xref: /petsc/src/mat/impls/baij/seq/baijsolvtrannat3.c (revision 31d78bcd2b98084dc1368b20eb1129c8b9fb39fe)

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

PetscErrorCode MatSolveTranspose_SeqBAIJ_3_NaturalOrdering_inplace(Mat A, Vec bb, Vec xx)
{
  Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
  const PetscInt   n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
  PetscInt         i, nz, idx, idt, oidx;
  const MatScalar *aa = a->a, *v;
  PetscScalar      s1, s2, s3, x1, x2, x3, *x;

  PetscFunctionBegin;
  PetscCall(VecCopy(bb, xx));
  PetscCall(VecGetArray(xx, &x));

  /* forward solve the U^T */
  idx = 0;
  for (i = 0; i < n; i++) {
    v = aa + 9 * diag[i];
    /* multiply by the inverse of the block diagonal */
    x1 = x[idx];
    x2 = x[1 + idx];
    x3 = x[2 + idx];
    s1 = v[0] * x1 + v[1] * x2 + v[2] * x3;
    s2 = v[3] * x1 + v[4] * x2 + v[5] * x3;
    s3 = v[6] * x1 + v[7] * x2 + v[8] * x3;
    v += 9;

    vi = aj + diag[i] + 1;
    nz = ai[i + 1] - diag[i] - 1;
    while (nz--) {
      oidx = 3 * (*vi++);
      x[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
      x[oidx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
      x[oidx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
      v += 9;
    }
    x[idx]     = s1;
    x[1 + idx] = s2;
    x[2 + idx] = s3;
    idx += 3;
  }
  /* backward solve the L^T */
  for (i = n - 1; i >= 0; i--) {
    v   = aa + 9 * diag[i] - 9;
    vi  = aj + diag[i] - 1;
    nz  = diag[i] - ai[i];
    idt = 3 * i;
    s1  = x[idt];
    s2  = x[1 + idt];
    s3  = x[2 + idt];
    while (nz--) {
      idx = 3 * (*vi--);
      x[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
      x[idx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
      x[idx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
      v -= 9;
    }
  }
  PetscCall(VecRestoreArray(xx, &x));
  PetscCall(PetscLogFlops(2.0 * 9.0 * (a->nz) - 3.0 * A->cmap->n));
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

  PetscFunctionBegin;
  PetscCall(VecCopy(bb, xx));
  PetscCall(VecGetArray(xx, &x));

  /* forward solve the U^T */
  idx = 0;
  for (i = 0; i < n; i++) {
    v = aa + bs2 * diag[i];
    /* multiply by the inverse of the block diagonal */
    x1 = x[idx];
    x2 = x[1 + idx];
    x3 = x[2 + idx];
    s1 = v[0] * x1 + v[1] * x2 + v[2] * x3;
    s2 = v[3] * x1 + v[4] * x2 + v[5] * x3;
    s3 = v[6] * x1 + v[7] * x2 + v[8] * x3;
    v -= bs2;

    vi = aj + diag[i] - 1;
    nz = diag[i] - diag[i + 1] - 1;
    for (j = 0; j > -nz; j--) {
      oidx = bs * vi[j];
      x[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
      x[oidx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
      x[oidx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
      v -= bs2;
    }
    x[idx]     = s1;
    x[1 + idx] = s2;
    x[2 + idx] = s3;
    idx += bs;
  }
  /* backward solve the L^T */
  for (i = n - 1; i >= 0; i--) {
    v   = aa + bs2 * ai[i];
    vi  = aj + ai[i];
    nz  = ai[i + 1] - ai[i];
    idt = bs * i;
    s1  = x[idt];
    s2  = x[1 + idt];
    s3  = x[2 + idt];
    for (j = 0; j < nz; j++) {
      idx = bs * vi[j];
      x[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
      x[idx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
      x[idx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
      v += bs2;
    }
  }
  PetscCall(VecRestoreArray(xx, &x));
  PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n));
  PetscFunctionReturn(PETSC_SUCCESS);
}