xref: /petsc/src/mat/impls/baij/seq/baijsolvnat3.c (revision 9371c9d470a9602b6d10a8bf50c9b2280a79e45a)

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

/*
      Special case where the matrix was ILU(0) factored in the natural
   ordering. This eliminates the need for the column and row permutation.
*/
PetscErrorCode MatSolve_SeqBAIJ_3_NaturalOrdering_inplace(Mat A, Vec bb, Vec xx) {
  Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
  const PetscInt     n = a->mbs, *ai = a->i, *aj = a->j;
  const PetscInt    *diag = a->diag, *vi;
  const MatScalar   *aa   = a->a, *v;
  PetscScalar       *x, s1, s2, s3, x1, x2, x3;
  const PetscScalar *b;
  PetscInt           jdx, idt, idx, nz, i;

  PetscFunctionBegin;
  PetscCall(VecGetArrayRead(bb, &b));
  PetscCall(VecGetArray(xx, &x));

  /* forward solve the lower triangular */
  idx  = 0;
  x[0] = b[0];
  x[1] = b[1];
  x[2] = b[2];
  for (i = 1; i < n; i++) {
    v  = aa + 9 * ai[i];
    vi = aj + ai[i];
    nz = diag[i] - ai[i];
    idx += 3;
    s1 = b[idx];
    s2 = b[1 + idx];
    s3 = b[2 + idx];
    while (nz--) {
      jdx = 3 * (*vi++);
      x1  = x[jdx];
      x2  = x[1 + jdx];
      x3  = x[2 + jdx];
      s1 -= v[0] * x1 + v[3] * x2 + v[6] * x3;
      s2 -= v[1] * x1 + v[4] * x2 + v[7] * x3;
      s3 -= v[2] * x1 + v[5] * x2 + v[8] * x3;
      v += 9;
    }
    x[idx]     = s1;
    x[1 + idx] = s2;
    x[2 + idx] = s3;
  }
  /* backward solve the upper triangular */
  for (i = n - 1; i >= 0; i--) {
    v   = aa + 9 * diag[i] + 9;
    vi  = aj + diag[i] + 1;
    nz  = ai[i + 1] - diag[i] - 1;
    idt = 3 * i;
    s1  = x[idt];
    s2  = x[1 + idt];
    s3  = x[2 + idt];
    while (nz--) {
      idx = 3 * (*vi++);
      x1  = x[idx];
      x2  = x[1 + idx];
      x3  = x[2 + idx];
      s1 -= v[0] * x1 + v[3] * x2 + v[6] * x3;
      s2 -= v[1] * x1 + v[4] * x2 + v[7] * x3;
      s3 -= v[2] * x1 + v[5] * x2 + v[8] * x3;
      v += 9;
    }
    v          = aa + 9 * diag[i];
    x[idt]     = v[0] * s1 + v[3] * s2 + v[6] * s3;
    x[1 + idt] = v[1] * s1 + v[4] * s2 + v[7] * s3;
    x[2 + idt] = v[2] * s1 + v[5] * s2 + v[8] * s3;
  }

  PetscCall(VecRestoreArrayRead(bb, &b));
  PetscCall(VecRestoreArray(xx, &x));
  PetscCall(PetscLogFlops(2.0 * 9 * (a->nz) - 3.0 * A->cmap->n));
  PetscFunctionReturn(0);
}

PetscErrorCode MatSolve_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, *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, x1, x2, x3;

  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];
  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];
    for (k = 0; k < nz; k++) {
      jdx = bs * vi[k];
      x1  = x[jdx];
      x2  = x[1 + jdx];
      x3  = x[2 + jdx];
      s1 -= v[0] * x1 + v[3] * x2 + v[6] * x3;
      s2 -= v[1] * x1 + v[4] * x2 + v[7] * x3;
      s3 -= v[2] * x1 + v[5] * x2 + v[8] * x3;

      v += bs2;
    }

    x[idx]     = s1;
    x[1 + idx] = s2;
    x[2 + idx] = s3;
  }

  /* 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];

    for (k = 0; k < nz; k++) {
      idx = bs * vi[k];
      x1  = x[idx];
      x2  = x[1 + idx];
      x3  = x[2 + idx];
      s1 -= v[0] * x1 + v[3] * x2 + v[6] * x3;
      s2 -= v[1] * x1 + v[4] * x2 + v[7] * x3;
      s3 -= v[2] * x1 + v[5] * x2 + v[8] * x3;

      v += bs2;
    }
    /* x = inv_diagonal*x */
    x[idt]     = v[0] * s1 + v[3] * s2 + v[6] * s3;
    x[1 + idt] = v[1] * s1 + v[4] * s2 + v[7] * s3;
    x[2 + idt] = v[2] * s1 + v[5] * s2 + v[8] * s3;
  }

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

PetscErrorCode MatForwardSolve_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;
  PetscInt           i, k, nz, idx, jdx;
  const PetscInt     bs = A->rmap->bs, bs2 = a->bs2;
  const MatScalar   *aa = a->a, *v;
  PetscScalar       *x;
  const PetscScalar *b;
  PetscScalar        s1, s2, s3, x1, x2, x3;

  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];
  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];
    for (k = 0; k < nz; k++) {
      jdx = bs * vi[k];
      x1  = x[jdx];
      x2  = x[1 + jdx];
      x3  = x[2 + jdx];
      s1 -= v[0] * x1 + v[3] * x2 + v[6] * x3;
      s2 -= v[1] * x1 + v[4] * x2 + v[7] * x3;
      s3 -= v[2] * x1 + v[5] * x2 + v[8] * x3;

      v += bs2;
    }

    x[idx]     = s1;
    x[1 + idx] = s2;
    x[2 + idx] = s3;
  }

  PetscCall(VecRestoreArrayRead(bb, &b));
  PetscCall(VecRestoreArray(xx, &x));
  PetscCall(PetscLogFlops(1.0 * bs2 * (a->nz) - bs * A->cmap->n));
  PetscFunctionReturn(0);
}

PetscErrorCode MatBackwardSolve_SeqBAIJ_3_NaturalOrdering(Mat A, Vec bb, Vec xx) {
  Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
  const PetscInt     n = a->mbs, *vi, *aj = a->j, *adiag = a->diag;
  PetscInt           i, k, nz, idx, 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, x1, x2, x3;

  PetscFunctionBegin;
  PetscCall(VecGetArrayRead(bb, &b));
  PetscCall(VecGetArray(xx, &x));

  /* 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  = b[idt];
    s2  = b[1 + idt];
    s3  = b[2 + idt];

    for (k = 0; k < nz; k++) {
      idx = bs * vi[k];
      x1  = x[idx];
      x2  = x[1 + idx];
      x3  = x[2 + idx];
      s1 -= v[0] * x1 + v[3] * x2 + v[6] * x3;
      s2 -= v[1] * x1 + v[4] * x2 + v[7] * x3;
      s3 -= v[2] * x1 + v[5] * x2 + v[8] * x3;

      v += bs2;
    }
    /* x = inv_diagonal*x */
    x[idt]     = v[0] * s1 + v[3] * s2 + v[6] * s3;
    x[1 + idt] = v[1] * s1 + v[4] * s2 + v[7] * s3;
    x[2 + idt] = v[2] * s1 + v[5] * s2 + v[8] * s3;
  }

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