Actual source code: sbaijfact4.c

      1: #include <../src/mat/impls/sbaij/seq/sbaij.h>
      2: #include <petsc/private/kernels/blockinvert.h>

      4: /*
      5:       Version for when blocks are 3 by 3 Using natural ordering
      6: */
      7: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat C, Mat A, const MatFactorInfo *info)
      8: {
      9:   Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ *)A->data, *b = (Mat_SeqSBAIJ *)C->data;
     10:   PetscInt      i, j, mbs = a->mbs, *bi = b->i, *bj = b->j;
     11:   PetscInt     *ai, *aj, k, k1, jmin, jmax, *jl, *il, vj, nexti, ili;
     12:   MatScalar    *ba = b->a, *aa, *ap, *dk, *uik;
     13:   MatScalar    *u, *diag, *rtmp, *rtmp_ptr;
     14:   PetscReal     shift = info->shiftamount;
     15:   PetscBool     allowzeropivot, zeropivotdetected;

     17:   PetscFunctionBegin;
     18:   /* initialization */
     19:   allowzeropivot = PetscNot(A->erroriffailure);
     20:   PetscCall(PetscCalloc1(9 * mbs, &rtmp));
     21:   PetscCall(PetscMalloc2(mbs, &il, mbs, &jl));
     22:   il[0] = 0;
     23:   for (i = 0; i < mbs; i++) jl[i] = mbs;

     25:   PetscCall(PetscMalloc2(9, &dk, 9, &uik));
     26:   ai = a->i;
     27:   aj = a->j;
     28:   aa = a->a;

     30:   /* for each row k */
     31:   for (k = 0; k < mbs; k++) {
     32:     /*initialize k-th row with elements nonzero in row k of A */
     33:     jmin = ai[k];
     34:     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:     PetscCall(PetscArraycpy(dk, rtmp + k * 9, 9));
     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:       PetscCall(PetscLogFlops(27.0 * 4.0));

     85:       /* update -U(i,k) */
     86:       PetscCall(PetscArraycpy(ba + ili * 9, uik, 9));

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

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

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

    110:         /* ... add i to row list for next nonzero entry */
    111:         il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
    112:         j     = bj[jmin];
    113:         jl[i] = jl[j];
    114:         jl[j] = i; /* update jl */
    115:       }
    116:       i = nexti;
    117:     }

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

    121:     /* invert diagonal block */
    122:     diag = ba + k * 9;
    123:     PetscCall(PetscArraycpy(diag, dk, 9));
    124:     PetscCall(PetscKernel_A_gets_inverse_A_3(diag, shift, allowzeropivot, &zeropivotdetected));
    125:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    127:     jmin = bi[k];
    128:     jmax = bi[k + 1];
    129:     if (jmin < jmax) {
    130:       for (j = jmin; j < jmax; j++) {
    131:         vj       = bj[j]; /* block col. index of U */
    132:         u        = ba + j * 9;
    133:         rtmp_ptr = rtmp + vj * 9;
    134:         for (k1 = 0; k1 < 9; k1++) {
    135:           *u++        = *rtmp_ptr;
    136:           *rtmp_ptr++ = 0.0;
    137:         }
    138:       }

    140:       /* ... add k to row list for first nonzero entry in k-th row */
    141:       il[k] = jmin;
    142:       i     = bj[jmin];
    143:       jl[k] = jl[i];
    144:       jl[i] = k;
    145:     }
    146:   }

    148:   PetscCall(PetscFree(rtmp));
    149:   PetscCall(PetscFree2(il, jl));
    150:   PetscCall(PetscFree2(dk, uik));

    152:   C->ops->solve          = MatSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
    153:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
    154:   C->ops->forwardsolve   = MatForwardSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
    155:   C->ops->backwardsolve  = MatBackwardSolve_SeqSBAIJ_3_NaturalOrdering_inplace;

    157:   C->assembled    = PETSC_TRUE;
    158:   C->preallocated = PETSC_TRUE;

    160:   PetscCall(PetscLogFlops(1.3333 * 27 * b->mbs)); /* from inverting diagonal blocks */
    161:   PetscFunctionReturn(PETSC_SUCCESS);
    162: }