative Methods ..." by Saad) for the output matrix B - bad choise!
    395:    Then it is rewritten so the factor B takes seqsbaij format. However the associated
    396:    MatCholeskyFactorNumeric_() have not been modified for the cases of bs>1 or !perm_identity,
    397:    thus the original code in MSR format is still used for these cases.
    398:    The code below should replace MatCholeskyFactorSymbolic_SeqSBAIJ_MSR() whenever
    399:    MatCholeskyFactorNumeric_() is modified for using sbaij symbolic factor.
    400:   */
    401:   if (bs > 1) {
    402:     MatCholeskyFactorSymbolic_SeqSBAIJ_MSR(fact,A,perm,info);
    403:     return(0);
    404:   }

    406:   /* check whether perm is the identity mapping */
    407:   ISIdentity(perm,&perm_identity);

    409:   if (perm_identity) {
    410:     a->permute = PETSC_FALSE;

    412:     ai = a->i; aj = a->j;
    413:   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix reordering is not supported for sbaij matrix. Use aij format");
    414:   ISGetIndices(perm,&rip);

    416:   /* initialization */
    417:   PetscMalloc1(mbs+1,&ui);
    418:   ui[0] = 0;

    420:   /* jl: linked list for storing indices of the pivot rows
    421:      il: il[i] points to the 1st nonzero entry of U(i,k:mbs-1) */
    422:   PetscMalloc4(mbs,&ui_ptr,mbs,&il,mbs,&jl,mbs,&cols);
    423:   for (i=0; i<mbs; i++) {
    424:     jl[i] = mbs; il[i] = 0;
    425:   }

    427:   /* create and initialize a linked list for storing column indices of the active row k */
    428:   nlnk = mbs + 1;
    429:   PetscLLCreate(mbs,mbs,nlnk,lnk,lnkbt);

    431:   /* initial FreeSpace size is fill*(ai[mbs]+1) */
    432:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,ai[mbs]+1),&free_space);
    433:   current_space = free_space;

    435:   for (k=0; k<mbs; k++) {  /* for each active row k */
    436:     /* initialize lnk by the column indices of row rip[k] of A */
    437:     nzk   = 0;
    438:     ncols = ai[rip[k]+1] - ai[rip[k]];
    439:     for (j=0; j<ncols; j++) {
    440:       i       = *(aj + ai[rip[k]] + j);
    441:       cols[j] = rip[i];
    442:     }
    443:     PetscLLAdd(ncols,cols,mbs,nlnk,lnk,lnkbt);
    444:     nzk += nlnk;

    446:     /* update lnk by computing fill-in for each pivot row to be merged in */
    447:     prow = jl[k]; /* 1st pivot row */

    449:     while (prow < k) {
    450:       nextprow = jl[prow];
    451:       /* merge prow into k-th row */
    452:       jmin   = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:mbs-1) */
    453:       jmax   = ui[prow+1];
    454:       ncols  = jmax-jmin;
    455:       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:mbs-1) */
    456:       PetscLLAddSorted(ncols,uj_ptr,mbs,nlnk,lnk,lnkbt);
    457:       nzk   += nlnk;

    459:       /* update il and jl for prow */
    460:       if (jmin < jmax) {
    461:         il[prow] = jmin;

    463:         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
    464:       }
    465:       prow = nextprow;
    466:     }

    468:     /* if free space is not available, make more free space */
    469:     if (current_space->local_remaining<nzk) {
    470:       i    = mbs - k + 1; /* num of unfactored rows */
    471:       i    = PetscMin(PetscIntMultTruncate(i,nzk), PetscIntMultTruncate(i,i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
    472:       PetscFreeSpaceGet(i,&current_space);
    473:       reallocs++;
    474:     }

    476:     /* copy data into free space, then initialize lnk */
    477:     PetscLLClean(mbs,mbs,nzk,lnk,current_space->array,lnkbt);

    479:     /* add the k-th row into il and jl */
    480:     if (nzk-1 > 0) {
    481:       i     = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:mbs-1) */
    482:       jl[k] = jl[i]; jl[i] = k;
    483:       il[k] = ui[k] + 1;
    484:     }
    485:     ui_ptr[k] = current_space->array;

    487:     current_space->array           += nzk;
    488:     current_space->local_used      += nzk;
    489:     current_space->local_remaining -= nzk;

    491:     ui[k+1] = ui[k] + nzk;
    492:   }

    494:   ISRestoreIndices(perm,&rip);
    495:   PetscFree4(ui_ptr,il,jl,cols);

    497:   /* destroy list of free space and other temporary array(s) */
    498:   PetscMalloc1(ui[mbs]+1,&uj);
    499:   PetscFreeSpaceContiguous(&free_space,uj);
    500:   PetscLLDestroy(lnk,lnkbt);

    502:   /* put together the new matrix in MATSEQSBAIJ format */
    503:   MatSeqSBAIJSetPreallocation(fact,bs,MAT_SKIP_ALLOCATION,NULL);

    505:   b               = (Mat_SeqSBAIJ*)fact->data;
    506:   b->singlemalloc = PETSC_FALSE;
    507:   b->free_a       = PETSC_TRUE;
    508:   b->free_ij      = PETSC_TRUE;

    510:   PetscMalloc1(ui[mbs]+1,&b->a);

    512:   b->j    = uj;
    513:   b->i    = ui;
    514:   b->diag = NULL;
    515:   b->ilen = NULL;
    516:   b->imax = NULL;
    517:   b->row  = perm;

    519:   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */

    521:   PetscObjectReference((PetscObject)perm);
    522:   b->icol  = perm;
    523:   PetscObjectReference((PetscObject)perm);
    524:   PetscMalloc1(mbs+1,&b->solve_work);
    525:   PetscLogObjectMemory((PetscObject)fact,(ui[mbs]-mbs)*(sizeof(PetscInt)+sizeof(MatScalar)));
    526:   b->maxnz = b->nz = ui[mbs];

    528:   fact->info.factor_mallocs   = reallocs;
    529:   fact->info.fill_ratio_given = fill;
    530:   if (ai[mbs] != 0) {
    531:     fact->info.fill_ratio_needed = ((PetscReal)ui[mbs])/ai[mbs];
    532:   } else {
    533:     fact->info.fill_ratio_needed = 0.0;
    534:   }
    535: #if defined(PETSC_USE_INFO)
    536:   if (ai[mbs] != 0) {
    537:     PetscReal af = fact->info.fill_ratio_needed;
    538:     PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);
    539:     PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
    540:     PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);
    541:   } else {
    542:     PetscInfo(A,"Empty matrix\n");
    543:   }
    544: #endif
    545:   MatSeqSBAIJSetNumericFactorization_inplace(fact,perm_identity);
    546:   return(0);
    547: }

    549: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_N(Mat C,Mat A,const MatFactorInfo *info)
    550: {
    551:   Mat_SeqSBAIJ   *a   = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
    552:   IS             perm = b->row;
    554:   const PetscInt *ai,*aj,*perm_ptr,mbs=a->mbs,*bi=b->i,*bj=b->j;
    555:   PetscInt       i,j;
    556:   PetscInt       *a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
    557:   PetscInt       bs  =A->rmap->bs,bs2 = a->bs2;
    558:   MatScalar      *ba = b->a,*aa,*ap,*dk,*uik;
    559:   MatScalar      *u,*diag,*rtmp,*rtmp_ptr;
    560:   MatScalar      *work;
    561:   PetscInt       *pivots;
    562:   PetscBool      allowzeropivot,zeropivotdetected;

    565:   /* initialization */
    566:   PetscCalloc1(bs2*mbs,&rtmp);
    567:   PetscMalloc2(mbs,&il,mbs,&jl);
    568:   allowzeropivot = PetscNot(A->erroriffailure);

    570:   il[0] = 0;
    571:   for (i=0; i<mbs; i++) jl[i] = mbs;

    573:   PetscMalloc3(bs2,&dk,bs2,&uik,bs,&work);
    574:   PetscMalloc1(bs,&pivots);

    576:   ISGetIndices(perm,&perm_ptr);

    578:   /* check permutation */
    579:   if (!a->permute) {
    580:     ai = a->i; aj = a->j; aa = a->a;
    581:   } else {
    582:     ai   = a->inew; aj = a->jnew;
    583:     PetscMalloc1(bs2*ai[mbs],&aa);
    584:     PetscArraycpy(aa,a->a,bs2*ai[mbs]);
    585:     PetscMalloc1(ai[mbs],&a2anew);
    586:     PetscArraycpy(a2anew,a->a2anew,ai[mbs]);

    588:     for (i=0; i<mbs; i++) {
    589:       jmin = ai[i]; jmax = ai[i+1];
    590:       for (j=jmin; j<jmax; j++) {
    591:         while (a2anew[j] != j) {
    592:           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
    593:           for (k1=0; k1<bs2; k1++) {
    594:             dk[k1]       = aa[k*bs2+k1];
    595:             aa[k*bs2+k1] = aa[j*bs2+k1];
    596:             aa[j*bs2+k1] = dk[k1];
    597:           }
    598:         }
    599:         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
    600:         if (i > aj[j]) {
    601:           ap = aa + j*bs2;                     /* ptr to the beginning of j-th block of aa */
    602:           for (k=0; k<bs2; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
    603:           for (k=0; k<bs; k++) {               /* j-th block of aa <- dk^T */
    604:             for (k1=0; k1<bs; k1++) *ap++ = dk[k + bs*k1];
    605:           }
    606:         }
    607:       }
    608:     }
    609:     PetscFree(a2anew);
    610:   }

    612:   /* for each row k */
    613:   for (k = 0; k<mbs; k++) {

    615:     /*initialize k-th row with elements nonzero in row perm(k) of A */
    616:     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];

    618:     ap = aa + jmin*bs2;
    619:     for (j = jmin; j < jmax; j++) {
    620:       vj       = perm_ptr[aj[j]];   /* block col. index */
    621:       rtmp_ptr = rtmp + vj*bs2;
    622:       for (i=0; i<bs2; i++) *rtmp_ptr++ = *ap++;
    623:     }

    625:     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
    626:     PetscArraycpy(dk,rtmp+k*bs2,bs2);
    627:     i    = jl[k]; /* first row to be added to k_th row  */

    629:     while (i < k) {
    630:       nexti = jl[i]; /* next row to be added to k_th row */

    632:       /* compute multiplier */
    633:       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */

    635:       /* uik = -inv(Di)*U_bar(i,k) */
    636:       diag = ba + i*bs2;
    637:       u    = ba + ili*bs2;
    638:       PetscArrayzero(uik,bs2);
    639:       PetscKernel_A_gets_A_minus_B_times_C(bs,uik,diag,u);

    641:       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
    642:       PetscKernel_A_gets_A_plus_Btranspose_times_C(bs,dk,uik,u);
    643:       PetscLogFlops(4.0*bs*bs2);

    645:       /* update -U(i,k) */
    646:       PetscArraycpy(ba+ili*bs2,uik,bs2);

    648:       /* add multiple of row i to k-th row ... */
    649:       jmin = ili + 1; jmax = bi[i+1];
    650:       if (jmin < jmax) {
    651:         for (j=jmin; j<jmax; j++) {
    652:           /* rtmp += -U(i,k)^T * U_bar(i,j) */
    653:           rtmp_ptr = rtmp + bj[j]*bs2;
    654:           u        = ba + j*bs2;
    655:           PetscKernel_A_gets_A_plus_Btranspose_times_C(bs,rtmp_ptr,uik,u);
    656:         }
    657:         PetscLogFlops(2.0*bs*bs2*(jmax-jmin));

    659:         /* ... add i to row list for next nonzero entry */
    660:         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
    661:         j     = bj[jmin];
    662:         jl[i] = jl[j]; jl[j] = i; /* update jl */
    663:       }
    664:       i = nexti;
    665:     }

    667:     /* save nonzero entries in k-th row of U ... */

    669:     /* invert diagonal block */
    670:     diag = ba+k*bs2;
    671:     PetscArraycpy(diag,dk,bs2);

    673:     PetscKernel_A_gets_inverse_A(bs,diag,pivots,work,allowzeropivot,&zeropivotdetected);
    674:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    676:     jmin = bi[k]; jmax = bi[k+1];
    677:     if (jmin < jmax) {
    678:       for (j=jmin; j<jmax; j++) {
    679:         vj       = bj[j];      /* block col. index of U */
    680:         u        = ba + j*bs2;
    681:         rtmp_ptr = rtmp + vj*bs2;
    682:         for (k1=0; k1<bs2; k1++) {
    683:           *u++        = *rtmp_ptr;
    684:           *rtmp_ptr++ = 0.0;
    685:         }
    686:       }

    688:       /* ... add k to row list for first nonzero entry in k-th row */
    689:       il[k] = jmin;
    690:       i     = bj[jmin];
    691:       jl[k] = jl[i]; jl[i] = k;
    692:     }
    693:   }

    695:   PetscFree(rtmp);
    696:   PetscFree2(il,jl);
    697:   PetscFree3(dk,uik,work);
    698:   PetscFree(pivots);
    699:   if (a->permute) {
    700:     PetscFree(aa);
    701:   }

    703:   ISRestoreIndices(perm,&perm_ptr);

    705:   C->ops->solve          = MatSolve_SeqSBAIJ_N_inplace;
    706:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_N_inplace;
    707:   C->ops->forwardsolve   = MatForwardSolve_SeqSBAIJ_N_inplace;
    708:   C->ops->backwardsolve  = MatBackwardSolve_SeqSBAIJ_N_inplace;

    710:   C->assembled    = PETSC_TRUE;
    711:   C->preallocated = PETSC_TRUE;

    713:   PetscLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
    714:   return(0);
    715: }

    717: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_N_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info)
    718: {
    719:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
    721:   PetscInt       i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
    722:   PetscInt       *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
    723:   PetscInt       bs  =A->rmap->bs,bs2 = a->bs2;
    724:   MatScalar      *ba = b->a,*aa,*ap,*dk,*uik;
    725:   MatScalar      *u,*diag,*rtmp,*rtmp_ptr;
    726:   MatScalar      *work;
    727:   PetscInt       *pivots;
    728:   PetscBool      allowzeropivot,zeropivotdetected;

    731:   PetscCalloc1(bs2*mbs,&rtmp);
    732:   PetscMalloc2(mbs,&il,mbs,&jl);
    733:   il[0] = 0;
    734:   for (i=0; i<mbs; i++) jl[i] = mbs;

    736:   PetscMalloc3(bs2,&dk,bs2,&uik,bs,&work);
    737:   PetscMalloc1(bs,&pivots);
    738:   allowzeropivot = PetscNot(A->erroriffailure);

    740:   ai = a->i; aj = a->j; aa = a->a;

    742:   /* for each row k */
    743:   for (k = 0; k<mbs; k++) {

    745:     /*initialize k-th row with elements nonzero in row k of A */
    746:     jmin = ai[k]; jmax = ai[k+1];
    747:     ap   = aa + jmin*bs2;
    748:     for (j = jmin; j < jmax; j++) {
    749:       vj       = aj[j];   /* block col. index */
    750:       rtmp_ptr = rtmp + vj*bs2;
    751:       for (i=0; i<bs2; i++) *rtmp_ptr++ = *ap++;
    752:     }

    754:     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
    755:     PetscArraycpy(dk,rtmp+k*bs2,bs2);
    756:     i    = jl[k]; /* first row to be added to k_th row  */

    758:     while (i < k) {
    759:       nexti = jl[i]; /* next row to be added to k_th row */

    761:       /* compute multiplier */
    762:       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */

    764:       /* uik = -inv(Di)*U_bar(i,k) */
    765:       diag = ba + i*bs2;
    766:       u    = ba + ili*bs2;
    767:       PetscArrayzero(uik,bs2);
    768:       PetscKernel_A_gets_A_minus_B_times_C(bs,uik,diag,u);

    770:       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
    771:       PetscKernel_A_gets_A_plus_Btranspose_times_C(bs,dk,uik,u);
    772:       PetscLogFlops(2.0*bs*bs2);

    774:       /* update -U(i,k) */
    775:       PetscArraycpy(ba+ili*bs2,uik,bs2);

    777:       /* add multiple of row i to k-th row ... */
    778:       jmin = ili + 1; jmax = bi[i+1];
    779:       if (jmin < jmax) {
    780:         for (j=jmin; j<jmax; j++) {
    781:           /* rtmp += -U(i,k)^T * U_bar(i,j) */
    782:           rtmp_ptr = rtmp + bj[j]*bs2;
    783:           u        = ba + j*bs2;
    784:           PetscKernel_A_gets_A_plus_Btranspose_times_C(bs,rtmp_ptr,uik,u);
    785:         }
    786:         PetscLogFlops(2.0*bs*bs2*(jmax-jmin));

    788:         /* ... add i to row list for next nonzero entry */
    789:         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
    790:         j     = bj[jmin];
    791:         jl[i] = jl[j]; jl[j] = i; /* update jl */
    792:       }
    793:       i = nexti;
    794:     }

    796:     /* save nonzero entries in k-th row of U ... */

    798:     /* invert diagonal block */
    799:     diag = ba+k*bs2;
    800:     PetscArraycpy(diag,dk,bs2);

    802:     PetscKernel_A_gets_inverse_A(bs,diag,pivots,work,allowzeropivot,&zeropivotdetected);
    803:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    805:     jmin = bi[k]; jmax = bi[k+1];
    806:     if (jmin < jmax) {
    807:       for (j=jmin; j<jmax; j++) {
    808:         vj       = bj[j];      /* block col. index of U */
    809:         u        = ba + j*bs2;
    810:         rtmp_ptr = rtmp + vj*bs2;
    811:         for (k1=0; k1<bs2; k1++) {
    812:           *u++        = *rtmp_ptr;
    813:           *rtmp_ptr++ = 0.0;
    814:         }
    815:       }

    817:       /* ... add k to row list for first nonzero entry in k-th row */
    818:       il[k] = jmin;
    819:       i     = bj[jmin];
    820:       jl[k] = jl[i]; jl[i] = k;
    821:     }
    822:   }

    824:   PetscFree(rtmp);
    825:   PetscFree2(il,jl);
    826:   PetscFree3(dk,uik,work);
    827:   PetscFree(pivots);

    829:   C->ops->solve          = MatSolve_SeqSBAIJ_N_NaturalOrdering_inplace;
    830:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_N_NaturalOrdering_inplace;
    831:   C->ops->forwardsolve   = MatForwardSolve_SeqSBAIJ_N_NaturalOrdering_inplace;
    832:   C->ops->backwardsolve  = MatBackwardSolve_SeqSBAIJ_N_NaturalOrdering_inplace;
    833:   C->assembled           = PETSC_TRUE;
    834:   C->preallocated        = PETSC_TRUE;

    836:   PetscLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
    837:   return(0);
    838: }

    840: /*
    841:     Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP.
    842:     Version for blocks 2 by 2.
    843: */
    844: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_2(Mat C,Mat A,const MatFactorInfo *info)
    845: {
    846:   Mat_SeqSBAIJ   *a   = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
    847:   IS             perm = b->row;
    849:   const PetscInt *ai,*aj,*perm_ptr;
    850:   PetscInt       i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
    851:   PetscInt       *a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
    852:   MatScalar      *ba = b->a,*aa,*ap;
    853:   MatScalar      *u,*diag,*rtmp,*rtmp_ptr,dk[4],uik[4];
    854:   PetscReal      shift = info->shiftamount;
    855:   PetscBool      allowzeropivot,zeropivotdetected;

    858:   allowzeropivot = PetscNot(A->erroriffailure);

    860:   /* initialization */
    861:   /* il and jl record the first nonzero element in each row of the accessing
    862:      window U(0:k, k:mbs-1).
    863:      jl:    list of rows to be added to uneliminated rows
    864:             i>= k: jl(i) is the first row to be added to row i
    865:             i<  k: jl(i) is the row following row i in some list of rows
    866:             jl(i) = mbs indicates the end of a list
    867:      il(i): points to the first nonzero element in columns k,...,mbs-1 of
    868:             row i of U */
    869:   PetscCalloc1(4*mbs,&rtmp);
    870:   PetscMalloc2(mbs,&il,mbs,&jl);
    871:   il[0] = 0;
    872:   for (i=0; i<mbs; i++) jl[i] = mbs;

    874:   ISGetIndices(perm,&perm_ptr);

    876:   /* check permutation */
    877:   if (!a->permute) {
    878:     ai = a->i; aj = a->j; aa = a->a;
    879:   } else {
    880:     ai   = a->inew; aj = a->jnew;
    881:     PetscMalloc1(4*ai[mbs],&aa);
    882:     PetscArraycpy(aa,a->a,4*ai[mbs]);
    883:     PetscMalloc1(ai[mbs],&a2anew);
    884:     PetscArraycpy(a2anew,a->a2anew,ai[mbs]);

    886:     for (i=0; i<mbs; i++) {
    887:       jmin = ai[i]; jmax = ai[i+1];
    888:       for (j=jmin; j<jmax; j++) {
    889:         while (a2anew[j] != j) {
    890:           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
    891:           for (k1=0; k1<4; k1++) {
    892:             dk[k1]     = aa[k*4+k1];
    893:             aa[k*4+k1] = aa[j*4+k1];
    894:             aa[j*4+k1] = dk[k1];
    895:           }
    896:         }
    897:         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
    898:         if (i > aj[j]) {
    899:           ap    = aa + j*4;  /* ptr to the beginning of the block */
    900:           dk[1] = ap[1];     /* swap ap[1] and ap[2] */
    901:           ap[1] = ap[2];
    902:           ap[2] = dk[1];
    903:         }
    904:       }
    905:     }
    906:     PetscFree(a2anew);
    907:   }

    909:   /* for each row k */
    910:   for (k = 0; k<mbs; k++) {

    912:     /*initialize k-th row with elements nonzero in row perm(k) of A */
    913:     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
    914:     ap   = aa + jmin*4;
    915:     for (j = jmin; j < jmax; j++) {
    916:       vj       = perm_ptr[aj[j]];   /* block col. index */
    917:       rtmp_ptr = rtmp + vj*4;
    918:       for (i=0; i<4; i++) *rtmp_ptr++ = *ap++;
    919:     }

    921:     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
    922:     PetscArraycpy(dk,rtmp+k*4,4);
    923:     i    = jl[k]; /* first row to be added to k_th row  */

    925:     while (i < k) {
    926:       nexti = jl[i]; /* next row to be added to k_th row */

    928:       /* compute multiplier */
    929:       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */

    931:       /* uik = -inv(Di)*U_bar(i,k): - ba[ili]*ba[i] */
    932:       diag   = ba + i*4;
    933:       u      = ba + ili*4;
    934:       uik[0] = -(diag[0]*u[0] + diag[2]*u[1]);
    935:       uik[1] = -(diag[1]*u[0] + diag[3]*u[1]);
    936:       uik[2] = -(diag[0]*u[2] + diag[2]*u[3]);
    937:       uik[3] = -(diag[1]*u[2] + diag[3]*u[3]);

    939:       /* update D(k) += -U(i,k)^T * U_bar(i,k): dk += uik*ba[ili] */
    940:       dk[0] += uik[0]*u[0] + uik[1]*u[1];
    941:       dk[1] += uik[2]*u[0] + uik[3]*u[1];
    942:       dk[2] += uik[0]*u[2] + uik[1]*u[3];
    943:       dk[3] += uik[2]*u[2] + uik[3]*u[3];

    945:       PetscLogFlops(16.0*2.0);

    947:       /* update -U(i,k): ba[ili] = uik */
    948:       PetscArraycpy(ba+ili*4,uik,4);

    950:       /* add multiple of row i to k-th row ... */
    951:       jmin = ili + 1; jmax = bi[i+1];
    952:       if (jmin < jmax) {
    953:         for (j=jmin; j<jmax; j++) {
    954:           /* rtmp += -U(i,k)^T * U_bar(i,j): rtmp[bj[j]] += uik*ba[j]; */
    955:           rtmp_ptr     = rtmp + bj[j]*4;
    956:           u            = ba + j*4;
    957:           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1];
    958:           rtmp_ptr[1] += uik[2]*u[0] + uik[3]*u[1];
    959:           rtmp_ptr[2] += uik[0]*u[2] + uik[1]*u[3];
    960:           rtmp_ptr[3] += uik[2]*u[2] + uik[3]*u[3];
    961:         }
    962:         PetscLogFlops(16.0*(jmax-jmin));

    964:         /* ... add i to row list for next nonzero entry */
    965:         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
    966:         j     = bj[jmin];
    967:         jl[i] = jl[j]; jl[j] = i; /* update jl */
    968:       }
    969:       i = nexti;
    970:     }

    972:     /* save nonzero entries in k-th row of U ... */

    974:     /* invert diagonal block */
    975:     diag = ba+k*4;
    976:     PetscArraycpy(diag,dk,4);
    977:     PetscKernel_A_gets_inverse_A_2(diag,shift,allowzeropivot,&zeropivotdetected);
    978:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    980:     jmin = bi[k]; jmax = bi[k+1];
    981:     if (jmin < jmax) {
    982:       for (j=jmin; j<jmax; j++) {
    983:         vj       = bj[j];      /* block col. index of U */
    984:         u        = ba + j*4;
    985:         rtmp_ptr = rtmp + vj*4;
    986:         for (k1=0; k1<4; k1++) {
    987:           *u++        = *rtmp_ptr;
    988:           *rtmp_ptr++ = 0.0;
    989:         }
    990:       }

    992:       /* ... add k to row list for first nonzero entry in k-th row */
    993:       il[k] = jmin;
    994:       i     = bj[jmin];
    995:       jl[k] = jl[i]; jl[i] = k;
    996:     }
    997:   }

    999:   PetscFree(rtmp);
    1000:   PetscFree2(il,jl);
    1001:   if (a->permute) {
    1002:     PetscFree(aa);
    1003:   }
    1004:   ISRestoreIndices(perm,&perm_ptr);

    1006:   C->ops->solve          = MatSolve_SeqSBAIJ_2_inplace;
    1007:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_2_inplace;
    1008:   C->assembled           = PETSC_TRUE;
    1009:   C->preallocated        = PETSC_TRUE;

    1011:   PetscLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
    1012:   return(0);
    1013: }

    1015: /*
    1016:       Version for when blocks are 2 by 2 Using natural ordering
    1017: */
    1018: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info)
    1019: {
    1020:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
    1022:   PetscInt       i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
    1023:   PetscInt       *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
    1024:   MatScalar      *ba = b->a,*aa,*ap,dk[8],uik[8];
    1025:   MatScalar      *u,*diag,*rtmp,*rtmp_ptr;
    1026:   PetscReal      shift = info->shiftamount;
    1027:   PetscBool      allowzeropivot,zeropivotdetected;

    1030:   allowzeropivot = PetscNot(A->erroriffailure);

    1032:   /* initialization */
    1033:   /* il and jl record the first nonzero element in each row of the accessing
    1034:      window U(0:k, k:mbs-1).
    1035:      jl:    list of rows to be added to uneliminated rows
    1036:             i>= k: jl(i) is the first row to be added to row i
    1037:             i<  k: jl(i) is the row following row i in some list of rows
    1038:             jl(i) = mbs indicates the end of a list
    1039:      il(i): points to the first nonzero element in columns k,...,mbs-1 of
    1040:             row i of U */
    1041:   PetscCalloc1(4*mbs,&rtmp);
    1042:   PetscMalloc2(mbs,&il,mbs,&jl);
    1043:   il[0] = 0;
    1044:   for (i=0; i<mbs; i++) jl[i] = mbs;

    1046:   ai = a->i; aj = a->j; aa = a->a;

    1048:   /* for each row k */
    1049:   for (k = 0; k<mbs; k++) {

    1051:     /*initialize k-th row with elements nonzero in row k of A */
    1052:     jmin = ai[k]; jmax = ai[k+1];
    1053:     ap   = aa + jmin*4;
    1054:     for (j = jmin; j < jmax; j++) {
    1055:       vj       = aj[j];   /* block col. index */
    1056:       rtmp_ptr = rtmp + vj*4;
    1057:       for (i=0; i<4; i++) *rtmp_ptr++ = *ap++;
    1058:     }

    1060:     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
    1061:     PetscArraycpy(dk,rtmp+k*4,4);
    1062:     i    = jl[k]; /* first row to be added to k_th row  */

    1064:     while (i < k) {
    1065:       nexti = jl[i]; /* next row to be added to k_th row */

    1067:       /* compute multiplier */
    1068:       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */

    1070:       /* uik = -inv(Di)*U_bar(i,k): - ba[ili]*ba[i] */
    1071:       diag   = ba + i*4;
    1072:       u      = ba + ili*4;
    1073:       uik[0] = -(diag[0]*u[0] + diag[2]*u[1]);
    1074:       uik[1] = -(diag[1]*u[0] + diag[3]*u[1]);
    1075:       uik[2] = -(diag[0]*u[2] + diag[2]*u[3]);
    1076:       uik[3] = -(diag[1]*u[2] + diag[3]*u[3]);

    1078:       /* update D(k) += -U(i,k)^T * U_bar(i,k): dk += uik*ba[ili] */
    1079:       dk[0] += uik[0]*u[0] + uik[1]*u[1];
    1080:       dk[1] += uik[2]*u[0] + uik[3]*u[1];
    1081:       dk[2] += uik[0]*u[2] + uik[1]*u[3];
    1082:       dk[3] += uik[2]*u[2] + uik[3]*u[3];

    1084:       PetscLogFlops(16.0*2.0);

    1086:       /* update -U(i,k): ba[ili] = uik */
    1087:       PetscArraycpy(ba+ili*4,uik,4);

    1089:       /* add multiple of row i to k-th row ... */
    1090:       jmin = ili + 1; jmax = bi[i+1];
    1091:       if (jmin < jmax) {
    1092:         for (j=jmin; j<jmax; j++) {
    1093:           /* rtmp += -U(i,k)^T * U_bar(i,j): rtmp[bj[j]] += uik*ba[j]; */
    1094:           rtmp_ptr     = rtmp + bj[j]*4;
    1095:           u            = ba + j*4;
    1096:           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1];
    1097:           rtmp_ptr[1] += uik[2]*u[0] + uik[3]*u[1];
    1098:           rtmp_ptr[2] += uik[0]*u[2] + uik[1]*u[3];
    1099:           rtmp_ptr[3] += uik[2]*u[2] + uik[3]*u[3];
    1100:         }
    1101:         PetscLogFlops(16.0*(jmax-jmin));

    1103:         /* ... add i to row list for next nonzero entry */
    1104:         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
    1105:         j     = bj[jmin];
    1106:         jl[i] = jl[j]; jl[j] = i; /* update jl */
    1107:       }
    1108:       i = nexti;
    1109:     }

    1111:     /* save nonzero entries in k-th row of U ... */

    1113:     /* invert diagonal block */
    1114:     diag = ba+k*4;
    1115:     PetscArraycpy(diag,dk,4);
    1116:     PetscKernel_A_gets_inverse_A_2(diag,shift,allowzeropivot,&zeropivotdetected);
    1117:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    1119:     jmin = bi[k]; jmax = bi[k+1];
    1120:     if (jmin < jmax) {
    1121:       for (j=jmin; j<jmax; j++) {
    1122:         vj       = bj[j];      /* block col. index of U */
    1123:         u        = ba + j*4;
    1124:         rtmp_ptr = rtmp + vj*4;
    1125:         for (k1=0; k1<4; k1++) {
    1126:           *u++        = *rtmp_ptr;
    1127:           *rtmp_ptr++ = 0.0;
    1128:         }
    1129:       }

    1131:       /* ... add k to row list for first nonzero entry in k-th row */
    1132:       il[k] = jmin;
    1133:       i     = bj[jmin];
    1134:       jl[k] = jl[i]; jl[i] = k;
    1135:     }
    1136:   }

    1138:   PetscFree(rtmp);
    1139:   PetscFree2(il,jl);

    1141:   C->ops->solve          = MatSolve_SeqSBAIJ_2_NaturalOrdering_inplace;
    1142:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_2_NaturalOrdering_inplace;
    1143:   C->ops->forwardsolve   = MatForwardSolve_SeqSBAIJ_2_NaturalOrdering_inplace;
    1144:   C->ops->backwardsolve  = MatBackwardSolve_SeqSBAIJ_2_NaturalOrdering_inplace;
    1145:   C->assembled           = PETSC_TRUE;
    1146:   C->preallocated        = PETSC_TRUE;

    1148:   PetscLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
    1149:   return(0);
    1150: }

    1152: /*
    1153:     Numeric U^T*D*U factorization for SBAIJ format.
    1154:     Version for blocks are 1 by 1.
    1155: */
    1156: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_1_inplace(Mat C,Mat A,const MatFactorInfo *info)
    1157: {
    1158:   Mat_SeqSBAIJ   *a=(Mat_SeqSBAIJ*)A->data,*b=(Mat_SeqSBAIJ*)C->data;
    1159:   IS             ip=b->row;
    1161:   const PetscInt *ai,*aj,*rip;
    1162:   PetscInt       *a2anew,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j,*bcol;
    1163:   PetscInt       k,jmin,jmax,*jl,*il,col,nexti,ili,nz;
    1164:   MatScalar      *rtmp,*ba=b->a,*bval,*aa,dk,uikdi;
    1165:   PetscReal      rs;
    1166:   FactorShiftCtx sctx;

    1169:   /* MatPivotSetUp(): initialize shift context sctx */
    1170:   PetscMemzero(&sctx,sizeof(FactorShiftCtx));

    1172:   ISGetIndices(ip,&rip);
    1173:   if (!a->permute) {
    1174:     ai = a->i; aj = a->j; aa = a->a;
    1175:   } else {
    1176:     ai     = a->inew; aj = a->jnew;
    1177:     nz     = ai[mbs];
    1178:     PetscMalloc1(nz,&aa);
    1179:     a2anew = a->a2anew;
    1180:     bval   = a->a;
    1181:     for (j=0; j<nz; j++) {
    1182:       aa[a2anew[j]] = *(bval++);
    1183:     }
    1184:   }

    1186:   /* initialization */
    1187:   /* il and jl record the first nonzero element in each row of the accessing
    1188:      window U(0:k, k:mbs-1).
    1189:      jl:    list of rows to be added to uneliminated rows
    1190:             i>= k: jl(i) is the first row to be added to row i
    1191:             i<  k: jl(i) is the row following row i in some list of rows
    1192:             jl(i) = mbs indicates the end of a list
    1193:      il(i): points to the first nonzero element in columns k,...,mbs-1 of
    1194:             row i of U */
    1195:   PetscMalloc3(mbs,&rtmp,mbs,&il,mbs,&jl);

    1197:   do {
    1198:     sctx.newshift = PETSC_FALSE;
    1199:     il[0] = 0;
    1200:     for (i=0; i<mbs; i++) {
    1201:       rtmp[i] = 0.0; jl[i] = mbs;
    1202:     }

    1204:     for (k = 0; k<mbs; k++) {
    1205:       /*initialize k-th row by the perm[k]-th row of A */
    1206:       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
    1207:       bval = ba + bi[k];
    1208:       for (j = jmin; j < jmax; j++) {
    1209:         col       = rip[aj[j]];
    1210:         rtmp[col] = aa[j];
    1211:         *bval++   = 0.0; /* for in-place factorization */
    1212:       }

    1214:       /* shift the diagonal of the matrix */
    1215:       if (sctx.nshift) rtmp[k] += sctx.shift_amount;

    1217:       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
    1218:       dk = rtmp[k];
    1219:       i  = jl[k]; /* first row to be added to k_th row  */

    1221:       while (i < k) {
    1222:         nexti = jl[i]; /* next row to be added to k_th row */

    1224:         /* compute multiplier, update diag(k) and U(i,k) */
    1225:         ili     = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
    1226:         uikdi   = -ba[ili]*ba[bi[i]]; /* diagonal(k) */
    1227:         dk     += uikdi*ba[ili];
    1228:         ba[ili] = uikdi; /* -U(i,k) */

    1230:         /* add multiple of row i to k-th row */
    1231:         jmin = ili + 1; jmax = bi[i+1];
    1232:         if (jmin < jmax) {
    1233:           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
    1234:           PetscLogFlops(2.0*(jmax-jmin));

    1236:           /* update il and jl for row i */
    1237:           il[i] = jmin;
    1238:           j     = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
    1239:         }
    1240:         i = nexti;
    1241:       }

    1243:       /* shift the diagonals when zero pivot is detected */
    1244:       /* compute rs=sum of abs(off-diagonal) */
    1245:       rs   = 0.0;
    1246:       jmin = bi[k]+1;
    1247:       nz   = bi[k+1] - jmin;
    1248:       if (nz) {
    1249:         bcol = bj + jmin;
    1250:         while (nz--) {
    1251:           rs += PetscAbsScalar(rtmp[*bcol]);
    1252:           bcol++;
    1253:         }
    1254:       }

    1256:       sctx.rs = rs;
    1257:       sctx.pv = dk;
    1258:       MatPivotCheck(C,A,info,&sctx,k);
    1259:       if (sctx.newshift) break;    /* sctx.shift_amount is updated */
    1260:       dk = sctx.pv;

    1262:       /* copy data into U(k,:) */
    1263:       ba[bi[k]] = 1.0/dk; /* U(k,k) */
    1264:       jmin      = bi[k]+1; jmax = bi[k+1];
    1265:       if (jmin < jmax) {
    1266:         for (j=jmin; j<jmax; j++) {
    1267:           col = bj[j]; ba[j] = rtmp[col]; rtmp[col] = 0.0;
    1268:         }
    1269:         /* add the k-th row into il and jl */
    1270:         il[k] = jmin;
    1271:         i     = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
    1272:       }
    1273:     }
    1274:   } while (sctx.newshift);
    1275:   PetscFree3(rtmp,il,jl);
    1276:   if (a->permute) {PetscFree(aa);}

    1278:   ISRestoreIndices(ip,&rip);

    1280:   C->ops->solve          = MatSolve_SeqSBAIJ_1_inplace;
    1281:   C->ops->solves         = MatSolves_SeqSBAIJ_1_inplace;
    1282:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_1_inplace;
    1283:   C->ops->forwardsolve   = MatForwardSolve_SeqSBAIJ_1_inplace;
    1284:   C->ops->backwardsolve  = MatBackwardSolve_SeqSBAIJ_1_inplace;
    1285:   C->assembled           = PETSC_TRUE;
    1286:   C->preallocated        = PETSC_TRUE;

    1288:   PetscLogFlops(C->rmap->N);
    1289:   if (sctx.nshift) {
    1290:     if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
    1291:       PetscInfo2(A,"number of shiftnz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
    1292:     } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
    1293:       PetscInfo2(A,"number of shiftpd tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
    1294:     }
    1295:   }
    1296:   return(0);
    1297: }

    1299: /*
    1300:   Version for when blocks are 1 by 1 Using natural ordering under new datastructure
    1301:   Modified from MatCholeskyFactorNumeric_SeqAIJ()
    1302: */
    1303: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_1_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
    1304: {
    1305:   Mat_SeqSBAIJ   *a=(Mat_SeqSBAIJ*)A->data;
    1306:   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)B->data;
    1308:   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp;
    1309:   PetscInt       *ai=a->i,*aj=a->j,*ajtmp;
    1310:   PetscInt       k,jmin,jmax,*c2r,*il,col,nexti,ili,nz;
    1311:   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
    1312:   FactorShiftCtx sctx;
    1313:   PetscReal      rs;
    1314:   MatScalar      d,*v;

    1317:   PetscMalloc3(mbs,&rtmp,mbs,&il,mbs,&c2r);

    1319:   /* MatPivotSetUp(): initialize shift context sctx */
    1320:   PetscMemzero(&sctx,sizeof(FactorShiftCtx));

    1322:   if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
    1323:     sctx.shift_top = info->zeropivot;

    1325:     PetscArrayzero(rtmp,mbs);

    1327:     for (i=0; i<mbs; i++) {
    1328:       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
    1329:       d        = (aa)[a->diag[i]];
    1330:       rtmp[i] += -PetscRealPart(d);  /* diagonal entry */
    1331:       ajtmp    = aj + ai[i] + 1;     /* exclude diagonal */
    1332:       v        = aa + ai[i] + 1;
    1333:       nz       = ai[i+1] - ai[i] - 1;
    1334:       for (j=0; j<nz; j++) {
    1335:         rtmp[i]        += PetscAbsScalar(v[j]);
    1336:         rtmp[ajtmp[j]] += PetscAbsScalar(v[j]);
    1337:       }
    1338:       if (PetscRealPart(rtmp[i]) > sctx.shift_top) sctx.shift_top = PetscRealPart(rtmp[i]);
    1339:     }
    1340:     sctx.shift_top *= 1.1;
    1341:     sctx.nshift_max = 5;
    1342:     sctx.shift_lo   = 0.;
    1343:     sctx.shift_hi   = 1.;
    1344:   }

    1346:   /* allocate working arrays
    1347:      c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col
    1348:      il:  for active k row, il[i] gives the index of the 1st nonzero entry in U[i,k:n-1] in bj and ba arrays
    1349:   */
    1350:   do {
    1351:     sctx.newshift = PETSC_FALSE;

    1353:     for (i=0; i<mbs; i++) c2r[i] = mbs;
    1354:     if (mbs) il[0] = 0;

    1356:     for (k = 0; k<mbs; k++) {
    1357:       /* zero rtmp */
    1358:       nz    = bi[k+1] - bi[k];
    1359:       bjtmp = bj + bi[k];
    1360:       for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;

    1362:       /* load in initial unfactored row */
    1363:       bval = ba + bi[k];
    1364:       jmin = ai[k]; jmax = ai[k+1];
    1365:       for (j = jmin; j < jmax; j++) {
    1366:         col       = aj[j];
    1367:         rtmp[col] = aa[j];
    1368:         *bval++   = 0.0; /* for in-place factorization */
    1369:       }
    1370:       /* shift the diagonal of the matrix: ZeropivotApply() */
    1371:       rtmp[k] += sctx.shift_amount;  /* shift the diagonal of the matrix */

    1373:       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
    1374:       dk = rtmp[k];
    1375:       i  = c2r[k]; /* first row to be added to k_th row  */

    1377:       while (i < k) {
    1378:         nexti = c2r[i]; /* next row to be added to k_th row */

    1380:         /* compute multiplier, update diag(k) and U(i,k) */
    1381:         ili     = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
    1382:         uikdi   = -ba[ili]*ba[bdiag[i]]; /* diagonal(k) */
    1383:         dk     += uikdi*ba[ili]; /* update diag[k] */
    1384:         ba[ili] = uikdi; /* -U(i,k) */

    1386:         /* add multiple of row i to k-th row */
    1387:         jmin = ili + 1; jmax = bi[i+1];
    1388:         if (jmin < jmax) {
    1389:           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
    1390:           /* update il and c2r for row i */
    1391:           il[i] = jmin;
    1392:           j     = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i;
    1393:         }
    1394:         i = nexti;
    1395:       }

    1397:       /* copy data into U(k,:) */
    1398:       rs   = 0.0;
    1399:       jmin = bi[k]; jmax = bi[k+1]-1;
    1400:       if (jmin < jmax) {
    1401:         for (j=jmin; j<jmax; j++) {
    1402:           col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]);
    1403:         }
    1404:         /* add the k-th row into il and c2r */
    1405:         il[k] = jmin;
    1406:         i     = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k;
    1407:       }

    1409:       sctx.rs = rs;
    1410:       sctx.pv = dk;
    1411:       MatPivotCheck(B,A,info,&sctx,k);
    1412:       if (sctx.newshift) break;
    1413:       dk = sctx.pv;

    1415:       ba[bdiag[k]] = 1.0/dk; /* U(k,k) */
    1416:     }
    1417:   } while (sctx.newshift);

    1419:   PetscFree3(rtmp,il,c2r);

    1421:   B->ops->solve          = MatSolve_SeqSBAIJ_1_NaturalOrdering;
    1422:   B->ops->solves         = MatSolves_SeqSBAIJ_1;
    1423:   B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering;
    1424:   B->ops->matsolve       = MatMatSolve_SeqSBAIJ_1_NaturalOrdering;
    1425:   B->ops->forwardsolve   = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering;
    1426:   B->ops->backwardsolve  = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering;

    1428:   B->assembled    = PETSC_TRUE;
    1429:   B->preallocated = PETSC_TRUE;

    1431:   PetscLogFlops(B->rmap->n);

    1433:   /* MatPivotView() */
    1434:   if (sctx.nshift) {
    1435:     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
    1436:       PetscInfo4(A,"number of shift_pd tries %D, shift_amount %g, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,(double)sctx.shift_amount,(double)sctx.shift_fraction,(double)sctx.shift_top);
    1437:     } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
    1438:       PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
    1439:     } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS) {
    1440:       PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %g\n",sctx.nshift,(double)info->shiftamount);
    1441:     }
    1442:   }
    1443:   return(0);
    1444: }

    1446: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_1_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
    1447: {
    1448:   Mat_SeqSBAIJ   *a=(Mat_SeqSBAIJ*)A->data,*b=(Mat_SeqSBAIJ*)C->data;
    1450:   PetscInt       i,j,mbs = a->mbs;
    1451:   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
    1452:   PetscInt       k,jmin,*jl,*il,nexti,ili,*acol,*bcol,nz;
    1453:   MatScalar      *rtmp,*ba=b->a,*aa=a->a,dk,uikdi,*aval,*bval;
    1454:   PetscReal      rs;
    1455:   FactorShiftCtx sctx;

    1458:   /* MatPivotSetUp(): initialize shift context sctx */
    1459:   PetscMemzero(&sctx,sizeof(FactorShiftCtx));

    1461:   /* initialization */
    1462:   /* il and jl record the first nonzero element in each row of the accessing
    1463:      window U(0:k, k:mbs-1).
    1464:      jl:    list of rows to be added to uneliminated rows
    1465:             i>= k: jl(i) is the first row to be added to row i
    1466:             i<  k: jl(i) is the row following row i in some list of rows
    1467:             jl(i) = mbs indicates the end of a list
    1468:      il(i): points to the first nonzero element in U(i,k:mbs-1)
    1469:   */
    1470:   PetscMalloc1(mbs,&rtmp);
    1471:   PetscMalloc2(mbs,&il,mbs,&jl);

    1473:   do {
    1474:     sctx.newshift = PETSC_FALSE;
    1475:     il[0] = 0;
    1476:     for (i=0; i<mbs; i++) {
    1477:       rtmp[i] = 0.0; jl[i] = mbs;
    1478:     }

    1480:     for (k = 0; k<mbs; k++) {
    1481:       /*initialize k-th row with elements nonzero in row perm(k) of A */
    1482:       nz   = ai[k+1] - ai[k];
    1483:       acol = aj + ai[k];
    1484:       aval = aa + ai[k];
    1485:       bval = ba + bi[k];
    1486:       while (nz--) {
    1487:         rtmp[*acol++] = *aval++;
    1488:         *bval++       = 0.0; /* for in-place factorization */
    1489:       }

    1491:       /* shift the diagonal of the matrix */
    1492:       if (sctx.nshift) rtmp[k] += sctx.shift_amount;

    1494:       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
    1495:       dk = rtmp[k];
    1496:       i  = jl[k]; /* first row to be added to k_th row  */

    1498:       while (i < k) {
    1499:         nexti = jl[i]; /* next row to be added to k_th row */
    1500:         /* compute multiplier, update D(k) and U(i,k) */
    1501:         ili     = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
    1502:         uikdi   = -ba[ili]*ba[bi[i]];
    1503:         dk     += uikdi*ba[ili];
    1504:         ba[ili] = uikdi; /* -U(i,k) */

    1506:         /* add multiple of row i to k-th row ... */
    1507:         jmin = ili + 1;
    1508:         nz   = bi[i+1] - jmin;
    1509:         if (nz > 0) {
    1510:           bcol = bj + jmin;
    1511:           bval = ba + jmin;
    1512:           PetscLogFlops(2.0*nz);
    1513:           while (nz--) rtmp[*bcol++] += uikdi*(*bval++);

    1515:           /* update il and jl for i-th row */
    1516:           il[i] = jmin;
    1517:           j     = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
    1518:         }
    1519:         i = nexti;
    1520:       }

    1522:       /* shift the diagonals when zero pivot is detected */
    1523:       /* compute rs=sum of abs(off-diagonal) */
    1524:       rs   = 0.0;
    1525:       jmin = bi[k]+1;
    1526:       nz   = bi[k+1] - jmin;
    1527:       if (nz) {
    1528:         bcol = bj + jmin;
    1529:         while (nz--) {
    1530:           rs += PetscAbsScalar(rtmp[*bcol]);
    1531:           bcol++;
    1532:         }
    1533:       }

    1535:       sctx.rs = rs;
    1536:       sctx.pv = dk;
    1537:       MatPivotCheck(C,A,info,&sctx,k);
    1538:       if (sctx.newshift) break;    /* sctx.shift_amount is updated */
    1539:       dk = sctx.pv;

    1541:       /* copy data into U(k,:) */
    1542:       ba[bi[k]] = 1.0/dk;
    1543:       jmin      = bi[k]+1;
    1544:       nz        = bi[k+1] - jmin;
    1545:       if (nz) {
    1546:         bcol = bj + jmin;
    1547:         bval = ba + jmin;
    1548:         while (nz--) {
    1549:           *bval++       = rtmp[*bcol];
    1550:           rtmp[*bcol++] = 0.0;
    1551:         }
    1552:         /* add k-th row into il and jl */
    1553:         il[k] = jmin;
    1554:         i     = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
    1555:       }
    1556:     } /* end of for (k = 0; k<mbs; k++) */
    1557:   } while (sctx.newshift);
    1558:   PetscFree(rtmp);
    1559:   PetscFree2(il,jl);

    1561:   C->ops->solve          = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
    1562:   C->ops->solves         = MatSolves_SeqSBAIJ_1_inplace;
    1563:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
    1564:   C->ops->forwardsolve   = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
    1565:   C->ops->backwardsolve  = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace;

    1567:   C->assembled    = PETSC_TRUE;
    1568:   C->preallocated = PETSC_TRUE;

    1570:   PetscLogFlops(C->rmap->N);
    1571:   if (sctx.nshift) {
    1572:     if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
    1573:       PetscInfo2(A,"number of shiftnz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
    1574:     } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
    1575:       PetscInfo2(A,"number of shiftpd tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
    1576:     }
    1577:   }
    1578:   return(0);
    1579: }

    1581: PetscErrorCode MatCholeskyFactor_SeqSBAIJ(Mat A,IS perm,const MatFactorInfo *info)
    1582: {
    1584:   Mat            C;

    1587:   MatGetFactor(A,"petsc",MAT_FACTOR_CHOLESKY,&C);
    1588:   MatCholeskyFactorSymbolic(C,A,perm,info);
    1589:   MatCholeskyFactorNumeric(C,A,info);

    1591:   A->ops->solve          = C->ops->solve;
    1592:   A->ops->solvetranspose = C->ops->solvetranspose;

    1594:   MatHeaderMerge(A,&C);
    1595:   return(0);
    1596: }