Date: 2022-08-02T03:13:46+00:00

Actual source code: inode.c

      2: /*
      3:   This file provides high performance routines for the Inode format (compressed sparse row)
      4:   by taking advantage of rows with identical nonzero structure (I-nodes).
      5: */
      6: #include <../src/mat/impls/aij/seq/aij.h>

      8: static PetscErrorCode MatCreateColInode_Private(Mat A,PetscInt *size,PetscInt **ns)
      9: {
     10:   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
     11:   PetscInt       i,count,m,n,min_mn,*ns_row,*ns_col;

     13:   n = A->cmap->n;
     14:   m = A->rmap->n;
     16:   ns_row = a->inode.size;

     18:   min_mn = (m < n) ? m : n;
     19:   if (!ns) {
     20:     for (count=0,i=0; count<min_mn; count+=ns_row[i],i++) ;
     21:     for (; count+1 < n; count++,i++) ;
     22:     if (count < n)  {
     23:       i++;
     24:     }
     25:     *size = i;
     26:     return 0;
     27:   }
     28:   PetscMalloc1(n+1,&ns_col);

     30:   /* Use the same row structure wherever feasible. */
     31:   for (count=0,i=0; count<min_mn; count+=ns_row[i],i++) {
     32:     ns_col[i] = ns_row[i];
     33:   }

     35:   /* if m < n; pad up the remainder with inode_limit */
     36:   for (; count+1 < n; count++,i++) {
     37:     ns_col[i] = 1;
     38:   }
     39:   /* The last node is the odd ball. padd it up with the remaining rows; */
     40:   if (count < n) {
     41:     ns_col[i] = n - count;
     42:     i++;
     43:   } else if (count > n) {
     44:     /* Adjust for the over estimation */
     45:     ns_col[i-1] += n - count;
     46:   }
     47:   *size = i;
     48:   *ns   = ns_col;
     49:   return 0;
     50: }

     52: /*
     53:       This builds symmetric version of nonzero structure,
     54: */
     55: static PetscErrorCode MatGetRowIJ_SeqAIJ_Inode_Symmetric(Mat A,const PetscInt *iia[],const PetscInt *jja[],PetscInt ishift,PetscInt oshift)
     56: {
     57:   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
     58:   PetscInt       *work,*ia,*ja,nz,nslim_row,nslim_col,m,row,col,n;
     59:   PetscInt       *tns,*tvc,*ns_row = a->inode.size,*ns_col,nsz,i1,i2;
     60:   const PetscInt *j,*jmax,*ai= a->i,*aj = a->j;

     62:   nslim_row = a->inode.node_count;
     63:   m         = A->rmap->n;
     64:   n         = A->cmap->n;

     68:   /* Use the row_inode as column_inode */
     69:   nslim_col = nslim_row;
     70:   ns_col    = ns_row;

     72:   /* allocate space for reformated inode structure */
     73:   PetscMalloc2(nslim_col+1,&tns,n+1,&tvc);
     74:   for (i1=0,tns[0]=0; i1<nslim_col; ++i1) tns[i1+1] = tns[i1]+ ns_row[i1];

     76:   for (i1=0,col=0; i1<nslim_col; ++i1) {
     77:     nsz = ns_col[i1];
     78:     for (i2=0; i2<nsz; ++i2,++col) tvc[col] = i1;
     79:   }
     80:   /* allocate space for row pointers */
     81:   PetscCalloc1(nslim_row+1,&ia);
     82:   *iia = ia;
     83:   PetscMalloc1(nslim_row+1,&work);

     85:   /* determine the number of columns in each row */
     86:   ia[0] = oshift;
     87:   for (i1=0,row=0; i1<nslim_row; row+=ns_row[i1],i1++) {

     89:     j    = aj + ai[row] + ishift;
     90:     jmax = aj + ai[row+1] + ishift;
     91:     if (j==jmax) continue; /* empty row */
     92:     col  = *j++ + ishift;
     93:     i2   = tvc[col];
     94:     while (i2<i1 && j<jmax) { /* 1.[-xx-d-xx--] 2.[-xx-------],off-diagonal elements */
     95:       ia[i1+1]++;
     96:       ia[i2+1]++;
     97:       i2++;                     /* Start col of next node */
     98:       while ((j<jmax) && ((col=*j+ishift)<tns[i2])) ++j;
     99:       i2 = tvc[col];
    100:     }
    101:     if (i2 == i1) ia[i2+1]++;    /* now the diagonal element */
    102:   }

    104:   /* shift ia[i] to point to next row */
    105:   for (i1=1; i1<nslim_row+1; i1++) {
    106:     row        = ia[i1-1];
    107:     ia[i1]    += row;
    108:     work[i1-1] = row - oshift;
    109:   }

    111:   /* allocate space for column pointers */
    112:   nz   = ia[nslim_row] + (!ishift);
    113:   PetscMalloc1(nz,&ja);
    114:   *jja = ja;

    116:   /* loop over lower triangular part putting into ja */
    117:   for (i1=0,row=0; i1<nslim_row; row += ns_row[i1],i1++) {
    118:     j    = aj + ai[row] + ishift;
    119:     jmax = aj + ai[row+1] + ishift;
    120:     if (j==jmax) continue; /* empty row */
    121:     col  = *j++ + ishift;
    122:     i2   = tvc[col];
    123:     while (i2<i1 && j<jmax) {
    124:       ja[work[i2]++] = i1 + oshift;
    125:       ja[work[i1]++] = i2 + oshift;
    126:       ++i2;
    127:       while ((j<jmax) && ((col=*j+ishift)< tns[i2])) ++j; /* Skip rest col indices in this node */
    128:       i2 = tvc[col];
    129:     }
    130:     if (i2 == i1) ja[work[i1]++] = i2 + oshift;

    132:   }
    133:   PetscFree(work);
    134:   PetscFree2(tns,tvc);
    135:   return 0;
    136: }

    138: /*
    139:       This builds nonsymmetric version of nonzero structure,
    140: */
    141: static PetscErrorCode MatGetRowIJ_SeqAIJ_Inode_Nonsymmetric(Mat A,const PetscInt *iia[],const PetscInt *jja[],PetscInt ishift,PetscInt oshift)
    142: {
    143:   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
    144:   PetscInt       *work,*ia,*ja,nz,nslim_row,n,row,col,*ns_col,nslim_col;
    145:   PetscInt       *tns,*tvc,nsz,i1,i2;
    146:   const PetscInt *j,*ai= a->i,*aj = a->j,*ns_row = a->inode.size;

    149:   nslim_row = a->inode.node_count;
    150:   n         = A->cmap->n;

    152:   /* Create The column_inode for this matrix */
    153:   MatCreateColInode_Private(A,&nslim_col,&ns_col);

    155:   /* allocate space for reformated column_inode structure */
    156:   PetscMalloc2(nslim_col +1,&tns,n + 1,&tvc);
    157:   for (i1=0,tns[0]=0; i1<nslim_col; ++i1) tns[i1+1] = tns[i1] + ns_col[i1];

    159:   for (i1=0,col=0; i1<nslim_col; ++i1) {
    160:     nsz = ns_col[i1];
    161:     for (i2=0; i2<nsz; ++i2,++col) tvc[col] = i1;
    162:   }
    163:   /* allocate space for row pointers */
    164:   PetscCalloc1(nslim_row+1,&ia);
    165:   *iia = ia;
    166:   PetscMalloc1(nslim_row+1,&work);

    168:   /* determine the number of columns in each row */
    169:   ia[0] = oshift;
    170:   for (i1=0,row=0; i1<nslim_row; row+=ns_row[i1],i1++) {
    171:     j   = aj + ai[row] + ishift;
    172:     nz  = ai[row+1] - ai[row];
    173:     if (!nz) continue; /* empty row */
    174:     col = *j++ + ishift;
    175:     i2  = tvc[col];
    176:     while (nz-- > 0) {           /* off-diagonal elements */
    177:       ia[i1+1]++;
    178:       i2++;                     /* Start col of next node */
    179:       while (nz > 0 && ((col = *j++ + ishift) < tns[i2])) nz--;
    180:       if (nz > 0) i2 = tvc[col];
    181:     }
    182:   }

    184:   /* shift ia[i] to point to next row */
    185:   for (i1=1; i1<nslim_row+1; i1++) {
    186:     row        = ia[i1-1];
    187:     ia[i1]    += row;
    188:     work[i1-1] = row - oshift;
    189:   }

    191:   /* allocate space for column pointers */
    192:   nz   = ia[nslim_row] + (!ishift);
    193:   PetscMalloc1(nz,&ja);
    194:   *jja = ja;

    196:   /* loop over matrix putting into ja */
    197:   for (i1=0,row=0; i1<nslim_row; row+=ns_row[i1],i1++) {
    198:     j   = aj + ai[row] + ishift;
    199:     nz  = ai[row+1] - ai[row];
    200:     if (!nz) continue; /* empty row */
    201:     col = *j++ + ishift;
    202:     i2  = tvc[col];
    203:     while (nz-- > 0) {
    204:       ja[work[i1]++] = i2 + oshift;
    205:       ++i2;
    206:       while (nz > 0 && ((col = *j++ + ishift) < tns[i2])) nz--;
    207:       if (nz > 0) i2 = tvc[col];
    208:     }
    209:   }
    210:   PetscFree(ns_col);
    211:   PetscFree(work);
    212:   PetscFree2(tns,tvc);
    213:   return 0;
    214: }

    216: static PetscErrorCode MatGetRowIJ_SeqAIJ_Inode(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool blockcompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
    217: {
    218:   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;

    220:   *n = a->inode.node_count;
    221:   if (!ia) return 0;
    222:   if (!blockcompressed) {
    223:     MatGetRowIJ_SeqAIJ(A,oshift,symmetric,blockcompressed,n,ia,ja,done);
    224:   } else if (symmetric) {
    225:     MatGetRowIJ_SeqAIJ_Inode_Symmetric(A,ia,ja,0,oshift);
    226:   } else {
    227:     MatGetRowIJ_SeqAIJ_Inode_Nonsymmetric(A,ia,ja,0,oshift);
    228:   }
    229:   return 0;
    230: }

    232: static PetscErrorCode MatRestoreRowIJ_SeqAIJ_Inode(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool blockcompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
    233: {
    234:   if (!ia) return 0;

    236:   if (!blockcompressed) {
    237:     MatRestoreRowIJ_SeqAIJ(A,oshift,symmetric,blockcompressed,n,ia,ja,done);
    238:   } else {
    239:     PetscFree(*ia);
    240:     PetscFree(*ja);
    241:   }
    242:   return 0;
    243: }

    245: /* ----------------------------------------------------------- */

    247: static PetscErrorCode MatGetColumnIJ_SeqAIJ_Inode_Nonsymmetric(Mat A,const PetscInt *iia[],const PetscInt *jja[],PetscInt ishift,PetscInt oshift)
    248: {
    249:   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
    250:   PetscInt       *work,*ia,*ja,*j,nz,nslim_row, n,row,col,*ns_col,nslim_col;
    251:   PetscInt       *tns,*tvc,*ns_row = a->inode.size,nsz,i1,i2,*ai= a->i,*aj = a->j;

    254:   nslim_row = a->inode.node_count;
    255:   n         = A->cmap->n;

    257:   /* Create The column_inode for this matrix */
    258:   MatCreateColInode_Private(A,&nslim_col,&ns_col);

    260:   /* allocate space for reformated column_inode structure */
    261:   PetscMalloc2(nslim_col + 1,&tns,n + 1,&tvc);
    262:   for (i1=0,tns[0]=0; i1<nslim_col; ++i1) tns[i1+1] = tns[i1] + ns_col[i1];

    264:   for (i1=0,col=0; i1<nslim_col; ++i1) {
    265:     nsz = ns_col[i1];
    266:     for (i2=0; i2<nsz; ++i2,++col) tvc[col] = i1;
    267:   }
    268:   /* allocate space for column pointers */
    269:   PetscCalloc1(nslim_col+1,&ia);
    270:   *iia = ia;
    271:   PetscMalloc1(nslim_col+1,&work);

    273:   /* determine the number of columns in each row */
    274:   ia[0] = oshift;
    275:   for (i1=0,row=0; i1<nslim_row; row+=ns_row[i1],i1++) {
    276:     j   = aj + ai[row] + ishift;
    277:     col = *j++ + ishift;
    278:     i2  = tvc[col];
    279:     nz  = ai[row+1] - ai[row];
    280:     while (nz-- > 0) {           /* off-diagonal elements */
    281:       /* ia[i1+1]++; */
    282:       ia[i2+1]++;
    283:       i2++;
    284:       while (nz > 0 && ((col = *j++ + ishift) < tns[i2])) nz--;
    285:       if (nz > 0) i2 = tvc[col];
    286:     }
    287:   }

    289:   /* shift ia[i] to point to next col */
    290:   for (i1=1; i1<nslim_col+1; i1++) {
    291:     col        = ia[i1-1];
    292:     ia[i1]    += col;
    293:     work[i1-1] = col - oshift;
    294:   }

    296:   /* allocate space for column pointers */
    297:   nz   = ia[nslim_col] + (!ishift);
    298:   PetscMalloc1(nz,&ja);
    299:   *jja = ja;

    301:   /* loop over matrix putting into ja */
    302:   for (i1=0,row=0; i1<nslim_row; row+=ns_row[i1],i1++) {
    303:     j   = aj + ai[row] + ishift;
    304:     col = *j++ + ishift;
    305:     i2  = tvc[col];
    306:     nz  = ai[row+1] - ai[row];
    307:     while (nz-- > 0) {
    308:       /* ja[work[i1]++] = i2 + oshift; */
    309:       ja[work[i2]++] = i1 + oshift;
    310:       i2++;
    311:       while (nz > 0 && ((col = *j++ + ishift) < tns[i2])) nz--;
    312:       if (nz > 0) i2 = tvc[col];
    313:     }
    314:   }
    315:   PetscFree(ns_col);
    316:   PetscFree(work);
    317:   PetscFree2(tns,tvc);
    318:   return 0;
    319: }

    321: static PetscErrorCode MatGetColumnIJ_SeqAIJ_Inode(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool blockcompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
    322: {
    323:   MatCreateColInode_Private(A,n,NULL);
    324:   if (!ia) return 0;

    326:   if (!blockcompressed) {
    327:     MatGetColumnIJ_SeqAIJ(A,oshift,symmetric,blockcompressed,n,ia,ja,done);
    328:   } else if (symmetric) {
    329:     /* Since the indices are symmetric it doesn't matter */
    330:     MatGetRowIJ_SeqAIJ_Inode_Symmetric(A,ia,ja,0,oshift);
    331:   } else {
    332:     MatGetColumnIJ_SeqAIJ_Inode_Nonsymmetric(A,ia,ja,0,oshift);
    333:   }
    334:   return 0;
    335: }

    337: static PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Inode(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool blockcompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
    338: {
    339:   if (!ia) return 0;
    340:   if (!blockcompressed) {
    341:     MatRestoreColumnIJ_SeqAIJ(A,oshift,symmetric,blockcompressed,n,ia,ja,done);
    342:   } else {
    343:     PetscFree(*ia);
    344:     PetscFree(*ja);
    345:   }
    346:   return 0;
    347: }

    349: /* ----------------------------------------------------------- */

    351: PetscErrorCode MatMult_SeqAIJ_Inode(Mat A,Vec xx,Vec yy)
    352: {
    353:   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
    354:   PetscScalar       sum1,sum2,sum3,sum4,sum5,tmp0,tmp1;
    355:   PetscScalar       *y;
    356:   const PetscScalar *x;
    357:   const MatScalar   *v1,*v2,*v3,*v4,*v5;
    358:   PetscInt          i1,i2,n,i,row,node_max,nsz,sz,nonzerorow=0;
    359:   const PetscInt    *idx,*ns,*ii;

    361: #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
    362: #pragma disjoint(*x,*y,*v1,*v2,*v3,*v4,*v5)
    363: #endif

    366:   node_max = a->inode.node_count;
    367:   ns       = a->inode.size;     /* Node Size array */
    368:   VecGetArrayRead(xx,&x);
    369:   VecGetArray(yy,&y);
    370:   idx      = a->j;
    371:   v1       = a->a;
    372:   ii       = a->i;

    374:   for (i = 0,row = 0; i< node_max; ++i) {
    375:     nsz         = ns[i];
    376:     n           = ii[1] - ii[0];
    377:     nonzerorow += (n>0)*nsz;
    378:     ii         += nsz;
    379:     PetscPrefetchBlock(idx+nsz*n,n,0,PETSC_PREFETCH_HINT_NTA);    /* Prefetch the indices for the block row after the current one */
    380:     PetscPrefetchBlock(v1+nsz*n,nsz*n,0,PETSC_PREFETCH_HINT_NTA); /* Prefetch the values for the block row after the current one  */
    381:     sz = n;                     /* No of non zeros in this row */
    382:                                 /* Switch on the size of Node */
    383:     switch (nsz) {               /* Each loop in 'case' is unrolled */
    384:     case 1:
    385:       sum1 = 0.;

    387:       for (n = 0; n< sz-1; n+=2) {
    388:         i1    = idx[0];         /* The instructions are ordered to */
    389:         i2    = idx[1];         /* make the compiler's job easy */
    390:         idx  += 2;
    391:         tmp0  = x[i1];
    392:         tmp1  = x[i2];
    393:         sum1 += v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    394:       }

    396:       if (n == sz-1) {          /* Take care of the last nonzero  */
    397:         tmp0  = x[*idx++];
    398:         sum1 += *v1++ *tmp0;
    399:       }
    400:       y[row++]=sum1;
    401:       break;
    402:     case 2:
    403:       sum1 = 0.;
    404:       sum2 = 0.;
    405:       v2   = v1 + n;

    407:       for (n = 0; n< sz-1; n+=2) {
    408:         i1    = idx[0];
    409:         i2    = idx[1];
    410:         idx  += 2;
    411:         tmp0  = x[i1];
    412:         tmp1  = x[i2];
    413:         sum1 += v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    414:         sum2 += v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    415:       }
    416:       if (n == sz-1) {
    417:         tmp0  = x[*idx++];
    418:         sum1 += *v1++ * tmp0;
    419:         sum2 += *v2++ * tmp0;
    420:       }
    421:       y[row++]=sum1;
    422:       y[row++]=sum2;
    423:       v1      =v2;              /* Since the next block to be processed starts there*/
    424:       idx    +=sz;
    425:       break;
    426:     case 3:
    427:       sum1 = 0.;
    428:       sum2 = 0.;
    429:       sum3 = 0.;
    430:       v2   = v1 + n;
    431:       v3   = v2 + n;

    433:       for (n = 0; n< sz-1; n+=2) {
    434:         i1    = idx[0];
    435:         i2    = idx[1];
    436:         idx  += 2;
    437:         tmp0  = x[i1];
    438:         tmp1  = x[i2];
    439:         sum1 += v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    440:         sum2 += v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    441:         sum3 += v3[0] * tmp0 + v3[1] * tmp1; v3 += 2;
    442:       }
    443:       if (n == sz-1) {
    444:         tmp0  = x[*idx++];
    445:         sum1 += *v1++ * tmp0;
    446:         sum2 += *v2++ * tmp0;
    447:         sum3 += *v3++ * tmp0;
    448:       }
    449:       y[row++]=sum1;
    450:       y[row++]=sum2;
    451:       y[row++]=sum3;
    452:       v1      =v3;              /* Since the next block to be processed starts there*/
    453:       idx    +=2*sz;
    454:       break;
    455:     case 4:
    456:       sum1 = 0.;
    457:       sum2 = 0.;
    458:       sum3 = 0.;
    459:       sum4 = 0.;
    460:       v2   = v1 + n;
    461:       v3   = v2 + n;
    462:       v4   = v3 + n;

    464:       for (n = 0; n< sz-1; n+=2) {
    465:         i1    = idx[0];
    466:         i2    = idx[1];
    467:         idx  += 2;
    468:         tmp0  = x[i1];
    469:         tmp1  = x[i2];
    470:         sum1 += v1[0] * tmp0 + v1[1] *tmp1; v1 += 2;
    471:         sum2 += v2[0] * tmp0 + v2[1] *tmp1; v2 += 2;
    472:         sum3 += v3[0] * tmp0 + v3[1] *tmp1; v3 += 2;
    473:         sum4 += v4[0] * tmp0 + v4[1] *tmp1; v4 += 2;
    474:       }
    475:       if (n == sz-1) {
    476:         tmp0  = x[*idx++];
    477:         sum1 += *v1++ * tmp0;
    478:         sum2 += *v2++ * tmp0;
    479:         sum3 += *v3++ * tmp0;
    480:         sum4 += *v4++ * tmp0;
    481:       }
    482:       y[row++]=sum1;
    483:       y[row++]=sum2;
    484:       y[row++]=sum3;
    485:       y[row++]=sum4;
    486:       v1      =v4;              /* Since the next block to be processed starts there*/
    487:       idx    +=3*sz;
    488:       break;
    489:     case 5:
    490:       sum1 = 0.;
    491:       sum2 = 0.;
    492:       sum3 = 0.;
    493:       sum4 = 0.;
    494:       sum5 = 0.;
    495:       v2   = v1 + n;
    496:       v3   = v2 + n;
    497:       v4   = v3 + n;
    498:       v5   = v4 + n;

    500:       for (n = 0; n<sz-1; n+=2) {
    501:         i1    = idx[0];
    502:         i2    = idx[1];
    503:         idx  += 2;
    504:         tmp0  = x[i1];
    505:         tmp1  = x[i2];
    506:         sum1 += v1[0] * tmp0 + v1[1] *tmp1; v1 += 2;
    507:         sum2 += v2[0] * tmp0 + v2[1] *tmp1; v2 += 2;
    508:         sum3 += v3[0] * tmp0 + v3[1] *tmp1; v3 += 2;
    509:         sum4 += v4[0] * tmp0 + v4[1] *tmp1; v4 += 2;
    510:         sum5 += v5[0] * tmp0 + v5[1] *tmp1; v5 += 2;
    511:       }
    512:       if (n == sz-1) {
    513:         tmp0  = x[*idx++];
    514:         sum1 += *v1++ * tmp0;
    515:         sum2 += *v2++ * tmp0;
    516:         sum3 += *v3++ * tmp0;
    517:         sum4 += *v4++ * tmp0;
    518:         sum5 += *v5++ * tmp0;
    519:       }
    520:       y[row++]=sum1;
    521:       y[row++]=sum2;
    522:       y[row++]=sum3;
    523:       y[row++]=sum4;
    524:       y[row++]=sum5;
    525:       v1      =v5;       /* Since the next block to be processed starts there */
    526:       idx    +=4*sz;
    527:       break;
    528:     default:
    529:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_COR,"Node size not yet supported");
    530:     }
    531:   }
    532:   VecRestoreArrayRead(xx,&x);
    533:   VecRestoreArray(yy,&y);
    534:   PetscLogFlops(2.0*a->nz - nonzerorow);
    535:   return 0;
    536: }
    537: /* ----------------------------------------------------------- */
    538: /* Almost same code as the MatMult_SeqAIJ_Inode() */
    539: PetscErrorCode MatMultAdd_SeqAIJ_Inode(Mat A,Vec xx,Vec zz,Vec yy)
    540: {
    541:   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
    542:   PetscScalar       sum1,sum2,sum3,sum4,sum5,tmp0,tmp1;
    543:   const MatScalar   *v1,*v2,*v3,*v4,*v5;
    544:   const PetscScalar *x;
    545:   PetscScalar       *y,*z,*zt;
    546:   PetscInt          i1,i2,n,i,row,node_max,nsz,sz;
    547:   const PetscInt    *idx,*ns,*ii;

    550:   node_max = a->inode.node_count;
    551:   ns       = a->inode.size;     /* Node Size array */

    553:   VecGetArrayRead(xx,&x);
    554:   VecGetArrayPair(zz,yy,&z,&y);
    555:   zt = z;

    557:   idx = a->j;
    558:   v1  = a->a;
    559:   ii  = a->i;

    561:   for (i = 0,row = 0; i< node_max; ++i) {
    562:     nsz = ns[i];
    563:     n   = ii[1] - ii[0];
    564:     ii += nsz;
    565:     sz  = n;                    /* No of non zeros in this row */
    566:                                 /* Switch on the size of Node */
    567:     switch (nsz) {               /* Each loop in 'case' is unrolled */
    568:     case 1:
    569:       sum1 = *zt++;

    571:       for (n = 0; n< sz-1; n+=2) {
    572:         i1    = idx[0];         /* The instructions are ordered to */
    573:         i2    = idx[1];         /* make the compiler's job easy */
    574:         idx  += 2;
    575:         tmp0  = x[i1];
    576:         tmp1  = x[i2];
    577:         sum1 += v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    578:       }

    580:       if (n   == sz-1) {          /* Take care of the last nonzero  */
    581:         tmp0  = x[*idx++];
    582:         sum1 += *v1++ * tmp0;
    583:       }
    584:       y[row++]=sum1;
    585:       break;
    586:     case 2:
    587:       sum1 = *zt++;
    588:       sum2 = *zt++;
    589:       v2   = v1 + n;

    591:       for (n = 0; n< sz-1; n+=2) {
    592:         i1    = idx[0];
    593:         i2    = idx[1];
    594:         idx  += 2;
    595:         tmp0  = x[i1];
    596:         tmp1  = x[i2];
    597:         sum1 += v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    598:         sum2 += v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    599:       }
    600:       if (n   == sz-1) {
    601:         tmp0  = x[*idx++];
    602:         sum1 += *v1++ * tmp0;
    603:         sum2 += *v2++ * tmp0;
    604:       }
    605:       y[row++]=sum1;
    606:       y[row++]=sum2;
    607:       v1      =v2;              /* Since the next block to be processed starts there*/
    608:       idx    +=sz;
    609:       break;
    610:     case 3:
    611:       sum1 = *zt++;
    612:       sum2 = *zt++;
    613:       sum3 = *zt++;
    614:       v2   = v1 + n;
    615:       v3   = v2 + n;

    617:       for (n = 0; n< sz-1; n+=2) {
    618:         i1    = idx[0];
    619:         i2    = idx[1];
    620:         idx  += 2;
    621:         tmp0  = x[i1];
    622:         tmp1  = x[i2];
    623:         sum1 += v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    624:         sum2 += v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    625:         sum3 += v3[0] * tmp0 + v3[1] * tmp1; v3 += 2;
    626:       }
    627:       if (n == sz-1) {
    628:         tmp0  = x[*idx++];
    629:         sum1 += *v1++ * tmp0;
    630:         sum2 += *v2++ * tmp0;
    631:         sum3 += *v3++ * tmp0;
    632:       }
    633:       y[row++]=sum1;
    634:       y[row++]=sum2;
    635:       y[row++]=sum3;
    636:       v1      =v3;              /* Since the next block to be processed starts there*/
    637:       idx    +=2*sz;
    638:       break;
    639:     case 4:
    640:       sum1 = *zt++;
    641:       sum2 = *zt++;
    642:       sum3 = *zt++;
    643:       sum4 = *zt++;
    644:       v2   = v1 + n;
    645:       v3   = v2 + n;
    646:       v4   = v3 + n;

    648:       for (n = 0; n< sz-1; n+=2) {
    649:         i1    = idx[0];
    650:         i2    = idx[1];
    651:         idx  += 2;
    652:         tmp0  = x[i1];
    653:         tmp1  = x[i2];
    654:         sum1 += v1[0] * tmp0 + v1[1] *tmp1; v1 += 2;
    655:         sum2 += v2[0] * tmp0 + v2[1] *tmp1; v2 += 2;
    656:         sum3 += v3[0] * tmp0 + v3[1] *tmp1; v3 += 2;
    657:         sum4 += v4[0] * tmp0 + v4[1] *tmp1; v4 += 2;
    658:       }
    659:       if (n == sz-1) {
    660:         tmp0  = x[*idx++];
    661:         sum1 += *v1++ * tmp0;
    662:         sum2 += *v2++ * tmp0;
    663:         sum3 += *v3++ * tmp0;
    664:         sum4 += *v4++ * tmp0;
    665:       }
    666:       y[row++]=sum1;
    667:       y[row++]=sum2;
    668:       y[row++]=sum3;
    669:       y[row++]=sum4;
    670:       v1      =v4;              /* Since the next block to be processed starts there*/
    671:       idx    +=3*sz;
    672:       break;
    673:     case 5:
    674:       sum1 = *zt++;
    675:       sum2 = *zt++;
    676:       sum3 = *zt++;
    677:       sum4 = *zt++;
    678:       sum5 = *zt++;
    679:       v2   = v1 + n;
    680:       v3   = v2 + n;
    681:       v4   = v3 + n;
    682:       v5   = v4 + n;

    684:       for (n = 0; n<sz-1; n+=2) {
    685:         i1    = idx[0];
    686:         i2    = idx[1];
    687:         idx  += 2;
    688:         tmp0  = x[i1];
    689:         tmp1  = x[i2];
    690:         sum1 += v1[0] * tmp0 + v1[1] *tmp1; v1 += 2;
    691:         sum2 += v2[0] * tmp0 + v2[1] *tmp1; v2 += 2;
    692:         sum3 += v3[0] * tmp0 + v3[1] *tmp1; v3 += 2;
    693:         sum4 += v4[0] * tmp0 + v4[1] *tmp1; v4 += 2;
    694:         sum5 += v5[0] * tmp0 + v5[1] *tmp1; v5 += 2;
    695:       }
    696:       if (n   == sz-1) {
    697:         tmp0  = x[*idx++];
    698:         sum1 += *v1++ * tmp0;
    699:         sum2 += *v2++ * tmp0;
    700:         sum3 += *v3++ * tmp0;
    701:         sum4 += *v4++ * tmp0;
    702:         sum5 += *v5++ * tmp0;
    703:       }
    704:       y[row++]=sum1;
    705:       y[row++]=sum2;
    706:       y[row++]=sum3;
    707:       y[row++]=sum4;
    708:       y[row++]=sum5;
    709:       v1      =v5;       /* Since the next block to be processed starts there */
    710:       idx    +=4*sz;
    711:       break;
    712:     default:
    713:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_COR,"Node size not yet supported");
    714:     }
    715:   }
    716:   VecRestoreArrayRead(xx,&x);
    717:   VecRestoreArrayPair(zz,yy,&z,&y);
    718:   PetscLogFlops(2.0*a->nz);
    719:   return 0;
    720: }

    722: /* ----------------------------------------------------------- */
    723: PetscErrorCode MatSolve_SeqAIJ_Inode_inplace(Mat A,Vec bb,Vec xx)
    724: {
    725:   Mat_SeqAIJ        *a    = (Mat_SeqAIJ*)A->data;
    726:   IS                iscol = a->col,isrow = a->row;
    727:   const PetscInt    *r,*c,*rout,*cout;
    728:   PetscInt          i,j,n = A->rmap->n,nz;
    729:   PetscInt          node_max,*ns,row,nsz,aii,i0,i1;
    730:   const PetscInt    *ai = a->i,*a_j = a->j,*vi,*ad,*aj;
    731:   PetscScalar       *x,*tmp,*tmps,tmp0,tmp1;
    732:   PetscScalar       sum1,sum2,sum3,sum4,sum5;
    733:   const MatScalar   *v1,*v2,*v3,*v4,*v5,*a_a = a->a,*aa;
    734:   const PetscScalar *b;

    737:   node_max = a->inode.node_count;
    738:   ns       = a->inode.size;     /* Node Size array */

    740:   VecGetArrayRead(bb,&b);
    741:   VecGetArrayWrite(xx,&x);
    742:   tmp  = a->solve_work;

    744:   ISGetIndices(isrow,&rout); r = rout;
    745:   ISGetIndices(iscol,&cout)); c = cout + (n-1;

    747:   /* forward solve the lower triangular */
    748:   tmps = tmp;
    749:   aa   = a_a;
    750:   aj   = a_j;
    751:   ad   = a->diag;

    753:   for (i = 0,row = 0; i< node_max; ++i) {
    754:     nsz = ns[i];
    755:     aii = ai[row];
    756:     v1  = aa + aii;
    757:     vi  = aj + aii;
    758:     nz  = ad[row]- aii;
    759:     if (i < node_max-1) {
    760:       /* Prefetch the block after the current one, the prefetch itself can't cause a memory error,
    761:       * but our indexing to determine it's size could. */
    762:       PetscPrefetchBlock(aj+ai[row+nsz],ad[row+nsz]-ai[row+nsz],0,PETSC_PREFETCH_HINT_NTA); /* indices */
    763:       /* In my tests, it seems to be better to fetch entire rows instead of just the lower-triangular part */
    764:       PetscPrefetchBlock(aa+ai[row+nsz],ad[row+nsz+ns[i+1]-1]-ai[row+nsz],0,PETSC_PREFETCH_HINT_NTA);
    765:       /* for (j=0; j<ns[i+1]; j++) PetscPrefetchBlock(aa+ai[row+nsz+j],ad[row+nsz+j]-ai[row+nsz+j],0,0); */
    766:     }

    768:     switch (nsz) {               /* Each loop in 'case' is unrolled */
    769:     case 1:
    770:       sum1 = b[*r++];
    771:       for (j=0; j<nz-1; j+=2) {
    772:         i0    = vi[0];
    773:         i1    = vi[1];
    774:         vi   +=2;
    775:         tmp0  = tmps[i0];
    776:         tmp1  = tmps[i1];
    777:         sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    778:       }
    779:       if (j == nz-1) {
    780:         tmp0  = tmps[*vi++];
    781:         sum1 -= *v1++ *tmp0;
    782:       }
    783:       tmp[row++]=sum1;
    784:       break;
    785:     case 2:
    786:       sum1 = b[*r++];
    787:       sum2 = b[*r++];
    788:       v2   = aa + ai[row+1];

    790:       for (j=0; j<nz-1; j+=2) {
    791:         i0    = vi[0];
    792:         i1    = vi[1];
    793:         vi   +=2;
    794:         tmp0  = tmps[i0];
    795:         tmp1  = tmps[i1];
    796:         sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    797:         sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    798:       }
    799:       if (j == nz-1) {
    800:         tmp0  = tmps[*vi++];
    801:         sum1 -= *v1++ *tmp0;
    802:         sum2 -= *v2++ *tmp0;
    803:       }
    804:       sum2     -= *v2++ *sum1;
    805:       tmp[row++]=sum1;
    806:       tmp[row++]=sum2;
    807:       break;
    808:     case 3:
    809:       sum1 = b[*r++];
    810:       sum2 = b[*r++];
    811:       sum3 = b[*r++];
    812:       v2   = aa + ai[row+1];
    813:       v3   = aa + ai[row+2];

    815:       for (j=0; j<nz-1; j+=2) {
    816:         i0    = vi[0];
    817:         i1    = vi[1];
    818:         vi   +=2;
    819:         tmp0  = tmps[i0];
    820:         tmp1  = tmps[i1];
    821:         sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    822:         sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    823:         sum3 -= v3[0] * tmp0 + v3[1] * tmp1; v3 += 2;
    824:       }
    825:       if (j == nz-1) {
    826:         tmp0  = tmps[*vi++];
    827:         sum1 -= *v1++ *tmp0;
    828:         sum2 -= *v2++ *tmp0;
    829:         sum3 -= *v3++ *tmp0;
    830:       }
    831:       sum2 -= *v2++ * sum1;
    832:       sum3 -= *v3++ * sum1;
    833:       sum3 -= *v3++ * sum2;

    835:       tmp[row++]=sum1;
    836:       tmp[row++]=sum2;
    837:       tmp[row++]=sum3;
    838:       break;

    840:     case 4:
    841:       sum1 = b[*r++];
    842:       sum2 = b[*r++];
    843:       sum3 = b[*r++];
    844:       sum4 = b[*r++];
    845:       v2   = aa + ai[row+1];
    846:       v3   = aa + ai[row+2];
    847:       v4   = aa + ai[row+3];

    849:       for (j=0; j<nz-1; j+=2) {
    850:         i0    = vi[0];
    851:         i1    = vi[1];
    852:         vi   +=2;
    853:         tmp0  = tmps[i0];
    854:         tmp1  = tmps[i1];
    855:         sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    856:         sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    857:         sum3 -= v3[0] * tmp0 + v3[1] * tmp1; v3 += 2;
    858:         sum4 -= v4[0] * tmp0 + v4[1] * tmp1; v4 += 2;
    859:       }
    860:       if (j == nz-1) {
    861:         tmp0  = tmps[*vi++];
    862:         sum1 -= *v1++ *tmp0;
    863:         sum2 -= *v2++ *tmp0;
    864:         sum3 -= *v3++ *tmp0;
    865:         sum4 -= *v4++ *tmp0;
    866:       }
    867:       sum2 -= *v2++ * sum1;
    868:       sum3 -= *v3++ * sum1;
    869:       sum4 -= *v4++ * sum1;
    870:       sum3 -= *v3++ * sum2;
    871:       sum4 -= *v4++ * sum2;
    872:       sum4 -= *v4++ * sum3;

    874:       tmp[row++]=sum1;
    875:       tmp[row++]=sum2;
    876:       tmp[row++]=sum3;
    877:       tmp[row++]=sum4;
    878:       break;
    879:     case 5:
    880:       sum1 = b[*r++];
    881:       sum2 = b[*r++];
    882:       sum3 = b[*r++];
    883:       sum4 = b[*r++];
    884:       sum5 = b[*r++];
    885:       v2   = aa + ai[row+1];
    886:       v3   = aa + ai[row+2];
    887:       v4   = aa + ai[row+3];
    888:       v5   = aa + ai[row+4];

    890:       for (j=0; j<nz-1; j+=2) {
    891:         i0    = vi[0];
    892:         i1    = vi[1];
    893:         vi   +=2;
    894:         tmp0  = tmps[i0];
    895:         tmp1  = tmps[i1];
    896:         sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    897:         sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    898:         sum3 -= v3[0] * tmp0 + v3[1] * tmp1; v3 += 2;
    899:         sum4 -= v4[0] * tmp0 + v4[1] * tmp1; v4 += 2;
    900:         sum5 -= v5[0] * tmp0 + v5[1] * tmp1; v5 += 2;
    901:       }
    902:       if (j == nz-1) {
    903:         tmp0  = tmps[*vi++];
    904:         sum1 -= *v1++ *tmp0;
    905:         sum2 -= *v2++ *tmp0;
    906:         sum3 -= *v3++ *tmp0;
    907:         sum4 -= *v4++ *tmp0;
    908:         sum5 -= *v5++ *tmp0;
    909:       }

    911:       sum2 -= *v2++ * sum1;
    912:       sum3 -= *v3++ * sum1;
    913:       sum4 -= *v4++ * sum1;
    914:       sum5 -= *v5++ * sum1;
    915:       sum3 -= *v3++ * sum2;
    916:       sum4 -= *v4++ * sum2;
    917:       sum5 -= *v5++ * sum2;
    918:       sum4 -= *v4++ * sum3;
    919:       sum5 -= *v5++ * sum3;
    920:       sum5 -= *v5++ * sum4;

    922:       tmp[row++]=sum1;
    923:       tmp[row++]=sum2;
    924:       tmp[row++]=sum3;
    925:       tmp[row++]=sum4;
    926:       tmp[row++]=sum5;
    927:       break;
    928:     default:
    929:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_COR,"Node size not yet supported ");
    930:     }
    931:   }
    932:   /* backward solve the upper triangular */
    933:   for (i=node_max -1,row = n-1; i>=0; i--) {
    934:     nsz = ns[i];
    935:     aii = ai[row+1] -1;
    936:     v1  = aa + aii;
    937:     vi  = aj + aii;
    938:     nz  = aii- ad[row];
    939:     switch (nsz) {               /* Each loop in 'case' is unrolled */
    940:     case 1:
    941:       sum1 = tmp[row];

    943:       for (j=nz; j>1; j-=2) {
    944:         vi   -=2;
    945:         i0    = vi[2];
    946:         i1    = vi[1];
    947:         tmp0  = tmps[i0];
    948:         tmp1  = tmps[i1];
    949:         v1   -= 2;
    950:         sum1 -= v1[2] * tmp0 + v1[1] * tmp1;
    951:       }
    952:       if (j==1) {
    953:         tmp0  = tmps[*vi--];
    954:         sum1 -= *v1-- * tmp0;
    955:       }
    956:       x[*c--] = tmp[row] = sum1*a_a[ad[row]]; row--;
    957:       break;
    958:     case 2:
    959:       sum1 = tmp[row];
    960:       sum2 = tmp[row -1];
    961:       v2   = aa + ai[row]-1;
    962:       for (j=nz; j>1; j-=2) {
    963:         vi   -=2;
    964:         i0    = vi[2];
    965:         i1    = vi[1];
    966:         tmp0  = tmps[i0];
    967:         tmp1  = tmps[i1];
    968:         v1   -= 2;
    969:         v2   -= 2;
    970:         sum1 -= v1[2] * tmp0 + v1[1] * tmp1;
    971:         sum2 -= v2[2] * tmp0 + v2[1] * tmp1;
    972:       }
    973:       if (j==1) {
    974:         tmp0  = tmps[*vi--];
    975:         sum1 -= *v1-- * tmp0;
    976:         sum2 -= *v2-- * tmp0;
    977:       }

    979:       tmp0    = x[*c--] = tmp[row] = sum1*a_a[ad[row]]; row--;
    980:       sum2   -= *v2-- * tmp0;
    981:       x[*c--] = tmp[row] = sum2*a_a[ad[row]]; row--;
    982:       break;
    983:     case 3:
    984:       sum1 = tmp[row];
    985:       sum2 = tmp[row -1];
    986:       sum3 = tmp[row -2];
    987:       v2   = aa + ai[row]-1;
    988:       v3   = aa + ai[row -1]-1;
    989:       for (j=nz; j>1; j-=2) {
    990:         vi   -=2;
    991:         i0    = vi[2];
    992:         i1    = vi[1];
    993:         tmp0  = tmps[i0];
    994:         tmp1  = tmps[i1];
    995:         v1   -= 2;
    996:         v2   -= 2;
    997:         v3   -= 2;
    998:         sum1 -= v1[2] * tmp0 + v1[1] * tmp1;
    999:         sum2 -= v2[2] * tmp0 + v2[1] * tmp1;
    1000:         sum3 -= v3[2] * tmp0 + v3[1] * tmp1;
    1001:       }
    1002:       if (j==1) {
    1003:         tmp0  = tmps[*vi--];
    1004:         sum1 -= *v1-- * tmp0;
    1005:         sum2 -= *v2-- * tmp0;
    1006:         sum3 -= *v3-- * tmp0;
    1007:       }
    1008:       tmp0    = x[*c--] = tmp[row] = sum1*a_a[ad[row]]; row--;
    1009:       sum2   -= *v2-- * tmp0;
    1010:       sum3   -= *v3-- * tmp0;
    1011:       tmp0    = x[*c--] = tmp[row] = sum2*a_a[ad[row]]; row--;
    1012:       sum3   -= *v3-- * tmp0;
    1013:       x[*c--] = tmp[row] = sum3*a_a[ad[row]]; row--;

    1015:       break;
    1016:     case 4:
    1017:       sum1 = tmp[row];
    1018:       sum2 = tmp[row -1];
    1019:       sum3 = tmp[row -2];
    1020:       sum4 = tmp[row -3];
    1021:       v2   = aa + ai[row]-1;
    1022:       v3   = aa + ai[row -1]-1;
    1023:       v4   = aa + ai[row -2]-1;

    1025:       for (j=nz; j>1; j-=2) {
    1026:         vi   -=2;
    1027:         i0    = vi[2];
    1028:         i1    = vi[1];
    1029:         tmp0  = tmps[i0];
    1030:         tmp1  = tmps[i1];
    1031:         v1   -= 2;
    1032:         v2   -= 2;
    1033:         v3   -= 2;
    1034:         v4   -= 2;
    1035:         sum1 -= v1[2] * tmp0 + v1[1] * tmp1;
    1036:         sum2 -= v2[2] * tmp0 + v2[1] * tmp1;
    1037:         sum3 -= v3[2] * tmp0 + v3[1] * tmp1;
    1038:         sum4 -= v4[2] * tmp0 + v4[1] * tmp1;
    1039:       }
    1040:       if (j==1) {
    1041:         tmp0  = tmps[*vi--];
    1042:         sum1 -= *v1-- * tmp0;
    1043:         sum2 -= *v2-- * tmp0;
    1044:         sum3 -= *v3-- * tmp0;
    1045:         sum4 -= *v4-- * tmp0;
    1046:       }

    1048:       tmp0    = x[*c--] = tmp[row] = sum1*a_a[ad[row]]; row--;
    1049:       sum2   -= *v2-- * tmp0;
    1050:       sum3   -= *v3-- * tmp0;
    1051:       sum4   -= *v4-- * tmp0;
    1052:       tmp0    = x[*c--] = tmp[row] = sum2*a_a[ad[row]]; row--;
    1053:       sum3   -= *v3-- * tmp0;
    1054:       sum4   -= *v4-- * tmp0;
    1055:       tmp0    = x[*c--] = tmp[row] = sum3*a_a[ad[row]]; row--;
    1056:       sum4   -= *v4-- * tmp0;
    1057:       x[*c--] = tmp[row] = sum4*a_a[ad[row]]; row--;
    1058:       break;
    1059:     case 5:
    1060:       sum1 = tmp[row];
    1061:       sum2 = tmp[row -1];
    1062:       sum3 = tmp[row -2];
    1063:       sum4 = tmp[row -3];
    1064:       sum5 = tmp[row -4];
    1065:       v2   = aa + ai[row]-1;
    1066:       v3   = aa + ai[row -1]-1;
    1067:       v4   = aa + ai[row -2]-1;
    1068:       v5   = aa + ai[row -3]-1;
    1069:       for (j=nz; j>1; j-=2) {
    1070:         vi   -= 2;
    1071:         i0    = vi[2];
    1072:         i1    = vi[1];
    1073:         tmp0  = tmps[i0];
    1074:         tmp1  = tmps[i1];
    1075:         v1   -= 2;
    1076:         v2   -= 2;
    1077:         v3   -= 2;
    1078:         v4   -= 2;
    1079:         v5   -= 2;
    1080:         sum1 -= v1[2] * tmp0 + v1[1] * tmp1;
    1081:         sum2 -= v2[2] * tmp0 + v2[1] * tmp1;
    1082:         sum3 -= v3[2] * tmp0 + v3[1] * tmp1;
    1083:         sum4 -= v4[2] * tmp0 + v4[1] * tmp1;
    1084:         sum5 -= v5[2] * tmp0 + v5[1] * tmp1;
    1085:       }
    1086:       if (j==1) {
    1087:         tmp0  = tmps[*vi--];
    1088:         sum1 -= *v1-- * tmp0;
    1089:         sum2 -= *v2-- * tmp0;
    1090:         sum3 -= *v3-- * tmp0;
    1091:         sum4 -= *v4-- * tmp0;
    1092:         sum5 -= *v5-- * tmp0;
    1093:       }

    1095:       tmp0    = x[*c--] = tmp[row] = sum1*a_a[ad[row]]; row--;
    1096:       sum2   -= *v2-- * tmp0;
    1097:       sum3   -= *v3-- * tmp0;
    1098:       sum4   -= *v4-- * tmp0;
    1099:       sum5   -= *v5-- * tmp0;
    1100:       tmp0    = x[*c--] = tmp[row] = sum2*a_a[ad[row]]; row--;
    1101:       sum3   -= *v3-- * tmp0;
    1102:       sum4   -= *v4-- * tmp0;
    1103:       sum5   -= *v5-- * tmp0;
    1104:       tmp0    = x[*c--] = tmp[row] = sum3*a_a[ad[row]]; row--;
    1105:       sum4   -= *v4-- * tmp0;
    1106:       sum5   -= *v5-- * tmp0;
    1107:       tmp0    = x[*c--] = tmp[row] = sum4*a_a[ad[row]]; row--;
    1108:       sum5   -= *v5-- * tmp0;
    1109:       x[*c--] = tmp[row] = sum5*a_a[ad[row]]; row--;
    1110:       break;
    1111:     default:
    1112:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_COR,"Node size not yet supported ");
    1113:     }
    1114:   }
    1115:   ISRestoreIndices(isrow,&rout);
    1116:   ISRestoreIndices(iscol,&cout);
    1117:   VecRestoreArrayRead(bb,&b);
    1118:   VecRestoreArrayWrite(xx,&x);
    1119:   PetscLogFlops(2.0*a->nz - A->cmap->n);
    1120:   return 0;
    1121: }

    1123: PetscErrorCode MatLUFactorNumeric_SeqAIJ_Inode(Mat B,Mat A,const MatFactorInfo *info)
    1124: {
    1125:   Mat             C     =B;
    1126:   Mat_SeqAIJ      *a    =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)C->data;
    1127:   IS              isrow = b->row,isicol = b->icol;
    1128:   const PetscInt  *r,*ic,*ics;
    1129:   const PetscInt  n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bdiag=b->diag;
    1130:   PetscInt        i,j,k,nz,nzL,row,*pj;
    1131:   const PetscInt  *ajtmp,*bjtmp;
    1132:   MatScalar       *pc,*pc1,*pc2,*pc3,*pc4,mul1,mul2,mul3,mul4,*pv,*rtmp1,*rtmp2,*rtmp3,*rtmp4;
    1133:   const MatScalar *aa=a->a,*v,*v1,*v2,*v3,*v4;
    1134:   FactorShiftCtx  sctx;
    1135:   const PetscInt  *ddiag;
    1136:   PetscReal       rs;
    1137:   MatScalar       d;
    1138:   PetscInt        inod,nodesz,node_max,col;
    1139:   const PetscInt  *ns;
    1140:   PetscInt        *tmp_vec1,*tmp_vec2,*nsmap;

    1142:   /* MatPivotSetUp(): initialize shift context sctx */
    1143:   PetscMemzero(&sctx,sizeof(FactorShiftCtx));

    1145:   if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
    1146:     ddiag          = a->diag;
    1147:     sctx.shift_top = info->zeropivot;
    1148:     for (i=0; i<n; i++) {
    1149:       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
    1150:       d  = (aa)[ddiag[i]];
    1151:       rs = -PetscAbsScalar(d) - PetscRealPart(d);
    1152:       v  = aa+ai[i];
    1153:       nz = ai[i+1] - ai[i];
    1154:       for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]);
    1155:       if (rs>sctx.shift_top) sctx.shift_top = rs;
    1156:     }
    1157:     sctx.shift_top *= 1.1;
    1158:     sctx.nshift_max = 5;
    1159:     sctx.shift_lo   = 0.;
    1160:     sctx.shift_hi   = 1.;
    1161:   }

    1163:   ISGetIndices(isrow,&r);
    1164:   ISGetIndices(isicol,&ic);

    1166:   PetscCalloc4(n,&rtmp1,n,&rtmp2,n,&rtmp3,n,&rtmp4);
    1167:   ics   = ic;

    1169:   node_max = a->inode.node_count;
    1170:   ns       = a->inode.size;

    1173:   /* If max inode size > 4, split it into two inodes.*/
    1174:   /* also map the inode sizes according to the ordering */
    1175:   PetscMalloc1(n+1,&tmp_vec1);
    1176:   for (i=0,j=0; i<node_max; ++i,++j) {
    1177:     if (ns[i] > 4) {
    1178:       tmp_vec1[j] = 4;
    1179:       ++j;
    1180:       tmp_vec1[j] = ns[i] - tmp_vec1[j-1];
    1181:     } else {
    1182:       tmp_vec1[j] = ns[i];
    1183:     }
    1184:   }
    1185:   /* Use the correct node_max */
    1186:   node_max = j;

    1188:   /* Now reorder the inode info based on mat re-ordering info */
    1189:   /* First create a row -> inode_size_array_index map */
    1190:   PetscMalloc1(n+1,&nsmap);
    1191:   PetscMalloc1(node_max+1,&tmp_vec2);
    1192:   for (i=0,row=0; i<node_max; i++) {
    1193:     nodesz = tmp_vec1[i];
    1194:     for (j=0; j<nodesz; j++,row++) {
    1195:       nsmap[row] = i;
    1196:     }
    1197:   }
    1198:   /* Using nsmap, create a reordered ns structure */
    1199:   for (i=0,j=0; i< node_max; i++) {
    1200:     nodesz      = tmp_vec1[nsmap[r[j]]];     /* here the reordered row_no is in r[] */
    1201:     tmp_vec2[i] = nodesz;
    1202:     j          += nodesz;
    1203:   }
    1204:   PetscFree(nsmap);
    1205:   PetscFree(tmp_vec1);

    1207:   /* Now use the correct ns */
    1208:   ns = tmp_vec2;

    1210:   do {
    1211:     sctx.newshift = PETSC_FALSE;
    1212:     /* Now loop over each block-row, and do the factorization */
    1213:     for (inod=0,i=0; inod<node_max; inod++) { /* i: row index; inod: inode index */
    1214:       nodesz = ns[inod];

    1216:       switch (nodesz) {
    1217:       case 1:
    1218:         /*----------*/
    1219:         /* zero rtmp1 */
    1220:         /* L part */
    1221:         nz    = bi[i+1] - bi[i];
    1222:         bjtmp = bj + bi[i];
    1223:         for (j=0; j<nz; j++) rtmp1[bjtmp[j]] = 0.0;

    1225:         /* U part */
    1226:         nz    = bdiag[i]-bdiag[i+1];
    1227:         bjtmp = bj + bdiag[i+1]+1;
    1228:         for (j=0; j<nz; j++) rtmp1[bjtmp[j]] = 0.0;

    1230:         /* load in initial (unfactored row) */
    1231:         nz    = ai[r[i]+1] - ai[r[i]];
    1232:         ajtmp = aj + ai[r[i]];
    1233:         v     = aa + ai[r[i]];
    1234:         for (j=0; j<nz; j++) rtmp1[ics[ajtmp[j]]] = v[j];

    1236:         /* ZeropivotApply() */
    1237:         rtmp1[i] += sctx.shift_amount;  /* shift the diagonal of the matrix */

    1239:         /* elimination */
    1240:         bjtmp = bj + bi[i];
    1241:         row   = *bjtmp++;
    1242:         nzL   = bi[i+1] - bi[i];
    1243:         for (k=0; k < nzL; k++) {
    1244:           pc = rtmp1 + row;
    1245:           if (*pc != 0.0) {
    1246:             pv   = b->a + bdiag[row];
    1247:             mul1 = *pc * (*pv);
    1248:             *pc  = mul1;
    1249:             pj   = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
    1250:             pv   = b->a + bdiag[row+1]+1;
    1251:             nz   = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */
    1252:             for (j=0; j<nz; j++) rtmp1[pj[j]] -= mul1 * pv[j];
    1253:             PetscLogFlops(1+2.0*nz);
    1254:           }
    1255:           row = *bjtmp++;
    1256:         }

    1258:         /* finished row so stick it into b->a */
    1259:         rs = 0.0;
    1260:         /* L part */
    1261:         pv = b->a + bi[i];
    1262:         pj = b->j + bi[i];
    1263:         nz = bi[i+1] - bi[i];
    1264:         for (j=0; j<nz; j++) {
    1265:           pv[j] = rtmp1[pj[j]]; rs += PetscAbsScalar(pv[j]);
    1266:         }

    1268:         /* U part */
    1269:         pv = b->a + bdiag[i+1]+1;
    1270:         pj = b->j + bdiag[i+1]+1;
    1271:         nz = bdiag[i] - bdiag[i+1]-1;
    1272:         for (j=0; j<nz; j++) {
    1273:           pv[j] = rtmp1[pj[j]]; rs += PetscAbsScalar(pv[j]);
    1274:         }

    1276:         /* Check zero pivot */
    1277:         sctx.rs = rs;
    1278:         sctx.pv = rtmp1[i];
    1279:         MatPivotCheck(B,A,info,&sctx,i);
    1280:         if (sctx.newshift) break;

    1282:         /* Mark diagonal and invert diagonal for simpler triangular solves */
    1283:         pv  = b->a + bdiag[i];
    1284:         *pv = 1.0/sctx.pv; /* sctx.pv = rtmp1[i]+shiftamount if shifttype==MAT_SHIFT_INBLOCKS */
    1285:         break;

    1287:       case 2:
    1288:         /*----------*/
    1289:         /* zero rtmp1 and rtmp2 */
    1290:         /* L part */
    1291:         nz    = bi[i+1] - bi[i];
    1292:         bjtmp = bj + bi[i];
    1293:         for  (j=0; j<nz; j++) {
    1294:           col        = bjtmp[j];
    1295:           rtmp1[col] = 0.0; rtmp2[col] = 0.0;
    1296:         }

    1298:         /* U part */
    1299:         nz    = bdiag[i]-bdiag[i+1];
    1300:         bjtmp = bj + bdiag[i+1]+1;
    1301:         for  (j=0; j<nz; j++) {
    1302:           col        = bjtmp[j];
    1303:           rtmp1[col] = 0.0; rtmp2[col] = 0.0;
    1304:         }

    1306:         /* load in initial (unfactored row) */
    1307:         nz    = ai[r[i]+1] - ai[r[i]];
    1308:         ajtmp = aj + ai[r[i]];
    1309:         v1    = aa + ai[r[i]]; v2 = aa + ai[r[i]+1];
    1310:         for (j=0; j<nz; j++) {
    1311:           col        = ics[ajtmp[j]];
    1312:           rtmp1[col] = v1[j]; rtmp2[col] = v2[j];
    1313:         }
    1314:         /* ZeropivotApply(): shift the diagonal of the matrix  */
    1315:         rtmp1[i] += sctx.shift_amount; rtmp2[i+1] += sctx.shift_amount;

    1317:         /* elimination */
    1318:         bjtmp = bj + bi[i];
    1319:         row   = *bjtmp++; /* pivot row */
    1320:         nzL   = bi[i+1] - bi[i];
    1321:         for (k=0; k < nzL; k++) {
    1322:           pc1 = rtmp1 + row;
    1323:           pc2 = rtmp2 + row;
    1324:           if (*pc1 != 0.0 || *pc2 != 0.0) {
    1325:             pv   = b->a + bdiag[row];
    1326:             mul1 = *pc1*(*pv); mul2 = *pc2*(*pv);
    1327:             *pc1 = mul1;       *pc2 = mul2;

    1329:             pj = b->j + bdiag[row+1]+1;     /* beginning of U(row,:) */
    1330:             pv = b->a + bdiag[row+1]+1;
    1331:             nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */
    1332:             for (j=0; j<nz; j++) {
    1333:               col         = pj[j];
    1334:               rtmp1[col] -= mul1 * pv[j];
    1335:               rtmp2[col] -= mul2 * pv[j];
    1336:             }
    1337:             PetscLogFlops(2+4.0*nz);
    1338:           }
    1339:           row = *bjtmp++;
    1340:         }

    1342:         /* finished row i; check zero pivot, then stick row i into b->a */
    1343:         rs = 0.0;
    1344:         /* L part */
    1345:         pc1 = b->a + bi[i];
    1346:         pj  = b->j + bi[i];
    1347:         nz  = bi[i+1] - bi[i];
    1348:         for (j=0; j<nz; j++) {
    1349:           col    = pj[j];
    1350:           pc1[j] = rtmp1[col]; rs += PetscAbsScalar(pc1[j]);
    1351:         }
    1352:         /* U part */
    1353:         pc1 = b->a + bdiag[i+1]+1;
    1354:         pj  = b->j + bdiag[i+1]+1;
    1355:         nz  = bdiag[i] - bdiag[i+1] - 1; /* exclude diagonal */
    1356:         for (j=0; j<nz; j++) {
    1357:           col    = pj[j];
    1358:           pc1[j] = rtmp1[col]; rs += PetscAbsScalar(pc1[j]);
    1359:         }

    1361:         sctx.rs = rs;
    1362:         sctx.pv = rtmp1[i];
    1363:         MatPivotCheck(B,A,info,&sctx,i);
    1364:         if (sctx.newshift) break;
    1365:         pc1  = b->a + bdiag[i]; /* Mark diagonal */
    1366:         *pc1 = 1.0/sctx.pv;

    1368:         /* Now take care of diagonal 2x2 block. */
    1369:         pc2 = rtmp2 + i;
    1370:         if (*pc2 != 0.0) {
    1371:           mul1 = (*pc2)*(*pc1); /* *pc1=diag[i] is inverted! */
    1372:           *pc2 = mul1;          /* insert L entry */
    1373:           pj   = b->j + bdiag[i+1]+1;   /* beginning of U(i,:) */
    1374:           nz   = bdiag[i]-bdiag[i+1]-1; /* num of entries in U(i,:) excluding diag */
    1375:           for (j=0; j<nz; j++) {
    1376:             col = pj[j]; rtmp2[col] -= mul1 * rtmp1[col];
    1377:           }
    1378:           PetscLogFlops(1+2.0*nz);
    1379:         }

    1381:         /* finished row i+1; check zero pivot, then stick row i+1 into b->a */
    1382:         rs = 0.0;
    1383:         /* L part */
    1384:         pc2 = b->a + bi[i+1];
    1385:         pj  = b->j + bi[i+1];
    1386:         nz  = bi[i+2] - bi[i+1];
    1387:         for (j=0; j<nz; j++) {
    1388:           col    = pj[j];
    1389:           pc2[j] = rtmp2[col]; rs += PetscAbsScalar(pc2[j]);
    1390:         }
    1391:         /* U part */
    1392:         pc2 = b->a + bdiag[i+2]+1;
    1393:         pj  = b->j + bdiag[i+2]+1;
    1394:         nz  = bdiag[i+1] - bdiag[i+2] - 1; /* exclude diagonal */
    1395:         for (j=0; j<nz; j++) {
    1396:           col    = pj[j];
    1397:           pc2[j] = rtmp2[col]; rs += PetscAbsScalar(pc2[j]);
    1398:         }

    1400:         sctx.rs = rs;
    1401:         sctx.pv = rtmp2[i+1];
    1402:         MatPivotCheck(B,A,info,&sctx,i+1);
    1403:         if (sctx.newshift) break;
    1404:         pc2  = b->a + bdiag[i+1];
    1405:         *pc2 = 1.0/sctx.pv;
    1406:         break;

    1408:       case 3:
    1409:         /*----------*/
    1410:         /* zero rtmp */
    1411:         /* L part */
    1412:         nz    = bi[i+1] - bi[i];
    1413:         bjtmp = bj + bi[i];
    1414:         for  (j=0; j<nz; j++) {
    1415:           col        = bjtmp[j];
    1416:           rtmp1[col] = 0.0; rtmp2[col] = 0.0; rtmp3[col] = 0.0;
    1417:         }

    1419:         /* U part */
    1420:         nz    = bdiag[i]-bdiag[i+1];
    1421:         bjtmp = bj + bdiag[i+1]+1;
    1422:         for  (j=0; j<nz; j++) {
    1423:           col        = bjtmp[j];
    1424:           rtmp1[col] = 0.0; rtmp2[col] = 0.0; rtmp3[col] = 0.0;
    1425:         }

    1427:         /* load in initial (unfactored row) */
    1428:         nz    = ai[r[i]+1] - ai[r[i]];
    1429:         ajtmp = aj + ai[r[i]];
    1430:         v1    = aa + ai[r[i]]; v2 = aa + ai[r[i]+1]; v3 = aa + ai[r[i]+2];
    1431:         for (j=0; j<nz; j++) {
    1432:           col        = ics[ajtmp[j]];
    1433:           rtmp1[col] = v1[j]; rtmp2[col] = v2[j]; rtmp3[col] = v3[j];
    1434:         }
    1435:         /* ZeropivotApply(): shift the diagonal of the matrix  */
    1436:         rtmp1[i] += sctx.shift_amount; rtmp2[i+1] += sctx.shift_amount; rtmp3[i+2] += sctx.shift_amount;

    1438:         /* elimination */
    1439:         bjtmp = bj + bi[i];
    1440:         row   = *bjtmp++; /* pivot row */
    1441:         nzL   = bi[i+1] - bi[i];
    1442:         for (k=0; k < nzL; k++) {
    1443:           pc1 = rtmp1 + row;
    1444:           pc2 = rtmp2 + row;
    1445:           pc3 = rtmp3 + row;
    1446:           if (*pc1 != 0.0 || *pc2 != 0.0 || *pc3 != 0.0) {
    1447:             pv   = b->a + bdiag[row];
    1448:             mul1 = *pc1*(*pv); mul2 = *pc2*(*pv); mul3 = *pc3*(*pv);
    1449:             *pc1 = mul1; *pc2 = mul2; *pc3 = mul3;

    1451:             pj = b->j + bdiag[row+1]+1;     /* beginning of U(row,:) */
    1452:             pv = b->a + bdiag[row+1]+1;
    1453:             nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */
    1454:             for (j=0; j<nz; j++) {
    1455:               col         = pj[j];
    1456:               rtmp1[col] -= mul1 * pv[j];
    1457:               rtmp2[col] -= mul2 * pv[j];
    1458:               rtmp3[col] -= mul3 * pv[j];
    1459:             }
    1460:             PetscLogFlops(3+6.0*nz);
    1461:           }
    1462:           row = *bjtmp++;
    1463:         }

    1465:         /* finished row i; check zero pivot, then stick row i into b->a */
    1466:         rs = 0.0;
    1467:         /* L part */
    1468:         pc1 = b->a + bi[i];
    1469:         pj  = b->j + bi[i];
    1470:         nz  = bi[i+1] - bi[i];
    1471:         for (j=0; j<nz; j++) {
    1472:           col    = pj[j];
    1473:           pc1[j] = rtmp1[col]; rs += PetscAbsScalar(pc1[j]);
    1474:         }
    1475:         /* U part */
    1476:         pc1 = b->a + bdiag[i+1]+1;
    1477:         pj  = b->j + bdiag[i+1]+1;
    1478:         nz  = bdiag[i] - bdiag[i+1] - 1; /* exclude diagonal */
    1479:         for (j=0; j<nz; j++) {
    1480:           col    = pj[j];
    1481:           pc1[j] = rtmp1[col]; rs += PetscAbsScalar(pc1[j]);
    1482:         }

    1484:         sctx.rs = rs;
    1485:         sctx.pv = rtmp1[i];
    1486:         MatPivotCheck(B,A,info,&sctx,i);
    1487:         if (sctx.newshift) break;
    1488:         pc1  = b->a + bdiag[i]; /* Mark diag[i] */
    1489:         *pc1 = 1.0/sctx.pv;

    1491:         /* Now take care of 1st column of diagonal 3x3 block. */
    1492:         pc2 = rtmp2 + i;
    1493:         pc3 = rtmp3 + i;
    1494:         if (*pc2 != 0.0 || *pc3 != 0.0) {
    1495:           mul2 = (*pc2)*(*pc1); *pc2 = mul2;
    1496:           mul3 = (*pc3)*(*pc1); *pc3 = mul3;
    1497:           pj   = b->j + bdiag[i+1]+1;   /* beginning of U(i,:) */
    1498:           nz   = bdiag[i]-bdiag[i+1]-1; /* num of entries in U(i,:) excluding diag */
    1499:           for (j=0; j<nz; j++) {
    1500:             col         = pj[j];
    1501:             rtmp2[col] -= mul2 * rtmp1[col];
    1502:             rtmp3[col] -= mul3 * rtmp1[col];
    1503:           }
    1504:           PetscLogFlops(2+4.0*nz);
    1505:         }

    1507:         /* finished row i+1; check zero pivot, then stick row i+1 into b->a */
    1508:         rs = 0.0;
    1509:         /* L part */
    1510:         pc2 = b->a + bi[i+1];
    1511:         pj  = b->j + bi[i+1];
    1512:         nz  = bi[i+2] - bi[i+1];
    1513:         for (j=0; j<nz; j++) {
    1514:           col    = pj[j];
    1515:           pc2[j] = rtmp2[col]; rs += PetscAbsScalar(pc2[j]);
    1516:         }
    1517:         /* U part */
    1518:         pc2 = b->a + bdiag[i+2]+1;
    1519:         pj  = b->j + bdiag[i+2]+1;
    1520:         nz  = bdiag[i+1] - bdiag[i+2] - 1; /* exclude diagonal */
    1521:         for (j=0; j<nz; j++) {
    1522:           col    = pj[j];
    1523:           pc2[j] = rtmp2[col]; rs += PetscAbsScalar(pc2[j]);
    1524:         }

    1526:         sctx.rs = rs;
    1527:         sctx.pv = rtmp2[i+1];
    1528:         MatPivotCheck(B,A,info,&sctx,i+1);
    1529:         if (sctx.newshift) break;
    1530:         pc2  = b->a + bdiag[i+1];
    1531:         *pc2 = 1.0/sctx.pv; /* Mark diag[i+1] */

    1533:         /* Now take care of 2nd column of diagonal 3x3 block. */
    1534:         pc3 = rtmp3 + i+1;
    1535:         if (*pc3 != 0.0) {
    1536:           mul3 = (*pc3)*(*pc2); *pc3 = mul3;
    1537:           pj   = b->j + bdiag[i+2]+1;     /* beginning of U(i+1,:) */
    1538:           nz   = bdiag[i+1]-bdiag[i+2]-1; /* num of entries in U(i+1,:) excluding diag */
    1539:           for (j=0; j<nz; j++) {
    1540:             col         = pj[j];
    1541:             rtmp3[col] -= mul3 * rtmp2[col];
    1542:           }
    1543:           PetscLogFlops(1+2.0*nz);
    1544:         }

    1546:         /* finished i+2; check zero pivot, then stick row i+2 into b->a */
    1547:         rs = 0.0;
    1548:         /* L part */
    1549:         pc3 = b->a + bi[i+2];
    1550:         pj  = b->j + bi[i+2];
    1551:         nz  = bi[i+3] - bi[i+2];
    1552:         for (j=0; j<nz; j++) {
    1553:           col    = pj[j];
    1554:           pc3[j] = rtmp3[col]; rs += PetscAbsScalar(pc3[j]);
    1555:         }
    1556:         /* U part */
    1557:         pc3 = b->a + bdiag[i+3]+1;
    1558:         pj  = b->j + bdiag[i+3]+1;
    1559:         nz  = bdiag[i+2] - bdiag[i+3] - 1; /* exclude diagonal */
    1560:         for (j=0; j<nz; j++) {
    1561:           col    = pj[j];
    1562:           pc3[j] = rtmp3[col]; rs += PetscAbsScalar(pc3[j]);
    1563:         }

    1565:         sctx.rs = rs;
    1566:         sctx.pv = rtmp3[i+2];
    1567:         MatPivotCheck(B,A,info,&sctx,i+2);
    1568:         if (sctx.newshift) break;
    1569:         pc3  = b->a + bdiag[i+2];
    1570:         *pc3 = 1.0/sctx.pv; /* Mark diag[i+2] */
    1571:         break;
    1572:       case 4:
    1573:         /*----------*/
    1574:         /* zero rtmp */
    1575:         /* L part */
    1576:         nz    = bi[i+1] - bi[i];
    1577:         bjtmp = bj + bi[i];
    1578:         for  (j=0; j<nz; j++) {
    1579:           col        = bjtmp[j];
    1580:           rtmp1[col] = 0.0; rtmp2[col] = 0.0; rtmp3[col] = 0.0;rtmp4[col] = 0.0;
    1581:         }

    1583:         /* U part */
    1584:         nz    = bdiag[i]-bdiag[i+1];
    1585:         bjtmp = bj + bdiag[i+1]+1;
    1586:         for  (j=0; j<nz; j++) {
    1587:           col        = bjtmp[j];
    1588:           rtmp1[col] = 0.0; rtmp2[col] = 0.0; rtmp3[col] = 0.0; rtmp4[col] = 0.0;
    1589:         }

    1591:         /* load in initial (unfactored row) */
    1592:         nz    = ai[r[i]+1] - ai[r[i]];
    1593:         ajtmp = aj + ai[r[i]];
    1594:         v1    = aa + ai[r[i]]; v2 = aa + ai[r[i]+1]; v3 = aa + ai[r[i]+2]; v4 = aa + ai[r[i]+3];
    1595:         for (j=0; j<nz; j++) {
    1596:           col        = ics[ajtmp[j]];
    1597:           rtmp1[col] = v1[j]; rtmp2[col] = v2[j]; rtmp3[col] = v3[j]; rtmp4[col] = v4[j];
    1598:         }
    1599:         /* ZeropivotApply(): shift the diagonal of the matrix  */
    1600:         rtmp1[i] += sctx.shift_amount; rtmp2[i+1] += sctx.shift_amount; rtmp3[i+2] += sctx.shift_amount; rtmp4[i+3] += sctx.shift_amount;

    1602:         /* elimination */
    1603:         bjtmp = bj + bi[i];
    1604:         row   = *bjtmp++; /* pivot row */
    1605:         nzL   = bi[i+1] - bi[i];
    1606:         for (k=0; k < nzL; k++) {
    1607:           pc1 = rtmp1 + row;
    1608:           pc2 = rtmp2 + row;
    1609:           pc3 = rtmp3 + row;
    1610:           pc4 = rtmp4 + row;
    1611:           if (*pc1 != 0.0 || *pc2 != 0.0 || *pc3 != 0.0 || *pc4 != 0.0) {
    1612:             pv   = b->a + bdiag[row];
    1613:             mul1 = *pc1*(*pv); mul2 = *pc2*(*pv); mul3 = *pc3*(*pv); mul4 = *pc4*(*pv);
    1614:             *pc1 = mul1; *pc2 = mul2; *pc3 = mul3; *pc4 = mul4;

    1616:             pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
    1617:             pv = b->a + bdiag[row+1]+1;
    1618:             nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */
    1619:             for (j=0; j<nz; j++) {
    1620:               col         = pj[j];
    1621:               rtmp1[col] -= mul1 * pv[j];
    1622:               rtmp2[col] -= mul2 * pv[j];
    1623:               rtmp3[col] -= mul3 * pv[j];
    1624:               rtmp4[col] -= mul4 * pv[j];
    1625:             }
    1626:             PetscLogFlops(4+8.0*nz);
    1627:           }
    1628:           row = *bjtmp++;
    1629:         }

    1631:         /* finished row i; check zero pivot, then stick row i into b->a */
    1632:         rs = 0.0;
    1633:         /* L part */
    1634:         pc1 = b->a + bi[i];
    1635:         pj  = b->j + bi[i];
    1636:         nz  = bi[i+1] - bi[i];
    1637:         for (j=0; j<nz; j++) {
    1638:           col    = pj[j];
    1639:           pc1[j] = rtmp1[col]; rs += PetscAbsScalar(pc1[j]);
    1640:         }
    1641:         /* U part */
    1642:         pc1 = b->a + bdiag[i+1]+1;
    1643:         pj  = b->j + bdiag[i+1]+1;
    1644:         nz  = bdiag[i] - bdiag[i+1] - 1; /* exclude diagonal */
    1645:         for (j=0; j<nz; j++) {
    1646:           col    = pj[j];
    1647:           pc1[j] = rtmp1[col]; rs += PetscAbsScalar(pc1[j]);
    1648:         }

    1650:         sctx.rs = rs;
    1651:         sctx.pv = rtmp1[i];
    1652:         MatPivotCheck(B,A,info,&sctx,i);
    1653:         if (sctx.newshift) break;
    1654:         pc1  = b->a + bdiag[i]; /* Mark diag[i] */
    1655:         *pc1 = 1.0/sctx.pv;

    1657:         /* Now take care of 1st column of diagonal 4x4 block. */
    1658:         pc2 = rtmp2 + i;
    1659:         pc3 = rtmp3 + i;
    1660:         pc4 = rtmp4 + i;
    1661:         if (*pc2 != 0.0 || *pc3 != 0.0 || *pc4 != 0.0) {
    1662:           mul2 = (*pc2)*(*pc1); *pc2 = mul2;
    1663:           mul3 = (*pc3)*(*pc1); *pc3 = mul3;
    1664:           mul4 = (*pc4)*(*pc1); *pc4 = mul4;
    1665:           pj   = b->j + bdiag[i+1]+1;   /* beginning of U(i,:) */
    1666:           nz   = bdiag[i]-bdiag[i+1]-1; /* num of entries in U(i,:) excluding diag */
    1667:           for (j=0; j<nz; j++) {
    1668:             col         = pj[j];
    1669:             rtmp2[col] -= mul2 * rtmp1[col];
    1670:             rtmp3[col] -= mul3 * rtmp1[col];
    1671:             rtmp4[col] -= mul4 * rtmp1[col];
    1672:           }
    1673:           PetscLogFlops(3+6.0*nz);
    1674:         }

    1676:         /* finished row i+1; check zero pivot, then stick row i+1 into b->a */
    1677:         rs = 0.0;
    1678:         /* L part */
    1679:         pc2 = b->a + bi[i+1];
    1680:         pj  = b->j + bi[i+1];
    1681:         nz  = bi[i+2] - bi[i+1];
    1682:         for (j=0; j<nz; j++) {
    1683:           col    = pj[j];
    1684:           pc2[j] = rtmp2[col]; rs += PetscAbsScalar(pc2[j]);
    1685:         }
    1686:         /* U part */
    1687:         pc2 = b->a + bdiag[i+2]+1;
    1688:         pj  = b->j + bdiag[i+2]+1;
    1689:         nz  = bdiag[i+1] - bdiag[i+2] - 1; /* exclude diagonal */
    1690:         for (j=0; j<nz; j++) {
    1691:           col    = pj[j];
    1692:           pc2[j] = rtmp2[col]; rs += PetscAbsScalar(pc2[j]);
    1693:         }

    1695:         sctx.rs = rs;
    1696:         sctx.pv = rtmp2[i+1];
    1697:         MatPivotCheck(B,A,info,&sctx,i+1);
    1698:         if (sctx.newshift) break;
    1699:         pc2  = b->a + bdiag[i+1];
    1700:         *pc2 = 1.0/sctx.pv; /* Mark diag[i+1] */

    1702:         /* Now take care of 2nd column of diagonal 4x4 block. */
    1703:         pc3 = rtmp3 + i+1;
    1704:         pc4 = rtmp4 + i+1;
    1705:         if (*pc3 != 0.0 || *pc4 != 0.0) {
    1706:           mul3 = (*pc3)*(*pc2); *pc3 = mul3;
    1707:           mul4 = (*pc4)*(*pc2); *pc4 = mul4;
    1708:           pj   = b->j + bdiag[i+2]+1;     /* beginning of U(i+1,:) */
    1709:           nz   = bdiag[i+1]-bdiag[i+2]-1; /* num of entries in U(i+1,:) excluding diag */
    1710:           for (j=0; j<nz; j++) {
    1711:             col         = pj[j];
    1712:             rtmp3[col] -= mul3 * rtmp2[col];
    1713:             rtmp4[col] -= mul4 * rtmp2[col];
    1714:           }
    1715:           PetscLogFlops(4.0*nz);
    1716:         }

    1718:         /* finished i+2; check zero pivot, then stick row i+2 into b->a */
    1719:         rs = 0.0;
    1720:         /* L part */
    1721:         pc3 = b->a + bi[i+2];
    1722:         pj  = b->j + bi[i+2];
    1723:         nz  = bi[i+3] - bi[i+2];
    1724:         for (j=0; j<nz; j++) {
    1725:           col    = pj[j];
    1726:           pc3[j] = rtmp3[col]; rs += PetscAbsScalar(pc3[j]);
    1727:         }
    1728:         /* U part */
    1729:         pc3 = b->a + bdiag[i+3]+1;
    1730:         pj  = b->j + bdiag[i+3]+1;
    1731:         nz  = bdiag[i+2] - bdiag[i+3] - 1; /* exclude diagonal */
    1732:         for (j=0; j<nz; j++) {
    1733:           col    = pj[j];
    1734:           pc3[j] = rtmp3[col]; rs += PetscAbsScalar(pc3[j]);
    1735:         }

    1737:         sctx.rs = rs;
    1738:         sctx.pv = rtmp3[i+2];
    1739:         MatPivotCheck(B,A,info,&sctx,i+2);
    1740:         if (sctx.newshift) break;
    1741:         pc3  = b->a + bdiag[i+2];
    1742:         *pc3 = 1.0/sctx.pv; /* Mark diag[i+2] */

    1744:         /* Now take care of 3rd column of diagonal 4x4 block. */
    1745:         pc4 = rtmp4 + i+2;
    1746:         if (*pc4 != 0.0) {
    1747:           mul4 = (*pc4)*(*pc3); *pc4 = mul4;
    1748:           pj   = b->j + bdiag[i+3]+1;     /* beginning of U(i+2,:) */
    1749:           nz   = bdiag[i+2]-bdiag[i+3]-1; /* num of entries in U(i+2,:) excluding diag */
    1750:           for (j=0; j<nz; j++) {
    1751:             col         = pj[j];
    1752:             rtmp4[col] -= mul4 * rtmp3[col];
    1753:           }
    1754:           PetscLogFlops(1+2.0*nz);
    1755:         }

    1757:         /* finished i+3; check zero pivot, then stick row i+3 into b->a */
    1758:         rs = 0.0;
    1759:         /* L part */
    1760:         pc4 = b->a + bi[i+3];
    1761:         pj  = b->j + bi[i+3];
    1762:         nz  = bi[i+4] - bi[i+3];
    1763:         for (j=0; j<nz; j++) {
    1764:           col    = pj[j];
    1765:           pc4[j] = rtmp4[col]; rs += PetscAbsScalar(pc4[j]);
    1766:         }
    1767:         /* U part */
    1768:         pc4 = b->a + bdiag[i+4]+1;
    1769:         pj  = b->j + bdiag[i+4]+1;
    1770:         nz  = bdiag[i+3] - bdiag[i+4] - 1; /* exclude diagonal */
    1771:         for (j=0; j<nz; j++) {
    1772:           col    = pj[j];
    1773:           pc4[j] = rtmp4[col]; rs += PetscAbsScalar(pc4[j]);
    1774:         }

    1776:         sctx.rs = rs;
    1777:         sctx.pv = rtmp4[i+3];
    1778:         MatPivotCheck(B,A,info,&sctx,i+3);
    1779:         if (sctx.newshift) break;
    1780:         pc4  = b->a + bdiag[i+3];
    1781:         *pc4 = 1.0/sctx.pv; /* Mark diag[i+3] */
    1782:         break;

    1784:       default:
    1785:         SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Node size not yet supported ");
    1786:       }
    1787:       if (sctx.newshift) break; /* break for (inod=0,i=0; inod<node_max; inod++) */
    1788:       i += nodesz;                 /* Update the row */
    1789:     }

    1791:     /* MatPivotRefine() */
    1792:     if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
    1793:       /*
    1794:        * if no shift in this attempt & shifting & started shifting & can refine,
    1795:        * then try lower shift
    1796:        */
    1797:       sctx.shift_hi       = sctx.shift_fraction;
    1798:       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
    1799:       sctx.shift_amount   = sctx.shift_fraction * sctx.shift_top;
    1800:       sctx.newshift       = PETSC_TRUE;
    1801:       sctx.nshift++;
    1802:     }
    1803:   } while (sctx.newshift);

    1805:   PetscFree4(rtmp1,rtmp2,rtmp3,rtmp4);
    1806:   PetscFree(tmp_vec2);
    1807:   ISRestoreIndices(isicol,&ic);
    1808:   ISRestoreIndices(isrow,&r);

    1810:   if (b->inode.size) {
    1811:     C->ops->solve           = MatSolve_SeqAIJ_Inode;
    1812:   } else {
    1813:     C->ops->solve           = MatSolve_SeqAIJ;
    1814:   }
    1815:   C->ops->solveadd          = MatSolveAdd_SeqAIJ;
    1816:   C->ops->solvetranspose    = MatSolveTranspose_SeqAIJ;
    1817:   C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ;
    1818:   C->ops->matsolve          = MatMatSolve_SeqAIJ;
    1819:   C->assembled              = PETSC_TRUE;
    1820:   C->preallocated           = PETSC_TRUE;

    1822:   PetscLogFlops(C->cmap->n);

    1824:   /* MatShiftView(A,info,&sctx) */
    1825:   if (sctx.nshift) {
    1826:     if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) {
    1827:       PetscInfo(A,"number of shift_pd tries %" PetscInt_FMT ", 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);
    1828:     } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
    1829:       PetscInfo(A,"number of shift_nz tries %" PetscInt_FMT ", shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
    1830:     } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS) {
    1831:       PetscInfo(A,"number of shift_inblocks applied %" PetscInt_FMT ", each shift_amount %g\n",sctx.nshift,(double)info->shiftamount);
    1832:     }
    1833:   }
    1834:   return 0;
    1835: }

    1837: PetscErrorCode MatLUFactorNumeric_SeqAIJ_Inode_inplace(Mat B,Mat A,const MatFactorInfo *info)
    1838: {
    1839:   Mat             C     = B;
    1840:   Mat_SeqAIJ      *a    = (Mat_SeqAIJ*)A->data,*b = (Mat_SeqAIJ*)C->data;
    1841:   IS              iscol = b->col,isrow = b->row,isicol = b->icol;
    1842:   const PetscInt  *r,*ic,*c,*ics;
    1843:   PetscInt        n   = A->rmap->n,*bi = b->i;
    1844:   PetscInt        *bj = b->j,*nbj=b->j +1,*ajtmp,*bjtmp,nz,nz_tmp,row,prow;
    1845:   PetscInt        i,j,idx,*bd = b->diag,node_max,nodesz;
    1846:   PetscInt        *ai = a->i,*aj = a->j;
    1847:   PetscInt        *ns,*tmp_vec1,*tmp_vec2,*nsmap,*pj;
    1848:   PetscScalar     mul1,mul2,mul3,tmp;
    1849:   MatScalar       *pc1,*pc2,*pc3,*ba = b->a,*pv,*rtmp11,*rtmp22,*rtmp33;
    1850:   const MatScalar *v1,*v2,*v3,*aa = a->a,*rtmp1;
    1851:   PetscReal       rs=0.0;
    1852:   FactorShiftCtx  sctx;

    1854:   sctx.shift_top      = 0;
    1855:   sctx.nshift_max     = 0;
    1856:   sctx.shift_lo       = 0;
    1857:   sctx.shift_hi       = 0;
    1858:   sctx.shift_fraction = 0;

    1860:   /* if both shift schemes are chosen by user, only use info->shiftpd */
    1861:   if (info->shifttype==(PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
    1862:     sctx.shift_top = 0;
    1863:     for (i=0; i<n; i++) {
    1864:       /* calculate rs = sum(|aij|)-RealPart(aii), amt of shift needed for this row */
    1865:       rs    = 0.0;
    1866:       ajtmp = aj + ai[i];
    1867:       rtmp1 = aa + ai[i];
    1868:       nz    = ai[i+1] - ai[i];
    1869:       for (j=0; j<nz; j++) {
    1870:         if (*ajtmp != i) {
    1871:           rs += PetscAbsScalar(*rtmp1++);
    1872:         } else {
    1873:           rs -= PetscRealPart(*rtmp1++);
    1874:         }
    1875:         ajtmp++;
    1876:       }
    1877:       if (rs>sctx.shift_top) sctx.shift_top = rs;
    1878:     }
    1879:     if (sctx.shift_top == 0.0) sctx.shift_top += 1.e-12;
    1880:     sctx.shift_top *= 1.1;
    1881:     sctx.nshift_max = 5;
    1882:     sctx.shift_lo   = 0.;
    1883:     sctx.shift_hi   = 1.;
    1884:   }
    1885:   sctx.shift_amount = 0;
    1886:   sctx.nshift       = 0;

    1888:   ISGetIndices(isrow,&r);
    1889:   ISGetIndices(iscol,&c);
    1890:   ISGetIndices(isicol,&ic);
    1891:   PetscCalloc3(n,&rtmp11,n,&rtmp22,n,&rtmp33);
    1892:   ics    = ic;

    1894:   node_max = a->inode.node_count;
    1895:   ns       = a->inode.size;

    1898:   /* If max inode size > 3, split it into two inodes.*/
    1899:   /* also map the inode sizes according to the ordering */
    1900:   PetscMalloc1(n+1,&tmp_vec1);
    1901:   for (i=0,j=0; i<node_max; ++i,++j) {
    1902:     if (ns[i]>3) {
    1903:       tmp_vec1[j] = ns[i]/2; /* Assuming ns[i] < =5  */
    1904:       ++j;
    1905:       tmp_vec1[j] = ns[i] - tmp_vec1[j-1];
    1906:     } else {
    1907:       tmp_vec1[j] = ns[i];
    1908:     }
    1909:   }
    1910:   /* Use the correct node_max */
    1911:   node_max = j;

    1913:   /* Now reorder the inode info based on mat re-ordering info */
    1914:   /* First create a row -> inode_size_array_index map */
    1915:   PetscMalloc2(n+1,&nsmap,node_max+1,&tmp_vec2);
    1916:   for (i=0,row=0; i<node_max; i++) {
    1917:     nodesz = tmp_vec1[i];
    1918:     for (j=0; j<nodesz; j++,row++) {
    1919:       nsmap[row] = i;
    1920:     }
    1921:   }
    1922:   /* Using nsmap, create a reordered ns structure */
    1923:   for (i=0,j=0; i< node_max; i++) {
    1924:     nodesz      = tmp_vec1[nsmap[r[j]]];     /* here the reordered row_no is in r[] */
    1925:     tmp_vec2[i] = nodesz;
    1926:     j          += nodesz;
    1927:   }
    1928:   PetscFree2(nsmap,tmp_vec1);
    1929:   /* Now use the correct ns */
    1930:   ns = tmp_vec2;

    1932:   do {
    1933:     sctx.newshift = PETSC_FALSE;
    1934:     /* Now loop over each block-row, and do the factorization */
    1935:     for (i=0,row=0; i<node_max; i++) {
    1936:       nodesz = ns[i];
    1937:       nz     = bi[row+1] - bi[row];
    1938:       bjtmp  = bj + bi[row];

    1940:       switch (nodesz) {
    1941:       case 1:
    1942:         for  (j=0; j<nz; j++) {
    1943:           idx         = bjtmp[j];
    1944:           rtmp11[idx] = 0.0;
    1945:         }

    1947:         /* load in initial (unfactored row) */
    1948:         idx    = r[row];
    1949:         nz_tmp = ai[idx+1] - ai[idx];
    1950:         ajtmp  = aj + ai[idx];
    1951:         v1     = aa + ai[idx];

    1953:         for (j=0; j<nz_tmp; j++) {
    1954:           idx         = ics[ajtmp[j]];
    1955:           rtmp11[idx] = v1[j];
    1956:         }
    1957:         rtmp11[ics[r[row]]] += sctx.shift_amount;

    1959:         prow = *bjtmp++;
    1960:         while (prow < row) {
    1961:           pc1 = rtmp11 + prow;
    1962:           if (*pc1 != 0.0) {
    1963:             pv     = ba + bd[prow];
    1964:             pj     = nbj + bd[prow];
    1965:             mul1   = *pc1 * *pv++;
    1966:             *pc1   = mul1;
    1967:             nz_tmp = bi[prow+1] - bd[prow] - 1;
    1968:             PetscLogFlops(1+2.0*nz_tmp);
    1969:             for (j=0; j<nz_tmp; j++) {
    1970:               tmp          = pv[j];
    1971:               idx          = pj[j];
    1972:               rtmp11[idx] -= mul1 * tmp;
    1973:             }
    1974:           }
    1975:           prow = *bjtmp++;
    1976:         }
    1977:         pj  = bj + bi[row];
    1978:         pc1 = ba + bi[row];

    1980:         sctx.pv     = rtmp11[row];
    1981:         rtmp11[row] = 1.0/rtmp11[row]; /* invert diag */
    1982:         rs          = 0.0;
    1983:         for (j=0; j<nz; j++) {
    1984:           idx    = pj[j];
    1985:           pc1[j] = rtmp11[idx]; /* rtmp11 -> ba */
    1986:           if (idx != row) rs += PetscAbsScalar(pc1[j]);
    1987:         }
    1988:         sctx.rs = rs;
    1989:         MatPivotCheck(B,A,info,&sctx,row);
    1990:         if (sctx.newshift) goto endofwhile;
    1991:         break;

    1993:       case 2:
    1994:         for (j=0; j<nz; j++) {
    1995:           idx         = bjtmp[j];
    1996:           rtmp11[idx] = 0.0;
    1997:           rtmp22[idx] = 0.0;
    1998:         }

    2000:         /* load in initial (unfactored row) */
    2001:         idx    = r[row];
    2002:         nz_tmp = ai[idx+1] - ai[idx];
    2003:         ajtmp  = aj + ai[idx];
    2004:         v1     = aa + ai[idx];
    2005:         v2     = aa + ai[idx+1];
    2006:         for (j=0; j<nz_tmp; j++) {
    2007:           idx         = ics[ajtmp[j]];
    2008:           rtmp11[idx] = v1[j];
    2009:           rtmp22[idx] = v2[j];
    2010:         }
    2011:         rtmp11[ics[r[row]]]   += sctx.shift_amount;
    2012:         rtmp22[ics[r[row+1]]] += sctx.shift_amount;

    2014:         prow = *bjtmp++;
    2015:         while (prow < row) {
    2016:           pc1 = rtmp11 + prow;
    2017:           pc2 = rtmp22 + prow;
    2018:           if (*pc1 != 0.0 || *pc2 != 0.0) {
    2019:             pv   = ba + bd[prow];
    2020:             pj   = nbj + bd[prow];
    2021:             mul1 = *pc1 * *pv;
    2022:             mul2 = *pc2 * *pv;
    2023:             ++pv;
    2024:             *pc1 = mul1;
    2025:             *pc2 = mul2;

    2027:             nz_tmp = bi[prow+1] - bd[prow] - 1;
    2028:             for (j=0; j<nz_tmp; j++) {
    2029:               tmp          = pv[j];
    2030:               idx          = pj[j];
    2031:               rtmp11[idx] -= mul1 * tmp;
    2032:               rtmp22[idx] -= mul2 * tmp;
    2033:             }
    2034:             PetscLogFlops(2+4.0*nz_tmp);
    2035:           }
    2036:           prow = *bjtmp++;
    2037:         }

    2039:         /* Now take care of diagonal 2x2 block. Note: prow = row here */
    2040:         pc1 = rtmp11 + prow;
    2041:         pc2 = rtmp22 + prow;

    2043:         sctx.pv = *pc1;
    2044:         pj      = bj + bi[prow];
    2045:         rs      = 0.0;
    2046:         for (j=0; j<nz; j++) {
    2047:           idx = pj[j];
    2048:           if (idx != prow) rs += PetscAbsScalar(rtmp11[idx]);
    2049:         }
    2050:         sctx.rs = rs;
    2051:         MatPivotCheck(B,A,info,&sctx,row);
    2052:         if (sctx.newshift) goto endofwhile;

    2054:         if (*pc2 != 0.0) {
    2055:           pj     = nbj + bd[prow];
    2056:           mul2   = (*pc2)/(*pc1); /* since diag is not yet inverted.*/
    2057:           *pc2   = mul2;
    2058:           nz_tmp = bi[prow+1] - bd[prow] - 1;
    2059:           for (j=0; j<nz_tmp; j++) {
    2060:             idx          = pj[j];
    2061:             tmp          = rtmp11[idx];
    2062:             rtmp22[idx] -= mul2 * tmp;
    2063:           }
    2064:           PetscLogFlops(1+2.0*nz_tmp);
    2065:         }

    2067:         pj  = bj + bi[row];
    2068:         pc1 = ba + bi[row];
    2069:         pc2 = ba + bi[row+1];

    2071:         sctx.pv       = rtmp22[row+1];
    2072:         rs            = 0.0;
    2073:         rtmp11[row]   = 1.0/rtmp11[row];
    2074:         rtmp22[row+1] = 1.0/rtmp22[row+1];
    2075:         /* copy row entries from dense representation to sparse */
    2076:         for (j=0; j<nz; j++) {
    2077:           idx    = pj[j];
    2078:           pc1[j] = rtmp11[idx];
    2079:           pc2[j] = rtmp22[idx];
    2080:           if (idx != row+1) rs += PetscAbsScalar(pc2[j]);
    2081:         }
    2082:         sctx.rs = rs;
    2083:         MatPivotCheck(B,A,info,&sctx,row+1);
    2084:         if (sctx.newshift) goto endofwhile;
    2085:         break;

    2087:       case 3:
    2088:         for  (j=0; j<nz; j++) {
    2089:           idx         = bjtmp[j];
    2090:           rtmp11[idx] = 0.0;
    2091:           rtmp22[idx] = 0.0;
    2092:           rtmp33[idx] = 0.0;
    2093:         }
    2094:         /* copy the nonzeros for the 3 rows from sparse representation to dense in rtmp*[] */
    2095:         idx    = r[row];
    2096:         nz_tmp = ai[idx+1] - ai[idx];
    2097:         ajtmp  = aj + ai[idx];
    2098:         v1     = aa + ai[idx];
    2099:         v2     = aa + ai[idx+1];
    2100:         v3     = aa + ai[idx+2];
    2101:         for (j=0; j<nz_tmp; j++) {
    2102:           idx         = ics[ajtmp[j]];
    2103:           rtmp11[idx] = v1[j];
    2104:           rtmp22[idx] = v2[j];
    2105:           rtmp33[idx] = v3[j];
    2106:         }
    2107:         rtmp11[ics[r[row]]]   += sctx.shift_amount;
    2108:         rtmp22[ics[r[row+1]]] += sctx.shift_amount;
    2109:         rtmp33[ics[r[row+2]]] += sctx.shift_amount;

    2111:         /* loop over all pivot row blocks above this row block */
    2112:         prow = *bjtmp++;
    2113:         while (prow < row) {
    2114:           pc1 = rtmp11 + prow;
    2115:           pc2 = rtmp22 + prow;
    2116:           pc3 = rtmp33 + prow;
    2117:           if (*pc1 != 0.0 || *pc2 != 0.0 || *pc3 !=0.0) {
    2118:             pv   = ba  + bd[prow];
    2119:             pj   = nbj + bd[prow];
    2120:             mul1 = *pc1 * *pv;
    2121:             mul2 = *pc2 * *pv;
    2122:             mul3 = *pc3 * *pv;
    2123:             ++pv;
    2124:             *pc1 = mul1;
    2125:             *pc2 = mul2;
    2126:             *pc3 = mul3;

    2128:             nz_tmp = bi[prow+1] - bd[prow] - 1;
    2129:             /* update this row based on pivot row */
    2130:             for (j=0; j<nz_tmp; j++) {
    2131:               tmp          = pv[j];
    2132:               idx          = pj[j];
    2133:               rtmp11[idx] -= mul1 * tmp;
    2134:               rtmp22[idx] -= mul2 * tmp;
    2135:               rtmp33[idx] -= mul3 * tmp;
    2136:             }
    2137:             PetscLogFlops(3+6.0*nz_tmp);
    2138:           }
    2139:           prow = *bjtmp++;
    2140:         }

    2142:         /* Now take care of diagonal 3x3 block in this set of rows */
    2143:         /* note: prow = row here */
    2144:         pc1 = rtmp11 + prow;
    2145:         pc2 = rtmp22 + prow;
    2146:         pc3 = rtmp33 + prow;

    2148:         sctx.pv = *pc1;
    2149:         pj      = bj + bi[prow];
    2150:         rs      = 0.0;
    2151:         for (j=0; j<nz; j++) {
    2152:           idx = pj[j];
    2153:           if (idx != row) rs += PetscAbsScalar(rtmp11[idx]);
    2154:         }
    2155:         sctx.rs = rs;
    2156:         MatPivotCheck(B,A,info,&sctx,row);
    2157:         if (sctx.newshift) goto endofwhile;

    2159:         if (*pc2 != 0.0 || *pc3 != 0.0) {
    2160:           mul2   = (*pc2)/(*pc1);
    2161:           mul3   = (*pc3)/(*pc1);
    2162:           *pc2   = mul2;
    2163:           *pc3   = mul3;
    2164:           nz_tmp = bi[prow+1] - bd[prow] - 1;
    2165:           pj     = nbj + bd[prow];
    2166:           for (j=0; j<nz_tmp; j++) {
    2167:             idx          = pj[j];
    2168:             tmp          = rtmp11[idx];
    2169:             rtmp22[idx] -= mul2 * tmp;
    2170:             rtmp33[idx] -= mul3 * tmp;
    2171:           }
    2172:           PetscLogFlops(2+4.0*nz_tmp);
    2173:         }
    2174:         ++prow;

    2176:         pc2     = rtmp22 + prow;
    2177:         pc3     = rtmp33 + prow;
    2178:         sctx.pv = *pc2;
    2179:         pj      = bj + bi[prow];
    2180:         rs      = 0.0;
    2181:         for (j=0; j<nz; j++) {
    2182:           idx = pj[j];
    2183:           if (idx != prow) rs += PetscAbsScalar(rtmp22[idx]);
    2184:         }
    2185:         sctx.rs = rs;
    2186:         MatPivotCheck(B,A,info,&sctx,row+1);
    2187:         if (sctx.newshift) goto endofwhile;

    2189:         if (*pc3 != 0.0) {
    2190:           mul3   = (*pc3)/(*pc2);
    2191:           *pc3   = mul3;
    2192:           pj     = nbj + bd[prow];
    2193:           nz_tmp = bi[prow+1] - bd[prow] - 1;
    2194:           for (j=0; j<nz_tmp; j++) {
    2195:             idx          = pj[j];
    2196:             tmp          = rtmp22[idx];
    2197:             rtmp33[idx] -= mul3 * tmp;
    2198:           }
    2199:           PetscLogFlops(1+2.0*nz_tmp);
    2200:         }

    2202:         pj  = bj + bi[row];
    2203:         pc1 = ba + bi[row];
    2204:         pc2 = ba + bi[row+1];
    2205:         pc3 = ba + bi[row+2];

    2207:         sctx.pv       = rtmp33[row+2];
    2208:         rs            = 0.0;
    2209:         rtmp11[row]   = 1.0/rtmp11[row];
    2210:         rtmp22[row+1] = 1.0/rtmp22[row+1];
    2211:         rtmp33[row+2] = 1.0/rtmp33[row+2];
    2212:         /* copy row entries from dense representation to sparse */
    2213:         for (j=0; j<nz; j++) {
    2214:           idx    = pj[j];
    2215:           pc1[j] = rtmp11[idx];
    2216:           pc2[j] = rtmp22[idx];
    2217:           pc3[j] = rtmp33[idx];
    2218:           if (idx != row+2) rs += PetscAbsScalar(pc3[j]);
    2219:         }

    2221:         sctx.rs = rs;
    2222:         MatPivotCheck(B,A,info,&sctx,row+2);
    2223:         if (sctx.newshift) goto endofwhile;
    2224:         break;

    2226:       default:
    2227:         SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Node size not yet supported ");
    2228:       }
    2229:       row += nodesz;                 /* Update the row */
    2230:     }
    2231: endofwhile:;
    2232:   } while (sctx.newshift);
    2233:   PetscFree3(rtmp11,rtmp22,rtmp33);
    2234:   PetscFree(tmp_vec2);
    2235:   ISRestoreIndices(isicol,&ic);
    2236:   ISRestoreIndices(isrow,&r);
    2237:   ISRestoreIndices(iscol,&c);

    2239:   (B)->ops->solve = MatSolve_SeqAIJ_inplace;
    2240:   /* do not set solve add, since MatSolve_Inode + Add is faster */
    2241:   C->ops->solvetranspose    = MatSolveTranspose_SeqAIJ_inplace;
    2242:   C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace;
    2243:   C->assembled              = PETSC_TRUE;
    2244:   C->preallocated           = PETSC_TRUE;
    2245:   if (sctx.nshift) {
    2246:     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
    2247:       PetscInfo(A,"number of shift_pd tries %" PetscInt_FMT ", 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);
    2248:     } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
    2249:       PetscInfo(A,"number of shift_nz tries %" PetscInt_FMT ", shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
    2250:     }
    2251:   }
    2252:   PetscLogFlops(C->cmap->n);
    2253:   MatSeqAIJCheckInode(C);
    2254:   return 0;
    2255: }

    2257: /* ----------------------------------------------------------- */
    2258: PetscErrorCode MatSolve_SeqAIJ_Inode(Mat A,Vec bb,Vec xx)
    2259: {
    2260:   Mat_SeqAIJ        *a    = (Mat_SeqAIJ*)A->data;
    2261:   IS                iscol = a->col,isrow = a->row;
    2262:   const PetscInt    *r,*c,*rout,*cout;
    2263:   PetscInt          i,j,n = A->rmap->n;
    2264:   PetscInt          node_max,row,nsz,aii,i0,i1,nz;
    2265:   const PetscInt    *ai = a->i,*a_j = a->j,*ns,*vi,*ad,*aj;
    2266:   PetscScalar       *x,*tmp,*tmps,tmp0,tmp1;
    2267:   PetscScalar       sum1,sum2,sum3,sum4,sum5;
    2268:   const MatScalar   *v1,*v2,*v3,*v4,*v5,*a_a = a->a,*aa;
    2269:   const PetscScalar *b;

    2272:   node_max = a->inode.node_count;
    2273:   ns       = a->inode.size;     /* Node Size array */

    2275:   VecGetArrayRead(bb,&b);
    2276:   VecGetArrayWrite(xx,&x);
    2277:   tmp  = a->solve_work;

    2279:   ISGetIndices(isrow,&rout); r = rout;
    2280:   ISGetIndices(iscol,&cout); c = cout;

    2282:   /* forward solve the lower triangular */
    2283:   tmps = tmp;
    2284:   aa   = a_a;
    2285:   aj   = a_j;
    2286:   ad   = a->diag;

    2288:   for (i = 0,row = 0; i< node_max; ++i) {
    2289:     nsz = ns[i];
    2290:     aii = ai[row];
    2291:     v1  = aa + aii;
    2292:     vi  = aj + aii;
    2293:     nz  = ai[row+1]- ai[row];

    2295:     if (i < node_max-1) {
    2296:       /* Prefetch the indices for the next block */
    2297:       PetscPrefetchBlock(aj+ai[row+nsz],ai[row+nsz+1]-ai[row+nsz],0,PETSC_PREFETCH_HINT_NTA); /* indices */
    2298:       /* Prefetch the data for the next block */
    2299:       PetscPrefetchBlock(aa+ai[row+nsz],ai[row+nsz+ns[i+1]]-ai[row+nsz],0,PETSC_PREFETCH_HINT_NTA);
    2300:     }

    2302:     switch (nsz) {               /* Each loop in 'case' is unrolled */
    2303:     case 1:
    2304:       sum1 = b[r[row]];
    2305:       for (j=0; j<nz-1; j+=2) {
    2306:         i0    = vi[j];
    2307:         i1    = vi[j+1];
    2308:         tmp0  = tmps[i0];
    2309:         tmp1  = tmps[i1];
    2310:         sum1 -= v1[j]*tmp0 + v1[j+1]*tmp1;
    2311:       }
    2312:       if (j == nz-1) {
    2313:         tmp0  = tmps[vi[j]];
    2314:         sum1 -= v1[j]*tmp0;
    2315:       }
    2316:       tmp[row++]=sum1;
    2317:       break;
    2318:     case 2:
    2319:       sum1 = b[r[row]];
    2320:       sum2 = b[r[row+1]];
    2321:       v2   = aa + ai[row+1];

    2323:       for (j=0; j<nz-1; j+=2) {
    2324:         i0    = vi[j];
    2325:         i1    = vi[j+1];
    2326:         tmp0  = tmps[i0];
    2327:         tmp1  = tmps[i1];
    2328:         sum1 -= v1[j] * tmp0 + v1[j+1] * tmp1;
    2329:         sum2 -= v2[j] * tmp0 + v2[j+1] * tmp1;
    2330:       }
    2331:       if (j == nz-1) {
    2332:         tmp0  = tmps[vi[j]];
    2333:         sum1 -= v1[j] *tmp0;
    2334:         sum2 -= v2[j] *tmp0;
    2335:       }
    2336:       sum2     -= v2[nz] * sum1;
    2337:       tmp[row++]=sum1;
    2338:       tmp[row++]=sum2;
    2339:       break;
    2340:     case 3:
    2341:       sum1 = b[r[row]];
    2342:       sum2 = b[r[row+1]];
    2343:       sum3 = b[r[row+2]];
    2344:       v2   = aa + ai[row+1];
    2345:       v3   = aa + ai[row+2];

    2347:       for (j=0; j<nz-1; j+=2) {
    2348:         i0    = vi[j];
    2349:         i1    = vi[j+1];
    2350:         tmp0  = tmps[i0];
    2351:         tmp1  = tmps[i1];
    2352:         sum1 -= v1[j] * tmp0 + v1[j+1] * tmp1;
    2353:         sum2 -= v2[j] * tmp0 + v2[j+1] * tmp1;
    2354:         sum3 -= v3[j] * tmp0 + v3[j+1] * tmp1;
    2355:       }
    2356:       if (j == nz-1) {
    2357:         tmp0  = tmps[vi[j]];
    2358:         sum1 -= v1[j] *tmp0;
    2359:         sum2 -= v2[j] *tmp0;
    2360:         sum3 -= v3[j] *tmp0;
    2361:       }
    2362:       sum2     -= v2[nz] * sum1;
    2363:       sum3     -= v3[nz] * sum1;
    2364:       sum3     -= v3[nz+1] * sum2;
    2365:       tmp[row++]=sum1;
    2366:       tmp[row++]=sum2;
    2367:       tmp[row++]=sum3;
    2368:       break;

    2370:     case 4:
    2371:       sum1 = b[r[row]];
    2372:       sum2 = b[r[row+1]];
    2373:       sum3 = b[r[row+2]];
    2374:       sum4 = b[r[row+3]];
    2375:       v2   = aa + ai[row+1];
    2376:       v3   = aa + ai[row+2];
    2377:       v4   = aa + ai[row+3];

    2379:       for (j=0; j<nz-1; j+=2) {
    2380:         i0    = vi[j];
    2381:         i1    = vi[j+1];
    2382:         tmp0  = tmps[i0];
    2383:         tmp1  = tmps[i1];
    2384:         sum1 -= v1[j] * tmp0 + v1[j+1] * tmp1;
    2385:         sum2 -= v2[j] * tmp0 + v2[j+1] * tmp1;
    2386:         sum3 -= v3[j] * tmp0 + v3[j+1] * tmp1;
    2387:         sum4 -= v4[j] * tmp0 + v4[j+1] * tmp1;
    2388:       }
    2389:       if (j == nz-1) {
    2390:         tmp0  = tmps[vi[j]];
    2391:         sum1 -= v1[j] *tmp0;
    2392:         sum2 -= v2[j] *tmp0;
    2393:         sum3 -= v3[j] *tmp0;
    2394:         sum4 -= v4[j] *tmp0;
    2395:       }
    2396:       sum2 -= v2[nz] * sum1;
    2397:       sum3 -= v3[nz] * sum1;
    2398:       sum4 -= v4[nz] * sum1;
    2399:       sum3 -= v3[nz+1] * sum2;
    2400:       sum4 -= v4[nz+1] * sum2;
    2401:       sum4 -= v4[nz+2] * sum3;

    2403:       tmp[row++]=sum1;
    2404:       tmp[row++]=sum2;
    2405:       tmp[row++]=sum3;
    2406:       tmp[row++]=sum4;
    2407:       break;
    2408:     case 5:
    2409:       sum1 = b[r[row]];
    2410:       sum2 = b[r[row+1]];
    2411:       sum3 = b[r[row+2]];
    2412:       sum4 = b[r[row+3]];
    2413:       sum5 = b[r[row+4]];
    2414:       v2   = aa + ai[row+1];
    2415:       v3   = aa + ai[row+2];
    2416:       v4   = aa + ai[row+3];
    2417:       v5   = aa + ai[row+4];

    2419:       for (j=0; j<nz-1; j+=2) {
    2420:         i0    = vi[j];
    2421:         i1    = vi[j+1];
    2422:         tmp0  = tmps[i0];
    2423:         tmp1  = tmps[i1];
    2424:         sum1 -= v1[j] * tmp0 + v1[j+1] * tmp1;
    2425:         sum2 -= v2[j] * tmp0 + v2[j+1] * tmp1;
    2426:         sum3 -= v3[j] * tmp0 + v3[j+1] * tmp1;
    2427:         sum4 -= v4[j] * tmp0 + v4[j+1] * tmp1;
    2428:         sum5 -= v5[j] * tmp0 + v5[j+1] * tmp1;
    2429:       }
    2430:       if (j == nz-1) {
    2431:         tmp0  = tmps[vi[j]];
    2432:         sum1 -= v1[j] *tmp0;
    2433:         sum2 -= v2[j] *tmp0;
    2434:         sum3 -= v3[j] *tmp0;
    2435:         sum4 -= v4[j] *tmp0;
    2436:         sum5 -= v5[j] *tmp0;
    2437:       }

    2439:       sum2 -= v2[nz] * sum1;
    2440:       sum3 -= v3[nz] * sum1;
    2441:       sum4 -= v4[nz] * sum1;
    2442:       sum5 -= v5[nz] * sum1;
    2443:       sum3 -= v3[nz+1] * sum2;
    2444:       sum4 -= v4[nz+1] * sum2;
    2445:       sum5 -= v5[nz+1] * sum2;
    2446:       sum4 -= v4[nz+2] * sum3;
    2447:       sum5 -= v5[nz+2] * sum3;
    2448:       sum5 -= v5[nz+3] * sum4;

    2450:       tmp[row++]=sum1;
    2451:       tmp[row++]=sum2;
    2452:       tmp[row++]=sum3;
    2453:       tmp[row++]=sum4;
    2454:       tmp[row++]=sum5;
    2455:       break;
    2456:     default:
    2457:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_COR,"Node size not yet supported ");
    2458:     }
    2459:   }
    2460:   /* backward solve the upper triangular */
    2461:   for (i=node_max -1,row = n-1; i>=0; i--) {
    2462:     nsz = ns[i];
    2463:     aii = ad[row+1] + 1;
    2464:     v1  = aa + aii;
    2465:     vi  = aj + aii;
    2466:     nz  = ad[row]- ad[row+1] - 1;

    2468:     if (i > 0) {
    2469:       /* Prefetch the indices for the next block */
    2470:       PetscPrefetchBlock(aj+ad[row-nsz+1]+1,ad[row-nsz]-ad[row-nsz+1],0,PETSC_PREFETCH_HINT_NTA);
    2471:       /* Prefetch the data for the next block */
    2472:       PetscPrefetchBlock(aa+ad[row-nsz+1]+1,ad[row-nsz-ns[i-1]+1]-ad[row-nsz+1],0,PETSC_PREFETCH_HINT_NTA);
    2473:     }

    2475:     switch (nsz) {               /* Each loop in 'case' is unrolled */
    2476:     case 1:
    2477:       sum1 = tmp[row];

    2479:       for (j=0; j<nz-1; j+=2) {
    2480:         i0    = vi[j];
    2481:         i1    = vi[j+1];
    2482:         tmp0  = tmps[i0];
    2483:         tmp1  = tmps[i1];
    2484:         sum1 -= v1[j] * tmp0 + v1[j+1] * tmp1;
    2485:       }
    2486:       if (j == nz-1) {
    2487:         tmp0  = tmps[vi[j]];
    2488:         sum1 -= v1[j]*tmp0;
    2489:       }
    2490:       x[c[row]] = tmp[row] = sum1*v1[nz]; row--;
    2491:       break;
    2492:     case 2:
    2493:       sum1 = tmp[row];
    2494:       sum2 = tmp[row-1];
    2495:       v2   = aa + ad[row] + 1;
    2496:       for (j=0; j<nz-1; j+=2) {
    2497:         i0    = vi[j];
    2498:         i1    = vi[j+1];
    2499:         tmp0  = tmps[i0];
    2500:         tmp1  = tmps[i1];
    2501:         sum1 -= v1[j] * tmp0 + v1[j+1] * tmp1;
    2502:         sum2 -= v2[j+1] * tmp0 + v2[j+2] * tmp1;
    2503:       }
    2504:       if (j == nz-1) {
    2505:         tmp0  = tmps[vi[j]];
    2506:         sum1 -= v1[j]* tmp0;
    2507:         sum2 -= v2[j+1]* tmp0;
    2508:       }

    2510:       tmp0      = x[c[row]] = tmp[row] = sum1*v1[nz]; row--;
    2511:       sum2     -= v2[0] * tmp0;
    2512:       x[c[row]] = tmp[row] = sum2*v2[nz+1]; row--;
    2513:       break;
    2514:     case 3:
    2515:       sum1 = tmp[row];
    2516:       sum2 = tmp[row -1];
    2517:       sum3 = tmp[row -2];
    2518:       v2   = aa + ad[row] + 1;
    2519:       v3   = aa + ad[row -1] + 1;
    2520:       for (j=0; j<nz-1; j+=2) {
    2521:         i0    = vi[j];
    2522:         i1    = vi[j+1];
    2523:         tmp0  = tmps[i0];
    2524:         tmp1  = tmps[i1];
    2525:         sum1 -= v1[j] * tmp0 + v1[j+1] * tmp1;
    2526:         sum2 -= v2[j+1] * tmp0 + v2[j+2] * tmp1;
    2527:         sum3 -= v3[j+2] * tmp0 + v3[j+3] * tmp1;
    2528:       }
    2529:       if (j== nz-1) {
    2530:         tmp0  = tmps[vi[j]];
    2531:         sum1 -= v1[j] * tmp0;
    2532:         sum2 -= v2[j+1] * tmp0;
    2533:         sum3 -= v3[j+2] * tmp0;
    2534:       }
    2535:       tmp0      = x[c[row]] = tmp[row] = sum1*v1[nz]; row--;
    2536:       sum2     -= v2[0]* tmp0;
    2537:       sum3     -= v3[1] * tmp0;
    2538:       tmp0      = x[c[row]] = tmp[row] = sum2*v2[nz+1]; row--;
    2539:       sum3     -= v3[0]* tmp0;
    2540:       x[c[row]] = tmp[row] = sum3*v3[nz+2]; row--;

    2542:       break;
    2543:     case 4:
    2544:       sum1 = tmp[row];
    2545:       sum2 = tmp[row -1];
    2546:       sum3 = tmp[row -2];
    2547:       sum4 = tmp[row -3];
    2548:       v2   = aa + ad[row]+1;
    2549:       v3   = aa + ad[row -1]+1;
    2550:       v4   = aa + ad[row -2]+1;

    2552:       for (j=0; j<nz-1; j+=2) {
    2553:         i0    = vi[j];
    2554:         i1    = vi[j+1];
    2555:         tmp0  = tmps[i0];
    2556:         tmp1  = tmps[i1];
    2557:         sum1 -= v1[j] * tmp0   + v1[j+1] * tmp1;
    2558:         sum2 -= v2[j+1] * tmp0 + v2[j+2] * tmp1;
    2559:         sum3 -= v3[j+2] * tmp0 + v3[j+3] * tmp1;
    2560:         sum4 -= v4[j+3] * tmp0 + v4[j+4] * tmp1;
    2561:       }
    2562:       if (j== nz-1) {
    2563:         tmp0  = tmps[vi[j]];
    2564:         sum1 -= v1[j] * tmp0;
    2565:         sum2 -= v2[j+1] * tmp0;
    2566:         sum3 -= v3[j+2] * tmp0;
    2567:         sum4 -= v4[j+3] * tmp0;
    2568:       }

    2570:       tmp0      = x[c[row]] = tmp[row] = sum1*v1[nz]; row--;
    2571:       sum2     -= v2[0] * tmp0;
    2572:       sum3     -= v3[1] * tmp0;
    2573:       sum4     -= v4[2] * tmp0;
    2574:       tmp0      = x[c[row]] = tmp[row] = sum2*v2[nz+1]; row--;
    2575:       sum3     -= v3[0] * tmp0;
    2576:       sum4     -= v4[1] * tmp0;
    2577:       tmp0      = x[c[row]] = tmp[row] = sum3*v3[nz+2]; row--;
    2578:       sum4     -= v4[0] * tmp0;
    2579:       x[c[row]] = tmp[row] = sum4*v4[nz+3]; row--;
    2580:       break;
    2581:     case 5:
    2582:       sum1 = tmp[row];
    2583:       sum2 = tmp[row -1];
    2584:       sum3 = tmp[row -2];
    2585:       sum4 = tmp[row -3];
    2586:       sum5 = tmp[row -4];
    2587:       v2   = aa + ad[row]+1;
    2588:       v3   = aa + ad[row -1]+1;
    2589:       v4   = aa + ad[row -2]+1;
    2590:       v5   = aa + ad[row -3]+1;
    2591:       for (j=0; j<nz-1; j+=2) {
    2592:         i0    = vi[j];
    2593:         i1    = vi[j+1];
    2594:         tmp0  = tmps[i0];
    2595:         tmp1  = tmps[i1];
    2596:         sum1 -= v1[j] * tmp0 + v1[j+1] * tmp1;
    2597:         sum2 -= v2[j+1] * tmp0 + v2[j+2] * tmp1;
    2598:         sum3 -= v3[j+2] * tmp0 + v3[j+3] * tmp1;
    2599:         sum4 -= v4[j+3] * tmp0 + v4[j+4] * tmp1;
    2600:         sum5 -= v5[j+4] * tmp0 + v5[j+5] * tmp1;
    2601:       }
    2602:       if (j==nz-1) {
    2603:         tmp0  = tmps[vi[j]];
    2604:         sum1 -= v1[j] * tmp0;
    2605:         sum2 -= v2[j+1] * tmp0;
    2606:         sum3 -= v3[j+2] * tmp0;
    2607:         sum4 -= v4[j+3] * tmp0;
    2608:         sum5 -= v5[j+4] * tmp0;
    2609:       }

    2611:       tmp0      = x[c[row]] = tmp[row] = sum1*v1[nz]; row--;
    2612:       sum2     -= v2[0] * tmp0;
    2613:       sum3     -= v3[1] * tmp0;
    2614:       sum4     -= v4[2] * tmp0;
    2615:       sum5     -= v5[3] * tmp0;
    2616:       tmp0      = x[c[row]] = tmp[row] = sum2*v2[nz+1]; row--;
    2617:       sum3     -= v3[0] * tmp0;
    2618:       sum4     -= v4[1] * tmp0;
    2619:       sum5     -= v5[2] * tmp0;
    2620:       tmp0      = x[c[row]] = tmp[row] = sum3*v3[nz+2]; row--;
    2621:       sum4     -= v4[0] * tmp0;
    2622:       sum5     -= v5[1] * tmp0;
    2623:       tmp0      = x[c[row]] = tmp[row] = sum4*v4[nz+3]; row--;
    2624:       sum5     -= v5[0] * tmp0;
    2625:       x[c[row]] = tmp[row] = sum5*v5[nz+4]; row--;
    2626:       break;
    2627:     default:
    2628:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_COR,"Node size not yet supported ");
    2629:     }
    2630:   }
    2631:   ISRestoreIndices(isrow,&rout);
    2632:   ISRestoreIndices(iscol,&cout);
    2633:   VecRestoreArrayRead(bb,&b);
    2634:   VecRestoreArrayWrite(xx,&x);
    2635:   PetscLogFlops(2.0*a->nz - A->cmap->n);
    2636:   return 0;
    2637: }

    2639: /*
    2640:      Makes a longer coloring[] array and calls the usual code with that
    2641: */
    2642: PetscErrorCode MatColoringPatch_SeqAIJ_Inode(Mat mat,PetscInt ncolors,PetscInt nin,ISColoringValue coloring[],ISColoring *iscoloring)
    2643: {
    2644:   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)mat->data;
    2645:   PetscInt        n = mat->cmap->n,m = a->inode.node_count,j,*ns = a->inode.size,row;
    2646:   PetscInt        *colorused,i;
    2647:   ISColoringValue *newcolor;

    2650:   PetscMalloc1(n+1,&newcolor);
    2651:   /* loop over inodes, marking a color for each column*/
    2652:   row = 0;
    2653:   for (i=0; i<m; i++) {
    2654:     for (j=0; j<ns[i]; j++) {
    2655:       newcolor[row++] = coloring[i] + j*ncolors;
    2656:     }
    2657:   }

    2659:   /* eliminate unneeded colors */
    2660:   PetscCalloc1(5*ncolors,&colorused);
    2661:   for (i=0; i<n; i++) {
    2662:     colorused[newcolor[i]] = 1;
    2663:   }

    2665:   for (i=1; i<5*ncolors; i++) {
    2666:     colorused[i] += colorused[i-1];
    2667:   }
    2668:   ncolors = colorused[5*ncolors-1];
    2669:   for (i=0; i<n; i++) {
    2670:     newcolor[i] = colorused[newcolor[i]]-1;
    2671:   }
    2672:   PetscFree(colorused);
    2673:   ISColoringCreate(PetscObjectComm((PetscObject)mat),ncolors,n,newcolor,PETSC_OWN_POINTER,iscoloring);
    2674:   PetscFree(coloring);
    2675:   return 0;
    2676: }

    2678: #include <petsc/private/kernels/blockinvert.h>

    2680: PetscErrorCode MatSOR_SeqAIJ_Inode(Mat A,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
    2681: {
    2682:   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
    2683:   PetscScalar       sum1 = 0.0,sum2 = 0.0,sum3 = 0.0,sum4 = 0.0,sum5 = 0.0,tmp0,tmp1,tmp2,tmp3;
    2684:   MatScalar         *ibdiag,*bdiag,work[25],*t;
    2685:   PetscScalar       *x,tmp4,tmp5,x1,x2,x3,x4,x5;
    2686:   const MatScalar   *v = a->a,*v1 = NULL,*v2 = NULL,*v3 = NULL,*v4 = NULL,*v5 = NULL;
    2687:   const PetscScalar *xb, *b;
    2688:   PetscReal         zeropivot = 100.*PETSC_MACHINE_EPSILON, shift = 0.0;
    2689:   PetscInt          n,m = a->inode.node_count,cnt = 0,i,j,row,i1,i2;
    2690:   PetscInt          sz,k,ipvt[5];
    2691:   PetscBool         allowzeropivot,zeropivotdetected;
    2692:   const PetscInt    *sizes = a->inode.size,*idx,*diag = a->diag,*ii = a->i;

    2694:   allowzeropivot = PetscNot(A->erroriffailure);

    2699:   if (!a->inode.ibdiagvalid) {
    2700:     if (!a->inode.ibdiag) {
    2701:       /* calculate space needed for diagonal blocks */
    2702:       for (i=0; i<m; i++) {
    2703:         cnt += sizes[i]*sizes[i];
    2704:       }
    2705:       a->inode.bdiagsize = cnt;

    2707:       PetscMalloc3(cnt,&a->inode.ibdiag,cnt,&a->inode.bdiag,A->rmap->n,&a->inode.ssor_work);
    2708:     }

    2710:     /* copy over the diagonal blocks and invert them */
    2711:     ibdiag = a->inode.ibdiag;
    2712:     bdiag  = a->inode.bdiag;
    2713:     cnt    = 0;
    2714:     for (i=0, row = 0; i<m; i++) {
    2715:       for (j=0; j<sizes[i]; j++) {
    2716:         for (k=0; k<sizes[i]; k++) {
    2717:           bdiag[cnt+k*sizes[i]+j] = v[diag[row+j] - j + k];
    2718:         }
    2719:       }
    2720:       PetscArraycpy(ibdiag+cnt,bdiag+cnt,sizes[i]*sizes[i]);

    2722:       switch (sizes[i]) {
    2723:       case 1:
    2724:         /* Create matrix data structure */
    2725:         if (PetscAbsScalar(ibdiag[cnt]) < zeropivot) {
    2726:           if (allowzeropivot) {
    2727:             A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    2728:             A->factorerror_zeropivot_value = PetscAbsScalar(ibdiag[cnt]);
    2729:             A->factorerror_zeropivot_row   = row;
    2730:             PetscInfo(A,"Zero pivot, row %" PetscInt_FMT "\n",row);
    2731:           } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot on row %" PetscInt_FMT,row);
    2732:         }
    2733:         ibdiag[cnt] = 1.0/ibdiag[cnt];
    2734:         break;
    2735:       case 2:
    2736:         PetscKernel_A_gets_inverse_A_2(ibdiag+cnt,shift,allowzeropivot,&zeropivotdetected);
    2737:         if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    2738:         break;
    2739:       case 3:
    2740:         PetscKernel_A_gets_inverse_A_3(ibdiag+cnt,shift,allowzeropivot,&zeropivotdetected);
    2741:         if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    2742:         break;
    2743:       case 4:
    2744:         PetscKernel_A_gets_inverse_A_4(ibdiag+cnt,shift,allowzeropivot,&zeropivotdetected);
    2745:         if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    2746:         break;
    2747:       case 5:
    2748:         PetscKernel_A_gets_inverse_A_5(ibdiag+cnt,ipvt,work,shift,allowzeropivot,&zeropivotdetected);
    2749:         if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    2750:         break;
    2751:       default:
    2752:         SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Inode size %" PetscInt_FMT " not supported",sizes[i]);
    2753:       }
    2754:       cnt += sizes[i]*sizes[i];
    2755:       row += sizes[i];
    2756:     }
    2757:     a->inode.ibdiagvalid = PETSC_TRUE;
    2758:   }
    2759:   ibdiag = a->inode.ibdiag;
    2760:   bdiag  = a->inode.bdiag;
    2761:   t      = a->inode.ssor_work;

    2763:   VecGetArray(xx,&x);
    2764:   VecGetArrayRead(bb,&b);
    2765:   /* We count flops by assuming the upper triangular and lower triangular parts have the same number of nonzeros */
    2766:   if (flag & SOR_ZERO_INITIAL_GUESS) {
    2767:     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {

    2769:       for (i=0, row=0; i<m; i++) {
    2770:         sz  = diag[row] - ii[row];
    2771:         v1  = a->a + ii[row];
    2772:         idx = a->j + ii[row];

    2774:         /* see comments for MatMult_SeqAIJ_Inode() for how this is coded */
    2775:         switch (sizes[i]) {
    2776:         case 1:

    2778:           sum1 = b[row];
    2779:           for (n = 0; n<sz-1; n+=2) {
    2780:             i1    = idx[0];
    2781:             i2    = idx[1];
    2782:             idx  += 2;
    2783:             tmp0  = x[i1];
    2784:             tmp1  = x[i2];
    2785:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    2786:           }

    2788:           if (n == sz-1) {
    2789:             tmp0  = x[*idx];
    2790:             sum1 -= *v1 * tmp0;
    2791:           }
    2792:           t[row]   = sum1;
    2793:           x[row++] = sum1*(*ibdiag++);
    2794:           break;
    2795:         case 2:
    2796:           v2   = a->a + ii[row+1];
    2797:           sum1 = b[row];
    2798:           sum2 = b[row+1];
    2799:           for (n = 0; n<sz-1; n+=2) {
    2800:             i1    = idx[0];
    2801:             i2    = idx[1];
    2802:             idx  += 2;
    2803:             tmp0  = x[i1];
    2804:             tmp1  = x[i2];
    2805:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    2806:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    2807:           }

    2809:           if (n == sz-1) {
    2810:             tmp0  = x[*idx];
    2811:             sum1 -= v1[0] * tmp0;
    2812:             sum2 -= v2[0] * tmp0;
    2813:           }
    2814:           t[row]   = sum1;
    2815:           t[row+1] = sum2;
    2816:           x[row++] = sum1*ibdiag[0] + sum2*ibdiag[2];
    2817:           x[row++] = sum1*ibdiag[1] + sum2*ibdiag[3];
    2818:           ibdiag  += 4;
    2819:           break;
    2820:         case 3:
    2821:           v2   = a->a + ii[row+1];
    2822:           v3   = a->a + ii[row+2];
    2823:           sum1 = b[row];
    2824:           sum2 = b[row+1];
    2825:           sum3 = b[row+2];
    2826:           for (n = 0; n<sz-1; n+=2) {
    2827:             i1    = idx[0];
    2828:             i2    = idx[1];
    2829:             idx  += 2;
    2830:             tmp0  = x[i1];
    2831:             tmp1  = x[i2];
    2832:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    2833:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    2834:             sum3 -= v3[0] * tmp0 + v3[1] * tmp1; v3 += 2;
    2835:           }

    2837:           if (n == sz-1) {
    2838:             tmp0  = x[*idx];
    2839:             sum1 -= v1[0] * tmp0;
    2840:             sum2 -= v2[0] * tmp0;
    2841:             sum3 -= v3[0] * tmp0;
    2842:           }
    2843:           t[row]   = sum1;
    2844:           t[row+1] = sum2;
    2845:           t[row+2] = sum3;
    2846:           x[row++] = sum1*ibdiag[0] + sum2*ibdiag[3] + sum3*ibdiag[6];
    2847:           x[row++] = sum1*ibdiag[1] + sum2*ibdiag[4] + sum3*ibdiag[7];
    2848:           x[row++] = sum1*ibdiag[2] + sum2*ibdiag[5] + sum3*ibdiag[8];
    2849:           ibdiag  += 9;
    2850:           break;
    2851:         case 4:
    2852:           v2   = a->a + ii[row+1];
    2853:           v3   = a->a + ii[row+2];
    2854:           v4   = a->a + ii[row+3];
    2855:           sum1 = b[row];
    2856:           sum2 = b[row+1];
    2857:           sum3 = b[row+2];
    2858:           sum4 = b[row+3];
    2859:           for (n = 0; n<sz-1; n+=2) {
    2860:             i1    = idx[0];
    2861:             i2    = idx[1];
    2862:             idx  += 2;
    2863:             tmp0  = x[i1];
    2864:             tmp1  = x[i2];
    2865:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    2866:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    2867:             sum3 -= v3[0] * tmp0 + v3[1] * tmp1; v3 += 2;
    2868:             sum4 -= v4[0] * tmp0 + v4[1] * tmp1; v4 += 2;
    2869:           }

    2871:           if (n == sz-1) {
    2872:             tmp0  = x[*idx];
    2873:             sum1 -= v1[0] * tmp0;
    2874:             sum2 -= v2[0] * tmp0;
    2875:             sum3 -= v3[0] * tmp0;
    2876:             sum4 -= v4[0] * tmp0;
    2877:           }
    2878:           t[row]   = sum1;
    2879:           t[row+1] = sum2;
    2880:           t[row+2] = sum3;
    2881:           t[row+3] = sum4;
    2882:           x[row++] = sum1*ibdiag[0] + sum2*ibdiag[4] + sum3*ibdiag[8] + sum4*ibdiag[12];
    2883:           x[row++] = sum1*ibdiag[1] + sum2*ibdiag[5] + sum3*ibdiag[9] + sum4*ibdiag[13];
    2884:           x[row++] = sum1*ibdiag[2] + sum2*ibdiag[6] + sum3*ibdiag[10] + sum4*ibdiag[14];
    2885:           x[row++] = sum1*ibdiag[3] + sum2*ibdiag[7] + sum3*ibdiag[11] + sum4*ibdiag[15];
    2886:           ibdiag  += 16;
    2887:           break;
    2888:         case 5:
    2889:           v2   = a->a + ii[row+1];
    2890:           v3   = a->a + ii[row+2];
    2891:           v4   = a->a + ii[row+3];
    2892:           v5   = a->a + ii[row+4];
    2893:           sum1 = b[row];
    2894:           sum2 = b[row+1];
    2895:           sum3 = b[row+2];
    2896:           sum4 = b[row+3];
    2897:           sum5 = b[row+4];
    2898:           for (n = 0; n<sz-1; n+=2) {
    2899:             i1    = idx[0];
    2900:             i2    = idx[1];
    2901:             idx  += 2;
    2902:             tmp0  = x[i1];
    2903:             tmp1  = x[i2];
    2904:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    2905:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    2906:             sum3 -= v3[0] * tmp0 + v3[1] * tmp1; v3 += 2;
    2907:             sum4 -= v4[0] * tmp0 + v4[1] * tmp1; v4 += 2;
    2908:             sum5 -= v5[0] * tmp0 + v5[1] * tmp1; v5 += 2;
    2909:           }

    2911:           if (n == sz-1) {
    2912:             tmp0  = x[*idx];
    2913:             sum1 -= v1[0] * tmp0;
    2914:             sum2 -= v2[0] * tmp0;
    2915:             sum3 -= v3[0] * tmp0;
    2916:             sum4 -= v4[0] * tmp0;
    2917:             sum5 -= v5[0] * tmp0;
    2918:           }
    2919:           t[row]   = sum1;
    2920:           t[row+1] = sum2;
    2921:           t[row+2] = sum3;
    2922:           t[row+3] = sum4;
    2923:           t[row+4] = sum5;
    2924:           x[row++] = sum1*ibdiag[0] + sum2*ibdiag[5] + sum3*ibdiag[10] + sum4*ibdiag[15] + sum5*ibdiag[20];
    2925:           x[row++] = sum1*ibdiag[1] + sum2*ibdiag[6] + sum3*ibdiag[11] + sum4*ibdiag[16] + sum5*ibdiag[21];
    2926:           x[row++] = sum1*ibdiag[2] + sum2*ibdiag[7] + sum3*ibdiag[12] + sum4*ibdiag[17] + sum5*ibdiag[22];
    2927:           x[row++] = sum1*ibdiag[3] + sum2*ibdiag[8] + sum3*ibdiag[13] + sum4*ibdiag[18] + sum5*ibdiag[23];
    2928:           x[row++] = sum1*ibdiag[4] + sum2*ibdiag[9] + sum3*ibdiag[14] + sum4*ibdiag[19] + sum5*ibdiag[24];
    2929:           ibdiag  += 25;
    2930:           break;
    2931:         default:
    2932:           SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Inode size %" PetscInt_FMT " not supported",sizes[i]);
    2933:         }
    2934:       }

    2936:       xb   = t;
    2937:       PetscLogFlops(a->nz);
    2938:     } else xb = b;
    2939:     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {

    2941:       ibdiag = a->inode.ibdiag+a->inode.bdiagsize;
    2942:       for (i=m-1, row=A->rmap->n-1; i>=0; i--) {
    2943:         ibdiag -= sizes[i]*sizes[i];
    2944:         sz      = ii[row+1] - diag[row] - 1;
    2945:         v1      = a->a + diag[row] + 1;
    2946:         idx     = a->j + diag[row] + 1;

    2948:         /* see comments for MatMult_SeqAIJ_Inode() for how this is coded */
    2949:         switch (sizes[i]) {
    2950:         case 1:

    2952:           sum1 = xb[row];
    2953:           for (n = 0; n<sz-1; n+=2) {
    2954:             i1    = idx[0];
    2955:             i2    = idx[1];
    2956:             idx  += 2;
    2957:             tmp0  = x[i1];
    2958:             tmp1  = x[i2];
    2959:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    2960:           }

    2962:           if (n == sz-1) {
    2963:             tmp0  = x[*idx];
    2964:             sum1 -= *v1*tmp0;
    2965:           }
    2966:           x[row--] = sum1*(*ibdiag);
    2967:           break;

    2969:         case 2:

    2971:           sum1 = xb[row];
    2972:           sum2 = xb[row-1];
    2973:           /* note that sum1 is associated with the second of the two rows */
    2974:           v2 = a->a + diag[row-1] + 2;
    2975:           for (n = 0; n<sz-1; n+=2) {
    2976:             i1    = idx[0];
    2977:             i2    = idx[1];
    2978:             idx  += 2;
    2979:             tmp0  = x[i1];
    2980:             tmp1  = x[i2];
    2981:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    2982:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    2983:           }

    2985:           if (n == sz-1) {
    2986:             tmp0  = x[*idx];
    2987:             sum1 -= *v1*tmp0;
    2988:             sum2 -= *v2*tmp0;
    2989:           }
    2990:           x[row--] = sum2*ibdiag[1] + sum1*ibdiag[3];
    2991:           x[row--] = sum2*ibdiag[0] + sum1*ibdiag[2];
    2992:           break;
    2993:         case 3:

    2995:           sum1 = xb[row];
    2996:           sum2 = xb[row-1];
    2997:           sum3 = xb[row-2];
    2998:           v2   = a->a + diag[row-1] + 2;
    2999:           v3   = a->a + diag[row-2] + 3;
    3000:           for (n = 0; n<sz-1; n+=2) {
    3001:             i1    = idx[0];
    3002:             i2    = idx[1];
    3003:             idx  += 2;
    3004:             tmp0  = x[i1];
    3005:             tmp1  = x[i2];
    3006:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    3007:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    3008:             sum3 -= v3[0] * tmp0 + v3[1] * tmp1; v3 += 2;
    3009:           }

    3011:           if (n == sz-1) {
    3012:             tmp0  = x[*idx];
    3013:             sum1 -= *v1*tmp0;
    3014:             sum2 -= *v2*tmp0;
    3015:             sum3 -= *v3*tmp0;
    3016:           }
    3017:           x[row--] = sum3*ibdiag[2] + sum2*ibdiag[5] + sum1*ibdiag[8];
    3018:           x[row--] = sum3*ibdiag[1] + sum2*ibdiag[4] + sum1*ibdiag[7];
    3019:           x[row--] = sum3*ibdiag[0] + sum2*ibdiag[3] + sum1*ibdiag[6];
    3020:           break;
    3021:         case 4:

    3023:           sum1 = xb[row];
    3024:           sum2 = xb[row-1];
    3025:           sum3 = xb[row-2];
    3026:           sum4 = xb[row-3];
    3027:           v2   = a->a + diag[row-1] + 2;
    3028:           v3   = a->a + diag[row-2] + 3;
    3029:           v4   = a->a + diag[row-3] + 4;
    3030:           for (n = 0; n<sz-1; n+=2) {
    3031:             i1    = idx[0];
    3032:             i2    = idx[1];
    3033:             idx  += 2;
    3034:             tmp0  = x[i1];
    3035:             tmp1  = x[i2];
    3036:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    3037:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    3038:             sum3 -= v3[0] * tmp0 + v3[1] * tmp1; v3 += 2;
    3039:             sum4 -= v4[0] * tmp0 + v4[1] * tmp1; v4 += 2;
    3040:           }

    3042:           if (n == sz-1) {
    3043:             tmp0  = x[*idx];
    3044:             sum1 -= *v1*tmp0;
    3045:             sum2 -= *v2*tmp0;
    3046:             sum3 -= *v3*tmp0;
    3047:             sum4 -= *v4*tmp0;
    3048:           }
    3049:           x[row--] = sum4*ibdiag[3] + sum3*ibdiag[7] + sum2*ibdiag[11] + sum1*ibdiag[15];
    3050:           x[row--] = sum4*ibdiag[2] + sum3*ibdiag[6] + sum2*ibdiag[10] + sum1*ibdiag[14];
    3051:           x[row--] = sum4*ibdiag[1] + sum3*ibdiag[5] + sum2*ibdiag[9] + sum1*ibdiag[13];
    3052:           x[row--] = sum4*ibdiag[0] + sum3*ibdiag[4] + sum2*ibdiag[8] + sum1*ibdiag[12];
    3053:           break;
    3054:         case 5:

    3056:           sum1 = xb[row];
    3057:           sum2 = xb[row-1];
    3058:           sum3 = xb[row-2];
    3059:           sum4 = xb[row-3];
    3060:           sum5 = xb[row-4];
    3061:           v2   = a->a + diag[row-1] + 2;
    3062:           v3   = a->a + diag[row-2] + 3;
    3063:           v4   = a->a + diag[row-3] + 4;
    3064:           v5   = a->a + diag[row-4] + 5;
    3065:           for (n = 0; n<sz-1; n+=2) {
    3066:             i1    = idx[0];
    3067:             i2    = idx[1];
    3068:             idx  += 2;
    3069:             tmp0  = x[i1];
    3070:             tmp1  = x[i2];
    3071:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    3072:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    3073:             sum3 -= v3[0] * tmp0 + v3[1] * tmp1; v3 += 2;
    3074:             sum4 -= v4[0] * tmp0 + v4[1] * tmp1; v4 += 2;
    3075:             sum5 -= v5[0] * tmp0 + v5[1] * tmp1; v5 += 2;
    3076:           }

    3078:           if (n == sz-1) {
    3079:             tmp0  = x[*idx];
    3080:             sum1 -= *v1*tmp0;
    3081:             sum2 -= *v2*tmp0;
    3082:             sum3 -= *v3*tmp0;
    3083:             sum4 -= *v4*tmp0;
    3084:             sum5 -= *v5*tmp0;
    3085:           }
    3086:           x[row--] = sum5*ibdiag[4] + sum4*ibdiag[9] + sum3*ibdiag[14] + sum2*ibdiag[19] + sum1*ibdiag[24];
    3087:           x[row--] = sum5*ibdiag[3] + sum4*ibdiag[8] + sum3*ibdiag[13] + sum2*ibdiag[18] + sum1*ibdiag[23];
    3088:           x[row--] = sum5*ibdiag[2] + sum4*ibdiag[7] + sum3*ibdiag[12] + sum2*ibdiag[17] + sum1*ibdiag[22];
    3089:           x[row--] = sum5*ibdiag[1] + sum4*ibdiag[6] + sum3*ibdiag[11] + sum2*ibdiag[16] + sum1*ibdiag[21];
    3090:           x[row--] = sum5*ibdiag[0] + sum4*ibdiag[5] + sum3*ibdiag[10] + sum2*ibdiag[15] + sum1*ibdiag[20];
    3091:           break;
    3092:         default:
    3093:           SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Inode size %" PetscInt_FMT " not supported",sizes[i]);
    3094:         }
    3095:       }

    3097:       PetscLogFlops(a->nz);
    3098:     }
    3099:     its--;
    3100:   }
    3101:   while (its--) {

    3103:     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
    3104:       for (i=0, row=0, ibdiag = a->inode.ibdiag;
    3105:            i<m;
    3106:            row += sizes[i], ibdiag += sizes[i]*sizes[i], i++) {

    3108:         sz  = diag[row] - ii[row];
    3109:         v1  = a->a + ii[row];
    3110:         idx = a->j + ii[row];
    3111:         /* see comments for MatMult_SeqAIJ_Inode() for how this is coded */
    3112:         switch (sizes[i]) {
    3113:         case 1:
    3114:           sum1 = b[row];
    3115:           for (n = 0; n<sz-1; n+=2) {
    3116:             i1    = idx[0];
    3117:             i2    = idx[1];
    3118:             idx  += 2;
    3119:             tmp0  = x[i1];
    3120:             tmp1  = x[i2];
    3121:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    3122:           }
    3123:           if (n == sz-1) {
    3124:             tmp0  = x[*idx++];
    3125:             sum1 -= *v1 * tmp0;
    3126:             v1++;
    3127:           }
    3128:           t[row]   = sum1;
    3129:           sz      = ii[row+1] - diag[row] - 1;
    3130:           idx     = a->j + diag[row] + 1;
    3131:           v1 += 1;
    3132:           for (n = 0; n<sz-1; n+=2) {
    3133:             i1    = idx[0];
    3134:             i2    = idx[1];
    3135:             idx  += 2;
    3136:             tmp0  = x[i1];
    3137:             tmp1  = x[i2];
    3138:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    3139:           }
    3140:           if (n == sz-1) {
    3141:             tmp0  = x[*idx++];
    3142:             sum1 -= *v1 * tmp0;
    3143:           }
    3144:           /* in MatSOR_SeqAIJ this line would be
    3145:            *
    3146:            * x[row] = (1-omega)*x[row]+(sum1+(*bdiag++)*x[row])*(*ibdiag++);
    3147:            *
    3148:            * but omega == 1, so this becomes
    3149:            *
    3150:            * x[row] = sum1*(*ibdiag++);
    3151:            *
    3152:            */
    3153:           x[row] = sum1*(*ibdiag);
    3154:           break;
    3155:         case 2:
    3156:           v2   = a->a + ii[row+1];
    3157:           sum1 = b[row];
    3158:           sum2 = b[row+1];
    3159:           for (n = 0; n<sz-1; n+=2) {
    3160:             i1    = idx[0];
    3161:             i2    = idx[1];
    3162:             idx  += 2;
    3163:             tmp0  = x[i1];
    3164:             tmp1  = x[i2];
    3165:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    3166:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    3167:           }
    3168:           if (n == sz-1) {
    3169:             tmp0  = x[*idx++];
    3170:             sum1 -= v1[0] * tmp0;
    3171:             sum2 -= v2[0] * tmp0;
    3172:             v1++; v2++;
    3173:           }
    3174:           t[row]   = sum1;
    3175:           t[row+1] = sum2;
    3176:           sz      = ii[row+1] - diag[row] - 2;
    3177:           idx     = a->j + diag[row] + 2;
    3178:           v1 += 2;
    3179:           v2 += 2;
    3180:           for (n = 0; n<sz-1; n+=2) {
    3181:             i1    = idx[0];
    3182:             i2    = idx[1];
    3183:             idx  += 2;
    3184:             tmp0  = x[i1];
    3185:             tmp1  = x[i2];
    3186:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    3187:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    3188:           }
    3189:           if (n == sz-1) {
    3190:             tmp0  = x[*idx];
    3191:             sum1 -= v1[0] * tmp0;
    3192:             sum2 -= v2[0] * tmp0;
    3193:           }
    3194:           x[row] = sum1*ibdiag[0] + sum2*ibdiag[2];
    3195:           x[row+1] = sum1*ibdiag[1] + sum2*ibdiag[3];
    3196:           break;
    3197:         case 3:
    3198:           v2   = a->a + ii[row+1];
    3199:           v3   = a->a + ii[row+2];
    3200:           sum1 = b[row];
    3201:           sum2 = b[row+1];
    3202:           sum3 = b[row+2];
    3203:           for (n = 0; n<sz-1; n+=2) {
    3204:             i1    = idx[0];
    3205:             i2    = idx[1];
    3206:             idx  += 2;
    3207:             tmp0  = x[i1];
    3208:             tmp1  = x[i2];
    3209:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    3210:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    3211:             sum3 -= v3[0] * tmp0 + v3[1] * tmp1; v3 += 2;
    3212:           }
    3213:           if (n == sz-1) {
    3214:             tmp0  = x[*idx++];
    3215:             sum1 -= v1[0] * tmp0;
    3216:             sum2 -= v2[0] * tmp0;
    3217:             sum3 -= v3[0] * tmp0;
    3218:             v1++; v2++; v3++;
    3219:           }
    3220:           t[row]   = sum1;
    3221:           t[row+1] = sum2;
    3222:           t[row+2] = sum3;
    3223:           sz      = ii[row+1] - diag[row] - 3;
    3224:           idx     = a->j + diag[row] + 3;
    3225:           v1 += 3;
    3226:           v2 += 3;
    3227:           v3 += 3;
    3228:           for (n = 0; n<sz-1; n+=2) {
    3229:             i1    = idx[0];
    3230:             i2    = idx[1];
    3231:             idx  += 2;
    3232:             tmp0  = x[i1];
    3233:             tmp1  = x[i2];
    3234:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    3235:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    3236:             sum3 -= v3[0] * tmp0 + v3[1] * tmp1; v3 += 2;
    3237:           }
    3238:           if (n == sz-1) {
    3239:             tmp0  = x[*idx];
    3240:             sum1 -= v1[0] * tmp0;
    3241:             sum2 -= v2[0] * tmp0;
    3242:             sum3 -= v3[0] * tmp0;
    3243:           }
    3244:           x[row] = sum1*ibdiag[0] + sum2*ibdiag[3] + sum3*ibdiag[6];
    3245:           x[row+1] = sum1*ibdiag[1] + sum2*ibdiag[4] + sum3*ibdiag[7];
    3246:           x[row+2] = sum1*ibdiag[2] + sum2*ibdiag[5] + sum3*ibdiag[8];
    3247:           break;
    3248:         case 4:
    3249:           v2   = a->a + ii[row+1];
    3250:           v3   = a->a + ii[row+2];
    3251:           v4   = a->a + ii[row+3];
    3252:           sum1 = b[row];
    3253:           sum2 = b[row+1];
    3254:           sum3 = b[row+2];
    3255:           sum4 = b[row+3];
    3256:           for (n = 0; n<sz-1; n+=2) {
    3257:             i1    = idx[0];
    3258:             i2    = idx[1];
    3259:             idx  += 2;
    3260:             tmp0  = x[i1];
    3261:             tmp1  = x[i2];
    3262:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    3263:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    3264:             sum3 -= v3[0] * tmp0 + v3[1] * tmp1; v3 += 2;
    3265:             sum4 -= v4[0] * tmp0 + v4[1] * tmp1; v4 += 2;
    3266:           }
    3267:           if (n == sz-1) {
    3268:             tmp0  = x[*idx++];
    3269:             sum1 -= v1[0] * tmp0;
    3270:             sum2 -= v2[0] * tmp0;
    3271:             sum3 -= v3[0] * tmp0;
    3272:             sum4 -= v4[0] * tmp0;
    3273:             v1++; v2++; v3++; v4++;
    3274:           }
    3275:           t[row]   = sum1;
    3276:           t[row+1] = sum2;
    3277:           t[row+2] = sum3;
    3278:           t[row+3] = sum4;
    3279:           sz      = ii[row+1] - diag[row] - 4;
    3280:           idx     = a->j + diag[row] + 4;
    3281:           v1 += 4;
    3282:           v2 += 4;
    3283:           v3 += 4;
    3284:           v4 += 4;
    3285:           for (n = 0; n<sz-1; n+=2) {
    3286:             i1    = idx[0];
    3287:             i2    = idx[1];
    3288:             idx  += 2;
    3289:             tmp0  = x[i1];
    3290:             tmp1  = x[i2];
    3291:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    3292:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    3293:             sum3 -= v3[0] * tmp0 + v3[1] * tmp1; v3 += 2;
    3294:             sum4 -= v4[0] * tmp0 + v4[1] * tmp1; v4 += 2;
    3295:           }
    3296:           if (n == sz-1) {
    3297:             tmp0  = x[*idx];
    3298:             sum1 -= v1[0] * tmp0;
    3299:             sum2 -= v2[0] * tmp0;
    3300:             sum3 -= v3[0] * tmp0;
    3301:             sum4 -= v4[0] * tmp0;
    3302:           }
    3303:           x[row] =   sum1*ibdiag[0] + sum2*ibdiag[4] + sum3*ibdiag[8] + sum4*ibdiag[12];
    3304:           x[row+1] = sum1*ibdiag[1] + sum2*ibdiag[5] + sum3*ibdiag[9] + sum4*ibdiag[13];
    3305:           x[row+2] = sum1*ibdiag[2] + sum2*ibdiag[6] + sum3*ibdiag[10] + sum4*ibdiag[14];
    3306:           x[row+3] = sum1*ibdiag[3] + sum2*ibdiag[7] + sum3*ibdiag[11] + sum4*ibdiag[15];
    3307:           break;
    3308:         case 5:
    3309:           v2   = a->a + ii[row+1];
    3310:           v3   = a->a + ii[row+2];
    3311:           v4   = a->a + ii[row+3];
    3312:           v5   = a->a + ii[row+4];
    3313:           sum1 = b[row];
    3314:           sum2 = b[row+1];
    3315:           sum3 = b[row+2];
    3316:           sum4 = b[row+3];
    3317:           sum5 = b[row+4];
    3318:           for (n = 0; n<sz-1; n+=2) {
    3319:             i1    = idx[0];
    3320:             i2    = idx[1];
    3321:             idx  += 2;
    3322:             tmp0  = x[i1];
    3323:             tmp1  = x[i2];
    3324:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    3325:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    3326:             sum3 -= v3[0] * tmp0 + v3[1] * tmp1; v3 += 2;
    3327:             sum4 -= v4[0] * tmp0 + v4[1] * tmp1; v4 += 2;
    3328:             sum5 -= v5[0] * tmp0 + v5[1] * tmp1; v5 += 2;
    3329:           }
    3330:           if (n == sz-1) {
    3331:             tmp0  = x[*idx++];
    3332:             sum1 -= v1[0] * tmp0;
    3333:             sum2 -= v2[0] * tmp0;
    3334:             sum3 -= v3[0] * tmp0;
    3335:             sum4 -= v4[0] * tmp0;
    3336:             sum5 -= v5[0] * tmp0;
    3337:             v1++; v2++; v3++; v4++; v5++;
    3338:           }
    3339:           t[row]   = sum1;
    3340:           t[row+1] = sum2;
    3341:           t[row+2] = sum3;
    3342:           t[row+3] = sum4;
    3343:           t[row+4] = sum5;
    3344:           sz      = ii[row+1] - diag[row] - 5;
    3345:           idx     = a->j + diag[row] + 5;
    3346:           v1 += 5;
    3347:           v2 += 5;
    3348:           v3 += 5;
    3349:           v4 += 5;
    3350:           v5 += 5;
    3351:           for (n = 0; n<sz-1; n+=2) {
    3352:             i1    = idx[0];
    3353:             i2    = idx[1];
    3354:             idx  += 2;
    3355:             tmp0  = x[i1];
    3356:             tmp1  = x[i2];
    3357:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    3358:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    3359:             sum3 -= v3[0] * tmp0 + v3[1] * tmp1; v3 += 2;
    3360:             sum4 -= v4[0] * tmp0 + v4[1] * tmp1; v4 += 2;
    3361:             sum5 -= v5[0] * tmp0 + v5[1] * tmp1; v5 += 2;
    3362:           }
    3363:           if (n == sz-1) {
    3364:             tmp0  = x[*idx];
    3365:             sum1 -= v1[0] * tmp0;
    3366:             sum2 -= v2[0] * tmp0;
    3367:             sum3 -= v3[0] * tmp0;
    3368:             sum4 -= v4[0] * tmp0;
    3369:             sum5 -= v5[0] * tmp0;
    3370:           }
    3371:           x[row]   = sum1*ibdiag[0] + sum2*ibdiag[5] + sum3*ibdiag[10] + sum4*ibdiag[15] + sum5*ibdiag[20];
    3372:           x[row+1] = sum1*ibdiag[1] + sum2*ibdiag[6] + sum3*ibdiag[11] + sum4*ibdiag[16] + sum5*ibdiag[21];
    3373:           x[row+2] = sum1*ibdiag[2] + sum2*ibdiag[7] + sum3*ibdiag[12] + sum4*ibdiag[17] + sum5*ibdiag[22];
    3374:           x[row+3] = sum1*ibdiag[3] + sum2*ibdiag[8] + sum3*ibdiag[13] + sum4*ibdiag[18] + sum5*ibdiag[23];
    3375:           x[row+4] = sum1*ibdiag[4] + sum2*ibdiag[9] + sum3*ibdiag[14] + sum4*ibdiag[19] + sum5*ibdiag[24];
    3376:           break;
    3377:         default:
    3378:           SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Inode size %" PetscInt_FMT " not supported",sizes[i]);
    3379:         }
    3380:       }
    3381:       xb   = t;
    3382:       PetscLogFlops(2.0*a->nz);  /* undercounts diag inverse */
    3383:     } else xb = b;

    3385:     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {

    3387:       ibdiag = a->inode.ibdiag+a->inode.bdiagsize;
    3388:       for (i=m-1, row=A->rmap->n-1; i>=0; i--) {
    3389:         ibdiag -= sizes[i]*sizes[i];

    3391:         /* set RHS */
    3392:         if (xb == b) {
    3393:           /* whole (old way) */
    3394:           sz      = ii[row+1] - ii[row];
    3395:           idx     = a->j + ii[row];
    3396:           switch (sizes[i]) {
    3397:           case 5:
    3398:             v5      = a->a + ii[row-4];
    3399:           case 4: /* fall through */
    3400:             v4      = a->a + ii[row-3];
    3401:           case 3:
    3402:             v3      = a->a + ii[row-2];
    3403:           case 2:
    3404:             v2      = a->a + ii[row-1];
    3405:           case 1:
    3406:             v1      = a->a + ii[row];
    3407:             break;
    3408:           default:
    3409:             SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Inode size %" PetscInt_FMT " not supported",sizes[i]);
    3410:           }
    3411:         } else {
    3412:           /* upper, no diag */
    3413:           sz      = ii[row+1] - diag[row] - 1;
    3414:           idx     = a->j + diag[row] + 1;
    3415:           switch (sizes[i]) {
    3416:           case 5:
    3417:             v5      = a->a + diag[row-4] + 5;
    3418:           case 4: /* fall through */
    3419:             v4      = a->a + diag[row-3] + 4;
    3420:           case 3:
    3421:             v3      = a->a + diag[row-2] + 3;
    3422:           case 2:
    3423:             v2      = a->a + diag[row-1] + 2;
    3424:           case 1:
    3425:             v1      = a->a + diag[row] + 1;
    3426:           }
    3427:         }
    3428:         /* set sum */
    3429:         switch (sizes[i]) {
    3430:         case 5:
    3431:           sum5 = xb[row-4];
    3432:         case 4: /* fall through */
    3433:           sum4 = xb[row-3];
    3434:         case 3:
    3435:           sum3 = xb[row-2];
    3436:         case 2:
    3437:           sum2 = xb[row-1];
    3438:         case 1:
    3439:           /* note that sum1 is associated with the last row */
    3440:           sum1 = xb[row];
    3441:         }
    3442:         /* do sums */
    3443:         for (n = 0; n<sz-1; n+=2) {
    3444:             i1    = idx[0];
    3445:             i2    = idx[1];
    3446:             idx  += 2;
    3447:             tmp0  = x[i1];
    3448:             tmp1  = x[i2];
    3449:             switch (sizes[i]) {
    3450:             case 5:
    3451:               sum5 -= v5[0] * tmp0 + v5[1] * tmp1; v5 += 2;
    3452:             case 4: /* fall through */
    3453:               sum4 -= v4[0] * tmp0 + v4[1] * tmp1; v4 += 2;
    3454:             case 3:
    3455:               sum3 -= v3[0] * tmp0 + v3[1] * tmp1; v3 += 2;
    3456:             case 2:
    3457:               sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    3458:             case 1:
    3459:               sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    3460:             }
    3461:         }
    3462:         /* ragged edge */
    3463:         if (n == sz-1) {
    3464:           tmp0  = x[*idx];
    3465:           switch (sizes[i]) {
    3466:           case 5:
    3467:             sum5 -= *v5*tmp0;
    3468:           case 4: /* fall through */
    3469:             sum4 -= *v4*tmp0;
    3470:           case 3:
    3471:             sum3 -= *v3*tmp0;
    3472:           case 2:
    3473:             sum2 -= *v2*tmp0;
    3474:           case 1:
    3475:             sum1 -= *v1*tmp0;
    3476:           }
    3477:         }
    3478:         /* update */
    3479:         if (xb == b) {
    3480:           /* whole (old way) w/ diag */
    3481:           switch (sizes[i]) {
    3482:           case 5:
    3483:             x[row--] += sum5*ibdiag[4] + sum4*ibdiag[9] + sum3*ibdiag[14] + sum2*ibdiag[19] + sum1*ibdiag[24];
    3484:             x[row--] += sum5*ibdiag[3] + sum4*ibdiag[8] + sum3*ibdiag[13] + sum2*ibdiag[18] + sum1*ibdiag[23];
    3485:             x[row--] += sum5*ibdiag[2] + sum4*ibdiag[7] + sum3*ibdiag[12] + sum2*ibdiag[17] + sum1*ibdiag[22];
    3486:             x[row--] += sum5*ibdiag[1] + sum4*ibdiag[6] + sum3*ibdiag[11] + sum2*ibdiag[16] + sum1*ibdiag[21];
    3487:             x[row--] += sum5*ibdiag[0] + sum4*ibdiag[5] + sum3*ibdiag[10] + sum2*ibdiag[15] + sum1*ibdiag[20];
    3488:             break;
    3489:           case 4:
    3490:             x[row--] += sum4*ibdiag[3] + sum3*ibdiag[7] + sum2*ibdiag[11] + sum1*ibdiag[15];
    3491:             x[row--] += sum4*ibdiag[2] + sum3*ibdiag[6] + sum2*ibdiag[10] + sum1*ibdiag[14];
    3492:             x[row--] += sum4*ibdiag[1] + sum3*ibdiag[5] + sum2*ibdiag[9] + sum1*ibdiag[13];
    3493:             x[row--] += sum4*ibdiag[0] + sum3*ibdiag[4] + sum2*ibdiag[8] + sum1*ibdiag[12];
    3494:             break;
    3495:           case 3:
    3496:             x[row--] += sum3*ibdiag[2] + sum2*ibdiag[5] + sum1*ibdiag[8];
    3497:             x[row--] += sum3*ibdiag[1] + sum2*ibdiag[4] + sum1*ibdiag[7];
    3498:             x[row--] += sum3*ibdiag[0] + sum2*ibdiag[3] + sum1*ibdiag[6];
    3499:             break;
    3500:           case 2:
    3501:             x[row--] += sum2*ibdiag[1] + sum1*ibdiag[3];
    3502:             x[row--] += sum2*ibdiag[0] + sum1*ibdiag[2];
    3503:             break;
    3504:           case 1:
    3505:             x[row--] += sum1*(*ibdiag);
    3506:             break;
    3507:           }
    3508:         } else {
    3509:           /* no diag so set =  */
    3510:           switch (sizes[i]) {
    3511:           case 5:
    3512:             x[row--] = sum5*ibdiag[4] + sum4*ibdiag[9] + sum3*ibdiag[14] + sum2*ibdiag[19] + sum1*ibdiag[24];
    3513:             x[row--] = sum5*ibdiag[3] + sum4*ibdiag[8] + sum3*ibdiag[13] + sum2*ibdiag[18] + sum1*ibdiag[23];
    3514:             x[row--] = sum5*ibdiag[2] + sum4*ibdiag[7] + sum3*ibdiag[12] + sum2*ibdiag[17] + sum1*ibdiag[22];
    3515:             x[row--] = sum5*ibdiag[1] + sum4*ibdiag[6] + sum3*ibdiag[11] + sum2*ibdiag[16] + sum1*ibdiag[21];
    3516:             x[row--] = sum5*ibdiag[0] + sum4*ibdiag[5] + sum3*ibdiag[10] + sum2*ibdiag[15] + sum1*ibdiag[20];
    3517:             break;
    3518:           case 4:
    3519:             x[row--] = sum4*ibdiag[3] + sum3*ibdiag[7] + sum2*ibdiag[11] + sum1*ibdiag[15];
    3520:             x[row--] = sum4*ibdiag[2] + sum3*ibdiag[6] + sum2*ibdiag[10] + sum1*ibdiag[14];
    3521:             x[row--] = sum4*ibdiag[1] + sum3*ibdiag[5] + sum2*ibdiag[9] + sum1*ibdiag[13];
    3522:             x[row--] = sum4*ibdiag[0] + sum3*ibdiag[4] + sum2*ibdiag[8] + sum1*ibdiag[12];
    3523:             break;
    3524:           case 3:
    3525:             x[row--] = sum3*ibdiag[2] + sum2*ibdiag[5] + sum1*ibdiag[8];
    3526:             x[row--] = sum3*ibdiag[1] + sum2*ibdiag[4] + sum1*ibdiag[7];
    3527:             x[row--] = sum3*ibdiag[0] + sum2*ibdiag[3] + sum1*ibdiag[6];
    3528:             break;
    3529:           case 2:
    3530:             x[row--] = sum2*ibdiag[1] + sum1*ibdiag[3];
    3531:             x[row--] = sum2*ibdiag[0] + sum1*ibdiag[2];
    3532:             break;
    3533:           case 1:
    3534:             x[row--] = sum1*(*ibdiag);
    3535:             break;
    3536:           }
    3537:         }
    3538:       }
    3539:       if (xb == b) {
    3540:         PetscLogFlops(2.0*a->nz);
    3541:       } else {
    3542:         PetscLogFlops(a->nz); /* assumes 1/2 in upper, undercounts diag inverse */
    3543:       }
    3544:     }
    3545:   }
    3546:   if (flag & SOR_EISENSTAT) {
    3547:     /*
    3548:           Apply  (U + D)^-1  where D is now the block diagonal
    3549:     */
    3550:     ibdiag = a->inode.ibdiag+a->inode.bdiagsize;
    3551:     for (i=m-1, row=A->rmap->n-1; i>=0; i--) {
    3552:       ibdiag -= sizes[i]*sizes[i];
    3553:       sz      = ii[row+1] - diag[row] - 1;
    3554:       v1      = a->a + diag[row] + 1;
    3555:       idx     = a->j + diag[row] + 1;
    3556:       /* see comments for MatMult_SeqAIJ_Inode() for how this is coded */
    3557:       switch (sizes[i]) {
    3558:       case 1:

    3560:         sum1 = b[row];
    3561:         for (n = 0; n<sz-1; n+=2) {
    3562:           i1    = idx[0];
    3563:           i2    = idx[1];
    3564:           idx  += 2;
    3565:           tmp0  = x[i1];
    3566:           tmp1  = x[i2];
    3567:           sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    3568:         }

    3570:         if (n == sz-1) {
    3571:           tmp0  = x[*idx];
    3572:           sum1 -= *v1*tmp0;
    3573:         }
    3574:         x[row] = sum1*(*ibdiag);row--;
    3575:         break;

    3577:       case 2:

    3579:         sum1 = b[row];
    3580:         sum2 = b[row-1];
    3581:         /* note that sum1 is associated with the second of the two rows */
    3582:         v2 = a->a + diag[row-1] + 2;
    3583:         for (n = 0; n<sz-1; n+=2) {
    3584:           i1    = idx[0];
    3585:           i2    = idx[1];
    3586:           idx  += 2;
    3587:           tmp0  = x[i1];
    3588:           tmp1  = x[i2];
    3589:           sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    3590:           sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    3591:         }

    3593:         if (n == sz-1) {
    3594:           tmp0  = x[*idx];
    3595:           sum1 -= *v1*tmp0;
    3596:           sum2 -= *v2*tmp0;
    3597:         }
    3598:         x[row]   = sum2*ibdiag[1] + sum1*ibdiag[3];
    3599:         x[row-1] = sum2*ibdiag[0] + sum1*ibdiag[2];
    3600:         row     -= 2;
    3601:         break;
    3602:       case 3:

    3604:         sum1 = b[row];
    3605:         sum2 = b[row-1];
    3606:         sum3 = b[row-2];
    3607:         v2   = a->a + diag[row-1] + 2;
    3608:         v3   = a->a + diag[row-2] + 3;
    3609:         for (n = 0; n<sz-1; n+=2) {
    3610:           i1    = idx[0];
    3611:           i2    = idx[1];
    3612:           idx  += 2;
    3613:           tmp0  = x[i1];
    3614:           tmp1  = x[i2];
    3615:           sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    3616:           sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    3617:           sum3 -= v3[0] * tmp0 + v3[1] * tmp1; v3 += 2;
    3618:         }

    3620:         if (n == sz-1) {
    3621:           tmp0  = x[*idx];
    3622:           sum1 -= *v1*tmp0;
    3623:           sum2 -= *v2*tmp0;
    3624:           sum3 -= *v3*tmp0;
    3625:         }
    3626:         x[row]   = sum3*ibdiag[2] + sum2*ibdiag[5] + sum1*ibdiag[8];
    3627:         x[row-1] = sum3*ibdiag[1] + sum2*ibdiag[4] + sum1*ibdiag[7];
    3628:         x[row-2] = sum3*ibdiag[0] + sum2*ibdiag[3] + sum1*ibdiag[6];
    3629:         row     -= 3;
    3630:         break;
    3631:       case 4:

    3633:         sum1 = b[row];
    3634:         sum2 = b[row-1];
    3635:         sum3 = b[row-2];
    3636:         sum4 = b[row-3];
    3637:         v2   = a->a + diag[row-1] + 2;
    3638:         v3   = a->a + diag[row-2] + 3;
    3639:         v4   = a->a + diag[row-3] + 4;
    3640:         for (n = 0; n<sz-1; n+=2) {
    3641:           i1    = idx[0];
    3642:           i2    = idx[1];
    3643:           idx  += 2;
    3644:           tmp0  = x[i1];
    3645:           tmp1  = x[i2];
    3646:           sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    3647:           sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    3648:           sum3 -= v3[0] * tmp0 + v3[1] * tmp1; v3 += 2;
    3649:           sum4 -= v4[0] * tmp0 + v4[1] * tmp1; v4 += 2;
    3650:         }

    3652:         if (n == sz-1) {
    3653:           tmp0  = x[*idx];
    3654:           sum1 -= *v1*tmp0;
    3655:           sum2 -= *v2*tmp0;
    3656:           sum3 -= *v3*tmp0;
    3657:           sum4 -= *v4*tmp0;
    3658:         }
    3659:         x[row]   = sum4*ibdiag[3] + sum3*ibdiag[7] + sum2*ibdiag[11] + sum1*ibdiag[15];
    3660:         x[row-1] = sum4*ibdiag[2] + sum3*ibdiag[6] + sum2*ibdiag[10] + sum1*ibdiag[14];
    3661:         x[row-2] = sum4*ibdiag[1] + sum3*ibdiag[5] + sum2*ibdiag[9] + sum1*ibdiag[13];
    3662:         x[row-3] = sum4*ibdiag[0] + sum3*ibdiag[4] + sum2*ibdiag[8] + sum1*ibdiag[12];
    3663:         row     -= 4;
    3664:         break;
    3665:       case 5:

    3667:         sum1 = b[row];
    3668:         sum2 = b[row-1];
    3669:         sum3 = b[row-2];
    3670:         sum4 = b[row-3];
    3671:         sum5 = b[row-4];
    3672:         v2   = a->a + diag[row-1] + 2;
    3673:         v3   = a->a + diag[row-2] + 3;
    3674:         v4   = a->a + diag[row-3] + 4;
    3675:         v5   = a->a + diag[row-4] + 5;
    3676:         for (n = 0; n<sz-1; n+=2) {
    3677:           i1    = idx[0];
    3678:           i2    = idx[1];
    3679:           idx  += 2;
    3680:           tmp0  = x[i1];
    3681:           tmp1  = x[i2];
    3682:           sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    3683:           sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    3684:           sum3 -= v3[0] * tmp0 + v3[1] * tmp1; v3 += 2;
    3685:           sum4 -= v4[0] * tmp0 + v4[1] * tmp1; v4 += 2;
    3686:           sum5 -= v5[0] * tmp0 + v5[1] * tmp1; v5 += 2;
    3687:         }

    3689:         if (n == sz-1) {
    3690:           tmp0  = x[*idx];
    3691:           sum1 -= *v1*tmp0;
    3692:           sum2 -= *v2*tmp0;
    3693:           sum3 -= *v3*tmp0;
    3694:           sum4 -= *v4*tmp0;
    3695:           sum5 -= *v5*tmp0;
    3696:         }
    3697:         x[row]   = sum5*ibdiag[4] + sum4*ibdiag[9] + sum3*ibdiag[14] + sum2*ibdiag[19] + sum1*ibdiag[24];
    3698:         x[row-1] = sum5*ibdiag[3] + sum4*ibdiag[8] + sum3*ibdiag[13] + sum2*ibdiag[18] + sum1*ibdiag[23];
    3699:         x[row-2] = sum5*ibdiag[2] + sum4*ibdiag[7] + sum3*ibdiag[12] + sum2*ibdiag[17] + sum1*ibdiag[22];
    3700:         x[row-3] = sum5*ibdiag[1] + sum4*ibdiag[6] + sum3*ibdiag[11] + sum2*ibdiag[16] + sum1*ibdiag[21];
    3701:         x[row-4] = sum5*ibdiag[0] + sum4*ibdiag[5] + sum3*ibdiag[10] + sum2*ibdiag[15] + sum1*ibdiag[20];
    3702:         row     -= 5;
    3703:         break;
    3704:       default:
    3705:         SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Inode size %" PetscInt_FMT " not supported",sizes[i]);
    3706:       }
    3707:     }
    3708:     PetscLogFlops(a->nz);

    3710:     /*
    3711:            t = b - D x    where D is the block diagonal
    3712:     */
    3713:     cnt = 0;
    3714:     for (i=0, row=0; i<m; i++) {
    3715:       switch (sizes[i]) {
    3716:       case 1:
    3717:         t[row] = b[row] - bdiag[cnt++]*x[row]; row++;
    3718:         break;
    3719:       case 2:
    3720:         x1       = x[row]; x2 = x[row+1];
    3721:         tmp1     = x1*bdiag[cnt] + x2*bdiag[cnt+2];
    3722:         tmp2     = x1*bdiag[cnt+1] + x2*bdiag[cnt+3];
    3723:         t[row]   = b[row] - tmp1;
    3724:         t[row+1] = b[row+1] - tmp2; row += 2;
    3725:         cnt     += 4;
    3726:         break;
    3727:       case 3:
    3728:         x1       = x[row]; x2 = x[row+1]; x3 = x[row+2];
    3729:         tmp1     = x1*bdiag[cnt] + x2*bdiag[cnt+3] + x3*bdiag[cnt+6];
    3730:         tmp2     = x1*bdiag[cnt+1] + x2*bdiag[cnt+4] + x3*bdiag[cnt+7];
    3731:         tmp3     = x1*bdiag[cnt+2] + x2*bdiag[cnt+5] + x3*bdiag[cnt+8];
    3732:         t[row]   = b[row] - tmp1;
    3733:         t[row+1] = b[row+1] - tmp2;
    3734:         t[row+2] = b[row+2] - tmp3; row += 3;
    3735:         cnt     += 9;
    3736:         break;
    3737:       case 4:
    3738:         x1       = x[row]; x2 = x[row+1]; x3 = x[row+2]; x4 = x[row+3];
    3739:         tmp1     = x1*bdiag[cnt] + x2*bdiag[cnt+4] + x3*bdiag[cnt+8] + x4*bdiag[cnt+12];
    3740:         tmp2     = x1*bdiag[cnt+1] + x2*bdiag[cnt+5] + x3*bdiag[cnt+9] + x4*bdiag[cnt+13];
    3741:         tmp3     = x1*bdiag[cnt+2] + x2*bdiag[cnt+6] + x3*bdiag[cnt+10] + x4*bdiag[cnt+14];
    3742:         tmp4     = x1*bdiag[cnt+3] + x2*bdiag[cnt+7] + x3*bdiag[cnt+11] + x4*bdiag[cnt+15];
    3743:         t[row]   = b[row] - tmp1;
    3744:         t[row+1] = b[row+1] - tmp2;
    3745:         t[row+2] = b[row+2] - tmp3;
    3746:         t[row+3] = b[row+3] - tmp4; row += 4;
    3747:         cnt     += 16;
    3748:         break;
    3749:       case 5:
    3750:         x1       = x[row]; x2 = x[row+1]; x3 = x[row+2]; x4 = x[row+3]; x5 = x[row+4];
    3751:         tmp1     = x1*bdiag[cnt] + x2*bdiag[cnt+5] + x3*bdiag[cnt+10] + x4*bdiag[cnt+15] + x5*bdiag[cnt+20];
    3752:         tmp2     = x1*bdiag[cnt+1] + x2*bdiag[cnt+6] + x3*bdiag[cnt+11] + x4*bdiag[cnt+16] + x5*bdiag[cnt+21];
    3753:         tmp3     = x1*bdiag[cnt+2] + x2*bdiag[cnt+7] + x3*bdiag[cnt+12] + x4*bdiag[cnt+17] + x5*bdiag[cnt+22];
    3754:         tmp4     = x1*bdiag[cnt+3] + x2*bdiag[cnt+8] + x3*bdiag[cnt+13] + x4*bdiag[cnt+18] + x5*bdiag[cnt+23];
    3755:         tmp5     = x1*bdiag[cnt+4] + x2*bdiag[cnt+9] + x3*bdiag[cnt+14] + x4*bdiag[cnt+19] + x5*bdiag[cnt+24];
    3756:         t[row]   = b[row] - tmp1;
    3757:         t[row+1] = b[row+1] - tmp2;
    3758:         t[row+2] = b[row+2] - tmp3;
    3759:         t[row+3] = b[row+3] - tmp4;
    3760:         t[row+4] = b[row+4] - tmp5;row += 5;
    3761:         cnt     += 25;
    3762:         break;
    3763:       default:
    3764:         SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Inode size %" PetscInt_FMT " not supported",sizes[i]);
    3765:       }
    3766:     }
    3767:     PetscLogFlops(m);

    3769:     /*
    3770:           Apply (L + D)^-1 where D is the block diagonal
    3771:     */
    3772:     for (i=0, row=0; i<m; i++) {
    3773:       sz  = diag[row] - ii[row];
    3774:       v1  = a->a + ii[row];
    3775:       idx = a->j + ii[row];
    3776:       /* see comments for MatMult_SeqAIJ_Inode() for how this is coded */
    3777:       switch (sizes[i]) {
    3778:       case 1:

    3780:         sum1 = t[row];
    3781:         for (n = 0; n<sz-1; n+=2) {
    3782:           i1    = idx[0];
    3783:           i2    = idx[1];
    3784:           idx  += 2;
    3785:           tmp0  = t[i1];
    3786:           tmp1  = t[i2];
    3787:           sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    3788:         }

    3790:         if (n == sz-1) {
    3791:           tmp0  = t[*idx];
    3792:           sum1 -= *v1 * tmp0;
    3793:         }
    3794:         x[row] += t[row] = sum1*(*ibdiag++); row++;
    3795:         break;
    3796:       case 2:
    3797:         v2   = a->a + ii[row+1];
    3798:         sum1 = t[row];
    3799:         sum2 = t[row+1];
    3800:         for (n = 0; n<sz-1; n+=2) {
    3801:           i1    = idx[0];
    3802:           i2    = idx[1];
    3803:           idx  += 2;
    3804:           tmp0  = t[i1];
    3805:           tmp1  = t[i2];
    3806:           sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    3807:           sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    3808:         }

    3810:         if (n == sz-1) {
    3811:           tmp0  = t[*idx];
    3812:           sum1 -= v1[0] * tmp0;
    3813:           sum2 -= v2[0] * tmp0;
    3814:         }
    3815:         x[row]   += t[row] = sum1*ibdiag[0] + sum2*ibdiag[2];
    3816:         x[row+1] += t[row+1] = sum1*ibdiag[1] + sum2*ibdiag[3];
    3817:         ibdiag   += 4; row += 2;
    3818:         break;
    3819:       case 3:
    3820:         v2   = a->a + ii[row+1];
    3821:         v3   = a->a + ii[row+2];
    3822:         sum1 = t[row];
    3823:         sum2 = t[row+1];
    3824:         sum3 = t[row+2];
    3825:         for (n = 0; n<sz-1; n+=2) {
    3826:           i1    = idx[0];
    3827:           i2    = idx[1];
    3828:           idx  += 2;
    3829:           tmp0  = t[i1];
    3830:           tmp1  = t[i2];
    3831:           sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    3832:           sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    3833:           sum3 -= v3[0] * tmp0 + v3[1] * tmp1; v3 += 2;
    3834:         }

    3836:         if (n == sz-1) {
    3837:           tmp0  = t[*idx];
    3838:           sum1 -= v1[0] * tmp0;
    3839:           sum2 -= v2[0] * tmp0;
    3840:           sum3 -= v3[0] * tmp0;
    3841:         }
    3842:         x[row]   += t[row] = sum1*ibdiag[0] + sum2*ibdiag[3] + sum3*ibdiag[6];
    3843:         x[row+1] += t[row+1] = sum1*ibdiag[1] + sum2*ibdiag[4] + sum3*ibdiag[7];
    3844:         x[row+2] += t[row+2] = sum1*ibdiag[2] + sum2*ibdiag[5] + sum3*ibdiag[8];
    3845:         ibdiag   += 9; row += 3;
    3846:         break;
    3847:       case 4:
    3848:         v2   = a->a + ii[row+1];
    3849:         v3   = a->a + ii[row+2];
    3850:         v4   = a->a + ii[row+3];
    3851:         sum1 = t[row];
    3852:         sum2 = t[row+1];
    3853:         sum3 = t[row+2];
    3854:         sum4 = t[row+3];
    3855:         for (n = 0; n<sz-1; n+=2) {
    3856:           i1    = idx[0];
    3857:           i2    = idx[1];
    3858:           idx  += 2;
    3859:           tmp0  = t[i1];
    3860:           tmp1  = t[i2];
    3861:           sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    3862:           sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    3863:           sum3 -= v3[0] * tmp0 + v3[1] * tmp1; v3 += 2;
    3864:           sum4 -= v4[0] * tmp0 + v4[1] * tmp1; v4 += 2;
    3865:         }

    3867:         if (n == sz-1) {
    3868:           tmp0  = t[*idx];
    3869:           sum1 -= v1[0] * tmp0;
    3870:           sum2 -= v2[0] * tmp0;
    3871:           sum3 -= v3[0] * tmp0;
    3872:           sum4 -= v4[0] * tmp0;
    3873:         }
    3874:         x[row]   += t[row] = sum1*ibdiag[0] + sum2*ibdiag[4] + sum3*ibdiag[8] + sum4*ibdiag[12];
    3875:         x[row+1] += t[row+1] = sum1*ibdiag[1] + sum2*ibdiag[5] + sum3*ibdiag[9] + sum4*ibdiag[13];
    3876:         x[row+2] += t[row+2] = sum1*ibdiag[2] + sum2*ibdiag[6] + sum3*ibdiag[10] + sum4*ibdiag[14];
    3877:         x[row+3] += t[row+3] = sum1*ibdiag[3] + sum2*ibdiag[7] + sum3*ibdiag[11] + sum4*ibdiag[15];
    3878:         ibdiag   += 16; row += 4;
    3879:         break;
    3880:       case 5:
    3881:         v2   = a->a + ii[row+1];
    3882:         v3   = a->a + ii[row+2];
    3883:         v4   = a->a + ii[row+3];
    3884:         v5   = a->a + ii[row+4];
    3885:         sum1 = t[row];
    3886:         sum2 = t[row+1];
    3887:         sum3 = t[row+2];
    3888:         sum4 = t[row+3];
    3889:         sum5 = t[row+4];
    3890:         for (n = 0; n<sz-1; n+=2) {
    3891:           i1    = idx[0];
    3892:           i2    = idx[1];
    3893:           idx  += 2;
    3894:           tmp0  = t[i1];
    3895:           tmp1  = t[i2];
    3896:           sum1 -= v1[0] * tmp0 + v1[1] * tmp1; v1 += 2;
    3897:           sum2 -= v2[0] * tmp0 + v2[1] * tmp1; v2 += 2;
    3898:           sum3 -= v3[0] * tmp0 + v3[1] * tmp1; v3 += 2;
    3899:           sum4 -= v4[0] * tmp0 + v4[1] * tmp1; v4 += 2;
    3900:           sum5 -= v5[0] * tmp0 + v5[1] * tmp1; v5 += 2;
    3901:         }

    3903:         if (n == sz-1) {
    3904:           tmp0  = t[*idx];
    3905:           sum1 -= v1[0] * tmp0;
    3906:           sum2 -= v2[0] * tmp0;
    3907:           sum3 -= v3[0] * tmp0;
    3908:           sum4 -= v4[0] * tmp0;
    3909:           sum5 -= v5[0] * tmp0;
    3910:         }
    3911:         x[row]   += t[row] = sum1*ibdiag[0] + sum2*ibdiag[5] + sum3*ibdiag[10] + sum4*ibdiag[15] + sum5*ibdiag[20];
    3912:         x[row+1] += t[row+1] = sum1*ibdiag[1] + sum2*ibdiag[6] + sum3*ibdiag[11] + sum4*ibdiag[16] + sum5*ibdiag[21];
    3913:         x[row+2] += t[row+2] = sum1*ibdiag[2] + sum2*ibdiag[7] + sum3*ibdiag[12] + sum4*ibdiag[17] + sum5*ibdiag[22];
    3914:         x[row+3] += t[row+3] = sum1*ibdiag[3] + sum2*ibdiag[8] + sum3*ibdiag[13] + sum4*ibdiag[18] + sum5*ibdiag[23];
    3915:         x[row+4] += t[row+4] = sum1*ibdiag[4] + sum2*ibdiag[9] + sum3*ibdiag[14] + sum4*ibdiag[19] + sum5*ibdiag[24];
    3916:         ibdiag   += 25; row += 5;
    3917:         break;
    3918:       default:
    3919:         SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Inode size %" PetscInt_FMT " not supported",sizes[i]);
    3920:       }
    3921:     }
    3922:     PetscLogFlops(a->nz);
    3923:   }
    3924:   VecRestoreArray(xx,&x);
    3925:   VecRestoreArrayRead(bb,&b);
    3926:   return 0;
    3927: }

    3929: PetscErrorCode MatMultDiagonalBlock_SeqAIJ_Inode(Mat A,Vec bb,Vec xx)
    3930: {
    3931:   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
    3932:   PetscScalar       *x,tmp1,tmp2,tmp3,tmp4,tmp5,x1,x2,x3,x4,x5;
    3933:   const MatScalar   *bdiag = a->inode.bdiag;
    3934:   const PetscScalar *b;
    3935:   PetscInt          m      = a->inode.node_count,cnt = 0,i,row;
    3936:   const PetscInt    *sizes = a->inode.size;

    3939:   VecGetArray(xx,&x);
    3940:   VecGetArrayRead(bb,&b);
    3941:   cnt  = 0;
    3942:   for (i=0, row=0; i<m; i++) {
    3943:     switch (sizes[i]) {
    3944:     case 1:
    3945:       x[row] = b[row]*bdiag[cnt++];row++;
    3946:       break;
    3947:     case 2:
    3948:       x1       = b[row]; x2 = b[row+1];
    3949:       tmp1     = x1*bdiag[cnt] + x2*bdiag[cnt+2];
    3950:       tmp2     = x1*bdiag[cnt+1] + x2*bdiag[cnt+3];
    3951:       x[row++] = tmp1;
    3952:       x[row++] = tmp2;
    3953:       cnt     += 4;
    3954:       break;
    3955:     case 3:
    3956:       x1       = b[row]; x2 = b[row+1]; x3 = b[row+2];
    3957:       tmp1     = x1*bdiag[cnt] + x2*bdiag[cnt+3] + x3*bdiag[cnt+6];
    3958:       tmp2     = x1*bdiag[cnt+1] + x2*bdiag[cnt+4] + x3*bdiag[cnt+7];
    3959:       tmp3     = x1*bdiag[cnt+2] + x2*bdiag[cnt+5] + x3*bdiag[cnt+8];
    3960:       x[row++] = tmp1;
    3961:       x[row++] = tmp2;
    3962:       x[row++] = tmp3;
    3963:       cnt     += 9;
    3964:       break;
    3965:     case 4:
    3966:       x1       = b[row]; x2 = b[row+1]; x3 = b[row+2]; x4 = b[row+3];
    3967:       tmp1     = x1*bdiag[cnt] + x2*bdiag[cnt+4] + x3*bdiag[cnt+8] + x4*bdiag[cnt+12];
    3968:       tmp2     = x1*bdiag[cnt+1] + x2*bdiag[cnt+5] + x3*bdiag[cnt+9] + x4*bdiag[cnt+13];
    3969:       tmp3     = x1*bdiag[cnt+2] + x2*bdiag[cnt+6] + x3*bdiag[cnt+10] + x4*bdiag[cnt+14];
    3970:       tmp4     = x1*bdiag[cnt+3] + x2*bdiag[cnt+7] + x3*bdiag[cnt+11] + x4*bdiag[cnt+15];
    3971:       x[row++] = tmp1;
    3972:       x[row++] = tmp2;
    3973:       x[row++] = tmp3;
    3974:       x[row++] = tmp4;
    3975:       cnt     += 16;
    3976:       break;
    3977:     case 5:
    3978:       x1       = b[row]; x2 = b[row+1]; x3 = b[row+2]; x4 = b[row+3]; x5 = b[row+4];
    3979:       tmp1     = x1*bdiag[cnt] + x2*bdiag[cnt+5] + x3*bdiag[cnt+10] + x4*bdiag[cnt+15] + x5*bdiag[cnt+20];
    3980:       tmp2     = x1*bdiag[cnt+1] + x2*bdiag[cnt+6] + x3*bdiag[cnt+11] + x4*bdiag[cnt+16] + x5*bdiag[cnt+21];
    3981:       tmp3     = x1*bdiag[cnt+2] + x2*bdiag[cnt+7] + x3*bdiag[cnt+12] + x4*bdiag[cnt+17] + x5*bdiag[cnt+22];
    3982:       tmp4     = x1*bdiag[cnt+3] + x2*bdiag[cnt+8] + x3*bdiag[cnt+13] + x4*bdiag[cnt+18] + x5*bdiag[cnt+23];
    3983:       tmp5     = x1*bdiag[cnt+4] + x2*bdiag[cnt+9] + x3*bdiag[cnt+14] + x4*bdiag[cnt+19] + x5*bdiag[cnt+24];
    3984:       x[row++] = tmp1;
    3985:       x[row++] = tmp2;
    3986:       x[row++] = tmp3;
    3987:       x[row++] = tmp4;
    3988:       x[row++] = tmp5;
    3989:       cnt     += 25;
    3990:       break;
    3991:     default:
    3992:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Inode size %" PetscInt_FMT " not supported",sizes[i]);
    3993:     }
    3994:   }
    3995:   PetscLogFlops(2.0*cnt);
    3996:   VecRestoreArray(xx,&x);
    3997:   VecRestoreArrayRead(bb,&b);
    3998:   return 0;
    3999: }

    4001: static PetscErrorCode MatSeqAIJ_Inode_ResetOps(Mat A)
    4002: {
    4003:   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;

    4005:   a->inode.node_count       = 0;
    4006:   a->inode.use              = PETSC_FALSE;
    4007:   a->inode.checked          = PETSC_FALSE;
    4008:   a->inode.mat_nonzerostate = -1;
    4009:   A->ops->getrowij          = MatGetRowIJ_SeqAIJ;
    4010:   A->ops->restorerowij      = MatRestoreRowIJ_SeqAIJ;
    4011:   A->ops->getcolumnij       = MatGetColumnIJ_SeqAIJ;
    4012:   A->ops->restorecolumnij   = MatRestoreColumnIJ_SeqAIJ;
    4013:   A->ops->coloringpatch     = NULL;
    4014:   A->ops->multdiagonalblock = NULL;
    4015:   if (A->factortype) {
    4016:     A->ops->solve = MatSolve_SeqAIJ_inplace;
    4017:   }
    4018:   return 0;
    4019: }

    4021: /*
    4022:     samestructure indicates that the matrix has not changed its nonzero structure so we
    4023:     do not need to recompute the inodes
    4024: */
    4025: PetscErrorCode MatSeqAIJCheckInode(Mat A)
    4026: {
    4027:   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
    4028:   PetscInt       i,j,m,nzx,nzy,*ns,node_count,blk_size;
    4029:   PetscBool      flag;
    4030:   const PetscInt *idx,*idy,*ii;

    4032:   if (!a->inode.use) {
    4033:     MatSeqAIJ_Inode_ResetOps(A);
    4034:     PetscFree(a->inode.size);
    4035:     return 0;
    4036:   }
    4037:   if (a->inode.checked && A->nonzerostate == a->inode.mat_nonzerostate) return 0;

    4039:   m = A->rmap->n;
    4040:   if (!a->inode.size) PetscMalloc1(m+1,&a->inode.size);
    4041:   ns = a->inode.size;

    4043:   i          = 0;
    4044:   node_count = 0;
    4045:   idx        = a->j;
    4046:   ii         = a->i;
    4047:   while (i < m) {                /* For each row */
    4048:     nzx = ii[i+1] - ii[i];       /* Number of nonzeros */
    4049:     /* Limits the number of elements in a node to 'a->inode.limit' */
    4050:     for (j=i+1,idy=idx,blk_size=1; j<m && blk_size <a->inode.limit; ++j,++blk_size) {
    4051:       nzy = ii[j+1] - ii[j];     /* Same number of nonzeros */
    4052:       if (nzy != nzx) break;
    4053:       idy += nzx;              /* Same nonzero pattern */
    4054:       PetscArraycmp(idx,idy,nzx,&flag);
    4055:       if (!flag) break;
    4056:     }
    4057:     ns[node_count++] = blk_size;
    4058:     idx             += blk_size*nzx;
    4059:     i                = j;
    4060:   }

    4062:   /* If not enough inodes found,, do not use inode version of the routines */
    4063:   if (!m || node_count > .8*m) {
    4064:     MatSeqAIJ_Inode_ResetOps(A);
    4065:     PetscFree(a->inode.size);
    4066:     PetscInfo(A,"Found %" PetscInt_FMT " nodes out of %" PetscInt_FMT " rows. Not using Inode routines\n",node_count,m);
    4067:   } else {
    4068:     if (!A->factortype) {
    4069:       A->ops->multdiagonalblock = MatMultDiagonalBlock_SeqAIJ_Inode;
    4070:       if (A->rmap->n == A->cmap->n) {
    4071:         A->ops->getrowij        = MatGetRowIJ_SeqAIJ_Inode;
    4072:         A->ops->restorerowij    = MatRestoreRowIJ_SeqAIJ_Inode;
    4073:         A->ops->getcolumnij     = MatGetColumnIJ_SeqAIJ_Inode;
    4074:         A->ops->restorecolumnij = MatRestoreColumnIJ_SeqAIJ_Inode;
    4075:         A->ops->coloringpatch   = MatColoringPatch_SeqAIJ_Inode;
    4076:       }
    4077:     } else {
    4078:       A->ops->solve = MatSolve_SeqAIJ_Inode_inplace;
    4079:     }
    4080:     a->inode.node_count = node_count;
    4081:     PetscInfo(A,"Found %" PetscInt_FMT " nodes of %" PetscInt_FMT ". Limit used: %" PetscInt_FMT ". Using Inode routines\n",node_count,m,a->inode.limit);
    4082:   }
    4083:   a->inode.checked          = PETSC_TRUE;
    4084:   a->inode.mat_nonzerostate = A->nonzerostate;
    4085:   return 0;
    4086: }

    4088: PetscErrorCode MatDuplicate_SeqAIJ_Inode(Mat A,MatDuplicateOption cpvalues,Mat *C)
    4089: {
    4090:   Mat            B =*C;
    4091:   Mat_SeqAIJ     *c=(Mat_SeqAIJ*)B->data,*a=(Mat_SeqAIJ*)A->data;
    4092:   PetscInt       m=A->rmap->n;

    4094:   c->inode.use              = a->inode.use;
    4095:   c->inode.limit            = a->inode.limit;
    4096:   c->inode.max_limit        = a->inode.max_limit;
    4097:   c->inode.checked          = PETSC_FALSE;
    4098:   c->inode.size             = NULL;
    4099:   c->inode.node_count       = 0;
    4100:   c->inode.ibdiagvalid      = PETSC_FALSE;
    4101:   c->inode.ibdiag           = NULL;
    4102:   c->inode.bdiag            = NULL;
    4103:   c->inode.mat_nonzerostate = -1;
    4104:   if (a->inode.use) {
    4105:     if (a->inode.checked && a->inode.size) {
    4106:       PetscMalloc1(m+1,&c->inode.size);
    4107:       PetscArraycpy(c->inode.size,a->inode.size,m+1);

    4109:       c->inode.checked          = PETSC_TRUE;
    4110:       c->inode.node_count       = a->inode.node_count;
    4111:       c->inode.mat_nonzerostate = (*C)->nonzerostate;
    4112:     }
    4113:     /* note the table of functions below should match that in MatSeqAIJCheckInode() */
    4114:     if (!B->factortype) {
    4115:       B->ops->getrowij          = MatGetRowIJ_SeqAIJ_Inode;
    4116:       B->ops->restorerowij      = MatRestoreRowIJ_SeqAIJ_Inode;
    4117:       B->ops->getcolumnij       = MatGetColumnIJ_SeqAIJ_Inode;
    4118:       B->ops->restorecolumnij   = MatRestoreColumnIJ_SeqAIJ_Inode;
    4119:       B->ops->coloringpatch     = MatColoringPatch_SeqAIJ_Inode;
    4120:       B->ops->multdiagonalblock = MatMultDiagonalBlock_SeqAIJ_Inode;
    4121:     } else {
    4122:       B->ops->solve = MatSolve_SeqAIJ_Inode_inplace;
    4123:     }
    4124:   }
    4125:   return 0;
    4126: }

    4128: static inline PetscErrorCode MatGetRow_FactoredLU(PetscInt *cols,PetscInt nzl,PetscInt nzu,PetscInt nz,const PetscInt *ai,const PetscInt *aj,const PetscInt *adiag,PetscInt row)
    4129: {
    4130:   PetscInt       k;
    4131:   const PetscInt *vi;

    4133:   vi = aj + ai[row];
    4134:   for (k=0; k<nzl; k++) cols[k] = vi[k];
    4135:   vi        = aj + adiag[row];
    4136:   cols[nzl] = vi[0];
    4137:   vi        = aj + adiag[row+1]+1;
    4138:   for (k=0; k<nzu; k++) cols[nzl+1+k] = vi[k];
    4139:   return 0;
    4140: }
    4141: /*
    4142:    MatSeqAIJCheckInode_FactorLU - Check Inode for factored seqaij matrix.
    4143:    Modified from MatSeqAIJCheckInode().

    4145:    Input Parameters:
    4146: .  Mat A - ILU or LU matrix factor

    4148: */
    4149: PetscErrorCode MatSeqAIJCheckInode_FactorLU(Mat A)
    4150: {
    4151:   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
    4152:   PetscInt       i,j,m,nzl1,nzu1,nzl2,nzu2,nzx,nzy,node_count,blk_size;
    4153:   PetscInt       *cols1,*cols2,*ns;
    4154:   const PetscInt *ai = a->i,*aj = a->j, *adiag = a->diag;
    4155:   PetscBool      flag;

    4157:   if (!a->inode.use)    return 0;
    4158:   if (a->inode.checked) return 0;

    4160:   m = A->rmap->n;
    4161:   if (a->inode.size) ns = a->inode.size;
    4162:   else {
    4163:     PetscMalloc1(m+1,&ns);
    4164:   }

    4166:   i          = 0;
    4167:   node_count = 0;
    4168:   PetscMalloc2(m,&cols1,m,&cols2);
    4169:   while (i < m) {                /* For each row */
    4170:     nzl1 = ai[i+1] - ai[i];       /* Number of nonzeros in L */
    4171:     nzu1 = adiag[i] - adiag[i+1] - 1; /* Number of nonzeros in U excluding diagonal*/
    4172:     nzx  = nzl1 + nzu1 + 1;
    4173:     MatGetRow_FactoredLU(cols1,nzl1,nzu1,nzx,ai,aj,adiag,i);

    4175:     /* Limits the number of elements in a node to 'a->inode.limit' */
    4176:     for (j=i+1,blk_size=1; j<m && blk_size <a->inode.limit; ++j,++blk_size) {
    4177:       nzl2 = ai[j+1] - ai[j];
    4178:       nzu2 = adiag[j] - adiag[j+1] - 1;
    4179:       nzy  = nzl2 + nzu2 + 1;
    4180:       if (nzy != nzx) break;
    4181:       MatGetRow_FactoredLU(cols2,nzl2,nzu2,nzy,ai,aj,adiag,j);
    4182:       PetscArraycmp(cols1,cols2,nzx,&flag);
    4183:       if (!flag) break;
    4184:     }
    4185:     ns[node_count++] = blk_size;
    4186:     i                = j;
    4187:   }
    4188:   PetscFree2(cols1,cols2);
    4189:   /* If not enough inodes found,, do not use inode version of the routines */
    4190:   if (!m || node_count > .8*m) {
    4191:     PetscFree(ns);

    4193:     a->inode.node_count = 0;
    4194:     a->inode.size       = NULL;
    4195:     a->inode.use        = PETSC_FALSE;

    4197:     PetscInfo(A,"Found %" PetscInt_FMT " nodes out of %" PetscInt_FMT " rows. Not using Inode routines\n",node_count,m);
    4198:   } else {
    4199:     A->ops->mult              = NULL;
    4200:     A->ops->sor               = NULL;
    4201:     A->ops->multadd           = NULL;
    4202:     A->ops->getrowij          = NULL;
    4203:     A->ops->restorerowij      = NULL;
    4204:     A->ops->getcolumnij       = NULL;
    4205:     A->ops->restorecolumnij   = NULL;
    4206:     A->ops->coloringpatch     = NULL;
    4207:     A->ops->multdiagonalblock = NULL;
    4208:     a->inode.node_count       = node_count;
    4209:     a->inode.size             = ns;

    4211:     PetscInfo(A,"Found %" PetscInt_FMT " nodes of %" PetscInt_FMT ". Limit used: %" PetscInt_FMT ". Using Inode routines\n",node_count,m,a->inode.limit);
    4212:   }
    4213:   a->inode.checked = PETSC_TRUE;
    4214:   return 0;
    4215: }

    4217: PetscErrorCode MatSeqAIJInvalidateDiagonal_Inode(Mat A)
    4218: {
    4219:   Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data;

    4221:   a->inode.ibdiagvalid = PETSC_FALSE;
    4222:   return 0;
    4223: }

    4225: /*
    4226:      This is really ugly. if inodes are used this replaces the
    4227:   permutations with ones that correspond to rows/cols of the matrix
    4228:   rather then inode blocks
    4229: */
    4230: PetscErrorCode  MatInodeAdjustForInodes(Mat A,IS *rperm,IS *cperm)
    4231: {
    4232:   PetscTryMethod(A,"MatInodeAdjustForInodes_C",(Mat,IS*,IS*),(A,rperm,cperm));
    4233:   return 0;
    4234: }

    4236: PetscErrorCode  MatInodeAdjustForInodes_SeqAIJ_Inode(Mat A,IS *rperm,IS *cperm)
    4237: {
    4238:   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
    4239:   PetscInt       m = A->rmap->n,n = A->cmap->n,i,j,nslim_row = a->inode.node_count;
    4240:   const PetscInt *ridx,*cidx;
    4241:   PetscInt       row,col,*permr,*permc,*ns_row =  a->inode.size,*tns,start_val,end_val,indx;
    4242:   PetscInt       nslim_col,*ns_col;
    4243:   IS             ris = *rperm,cis = *cperm;

    4245:   if (!a->inode.size) return 0; /* no inodes so return */
    4246:   if (a->inode.node_count == m) return 0; /* all inodes are of size 1 */

    4248:   MatCreateColInode_Private(A,&nslim_col,&ns_col);
    4249:   PetscMalloc1(((nslim_row>nslim_col) ? nslim_row : nslim_col)+1,&tns);
    4250:   PetscMalloc2(m,&permr,n,&permc);

    4252:   ISGetIndices(ris,&ridx);
    4253:   ISGetIndices(cis,&cidx);

    4255:   /* Form the inode structure for the rows of permuted matric using inv perm*/
    4256:   for (i=0,tns[0]=0; i<nslim_row; ++i) tns[i+1] = tns[i] + ns_row[i];

    4258:   /* Construct the permutations for rows*/
    4259:   for (i=0,row = 0; i<nslim_row; ++i) {
    4260:     indx      = ridx[i];
    4261:     start_val = tns[indx];
    4262:     end_val   = tns[indx + 1];
    4263:     for (j=start_val; j<end_val; ++j,++row) permr[row]= j;
    4264:   }

    4266:   /* Form the inode structure for the columns of permuted matrix using inv perm*/
    4267:   for (i=0,tns[0]=0; i<nslim_col; ++i) tns[i+1] = tns[i] + ns_col[i];

    4269:   /* Construct permutations for columns */
    4270:   for (i=0,col=0; i<nslim_col; ++i) {
    4271:     indx      = cidx[i];
    4272:     start_val = tns[indx];
    4273:     end_val   = tns[indx + 1];
    4274:     for (j = start_val; j<end_val; ++j,++col) permc[col]= j;
    4275:   }

    4277:   ISCreateGeneral(PETSC_COMM_SELF,n,permr,PETSC_COPY_VALUES,rperm);
    4278:   ISSetPermutation(*rperm);
    4279:   ISCreateGeneral(PETSC_COMM_SELF,n,permc,PETSC_COPY_VALUES,cperm);
    4280:   ISSetPermutation(*cperm);

    4282:   ISRestoreIndices(ris,&ridx);
    4283:   ISRestoreIndices(cis,&cidx);

    4285:   PetscFree(ns_col);
    4286:   PetscFree2(permr,permc);
    4287:   ISDestroy(&cis);
    4288:   ISDestroy(&ris);
    4289:   PetscFree(tns);
    4290:   return 0;
    4291: }

    4293: /*@C
    4294:    MatInodeGetInodeSizes - Returns the inode information of the Inode matrix.

    4296:    Not Collective

    4298:    Input Parameter:
    4299: .  A - the Inode matrix or matrix derived from the Inode class -- e.g., SeqAIJ

    4301:    Output Parameters:
    4302: +  node_count - no of inodes present in the matrix.
    4303: .  sizes      - an array of size node_count,with sizes of each inode.
    4304: -  limit      - the max size used to generate the inodes.

    4306:    Level: advanced

    4308:    Notes:
    4309:     This routine returns some internal storage information
    4310:    of the matrix, it is intended to be used by advanced users.
    4311:    It should be called after the matrix is assembled.
    4312:    The contents of the sizes[] array should not be changed.
    4313:    NULL may be passed for information not requested.

    4315: .seealso: MatGetInfo()
    4316: @*/
    4317: PetscErrorCode  MatInodeGetInodeSizes(Mat A,PetscInt *node_count,PetscInt *sizes[],PetscInt *limit)
    4318: {
    4319:   PetscErrorCode (*f)(Mat,PetscInt*,PetscInt**,PetscInt*);

    4322:   PetscObjectQueryFunction((PetscObject)A,"MatInodeGetInodeSizes_C",&f);
    4323:   if (f) (*f)(A,node_count,sizes,limit);
    4324:   return 0;
    4325: }

    4327: PetscErrorCode  MatInodeGetInodeSizes_SeqAIJ_Inode(Mat A,PetscInt *node_count,PetscInt *sizes[],PetscInt *limit)
    4328: {
    4329:   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;

    4331:   if (node_count) *node_count = a->inode.node_count;
    4332:   if (sizes)      *sizes      = a->inode.size;
    4333:   if (limit)      *limit      = a->inode.limit;
    4334:   return 0;
    4335: }