Actual source code: baijfact2.c

      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);

     14: /*
     15:    This is not much faster than MatLUFactorNumeric_SeqBAIJ_N() but the solve is faster at least sometimes
     16: */
     17: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_15_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
     18: {
     19:   Mat             C =B;
     20:   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
     21:   PetscErrorCode  ierr;
     22:   PetscInt        i,j,k,ipvt[15];
     23:   const PetscInt  n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*ajtmp,*bjtmp,*bdiag=b->diag,*pj;
     24:   PetscInt        nz,nzL,row;
     25:   MatScalar       *rtmp,*pc,*mwork,*pv,*vv,work[225];
     26:   const MatScalar *v,*aa=a->a;
     27:   PetscInt        bs2 = a->bs2,bs=A->rmap->bs,flg;
     28:   PetscInt        sol_ver;
     29:   PetscBool       allowzeropivot,zeropivotdetected;

     32:   allowzeropivot = PetscNot(A->erroriffailure);
     33:   PetscOptionsGetInt(NULL,((PetscObject)A)->prefix,"-sol_ver",&sol_ver,NULL);

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

     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:       PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
     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:       PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
     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:       PetscArraycpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2);
     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(2.0*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:       PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
     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:     PetscArraycpy(pv,rtmp+bs2*pj[0],bs2);
    105:     PetscKernel_A_gets_inverse_A_15(pv,ipvt,work,info->shiftamount,allowzeropivot,&zeropivotdetected);
    106:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    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:       PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
    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: }

    127: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_N(Mat B,Mat A,const MatFactorInfo *info)
    128: {
    129:   Mat            C     =B;
    130:   Mat_SeqBAIJ    *a    =(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
    131:   IS             isrow = b->row,isicol = b->icol;
    133:   const PetscInt *r,*ic;
    134:   PetscInt       i,j,k,n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
    135:   PetscInt       *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj;
    136:   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
    137:   PetscInt       bs=A->rmap->bs,bs2 = a->bs2,*v_pivots,flg;
    138:   MatScalar      *v_work;
    139:   PetscBool      col_identity,row_identity,both_identity;
    140:   PetscBool      allowzeropivot,zeropivotdetected;

    143:   ISGetIndices(isrow,&r);
    144:   ISGetIndices(isicol,&ic);
    145:   allowzeropivot = PetscNot(A->erroriffailure);

    147:   PetscCalloc1(bs2*n,&rtmp);

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

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

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

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

    176:     /* elimination */
    177:     bjtmp = bj + bi[i];
    178:     nzL   = bi[i+1] - bi[i];
    179:     for (k=0; k < nzL; k++) {
    180:       row = bjtmp[k];
    181:       pc  = rtmp + bs2*row;
    182:       for (flg=0,j=0; j<bs2; j++) {
    183:         if (pc[j]!=0.0) {
    184:           flg = 1;
    185:           break;
    186:         }
    187:       }
    188:       if (flg) {
    189:         pv = b->a + bs2*bdiag[row];
    190:         PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); /* *pc = *pc * (*pv); */
    191:         pj = b->j + bdiag[row+1]+1;         /* begining of U(row,:) */
    192:         pv = b->a + bs2*(bdiag[row+1]+1);
    193:         nz = bdiag[row] - bdiag[row+1] - 1;         /* num of entries inU(row,:), excluding diag */
    194:         for (j=0; j<nz; j++) {
    195:           PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
    196:         }
    197:         PetscLogFlops(2.0*bs2*bs*(nz+1)-bs2); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
    198:       }
    199:     }

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

    210:     /* Mark diagonal and invert diagonal for simplier triangular solves */
    211:     pv = b->a + bs2*bdiag[i];
    212:     pj = b->j + bdiag[i];
    213:     PetscArraycpy(pv,rtmp+bs2*pj[0],bs2);

    215:     PetscKernel_A_gets_inverse_A(bs,pv,v_pivots,v_work,allowzeropivot,&zeropivotdetected);
    216:     if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    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:       PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
    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:     switch (bs) {
    238:     case  9:
    239: #if defined(PETSC_HAVE_IMMINTRIN_H) && defined(__AVX2__) && defined(__FMA__) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES)
    240:       C->ops->solve = MatSolve_SeqBAIJ_9_NaturalOrdering;
    241: #else
    242:       C->ops->solve = MatSolve_SeqBAIJ_N_NaturalOrdering;
    243: #endif
    244:       break;
    245:     case 11:
    246:       C->ops->solve = MatSolve_SeqBAIJ_11_NaturalOrdering;
    247:       break;
    248:     case 12:
    249:       C->ops->solve = MatSolve_SeqBAIJ_12_NaturalOrdering;
    250:       break;
    251:     case 13:
    252:       C->ops->solve = MatSolve_SeqBAIJ_13_NaturalOrdering;
    253:       break;
    254:     case 14:
    255:       C->ops->solve = MatSolve_SeqBAIJ_14_NaturalOrdering;
    256:       break;
    257:     default:
    258:       C->ops->solve = MatSolve_SeqBAIJ_N_NaturalOrdering;
    259:       break;
    260:     }
    261:   } else {
    262:     C->ops->solve = MatSolve_SeqBAIJ_N;
    263:   }
    264:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_N;

    266:   C->assembled = PETSC_TRUE;

    268:   PetscLogFlops(1.333333333333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
    269:   return(0);
    270: }

    272: /*
    273:    ilu(0) with natural ordering under new data structure.
    274:    See MatILUFactorSymbolic_SeqAIJ_ilu0() for detailed description
    275:    because this code is almost identical to MatILUFactorSymbolic_SeqAIJ_ilu0_inplace().
    276: */

    278: PetscErrorCode MatILUFactorSymbolic_SeqBAIJ_ilu0(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
    279: {

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

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

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

    294:   b->singlemalloc    = PETSC_TRUE;
    295:   b->free_a          = PETSC_TRUE;
    296:   b->free_ij         = PETSC_TRUE;
    297:   fact->preallocated = PETSC_TRUE;
    298:   fact->assembled    = PETSC_TRUE;
    299:   if (!b->diag) {
    300:     PetscMalloc1(n+1,&b->diag);
    301:     PetscLogObjectMemory((PetscObject)fact,(n+1)*sizeof(PetscInt));
    302:   }
    303:   bdiag = b->diag;

    305:   if (n > 0) {
    306:     PetscArrayzero(b->a,bs2*ai[n]);
    307:   }

    309:   /* set bi and bj with new data structure */
    310:   bi = b->i;
    311:   bj = b->j;

    313:   /* L part */
    314:   bi[0] = 0;
    315:   for (i=0; i<n; i++) {
    316:     nz      = adiag[i] - ai[i];
    317:     bi[i+1] = bi[i] + nz;
    318:     aj      = a->j + ai[i];
    319:     for (j=0; j<nz; j++) {
    320:       *bj = aj[j]; bj++;
    321:     }
    322:   }

    324:   /* U part */
    325:   bi_temp  = bi[n];
    326:   bdiag[n] = bi[n]-1;
    327:   for (i=n-1; i>=0; i--) {
    328:     nz      = ai[i+1] - adiag[i] - 1;
    329:     bi_temp = bi_temp + nz + 1;
    330:     aj      = a->j + adiag[i] + 1;
    331:     for (j=0; j<nz; j++) {
    332:       *bj = aj[j]; bj++;
    333:     }
    334:     /* diag[i] */
    335:     *bj      = i; bj++;
    336:     bdiag[i] = bi_temp - 1;
    337:   }
    338:   return(0);
    339: }

    341: PetscErrorCode MatILUFactorSymbolic_SeqBAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
    342: {
    343:   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b;
    344:   IS                 isicol;
    345:   PetscErrorCode     ierr;
    346:   const PetscInt     *r,*ic;
    347:   PetscInt           n=a->mbs,*ai=a->i,*aj=a->j,d;
    348:   PetscInt           *bi,*cols,nnz,*cols_lvl;
    349:   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
    350:   PetscInt           i,levels,diagonal_fill;
    351:   PetscBool          col_identity,row_identity,both_identity;
    352:   PetscReal          f;
    353:   PetscInt           nlnk,*lnk,*lnk_lvl=NULL;
    354:   PetscBT            lnkbt;
    355:   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
    356:   PetscFreeSpaceList free_space    =NULL,current_space=NULL;
    357:   PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL;
    358:   PetscBool          missing;
    359:   PetscInt           bs=A->rmap->bs,bs2=a->bs2;

    362:   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);
    363:   if (bs>1) {  /* check shifttype */
    364:     if (info->shifttype == MAT_SHIFT_NONZERO || info->shifttype == MAT_SHIFT_POSITIVE_DEFINITE) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only MAT_SHIFT_NONE and MAT_SHIFT_INBLOCKS are supported for BAIJ matrix");
    365:   }

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

    370:   f             = info->fill;
    371:   levels        = (PetscInt)info->levels;
    372:   diagonal_fill = (PetscInt)info->diagonal_fill;

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

    376:   ISIdentity(isrow,&row_identity);
    377:   ISIdentity(iscol,&col_identity);

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

    381:   if (!levels && both_identity) {
    382:     /* special case: ilu(0) with natural ordering */
    383:     MatILUFactorSymbolic_SeqBAIJ_ilu0(fact,A,isrow,iscol,info);
    384:     MatSeqBAIJSetNumericFactorization(fact,both_identity);

    386:     fact->factortype               = MAT_FACTOR_ILU;
    387:     (fact)->info.factor_mallocs    = 0;
    388:     (fact)->info.fill_ratio_given  = info->fill;
    389:     (fact)->info.fill_ratio_needed = 1.0;

    391:     b                = (Mat_SeqBAIJ*)(fact)->data;
    392:     b->row           = isrow;
    393:     b->col           = iscol;
    394:     b->icol          = isicol;
    395:     PetscObjectReference((PetscObject)isrow);
    396:     PetscObjectReference((PetscObject)iscol);
    397:     b->pivotinblocks = (info->pivotinblocks) ? PETSC_TRUE : PETSC_FALSE;

    399:     PetscMalloc1((n+1)*bs,&b->solve_work);
    400:     return(0);
    401:   }

    403:   ISGetIndices(isrow,&r);
    404:   ISGetIndices(isicol,&ic);

    406:   /* get new row pointers */
    407:   PetscMalloc1(n+1,&bi);
    408:   bi[0] = 0;
    409:   /* bdiag is location of diagonal in factor */
    410:   PetscMalloc1(n+1,&bdiag);
    411:   bdiag[0] = 0;

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

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

    419:   /* initial FreeSpace size is f*(ai[n]+1) */
    420:   PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space);
    421:   current_space     = free_space;
    422:   PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space_lvl);
    423:   current_space_lvl = free_space_lvl;

    425:   for (i=0; i<n; i++) {
    426:     nzi = 0;
    427:     /* copy current row into linked list */
    428:     nnz = ai[r[i]+1] - ai[r[i]];
    429:     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);
    430:     cols   = aj + ai[r[i]];
    431:     lnk[i] = -1; /* marker to indicate if diagonal exists */
    432:     PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);
    433:     nzi   += nlnk;

    435:     /* make sure diagonal entry is included */
    436:     if (diagonal_fill && lnk[i] == -1) {
    437:       fm = n;
    438:       while (lnk[fm] < i) fm = lnk[fm];
    439:       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
    440:       lnk[fm]    = i;
    441:       lnk_lvl[i] = 0;
    442:       nzi++; dcount++;
    443:     }

    445:     /* add pivot rows into the active row */
    446:     nzbd = 0;
    447:     prow = lnk[n];
    448:     while (prow < i) {
    449:       nnz      = bdiag[prow];
    450:       cols     = bj_ptr[prow] + nnz + 1;
    451:       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
    452:       nnz      = bi[prow+1] - bi[prow] - nnz - 1;

    454:       PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);
    455:       nzi += nlnk;
    456:       prow = lnk[prow];
    457:       nzbd++;
    458:     }
    459:     bdiag[i] = nzbd;
    460:     bi[i+1]  = bi[i] + nzi;

    462:     /* if free space is not available, make more free space */
    463:     if (current_space->local_remaining<nzi) {
    464:       nnz  = PetscIntMultTruncate(2,PetscIntMultTruncate(nzi,(n - i))); /* estimated and max additional space needed */
    465:       PetscFreeSpaceGet(nnz,&current_space);
    466:       PetscFreeSpaceGet(nnz,&current_space_lvl);
    467:       reallocs++;
    468:     }

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

    473:     bj_ptr[i]    = current_space->array;
    474:     bjlvl_ptr[i] = current_space_lvl->array;

    476:     /* make sure the active row i has diagonal entry */
    477:     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);

    479:     current_space->array           += nzi;
    480:     current_space->local_used      += nzi;
    481:     current_space->local_remaining -= nzi;

    483:     current_space_lvl->array           += nzi;
    484:     current_space_lvl->local_used      += nzi;
    485:     current_space_lvl->local_remaining -= nzi;
    486:   }

    488:   ISRestoreIndices(isrow,&r);
    489:   ISRestoreIndices(isicol,&ic);

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

    495:   PetscIncompleteLLDestroy(lnk,lnkbt);
    496:   PetscFreeSpaceDestroy(free_space_lvl);
    497:   PetscFree2(bj_ptr,bjlvl_ptr);

    499: #if defined(PETSC_USE_INFO)
    500:   {
    501:     PetscReal af = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
    502:     PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);
    503:     PetscInfo1(A,"Run with -[sub_]pc_factor_fill %g or use \n",(double)af);
    504:     PetscInfo1(A,"PCFactorSetFill([sub]pc,%g);\n",(double)af);
    505:     PetscInfo(A,"for best performance.\n");
    506:     if (diagonal_fill) {
    507:       PetscInfo1(A,"Detected and replaced %D missing diagonals\n",dcount);
    508:     }
    509:   }
    510: #endif

    512:   /* put together the new matrix */
    513:   MatSeqBAIJSetPreallocation(fact,bs,MAT_SKIP_ALLOCATION,NULL);
    514:   PetscLogObjectParent((PetscObject)fact,(PetscObject)isicol);

    516:   b               = (Mat_SeqBAIJ*)(fact)->data;
    517:   b->free_a       = PETSC_TRUE;
    518:   b->free_ij      = PETSC_TRUE;
    519:   b->singlemalloc = PETSC_FALSE;

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

    523:   b->j          = bj;
    524:   b->i          = bi;
    525:   b->diag       = bdiag;
    526:   b->free_diag  = PETSC_TRUE;
    527:   b->ilen       = NULL;
    528:   b->imax       = NULL;
    529:   b->row        = isrow;
    530:   b->col        = iscol;
    531:   PetscObjectReference((PetscObject)isrow);
    532:   PetscObjectReference((PetscObject)iscol);
    533:   b->icol       = isicol;

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

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

    545:   MatSeqBAIJSetNumericFactorization(fact,both_identity);
    546:   return(0);
    547: }

    549: /*
    550:      This code is virtually identical to MatILUFactorSymbolic_SeqAIJ
    551:    except that the data structure of Mat_SeqAIJ is slightly different.
    552:    Not a good example of code reuse.
    553: */
    554: PetscErrorCode MatILUFactorSymbolic_SeqBAIJ_inplace(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
    555: {
    556:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b;
    557:   IS             isicol;
    559:   const PetscInt *r,*ic,*ai = a->i,*aj = a->j,*xi;
    560:   PetscInt       prow,n = a->mbs,*ainew,*ajnew,jmax,*fill,nz,*im,*ajfill,*flev,*xitmp;
    561:   PetscInt       *dloc,idx,row,m,fm,nzf,nzi,reallocate = 0,dcount = 0;
    562:   PetscInt       incrlev,nnz,i,bs = A->rmap->bs,bs2 = a->bs2,levels,diagonal_fill,dd;
    563:   PetscBool      col_identity,row_identity,both_identity,flg;
    564:   PetscReal      f;

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

    570:   f             = info->fill;
    571:   levels        = (PetscInt)info->levels;
    572:   diagonal_fill = (PetscInt)info->diagonal_fill;

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

    576:   ISIdentity(isrow,&row_identity);
    577:   ISIdentity(iscol,&col_identity);
    578:   both_identity = (PetscBool) (row_identity && col_identity);

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

    584:     fact->factortype = MAT_FACTOR_ILU;
    585:     b                = (Mat_SeqBAIJ*)fact->data;
    586:     b->row           = isrow;
    587:     b->col           = iscol;
    588:     PetscObjectReference((PetscObject)isrow);
    589:     PetscObjectReference((PetscObject)iscol);
    590:     b->icol          = isicol;
    591:     b->pivotinblocks = (info->pivotinblocks) ? PETSC_TRUE : PETSC_FALSE;

    593:     PetscMalloc1((n+1)*bs,&b->solve_work);
    594:     return(0);
    595:   }

    597:   /* general case perform the symbolic factorization */
    598:   ISGetIndices(isrow,&r);
    599:   ISGetIndices(isicol,&ic);

    601:   /* get new row pointers */
    602:   PetscMalloc1(n+1,&ainew);
    603:   ainew[0] = 0;
    604:   /* don't know how many column pointers are needed so estimate */
    605:   jmax = (PetscInt)(f*ai[n] + 1);
    606:   PetscMalloc1(jmax,&ajnew);
    607:   /* ajfill is level of fill for each fill entry */
    608:   PetscMalloc1(jmax,&ajfill);
    609:   /* fill is a linked list of nonzeros in active row */
    610:   PetscMalloc1(n+1,&fill);
    611:   /* im is level for each filled value */
    612:   PetscMalloc1(n+1,&im);
    613:   /* dloc is location of diagonal in factor */
    614:   PetscMalloc1(n+1,&dloc);
    615:   dloc[0] = 0;
    616:   for (prow=0; prow<n; prow++) {

    618:     /* copy prow into linked list */
    619:     nzf = nz = ai[r[prow]+1] - ai[r[prow]];
    620:     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);
    621:     xi         = aj + ai[r[prow]];
    622:     fill[n]    = n;
    623:     fill[prow] = -1;   /* marker for diagonal entry */
    624:     while (nz--) {
    625:       fm  = n;
    626:       idx = ic[*xi++];
    627:       do {
    628:         m  = fm;
    629:         fm = fill[m];
    630:       } while (fm < idx);
    631:       fill[m]   = idx;
    632:       fill[idx] = fm;
    633:       im[idx]   = 0;
    634:     }

    636:     /* make sure diagonal entry is included */
    637:     if (diagonal_fill && fill[prow] == -1) {
    638:       fm = n;
    639:       while (fill[fm] < prow) fm = fill[fm];
    640:       fill[prow] = fill[fm];    /* insert diagonal into linked list */
    641:       fill[fm]   = prow;
    642:       im[prow]   = 0;
    643:       nzf++;
    644:       dcount++;
    645:     }

    647:     nzi = 0;
    648:     row = fill[n];
    649:     while (row < prow) {
    650:       incrlev = im[row] + 1;
    651:       nz      = dloc[row];
    652:       xi      = ajnew  + ainew[row] + nz + 1;
    653:       flev    = ajfill + ainew[row] + nz + 1;
    654:       nnz     = ainew[row+1] - ainew[row] - nz - 1;
    655:       fm      = row;
    656:       while (nnz-- > 0) {
    657:         idx = *xi++;
    658:         if (*flev + incrlev > levels) {
    659:           flev++;
    660:           continue;
    661:         }
    662:         do {
    663:           m  = fm;
    664:           fm = fill[m];
    665:         } while (fm < idx);
    666:         if (fm != idx) {
    667:           im[idx]   = *flev + incrlev;
    668:           fill[m]   = idx;
    669:           fill[idx] = fm;
    670:           fm        = idx;
    671:           nzf++;
    672:         } else if (im[idx] > *flev + incrlev) im[idx] = *flev+incrlev;
    673:         flev++;
    674:       }
    675:       row = fill[row];
    676:       nzi++;
    677:     }
    678:     /* copy new filled row into permanent storage */
    679:     ainew[prow+1] = ainew[prow] + nzf;
    680:     if (ainew[prow+1] > jmax) {

    682:       /* estimate how much additional space we will need */
    683:       /* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */
    684:       /* just double the memory each time */
    685:       PetscInt maxadd = jmax;
    686:       /* maxadd = (int)(((f*ai[n]+1)*(n-prow+5))/n); */
    687:       if (maxadd < nzf) maxadd = (n-prow)*(nzf+1);
    688:       jmax += maxadd;

    690:       /* allocate a longer ajnew and ajfill */
    691:       PetscMalloc1(jmax,&xitmp);
    692:       PetscArraycpy(xitmp,ajnew,ainew[prow]);
    693:       PetscFree(ajnew);
    694:       ajnew  = xitmp;
    695:       PetscMalloc1(jmax,&xitmp);
    696:       PetscArraycpy(xitmp,ajfill,ainew[prow]);
    697:       PetscFree(ajfill);
    698:       ajfill = xitmp;
    699:       reallocate++;   /* count how many reallocations are needed */
    700:     }
    701:     xitmp      = ajnew + ainew[prow];
    702:     flev       = ajfill + ainew[prow];
    703:     dloc[prow] = nzi;
    704:     fm         = fill[n];
    705:     while (nzf--) {
    706:       *xitmp++ = fm;
    707:       *flev++  = im[fm];
    708:       fm       = fill[fm];
    709:     }
    710:     /* make sure row has diagonal entry */
    711:     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\
    712:                                                         try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",prow);
    713:   }
    714:   PetscFree(ajfill);
    715:   ISRestoreIndices(isrow,&r);
    716:   ISRestoreIndices(isicol,&ic);
    717:   PetscFree(fill);
    718:   PetscFree(im);

    720: #if defined(PETSC_USE_INFO)
    721:   {
    722:     PetscReal af = ((PetscReal)ainew[n])/((PetscReal)ai[n]);
    723:     PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocate,(double)f,(double)af);
    724:     PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
    725:     PetscInfo1(A,"PCFactorSetFill(pc,%g);\n",(double)af);
    726:     PetscInfo(A,"for best performance.\n");
    727:     if (diagonal_fill) {
    728:       PetscInfo1(A,"Detected and replaced %D missing diagonals\n",dcount);
    729:     }
    730:   }
    731: #endif

    733:   /* put together the new matrix */
    734:   MatSeqBAIJSetPreallocation(fact,bs,MAT_SKIP_ALLOCATION,NULL);
    735:   PetscLogObjectParent((PetscObject)fact,(PetscObject)isicol);
    736:   b    = (Mat_SeqBAIJ*)fact->data;

    738:   b->free_a       = PETSC_TRUE;
    739:   b->free_ij      = PETSC_TRUE;
    740:   b->singlemalloc = PETSC_FALSE;

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

    744:   b->j          = ajnew;
    745:   b->i          = ainew;
    746:   for (i=0; i<n; i++) dloc[i] += ainew[i];
    747:   b->diag          = dloc;
    748:   b->free_diag     = PETSC_TRUE;
    749:   b->ilen          = NULL;
    750:   b->imax          = NULL;
    751:   b->row           = isrow;
    752:   b->col           = iscol;
    753:   b->pivotinblocks = (info->pivotinblocks) ? PETSC_TRUE : PETSC_FALSE;

    755:   PetscObjectReference((PetscObject)isrow);
    756:   PetscObjectReference((PetscObject)iscol);
    757:   b->icol = isicol;
    758:   PetscMalloc1(bs*n+bs,&b->solve_work);
    759:   /* In b structure:  Free imax, ilen, old a, old j.
    760:      Allocate dloc, solve_work, new a, new j */
    761:   PetscLogObjectMemory((PetscObject)fact,(ainew[n]-n)*(sizeof(PetscInt))+bs2*ainew[n]*sizeof(PetscScalar));
    762:   b->maxnz = b->nz = ainew[n];

    764:   fact->info.factor_mallocs    = reallocate;
    765:   fact->info.fill_ratio_given  = f;
    766:   fact->info.fill_ratio_needed = ((PetscReal)ainew[n])/((PetscReal)ai[prow]);

    768:   MatSeqBAIJSetNumericFactorization_inplace(fact,both_identity);
    769:   return(0);
    770: }

    772: PetscErrorCode MatSetUnfactored_SeqBAIJ_4_NaturalOrdering_SSE(Mat A)
    773: {
    774:   /* Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data; */
    775:   /* int i,*AJ=a->j,nz=a->nz; */

    778:   /* Undo Column scaling */
    779:   /*    while (nz--) { */
    780:   /*      AJ[i] = AJ[i]/4; */
    781:   /*    } */
    782:   /* This should really invoke a push/pop logic, but we don't have that yet. */
    783:   A->ops->setunfactored = NULL;
    784:   return(0);
    785: }

    787: PetscErrorCode MatSetUnfactored_SeqBAIJ_4_NaturalOrdering_SSE_usj(Mat A)
    788: {
    789:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data;
    790:   PetscInt       *AJ=a->j,nz=a->nz;
    791:   unsigned short *aj=(unsigned short*)AJ;

    794:   /* Is this really necessary? */
    795:   while (nz--) {
    796:     AJ[nz] = (int)((unsigned int)aj[nz]); /* First extend, then convert to signed. */
    797:   }
    798:   A->ops->setunfactored = NULL;
    799:   return(0);
    800: }