xref: /petsc/src/mat/impls/sbaij/seq/relax.h (revision 08401ef684002a709c6d3db98a0c9f54a8bcf1ec)

/*
    This is included by sbaij.c to generate unsigned short and regular versions of these two functions
*/

/* We cut-and-past below from aij.h to make a "no_function" version of PetscSparseDensePlusDot().
 * This is necessary because the USESHORT case cannot use the inlined functions that may be employed. */

#if defined(PETSC_KERNEL_USE_UNROLL_4)
#define PetscSparseDensePlusDot_no_function(sum,r,xv,xi,nnz) { \
    if (nnz > 0) { \
      PetscInt nnz2=nnz,rem=nnz&0x3; \
      switch (rem) { \
      case 3: sum += *xv++ *r[*xi++]; \
      case 2: sum += *xv++ *r[*xi++]; \
      case 1: sum += *xv++ *r[*xi++]; \
        nnz2      -= rem;} \
      while (nnz2 > 0) { \
        sum +=  xv[0] * r[xi[0]] + xv[1] * r[xi[1]] + \
                xv[2] * r[xi[2]] + xv[3] * r[xi[3]]; \
        xv += 4; xi += 4; nnz2 -= 4; \
      } \
      xv -= nnz; xi -= nnz; \
    } \
  }

#elif defined(PETSC_KERNEL_USE_UNROLL_2)
#define PetscSparseDensePlusDot_no_function(sum,r,xv,xi,nnz) { \
    PetscInt __i,__i1,__i2; \
    for (__i=0; __i<nnz-1; __i+=2) {__i1 = xi[__i]; __i2=xi[__i+1]; \
                                    sum += (xv[__i]*r[__i1] + xv[__i+1]*r[__i2]);} \
    if (nnz & 0x1) sum += xv[__i] * r[xi[__i]];}

#else
#define PetscSparseDensePlusDot_no_function(sum,r,xv,xi,nnz) { \
    PetscInt __i; \
    for (__i=0; __i<nnz; __i++) sum += xv[__i] * r[xi[__i]];}
#endif

#if defined(USESHORT)
PetscErrorCode MatMult_SeqSBAIJ_1_ushort(Mat A,Vec xx,Vec zz)
#else
PetscErrorCode MatMult_SeqSBAIJ_1(Mat A,Vec xx,Vec zz)
#endif
{
  Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
  const PetscScalar *x;
  PetscScalar       *z,x1,sum;
  const MatScalar   *v;
  MatScalar         vj;
  PetscInt          mbs=a->mbs,i,j,nz;
  const PetscInt    *ai=a->i;
#if defined(USESHORT)
  const unsigned short *ib=a->jshort;
  unsigned short       ibt;
#else
  const PetscInt *ib=a->j;
  PetscInt       ibt;
#endif
  PetscInt nonzerorow=0,jmin;
#if defined(PETSC_USE_COMPLEX)
  const int aconj = A->hermitian;
#else
  const int aconj = 0;
#endif

  PetscFunctionBegin;
  PetscCall(VecSet(zz,0.0));
  PetscCall(VecGetArrayRead(xx,&x));
  PetscCall(VecGetArray(zz,&z));

  v = a->a;
  for (i=0; i<mbs; i++) {
    nz = ai[i+1] - ai[i];          /* length of i_th row of A */
    if (!nz) continue; /* Move to the next row if the current row is empty */
    nonzerorow++;
    sum  = 0.0;
    jmin = 0;
    x1   = x[i];
    if (ib[0] == i) {
      sum = v[0]*x1;                 /* diagonal term */
      jmin++;
    }
    PetscPrefetchBlock(ib+nz,nz,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
    PetscPrefetchBlock(v+nz,nz,0,PETSC_PREFETCH_HINT_NTA);  /* Entries for the next row */
    if (aconj) {
      for (j=jmin; j<nz; j++) {
        ibt     = ib[j];
        vj      = v[j];
        z[ibt] += PetscConj(vj) * x1; /* (strict lower triangular part of A)*x  */
        sum    += vj * x[ibt];        /* (strict upper triangular part of A)*x  */
      }
    } else {
      for (j=jmin; j<nz; j++) {
        ibt     = ib[j];
        vj      = v[j];
        z[ibt] += vj * x1;       /* (strict lower triangular part of A)*x  */
        sum    += vj * x[ibt];   /* (strict upper triangular part of A)*x  */
      }
    }
    z[i] += sum;
    v    += nz;
    ib   += nz;
  }

  PetscCall(VecRestoreArrayRead(xx,&x));
  PetscCall(VecRestoreArray(zz,&z));
  PetscCall(PetscLogFlops(2.0*(2.0*a->nz - nonzerorow) - nonzerorow));
  PetscFunctionReturn(0);
}

#if defined(USESHORT)
PetscErrorCode MatSOR_SeqSBAIJ_ushort(Mat A,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
#else
PetscErrorCode MatSOR_SeqSBAIJ(Mat A,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
#endif
{
  Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
  const MatScalar   *aa=a->a,*v,*v1,*aidiag;
  PetscScalar       *x,*t,sum;
  const PetscScalar *b;
  MatScalar         tmp;
  PetscInt          m  =a->mbs,bs=A->rmap->bs,j;
  const PetscInt    *ai=a->i;
#if defined(USESHORT)
  const unsigned short *aj=a->jshort,*vj,*vj1;
#else
  const PetscInt *aj=a->j,*vj,*vj1;
#endif
  PetscInt nz,nz1,i;

  PetscFunctionBegin;
  if (fshift == -1.0) fshift = 0.0; /* negative fshift indicates do not error on zero diagonal; this code never errors on zero diagonal */
  PetscCheckFalse(flag & SOR_EISENSTAT,PETSC_COMM_SELF,PETSC_ERR_SUP,"No support yet for Eisenstat");

  its = its*lits;
  PetscCheck(its > 0,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Relaxation requires global its %" PetscInt_FMT " and local its %" PetscInt_FMT " both positive",its,lits);

  PetscCheck(bs <= 1,PETSC_COMM_SELF,PETSC_ERR_SUP,"SSOR for block size > 1 is not yet implemented");

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

  if (!a->idiagvalid) {
    if (!a->idiag) {
      PetscCall(PetscMalloc1(m,&a->idiag));
    }
    for (i=0; i<a->mbs; i++) a->idiag[i] = 1.0/a->a[a->i[i]];
    a->idiagvalid = PETSC_TRUE;
  }

  if (!a->sor_work) {
    PetscCall(PetscMalloc1(m,&a->sor_work));
  }
  t = a->sor_work;

  aidiag = a->idiag;

  if (flag == SOR_APPLY_UPPER) {
    /* apply (U + D/omega) to the vector */
    PetscScalar d;
    for (i=0; i<m; i++) {
      d   = fshift + aa[ai[i]];
      nz  = ai[i+1] - ai[i] - 1;
      vj  = aj + ai[i] + 1;
      v   = aa + ai[i] + 1;
      sum = b[i]*d/omega;
#ifdef USESHORT
      PetscSparseDensePlusDot_no_function(sum,b,v,vj,nz);
#else
      PetscSparseDensePlusDot(sum,b,v,vj,nz);
#endif
      x[i] = sum;
    }
    PetscCall(PetscLogFlops(a->nz));
  }

  if (flag & SOR_ZERO_INITIAL_GUESS) {
    if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
      PetscCall(PetscArraycpy(t,b,m));

      v  = aa + 1;
      vj = aj + 1;
      for (i=0; i<m; i++) {
        nz  = ai[i+1] - ai[i] - 1;
        tmp = -(x[i] = omega*t[i]*aidiag[i]);
        for (j=0; j<nz; j++) t[vj[j]] += tmp*v[j];
        v  += nz + 1;
        vj += nz + 1;
      }
      PetscCall(PetscLogFlops(2.0*a->nz));
    }

    if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
      int nz2;
      if (!(flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP)) {
#if defined(PETSC_USE_BACKWARD_LOOP)
        v  = aa + ai[m] - 1;
        vj = aj + ai[m] - 1;
        for (i=m-1; i>=0; i--) {
          sum = b[i];
          nz  = ai[i+1] - ai[i] - 1;
          {PetscInt __i;for (__i=0; __i<nz; __i++) sum -= v[-__i] * x[vj[-__i]];}
#else
        v  = aa + ai[m-1] + 1;
        vj = aj + ai[m-1] + 1;
        nz = 0;
        for (i=m-1; i>=0; i--) {
          sum = b[i];
          nz2 = ai[i] - ai[PetscMax(i-1,0)] - 1; /* avoid referencing ai[-1], nonsense nz2 is okay on last iteration */
          PETSC_Prefetch(v-nz2-1,0,PETSC_PREFETCH_HINT_NTA);
          PETSC_Prefetch(vj-nz2-1,0,PETSC_PREFETCH_HINT_NTA);
          PetscSparseDenseMinusDot(sum,x,v,vj,nz);
          nz = nz2;
#endif
          x[i] = omega*sum*aidiag[i];
          v   -= nz + 1;
          vj  -= nz + 1;
        }
        PetscCall(PetscLogFlops(2.0*a->nz));
      } else {
        v  = aa + ai[m-1] + 1;
        vj = aj + ai[m-1] + 1;
        nz = 0;
        for (i=m-1; i>=0; i--) {
          sum = t[i];
          nz2 = ai[i] - ai[PetscMax(i-1,0)] - 1; /* avoid referencing ai[-1], nonsense nz2 is okay on last iteration */
          PETSC_Prefetch(v-nz2-1,0,PETSC_PREFETCH_HINT_NTA);
          PETSC_Prefetch(vj-nz2-1,0,PETSC_PREFETCH_HINT_NTA);
          PetscSparseDenseMinusDot(sum,x,v,vj,nz);
          x[i] = (1-omega)*x[i] + omega*sum*aidiag[i];
          nz   = nz2;
          v   -= nz + 1;
          vj  -= nz + 1;
        }
        PetscCall(PetscLogFlops(2.0*a->nz));
      }
    }
    its--;
  }

  while (its--) {
    /*
       forward sweep:
       for i=0,...,m-1:
         sum[i] = (b[i] - U(i,:)x)/d[i];
         x[i]   = (1-omega)x[i] + omega*sum[i];
         b      = b - x[i]*U^T(i,:);

    */
    if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
      PetscCall(PetscArraycpy(t,b,m));

      for (i=0; i<m; i++) {
        v    = aa + ai[i] + 1; v1=v;
        vj   = aj + ai[i] + 1; vj1=vj;
        nz   = ai[i+1] - ai[i] - 1; nz1=nz;
        sum  = t[i];
        while (nz1--) sum -= (*v1++)*x[*vj1++];
        x[i] = (1-omega)*x[i] + omega*sum*aidiag[i];
        while (nz--) t[*vj++] -= x[i]*(*v++);
      }
      PetscCall(PetscLogFlops(4.0*a->nz));
    }

    if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
      /*
       backward sweep:
       b = b - x[i]*U^T(i,:), i=0,...,n-2
       for i=m-1,...,0:
         sum[i] = (b[i] - U(i,:)x)/d[i];
         x[i]   = (1-omega)x[i] + omega*sum[i];
      */
      /* if there was a forward sweep done above then I thing the next two for loops are not needed */
      PetscCall(PetscArraycpy(t,b,m));

      for (i=0; i<m-1; i++) {  /* update rhs */
        v    = aa + ai[i] + 1;
        vj   = aj + ai[i] + 1;
        nz   = ai[i+1] - ai[i] - 1;
        while (nz--) t[*vj++] -= x[i]*(*v++);
      }
      PetscCall(PetscLogFlops(2.0*(a->nz - m)));
      for (i=m-1; i>=0; i--) {
        v    = aa + ai[i] + 1;
        vj   = aj + ai[i] + 1;
        nz   = ai[i+1] - ai[i] - 1;
        sum  = t[i];
        while (nz--) sum -= x[*vj++]*(*v++);
        x[i] =   (1-omega)*x[i] + omega*sum*aidiag[i];
      }
      PetscCall(PetscLogFlops(2.0*(a->nz + m)));
    }
  }

  PetscCall(VecRestoreArray(xx,&x));
  PetscCall(VecRestoreArrayRead(bb,&b));
  PetscFunctionReturn(0);
}