Date: 2025-03-29T05:58:34+00:00

Actual source code: baijsolvtrannat2.c

      1: #include <../src/mat/impls/baij/seq/baij.h>

      3: PetscErrorCode MatSolveTranspose_SeqBAIJ_2_NaturalOrdering_inplace(Mat A, Vec bb, Vec xx)
      4: {
      5:   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
      6:   PetscInt         i, nz, idx, idt, oidx;
      7:   const PetscInt  *diag = a->diag, *vi, n = a->mbs, *ai = a->i, *aj = a->j;
      8:   const MatScalar *aa = a->a, *v;
      9:   PetscScalar      s1, s2, x1, x2, *x;

     11:   PetscFunctionBegin;
     12:   PetscCall(VecCopy(bb, xx));
     13:   PetscCall(VecGetArray(xx, &x));

     15:   /* forward solve the U^T */
     16:   idx = 0;
     17:   for (i = 0; i < n; i++) {
     18:     v = aa + 4 * diag[i];
     19:     /* multiply by the inverse of the block diagonal */
     20:     x1 = x[idx];
     21:     x2 = x[1 + idx];
     22:     s1 = v[0] * x1 + v[1] * x2;
     23:     s2 = v[2] * x1 + v[3] * x2;
     24:     v += 4;

     26:     vi = aj + diag[i] + 1;
     27:     nz = ai[i + 1] - diag[i] - 1;
     28:     while (nz--) {
     29:       oidx = 2 * (*vi++);
     30:       x[oidx] -= v[0] * s1 + v[1] * s2;
     31:       x[oidx + 1] -= v[2] * s1 + v[3] * s2;
     32:       v += 4;
     33:     }
     34:     x[idx]     = s1;
     35:     x[1 + idx] = s2;
     36:     idx += 2;
     37:   }
     38:   /* backward solve the L^T */
     39:   for (i = n - 1; i >= 0; i--) {
     40:     v   = aa + 4 * diag[i] - 4;
     41:     vi  = aj + diag[i] - 1;
     42:     nz  = diag[i] - ai[i];
     43:     idt = 2 * i;
     44:     s1  = x[idt];
     45:     s2  = x[1 + idt];
     46:     while (nz--) {
     47:       idx = 2 * (*vi--);
     48:       x[idx] -= v[0] * s1 + v[1] * s2;
     49:       x[idx + 1] -= v[2] * s1 + v[3] * s2;
     50:       v -= 4;
     51:     }
     52:   }
     53:   PetscCall(VecRestoreArray(xx, &x));
     54:   PetscCall(PetscLogFlops(2.0 * 4.0 * (a->nz) - 2.0 * A->cmap->n));
     55:   PetscFunctionReturn(PETSC_SUCCESS);
     56: }

     58: PetscErrorCode MatSolveTranspose_SeqBAIJ_2_NaturalOrdering(Mat A, Vec bb, Vec xx)
     59: {
     60:   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
     61:   const PetscInt   n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
     62:   PetscInt         nz, idx, idt, j, i, oidx;
     63:   const PetscInt   bs = A->rmap->bs, bs2 = a->bs2;
     64:   const MatScalar *aa = a->a, *v;
     65:   PetscScalar      s1, s2, x1, x2, *x;

     67:   PetscFunctionBegin;
     68:   PetscCall(VecCopy(bb, xx));
     69:   PetscCall(VecGetArray(xx, &x));

     71:   /* forward solve the U^T */
     72:   idx = 0;
     73:   for (i = 0; i < n; i++) {
     74:     v = aa + bs2 * diag[i];
     75:     /* multiply by the inverse of the block diagonal */
     76:     x1 = x[idx];
     77:     x2 = x[1 + idx];
     78:     s1 = v[0] * x1 + v[1] * x2;
     79:     s2 = v[2] * x1 + v[3] * x2;
     80:     v -= bs2;

     82:     vi = aj + diag[i] - 1;
     83:     nz = diag[i] - diag[i + 1] - 1;
     84:     for (j = 0; j > -nz; j--) {
     85:       oidx = bs * vi[j];
     86:       x[oidx] -= v[0] * s1 + v[1] * s2;
     87:       x[oidx + 1] -= v[2] * s1 + v[3] * s2;
     88:       v -= bs2;
     89:     }
     90:     x[idx]     = s1;
     91:     x[1 + idx] = s2;
     92:     idx += bs;
     93:   }
     94:   /* backward solve the L^T */
     95:   for (i = n - 1; i >= 0; i--) {
     96:     v   = aa + bs2 * ai[i];
     97:     vi  = aj + ai[i];
     98:     nz  = ai[i + 1] - ai[i];
     99:     idt = bs * i;
    100:     s1  = x[idt];
    101:     s2  = x[1 + idt];
    102:     for (j = 0; j < nz; j++) {
    103:       idx = bs * vi[j];
    104:       x[idx] -= v[0] * s1 + v[1] * s2;
    105:       x[idx + 1] -= v[2] * s1 + v[3] * s2;
    106:       v += bs2;
    107:     }
    108:   }
    109:   PetscCall(VecRestoreArray(xx, &x));
    110:   PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n));
    111:   PetscFunctionReturn(PETSC_SUCCESS);
    112: }