Actual source code: sbaijfact4.c
petsc-3.10.5 2019-03-28
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      2:  #include <../src/mat/impls/sbaij/seq/sbaij.h>
      3:  #include <petsc/private/kernels/blockinvert.h>

      5: /*
      6:       Version for when blocks are 3 by 3 Using natural ordering
      7: */
      8: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info)
      9: {
     10:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
     12:   PetscInt       i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
     13:   PetscInt       *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
     14:   MatScalar      *ba = b->a,*aa,*ap,*dk,*uik;
     15:   MatScalar      *u,*diag,*rtmp,*rtmp_ptr;
     16:   PetscReal      shift = info->shiftamount;
     17:   PetscBool      allowzeropivot,zeropivotdetected;

     20:   /* initialization */
     21:   allowzeropivot = PetscNot(A->erroriffailure);
     22:   PetscCalloc1(9*mbs,&rtmp);
     23:   PetscMalloc2(mbs,&il,mbs,&jl);
     24:   il[0] = 0;
     25:   for (i=0; i<mbs; i++) jl[i] = mbs;
     26:
     27:   PetscMalloc2(9,&dk,9,&uik);
     28:   ai   = a->i; aj = a->j; aa = a->a;

     30:   /* for each row k */
     31:   for (k = 0; k<mbs; k++) {

     33:     /*initialize k-th row with elements nonzero in row k of A */
     34:     jmin = ai[k]; jmax = ai[k+1];
     35:     if (jmin < jmax) {
     36:       ap = aa + jmin*9;
     37:       for (j = jmin; j < jmax; j++) {
     38:         vj       = aj[j];   /* block col. index */
     39:         rtmp_ptr = rtmp + vj*9;
     40:         for (i=0; i<9; i++) *rtmp_ptr++ = *ap++;
     41:       }
     42:     }

     44:     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
     45:     PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));
     46:     i    = jl[k]; /* first row to be added to k_th row  */

     48:     while (i < mbs) {
     49:       nexti = jl[i]; /* next row to be added to k_th row */

     51:       /* compute multiplier */
     52:       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */

     54:       /* uik = -inv(Di)*U_bar(i,k) */
     55:       diag = ba + i*9;
     56:       u    = ba + ili*9;

     58:       uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]);
     59:       uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]);
     60:       uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]);

     62:       uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]);
     63:       uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]);
     64:       uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]);

     66:       uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]);
     67:       uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]);
     68:       uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]);

     70:       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
     71:       dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
     72:       dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
     73:       dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];

     75:       dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
     76:       dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
     77:       dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];

     79:       dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
     80:       dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
     81:       dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];

     83:       PetscLogFlops(27.0*4.0);

     85:       /* update -U(i,k) */
     86:       PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));

     88:       /* add multiple of row i to k-th row ... */
     89:       jmin = ili + 1; jmax = bi[i+1];
     90:       if (jmin < jmax) {
     91:         for (j=jmin; j<jmax; j++) {
     92:           /* rtmp += -U(i,k)^T * U_bar(i,j) */
     93:           rtmp_ptr     = rtmp + bj[j]*9;
     94:           u            = ba + j*9;
     95:           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
     96:           rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
     97:           rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];

     99:           rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
    100:           rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
    101:           rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];

    103:           rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
    104:           rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
    105:           rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
    106:         }
    107:         PetscLogFlops(2.0*27.0*(jmax-jmin));

    109:         /* ... add i to row list for next nonzero entry */
    110:         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
    111:         j     = bj[jmin];
    112:         jl[i] = jl[j]; jl[j] = i; /* update jl */
    113:       }
    114:       i = nexti;
    115:     }

    117:     /* save nonzero entries in k-th row of U ... */

    119:     /* invert diagonal block */
    120:     diag = ba+k*9;
    121:     PetscMemcpy(diag,dk,9*sizeof(MatScalar));
    122:     PetscKernel_A_gets_inverse_A_3(diag,shift,allowzeropivot,&zeropivotdetected);
    123:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    125:     jmin = bi[k]; jmax = bi[k+1];
    126:     if (jmin < jmax) {
    127:       for (j=jmin; j<jmax; j++) {
    128:         vj       = bj[j];      /* block col. index of U */
    129:         u        = ba + j*9;
    130:         rtmp_ptr = rtmp + vj*9;
    131:         for (k1=0; k1<9; k1++) {
    132:           *u++        = *rtmp_ptr;
    133:           *rtmp_ptr++ = 0.0;
    134:         }
    135:       }

    137:       /* ... add k to row list for first nonzero entry in k-th row */
    138:       il[k] = jmin;
    139:       i     = bj[jmin];
    140:       jl[k] = jl[i]; jl[i] = k;
    141:     }
    142:   }

    144:   PetscFree(rtmp);
    145:   PetscFree2(il,jl);
    146:   PetscFree2(dk,uik);

    148:   C->ops->solve          = MatSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
    149:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
    150:   C->ops->forwardsolve   = MatForwardSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
    151:   C->ops->backwardsolve  = MatBackwardSolve_SeqSBAIJ_3_NaturalOrdering_inplace;

    153:   C->assembled    = PETSC_TRUE;
    154:   C->preallocated = PETSC_TRUE;

    156:   PetscLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
    157:   return(0);
    158: }