xref: /petsc/src/mat/impls/baij/seq/baijsolvnat1.c (revision 31d78bcd2b98084dc1368b20eb1129c8b9fb39fe)

#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_1_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;
  const MatScalar   *aa = a->a, *v;
  PetscScalar       *x;
  const PetscScalar *b;
  PetscScalar        s1, x1;
  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];
  for (i = 1; i < n; i++) {
    v  = aa + ai[i];
    vi = aj + ai[i];
    nz = diag[i] - ai[i];
    idx += 1;
    s1 = b[idx];
    while (nz--) {
      jdx = *vi++;
      x1  = x[jdx];
      s1 -= v[0] * x1;
      v += 1;
    }
    x[idx] = s1;
  }
  /* backward solve the upper triangular */
  for (i = n - 1; i >= 0; i--) {
    v   = aa + diag[i] + 1;
    vi  = aj + diag[i] + 1;
    nz  = ai[i + 1] - diag[i] - 1;
    idt = i;
    s1  = x[idt];
    while (nz--) {
      idx = *vi++;
      x1  = x[idx];
      s1 -= v[0] * x1;
      v += 1;
    }
    v      = aa + diag[i];
    x[idt] = v[0] * s1;
  }
  PetscCall(VecRestoreArrayRead(bb, &b));
  PetscCall(VecRestoreArray(xx, &x));
  PetscCall(PetscLogFlops(2.0 * (a->nz) - A->cmap->n));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatForwardSolve_SeqBAIJ_1_NaturalOrdering(Mat A, Vec bb, Vec xx)
{
  Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
  const PetscInt     n = a->mbs, *ai = a->i, *aj = a->j, *vi;
  PetscScalar       *x, sum;
  const PetscScalar *b;
  const MatScalar   *aa = a->a, *v;
  PetscInt           i, nz;

  PetscFunctionBegin;
  if (!n) PetscFunctionReturn(PETSC_SUCCESS);

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

  /* forward solve the lower triangular */
  x[0] = b[0];
  v    = aa;
  vi   = aj;
  for (i = 1; i < n; i++) {
    nz  = ai[i + 1] - ai[i];
    sum = b[i];
    PetscSparseDenseMinusDot(sum, x, v, vi, nz);
    v += nz;
    vi += nz;
    x[i] = sum;
  }
  PetscCall(PetscLogFlops(a->nz - A->cmap->n));
  PetscCall(VecRestoreArrayRead(bb, &b));
  PetscCall(VecRestoreArray(xx, &x));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatBackwardSolve_SeqBAIJ_1_NaturalOrdering(Mat A, Vec bb, Vec xx)
{
  Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
  const PetscInt     n = a->mbs, *aj = a->j, *adiag = a->diag, *vi;
  PetscScalar       *x, sum;
  const PetscScalar *b;
  const MatScalar   *aa = a->a, *v;
  PetscInt           i, nz;

  PetscFunctionBegin;
  if (!n) PetscFunctionReturn(PETSC_SUCCESS);

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

  /* backward solve the upper triangular */
  for (i = n - 1; i >= 0; i--) {
    v   = aa + adiag[i + 1] + 1;
    vi  = aj + adiag[i + 1] + 1;
    nz  = adiag[i] - adiag[i + 1] - 1;
    sum = b[i];
    PetscSparseDenseMinusDot(sum, x, v, vi, nz);
    x[i] = sum * v[nz]; /* x[i]=aa[adiag[i]]*sum; v++; */
  }

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

PetscErrorCode MatSolve_SeqBAIJ_1_NaturalOrdering(Mat A, Vec bb, Vec xx)
{
  Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
  const PetscInt     n = a->mbs, *ai = a->i, *aj = a->j, *adiag = a->diag, *vi;
  PetscScalar       *x, sum;
  const PetscScalar *b;
  const MatScalar   *aa = a->a, *v;
  PetscInt           i, nz;

  PetscFunctionBegin;
  if (!n) PetscFunctionReturn(PETSC_SUCCESS);

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

  /* forward solve the lower triangular */
  x[0] = b[0];
  v    = aa;
  vi   = aj;
  for (i = 1; i < n; i++) {
    nz  = ai[i + 1] - ai[i];
    sum = b[i];
    PetscSparseDenseMinusDot(sum, x, v, vi, nz);
    v += nz;
    vi += nz;
    x[i] = sum;
  }

  /* backward solve the upper triangular */
  for (i = n - 1; i >= 0; i--) {
    v   = aa + adiag[i + 1] + 1;
    vi  = aj + adiag[i + 1] + 1;
    nz  = adiag[i] - adiag[i + 1] - 1;
    sum = x[i];
    PetscSparseDenseMinusDot(sum, x, v, vi, nz);
    x[i] = sum * v[nz]; /* x[i]=aa[adiag[i]]*sum; v++; */
  }

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