Date: 2015-10-02T22:08:03+00:00

Actual source code: baijfact2.c
petsc-3.6.2 2015-10-02
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      2: /*
      3:     Factorization code for BAIJ format.
      4: */

      6: #include <../src/mat/impls/baij/seq/baij.h>
      7: #include <petsc/private/kernels/blockinvert.h>
      8: #include <petscbt.h>
      9: #include <../src/mat/utils/freespace.h>

     11: /* ----------------------------------------------------------------*/
     12: extern PetscErrorCode MatDuplicateNoCreate_SeqBAIJ(Mat,Mat,MatDuplicateOption,PetscBool);

     16: /*
     17:    This is not much faster than MatLUFactorNumeric_SeqBAIJ_N() but the solve is faster at least sometimes
     18: */
     19: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_15_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
     20: {
     21:   Mat             C =B;
     22:   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
     23:   PetscErrorCode  ierr;
     24:   PetscInt        i,j,k,ipvt[15];
     25:   const PetscInt  n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*ajtmp,*bjtmp,*bdiag=b->diag,*pj;
     26:   PetscInt        nz,nzL,row;
     27:   MatScalar       *rtmp,*pc,*mwork,*pv,*vv,work[225];
     28:   const MatScalar *v,*aa=a->a;
     29:   PetscInt        bs2 = a->bs2,bs=A->rmap->bs,flg;
     30:   PetscInt        sol_ver;

     33:   PetscOptionsGetInt(((PetscObject)A)->prefix,"-sol_ver",&sol_ver,NULL);

     35:   /* generate work space needed by the factorization */
     36:   PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
     37:   PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));

     39:   for (i=0; i<n; i++) {
     40:     /* zero rtmp */
     41:     /* L part */
     42:     nz    = bi[i+1] - bi[i];
     43:     bjtmp = bj + bi[i];
     44:     for  (j=0; j<nz; j++) {
     45:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
     46:     }

     48:     /* U part */
     49:     nz    = bdiag[i] - bdiag[i+1];
     50:     bjtmp = bj + bdiag[i+1]+1;
     51:     for  (j=0; j<nz; j++) {
     52:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
     53:     }

     55:     /* load in initial (unfactored row) */
     56:     nz    = ai[i+1] - ai[i];
     57:     ajtmp = aj + ai[i];
     58:     v     = aa + bs2*ai[i];
     59:     for (j=0; j<nz; j++) {
     60:       PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));
     61:     }

     63:     /* elimination */
     64:     bjtmp = bj + bi[i];
     65:     nzL   = bi[i+1] - bi[i];
     66:     for (k=0; k < nzL; k++) {
     67:       row = bjtmp[k];
     68:       pc  = rtmp + bs2*row;
     69:       for (flg=0,j=0; j<bs2; j++) {
     70:         if (pc[j]!=0.0) {
     71:           flg = 1;
     72:           break;
     73:         }
     74:       }
     75:       if (flg) {
     76:         pv = b->a + bs2*bdiag[row];
     77:         PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork);
     78:         /*PetscKernel_A_gets_A_times_B_15(pc,pv,mwork);*/
     79:         pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
     80:         pv = b->a + bs2*(bdiag[row+1]+1);
     81:         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
     82:         for (j=0; j<nz; j++) {
     83:           vv = rtmp + bs2*pj[j];
     84:           PetscKernel_A_gets_A_minus_B_times_C(bs,vv,pc,pv);
     85:           /* PetscKernel_A_gets_A_minus_B_times_C_15(vv,pc,pv); */
     86:           pv += bs2;
     87:         }
     88:         PetscLogFlops(2*bs2*bs*(nz+1)-bs2); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
     89:       }
     90:     }

     92:     /* finished row so stick it into b->a */
     93:     /* L part */
     94:     pv = b->a + bs2*bi[i];
     95:     pj = b->j + bi[i];
     96:     nz = bi[i+1] - bi[i];
     97:     for (j=0; j<nz; j++) {
     98:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
     99:     }

    101:     /* Mark diagonal and invert diagonal for simplier triangular solves */
    102:     pv   = b->a + bs2*bdiag[i];
    103:     pj   = b->j + bdiag[i];
    104:     PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
    105:     /* PetscKernel_A_gets_inverse_A(bs,pv,pivots,work); */
    106:     PetscKernel_A_gets_inverse_A_15(pv,ipvt,work,info->shiftamount);

    108:     /* U part */
    109:     pv = b->a + bs2*(bdiag[i+1]+1);
    110:     pj = b->j + bdiag[i+1]+1;
    111:     nz = bdiag[i] - bdiag[i+1] - 1;
    112:     for (j=0; j<nz; j++) {
    113:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
    114:     }
    115:   }

    117:   PetscFree2(rtmp,mwork);

    119:   C->ops->solve          = MatSolve_SeqBAIJ_15_NaturalOrdering_ver1;
    120:   C->ops->solvetranspose = MatSolve_SeqBAIJ_N_NaturalOrdering;
    121:   C->assembled           = PETSC_TRUE;

    123:   PetscLogFlops(1.333333333333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
    124:   return(0);
    125: }

    129: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_N(Mat B,Mat A,const MatFactorInfo *info)
    130: {
    131:   Mat            C     =B;
    132:   Mat_SeqBAIJ    *a    =(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
    133:   IS             isrow = b->row,isicol = b->icol;
    135:   const PetscInt *r,*ic;
    136:   PetscInt       i,j,k,n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
    137:   PetscInt       *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj;
    138:   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
    139:   PetscInt       bs=A->rmap->bs,bs2 = a->bs2,*v_pivots,flg;
    140:   MatScalar      *v_work;
    141:   PetscBool      col_identity,row_identity,both_identity;

    144:   ISGetIndices(isrow,&r);
    145:   ISGetIndices(isicol,&ic);

    147:   PetscMalloc1(bs2*n,&rtmp);
    148:   PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));

    150:   /* generate work space needed by dense LU factorization */
    151:   PetscMalloc3(bs,&v_work,bs2,&mwork,bs,&v_pivots);

    153:   for (i=0; i<n; i++) {
    154:     /* zero rtmp */
    155:     /* L part */
    156:     nz    = bi[i+1] - bi[i];
    157:     bjtmp = bj + bi[i];
    158:     for  (j=0; j<nz; j++) {
    159:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
    160:     }

    162:     /* U part */
    163:     nz    = bdiag[i] - bdiag[i+1];
    164:     bjtmp = bj + bdiag[i+1]+1;
    165:     for  (j=0; j<nz; j++) {
    166:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
    167:     }

    169:     /* load in initial (unfactored row) */
    170:     nz    = ai[r[i]+1] - ai[r[i]];
    171:     ajtmp = aj + ai[r[i]];
    172:     v     = aa + bs2*ai[r[i]];
    173:     for (j=0; j<nz; j++) {
    174:       PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));
    175:     }

    177:     /* elimination */
    178:     bjtmp = bj + bi[i];
    179:     nzL   = bi[i+1] - bi[i];
    180:     for (k=0; k < nzL; k++) {
    181:       row = bjtmp[k];
    182:       pc  = rtmp + bs2*row;
    183:       for (flg=0,j=0; j<bs2; j++) {
    184:         if (pc[j]!=0.0) {
    185:           flg = 1;
    186:           break;
    187:         }
    188:       }
    189:       if (flg) {
    190:         pv = b->a + bs2*bdiag[row];
    191:         PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); /* *pc = *pc * (*pv); */
    192:         pj = b->j + bdiag[row+1]+1;         /* begining of U(row,:) */
    193:         pv = b->a + bs2*(bdiag[row+1]+1);
    194:         nz = bdiag[row] - bdiag[row+1] - 1;         /* num of entries inU(row,:), excluding diag */
    195:         for (j=0; j<nz; j++) {
    196:           PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
    197:         }
    198:         PetscLogFlops(2*bs2*bs*(nz+1)-bs2); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
    199:       }
    200:     }

    202:     /* finished row so stick it into b->a */
    203:     /* L part */
    204:     pv = b->a + bs2*bi[i];
    205:     pj = b->j + bi[i];
    206:     nz = bi[i+1] - bi[i];
    207:     for (j=0; j<nz; j++) {
    208:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
    209:     }

    211:     /* Mark diagonal and invert diagonal for simplier triangular solves */
    212:     pv = b->a + bs2*bdiag[i];
    213:     pj = b->j + bdiag[i];
    214:     /* if (*pj != i)SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"row %d != *pj %d",i,*pj); */
    215:     PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
    216:     PetscKernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);

    218:     /* U part */
    219:     pv = b->a + bs2*(bdiag[i+1]+1);
    220:     pj = b->j + bdiag[i+1]+1;
    221:     nz = bdiag[i] - bdiag[i+1] - 1;
    222:     for (j=0; j<nz; j++) {
    223:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
    224:     }
    225:   }

    227:   PetscFree(rtmp);
    228:   PetscFree3(v_work,mwork,v_pivots);
    229:   ISRestoreIndices(isicol,&ic);
    230:   ISRestoreIndices(isrow,&r);

    232:   ISIdentity(isrow,&row_identity);
    233:   ISIdentity(isicol,&col_identity);

    235:   both_identity = (PetscBool) (row_identity && col_identity);
    236:   if (both_identity) {
    237:     C->ops->solve = MatSolve_SeqBAIJ_N_NaturalOrdering;
    238:   } else {
    239:     C->ops->solve = MatSolve_SeqBAIJ_N;
    240:   }
    241:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_N;

    243:   C->assembled = PETSC_TRUE;

    245:   PetscLogFlops(1.333333333333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
    246:   return(0);
    247: }

    249: /*
    250:    ilu(0) with natural ordering under new data structure.
    251:    See MatILUFactorSymbolic_SeqAIJ_ilu0() for detailed description
    252:    because this code is almost identical to MatILUFactorSymbolic_SeqAIJ_ilu0_inplace().
    253: */

    257: PetscErrorCode MatILUFactorSymbolic_SeqBAIJ_ilu0(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
    258: {

    260:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b;
    262:   PetscInt       n=a->mbs,*ai=a->i,*aj,*adiag=a->diag,bs2 = a->bs2;
    263:   PetscInt       i,j,nz,*bi,*bj,*bdiag,bi_temp;

    266:   MatDuplicateNoCreate_SeqBAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);
    267:   b    = (Mat_SeqBAIJ*)(fact)->data;

    269:   /* allocate matrix arrays for new data structure */
    270:   PetscMalloc3(bs2*ai[n]+1,&b->a,ai[n]+1,&b->j,n+1,&b->i);
    271:   PetscLogObjectMemory((PetscObject)fact,ai[n]*(bs2*sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));

    273:   b->singlemalloc    = PETSC_TRUE;
    274:   b->free_a          = PETSC_TRUE;
    275:   b->free_ij         = PETSC_TRUE;
    276:   fact->preallocated = PETSC_TRUE;
    277:   fact->assembled    = PETSC_TRUE;
    278:   if (!b->diag) {
    279:     PetscMalloc1(n+1,&b->diag);
    280:     PetscLogObjectMemory((PetscObject)fact,(n+1)*sizeof(PetscInt));
    281:   }
    282:   bdiag = b->diag;

    284:   if (n > 0) {
    285:     PetscMemzero(b->a,bs2*ai[n]*sizeof(MatScalar));
    286:   }

    288:   /* set bi and bj with new data structure */
    289:   bi = b->i;
    290:   bj = b->j;

    292:   /* L part */
    293:   bi[0] = 0;
    294:   for (i=0; i<n; i++) {
    295:     nz      = adiag[i] - ai[i];
    296:     bi[i+1] = bi[i] + nz;
    297:     aj      = a->j + ai[i];
    298:     for (j=0; j<nz; j++) {
    299:       *bj = aj[j]; bj++;
    300:     }
    301:   }

    303:   /* U part */
    304:   bi_temp  = bi[n];
    305:   bdiag[n] = bi[n]-1;
    306:   for (i=n-1; i>=0; i--) {
    307:     nz      = ai[i+1] - adiag[i] - 1;
    308:     bi_temp = bi_temp + nz + 1;
    309:     aj      = a->j + adiag[i] + 1;
    310:     for (j=0; j<nz; j++) {
    311:       *bj = aj[j]; bj++;
    312:     }
    313:     /* diag[i] */
    314:     *bj      = i; bj++;
    315:     bdiag[i] = bi_temp - 1;
    316:   }
    317:   return(0);
    318: }

    322: PetscErrorCode MatILUFactorSymbolic_SeqBAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
    323: {
    324:   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b;
    325:   IS                 isicol;
    326:   PetscErrorCode     ierr;
    327:   const PetscInt     *r,*ic;
    328:   PetscInt           n=a->mbs,*ai=a->i,*aj=a->j,d;
    329:   PetscInt           *bi,*cols,nnz,*cols_lvl;
    330:   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
    331:   PetscInt           i,levels,diagonal_fill;
    332:   PetscBool          col_identity,row_identity,both_identity;
    333:   PetscReal          f;
    334:   PetscInt           nlnk,*lnk,*lnk_lvl=NULL;
    335:   PetscBT            lnkbt;
    336:   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
    337:   PetscFreeSpaceList free_space    =NULL,current_space=NULL;
    338:   PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL;
    339:   PetscBool          missing;
    340:   PetscInt           bs=A->rmap->bs,bs2=a->bs2;

    343:   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);
    344:   if (bs>1) {  /* check shifttype */
    345:     if (info->shifttype == MAT_SHIFT_NONZERO || info->shifttype == MAT_SHIFT_POSITIVE_DEFINITE)
    346:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only MAT_SHIFT_NONE and MAT_SHIFT_INBLOCKS are supported for BAIJ matrix");
    347:   }

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

    352:   f             = info->fill;
    353:   levels        = (PetscInt)info->levels;
    354:   diagonal_fill = (PetscInt)info->diagonal_fill;

    356:   ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);

    358:   ISIdentity(isrow,&row_identity);
    359:   ISIdentity(iscol,&col_identity);

    361:   both_identity = (PetscBool) (row_identity && col_identity);

    363:   if (!levels && both_identity) {
    364:     /* special case: ilu(0) with natural ordering */
    365:     MatILUFactorSymbolic_SeqBAIJ_ilu0(fact,A,isrow,iscol,info);
    366:     MatSeqBAIJSetNumericFactorization(fact,both_identity);

    368:     fact->factortype               = MAT_FACTOR_ILU;
    369:     (fact)->info.factor_mallocs    = 0;
    370:     (fact)->info.fill_ratio_given  = info->fill;
    371:     (fact)->info.fill_ratio_needed = 1.0;

    373:     b                = (Mat_SeqBAIJ*)(fact)->data;
    374:     b->row           = isrow;
    375:     b->col           = iscol;
    376:     b->icol          = isicol;
    377:     PetscObjectReference((PetscObject)isrow);
    378:     PetscObjectReference((PetscObject)iscol);
    379:     b->pivotinblocks = (info->pivotinblocks) ? PETSC_TRUE : PETSC_FALSE;

    381:     PetscMalloc1((n+1)*bs,&b->solve_work);
    382:     return(0);
    383:   }

    385:   ISGetIndices(isrow,&r);
    386:   ISGetIndices(isicol,&ic);

    388:   /* get new row pointers */
    389:   PetscMalloc1(n+1,&bi);
    390:   bi[0] = 0;
    391:   /* bdiag is location of diagonal in factor */
    392:   PetscMalloc1(n+1,&bdiag);
    393:   bdiag[0] = 0;

    395:   PetscMalloc2(n,&bj_ptr,n,&bjlvl_ptr);

    397:   /* create a linked list for storing column indices of the active row */
    398:   nlnk = n + 1;
    399:   PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);

    401:   /* initial FreeSpace size is f*(ai[n]+1) */
    402:   PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);
    403:   current_space     = free_space;
    404:   PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);
    405:   current_space_lvl = free_space_lvl;

    407:   for (i=0; i<n; i++) {
    408:     nzi = 0;
    409:     /* copy current row into linked list */
    410:     nnz = ai[r[i]+1] - ai[r[i]];
    411:     if (!nnz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
    412:     cols   = aj + ai[r[i]];
    413:     lnk[i] = -1; /* marker to indicate if diagonal exists */
    414:     PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);
    415:     nzi   += nlnk;

    417:     /* make sure diagonal entry is included */
    418:     if (diagonal_fill && lnk[i] == -1) {
    419:       fm = n;
    420:       while (lnk[fm] < i) fm = lnk[fm];
    421:       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
    422:       lnk[fm]    = i;
    423:       lnk_lvl[i] = 0;
    424:       nzi++; dcount++;
    425:     }

    427:     /* add pivot rows into the active row */
    428:     nzbd = 0;
    429:     prow = lnk[n];
    430:     while (prow < i) {
    431:       nnz      = bdiag[prow];
    432:       cols     = bj_ptr[prow] + nnz + 1;
    433:       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
    434:       nnz      = bi[prow+1] - bi[prow] - nnz - 1;

    436:       PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);
    437:       nzi += nlnk;
    438:       prow = lnk[prow];
    439:       nzbd++;
    440:     }
    441:     bdiag[i] = nzbd;
    442:     bi[i+1]  = bi[i] + nzi;

    444:     /* if free space is not available, make more free space */
    445:     if (current_space->local_remaining<nzi) {
    446:       nnz  = 2*nzi*(n - i); /* estimated and max additional space needed */
    447:       PetscFreeSpaceGet(nnz,&current_space);
    448:       PetscFreeSpaceGet(nnz,&current_space_lvl);
    449:       reallocs++;
    450:     }

    452:     /* copy data into free_space and free_space_lvl, then initialize lnk */
    453:     PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);

    455:     bj_ptr[i]    = current_space->array;
    456:     bjlvl_ptr[i] = current_space_lvl->array;

    458:     /* make sure the active row i has diagonal entry */
    459:     if (*(bj_ptr[i]+bdiag[i]) != i) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\ntry running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);

    461:     current_space->array           += nzi;
    462:     current_space->local_used      += nzi;
    463:     current_space->local_remaining -= nzi;

    465:     current_space_lvl->array           += nzi;
    466:     current_space_lvl->local_used      += nzi;
    467:     current_space_lvl->local_remaining -= nzi;
    468:   }

    470:   ISRestoreIndices(isrow,&r);
    471:   ISRestoreIndices(isicol,&ic);

    473:   /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */
    474:   PetscMalloc1(bi[n]+1,&bj);
    475:   PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);

    477:   PetscIncompleteLLDestroy(lnk,lnkbt);
    478:   PetscFreeSpaceDestroy(free_space_lvl);
    479:   PetscFree2(bj_ptr,bjlvl_ptr);

    481: #if defined(PETSC_USE_INFO)
    482:   {
    483:     PetscReal af = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
    484:     PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);
    485:     PetscInfo1(A,"Run with -[sub_]pc_factor_fill %g or use \n",(double)af);
    486:     PetscInfo1(A,"PCFactorSetFill([sub]pc,%g);\n",(double)af);
    487:     PetscInfo(A,"for best performance.\n");
    488:     if (diagonal_fill) {
    489:       PetscInfo1(A,"Detected and replaced %D missing diagonals\n",dcount);
    490:     }
    491:   }
    492: #endif

    494:   /* put together the new matrix */
    495:   MatSeqBAIJSetPreallocation_SeqBAIJ(fact,bs,MAT_SKIP_ALLOCATION,NULL);
    496:   PetscLogObjectParent((PetscObject)fact,(PetscObject)isicol);

    498:   b               = (Mat_SeqBAIJ*)(fact)->data;
    499:   b->free_a       = PETSC_TRUE;
    500:   b->free_ij      = PETSC_TRUE;
    501:   b->singlemalloc = PETSC_FALSE;

    503:   PetscMalloc1(bs2*(bdiag[0]+1),&b->a);

    505:   b->j          = bj;
    506:   b->i          = bi;
    507:   b->diag       = bdiag;
    508:   b->free_diag  = PETSC_TRUE;
    509:   b->ilen       = 0;
    510:   b->imax       = 0;
    511:   b->row        = isrow;
    512:   b->col        = iscol;
    513:   PetscObjectReference((PetscObject)isrow);
    514:   PetscObjectReference((PetscObject)iscol);
    515:   b->icol       = isicol;

    517:   PetscMalloc1(bs*n+bs,&b->solve_work);
    518:   /* In b structure:  Free imax, ilen, old a, old j.
    519:      Allocate bdiag, solve_work, new a, new j */
    520:   PetscLogObjectMemory((PetscObject)fact,(bdiag[0]+1) * (sizeof(PetscInt)+bs2*sizeof(PetscScalar)));
    521:   b->maxnz = b->nz = bdiag[0]+1;

    523:   fact->info.factor_mallocs    = reallocs;
    524:   fact->info.fill_ratio_given  = f;
    525:   fact->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);

    527:   MatSeqBAIJSetNumericFactorization(fact,both_identity);
    528:   return(0);
    529: }

    531: /*
    532:      This code is virtually identical to MatILUFactorSymbolic_SeqAIJ
    533:    except that the data structure of Mat_SeqAIJ is slightly different.
    534:    Not a good example of code reuse.
    535: */
    538: PetscErrorCode MatILUFactorSymbolic_SeqBAIJ_inplace(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
    539: {
    540:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b;
    541:   IS             isicol;
    543:   const PetscInt *r,*ic,*ai = a->i,*aj = a->j,*xi;
    544:   PetscInt       prow,n = a->mbs,*ainew,*ajnew,jmax,*fill,nz,*im,*ajfill,*flev,*xitmp;
    545:   PetscInt       *dloc,idx,row,m,fm,nzf,nzi,reallocate = 0,dcount = 0;
    546:   PetscInt       incrlev,nnz,i,bs = A->rmap->bs,bs2 = a->bs2,levels,diagonal_fill,dd;
    547:   PetscBool      col_identity,row_identity,both_identity,flg;
    548:   PetscReal      f;

    551:   MatMissingDiagonal_SeqBAIJ(A,&flg,&dd);
    552:   if (flg) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix A is missing diagonal entry in row %D",dd);

    554:   f             = info->fill;
    555:   levels        = (PetscInt)info->levels;
    556:   diagonal_fill = (PetscInt)info->diagonal_fill;

    558:   ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);

    560:   ISIdentity(isrow,&row_identity);
    561:   ISIdentity(iscol,&col_identity);
    562:   both_identity = (PetscBool) (row_identity && col_identity);

    564:   if (!levels && both_identity) {  /* special case copy the nonzero structure */
    565:     MatDuplicateNoCreate_SeqBAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);
    566:     MatSeqBAIJSetNumericFactorization_inplace(fact,both_identity);

    568:     fact->factortype = MAT_FACTOR_ILU;
    569:     b                = (Mat_SeqBAIJ*)fact->data;
    570:     b->row           = isrow;
    571:     b->col           = iscol;
    572:     PetscObjectReference((PetscObject)isrow);
    573:     PetscObjectReference((PetscObject)iscol);
    574:     b->icol          = isicol;
    575:     b->pivotinblocks = (info->pivotinblocks) ? PETSC_TRUE : PETSC_FALSE;

    577:     PetscMalloc1((n+1)*bs,&b->solve_work);
    578:     return(0);
    579:   }

    581:   /* general case perform the symbolic factorization */
    582:   ISGetIndices(isrow,&r);
    583:   ISGetIndices(isicol,&ic);

    585:   /* get new row pointers */
    586:   PetscMalloc1(n+1,&ainew);
    587:   ainew[0] = 0;
    588:   /* don't know how many column pointers are needed so estimate */
    589:   jmax = (PetscInt)(f*ai[n] + 1);
    590:   PetscMalloc1(jmax,&ajnew);
    591:   /* ajfill is level of fill for each fill entry */
    592:   PetscMalloc1(jmax,&ajfill);
    593:   /* fill is a linked list of nonzeros in active row */
    594:   PetscMalloc1(n+1,&fill);
    595:   /* im is level for each filled value */
    596:   PetscMalloc1(n+1,&im);
    597:   /* dloc is location of diagonal in factor */
    598:   PetscMalloc1(n+1,&dloc);
    599:   dloc[0] = 0;
    600:   for (prow=0; prow<n; prow++) {

    602:     /* copy prow into linked list */
    603:     nzf = nz = ai[r[prow]+1] - ai[r[prow]];
    604:     if (!nz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[prow],prow);
    605:     xi         = aj + ai[r[prow]];
    606:     fill[n]    = n;
    607:     fill[prow] = -1;   /* marker for diagonal entry */
    608:     while (nz--) {
    609:       fm  = n;
    610:       idx = ic[*xi++];
    611:       do {
    612:         m  = fm;
    613:         fm = fill[m];
    614:       } while (fm < idx);
    615:       fill[m]   = idx;
    616:       fill[idx] = fm;
    617:       im[idx]   = 0;
    618:     }

    620:     /* make sure diagonal entry is included */
    621:     if (diagonal_fill && fill[prow] == -1) {
    622:       fm = n;
    623:       while (fill[fm] < prow) fm = fill[fm];
    624:       fill[prow] = fill[fm];    /* insert diagonal into linked list */
    625:       fill[fm]   = prow;
    626:       im[prow]   = 0;
    627:       nzf++;
    628:       dcount++;
    629:     }

    631:     nzi = 0;
    632:     row = fill[n];
    633:     while (row < prow) {
    634:       incrlev = im[row] + 1;
    635:       nz      = dloc[row];
    636:       xi      = ajnew  + ainew[row] + nz + 1;
    637:       flev    = ajfill + ainew[row] + nz + 1;
    638:       nnz     = ainew[row+1] - ainew[row] - nz - 1;
    639:       fm      = row;
    640:       while (nnz-- > 0) {
    641:         idx = *xi++;
    642:         if (*flev + incrlev > levels) {
    643:           flev++;
    644:           continue;
    645:         }
    646:         do {
    647:           m  = fm;
    648:           fm = fill[m];
    649:         } while (fm < idx);
    650:         if (fm != idx) {
    651:           im[idx]   = *flev + incrlev;
    652:           fill[m]   = idx;
    653:           fill[idx] = fm;
    654:           fm        = idx;
    655:           nzf++;
    656:         } else if (im[idx] > *flev + incrlev) im[idx] = *flev+incrlev;
    657:         flev++;
    658:       }
    659:       row = fill[row];
    660:       nzi++;
    661:     }
    662:     /* copy new filled row into permanent storage */
    663:     ainew[prow+1] = ainew[prow] + nzf;
    664:     if (ainew[prow+1] > jmax) {

    666:       /* estimate how much additional space we will need */
    667:       /* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */
    668:       /* just double the memory each time */
    669:       PetscInt maxadd = jmax;
    670:       /* maxadd = (int)(((f*ai[n]+1)*(n-prow+5))/n); */
    671:       if (maxadd < nzf) maxadd = (n-prow)*(nzf+1);
    672:       jmax += maxadd;

    674:       /* allocate a longer ajnew and ajfill */
    675:       PetscMalloc1(jmax,&xitmp);
    676:       PetscMemcpy(xitmp,ajnew,ainew[prow]*sizeof(PetscInt));
    677:       PetscFree(ajnew);
    678:       ajnew  = xitmp;
    679:       PetscMalloc1(jmax,&xitmp);
    680:       PetscMemcpy(xitmp,ajfill,ainew[prow]*sizeof(PetscInt));
    681:       PetscFree(ajfill);
    682:       ajfill = xitmp;
    683:       reallocate++;   /* count how many reallocations are needed */
    684:     }
    685:     xitmp      = ajnew + ainew[prow];
    686:     flev       = ajfill + ainew[prow];
    687:     dloc[prow] = nzi;
    688:     fm         = fill[n];
    689:     while (nzf--) {
    690:       *xitmp++ = fm;
    691:       *flev++  = im[fm];
    692:       fm       = fill[fm];
    693:     }
    694:     /* make sure row has diagonal entry */
    695:     if (ajnew[ainew[prow]+dloc[prow]] != prow) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
    696:                                                         try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",prow);
    697:   }
    698:   PetscFree(ajfill);
    699:   ISRestoreIndices(isrow,&r);
    700:   ISRestoreIndices(isicol,&ic);
    701:   PetscFree(fill);
    702:   PetscFree(im);

    704: #if defined(PETSC_USE_INFO)
    705:   {
    706:     PetscReal af = ((PetscReal)ainew[n])/((PetscReal)ai[n]);
    707:     PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocate,(double)f,(double)af);
    708:     PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
    709:     PetscInfo1(A,"PCFactorSetFill(pc,%g);\n",(double)af);
    710:     PetscInfo(A,"for best performance.\n");
    711:     if (diagonal_fill) {
    712:       PetscInfo1(A,"Detected and replaced %D missing diagonals\n",dcount);
    713:     }
    714:   }
    715: #endif

    717:   /* put together the new matrix */
    718:   MatSeqBAIJSetPreallocation_SeqBAIJ(fact,bs,MAT_SKIP_ALLOCATION,NULL);
    719:   PetscLogObjectParent((PetscObject)fact,(PetscObject)isicol);
    720:   b    = (Mat_SeqBAIJ*)fact->data;

    722:   b->free_a       = PETSC_TRUE;
    723:   b->free_ij      = PETSC_TRUE;
    724:   b->singlemalloc = PETSC_FALSE;

    726:   PetscMalloc1(bs2*ainew[n],&b->a);

    728:   b->j          = ajnew;
    729:   b->i          = ainew;
    730:   for (i=0; i<n; i++) dloc[i] += ainew[i];
    731:   b->diag          = dloc;
    732:   b->free_diag     = PETSC_TRUE;
    733:   b->ilen          = 0;
    734:   b->imax          = 0;
    735:   b->row           = isrow;
    736:   b->col           = iscol;
    737:   b->pivotinblocks = (info->pivotinblocks) ? PETSC_TRUE : PETSC_FALSE;

    739:   PetscObjectReference((PetscObject)isrow);
    740:   PetscObjectReference((PetscObject)iscol);
    741:   b->icol = isicol;
    742:   PetscMalloc1(bs*n+bs,&b->solve_work);
    743:   /* In b structure:  Free imax, ilen, old a, old j.
    744:      Allocate dloc, solve_work, new a, new j */
    745:   PetscLogObjectMemory((PetscObject)fact,(ainew[n]-n)*(sizeof(PetscInt))+bs2*ainew[n]*sizeof(PetscScalar));
    746:   b->maxnz = b->nz = ainew[n];

    748:   fact->info.factor_mallocs    = reallocate;
    749:   fact->info.fill_ratio_given  = f;
    750:   fact->info.fill_ratio_needed = ((PetscReal)ainew[n])/((PetscReal)ai[prow]);

    752:   MatSeqBAIJSetNumericFactorization_inplace(fact,both_identity);
    753:   return(0);
    754: }

    758: PetscErrorCode MatSetUnfactored_SeqBAIJ_4_NaturalOrdering_SSE(Mat A)
    759: {
    760:   /* Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data; */
    761:   /* int i,*AJ=a->j,nz=a->nz; */

    764:   /* Undo Column scaling */
    765:   /*    while (nz--) { */
    766:   /*      AJ[i] = AJ[i]/4; */
    767:   /*    } */
    768:   /* This should really invoke a push/pop logic, but we don't have that yet. */
    769:   A->ops->setunfactored = NULL;
    770:   return(0);
    771: }

    775: PetscErrorCode MatSetUnfactored_SeqBAIJ_4_NaturalOrdering_SSE_usj(Mat A)
    776: {
    777:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data;
    778:   PetscInt       *AJ=a->j,nz=a->nz;
    779:   unsigned short *aj=(unsigned short*)AJ;

    782:   /* Is this really necessary? */
    783:   while (nz--) {
    784:     AJ[nz] = (int)((unsigned int)aj[nz]); /* First extend, then convert to signed. */
    785:   }
    786:   A->ops->setunfactored = NULL;
    787:   return(0);
    788: }