text: // Copyright (C) 2011-2013 Ryan Curtin
  // Copyright (C) 2012-2013 Conrad Sanderson
  // Copyright (C) 2011 Matthew Amidon
  // 
  // This Source Code Form is subject to the terms of the Mozilla Public
  // License, v. 2.0. If a copy of the MPL was not distributed with this
  // file, You can obtain one at http://mozilla.org/MPL/2.0/.
  
  //! \addtogroup SpMat
  //! @{
  
  /**
   * Initialize a sparse matrix with size 0x0 (empty).
   */
  template<typename eT>
  inline
  SpMat<eT>::SpMat()
    : n_rows(0)
    , n_cols(0)
    , n_elem(0)
    , n_nonzero(0)
    , vec_state(0)
    , values(memory::acquire_chunked<eT>(1))
    , row_indices(memory::acquire_chunked<uword>(1))
    , col_ptrs(memory::acquire<uword>(2))
    {
    arma_extra_debug_sigprint_this(this);
    
    access::rw(values[0]) = 0;
    access::rw(row_indices[0]) = 0;
    
    access::rw(col_ptrs[0]) = 0; // No elements.
    access::rw(col_ptrs[1]) = std::numeric_limits<uword>::max();
    }
  
  
  
  /**
   * Clean up the memory of a sparse matrix and destruct it.
   */
  template<typename eT>
  inline
  SpMat<eT>::~SpMat()
    {
    arma_extra_debug_sigprint_this(this);
    
    if(values     )  { memory::release(access::rw(values));      }
    if(row_indices)  { memory::release(access::rw(row_indices)); }
    if(col_ptrs   )  { memory::release(access::rw(col_ptrs));    }
    }
  
  
  
  /**
   * Constructor with size given.
   */
  template<typename eT>
  inline
  SpMat<eT>::SpMat(const uword in_rows, const uword in_cols)
    : n_rows(0)
    , n_cols(0)
    , n_elem(0)
    , n_nonzero(0)
    , vec_state(0)
    , values(NULL)
    , row_indices(NULL)
    , col_ptrs(NULL)
    {
    arma_extra_debug_sigprint_this(this);
  
    init(in_rows, in_cols);
    }
  
  
  
  /**
   * Assemble from text.
   */
  template<typename eT>
  inline
  SpMat<eT>::SpMat(const char* text)
    : n_rows(0)
    , n_cols(0)
    , n_elem(0)
    , n_nonzero(0)
    , vec_state(0)
    , values(NULL)
    , row_indices(NULL)
    , col_ptrs(NULL)
    {
    arma_extra_debug_sigprint_this(this);
  
    init(std::string(text));
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator=(const char* text)
    {
    arma_extra_debug_sigprint();
  
    init(std::string(text));
    }
  
  
  
  template<typename eT>
  inline
  SpMat<eT>::SpMat(const std::string& text)
    : n_rows(0)
    , n_cols(0)
    , n_elem(0)
    , n_nonzero(0)
    , vec_state(0)
    , values(NULL)
    , row_indices(NULL)
    , col_ptrs(NULL)
    {
    arma_extra_debug_sigprint();
  
    init(text);
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator=(const std::string& text)
    {
    arma_extra_debug_sigprint();
  
    init(text);
    }
  
  
  
  template<typename eT>
  inline
  SpMat<eT>::SpMat(const SpMat<eT>& x)
    : n_rows(0)
    , n_cols(0)
    , n_elem(0)
    , n_nonzero(0)
    , vec_state(0)
    , values(NULL)
    , row_indices(NULL)
    , col_ptrs(NULL)
    {
    arma_extra_debug_sigprint_this(this);
  
    init(x);
    }
  
  
  
  #if defined(ARMA_USE_CXX11)
    
    template<typename eT>
    inline
    SpMat<eT>::SpMat(SpMat<eT>&& in_mat)
      : n_rows(0)
      , n_cols(0)
      , n_elem(0)
      , n_nonzero(0)
      , vec_state(0)
      , values(NULL)
      , row_indices(NULL)
      , col_ptrs(NULL)
      {
      arma_extra_debug_sigprint_this(this);
      arma_extra_debug_sigprint(arma_boost::format("this = %x   in_mat = %x") % this % &in_mat);
      
      (*this).steal_mem(in_mat);
      }
    
    
    
    template<typename eT>
    inline
    const SpMat<eT>&
    SpMat<eT>::operator=(SpMat<eT>&& in_mat)
      {
      arma_extra_debug_sigprint(arma_boost::format("this = %x   in_mat = %x") % this % &in_mat);
      
      (*this).steal_mem(in_mat);
      
      return *this;
      }
    
  #endif
  
  
  
  //! Insert a large number of values at once.
  //! locations.row[0] should be row indices, locations.row[1] should be column indices,
  //! and values should be the corresponding values.
  //! If sort_locations is false, then it is assumed that the locations and values
  //! are already sorted in column-major ordering.
  template<typename eT>
  template<typename T1, typename T2>
  inline
  SpMat<eT>::SpMat(const Base<uword,T1>& locations_expr, const Base<eT,T2>& vals_expr, const bool sort_locations)
    : n_rows(0)
    , n_cols(0)
    , n_elem(0)
    , n_nonzero(0)
    , vec_state(0)
    , values(NULL)
    , row_indices(NULL)
    , col_ptrs(NULL)
    {
    arma_extra_debug_sigprint_this(this);
    
    const unwrap<T1>         locs_tmp( locations_expr.get_ref() );
    const Mat<uword>& locs = locs_tmp.M;
    
    const unwrap<T2> vals_tmp( vals_expr.get_ref() );
    const Mat<eT>& vals = vals_tmp.M;
    
    arma_debug_check( (vals.is_vec() == false), "SpMat::SpMat(): given 'values' object is not a vector" );
    
    arma_debug_check((locs.n_cols != vals.n_elem), "SpMat::SpMat(): number of locations is different than number of values");
    
    // If there are no elements in the list, max() will fail.
    if (locs.n_cols == 0)
      {
      init(0, 0);
      return;
      }
  
    arma_debug_check((locs.n_rows != 2), "SpMat::SpMat(): locations matrix must have two rows");
  
    // Automatically determine size (and check if it's sorted).
    uvec bounds = arma::max(locs, 1);
    init(bounds[0] + 1, bounds[1] + 1);
  
    // Resize to correct number of elements.
    mem_resize(vals.n_elem);
  
    // Reset column pointers to zero.
    arrayops::inplace_set(access::rwp(col_ptrs), uword(0), n_cols + 1);
  
    bool actually_sorted = true;
    if(sort_locations == true)
      {
      // sort_index() uses std::sort() which may use quicksort... so we better
      // make sure it's not already sorted before taking an O(N^2) sort penalty.
      for (uword i = 1; i < locs.n_cols; ++i)
        {
        if ((locs.at(1, i) < locs.at(1, i - 1)) || (locs.at(1, i) == locs.at(1, i - 1) && locs.at(0, i) <= locs.at(0, i - 1)))
          {
          actually_sorted = false;
          break;
          }
        }
      
      if(actually_sorted == false)
        {
        // This may not be the fastest possible implementation but it maximizes code reuse.
        Col<uword> abslocs(locs.n_cols);
        
        for (uword i = 0; i < locs.n_cols; ++i)
          {
          abslocs[i] = locs.at(1, i) * n_rows + locs.at(0, i);
          }
        
        // Now we will sort with sort_index().
        uvec sorted_indices = sort_index(abslocs); // Ascending sort.
        
        // Now we add the elements in this sorted order.
        for (uword i = 0; i < sorted_indices.n_elem; ++i)
          {
          arma_debug_check((locs.at(0, sorted_indices[i]) >= n_rows), "SpMat::SpMat(): invalid row index");
          arma_debug_check((locs.at(1, sorted_indices[i]) >= n_cols), "SpMat::SpMat(): invalid column index");
          
          access::rw(values[i])      = vals[sorted_indices[i]];
          access::rw(row_indices[i]) = locs.at(0, sorted_indices[i]);
          
          access::rw(col_ptrs[locs.at(1, sorted_indices[i]) + 1])++;
          }
        }
      }
    
    if( (sort_locations == false) || (actually_sorted == true) )
      {
      // Now set the values and row indices correctly.
      // Increment the column pointers in each column (so they are column "counts").
      for (uword i = 0; i < vals.n_elem; ++i)
        {
        arma_debug_check((locs.at(0, i) >= n_rows), "SpMat::SpMat(): invalid row index");
        arma_debug_check((locs.at(1, i) >= n_cols), "SpMat::SpMat(): invalid column index");
        
        // Check ordering in debug mode.
        if(i > 0)
          {
          arma_debug_check
            (
            ( (locs.at(1, i) < locs.at(1, i - 1)) || (locs.at(1, i) == locs.at(1, i - 1) && locs.at(0, i) < locs.at(0, i - 1)) ),
            "SpMat::SpMat(): out of order points; either pass sort_locations = true, or sort points in column-major ordering"
            );
          arma_debug_check((locs.at(1, i) == locs.at(1, i - 1) && locs.at(0, i) == locs.at(0, i - 1)), "SpMat::SpMat(): two identical point locations in list");
          }
        
        access::rw(values[i])      = vals[i];
        access::rw(row_indices[i]) = locs.at(0, i);
        
        access::rw(col_ptrs[locs.at(1, i) + 1])++;
        }
      }
    
    // Now fix the column pointers.
    for (uword i = 0; i <= n_cols; ++i)
      {
      access::rw(col_ptrs[i + 1]) += col_ptrs[i];
      }
    }
  
  
  
  //! Insert a large number of values at once.
  //! locations.row[0] should be row indices, locations.row[1] should be column indices,
  //! and values should be the corresponding values.
  //! If sort_locations is false, then it is assumed that the locations and values
  //! are already sorted in column-major ordering.
  //! In this constructor the size is explicitly given.
  template<typename eT>
  template<typename T1, typename T2>
  inline
  SpMat<eT>::SpMat(const Base<uword,T1>& locations_expr, const Base<eT,T2>& vals_expr, const uword in_n_rows, const uword in_n_cols, const bool sort_locations)
    : n_rows(0)
    , n_cols(0)
    , n_elem(0)
    , n_nonzero(0)
    , vec_state(0)
    , values(NULL)
    , row_indices(NULL)
    , col_ptrs(NULL)
    {
    arma_extra_debug_sigprint_this(this);
    
    init(in_n_rows, in_n_cols);
    
    const unwrap<T1> locs_tmp( locations_expr.get_ref() );
    const unwrap<T2> vals_tmp( vals_expr.get_ref() );
    
    const Mat<uword>& locs = locs_tmp.M;
    const Mat<eT>&    vals = vals_tmp.M;
    
    arma_debug_check( (vals.is_vec() == false),     "SpMat::SpMat(): given 'values' object is not a vector" );
    arma_debug_check( (locs.n_rows != 2),           "SpMat::SpMat(): locations matrix must have two rows" );
    arma_debug_check( (locs.n_cols != vals.n_elem), "SpMat::SpMat(): number of locations is different than number of values" );
    
    // Resize to correct number of elements.
    mem_resize(vals.n_elem);
    
    // Reset column pointers to zero.
    arrayops::inplace_set(access::rwp(col_ptrs), uword(0), n_cols + 1);
    
    
    bool actually_sorted = true;
    
    if(sort_locations == true)
      {
      // sort_index() uses std::sort() which may use quicksort... so we better
      // make sure it's not already sorted before taking an O(N^2) sort penalty.
      for (uword i = 1; i < locs.n_cols; ++i)
        {
        if ((locs.at(1, i) < locs.at(1, i - 1)) || (locs.at(1, i) == locs.at(1, i - 1) && locs.at(0, i) <= locs.at(0, i - 1)))
          {
          actually_sorted = false;
          break;
          }
        }
      
      if(actually_sorted == false)
        {
        // This may not be the fastest possible implementation but it maximizes code reuse.
        Col<uword> abslocs(locs.n_cols);
        
        for (uword i = 0; i < locs.n_cols; ++i)
          {
          abslocs[i] = locs.at(1, i) * n_rows + locs.at(0, i);
          }
  
        // Now we will sort with sort_index().
        uvec sorted_indices = sort_index(abslocs); // Ascending sort.
  
        // Now we add the elements in this sorted order.
        for (uword i = 0; i < sorted_indices.n_elem; ++i)
          {
          arma_debug_check((locs.at(0, sorted_indices[i]) >= n_rows), "SpMat::SpMat(): invalid row index");
          arma_debug_check((locs.at(1, sorted_indices[i]) >= n_cols), "SpMat::SpMat(): invalid column index");
  
          access::rw(values[i])      = vals[sorted_indices[i]];
          access::rw(row_indices[i]) = locs.at(0, sorted_indices[i]);
  
          access::rw(col_ptrs[locs.at(1, sorted_indices[i]) + 1])++;
          }
        }
      }
  
    if( (sort_locations == false) || (actually_sorted == true) )
      {
      // Now set the values and row indices correctly.
      // Increment the column pointers in each column (so they are column "counts").
      for (uword i = 0; i < vals.n_elem; ++i)
        {
        arma_debug_check((locs.at(0, i) >= n_rows), "SpMat::SpMat(): invalid row index");
        arma_debug_check((locs.at(1, i) >= n_cols), "SpMat::SpMat(): invalid column index");
  
        // Check ordering in debug mode.
        if(i > 0)
          {
          arma_debug_check
            (
            ( (locs.at(1, i) < locs.at(1, i - 1)) || (locs.at(1, i) == locs.at(1, i - 1) && locs.at(0, i) < locs.at(0, i - 1)) ),
            "SpMat::SpMat(): out of order points; either pass sort_locations = true or sort points in column-major ordering"
            );
          arma_debug_check((locs.at(1, i) == locs.at(1, i - 1) && locs.at(0, i) == locs.at(0, i - 1)), "SpMat::SpMat(): two identical point locations in list");
          }
  //! If sort_locations is false, then it is assumed that the locations and values
  //! are already sorted in column-major ordering.
  
        access::rw(values[i])      = vals[i];
        access::rw(row_indices[i]) = locs.at(0, i);
  
        access::rw(col_ptrs[locs.at(1, i) + 1])++;
        }
      }
  
    // Now fix the column pointers.
    for (uword i = 0; i <= n_cols; ++i)
      {
      access::rw(col_ptrs[i + 1]) += col_ptrs[i];
      }
    }
  
  
  
  //! Insert a large number of values at once.
  //! Per CSC format, rowind_expr should be row indices, 
  //! colptr_expr should column ptr indices locations,
  //! and values should be the corresponding values.
  //! In this constructor the size is explicitly given.
  //! Values are assumed to be sorted, and the size 
  //! information is trusted
  template<typename eT>
  template<typename T1, typename T2, typename T3>
  inline
  SpMat<eT>::SpMat
    (
    const Base<uword,T1>& rowind_expr, 
    const Base<uword,T2>& colptr_expr, 
    const Base<eT,   T3>& values_expr, 
    const uword           in_n_rows, 
    const uword           in_n_cols
    )
    : n_rows(0)
    , n_cols(0)
    , n_elem(0)
    , n_nonzero(0)
    , vec_state(0)
    , values(NULL)
    , row_indices(NULL)
    , col_ptrs(NULL)
    {
    arma_extra_debug_sigprint_this(this);
    
    init(in_n_rows, in_n_cols);
    
    const unwrap<T1> rowind_tmp( rowind_expr.get_ref() );
    const unwrap<T2> colptr_tmp( colptr_expr.get_ref() );
    const unwrap<T3>   vals_tmp( values_expr.get_ref() );
    
    const Mat<uword>& rowind = rowind_tmp.M;
    const Mat<uword>& colptr = colptr_tmp.M;
    const Mat<eT>&      vals = vals_tmp.M;
    
    arma_debug_check( (rowind.is_vec() == false), "SpMat::SpMat(): given 'rowind' object is not a vector" );
    arma_debug_check( (colptr.is_vec() == false), "SpMat::SpMat(): given 'colptr' object is not a vector" );
    arma_debug_check( (vals.is_vec()   == false), "SpMat::SpMat(): given 'values' object is not a vector" );
    
    arma_debug_check( (rowind.n_elem != vals.n_elem), "SpMat::SpMat(): number of row indices is not equal to number of values" );
    arma_debug_check( (colptr.n_elem != (n_cols+1) ), "SpMat::SpMat(): number of column pointers is not equal to n_cols+1" );
    
    // Resize to correct number of elements (this also sets n_nonzero)
    mem_resize(vals.n_elem);
    
    // copy supplied values into sparse matrix -- not checked for consistency
    arrayops::copy(access::rwp(row_indices), rowind.memptr(), rowind.n_elem );
    arrayops::copy(access::rwp(col_ptrs),    colptr.memptr(), colptr.n_elem );
    arrayops::copy(access::rwp(values),      vals.memptr(),   vals.n_elem   );
    
    // important: set the sentinel as well
    access::rw(col_ptrs[n_cols + 1]) = std::numeric_limits<uword>::max();
    }
  
  
  
  /**
   * Simple operators with plain values.  These operate on every value in the
   * matrix, so a sparse matrix += 1 will turn all those zeroes into ones.  Be
   * careful and make sure that's what you really want!
   */
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator=(const eT val)
    {
    arma_extra_debug_sigprint();
  
    // Resize to 1x1 then set that to the right value.
    init(1, 1); // Sets col_ptrs to 0.
    mem_resize(1); // One element.
  
    // Manually set element.
    access::rw(values[0]) = val;
    access::rw(row_indices[0]) = 0;
    access::rw(col_ptrs[1]) = 1;
  
    return *this;
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator*=(const eT val)
    {
    arma_extra_debug_sigprint();
    
    if(val == eT(0))
      {
      // Everything will be zero.
      init(n_rows, n_cols);
      return *this;
      }
    
    arrayops::inplace_mul( access::rwp(values), val, n_nonzero );
    
    return *this;
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator/=(const eT val)
    {
    arma_extra_debug_sigprint();
    
    arma_debug_check( (val == eT(0)), "element-wise division: division by zero" );
    
    arrayops::inplace_div( access::rwp(values), val, n_nonzero );
    
    return *this;
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator=(const SpMat<eT>& x)
    {
    arma_extra_debug_sigprint();
    
    init(x);
    
    return *this;
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator+=(const SpMat<eT>& x)
    {
    arma_extra_debug_sigprint();
    
    SpMat<eT> out;
    out = (*this) + x;
    steal_mem(out);
    
    return *this;
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator-=(const SpMat<eT>& x)
    {
    arma_extra_debug_sigprint();
    
    SpMat<eT> out;
    out = (*this) - x;
    steal_mem(out);
    
    return *this;
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator*=(const SpMat<eT>& y)
    {
    arma_extra_debug_sigprint();
    
    SpMat<eT> z;
    z = (*this) * y;
    steal_mem(z);
    
    return *this;
    }
  
  
  
  // This is in-place element-wise matrix multiplication.
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator%=(const SpMat<eT>& x)
    {
    arma_extra_debug_sigprint();
    
    arma_debug_assert_same_size(n_rows, n_cols, x.n_rows, x.n_cols, "element-wise multiplication");
    
    // We can do this with two iterators rather simply.
          iterator it    = begin();
    const_iterator x_it  = x.begin();
    
    while (it != end() && x_it != x.end())
      {
      // One of these will be further advanced than the other (or they will be at the same place).
      if ((it.row() == x_it.row()) && (it.col() == x_it.col()))
        {
        // There is an element at this place in both matrices.  Multiply.
        (*it) *= (*x_it);
  
        // Now move on to the next position.
        it++;
        x_it++;
        }
  
      else if ((it.col() < x_it.col()) || ((it.col() == x_it.col()) && (it.row() < x_it.row())))
        {
        // This case is when our matrix has an element which the other matrix does not.
        // So we must delete this element.
        (*it) = 0;
  
        // Because we have deleted the element, we now have to manually set the position...
        it.internal_pos--;
  
        // Now we can increment our iterator.
        it++;
        }
  
      else /* if our iterator is ahead of the other matrix */
        {
        // In this case we don't need to set anything to 0; our element is already 0.
        // We can just increment the iterator of the other matrix.
        x_it++;
        }
  
      }
  
    // If we are not at the end of our matrix, then we must terminate the remaining elements.
    while (it != end())
      {
      (*it) = 0;
  
      // Hack to manually set the position right...
      it.internal_pos--;
      it++; // ...and then an increment.
      }
  
    return *this;
    }
  
  
  
  // Construct a complex matrix out of two non-complex matrices
  template<typename eT>
  template<typename T1, typename T2>
  inline
  SpMat<eT>::SpMat
    (
    const SpBase<typename SpMat<eT>::pod_type, T1>& A,
    const SpBase<typename SpMat<eT>::pod_type, T2>& B
    )
    : n_rows(0)
    , n_cols(0)
    , n_elem(0)
    , n_nonzero(0)
    , vec_state(0)
    , values(NULL) // extra element is set when mem_resize is called
    , row_indices(NULL)
    , col_ptrs(NULL)
    {
    arma_extra_debug_sigprint();
    
    typedef typename T1::elem_type T;
    
    // Make sure eT is complex and T is not (compile-time check).
    arma_type_check(( is_complex<eT>::value == false ));
    arma_type_check(( is_complex< T>::value == true  ));
    
    // Compile-time abort if types are not compatible.
    arma_type_check(( is_same_type< std::complex<T>, eT >::no ));
    
    const unwrap_spmat<T1> tmp1(A.get_ref());
    const unwrap_spmat<T2> tmp2(B.get_ref());
    
    const SpMat<T>& X = tmp1.M;
    const SpMat<T>& Y = tmp2.M;
    
    arma_debug_assert_same_size(X.n_rows, X.n_cols, Y.n_rows, Y.n_cols, "SpMat()");
    
    const uword l_n_rows = X.n_rows;
    const uword l_n_cols = X.n_cols;
    
    // Set size of matrix correctly.
    init(l_n_rows, l_n_cols);
    mem_resize(n_unique(X, Y, op_n_unique_count()));
    
    // Now on a second iteration, fill it.
    typename SpMat<T>::const_iterator x_it  = X.begin();
    typename SpMat<T>::const_iterator x_end = X.end();
    
    typename SpMat<T>::const_iterator y_it  = Y.begin();
    typename SpMat<T>::const_iterator y_end = Y.end();
    
    uword cur_pos = 0;
    
    while ((x_it != x_end) || (y_it != y_end))
      {
      if(x_it == y_it) // if we are at the same place
        {
        access::rw(values[cur_pos]) = std::complex<T>((T) *x_it, (T) *y_it);
        access::rw(row_indices[cur_pos]) = x_it.row();
        ++access::rw(col_ptrs[x_it.col() + 1]);
        
        ++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
          {
          access::rw(values[cur_pos]) = std::complex<T>((T) *x_it, T(0));
          access::rw(row_indices[cur_pos]) = x_it.row();
          ++access::rw(col_ptrs[x_it.col() + 1]);
          
          ++x_it;
          }
        else // x is closer to the end
          {
          access::rw(values[cur_pos]) = std::complex<T>(T(0), (T) *y_it);
          access::rw(row_indices[cur_pos]) = y_it.row();
          ++access::rw(col_ptrs[y_it.col() + 1]);
          
          ++y_it;
          }
        }
      
      ++cur_pos;
      }
    
    // Now fix the column pointers; they are supposed to be a sum.
    for (uword c = 1; c <= n_cols; ++c)
      {
      access::rw(col_ptrs[c]) += col_ptrs[c - 1];
      }
    
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator/=(const SpMat<eT>& x)
    {
    arma_extra_debug_sigprint();
    
    arma_debug_assert_same_size(n_rows, n_cols, x.n_rows, x.n_cols, "element-wise division");
    
    // If you use this method, you are probably stupid or misguided, but for compatibility with Mat, we have implemented it anyway.
    // We have to loop over every element, which is not good.  In fact, it makes me physically sad to write this.
    for(uword c = 0; c < n_cols; ++c)
      {
      for(uword r = 0; r < n_rows; ++r)
        {
        at(r, c) /= x.at(r, c);
        }
      }
  
    return *this;
    }
  
  
  
  template<typename eT>
  template<typename T1>
  inline
  SpMat<eT>::SpMat(const Base<eT, T1>& x)
    : n_rows(0)
    , n_cols(0)
    , n_elem(0)
    , n_nonzero(0)
    , vec_state(0)
    , values(NULL) // extra element is set when mem_resize is called in operator=()
    , row_indices(NULL)
    , col_ptrs(NULL)
    {
    arma_extra_debug_sigprint_this(this);
  
    (*this).operator=(x);
    }
  
  
  
  template<typename eT>
  template<typename T1>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator=(const Base<eT, T1>& x)
    {
    arma_extra_debug_sigprint();
    
    const Proxy<T1> p(x.get_ref());
    
    const uword x_n_rows = p.get_n_rows();
    const uword x_n_cols = p.get_n_cols();
    const uword x_n_elem = p.get_n_elem();
  
    init(x_n_rows, x_n_cols);
  
    // Count number of nonzero elements in base object.
    uword n = 0;
    if(Proxy<T1>::prefer_at_accessor == true)
      {
      for(uword j = 0; j < x_n_cols; ++j)
      for(uword i = 0; i < x_n_rows; ++i)
        {
        if(p.at(i, j) != eT(0)) { ++n; }
        }
      }
    else
      {
      for(uword i = 0; i < x_n_elem; ++i)
        {
        if(p[i] != eT(0)) { ++n; }
        }
      }
  
    mem_resize(n);
  
    // Now the memory is resized correctly; add nonzero elements.
    n = 0;
    for(uword j = 0; j < x_n_cols; ++j)
    for(uword i = 0; i < x_n_rows; ++i)
      {
      const eT val = p.at(i, j);
      
      if(val != eT(0))
        {
        access::rw(values[n])      = val;
        access::rw(row_indices[n]) = i;
        access::rw(col_ptrs[j + 1])++;
        ++n;
        }
      }
  
    // Sum column counts to be column pointers.
    for(uword c = 1; c <= n_cols; ++c)
      {
      access::rw(col_ptrs[c]) += col_ptrs[c - 1];
      }
    
    return *this;
    }
  
  
  
  template<typename eT>
  template<typename T1>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator*=(const Base<eT, T1>& y)
    {
    arma_extra_debug_sigprint();
  
    const Proxy<T1> p(y.get_ref());
  
    arma_debug_assert_mul_size(n_rows, n_cols, p.get_n_rows(), p.get_n_cols(), "matrix multiplication");
  
    // We assume the matrix structure is such that we will end up with a sparse
    // matrix.  Assuming that every entry in the dense matrix is nonzero (which is
    // a fairly valid assumption), each row with any nonzero elements in it (in this
    // matrix) implies an entire nonzero column.  Therefore, we iterate over all
    // the row_indices and count the number of rows with any elements in them
    // (using the quasi-linked-list idea from SYMBMM -- see operator_times.hpp).
    podarray<uword> index(n_rows);
    index.fill(n_rows); // Fill with invalid links.
  
    uword last_index = n_rows + 1;
    for(uword i = 0; i < n_nonzero; ++i)
      {
      if(index[row_indices[i]] == n_rows)
        {
        index[row_indices[i]] = last_index;
        last_index = row_indices[i];
        }
      }
  
    // Now count the number of rows which have nonzero elements.
    uword nonzero_rows = 0;
    while(last_index != n_rows + 1)
      {
      ++nonzero_rows;
      last_index = index[last_index];
      }
  
    SpMat<eT> z(n_rows, p.get_n_cols());
  
    z.mem_resize(nonzero_rows * p.get_n_cols()); // upper bound on size
  
    // Now we have to fill all the elements using a modification of the NUMBMM algorithm.
    uword cur_pos = 0;
  
    podarray<eT> partial_sums(n_rows);
    partial_sums.zeros();
  
    for(uword lcol = 0; lcol < n_cols; ++lcol)
      {
      const_iterator it = begin();
  
      while(it != end())
        {
        const eT value = (*it);
  
        partial_sums[it.row()] += (value * p.at(it.col(), lcol));
  
        ++it;
        }
  
      // Now add all partial sums to the matrix.
      for(uword i = 0; i < n_rows; ++i)
        {
        if(partial_sums[i] != eT(0))
          {
          access::rw(z.values[cur_pos]) = partial_sums[i];
          access::rw(z.row_indices[cur_pos]) = i;
          ++access::rw(z.col_ptrs[lcol + 1]);
          //printf("colptr %d now %d\n", lcol + 1, z.col_ptrs[lcol + 1]);
          ++cur_pos;
          partial_sums[i] = 0; // Would it be faster to do this in batch later?
          }
        }
      }
  
    // Now fix the column pointers.
    for(uword c = 1; c <= z.n_cols; ++c)
      {
      access::rw(z.col_ptrs[c]) += z.col_ptrs[c - 1];
      }
  
    // Resize to final correct size.
    z.mem_resize(z.col_ptrs[z.n_cols]);
    
    // Now take the memory of the temporary matrix.
    steal_mem(z);
    
    return *this;
    }
  
  
  
  /**
   * Don't use this function.  It's not mathematically well-defined and wastes
   * cycles to trash all your data.  This is dumb.
   */
  template<typename eT>
  template<typename T1>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator/=(const Base<eT, T1>& x)
    {
    arma_extra_debug_sigprint();
  
    SpMat<eT> tmp = (*this) / x.get_ref();
    
    steal_mem(tmp);
    
    return *this;
    }
  
  
  
  template<typename eT>
  template<typename T1>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator%=(const Base<eT, T1>& x)
    {
    arma_extra_debug_sigprint();
  
    const Proxy<T1> p(x.get_ref());
    
    arma_debug_assert_same_size(n_rows, n_cols, p.get_n_rows(), p.get_n_cols(), "element-wise multiplication");
    
    // Count the number of elements we will need.
    SpMat<eT> tmp(n_rows, n_cols);
    const_iterator it = begin();
    uword new_n_nonzero = 0;
  
    while(it != end())
      {
      // prefer_at_accessor == false can't save us any work here
      if(((*it) * p.at(it.row(), it.col())) != eT(0))
        {
        ++new_n_nonzero;
        }
      ++it;
      }
  
    // Resize.
    tmp.mem_resize(new_n_nonzero);
  
    const_iterator c_it = begin();
    uword cur_pos = 0;
    while(c_it != end())
      {
      // prefer_at_accessor == false can't save us any work here
      const eT val = (*c_it) * p.at(c_it.row(), c_it.col());
      if(val != eT(0))
        {
        access::rw(tmp.values[cur_pos]) = val;
        access::rw(tmp.row_indices[cur_pos]) = c_it.row();
        ++access::rw(tmp.col_ptrs[c_it.col() + 1]);
        ++cur_pos;
        }
  
      ++c_it;
      }
  
    // Fix column pointers.
    for(uword c = 1; c <= n_cols; ++c)
      {
      access::rw(tmp.col_ptrs[c]) += tmp.col_ptrs[c - 1];
      }
  
    steal_mem(tmp);
  
    return *this;
    }
  
  
  
  /**
   * Functions on subviews.
   */
  template<typename eT>
  inline
  SpMat<eT>::SpMat(const SpSubview<eT>& X)
    : n_rows(0)
    , n_cols(0)
    , n_elem(0)
    , n_nonzero(0)
    , vec_state(0)
    , values(NULL) // extra element added when mem_resize is called
    , row_indices(NULL)
    , col_ptrs(NULL)
    {
    arma_extra_debug_sigprint_this(this);
  
    (*this).operator=(X);
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator=(const SpSubview<eT>& X)
    {
    arma_extra_debug_sigprint();
    
    const uword in_n_cols = X.n_cols;
    const uword in_n_rows = X.n_rows;
    
    const bool alias = (this == &(X.m));
  
    if(alias == false)
      {
      init(in_n_rows, in_n_cols);
  
      const uword x_n_nonzero = X.n_nonzero;
  
      mem_resize(x_n_nonzero);
  
      typename SpSubview<eT>::const_iterator it = X.begin();
  
      while(it != X.end())
        {
        access::rw(row_indices[it.pos()]) = it.row();
        access::rw(values[it.pos()]) = (*it);
        ++access::rw(col_ptrs[it.col() + 1]);
        ++it;
        }
  
      // Now sum column pointers.
      for(uword c = 1; c <= n_cols; ++c)
        {
        access::rw(col_ptrs[c]) += col_ptrs[c - 1];
        }
      }
    else
      {
      // Create it in a temporary.
      SpMat<eT> tmp(X);
  
      steal_mem(tmp);
      }
    
    return *this;
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator+=(const SpSubview<eT>& X)
    {
    arma_extra_debug_sigprint();
    
    arma_debug_assert_same_size(n_rows, n_cols, X.n_rows, X.n_cols, "addition");
    
    typename SpSubview<eT>::const_iterator it = X.begin();
  
    while(it != X.end())
      {
      at(it.row(), it.col()) += (*it);
      ++it;
      }
  
    return *this;
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator-=(const SpSubview<eT>& X)
    {
    arma_extra_debug_sigprint();
    
    arma_debug_assert_same_size(n_rows, n_cols, X.n_rows, X.n_cols, "subtraction");
    
    typename SpSubview<eT>::const_iterator it = X.begin();
    
    while(it != X.end())
      {
      at(it.row(), it.col()) -= (*it);
      ++it;
      }
    
    return *this;
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator*=(const SpSubview<eT>& y)
    {
    arma_extra_debug_sigprint();
    
    arma_debug_assert_mul_size(n_rows, n_cols, y.n_rows, y.n_cols, "matrix multiplication");
    
    // Cannot be done in-place (easily).
    SpMat<eT> z = (*this) * y;
    steal_mem(z);
    
    return *this;
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator%=(const SpSubview<eT>& x)
    {
    arma_extra_debug_sigprint();
    
    arma_debug_assert_same_size(n_rows, n_cols, x.n_rows, x.n_cols, "element-wise multiplication");
  
    iterator it = begin();
    typename SpSubview<eT>::const_iterator xit = x.begin();
  
    while((it != end()) || (xit != x.end()))
      {
      if((xit.row() == it.row()) && (xit.col() == it.col()))
        {
        (*it) *= (*xit);
        ++it;
        ++xit;
        }
      else
        {
        if((xit.col() > it.col()) || ((xit.col() == it.col()) && (xit.row() > it.row())))
          {
          // xit is "ahead"
          (*it) = eT(0); // erase element; x has a zero here
          it.internal_pos--; // update iterator so it still works
          ++it;
          }
        else
          {
          // it is "ahead"
          ++xit;
          }
        }
      }
  
    return *this;
    }
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator/=(const SpSubview<eT>& x)
    {
    arma_extra_debug_sigprint();
    
    arma_debug_assert_same_size(n_rows, n_cols, x.n_rows, x.n_cols, "element-wise division");
    
    // There is no pretty way to do this.
    for(uword elem = 0; elem < n_elem; elem++)
      {
      at(elem) /= x(elem);
      }
    
    return *this;
    }
  
  
  
  /**
   * Operators on regular subviews.
   */
  template<typename eT>
  inline
  SpMat<eT>::SpMat(const subview<eT>& x)
    : n_rows(0)
    , n_cols(0)
    , n_elem(0)
    , n_nonzero(0)
    , vec_state(0)
    , values(NULL) // extra value set in operator=()
    , row_indices(NULL)
    , col_ptrs(NULL)
    {
    arma_extra_debug_sigprint_this(this);
  
    (*this).operator=(x);
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator=(const subview<eT>& x)
    {
    arma_extra_debug_sigprint();
    
    const uword x_n_rows = x.n_rows;
    const uword x_n_cols = x.n_cols;
    
    // Set the size correctly.
    init(x_n_rows, x_n_cols);
  
    // Count number of nonzero elements.
    uword n = 0;
    for(uword c = 0; c < x_n_cols; ++c)
      {
      for(uword r = 0; r < x_n_rows; ++r)
        {
        if(x.at(r, c) != eT(0))
          {
          ++n;
          }
        }
      }
  
    // Resize memory appropriately.
    mem_resize(n);
  
    n = 0;
    for(uword c = 0; c < x_n_cols; ++c)
      {
      for(uword r = 0; r < x_n_rows; ++r)
        {
        const eT val = x.at(r, c);
        
        if(val != eT(0))
          {
          access::rw(values[n]) = val;
          access::rw(row_indices[n]) = r;
          ++access::rw(col_ptrs[c + 1]);
          ++n;
          }
        }
      }
  
    // Fix column counts into column pointers.
    for(uword c = 1; c <= n_cols; ++c)
      {
      access::rw(col_ptrs[c]) += col_ptrs[c - 1];
      }
    
    return *this;
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator+=(const subview<eT>& x)
    {
    arma_extra_debug_sigprint();
    
    arma_debug_assert_same_size(n_rows, n_cols, x.n_rows, x.n_cols, "addition");
    
    // Loop over every element.  This could probably be written in a more
    // efficient way, by calculating the number of nonzero elements the output
    // matrix will have, allocating the memory correctly, and then filling the
    // matrix correctly.  However... for now, this works okay.
    for(uword lcol = 0; lcol < n_cols; ++lcol)
    for(uword lrow = 0; lrow < n_rows; ++lrow)
      {
      at(lrow, lcol) += x.at(lrow, lcol);
      }
    
    return *this;
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator-=(const subview<eT>& x)
    {
    arma_extra_debug_sigprint();
    
    arma_debug_assert_same_size(n_rows, n_cols, x.n_rows, x.n_cols, "subtraction");
    
    // Loop over every element.
    for(uword lcol = 0; lcol < n_cols; ++lcol)
    for(uword lrow = 0; lrow < n_rows; ++lrow)
      {
      at(lrow, lcol) -= x.at(lrow, lcol);
      }
    
    return *this;
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator*=(const subview<eT>& y)
    {
    arma_extra_debug_sigprint();
  
    arma_debug_assert_mul_size(n_rows, n_cols, y.n_rows, y.n_cols, "matrix multiplication");
  
    SpMat<eT> z(n_rows, y.n_cols);
  
    // Performed in the same fashion as operator*=(SpMat).
    for (const_row_iterator x_row_it = begin_row(); x_row_it.pos() < n_nonzero; ++x_row_it)
      {
      for (uword lcol = 0; lcol < y.n_cols; ++lcol)
        {
        // At this moment in the loop, we are calculating anything that is contributed to by *x_row_it and *y_col_it.
        // Given that our position is x_ab and y_bc, there will only be a contribution if x.col == y.row, and that
        // contribution will be in location z_ac.
        z.at(x_row_it.row, lcol) += (*x_row_it) * y.at(x_row_it.col, lcol);
        }
      }
  
    steal_mem(z);
  
    return *this;
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator%=(const subview<eT>& x)
    {
    arma_extra_debug_sigprint();
    
    arma_debug_assert_same_size(n_rows, n_cols, x.n_rows, x.n_cols, "element-wise multiplication");
    
    // Loop over every element.
    for(uword lcol = 0; lcol < n_cols; ++lcol)
    for(uword lrow = 0; lrow < n_rows; ++lrow)
      {
      at(lrow, lcol) *= x.at(lrow, lcol);
      }
  
    return *this;
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator/=(const subview<eT>& x)
    {
    arma_extra_debug_sigprint();
    
    arma_debug_assert_same_size(n_rows, n_cols, x.n_rows, x.n_cols, "element-wise division");
    
    // Loop over every element.
    for(uword lcol = 0; lcol < n_cols; ++lcol)
    for(uword lrow = 0; lrow < n_rows; ++lrow)
      {
      at(lrow, lcol) /= x.at(lrow, lcol);
      }
  
    return *this;
    }
  
  
  
  template<typename eT>
  template<typename T1, typename spop_type>
  inline
  SpMat<eT>::SpMat(const SpOp<T1, spop_type>& X)
    : n_rows(0)
    , n_cols(0)
    , n_elem(0)
    , n_nonzero(0)
    , vec_state(0)
    , values(NULL) // set in application of sparse operation
    , row_indices(NULL)
    , col_ptrs(NULL)
    {
    arma_extra_debug_sigprint_this(this);
  
    arma_type_check(( is_same_type< eT, typename T1::elem_type >::no ));
    
    spop_type::apply(*this, X);
    }
  
  
  
  template<typename eT>
  template<typename T1, typename spop_type>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator=(const SpOp<T1, spop_type>& X)
    {
    arma_extra_debug_sigprint();
  
    arma_type_check(( is_same_type< eT, typename T1::elem_type >::no ));
    
    spop_type::apply(*this, X);
    
    return *this;
    }
  
  
  
  template<typename eT>
  template<typename T1, typename spop_type>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator+=(const SpOp<T1, spop_type>& X)
    {
    arma_extra_debug_sigprint();
    
    arma_type_check(( is_same_type< eT, typename T1::elem_type >::no ));
    
    const SpMat<eT> m(X);
    
    return (*this).operator+=(m);
    }
  
  
  
  template<typename eT>
  template<typename T1, typename spop_type>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator-=(const SpOp<T1, spop_type>& X)
    {
    arma_extra_debug_sigprint();
    
    arma_type_check(( is_same_type< eT, typename T1::elem_type >::no ));
    
    const SpMat<eT> m(X);
    
    return (*this).operator-=(m);
    }
  
  
  
  template<typename eT>
  template<typename T1, typename spop_type>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator*=(const SpOp<T1, spop_type>& X)
    {
    arma_extra_debug_sigprint();
    
    arma_type_check(( is_same_type< eT, typename T1::elem_type >::no ));
    
    const SpMat<eT> m(X);
    
    return (*this).operator*=(m);
    }
  
  
  
  template<typename eT>
  template<typename T1, typename spop_type>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator%=(const SpOp<T1, spop_type>& X)
    {
    arma_extra_debug_sigprint();
    
    arma_type_check(( is_same_type< eT, typename T1::elem_type >::no ));
    
    const SpMat<eT> m(X);
    
    return (*this).operator%=(m);
    }
  
  
  
  template<typename eT>
  template<typename T1, typename spop_type>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator/=(const SpOp<T1, spop_type>& X)
    {
    arma_extra_debug_sigprint();
    
    arma_type_check(( is_same_type< eT, typename T1::elem_type >::no ));
    
    const SpMat<eT> m(X);
    
    return (*this).operator/=(m);
    }
  
  
  
  template<typename eT>
  template<typename T1, typename T2, typename spglue_type>
  inline
  SpMat<eT>::SpMat(const SpGlue<T1, T2, spglue_type>& X)
    : n_rows(0)
    , n_cols(0)
    , n_elem(0)
    , n_nonzero(0)
    , vec_state(0)
    , values(NULL) // extra element set in application of sparse glue
    , row_indices(NULL)
    , col_ptrs(NULL)
    {
    arma_extra_debug_sigprint_this(this);
  
    arma_type_check(( is_same_type< eT, typename T1::elem_type >::no ));
    
    spglue_type::apply(*this, X);
    }
  
  
  
  template<typename eT>
  template<typename T1, typename spop_type>
  inline
  SpMat<eT>::SpMat(const mtSpOp<eT, T1, spop_type>& X)
    : n_rows(0)
    , n_cols(0)
    , n_elem(0)
    , n_nonzero(0)
    , vec_state(0)
    , values(NULL) // extra element set in application of sparse glue
    , row_indices(NULL)
    , col_ptrs(NULL)
    {
    arma_extra_debug_sigprint_this(this);
  
    spop_type::apply(*this, X);
    }
  
  
  
  template<typename eT>
  template<typename T1, typename spop_type>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator=(const mtSpOp<eT, T1, spop_type>& X)
    {
    arma_extra_debug_sigprint();
  
    spop_type::apply(*this, X);
  
    return *this;
    }
  
  
  
  template<typename eT>
  template<typename T1, typename spop_type>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator+=(const mtSpOp<eT, T1, spop_type>& X)
    {
    arma_extra_debug_sigprint();
  
    const SpMat<eT> m(X);
  
    return (*this).operator+=(m);
    }
  
  
  
  template<typename eT>
  template<typename T1, typename spop_type>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator-=(const mtSpOp<eT, T1, spop_type>& X)
    {
    arma_extra_debug_sigprint();
  
    const SpMat<eT> m(X);
  
    return (*this).operator-=(m);
    }
  
  
  
  template<typename eT>
  template<typename T1, typename spop_type>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator*=(const mtSpOp<eT, T1, spop_type>& X)
    {
    arma_extra_debug_sigprint();
  
    const SpMat<eT> m(X);
  
    return (*this).operator*=(m);
    }
  
  
  
  template<typename eT>
  template<typename T1, typename spop_type>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator%=(const mtSpOp<eT, T1, spop_type>& X)
    {
    arma_extra_debug_sigprint();
  
    const SpMat<eT> m(X);
  
    return (*this).operator%=(m);
    }
  
  
  
  template<typename eT>
  template<typename T1, typename spop_type>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator/=(const mtSpOp<eT, T1, spop_type>& X)
    {
    arma_extra_debug_sigprint();
  
    const SpMat<eT> m(X);
  
    return (*this).operator/=(m);
    }
  
  
  
  template<typename eT>
  template<typename T1, typename T2, typename spglue_type>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator=(const SpGlue<T1, T2, spglue_type>& X)
    {
    arma_extra_debug_sigprint();
  
    arma_type_check(( is_same_type< eT, typename T1::elem_type >::no ));
    
    spglue_type::apply(*this, X);
    
    return *this;
    }
  
  
  
  template<typename eT>
  template<typename T1, typename T2, typename spglue_type>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator+=(const SpGlue<T1, T2, spglue_type>& X)
    {
    arma_extra_debug_sigprint();
    
    arma_type_check(( is_same_type< eT, typename T1::elem_type >::no ));
    
    const SpMat<eT> m(X);
    
    return (*this).operator+=(m);
    }
  
  
  
  template<typename eT>
  template<typename T1, typename T2, typename spglue_type>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator-=(const SpGlue<T1, T2, spglue_type>& X)
    {
    arma_extra_debug_sigprint();
    
    arma_type_check(( is_same_type< eT, typename T1::elem_type >::no ));
    
    const SpMat<eT> m(X);
    
    return (*this).operator-=(m);
    }
  
  
  
  template<typename eT>
  template<typename T1, typename T2, typename spglue_type>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator*=(const SpGlue<T1, T2, spglue_type>& X)
    {
    arma_extra_debug_sigprint();
    
    arma_type_check(( is_same_type< eT, typename T1::elem_type >::no ));
    
    const SpMat<eT> m(X);
    
    return (*this).operator*=(m);
    }
  
  
  
  template<typename eT>
  template<typename T1, typename T2, typename spglue_type>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator%=(const SpGlue<T1, T2, spglue_type>& X)
    {
    arma_extra_debug_sigprint();
    
    arma_type_check(( is_same_type< eT, typename T1::elem_type >::no ));
    
    const SpMat<eT> m(X);
    
    return (*this).operator%=(m);
    }
  
  
  
  template<typename eT>
  template<typename T1, typename T2, typename spglue_type>
  inline
  const SpMat<eT>&
  SpMat<eT>::operator/=(const SpGlue<T1, T2, spglue_type>& X)
    {
    arma_extra_debug_sigprint();
    
    arma_type_check(( is_same_type< eT, typename T1::elem_type >::no ));
    
    const SpMat<eT> m(X);
    
    return (*this).operator/=(m);
    }
  
  
  
  template<typename eT>
  arma_inline
  SpSubview<eT>
  SpMat<eT>::row(const uword row_num)
    {
    arma_extra_debug_sigprint();
  
    arma_debug_check(row_num >= n_rows, "SpMat::row(): out of bounds");
  
    return SpSubview<eT>(*this, row_num, 0, 1, n_cols);
    }
  
  
  
  template<typename eT>
  arma_inline
  const SpSubview<eT>
  SpMat<eT>::row(const uword row_num) const
    {
    arma_extra_debug_sigprint();
  
    arma_debug_check(row_num >= n_rows, "SpMat::row(): out of bounds");
  
    return SpSubview<eT>(*this, row_num, 0, 1, n_cols);
    }
  
  
  
  template<typename eT>
  inline
  SpSubview<eT>
  SpMat<eT>::operator()(const uword row_num, const span& col_span)
    {
    arma_extra_debug_sigprint();
    
    const bool col_all = col_span.whole;
    
    const uword local_n_cols = n_cols;
    
    const uword in_col1       = col_all ? 0            : col_span.a;
    const uword in_col2       =                          col_span.b;
    const uword submat_n_cols = col_all ? local_n_cols : in_col2 - in_col1 + 1;
    
    arma_debug_check
      (
      (row_num >= n_rows)
      ||
      ( col_all ? false : ((in_col1 > in_col2) || (in_col2 >= local_n_cols)) )
      ,
      "SpMat::operator(): indices out of bounds or incorrectly used"
      );
    
    return SpSubview<eT>(*this, row_num, in_col1, 1, submat_n_cols);
    }
  
  
  
  template<typename eT>
  inline
  const SpSubview<eT>
  SpMat<eT>::operator()(const uword row_num, const span& col_span) const
    {
    arma_extra_debug_sigprint();
    
    const bool col_all = col_span.whole;
    
    const uword local_n_cols = n_cols;
    
    const uword in_col1       = col_all ? 0            : col_span.a;
    const uword in_col2       =                          col_span.b;
    const uword submat_n_cols = col_all ? local_n_cols : in_col2 - in_col1 + 1;
    
    arma_debug_check
      (
      (row_num >= n_rows)
      ||
      ( col_all ? false : ((in_col1 > in_col2) || (in_col2 >= local_n_cols)) )
      ,
      "SpMat::operator(): indices out of bounds or incorrectly used"
      );
    
    return SpSubview<eT>(*this, row_num, in_col1, 1, submat_n_cols);
    }
  
  
  
  template<typename eT>
  arma_inline
  SpSubview<eT>
  SpMat<eT>::col(const uword col_num)
    {
    arma_extra_debug_sigprint();
  
    arma_debug_check(col_num >= n_cols, "SpMat::col(): out of bounds");
  
    return SpSubview<eT>(*this, 0, col_num, n_rows, 1);
    }
  
  
  
  template<typename eT>
  arma_inline
  const SpSubview<eT>
  SpMat<eT>::col(const uword col_num) const
    {
    arma_extra_debug_sigprint();
  
    arma_debug_check(col_num >= n_cols, "SpMat::col(): out of bounds");
  
    return SpSubview<eT>(*this, 0, col_num, n_rows, 1);
    }
  
  
  
  template<typename eT>
  inline
  SpSubview<eT>
  SpMat<eT>::operator()(const span& row_span, const uword col_num)
    {
    arma_extra_debug_sigprint();
    
    const bool row_all = row_span.whole;
    
    const uword local_n_rows = n_rows;
    
    const uword in_row1       = row_all ? 0            : row_span.a;
    const uword in_row2       =                          row_span.b;
    const uword submat_n_rows = row_all ? local_n_rows : in_row2 - in_row1 + 1;
    
    arma_debug_check
      (
      (col_num >= n_cols)
      ||
      ( row_all ? false : ((in_row1 > in_row2) || (in_row2 >= local_n_rows)) )
      ,
      "SpMat::operator(): indices out of bounds or incorrectly used"
      );
    
    return SpSubview<eT>(*this, in_row1, col_num, submat_n_rows, 1);
    }
  
  
  
  template<typename eT>
  inline
  const SpSubview<eT>
  SpMat<eT>::operator()(const span& row_span, const uword col_num) const
    {
    arma_extra_debug_sigprint();
    
    const bool row_all = row_span.whole;
    
    const uword local_n_rows = n_rows;
    
    const uword in_row1       = row_all ? 0            : row_span.a;
    const uword in_row2       =                          row_span.b;
    const uword submat_n_rows = row_all ? local_n_rows : in_row2 - in_row1 + 1;
    
    arma_debug_check
      (
      (col_num >= n_cols)
      ||
      ( row_all ? false : ((in_row1 > in_row2) || (in_row2 >= local_n_rows)) )
      ,
      "SpMat::operator(): indices out of bounds or incorrectly used"
      );
    
    return SpSubview<eT>(*this, in_row1, col_num, submat_n_rows, 1);
    }
  
  
  
  /**
   * Swap in_row1 with in_row2.
   */
  template<typename eT>
  inline
  void
  SpMat<eT>::swap_rows(const uword in_row1, const uword in_row2)
    {
    arma_extra_debug_sigprint();
  
    arma_debug_check
      (
      (in_row1 >= n_rows) || (in_row2 >= n_rows),
      "SpMat::swap_rows(): out of bounds"
      );
  
    // Sanity check.
    if (in_row1 == in_row2)
      {
      return;
      }
  
    // The easier way to do this, instead of collecting all the elements in one row and then swapping with the other, will be
    // to iterate over each column of the matrix (since we store in column-major format) and then swap the two elements in the two rows at that time.
    // We will try to avoid using the at() call since it is expensive, instead preferring to use an iterator to track our position.
    uword col1 = (in_row1 < in_row2) ? in_row1 : in_row2;
    uword col2 = (in_row1 < in_row2) ? in_row2 : in_row1;
  
    for (uword lcol = 0; lcol < n_cols; lcol++)
      {
      // If there is nothing in this column we can ignore it.
      if (col_ptrs[lcol] == col_ptrs[lcol + 1])
        {
        continue;
        }
  
      // These will represent the positions of the items themselves.
      uword loc1 = n_nonzero + 1;
      uword loc2 = n_nonzero + 1;
  
      for (uword search_pos = col_ptrs[lcol]; search_pos < col_ptrs[lcol + 1]; search_pos++)
        {
        if (row_indices[search_pos] == col1)
          {
          loc1 = search_pos;
          }
  
        if (row_indices[search_pos] == col2)
          {
          loc2 = search_pos;
          break; // No need to look any further.
          }
        }
  
      // There are four cases: we found both elements; we found one element (loc1); we found one element (loc2); we found zero elements.
      // If we found zero elements no work needs to be done and we can continue to the next column.
      if ((loc1 != (n_nonzero + 1)) && (loc2 != (n_nonzero + 1)))
        {
        // This is an easy case: just swap the values.  No index modifying necessary.
        eT tmp = values[loc1];
        access::rw(values[loc1]) = values[loc2];
        access::rw(values[loc2]) = tmp;
        }
      else if (loc1 != (n_nonzero + 1)) // We only found loc1 and not loc2.
        {
        // We need to find the correct place to move our value to.  It will be forward (not backwards) because in_row2 > in_row1.
        // Each iteration of the loop swaps the current value (loc1) with (loc1 + 1); in this manner we move our value down to where it should be.
        while (((loc1 + 1) < col_ptrs[lcol + 1]) && (row_indices[loc1 + 1] < in_row2))
          {
          // Swap both the values and the indices.  The column should not change.
          eT tmp = values[loc1];
          access::rw(values[loc1]) = values[loc1 + 1];
          access::rw(values[loc1 + 1]) = tmp;
  
          uword tmp_index = row_indices[loc1];
          access::rw(row_indices[loc1]) = row_indices[loc1 + 1];
          access::rw(row_indices[loc1 + 1]) = tmp_index;
  
          loc1++; // And increment the counter.
          }
  
        // Now set the row index correctly.
        access::rw(row_indices[loc1]) = in_row2;
  
        }
      else if (loc2 != (n_nonzero + 1))
        {
        // We need to find the correct place to move our value to.  It will be backwards (not forwards) because in_row1 < in_row2.
        // Each iteration of the loop swaps the current value (loc2) with (loc2 - 1); in this manner we move our value up to where it should be.
        while (((loc2 - 1) >= col_ptrs[lcol]) && (row_indices[loc2 - 1] > in_row1))
          {
          // Swap both the values and the indices.  The column should not change.
          eT tmp = values[loc2];
          access::rw(values[loc2]) = values[loc2 - 1];
          access::rw(values[loc2 - 1]) = tmp;
  
          uword tmp_index = row_indices[loc2];
          access::rw(row_indices[loc2]) = row_indices[loc2 - 1];
          access::rw(row_indices[loc2 - 1]) = tmp_index;
  
          loc2--; // And decrement the counter.
          }
  
        // Now set the row index correctly.
        access::rw(row_indices[loc2]) = in_row1;
  
        }
      /* else: no need to swap anything; both values are zero */
      }
    }
  
  /**
   * Swap in_col1 with in_col2.
   */
  template<typename eT>
  inline
  void
  SpMat<eT>::swap_cols(const uword in_col1, const uword in_col2)
    {
    arma_extra_debug_sigprint();
  
    // slow but works
    for(uword lrow = 0; lrow < n_rows; ++lrow)
      {
      eT tmp = at(lrow, in_col1);
      at(lrow, in_col1) = at(lrow, in_col2);
      at(lrow, in_col2) = tmp;
      }
    }
  
  /**
   * Remove the row row_num.
   */
  template<typename eT>
  inline
  void
  SpMat<eT>::shed_row(const uword row_num)
    {
    arma_extra_debug_sigprint();
    arma_debug_check (row_num >= n_rows, "SpMat::shed_row(): out of bounds");
  
    shed_rows (row_num, row_num);
    }
  
  /**
   * Remove the column col_num.
   */
  template<typename eT>
  inline
  void
  SpMat<eT>::shed_col(const uword col_num)
    {
    arma_extra_debug_sigprint();
    arma_debug_check (col_num >= n_cols, "SpMat::shed_col(): out of bounds");
  
    shed_cols(col_num, col_num);
    }
  
  /**
   * Remove all rows between (and including) in_row1 and in_row2.
   */
  template<typename eT>
  inline
  void
  SpMat<eT>::shed_rows(const uword in_row1, const uword in_row2)
    {
    arma_extra_debug_sigprint();
  
    arma_debug_check
      (
      (in_row1 > in_row2) || (in_row2 >= n_rows),
      "SpMat::shed_rows(): indices out of bounds or incorectly used"
      );
  
    uword i, j;
    // Store the length of values
    uword vlength = n_nonzero;
    // Store the length of col_ptrs
    uword clength = n_cols + 1;
  
    // This is O(n * n_cols) and inplace, there may be a faster way, though.
    for (i = 0, j = 0; i < vlength; ++i)
      {
      // Store the row of the ith element.
      const uword lrow = row_indices[i];
      // Is the ith element in the range of rows we want to remove?
      if (lrow >= in_row1 && lrow <= in_row2)
        {
        // Increment our "removed elements" counter.
        ++j;
  
        // Adjust the values of col_ptrs each time we remove an element.
        // Basically, the length of one column reduces by one, and everything to
        // its right gets reduced by one to represent all the elements being
        // shifted to the left by one.
        for(uword k = 0; k < clength; ++k)
          {
          if (col_ptrs[k] > (i - j + 1))
            {
            --access::rw(col_ptrs[k]);
            }
          }
        }
      else
        {
        // We shift the element we checked to the left by how many elements
        // we have removed.
        // j = 0 until we remove the first element.
        if (j != 0)
          {
          access::rw(row_indices[i - j]) = (lrow > in_row2) ? (lrow - (in_row2 - in_row1 + 1)) : lrow;
          access::rw(values[i - j]) = values[i];
          }
        }
      }
  
    // j is the number of elements removed.
  
    // Shrink the vectors.  This will copy the memory.
    mem_resize(n_nonzero - j);
  
    // Adjust row and element counts.
    access::rw(n_rows)    = n_rows - (in_row2 - in_row1) - 1;
    access::rw(n_elem)    = n_rows * n_cols;
    }
  
  /**
   * Remove all columns between (and including) in_col1 and in_col2.
   */
  template<typename eT>
  inline
  void
  SpMat<eT>::shed_cols(const uword in_col1, const uword in_col2)
    {
    arma_extra_debug_sigprint();
  
    arma_debug_check
      (
      (in_col1 > in_col2) || (in_col2 >= n_cols),
      "SpMat::shed_cols(): indices out of bounds or incorrectly used"
      );
  
    // First we find the locations in values and row_indices for the column entries.
    uword col_beg = col_ptrs[in_col1];
    uword col_end = col_ptrs[in_col2 + 1];
  
    // Then we find the number of entries in the column.
    uword diff = col_end - col_beg;
  
    if (diff > 0)
      {
      eT*    new_values      = memory::acquire_chunked<eT>   (n_nonzero - diff);
      uword* new_row_indices = memory::acquire_chunked<uword>(n_nonzero - diff);
  
      // Copy first part.
      if (col_beg != 0)
        {
        arrayops::copy(new_values, values, col_beg);
        arrayops::copy(new_row_indices, row_indices, col_beg);
        }
  
      // Copy second part.
      if (col_end != n_nonzero)
        {
        arrayops::copy(new_values + col_beg, values + col_end, n_nonzero - col_end);
        arrayops::copy(new_row_indices + col_beg, row_indices + col_end, n_nonzero - col_end);
        }
  
      memory::release(values);
      memory::release(row_indices);
  
      access::rw(values)      = new_values;
      access::rw(row_indices) = new_row_indices;
  
      // Update counts and such.
      access::rw(n_nonzero) -= diff;
      }
    
    // Update column pointers.
    const uword new_n_cols = n_cols - ((in_col2 - in_col1) + 1);
    
    uword* new_col_ptrs = memory::acquire<uword>(new_n_cols + 2);
    new_col_ptrs[new_n_cols + 1] = std::numeric_limits<uword>::max();
    
    // Copy first set of columns (no manipulation required).
    if (in_col1 != 0)
      {
      arrayops::copy(new_col_ptrs, col_ptrs, in_col1);
      }
    
    // Copy second set of columns (manipulation required).
    uword cur_col = in_col1;
    for (uword i = in_col2 + 1; i <= n_cols; ++i, ++cur_col)
      {
      new_col_ptrs[cur_col] = col_ptrs[i] - diff;
      }
    
    memory::release(col_ptrs);
    access::rw(col_ptrs) = new_col_ptrs;
    
    // We update the element and column counts, and we're done.
    access::rw(n_cols) = new_n_cols;
    access::rw(n_elem) = n_cols * n_rows;
    }
  
  
  
  template<typename eT>
  arma_inline
  SpSubview<eT>
  SpMat<eT>::rows(const uword in_row1, const uword in_row2)
    {
    arma_extra_debug_sigprint();
  
    arma_debug_check
      (
      (in_row1 > in_row2) || (in_row2 >= n_rows),
      "SpMat::rows(): indices out of bounds or incorrectly used"
      );
  
    const uword subview_n_rows = in_row2 - in_row1 + 1;
  
    return SpSubview<eT>(*this, in_row1, 0, subview_n_rows, n_cols);
    }
  
  
  
  template<typename eT>
  arma_inline
  const SpSubview<eT>
  SpMat<eT>::rows(const uword in_row1, const uword in_row2) const
    {
    arma_extra_debug_sigprint();
  
    arma_debug_check
      (
      (in_row1 > in_row2) || (in_row2 >= n_rows),
      "SpMat::rows(): indices out of bounds or incorrectly used"
      );
  
    const uword subview_n_rows = in_row2 - in_row1 + 1;
  
    return SpSubview<eT>(*this, in_row1, 0, subview_n_rows, n_cols);
    }
  
  
  
  template<typename eT>
  arma_inline
  SpSubview<eT>
  SpMat<eT>::cols(const uword in_col1, const uword in_col2)
    {
    arma_extra_debug_sigprint();
  
    arma_debug_check
      (
      (in_col1 > in_col2) || (in_col2 >= n_cols),
      "SpMat::cols(): indices out of bounds or incorrectly used"
      );
  
    const uword subview_n_cols = in_col2 - in_col1 + 1;
  
    return SpSubview<eT>(*this, 0, in_col1, n_rows, subview_n_cols);
    }
  
  
  
  template<typename eT>
  arma_inline
  const SpSubview<eT>
  SpMat<eT>::cols(const uword in_col1, const uword in_col2) const
    {
    arma_extra_debug_sigprint();
  
    arma_debug_check
      (
      (in_col1 > in_col2) || (in_col2 >= n_cols),
      "SpMat::cols(): indices out of bounds or incorrectly used"
      );
  
    const uword subview_n_cols = in_col2 - in_col1 + 1;
  
    return SpSubview<eT>(*this, 0, in_col1, n_rows, subview_n_cols);
    }
  
  
  
  template<typename eT>
  arma_inline
  SpSubview<eT>
  SpMat<eT>::submat(const uword in_row1, const uword in_col1, const uword in_row2, const uword in_col2)
    {
    arma_extra_debug_sigprint();
  
    arma_debug_check
      (
      (in_row1 > in_row2) || (in_col1 >  in_col2) || (in_row2 >= n_rows) || (in_col2 >= n_cols),
      "SpMat::submat(): indices out of bounds or incorrectly used"
      );
  
    const uword subview_n_rows = in_row2 - in_row1 + 1;
    const uword subview_n_cols = in_col2 - in_col1 + 1;
  
    return SpSubview<eT>(*this, in_row1, in_col1, subview_n_rows, subview_n_cols);
    }
  
  
  
  template<typename eT>
  arma_inline
  const SpSubview<eT>
  SpMat<eT>::submat(const uword in_row1, const uword in_col1, const uword in_row2, const uword in_col2) const
    {
    arma_extra_debug_sigprint();
  
    arma_debug_check
      (
      (in_row1 > in_row2) || (in_col1 >  in_col2) || (in_row2 >= n_rows) || (in_col2 >= n_cols),
      "SpMat::submat(): indices out of bounds or incorrectly used"
      );
  
    const uword subview_n_rows = in_row2 - in_row1 + 1;
    const uword subview_n_cols = in_col2 - in_col1 + 1;
  
    return SpSubview<eT>(*this, in_row1, in_col1, subview_n_rows, subview_n_cols);
    }
  
  
  
  template<typename eT>
  arma_inline
  SpSubview<eT>
  SpMat<eT>::submat(const uword in_row1, const uword in_col1, const SizeMat& s)
    {
    arma_extra_debug_sigprint();
    
    const uword l_n_rows = n_rows;
    const uword l_n_cols = n_cols;
    
    const uword s_n_rows = s.n_rows;
    const uword s_n_cols = s.n_cols;
    
    arma_debug_check
      (
      ((in_row1 >= l_n_rows) || (in_col1 >= l_n_cols) || ((in_row1 + s_n_rows) > l_n_rows) || ((in_col1 + s_n_cols) > l_n_cols)),
      "SpMat::submat(): indices or size out of bounds"
      );
    
    return SpSubview<eT>(*this, in_row1, in_col1, s_n_rows, s_n_cols);
    }
  
  
  
  template<typename eT>
  arma_inline
  const SpSubview<eT>
  SpMat<eT>::submat(const uword in_row1, const uword in_col1, const SizeMat& s) const
    {
    arma_extra_debug_sigprint();
    
    const uword l_n_rows = n_rows;
    const uword l_n_cols = n_cols;
    
    const uword s_n_rows = s.n_rows;
    const uword s_n_cols = s.n_cols;
    
    arma_debug_check
      (
      ((in_row1 >= l_n_rows) || (in_col1 >= l_n_cols) || ((in_row1 + s_n_rows) > l_n_rows) || ((in_col1 + s_n_cols) > l_n_cols)),
      "SpMat::submat(): indices or size out of bounds"
      );
    
    return SpSubview<eT>(*this, in_row1, in_col1, s_n_rows, s_n_cols);
    }
  
  
  
  template<typename eT>
  inline
  SpSubview<eT>
  SpMat<eT>::submat(const span& row_span, const span& col_span)
    {
    arma_extra_debug_sigprint();
  
    const bool row_all = row_span.whole;
    const bool col_all = col_span.whole;
    
    const uword local_n_rows = n_rows;
    const uword local_n_cols = n_cols;
    
    const uword in_row1       = row_all ? 0            : row_span.a;
    const uword in_row2       =                          row_span.b;
    const uword submat_n_rows = row_all ? local_n_rows : in_row2 - in_row1 + 1; 
    
    const uword in_col1       = col_all ? 0            : col_span.a;
    const uword in_col2       =                          col_span.b;
    const uword submat_n_cols = col_all ? local_n_cols : in_col2 - in_col1 + 1; 
    
    arma_debug_check
      (    
      ( row_all ? false : ((in_row1 > in_row2) || (in_row2 >= local_n_rows)) )
      ||   
      ( col_all ? false : ((in_col1 > in_col2) || (in_col2 >= local_n_cols)) )
      ,    
      "SpMat::submat(): indices out of bounds or incorrectly used"
      );   
    
    return SpSubview<eT>(*this, in_row1, in_col1, submat_n_rows, submat_n_cols);
    }
  
  
  
  template<typename eT>
  inline
  const SpSubview<eT>
  SpMat<eT>::submat(const span& row_span, const span& col_span) const
    {
    arma_extra_debug_sigprint();
  
    const bool row_all = row_span.whole;
    const bool col_all = col_span.whole;
    
    const uword local_n_rows = n_rows;
    const uword local_n_cols = n_cols;
    
    const uword in_row1       = row_all ? 0            : row_span.a;
    const uword in_row2       =                          row_span.b;
    const uword submat_n_rows = row_all ? local_n_rows : in_row2 - in_row1 + 1; 
    
    const uword in_col1       = col_all ? 0            : col_span.a;
    const uword in_col2       =                          col_span.b;
    const uword submat_n_cols = col_all ? local_n_cols : in_col2 - in_col1 + 1; 
    
    arma_debug_check
      (    
      ( row_all ? false : ((in_row1 > in_row2) || (in_row2 >= local_n_rows)) )
      ||   
      ( col_all ? false : ((in_col1 > in_col2) || (in_col2 >= local_n_cols)) )
      ,    
      "SpMat::submat(): indices out of bounds or incorrectly used"
      );   
    
    return SpSubview<eT>(*this, in_row1, in_col1, submat_n_rows, submat_n_cols);
    }
  
  
  
  template<typename eT>
  inline
  SpSubview<eT>
  SpMat<eT>::operator()(const span& row_span, const span& col_span)
    {
    arma_extra_debug_sigprint();
  
    return submat(row_span, col_span);
    }
  
  
  
  template<typename eT>
  inline
  const SpSubview<eT>
  SpMat<eT>::operator()(const span& row_span, const span& col_span) const
    {
    arma_extra_debug_sigprint();
  
    return submat(row_span, col_span);
    }
  
  
  
  template<typename eT>
  arma_inline
  SpSubview<eT>
  SpMat<eT>::operator()(const uword in_row1, const uword in_col1, const SizeMat& s)
    {
    arma_extra_debug_sigprint();
    
    return (*this).submat(in_row1, in_col1, s);
    }
  
  
  
  template<typename eT>
  arma_inline
  const SpSubview<eT>
  SpMat<eT>::operator()(const uword in_row1, const uword in_col1, const SizeMat& s) const
    {
    arma_extra_debug_sigprint();
    
    return (*this).submat(in_row1, in_col1, s);
    }
  
  
  
  /**
   * Element access; acces the i'th element (works identically to the Mat accessors).
   * If there is nothing at element i, 0 is returned.
   *
   * @param i Element to access.
   */
  
  template<typename eT>
  arma_inline
  arma_warn_unused
  SpValProxy<SpMat<eT> >
  SpMat<eT>::operator[](const uword i)
    {
    return get_value(i);
    }
  
  
  
  template<typename eT>
  arma_inline
  arma_warn_unused
  eT
  SpMat<eT>::operator[](const uword i) const
    {
    return get_value(i);
    }
  
  
  
  template<typename eT>
  arma_inline
  arma_warn_unused
  SpValProxy<SpMat<eT> >
  SpMat<eT>::at(const uword i)
    {
    return get_value(i);
    }
  
  
  
  template<typename eT>
  arma_inline
  arma_warn_unused
  eT
  SpMat<eT>::at(const uword i) const
    {
    return get_value(i);
    }
  
  
  
  template<typename eT>
  arma_inline
  arma_warn_unused
  SpValProxy<SpMat<eT> >
  SpMat<eT>::operator()(const uword i)
    {
    arma_debug_check( (i >= n_elem), "SpMat::operator(): out of bounds");
    return get_value(i);
    }
  
  
  
  template<typename eT>
  arma_inline
  arma_warn_unused
  eT
  SpMat<eT>::operator()(const uword i) const
    {
    arma_debug_check( (i >= n_elem), "SpMat::operator(): out of bounds");
    return get_value(i);
    }
  
  
  
  /**
   * Element access; access the element at row in_rows and column in_col.
   * If there is nothing at that position, 0 is returned.
   */
  
  template<typename eT>
  arma_inline
  arma_warn_unused
  SpValProxy<SpMat<eT> >
  SpMat<eT>::at(const uword in_row, const uword in_col)
    {
    return get_value(in_row, in_col);
    }
  
  
  
  template<typename eT>
  arma_inline
  arma_warn_unused
  eT
  SpMat<eT>::at(const uword in_row, const uword in_col) const
    {
    return get_value(in_row, in_col);
    }
  
  
  
  template<typename eT>
  arma_inline
  arma_warn_unused
  SpValProxy<SpMat<eT> >
  SpMat<eT>::operator()(const uword in_row, const uword in_col)
    {
    arma_debug_check( ((in_row >= n_rows) || (in_col >= n_cols)), "SpMat::operator(): out of bounds");
    return get_value(in_row, in_col);
    }
  
  
  
  template<typename eT>
  arma_inline
  arma_warn_unused
  eT
  SpMat<eT>::operator()(const uword in_row, const uword in_col) const
    {
    arma_debug_check( ((in_row >= n_rows) || (in_col >= n_cols)), "SpMat::operator(): out of bounds");
    return get_value(in_row, in_col);
    }
  
  
  
  /**
   * Check if matrix is empty (no size, no values).
   */
  template<typename eT>
  arma_inline
  arma_warn_unused
  bool
  SpMat<eT>::is_empty() const
    {
    return(n_elem == 0);
    }
  
  
  
  //! returns true if the object can be interpreted as a column or row vector
  template<typename eT>
  arma_inline
  arma_warn_unused
  bool
  SpMat<eT>::is_vec() const
    {
    return ( (n_rows == 1) || (n_cols == 1) );
    }
  
  
  
  //! returns true if the object can be interpreted as a row vector
  template<typename eT>
  arma_inline
  arma_warn_unused
  bool
  SpMat<eT>::is_rowvec() const
    {
    return (n_rows == 1);
    }
  
  
  
  //! returns true if the object can be interpreted as a column vector
  template<typename eT>
  arma_inline
  arma_warn_unused
  bool
  SpMat<eT>::is_colvec() const
    {
    return (n_cols == 1);
    }
  
  
  
  //! returns true if the object has the same number of non-zero rows and columnns
  template<typename eT>
  arma_inline
  arma_warn_unused
  bool
  SpMat<eT>::is_square() const
    {
    return (n_rows == n_cols);
    }
  
  
  
  //! returns true if all of the elements are finite
  template<typename eT>
  inline
  arma_warn_unused
  bool
  SpMat<eT>::is_finite() const
    {
    for(uword i = 0; i < n_nonzero; i++)
      {
      if(arma_isfinite(values[i]) == false)
        {
        return false;
        }
      }
  
    return true; // No infinite values.
    }
  
  
  
  //! returns true if the given index is currently in range
  template<typename eT>
  arma_inline
  arma_warn_unused
  bool
  SpMat<eT>::in_range(const uword i) const
    {
    return (i < n_elem);
    }
  
  
  //! returns true if the given start and end indices are currently in range
  template<typename eT>
  arma_inline
  arma_warn_unused
  bool
  SpMat<eT>::in_range(const span& x) const
    {
    arma_extra_debug_sigprint();
  
    if(x.whole == true)
      {
      return true;
      }
    else
      {
      const uword a = x.a;
      const uword b = x.b;
  
      return ( (a <= b) && (b < n_elem) );
      }
    }
  
  
  
  //! returns true if the given location is currently in range
  template<typename eT>
  arma_inline
  arma_warn_unused
  bool
  SpMat<eT>::in_range(const uword in_row, const uword in_col) const
    {
    return ( (in_row < n_rows) && (in_col < n_cols) );
    }
  
  
  
  template<typename eT>
  arma_inline
  arma_warn_unused
  bool
  SpMat<eT>::in_range(const span& row_span, const uword in_col) const
    {
    arma_extra_debug_sigprint();
  
    if(row_span.whole == true)
      {
      return (in_col < n_cols);
      }
    else
      {
      const uword in_row1 = row_span.a;
      const uword in_row2 = row_span.b;
  
      return ( (in_row1 <= in_row2) && (in_row2 < n_rows) && (in_col < n_cols) );
      }
    }
  
  
  
  template<typename eT>
  arma_inline
  arma_warn_unused
  bool
  SpMat<eT>::in_range(const uword in_row, const span& col_span) const
    {
    arma_extra_debug_sigprint();
  
    if(col_span.whole == true)
      {
      return (in_row < n_rows);
      }
    else
      {
      const uword in_col1 = col_span.a;
      const uword in_col2 = col_span.b;
  
      return ( (in_row < n_rows) && (in_col1 <= in_col2) && (in_col2 < n_cols) );
      }
    }
  
  
  
  template<typename eT>
  arma_inline
  arma_warn_unused
  bool
  SpMat<eT>::in_range(const span& row_span, const span& col_span) const
    {
    arma_extra_debug_sigprint();
  
    const uword in_row1 = row_span.a;
    const uword in_row2 = row_span.b;
  
    const uword in_col1 = col_span.a;
    const uword in_col2 = col_span.b;
  
    const bool rows_ok = row_span.whole ? true : ( (in_row1 <= in_row2) && (in_row2 < n_rows) );
    const bool cols_ok = col_span.whole ? true : ( (in_col1 <= in_col2) && (in_col2 < n_cols) );
  
    return ( (rows_ok == true) && (cols_ok == true) );
    }
  
  
  
  template<typename eT>
  arma_inline
  arma_warn_unused
  bool
  SpMat<eT>::in_range(const uword in_row, const uword in_col, const SizeMat& s) const
    {
    const uword l_n_rows = n_rows;
    const uword l_n_cols = n_cols;
    
    if( (in_row >= l_n_rows) || (in_col >= l_n_cols) || ((in_row + s.n_rows) > l_n_rows) || ((in_col + s.n_cols) > l_n_cols) )
      {
      return false;
      }
    else
      {
      return true;
      }
    }
  
  
  
  template<typename eT>
  inline
  void
  SpMat<eT>::impl_print(const std::string& extra_text) const
    {
    arma_extra_debug_sigprint();
  
    if(extra_text.length() != 0)
      {
      const std::streamsize orig_width = ARMA_DEFAULT_OSTREAM.width();
  
      ARMA_DEFAULT_OSTREAM << extra_text << '\n';
  
      ARMA_DEFAULT_OSTREAM.width(orig_width);
      }
  
    arma_ostream::print(ARMA_DEFAULT_OSTREAM, *this, true);
    }
  
  
  
  template<typename eT>
  inline
  void
  SpMat<eT>::impl_print(std::ostream& user_stream, const std::string& extra_text) const
    {
    arma_extra_debug_sigprint();
  
    if(extra_text.length() != 0)
      {
      const std::streamsize orig_width = user_stream.width();
  
      user_stream << extra_text << '\n';
  
      user_stream.width(orig_width);
      }
  
    arma_ostream::print(user_stream, *this, true);
    }
  
  
  
  template<typename eT>
  inline
  void
  SpMat<eT>::impl_raw_print(const std::string& extra_text) const
    {
    arma_extra_debug_sigprint();
  
    if(extra_text.length() != 0)
      {
      const std::streamsize orig_width = ARMA_DEFAULT_OSTREAM.width();
  
      ARMA_DEFAULT_OSTREAM << extra_text << '\n';
  
      ARMA_DEFAULT_OSTREAM.width(orig_width);
      }
  
    arma_ostream::print(ARMA_DEFAULT_OSTREAM, *this, false);
    }
  
  
  template<typename eT>
  inline
  void
  SpMat<eT>::impl_raw_print(std::ostream& user_stream, const std::string& extra_text) const
    {
    arma_extra_debug_sigprint();
  
    if(extra_text.length() != 0)
      {
      const std::streamsize orig_width = user_stream.width();
  
      user_stream << extra_text << '\n';
  
      user_stream.width(orig_width);
      }
  
    arma_ostream::print(user_stream, *this, false);
    }
  
  
  
  /**
   * Matrix printing, prepends supplied text.
   * Prints 0 wherever no element exists.
   */
  template<typename eT>
  inline
  void
  SpMat<eT>::impl_print_dense(const std::string& extra_text) const
    {
    arma_extra_debug_sigprint();
  
    if(extra_text.length() != 0)
      {
      const std::streamsize orig_width = ARMA_DEFAULT_OSTREAM.width();
  
      ARMA_DEFAULT_OSTREAM << extra_text << '\n';
  
      ARMA_DEFAULT_OSTREAM.width(orig_width);
      }
  
    arma_ostream::print_dense(ARMA_DEFAULT_OSTREAM, *this, true);
    }
  
  
  
  template<typename eT>
  inline
  void
  SpMat<eT>::impl_print_dense(std::ostream& user_stream, const std::string& extra_text) const
    {
    arma_extra_debug_sigprint();
  
    if(extra_text.length() != 0)
      {
      const std::streamsize orig_width = user_stream.width();
  
      user_stream << extra_text << '\n';
  
      user_stream.width(orig_width);
      }
  
    arma_ostream::print_dense(user_stream, *this, true);
    }
  
  
  
  template<typename eT>
  inline
  void
  SpMat<eT>::impl_raw_print_dense(const std::string& extra_text) const
    {
    arma_extra_debug_sigprint();
  
    if(extra_text.length() != 0)
      {
      const std::streamsize orig_width = ARMA_DEFAULT_OSTREAM.width();
  
      ARMA_DEFAULT_OSTREAM << extra_text << '\n';
  
      ARMA_DEFAULT_OSTREAM.width(orig_width);
      }
  
    arma_ostream::print_dense(ARMA_DEFAULT_OSTREAM, *this, false);
    }
  
  
  
  template<typename eT>
  inline
  void
  SpMat<eT>::impl_raw_print_dense(std::ostream& user_stream, const std::string& extra_text) const
    {
    arma_extra_debug_sigprint();
  
    if(extra_text.length() != 0)
      {
      const std::streamsize orig_width = user_stream.width();
  
      user_stream << extra_text << '\n';
  
      user_stream.width(orig_width);
      }
  
    arma_ostream::print_dense(user_stream, *this, false);
    }
  
  
  
  //! Set the size to the size of another matrix.
  template<typename eT>
  template<typename eT2>
  inline
  void
  SpMat<eT>::copy_size(const SpMat<eT2>& m)
    {
    arma_extra_debug_sigprint();
  
    init(m.n_rows, m.n_cols);
    }
  
  
  
  template<typename eT>
  template<typename eT2>
  inline
  void
  SpMat<eT>::copy_size(const Mat<eT2>& m)
    {
    arma_extra_debug_sigprint();
  
    init(m.n_rows, m.n_cols);
    }
  
  
  
  /**
   * Resize the matrix to a given size.  The matrix will be resized to be a column vector (i.e. in_elem columns, 1 row).
   *
   * @param in_elem Number of elements to allow.
   */
  template<typename eT>
  inline
  void
  SpMat<eT>::set_size(const uword in_elem)
    {
    arma_extra_debug_sigprint();
  
    // If this is a row vector, we resize to a row vector.
    if(vec_state == 2)
      {
      init(1, in_elem);
      }
    else
      {
      init(in_elem, 1);
      }
    }
  
  
  
  /**
   * Resize the matrix to a given size.
   *
   * @param in_rows Number of rows to allow.
   * @param in_cols Number of columns to allow.
   */
  template<typename eT>
  inline
  void
  SpMat<eT>::set_size(const uword in_rows, const uword in_cols)
    {
    arma_extra_debug_sigprint();
  
    init(in_rows, in_cols);
    }
  
  
  
  template<typename eT>
  inline
  void
  SpMat<eT>::reshape(const uword in_rows, const uword in_cols, const uword dim)
    {
    arma_extra_debug_sigprint();
  
    if (dim == 0)
      {
      // We have to modify all of the relevant row indices and the relevant column pointers.
      // Iterate over all the points to do this.  We won't be deleting any points, but we will be modifying
      // columns and rows. We'll have to store a new set of column vectors.
      uword* new_col_ptrs    = memory::acquire<uword>(in_cols + 2);
      new_col_ptrs[in_cols + 1] = std::numeric_limits<uword>::max();
      
      uword* new_row_indices = memory::acquire_chunked<uword>(n_nonzero + 1);
      access::rw(new_row_indices[n_nonzero]) = 0;
  
      arrayops::inplace_set(new_col_ptrs, uword(0), in_cols + 1);
  
      for(const_iterator it = begin(); it != end(); it++)
        {
        uword vector_position = (it.col() * n_rows) + it.row();
        new_row_indices[it.pos()] = vector_position % in_rows;
        ++new_col_ptrs[vector_position / in_rows + 1];
        }
  
      // Now sum the column counts to get the new column pointers.
      for(uword i = 1; i <= in_cols; i++)
        {
        access::rw(new_col_ptrs[i]) += new_col_ptrs[i - 1];
        }
  
      // Copy the new row indices.
      memory::release(row_indices);
      access::rw(row_indices) = new_row_indices;
  
      memory::release(col_ptrs);
      access::rw(col_ptrs) = new_col_ptrs;
  
      // Now set the size.
      access::rw(n_rows) = in_rows;
      access::rw(n_cols) = in_cols;
      }
    else
      {
      // Row-wise reshaping.  This is more tedious and we will use a separate sparse matrix to do it.
      SpMat<eT> tmp(in_rows, in_cols);
  
      for(const_row_iterator it = begin_row(); it.pos() < n_nonzero; it++)
        {
        uword vector_position = (it.row() * n_cols) + it.col();
  
        tmp((vector_position / in_cols), (vector_position % in_cols)) = (*it);
        }
  
      (*this).operator=(tmp);
      }
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::zeros()
    {
    arma_extra_debug_sigprint();
  
    if (n_nonzero > 0)
      {
      memory::release(values);
      memory::release(row_indices);
  
      access::rw(values)      = memory::acquire_chunked<eT>(1);
      access::rw(row_indices) = memory::acquire_chunked<uword>(1);
  
      access::rw(values[0]) = 0;
      access::rw(row_indices[0]) = 0;
      }
  
    access::rw(n_nonzero) = 0;
    arrayops::inplace_set(access::rwp(col_ptrs), uword(0), n_cols + 1);
  
    return *this;
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::zeros(const uword in_elem)
    {
    arma_extra_debug_sigprint();
  
    if(vec_state == 2)
      {
      init(1, in_elem); // Row vector
      }
    else
      {
      init(in_elem, 1);
      }
  
    return *this;
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::zeros(const uword in_rows, const uword in_cols)
    {
    arma_extra_debug_sigprint();
  
    init(in_rows, in_cols);
  
    return *this;
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::eye()
    {
    arma_extra_debug_sigprint();
  
    return (*this).eye(n_rows, n_cols);
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::eye(const uword in_rows, const uword in_cols)
    {
    arma_extra_debug_sigprint();
    
    const uword N = (std::min)(in_rows, in_cols);
    
    init(in_rows, in_cols);
    
    mem_resize(N);
    
    arrayops::inplace_set(access::rwp(values), eT(1), N);
    
    for(uword i = 0; i <  N; ++i) { access::rw(row_indices[i]) = i; }
    
    for(uword i = 0; i <= N; ++i) { access::rw(col_ptrs[i])    = i; }
    
    access::rw(n_nonzero) = N;
    
    return *this;
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::speye()
    {
    arma_extra_debug_sigprint();
  
    return (*this).eye(n_rows, n_cols);
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::speye(const uword in_n_rows, const uword in_n_cols)
    {
    arma_extra_debug_sigprint();
    
    return (*this).eye(in_n_rows, in_n_cols);
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::sprandu(const uword in_rows, const uword in_cols, const double density)
    {
    arma_extra_debug_sigprint();
    
    arma_debug_check( ( (density < double(0)) || (density > double(1)) ), "sprandu(): density must be in the [0,1] interval" );
    
    zeros(in_rows, in_cols);
    
    mem_resize( uword(density * double(in_rows) * double(in_cols) + 0.5) );
    
    if(n_nonzero == 0)
      {
      return *this;
      }
    
    arma_rng::randu<eT>::fill( access::rwp(values), n_nonzero );
    
    uvec indices = linspace<uvec>( 0u, in_rows*in_cols-1, n_nonzero );
    
    // perturb the indices
    for(uword i=1; i < n_nonzero-1; ++i)
      {
      const uword index_left  = indices[i-1];
      const uword index_right = indices[i+1];
      
      const uword center = (index_left + index_right) / 2;
      
      const uword delta1 = center      - index_left - 1;
      const uword delta2 = index_right - center     - 1;
      
      const uword min_delta = (std::min)(delta1, delta2);
      
      uword index_new = uword( double(center) + double(min_delta) * (2.0*randu()-1.0) );
      
      // paranoia, but better be safe than sorry
      if( (index_left < index_new) && (index_new < index_right) )
        {
        indices[i] = index_new;
        }
      }
    
    uword cur_index = 0;
    uword count     = 0;  
    
    for(uword lcol = 0; lcol < in_cols; ++lcol)
    for(uword lrow = 0; lrow < in_rows; ++lrow)
      {
      if(count == indices[cur_index])
        {
        access::rw(row_indices[cur_index]) = lrow;
        access::rw(col_ptrs[lcol + 1])++;
        ++cur_index;
        }
      
      ++count;
      }
    
    if(cur_index != n_nonzero)
      {
      // Fix size to correct size.
      mem_resize(cur_index);
      }
    
    // Sum column pointers.
    for(uword lcol = 1; lcol <= in_cols; ++lcol)
      {
      access::rw(col_ptrs[lcol]) += col_ptrs[lcol - 1];
      }
    
    return *this;
    }
  
  
  
  template<typename eT>
  inline
  const SpMat<eT>&
  SpMat<eT>::sprandn(const uword in_rows, const uword in_cols, const double density)
    {
    arma_extra_debug_sigprint();
    
    arma_debug_check( ( (density < double(0)) || (density > double(1)) ), "sprandn(): density must be in the [0,1] interval" );
    
    zeros(in_rows, in_cols);
    
    mem_resize( uword(density * double(in_rows) * double(in_cols) + 0.5) );
    
    if(n_nonzero == 0)
      {
      return *this;
      }
    
    arma_rng::randn<eT>::fill( access::rwp(values), n_nonzero );
    
    uvec indices = linspace<uvec>( 0u, in_rows*in_cols-1, n_nonzero );
    
    // perturb the indices
    for(uword i=1; i < n_nonzero-1; ++i)
      {
      const uword index_left  = indices[i-1];
      const uword index_right = indices[i+1];
      
      const uword center = (index_left + index_right) / 2;
      
      const uword delta1 = center      - index_left - 1;
      const uword delta2 = index_right - center     - 1;
      
      const uword min_delta = (std::min)(delta1, delta2);
      
      uword index_new = uword( double(center) + double(min_delta) * (2.0*randu()-1.0) );
      
      // paranoia, but better be safe than sorry
      if( (index_left < index_new) && (index_new < index_right) )
        {
        indices[i] = index_new;
        }
      }
    
    uword cur_index = 0;
    uword count     = 0;  
    
    for(uword lcol = 0; lcol < in_cols; ++lcol)
    for(uword lrow = 0; lrow < in_rows; ++lrow)
      {
      if(count == indices[cur_index])
        {
        access::rw(row_indices[cur_index]) = lrow;
        access::rw(col_ptrs[lcol + 1])++;
        ++cur_index;
        }
      
      ++count;
      }
    
    if(cur_index != n_nonzero)
      {
      // Fix size to correct size.
      mem_resize(cur_index);
      }
    
    // Sum column pointers.
    for(uword lcol = 1; lcol <= in_cols; ++lcol)
      {
      access::rw(col_ptrs[lcol]) += col_ptrs[lcol - 1];
      }
    
    return *this;
    }
  
  
  
  template<typename eT>
  inline
  void
  SpMat<eT>::reset()
    {
    arma_extra_debug_sigprint();
  
    switch(vec_state)
      {
      default:
        init(0, 0);
        break;
        
      case 1:
        init(0, 1);
        break;
      
      case 2:
        init(1, 0);
        break;
      }
    }
  
  
  
  /**
   * Get the minimum or the maximum of the matrix.
   */
  template<typename eT>
  inline
  arma_warn_unused
  eT
  SpMat<eT>::min() const
    {
    arma_extra_debug_sigprint();
  
    arma_debug_check((n_elem == 0), "min(): object has no elements");
  
    if (n_nonzero == 0)
      {
      return 0;
      }
  
    eT val = op_min::direct_min(values, n_nonzero);
  
    if ((val > 0) && (n_nonzero < n_elem)) // A sparse 0 is less.
      {
      val = 0;
      }
  
    return val;
    }
  
  
  
  template<typename eT>
  inline
  eT
  SpMat<eT>::min(uword& index_of_min_val) const
    {
    arma_extra_debug_sigprint();
  
    arma_debug_check((n_elem == 0), "min(): object has no elements");
  
    eT val = 0;
  
    if (n_nonzero == 0) // There are no other elements.  It must be 0.
      {
      index_of_min_val = 0;
      }
    else
      {
      uword location;
      val = op_min::direct_min(values, n_nonzero, location);
  
      if ((val > 0) && (n_nonzero < n_elem)) // A sparse 0 is less.
        {
        val = 0;
  
        // Give back the index to the first zero position.
        index_of_min_val = 0;
        while (get_position(index_of_min_val) == index_of_min_val) // An element exists at that position.
          {
          index_of_min_val++;
          }
  
        }
      else
        {
        index_of_min_val = get_position(location);
        }
      }
  
    return val;
  
    }
  
  
  
  template<typename eT>
  inline
  eT
  SpMat<eT>::min(uword& row_of_min_val, uword& col_of_min_val) const
    {
    arma_extra_debug_sigprint();
  
    arma_debug_check((n_elem == 0), "min(): object has no elements");
  
    eT val = 0;
  
    if (n_nonzero == 0) // There are no other elements.  It must be 0.
      {
      row_of_min_val = 0;
      col_of_min_val = 0;
      }
    else
      {
      uword location;
      val = op_min::direct_min(values, n_nonzero, location);
  
      if ((val > 0) && (n_nonzero < n_elem)) // A sparse 0 is less.
        {
        val = 0;
  
        location = 0;
        while (get_position(location) == location) // An element exists at that position.
          {
          location++;
          }
  
        row_of_min_val = location % n_rows;
        col_of_min_val = location / n_rows;
        }
      else
        {
        get_position(location, row_of_min_val, col_of_min_val);
        }
      }
  
    return val;
  
    }
  
  
  
  template<typename eT>
  inline
  arma_warn_unused
  eT
  SpMat<eT>::max() const
    {
    arma_extra_debug_sigprint();
  
    arma_debug_check((n_elem == 0), "max(): object has no elements");
  
    if (n_nonzero == 0)
      {
      return 0;
      }
  
    eT val = op_max::direct_max(values, n_nonzero);
  
    if ((val < 0) && (n_nonzero < n_elem)) // A sparse 0 is more.
      {
      return 0;
      }
  
    return val;
  
    }
  
  
  
  template<typename eT>
  inline
  eT
  SpMat<eT>::max(uword& index_of_max_val) const
    {
    arma_extra_debug_sigprint();
  
    arma_debug_check((n_elem == 0), "max(): object has no elements");
  
    eT val = 0;
  
    if (n_nonzero == 0)
      {
      index_of_max_val = 0;
      }
    else
      {
      uword location;
      val = op_max::direct_max(values, n_nonzero, location);
  
      if ((val < 0) && (n_nonzero < n_elem)) // A sparse 0 is more.
        {
        val = 0;
  
        location = 0;
        while (get_position(location) == location) // An element exists at that position.
          {
          location++;
          }
  
        }
      else
        {
        index_of_max_val = get_position(location);
        }
  
      }
  
    return val;
  
    }
  
  
  
  template<typename eT>
  inline
  eT
  SpMat<eT>::max(uword& row_of_max_val, uword& col_of_max_val) const
    {
    arma_extra_debug_sigprint();
  
    arma_debug_check((n_elem == 0), "max(): object has no elements");
  
    eT val = 0;
  
    if (n_nonzero == 0)
      {
      row_of_max_val = 0;
      col_of_max_val = 0;
      }
    else
      {
      uword location;
      val = op_max::direct_max(values, n_nonzero, location);
  
      if ((val < 0) && (n_nonzero < n_elem)) // A sparse 0 is more.
        {
        val = 0;
  
        location = 0;
        while (get_position(location) == location) // An element exists at that position.
          {
          location++;
          }
  
        row_of_max_val = location % n_rows;
        col_of_max_val = location / n_rows;
  
        }
      else
        {
        get_position(location, row_of_max_val, col_of_max_val);
        }
  
      }
  
    return val;
  
    }
  
  
  
  //! save the matrix to a file
  template<typename eT>
  inline
  bool
  SpMat<eT>::save(const std::string name, const file_type type, const bool print_status) const
    {
    arma_extra_debug_sigprint();
    
    bool save_okay;
    
    switch(type)
      {
      // case raw_ascii:
      //   save_okay = diskio::save_raw_ascii(*this, name);
      //   break;
      
      // case csv_ascii:
      //   save_okay = diskio::save_csv_ascii(*this, name);
      //   break;
      
      case arma_binary:
        save_okay = diskio::save_arma_binary(*this, name);
        break;
      
      case coord_ascii:
        save_okay = diskio::save_coord_ascii(*this, name);
        break;
      
      default:
        arma_warn(true, "SpMat::save(): unsupported file type");
        save_okay = false;
      }
    
    arma_warn( (save_okay == false), "SpMat::save(): couldn't write to ", name);
    
    return save_okay;
    }
  
  
  
  //! save the matrix to a stream
  template<typename eT>
  inline
  bool
  SpMat<eT>::save(std::ostream& os, const file_type type, const bool print_status) const
    {
    arma_extra_debug_sigprint();
    
    bool save_okay;
    
    switch(type)
      {
      // case raw_ascii:
      //   save_okay = diskio::save_raw_ascii(*this, os);
      //   break;
      
      // case csv_ascii:
      //   save_okay = diskio::save_csv_ascii(*this, os);
      //   break;
      
      case arma_binary:
        save_okay = diskio::save_arma_binary(*this, os);
        break;
      
      case coord_ascii:
        save_okay = diskio::save_coord_ascii(*this, os);
        break;
      
      default:
        arma_warn(true, "SpMat::save(): unsupported file type");
        save_okay = false;
      }
    
    arma_warn( (save_okay == false), "SpMat::save(): couldn't write to the given stream");
    
    return save_okay;
    }
  
  
  
  //! load a matrix from a file
  template<typename eT>
  inline
  bool
  SpMat<eT>::load(const std::string name, const file_type type, const bool print_status)
    {
    arma_extra_debug_sigprint();
    
    bool load_okay;
    std::string err_msg;
    
    switch(type)
      {
      // case auto_detect:
      //   load_okay = diskio::load_auto_detect(*this, name, err_msg);
      //   break;
      
      // case raw_ascii:
      //   load_okay = diskio::load_raw_ascii(*this, name, err_msg);
      //   break;
      
      // case csv_ascii:
      //   load_okay = diskio::load_csv_ascii(*this, name, err_msg);
      //   break;
      
      case arma_binary:
        load_okay = diskio::load_arma_binary(*this, name, err_msg);
        break;
      
      case coord_ascii:
        load_okay = diskio::load_coord_ascii(*this, name, err_msg);
        break;
      
      default:
        arma_warn(true, "SpMat::load(): unsupported file type");
        load_okay = false;
      }
    
    if(load_okay == false)
      {
      if(err_msg.length() > 0)
        {
        arma_warn(true, "SpMat::load(): ", err_msg, name);
        }
      else
        {
        arma_warn(true, "SpMat::load(): couldn't read ", name);
        }
      }
    
    if(load_okay == false)
      {
      (*this).reset();
      }
      
    return load_okay;
    }
  
  
  
  //! load a matrix from a stream
  template<typename eT>
  inline
  bool
  SpMat<eT>::load(std::istream& is, const file_type type, const bool print_status)
    {
    arma_extra_debug_sigprint();
    
    bool load_okay;
    std::string err_msg;
    
    switch(type)
      {
      // case auto_detect:
      //   load_okay = diskio::load_auto_detect(*this, is, err_msg);
      //   break;
      
      // case raw_ascii:
      //   load_okay = diskio::load_raw_ascii(*this, is, err_msg);
      //   break;
      
      // case csv_ascii:
      //   load_okay = diskio::load_csv_ascii(*this, is, err_msg);
      //   break;
      
      case arma_binary:
        load_okay = diskio::load_arma_binary(*this, is, err_msg);
        break;
      
      case coord_ascii:
        load_okay = diskio::load_coord_ascii(*this, is, err_msg);
        break;
      
      default:
        arma_warn(true, "SpMat::load(): unsupported file type");
        load_okay = false;
      }
    
    
    if(load_okay == false)
      {
      if(err_msg.length() > 0)
        {
        arma_warn(true, "SpMat::load(): ", err_msg, "the given stream");
        }
      else
        {
        arma_warn(true, "SpMat::load(): couldn't load from the given stream");
        }
      }
    
    if(load_okay == false)
      {
      (*this).reset();
      }
      
    return load_okay;
    }
  
  
  
  //! save the matrix to a file, without printing any error messages
  template<typename eT>
  inline
  bool
  SpMat<eT>::quiet_save(const std::string name, const file_type type) const
    {
    arma_extra_debug_sigprint();
    
    return (*this).save(name, type, false);
    }
  
  
  
  //! save the matrix to a stream, without printing any error messages
  template<typename eT>
  inline
  bool
  SpMat<eT>::quiet_save(std::ostream& os, const file_type type) const
    {
    arma_extra_debug_sigprint();
    
    return (*this).save(os, type, false);
    }
  
  
  
  //! load a matrix from a file, without printing any error messages
  template<typename eT>
  inline
  bool
  SpMat<eT>::quiet_load(const std::string name, const file_type type)
    {
    arma_extra_debug_sigprint();
    
    return (*this).load(name, type, false);
    }
  
  
  
  //! load a matrix from a stream, without printing any error messages
  template<typename eT>
  inline
  bool
  SpMat<eT>::quiet_load(std::istream& is, const file_type type)
    {
    arma_extra_debug_sigprint();
    
    return (*this).load(is, type, false);
    }
  
  
  
  /**
   * Initialize the matrix to the specified size.  Data is not preserved, so the matrix is assumed to be entirely sparse (empty).
   */
  template<typename eT>
  inline
  void
  SpMat<eT>::init(uword in_rows, uword in_cols)
    {
    arma_extra_debug_sigprint();
  
    // Verify that we are allowed to do this.
    if(vec_state > 0)
      {
      if((in_rows == 0) && (in_cols == 0))
        {
        if(vec_state == 1)
          {
          in_cols = 1;
          }
        else
        if(vec_state == 2)
          {
          in_rows = 1;
          }
        }
      else
        {
        arma_debug_check
          (
          ( ((vec_state == 1) && (in_cols != 1)) || ((vec_state == 2) && (in_rows != 1)) ),
          "SpMat::init(): object is a row or column vector; requested size is not compatible"
          );
        }
      }
  
    // Ensure that n_elem can hold the result of (n_rows * n_cols)
    arma_debug_check
      (
        (
        ( (in_rows > ARMA_MAX_UHWORD) || (in_cols > ARMA_MAX_UHWORD) )
          ? ( (float(in_rows) * float(in_cols)) > float(ARMA_MAX_UWORD) )
          : false
        ),
        "SpMat::init(): requested size is too large"
      );
  
    // Clean out the existing memory.
    if (values)
      {
      memory::release(values);
      memory::release(row_indices);
      }
  
    access::rw(values)      = memory::acquire_chunked<eT>   (1);
    access::rw(row_indices) = memory::acquire_chunked<uword>(1);
  
    access::rw(values[0]) = 0;
    access::rw(row_indices[0]) = 0;
  
    memory::release(col_ptrs);
  
    // Set the new size accordingly.
    access::rw(n_rows)    = in_rows;
    access::rw(n_cols)    = in_cols;
    access::rw(n_elem)    = (in_rows * in_cols);
    access::rw(n_nonzero) = 0;
  
    // Try to allocate the column pointers, filling them with 0,
    // except for the last element which contains the maximum possible element
    // (so iterators terminate correctly).
    access::rw(col_ptrs) = memory::acquire<uword>(in_cols + 2);
    
    arrayops::inplace_set(access::rwp(col_ptrs), uword(0), in_cols + 1);
    
    access::rw(col_ptrs[in_cols + 1]) = std::numeric_limits<uword>::max();
    }
  
  
  
  /**
   * Initialize the matrix from a string.
   */
  template<typename eT>
  inline
  void
  SpMat<eT>::init(const std::string& text)
    {
    arma_extra_debug_sigprint();
  
    // Figure out the size first.
    uword t_n_rows = 0;
    uword t_n_cols = 0;
  
    bool t_n_cols_found = false;
  
    std::string token;
  
    std::string::size_type line_start = 0;
    std::string::size_type   line_end = 0;
  
    while (line_start < text.length())
      {
  
      line_end = text.find(';', line_start);
  
      if (line_end == std::string::npos)
        line_end = text.length() - 1;
  
      std::string::size_type line_len = line_end - line_start + 1;
      std::stringstream line_stream(text.substr(line_start, line_len));
  
      // Step through each column.
      uword line_n_cols = 0;
  
      while (line_stream >> token)
        {
        ++line_n_cols;
        }
  
      if (line_n_cols > 0)
        {
        if (t_n_cols_found == false)
          {
          t_n_cols = line_n_cols;
          t_n_cols_found = true;
          }
        else // Check it each time through, just to make sure.
          arma_check((line_n_cols != t_n_cols), "SpMat::init(): inconsistent number of columns in given string");
  
        ++t_n_rows;
        }
  
      line_start = line_end + 1;
  
      }
  
    set_size(t_n_rows, t_n_cols);
  
    // Second time through will pick up all the values.
    line_start = 0;
    line_end = 0;
  
    uword lrow = 0;
  
    while (line_start < text.length())
      {
  
      line_end = text.find(';', line_start);
  
      if (line_end == std::string::npos)
        line_end = text.length() - 1;
  
      std::string::size_type line_len = line_end - line_start + 1;
      std::stringstream line_stream(text.substr(line_start, line_len));
  
      uword lcol = 0;
      eT val;
  
      while (line_stream >> val)
        {
        // Only add nonzero elements.
        if (val != eT(0))
          {
          get_value(lrow, lcol) = val;
          }
  
        ++lcol;
        }
  
      ++lrow;
      line_start = line_end + 1;
  
      }
  
    }
  
  /**
   * Copy from another matrix.
   */
  template<typename eT>
  inline
  void
  SpMat<eT>::init(const SpMat<eT>& x)
    {
    arma_extra_debug_sigprint();
    
    // Ensure we are not initializing to ourselves.
    if (this != &x)
      {
      init(x.n_rows, x.n_cols);
  
      // values and row_indices may not be null.
      if (values != NULL)
        {
        memory::release(values);
        memory::release(row_indices);
        }
  
      access::rw(values)      = memory::acquire_chunked<eT>   (x.n_nonzero + 1);
      access::rw(row_indices) = memory::acquire_chunked<uword>(x.n_nonzero + 1);
  
      // Now copy over the elements.
      arrayops::copy(access::rwp(values),      x.values,      x.n_nonzero + 1);
      arrayops::copy(access::rwp(row_indices), x.row_indices, x.n_nonzero + 1);
      arrayops::copy(access::rwp(col_ptrs),    x.col_ptrs,    x.n_cols + 1);
      
      access::rw(n_nonzero) = x.n_nonzero;
      }
    }
  
  
  
  template<typename eT>
  inline
  void
  SpMat<eT>::mem_resize(const uword new_n_nonzero)
    {
    arma_extra_debug_sigprint();
    
    if(n_nonzero != new_n_nonzero)
      {
      if(new_n_nonzero == 0)
        {
        memory::release(values);
        memory::release(row_indices);
        
        access::rw(values)      = memory::acquire_chunked<eT>   (1);
        access::rw(row_indices) = memory::acquire_chunked<uword>(1);
  
        access::rw(     values[0]) = 0;
        access::rw(row_indices[0]) = 0;
        }
      else
        {
        // Figure out the actual amount of memory currently allocated
        // NOTE: this relies on memory::acquire_chunked() being used for the 'values' and 'row_indices' arrays
        const uword n_alloc = memory::enlarge_to_mult_of_chunksize(n_nonzero);
        
        if(n_alloc < new_n_nonzero)
          {
          eT*    new_values      = memory::acquire_chunked<eT>   (new_n_nonzero + 1);
          uword* new_row_indices = memory::acquire_chunked<uword>(new_n_nonzero + 1);
          
          if(n_nonzero > 0)
            {
            // Copy old elements.
            uword copy_len = std::min(n_nonzero, new_n_nonzero);
            
            arrayops::copy(new_values,      values,      copy_len);
            arrayops::copy(new_row_indices, row_indices, copy_len);
            }
          
          memory::release(values);
          memory::release(row_indices);
          
          access::rw(values)      = new_values;
          access::rw(row_indices) = new_row_indices;
          }
          
        // Set the "fake end" of the matrix by setting the last value and row
        // index to 0.  This helps the iterators work correctly.
        access::rw(     values[new_n_nonzero]) = 0;
        access::rw(row_indices[new_n_nonzero]) = 0;
        }
      
      access::rw(n_nonzero) = new_n_nonzero;
      }
    }
  
  
  
  // Steal memory from another matrix.
  template<typename eT>
  inline
  void
  SpMat<eT>::steal_mem(SpMat<eT>& x)
    {
    arma_extra_debug_sigprint();
    
    if(this != &x)
      {
      if(values     )  { memory::release(access::rw(values));      }
      if(row_indices)  { memory::release(access::rw(row_indices)); }
      if(col_ptrs   )  { memory::release(access::rw(col_ptrs));    }
      
      access::rw(n_rows)    = x.n_rows;
      access::rw(n_cols)    = x.n_cols;
      access::rw(n_elem)    = x.n_elem;
      access::rw(n_nonzero) = x.n_nonzero;
      
      access::rw(values)      = x.values;
      access::rw(row_indices) = x.row_indices;
      access::rw(col_ptrs)    = x.col_ptrs;
      
      // Set other matrix to empty.
      access::rw(x.n_rows)    = 0;
      access::rw(x.n_cols)    = 0;
      access::rw(x.n_elem)    = 0;
      access::rw(x.n_nonzero) = 0;
      
      access::rw(x.values)      = NULL;
      access::rw(x.row_indices) = NULL;
      access::rw(x.col_ptrs)    = NULL;
      }
    }
  
  
  
  template<typename eT>
  template<typename T1, typename Functor>
  arma_hot
  inline
  void
  SpMat<eT>::init_xform(const SpBase<eT,T1>& A, const Functor& func)
    {
    arma_extra_debug_sigprint();
    
    // if possible, avoid doing a copy and instead apply func to the generated elements
    if(SpProxy<T1>::Q_created_by_proxy == true)
      {
      (*this) = A.get_ref();
      
      const uword nnz = n_nonzero;
      
      eT* t_values = access::rwp(values);
      
      for(uword i=0; i < nnz; ++i)
        {
        t_values[i] = func(t_values[i]);
        }
      }
    else
      {
      init_xform_mt(A.get_ref(), func);
      }
    }
  
  
  
  template<typename eT>
  template<typename eT2, typename T1, typename Functor>
  arma_hot
  inline
  void
  SpMat<eT>::init_xform_mt(const SpBase<eT2,T1>& A, const Functor& func)
    {
    arma_extra_debug_sigprint();
    
    const SpProxy<T1> P(A.get_ref());
    
    if( (P.is_alias(*this) == true) || (is_SpMat<typename SpProxy<T1>::stored_type>::value == true) )
      {
      // NOTE: unwrap_spmat will convert a submatrix to a matrix, which in effect takes care of aliasing with submatrices;
      // NOTE: however, when more delayed ops are implemented, more elaborate handling of aliasing will be necessary
      const unwrap_spmat<typename SpProxy<T1>::stored_type> tmp(P.Q);
      
      const SpMat<eT2>& x = tmp.M;
      
      if(void_ptr(this) != void_ptr(&x))
        {
        init(x.n_rows, x.n_cols);
        
        // values and row_indices may not be null.
        if(values != NULL)
          {
          memory::release(values);
          memory::release(row_indices);
          }
        
        access::rw(values)      = memory::acquire_chunked<eT>   (x.n_nonzero + 1);
        access::rw(row_indices) = memory::acquire_chunked<uword>(x.n_nonzero + 1);
        
        arrayops::copy(access::rwp(row_indices), x.row_indices, x.n_nonzero + 1);
        arrayops::copy(access::rwp(col_ptrs),    x.col_ptrs,    x.n_cols    + 1);
        
        access::rw(n_nonzero) = x.n_nonzero;
        }
      
      
      // initialise the elements array with a transformed version of the elements from x
      
      const uword nnz = n_nonzero;
      
      const eT2* x_values = x.values;
            eT*  t_values = access::rwp(values);
      
      for(uword i=0; i < nnz; ++i)
        {
        t_values[i] = func(x_values[i]);   // NOTE: func() must produce a value of type eT (ie. act as a convertor between eT2 and eT)
        }
      }
    else
      {
      init(P.get_n_rows(), P.get_n_cols());
      
      mem_resize(P.get_n_nonzero());
      
      typename SpProxy<T1>::const_iterator_type it = P.begin();
      
      while(it != P.end())
        {
        access::rw(row_indices[it.pos()]) = it.row();
        access::rw(values[it.pos()]) = func(*it);   // NOTE: func() must produce a value of type eT (ie. act as a convertor between eT2 and eT)
        ++access::rw(col_ptrs[it.col() + 1]);
        ++it;
        }
      
      // Now sum column pointers.
      for(uword c = 1; c <= n_cols; ++c)
        {
        access::rw(col_ptrs[c]) += col_ptrs[c - 1];
        }
      }
    }
  
  
  
  template<typename eT>
  inline
  typename SpMat<eT>::iterator
  SpMat<eT>::begin()
    {
    return iterator(*this);
    }
  
  
  
  template<typename eT>
  inline
  typename SpMat<eT>::const_iterator
  SpMat<eT>::begin() const
    {
    return const_iterator(*this);
    }
  
  
  
  template<typename eT>
  inline
  typename SpMat<eT>::iterator
  SpMat<eT>::end()
    {
    return iterator(*this, 0, n_cols, n_nonzero);
    }
  
  
  
  template<typename eT>
  inline
  typename SpMat<eT>::const_iterator
  SpMat<eT>::end() const
    {
    return const_iterator(*this, 0, n_cols, n_nonzero);
    }
  
  
  
  template<typename eT>
  inline
  typename SpMat<eT>::iterator
  SpMat<eT>::begin_col(const uword col_num)
    {
    return iterator(*this, 0, col_num);
    }
  
  
  
  template<typename eT>
  inline
  typename SpMat<eT>::const_iterator
  SpMat<eT>::begin_col(const uword col_num) const
    {
    return const_iterator(*this, 0, col_num);
    }
  
  
  
  template<typename eT>
  inline
  typename SpMat<eT>::iterator
  SpMat<eT>::end_col(const uword col_num)
    {
    return iterator(*this, 0, col_num + 1);
    }
  
  
  
  template<typename eT>
  inline
  typename SpMat<eT>::const_iterator
  SpMat<eT>::end_col(const uword col_num) const
    {
    return const_iterator(*this, 0, col_num + 1);
    }
  
  
  
  template<typename eT>
  inline
  typename SpMat<eT>::row_iterator
  SpMat<eT>::begin_row(const uword row_num)
    {
    return row_iterator(*this, row_num, 0);
    }
  
  
  
  template<typename eT>
  inline
  typename SpMat<eT>::const_row_iterator
  SpMat<eT>::begin_row(const uword row_num) const
    {
    return const_row_iterator(*this, row_num, 0);
    }
  
  
  
  template<typename eT>
  inline
  typename SpMat<eT>::row_iterator
  SpMat<eT>::end_row()
    {
    return row_iterator(*this, n_nonzero);
    }
  
  
  
  template<typename eT>
  inline
  typename SpMat<eT>::const_row_iterator
  SpMat<eT>::end_row() const
    {
    return const_row_iterator(*this, n_nonzero);
    }
  
  
  
  template<typename eT>
  inline
  typename SpMat<eT>::row_iterator
  SpMat<eT>::end_row(const uword row_num)
    {
    return row_iterator(*this, row_num + 1, 0);
    }
  
  
  
  template<typename eT>
  inline
  typename SpMat<eT>::const_row_iterator
  SpMat<eT>::end_row(const uword row_num) const
    {
    return const_row_iterator(*this, row_num + 1, 0);
    }
  
  
  
  template<typename eT>
  inline
  void
  SpMat<eT>::clear()
    {
    (*this).reset();
    }
  
  
  
  template<typename eT>
  inline
  bool
  SpMat<eT>::empty() const
    {
    return (n_elem == 0);
    }
  
  
  
  template<typename eT>
  inline
  uword
  SpMat<eT>::size() const
    {
    return n_elem;
    }
  
  
  
  template<typename eT>
  inline
  arma_hot
  arma_warn_unused
  SpValProxy<SpMat<eT> >
  SpMat<eT>::get_value(const uword i)
    {
    // First convert to the actual location.
    uword lcol = i / n_rows; // Integer division.
    uword lrow = i % n_rows;
  
    return get_value(lrow, lcol);
    }
  
  
  
  template<typename eT>
  inline
  arma_hot
  arma_warn_unused
  eT
  SpMat<eT>::get_value(const uword i) const
    {
    // First convert to the actual location.
    uword lcol = i / n_rows; // Integer division.
    uword lrow = i % n_rows;
  
    return get_value(lrow, lcol);
    }
  
  
  
  template<typename eT>
  inline
  arma_hot
  arma_warn_unused
  SpValProxy<SpMat<eT> >
  SpMat<eT>::get_value(const uword in_row, const uword in_col)
    {
    const uword colptr      = col_ptrs[in_col];
    const uword next_colptr = col_ptrs[in_col + 1];
  
    // Step through the row indices to see if our element exists.
    for (uword i = colptr; i < next_colptr; ++i)
      {
      const uword row_index = row_indices[i];
      
      // First check that we have not stepped past it.
      if (in_row < row_index) // If we have, then it doesn't exist: return 0.
        {
        return SpValProxy<SpMat<eT> >(in_row, in_col, *this); // Proxy for a zero value.
        }
  
      // Now check if we are at the correct place.
      if (in_row == row_index) // If we are, return a reference to the value.
        {
        return SpValProxy<SpMat<eT> >(in_row, in_col, *this, &access::rw(values[i]));
        }
  
      }
  
    // We did not find it, so it does not exist: return 0.
    return SpValProxy<SpMat<eT> >(in_row, in_col, *this);
    }
  
  
  
  template<typename eT>
  inline
  arma_hot
  arma_warn_unused
  eT
  SpMat<eT>::get_value(const uword in_row, const uword in_col) const
    {
    const uword colptr      = col_ptrs[in_col];
    const uword next_colptr = col_ptrs[in_col + 1];
    
    // Step through the row indices to see if our element exists.
    for (uword i = colptr; i < next_colptr; ++i)
      {
      const uword row_index = row_indices[i];
      
      // First check that we have not stepped past it.
      if (in_row < row_index) // If we have, then it doesn't exist: return 0.
        {
        return eT(0);
        }
      
      // Now check if we are at the correct place.
      if (in_row == row_index) // If we are, return the value.
        {
        return values[i];
        }
      }
    
    // We did not find it, so it does not exist: return 0.
    return eT(0);
    }
  
  
  
  /**
   * Given the index representing which of the nonzero values this is, return its
   * actual location, either in row/col or just the index.
   */
  template<typename eT>
  arma_hot
  arma_inline
  arma_warn_unused
  uword
  SpMat<eT>::get_position(const uword i) const
    {
    uword lrow, lcol;
    
    get_position(i, lrow, lcol);
    
    // Assemble the row/col into the element's location in the matrix.
    return (lrow + n_rows * lcol);
    }
  
  
  
  template<typename eT>
  arma_hot
  arma_inline
  void
  SpMat<eT>::get_position(const uword i, uword& row_of_i, uword& col_of_i) const
    {
    arma_debug_check((i >= n_nonzero), "SpMat::get_position(): index out of bounds");
    
    col_of_i = 0;
    while (col_ptrs[col_of_i + 1] <= i)
      {
      col_of_i++;
      }
    
    row_of_i = row_indices[i];
    
    return;
    }
  
  
  
  /**
   * Add an element at the given position, and return a reference to it.  The
   * element will be set to 0 (unless otherwise specified).  If the element
   * already exists, its value will be overwritten.
   *
   * @param in_row Row of new element.
   * @param in_col Column of new element.
   * @param in_val Value to set new element to (default 0.0).
   */
  template<typename eT>
  inline
  arma_hot
  arma_warn_unused
  eT&
  SpMat<eT>::add_element(const uword in_row, const uword in_col, const eT val)
    {
    arma_extra_debug_sigprint();
    
    // We will assume the new element does not exist and begin the search for
    // where to insert it.  If we find that it already exists, we will then
    // overwrite it.
    uword colptr      = col_ptrs[in_col    ];
    uword next_colptr = col_ptrs[in_col + 1];
    
    uword pos = colptr; // The position in the matrix of this value.
    
    if (colptr != next_colptr)
      {
      // There are other elements in this column, so we must find where this
      // element will fit as compared to those.
      while (pos < next_colptr && in_row > row_indices[pos])
        {
        pos++;
        }
      
      // We aren't inserting into the last position, so it is still possible
      // that the element may exist.
      if (pos != next_colptr && row_indices[pos] == in_row)
        {
        // It already exists.  Then, just overwrite it.
        access::rw(values[pos]) = val;
        
        return access::rw(values[pos]);
        }
      }
    
    
    // 
    // Element doesn't exist, so we have to insert it
    // 
    
    // We have to update the rest of the column pointers.
    for (uword i = in_col + 1; i < n_cols + 1; i++)
      {
      access::rw(col_ptrs[i])++; // We are only inserting one new element.
      }
    
    
    // Figure out the actual amount of memory currently allocated
    // NOTE: this relies on memory::acquire_chunked() being used for the 'values' and 'row_indices' arrays
    const uword n_alloc = memory::enlarge_to_mult_of_chunksize(n_nonzero + 1);
    
    // If possible, avoid time-consuming memory allocation 
    if(n_alloc > (n_nonzero + 1))
      {
      arrayops::copy_backwards(access::rwp(values)      + pos + 1, values      + pos, (n_nonzero - pos) + 1);
      arrayops::copy_backwards(access::rwp(row_indices) + pos + 1, row_indices + pos, (n_nonzero - pos) + 1);
      
      // Insert the new element.
      access::rw(values[pos])      = val;
      access::rw(row_indices[pos]) = in_row;
      
      access::rw(n_nonzero)++;
      }
    else
      {
      const uword old_n_nonzero = n_nonzero;
      
      access::rw(n_nonzero)++; // Add to count of nonzero elements.
      
      // Allocate larger memory.
      eT*    new_values      = memory::acquire_chunked<eT>   (n_nonzero + 1);
      uword* new_row_indices = memory::acquire_chunked<uword>(n_nonzero + 1);
      
      // Copy things over, before the new element.
      if (pos > 0)
        {
        arrayops::copy(new_values,      values,      pos);
        arrayops::copy(new_row_indices, row_indices, pos);
        }
      
      // Insert the new element.
      new_values[pos]      = val;
      new_row_indices[pos] = in_row;
      
      // Copy the rest of things over (including the extra element at the end).
      arrayops::copy(new_values      + pos + 1, values      + pos, (old_n_nonzero - pos) + 1);
      arrayops::copy(new_row_indices + pos + 1, row_indices + pos, (old_n_nonzero - pos) + 1);
      
      // Assign new pointers.
      memory::release(values);
      memory::release(row_indices);
  
      access::rw(values)      = new_values;
      access::rw(row_indices) = new_row_indices;
      }
    
    return access::rw(values[pos]);
    }
  
  
  
  /**
   * Delete an element at the given position.
   *
   * @param in_row Row of element to be deleted.
   * @param in_col Column of element to be deleted.
   */
  template<typename eT>
  inline
  arma_hot
  void
  SpMat<eT>::delete_element(const uword in_row, const uword in_col)
    {
    arma_extra_debug_sigprint();
    
    // We assume the element exists (although... it may not) and look for its
    // exact position.  If it doesn't exist... well, we don't need to do anything.
    uword colptr      = col_ptrs[in_col];
    uword next_colptr = col_ptrs[in_col + 1];
  
    if (colptr != next_colptr)
      {
      // There's at least one element in this column.
      // Let's see if we are one of them.
      for (uword pos = colptr; pos < next_colptr; pos++)
        {
        if (in_row == row_indices[pos])
          {
          const uword old_n_nonzero = n_nonzero;
          
          --access::rw(n_nonzero); // Remove one from the count of nonzero elements.
          
          // Found it.  Now remove it.
            
          // Figure out the actual amount of memory currently allocated and the actual amount that will be required
          // NOTE: this relies on memory::acquire_chunked() being used for the 'values' and 'row_indices' arrays
            
          const uword n_alloc     = memory::enlarge_to_mult_of_chunksize(old_n_nonzero + 1);
          const uword n_alloc_mod = memory::enlarge_to_mult_of_chunksize(n_nonzero + 1);
            
          // If possible, avoid time-consuming memory allocation
          if(n_alloc_mod == n_alloc)
            {
            if (pos < n_nonzero)  // remember, we decremented n_nonzero
              {
              arrayops::copy_forwards(access::rwp(values)      + pos, values + pos + 1, (n_nonzero - pos) + 1);
              arrayops::copy_forwards(access::rwp(row_indices) + pos, row_indices + pos + 1, (n_nonzero - pos) + 1);
              }
            }
          else
            {
            // Make new arrays.
            eT*    new_values      = memory::acquire_chunked<eT>   (n_nonzero + 1);
            uword* new_row_indices = memory::acquire_chunked<uword>(n_nonzero + 1);
              
            if (pos > 0)
              {
              arrayops::copy(new_values,      values,      pos);
              arrayops::copy(new_row_indices, row_indices, pos);
              }
              
            arrayops::copy(new_values      + pos, values      + pos + 1, (n_nonzero - pos) + 1);
            arrayops::copy(new_row_indices + pos, row_indices + pos + 1, (n_nonzero - pos) + 1);
              
            memory::release(values);
            memory::release(row_indices);
              
            access::rw(values)      = new_values;
            access::rw(row_indices) = new_row_indices;
            }
          
          // And lastly, update all the column pointers (decrement by one).
          for (uword i = in_col + 1; i < n_cols + 1; i++)
            {
            --access::rw(col_ptrs[i]); // We only removed one element.
            }
          
          return; // There is nothing left to do.
          }
        }
      }
    
    return; // The element does not exist, so there's nothing for us to do.
    }
  
  
  
  #ifdef ARMA_EXTRA_SPMAT_MEAT
    #include ARMA_INCFILE_WRAP(ARMA_EXTRA_SPMAT_MEAT)
  #endif
  
  
  
  //! @}
  