Date: 2015-10-02T22:09:38+00:00

Actual source code: sbaijfact.c
petsc-3.6.2 2015-10-02
Report Typos and Errors

      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: /*
      8:   input:
      9:    F -- numeric factor
     10:   output:
     11:    nneg, nzero, npos: matrix inertia
     12: */

     16: PetscErrorCode MatGetInertia_SeqSBAIJ(Mat F,PetscInt *nneig,PetscInt *nzero,PetscInt *npos)
     17: {
     18:   Mat_SeqSBAIJ *fact_ptr = (Mat_SeqSBAIJ*)F->data;
     19:   MatScalar    *dd       = fact_ptr->a;
     20:   PetscInt     mbs       =fact_ptr->mbs,bs=F->rmap->bs,i,nneig_tmp,npos_tmp,*fi = fact_ptr->diag;

     23:   if (bs != 1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for bs: %D >1 yet",bs);
     24:   nneig_tmp = 0; npos_tmp = 0;
     25:   for (i=0; i<mbs; i++) {
     26:     if (PetscRealPart(dd[*fi]) > 0.0) npos_tmp++;
     27:     else if (PetscRealPart(dd[*fi]) < 0.0) nneig_tmp++;
     28:     fi++;
     29:   }
     30:   if (nneig) *nneig = nneig_tmp;
     31:   if (npos)  *npos  = npos_tmp;
     32:   if (nzero) *nzero = mbs - nneig_tmp - npos_tmp;
     33:   return(0);
     34: }

     36: /*
     37:   Symbolic U^T*D*U factorization for SBAIJ format. Modified from SSF of YSMP.
     38:   Use Modified Sparse Row (MSR) storage for u and ju. See page 85, "Iterative Methods ..." by Saad.
     39: */
     42: PetscErrorCode MatCholeskyFactorSymbolic_SeqSBAIJ_MSR(Mat F,Mat A,IS perm,const MatFactorInfo *info)
     43: {
     44:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data,*b;
     46:   const PetscInt *rip,*ai,*aj;
     47:   PetscInt       i,mbs = a->mbs,*jutmp,bs = A->rmap->bs,bs2=a->bs2;
     48:   PetscInt       m,reallocs = 0,prow;
     49:   PetscInt       *jl,*q,jmin,jmax,juidx,nzk,qm,*iu,*ju,k,j,vj,umax,maxadd;
     50:   PetscReal      f = info->fill;
     51:   PetscBool      perm_identity;

     54:   /* check whether perm is the identity mapping */
     55:   ISIdentity(perm,&perm_identity);
     56:   ISGetIndices(perm,&rip);

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

     61:     ai = a->i; aj = a->j;
     62:   } else {            /* non-trivial permutation */
     63:     a->permute = PETSC_TRUE;

     65:     MatReorderingSeqSBAIJ(A,perm);

     67:     ai = a->inew; aj = a->jnew;
     68:   }

     70:   /* initialization */
     71:   PetscMalloc1(mbs+1,&iu);
     72:   umax  = (PetscInt)(f*ai[mbs] + 1); umax += mbs + 1;
     73:   PetscMalloc1(umax,&ju);
     74:   iu[0] = mbs+1;
     75:   juidx = mbs + 1; /* index for ju */
     76:   /* jl linked list for pivot row -- linked list for col index */
     77:   PetscMalloc2(mbs,&jl,mbs,&q);
     78:   for (i=0; i<mbs; i++) {
     79:     jl[i] = mbs;
     80:     q[i]  = 0;
     81:   }

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

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

    110:     while (prow < k) {
    111:       /* merge row prow into k-th row */
    112:       jmin = iu[prow] + 1; jmax = iu[prow+1];
    113:       qm   = k;
    114:       for (j=jmin; j<jmax; j++) {
    115:         vj = ju[j];
    116:         do {
    117:           m = qm; qm = q[m];
    118:         } while (qm < vj);
    119:         if (qm != vj) {
    120:           nzk++; q[m] = vj; q[vj] = qm; qm = vj;
    121:         }
    122:       }
    123:       prow = jl[prow]; /* next pivot row */
    124:     }

    126:     /* add k to row list for first nonzero element in k-th row */
    127:     if (nzk > 0) {
    128:       i     = q[k]; /* col value of first nonzero element in U(k, k+1:mbs-1) */
    129:       jl[k] = jl[i]; jl[i] = k;
    130:     }
    131:     iu[k+1] = iu[k] + nzk;

    133:     /* allocate more space to ju if needed */
    134:     if (iu[k+1] > umax) {
    135:       /* estimate how much additional space we will need */
    136:       /* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */
    137:       /* just double the memory each time */
    138:       maxadd = umax;
    139:       if (maxadd < nzk) maxadd = (mbs-k)*(nzk+1)/2;
    140:       umax += maxadd;

    142:       /* allocate a longer ju */
    143:       PetscMalloc1(umax,&jutmp);
    144:       PetscMemcpy(jutmp,ju,iu[k]*sizeof(PetscInt));
    145:       PetscFree(ju);
    146:       ju   = jutmp;
    147:       reallocs++; /* count how many times we realloc */
    148:     }

    150:     /* save nonzero structure of k-th row in ju */
    151:     i=k;
    152:     while (nzk--) {
    153:       i           = q[i];
    154:       ju[juidx++] = i;
    155:     }
    156:   }

    158: #if defined(PETSC_USE_INFO)
    159:   if (ai[mbs] != 0) {
    160:     PetscReal af = ((PetscReal)iu[mbs])/((PetscReal)ai[mbs]);
    161:     PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);
    162:     PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
    163:     PetscInfo1(A,"PCFactorSetFill(pc,%g);\n",(double)af);
    164:     PetscInfo(A,"for best performance.\n");
    165:   } else {
    166:     PetscInfo(A,"Empty matrix.\n");
    167:   }
    168: #endif

    170:   ISRestoreIndices(perm,&rip);
    171:   PetscFree2(jl,q);

    173:   /* put together the new matrix */
    174:   MatSeqSBAIJSetPreallocation_SeqSBAIJ(F,bs,MAT_SKIP_ALLOCATION,NULL);

    176:   /* PetscLogObjectParent((PetscObject)B,(PetscObject)iperm); */
    177:   b                = (Mat_SeqSBAIJ*)(F)->data;
    178:   b->singlemalloc  = PETSC_FALSE;
    179:   b->free_a        = PETSC_TRUE;
    180:   b->free_ij       = PETSC_TRUE;

    182:   PetscMalloc1((iu[mbs]+1)*bs2,&b->a);
    183:   b->j    = ju;
    184:   b->i    = iu;
    185:   b->diag = 0;
    186:   b->ilen = 0;
    187:   b->imax = 0;
    188:   b->row  = perm;

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

    192:   PetscObjectReference((PetscObject)perm);

    194:   b->icol = perm;
    195:   PetscObjectReference((PetscObject)perm);
    196:   PetscMalloc1(bs*mbs+bs,&b->solve_work);
    197:   /* In b structure:  Free imax, ilen, old a, old j.
    198:      Allocate idnew, solve_work, new a, new j */
    199:   PetscLogObjectMemory((PetscObject)F,(iu[mbs]-mbs)*(sizeof(PetscInt)+sizeof(MatScalar)));
    200:   b->maxnz = b->nz = iu[mbs];

    202:   (F)->info.factor_mallocs   = reallocs;
    203:   (F)->info.fill_ratio_given = f;
    204:   if (ai[mbs] != 0) {
    205:     (F)->info.fill_ratio_needed = ((PetscReal)iu[mbs])/((PetscReal)ai[mbs]);
    206:   } else {
    207:     (F)->info.fill_ratio_needed = 0.0;
    208:   }
    209:   MatSeqSBAIJSetNumericFactorization_inplace(F,perm_identity);
    210:   return(0);
    211: }
    212: /*
    213:     Symbolic U^T*D*U factorization for SBAIJ format.
    214:     See MatICCFactorSymbolic_SeqAIJ() for description of its data structure.
    215: */
    216: #include <petscbt.h>
    217: #include <../src/mat/utils/freespace.h>
    220: PetscErrorCode MatCholeskyFactorSymbolic_SeqSBAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
    221: {
    222:   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data;
    223:   Mat_SeqSBAIJ       *b;
    224:   PetscErrorCode     ierr;
    225:   PetscBool          perm_identity,missing;
    226:   PetscReal          fill = info->fill;
    227:   const PetscInt     *rip,*ai=a->i,*aj=a->j;
    228:   PetscInt           i,mbs=a->mbs,bs=A->rmap->bs,reallocs=0,prow;
    229:   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
    230:   PetscInt           nlnk,*lnk,ncols,*cols,*uj,**ui_ptr,*uj_ptr,*udiag;
    231:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
    232:   PetscBT            lnkbt;

    235:   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);
    236:   MatMissingDiagonal(A,&missing,&i);
    237:   if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
    238:   if (bs > 1) {
    239:     MatCholeskyFactorSymbolic_SeqSBAIJ_inplace(fact,A,perm,info);
    240:     return(0);
    241:   }

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

    249:   /* initialization */
    250:   PetscMalloc1(mbs+1,&ui);
    251:   PetscMalloc1(mbs+1,&udiag);
    252:   ui[0] = 0;

    254:   /* jl: linked list for storing indices of the pivot rows
    255:      il: il[i] points to the 1st nonzero entry of U(i,k:mbs-1) */
    256:   PetscMalloc4(mbs,&ui_ptr,mbs,&il,mbs,&jl,mbs,&cols);
    257:   for (i=0; i<mbs; i++) {
    258:     jl[i] = mbs; il[i] = 0;
    259:   }

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

    265:   /* initial FreeSpace size is fill*(ai[mbs]+1) */
    266:   PetscFreeSpaceGet((PetscInt)(fill*(ai[mbs]+1)),&free_space);
    267:   current_space = free_space;

    269:   for (k=0; k<mbs; k++) {  /* for each active row k */
    270:     /* initialize lnk by the column indices of row rip[k] of A */
    271:     nzk   = 0;
    272:     ncols = ai[k+1] - ai[k];
    273:     if (!ncols) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Empty row %D in matrix ",k);
    274:     for (j=0; j<ncols; j++) {
    275:       i       = *(aj + ai[k] + j);
    276:       cols[j] = i;
    277:     }
    278:     PetscLLAdd(ncols,cols,mbs,nlnk,lnk,lnkbt);
    279:     nzk += nlnk;

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

    284:     while (prow < k) {
    285:       nextprow = jl[prow];
    286:       /* merge prow into k-th row */
    287:       jmin   = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:mbs-1) */
    288:       jmax   = ui[prow+1];
    289:       ncols  = jmax-jmin;
    290:       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:mbs-1) */
    291:       PetscLLAddSorted(ncols,uj_ptr,mbs,nlnk,lnk,lnkbt);
    292:       nzk   += nlnk;

    294:       /* update il and jl for prow */
    295:       if (jmin < jmax) {
    296:         il[prow] = jmin;
    297:         j        = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
    298:       }
    299:       prow = nextprow;
    300:     }

    302:     /* if free space is not available, make more free space */
    303:     if (current_space->local_remaining<nzk) {
    304:       i    = mbs - k + 1; /* num of unfactored rows */
    305:       i   *= PetscMin(nzk, i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */
    306:       PetscFreeSpaceGet(i,&current_space);
    307:       reallocs++;
    308:     }

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

    313:     /* add the k-th row into il and jl */
    314:     if (nzk > 1) {
    315:       i     = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:mbs-1) */
    316:       jl[k] = jl[i]; jl[i] = k;
    317:       il[k] = ui[k] + 1;
    318:     }
    319:     ui_ptr[k] = current_space->array;

    321:     current_space->array           += nzk;
    322:     current_space->local_used      += nzk;
    323:     current_space->local_remaining -= nzk;

    325:     ui[k+1] = ui[k] + nzk;
    326:   }

    328:   ISRestoreIndices(perm,&rip);
    329:   PetscFree4(ui_ptr,il,jl,cols);

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

    336:   /* put together the new matrix in MATSEQSBAIJ format */
    337:   MatSeqSBAIJSetPreallocation_SeqSBAIJ(fact,bs,MAT_SKIP_ALLOCATION,NULL);

    339:   b               = (Mat_SeqSBAIJ*)fact->data;
    340:   b->singlemalloc = PETSC_FALSE;
    341:   b->free_a       = PETSC_TRUE;
    342:   b->free_ij      = PETSC_TRUE;

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

    346:   b->j         = uj;
    347:   b->i         = ui;
    348:   b->diag      = udiag;
    349:   b->free_diag = PETSC_TRUE;
    350:   b->ilen      = 0;
    351:   b->imax      = 0;
    352:   b->row       = perm;
    353:   b->icol      = perm;

    355:   PetscObjectReference((PetscObject)perm);
    356:   PetscObjectReference((PetscObject)perm);

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

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

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

    365:   fact->info.factor_mallocs   = reallocs;
    366:   fact->info.fill_ratio_given = fill;
    367:   if (ai[mbs] != 0) {
    368:     fact->info.fill_ratio_needed = ((PetscReal)ui[mbs])/ai[mbs];
    369:   } else {
    370:     fact->info.fill_ratio_needed = 0.0;
    371:   }
    372: #if defined(PETSC_USE_INFO)
    373:   if (ai[mbs] != 0) {
    374:     PetscReal af = fact->info.fill_ratio_needed;
    375:     PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);
    376:     PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
    377:     PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);
    378:   } else {
    379:     PetscInfo(A,"Empty matrix.\n");
    380:   }
    381: #endif
    382:   fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqSBAIJ_1_NaturalOrdering;
    383:   return(0);
    384: }

    388: PetscErrorCode MatCholeskyFactorSymbolic_SeqSBAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
    389: {
    390:   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data;
    391:   Mat_SeqSBAIJ       *b;
    392:   PetscErrorCode     ierr;
    393:   PetscBool          perm_identity,missing;
    394:   PetscReal          fill = info->fill;
    395:   const PetscInt     *rip,*ai,*aj;
    396:   PetscInt           i,mbs=a->mbs,bs=A->rmap->bs,reallocs=0,prow,d;
    397:   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
    398:   PetscInt           nlnk,*lnk,ncols,*cols,*uj,**ui_ptr,*uj_ptr;
    399:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
    400:   PetscBT            lnkbt;

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

    406:   /*
    407:    This code originally uses Modified Sparse Row (MSR) storage
    408:    (see page 85, "Iterative Methods ..." by Saad) for the output matrix B - bad choise!
    409:    Then it is rewritten so the factor B takes seqsbaij format. However the associated
    410:    MatCholeskyFactorNumeric_() have not been modified for the cases of bs>1 or !perm_identity,
    411:    thus the original code in MSR format is still used for these cases.
    412:    The code below should replace MatCholeskyFactorSymbolic_SeqSBAIJ_MSR() whenever
    413:    MatCholeskyFactorNumeric_() is modified for using sbaij symbolic factor.
    414:   */
    415:   if (bs > 1) {
    416:     MatCholeskyFactorSymbolic_SeqSBAIJ_MSR(fact,A,perm,info);
    417:     return(0);
    418:   }

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

    423:   if (perm_identity) {
    424:     a->permute = PETSC_FALSE;

    426:     ai = a->i; aj = a->j;
    427:   } else {
    428:     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix reordering is not supported for sbaij matrix. Use aij format");
    429: #if 0
    430:     /* There are bugs for reordeing. Needs further work.
    431:        MatReordering for sbaij cannot be efficient. User should use aij formt! */
    432:     a->permute = PETSC_TRUE;

    434:     MatReorderingSeqSBAIJ(A,perm);
    435:     ai   = a->inew; aj = a->jnew;
    436: #endif
    437:   }
    438:   ISGetIndices(perm,&rip);

    440:   /* initialization */
    441:   PetscMalloc1(mbs+1,&ui);
    442:   ui[0] = 0;

    444:   /* jl: linked list for storing indices of the pivot rows
    445:      il: il[i] points to the 1st nonzero entry of U(i,k:mbs-1) */
    446:   PetscMalloc4(mbs,&ui_ptr,mbs,&il,mbs,&jl,mbs,&cols);
    447:   for (i=0; i<mbs; i++) {
    448:     jl[i] = mbs; il[i] = 0;
    449:   }

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

    455:   /* initial FreeSpace size is fill*(ai[mbs]+1) */
    456:   PetscFreeSpaceGet((PetscInt)(fill*(ai[mbs]+1)),&free_space);
    457:   current_space = free_space;

    459:   for (k=0; k<mbs; k++) {  /* for each active row k */
    460:     /* initialize lnk by the column indices of row rip[k] of A */
    461:     nzk   = 0;
    462:     ncols = ai[rip[k]+1] - ai[rip[k]];
    463:     for (j=0; j<ncols; j++) {
    464:       i       = *(aj + ai[rip[k]] + j);
    465:       cols[j] = rip[i];
    466:     }
    467:     PetscLLAdd(ncols,cols,mbs,nlnk,lnk,lnkbt);
    468:     nzk += nlnk;

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

    473:     while (prow < k) {
    474:       nextprow = jl[prow];
    475:       /* merge prow into k-th row */
    476:       jmin   = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:mbs-1) */
    477:       jmax   = ui[prow+1];
    478:       ncols  = jmax-jmin;
    479:       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:mbs-1) */
    480:       PetscLLAddSorted(ncols,uj_ptr,mbs,nlnk,lnk,lnkbt);
    481:       nzk   += nlnk;

    483:       /* update il and jl for prow */
    484:       if (jmin < jmax) {
    485:         il[prow] = jmin;

    487:         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
    488:       }
    489:       prow = nextprow;
    490:     }

    492:     /* if free space is not available, make more free space */
    493:     if (current_space->local_remaining<nzk) {
    494:       i    = mbs - k + 1; /* num of unfactored rows */
    495:       i    = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
    496:       PetscFreeSpaceGet(i,&current_space);
    497:       reallocs++;
    498:     }

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

    503:     /* add the k-th row into il and jl */
    504:     if (nzk-1 > 0) {
    505:       i     = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:mbs-1) */
    506:       jl[k] = jl[i]; jl[i] = k;
    507:       il[k] = ui[k] + 1;
    508:     }
    509:     ui_ptr[k] = current_space->array;

    511:     current_space->array           += nzk;
    512:     current_space->local_used      += nzk;
    513:     current_space->local_remaining -= nzk;

    515:     ui[k+1] = ui[k] + nzk;
    516:   }

    518:   ISRestoreIndices(perm,&rip);
    519:   PetscFree4(ui_ptr,il,jl,cols);

    521:   /* destroy list of free space and other temporary array(s) */
    522:   PetscMalloc1(ui[mbs]+1,&uj);
    523:   PetscFreeSpaceContiguous(&free_space,uj);
    524:   PetscLLDestroy(lnk,lnkbt);

    526:   /* put together the new matrix in MATSEQSBAIJ format */
    527:   MatSeqSBAIJSetPreallocation_SeqSBAIJ(fact,bs,MAT_SKIP_ALLOCATION,NULL);

    529:   b               = (Mat_SeqSBAIJ*)fact->data;
    530:   b->singlemalloc = PETSC_FALSE;
    531:   b->free_a       = PETSC_TRUE;
    532:   b->free_ij      = PETSC_TRUE;

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

    536:   b->j    = uj;
    537:   b->i    = ui;
    538:   b->diag = 0;
    539:   b->ilen = 0;
    540:   b->imax = 0;
    541:   b->row  = perm;

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

    545:   PetscObjectReference((PetscObject)perm);
    546:   b->icol  = perm;
    547:   PetscObjectReference((PetscObject)perm);
    548:   PetscMalloc1(mbs+1,&b->solve_work);
    549:   PetscLogObjectMemory((PetscObject)fact,(ui[mbs]-mbs)*(sizeof(PetscInt)+sizeof(MatScalar)));
    550:   b->maxnz = b->nz = ui[mbs];

    552:   fact->info.factor_mallocs   = reallocs;
    553:   fact->info.fill_ratio_given = fill;
    554:   if (ai[mbs] != 0) {
    555:     fact->info.fill_ratio_needed = ((PetscReal)ui[mbs])/ai[mbs];
    556:   } else {
    557:     fact->info.fill_ratio_needed = 0.0;
    558:   }
    559: #if defined(PETSC_USE_INFO)
    560:   if (ai[mbs] != 0) {
    561:     PetscReal af = fact->info.fill_ratio_needed;
    562:     PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);
    563:     PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
    564:     PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);
    565:   } else {
    566:     PetscInfo(A,"Empty matrix.\n");
    567:   }
    568: #endif
    569:   MatSeqSBAIJSetNumericFactorization_inplace(fact,perm_identity);
    570:   return(0);
    571: }

    575: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_N(Mat C,Mat A,const MatFactorInfo *info)
    576: {
    577:   Mat_SeqSBAIJ   *a   = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
    578:   IS             perm = b->row;
    580:   const PetscInt *ai,*aj,*perm_ptr,mbs=a->mbs,*bi=b->i,*bj=b->j;
    581:   PetscInt       i,j;
    582:   PetscInt       *a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
    583:   PetscInt       bs  =A->rmap->bs,bs2 = a->bs2,bslog = 0;
    584:   MatScalar      *ba = b->a,*aa,*ap,*dk,*uik;
    585:   MatScalar      *u,*diag,*rtmp,*rtmp_ptr;
    586:   MatScalar      *work;
    587:   PetscInt       *pivots;

    590:   /* initialization */
    591:   PetscCalloc1(bs2*mbs,&rtmp);
    592:   PetscMalloc2(mbs,&il,mbs,&jl);
    593:   for (i=0; i<mbs; i++) {
    594:     jl[i] = mbs; il[0] = 0;
    595:   }
    596:   PetscMalloc3(bs2,&dk,bs2,&uik,bs,&work);
    597:   PetscMalloc1(bs,&pivots);

    599:   ISGetIndices(perm,&perm_ptr);

    601:   /* check permutation */
    602:   if (!a->permute) {
    603:     ai = a->i; aj = a->j; aa = a->a;
    604:   } else {
    605:     ai   = a->inew; aj = a->jnew;
    606:     PetscMalloc1(bs2*ai[mbs],&aa);
    607:     PetscMemcpy(aa,a->a,bs2*ai[mbs]*sizeof(MatScalar));
    608:     PetscMalloc1(ai[mbs],&a2anew);
    609:     PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(PetscInt));

    611:     /* flops in while loop */
    612:     bslog = 2*bs*bs2;

    614:     for (i=0; i<mbs; i++) {
    615:       jmin = ai[i]; jmax = ai[i+1];
    616:       for (j=jmin; j<jmax; j++) {
    617:         while (a2anew[j] != j) {
    618:           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
    619:           for (k1=0; k1<bs2; k1++) {
    620:             dk[k1]       = aa[k*bs2+k1];
    621:             aa[k*bs2+k1] = aa[j*bs2+k1];
    622:             aa[j*bs2+k1] = dk[k1];
    623:           }
    624:         }
    625:         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
    626:         if (i > aj[j]) {
    627:           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
    628:           ap = aa + j*bs2;                     /* ptr to the beginning of j-th block of aa */
    629:           for (k=0; k<bs2; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
    630:           for (k=0; k<bs; k++) {               /* j-th block of aa <- dk^T */
    631:             for (k1=0; k1<bs; k1++) *ap++ = dk[k + bs*k1];
    632:           }
    633:         }
    634:       }
    635:     }
    636:     PetscFree(a2anew);
    637:   }

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

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

    645:     ap = aa + jmin*bs2;
    646:     for (j = jmin; j < jmax; j++) {
    647:       vj       = perm_ptr[aj[j]];   /* block col. index */
    648:       rtmp_ptr = rtmp + vj*bs2;
    649:       for (i=0; i<bs2; i++) *rtmp_ptr++ = *ap++;
    650:     }

    652:     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
    653:     PetscMemcpy(dk,rtmp+k*bs2,bs2*sizeof(MatScalar));
    654:     i    = jl[k]; /* first row to be added to k_th row  */

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

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

    662:       /* uik = -inv(Di)*U_bar(i,k) */
    663:       diag = ba + i*bs2;
    664:       u    = ba + ili*bs2;
    665:       PetscMemzero(uik,bs2*sizeof(MatScalar));
    666:       PetscKernel_A_gets_A_minus_B_times_C(bs,uik,diag,u);

    668:       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
    669:       PetscKernel_A_gets_A_plus_Btranspose_times_C(bs,dk,uik,u);
    670:       PetscLogFlops(bslog*2.0);

    672:       /* update -U(i,k) */
    673:       PetscMemcpy(ba+ili*bs2,uik,bs2*sizeof(MatScalar));

    675:       /* add multiple of row i to k-th row ... */
    676:       jmin = ili + 1; jmax = bi[i+1];
    677:       if (jmin < jmax) {
    678:         for (j=jmin; j<jmax; j++) {
    679:           /* rtmp += -U(i,k)^T * U_bar(i,j) */
    680:           rtmp_ptr = rtmp + bj[j]*bs2;
    681:           u        = ba + j*bs2;
    682:           PetscKernel_A_gets_A_plus_Btranspose_times_C(bs,rtmp_ptr,uik,u);
    683:         }
    684:         PetscLogFlops(bslog*(jmax-jmin));

    686:         /* ... add i to row list for next nonzero entry */
    687:         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
    688:         j     = bj[jmin];
    689:         jl[i] = jl[j]; jl[j] = i; /* update jl */
    690:       }
    691:       i = nexti;
    692:     }

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

    696:     /* invert diagonal block */
    697:     diag = ba+k*bs2;
    698:     PetscMemcpy(diag,dk,bs2*sizeof(MatScalar));
    699:     PetscKernel_A_gets_inverse_A(bs,diag,pivots,work);

    701:     jmin = bi[k]; jmax = bi[k+1];
    702:     if (jmin < jmax) {
    703:       for (j=jmin; j<jmax; j++) {
    704:         vj       = bj[j];      /* block col. index of U */
    705:         u        = ba + j*bs2;
    706:         rtmp_ptr = rtmp + vj*bs2;
    707:         for (k1=0; k1<bs2; k1++) {
    708:           *u++        = *rtmp_ptr;
    709:           *rtmp_ptr++ = 0.0;
    710:         }
    711:       }

    713:       /* ... add k to row list for first nonzero entry in k-th row */
    714:       il[k] = jmin;
    715:       i     = bj[jmin];
    716:       jl[k] = jl[i]; jl[i] = k;
    717:     }
    718:   }

    720:   PetscFree(rtmp);
    721:   PetscFree2(il,jl);
    722:   PetscFree3(dk,uik,work);
    723:   PetscFree(pivots);
    724:   if (a->permute) {
    725:     PetscFree(aa);
    726:   }

    728:   ISRestoreIndices(perm,&perm_ptr);

    730:   C->ops->solve          = MatSolve_SeqSBAIJ_N_inplace;
    731:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_N_inplace;
    732:   C->ops->forwardsolve   = MatForwardSolve_SeqSBAIJ_N_inplace;
    733:   C->ops->backwardsolve  = MatBackwardSolve_SeqSBAIJ_N_inplace;

    735:   C->assembled    = PETSC_TRUE;
    736:   C->preallocated = PETSC_TRUE;

    738:   PetscLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
    739:   return(0);
    740: }

    744: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_N_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info)
    745: {
    746:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
    748:   PetscInt       i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
    749:   PetscInt       *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
    750:   PetscInt       bs  =A->rmap->bs,bs2 = a->bs2,bslog;
    751:   MatScalar      *ba = b->a,*aa,*ap,*dk,*uik;
    752:   MatScalar      *u,*diag,*rtmp,*rtmp_ptr;
    753:   MatScalar      *work;
    754:   PetscInt       *pivots;

    757:   PetscCalloc1(bs2*mbs,&rtmp);
    758:   PetscMalloc2(mbs,&il,mbs,&jl);
    759:   for (i=0; i<mbs; i++) {
    760:     jl[i] = mbs; il[0] = 0;
    761:   }
    762:   PetscMalloc3(bs2,&dk,bs2,&uik,bs,&work);
    763:   PetscMalloc1(bs,&pivots);

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

    767:   /* flops in while loop */
    768:   bslog = 2*bs*bs2;

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

    773:     /*initialize k-th row with elements nonzero in row k of A */
    774:     jmin = ai[k]; jmax = ai[k+1];
    775:     ap   = aa + jmin*bs2;
    776:     for (j = jmin; j < jmax; j++) {
    777:       vj       = aj[j];   /* block col. index */
    778:       rtmp_ptr = rtmp + vj*bs2;
    779:       for (i=0; i<bs2; i++) *rtmp_ptr++ = *ap++;
    780:     }

    782:     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
    783:     PetscMemcpy(dk,rtmp+k*bs2,bs2*sizeof(MatScalar));
    784:     i    = jl[k]; /* first row to be added to k_th row  */

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

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

    792:       /* uik = -inv(Di)*U_bar(i,k) */
    793:       diag = ba + i*bs2;
    794:       u    = ba + ili*bs2;
    795:       PetscMemzero(uik,bs2*sizeof(MatScalar));
    796:       PetscKernel_A_gets_A_minus_B_times_C(bs,uik,diag,u);

    798:       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
    799:       PetscKernel_A_gets_A_plus_Btranspose_times_C(bs,dk,uik,u);
    800:       PetscLogFlops(bslog*2.0);

    802:       /* update -U(i,k) */
    803:       PetscMemcpy(ba+ili*bs2,uik,bs2*sizeof(MatScalar));

    805:       /* add multiple of row i to k-th row ... */
    806:       jmin = ili + 1; jmax = bi[i+1];
    807:       if (jmin < jmax) {
    808:         for (j=jmin; j<jmax; j++) {
    809:           /* rtmp += -U(i,k)^T * U_bar(i,j) */
    810:           rtmp_ptr = rtmp + bj[j]*bs2;
    811:           u        = ba + j*bs2;
    812:           PetscKernel_A_gets_A_plus_Btranspose_times_C(bs,rtmp_ptr,uik,u);
    813:         }
    814:         PetscLogFlops(bslog*(jmax-jmin));

    816:         /* ... add i to row list for next nonzero entry */
    817:         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
    818:         j     = bj[jmin];
    819:         jl[i] = jl[j]; jl[j] = i; /* update jl */
    820:       }
    821:       i = nexti;
    822:     }

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

    826:     /* invert diagonal block */
    827:     diag = ba+k*bs2;
    828:     PetscMemcpy(diag,dk,bs2*sizeof(MatScalar));
    829:     PetscKernel_A_gets_inverse_A(bs,diag,pivots,work);

    831:     jmin = bi[k]; jmax = bi[k+1];
    832:     if (jmin < jmax) {
    833:       for (j=jmin; j<jmax; j++) {
    834:         vj       = bj[j];      /* block col. index of U */
    835:         u        = ba + j*bs2;
    836:         rtmp_ptr = rtmp + vj*bs2;
    837:         for (k1=0; k1<bs2; k1++) {
    838:           *u++        = *rtmp_ptr;
    839:           *rtmp_ptr++ = 0.0;
    840:         }
    841:       }

    843:       /* ... add k to row list for first nonzero entry in k-th row */
    844:       il[k] = jmin;
    845:       i     = bj[jmin];
    846:       jl[k] = jl[i]; jl[i] = k;
    847:     }
    848:   }

    850:   PetscFree(rtmp);
    851:   PetscFree2(il,jl);
    852:   PetscFree3(dk,uik,work);
    853:   PetscFree(pivots);

    855:   C->ops->solve          = MatSolve_SeqSBAIJ_N_NaturalOrdering_inplace;
    856:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_N_NaturalOrdering_inplace;
    857:   C->ops->forwardsolve   = MatForwardSolve_SeqSBAIJ_N_NaturalOrdering_inplace;
    858:   C->ops->backwardsolve  = MatBackwardSolve_SeqSBAIJ_N_NaturalOrdering_inplace;
    859:   C->assembled           = PETSC_TRUE;
    860:   C->preallocated        = PETSC_TRUE;

    862:   PetscLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
    863:   return(0);
    864: }

    866: /*
    867:     Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP.
    868:     Version for blocks 2 by 2.
    869: */
    872: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_2(Mat C,Mat A,const MatFactorInfo *info)
    873: {
    874:   Mat_SeqSBAIJ   *a   = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
    875:   IS             perm = b->row;
    877:   const PetscInt *ai,*aj,*perm_ptr;
    878:   PetscInt       i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
    879:   PetscInt       *a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
    880:   MatScalar      *ba = b->a,*aa,*ap;
    881:   MatScalar      *u,*diag,*rtmp,*rtmp_ptr,dk[4],uik[4];
    882:   PetscReal      shift = info->shiftamount;

    885:   /* initialization */
    886:   /* il and jl record the first nonzero element in each row of the accessing
    887:      window U(0:k, k:mbs-1).
    888:      jl:    list of rows to be added to uneliminated rows
    889:             i>= k: jl(i) is the first row to be added to row i
    890:             i<  k: jl(i) is the row following row i in some list of rows
    891:             jl(i) = mbs indicates the end of a list
    892:      il(i): points to the first nonzero element in columns k,...,mbs-1 of
    893:             row i of U */
    894:   PetscCalloc1(4*mbs,&rtmp);
    895:   PetscMalloc2(mbs,&il,mbs,&jl);
    896:   for (i=0; i<mbs; i++) {
    897:     jl[i] = mbs; il[0] = 0;
    898:   }
    899:   ISGetIndices(perm,&perm_ptr);

    901:   /* check permutation */
    902:   if (!a->permute) {
    903:     ai = a->i; aj = a->j; aa = a->a;
    904:   } else {
    905:     ai   = a->inew; aj = a->jnew;
    906:     PetscMalloc1(4*ai[mbs],&aa);
    907:     PetscMemcpy(aa,a->a,4*ai[mbs]*sizeof(MatScalar));
    908:     PetscMalloc1(ai[mbs],&a2anew);
    909:     PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(PetscInt));

    911:     for (i=0; i<mbs; i++) {
    912:       jmin = ai[i]; jmax = ai[i+1];
    913:       for (j=jmin; j<jmax; j++) {
    914:         while (a2anew[j] != j) {
    915:           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
    916:           for (k1=0; k1<4; k1++) {
    917:             dk[k1]     = aa[k*4+k1];
    918:             aa[k*4+k1] = aa[j*4+k1];
    919:             aa[j*4+k1] = dk[k1];
    920:           }
    921:         }
    922:         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
    923:         if (i > aj[j]) {
    924:           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
    925:           ap    = aa + j*4;  /* ptr to the beginning of the block */
    926:           dk[1] = ap[1];     /* swap ap[1] and ap[2] */
    927:           ap[1] = ap[2];
    928:           ap[2] = dk[1];
    929:         }
    930:       }
    931:     }
    932:     PetscFree(a2anew);
    933:   }

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

    938:     /*initialize k-th row with elements nonzero in row perm(k) of A */
    939:     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
    940:     ap   = aa + jmin*4;
    941:     for (j = jmin; j < jmax; j++) {
    942:       vj       = perm_ptr[aj[j]];   /* block col. index */
    943:       rtmp_ptr = rtmp + vj*4;
    944:       for (i=0; i<4; i++) *rtmp_ptr++ = *ap++;
    945:     }

    947:     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
    948:     PetscMemcpy(dk,rtmp+k*4,4*sizeof(MatScalar));
    949:     i    = jl[k]; /* first row to be added to k_th row  */

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

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

    957:       /* uik = -inv(Di)*U_bar(i,k): - ba[ili]*ba[i] */
    958:       diag   = ba + i*4;
    959:       u      = ba + ili*4;
    960:       uik[0] = -(diag[0]*u[0] + diag[2]*u[1]);
    961:       uik[1] = -(diag[1]*u[0] + diag[3]*u[1]);
    962:       uik[2] = -(diag[0]*u[2] + diag[2]*u[3]);
    963:       uik[3] = -(diag[1]*u[2] + diag[3]*u[3]);

    965:       /* update D(k) += -U(i,k)^T * U_bar(i,k): dk += uik*ba[ili] */
    966:       dk[0] += uik[0]*u[0] + uik[1]*u[1];
    967:       dk[1] += uik[2]*u[0] + uik[3]*u[1];
    968:       dk[2] += uik[0]*u[2] + uik[1]*u[3];
    969:       dk[3] += uik[2]*u[2] + uik[3]*u[3];

    971:       PetscLogFlops(16.0*2.0);

    973:       /* update -U(i,k): ba[ili] = uik */
    974:       PetscMemcpy(ba+ili*4,uik,4*sizeof(MatScalar));

    976:       /* add multiple of row i to k-th row ... */
    977:       jmin = ili + 1; jmax = bi[i+1];
    978:       if (jmin < jmax) {
    979:         for (j=jmin; j<jmax; j++) {
    980:           /* rtmp += -U(i,k)^T * U_bar(i,j): rtmp[bj[j]] += uik*ba[j]; */
    981:           rtmp_ptr     = rtmp + bj[j]*4;
    982:           u            = ba + j*4;
    983:           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1];
    984:           rtmp_ptr[1] += uik[2]*u[0] + uik[3]*u[1];
    985:           rtmp_ptr[2] += uik[0]*u[2] + uik[1]*u[3];
    986:           rtmp_ptr[3] += uik[2]*u[2] + uik[3]*u[3];
    987:         }
    988:         PetscLogFlops(16.0*(jmax-jmin));

    990:         /* ... add i to row list for next nonzero entry */
    991:         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
    992:         j     = bj[jmin];
    993:         jl[i] = jl[j]; jl[j] = i; /* update jl */
    994:       }
    995:       i = nexti;
    996:     }

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

    1000:     /* invert diagonal block */
    1001:     diag = ba+k*4;
    1002:     PetscMemcpy(diag,dk,4*sizeof(MatScalar));
    1003:     PetscKernel_A_gets_inverse_A_2(diag,shift);

    1005:     jmin = bi[k]; jmax = bi[k+1];
    1006:     if (jmin < jmax) {
    1007:       for (j=jmin; j<jmax; j++) {
    1008:         vj       = bj[j];      /* block col. index of U */
    1009:         u        = ba + j*4;
    1010:         rtmp_ptr = rtmp + vj*4;
    1011:         for (k1=0; k1<4; k1++) {
    1012:           *u++        = *rtmp_ptr;
    1013:           *rtmp_ptr++ = 0.0;
    1014:         }
    1015:       }

    1017:       /* ... add k to row list for first nonzero entry in k-th row */
    1018:       il[k] = jmin;
    1019:       i     = bj[jmin];
    1020:       jl[k] = jl[i]; jl[i] = k;
    1021:     }
    1022:   }

    1024:   PetscFree(rtmp);
    1025:   PetscFree2(il,jl);
    1026:   if (a->permute) {
    1027:     PetscFree(aa);
    1028:   }
    1029:   ISRestoreIndices(perm,&perm_ptr);

    1031:   C->ops->solve          = MatSolve_SeqSBAIJ_2_inplace;
    1032:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_2_inplace;
    1033:   C->assembled           = PETSC_TRUE;
    1034:   C->preallocated        = PETSC_TRUE;

    1036:   PetscLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
    1037:   return(0);
    1038: }

    1040: /*
    1041:       Version for when blocks are 2 by 2 Using natural ordering
    1042: */
    1045: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info)
    1046: {
    1047:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
    1049:   PetscInt       i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
    1050:   PetscInt       *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
    1051:   MatScalar      *ba = b->a,*aa,*ap,dk[8],uik[8];
    1052:   MatScalar      *u,*diag,*rtmp,*rtmp_ptr;
    1053:   PetscReal      shift = info->shiftamount;

    1056:   /* initialization */
    1057:   /* il and jl record the first nonzero element in each row of the accessing
    1058:      window U(0:k, k:mbs-1).
    1059:      jl:    list of rows to be added to uneliminated rows
    1060:             i>= k: jl(i) is the first row to be added to row i
    1061:             i<  k: jl(i) is the row following row i in some list of rows
    1062:             jl(i) = mbs indicates the end of a list
    1063:      il(i): points to the first nonzero element in columns k,...,mbs-1 of
    1064:             row i of U */
    1065:   PetscCalloc1(4*mbs,&rtmp);
    1066:   PetscMalloc2(mbs,&il,mbs,&jl);
    1067:   for (i=0; i<mbs; i++) {
    1068:     jl[i] = mbs; il[0] = 0;
    1069:   }
    1070:   ai = a->i; aj = a->j; aa = a->a;

    1072:   /* for each row k */
    1073:   for (k = 0; k<mbs; k++) {

    1075:     /*initialize k-th row with elements nonzero in row k of A */
    1076:     jmin = ai[k]; jmax = ai[k+1];
    1077:     ap   = aa + jmin*4;
    1078:     for (j = jmin; j < jmax; j++) {
    1079:       vj       = aj[j];   /* block col. index */
    1080:       rtmp_ptr = rtmp + vj*4;
    1081:       for (i=0; i<4; i++) *rtmp_ptr++ = *ap++;
    1082:     }

    1084:     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
    1085:     PetscMemcpy(dk,rtmp+k*4,4*sizeof(MatScalar));
    1086:     i    = jl[k]; /* first row to be added to k_th row  */

    1088:     while (i < k) {
    1089:       nexti = jl[i]; /* next row to be added to k_th row */

    1091:       /* compute multiplier */
    1092:       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */

    1094:       /* uik = -inv(Di)*U_bar(i,k): - ba[ili]*ba[i] */
    1095:       diag   = ba + i*4;
    1096:       u      = ba + ili*4;
    1097:       uik[0] = -(diag[0]*u[0] + diag[2]*u[1]);
    1098:       uik[1] = -(diag[1]*u[0] + diag[3]*u[1]);
    1099:       uik[2] = -(diag[0]*u[2] + diag[2]*u[3]);
    1100:       uik[3] = -(diag[1]*u[2] + diag[3]*u[3]);

    1102:       /* update D(k) += -U(i,k)^T * U_bar(i,k): dk += uik*ba[ili] */
    1103:       dk[0] += uik[0]*u[0] + uik[1]*u[1];
    1104:       dk[1] += uik[2]*u[0] + uik[3]*u[1];
    1105:       dk[2] += uik[0]*u[2] + uik[1]*u[3];
    1106:       dk[3] += uik[2]*u[2] + uik[3]*u[3];

    1108:       PetscLogFlops(16.0*2.0);

    1110:       /* update -U(i,k): ba[ili] = uik */
    1111:       PetscMemcpy(ba+ili*4,uik,4*sizeof(MatScalar));

    1113:       /* add multiple of row i to k-th row ... */
    1114:       jmin = ili + 1; jmax = bi[i+1];
    1115:       if (jmin < jmax) {
    1116:         for (j=jmin; j<jmax; j++) {
    1117:           /* rtmp += -U(i,k)^T * U_bar(i,j): rtmp[bj[j]] += uik*ba[j]; */
    1118:           rtmp_ptr     = rtmp + bj[j]*4;
    1119:           u            = ba + j*4;
    1120:           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1];
    1121:           rtmp_ptr[1] += uik[2]*u[0] + uik[3]*u[1];
    1122:           rtmp_ptr[2] += uik[0]*u[2] + uik[1]*u[3];
    1123:           rtmp_ptr[3] += uik[2]*u[2] + uik[3]*u[3];
    1124:         }
    1125:         PetscLogFlops(16.0*(jmax-jmin));

    1127:         /* ... add i to row list for next nonzero entry */
    1128:         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
    1129:         j     = bj[jmin];
    1130:         jl[i] = jl[j]; jl[j] = i; /* update jl */
    1131:       }
    1132:       i = nexti;
    1133:     }

    1135:     /* save nonzero entries in k-th row of U ... */

    1137:     /* invert diagonal block */
    1138:     diag = ba+k*4;
    1139:     PetscMemcpy(diag,dk,4*sizeof(MatScalar));
    1140:     PetscKernel_A_gets_inverse_A_2(diag,shift);

    1142:     jmin = bi[k]; jmax = bi[k+1];
    1143:     if (jmin < jmax) {
    1144:       for (j=jmin; j<jmax; j++) {
    1145:         vj       = bj[j];      /* block col. index of U */
    1146:         u        = ba + j*4;
    1147:         rtmp_ptr = rtmp + vj*4;
    1148:         for (k1=0; k1<4; k1++) {
    1149:           *u++        = *rtmp_ptr;
    1150:           *rtmp_ptr++ = 0.0;
    1151:         }
    1152:       }

    1154:       /* ... add k to row list for first nonzero entry in k-th row */
    1155:       il[k] = jmin;
    1156:       i     = bj[jmin];
    1157:       jl[k] = jl[i]; jl[i] = k;
    1158:     }
    1159:   }

    1161:   PetscFree(rtmp);
    1162:   PetscFree2(il,jl);

    1164:   C->ops->solve          = MatSolve_SeqSBAIJ_2_NaturalOrdering_inplace;
    1165:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_2_NaturalOrdering_inplace;
    1166:   C->ops->forwardsolve   = MatForwardSolve_SeqSBAIJ_2_NaturalOrdering_inplace;
    1167:   C->ops->backwardsolve  = MatBackwardSolve_SeqSBAIJ_2_NaturalOrdering_inplace;
    1168:   C->assembled           = PETSC_TRUE;
    1169:   C->preallocated        = PETSC_TRUE;

    1171:   PetscLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
    1172:   return(0);
    1173: }

    1175: /*
    1176:     Numeric U^T*D*U factorization for SBAIJ format.
    1177:     Version for blocks are 1 by 1.
    1178: */
    1181: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_1_inplace(Mat C,Mat A,const MatFactorInfo *info)
    1182: {
    1183:   Mat_SeqSBAIJ   *a=(Mat_SeqSBAIJ*)A->data,*b=(Mat_SeqSBAIJ*)C->data;
    1184:   IS             ip=b->row;
    1186:   const PetscInt *ai,*aj,*rip;
    1187:   PetscInt       *a2anew,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j,*bcol;
    1188:   PetscInt       k,jmin,jmax,*jl,*il,col,nexti,ili,nz;
    1189:   MatScalar      *rtmp,*ba=b->a,*bval,*aa,dk,uikdi;
    1190:   PetscReal      rs;
    1191:   FactorShiftCtx sctx;

    1194:   /* MatPivotSetUp(): initialize shift context sctx */
    1195:   PetscMemzero(&sctx,sizeof(FactorShiftCtx));

    1197:   ISGetIndices(ip,&rip);
    1198:   if (!a->permute) {
    1199:     ai = a->i; aj = a->j; aa = a->a;
    1200:   } else {
    1201:     ai     = a->inew; aj = a->jnew;
    1202:     nz     = ai[mbs];
    1203:     PetscMalloc1(nz,&aa);
    1204:     a2anew = a->a2anew;
    1205:     bval   = a->a;
    1206:     for (j=0; j<nz; j++) {
    1207:       aa[a2anew[j]] = *(bval++);
    1208:     }
    1209:   }

    1211:   /* initialization */
    1212:   /* il and jl record the first nonzero element in each row of the accessing
    1213:      window U(0:k, k:mbs-1).
    1214:      jl:    list of rows to be added to uneliminated rows
    1215:             i>= k: jl(i) is the first row to be added to row i
    1216:             i<  k: jl(i) is the row following row i in some list of rows
    1217:             jl(i) = mbs indicates the end of a list
    1218:      il(i): points to the first nonzero element in columns k,...,mbs-1 of
    1219:             row i of U */
    1220:   PetscMalloc3(mbs,&rtmp,mbs,&il,mbs,&jl);

    1222:   do {
    1223:     sctx.newshift = PETSC_FALSE;
    1224:     for (i=0; i<mbs; i++) {
    1225:       rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
    1226:     }

    1228:     for (k = 0; k<mbs; k++) {
    1229:       /*initialize k-th row by the perm[k]-th row of A */
    1230:       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
    1231:       bval = ba + bi[k];
    1232:       for (j = jmin; j < jmax; j++) {
    1233:         col       = rip[aj[j]];
    1234:         rtmp[col] = aa[j];
    1235:         *bval++   = 0.0; /* for in-place factorization */
    1236:       }

    1238:       /* shift the diagonal of the matrix */
    1239:       if (sctx.nshift) rtmp[k] += sctx.shift_amount;

    1241:       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
    1242:       dk = rtmp[k];
    1243:       i  = jl[k]; /* first row to be added to k_th row  */

    1245:       while (i < k) {
    1246:         nexti = jl[i]; /* next row to be added to k_th row */

    1248:         /* compute multiplier, update diag(k) and U(i,k) */
    1249:         ili     = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
    1250:         uikdi   = -ba[ili]*ba[bi[i]]; /* diagonal(k) */
    1251:         dk     += uikdi*ba[ili];
    1252:         ba[ili] = uikdi; /* -U(i,k) */

    1254:         /* add multiple of row i to k-th row */
    1255:         jmin = ili + 1; jmax = bi[i+1];
    1256:         if (jmin < jmax) {
    1257:           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
    1258:           PetscLogFlops(2.0*(jmax-jmin));

    1260:           /* update il and jl for row i */
    1261:           il[i] = jmin;
    1262:           j     = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
    1263:         }
    1264:         i = nexti;
    1265:       }

    1267:       /* shift the diagonals when zero pivot is detected */
    1268:       /* compute rs=sum of abs(off-diagonal) */
    1269:       rs   = 0.0;
    1270:       jmin = bi[k]+1;
    1271:       nz   = bi[k+1] - jmin;
    1272:       if (nz) {
    1273:         bcol = bj + jmin;
    1274:         while (nz--) {
    1275:           rs += PetscAbsScalar(rtmp[*bcol]);
    1276:           bcol++;
    1277:         }
    1278:       }

    1280:       sctx.rs = rs;
    1281:       sctx.pv = dk;
    1282:       MatPivotCheck(A,info,&sctx,k);
    1283:       if (sctx.newshift) break;    /* sctx.shift_amount is updated */
    1284:       dk = sctx.pv;

    1286:       /* copy data into U(k,:) */
    1287:       ba[bi[k]] = 1.0/dk; /* U(k,k) */
    1288:       jmin      = bi[k]+1; jmax = bi[k+1];
    1289:       if (jmin < jmax) {
    1290:         for (j=jmin; j<jmax; j++) {
    1291:           col = bj[j]; ba[j] = rtmp[col]; rtmp[col] = 0.0;
    1292:         }
    1293:         /* add the k-th row into il and jl */
    1294:         il[k] = jmin;
    1295:         i     = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
    1296:       }
    1297:     }
    1298:   } while (sctx.newshift);
    1299:   PetscFree3(rtmp,il,jl);
    1300:   if (a->permute) {PetscFree(aa);}

    1302:   ISRestoreIndices(ip,&rip);

    1304:   C->ops->solve          = MatSolve_SeqSBAIJ_1_inplace;
    1305:   C->ops->solves         = MatSolves_SeqSBAIJ_1_inplace;
    1306:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_1_inplace;
    1307:   C->ops->forwardsolve   = MatForwardSolve_SeqSBAIJ_1_inplace;
    1308:   C->ops->backwardsolve  = MatBackwardSolve_SeqSBAIJ_1_inplace;
    1309:   C->assembled           = PETSC_TRUE;
    1310:   C->preallocated        = PETSC_TRUE;

    1312:   PetscLogFlops(C->rmap->N);
    1313:   if (sctx.nshift) {
    1314:     if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
    1315:       PetscInfo2(A,"number of shiftnz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
    1316:     } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
    1317:       PetscInfo2(A,"number of shiftpd tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
    1318:     }
    1319:   }
    1320:   return(0);
    1321: }

    1323: /*
    1324:   Version for when blocks are 1 by 1 Using natural ordering under new datastructure
    1325:   Modified from MatCholeskyFactorNumeric_SeqAIJ()
    1326: */
    1329: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_1_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
    1330: {
    1331:   Mat_SeqSBAIJ   *a=(Mat_SeqSBAIJ*)A->data;
    1332:   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)B->data;
    1334:   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp;
    1335:   PetscInt       *ai=a->i,*aj=a->j,*ajtmp;
    1336:   PetscInt       k,jmin,jmax,*c2r,*il,col,nexti,ili,nz;
    1337:   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
    1338:   FactorShiftCtx sctx;
    1339:   PetscReal      rs;
    1340:   MatScalar      d,*v;

    1343:   PetscMalloc3(mbs,&rtmp,mbs,&il,mbs,&c2r);

    1345:   /* MatPivotSetUp(): initialize shift context sctx */
    1346:   PetscMemzero(&sctx,sizeof(FactorShiftCtx));

    1348:   if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
    1349:     sctx.shift_top = info->zeropivot;

    1351:     PetscMemzero(rtmp,mbs*sizeof(MatScalar));

    1353:     for (i=0; i<mbs; i++) {
    1354:       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
    1355:       d        = (aa)[a->diag[i]];
    1356:       rtmp[i] += -PetscRealPart(d);  /* diagonal entry */
    1357:       ajtmp    = aj + ai[i] + 1;     /* exclude diagonal */
    1358:       v        = aa + ai[i] + 1;
    1359:       nz       = ai[i+1] - ai[i] - 1;
    1360:       for (j=0; j<nz; j++) {
    1361:         rtmp[i]        += PetscAbsScalar(v[j]);
    1362:         rtmp[ajtmp[j]] += PetscAbsScalar(v[j]);
    1363:       }
    1364:       if (PetscRealPart(rtmp[i]) > sctx.shift_top) sctx.shift_top = PetscRealPart(rtmp[i]);
    1365:     }
    1366:     sctx.shift_top *= 1.1;
    1367:     sctx.nshift_max = 5;
    1368:     sctx.shift_lo   = 0.;
    1369:     sctx.shift_hi   = 1.;
    1370:   }

    1372:   /* allocate working arrays
    1373:      c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col
    1374:      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
    1375:   */
    1376:   do {
    1377:     sctx.newshift = PETSC_FALSE;

    1379:     for (i=0; i<mbs; i++) c2r[i] = mbs;
    1380:     if (mbs) il[0] = 0;

    1382:     for (k = 0; k<mbs; k++) {
    1383:       /* zero rtmp */
    1384:       nz    = bi[k+1] - bi[k];
    1385:       bjtmp = bj + bi[k];
    1386:       for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;

    1388:       /* load in initial unfactored row */
    1389:       bval = ba + bi[k];
    1390:       jmin = ai[k]; jmax = ai[k+1];
    1391:       for (j = jmin; j < jmax; j++) {
    1392:         col       = aj[j];
    1393:         rtmp[col] = aa[j];
    1394:         *bval++   = 0.0; /* for in-place factorization */
    1395:       }
    1396:       /* shift the diagonal of the matrix: ZeropivotApply() */
    1397:       rtmp[k] += sctx.shift_amount;  /* shift the diagonal of the matrix */

    1399:       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
    1400:       dk = rtmp[k];
    1401:       i  = c2r[k]; /* first row to be added to k_th row  */

    1403:       while (i < k) {
    1404:         nexti = c2r[i]; /* next row to be added to k_th row */

    1406:         /* compute multiplier, update diag(k) and U(i,k) */
    1407:         ili     = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
    1408:         uikdi   = -ba[ili]*ba[bdiag[i]]; /* diagonal(k) */
    1409:         dk     += uikdi*ba[ili]; /* update diag[k] */
    1410:         ba[ili] = uikdi; /* -U(i,k) */

    1412:         /* add multiple of row i to k-th row */
    1413:         jmin = ili + 1; jmax = bi[i+1];
    1414:         if (jmin < jmax) {
    1415:           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
    1416:           /* update il and c2r for row i */
    1417:           il[i] = jmin;
    1418:           j     = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i;
    1419:         }
    1420:         i = nexti;
    1421:       }

    1423:       /* copy data into U(k,:) */
    1424:       rs   = 0.0;
    1425:       jmin = bi[k]; jmax = bi[k+1]-1;
    1426:       if (jmin < jmax) {
    1427:         for (j=jmin; j<jmax; j++) {
    1428:           col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]);
    1429:         }
    1430:         /* add the k-th row into il and c2r */
    1431:         il[k] = jmin;
    1432:         i     = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k;
    1433:       }

    1435:       sctx.rs = rs;
    1436:       sctx.pv = dk;
    1437:       MatPivotCheck(A,info,&sctx,k);
    1438:       if (sctx.newshift) break;
    1439:       dk = sctx.pv;

    1441:       ba[bdiag[k]] = 1.0/dk; /* U(k,k) */
    1442:     }
    1443:   } while (sctx.newshift);

    1445:   PetscFree3(rtmp,il,c2r);

    1447:   B->ops->solve          = MatSolve_SeqSBAIJ_1_NaturalOrdering;
    1448:   B->ops->solves         = MatSolves_SeqSBAIJ_1;
    1449:   B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering;
    1450:   B->ops->forwardsolve   = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering;
    1451:   B->ops->backwardsolve  = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering;

    1453:   B->assembled    = PETSC_TRUE;
    1454:   B->preallocated = PETSC_TRUE;

    1456:   PetscLogFlops(B->rmap->n);

    1458:   /* MatPivotView() */
    1459:   if (sctx.nshift) {
    1460:     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
    1461:       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);
    1462:     } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
    1463:       PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
    1464:     } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS) {
    1465:       PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %g\n",sctx.nshift,(double)info->shiftamount);
    1466:     }
    1467:   }
    1468:   return(0);
    1469: }

    1473: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_1_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
    1474: {
    1475:   Mat_SeqSBAIJ   *a=(Mat_SeqSBAIJ*)A->data,*b=(Mat_SeqSBAIJ*)C->data;
    1477:   PetscInt       i,j,mbs = a->mbs;
    1478:   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
    1479:   PetscInt       k,jmin,*jl,*il,nexti,ili,*acol,*bcol,nz;
    1480:   MatScalar      *rtmp,*ba=b->a,*aa=a->a,dk,uikdi,*aval,*bval;
    1481:   PetscReal      rs;
    1482:   FactorShiftCtx sctx;

    1485:   /* MatPivotSetUp(): initialize shift context sctx */
    1486:   PetscMemzero(&sctx,sizeof(FactorShiftCtx));

    1488:   /* initialization */
    1489:   /* il and jl record the first nonzero element in each row of the accessing
    1490:      window U(0:k, k:mbs-1).
    1491:      jl:    list of rows to be added to uneliminated rows
    1492:             i>= k: jl(i) is the first row to be added to row i
    1493:             i<  k: jl(i) is the row following row i in some list of rows
    1494:             jl(i) = mbs indicates the end of a list
    1495:      il(i): points to the first nonzero element in U(i,k:mbs-1)
    1496:   */
    1497:   PetscMalloc1(mbs,&rtmp);
    1498:   PetscMalloc2(mbs,&il,mbs,&jl);

    1500:   do {
    1501:     sctx.newshift = PETSC_FALSE;
    1502:     for (i=0; i<mbs; i++) {
    1503:       rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
    1504:     }

    1506:     for (k = 0; k<mbs; k++) {
    1507:       /*initialize k-th row with elements nonzero in row perm(k) of A */
    1508:       nz   = ai[k+1] - ai[k];
    1509:       acol = aj + ai[k];
    1510:       aval = aa + ai[k];
    1511:       bval = ba + bi[k];
    1512:       while (nz--) {
    1513:         rtmp[*acol++] = *aval++;
    1514:         *bval++       = 0.0; /* for in-place factorization */
    1515:       }

    1517:       /* shift the diagonal of the matrix */
    1518:       if (sctx.nshift) rtmp[k] += sctx.shift_amount;

    1520:       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
    1521:       dk = rtmp[k];
    1522:       i  = jl[k]; /* first row to be added to k_th row  */

    1524:       while (i < k) {
    1525:         nexti = jl[i]; /* next row to be added to k_th row */
    1526:         /* compute multiplier, update D(k) and U(i,k) */
    1527:         ili     = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
    1528:         uikdi   = -ba[ili]*ba[bi[i]];
    1529:         dk     += uikdi*ba[ili];
    1530:         ba[ili] = uikdi; /* -U(i,k) */

    1532:         /* add multiple of row i to k-th row ... */
    1533:         jmin = ili + 1;
    1534:         nz   = bi[i+1] - jmin;
    1535:         if (nz > 0) {
    1536:           bcol = bj + jmin;
    1537:           bval = ba + jmin;
    1538:           PetscLogFlops(2.0*nz);
    1539:           while (nz--) rtmp[*bcol++] += uikdi*(*bval++);

    1541:           /* update il and jl for i-th row */
    1542:           il[i] = jmin;
    1543:           j     = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
    1544:         }
    1545:         i = nexti;
    1546:       }

    1548:       /* shift the diagonals when zero pivot is detected */
    1549:       /* compute rs=sum of abs(off-diagonal) */
    1550:       rs   = 0.0;
    1551:       jmin = bi[k]+1;
    1552:       nz   = bi[k+1] - jmin;
    1553:       if (nz) {
    1554:         bcol = bj + jmin;
    1555:         while (nz--) {
    1556:           rs += PetscAbsScalar(rtmp[*bcol]);
    1557:           bcol++;
    1558:         }
    1559:       }

    1561:       sctx.rs = rs;
    1562:       sctx.pv = dk;
    1563:       MatPivotCheck(A,info,&sctx,k);
    1564:       if (sctx.newshift) break;    /* sctx.shift_amount is updated */
    1565:       dk = sctx.pv;

    1567:       /* copy data into U(k,:) */
    1568:       ba[bi[k]] = 1.0/dk;
    1569:       jmin      = bi[k]+1;
    1570:       nz        = bi[k+1] - jmin;
    1571:       if (nz) {
    1572:         bcol = bj + jmin;
    1573:         bval = ba + jmin;
    1574:         while (nz--) {
    1575:           *bval++       = rtmp[*bcol];
    1576:           rtmp[*bcol++] = 0.0;
    1577:         }
    1578:         /* add k-th row into il and jl */
    1579:         il[k] = jmin;
    1580:         i     = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
    1581:       }
    1582:     } /* end of for (k = 0; k<mbs; k++) */
    1583:   } while (sctx.newshift);
    1584:   PetscFree(rtmp);
    1585:   PetscFree2(il,jl);

    1587:   C->ops->solve          = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
    1588:   C->ops->solves         = MatSolves_SeqSBAIJ_1_inplace;
    1589:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
    1590:   C->ops->forwardsolve   = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
    1591:   C->ops->backwardsolve  = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace;

    1593:   C->assembled    = PETSC_TRUE;
    1594:   C->preallocated = PETSC_TRUE;

    1596:   PetscLogFlops(C->rmap->N);
    1597:   if (sctx.nshift) {
    1598:     if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
    1599:       PetscInfo2(A,"number of shiftnz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
    1600:     } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
    1601:       PetscInfo2(A,"number of shiftpd tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
    1602:     }
    1603:   }
    1604:   return(0);
    1605: }

    1609: PetscErrorCode MatCholeskyFactor_SeqSBAIJ(Mat A,IS perm,const MatFactorInfo *info)
    1610: {
    1612:   Mat            C;

    1615:   MatGetFactor(A,"petsc",MAT_FACTOR_CHOLESKY,&C);
    1616:   MatCholeskyFactorSymbolic(C,A,perm,info);
    1617:   MatCholeskyFactorNumeric(C,A,info);

    1619:   A->ops->solve          = C->ops->solve;
    1620:   A->ops->solvetranspose = C->ops->solvetranspose;

    1622:   MatHeaderMerge(A,C);
    1623:   return(0);
    1624: }