// SPDX-License-Identifier: Apache-2.0
// 
// Copyright 2008-2016 Conrad Sanderson (https://conradsanderson.id.au)
// Copyright 2008-2016 National ICT Australia (NICTA)
// 
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
// https://www.apache.org/licenses/LICENSE-2.0
// 
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
// ------------------------------------------------------------------------


//! \addtogroup SpProxy
//! @{


// TODO: clarify and check which variables and functions are valid when 'use_iterator' is either true or false


// within each specialisation of the SpProxy struct:
// 
// elem_type               = type of the elements obtained from object Q
// pod_type                = underlying type of elements if elem_type is std::complex
// stored_type             = type of Q object
// 
// const_iterator_type     = type of iterator provided by begin() and begin_col()
// const_row_iterator_type = type of iterator provided by begin_row()
// 
// use_iterator            = boolean to indicate that provided iterators must be used for accessing elements
// Q_is_generated          = boolean to indicate Q object was generated by SpProxy
// 
// is_row                  = boolean to indicate Q object can be treated a row vector
// is_col                  = boolean to indicate Q object can be treated a column vector
// is_xvec                 = boolean to indicate Q object is a vector with unknown orientation
// 
// Q                       = object that can be unwrapped via unwrap_spmat family of classes (ie. Q must be convertible to SpMat)
// 
// get_n_rows()            = return number of rows in Q
// get_n_cols()            = return number of columns in Q
// get_n_elem()            = return number of elements in Q
// get_n_nonzero()         = return number of non-zero elements in Q
// 
// operator[i]             = linear element accessor;       valid only if the 'use_iterator' boolean is false
// at(row,col)             = access elements via (row,col); valid only if the 'use_iterator' boolean is false
// 
// get_values()            = return pointer to CSC          values array in Q; valid only if the 'use_iterator' boolean is false
// get_row_indices()       = return pointer to CSC     row indices array in Q; valid only if the 'use_iterator' boolean is false
// get_col_ptrs()          = return pointer to CSC column pointers array in Q; valid only if the 'use_iterator' boolean is false
// 
// begin()                 = column-wise iterator indicating first element in Q
// begin_col(col_num)      = column-wise iterator indicating first element in column 'col_num' in Q
// begin_row(row_num = 0)  =    row-wise iterator indicating first element in row    'row_num' in Q
// 
// end()                   = column-wise iterator indicating "one-past-end" element in Q
// end_row()               =    row-wise iterator indicating "one-past-end" element in Q
// end_row(row_num)        =    row-wise iterator indicating "one-past-end" element in row 'row_num' in Q
// 
// is_alias(X)             = return true/false to indicate Q object aliases matrix X



template<typename eT>
struct SpProxy< SpMat<eT> >
  {
  typedef eT                                       elem_type;
  typedef typename get_pod_type<elem_type>::result pod_type;
  typedef SpMat<eT>                                stored_type;
  
  typedef typename SpMat<eT>::const_iterator       const_iterator_type;
  typedef typename SpMat<eT>::const_row_iterator   const_row_iterator_type;
  
  static constexpr bool use_iterator   = false;
  static constexpr bool Q_is_generated = false;
  
  static constexpr bool is_row  = false;
  static constexpr bool is_col  = false;
  static constexpr bool is_xvec = false;
  
  const SpMat<eT>& Q;
  
  inline explicit SpProxy(const SpMat<eT>& A)
    : Q(A)
    {
    arma_debug_sigprint();
    Q.sync();
    }
  
  arma_inline uword get_n_rows()    const { return Q.n_rows;    }
  arma_inline uword get_n_cols()    const { return Q.n_cols;    }
  arma_inline uword get_n_elem()    const { return Q.n_elem;    }
  arma_inline uword get_n_nonzero() const { return Q.n_nonzero; }
  
  arma_inline elem_type operator[](const uword i)                    const { return Q[i];           }
  arma_inline elem_type at        (const uword row, const uword col) const { return Q.at(row, col); }
  
  arma_inline const eT*    get_values()      const { return Q.values;      }
  arma_inline const uword* get_row_indices() const { return Q.row_indices; }
  arma_inline const uword* get_col_ptrs()    const { return Q.col_ptrs;    }
  
  arma_inline const_iterator_type     begin()                            const { return Q.begin();            }
  arma_inline const_iterator_type     begin_col(const uword col_num)     const { return Q.begin_col(col_num); }
  arma_inline const_row_iterator_type begin_row(const uword row_num = 0) const { return Q.begin_row(row_num); }
  
  arma_inline const_iterator_type     end()                        const { return Q.end();            }
  arma_inline const_row_iterator_type end_row()                    const { return Q.end_row();        }
  arma_inline const_row_iterator_type end_row(const uword row_num) const { return Q.end_row(row_num); }
  
  template<typename eT2>
  arma_inline bool is_alias(const SpMat<eT2>& X) const { return (is_same_type<eT,eT2>::yes) && (void_ptr(&Q) == void_ptr(&X)); }
  };



template<typename eT>
struct SpProxy< SpCol<eT> >
  {
  typedef eT                                       elem_type;
  typedef typename get_pod_type<elem_type>::result pod_type;
  typedef SpCol<eT>                                stored_type;
  
  typedef typename SpCol<eT>::const_iterator       const_iterator_type;
  typedef typename SpCol<eT>::const_row_iterator   const_row_iterator_type;
  
  static constexpr bool use_iterator   = false;
  static constexpr bool Q_is_generated = false;
  
  static constexpr bool is_row  = false;
  static constexpr bool is_col  = true;
  static constexpr bool is_xvec = false;
  
  const SpCol<eT>& Q;
  
  inline explicit SpProxy(const SpCol<eT>& A)
    : Q(A)
    {
    arma_debug_sigprint();
    Q.sync();
    }
  
  arma_inline uword get_n_rows()    const { return Q.n_rows;    }
  constexpr   uword get_n_cols()    const { return 1;           }
  arma_inline uword get_n_elem()    const { return Q.n_elem;    }
  arma_inline uword get_n_nonzero() const { return Q.n_nonzero; }
  
  arma_inline elem_type operator[](const uword i)                    const { return Q[i];           }
  arma_inline elem_type at        (const uword row, const uword col) const { return Q.at(row, col); }
  
  arma_inline const eT*    get_values()      const { return Q.values;      }
  arma_inline const uword* get_row_indices() const { return Q.row_indices; }
  arma_inline const uword* get_col_ptrs()    const { return Q.col_ptrs;    }
  
  arma_inline const_iterator_type     begin()                            const { return Q.begin();            }
  arma_inline const_iterator_type     begin_col(const uword)             const { return Q.begin();            }
  arma_inline const_row_iterator_type begin_row(const uword row_num = 0) const { return Q.begin_row(row_num); }
  
  arma_inline const_iterator_type     end()                        const { return Q.end();            }
  arma_inline const_row_iterator_type end_row()                    const { return Q.end_row();        }
  arma_inline const_row_iterator_type end_row(const uword row_num) const { return Q.end_row(row_num); }
  
  template<typename eT2>
  arma_inline bool is_alias(const SpMat<eT2>& X) const { return (is_same_type<eT,eT2>::yes) && (void_ptr(&Q) == void_ptr(&X)); }
  };



template<typename eT>
struct SpProxy< SpRow<eT> >
  {
  typedef eT                                       elem_type;
  typedef typename get_pod_type<elem_type>::result pod_type;
  typedef SpRow<eT>                                stored_type;
  
  typedef typename SpRow<eT>::const_iterator       const_iterator_type;
  typedef typename SpRow<eT>::const_row_iterator   const_row_iterator_type;
  
  static constexpr bool use_iterator   = false;
  static constexpr bool Q_is_generated = false;
  
  static constexpr bool is_row  = true;
  static constexpr bool is_col  = false;
  static constexpr bool is_xvec = false;
  
  const SpRow<eT>& Q;
  
  inline explicit SpProxy(const SpRow<eT>& A)
    : Q(A)
    {
    arma_debug_sigprint();
    Q.sync();
    }
  
  constexpr   uword get_n_rows()    const { return 1;           }
  arma_inline uword get_n_cols()    const { return Q.n_cols;    }
  arma_inline uword get_n_elem()    const { return Q.n_elem;    }
  arma_inline uword get_n_nonzero() const { return Q.n_nonzero; }
  
  arma_inline elem_type operator[](const uword i)                    const { return Q[i];           }
  arma_inline elem_type at        (const uword row, const uword col) const { return Q.at(row, col); }
  
  arma_inline const eT*    get_values()      const { return Q.values;      }
  arma_inline const uword* get_row_indices() const { return Q.row_indices; }
  arma_inline const uword* get_col_ptrs()    const { return Q.col_ptrs;    }
  
  arma_inline const_iterator_type     begin()                            const { return Q.begin();            }
  arma_inline const_iterator_type     begin_col(const uword col_num)     const { return Q.begin_col(col_num); }
  arma_inline const_row_iterator_type begin_row(const uword row_num = 0) const { return Q.begin_row(row_num); }
  
  arma_inline const_iterator_type     end()                        const { return Q.end();            }
  arma_inline const_row_iterator_type end_row()                    const { return Q.end_row();        }
  arma_inline const_row_iterator_type end_row(const uword row_num) const { return Q.end_row(row_num); }
  
  template<typename eT2>
  arma_inline bool is_alias(const SpMat<eT2>& X) const { return (is_same_type<eT,eT2>::yes) && (void_ptr(&Q) == void_ptr(&X)); }
  };



template<typename eT>
struct SpProxy< SpSubview<eT> >
  {
  typedef eT                                           elem_type;
  typedef typename get_pod_type<elem_type>::result     pod_type;
  typedef SpSubview<eT>                                stored_type;
  
  typedef typename SpSubview<eT>::const_iterator       const_iterator_type;
  typedef typename SpSubview<eT>::const_row_iterator   const_row_iterator_type;
  
  static constexpr bool use_iterator   = true;
  static constexpr bool Q_is_generated = false;
  
  static constexpr bool is_row  = false;
  static constexpr bool is_col  = false;
  static constexpr bool is_xvec = false;
  
  const SpSubview<eT>& Q;
  
  inline explicit SpProxy(const SpSubview<eT>& A)
    : Q(A)
    {
    arma_debug_sigprint();
    Q.m.sync();
    }
  
  arma_inline uword get_n_rows()    const { return Q.n_rows;    }
  arma_inline uword get_n_cols()    const { return Q.n_cols;    }
  arma_inline uword get_n_elem()    const { return Q.n_elem;    }
  arma_inline uword get_n_nonzero() const { return Q.n_nonzero; }
  
  arma_inline elem_type operator[](const uword i)                    const { return Q[i];           }
  arma_inline elem_type at        (const uword row, const uword col) const { return Q.at(row, col); }
  
  arma_inline const eT*    get_values()      const { return Q.m.values;      }
  arma_inline const uword* get_row_indices() const { return Q.m.row_indices; }
  arma_inline const uword* get_col_ptrs()    const { return Q.m.col_ptrs;    }
  
  arma_inline const_iterator_type     begin()                            const { return Q.begin();            }
  arma_inline const_iterator_type     begin_col(const uword col_num)     const { return Q.begin_col(col_num); }
  arma_inline const_row_iterator_type begin_row(const uword row_num = 0) const { return Q.begin_row(row_num); }
  
  arma_inline const_iterator_type     end()                        const { return Q.end();            }
  arma_inline const_row_iterator_type end_row()                    const { return Q.end_row();        }
  arma_inline const_row_iterator_type end_row(const uword row_num) const { return Q.end_row(row_num); }
  
  template<typename eT2>
  arma_inline bool is_alias(const SpMat<eT2>& X) const { return (is_same_type<eT,eT2>::yes) && (void_ptr(&Q.m) == void_ptr(&X)); }
  };



template<typename eT>
struct SpProxy< SpSubview_col<eT> >
  {
  typedef eT                                           elem_type;
  typedef typename get_pod_type<elem_type>::result     pod_type;
  typedef SpSubview_col<eT>                            stored_type;
  
  typedef typename SpSubview<eT>::const_iterator       const_iterator_type;
  typedef typename SpSubview<eT>::const_row_iterator   const_row_iterator_type;
  
  static constexpr bool use_iterator   = true;
  static constexpr bool Q_is_generated = false;
  
  static constexpr bool is_row  = false;
  static constexpr bool is_col  = true;
  static constexpr bool is_xvec = false;
  
  const SpSubview_col<eT>& Q;
  
  inline explicit SpProxy(const SpSubview_col<eT>& A)
    : Q(A)
    {
    arma_debug_sigprint();
    Q.m.sync();
    }
  
  arma_inline uword get_n_rows()    const { return Q.n_rows;    }
  constexpr   uword get_n_cols()    const { return 1;           }
  arma_inline uword get_n_elem()    const { return Q.n_elem;    }
  arma_inline uword get_n_nonzero() const { return Q.n_nonzero; }
  
  arma_inline elem_type operator[](const uword i)                const { return Q.at(i,   0); }
  arma_inline elem_type at        (const uword row, const uword) const { return Q.at(row, 0); }
  
  arma_inline const eT*    get_values()      const { return Q.m.values;      }
  arma_inline const uword* get_row_indices() const { return Q.m.row_indices; }
  arma_inline const uword* get_col_ptrs()    const { return Q.m.col_ptrs;    }
  
  arma_inline const_iterator_type     begin()                            const { return Q.begin();            }
  arma_inline const_iterator_type     begin_col(const uword col_num)     const { return Q.begin_col(col_num); }
  arma_inline const_row_iterator_type begin_row(const uword row_num = 0) const { return Q.begin_row(row_num); }
  
  arma_inline const_iterator_type     end()                        const { return Q.end();            }
  arma_inline const_row_iterator_type end_row()                    const { return Q.end_row();        }
  arma_inline const_row_iterator_type end_row(const uword row_num) const { return Q.end_row(row_num); }
  
  template<typename eT2>
  arma_inline bool is_alias(const SpMat<eT2>& X) const { return (is_same_type<eT,eT2>::yes) && (void_ptr(&Q.m) == void_ptr(&X)); }
  };



template<typename eT, typename T1>
struct SpProxy< SpSubview_col_list<eT,T1> >
  {
  typedef eT                                       elem_type;
  typedef typename get_pod_type<elem_type>::result pod_type;
  typedef SpMat<eT>                                stored_type;
  
  typedef typename SpMat<eT>::const_iterator       const_iterator_type;
  typedef typename SpMat<eT>::const_row_iterator   const_row_iterator_type;
  
  static constexpr bool use_iterator   = false;
  static constexpr bool Q_is_generated = true;
  
  static constexpr bool is_row  = false;
  static constexpr bool is_col  = false;
  static constexpr bool is_xvec = false;
  
  const SpMat<eT> Q;
  
  inline explicit SpProxy(const SpSubview_col_list<eT,T1>& A)
    : Q(A)
    {
    arma_debug_sigprint();
    }
  
  arma_inline uword get_n_rows()    const { return Q.n_rows;    }
  arma_inline uword get_n_cols()    const { return Q.n_cols;    }
  arma_inline uword get_n_elem()    const { return Q.n_elem;    }
  arma_inline uword get_n_nonzero() const { return Q.n_nonzero; }
  
  arma_inline elem_type operator[](const uword i)                    const { return Q[i];           }
  arma_inline elem_type at        (const uword row, const uword col) const { return Q.at(row, col); }
  
  arma_inline const eT*    get_values()      const { return Q.values;      }
  arma_inline const uword* get_row_indices() const { return Q.row_indices; }
  arma_inline const uword* get_col_ptrs()    const { return Q.col_ptrs;    }
  
  arma_inline const_iterator_type     begin()                            const { return Q.begin();            }
  arma_inline const_iterator_type     begin_col(const uword col_num)     const { return Q.begin_col(col_num); }
  arma_inline const_row_iterator_type begin_row(const uword row_num = 0) const { return Q.begin_row(row_num); }
  
  arma_inline const_iterator_type     end()                        const { return Q.end();            }
  arma_inline const_row_iterator_type end_row()                    const { return Q.end_row();        }
  arma_inline const_row_iterator_type end_row(const uword row_num) const { return Q.end_row(row_num); }
  
  template<typename eT2>
  constexpr bool is_alias(const SpMat<eT2>&) const { return false; }
  };



template<typename eT>
struct SpProxy< SpSubview_row<eT> >
  {
  typedef eT                                           elem_type;
  typedef typename get_pod_type<elem_type>::result     pod_type;
  typedef SpSubview_row<eT>                            stored_type;
  
  typedef typename SpSubview<eT>::const_iterator       const_iterator_type;
  typedef typename SpSubview<eT>::const_row_iterator   const_row_iterator_type;
  
  static constexpr bool use_iterator   = true;
  static constexpr bool Q_is_generated = false;
  
  static constexpr bool is_row  = true;
  static constexpr bool is_col  = false;
  static constexpr bool is_xvec = false;
  
  const SpSubview_row<eT>& Q;
  
  inline explicit SpProxy(const SpSubview_row<eT>& A)
    : Q(A)
    {
    arma_debug_sigprint();
    Q.m.sync();
    }
  
  constexpr   uword get_n_rows()    const { return 1;           }
  arma_inline uword get_n_cols()    const { return Q.n_cols;    }
  arma_inline uword get_n_elem()    const { return Q.n_elem;    }
  arma_inline uword get_n_nonzero() const { return Q.n_nonzero; }
  
  arma_inline elem_type operator[](const uword i)                const { return Q.at(0, i  ); }
  arma_inline elem_type at        (const uword, const uword col) const { return Q.at(0, col); }
  
  arma_inline const eT*    get_values()      const { return Q.m.values;      }
  arma_inline const uword* get_row_indices() const { return Q.m.row_indices; }
  arma_inline const uword* get_col_ptrs()    const { return Q.m.col_ptrs;    }
  
  arma_inline const_iterator_type     begin()                            const { return Q.begin();            }
  arma_inline const_iterator_type     begin_col(const uword col_num)     const { return Q.begin_col(col_num); }
  arma_inline const_row_iterator_type begin_row(const uword row_num = 0) const { return Q.begin_row(row_num); }
  
  arma_inline const_iterator_type     end()                        const { return Q.end();            }
  arma_inline const_row_iterator_type end_row()                    const { return Q.end_row();        }
  arma_inline const_row_iterator_type end_row(const uword row_num) const { return Q.end_row(row_num); }
  
  template<typename eT2>
  arma_inline bool is_alias(const SpMat<eT2>& X) const { return (is_same_type<eT,eT2>::yes) && (void_ptr(&Q.m) == void_ptr(&X)); }
  };



template<typename eT>
struct SpProxy< spdiagview<eT> >
  {
  typedef eT                                       elem_type;
  typedef typename get_pod_type<elem_type>::result pod_type;
  typedef SpMat<eT>                                stored_type;
  
  typedef typename SpMat<eT>::const_iterator       const_iterator_type;
  typedef typename SpMat<eT>::const_row_iterator   const_row_iterator_type;
  
  static constexpr bool use_iterator   = false;
  static constexpr bool Q_is_generated = true;
  
  static constexpr bool is_row  = false;
  static constexpr bool is_col  = true;
  static constexpr bool is_xvec = false;
  
  const SpMat<eT> Q;
  
  inline explicit SpProxy(const spdiagview<eT>& A)
    : Q(A)
    {
    arma_debug_sigprint();
    }
  
  arma_inline uword get_n_rows()    const { return Q.n_rows;    }
  constexpr   uword get_n_cols()    const { return 1;           }
  arma_inline uword get_n_elem()    const { return Q.n_elem;    }
  arma_inline uword get_n_nonzero() const { return Q.n_nonzero; }
  
  arma_inline elem_type operator[](const uword i)                    const { return Q[i];           }
  arma_inline elem_type at        (const uword row, const uword col) const { return Q.at(row, col); }
  
  arma_inline const eT*    get_values()      const { return Q.values;      }
  arma_inline const uword* get_row_indices() const { return Q.row_indices; }
  arma_inline const uword* get_col_ptrs()    const { return Q.col_ptrs;    }
  
  arma_inline const_iterator_type     begin()                            const { return Q.begin();            }
  arma_inline const_iterator_type     begin_col(const uword col_num)     const { return Q.begin_col(col_num); }
  arma_inline const_row_iterator_type begin_row(const uword row_num = 0) const { return Q.begin_row(row_num); }
  
  arma_inline const_iterator_type     end()                        const { return Q.end();            }
  arma_inline const_row_iterator_type end_row()                    const { return Q.end_row();        }
  arma_inline const_row_iterator_type end_row(const uword row_num) const { return Q.end_row(row_num); }
  
  template<typename eT2>
  constexpr bool is_alias(const SpMat<eT2>&) const { return false; }
  };



template<typename T1, typename spop_type>
struct SpProxy< SpOp<T1, spop_type> >
  {
  typedef typename T1::elem_type                   elem_type;
  typedef typename T1::elem_type                   eT;
  typedef typename get_pod_type<elem_type>::result pod_type;
  typedef SpMat<eT>                                stored_type;
  
  typedef typename SpMat<eT>::const_iterator       const_iterator_type;
  typedef typename SpMat<eT>::const_row_iterator   const_row_iterator_type;
  
  static constexpr bool use_iterator   = false;
  static constexpr bool Q_is_generated = true;
  
  static constexpr bool is_row  = SpOp<T1, spop_type>::is_row;
  static constexpr bool is_col  = SpOp<T1, spop_type>::is_col;
  static constexpr bool is_xvec = SpOp<T1, spop_type>::is_xvec;
  
  const SpMat<eT> Q;
  
  inline explicit SpProxy(const SpOp<T1, spop_type>& A)
    : Q(A)
    {
    arma_debug_sigprint();
    }
  
  arma_inline uword get_n_rows()    const { return is_row ? 1 : Q.n_rows; }
  arma_inline uword get_n_cols()    const { return is_col ? 1 : Q.n_cols; }
  arma_inline uword get_n_elem()    const { return Q.n_elem;              }
  arma_inline uword get_n_nonzero() const { return Q.n_nonzero;           }
  
  arma_inline elem_type operator[](const uword i)                    const { return Q[i];           }
  arma_inline elem_type at        (const uword row, const uword col) const { return Q.at(row, col); }
  
  arma_inline const eT*    get_values()      const { return Q.values;      }
  arma_inline const uword* get_row_indices() const { return Q.row_indices; }
  arma_inline const uword* get_col_ptrs()    const { return Q.col_ptrs;    }
  
  arma_inline const_iterator_type     begin()                            const { return Q.begin();            }
  arma_inline const_iterator_type     begin_col(const uword col_num)     const { return Q.begin_col(col_num); }
  arma_inline const_row_iterator_type begin_row(const uword row_num = 0) const { return Q.begin_row(row_num); }
  
  arma_inline const_iterator_type     end()                        const { return Q.end();            }
  arma_inline const_row_iterator_type end_row()                    const { return Q.end_row();        }
  arma_inline const_row_iterator_type end_row(const uword row_num) const { return Q.end_row(row_num); }
  
  template<typename eT2>
  constexpr bool is_alias(const SpMat<eT2>&) const { return false; }
  };



template<typename T1, typename T2, typename spglue_type>
struct SpProxy< SpGlue<T1, T2, spglue_type> >
  {
  typedef typename T1::elem_type                   elem_type;
  typedef typename T1::elem_type                   eT;
  typedef typename get_pod_type<elem_type>::result pod_type;
  typedef SpMat<eT>                                stored_type;
  
  typedef typename SpMat<eT>::const_iterator       const_iterator_type;
  typedef typename SpMat<eT>::const_row_iterator   const_row_iterator_type;
  
  static constexpr bool use_iterator   = false;
  static constexpr bool Q_is_generated = true;
  
  static constexpr bool is_row  = SpGlue<T1, T2, spglue_type>::is_row;
  static constexpr bool is_col  = SpGlue<T1, T2, spglue_type>::is_col;
  static constexpr bool is_xvec = SpGlue<T1, T2, spglue_type>::is_xvec;
  
  const SpMat<eT> Q;
  
  inline explicit SpProxy(const SpGlue<T1, T2, spglue_type>& A)
    : Q(A)
    {
    arma_debug_sigprint();
    }
  
  arma_inline uword get_n_rows()    const { return is_row ? 1 : Q.n_rows; }
  arma_inline uword get_n_cols()    const { return is_col ? 1 : Q.n_cols; }
  arma_inline uword get_n_elem()    const { return Q.n_elem;              }
  arma_inline uword get_n_nonzero() const { return Q.n_nonzero;           }
  
  arma_inline elem_type operator[](const uword i)                    const { return Q[i];           }
  arma_inline elem_type at        (const uword row, const uword col) const { return Q.at(row, col); }
  
  arma_inline const eT*    get_values()      const { return Q.values;      }
  arma_inline const uword* get_row_indices() const { return Q.row_indices; }
  arma_inline const uword* get_col_ptrs()    const { return Q.col_ptrs;    }
  
  arma_inline const_iterator_type     begin()                            const { return Q.begin();            }
  arma_inline const_iterator_type     begin_col(const uword col_num)     const { return Q.begin_col(col_num); }
  arma_inline const_row_iterator_type begin_row(const uword row_num = 0) const { return Q.begin_row(row_num); }
  
  arma_inline const_iterator_type     end()                        const { return Q.end();            }
  arma_inline const_row_iterator_type end_row()                    const { return Q.end_row();        }
  arma_inline const_row_iterator_type end_row(const uword row_num) const { return Q.end_row(row_num); }
  
  template<typename eT2>
  constexpr bool is_alias(const SpMat<eT2>&) const { return false; }
  };



template<typename out_eT, typename T1, typename spop_type>
struct SpProxy< mtSpOp<out_eT, T1, spop_type> >
  {
  typedef          out_eT                          elem_type;
  typedef typename get_pod_type<elem_type>::result pod_type;
  typedef SpMat<out_eT>                            stored_type;
  
  typedef typename SpMat<out_eT>::const_iterator       const_iterator_type;
  typedef typename SpMat<out_eT>::const_row_iterator   const_row_iterator_type;
  
  static constexpr bool use_iterator   = false;
  static constexpr bool Q_is_generated = true;
  
  static constexpr bool is_row  = mtSpOp<out_eT, T1, spop_type>::is_row;
  static constexpr bool is_col  = mtSpOp<out_eT, T1, spop_type>::is_col;
  static constexpr bool is_xvec = mtSpOp<out_eT, T1, spop_type>::is_xvec;
  
  const SpMat<out_eT> Q;
  
  inline explicit SpProxy(const mtSpOp<out_eT, T1, spop_type>& A)
    : Q(A)
    {
    arma_debug_sigprint();
    }
  
  arma_inline uword get_n_rows()    const { return is_row ? 1 : Q.n_rows; }
  arma_inline uword get_n_cols()    const { return is_col ? 1 : Q.n_cols; }
  arma_inline uword get_n_elem()    const { return Q.n_elem;              }
  arma_inline uword get_n_nonzero() const { return Q.n_nonzero;           }
  
  arma_inline elem_type operator[](const uword i)                    const { return Q[i];           }
  arma_inline elem_type at        (const uword row, const uword col) const { return Q.at(row, col); }
  
  arma_inline const out_eT* get_values()      const { return Q.values;      }
  arma_inline const uword*  get_row_indices() const { return Q.row_indices; }
  arma_inline const uword*  get_col_ptrs()    const { return Q.col_ptrs;    }
  
  arma_inline const_iterator_type     begin()                            const { return Q.begin();            }
  arma_inline const_iterator_type     begin_col(const uword col_num)     const { return Q.begin_col(col_num); }
  arma_inline const_row_iterator_type begin_row(const uword row_num = 0) const { return Q.begin_row(row_num); }
  
  arma_inline const_iterator_type     end()                        const { return Q.end();            }
  arma_inline const_row_iterator_type end_row()                    const { return Q.end_row();        }
  arma_inline const_row_iterator_type end_row(const uword row_num) const { return Q.end_row(row_num); }
  
  template<typename eT2>
  constexpr bool is_alias(const SpMat<eT2>&) const { return false; }
  };



template<typename out_eT, typename T1, typename T2, typename spglue_type>
struct SpProxy< mtSpGlue<out_eT, T1, T2, spglue_type> >
  {
  typedef          out_eT                          elem_type;
  typedef typename get_pod_type<elem_type>::result pod_type;
  typedef SpMat<out_eT>                            stored_type;
  
  typedef typename SpMat<out_eT>::const_iterator       const_iterator_type;
  typedef typename SpMat<out_eT>::const_row_iterator   const_row_iterator_type;
  
  static constexpr bool use_iterator   = false;
  static constexpr bool Q_is_generated = true;
  
  static constexpr bool is_row  = mtSpGlue<out_eT, T1, T2, spglue_type>::is_row;
  static constexpr bool is_col  = mtSpGlue<out_eT, T1, T2, spglue_type>::is_col;
  static constexpr bool is_xvec = mtSpGlue<out_eT, T1, T2, spglue_type>::is_xvec;
  
  const SpMat<out_eT> Q;
  
  inline explicit SpProxy(const mtSpGlue<out_eT, T1, T2, spglue_type>& A)
    : Q(A)
    {
    arma_debug_sigprint();
    }
  
  arma_inline uword get_n_rows()    const { return is_row ? 1 : Q.n_rows; }
  arma_inline uword get_n_cols()    const { return is_col ? 1 : Q.n_cols; }
  arma_inline uword get_n_elem()    const { return Q.n_elem;              }
  arma_inline uword get_n_nonzero() const { return Q.n_nonzero;           }
  
  arma_inline elem_type operator[](const uword i)                    const { return Q[i];           }
  arma_inline elem_type at        (const uword row, const uword col) const { return Q.at(row, col); }
  
  arma_inline const out_eT* get_values()      const { return Q.values;      }
  arma_inline const uword*  get_row_indices() const { return Q.row_indices; }
  arma_inline const uword*  get_col_ptrs()    const { return Q.col_ptrs;    }
  
  arma_inline const_iterator_type     begin()                            const { return Q.begin();            }
  arma_inline const_iterator_type     begin_col(const uword col_num)     const { return Q.begin_col(col_num); }
  arma_inline const_row_iterator_type begin_row(const uword row_num = 0) const { return Q.begin_row(row_num); }
  
  arma_inline const_iterator_type     end()                        const { return Q.end();            }
  arma_inline const_row_iterator_type end_row()                    const { return Q.end_row();        }
  arma_inline const_row_iterator_type end_row(const uword row_num) const { return Q.end_row(row_num); }
  
  template<typename eT2>
  constexpr bool is_alias(const SpMat<eT2>&) const { return false; }
  };



template<typename out_eT, typename T1, typename op_type>
struct SpProxy< mtSpReduceOp<out_eT, T1, op_type> >
  {
  typedef          out_eT                          elem_type;
  typedef typename get_pod_type<elem_type>::result pod_type;
  typedef SpMat<out_eT>                            stored_type;
  
  typedef typename SpMat<out_eT>::const_iterator       const_iterator_type;
  typedef typename SpMat<out_eT>::const_row_iterator   const_row_iterator_type;
  
  static constexpr bool use_iterator   = false;
  static constexpr bool Q_is_generated = true;
  
  static constexpr bool is_row  = mtSpReduceOp<out_eT, T1, op_type>::is_row;
  static constexpr bool is_col  = mtSpReduceOp<out_eT, T1, op_type>::is_col;
  static constexpr bool is_xvec = mtSpReduceOp<out_eT, T1, op_type>::is_xvec;
  
  const SpMat<out_eT> Q;
  
  inline explicit SpProxy(const mtSpReduceOp<out_eT, T1, op_type>& A)
    : Q(A)
    {
    arma_debug_sigprint();
    }
  
  arma_inline uword get_n_rows()    const { return is_row ? 1 : Q.n_rows; }
  arma_inline uword get_n_cols()    const { return is_col ? 1 : Q.n_cols; }
  arma_inline uword get_n_elem()    const { return Q.n_elem;              }
  arma_inline uword get_n_nonzero() const { return Q.n_nonzero;           }
  
  arma_inline elem_type operator[](const uword i)                    const { return Q[i];           }
  arma_inline elem_type at        (const uword row, const uword col) const { return Q.at(row, col); }
  
  arma_inline const out_eT* get_values()      const { return Q.values;      }
  arma_inline const uword*  get_row_indices() const { return Q.row_indices; }
  arma_inline const uword*  get_col_ptrs()    const { return Q.col_ptrs;    }
  
  arma_inline const_iterator_type     begin()                            const { return Q.begin();            }
  arma_inline const_iterator_type     begin_col(const uword col_num)     const { return Q.begin_col(col_num); }
  arma_inline const_row_iterator_type begin_row(const uword row_num = 0) const { return Q.begin_row(row_num); }
  
  arma_inline const_iterator_type     end()                        const { return Q.end();            }
  arma_inline const_row_iterator_type end_row()                    const { return Q.end_row();        }
  arma_inline const_row_iterator_type end_row(const uword row_num) const { return Q.end_row(row_num); }
  
  template<typename eT2>
  constexpr bool is_alias(const SpMat<eT2>&) const { return false; }
  };



//! @}