Date: 2013-07-02T14:42:44+00:00

Actual source code: baijfact13.c
petsc-3.4.2 2013-07-02

      2: /*
      3:     Factorization code for BAIJ format.
      4: */
      5: #include <../src/mat/impls/baij/seq/baij.h>
      6: #include <petsc-private/kernels/blockinvert.h>

      8: /*
      9:       Version for when blocks are 3 by 3
     10: */
     13: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_inplace(Mat C,Mat A,const MatFactorInfo *info)
     14: {
     15:   Mat_SeqBAIJ    *a    = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
     16:   IS             isrow = b->row,isicol = b->icol;
     18:   const PetscInt *r,*ic;
     19:   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
     20:   PetscInt       *ajtmpold,*ajtmp,nz,row,*ai=a->i,*aj=a->j;
     21:   PetscInt       *diag_offset = b->diag,idx,*pj;
     22:   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
     23:   MatScalar      p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
     24:   MatScalar      p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
     25:   MatScalar      *ba   = b->a,*aa = a->a;
     26:   PetscReal      shift = info->shiftamount;

     29:   ISGetIndices(isrow,&r);
     30:   ISGetIndices(isicol,&ic);
     31:   PetscMalloc(9*(n+1)*sizeof(MatScalar),&rtmp);

     33:   for (i=0; i<n; i++) {
     34:     nz    = bi[i+1] - bi[i];
     35:     ajtmp = bj + bi[i];
     36:     for  (j=0; j<nz; j++) {
     37:       x    = rtmp + 9*ajtmp[j];
     38:       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = 0.0;
     39:     }
     40:     /* load in initial (unfactored row) */
     41:     idx      = r[i];
     42:     nz       = ai[idx+1] - ai[idx];
     43:     ajtmpold = aj + ai[idx];
     44:     v        = aa + 9*ai[idx];
     45:     for (j=0; j<nz; j++) {
     46:       x    = rtmp + 9*ic[ajtmpold[j]];
     47:       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
     48:       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
     49:       v   += 9;
     50:     }
     51:     row = *ajtmp++;
     52:     while (row < i) {
     53:       pc = rtmp + 9*row;
     54:       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
     55:       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
     56:       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
     57:           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
     58:         pv    = ba + 9*diag_offset[row];
     59:         pj    = bj + diag_offset[row] + 1;
     60:         x1    = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
     61:         x5    = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
     62:         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
     63:         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
     64:         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;

     66:         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
     67:         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
     68:         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;

     70:         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
     71:         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
     72:         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
     73:         nz    = bi[row+1] - diag_offset[row] - 1;
     74:         pv   += 9;
     75:         for (j=0; j<nz; j++) {
     76:           x1    = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
     77:           x5    = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
     78:           x     = rtmp + 9*pj[j];
     79:           x[0] -= m1*x1 + m4*x2 + m7*x3;
     80:           x[1] -= m2*x1 + m5*x2 + m8*x3;
     81:           x[2] -= m3*x1 + m6*x2 + m9*x3;

     83:           x[3] -= m1*x4 + m4*x5 + m7*x6;
     84:           x[4] -= m2*x4 + m5*x5 + m8*x6;
     85:           x[5] -= m3*x4 + m6*x5 + m9*x6;

     87:           x[6] -= m1*x7 + m4*x8 + m7*x9;
     88:           x[7] -= m2*x7 + m5*x8 + m8*x9;
     89:           x[8] -= m3*x7 + m6*x8 + m9*x9;
     90:           pv   += 9;
     91:         }
     92:         PetscLogFlops(54.0*nz+36.0);
     93:       }
     94:       row = *ajtmp++;
     95:     }
     96:     /* finished row so stick it into b->a */
     97:     pv = ba + 9*bi[i];
     98:     pj = bj + bi[i];
     99:     nz = bi[i+1] - bi[i];
    100:     for (j=0; j<nz; j++) {
    101:       x     = rtmp + 9*pj[j];
    102:       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
    103:       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
    104:       pv   += 9;
    105:     }
    106:     /* invert diagonal block */
    107:     w    = ba + 9*diag_offset[i];
    108:     PetscKernel_A_gets_inverse_A_3(w,shift);
    109:   }

    111:   PetscFree(rtmp);
    112:   ISRestoreIndices(isicol,&ic);
    113:   ISRestoreIndices(isrow,&r);

    115:   C->ops->solve          = MatSolve_SeqBAIJ_3_inplace;
    116:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_inplace;
    117:   C->assembled           = PETSC_TRUE;

    119:   PetscLogFlops(1.333333333333*3*3*3*b->mbs); /* from inverting diagonal blocks */
    120:   return(0);
    121: }

    123: /* MatLUFactorNumeric_SeqBAIJ_3 -
    124:      copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
    125:        PetscKernel_A_gets_A_times_B()
    126:        PetscKernel_A_gets_A_minus_B_times_C()
    127:        PetscKernel_A_gets_inverse_A()
    128: */
    131: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3(Mat B,Mat A,const MatFactorInfo *info)
    132: {
    133:   Mat            C     =B;
    134:   Mat_SeqBAIJ    *a    =(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
    135:   IS             isrow = b->row,isicol = b->icol;
    137:   const PetscInt *r,*ic;
    138:   PetscInt       i,j,k,nz,nzL,row;
    139:   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
    140:   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
    141:   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
    142:   PetscInt       flg;
    143:   PetscReal      shift = info->shiftamount;

    146:   ISGetIndices(isrow,&r);
    147:   ISGetIndices(isicol,&ic);

    149:   /* generate work space needed by the factorization */
    150:   PetscMalloc2(bs2*n,MatScalar,&rtmp,bs2,MatScalar,&mwork);
    151:   PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));

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

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

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

    177:     /* elimination */
    178:     bjtmp = bj + bi[i];
    179:     nzL   = bi[i+1] - bi[i];
    180:     for (k = 0; k < nzL; k++) {
    181:       row = bjtmp[k];
    182:       pc  = rtmp + bs2*row;
    183:       for (flg=0,j=0; j<bs2; j++) {
    184:         if (pc[j]!=0.0) {
    185:           flg = 1;
    186:           break;
    187:         }
    188:       }
    189:       if (flg) {
    190:         pv = b->a + bs2*bdiag[row];
    191:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
    192:         PetscKernel_A_gets_A_times_B_3(pc,pv,mwork);

    194:         pj = b->j + bdiag[row+1] + 1; /* beginning of U(row,:) */
    195:         pv = b->a + bs2*(bdiag[row+1]+1);
    196:         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
    197:         for (j=0; j<nz; j++) {
    198:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
    199:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
    200:           v    = rtmp + bs2*pj[j];
    201:           PetscKernel_A_gets_A_minus_B_times_C_3(v,pc,pv);
    202:           pv  += bs2;
    203:         }
    204:         PetscLogFlops(54*nz+45); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
    205:       }
    206:     }

    208:     /* finished row so stick it into b->a */
    209:     /* L part */
    210:     pv = b->a + bs2*bi[i];
    211:     pj = b->j + bi[i];
    212:     nz = bi[i+1] - bi[i];
    213:     for (j=0; j<nz; j++) {
    214:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
    215:     }

    217:     /* Mark diagonal and invert diagonal for simplier triangular solves */
    218:     pv   = b->a + bs2*bdiag[i];
    219:     pj   = b->j + bdiag[i];
    220:     PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
    221:     /* PetscKernel_A_gets_inverse_A(bs,pv,v_pivots,v_work); */
    222:     PetscKernel_A_gets_inverse_A_3(pv,shift);

    224:     /* U part */
    225:     pj = b->j + bdiag[i+1] + 1;
    226:     pv = b->a + bs2*(bdiag[i+1]+1);
    227:     nz = bdiag[i] - bdiag[i+1] - 1;
    228:     for (j=0; j<nz; j++) {
    229:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
    230:     }
    231:   }

    233:   PetscFree2(rtmp,mwork);
    234:   ISRestoreIndices(isicol,&ic);
    235:   ISRestoreIndices(isrow,&r);

    237:   C->ops->solve          = MatSolve_SeqBAIJ_3;
    238:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3;
    239:   C->assembled           = PETSC_TRUE;

    241:   PetscLogFlops(1.333333333333*3*3*3*n); /* from inverting diagonal blocks */
    242:   return(0);
    243: }

    247: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
    248: {
    249:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
    251:   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
    252:   PetscInt       *ajtmpold,*ajtmp,nz,row;
    253:   PetscInt       *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
    254:   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
    255:   MatScalar      p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
    256:   MatScalar      p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
    257:   MatScalar      *ba   = b->a,*aa = a->a;
    258:   PetscReal      shift = info->shiftamount;

    261:   PetscMalloc(9*(n+1)*sizeof(MatScalar),&rtmp);

    263:   for (i=0; i<n; i++) {
    264:     nz    = bi[i+1] - bi[i];
    265:     ajtmp = bj + bi[i];
    266:     for  (j=0; j<nz; j++) {
    267:       x    = rtmp+9*ajtmp[j];
    268:       x[0] = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = 0.0;
    269:     }
    270:     /* load in initial (unfactored row) */
    271:     nz       = ai[i+1] - ai[i];
    272:     ajtmpold = aj + ai[i];
    273:     v        = aa + 9*ai[i];
    274:     for (j=0; j<nz; j++) {
    275:       x    = rtmp+9*ajtmpold[j];
    276:       x[0] = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
    277:       x[4] = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
    278:       v   += 9;
    279:     }
    280:     row = *ajtmp++;
    281:     while (row < i) {
    282:       pc = rtmp + 9*row;
    283:       p1 = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
    284:       p5 = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
    285:       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
    286:           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
    287:         pv    = ba + 9*diag_offset[row];
    288:         pj    = bj + diag_offset[row] + 1;
    289:         x1    = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
    290:         x5    = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
    291:         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
    292:         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
    293:         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;

    295:         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
    296:         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
    297:         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;

    299:         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
    300:         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
    301:         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;

    303:         nz  = bi[row+1] - diag_offset[row] - 1;
    304:         pv += 9;
    305:         for (j=0; j<nz; j++) {
    306:           x1    = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
    307:           x5    = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
    308:           x     = rtmp + 9*pj[j];
    309:           x[0] -= m1*x1 + m4*x2 + m7*x3;
    310:           x[1] -= m2*x1 + m5*x2 + m8*x3;
    311:           x[2] -= m3*x1 + m6*x2 + m9*x3;

    313:           x[3] -= m1*x4 + m4*x5 + m7*x6;
    314:           x[4] -= m2*x4 + m5*x5 + m8*x6;
    315:           x[5] -= m3*x4 + m6*x5 + m9*x6;

    317:           x[6] -= m1*x7 + m4*x8 + m7*x9;
    318:           x[7] -= m2*x7 + m5*x8 + m8*x9;
    319:           x[8] -= m3*x7 + m6*x8 + m9*x9;
    320:           pv   += 9;
    321:         }
    322:         PetscLogFlops(54.0*nz+36.0);
    323:       }
    324:       row = *ajtmp++;
    325:     }
    326:     /* finished row so stick it into b->a */
    327:     pv = ba + 9*bi[i];
    328:     pj = bj + bi[i];
    329:     nz = bi[i+1] - bi[i];
    330:     for (j=0; j<nz; j++) {
    331:       x     = rtmp+9*pj[j];
    332:       pv[0] = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
    333:       pv[4] = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
    334:       pv   += 9;
    335:     }
    336:     /* invert diagonal block */
    337:     w    = ba + 9*diag_offset[i];
    338:     PetscKernel_A_gets_inverse_A_3(w,shift);
    339:   }

    341:   PetscFree(rtmp);

    343:   C->ops->solve          = MatSolve_SeqBAIJ_3_NaturalOrdering_inplace;
    344:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering_inplace;
    345:   C->assembled           = PETSC_TRUE;

    347:   PetscLogFlops(1.333333333333*3*3*3*b->mbs); /* from inverting diagonal blocks */
    348:   return(0);
    349: }

    351: /*
    352:   MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering -
    353:     copied from MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering_inplace()
    354: */
    357: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
    358: {
    359:   Mat            C =B;
    360:   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
    362:   PetscInt       i,j,k,nz,nzL,row;
    363:   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
    364:   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
    365:   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
    366:   PetscInt       flg;
    367:   PetscReal      shift = info->shiftamount;

    370:   /* generate work space needed by the factorization */
    371:   PetscMalloc2(bs2*n,MatScalar,&rtmp,bs2,MatScalar,&mwork);
    372:   PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));

    374:   for (i=0; i<n; i++) {
    375:     /* zero rtmp */
    376:     /* L part */
    377:     nz    = bi[i+1] - bi[i];
    378:     bjtmp = bj + bi[i];
    379:     for  (j=0; j<nz; j++) {
    380:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
    381:     }

    383:     /* U part */
    384:     nz    = bdiag[i] - bdiag[i+1];
    385:     bjtmp = bj + bdiag[i+1] + 1;
    386:     for  (j=0; j<nz; j++) {
    387:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
    388:     }

    390:     /* load in initial (unfactored row) */
    391:     nz    = ai[i+1] - ai[i];
    392:     ajtmp = aj + ai[i];
    393:     v     = aa + bs2*ai[i];
    394:     for (j=0; j<nz; j++) {
    395:       PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));
    396:     }

    398:     /* elimination */
    399:     bjtmp = bj + bi[i];
    400:     nzL   = bi[i+1] - bi[i];
    401:     for (k=0; k<nzL; k++) {
    402:       row = bjtmp[k];
    403:       pc  = rtmp + bs2*row;
    404:       for (flg=0,j=0; j<bs2; j++) {
    405:         if (pc[j]!=0.0) {
    406:           flg = 1;
    407:           break;
    408:         }
    409:       }
    410:       if (flg) {
    411:         pv = b->a + bs2*bdiag[row];
    412:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
    413:         PetscKernel_A_gets_A_times_B_3(pc,pv,mwork);

    415:         pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
    416:         pv = b->a + bs2*(bdiag[row+1]+1);
    417:         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
    418:         for (j=0; j<nz; j++) {
    419:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
    420:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
    421:           v    = rtmp + bs2*pj[j];
    422:           PetscKernel_A_gets_A_minus_B_times_C_3(v,pc,pv);
    423:           pv  += bs2;
    424:         }
    425:         PetscLogFlops(54*nz+45); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
    426:       }
    427:     }

    429:     /* finished row so stick it into b->a */
    430:     /* L part */
    431:     pv = b->a + bs2*bi[i];
    432:     pj = b->j + bi[i];
    433:     nz = bi[i+1] - bi[i];
    434:     for (j=0; j<nz; j++) {
    435:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
    436:     }

    438:     /* Mark diagonal and invert diagonal for simplier triangular solves */
    439:     pv   = b->a + bs2*bdiag[i];
    440:     pj   = b->j + bdiag[i];
    441:     PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
    442:     /* PetscKernel_A_gets_inverse_A(bs,pv,v_pivots,v_work); */
    443:     PetscKernel_A_gets_inverse_A_3(pv,shift);

    445:     /* U part */
    446:     pv = b->a + bs2*(bdiag[i+1]+1);
    447:     pj = b->j + bdiag[i+1]+1;
    448:     nz = bdiag[i] - bdiag[i+1] - 1;
    449:     for (j=0; j<nz; j++) {
    450:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
    451:     }
    452:   }
    453:   PetscFree2(rtmp,mwork);

    455:   C->ops->solve          = MatSolve_SeqBAIJ_3_NaturalOrdering;
    456:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering;
    457:   C->assembled           = PETSC_TRUE;

    459:   PetscLogFlops(1.333333333333*3*3*3*n); /* from inverting diagonal blocks */
    460:   return(0);
    461: }