xref: /petsc/src/mat/impls/baij/seq/baijsolvnat2.c (revision 9566063d113dddea24716c546802770db7481bc0)

#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_2_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,s1,s2,x1,x2;
  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];
  for (i=1; i<n; i++) {
    v    =  aa      + 4*ai[i];
    vi   =  aj      + ai[i];
    nz   =  diag[i] - ai[i];
    idx +=  2;
    s1   =  b[idx];s2 = b[1+idx];
    while (nz--) {
      jdx = 2*(*vi++);
      x1  = x[jdx];x2 = x[1+jdx];
      s1 -= v[0]*x1 + v[2]*x2;
      s2 -= v[1]*x1 + v[3]*x2;
      v  += 4;
    }
    x[idx]   = s1;
    x[1+idx] = s2;
  }
  /* backward solve the upper triangular */
  for (i=n-1; i>=0; i--) {
    v   = aa + 4*diag[i] + 4;
    vi  = aj + diag[i] + 1;
    nz  = ai[i+1] - diag[i] - 1;
    idt = 2*i;
    s1  = x[idt];  s2 = x[1+idt];
    while (nz--) {
      idx = 2*(*vi++);
      x1  = x[idx];   x2 = x[1+idx];
      s1 -= v[0]*x1 + v[2]*x2;
      s2 -= v[1]*x1 + v[3]*x2;
      v  += 4;
    }
    v        = aa +  4*diag[i];
    x[idt]   = v[0]*s1 + v[2]*s2;
    x[1+idt] = v[1]*s1 + v[3]*s2;
  }

  PetscCall(VecRestoreArrayRead(bb,&b));
  PetscCall(VecRestoreArray(xx,&x));
  PetscCall(PetscLogFlops(2.0*4*(a->nz) - 2.0*A->cmap->n));
  PetscFunctionReturn(0);
}

PetscErrorCode MatSolve_SeqBAIJ_2_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,idt,jdx;
  const MatScalar   *aa=a->a,*v;
  PetscScalar       *x,s1,s2,x1,x2;
  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];
  for (i=1; i<n; i++) {
    v   = aa + 4*ai[i];
    vi  = aj + ai[i];
    nz  = ai[i+1] - ai[i];
    idx = 2*i;
    s1  = b[idx];s2 = b[1+idx];
    PetscPrefetchBlock(vi+nz,nz,0,PETSC_PREFETCH_HINT_NTA);
    PetscPrefetchBlock(v+4*nz,4*nz,0,PETSC_PREFETCH_HINT_NTA);
    for (k=0; k<nz; k++) {
      jdx = 2*vi[k];
      x1  = x[jdx];x2 = x[1+jdx];
      s1 -= v[0]*x1 + v[2]*x2;
      s2 -= v[1]*x1 + v[3]*x2;
      v  +=  4;
    }
    x[idx]   = s1;
    x[1+idx] = s2;
  }

  /* backward solve the upper triangular */
  for (i=n-1; i>=0; i--) {
    v   = aa + 4*(adiag[i+1]+1);
    vi  = aj + adiag[i+1]+1;
    nz  = adiag[i] - adiag[i+1]-1;
    idt = 2*i;
    s1  = x[idt];  s2 = x[1+idt];
    PetscPrefetchBlock(vi+nz,nz,0,PETSC_PREFETCH_HINT_NTA);
    PetscPrefetchBlock(v+4*nz,4*nz,0,PETSC_PREFETCH_HINT_NTA);
    for (k=0; k<nz; k++) {
      idx = 2*vi[k];
      x1  = x[idx];   x2 = x[1+idx];
      s1 -= v[0]*x1 + v[2]*x2;
      s2 -= v[1]*x1 + v[3]*x2;
      v  += 4;
    }
    /* x = inv_diagonal*x */
    x[idt]   = v[0]*s1 + v[2]*s2;
    x[1+idt] = v[1]*s1 + v[3]*s2;
  }

  PetscCall(VecRestoreArrayRead(bb,&b));
  PetscCall(VecRestoreArray(xx,&x));
  PetscCall(PetscLogFlops(2.0*4*(a->nz) - 2.0*A->cmap->n));
  PetscFunctionReturn(0);
}

PetscErrorCode MatForwardSolve_SeqBAIJ_2_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 MatScalar   *aa=a->a,*v;
  PetscScalar       *x,s1,s2,x1,x2;
  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];
  for (i=1; i<n; i++) {
    v   = aa + 4*ai[i];
    vi  = aj + ai[i];
    nz  = ai[i+1] - ai[i];
    idx = 2*i;
    s1  = b[idx];s2 = b[1+idx];
    PetscPrefetchBlock(vi+nz,nz,0,PETSC_PREFETCH_HINT_NTA);
    PetscPrefetchBlock(v+4*nz,4*nz,0,PETSC_PREFETCH_HINT_NTA);
    for (k=0; k<nz; k++) {
      jdx = 2*vi[k];
      x1  = x[jdx];x2 = x[1+jdx];
      s1 -= v[0]*x1 + v[2]*x2;
      s2 -= v[1]*x1 + v[3]*x2;
      v  +=  4;
    }
    x[idx]   = s1;
    x[1+idx] = s2;
  }

  PetscCall(VecRestoreArrayRead(bb,&b));
  PetscCall(VecRestoreArray(xx,&x));
  PetscCall(PetscLogFlops(4.0*(a->nz) - A->cmap->n));
  PetscFunctionReturn(0);
}

PetscErrorCode MatBackwardSolve_SeqBAIJ_2_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 MatScalar   *aa=a->a,*v;
  PetscScalar       *x,s1,s2,x1,x2;
  const PetscScalar *b;

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

  /* backward solve the upper triangular */
  for (i=n-1; i>=0; i--) {
    v   = aa + 4*(adiag[i+1]+1);
    vi  = aj + adiag[i+1]+1;
    nz  = adiag[i] - adiag[i+1]-1;
    idt = 2*i;
    s1  = b[idt];  s2 = b[1+idt];
    PetscPrefetchBlock(vi+nz,nz,0,PETSC_PREFETCH_HINT_NTA);
    PetscPrefetchBlock(v+4*nz,4*nz,0,PETSC_PREFETCH_HINT_NTA);
    for (k=0; k<nz; k++) {
      idx = 2*vi[k];
      x1  = x[idx];   x2 = x[1+idx];
      s1 -= v[0]*x1 + v[2]*x2;
      s2 -= v[1]*x1 + v[3]*x2;
      v  += 4;
    }
    /* x = inv_diagonal*x */
    x[idt]   = v[0]*s1 + v[2]*s2;
    x[1+idt] = v[1]*s1 + v[3]*s2;
  }

  PetscCall(VecRestoreArrayRead(bb,&b));
  PetscCall(VecRestoreArray(xx,&x));
  PetscCall(PetscLogFlops(4.0*a->nz - A->cmap->n));
  PetscFunctionReturn(0);
}