xref: /petsc/src/mat/impls/baij/seq/baijsolvtran1.c (revision 9566063d113dddea24716c546802770db7481bc0)

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

PetscErrorCode MatSolveTranspose_SeqBAIJ_1(Mat A,Vec bb,Vec xx)
{
  Mat_SeqBAIJ       *a    = (Mat_SeqBAIJ*)A->data;
  IS                iscol = a->col,isrow = a->row;
  const PetscInt    *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi;
  PetscInt          i,n = a->mbs,j;
  PetscInt          nz;
  PetscScalar       *x,*tmp,s1;
  const MatScalar   *aa = a->a,*v;
  const PetscScalar *b;

  PetscFunctionBegin;
  PetscCall(VecGetArrayRead(bb,&b));
  PetscCall(VecGetArray(xx,&x));
  tmp  = a->solve_work;

  PetscCall(ISGetIndices(isrow,&rout)); r = rout;
  PetscCall(ISGetIndices(iscol,&cout)); c = cout;

  /* copy the b into temp work space according to permutation */
  for (i=0; i<n; i++) tmp[i] = b[c[i]];

  /* forward solve the U^T */
  for (i=0; i<n; i++) {
    v   = aa + adiag[i+1] + 1;
    vi  = aj + adiag[i+1] + 1;
    nz  = adiag[i] - adiag[i+1] - 1;
    s1  = tmp[i];
    s1 *= v[nz];  /* multiply by inverse of diagonal entry */
    for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
    tmp[i] = s1;
  }

  /* backward solve the L^T */
  for (i=n-1; i>=0; i--) {
    v  = aa + ai[i];
    vi = aj + ai[i];
    nz = ai[i+1] - ai[i];
    s1 = tmp[i];
    for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
  }

  /* copy tmp into x according to permutation */
  for (i=0; i<n; i++) x[r[i]] = tmp[i];

  PetscCall(ISRestoreIndices(isrow,&rout));
  PetscCall(ISRestoreIndices(iscol,&cout));
  PetscCall(VecRestoreArrayRead(bb,&b));
  PetscCall(VecRestoreArray(xx,&x));

  PetscCall(PetscLogFlops(2.0*a->nz-A->cmap->n));
  PetscFunctionReturn(0);
}

PetscErrorCode MatSolveTranspose_SeqBAIJ_1_inplace(Mat A,Vec bb,Vec xx)
{
  Mat_SeqBAIJ       *a   =(Mat_SeqBAIJ*)A->data;
  IS                iscol=a->col,isrow=a->row;
  const PetscInt    *r,*c,*rout,*cout;
  const PetscInt    *diag=a->diag,n=a->mbs,*vi,*ai=a->i,*aj=a->j;
  PetscInt          i,nz;
  const MatScalar   *aa=a->a,*v;
  PetscScalar       s1,*x,*t;
  const PetscScalar *b;

  PetscFunctionBegin;
  PetscCall(VecGetArrayRead(bb,&b));
  PetscCall(VecGetArray(xx,&x));
  t    = a->solve_work;

  PetscCall(ISGetIndices(isrow,&rout)); r = rout;
  PetscCall(ISGetIndices(iscol,&cout)); c = cout;

  /* copy the b into temp work space according to permutation */
  for (i=0; i<n; i++) t[i] = b[c[i]];

  /* forward solve the U^T */
  for (i=0; i<n; i++) {

    v = aa + diag[i];
    /* multiply by the inverse of the block diagonal */
    s1 = (*v++)*t[i];
    vi = aj + diag[i] + 1;
    nz = ai[i+1] - diag[i] - 1;
    while (nz--) {
      t[*vi++] -= (*v++)*s1;
    }
    t[i] = s1;
  }
  /* backward solve the L^T */
  for (i=n-1; i>=0; i--) {
    v  = aa + diag[i] - 1;
    vi = aj + diag[i] - 1;
    nz = diag[i] - ai[i];
    s1 = t[i];
    while (nz--) {
      t[*vi--] -=  (*v--)*s1;
    }
  }

  /* copy t into x according to permutation */
  for (i=0; i<n; i++) x[r[i]] = t[i];

  PetscCall(ISRestoreIndices(isrow,&rout));
  PetscCall(ISRestoreIndices(iscol,&cout));
  PetscCall(VecRestoreArrayRead(bb,&b));
  PetscCall(VecRestoreArray(xx,&x));
  PetscCall(PetscLogFlops(2.0*(a->nz) - A->cmap->n));
  PetscFunctionReturn(0);
}