Actual source code: baijfact.c

      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:   PetscArrayzero(rtmp,bs2*n);

     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:       PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
     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:       PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
     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:       PetscArraycpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2);
     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(16.0*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:       PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
     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:     PetscArraycpy(pv,rtmp+bs2*pj[0],bs2);
    101:     PetscKernel_A_gets_inverse_A_2(pv,shift,allowzeropivot,&zeropivotdetected);
    102:     if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

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

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

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

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

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

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

    142:   /* generate work space needed by the factorization */
    143:   PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
    144:   PetscArrayzero(rtmp,bs2*n);

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

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

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

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

    187:         pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
    188:         pv = b->a + bs2*(bdiag[row+1]+1);
    189:         nz = bdiag[row]-bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
    190:         for (j=0; j<nz; j++) {
    191:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
    192:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
    193:           v    = rtmp + 4*pj[j];
    194:           PetscKernel_A_gets_A_minus_B_times_C_2(v,pc,pv);
    195:           pv  += 4;
    196:         }
    197:         PetscLogFlops(16.0*nz+12); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
    198:       }
    199:     }

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

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

    217:     /* U part */
    218:     /*
    219:     pv = b->a + bs2*bi[2*n-i];
    220:     pj = b->j + bi[2*n-i];
    221:     nz = bi[2*n-i+1] - bi[2*n-i] - 1;
    222:     */
    223:     pv = b->a + bs2*(bdiag[i+1]+1);
    224:     pj = b->j + bdiag[i+1]+1;
    225:     nz = bdiag[i] - bdiag[i+1] - 1;
    226:     for (j=0; j<nz; j++) {
    227:       PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
    228:     }
    229:   }
    230:   PetscFree2(rtmp,mwork);

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

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

    242: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_2_inplace(Mat B,Mat A,const MatFactorInfo *info)
    243: {
    244:   Mat            C     = B;
    245:   Mat_SeqBAIJ    *a    = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
    246:   IS             isrow = b->row,isicol = b->icol;
    248:   const PetscInt *r,*ic;
    249:   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
    250:   PetscInt       *ajtmpold,*ajtmp,nz,row;
    251:   PetscInt       *diag_offset=b->diag,idx,*ai=a->i,*aj=a->j,*pj;
    252:   MatScalar      *pv,*v,*rtmp,m1,m2,m3,m4,*pc,*w,*x,x1,x2,x3,x4;
    253:   MatScalar      p1,p2,p3,p4;
    254:   MatScalar      *ba   = b->a,*aa = a->a;
    255:   PetscReal      shift = info->shiftamount;
    256:   PetscBool      allowzeropivot,zeropivotdetected;

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

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

    322:   PetscFree(rtmp);
    323:   ISRestoreIndices(isicol,&ic);
    324:   ISRestoreIndices(isrow,&r);

    326:   C->ops->solve          = MatSolve_SeqBAIJ_2_inplace;
    327:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_2_inplace;
    328:   C->assembled           = PETSC_TRUE;

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

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

    416:   PetscFree(rtmp);

    418:   C->ops->solve          = MatSolve_SeqBAIJ_2_NaturalOrdering_inplace;
    419:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_2_NaturalOrdering_inplace;
    420:   C->assembled           = PETSC_TRUE;

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

    426: /* ----------------------------------------------------------- */
    427: /*
    428:      Version for when blocks are 1 by 1.
    429: */
    430: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_1(Mat B,Mat A,const MatFactorInfo *info)
    431: {
    432:   Mat             C     =B;
    433:   Mat_SeqBAIJ     *a    =(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
    434:   IS              isrow = b->row,isicol = b->icol;
    435:   PetscErrorCode  ierr;
    436:   const PetscInt  *r,*ic,*ics;
    437:   const PetscInt  n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bdiag=b->diag;
    438:   PetscInt        i,j,k,nz,nzL,row,*pj;
    439:   const PetscInt  *ajtmp,*bjtmp;
    440:   MatScalar       *rtmp,*pc,multiplier,*pv;
    441:   const MatScalar *aa=a->a,*v;
    442:   PetscBool       row_identity,col_identity;
    443:   FactorShiftCtx  sctx;
    444:   const PetscInt  *ddiag;
    445:   PetscReal       rs;
    446:   MatScalar       d;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    562:   PetscFree(rtmp);
    563:   ISRestoreIndices(isicol,&ic);
    564:   ISRestoreIndices(isrow,&r);

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

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

    593: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_1_inplace(Mat C,Mat A,const MatFactorInfo *info)
    594: {
    595:   Mat_SeqBAIJ    *a    = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
    596:   IS             isrow = b->row,isicol = b->icol;
    598:   const PetscInt *r,*ic;
    599:   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
    600:   PetscInt       *ajtmpold,*ajtmp,nz,row,*ai = a->i,*aj = a->j;
    601:   PetscInt       *diag_offset = b->diag,diag,*pj;
    602:   MatScalar      *pv,*v,*rtmp,multiplier,*pc;
    603:   MatScalar      *ba = b->a,*aa = a->a;
    604:   PetscBool      row_identity, col_identity;

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

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

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

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

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

    664: PETSC_INTERN PetscErrorCode MatGetFactor_seqbaij_petsc(Mat A,MatFactorType ftype,Mat *B)
    665: {
    666:   PetscInt       n = A->rmap->n;

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

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

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

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

    695: /* ----------------------------------------------------------- */
    696: PetscErrorCode MatLUFactor_SeqBAIJ(Mat A,IS row,IS col,const MatFactorInfo *info)
    697: {
    699:   Mat            C;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    826:   ISRestoreIndices(ip,&rip);

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    1007:     b  = (Mat_SeqSBAIJ*)B->data;
    1008:     uj = b->j;
    1009:     for (i=0; i<am; i++) {
    1010:       aj = a->j + a->diag[i];
    1011:       for (j=0; j<ui[i]; j++) *uj++ = *aj++;
    1012:       b->ilen[i] = ui[i];
    1013:     }
    1014:     PetscFree(ui);

    1016:     B->factortype = MAT_FACTOR_NONE;

    1018:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    1019:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    1020:     B->factortype = MAT_FACTOR_ICC;

    1022:     B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering;
    1023:     return(0);
    1024:   }

    1026:   /* initialization */
    1027:   PetscMalloc1(am+1,&ui);
    1028:   ui[0] = 0;
    1029:   PetscMalloc1(2*am+1,&cols_lvl);

    1031:   /* jl: linked list for storing indices of the pivot rows
    1032:      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
    1033:   PetscMalloc4(am,&uj_ptr,am,&uj_lvl_ptr,am,&il,am,&jl);
    1034:   for (i=0; i<am; i++) {
    1035:     jl[i] = am; il[i] = 0;
    1036:   }

    1038:   /* create and initialize a linked list for storing column indices of the active row k */
    1039:   nlnk = am + 1;
    1040:   PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);

    1042:   /* initial FreeSpace size is fill*(ai[am]+am)/2 */
    1043:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am]/2,am/2)),&free_space);

    1045:   current_space = free_space;

    1047:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am]/2,am/2)),&free_space_lvl);
    1048:   current_space_lvl = free_space_lvl;

    1050:   for (k=0; k<am; k++) {  /* for each active row k */
    1051:     /* initialize lnk by the column indices of row rip[k] of A */
    1052:     nzk         = 0;
    1053:     ncols       = ai[rip[k]+1] - ai[rip[k]];
    1054:     ncols_upper = 0;
    1055:     cols        = cols_lvl + am;
    1056:     for (j=0; j<ncols; j++) {
    1057:       i = rip[*(aj + ai[rip[k]] + j)];
    1058:       if (i >= k) { /* only take upper triangular entry */
    1059:         cols[ncols_upper]     = i;
    1060:         cols_lvl[ncols_upper] = -1;  /* initialize level for nonzero entries */
    1061:         ncols_upper++;
    1062:       }
    1063:     }
    1064:     PetscIncompleteLLAdd(ncols_upper,cols,levels,cols_lvl,am,nlnk,lnk,lnk_lvl,lnkbt);
    1065:     nzk += nlnk;

    1067:     /* update lnk by computing fill-in for each pivot row to be merged in */
    1068:     prow = jl[k]; /* 1st pivot row */

    1070:     while (prow < k) {
    1071:       nextprow = jl[prow];

    1073:       /* merge prow into k-th row */
    1074:       jmin  = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */
    1075:       jmax  = ui[prow+1];
    1076:       ncols = jmax-jmin;
    1077:       i     = jmin - ui[prow];
    1078:       cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
    1079:       for (j=0; j<ncols; j++) cols_lvl[j] = *(uj_lvl_ptr[prow] + i + j);
    1080:       PetscIncompleteLLAddSorted(ncols,cols,levels,cols_lvl,am,nlnk,lnk,lnk_lvl,lnkbt);
    1081:       nzk += nlnk;

    1083:       /* update il and jl for prow */
    1084:       if (jmin < jmax) {
    1085:         il[prow] = jmin;

    1087:         j = *cols; jl[prow] = jl[j]; jl[j] = prow;
    1088:       }
    1089:       prow = nextprow;
    1090:     }

    1092:     /* if free space is not available, make more free space */
    1093:     if (current_space->local_remaining<nzk) {
    1094:       i    = am - k + 1; /* num of unfactored rows */
    1095:       i    = PetscMin(PetscIntMultTruncate(i,nzk), PetscIntMultTruncate(i,i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
    1096:       PetscFreeSpaceGet(i,&current_space);
    1097:       PetscFreeSpaceGet(i,&current_space_lvl);
    1098:       reallocs++;
    1099:     }

    1101:     /* copy data into free_space and free_space_lvl, then initialize lnk */
    1102:     PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);

    1104:     /* add the k-th row into il and jl */
    1105:     if (nzk-1 > 0) {
    1106:       i     = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
    1107:       jl[k] = jl[i]; jl[i] = k;
    1108:       il[k] = ui[k] + 1;
    1109:     }
    1110:     uj_ptr[k]     = current_space->array;
    1111:     uj_lvl_ptr[k] = current_space_lvl->array;

    1113:     current_space->array           += nzk;
    1114:     current_space->local_used      += nzk;
    1115:     current_space->local_remaining -= nzk;

    1117:     current_space_lvl->array           += nzk;
    1118:     current_space_lvl->local_used      += nzk;
    1119:     current_space_lvl->local_remaining -= nzk;

    1121:     ui[k+1] = ui[k] + nzk;
    1122:   }

    1124:   ISRestoreIndices(perm,&rip);
    1125:   PetscFree4(uj_ptr,uj_lvl_ptr,il,jl);
    1126:   PetscFree(cols_lvl);

    1128:   /* copy free_space into uj and free free_space; set uj in new datastructure; */
    1129:   PetscMalloc1(ui[am]+1,&uj);
    1130:   PetscFreeSpaceContiguous(&free_space,uj);
    1131:   PetscIncompleteLLDestroy(lnk,lnkbt);
    1132:   PetscFreeSpaceDestroy(free_space_lvl);

    1134:   /* put together the new matrix in MATSEQSBAIJ format */
    1135:   B    = fact;
    1136:   MatSeqSBAIJSetPreallocation(B,1,MAT_SKIP_ALLOCATION,NULL);

    1138:   b                = (Mat_SeqSBAIJ*)B->data;
    1139:   b->singlemalloc  = PETSC_FALSE;
    1140:   b->free_a        = PETSC_TRUE;
    1141:   b->free_ij       = PETSC_TRUE;

    1143:   PetscMalloc1(ui[am]+1,&b->a);

    1145:   b->j             = uj;
    1146:   b->i             = ui;
    1147:   b->diag          = NULL;
    1148:   b->ilen          = NULL;
    1149:   b->imax          = NULL;
    1150:   b->row           = perm;
    1151:   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */

    1153:   PetscObjectReference((PetscObject)perm);

    1155:   b->icol = perm;

    1157:   PetscObjectReference((PetscObject)perm);
    1158:   PetscMalloc1(am+1,&b->solve_work);
    1159:   PetscLogObjectMemory((PetscObject)B,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));

    1161:   b->maxnz = b->nz = ui[am];

    1163:   B->info.factor_mallocs   = reallocs;
    1164:   B->info.fill_ratio_given = fill;
    1165:   if (ai[am] != 0.) {
    1166:     /* nonzeros in lower triangular part of A (includign diagonals)= (ai[am]+am)/2 */
    1167:     B->info.fill_ratio_needed = ((PetscReal)2*ui[am])/(ai[am]+am);
    1168:   } else {
    1169:     B->info.fill_ratio_needed = 0.0;
    1170:   }
    1171: #if defined(PETSC_USE_INFO)
    1172:   if (ai[am] != 0) {
    1173:     PetscReal af = B->info.fill_ratio_needed;
    1174:     PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);
    1175:     PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
    1176:     PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);
    1177:   } else {
    1178:     PetscInfo(A,"Empty matrix\n");
    1179:   }
    1180: #endif
    1181:   if (perm_identity) {
    1182:     B->ops->solve                 = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
    1183:     B->ops->solvetranspose        = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
    1184:     B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering;
    1185:   } else {
    1186:     (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N;
    1187:   }
    1188:   return(0);
    1189: }

    1191: PetscErrorCode MatCholeskyFactorSymbolic_SeqBAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
    1192: {
    1193:   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data;
    1194:   Mat_SeqSBAIJ       *b;
    1195:   Mat                B;
    1196:   PetscErrorCode     ierr;
    1197:   PetscBool          perm_identity,missing;
    1198:   PetscReal          fill = info->fill;
    1199:   const PetscInt     *rip;
    1200:   PetscInt           i,mbs=a->mbs,bs=A->rmap->bs,*ai=a->i,*aj=a->j,reallocs=0,prow;
    1201:   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
    1202:   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr;
    1203:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
    1204:   PetscBT            lnkbt;

    1207:   if (bs > 1) { /* convert to seqsbaij */
    1208:     if (!a->sbaijMat) {
    1209:       MatConvert(A,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&a->sbaijMat);
    1210:     }
    1211:     (fact)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqSBAIJ; /* undue the change made in MatGetFactor_seqbaij_petsc */

    1213:     MatCholeskyFactorSymbolic(fact,a->sbaijMat,perm,info);
    1214:     return(0);
    1215:   }

    1217:   MatMissingDiagonal(A,&missing,&i);
    1218:   if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);

    1220:   /* check whether perm is the identity mapping */
    1221:   ISIdentity(perm,&perm_identity);
    1222:   if (!perm_identity) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix reordering is not supported");
    1223:   ISGetIndices(perm,&rip);

    1225:   /* initialization */
    1226:   PetscMalloc1(mbs+1,&ui);
    1227:   ui[0] = 0;

    1229:   /* jl: linked list for storing indices of the pivot rows
    1230:      il: il[i] points to the 1st nonzero entry of U(i,k:mbs-1) */
    1231:   PetscMalloc4(mbs,&ui_ptr,mbs,&il,mbs,&jl,mbs,&cols);
    1232:   for (i=0; i<mbs; i++) {
    1233:     jl[i] = mbs; il[i] = 0;
    1234:   }

    1236:   /* create and initialize a linked list for storing column indices of the active row k */
    1237:   nlnk = mbs + 1;
    1238:   PetscLLCreate(mbs,mbs,nlnk,lnk,lnkbt);

    1240:   /* initial FreeSpace size is fill* (ai[mbs]+mbs)/2 */
    1241:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[mbs]/2,mbs/2)),&free_space);

    1243:   current_space = free_space;

    1245:   for (k=0; k<mbs; k++) {  /* for each active row k */
    1246:     /* initialize lnk by the column indices of row rip[k] of A */
    1247:     nzk         = 0;
    1248:     ncols       = ai[rip[k]+1] - ai[rip[k]];
    1249:     ncols_upper = 0;
    1250:     for (j=0; j<ncols; j++) {
    1251:       i = rip[*(aj + ai[rip[k]] + j)];
    1252:       if (i >= k) { /* only take upper triangular entry */
    1253:         cols[ncols_upper] = i;
    1254:         ncols_upper++;
    1255:       }
    1256:     }
    1257:     PetscLLAdd(ncols_upper,cols,mbs,nlnk,lnk,lnkbt);
    1258:     nzk += nlnk;

    1260:     /* update lnk by computing fill-in for each pivot row to be merged in */
    1261:     prow = jl[k]; /* 1st pivot row */

    1263:     while (prow < k) {
    1264:       nextprow = jl[prow];
    1265:       /* merge prow into k-th row */
    1266:       jmin   = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:mbs-1) */
    1267:       jmax   = ui[prow+1];
    1268:       ncols  = jmax-jmin;
    1269:       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:mbs-1) */
    1270:       PetscLLAddSorted(ncols,uj_ptr,mbs,nlnk,lnk,lnkbt);
    1271:       nzk   += nlnk;

    1273:       /* update il and jl for prow */
    1274:       if (jmin < jmax) {
    1275:         il[prow] = jmin;
    1276:         j        = *uj_ptr;
    1277:         jl[prow] = jl[j];
    1278:         jl[j]    = prow;
    1279:       }
    1280:       prow = nextprow;
    1281:     }

    1283:     /* if free space is not available, make more free space */
    1284:     if (current_space->local_remaining<nzk) {
    1285:       i    = mbs - k + 1; /* num of unfactored rows */
    1286:       i    = PetscMin(PetscIntMultTruncate(i,nzk), PetscIntMultTruncate(i,i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
    1287:       PetscFreeSpaceGet(i,&current_space);
    1288:       reallocs++;
    1289:     }

    1291:     /* copy data into free space, then initialize lnk */
    1292:     PetscLLClean(mbs,mbs,nzk,lnk,current_space->array,lnkbt);

    1294:     /* add the k-th row into il and jl */
    1295:     if (nzk-1 > 0) {
    1296:       i     = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:mbs-1) */
    1297:       jl[k] = jl[i]; jl[i] = k;
    1298:       il[k] = ui[k] + 1;
    1299:     }
    1300:     ui_ptr[k]                       = current_space->array;
    1301:     current_space->array           += nzk;
    1302:     current_space->local_used      += nzk;
    1303:     current_space->local_remaining -= nzk;

    1305:     ui[k+1] = ui[k] + nzk;
    1306:   }

    1308:   ISRestoreIndices(perm,&rip);
    1309:   PetscFree4(ui_ptr,il,jl,cols);

    1311:   /* copy free_space into uj and free free_space; set uj in new datastructure; */
    1312:   PetscMalloc1(ui[mbs]+1,&uj);
    1313:   PetscFreeSpaceContiguous(&free_space,uj);
    1314:   PetscLLDestroy(lnk,lnkbt);

    1316:   /* put together the new matrix in MATSEQSBAIJ format */
    1317:   B    = fact;
    1318:   MatSeqSBAIJSetPreallocation(B,bs,MAT_SKIP_ALLOCATION,NULL);

    1320:   b               = (Mat_SeqSBAIJ*)B->data;
    1321:   b->singlemalloc = PETSC_FALSE;
    1322:   b->free_a       = PETSC_TRUE;
    1323:   b->free_ij      = PETSC_TRUE;

    1325:   PetscMalloc1(ui[mbs]+1,&b->a);

    1327:   b->j             = uj;
    1328:   b->i             = ui;
    1329:   b->diag          = NULL;
    1330:   b->ilen          = NULL;
    1331:   b->imax          = NULL;
    1332:   b->row           = perm;
    1333:   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */

    1335:   PetscObjectReference((PetscObject)perm);
    1336:   b->icol  = perm;
    1337:   PetscObjectReference((PetscObject)perm);
    1338:   PetscMalloc1(mbs+1,&b->solve_work);
    1339:   PetscLogObjectMemory((PetscObject)B,(ui[mbs]-mbs)*(sizeof(PetscInt)+sizeof(MatScalar)));
    1340:   b->maxnz = b->nz = ui[mbs];

    1342:   B->info.factor_mallocs   = reallocs;
    1343:   B->info.fill_ratio_given = fill;
    1344:   if (ai[mbs] != 0.) {
    1345:     /* nonzeros in lower triangular part of A = (ai[mbs]+mbs)/2 */
    1346:     B->info.fill_ratio_needed = ((PetscReal)2*ui[mbs])/(ai[mbs]+mbs);
    1347:   } else {
    1348:     B->info.fill_ratio_needed = 0.0;
    1349:   }
    1350: #if defined(PETSC_USE_INFO)
    1351:   if (ai[mbs] != 0.) {
    1352:     PetscReal af = B->info.fill_ratio_needed;
    1353:     PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);
    1354:     PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
    1355:     PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);
    1356:   } else {
    1357:     PetscInfo(A,"Empty matrix\n");
    1358:   }
    1359: #endif
    1360:   if (perm_identity) {
    1361:     B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering;
    1362:   } else {
    1363:     B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N;
    1364:   }
    1365:   return(0);
    1366: }

    1368: PetscErrorCode MatSolve_SeqBAIJ_N_NaturalOrdering(Mat A,Vec bb,Vec xx)
    1369: {
    1370:   Mat_SeqBAIJ       *a=(Mat_SeqBAIJ*)A->data;
    1371:   PetscErrorCode    ierr;
    1372:   const PetscInt    *ai=a->i,*aj=a->j,*adiag=a->diag,*vi;
    1373:   PetscInt          i,k,n=a->mbs;
    1374:   PetscInt          nz,bs=A->rmap->bs,bs2=a->bs2;
    1375:   const MatScalar   *aa=a->a,*v;
    1376:   PetscScalar       *x,*s,*t,*ls;
    1377:   const PetscScalar *b;

    1380:   VecGetArrayRead(bb,&b);
    1381:   VecGetArray(xx,&x);
    1382:   t    = a->solve_work;

    1384:   /* forward solve the lower triangular */
    1385:   PetscArraycpy(t,b,bs); /* copy 1st block of b to t */

    1387:   for (i=1; i<n; i++) {
    1388:     v    = aa + bs2*ai[i];
    1389:     vi   = aj + ai[i];
    1390:     nz   = ai[i+1] - ai[i];
    1391:     s    = t + bs*i;
    1392:     PetscArraycpy(s,b+bs*i,bs); /* copy i_th block of b to t */
    1393:     for (k=0;k<nz;k++) {
    1394:       PetscKernel_v_gets_v_minus_A_times_w(bs,s,v,t+bs*vi[k]);
    1395:       v += bs2;
    1396:     }
    1397:   }

    1399:   /* backward solve the upper triangular */
    1400:   ls = a->solve_work + A->cmap->n;
    1401:   for (i=n-1; i>=0; i--) {
    1402:     v    = aa + bs2*(adiag[i+1]+1);
    1403:     vi   = aj + adiag[i+1]+1;
    1404:     nz   = adiag[i] - adiag[i+1]-1;
    1405:     PetscArraycpy(ls,t+i*bs,bs);
    1406:     for (k=0; k<nz; k++) {
    1407:       PetscKernel_v_gets_v_minus_A_times_w(bs,ls,v,t+bs*vi[k]);
    1408:       v += bs2;
    1409:     }
    1410:     PetscKernel_w_gets_A_times_v(bs,ls,aa+bs2*adiag[i],t+i*bs); /* *inv(diagonal[i]) */
    1411:     PetscArraycpy(x+i*bs,t+i*bs,bs);
    1412:   }

    1414:   VecRestoreArrayRead(bb,&b);
    1415:   VecRestoreArray(xx,&x);
    1416:   PetscLogFlops(2.0*(a->bs2)*(a->nz) - A->rmap->bs*A->cmap->n);
    1417:   return(0);
    1418: }

    1420: PetscErrorCode MatSolve_SeqBAIJ_N(Mat A,Vec bb,Vec xx)
    1421: {
    1422:   Mat_SeqBAIJ        *a   =(Mat_SeqBAIJ*)A->data;
    1423:   IS                 iscol=a->col,isrow=a->row;
    1424:   PetscErrorCode     ierr;
    1425:   const PetscInt     *r,*c,*rout,*cout,*ai=a->i,*aj=a->j,*adiag=a->diag,*vi;
    1426:   PetscInt           i,m,n=a->mbs;
    1427:   PetscInt           nz,bs=A->rmap->bs,bs2=a->bs2;
    1428:   const MatScalar    *aa=a->a,*v;
    1429:   PetscScalar        *x,*s,*t,*ls;
    1430:   const PetscScalar  *b;

    1433:   VecGetArrayRead(bb,&b);
    1434:   VecGetArray(xx,&x);
    1435:   t    = a->solve_work;

    1437:   ISGetIndices(isrow,&rout); r = rout;
    1438:   ISGetIndices(iscol,&cout); c = cout;

    1440:   /* forward solve the lower triangular */
    1441:   PetscArraycpy(t,b+bs*r[0],bs);
    1442:   for (i=1; i<n; i++) {
    1443:     v    = aa + bs2*ai[i];
    1444:     vi   = aj + ai[i];
    1445:     nz   = ai[i+1] - ai[i];
    1446:     s    = t + bs*i;
    1447:     PetscArraycpy(s,b+bs*r[i],bs);
    1448:     for (m=0; m<nz; m++) {
    1449:       PetscKernel_v_gets_v_minus_A_times_w(bs,s,v,t+bs*vi[m]);
    1450:       v += bs2;
    1451:     }
    1452:   }

    1454:   /* backward solve the upper triangular */
    1455:   ls = a->solve_work + A->cmap->n;
    1456:   for (i=n-1; i>=0; i--) {
    1457:     v    = aa + bs2*(adiag[i+1]+1);
    1458:     vi   = aj + adiag[i+1]+1;
    1459:     nz   = adiag[i] - adiag[i+1] - 1;
    1460:     PetscArraycpy(ls,t+i*bs,bs);
    1461:     for (m=0; m<nz; m++) {
    1462:       PetscKernel_v_gets_v_minus_A_times_w(bs,ls,v,t+bs*vi[m]);
    1463:       v += bs2;
    1464:     }
    1465:     PetscKernel_w_gets_A_times_v(bs,ls,v,t+i*bs); /* *inv(diagonal[i]) */
    1466:     PetscArraycpy(x + bs*c[i],t+i*bs,bs);
    1467:   }
    1468:   ISRestoreIndices(isrow,&rout);
    1469:   ISRestoreIndices(iscol,&cout);
    1470:   VecRestoreArrayRead(bb,&b);
    1471:   VecRestoreArray(xx,&x);
    1472:   PetscLogFlops(2.0*(a->bs2)*(a->nz) - A->rmap->bs*A->cmap->n);
    1473:   return(0);
    1474: }

    1476: /*
    1477:     For each block in an block array saves the largest absolute value in the block into another array
    1478: */
    1479: static PetscErrorCode MatBlockAbs_private(PetscInt nbs,PetscInt bs2,PetscScalar *blockarray,PetscReal *absarray)
    1480: {
    1482:   PetscInt       i,j;

    1485:   PetscArrayzero(absarray,nbs+1);
    1486:   for (i=0; i<nbs; i++) {
    1487:     for (j=0; j<bs2; j++) {
    1488:       if (absarray[i] < PetscAbsScalar(blockarray[i*nbs+j])) absarray[i] = PetscAbsScalar(blockarray[i*nbs+j]);
    1489:     }
    1490:   }
    1491:   return(0);
    1492: }

    1494: /*
    1495:      This needs to be renamed and called by the regular MatILUFactor_SeqBAIJ when drop tolerance is used
    1496: */
    1497: PetscErrorCode MatILUDTFactor_SeqBAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact)
    1498: {
    1499:   Mat            B = *fact;
    1500:   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b;
    1501:   IS             isicol;
    1503:   const PetscInt *r,*ic;
    1504:   PetscInt       i,mbs=a->mbs,bs=A->rmap->bs,bs2=a->bs2,*ai=a->i,*aj=a->j,*ajtmp,*adiag;
    1505:   PetscInt       *bi,*bj,*bdiag;

    1507:   PetscInt  row,nzi,nzi_bl,nzi_bu,*im,dtcount,nzi_al,nzi_au;
    1508:   PetscInt  nlnk,*lnk;
    1509:   PetscBT   lnkbt;
    1510:   PetscBool row_identity,icol_identity;
    1511:   MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,*multiplier,*vtmp;
    1512:   PetscInt  j,nz,*pj,*bjtmp,k,ncut,*jtmp;

    1514:   PetscReal dt=info->dt;          /* shift=info->shiftamount; */
    1515:   PetscInt  nnz_max;
    1516:   PetscBool missing;
    1517:   PetscReal *vtmp_abs;
    1518:   MatScalar *v_work;
    1519:   PetscInt  *v_pivots;
    1520:   PetscBool allowzeropivot,zeropivotdetected=PETSC_FALSE;

    1523:   /* ------- symbolic factorization, can be reused ---------*/
    1524:   MatMissingDiagonal(A,&missing,&i);
    1525:   if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
    1526:   adiag=a->diag;

    1528:   ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);

    1530:   /* bdiag is location of diagonal in factor */
    1531:   PetscMalloc1(mbs+1,&bdiag);

    1533:   /* allocate row pointers bi */
    1534:   PetscMalloc1(2*mbs+2,&bi);

    1536:   /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */
    1537:   dtcount = (PetscInt)info->dtcount;
    1538:   if (dtcount > mbs-1) dtcount = mbs-1;
    1539:   nnz_max = ai[mbs]+2*mbs*dtcount +2;
    1540:   /* printf("MatILUDTFactor_SeqBAIJ, bs %d, ai[mbs] %d, nnz_max  %d, dtcount %d\n",bs,ai[mbs],nnz_max,dtcount); */
    1541:   PetscMalloc1(nnz_max,&bj);
    1542:   nnz_max = nnz_max*bs2;
    1543:   PetscMalloc1(nnz_max,&ba);

    1545:   /* put together the new matrix */
    1546:   MatSeqBAIJSetPreallocation(B,bs,MAT_SKIP_ALLOCATION,NULL);
    1547:   PetscLogObjectParent((PetscObject)B,(PetscObject)isicol);

    1549:   b               = (Mat_SeqBAIJ*)(B)->data;
    1550:   b->free_a       = PETSC_TRUE;
    1551:   b->free_ij      = PETSC_TRUE;
    1552:   b->singlemalloc = PETSC_FALSE;

    1554:   b->a    = ba;
    1555:   b->j    = bj;
    1556:   b->i    = bi;
    1557:   b->diag = bdiag;
    1558:   b->ilen = NULL;
    1559:   b->imax = NULL;
    1560:   b->row  = isrow;
    1561:   b->col  = iscol;

    1563:   PetscObjectReference((PetscObject)isrow);
    1564:   PetscObjectReference((PetscObject)iscol);

    1566:   b->icol  = isicol;
    1567:   PetscMalloc1(bs*(mbs+1),&b->solve_work);
    1568:   PetscLogObjectMemory((PetscObject)B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));
    1569:   b->maxnz = nnz_max/bs2;

    1571:   (B)->factortype            = MAT_FACTOR_ILUDT;
    1572:   (B)->info.factor_mallocs   = 0;
    1573:   (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)(ai[mbs]*bs2));
    1574:   /* ------- end of symbolic factorization ---------*/
    1575:   ISGetIndices(isrow,&r);
    1576:   ISGetIndices(isicol,&ic);

    1578:   /* linked list for storing column indices of the active row */
    1579:   nlnk = mbs + 1;
    1580:   PetscLLCreate(mbs,mbs,nlnk,lnk,lnkbt);

    1582:   /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */
    1583:   PetscMalloc2(mbs,&im,mbs,&jtmp);
    1584:   /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */
    1585:   PetscMalloc2(mbs*bs2,&rtmp,mbs*bs2,&vtmp);
    1586:   PetscMalloc1(mbs+1,&vtmp_abs);
    1587:   PetscMalloc3(bs,&v_work,bs2,&multiplier,bs,&v_pivots);

    1589:   allowzeropivot = PetscNot(A->erroriffailure);
    1590:   bi[0]       = 0;
    1591:   bdiag[0]    = (nnz_max/bs2)-1; /* location of diagonal in factor B */
    1592:   bi[2*mbs+1] = bdiag[0]+1; /* endof bj and ba array */
    1593:   for (i=0; i<mbs; i++) {
    1594:     /* copy initial fill into linked list */
    1595:     nzi = ai[r[i]+1] - ai[r[i]];
    1596:     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);
    1597:     nzi_al = adiag[r[i]] - ai[r[i]];
    1598:     nzi_au = ai[r[i]+1] - adiag[r[i]] -1;

    1600:     /* load in initial unfactored row */
    1601:     ajtmp = aj + ai[r[i]];
    1602:     PetscLLAddPerm(nzi,ajtmp,ic,mbs,nlnk,lnk,lnkbt);
    1603:     PetscArrayzero(rtmp,mbs*bs2);
    1604:     aatmp = a->a + bs2*ai[r[i]];
    1605:     for (j=0; j<nzi; j++) {
    1606:       PetscArraycpy(rtmp+bs2*ic[ajtmp[j]],aatmp+bs2*j,bs2);
    1607:     }

    1609:     /* add pivot rows into linked list */
    1610:     row = lnk[mbs];
    1611:     while (row < i) {
    1612:       nzi_bl = bi[row+1] - bi[row] + 1;
    1613:       bjtmp  = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */
    1614:       PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);
    1615:       nzi   += nlnk;
    1616:       row    = lnk[row];
    1617:     }

    1619:     /* copy data from lnk into jtmp, then initialize lnk */
    1620:     PetscLLClean(mbs,mbs,nzi,lnk,jtmp,lnkbt);

    1622:     /* numerical factorization */
    1623:     bjtmp = jtmp;
    1624:     row   = *bjtmp++; /* 1st pivot row */

    1626:     while  (row < i) {
    1627:       pc = rtmp + bs2*row;
    1628:       pv = ba + bs2*bdiag[row]; /* inv(diag) of the pivot row */
    1629:       PetscKernel_A_gets_A_times_B(bs,pc,pv,multiplier); /* pc= multiplier = pc*inv(diag[row]) */
    1630:       MatBlockAbs_private(1,bs2,pc,vtmp_abs);
    1631:       if (vtmp_abs[0] > dt) { /* apply tolerance dropping rule */
    1632:         pj = bj + bdiag[row+1] + 1;         /* point to 1st entry of U(row,:) */
    1633:         pv = ba + bs2*(bdiag[row+1] + 1);
    1634:         nz = bdiag[row] - bdiag[row+1] - 1;         /* num of entries in U(row,:), excluding diagonal */
    1635:         for (j=0; j<nz; j++) {
    1636:           PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
    1637:         }
    1638:         /* PetscLogFlops(bslog*(nz+1.0)-bs); */
    1639:       }
    1640:       row = *bjtmp++;
    1641:     }

    1643:     /* copy sparse rtmp into contiguous vtmp; separate L and U part */
    1644:     nzi_bl = 0; j = 0;
    1645:     while (jtmp[j] < i) { /* L-part. Note: jtmp is sorted */
    1646:       PetscArraycpy(vtmp+bs2*j,rtmp+bs2*jtmp[j],bs2);
    1647:       nzi_bl++; j++;
    1648:     }
    1649:     nzi_bu = nzi - nzi_bl -1;

    1651:     while (j < nzi) { /* U-part */
    1652:       PetscArraycpy(vtmp+bs2*j,rtmp+bs2*jtmp[j],bs2);
    1653:       j++;
    1654:     }

    1656:     MatBlockAbs_private(nzi,bs2,vtmp,vtmp_abs);

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

    1675:     /* apply level dropping rule to U part */
    1676:     ncut = nzi_au + dtcount;
    1677:     if (ncut < nzi_bu) {
    1678:       PetscSortSplitReal(ncut,nzi_bu,vtmp_abs+nzi_bl+1,jtmp+nzi_bl+1);
    1679:       PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);
    1680:     } else {
    1681:       ncut = nzi_bu;
    1682:     }
    1683:     nzi += ncut;

    1685:     /* mark bdiagonal */
    1686:     bdiag[i+1]    = bdiag[i] - (ncut + 1);
    1687:     bi[2*mbs - i] = bi[2*mbs - i +1] - (ncut + 1);

    1689:     bjtmp  = bj + bdiag[i];
    1690:     batmp  = ba + bs2*bdiag[i];
    1691:     PetscArraycpy(batmp,rtmp+bs2*i,bs2);
    1692:     *bjtmp = i;

    1694:     bjtmp = bj + bdiag[i+1]+1;
    1695:     batmp = ba + (bdiag[i+1]+1)*bs2;

    1697:     for (k=0; k<ncut; k++) {
    1698:       bjtmp[k] = jtmp[nzi_bl+1+k];
    1699:       PetscArraycpy(batmp+bs2*k,rtmp+bs2*bjtmp[k],bs2);
    1700:     }

    1702:     im[i] = nzi; /* used by PetscLLAddSortedLU() */

    1704:     /* invert diagonal block for simplier triangular solves - add shift??? */
    1705:     batmp = ba + bs2*bdiag[i];

    1707:     PetscKernel_A_gets_inverse_A(bs,batmp,v_pivots,v_work,allowzeropivot,&zeropivotdetected);
    1708:     if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    1709:   } /* for (i=0; i<mbs; i++) */
    1710:   PetscFree3(v_work,multiplier,v_pivots);

    1712:   /* printf("end of L %d, beginning of U %d\n",bi[mbs],bdiag[mbs]); */
    1713:   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]);

    1715:   ISRestoreIndices(isrow,&r);
    1716:   ISRestoreIndices(isicol,&ic);

    1718:   PetscLLDestroy(lnk,lnkbt);

    1720:   PetscFree2(im,jtmp);
    1721:   PetscFree2(rtmp,vtmp);

    1723:   PetscLogFlops(bs2*B->cmap->n);
    1724:   b->maxnz = b->nz = bi[mbs] + bdiag[0] - bdiag[mbs];

    1726:   ISIdentity(isrow,&row_identity);
    1727:   ISIdentity(isicol,&icol_identity);
    1728:   if (row_identity && icol_identity) {
    1729:     B->ops->solve = MatSolve_SeqBAIJ_N_NaturalOrdering;
    1730:   } else {
    1731:     B->ops->solve = MatSolve_SeqBAIJ_N;
    1732:   }

    1734:   B->ops->solveadd          = NULL;
    1735:   B->ops->solvetranspose    = NULL;
    1736:   B->ops->solvetransposeadd = NULL;
    1737:   B->ops->matsolve          = NULL;
    1738:   B->assembled              = PETSC_TRUE;
    1739:   B->preallocated           = PETSC_TRUE;
    1740:   return(0);
    1741: }