Date: 2016-07-24T16:55:05+00:00

Actual source code: baijfact13.c
petsc-3.7.3 2016-07-24
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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: */
     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;
     27:   PetscBool      allowzeropivot,zeropivotdetected;

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

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

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

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

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

     89:           x[6] -= m1*x7 + m4*x8 + m7*x9;
     90:           x[7] -= m2*x7 + m5*x8 + m8*x9;
     91:           x[8] -= m3*x7 + m6*x8 + m9*x9;
     92:           pv   += 9;
     93:         }
     94:         PetscLogFlops(54.0*nz+36.0);
     95:       }
     96:       row = *ajtmp++;
     97:     }
     98:     /* finished row so stick it into b->a */
     99:     pv = ba + 9*bi[i];
    100:     pj = bj + bi[i];
    101:     nz = bi[i+1] - bi[i];
    102:     for (j=0; j<nz; j++) {
    103:       x     = rtmp + 9*pj[j];
    104:       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
    105:       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
    106:       pv   += 9;
    107:     }
    108:     /* invert diagonal block */
    109:     w    = ba + 9*diag_offset[i];
    110:     PetscKernel_A_gets_inverse_A_3(w,shift,allowzeropivot,&zeropivotdetected);
    111:     if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    112:   }

    114:   PetscFree(rtmp);
    115:   ISRestoreIndices(isicol,&ic);
    116:   ISRestoreIndices(isrow,&r);

    118:   C->ops->solve          = MatSolve_SeqBAIJ_3_inplace;
    119:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_inplace;
    120:   C->assembled           = PETSC_TRUE;

    122:   PetscLogFlops(1.333333333333*3*3*3*b->mbs); /* from inverting diagonal blocks */
    123:   return(0);
    124: }

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

    150:   ISGetIndices(isrow,&r);
    151:   ISGetIndices(isicol,&ic);
    152:   allowzeropivot = PetscNot(A->erroriffailure);

    154:   /* generate work space needed by the factorization */
    155:   PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
    156:   PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));

    158:   for (i=0; i<n; i++) {
    159:     /* zero rtmp */
    160:     /* L part */
    161:     nz    = bi[i+1] - bi[i];
    162:     bjtmp = bj + bi[i];
    163:     for  (j=0; j<nz; j++) {
    164:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
    165:     }

    167:     /* U part */
    168:     nz    = bdiag[i] - bdiag[i+1];
    169:     bjtmp = bj + bdiag[i+1]+1;
    170:     for  (j=0; j<nz; j++) {
    171:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
    172:     }

    174:     /* load in initial (unfactored row) */
    175:     nz    = ai[r[i]+1] - ai[r[i]];
    176:     ajtmp = aj + ai[r[i]];
    177:     v     = aa + bs2*ai[r[i]];
    178:     for (j=0; j<nz; j++) {
    179:       PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));
    180:     }

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

    199:         pj = b->j + bdiag[row+1] + 1; /* beginning of U(row,:) */
    200:         pv = b->a + bs2*(bdiag[row+1]+1);
    201:         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
    202:         for (j=0; j<nz; j++) {
    203:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
    204:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
    205:           v    = rtmp + bs2*pj[j];
    206:           PetscKernel_A_gets_A_minus_B_times_C_3(v,pc,pv);
    207:           pv  += bs2;
    208:         }
    209:         PetscLogFlops(54*nz+45); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
    210:       }
    211:     }

    213:     /* finished row so stick it into b->a */
    214:     /* L part */
    215:     pv = b->a + bs2*bi[i];
    216:     pj = b->j + bi[i];
    217:     nz = bi[i+1] - bi[i];
    218:     for (j=0; j<nz; j++) {
    219:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
    220:     }

    222:     /* Mark diagonal and invert diagonal for simplier triangular solves */
    223:     pv   = b->a + bs2*bdiag[i];
    224:     pj   = b->j + bdiag[i];
    225:     PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
    226:     PetscKernel_A_gets_inverse_A_3(pv,shift,allowzeropivot,&zeropivotdetected);
    227:     if (zeropivotdetected) B->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    229:     /* U part */
    230:     pj = b->j + bdiag[i+1] + 1;
    231:     pv = b->a + bs2*(bdiag[i+1]+1);
    232:     nz = bdiag[i] - bdiag[i+1] - 1;
    233:     for (j=0; j<nz; j++) {
    234:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
    235:     }
    236:   }

    238:   PetscFree2(rtmp,mwork);
    239:   ISRestoreIndices(isicol,&ic);
    240:   ISRestoreIndices(isrow,&r);

    242:   C->ops->solve          = MatSolve_SeqBAIJ_3;
    243:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3;
    244:   C->assembled           = PETSC_TRUE;

    246:   PetscLogFlops(1.333333333333*3*3*3*n); /* from inverting diagonal blocks */
    247:   return(0);
    248: }

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

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

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

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

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

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

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

    324:           x[6] -= m1*x7 + m4*x8 + m7*x9;
    325:           x[7] -= m2*x7 + m5*x8 + m8*x9;
    326:           x[8] -= m3*x7 + m6*x8 + m9*x9;
    327:           pv   += 9;
    328:         }
    329:         PetscLogFlops(54.0*nz+36.0);
    330:       }
    331:       row = *ajtmp++;
    332:     }
    333:     /* finished row so stick it into b->a */
    334:     pv = ba + 9*bi[i];
    335:     pj = bj + bi[i];
    336:     nz = bi[i+1] - bi[i];
    337:     for (j=0; j<nz; j++) {
    338:       x     = rtmp+9*pj[j];
    339:       pv[0] = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
    340:       pv[4] = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
    341:       pv   += 9;
    342:     }
    343:     /* invert diagonal block */
    344:     w    = ba + 9*diag_offset[i];
    345:     PetscKernel_A_gets_inverse_A_3(w,shift,allowzeropivot,&zeropivotdetected);
    346:     if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    347:   }

    349:   PetscFree(rtmp);

    351:   C->ops->solve          = MatSolve_SeqBAIJ_3_NaturalOrdering_inplace;
    352:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering_inplace;
    353:   C->assembled           = PETSC_TRUE;

    355:   PetscLogFlops(1.333333333333*3*3*3*b->mbs); /* from inverting diagonal blocks */
    356:   return(0);
    357: }

    359: /*
    360:   MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering -
    361:     copied from MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering_inplace()
    362: */
    365: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
    366: {
    367:   Mat            C =B;
    368:   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
    370:   PetscInt       i,j,k,nz,nzL,row;
    371:   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
    372:   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
    373:   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
    374:   PetscInt       flg;
    375:   PetscReal      shift = info->shiftamount;
    376:   PetscBool      allowzeropivot,zeropivotdetected;

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

    381:   /* generate work space needed by the factorization */
    382:   PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
    383:   PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));

    385:   for (i=0; i<n; i++) {
    386:     /* zero rtmp */
    387:     /* L part */
    388:     nz    = bi[i+1] - bi[i];
    389:     bjtmp = bj + bi[i];
    390:     for  (j=0; j<nz; j++) {
    391:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
    392:     }

    394:     /* U part */
    395:     nz    = bdiag[i] - bdiag[i+1];
    396:     bjtmp = bj + bdiag[i+1] + 1;
    397:     for  (j=0; j<nz; j++) {
    398:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
    399:     }

    401:     /* load in initial (unfactored row) */
    402:     nz    = ai[i+1] - ai[i];
    403:     ajtmp = aj + ai[i];
    404:     v     = aa + bs2*ai[i];
    405:     for (j=0; j<nz; j++) {
    406:       PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));
    407:     }

    409:     /* elimination */
    410:     bjtmp = bj + bi[i];
    411:     nzL   = bi[i+1] - bi[i];
    412:     for (k=0; k<nzL; k++) {
    413:       row = bjtmp[k];
    414:       pc  = rtmp + bs2*row;
    415:       for (flg=0,j=0; j<bs2; j++) {
    416:         if (pc[j]!=0.0) {
    417:           flg = 1;
    418:           break;
    419:         }
    420:       }
    421:       if (flg) {
    422:         pv = b->a + bs2*bdiag[row];
    423:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
    424:         PetscKernel_A_gets_A_times_B_3(pc,pv,mwork);

    426:         pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
    427:         pv = b->a + bs2*(bdiag[row+1]+1);
    428:         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
    429:         for (j=0; j<nz; j++) {
    430:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
    431:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
    432:           v    = rtmp + bs2*pj[j];
    433:           PetscKernel_A_gets_A_minus_B_times_C_3(v,pc,pv);
    434:           pv  += bs2;
    435:         }
    436:         PetscLogFlops(54*nz+45); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
    437:       }
    438:     }

    440:     /* finished row so stick it into b->a */
    441:     /* L part */
    442:     pv = b->a + bs2*bi[i];
    443:     pj = b->j + bi[i];
    444:     nz = bi[i+1] - bi[i];
    445:     for (j=0; j<nz; j++) {
    446:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
    447:     }

    449:     /* Mark diagonal and invert diagonal for simplier triangular solves */
    450:     pv   = b->a + bs2*bdiag[i];
    451:     pj   = b->j + bdiag[i];
    452:     PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
    453:     PetscKernel_A_gets_inverse_A_3(pv,shift,allowzeropivot,&zeropivotdetected);
    454:     if (zeropivotdetected) B->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    456:     /* U part */
    457:     pv = b->a + bs2*(bdiag[i+1]+1);
    458:     pj = b->j + bdiag[i+1]+1;
    459:     nz = bdiag[i] - bdiag[i+1] - 1;
    460:     for (j=0; j<nz; j++) {
    461:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
    462:     }
    463:   }
    464:   PetscFree2(rtmp,mwork);

    466:   C->ops->solve          = MatSolve_SeqBAIJ_3_NaturalOrdering;
    467:   C->ops->forwardsolve   = MatForwardSolve_SeqBAIJ_3_NaturalOrdering;
    468:   C->ops->backwardsolve  = MatBackwardSolve_SeqBAIJ_3_NaturalOrdering;
    469:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering;
    470:   C->assembled           = PETSC_TRUE;

    472:   PetscLogFlops(1.333333333333*3*3*3*n); /* from inverting diagonal blocks */
    473:   return(0);
    474: }