Date: 2021-03-03T22:26:17+00:00

Actual source code: baijfact13.c
petsc-3.14.5 2021-03-03
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      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: */
     11: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_inplace(Mat C,Mat A,const MatFactorInfo *info)
     12: {
     13:   Mat_SeqBAIJ    *a    = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
     14:   IS             isrow = b->row,isicol = b->icol;
     16:   const PetscInt *r,*ic;
     17:   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
     18:   PetscInt       *ajtmpold,*ajtmp,nz,row,*ai=a->i,*aj=a->j;
     19:   PetscInt       *diag_offset = b->diag,idx,*pj;
     20:   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
     21:   MatScalar      p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
     22:   MatScalar      p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
     23:   MatScalar      *ba   = b->a,*aa = a->a;
     24:   PetscReal      shift = info->shiftamount;
     25:   PetscBool      allowzeropivot,zeropivotdetected;

     28:   ISGetIndices(isrow,&r);
     29:   ISGetIndices(isicol,&ic);
     30:   PetscMalloc1(9*(n+1),&rtmp);
     31:   allowzeropivot = PetscNot(A->erroriffailure);

     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,allowzeropivot,&zeropivotdetected);
    109:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    110:   }

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

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

    120:   PetscLogFlops(1.333333333333*3*3*3*b->mbs); /* from inverting diagonal blocks */
    121:   return(0);
    122: }

    124: /* MatLUFactorNumeric_SeqBAIJ_3 -
    125:      copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
    126:        PetscKernel_A_gets_A_times_B()
    127:        PetscKernel_A_gets_A_minus_B_times_C()
    128:        PetscKernel_A_gets_inverse_A()
    129: */
    130: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3(Mat B,Mat A,const MatFactorInfo *info)
    131: {
    132:   Mat            C     =B;
    133:   Mat_SeqBAIJ    *a    =(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
    134:   IS             isrow = b->row,isicol = b->icol;
    136:   const PetscInt *r,*ic;
    137:   PetscInt       i,j,k,nz,nzL,row;
    138:   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
    139:   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
    140:   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
    141:   PetscInt       flg;
    142:   PetscReal      shift = info->shiftamount;
    143:   PetscBool      allowzeropivot,zeropivotdetected;

    146:   ISGetIndices(isrow,&r);
    147:   ISGetIndices(isicol,&ic);
    148:   allowzeropivot = PetscNot(A->erroriffailure);

    150:   /* generate work space needed by the factorization */
    151:   PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
    152:   PetscArrayzero(rtmp,bs2*n);

    154:   for (i=0; i<n; i++) {
    155:     /* zero rtmp */
    156:     /* L part */
    157:     nz    = bi[i+1] - bi[i];
    158:     bjtmp = bj + bi[i];
    159:     for  (j=0; j<nz; j++) {
    160:       PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
    161:     }

    163:     /* U part */
    164:     nz    = bdiag[i] - bdiag[i+1];
    165:     bjtmp = bj + bdiag[i+1]+1;
    166:     for  (j=0; j<nz; j++) {
    167:       PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
    168:     }

    170:     /* load in initial (unfactored row) */
    171:     nz    = ai[r[i]+1] - ai[r[i]];
    172:     ajtmp = aj + ai[r[i]];
    173:     v     = aa + bs2*ai[r[i]];
    174:     for (j=0; j<nz; j++) {
    175:       PetscArraycpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2);
    176:     }

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

    195:         pj = b->j + bdiag[row+1] + 1; /* beginning of U(row,:) */
    196:         pv = b->a + bs2*(bdiag[row+1]+1);
    197:         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
    198:         for (j=0; j<nz; j++) {
    199:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
    200:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
    201:           v    = rtmp + bs2*pj[j];
    202:           PetscKernel_A_gets_A_minus_B_times_C_3(v,pc,pv);
    203:           pv  += bs2;
    204:         }
    205:         PetscLogFlops(54.0*nz+45); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
    206:       }
    207:     }

    209:     /* finished row so stick it into b->a */
    210:     /* L part */
    211:     pv = b->a + bs2*bi[i];
    212:     pj = b->j + bi[i];
    213:     nz = bi[i+1] - bi[i];
    214:     for (j=0; j<nz; j++) {
    215:       PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
    216:     }

    218:     /* Mark diagonal and invert diagonal for simplier triangular solves */
    219:     pv   = b->a + bs2*bdiag[i];
    220:     pj   = b->j + bdiag[i];
    221:     PetscArraycpy(pv,rtmp+bs2*pj[0],bs2);
    222:     PetscKernel_A_gets_inverse_A_3(pv,shift,allowzeropivot,&zeropivotdetected);
    223:     if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    225:     /* U part */
    226:     pj = b->j + bdiag[i+1] + 1;
    227:     pv = b->a + bs2*(bdiag[i+1]+1);
    228:     nz = bdiag[i] - bdiag[i+1] - 1;
    229:     for (j=0; j<nz; j++) {
    230:       PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
    231:     }
    232:   }

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

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

    242:   PetscLogFlops(1.333333333333*3*3*3*n); /* from inverting diagonal blocks */
    243:   return(0);
    244: }

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

    261:   PetscMalloc1(9*(n+1),&rtmp);
    262:   allowzeropivot = PetscNot(A->erroriffailure);

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

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

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

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

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

    318:           x[6] -= m1*x7 + m4*x8 + m7*x9;
    319:           x[7] -= m2*x7 + m5*x8 + m8*x9;
    320:           x[8] -= m3*x7 + m6*x8 + m9*x9;
    321:           pv   += 9;
    322:         }
    323:         PetscLogFlops(54.0*nz+36.0);
    324:       }
    325:       row = *ajtmp++;
    326:     }
    327:     /* finished row so stick it into b->a */
    328:     pv = ba + 9*bi[i];
    329:     pj = bj + bi[i];
    330:     nz = bi[i+1] - bi[i];
    331:     for (j=0; j<nz; j++) {
    332:       x     = rtmp+9*pj[j];
    333:       pv[0] = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
    334:       pv[4] = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
    335:       pv   += 9;
    336:     }
    337:     /* invert diagonal block */
    338:     w    = ba + 9*diag_offset[i];
    339:     PetscKernel_A_gets_inverse_A_3(w,shift,allowzeropivot,&zeropivotdetected);
    340:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    341:   }

    343:   PetscFree(rtmp);

    345:   C->ops->solve          = MatSolve_SeqBAIJ_3_NaturalOrdering_inplace;
    346:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering_inplace;
    347:   C->assembled           = PETSC_TRUE;

    349:   PetscLogFlops(1.333333333333*3*3*3*b->mbs); /* from inverting diagonal blocks */
    350:   return(0);
    351: }

    353: /*
    354:   MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering -
    355:     copied from MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering_inplace()
    356: */
    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;
    368:   PetscBool      allowzeropivot,zeropivotdetected;

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

    373:   /* generate work space needed by the factorization */
    374:   PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
    375:   PetscArrayzero(rtmp,bs2*n);

    377:   for (i=0; i<n; i++) {
    378:     /* zero rtmp */
    379:     /* L part */
    380:     nz    = bi[i+1] - bi[i];
    381:     bjtmp = bj + bi[i];
    382:     for  (j=0; j<nz; j++) {
    383:       PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
    384:     }

    386:     /* U part */
    387:     nz    = bdiag[i] - bdiag[i+1];
    388:     bjtmp = bj + bdiag[i+1] + 1;
    389:     for  (j=0; j<nz; j++) {
    390:       PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
    391:     }

    393:     /* load in initial (unfactored row) */
    394:     nz    = ai[i+1] - ai[i];
    395:     ajtmp = aj + ai[i];
    396:     v     = aa + bs2*ai[i];
    397:     for (j=0; j<nz; j++) {
    398:       PetscArraycpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2);
    399:     }

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

    418:         pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
    419:         pv = b->a + bs2*(bdiag[row+1]+1);
    420:         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
    421:         for (j=0; j<nz; j++) {
    422:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
    423:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
    424:           v    = rtmp + bs2*pj[j];
    425:           PetscKernel_A_gets_A_minus_B_times_C_3(v,pc,pv);
    426:           pv  += bs2;
    427:         }
    428:         PetscLogFlops(54.0*nz+45); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
    429:       }
    430:     }

    432:     /* finished row so stick it into b->a */
    433:     /* L part */
    434:     pv = b->a + bs2*bi[i];
    435:     pj = b->j + bi[i];
    436:     nz = bi[i+1] - bi[i];
    437:     for (j=0; j<nz; j++) {
    438:       PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
    439:     }

    441:     /* Mark diagonal and invert diagonal for simplier triangular solves */
    442:     pv   = b->a + bs2*bdiag[i];
    443:     pj   = b->j + bdiag[i];
    444:     PetscArraycpy(pv,rtmp+bs2*pj[0],bs2);
    445:     PetscKernel_A_gets_inverse_A_3(pv,shift,allowzeropivot,&zeropivotdetected);
    446:     if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    448:     /* U part */
    449:     pv = b->a + bs2*(bdiag[i+1]+1);
    450:     pj = b->j + bdiag[i+1]+1;
    451:     nz = bdiag[i] - bdiag[i+1] - 1;
    452:     for (j=0; j<nz; j++) {
    453:       PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
    454:     }
    455:   }
    456:   PetscFree2(rtmp,mwork);

    458:   C->ops->solve          = MatSolve_SeqBAIJ_3_NaturalOrdering;
    459:   C->ops->forwardsolve   = MatForwardSolve_SeqBAIJ_3_NaturalOrdering;
    460:   C->ops->backwardsolve  = MatBackwardSolve_SeqBAIJ_3_NaturalOrdering;
    461:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering;
    462:   C->assembled           = PETSC_TRUE;

    464:   PetscLogFlops(1.333333333333*3*3*3*n); /* from inverting diagonal blocks */
    465:   return(0);
    466: }