xref: /petsc/src/mat/impls/baij/seq/baijsolvtrannat4.c (revision 9371c9d470a9602b6d10a8bf50c9b2280a79e45a)

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

PetscErrorCode MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_inplace(Mat A, Vec bb, Vec xx) {
  Mat_SeqBAIJ     *a    = (Mat_SeqBAIJ *)A->data;
  const PetscInt  *diag = a->diag, n = a->mbs, *vi, *ai = a->i, *aj = a->j;
  PetscInt         i, nz, idx, idt, oidx;
  const MatScalar *aa = a->a, *v;
  PetscScalar      s1, s2, s3, s4, x1, x2, x3, x4, *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 + 16 * diag[i];
    /* multiply by the inverse of the block diagonal */
    x1 = x[idx];
    x2 = x[1 + idx];
    x3 = x[2 + idx];
    x4 = x[3 + idx];
    s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4;
    s2 = v[4] * x1 + v[5] * x2 + v[6] * x3 + v[7] * x4;
    s3 = v[8] * x1 + v[9] * x2 + v[10] * x3 + v[11] * x4;
    s4 = v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4;
    v += 16;

    vi = aj + diag[i] + 1;
    nz = ai[i + 1] - diag[i] - 1;
    while (nz--) {
      oidx = 4 * (*vi++);
      x[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4;
      x[oidx + 1] -= v[4] * s1 + v[5] * s2 + v[6] * s3 + v[7] * s4;
      x[oidx + 2] -= v[8] * s1 + v[9] * s2 + v[10] * s3 + v[11] * s4;
      x[oidx + 3] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4;
      v += 16;
    }
    x[idx]     = s1;
    x[1 + idx] = s2;
    x[2 + idx] = s3;
    x[3 + idx] = s4;
    idx += 4;
  }
  /* backward solve the L^T */
  for (i = n - 1; i >= 0; i--) {
    v   = aa + 16 * diag[i] - 16;
    vi  = aj + diag[i] - 1;
    nz  = diag[i] - ai[i];
    idt = 4 * i;
    s1  = x[idt];
    s2  = x[1 + idt];
    s3  = x[2 + idt];
    s4  = x[3 + idt];
    while (nz--) {
      idx = 4 * (*vi--);
      x[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4;
      x[idx + 1] -= v[4] * s1 + v[5] * s2 + v[6] * s3 + v[7] * s4;
      x[idx + 2] -= v[8] * s1 + v[9] * s2 + v[10] * s3 + v[11] * s4;
      x[idx + 3] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4;
      v -= 16;
    }
  }
  PetscCall(VecRestoreArray(xx, &x));
  PetscCall(PetscLogFlops(2.0 * 16 * (a->nz) - 4.0 * A->cmap->n));
  PetscFunctionReturn(0);
}

PetscErrorCode MatSolveTranspose_SeqBAIJ_4_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, s4, x1, x2, x3, x4, *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];
    x4 = x[3 + idx];
    s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4;
    s2 = v[4] * x1 + v[5] * x2 + v[6] * x3 + v[7] * x4;
    s3 = v[8] * x1 + v[9] * x2 + v[10] * x3 + v[11] * x4;
    s4 = v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4;
    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 + v[3] * s4;
      x[oidx + 1] -= v[4] * s1 + v[5] * s2 + v[6] * s3 + v[7] * s4;
      x[oidx + 2] -= v[8] * s1 + v[9] * s2 + v[10] * s3 + v[11] * s4;
      x[oidx + 3] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4;
      v -= bs2;
    }
    x[idx]     = s1;
    x[1 + idx] = s2;
    x[2 + idx] = s3;
    x[3 + idx] = s4;
    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];
    s4  = x[3 + idt];
    for (j = 0; j < nz; j++) {
      idx = bs * vi[j];
      x[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4;
      x[idx + 1] -= v[4] * s1 + v[5] * s2 + v[6] * s3 + v[7] * s4;
      x[idx + 2] -= v[8] * s1 + v[9] * s2 + v[10] * s3 + v[11] * s4;
      x[idx + 3] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4;
      v += bs2;
    }
  }
  PetscCall(VecRestoreArray(xx, &x));
  PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n));
  PetscFunctionReturn(0);
}