C++ SpProxy::end方法代码示例

arma_hot
inline
uword
n_unique
  (
  const SpProxy<T1>& pa,
  const SpProxy<T2>& pb,
  const op_n_unique_type junk
  )
  {
  arma_extra_debug_sigprint();
  arma_ignore(junk);
  
  typename SpProxy<T1>::const_iterator_type x_it     = pa.begin();
  typename SpProxy<T1>::const_iterator_type x_it_end = pa.end();
  
  typename SpProxy<T2>::const_iterator_type y_it     = pb.begin();
  typename SpProxy<T2>::const_iterator_type y_it_end = pb.end();

  uword total_n_nonzero = 0;

  while( (x_it != x_it_end) || (y_it != y_it_end) )
    {
    if(x_it == y_it)
      {
      if(op_n_unique_type::eval((*x_it), (*y_it)) != typename T1::elem_type(0))
        {
        ++total_n_nonzero;
        }

      ++x_it;
      ++y_it;
      }
    else
      {
      if((x_it.col() < y_it.col()) || ((x_it.col() == y_it.col()) && (x_it.row() < y_it.row()))) // if y is closer to the end
        {
        if(op_n_unique_type::eval((*x_it), typename T1::elem_type(0)) != typename T1::elem_type(0))
          {
          ++total_n_nonzero;
          }

        ++x_it;
        }
      else // x is closer to the end
        {
        if(op_n_unique_type::eval(typename T1::elem_type(0), (*y_it)) != typename T1::elem_type(0))
          {
          ++total_n_nonzero;
          }

        ++y_it;
        }
      }
    }

  return total_n_nonzero;
  }

inline
typename
enable_if2
  <
  (is_arma_type<T1>::value && is_arma_sparse_type<T2>::value && is_same_type<typename T1::elem_type, typename T2::elem_type>::value),
  Mat<typename T1::elem_type>
  >::result
operator-
  (
  const T1& x,
  const T2& y
  )
  {
  arma_extra_debug_sigprint();
  
  Mat<typename T1::elem_type> result(x);
  
  const SpProxy<T2> pb(y.get_ref());
  
  arma_debug_assert_same_size( result.n_rows, result.n_cols, pb.get_n_rows(), pb.get_n_cols(), "subtraction" );
  
  typename SpProxy<T2>::const_iterator_type it     = pb.begin();
  typename SpProxy<T2>::const_iterator_type it_end = pb.end();

  while(it != it_end)
    {
    result.at(it.row(), it.col()) -= (*it);
    ++it;
    }
  
  return result;
  }

inline
arma_warn_unused
bool
is_finite(const SpBase<typename T1::elem_type,T1>& X)
  {
  arma_extra_debug_sigprint();
  
  const SpProxy<T1> P(X.get_ref());
  
  if(is_SpMat<typename SpProxy<T1>::stored_type>::value)
    {
    const unwrap_spmat<typename SpProxy<T1>::stored_type> tmp(P.Q);
    
    return tmp.M.is_finite();
    }
  else
    {
    typename SpProxy<T1>::const_iterator_type it     = P.begin();
    typename SpProxy<T1>::const_iterator_type it_end = P.end();
    
    while(it != it_end)
      {
      if(arma_isfinite(*it) == false)  { return false; }
      ++it;
      }
    }
  
  return true;
  }

 arma_hot
 inline
 typename T1::elem_type
 dot_helper(const SpProxy<T1>& pa, const SpProxy<T2>& pb)
   {
   typedef typename T1::elem_type eT;
   
   // Iterate over both objects and see when they are the same
   eT result = eT(0);
   
   typename SpProxy<T1>::const_iterator_type a_it  = pa.begin();
   typename SpProxy<T1>::const_iterator_type a_end = pa.end();
   
   typename SpProxy<T2>::const_iterator_type b_it  = pb.begin();
   typename SpProxy<T2>::const_iterator_type b_end = pb.end();
   
   while((a_it != a_end) && (b_it != b_end))
     {
     if(a_it == b_it)
       {
       result += (*a_it) * (*b_it);
       
       ++a_it;
       ++b_it;
       }
     else if((a_it.col() < b_it.col()) || ((a_it.col() == b_it.col()) && (a_it.row() < b_it.row())))
       {
       // a_it is "behind"
       ++a_it;
       }
     else
       {
       // b_it is "behind"
       ++b_it;
       }
     }
   
   return result;
   }

inline
void
op_sp_plus::apply(Mat<typename T1::elem_type>& out, const SpToDOp<T1,op_sp_plus>& in)
  {
  arma_extra_debug_sigprint();
  
  // Note that T1 will be a sparse type, so we use SpProxy.
  const SpProxy<T1> proxy(in.m);
  
  out.set_size(proxy.get_n_rows(), proxy.get_n_cols());
  out.fill(in.aux);
  
  typename SpProxy<T1>::const_iterator_type it     = proxy.begin();
  typename SpProxy<T1>::const_iterator_type it_end = proxy.end();
  
  for(; it != it_end; ++it)
    {
    out.at(it.row(), it.col()) += (*it);
    }
  }

arma_hot
inline
void
spglue_plus::apply_noalias(SpMat<eT>& out, const SpProxy<T1>& pa, const SpProxy<T2>& pb)
  {
  arma_extra_debug_sigprint();
  
  arma_debug_assert_same_size(pa.get_n_rows(), pa.get_n_cols(), pb.get_n_rows(), pb.get_n_cols(), "addition");

  if( (pa.get_n_nonzero() != 0) && (pb.get_n_nonzero() != 0) )
    {
    out.set_size(pa.get_n_rows(), pa.get_n_cols());
    
    // Resize memory to correct size.
    out.mem_resize(n_unique(pa, pb, op_n_unique_add()));
    
    // Now iterate across both matrices.
    typename SpProxy<T1>::const_iterator_type x_it = pa.begin();
    typename SpProxy<T2>::const_iterator_type y_it = pb.begin();
    
    typename SpProxy<T1>::const_iterator_type x_end = pa.end();
    typename SpProxy<T2>::const_iterator_type y_end = pb.end();
    
    uword cur_val = 0;
    while( (x_it != x_end) || (y_it != y_end) )
      {
      if(x_it == y_it)
        {
        const eT val = (*x_it) + (*y_it);
        
        if (val != eT(0))
          {
          access::rw(out.values[cur_val]) = val;
          access::rw(out.row_indices[cur_val]) = x_it.row();
          ++access::rw(out.col_ptrs[x_it.col() + 1]);
          ++cur_val;
          }

        ++x_it;
        ++y_it;
        }
      else
        {
        const uword x_it_row = x_it.row();
        const uword x_it_col = x_it.col();
        
        const uword y_it_row = y_it.row();
        const uword y_it_col = y_it.col();
        
        if((x_it_col < y_it_col) || ((x_it_col == y_it_col) && (x_it_row < y_it_row))) // if y is closer to the end
          {
          access::rw(out.values[cur_val]) = (*x_it);
          access::rw(out.row_indices[cur_val]) = x_it_row;
          ++access::rw(out.col_ptrs[x_it_col + 1]);
          ++cur_val;
          ++x_it;
          }
        else
          {
          access::rw(out.values[cur_val]) = (*y_it);
          access::rw(out.row_indices[cur_val]) = y_it_row;
          ++access::rw(out.col_ptrs[y_it_col + 1]);
          ++cur_val;
          ++y_it;
          }
        }
      }
    
    const uword out_n_cols = out.n_cols;
    
    uword* col_ptrs = access::rwp(out.col_ptrs);
    
    // Fix column pointers to be cumulative.
    for(uword c = 1; c <= out_n_cols; ++c)
      {
      col_ptrs[c] += col_ptrs[c - 1];
      }
    }
  else
    {
    if(pa.get_n_nonzero() == 0)
      {
      out = pb.Q;
      return;
      }
    
    if(pb.get_n_nonzero() == 0)
      {
      out = pa.Q;
      return;
      }
    }
  }

arma_hot
inline
void
spop_sum::apply(SpMat<typename T1::elem_type>& out, const SpOp<T1,spop_sum>& in)
  {
  arma_extra_debug_sigprint();
  
  typedef typename T1::elem_type eT;
  
  const uword dim = in.aux_uword_a;
  arma_debug_check( (dim > 1), "sum(): parameter 'dim' must be 0 or 1" );
  
  const SpProxy<T1> p(in.m);
  
  const uword p_n_rows = p.get_n_rows();
  const uword p_n_cols = p.get_n_cols();
  
  if(p.get_n_nonzero() == 0)
    {
    if(dim == 0)  { out.zeros(1,p_n_cols); }
    if(dim == 1)  { out.zeros(p_n_rows,1); }
    
    return;
    }
  
  if(dim == 0) // find the sum in each column
    {
    Row<eT> acc(p_n_cols, fill::zeros);
    
    if(SpProxy<T1>::must_use_iterator)
      {
      typename SpProxy<T1>::const_iterator_type it     = p.begin();
      typename SpProxy<T1>::const_iterator_type it_end = p.end();
      
      while(it != it_end)  { acc[it.col()] += (*it);  ++it; }
      }
    else
      {
      for(uword col = 0; col < p_n_cols; ++col)
        {
        acc[col] = arrayops::accumulate
          (
          &p.get_values()[p.get_col_ptrs()[col]],
          p.get_col_ptrs()[col + 1] - p.get_col_ptrs()[col]
          );
        }
      }
    
    out = acc;
    }
  else
  if(dim == 1)  // find the sum in each row
    {
    Col<eT> acc(p_n_rows, fill::zeros);
    
    typename SpProxy<T1>::const_iterator_type it     = p.begin();
    typename SpProxy<T1>::const_iterator_type it_end = p.end();
    
    while(it != it_end)  { acc[it.row()] += (*it);  ++it; }
    
    out = acc;
    }
  }

inline
void
spop_mean::apply_noalias_fast
  (
        SpMat<typename T1::elem_type>& out,
  const SpProxy<T1>&                   p,
  const uword                          dim
  )
  {
  arma_extra_debug_sigprint();
  
  typedef typename T1::elem_type eT;
  typedef typename T1::pod_type   T;
  
  const uword p_n_rows = p.get_n_rows();
  const uword p_n_cols = p.get_n_cols();
  
  if( (p_n_rows == 0) || (p_n_cols == 0) || (p.get_n_nonzero() == 0) )
    {
    if(dim == 0)  { out.zeros((p_n_rows > 0) ? 1 : 0, p_n_cols); }
    if(dim == 1)  { out.zeros(p_n_rows, (p_n_cols > 0) ? 1 : 0); }
    
    return;
    }
  
  if(dim == 0) // find the mean in each column
    {
    Row<eT> acc(p_n_cols, fill::zeros);
    
    if(SpProxy<T1>::must_use_iterator)
      {
      typename SpProxy<T1>::const_iterator_type it     = p.begin();
      typename SpProxy<T1>::const_iterator_type it_end = p.end();
      
      while(it != it_end)  { acc[it.col()] += (*it);  ++it; }
      
      acc /= T(p_n_rows);
      }
    else
      {
      for(uword col = 0; col < p_n_cols; ++col)
        {
        acc[col] = arrayops::accumulate
          (
          &p.get_values()[p.get_col_ptrs()[col]],
          p.get_col_ptrs()[col + 1] - p.get_col_ptrs()[col]
          ) / T(p_n_rows);
        }
      }
    
    out = acc;
    }
  else
  if(dim == 1)  // find the mean in each row
    {
    Col<eT> acc(p_n_rows, fill::zeros);
    
    typename SpProxy<T1>::const_iterator_type it     = p.begin();
    typename SpProxy<T1>::const_iterator_type it_end = p.end();
    
    while(it != it_end)  { acc[it.row()] += (*it);  ++it; }
    
    acc /= T(p_n_cols);
    
    out = acc;
    }
  
  if(out.is_finite() == false)
    {
    spop_mean::apply_noalias_slow(out, p, dim);
    }
  }

inline
typename
enable_if2
  <
  (is_arma_sparse_type<T1>::value && is_arma_sparse_type<T2>::value && is_same_type<typename T1::elem_type, typename T2::elem_type>::value),
  SpMat<typename T1::elem_type>
  >::result
operator%
  (
  const SpBase<typename T1::elem_type, T1>& x,
  const SpBase<typename T2::elem_type, T2>& y
  )
  {
  arma_extra_debug_sigprint();
  
  typedef typename T1::elem_type eT;

  const SpProxy<T1> pa(x.get_ref());
  const SpProxy<T2> pb(y.get_ref());

  arma_debug_assert_same_size(pa.get_n_rows(), pa.get_n_cols(), pb.get_n_rows(), pb.get_n_cols(), "element-wise multiplication");

  SpMat<typename T1::elem_type> result(pa.get_n_rows(), pa.get_n_cols());
  
  if( (pa.get_n_nonzero() != 0) && (pb.get_n_nonzero() != 0) )
    {
    // Resize memory to correct size.
    result.mem_resize(n_unique(x, y, op_n_unique_mul()));
    
    // Now iterate across both matrices.
    typename SpProxy<T1>::const_iterator_type x_it = pa.begin();
    typename SpProxy<T2>::const_iterator_type y_it = pb.begin();
    
    typename SpProxy<T1>::const_iterator_type x_end = pa.end();
    typename SpProxy<T2>::const_iterator_type y_end = pb.end();
    
    uword cur_val = 0;
    while((x_it != x_end) || (y_it != y_end))
      {
      if(x_it == y_it)
        {
        const eT val = (*x_it) * (*y_it);
        
        if (val != eT(0))
          {
          access::rw(result.values[cur_val]) = val;
          access::rw(result.row_indices[cur_val]) = x_it.row();
          ++access::rw(result.col_ptrs[x_it.col() + 1]);
          ++cur_val;
          }
        
        ++x_it;
        ++y_it;
        }
      else
        {
        const uword x_it_row = x_it.row();
        const uword x_it_col = x_it.col();
        
        const uword y_it_row = y_it.row();
        const uword y_it_col = y_it.col();
        
        if((x_it_col < y_it_col) || ((x_it_col == y_it_col) && (x_it_row < y_it_row))) // if y is closer to the end
          {
          ++x_it;
          }
        else
          {
          ++y_it;
          }
        }
      }
    
    // Fix column pointers to be cumulative.
    for(uword c = 1; c <= result.n_cols; ++c)
      {
      access::rw(result.col_ptrs[c]) += result.col_ptrs[c - 1];
      }
    }
  
  return result;
  }

inline
void
spop_diagmat::apply_noalias(SpMat<typename T1::elem_type>& out, const SpProxy<T1>& p)
  {
  arma_extra_debug_sigprint();
  
  const uword n_rows = p.get_n_rows();
  const uword n_cols = p.get_n_cols();
  
  const bool p_is_vec = (n_rows == 1) || (n_cols == 1);
  
  if(p_is_vec)    // generate a diagonal matrix out of a vector
    {
    const uword N = (n_rows == 1) ? n_cols : n_rows;
    
    out.zeros(N, N);
    
    if(p.get_n_nonzero() == 0)  { return; }
    
    typename SpProxy<T1>::const_iterator_type it     = p.begin();
    typename SpProxy<T1>::const_iterator_type it_end = p.end();
      
    if(n_cols == 1)
      {
      while(it != it_end)
        {
        const uword row = it.row();
        
        out.at(row,row) = (*it);
        
        ++it;
        }
      }
    else
    if(n_rows == 1)
      {
      while(it != it_end)
        {
        const uword col = it.col();
        
        out.at(col,col) = (*it);
        
        ++it;
        }
      }
    }
  else   // generate a diagonal matrix out of a matrix
    {
    arma_debug_check( (n_rows != n_cols), "diagmat(): given matrix is not square" );
    
    out.zeros(n_rows, n_rows);
    
    if(p.get_n_nonzero() == 0)  { return; }
    
    typename SpProxy<T1>::const_iterator_type it     = p.begin();
    typename SpProxy<T1>::const_iterator_type it_end = p.end();
      
    while(it != it_end)
      {
      const uword row = it.row();
      const uword col = it.col();
      
      if(row == col)
        {
        out.at(row,row) = (*it);
        }
      
      ++it;
      }
    }
  }

inline
const SpSubview<eT>&
SpSubview<eT>::operator_equ_common(const SpBase<eT, T1>& in)
  {
  arma_extra_debug_sigprint();
  
  // algorithm:
  // instead of directly inserting values into the matrix underlying the subview,
  // create a new matrix by merging the underlying matrix with the input object,
  // and then replacing the underlying matrix with the created matrix.
  // 
  // the merging process requires pretending that the input object
  // has the same size as the underlying matrix.
  // while iterating through the elements of the input object,
  // this requires adjusting the row and column locations of each element,
  // as well as providing fake zero elements.
  // in effect there is a proxy for a proxy.
  
  
  const SpProxy< SpMat<eT> > pa((*this).m   );
  const SpProxy< T1        > pb(in.get_ref());
  
  arma_debug_assert_same_size(n_rows, n_cols, pb.get_n_rows(), pb.get_n_cols(), "insertion into sparse submatrix");
  
  const uword pa_start_row = (*this).aux_row1;
  const uword pa_start_col = (*this).aux_col1;
  
  const uword pa_end_row = pa_start_row + (*this).n_rows - 1;
  const uword pa_end_col = pa_start_col + (*this).n_cols - 1;
  
  const uword pa_n_rows = pa.get_n_rows();
  
  SpMat<eT> out(pa.get_n_rows(), pa.get_n_cols());
  
  const uword alt_count = pa.get_n_nonzero() - (*this).n_nonzero + pb.get_n_nonzero();
  
  // Resize memory to correct size.
  out.mem_resize(alt_count);
  
  typename SpProxy< SpMat<eT> >::const_iterator_type x_it  = pa.begin();
  typename SpProxy< SpMat<eT> >::const_iterator_type x_end = pa.end();
  
  typename SpProxy<T1>::const_iterator_type y_it  = pb.begin();
  typename SpProxy<T1>::const_iterator_type y_end = pb.end();
  
  bool x_it_ok = (x_it != x_end);
  bool y_it_ok = (y_it != y_end);
  
  uword x_it_row = (x_it_ok) ? x_it.row() : 0;
  uword x_it_col = (x_it_ok) ? x_it.col() : 0;
  
  uword y_it_row = (y_it_ok) ? y_it.row() + pa_start_row : 0;
  uword y_it_col = (y_it_ok) ? y_it.col() + pa_start_col : 0;
    
  uword cur_val = 0;
  while(x_it_ok || y_it_ok)
    {
    const bool x_inside_box = (x_it_row >= pa_start_row) && (x_it_row <= pa_end_row) && (x_it_col >= pa_start_col) && (x_it_col <= pa_end_col);
    const bool y_inside_box = (y_it_row >= pa_start_row) && (y_it_row <= pa_end_row) && (y_it_col >= pa_start_col) && (y_it_col <= pa_end_col);
    
    const eT x_val = x_inside_box ? eT(0) : ( x_it_ok ? (*x_it) : eT(0) );
    
    const eT y_val = y_inside_box ? ( y_it_ok ? (*y_it) : eT(0) ) : eT(0);
    
    if( (x_it_row == y_it_row) && (x_it_col == y_it_col) )
      {
      if( (x_val != eT(0)) || (y_val != eT(0)) )  
        {
        access::rw(out.values[cur_val]) = (x_val != eT(0)) ? x_val : y_val;
        access::rw(out.row_indices[cur_val]) = x_it_row;
        ++access::rw(out.col_ptrs[x_it_col + 1]);
        ++cur_val;
        }
      
      if(x_it_ok)
        {
        ++x_it;
        
        if(x_it == x_end)  { x_it_ok = false; }
        }
      
      if(x_it_ok)
        {
        x_it_row = x_it.row();
        x_it_col = x_it.col();
        }
      else
        {
        x_it_row++;
        
        if(x_it_row >= pa_n_rows)  { x_it_row = 0; x_it_col++; }
        }
      
      if(y_it_ok)
        {
        ++y_it;
        
        if(y_it == y_end)  { y_it_ok = false; }
        }
      
//.........这里部分代码省略.........

arma_hot
inline
void
spglue_minus::apply_noalias(SpMat<eT>& out, const SpProxy<T1>& pa, const SpProxy<T2>& pb)
  {
  arma_extra_debug_sigprint();
  
  arma_debug_assert_same_size(pa.get_n_rows(), pa.get_n_cols(), pb.get_n_rows(), pb.get_n_cols(), "subtraction");
  
  if(pa.get_n_nonzero() == 0)  { out = pb.Q; out *= eT(-1); return; }
  if(pb.get_n_nonzero() == 0)  { out = pa.Q;                return; }
  
  const uword max_n_nonzero = spglue_elem_helper::max_n_nonzero_plus(pa, pb);
  
  // Resize memory to upper bound
  out.reserve(pa.get_n_rows(), pa.get_n_cols(), max_n_nonzero);
  
  // Now iterate across both matrices.
  typename SpProxy<T1>::const_iterator_type x_it  = pa.begin();
  typename SpProxy<T1>::const_iterator_type x_end = pa.end();
  
  typename SpProxy<T2>::const_iterator_type y_it  = pb.begin();
  typename SpProxy<T2>::const_iterator_type y_end = pb.end();
  
  uword count = 0;
  
  while( (x_it != x_end) || (y_it != y_end) )
    {
    eT out_val;
    
    const uword x_it_row = x_it.row();
    const uword x_it_col = x_it.col();
    
    const uword y_it_row = y_it.row();
    const uword y_it_col = y_it.col();
    
    bool use_y_loc = false;
    
    if(x_it == y_it)
      {
      out_val = (*x_it) - (*y_it);
      
      ++x_it;
      ++y_it;
      }
    else
      {
      if((x_it_col < y_it_col) || ((x_it_col == y_it_col) && (x_it_row < y_it_row))) // if y is closer to the end
        {
        out_val = (*x_it);
        
        ++x_it;
        }
      else
        {
        out_val = -(*y_it);  // take the negative
        
        ++y_it;
        
        use_y_loc = true;
        }
      }
    
    if(out_val != eT(0))
      {
      access::rw(out.values[count]) = out_val;
      
      const uword out_row = (use_y_loc == false) ? x_it_row : y_it_row;
      const uword out_col = (use_y_loc == false) ? x_it_col : y_it_col;
      
      access::rw(out.row_indices[count]) = out_row;
      access::rw(out.col_ptrs[out_col + 1])++;
      ++count;
      }
    }
  
  const uword out_n_cols = out.n_cols;
  
  uword* col_ptrs = access::rwp(out.col_ptrs);
  
  // Fix column pointers to be cumulative.
  for(uword c = 1; c <= out_n_cols; ++c)
    {
    col_ptrs[c] += col_ptrs[c - 1];
    }
  
  if(count < max_n_nonzero)
    {
    if(count <= (max_n_nonzero/2))
      {
      out.mem_resize(count);
      }
    else
      {
      // quick resize without reallocating memory and copying data
      access::rw(         out.n_nonzero) = count;
      access::rw(     out.values[count]) = eT(0);
      access::rw(out.row_indices[count]) = uword(0);
      }
    }
//.........这里部分代码省略.........

arma_hot
inline
void
spglue_times::apply_noalias(SpMat<eT>& c, const SpProxy<T1>& pa, const SpProxy<T2>& pb)
  {
  arma_extra_debug_sigprint();
  
  const uword x_n_rows = pa.get_n_rows();
  const uword x_n_cols = pa.get_n_cols();
  const uword y_n_rows = pb.get_n_rows();
  const uword y_n_cols = pb.get_n_cols();

  arma_debug_assert_mul_size(x_n_rows, x_n_cols, y_n_rows, y_n_cols, "matrix multiplication");

  // First we must determine the structure of the new matrix (column pointers).
  // This follows the algorithm described in 'Sparse Matrix Multiplication
  // Package (SMMP)' (R.E. Bank and C.C. Douglas, 2001).  Their description of
  // "SYMBMM" does not include anything about memory allocation.  In addition it
  // does not consider that there may be elements which space may be allocated
  // for but which evaluate to zero anyway.  So we have to modify the algorithm
  // to work that way.  For the "SYMBMM" implementation we will not determine
  // the row indices but instead just the column pointers.
  
  //SpMat<typename T1::elem_type> c(x_n_rows, y_n_cols); // Initializes col_ptrs to 0.
  c.zeros(x_n_rows, y_n_cols);
  
  //if( (pa.get_n_elem() == 0) || (pb.get_n_elem() == 0) )
  if( (pa.get_n_nonzero() == 0) || (pb.get_n_nonzero() == 0) )
    {
    return;
    }
  
  // Auxiliary storage which denotes when items have been found.
  podarray<uword> index(x_n_rows);
  index.fill(x_n_rows); // Fill with invalid links.
  
  typename SpProxy<T2>::const_iterator_type y_it  = pb.begin();
  typename SpProxy<T2>::const_iterator_type y_end = pb.end();

  // SYMBMM: calculate column pointers for resultant matrix to obtain a good
  // upper bound on the number of nonzero elements.
  uword cur_col_length = 0;
  uword last_ind = x_n_rows + 1;
  do
    {
    const uword y_it_row = y_it.row();
    
    // Look through the column that this point (*y_it) could affect.
    typename SpProxy<T1>::const_iterator_type x_it = pa.begin_col(y_it_row);
    
    while(x_it.col() == y_it_row)
      {
      // A point at x(i, j) and y(j, k) implies a point at c(i, k).
      if(index[x_it.row()] == x_n_rows)
        {
        index[x_it.row()] = last_ind;
        last_ind = x_it.row();
        ++cur_col_length;
        }

      ++x_it;
      }

    const uword old_col = y_it.col();
    ++y_it;

    // See if column incremented.
    if(old_col != y_it.col())
      {
      // Set column pointer (this is not a cumulative count; that is done later).
      access::rw(c.col_ptrs[old_col + 1]) = cur_col_length;
      cur_col_length = 0;

      // Return index markers to zero.  Use last_ind for traversal.
      while(last_ind != x_n_rows + 1)
        {
        const uword tmp = index[last_ind];
        index[last_ind] = x_n_rows;
        last_ind = tmp;
        }
      }
    }
  while(y_it != y_end);

  // Accumulate column pointers.
  for(uword i = 0; i < c.n_cols; ++i)
    {
    access::rw(c.col_ptrs[i + 1]) += c.col_ptrs[i];
    }

  // Now that we know a decent bound on the number of nonzero elements, allocate
  // the memory and fill it.
  c.mem_resize(c.col_ptrs[c.n_cols]);

  // Now the implementation of the NUMBMM algorithm.
  uword cur_pos = 0; // Current position in c matrix.
  podarray<eT> sums(x_n_rows); // Partial sums.
  sums.zeros();
  
  // setting the size of 'sorted_indices' to x_n_rows is a better-than-nothing guess;
//.........这里部分代码省略.........