Actual source code: baijfact.c
petsc-3.10.5 2019-03-28
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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: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_2(Mat B,Mat A,const MatFactorInfo *info)
      9: {
     10:   Mat            C     =B;
     11:   Mat_SeqBAIJ    *a    =(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
     12:   IS             isrow = b->row,isicol = b->icol;
     14:   const PetscInt *r,*ic;
     15:   PetscInt       i,j,k,nz,nzL,row,*pj;
     16:   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,bs2=a->bs2;
     17:   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag;
     18:   MatScalar      *rtmp,*pc,*mwork,*pv;
     19:   MatScalar      *aa=a->a,*v;
     20:   PetscInt       flg;
     21:   PetscReal      shift = info->shiftamount;
     22:   PetscBool      allowzeropivot,zeropivotdetected;

     25:   ISGetIndices(isrow,&r);
     26:   ISGetIndices(isicol,&ic);
     27:   allowzeropivot = PetscNot(A->erroriffailure);

     29:   /* generate work space needed by the factorization */
     30:   PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
     31:   PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));

     33:   for (i=0; i<n; i++) {
     34:     /* zero rtmp */
     35:     /* L part */
     36:     nz    = bi[i+1] - bi[i];
     37:     bjtmp = bj + bi[i];
     38:     for  (j=0; j<nz; j++) {
     39:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
     40:     }

     42:     /* U part */
     43:     nz    = bdiag[i] - bdiag[i+1];
     44:     bjtmp = bj + bdiag[i+1]+1;
     45:     for  (j=0; j<nz; j++) {
     46:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
     47:     }

     49:     /* load in initial (unfactored row) */
     50:     nz    = ai[r[i]+1] - ai[r[i]];
     51:     ajtmp = aj + ai[r[i]];
     52:     v     = aa + bs2*ai[r[i]];
     53:     for (j=0; j<nz; j++) {
     54:       PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));
     55:     }

     57:     /* elimination */
     58:     bjtmp = bj + bi[i];
     59:     nzL   = bi[i+1] - bi[i];
     60:     for (k=0; k < nzL; k++) {
     61:       row = bjtmp[k];
     62:       pc  = rtmp + bs2*row;
     63:       for (flg=0,j=0; j<bs2; j++) {
     64:         if (pc[j] != (PetscScalar)0.0) {
     65:           flg = 1;
     66:           break;
     67:         }
     68:       }
     69:       if (flg) {
     70:         pv = b->a + bs2*bdiag[row];
     71:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
     72:         PetscKernel_A_gets_A_times_B_2(pc,pv,mwork);

     74:         pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
     75:         pv = b->a + bs2*(bdiag[row+1]+1);
     76:         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
     77:         for (j=0; j<nz; j++) {
     78:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
     79:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
     80:           v    = rtmp + 4*pj[j];
     81:           PetscKernel_A_gets_A_minus_B_times_C_2(v,pc,pv);
     82:           pv  += 4;
     83:         }
     84:         PetscLogFlops(16*nz+12); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
     85:       }
     86:     }

     88:     /* finished row so stick it into b->a */
     89:     /* L part */
     90:     pv = b->a + bs2*bi[i];
     91:     pj = b->j + bi[i];
     92:     nz = bi[i+1] - bi[i];
     93:     for (j=0; j<nz; j++) {
     94:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
     95:     }

     97:     /* Mark diagonal and invert diagonal for simplier triangular solves */
     98:     pv   = b->a + bs2*bdiag[i];
     99:     pj   = b->j + bdiag[i];
    100:     PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
    101:
    102:     PetscKernel_A_gets_inverse_A_2(pv,shift,allowzeropivot,&zeropivotdetected);
    103:     if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    105:     /* U part */
    106:     pv = b->a + bs2*(bdiag[i+1]+1);
    107:     pj = b->j + bdiag[i+1]+1;
    108:     nz = bdiag[i] - bdiag[i+1] - 1;
    109:     for (j=0; j<nz; j++) {
    110:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
    111:     }
    112:   }

    114:   PetscFree2(rtmp,mwork);
    115:   ISRestoreIndices(isicol,&ic);
    116:   ISRestoreIndices(isrow,&r);

    118:   C->ops->solve          = MatSolve_SeqBAIJ_2;
    119:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_2;
    120:   C->assembled           = PETSC_TRUE;

    122:   PetscLogFlops(1.333333333333*2*2*2*n); /* from inverting diagonal blocks */
    123:   return(0);
    124: }

    126: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
    127: {
    128:   Mat            C =B;
    129:   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
    131:   PetscInt       i,j,k,nz,nzL,row,*pj;
    132:   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,bs2=a->bs2;
    133:   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag;
    134:   MatScalar      *rtmp,*pc,*mwork,*pv;
    135:   MatScalar      *aa=a->a,*v;
    136:   PetscInt       flg;
    137:   PetscReal      shift = info->shiftamount;
    138:   PetscBool      allowzeropivot,zeropivotdetected;

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

    143:   /* generate work space needed by the factorization */
    144:   PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
    145:   PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));

    147:   for (i=0; i<n; i++) {
    148:     /* zero rtmp */
    149:     /* L part */
    150:     nz    = bi[i+1] - bi[i];
    151:     bjtmp = bj + bi[i];
    152:     for  (j=0; j<nz; j++) {
    153:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
    154:     }

    156:     /* U part */
    157:     nz    = bdiag[i] - bdiag[i+1];
    158:     bjtmp = bj + bdiag[i+1]+1;
    159:     for  (j=0; j<nz; j++) {
    160:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
    161:     }

    163:     /* load in initial (unfactored row) */
    164:     nz    = ai[i+1] - ai[i];
    165:     ajtmp = aj + ai[i];
    166:     v     = aa + bs2*ai[i];
    167:     for (j=0; j<nz; j++) {
    168:       PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));
    169:     }

    171:     /* elimination */
    172:     bjtmp = bj + bi[i];
    173:     nzL   = bi[i+1] - bi[i];
    174:     for (k=0; k < nzL; k++) {
    175:       row = bjtmp[k];
    176:       pc  = rtmp + bs2*row;
    177:       for (flg=0,j=0; j<bs2; j++) {
    178:         if (pc[j]!=(PetscScalar)0.0) {
    179:           flg = 1;
    180:           break;
    181:         }
    182:       }
    183:       if (flg) {
    184:         pv = b->a + bs2*bdiag[row];
    185:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
    186:         PetscKernel_A_gets_A_times_B_2(pc,pv,mwork);

    188:         pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
    189:         pv = b->a + bs2*(bdiag[row+1]+1);
    190:         nz = bdiag[row]-bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
    191:         for (j=0; j<nz; j++) {
    192:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
    193:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
    194:           v    = rtmp + 4*pj[j];
    195:           PetscKernel_A_gets_A_minus_B_times_C_2(v,pc,pv);
    196:           pv  += 4;
    197:         }
    198:         PetscLogFlops(16*nz+12); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
    199:       }
    200:     }

    202:     /* finished row so stick it into b->a */
    203:     /* L part */
    204:     pv = b->a + bs2*bi[i];
    205:     pj = b->j + bi[i];
    206:     nz = bi[i+1] - bi[i];
    207:     for (j=0; j<nz; j++) {
    208:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
    209:     }

    211:     /* Mark diagonal and invert diagonal for simplier triangular solves */
    212:     pv   = b->a + bs2*bdiag[i];
    213:     pj   = b->j + bdiag[i];
    214:     PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
    215:
    216:     PetscKernel_A_gets_inverse_A_2(pv,shift,allowzeropivot,&zeropivotdetected);
    217:     if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    219:     /* U part */
    220:     /*
    221:     pv = b->a + bs2*bi[2*n-i];
    222:     pj = b->j + bi[2*n-i];
    223:     nz = bi[2*n-i+1] - bi[2*n-i] - 1;
    224:     */
    225:     pv = b->a + bs2*(bdiag[i+1]+1);
    226:     pj = b->j + 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:   }
    232:   PetscFree2(rtmp,mwork);

    234:   C->ops->solve          = MatSolve_SeqBAIJ_2_NaturalOrdering;
    235:   C->ops->forwardsolve   = MatForwardSolve_SeqBAIJ_2_NaturalOrdering;
    236:   C->ops->backwardsolve  = MatBackwardSolve_SeqBAIJ_2_NaturalOrdering;
    237:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_2_NaturalOrdering;
    238:   C->assembled           = PETSC_TRUE;

    240:   PetscLogFlops(1.333333333333*2*2*2*n); /* from inverting diagonal blocks */
    241:   return(0);
    242: }

    244: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_2_inplace(Mat B,Mat A,const MatFactorInfo *info)
    245: {
    246:   Mat            C     = B;
    247:   Mat_SeqBAIJ    *a    = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
    248:   IS             isrow = b->row,isicol = b->icol;
    250:   const PetscInt *r,*ic;
    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,idx,*ai=a->i,*aj=a->j,*pj;
    254:   MatScalar      *pv,*v,*rtmp,m1,m2,m3,m4,*pc,*w,*x,x1,x2,x3,x4;
    255:   MatScalar      p1,p2,p3,p4;
    256:   MatScalar      *ba   = b->a,*aa = a->a;
    257:   PetscReal      shift = info->shiftamount;
    258:   PetscBool      allowzeropivot,zeropivotdetected;

    261:   allowzeropivot = PetscNot(A->erroriffailure);
    262:   ISGetIndices(isrow,&r);
    263:   ISGetIndices(isicol,&ic);
    264:   PetscMalloc1(4*(n+1),&rtmp);

    266:   for (i=0; i<n; i++) {
    267:     nz    = bi[i+1] - bi[i];
    268:     ajtmp = bj + bi[i];
    269:     for  (j=0; j<nz; j++) {
    270:       x = rtmp+4*ajtmp[j]; x[0] = x[1] = x[2] = x[3] = 0.0;
    271:     }
    272:     /* load in initial (unfactored row) */
    273:     idx      = r[i];
    274:     nz       = ai[idx+1] - ai[idx];
    275:     ajtmpold = aj + ai[idx];
    276:     v        = aa + 4*ai[idx];
    277:     for (j=0; j<nz; j++) {
    278:       x    = rtmp+4*ic[ajtmpold[j]];
    279:       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
    280:       v   += 4;
    281:     }
    282:     row = *ajtmp++;
    283:     while (row < i) {
    284:       pc = rtmp + 4*row;
    285:       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
    286:       if (p1 != (PetscScalar)0.0 || p2 != (PetscScalar)0.0 || p3 != (PetscScalar)0.0 || p4 != (PetscScalar)0.0) {
    287:         pv    = ba + 4*diag_offset[row];
    288:         pj    = bj + diag_offset[row] + 1;
    289:         x1    = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
    290:         pc[0] = m1 = p1*x1 + p3*x2;
    291:         pc[1] = m2 = p2*x1 + p4*x2;
    292:         pc[2] = m3 = p1*x3 + p3*x4;
    293:         pc[3] = m4 = p2*x3 + p4*x4;
    294:         nz    = bi[row+1] - diag_offset[row] - 1;
    295:         pv   += 4;
    296:         for (j=0; j<nz; j++) {
    297:           x1    = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
    298:           x     = rtmp + 4*pj[j];
    299:           x[0] -= m1*x1 + m3*x2;
    300:           x[1] -= m2*x1 + m4*x2;
    301:           x[2] -= m1*x3 + m3*x4;
    302:           x[3] -= m2*x3 + m4*x4;
    303:           pv   += 4;
    304:         }
    305:         PetscLogFlops(16.0*nz+12.0);
    306:       }
    307:       row = *ajtmp++;
    308:     }
    309:     /* finished row so stick it into b->a */
    310:     pv = ba + 4*bi[i];
    311:     pj = bj + bi[i];
    312:     nz = bi[i+1] - bi[i];
    313:     for (j=0; j<nz; j++) {
    314:       x     = rtmp+4*pj[j];
    315:       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
    316:       pv   += 4;
    317:     }
    318:     /* invert diagonal block */
    319:     w    = ba + 4*diag_offset[i];
    320:     PetscKernel_A_gets_inverse_A_2(w,shift,allowzeropivot,&zeropivotdetected);
    321:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    322:   }

    324:   PetscFree(rtmp);
    325:   ISRestoreIndices(isicol,&ic);
    326:   ISRestoreIndices(isrow,&r);

    328:   C->ops->solve          = MatSolve_SeqBAIJ_2_inplace;
    329:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_2_inplace;
    330:   C->assembled           = PETSC_TRUE;

    332:   PetscLogFlops(1.333333333333*8*b->mbs); /* from inverting diagonal blocks */
    333:   return(0);
    334: }
    335: /*
    336:       Version for when blocks are 2 by 2 Using natural ordering
    337: */
    338: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
    339: {
    340:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
    342:   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
    343:   PetscInt       *ajtmpold,*ajtmp,nz,row;
    344:   PetscInt       *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
    345:   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
    346:   MatScalar      p1,p2,p3,p4,m1,m2,m3,m4,x1,x2,x3,x4;
    347:   MatScalar      *ba   = b->a,*aa = a->a;
    348:   PetscReal      shift = info->shiftamount;
    349:   PetscBool      allowzeropivot,zeropivotdetected;

    352:   allowzeropivot = PetscNot(A->erroriffailure);
    353:   PetscMalloc1(4*(n+1),&rtmp);
    354:   for (i=0; i<n; i++) {
    355:     nz    = bi[i+1] - bi[i];
    356:     ajtmp = bj + bi[i];
    357:     for  (j=0; j<nz; j++) {
    358:       x    = rtmp+4*ajtmp[j];
    359:       x[0] = x[1]  = x[2]  = x[3]  = 0.0;
    360:     }
    361:     /* load in initial (unfactored row) */
    362:     nz       = ai[i+1] - ai[i];
    363:     ajtmpold = aj + ai[i];
    364:     v        = aa + 4*ai[i];
    365:     for (j=0; j<nz; j++) {
    366:       x    = rtmp+4*ajtmpold[j];
    367:       x[0] = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
    368:       v   += 4;
    369:     }
    370:     row = *ajtmp++;
    371:     while (row < i) {
    372:       pc = rtmp + 4*row;
    373:       p1 = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
    374:       if (p1 != (PetscScalar)0.0 || p2 != (PetscScalar)0.0 || p3 != (PetscScalar)0.0 || p4 != (PetscScalar)0.0) {
    375:         pv    = ba + 4*diag_offset[row];
    376:         pj    = bj + diag_offset[row] + 1;
    377:         x1    = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
    378:         pc[0] = m1 = p1*x1 + p3*x2;
    379:         pc[1] = m2 = p2*x1 + p4*x2;
    380:         pc[2] = m3 = p1*x3 + p3*x4;
    381:         pc[3] = m4 = p2*x3 + p4*x4;
    382:         nz    = bi[row+1] - diag_offset[row] - 1;
    383:         pv   += 4;
    384:         for (j=0; j<nz; j++) {
    385:           x1    = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
    386:           x     = rtmp + 4*pj[j];
    387:           x[0] -= m1*x1 + m3*x2;
    388:           x[1] -= m2*x1 + m4*x2;
    389:           x[2] -= m1*x3 + m3*x4;
    390:           x[3] -= m2*x3 + m4*x4;
    391:           pv   += 4;
    392:         }
    393:         PetscLogFlops(16.0*nz+12.0);
    394:       }
    395:       row = *ajtmp++;
    396:     }
    397:     /* finished row so stick it into b->a */
    398:     pv = ba + 4*bi[i];
    399:     pj = bj + bi[i];
    400:     nz = bi[i+1] - bi[i];
    401:     for (j=0; j<nz; j++) {
    402:       x     = rtmp+4*pj[j];
    403:       pv[0] = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
    404:       /*
    405:       printf(" col %d:",pj[j]);
    406:       PetscInt j1;
    407:       for (j1=0; j1<4; j1++) printf(" %g,",*(pv+j1));
    408:       printf("\n");
    409:       */
    410:       pv += 4;
    411:     }
    412:     /* invert diagonal block */
    413:     w = ba + 4*diag_offset[i];
    414:     PetscKernel_A_gets_inverse_A_2(w,shift, allowzeropivot,&zeropivotdetected);
    415:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    416:   }

    418:   PetscFree(rtmp);

    420:   C->ops->solve          = MatSolve_SeqBAIJ_2_NaturalOrdering_inplace;
    421:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_2_NaturalOrdering_inplace;
    422:   C->assembled           = PETSC_TRUE;

    424:   PetscLogFlops(1.333333333333*8*b->mbs); /* from inverting diagonal blocks */
    425:   return(0);
    426: }

    428: /* ----------------------------------------------------------- */
    429: /*
    430:      Version for when blocks are 1 by 1.
    431: */
    432: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_1(Mat B,Mat A,const MatFactorInfo *info)
    433: {
    434:   Mat             C     =B;
    435:   Mat_SeqBAIJ     *a    =(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
    436:   IS              isrow = b->row,isicol = b->icol;
    437:   PetscErrorCode  ierr;
    438:   const PetscInt  *r,*ic,*ics;
    439:   const PetscInt  n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bdiag=b->diag;
    440:   PetscInt        i,j,k,nz,nzL,row,*pj;
    441:   const PetscInt  *ajtmp,*bjtmp;
    442:   MatScalar       *rtmp,*pc,multiplier,*pv;
    443:   const MatScalar *aa=a->a,*v;
    444:   PetscBool       row_identity,col_identity;
    445:   FactorShiftCtx  sctx;
    446:   const PetscInt  *ddiag;
    447:   PetscReal       rs;
    448:   MatScalar       d;

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

    454:   if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
    455:     ddiag          = a->diag;
    456:     sctx.shift_top = info->zeropivot;
    457:     for (i=0; i<n; i++) {
    458:       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
    459:       d  = (aa)[ddiag[i]];
    460:       rs = -PetscAbsScalar(d) - PetscRealPart(d);
    461:       v  = aa+ai[i];
    462:       nz = ai[i+1] - ai[i];
    463:       for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]);
    464:       if (rs>sctx.shift_top) sctx.shift_top = rs;
    465:     }
    466:     sctx.shift_top *= 1.1;
    467:     sctx.nshift_max = 5;
    468:     sctx.shift_lo   = 0.;
    469:     sctx.shift_hi   = 1.;
    470:   }

    472:   ISGetIndices(isrow,&r);
    473:   ISGetIndices(isicol,&ic);
    474:   PetscMalloc1(n+1,&rtmp);
    475:   ics  = ic;

    477:   do {
    478:     sctx.newshift = PETSC_FALSE;
    479:     for (i=0; i<n; i++) {
    480:       /* zero rtmp */
    481:       /* L part */
    482:       nz    = bi[i+1] - bi[i];
    483:       bjtmp = bj + bi[i];
    484:       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;

    486:       /* U part */
    487:       nz    = bdiag[i]-bdiag[i+1];
    488:       bjtmp = bj + bdiag[i+1]+1;
    489:       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;

    491:       /* load in initial (unfactored row) */
    492:       nz    = ai[r[i]+1] - ai[r[i]];
    493:       ajtmp = aj + ai[r[i]];
    494:       v     = aa + ai[r[i]];
    495:       for (j=0; j<nz; j++) rtmp[ics[ajtmp[j]]] = v[j];

    497:       /* ZeropivotApply() */
    498:       rtmp[i] += sctx.shift_amount;  /* shift the diagonal of the matrix */

    500:       /* elimination */
    501:       bjtmp = bj + bi[i];
    502:       row   = *bjtmp++;
    503:       nzL   = bi[i+1] - bi[i];
    504:       for (k=0; k < nzL; k++) {
    505:         pc = rtmp + row;
    506:         if (*pc != (PetscScalar)0.0) {
    507:           pv         = b->a + bdiag[row];
    508:           multiplier = *pc * (*pv);
    509:           *pc        = multiplier;

    511:           pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
    512:           pv = b->a + bdiag[row+1]+1;
    513:           nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */
    514:           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
    515:           PetscLogFlops(2.0*nz);
    516:         }
    517:         row = *bjtmp++;
    518:       }

    520:       /* finished row so stick it into b->a */
    521:       rs = 0.0;
    522:       /* L part */
    523:       pv = b->a + bi[i];
    524:       pj = b->j + bi[i];
    525:       nz = bi[i+1] - bi[i];
    526:       for (j=0; j<nz; j++) {
    527:         pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
    528:       }

    530:       /* U part */
    531:       pv = b->a + bdiag[i+1]+1;
    532:       pj = b->j + bdiag[i+1]+1;
    533:       nz = bdiag[i] - bdiag[i+1]-1;
    534:       for (j=0; j<nz; j++) {
    535:         pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
    536:       }

    538:       sctx.rs = rs;
    539:       sctx.pv = rtmp[i];
    540:       MatPivotCheck(B,A,info,&sctx,i);
    541:       if (sctx.newshift) break; /* break for-loop */
    542:       rtmp[i] = sctx.pv; /* sctx.pv might be updated in the case of MAT_SHIFT_INBLOCKS */

    544:       /* Mark diagonal and invert diagonal for simplier triangular solves */
    545:       pv  = b->a + bdiag[i];
    546:       *pv = (PetscScalar)1.0/rtmp[i];

    548:     } /* endof for (i=0; i<n; i++) { */

    550:     /* MatPivotRefine() */
    551:     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
    552:       /*
    553:        * if no shift in this attempt & shifting & started shifting & can refine,
    554:        * then try lower shift
    555:        */
    556:       sctx.shift_hi       = sctx.shift_fraction;
    557:       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
    558:       sctx.shift_amount   = sctx.shift_fraction * sctx.shift_top;
    559:       sctx.newshift       = PETSC_TRUE;
    560:       sctx.nshift++;
    561:     }
    562:   } while (sctx.newshift);

    564:   PetscFree(rtmp);
    565:   ISRestoreIndices(isicol,&ic);
    566:   ISRestoreIndices(isrow,&r);

    568:   ISIdentity(isrow,&row_identity);
    569:   ISIdentity(isicol,&col_identity);
    570:   if (row_identity && col_identity) {
    571:     C->ops->solve          = MatSolve_SeqBAIJ_1_NaturalOrdering;
    572:     C->ops->forwardsolve   = MatForwardSolve_SeqBAIJ_1_NaturalOrdering;
    573:     C->ops->backwardsolve  = MatBackwardSolve_SeqBAIJ_1_NaturalOrdering;
    574:     C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_1_NaturalOrdering;
    575:   } else {
    576:     C->ops->solve          = MatSolve_SeqBAIJ_1;
    577:     C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_1;
    578:   }
    579:   C->assembled = PETSC_TRUE;
    580:   PetscLogFlops(C->cmap->n);

    582:   /* MatShiftView(A,info,&sctx) */
    583:   if (sctx.nshift) {
    584:     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
    585:       PetscInfo4(A,"number of shift_pd tries %D, 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);
    586:     } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
    587:       PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
    588:     } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS) {
    589:       PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %g\n",sctx.nshift,(double)info->shiftamount);
    590:     }
    591:   }
    592:   return(0);
    593: }

    595: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_1_inplace(Mat C,Mat A,const MatFactorInfo *info)
    596: {
    597:   Mat_SeqBAIJ    *a    = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
    598:   IS             isrow = b->row,isicol = b->icol;
    600:   const PetscInt *r,*ic;
    601:   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
    602:   PetscInt       *ajtmpold,*ajtmp,nz,row,*ai = a->i,*aj = a->j;
    603:   PetscInt       *diag_offset = b->diag,diag,*pj;
    604:   MatScalar      *pv,*v,*rtmp,multiplier,*pc;
    605:   MatScalar      *ba = b->a,*aa = a->a;
    606:   PetscBool      row_identity, col_identity;

    609:   ISGetIndices(isrow,&r);
    610:   ISGetIndices(isicol,&ic);
    611:   PetscMalloc1(n+1,&rtmp);

    613:   for (i=0; i<n; i++) {
    614:     nz    = bi[i+1] - bi[i];
    615:     ajtmp = bj + bi[i];
    616:     for  (j=0; j<nz; j++) rtmp[ajtmp[j]] = 0.0;

    618:     /* load in initial (unfactored row) */
    619:     nz       = ai[r[i]+1] - ai[r[i]];
    620:     ajtmpold = aj + ai[r[i]];
    621:     v        = aa + ai[r[i]];
    622:     for (j=0; j<nz; j++) rtmp[ic[ajtmpold[j]]] =  v[j];

    624:     row = *ajtmp++;
    625:     while (row < i) {
    626:       pc = rtmp + row;
    627:       if (*pc != 0.0) {
    628:         pv         = ba + diag_offset[row];
    629:         pj         = bj + diag_offset[row] + 1;
    630:         multiplier = *pc * *pv++;
    631:         *pc        = multiplier;
    632:         nz         = bi[row+1] - diag_offset[row] - 1;
    633:         for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
    634:         PetscLogFlops(1.0+2.0*nz);
    635:       }
    636:       row = *ajtmp++;
    637:     }
    638:     /* finished row so stick it into b->a */
    639:     pv = ba + bi[i];
    640:     pj = bj + bi[i];
    641:     nz = bi[i+1] - bi[i];
    642:     for (j=0; j<nz; j++) pv[j] = rtmp[pj[j]];
    643:     diag = diag_offset[i] - bi[i];
    644:     /* check pivot entry for current row */
    645:     if (pv[diag] == 0.0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot: row in original ordering %D in permuted ordering %D",r[i],i);
    646:     pv[diag] = 1.0/pv[diag];
    647:   }

    649:   PetscFree(rtmp);
    650:   ISRestoreIndices(isicol,&ic);
    651:   ISRestoreIndices(isrow,&r);
    652:   ISIdentity(isrow,&row_identity);
    653:   ISIdentity(isicol,&col_identity);
    654:   if (row_identity && col_identity) {
    655:     C->ops->solve          = MatSolve_SeqBAIJ_1_NaturalOrdering_inplace;
    656:     C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_1_NaturalOrdering_inplace;
    657:   } else {
    658:     C->ops->solve          = MatSolve_SeqBAIJ_1_inplace;
    659:     C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_1_inplace;
    660:   }
    661:   C->assembled = PETSC_TRUE;
    662:   PetscLogFlops(C->cmap->n);
    663:   return(0);
    664: }

    666: PETSC_INTERN PetscErrorCode MatGetFactor_seqbaij_petsc(Mat A,MatFactorType ftype,Mat *B)
    667: {
    668:   PetscInt       n = A->rmap->n;

    672: #if defined(PETSC_USE_COMPLEX)
    673:   if (A->hermitian && (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Hermitian Factor is not supported");
    674: #endif
    675:   MatCreate(PetscObjectComm((PetscObject)A),B);
    676:   MatSetSizes(*B,n,n,n,n);
    677:   if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT) {
    678:     MatSetType(*B,MATSEQBAIJ);

    680:     (*B)->ops->lufactorsymbolic  = MatLUFactorSymbolic_SeqBAIJ;
    681:     (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqBAIJ;
    682:   } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) {
    683:     MatSetType(*B,MATSEQSBAIJ);
    684:     MatSeqSBAIJSetPreallocation(*B,A->rmap->bs,MAT_SKIP_ALLOCATION,NULL);

    686:     (*B)->ops->iccfactorsymbolic      = MatICCFactorSymbolic_SeqBAIJ;
    687:     (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqBAIJ;
    688:   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor type not supported");
    689:   (*B)->factortype = ftype;

    691:   PetscFree((*B)->solvertype);
    692:   PetscStrallocpy(MATSOLVERPETSC,&(*B)->solvertype);
    693:   return(0);
    694: }

    696: /* ----------------------------------------------------------- */
    697: PetscErrorCode MatLUFactor_SeqBAIJ(Mat A,IS row,IS col,const MatFactorInfo *info)
    698: {
    700:   Mat            C;

    703:   MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_LU,&C);
    704:   MatLUFactorSymbolic(C,A,row,col,info);
    705:   MatLUFactorNumeric(C,A,info);

    707:   A->ops->solve          = C->ops->solve;
    708:   A->ops->solvetranspose = C->ops->solvetranspose;

    710:   MatHeaderMerge(A,&C);
    711:   PetscLogObjectParent((PetscObject)A,(PetscObject)((Mat_SeqBAIJ*)(A->data))->icol);
    712:   return(0);
    713: }

    715:  #include <../src/mat/impls/sbaij/seq/sbaij.h>
    716: PetscErrorCode MatCholeskyFactorNumeric_SeqBAIJ_N(Mat C,Mat A,const MatFactorInfo *info)
    717: {
    719:   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data;
    720:   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
    721:   IS             ip=b->row;
    722:   const PetscInt *rip;
    723:   PetscInt       i,j,mbs=a->mbs,bs=A->rmap->bs,*bi=b->i,*bj=b->j,*bcol;
    724:   PetscInt       *ai=a->i,*aj=a->j;
    725:   PetscInt       k,jmin,jmax,*jl,*il,col,nexti,ili,nz;
    726:   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
    727:   PetscReal      rs;
    728:   FactorShiftCtx sctx;

    731:   if (bs > 1) { /* convert A to a SBAIJ matrix and apply Cholesky factorization from it */
    732:     if (!a->sbaijMat) {
    733:       MatConvert(A,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&a->sbaijMat);
    734:     }
    735:     (a->sbaijMat)->ops->choleskyfactornumeric(C,a->sbaijMat,info);
    736:     MatDestroy(&a->sbaijMat);
    737:     return(0);
    738:   }

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

    743:   ISGetIndices(ip,&rip);
    744:   PetscMalloc3(mbs,&rtmp,mbs,&il,mbs,&jl);

    746:   sctx.shift_amount = 0.;
    747:   sctx.nshift       = 0;
    748:   do {
    749:     sctx.newshift = PETSC_FALSE;
    750:     for (i=0; i<mbs; i++) {
    751:       rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
    752:     }

    754:     for (k = 0; k<mbs; k++) {
    755:       bval = ba + bi[k];
    756:       /* initialize k-th row by the perm[k]-th row of A */
    757:       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
    758:       for (j = jmin; j < jmax; j++) {
    759:         col = rip[aj[j]];
    760:         if (col >= k) { /* only take upper triangular entry */
    761:           rtmp[col] = aa[j];
    762:           *bval++   = 0.0; /* for in-place factorization */
    763:         }
    764:       }

    766:       /* shift the diagonal of the matrix */
    767:       if (sctx.nshift) rtmp[k] += sctx.shift_amount;

    769:       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
    770:       dk = rtmp[k];
    771:       i  = jl[k]; /* first row to be added to k_th row  */

    773:       while (i < k) {
    774:         nexti = jl[i]; /* next row to be added to k_th row */

    776:         /* compute multiplier, update diag(k) and U(i,k) */
    777:         ili     = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
    778:         uikdi   = -ba[ili]*ba[bi[i]]; /* diagonal(k) */
    779:         dk     += uikdi*ba[ili];
    780:         ba[ili] = uikdi; /* -U(i,k) */

    782:         /* add multiple of row i to k-th row */
    783:         jmin = ili + 1; jmax = bi[i+1];
    784:         if (jmin < jmax) {
    785:           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
    786:           /* update il and jl for row i */
    787:           il[i] = jmin;
    788:           j     = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
    789:         }
    790:         i = nexti;
    791:       }

    793:       /* shift the diagonals when zero pivot is detected */
    794:       /* compute rs=sum of abs(off-diagonal) */
    795:       rs   = 0.0;
    796:       jmin = bi[k]+1;
    797:       nz   = bi[k+1] - jmin;
    798:       if (nz) {
    799:         bcol = bj + jmin;
    800:         while (nz--) {
    801:           rs += PetscAbsScalar(rtmp[*bcol]);
    802:           bcol++;
    803:         }
    804:       }

    806:       sctx.rs = rs;
    807:       sctx.pv = dk;
    808:       MatPivotCheck(C,A,info,&sctx,k);
    809:       if (sctx.newshift) break;
    810:       dk = sctx.pv;

    812:       /* copy data into U(k,:) */
    813:       ba[bi[k]] = 1.0/dk; /* U(k,k) */
    814:       jmin      = bi[k]+1; jmax = bi[k+1];
    815:       if (jmin < jmax) {
    816:         for (j=jmin; j<jmax; j++) {
    817:           col = bj[j]; ba[j] = rtmp[col]; rtmp[col] = 0.0;
    818:         }
    819:         /* add the k-th row into il and jl */
    820:         il[k] = jmin;
    821:         i     = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
    822:       }
    823:     }
    824:   } while (sctx.newshift);
    825:   PetscFree3(rtmp,il,jl);

    827:   ISRestoreIndices(ip,&rip);

    829:   C->assembled    = PETSC_TRUE;
    830:   C->preallocated = PETSC_TRUE;

    832:   PetscLogFlops(C->rmap->N);
    833:   if (sctx.nshift) {
    834:     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
    835:       PetscInfo2(A,"number of shiftpd tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
    836:     } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
    837:       PetscInfo2(A,"number of shiftnz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
    838:     }
    839:   }
    840:   return(0);
    841: }

    843: PetscErrorCode MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info)
    844: {
    845:   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data;
    846:   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
    848:   PetscInt       i,j,am=a->mbs;
    849:   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
    850:   PetscInt       k,jmin,*jl,*il,nexti,ili,*acol,*bcol,nz;
    851:   MatScalar      *rtmp,*ba=b->a,*aa=a->a,dk,uikdi,*aval,*bval;
    852:   PetscReal      rs;
    853:   FactorShiftCtx sctx;

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

    859:   PetscMalloc3(am,&rtmp,am,&il,am,&jl);

    861:   do {
    862:     sctx.newshift = PETSC_FALSE;
    863:     for (i=0; i<am; i++) {
    864:       rtmp[i] = 0.0; jl[i] = am; il[0] = 0;
    865:     }

    867:     for (k = 0; k<am; k++) {
    868:       /* initialize k-th row with elements nonzero in row perm(k) of A */
    869:       nz   = ai[k+1] - ai[k];
    870:       acol = aj + ai[k];
    871:       aval = aa + ai[k];
    872:       bval = ba + bi[k];
    873:       while (nz--) {
    874:         if (*acol < k) { /* skip lower triangular entries */
    875:           acol++; aval++;
    876:         } else {
    877:           rtmp[*acol++] = *aval++;
    878:           *bval++       = 0.0; /* for in-place factorization */
    879:         }
    880:       }

    882:       /* shift the diagonal of the matrix */
    883:       if (sctx.nshift) rtmp[k] += sctx.shift_amount;

    885:       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
    886:       dk = rtmp[k];
    887:       i  = jl[k]; /* first row to be added to k_th row  */

    889:       while (i < k) {
    890:         nexti = jl[i]; /* next row to be added to k_th row */
    891:         /* compute multiplier, update D(k) and U(i,k) */
    892:         ili     = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
    893:         uikdi   = -ba[ili]*ba[bi[i]];
    894:         dk     += uikdi*ba[ili];
    895:         ba[ili] = uikdi; /* -U(i,k) */

    897:         /* add multiple of row i to k-th row ... */
    898:         jmin = ili + 1;
    899:         nz   = bi[i+1] - jmin;
    900:         if (nz > 0) {
    901:           bcol = bj + jmin;
    902:           bval = ba + jmin;
    903:           while (nz--) rtmp[*bcol++] += uikdi*(*bval++);
    904:           /* update il and jl for i-th row */
    905:           il[i] = jmin;
    906:           j     = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
    907:         }
    908:         i = nexti;
    909:       }

    911:       /* shift the diagonals when zero pivot is detected */
    912:       /* compute rs=sum of abs(off-diagonal) */
    913:       rs   = 0.0;
    914:       jmin = bi[k]+1;
    915:       nz   = bi[k+1] - jmin;
    916:       if (nz) {
    917:         bcol = bj + jmin;
    918:         while (nz--) {
    919:           rs += PetscAbsScalar(rtmp[*bcol]);
    920:           bcol++;
    921:         }
    922:       }

    924:       sctx.rs = rs;
    925:       sctx.pv = dk;
    926:       MatPivotCheck(C,A,info,&sctx,k);
    927:       if (sctx.newshift) break;    /* sctx.shift_amount is updated */
    928:       dk = sctx.pv;

    930:       /* copy data into U(k,:) */
    931:       ba[bi[k]] = 1.0/dk;
    932:       jmin      = bi[k]+1;
    933:       nz        = bi[k+1] - jmin;
    934:       if (nz) {
    935:         bcol = bj + jmin;
    936:         bval = ba + jmin;
    937:         while (nz--) {
    938:           *bval++       = rtmp[*bcol];
    939:           rtmp[*bcol++] = 0.0;
    940:         }
    941:         /* add k-th row into il and jl */
    942:         il[k] = jmin;
    943:         i     = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
    944:       }
    945:     }
    946:   } while (sctx.newshift);
    947:   PetscFree3(rtmp,il,jl);

    949:   C->ops->solve          = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
    950:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
    951:   C->assembled           = PETSC_TRUE;
    952:   C->preallocated        = PETSC_TRUE;

    954:   PetscLogFlops(C->rmap->N);
    955:   if (sctx.nshift) {
    956:     if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
    957:       PetscInfo2(A,"number of shiftnz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
    958:     } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
    959:       PetscInfo2(A,"number of shiftpd tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
    960:     }
    961:   }
    962:   return(0);
    963: }

    965:  #include <petscbt.h>
    966:  #include <../src/mat/utils/freespace.h>
    967: PetscErrorCode MatICCFactorSymbolic_SeqBAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
    968: {
    969:   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data;
    970:   Mat_SeqSBAIJ       *b;
    971:   Mat                B;
    972:   PetscErrorCode     ierr;
    973:   PetscBool          perm_identity,missing;
    974:   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=a->mbs,bs=A->rmap->bs,*ui;
    975:   const PetscInt     *rip;
    976:   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
    977:   PetscInt           nlnk,*lnk,*lnk_lvl=NULL,ncols,ncols_upper,*cols,*cols_lvl,*uj,**uj_ptr,**uj_lvl_ptr;
    978:   PetscReal          fill          =info->fill,levels=info->levels;
    979:   PetscFreeSpaceList free_space    =NULL,current_space=NULL;
    980:   PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL;
    981:   PetscBT            lnkbt;

    984:   MatMissingDiagonal(A,&missing,&i);
    985:   if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);

    987:   if (bs > 1) {
    988:     if (!a->sbaijMat) {
    989:       MatConvert(A,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&a->sbaijMat);
    990:     }
    991:     (fact)->ops->iccfactorsymbolic = MatICCFactorSymbolic_SeqSBAIJ;  /* undue the change made in MatGetFactor_seqbaij_petsc */

    993:     MatICCFactorSymbolic(fact,a->sbaijMat,perm,info);
    994:     return(0);
    995:   }

    997:   ISIdentity(perm,&perm_identity);
    998:   ISGetIndices(perm,&rip);

    1000:   /* special case that simply copies fill pattern */
    1001:   if (!levels && perm_identity) {
    1002:     PetscMalloc1(am+1,&ui);
    1003:     for (i=0; i<am; i++) ui[i] = ai[i+1] - a->diag[i]; /* ui: rowlengths - changes when !perm_identity */
    1004:     B    = fact;
    1005:     MatSeqSBAIJSetPreallocation(B,1,0,ui);

    1008:     b  = (Mat_SeqSBAIJ*)B->data;
    1009:     uj = b->j;
    1010:     for (i=0; i<am; i++) {
    1011:       aj = a->j + a->diag[i];
    1012:       for (j=0; j<ui[i]; j++) *uj++ = *aj++;
    1013:       b->ilen[i] = ui[i];
    1014:     }
    1015:     PetscFree(ui);

    1017:     B->factortype = MAT_FACTOR_NONE;

    1019:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    1020:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    1021:     B->factortype = MAT_FACTOR_ICC;

    1023:     B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering;
    1024:     return(0);
    1025:   }

    1027:   /* initialization */
    1028:   PetscMalloc1(am+1,&ui);
    1029:   ui[0] = 0;
    1030:   PetscMalloc1(2*am+1,&cols_lvl);

    1032:   /* jl: linked list for storing indices of the pivot rows
    1033:      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
    1034:   PetscMalloc4(am,&uj_ptr,am,&uj_lvl_ptr,am,&il,am,&jl);
    1035:   for (i=0; i<am; i++) {
    1036:     jl[i] = am; il[i] = 0;
    1037:   }

    1039:   /* create and initialize a linked list for storing column indices of the active row k */
    1040:   nlnk = am + 1;
    1041:   PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);

    1043:   /* initial FreeSpace size is fill*(ai[am]+am)/2 */
    1044:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am]/2,am/2)),&free_space);

    1046:   current_space = free_space;

    1048:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am]/2,am/2)),&free_space_lvl);
    1049:   current_space_lvl = free_space_lvl;

    1051:   for (k=0; k<am; k++) {  /* for each active row k */
    1052:     /* initialize lnk by the column indices of row rip[k] of A */
    1053:     nzk         = 0;
    1054:     ncols       = ai[rip[k]+1] - ai[rip[k]];
    1055:     ncols_upper = 0;
    1056:     cols        = cols_lvl + am;
    1057:     for (j=0; j<ncols; j++) {
    1058:       i = rip[*(aj + ai[rip[k]] + j)];
    1059:       if (i >= k) { /* only take upper triangular entry */
    1060:         cols[ncols_upper]     = i;
    1061:         cols_lvl[ncols_upper] = -1;  /* initialize level for nonzero entries */
    1062:         ncols_upper++;
    1063:       }
    1064:     }
    1065:     PetscIncompleteLLAdd(ncols_upper,cols,levels,cols_lvl,am,nlnk,lnk,lnk_lvl,lnkbt);
    1066:     nzk += nlnk;

    1068:     /* update lnk by computing fill-in for each pivot row to be merged in */
    1069:     prow = jl[k]; /* 1st pivot row */

    1071:     while (prow < k) {
    1072:       nextprow = jl[prow];

    1074:       /* merge prow into k-th row */
    1075:       jmin  = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */
    1076:       jmax  = ui[prow+1];
    1077:       ncols = jmax-jmin;
    1078:       i     = jmin - ui[prow];
    1079:       cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
    1080:       for (j=0; j<ncols; j++) cols_lvl[j] = *(uj_lvl_ptr[prow] + i + j);
    1081:       PetscIncompleteLLAddSorted(ncols,cols,levels,cols_lvl,am,nlnk,lnk,lnk_lvl,lnkbt);
    1082:       nzk += nlnk;

    1084:       /* update il and jl for prow */
    1085:       if (jmin < jmax) {
    1086:         il[prow] = jmin;

    1088:         j = *cols; jl[prow] = jl[j]; jl[j] = prow;
    1089:       }
    1090:       prow = nextprow;
    1091:     }

    1093:     /* if free space is not available, make more free space */
    1094:     if (current_space->local_remaining<nzk) {
    1095:       i    = am - k + 1; /* num of unfactored rows */
    1096:       i    = PetscMin(PetscIntMultTruncate(i,nzk), PetscIntMultTruncate(i,i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
    1097:       PetscFreeSpaceGet(i,&current_space);
    1098:       PetscFreeSpaceGet(i,&current_space_lvl);
    1099:       reallocs++;
    1100:     }

    1102:     /* copy data into free_space and free_space_lvl, then initialize lnk */
    1103:     PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);

    1105:     /* add the k-th row into il and jl */
    1106:     if (nzk-1 > 0) {
    1107:       i     = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
    1108:       jl[k] = jl[i]; jl[i] = k;
    1109:       il[k] = ui[k] + 1;
    1110:     }
    1111:     uj_ptr[k]     = current_space->array;
    1112:     uj_lvl_ptr[k] = current_space_lvl->array;

    1114:     current_space->array           += nzk;
    1115:     current_space->local_used      += nzk;
    1116:     current_space->local_remaining -= nzk;

    1118:     current_space_lvl->array           += nzk;
    1119:     current_space_lvl->local_used      += nzk;
    1120:     current_space_lvl->local_remaining -= nzk;

    1122:     ui[k+1] = ui[k] + nzk;
    1123:   }

    1125:   ISRestoreIndices(perm,&rip);
    1126:   PetscFree4(uj_ptr,uj_lvl_ptr,il,jl);
    1127:   PetscFree(cols_lvl);

    1129:   /* copy free_space into uj and free free_space; set uj in new datastructure; */
    1130:   PetscMalloc1(ui[am]+1,&uj);
    1131:   PetscFreeSpaceContiguous(&free_space,uj);
    1132:   PetscIncompleteLLDestroy(lnk,lnkbt);
    1133:   PetscFreeSpaceDestroy(free_space_lvl);

    1135:   /* put together the new matrix in MATSEQSBAIJ format */
    1136:   B    = fact;
    1137:   MatSeqSBAIJSetPreallocation(B,1,MAT_SKIP_ALLOCATION,NULL);

    1139:   b                = (Mat_SeqSBAIJ*)B->data;
    1140:   b->singlemalloc  = PETSC_FALSE;
    1141:   b->free_a        = PETSC_TRUE;
    1142:   b->free_ij       = PETSC_TRUE;

    1144:   PetscMalloc1(ui[am]+1,&b->a);

    1146:   b->j             = uj;
    1147:   b->i             = ui;
    1148:   b->diag          = 0;
    1149:   b->ilen          = 0;
    1150:   b->imax          = 0;
    1151:   b->row           = perm;
    1152:   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */

    1154:   PetscObjectReference((PetscObject)perm);

    1156:   b->icol = perm;

    1158:   PetscObjectReference((PetscObject)perm);
    1159:   PetscMalloc1(am+1,&b->solve_work);
    1160:   PetscLogObjectMemory((PetscObject)B,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));

    1162:   b->maxnz = b->nz = ui[am];

    1164:   B->info.factor_mallocs   = reallocs;
    1165:   B->info.fill_ratio_given = fill;
    1166:   if (ai[am] != 0.) {
    1167:     /* nonzeros in lower triangular part of A (includign diagonals)= (ai[am]+am)/2 */
    1168:     B->info.fill_ratio_needed = ((PetscReal)2*ui[am])/(ai[am]+am);
    1169:   } else {
    1170:     B->info.fill_ratio_needed = 0.0;
    1171:   }
    1172: #if defined(PETSC_USE_INFO)
    1173:   if (ai[am] != 0) {
    1174:     PetscReal af = B->info.fill_ratio_needed;
    1175:     PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);
    1176:     PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
    1177:     PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);
    1178:   } else {
    1179:     PetscInfo(A,"Empty matrix.\n");
    1180:   }
    1181: #endif
    1182:   if (perm_identity) {
    1183:     B->ops->solve                 = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
    1184:     B->ops->solvetranspose        = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
    1185:     B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering;
    1186:   } else {
    1187:     (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N;
    1188:   }
    1189:   return(0);
    1190: }

    1192: PetscErrorCode MatCholeskyFactorSymbolic_SeqBAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
    1193: {
    1194:   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data;
    1195:   Mat_SeqSBAIJ       *b;
    1196:   Mat                B;
    1197:   PetscErrorCode     ierr;
    1198:   PetscBool          perm_identity,missing;
    1199:   PetscReal          fill = info->fill;
    1200:   const PetscInt     *rip;
    1201:   PetscInt           i,mbs=a->mbs,bs=A->rmap->bs,*ai=a->i,*aj=a->j,reallocs=0,prow;
    1202:   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
    1203:   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr;
    1204:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
    1205:   PetscBT            lnkbt;

    1208:   if (bs > 1) { /* convert to seqsbaij */
    1209:     if (!a->sbaijMat) {
    1210:       MatConvert(A,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&a->sbaijMat);
    1211:     }
    1212:     (fact)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqSBAIJ; /* undue the change made in MatGetFactor_seqbaij_petsc */

    1214:     MatCholeskyFactorSymbolic(fact,a->sbaijMat,perm,info);
    1215:     return(0);
    1216:   }

    1218:   MatMissingDiagonal(A,&missing,&i);
    1219:   if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);

    1221:   /* check whether perm is the identity mapping */
    1222:   ISIdentity(perm,&perm_identity);
    1223:   if (!perm_identity) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix reordering is not supported");
    1224:   ISGetIndices(perm,&rip);

    1226:   /* initialization */
    1227:   PetscMalloc1(mbs+1,&ui);
    1228:   ui[0] = 0;

    1230:   /* jl: linked list for storing indices of the pivot rows
    1231:      il: il[i] points to the 1st nonzero entry of U(i,k:mbs-1) */
    1232:   PetscMalloc4(mbs,&ui_ptr,mbs,&il,mbs,&jl,mbs,&cols);
    1233:   for (i=0; i<mbs; i++) {
    1234:     jl[i] = mbs; il[i] = 0;
    1235:   }

    1237:   /* create and initialize a linked list for storing column indices of the active row k */
    1238:   nlnk = mbs + 1;
    1239:   PetscLLCreate(mbs,mbs,nlnk,lnk,lnkbt);

    1241:   /* initial FreeSpace size is fill* (ai[mbs]+mbs)/2 */
    1242:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[mbs]/2,mbs/2)),&free_space);

    1244:   current_space = free_space;

    1246:   for (k=0; k<mbs; k++) {  /* for each active row k */
    1247:     /* initialize lnk by the column indices of row rip[k] of A */
    1248:     nzk         = 0;
    1249:     ncols       = ai[rip[k]+1] - ai[rip[k]];
    1250:     ncols_upper = 0;
    1251:     for (j=0; j<ncols; j++) {
    1252:       i = rip[*(aj + ai[rip[k]] + j)];
    1253:       if (i >= k) { /* only take upper triangular entry */
    1254:         cols[ncols_upper] = i;
    1255:         ncols_upper++;
    1256:       }
    1257:     }
    1258:     PetscLLAdd(ncols_upper,cols,mbs,nlnk,lnk,lnkbt);
    1259:     nzk += nlnk;

    1261:     /* update lnk by computing fill-in for each pivot row to be merged in */
    1262:     prow = jl[k]; /* 1st pivot row */

    1264:     while (prow < k) {
    1265:       nextprow = jl[prow];
    1266:       /* merge prow into k-th row */
    1267:       jmin   = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:mbs-1) */
    1268:       jmax   = ui[prow+1];
    1269:       ncols  = jmax-jmin;
    1270:       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:mbs-1) */
    1271:       PetscLLAddSorted(ncols,uj_ptr,mbs,nlnk,lnk,lnkbt);
    1272:       nzk   += nlnk;

    1274:       /* update il and jl for prow */
    1275:       if (jmin < jmax) {
    1276:         il[prow] = jmin;
    1277:         j        = *uj_ptr;
    1278:         jl[prow] = jl[j];
    1279:         jl[j]    = prow;
    1280:       }
    1281:       prow = nextprow;
    1282:     }

    1284:     /* if free space is not available, make more free space */
    1285:     if (current_space->local_remaining<nzk) {
    1286:       i    = mbs - k + 1; /* num of unfactored rows */
    1287:       i    = PetscMin(PetscIntMultTruncate(i,nzk), PetscIntMultTruncate(i,i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
    1288:       PetscFreeSpaceGet(i,&current_space);
    1289:       reallocs++;
    1290:     }

    1292:     /* copy data into free space, then initialize lnk */
    1293:     PetscLLClean(mbs,mbs,nzk,lnk,current_space->array,lnkbt);

    1295:     /* add the k-th row into il and jl */
    1296:     if (nzk-1 > 0) {
    1297:       i     = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:mbs-1) */
    1298:       jl[k] = jl[i]; jl[i] = k;
    1299:       il[k] = ui[k] + 1;
    1300:     }
    1301:     ui_ptr[k]                       = current_space->array;
    1302:     current_space->array           += nzk;
    1303:     current_space->local_used      += nzk;
    1304:     current_space->local_remaining -= nzk;

    1306:     ui[k+1] = ui[k] + nzk;
    1307:   }

    1309:   ISRestoreIndices(perm,&rip);
    1310:   PetscFree4(ui_ptr,il,jl,cols);

    1312:   /* copy free_space into uj and free free_space; set uj in new datastructure; */
    1313:   PetscMalloc1(ui[mbs]+1,&uj);
    1314:   PetscFreeSpaceContiguous(&free_space,uj);
    1315:   PetscLLDestroy(lnk,lnkbt);

    1317:   /* put together the new matrix in MATSEQSBAIJ format */
    1318:   B    = fact;
    1319:   MatSeqSBAIJSetPreallocation(B,bs,MAT_SKIP_ALLOCATION,NULL);

    1321:   b               = (Mat_SeqSBAIJ*)B->data;
    1322:   b->singlemalloc = PETSC_FALSE;
    1323:   b->free_a       = PETSC_TRUE;
    1324:   b->free_ij      = PETSC_TRUE;

    1326:   PetscMalloc1(ui[mbs]+1,&b->a);

    1328:   b->j             = uj;
    1329:   b->i             = ui;
    1330:   b->diag          = 0;
    1331:   b->ilen          = 0;
    1332:   b->imax          = 0;
    1333:   b->row           = perm;
    1334:   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */

    1336:   PetscObjectReference((PetscObject)perm);
    1337:   b->icol  = perm;
    1338:   PetscObjectReference((PetscObject)perm);
    1339:   PetscMalloc1(mbs+1,&b->solve_work);
    1340:   PetscLogObjectMemory((PetscObject)B,(ui[mbs]-mbs)*(sizeof(PetscInt)+sizeof(MatScalar)));
    1341:   b->maxnz = b->nz = ui[mbs];

    1343:   B->info.factor_mallocs   = reallocs;
    1344:   B->info.fill_ratio_given = fill;
    1345:   if (ai[mbs] != 0.) {
    1346:     /* nonzeros in lower triangular part of A = (ai[mbs]+mbs)/2 */
    1347:     B->info.fill_ratio_needed = ((PetscReal)2*ui[mbs])/(ai[mbs]+mbs);
    1348:   } else {
    1349:     B->info.fill_ratio_needed = 0.0;
    1350:   }
    1351: #if defined(PETSC_USE_INFO)
    1352:   if (ai[mbs] != 0.) {
    1353:     PetscReal af = B->info.fill_ratio_needed;
    1354:     PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);
    1355:     PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
    1356:     PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);
    1357:   } else {
    1358:     PetscInfo(A,"Empty matrix.\n");
    1359:   }
    1360: #endif
    1361:   if (perm_identity) {
    1362:     B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering;
    1363:   } else {
    1364:     B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N;
    1365:   }
    1366:   return(0);
    1367: }

    1369: PetscErrorCode MatSolve_SeqBAIJ_N_NaturalOrdering(Mat A,Vec bb,Vec xx)
    1370: {
    1371:   Mat_SeqBAIJ       *a=(Mat_SeqBAIJ*)A->data;
    1372:   PetscErrorCode    ierr;
    1373:   const PetscInt    *ai=a->i,*aj=a->j,*adiag=a->diag,*vi;
    1374:   PetscInt          i,k,n=a->mbs;
    1375:   PetscInt          nz,bs=A->rmap->bs,bs2=a->bs2;
    1376:   const MatScalar   *aa=a->a,*v;
    1377:   PetscScalar       *x,*s,*t,*ls;
    1378:   const PetscScalar *b;

    1381:   VecGetArrayRead(bb,&b);
    1382:   VecGetArray(xx,&x);
    1383:   t    = a->solve_work;

    1385:   /* forward solve the lower triangular */
    1386:   PetscMemcpy(t,b,bs*sizeof(PetscScalar)); /* copy 1st block of b to t */

    1388:   for (i=1; i<n; i++) {
    1389:     v    = aa + bs2*ai[i];
    1390:     vi   = aj + ai[i];
    1391:     nz   = ai[i+1] - ai[i];
    1392:     s    = t + bs*i;
    1393:     PetscMemcpy(s,b+bs*i,bs*sizeof(PetscScalar)); /* copy i_th block of b to t */
    1394:     for (k=0;k<nz;k++) {
    1395:       PetscKernel_v_gets_v_minus_A_times_w(bs,s,v,t+bs*vi[k]);
    1396:       v += bs2;
    1397:     }
    1398:   }

    1400:   /* backward solve the upper triangular */
    1401:   ls = a->solve_work + A->cmap->n;
    1402:   for (i=n-1; i>=0; i--) {
    1403:     v    = aa + bs2*(adiag[i+1]+1);
    1404:     vi   = aj + adiag[i+1]+1;
    1405:     nz   = adiag[i] - adiag[i+1]-1;
    1406:     PetscMemcpy(ls,t+i*bs,bs*sizeof(PetscScalar));
    1407:     for (k=0; k<nz; k++) {
    1408:       PetscKernel_v_gets_v_minus_A_times_w(bs,ls,v,t+bs*vi[k]);
    1409:       v += bs2;
    1410:     }
    1411:     PetscKernel_w_gets_A_times_v(bs,ls,aa+bs2*adiag[i],t+i*bs); /* *inv(diagonal[i]) */
    1412:     PetscMemcpy(x+i*bs,t+i*bs,bs*sizeof(PetscScalar));
    1413:   }

    1415:   VecRestoreArrayRead(bb,&b);
    1416:   VecRestoreArray(xx,&x);
    1417:   PetscLogFlops(2.0*(a->bs2)*(a->nz) - A->rmap->bs*A->cmap->n);
    1418:   return(0);
    1419: }

    1421: PetscErrorCode MatSolve_SeqBAIJ_N(Mat A,Vec bb,Vec xx)
    1422: {
    1423:   Mat_SeqBAIJ        *a   =(Mat_SeqBAIJ*)A->data;
    1424:   IS                 iscol=a->col,isrow=a->row;
    1425:   PetscErrorCode     ierr;
    1426:   const PetscInt     *r,*c,*rout,*cout,*ai=a->i,*aj=a->j,*adiag=a->diag,*vi;
    1427:   PetscInt           i,m,n=a->mbs;
    1428:   PetscInt           nz,bs=A->rmap->bs,bs2=a->bs2;
    1429:   const MatScalar    *aa=a->a,*v;
    1430:   PetscScalar        *x,*s,*t,*ls;
    1431:   const PetscScalar  *b;

    1434:   VecGetArrayRead(bb,&b);
    1435:   VecGetArray(xx,&x);
    1436:   t    = a->solve_work;

    1438:   ISGetIndices(isrow,&rout); r = rout;
    1439:   ISGetIndices(iscol,&cout); c = cout;

    1441:   /* forward solve the lower triangular */
    1442:   PetscMemcpy(t,b+bs*r[0],bs*sizeof(PetscScalar));
    1443:   for (i=1; i<n; i++) {
    1444:     v    = aa + bs2*ai[i];
    1445:     vi   = aj + ai[i];
    1446:     nz   = ai[i+1] - ai[i];
    1447:     s    = t + bs*i;
    1448:     PetscMemcpy(s,b+bs*r[i],bs*sizeof(PetscScalar));
    1449:     for (m=0; m<nz; m++) {
    1450:       PetscKernel_v_gets_v_minus_A_times_w(bs,s,v,t+bs*vi[m]);
    1451:       v += bs2;
    1452:     }
    1453:   }

    1455:   /* backward solve the upper triangular */
    1456:   ls = a->solve_work + A->cmap->n;
    1457:   for (i=n-1; i>=0; i--) {
    1458:     v    = aa + bs2*(adiag[i+1]+1);
    1459:     vi   = aj + adiag[i+1]+1;
    1460:     nz   = adiag[i] - adiag[i+1] - 1;
    1461:     PetscMemcpy(ls,t+i*bs,bs*sizeof(PetscScalar));
    1462:     for (m=0; m<nz; m++) {
    1463:       PetscKernel_v_gets_v_minus_A_times_w(bs,ls,v,t+bs*vi[m]);
    1464:       v += bs2;
    1465:     }
    1466:     PetscKernel_w_gets_A_times_v(bs,ls,v,t+i*bs); /* *inv(diagonal[i]) */
    1467:     PetscMemcpy(x + bs*c[i],t+i*bs,bs*sizeof(PetscScalar));
    1468:   }
    1469:   ISRestoreIndices(isrow,&rout);
    1470:   ISRestoreIndices(iscol,&cout);
    1471:   VecRestoreArrayRead(bb,&b);
    1472:   VecRestoreArray(xx,&x);
    1473:   PetscLogFlops(2.0*(a->bs2)*(a->nz) - A->rmap->bs*A->cmap->n);
    1474:   return(0);
    1475: }

    1477: /*
    1478:     For each block in an block array saves the largest absolute value in the block into another array
    1479: */
    1480: static PetscErrorCode MatBlockAbs_private(PetscInt nbs,PetscInt bs2,PetscScalar *blockarray,PetscReal *absarray)
    1481: {
    1483:   PetscInt       i,j;

    1486:   PetscMemzero(absarray,(nbs+1)*sizeof(PetscReal));
    1487:   for (i=0; i<nbs; i++) {
    1488:     for (j=0; j<bs2; j++) {
    1489:       if (absarray[i] < PetscAbsScalar(blockarray[i*nbs+j])) absarray[i] = PetscAbsScalar(blockarray[i*nbs+j]);
    1490:     }
    1491:   }
    1492:   return(0);
    1493: }

    1495: /*
    1496:      This needs to be renamed and called by the regular MatILUFactor_SeqBAIJ when drop tolerance is used
    1497: */
    1498: PetscErrorCode MatILUDTFactor_SeqBAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact)
    1499: {
    1500:   Mat            B = *fact;
    1501:   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b;
    1502:   IS             isicol;
    1504:   const PetscInt *r,*ic;
    1505:   PetscInt       i,mbs=a->mbs,bs=A->rmap->bs,bs2=a->bs2,*ai=a->i,*aj=a->j,*ajtmp,*adiag;
    1506:   PetscInt       *bi,*bj,*bdiag;

    1508:   PetscInt  row,nzi,nzi_bl,nzi_bu,*im,dtcount,nzi_al,nzi_au;
    1509:   PetscInt  nlnk,*lnk;
    1510:   PetscBT   lnkbt;
    1511:   PetscBool row_identity,icol_identity;
    1512:   MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,*multiplier,*vtmp;
    1513:   PetscInt  j,nz,*pj,*bjtmp,k,ncut,*jtmp;

    1515:   PetscReal dt=info->dt;          /* shift=info->shiftamount; */
    1516:   PetscInt  nnz_max;
    1517:   PetscBool missing;
    1518:   PetscReal *vtmp_abs;
    1519:   MatScalar *v_work;
    1520:   PetscInt  *v_pivots;
    1521:   PetscBool allowzeropivot,zeropivotdetected=PETSC_FALSE;

    1524:   /* ------- symbolic factorization, can be reused ---------*/
    1525:   MatMissingDiagonal(A,&missing,&i);
    1526:   if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
    1527:   adiag=a->diag;

    1529:   ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);

    1531:   /* bdiag is location of diagonal in factor */
    1532:   PetscMalloc1(mbs+1,&bdiag);

    1534:   /* allocate row pointers bi */
    1535:   PetscMalloc1(2*mbs+2,&bi);

    1537:   /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */
    1538:   dtcount = (PetscInt)info->dtcount;
    1539:   if (dtcount > mbs-1) dtcount = mbs-1;
    1540:   nnz_max = ai[mbs]+2*mbs*dtcount +2;
    1541:   /* printf("MatILUDTFactor_SeqBAIJ, bs %d, ai[mbs] %d, nnz_max  %d, dtcount %d\n",bs,ai[mbs],nnz_max,dtcount); */
    1542:   PetscMalloc1(nnz_max,&bj);
    1543:   nnz_max = nnz_max*bs2;
    1544:   PetscMalloc1(nnz_max,&ba);

    1546:   /* put together the new matrix */
    1547:   MatSeqBAIJSetPreallocation(B,bs,MAT_SKIP_ALLOCATION,NULL);
    1548:   PetscLogObjectParent((PetscObject)B,(PetscObject)isicol);

    1550:   b               = (Mat_SeqBAIJ*)(B)->data;
    1551:   b->free_a       = PETSC_TRUE;
    1552:   b->free_ij      = PETSC_TRUE;
    1553:   b->singlemalloc = PETSC_FALSE;

    1555:   b->a    = ba;
    1556:   b->j    = bj;
    1557:   b->i    = bi;
    1558:   b->diag = bdiag;
    1559:   b->ilen = 0;
    1560:   b->imax = 0;
    1561:   b->row  = isrow;
    1562:   b->col  = iscol;

    1564:   PetscObjectReference((PetscObject)isrow);
    1565:   PetscObjectReference((PetscObject)iscol);

    1567:   b->icol  = isicol;
    1568:   PetscMalloc1(bs*(mbs+1),&b->solve_work);
    1569:   PetscLogObjectMemory((PetscObject)B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));
    1570:   b->maxnz = nnz_max/bs2;

    1572:   (B)->factortype            = MAT_FACTOR_ILUDT;
    1573:   (B)->info.factor_mallocs   = 0;
    1574:   (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)(ai[mbs]*bs2));
    1575:   /* ------- end of symbolic factorization ---------*/
    1576:   ISGetIndices(isrow,&r);
    1577:   ISGetIndices(isicol,&ic);

    1579:   /* linked list for storing column indices of the active row */
    1580:   nlnk = mbs + 1;
    1581:   PetscLLCreate(mbs,mbs,nlnk,lnk,lnkbt);

    1583:   /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */
    1584:   PetscMalloc2(mbs,&im,mbs,&jtmp);
    1585:   /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */
    1586:   PetscMalloc2(mbs*bs2,&rtmp,mbs*bs2,&vtmp);
    1587:   PetscMalloc1(mbs+1,&vtmp_abs);
    1588:   PetscMalloc3(bs,&v_work,bs2,&multiplier,bs,&v_pivots);

    1590:   allowzeropivot = PetscNot(A->erroriffailure);
    1591:   bi[0]       = 0;
    1592:   bdiag[0]    = (nnz_max/bs2)-1; /* location of diagonal in factor B */
    1593:   bi[2*mbs+1] = bdiag[0]+1; /* endof bj and ba array */
    1594:   for (i=0; i<mbs; i++) {
    1595:     /* copy initial fill into linked list */
    1596:     nzi = ai[r[i]+1] - ai[r[i]];
    1597:     if (!nzi) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
    1598:     nzi_al = adiag[r[i]] - ai[r[i]];
    1599:     nzi_au = ai[r[i]+1] - adiag[r[i]] -1;

    1601:     /* load in initial unfactored row */
    1602:     ajtmp = aj + ai[r[i]];
    1603:     PetscLLAddPerm(nzi,ajtmp,ic,mbs,nlnk,lnk,lnkbt);
    1604:     PetscMemzero(rtmp,mbs*bs2*sizeof(PetscScalar));
    1605:     aatmp = a->a + bs2*ai[r[i]];
    1606:     for (j=0; j<nzi; j++) {
    1607:       PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],aatmp+bs2*j,bs2*sizeof(MatScalar));
    1608:     }

    1610:     /* add pivot rows into linked list */
    1611:     row = lnk[mbs];
    1612:     while (row < i) {
    1613:       nzi_bl = bi[row+1] - bi[row] + 1;
    1614:       bjtmp  = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */
    1615:       PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);
    1616:       nzi   += nlnk;
    1617:       row    = lnk[row];
    1618:     }

    1620:     /* copy data from lnk into jtmp, then initialize lnk */
    1621:     PetscLLClean(mbs,mbs,nzi,lnk,jtmp,lnkbt);

    1623:     /* numerical factorization */
    1624:     bjtmp = jtmp;
    1625:     row   = *bjtmp++; /* 1st pivot row */

    1627:     while  (row < i) {
    1628:       pc = rtmp + bs2*row;
    1629:       pv = ba + bs2*bdiag[row]; /* inv(diag) of the pivot row */
    1630:       PetscKernel_A_gets_A_times_B(bs,pc,pv,multiplier); /* pc= multiplier = pc*inv(diag[row]) */
    1631:       MatBlockAbs_private(1,bs2,pc,vtmp_abs);
    1632:       if (vtmp_abs[0] > dt) { /* apply tolerance dropping rule */
    1633:         pj = bj + bdiag[row+1] + 1;         /* point to 1st entry of U(row,:) */
    1634:         pv = ba + bs2*(bdiag[row+1] + 1);
    1635:         nz = bdiag[row] - bdiag[row+1] - 1;         /* num of entries in U(row,:), excluding diagonal */
    1636:         for (j=0; j<nz; j++) {
    1637:           PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
    1638:         }
    1639:         /* PetscLogFlops(bslog*(nz+1.0)-bs); */
    1640:       }
    1641:       row = *bjtmp++;
    1642:     }

    1644:     /* copy sparse rtmp into contiguous vtmp; separate L and U part */
    1645:     nzi_bl = 0; j = 0;
    1646:     while (jtmp[j] < i) { /* L-part. Note: jtmp is sorted */
    1647:       PetscMemcpy(vtmp+bs2*j,rtmp+bs2*jtmp[j],bs2*sizeof(MatScalar));
    1648:       nzi_bl++; j++;
    1649:     }
    1650:     nzi_bu = nzi - nzi_bl -1;

    1652:     while (j < nzi) { /* U-part */
    1653:       PetscMemcpy(vtmp+bs2*j,rtmp+bs2*jtmp[j],bs2*sizeof(MatScalar));
    1654:       j++;
    1655:     }

    1657:     MatBlockAbs_private(nzi,bs2,vtmp,vtmp_abs);
    1658:
    1659:     bjtmp = bj + bi[i];
    1660:     batmp = ba + bs2*bi[i];
    1661:     /* apply level dropping rule to L part */
    1662:     ncut = nzi_al + dtcount;
    1663:     if (ncut < nzi_bl) {
    1664:       PetscSortSplitReal(ncut,nzi_bl,vtmp_abs,jtmp);
    1665:       PetscSortIntWithScalarArray(ncut,jtmp,vtmp);
    1666:     } else {
    1667:       ncut = nzi_bl;
    1668:     }
    1669:     for (j=0; j<ncut; j++) {
    1670:       bjtmp[j] = jtmp[j];
    1671:       PetscMemcpy(batmp+bs2*j,rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
    1672:     }
    1673:     bi[i+1] = bi[i] + ncut;
    1674:     nzi     = ncut + 1;

    1676:     /* apply level dropping rule to U part */
    1677:     ncut = nzi_au + dtcount;
    1678:     if (ncut < nzi_bu) {
    1679:       PetscSortSplitReal(ncut,nzi_bu,vtmp_abs+nzi_bl+1,jtmp+nzi_bl+1);
    1680:       PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);
    1681:     } else {
    1682:       ncut = nzi_bu;
    1683:     }
    1684:     nzi += ncut;

    1686:     /* mark bdiagonal */
    1687:     bdiag[i+1]    = bdiag[i] - (ncut + 1);
    1688:     bi[2*mbs - i] = bi[2*mbs - i +1] - (ncut + 1);

    1690:     bjtmp  = bj + bdiag[i];
    1691:     batmp  = ba + bs2*bdiag[i];
    1692:     PetscMemcpy(batmp,rtmp+bs2*i,bs2*sizeof(MatScalar));
    1693:     *bjtmp = i;
    1694:
    1695:     bjtmp = bj + bdiag[i+1]+1;
    1696:     batmp = ba + (bdiag[i+1]+1)*bs2;

    1698:     for (k=0; k<ncut; k++) {
    1699:       bjtmp[k] = jtmp[nzi_bl+1+k];
    1700:       PetscMemcpy(batmp+bs2*k,rtmp+bs2*bjtmp[k],bs2*sizeof(MatScalar));
    1701:     }

    1703:     im[i] = nzi; /* used by PetscLLAddSortedLU() */

    1705:     /* invert diagonal block for simplier triangular solves - add shift??? */
    1706:     batmp = ba + bs2*bdiag[i];

    1708:     PetscKernel_A_gets_inverse_A(bs,batmp,v_pivots,v_work,allowzeropivot,&zeropivotdetected);
    1709:     if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    1710:   } /* for (i=0; i<mbs; i++) */
    1711:   PetscFree3(v_work,multiplier,v_pivots);

    1713:   /* printf("end of L %d, beginning of U %d\n",bi[mbs],bdiag[mbs]); */
    1714:   if (bi[mbs] >= bdiag[mbs]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"end of L array %d cannot >= the beginning of U array %d",bi[mbs],bdiag[mbs]);

    1716:   ISRestoreIndices(isrow,&r);
    1717:   ISRestoreIndices(isicol,&ic);

    1719:   PetscLLDestroy(lnk,lnkbt);

    1721:   PetscFree2(im,jtmp);
    1722:   PetscFree2(rtmp,vtmp);

    1724:   PetscLogFlops(bs2*B->cmap->n);
    1725:   b->maxnz = b->nz = bi[mbs] + bdiag[0] - bdiag[mbs];

    1727:   ISIdentity(isrow,&row_identity);
    1728:   ISIdentity(isicol,&icol_identity);
    1729:   if (row_identity && icol_identity) {
    1730:     B->ops->solve = MatSolve_SeqBAIJ_N_NaturalOrdering;
    1731:   } else {
    1732:     B->ops->solve = MatSolve_SeqBAIJ_N;
    1733:   }

    1735:   B->ops->solveadd          = 0;
    1736:   B->ops->solvetranspose    = 0;
    1737:   B->ops->solvetransposeadd = 0;
    1738:   B->ops->matsolve          = 0;
    1739:   B->assembled              = PETSC_TRUE;
    1740:   B->preallocated           = PETSC_TRUE;
    1741:   return(0);
    1742: }