Mat_bones.hpp

// 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 Mat
//! @{



//! Dense matrix class

template<typename eT>
class Mat : public Base< eT, Mat<eT> >
  {
  public:
  
  typedef eT                                elem_type;  //!< the type of elements stored in the matrix
  typedef typename get_pod_type<eT>::result  pod_type;  //!< if eT is std::complex<T>, pod_type is T; otherwise pod_type is eT
  
  const uword  n_rows;    //!< number of rows               (read-only)
  const uword  n_cols;    //!< number of columns            (read-only)
  const uword  n_elem;    //!< number of elements           (read-only)
  const uword  n_alloc;   //!< number of allocated elements (read-only); NOTE: n_alloc can be 0, even if n_elem > 0
  const uhword vec_state; //!< 0: matrix layout; 1: column vector layout; 2: row vector layout
  const uhword mem_state;
  
  // mem_state = 0: normal matrix which manages its own memory
  // mem_state = 1: use auxiliary memory until a size change
  // mem_state = 2: use auxiliary memory and don't allow the number of elements to be changed
  // mem_state = 3: fixed size (eg. via template based size specification)
  
  arma_aligned const eT* const mem;  //!< pointer to the memory used for storing elements (memory is read-only)
  
  
  protected:
  
  arma_align_mem eT mem_local[ arma_config::mat_prealloc ];  // local storage, for small vectors and matrices
  
  
  public:
  
  static constexpr bool is_col  = false;
  static constexpr bool is_row  = false;
  static constexpr bool is_xvec = false;
  
  static constexpr bool has_subview = false;
  
  inline ~Mat();
  inline  Mat();
  
  inline explicit Mat(const uword in_n_rows, const uword in_n_cols);
  inline explicit Mat(const SizeMat& s);
  
  template<bool do_zeros> inline explicit Mat(const uword in_n_rows, const uword in_n_cols, const arma_initmode_indicator<do_zeros>&);
  template<bool do_zeros> inline explicit Mat(const SizeMat& s,                             const arma_initmode_indicator<do_zeros>&);
  
  template<typename fill_type> inline Mat(const uword in_n_rows, const uword in_n_cols, const fill::fill_class<fill_type>& f);
  template<typename fill_type> inline Mat(const SizeMat& s,                             const fill::fill_class<fill_type>& f);
  
  inline Mat(const uword in_n_rows, const uword in_n_cols, const fill::scalar_holder<eT> f);
  inline Mat(const SizeMat& s,                             const fill::scalar_holder<eT> f);
  
  arma_cold inline            Mat(const char*        text);
  arma_cold inline Mat& operator=(const char*        text);
  
  arma_cold inline            Mat(const std::string& text);
  arma_cold inline Mat& operator=(const std::string& text);
  
  inline            Mat(const std::vector<eT>& x);
  inline Mat& operator=(const std::vector<eT>& x);
  
  inline            Mat(const std::initializer_list<eT>& list);
  inline Mat& operator=(const std::initializer_list<eT>& list);
  
  inline            Mat(const std::initializer_list< std::initializer_list<eT> >& list);
  inline Mat& operator=(const std::initializer_list< std::initializer_list<eT> >& list);
  
  inline            Mat(Mat&& m);
  inline Mat& operator=(Mat&& m);
  
  inline Mat(      eT* aux_mem, const uword aux_n_rows, const uword aux_n_cols, const bool copy_aux_mem = true, const bool strict = false);
  inline Mat(const eT* aux_mem, const uword aux_n_rows, const uword aux_n_cols);
  
  inline Mat& operator= (const eT val);
  inline Mat& operator+=(const eT val);
  inline Mat& operator-=(const eT val);
  inline Mat& operator*=(const eT val);
  inline Mat& operator/=(const eT val);
  
  inline             Mat(const Mat& m, const arma_vec_indicator&, const uhword in_vec_state);
  inline             Mat(const Mat& m);
  inline Mat& operator= (const Mat& m);
  inline Mat& operator+=(const Mat& m);
  inline Mat& operator-=(const Mat& m);
  inline Mat& operator*=(const Mat& m);
  inline Mat& operator%=(const Mat& m);
  inline Mat& operator/=(const Mat& m);
  
  template<typename T1> inline             Mat(const BaseCube<eT,T1>& X, const arma_vec_indicator&, const uhword in_vec_state);
  template<typename T1> inline             Mat(const BaseCube<eT,T1>& X);
  template<typename T1> inline Mat& operator= (const BaseCube<eT,T1>& X);
  template<typename T1> inline Mat& operator+=(const BaseCube<eT,T1>& X);
  template<typename T1> inline Mat& operator-=(const BaseCube<eT,T1>& X);
  template<typename T1> inline Mat& operator*=(const BaseCube<eT,T1>& X);
  template<typename T1> inline Mat& operator%=(const BaseCube<eT,T1>& X);
  template<typename T1> inline Mat& operator/=(const BaseCube<eT,T1>& X);
  
  template<typename T1, typename T2> inline explicit Mat(const Base<pod_type,T1>& A, const Base<pod_type,T2>& B, const arma_vec_indicator&, const uhword in_vec_state);
  template<typename T1, typename T2> inline explicit Mat(const Base<pod_type,T1>& A, const Base<pod_type,T2>& B);
  
  inline explicit    Mat(const subview<eT>& X, const bool reuse_mem);  // only to be used by quasi_unwrap and partial_unwrap
  
  inline             Mat(const subview<eT>& X, const arma_vec_indicator&, const uhword in_vec_state);
  inline             Mat(const subview<eT>& X);
  inline Mat& operator= (const subview<eT>& X);
  inline Mat& operator+=(const subview<eT>& X);
  inline Mat& operator-=(const subview<eT>& X);
  inline Mat& operator*=(const subview<eT>& X);
  inline Mat& operator%=(const subview<eT>& X);
  inline Mat& operator/=(const subview<eT>& X);
  
  inline Mat(const subview_row_strans<eT>& X);  // subview_row_strans can only be generated by the Proxy class
  inline Mat(const subview_row_htrans<eT>& X);  // subview_row_htrans can only be generated by the Proxy class
  inline Mat(const        xvec_htrans<eT>& X);  //        xvec_htrans can only be generated by the Proxy class
  
  template<bool do_conj>
  inline Mat(const xtrans_mat<eT,do_conj>& X);  //        xtrans_mat can only be generated by the Proxy class
  
  inline             Mat(const subview_cube<eT>& X, const arma_vec_indicator&, const uhword in_vec_state);
  inline             Mat(const subview_cube<eT>& X);
  inline Mat& operator= (const subview_cube<eT>& X);
  inline Mat& operator+=(const subview_cube<eT>& X);
  inline Mat& operator-=(const subview_cube<eT>& X);
  inline Mat& operator*=(const subview_cube<eT>& X);
  inline Mat& operator%=(const subview_cube<eT>& X);
  inline Mat& operator/=(const subview_cube<eT>& X);
  
  inline             Mat(const diagview<eT>& X, const arma_vec_indicator&, const uhword in_vec_state);
  inline             Mat(const diagview<eT>& X);
  inline Mat& operator= (const diagview<eT>& X);
  inline Mat& operator+=(const diagview<eT>& X);
  inline Mat& operator-=(const diagview<eT>& X);
  inline Mat& operator*=(const diagview<eT>& X);
  inline Mat& operator%=(const diagview<eT>& X);
  inline Mat& operator/=(const diagview<eT>& X);
  
  template<typename T1> inline             Mat(const subview_elem1<eT,T1>& X, const arma_vec_indicator&, const uhword in_vec_state);
  template<typename T1> inline             Mat(const subview_elem1<eT,T1>& X);
  template<typename T1> inline Mat& operator= (const subview_elem1<eT,T1>& X);
  template<typename T1> inline Mat& operator+=(const subview_elem1<eT,T1>& X);
  template<typename T1> inline Mat& operator-=(const subview_elem1<eT,T1>& X);
  template<typename T1> inline Mat& operator*=(const subview_elem1<eT,T1>& X);
  template<typename T1> inline Mat& operator%=(const subview_elem1<eT,T1>& X);
  template<typename T1> inline Mat& operator/=(const subview_elem1<eT,T1>& X);
  
  template<typename T1, typename T2> inline             Mat(const subview_elem2<eT,T1,T2>& X, const arma_vec_indicator&, const uhword in_vec_state);
  template<typename T1, typename T2> inline             Mat(const subview_elem2<eT,T1,T2>& X);
  template<typename T1, typename T2> inline Mat& operator= (const subview_elem2<eT,T1,T2>& X);
  template<typename T1, typename T2> inline Mat& operator+=(const subview_elem2<eT,T1,T2>& X);
  template<typename T1, typename T2> inline Mat& operator-=(const subview_elem2<eT,T1,T2>& X);
  template<typename T1, typename T2> inline Mat& operator*=(const subview_elem2<eT,T1,T2>& X);
  template<typename T1, typename T2> inline Mat& operator%=(const subview_elem2<eT,T1,T2>& X);
  template<typename T1, typename T2> inline Mat& operator/=(const subview_elem2<eT,T1,T2>& X);

  // Operators on sparse matrices (and subviews)
  template<typename T1> inline explicit    Mat(const SpBase<eT, T1>& m, const arma_vec_indicator&, const uhword in_vec_state);
  template<typename T1> inline explicit    Mat(const SpBase<eT, T1>& m);
  template<typename T1> inline Mat& operator= (const SpBase<eT, T1>& m);
  template<typename T1> inline Mat& operator+=(const SpBase<eT, T1>& m);
  template<typename T1> inline Mat& operator-=(const SpBase<eT, T1>& m);
  template<typename T1> inline Mat& operator*=(const SpBase<eT, T1>& m);
  template<typename T1> inline Mat& operator%=(const SpBase<eT, T1>& m);
  template<typename T1> inline Mat& operator/=(const SpBase<eT, T1>& m);
  
  inline explicit    Mat(const SpSubview<eT>& X, const arma_vec_indicator&, const uhword in_vec_state);
  inline explicit    Mat(const SpSubview<eT>& X);
  inline Mat& operator= (const SpSubview<eT>& X);
  inline Mat& operator+=(const SpSubview<eT>& X);
  inline Mat& operator-=(const SpSubview<eT>& X);
  
  inline explicit    Mat(const spdiagview<eT>& X, const arma_vec_indicator&, const uhword in_vec_state);
  inline explicit    Mat(const spdiagview<eT>& X);
  inline Mat& operator= (const spdiagview<eT>& X);
  inline Mat& operator+=(const spdiagview<eT>& X);
  inline Mat& operator-=(const spdiagview<eT>& X);
  inline Mat& operator*=(const spdiagview<eT>& X);
  inline Mat& operator%=(const spdiagview<eT>& X);
  inline Mat& operator/=(const spdiagview<eT>& X);
  
  
  [[deprecated("use braced initialiser list instead")]] inline mat_injector<Mat> operator<<(const eT val);
  [[deprecated("use braced initialiser list instead")]] inline mat_injector<Mat> operator<<(const injector_end_of_row<>& x);
  
  
  arma_inline       subview_row<eT> row(const uword row_num);
  arma_inline const subview_row<eT> row(const uword row_num) const;
  
  inline            subview_row<eT> operator()(const uword row_num, const span& col_span);
  inline      const subview_row<eT> operator()(const uword row_num, const span& col_span) const;
  
  
  arma_inline       subview_col<eT> col(const uword col_num);
  arma_inline const subview_col<eT> col(const uword col_num) const;
  
  inline            subview_col<eT> operator()(const span& row_span, const uword col_num);
  inline      const subview_col<eT> operator()(const span& row_span, const uword col_num) const;
  
  inline            Col<eT>  unsafe_col(const uword col_num);
  inline      const Col<eT>  unsafe_col(const uword col_num) const;
  
  
  arma_inline       subview<eT>      rows(const uword in_row1, const uword in_row2);
  arma_inline const subview<eT>      rows(const uword in_row1, const uword in_row2) const;
  
  arma_inline       subview_cols<eT> cols(const uword in_col1, const uword in_col2);
  arma_inline const subview_cols<eT> cols(const uword in_col1, const uword in_col2) const;
  
  inline            subview<eT>      rows(const span& row_span);
  inline      const subview<eT>      rows(const span& row_span) const;
  
  arma_inline       subview_cols<eT> cols(const span& col_span);
  arma_inline const subview_cols<eT> cols(const span& col_span) const;
  
  
  arma_inline       subview<eT> submat(const uword in_row1, const uword in_col1, const uword in_row2, const uword in_col2);
  arma_inline const subview<eT> submat(const uword in_row1, const uword in_col1, const uword in_row2, const uword in_col2) const;
  
  arma_inline       subview<eT> submat(const uword in_row1, const uword in_col1, const SizeMat& s);
  arma_inline const subview<eT> submat(const uword in_row1, const uword in_col1, const SizeMat& s) const;
  
  inline            subview<eT> submat    (const span& row_span, const span& col_span);
  inline      const subview<eT> submat    (const span& row_span, const span& col_span) const;
  
  inline            subview<eT> operator()(const span& row_span, const span& col_span);
  inline      const subview<eT> operator()(const span& row_span, const span& col_span) const;
  
  inline            subview<eT> operator()(const uword in_row1, const uword in_col1, const SizeMat& s);
  inline      const subview<eT> operator()(const uword in_row1, const uword in_col1, const SizeMat& s) const;
  
  inline       subview<eT> head_rows(const uword N);
  inline const subview<eT> head_rows(const uword N) const;
  
  inline       subview<eT> tail_rows(const uword N);
  inline const subview<eT> tail_rows(const uword N) const;
  
  inline       subview_cols<eT> head_cols(const uword N);
  inline const subview_cols<eT> head_cols(const uword N) const;
  
  inline       subview_cols<eT> tail_cols(const uword N);
  inline const subview_cols<eT> tail_cols(const uword N) const;
  
  template<typename T1> arma_inline       subview_elem1<eT,T1> elem(const Base<uword,T1>& a);
  template<typename T1> arma_inline const subview_elem1<eT,T1> elem(const Base<uword,T1>& a) const;
  
  template<typename T1> arma_inline       subview_elem1<eT,T1> operator()(const Base<uword,T1>& a);
  template<typename T1> arma_inline const subview_elem1<eT,T1> operator()(const Base<uword,T1>& a) const;
  
  
  template<typename T1, typename T2> arma_inline       subview_elem2<eT,T1,T2> elem(const Base<uword,T1>& ri, const Base<uword,T2>& ci);
  template<typename T1, typename T2> arma_inline const subview_elem2<eT,T1,T2> elem(const Base<uword,T1>& ri, const Base<uword,T2>& ci) const;
  
  template<typename T1, typename T2> arma_inline       subview_elem2<eT,T1,T2> submat(const Base<uword,T1>& ri, const Base<uword,T2>& ci);
  template<typename T1, typename T2> arma_inline const subview_elem2<eT,T1,T2> submat(const Base<uword,T1>& ri, const Base<uword,T2>& ci) const;
  
  template<typename T1, typename T2> arma_inline       subview_elem2<eT,T1,T2> operator()(const Base<uword,T1>& ri, const Base<uword,T2>& ci);
  template<typename T1, typename T2> arma_inline const subview_elem2<eT,T1,T2> operator()(const Base<uword,T1>& ri, const Base<uword,T2>& ci) const;
  
  
  template<typename T1> arma_inline       subview_elem2<eT,T1,T1> rows(const Base<uword,T1>& ri);
  template<typename T1> arma_inline const subview_elem2<eT,T1,T1> rows(const Base<uword,T1>& ri) const;
  
  template<typename T2> arma_inline       subview_elem2<eT,T2,T2> cols(const Base<uword,T2>& ci);
  template<typename T2> arma_inline const subview_elem2<eT,T2,T2> cols(const Base<uword,T2>& ci) const;
  
  
  arma_inline       subview_each1< Mat<eT>, 0 > each_col();
  arma_inline       subview_each1< Mat<eT>, 1 > each_row();
  
  arma_inline const subview_each1< Mat<eT>, 0 > each_col() const;
  arma_inline const subview_each1< Mat<eT>, 1 > each_row() const;
  
  template<typename T1> inline       subview_each2< Mat<eT>, 0, T1 > each_col(const Base<uword, T1>& indices);
  template<typename T1> inline       subview_each2< Mat<eT>, 1, T1 > each_row(const Base<uword, T1>& indices);
  
  template<typename T1> inline const subview_each2< Mat<eT>, 0, T1 > each_col(const Base<uword, T1>& indices) const;
  template<typename T1> inline const subview_each2< Mat<eT>, 1, T1 > each_row(const Base<uword, T1>& indices) const;
  
  inline       Mat& each_col(const std::function< void(      Col<eT>&) >& F);
  inline const Mat& each_col(const std::function< void(const Col<eT>&) >& F) const;
  
  inline       Mat& each_row(const std::function< void(      Row<eT>&) >& F);
  inline const Mat& each_row(const std::function< void(const Row<eT>&) >& F) const;
  
  
  arma_inline       diagview<eT> diag(const sword in_id = 0);
  arma_inline const diagview<eT> diag(const sword in_id = 0) const;
  
  
  inline void swap_rows(const uword in_row1, const uword in_row2);
  inline void swap_cols(const uword in_col1, const uword in_col2);
  
  inline void shed_row(const uword row_num);
  inline void shed_col(const uword col_num);
  
  inline void shed_rows(const uword in_row1, const uword in_row2);
  inline void shed_cols(const uword in_col1, const uword in_col2);
  
  template<typename T1> inline void shed_rows(const Base<uword, T1>& indices);
  template<typename T1> inline void shed_cols(const Base<uword, T1>& indices);
  
  [[deprecated("use insert_rows(row_num, N) instead")]] inline void insert_rows(const uword row_num, const uword N, const bool set_to_zero);
  [[deprecated("use insert_cols(col_num, N) instead")]] inline void insert_cols(const uword col_num, const uword N, const bool set_to_zero);
  
  inline void insert_rows(const uword row_num, const uword N);
  inline void insert_cols(const uword col_num, const uword N);
  
  template<typename T1> inline void insert_rows(const uword row_num, const Base<eT,T1>& X);
  template<typename T1> inline void insert_cols(const uword col_num, const Base<eT,T1>& X);
  
  
  template<typename T1, typename gen_type> inline             Mat(const Gen<T1, gen_type>& X, const arma_vec_indicator&, const uhword in_vec_state);
  template<typename T1, typename gen_type> inline             Mat(const Gen<T1, gen_type>& X);
  template<typename T1, typename gen_type> inline Mat& operator= (const Gen<T1, gen_type>& X);
  template<typename T1, typename gen_type> inline Mat& operator+=(const Gen<T1, gen_type>& X);
  template<typename T1, typename gen_type> inline Mat& operator-=(const Gen<T1, gen_type>& X);
  template<typename T1, typename gen_type> inline Mat& operator*=(const Gen<T1, gen_type>& X);
  template<typename T1, typename gen_type> inline Mat& operator%=(const Gen<T1, gen_type>& X);
  template<typename T1, typename gen_type> inline Mat& operator/=(const Gen<T1, gen_type>& X);
  
  template<typename T1, typename op_type> inline             Mat(const Op<T1, op_type>& X, const arma_vec_indicator&, const uhword in_vec_state);
  template<typename T1, typename op_type> inline             Mat(const Op<T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator= (const Op<T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator+=(const Op<T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator-=(const Op<T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator*=(const Op<T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator%=(const Op<T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator/=(const Op<T1, op_type>& X);
  
  template<typename T1, typename eop_type> inline             Mat(const eOp<T1, eop_type>& X, const arma_vec_indicator&, const uhword in_vec_state);
  template<typename T1, typename eop_type> inline             Mat(const eOp<T1, eop_type>& X);
  template<typename T1, typename eop_type> inline Mat& operator= (const eOp<T1, eop_type>& X);
  template<typename T1, typename eop_type> inline Mat& operator+=(const eOp<T1, eop_type>& X);
  template<typename T1, typename eop_type> inline Mat& operator-=(const eOp<T1, eop_type>& X);
  template<typename T1, typename eop_type> inline Mat& operator*=(const eOp<T1, eop_type>& X);
  template<typename T1, typename eop_type> inline Mat& operator%=(const eOp<T1, eop_type>& X);
  template<typename T1, typename eop_type> inline Mat& operator/=(const eOp<T1, eop_type>& X);
  
  template<typename T1, typename op_type> inline             Mat(const mtOp<eT, T1, op_type>& X, const arma_vec_indicator&, const uhword in_vec_state);
  template<typename T1, typename op_type> inline             Mat(const mtOp<eT, T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator= (const mtOp<eT, T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator+=(const mtOp<eT, T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator-=(const mtOp<eT, T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator*=(const mtOp<eT, T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator%=(const mtOp<eT, T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator/=(const mtOp<eT, T1, op_type>& X);

  template<typename T1, typename op_type> inline             Mat(const CubeToMatOp<T1, op_type>& X, const arma_vec_indicator&, const uhword in_vec_state);
  template<typename T1, typename op_type> inline             Mat(const CubeToMatOp<T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator= (const CubeToMatOp<T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator+=(const CubeToMatOp<T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator-=(const CubeToMatOp<T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator*=(const CubeToMatOp<T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator%=(const CubeToMatOp<T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator/=(const CubeToMatOp<T1, op_type>& X);
  
  template<typename T1, typename op_type> inline             Mat(const SpToDOp<T1, op_type>& X, const arma_vec_indicator&, const uhword in_vec_state);
  template<typename T1, typename op_type> inline             Mat(const SpToDOp<T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator= (const SpToDOp<T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator+=(const SpToDOp<T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator-=(const SpToDOp<T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator*=(const SpToDOp<T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator%=(const SpToDOp<T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator/=(const SpToDOp<T1, op_type>& X);
  
  template<typename T1, typename op_type> inline explicit    Mat(const mtSpReduceOp<eT, T1, op_type>& X, const arma_vec_indicator&, const uhword in_vec_state);
  template<typename T1, typename op_type> inline explicit    Mat(const mtSpReduceOp<eT, T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator= (const mtSpReduceOp<eT, T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator+=(const mtSpReduceOp<eT, T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator-=(const mtSpReduceOp<eT, T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator*=(const mtSpReduceOp<eT, T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator%=(const mtSpReduceOp<eT, T1, op_type>& X);
  template<typename T1, typename op_type> inline Mat& operator/=(const mtSpReduceOp<eT, T1, op_type>& X);
  
  template<typename T1, typename T2, typename glue_type> inline             Mat(const Glue<T1, T2, glue_type>& X, const arma_vec_indicator&, const uhword in_vec_state);
  template<typename T1, typename T2, typename glue_type> inline             Mat(const Glue<T1, T2, glue_type>& X);
  template<typename T1, typename T2, typename glue_type> inline Mat& operator= (const Glue<T1, T2, glue_type>& X);
  template<typename T1, typename T2, typename glue_type> inline Mat& operator+=(const Glue<T1, T2, glue_type>& X);
  template<typename T1, typename T2, typename glue_type> inline Mat& operator-=(const Glue<T1, T2, glue_type>& X);
  template<typename T1, typename T2, typename glue_type> inline Mat& operator*=(const Glue<T1, T2, glue_type>& X);
  template<typename T1, typename T2, typename glue_type> inline Mat& operator%=(const Glue<T1, T2, glue_type>& X);
  template<typename T1, typename T2, typename glue_type> inline Mat& operator/=(const Glue<T1, T2, glue_type>& X);
  
  template<typename T1, typename T2>                     inline Mat& operator+=(const Glue<T1, T2, glue_times>& X);
  template<typename T1, typename T2>                     inline Mat& operator-=(const Glue<T1, T2, glue_times>& X);
  
  template<typename T1, typename T2, typename eglue_type> inline             Mat(const eGlue<T1, T2, eglue_type>& X, const arma_vec_indicator&, const uhword in_vec_state);
  template<typename T1, typename T2, typename eglue_type> inline             Mat(const eGlue<T1, T2, eglue_type>& X);
  template<typename T1, typename T2, typename eglue_type> inline Mat& operator= (const eGlue<T1, T2, eglue_type>& X);
  template<typename T1, typename T2, typename eglue_type> inline Mat& operator+=(const eGlue<T1, T2, eglue_type>& X);
  template<typename T1, typename T2, typename eglue_type> inline Mat& operator-=(const eGlue<T1, T2, eglue_type>& X);
  template<typename T1, typename T2, typename eglue_type> inline Mat& operator*=(const eGlue<T1, T2, eglue_type>& X);
  template<typename T1, typename T2, typename eglue_type> inline Mat& operator%=(const eGlue<T1, T2, eglue_type>& X);
  template<typename T1, typename T2, typename eglue_type> inline Mat& operator/=(const eGlue<T1, T2, eglue_type>& X);
  
  template<typename T1, typename T2, typename glue_type> inline             Mat(const mtGlue<eT, T1, T2, glue_type>& X, const arma_vec_indicator&, const uhword in_vec_state);
  template<typename T1, typename T2, typename glue_type> inline             Mat(const mtGlue<eT, T1, T2, glue_type>& X);
  template<typename T1, typename T2, typename glue_type> inline Mat& operator= (const mtGlue<eT, T1, T2, glue_type>& X);
  template<typename T1, typename T2, typename glue_type> inline Mat& operator+=(const mtGlue<eT, T1, T2, glue_type>& X);
  template<typename T1, typename T2, typename glue_type> inline Mat& operator-=(const mtGlue<eT, T1, T2, glue_type>& X);
  template<typename T1, typename T2, typename glue_type> inline Mat& operator*=(const mtGlue<eT, T1, T2, glue_type>& X);
  template<typename T1, typename T2, typename glue_type> inline Mat& operator%=(const mtGlue<eT, T1, T2, glue_type>& X);
  template<typename T1, typename T2, typename glue_type> inline Mat& operator/=(const mtGlue<eT, T1, T2, glue_type>& X);
  
  template<typename T1, typename T2, typename glue_type> inline             Mat(const SpToDGlue<T1, T2, glue_type>& X, const arma_vec_indicator&, const uhword in_vec_state);
  template<typename T1, typename T2, typename glue_type> inline             Mat(const SpToDGlue<T1, T2, glue_type>& X);
  template<typename T1, typename T2, typename glue_type> inline Mat& operator= (const SpToDGlue<T1, T2, glue_type>& X);
  template<typename T1, typename T2, typename glue_type> inline Mat& operator+=(const SpToDGlue<T1, T2, glue_type>& X);
  template<typename T1, typename T2, typename glue_type> inline Mat& operator-=(const SpToDGlue<T1, T2, glue_type>& X);
  template<typename T1, typename T2, typename glue_type> inline Mat& operator*=(const SpToDGlue<T1, T2, glue_type>& X);
  template<typename T1, typename T2, typename glue_type> inline Mat& operator%=(const SpToDGlue<T1, T2, glue_type>& X);
  template<typename T1, typename T2, typename glue_type> inline Mat& operator/=(const SpToDGlue<T1, T2, glue_type>& X);
  
  
  arma_warn_unused arma_inline const eT& at_alt     (const uword ii) const;
  
  arma_warn_unused arma_inline       eT& operator[] (const uword ii);
  arma_warn_unused arma_inline const eT& operator[] (const uword ii) const;
  arma_warn_unused arma_inline       eT& at         (const uword ii);
  arma_warn_unused arma_inline const eT& at         (const uword ii) const;
  arma_warn_unused arma_inline       eT& operator() (const uword ii);
  arma_warn_unused arma_inline const eT& operator() (const uword ii) const;
  
  #if defined(__cpp_multidimensional_subscript)
  arma_warn_unused arma_inline       eT& operator[] (const uword in_row, const uword in_col);
  arma_warn_unused arma_inline const eT& operator[] (const uword in_row, const uword in_col) const;
  #endif
  
  arma_warn_unused arma_inline       eT& at         (const uword in_row, const uword in_col);
  arma_warn_unused arma_inline const eT& at         (const uword in_row, const uword in_col) const;
  arma_warn_unused arma_inline       eT& operator() (const uword in_row, const uword in_col);
  arma_warn_unused arma_inline const eT& operator() (const uword in_row, const uword in_col) const;
  
  inline void push_back(const eT val);
  
  arma_inline const Mat& operator++();
  arma_inline void       operator++(int);
  
  arma_inline const Mat& operator--();
  arma_inline void       operator--(int);
  
  arma_warn_unused arma_inline bool is_empty()  const;
  arma_warn_unused arma_inline bool is_vec()    const;
  arma_warn_unused arma_inline bool is_rowvec() const;
  arma_warn_unused arma_inline bool is_colvec() const;
  arma_warn_unused arma_inline bool is_square() const;
  
  arma_warn_unused inline bool internal_is_finite()     const;
  arma_warn_unused inline bool internal_has_inf()       const;
  arma_warn_unused inline bool internal_has_nan()       const;
  arma_warn_unused inline bool internal_has_nonfinite() const;
  
  arma_warn_unused inline bool is_sorted(const char* direction = "ascend")       const;
  arma_warn_unused inline bool is_sorted(const char* direction, const uword dim) const;
  
  template<typename comparator>
  arma_warn_unused inline bool is_sorted_helper(const comparator& comp, const uword dim) const;
  
  arma_warn_unused arma_inline bool in_range(const uword ii) const;
  arma_warn_unused arma_inline bool in_range(const span& x ) const;
  
  arma_warn_unused arma_inline bool in_range(const uword   in_row, const uword   in_col) const;
  arma_warn_unused arma_inline bool in_range(const span& row_span, const uword   in_col) const;
  arma_warn_unused arma_inline bool in_range(const uword   in_row, const span& col_span) const;
  arma_warn_unused arma_inline bool in_range(const span& row_span, const span& col_span) const;
  
  arma_warn_unused arma_inline bool in_range(const uword in_row, const uword in_col, const SizeMat& s) const;
  
  arma_warn_unused arma_inline       eT* colptr(const uword in_col);
  arma_warn_unused arma_inline const eT* colptr(const uword in_col) const;
  
  arma_warn_unused arma_inline       eT* memptr();
  arma_warn_unused arma_inline const eT* memptr() const;
  
  
  template<typename eT2, typename expr>
  inline Mat& copy_size(const Base<eT2,expr>& X);
  
  inline Mat& set_size(const uword new_n_elem);
  inline Mat& set_size(const uword new_n_rows, const uword new_n_cols);
  inline Mat& set_size(const SizeMat& s);
  
  inline Mat&   resize(const uword new_n_elem);
  inline Mat&   resize(const uword new_n_rows, const uword new_n_cols);
  inline Mat&   resize(const SizeMat& s);
  
  inline Mat&  reshape(const uword new_n_rows, const uword new_n_cols);
  inline Mat&  reshape(const SizeMat& s);
  
  [[deprecated("use reshape(n_rows, n_cols) instead")]] inline void reshape(const uword new_n_rows, const uword new_n_cols, const uword dim);  //!< NOTE: don't use this form: it will be removed
  
  
  template<typename functor> inline       Mat&  for_each(functor F);
  template<typename functor> inline const Mat&  for_each(functor F) const;
  
  template<typename functor> inline       Mat& transform(functor F);
  template<typename functor> inline       Mat&     imbue(functor F);
  
  
  inline Mat& replace(const eT old_val, const eT new_val);
  
  inline Mat& clean(const pod_type threshold);
  
  inline Mat& clamp(const eT min_val, const eT max_val);
  
  inline Mat& fill(const eT val);
  
  template<typename fill_type>
  inline Mat& fill(const fill::fill_class<fill_type>& f);
  
  inline Mat& zeros();
  inline Mat& zeros(const uword new_n_elem);
  inline Mat& zeros(const uword new_n_rows, const uword new_n_cols);
  inline Mat& zeros(const SizeMat& s);
  
  inline Mat& ones();
  inline Mat& ones(const uword new_n_elem);
  inline Mat& ones(const uword new_n_rows, const uword new_n_cols);
  inline Mat& ones(const SizeMat& s);
  
  inline Mat& randu();
  inline Mat& randu(const uword new_n_elem);
  inline Mat& randu(const uword new_n_rows, const uword new_n_cols);
  inline Mat& randu(const SizeMat& s);
  
  inline Mat& randn();
  inline Mat& randn(const uword new_n_elem);
  inline Mat& randn(const uword new_n_rows, const uword new_n_cols);
  inline Mat& randn(const SizeMat& s);
  
  inline Mat& eye();
  inline Mat& eye(const uword new_n_rows, const uword new_n_cols);
  inline Mat& eye(const SizeMat& s);
  
  arma_cold inline void      reset();
  arma_cold inline void soft_reset();
  
  
  template<typename T1> inline void set_real(const Base<pod_type,T1>& X);
  template<typename T1> inline void set_imag(const Base<pod_type,T1>& X);
  
  
  arma_warn_unused inline eT min() const;
  arma_warn_unused inline eT max() const;
  
  [[deprecated("use .index_min() instead")]] inline eT min(uword& index_of_min_val) const;
  [[deprecated("use .index_max() instead")]] inline eT max(uword& index_of_max_val) const;
  
  [[deprecated("use .index_min() with ind2sub() instead")]] inline eT min(uword& row_of_min_val, uword& col_of_min_val) const;
  [[deprecated("use .index_max() with ind2sub() instead")]] inline eT max(uword& row_of_max_val, uword& col_of_max_val) const;
  
  
  arma_cold inline bool save(const std::string   name, const file_type type = arma_binary) const;
  arma_cold inline bool save(const hdf5_name&    spec, const file_type type = hdf5_binary) const;
  arma_cold inline bool save(const  csv_name&    spec, const file_type type =   csv_ascii) const;
  arma_cold inline bool save(      std::ostream& os,   const file_type type = arma_binary) const;
  
  arma_cold inline bool load(const std::string   name, const file_type type = auto_detect);
  arma_cold inline bool load(const hdf5_name&    spec, const file_type type = hdf5_binary);
  arma_cold inline bool load(const  csv_name&    spec, const file_type type =   csv_ascii);
  arma_cold inline bool load(      std::istream& is,   const file_type type = auto_detect);
  
  [[deprecated("use save() instead")]] inline bool quiet_save(const std::string   name, const file_type type = arma_binary) const;
  [[deprecated("use save() instead")]] inline bool quiet_save(const hdf5_name&    spec, const file_type type = hdf5_binary) const;
  [[deprecated("use save() instead")]] inline bool quiet_save(const  csv_name&    spec, const file_type type =   csv_ascii) const;
  [[deprecated("use save() instead")]] inline bool quiet_save(      std::ostream& os,   const file_type type = arma_binary) const;
  
  [[deprecated("use load() instead")]] inline bool quiet_load(const std::string   name, const file_type type = auto_detect);
  [[deprecated("use load() instead")]] inline bool quiet_load(const hdf5_name&    spec, const file_type type = hdf5_binary);
  [[deprecated("use load() instead")]] inline bool quiet_load(const  csv_name&    spec, const file_type type =   csv_ascii);
  [[deprecated("use load() instead")]] inline bool quiet_load(      std::istream& is,   const file_type type = auto_detect);
  
  
  // for container-like functionality
  
  typedef eT    value_type;
  typedef uword size_type;
  
  typedef       eT*       iterator;
  typedef const eT* const_iterator;
  
  typedef       eT*       col_iterator;
  typedef const eT* const_col_iterator;
  
  class const_row_iterator;
  
  class row_iterator
    {
    public:
    
    inline row_iterator();
    inline row_iterator(const row_iterator& X);
    inline row_iterator(Mat<eT>& in_M, const uword in_row, const uword in_col);
    
    arma_warn_unused inline eT& operator* ();
    
                     inline row_iterator& operator++();
    arma_warn_unused inline row_iterator  operator++(int);
    
                     inline row_iterator& operator--();
    arma_warn_unused inline row_iterator  operator--(int);
    
    arma_warn_unused inline bool operator!=(const       row_iterator& X) const;
    arma_warn_unused inline bool operator==(const       row_iterator& X) const;
    arma_warn_unused inline bool operator!=(const const_row_iterator& X) const;
    arma_warn_unused inline bool operator==(const const_row_iterator& X) const;
    
    typedef std::bidirectional_iterator_tag iterator_category;
    typedef eT                              value_type;
    typedef std::ptrdiff_t                  difference_type;  // TODO: not certain on this one
    typedef eT*                             pointer;
    typedef eT&                             reference;
    
    arma_aligned Mat<eT>* M;
    arma_aligned uword    current_row;
    arma_aligned uword    current_col;
    };
  
  
  class const_row_iterator
    {
    public:
    
    inline const_row_iterator();
    inline const_row_iterator(const       row_iterator& X);
    inline const_row_iterator(const const_row_iterator& X);
    inline const_row_iterator(const Mat<eT>& in_M, const uword in_row, const uword in_col);
    
    arma_warn_unused inline const eT& operator*() const;
    
                     inline const_row_iterator& operator++();
    arma_warn_unused inline const_row_iterator  operator++(int);
    
                     inline const_row_iterator& operator--();
    arma_warn_unused inline const_row_iterator  operator--(int);
    
    arma_warn_unused inline bool operator!=(const       row_iterator& X) const;
    arma_warn_unused inline bool operator==(const       row_iterator& X) const;
    arma_warn_unused inline bool operator!=(const const_row_iterator& X) const;
    arma_warn_unused inline bool operator==(const const_row_iterator& X) const;
    
    typedef std::bidirectional_iterator_tag iterator_category;
    typedef eT                              value_type;
    typedef std::ptrdiff_t                  difference_type;  // TODO: not certain on this one
    typedef const eT*                       pointer;
    typedef const eT&                       reference;
    
    arma_aligned const Mat<eT>* M;
    arma_aligned       uword    current_row;
    arma_aligned       uword    current_col;
    };
  
  
  class const_row_col_iterator;

  class row_col_iterator
    {
    public:
    
    inline row_col_iterator();
    inline row_col_iterator(const row_col_iterator& in_it);
    inline row_col_iterator(Mat<eT>& in_M, const uword row = 0, const uword col = 0);
    
    arma_warn_unused inline eT& operator*();
    
                     inline row_col_iterator& operator++();
    arma_warn_unused inline row_col_iterator  operator++(int);
    
                     inline row_col_iterator& operator--();
    arma_warn_unused inline row_col_iterator  operator--(int);
    
    arma_warn_unused inline uword row() const;
    arma_warn_unused inline uword col() const;
    
    arma_warn_unused inline bool operator==(const       row_col_iterator& rhs) const;
    arma_warn_unused inline bool operator!=(const       row_col_iterator& rhs) const;
    arma_warn_unused inline bool operator==(const const_row_col_iterator& rhs) const;
    arma_warn_unused inline bool operator!=(const const_row_col_iterator& rhs) const;
    
    typedef std::bidirectional_iterator_tag iterator_category;
    typedef eT                              value_type;
    typedef std::ptrdiff_t                  difference_type;  // TODO: not certain on this one
    typedef eT*                             pointer;
    typedef eT&                             reference;
    
    arma_aligned Mat<eT>* M;
    arma_aligned eT*      current_ptr;
    arma_aligned uword    current_col;
    arma_aligned uword    current_row;
    };
  
  
  class const_row_col_iterator
    {
    public:
    
    inline const_row_col_iterator();
    inline const_row_col_iterator(const       row_col_iterator& in_it);
    inline const_row_col_iterator(const const_row_col_iterator& in_it);
    inline const_row_col_iterator(const Mat<eT>& in_M, const uword row = 0, const uword col = 0);
    
    arma_warn_unused inline const eT& operator*() const;
    
                     inline const_row_col_iterator& operator++();
    arma_warn_unused inline const_row_col_iterator  operator++(int);
    
                     inline const_row_col_iterator& operator--();
    arma_warn_unused inline const_row_col_iterator  operator--(int);
    
    arma_warn_unused inline uword row() const;
    arma_warn_unused inline uword col() const;
    
    arma_warn_unused inline bool operator==(const const_row_col_iterator& rhs) const;
    arma_warn_unused inline bool operator!=(const const_row_col_iterator& rhs) const;
    arma_warn_unused inline bool operator==(const       row_col_iterator& rhs) const;
    arma_warn_unused inline bool operator!=(const       row_col_iterator& rhs) const;
    
    // So that we satisfy the STL iterator types.
    typedef std::bidirectional_iterator_tag iterator_category;
    typedef eT                              value_type;
    typedef std::ptrdiff_t                  difference_type;  // TODO: not certain on this one
    typedef const eT*                       pointer;
    typedef const eT&                       reference;
    
    arma_aligned const Mat<eT>* M;
    arma_aligned const eT*      current_ptr;
    arma_aligned       uword    current_col;
    arma_aligned       uword    current_row;
    };
  
  
  inline       iterator  begin();
  inline const_iterator  begin() const;
  inline const_iterator cbegin() const;
  
  inline       iterator  end();
  inline const_iterator  end() const;
  inline const_iterator cend() const;
  
  inline       col_iterator begin_col(const uword col_num);
  inline const_col_iterator begin_col(const uword col_num) const;
  
  inline       col_iterator end_col  (const uword col_num);
  inline const_col_iterator end_col  (const uword col_num) const;
  
  inline       row_iterator begin_row(const uword row_num);
  inline const_row_iterator begin_row(const uword row_num) const;
  
  inline       row_iterator end_row  (const uword row_num);
  inline const_row_iterator end_row  (const uword row_num) const;
  
  inline       row_col_iterator begin_row_col();
  inline const_row_col_iterator begin_row_col() const;
  
  inline       row_col_iterator end_row_col();
  inline const_row_col_iterator end_row_col() const;
  
  
  inline void  clear();
  inline bool  empty() const;
  inline uword size()  const;
  
  arma_warn_unused inline       eT& front();
  arma_warn_unused inline const eT& front() const;
  
  arma_warn_unused inline       eT& back();
  arma_warn_unused inline const eT& back() const;
  
  inline void swap(Mat& B);
  
  inline void steal_mem(Mat& X);                      //!< don't use this unless you're writing code internal to Armadillo
  inline void steal_mem(Mat& X, const bool is_move);  //!< don't use this unless you're writing code internal to Armadillo
  
  inline void steal_mem_col(Mat& X, const uword max_n_rows);
  
  template<typename eT2>
  arma_inline bool is_alias(const Mat<eT2>& X) const; //!< don't use this unless you're writing code internal to Armadillo
  
  
  template<uword fixed_n_rows, uword fixed_n_cols> class fixed;
  
  
  protected:
  
  inline void init_cold();
  inline void init_warm(uword in_n_rows, uword in_n_cols);
  
  arma_cold inline void init(const std::string& text);
  
  inline void init(const std::initializer_list<eT>& list);
  inline void init(const std::initializer_list< std::initializer_list<eT> >& list);
  
  template<typename T1, typename T2>
  inline void init(const Base<pod_type,T1>& A, const Base<pod_type,T2>& B);
  
  inline Mat(const char junk, const eT* aux_mem, const uword aux_n_rows, const uword aux_n_cols);
  
  inline Mat(const arma_vec_indicator&, const uhword in_vec_state);
  inline Mat(const arma_vec_indicator&, const uword in_n_rows, const uword in_n_cols, const uhword in_vec_state);
  
  inline Mat(const arma_fixed_indicator&, const uword in_n_rows, const uword in_n_cols, const uhword in_vec_state, const eT* in_mem);
  
  template<int vec_mode> inline void vec_push_back(const eT val, const arma_vec_mode_indicator<vec_mode>&);
  
  
  friend class Cube<eT>;
  friend class subview_cube<eT>;
  
  friend struct glue_join;
  friend struct op_strans;
  friend struct op_htrans;
  friend struct op_resize;
  friend struct op_mean;
  friend struct op_max;
  friend struct op_min;
  
  
  public:
  
  #if defined(ARMA_EXTRA_MAT_PROTO)
    #include ARMA_INCFILE_WRAP(ARMA_EXTRA_MAT_PROTO)
  #endif
  };



template<typename eT>
template<uword fixed_n_rows, uword fixed_n_cols> 
class Mat<eT>::fixed : public Mat<eT>
  {
  private:
  
  using Mat<eT>::mem_local;
  
  static constexpr uword fixed_n_elem = fixed_n_rows * fixed_n_cols;
  static constexpr bool  use_extra    = (fixed_n_elem > arma_config::mat_prealloc);
  
  arma_align_mem eT mem_local_extra[ (use_extra) ? fixed_n_elem : 1 ];
  
  
  public:
  
  typedef fixed<fixed_n_rows, fixed_n_cols> Mat_fixed_type;
  
  typedef eT                                elem_type;
  typedef typename get_pod_type<eT>::result pod_type;
  
  static constexpr bool is_col  = (fixed_n_cols == 1);
  static constexpr bool is_row  = (fixed_n_rows == 1);
  static constexpr bool is_xvec = false;
  
  static constexpr bool has_subview = false;
  
  static const uword n_rows;  // value provided below the class definition
  static const uword n_cols;  // value provided below the class definition
  static const uword n_elem;  // value provided below the class definition
  
  arma_inline fixed();
  arma_inline fixed(const fixed<fixed_n_rows, fixed_n_cols>& X);
  
                                     inline fixed(const fill::scalar_holder<eT> f);
  template<typename fill_type>       inline fixed(const fill::fill_class<fill_type>& f);
  template<typename T1>              inline fixed(const Base<eT,T1>& A);
  template<typename T1, typename T2> inline fixed(const Base<pod_type,T1>& A, const Base<pod_type,T2>& B);
  
  inline fixed(const eT* aux_mem);
  
  inline fixed(const char*        text);
  inline fixed(const std::string& text);
  
  using Mat<eT>::operator=;
  using Mat<eT>::operator();
  
  inline          fixed(const std::initializer_list<eT>& list);
  inline Mat& operator=(const std::initializer_list<eT>& list);
  
  inline          fixed(const std::initializer_list< std::initializer_list<eT> >& list);
  inline Mat& operator=(const std::initializer_list< std::initializer_list<eT> >& list);
  
  arma_inline Mat& operator=(const fixed<fixed_n_rows, fixed_n_cols>& X);
  
  #if defined(ARMA_GOOD_COMPILER)
    template<typename T1,              typename   eop_type> inline Mat& operator=(const   eOp<T1,       eop_type>& X);
    template<typename T1, typename T2, typename eglue_type> inline Mat& operator=(const eGlue<T1, T2, eglue_type>& X);
  #endif
  
  arma_warn_unused arma_inline const Op< Mat_fixed_type, op_htrans >  t() const;
  arma_warn_unused arma_inline const Op< Mat_fixed_type, op_htrans > ht() const;
  arma_warn_unused arma_inline const Op< Mat_fixed_type, op_strans > st() const;
  
  arma_warn_unused arma_inline const eT& at_alt     (const uword i) const;
  
  arma_warn_unused arma_inline       eT& operator[] (const uword i);
  arma_warn_unused arma_inline const eT& operator[] (const uword i) const;
  arma_warn_unused arma_inline       eT& at         (const uword i);
  arma_warn_unused arma_inline const eT& at         (const uword i) const;
  arma_warn_unused arma_inline       eT& operator() (const uword i);
  arma_warn_unused arma_inline const eT& operator() (const uword i) const;
  
  #if defined(__cpp_multidimensional_subscript)
  arma_warn_unused arma_inline       eT& operator[] (const uword in_row, const uword in_col);
  arma_warn_unused arma_inline const eT& operator[] (const uword in_row, const uword in_col) const;
  #endif
  
  arma_warn_unused arma_inline       eT& at         (const uword in_row, const uword in_col);
  arma_warn_unused arma_inline const eT& at         (const uword in_row, const uword in_col) const;
  arma_warn_unused arma_inline       eT& operator() (const uword in_row, const uword in_col);
  arma_warn_unused arma_inline const eT& operator() (const uword in_row, const uword in_col) const;
  
  inline void push_back(const eT) = delete;
  
  arma_warn_unused arma_inline       eT* colptr(const uword in_col);
  arma_warn_unused arma_inline const eT* colptr(const uword in_col) const;
  
  arma_warn_unused arma_inline       eT* memptr();
  arma_warn_unused arma_inline const eT* memptr() const;
  
  arma_inline       subview_row<eT> row(const uword row_num);
  arma_inline const subview_row<eT> row(const uword row_num) const;
  
  arma_inline       subview_col<eT> col(const uword col_num);
  arma_inline const subview_col<eT> col(const uword col_num) const;
  
  arma_warn_unused arma_inline bool is_vec() const;
  
  inline const Mat<eT>& fill(const eT val);
  inline const Mat<eT>& zeros();
  inline const Mat<eT>& ones();
  };



// these definitions are outside of the class due to bizarre C++ rules;
// C++17 has inline variables to address this shortcoming

template<typename eT>
template<uword fixed_n_rows, uword fixed_n_cols>
const uword Mat<eT>::fixed<fixed_n_rows, fixed_n_cols>::n_rows = fixed_n_rows;

template<typename eT>
template<uword fixed_n_rows, uword fixed_n_cols>
const uword Mat<eT>::fixed<fixed_n_rows, fixed_n_cols>::n_cols = fixed_n_cols;

template<typename eT>
template<uword fixed_n_rows, uword fixed_n_cols>
const uword Mat<eT>::fixed<fixed_n_rows, fixed_n_cols>::n_elem = fixed_n_rows * fixed_n_cols;



class Mat_aux
  {
  public:

  template<typename eT> inline static void prefix_pp(Mat<eT>& x);
  template<typename T>  inline static void prefix_pp(Mat< std::complex<T> >& x);
  
  template<typename eT> inline static void postfix_pp(Mat<eT>& x);
  template<typename T>  inline static void postfix_pp(Mat< std::complex<T> >& x);
  
  template<typename eT> inline static void prefix_mm(Mat<eT>& x);
  template<typename T>  inline static void prefix_mm(Mat< std::complex<T> >& x);
  
  template<typename eT> inline static void postfix_mm(Mat<eT>& x);
  template<typename T>  inline static void postfix_mm(Mat< std::complex<T> >& x);
  
  template<typename eT, typename T1> inline static void set_real(Mat<eT>&                out, const Base<eT,T1>& X);
  template<typename T,  typename T1> inline static void set_real(Mat< std::complex<T> >& out, const Base< T,T1>& X);
  
  template<typename eT, typename T1> inline static void set_imag(Mat<eT>&                out, const Base<eT,T1>& X);
  template<typename T,  typename T1> inline static void set_imag(Mat< std::complex<T> >& out, const Base< T,T1>& X);
  };



template<typename eT> class Mat_noalias : public Mat<eT> {};



//! @}