Actual source code: baijsolvtrannat3.c

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

  3: PetscErrorCode MatSolveTranspose_SeqBAIJ_3_NaturalOrdering_inplace(Mat A, Vec bb, Vec xx)
  4: {
  5:   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
  6:   const PetscInt   n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
  7:   PetscInt         i, nz, idx, idt, oidx;
  8:   const MatScalar *aa = a->a, *v;
  9:   PetscScalar      s1, s2, s3, x1, x2, x3, *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 + 9 * diag[i];
 19:     /* multiply by the inverse of the block diagonal */
 20:     x1 = x[idx];
 21:     x2 = x[1 + idx];
 22:     x3 = x[2 + idx];
 23:     s1 = v[0] * x1 + v[1] * x2 + v[2] * x3;
 24:     s2 = v[3] * x1 + v[4] * x2 + v[5] * x3;
 25:     s3 = v[6] * x1 + v[7] * x2 + v[8] * x3;
 26:     v += 9;

 28:     vi = aj + diag[i] + 1;
 29:     nz = ai[i + 1] - diag[i] - 1;
 30:     while (nz--) {
 31:       oidx = 3 * (*vi++);
 32:       x[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
 33:       x[oidx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
 34:       x[oidx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
 35:       v += 9;
 36:     }
 37:     x[idx]     = s1;
 38:     x[1 + idx] = s2;
 39:     x[2 + idx] = s3;
 40:     idx += 3;
 41:   }
 42:   /* backward solve the L^T */
 43:   for (i = n - 1; i >= 0; i--) {
 44:     v   = aa + 9 * diag[i] - 9;
 45:     vi  = aj + diag[i] - 1;
 46:     nz  = diag[i] - ai[i];
 47:     idt = 3 * i;
 48:     s1  = x[idt];
 49:     s2  = x[1 + idt];
 50:     s3  = x[2 + idt];
 51:     while (nz--) {
 52:       idx = 3 * (*vi--);
 53:       x[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
 54:       x[idx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
 55:       x[idx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
 56:       v -= 9;
 57:     }
 58:   }
 59:   PetscCall(VecRestoreArray(xx, &x));
 60:   PetscCall(PetscLogFlops(2.0 * 9.0 * (a->nz) - 3.0 * A->cmap->n));
 61:   PetscFunctionReturn(PETSC_SUCCESS);
 62: }

 64: PetscErrorCode MatSolveTranspose_SeqBAIJ_3_NaturalOrdering(Mat A, Vec bb, Vec xx)
 65: {
 66:   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
 67:   const PetscInt   n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
 68:   PetscInt         nz, idx, idt, j, i, oidx;
 69:   const PetscInt   bs = A->rmap->bs, bs2 = a->bs2;
 70:   const MatScalar *aa = a->a, *v;
 71:   PetscScalar      s1, s2, s3, x1, x2, x3, *x;

 73:   PetscFunctionBegin;
 74:   PetscCall(VecCopy(bb, xx));
 75:   PetscCall(VecGetArray(xx, &x));

 77:   /* forward solve the U^T */
 78:   idx = 0;
 79:   for (i = 0; i < n; i++) {
 80:     v = aa + bs2 * diag[i];
 81:     /* multiply by the inverse of the block diagonal */
 82:     x1 = x[idx];
 83:     x2 = x[1 + idx];
 84:     x3 = x[2 + idx];
 85:     s1 = v[0] * x1 + v[1] * x2 + v[2] * x3;
 86:     s2 = v[3] * x1 + v[4] * x2 + v[5] * x3;
 87:     s3 = v[6] * x1 + v[7] * x2 + v[8] * x3;
 88:     v -= bs2;

 90:     vi = aj + diag[i] - 1;
 91:     nz = diag[i] - diag[i + 1] - 1;
 92:     for (j = 0; j > -nz; j--) {
 93:       oidx = bs * vi[j];
 94:       x[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
 95:       x[oidx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
 96:       x[oidx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
 97:       v -= bs2;
 98:     }
 99:     x[idx]     = s1;
100:     x[1 + idx] = s2;
101:     x[2 + idx] = s3;
102:     idx += bs;
103:   }
104:   /* backward solve the L^T */
105:   for (i = n - 1; i >= 0; i--) {
106:     v   = aa + bs2 * ai[i];
107:     vi  = aj + ai[i];
108:     nz  = ai[i + 1] - ai[i];
109:     idt = bs * i;
110:     s1  = x[idt];
111:     s2  = x[1 + idt];
112:     s3  = x[2 + idt];
113:     for (j = 0; j < nz; j++) {
114:       idx = bs * vi[j];
115:       x[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
116:       x[idx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
117:       x[idx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
118:       v += bs2;
119:     }
120:   }
121:   PetscCall(VecRestoreArray(xx, &x));
122:   PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n));
123:   PetscFunctionReturn(PETSC_SUCCESS);
124: }