xref: /petsc/src/mat/impls/baij/seq/baijsolvnat6.c (revision 9371c9d470a9602b6d10a8bf50c9b2280a79e45a)

#include <../src/mat/impls/baij/seq/baij.h>
#include <petsc/private/kernels/blockinvert.h>

PetscErrorCode MatSolve_SeqBAIJ_6_NaturalOrdering_inplace(Mat A, Vec bb, Vec xx) {
  Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
  PetscInt           i, nz, idx, idt, jdx;
  const PetscInt    *diag = a->diag, *vi, n = a->mbs, *ai = a->i, *aj = a->j;
  const MatScalar   *aa = a->a, *v;
  PetscScalar       *x, s1, s2, s3, s4, s5, s6, x1, x2, x3, x4, x5, x6;
  const PetscScalar *b;

  PetscFunctionBegin;
  PetscCall(VecGetArrayRead(bb, &b));
  PetscCall(VecGetArray(xx, &x));
  /* forward solve the lower triangular */
  idx  = 0;
  x[0] = b[idx];
  x[1] = b[1 + idx];
  x[2] = b[2 + idx];
  x[3] = b[3 + idx];
  x[4] = b[4 + idx];
  x[5] = b[5 + idx];
  for (i = 1; i < n; i++) {
    v   = aa + 36 * ai[i];
    vi  = aj + ai[i];
    nz  = diag[i] - ai[i];
    idx = 6 * i;
    s1  = b[idx];
    s2  = b[1 + idx];
    s3  = b[2 + idx];
    s4  = b[3 + idx];
    s5  = b[4 + idx];
    s6  = b[5 + idx];
    while (nz--) {
      jdx = 6 * (*vi++);
      x1  = x[jdx];
      x2  = x[1 + jdx];
      x3  = x[2 + jdx];
      x4  = x[3 + jdx];
      x5  = x[4 + jdx];
      x6  = x[5 + jdx];
      s1 -= v[0] * x1 + v[6] * x2 + v[12] * x3 + v[18] * x4 + v[24] * x5 + v[30] * x6;
      s2 -= v[1] * x1 + v[7] * x2 + v[13] * x3 + v[19] * x4 + v[25] * x5 + v[31] * x6;
      s3 -= v[2] * x1 + v[8] * x2 + v[14] * x3 + v[20] * x4 + v[26] * x5 + v[32] * x6;
      s4 -= v[3] * x1 + v[9] * x2 + v[15] * x3 + v[21] * x4 + v[27] * x5 + v[33] * x6;
      s5 -= v[4] * x1 + v[10] * x2 + v[16] * x3 + v[22] * x4 + v[28] * x5 + v[34] * x6;
      s6 -= v[5] * x1 + v[11] * x2 + v[17] * x3 + v[23] * x4 + v[29] * x5 + v[35] * x6;
      v += 36;
    }
    x[idx]     = s1;
    x[1 + idx] = s2;
    x[2 + idx] = s3;
    x[3 + idx] = s4;
    x[4 + idx] = s5;
    x[5 + idx] = s6;
  }
  /* backward solve the upper triangular */
  for (i = n - 1; i >= 0; i--) {
    v   = aa + 36 * diag[i] + 36;
    vi  = aj + diag[i] + 1;
    nz  = ai[i + 1] - diag[i] - 1;
    idt = 6 * i;
    s1  = x[idt];
    s2  = x[1 + idt];
    s3  = x[2 + idt];
    s4  = x[3 + idt];
    s5  = x[4 + idt];
    s6  = x[5 + idt];
    while (nz--) {
      idx = 6 * (*vi++);
      x1  = x[idx];
      x2  = x[1 + idx];
      x3  = x[2 + idx];
      x4  = x[3 + idx];
      x5  = x[4 + idx];
      x6  = x[5 + idx];
      s1 -= v[0] * x1 + v[6] * x2 + v[12] * x3 + v[18] * x4 + v[24] * x5 + v[30] * x6;
      s2 -= v[1] * x1 + v[7] * x2 + v[13] * x3 + v[19] * x4 + v[25] * x5 + v[31] * x6;
      s3 -= v[2] * x1 + v[8] * x2 + v[14] * x3 + v[20] * x4 + v[26] * x5 + v[32] * x6;
      s4 -= v[3] * x1 + v[9] * x2 + v[15] * x3 + v[21] * x4 + v[27] * x5 + v[33] * x6;
      s5 -= v[4] * x1 + v[10] * x2 + v[16] * x3 + v[22] * x4 + v[28] * x5 + v[34] * x6;
      s6 -= v[5] * x1 + v[11] * x2 + v[17] * x3 + v[23] * x4 + v[29] * x5 + v[35] * x6;
      v += 36;
    }
    v          = aa + 36 * diag[i];
    x[idt]     = v[0] * s1 + v[6] * s2 + v[12] * s3 + v[18] * s4 + v[24] * s5 + v[30] * s6;
    x[1 + idt] = v[1] * s1 + v[7] * s2 + v[13] * s3 + v[19] * s4 + v[25] * s5 + v[31] * s6;
    x[2 + idt] = v[2] * s1 + v[8] * s2 + v[14] * s3 + v[20] * s4 + v[26] * s5 + v[32] * s6;
    x[3 + idt] = v[3] * s1 + v[9] * s2 + v[15] * s3 + v[21] * s4 + v[27] * s5 + v[33] * s6;
    x[4 + idt] = v[4] * s1 + v[10] * s2 + v[16] * s3 + v[22] * s4 + v[28] * s5 + v[34] * s6;
    x[5 + idt] = v[5] * s1 + v[11] * s2 + v[17] * s3 + v[23] * s4 + v[29] * s5 + v[35] * s6;
  }

  PetscCall(VecRestoreArrayRead(bb, &b));
  PetscCall(VecRestoreArray(xx, &x));
  PetscCall(PetscLogFlops(2.0 * 36 * (a->nz) - 6.0 * A->cmap->n));
  PetscFunctionReturn(0);
}

PetscErrorCode MatSolve_SeqBAIJ_6_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, *adiag = a->diag;
  PetscInt           i, k, nz, idx, jdx, idt;
  const PetscInt     bs = A->rmap->bs, bs2 = a->bs2;
  const MatScalar   *aa = a->a, *v;
  PetscScalar       *x;
  const PetscScalar *b;
  PetscScalar        s1, s2, s3, s4, s5, s6, x1, x2, x3, x4, x5, x6;

  PetscFunctionBegin;
  PetscCall(VecGetArrayRead(bb, &b));
  PetscCall(VecGetArray(xx, &x));
  /* forward solve the lower triangular */
  idx  = 0;
  x[0] = b[idx];
  x[1] = b[1 + idx];
  x[2] = b[2 + idx];
  x[3] = b[3 + idx];
  x[4] = b[4 + idx];
  x[5] = b[5 + idx];
  for (i = 1; i < n; i++) {
    v   = aa + bs2 * ai[i];
    vi  = aj + ai[i];
    nz  = ai[i + 1] - ai[i];
    idx = bs * i;
    s1  = b[idx];
    s2  = b[1 + idx];
    s3  = b[2 + idx];
    s4  = b[3 + idx];
    s5  = b[4 + idx];
    s6  = b[5 + idx];
    for (k = 0; k < nz; k++) {
      jdx = bs * vi[k];
      x1  = x[jdx];
      x2  = x[1 + jdx];
      x3  = x[2 + jdx];
      x4  = x[3 + jdx];
      x5  = x[4 + jdx];
      x6  = x[5 + jdx];
      s1 -= v[0] * x1 + v[6] * x2 + v[12] * x3 + v[18] * x4 + v[24] * x5 + v[30] * x6;
      s2 -= v[1] * x1 + v[7] * x2 + v[13] * x3 + v[19] * x4 + v[25] * x5 + v[31] * x6;
      s3 -= v[2] * x1 + v[8] * x2 + v[14] * x3 + v[20] * x4 + v[26] * x5 + v[32] * x6;
      s4 -= v[3] * x1 + v[9] * x2 + v[15] * x3 + v[21] * x4 + v[27] * x5 + v[33] * x6;
      s5 -= v[4] * x1 + v[10] * x2 + v[16] * x3 + v[22] * x4 + v[28] * x5 + v[34] * x6;
      s6 -= v[5] * x1 + v[11] * x2 + v[17] * x3 + v[23] * x4 + v[29] * x5 + v[35] * x6;
      v += bs2;
    }

    x[idx]     = s1;
    x[1 + idx] = s2;
    x[2 + idx] = s3;
    x[3 + idx] = s4;
    x[4 + idx] = s5;
    x[5 + idx] = s6;
  }

  /* backward solve the upper triangular */
  for (i = n - 1; i >= 0; i--) {
    v   = aa + bs2 * (adiag[i + 1] + 1);
    vi  = aj + adiag[i + 1] + 1;
    nz  = adiag[i] - adiag[i + 1] - 1;
    idt = bs * i;
    s1  = x[idt];
    s2  = x[1 + idt];
    s3  = x[2 + idt];
    s4  = x[3 + idt];
    s5  = x[4 + idt];
    s6  = x[5 + idt];
    for (k = 0; k < nz; k++) {
      idx = bs * vi[k];
      x1  = x[idx];
      x2  = x[1 + idx];
      x3  = x[2 + idx];
      x4  = x[3 + idx];
      x5  = x[4 + idx];
      x6  = x[5 + idx];
      s1 -= v[0] * x1 + v[6] * x2 + v[12] * x3 + v[18] * x4 + v[24] * x5 + v[30] * x6;
      s2 -= v[1] * x1 + v[7] * x2 + v[13] * x3 + v[19] * x4 + v[25] * x5 + v[31] * x6;
      s3 -= v[2] * x1 + v[8] * x2 + v[14] * x3 + v[20] * x4 + v[26] * x5 + v[32] * x6;
      s4 -= v[3] * x1 + v[9] * x2 + v[15] * x3 + v[21] * x4 + v[27] * x5 + v[33] * x6;
      s5 -= v[4] * x1 + v[10] * x2 + v[16] * x3 + v[22] * x4 + v[28] * x5 + v[34] * x6;
      s6 -= v[5] * x1 + v[11] * x2 + v[17] * x3 + v[23] * x4 + v[29] * x5 + v[35] * x6;
      v += bs2;
    }
    /* x = inv_diagonal*x */
    x[idt]     = v[0] * s1 + v[6] * s2 + v[12] * s3 + v[18] * s4 + v[24] * s5 + v[30] * s6;
    x[1 + idt] = v[1] * s1 + v[7] * s2 + v[13] * s3 + v[19] * s4 + v[25] * s5 + v[31] * s6;
    x[2 + idt] = v[2] * s1 + v[8] * s2 + v[14] * s3 + v[20] * s4 + v[26] * s5 + v[32] * s6;
    x[3 + idt] = v[3] * s1 + v[9] * s2 + v[15] * s3 + v[21] * s4 + v[27] * s5 + v[33] * s6;
    x[4 + idt] = v[4] * s1 + v[10] * s2 + v[16] * s3 + v[22] * s4 + v[28] * s5 + v[34] * s6;
    x[5 + idt] = v[5] * s1 + v[11] * s2 + v[17] * s3 + v[23] * s4 + v[29] * s5 + v[35] * s6;
  }

  PetscCall(VecRestoreArrayRead(bb, &b));
  PetscCall(VecRestoreArray(xx, &x));
  PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n));
  PetscFunctionReturn(0);
}