// SPDX-License-Identifier: Apache-2.0
//
// Copyright 2008-2016 Conrad Sanderson (http://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
// http://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;

  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);
  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);
  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);

  inline explicit Mat(
      const subview<eT>& X,
      const bool use_colmem);  // only to be used by the quasi_unwrap class

  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);
  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);
  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);
  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);
  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);
  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);
  inline Mat& operator=(const SpSubview<eT>& X);

  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);

  arma_frown("use braced initialiser list instead") inline mat_injector<Mat> operator<<(
      const eT val);
  arma_frown("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);

  arma_deprecated inline void insert_rows(const uword row_num, const uword N,
                                          const bool set_to_zero);
  arma_deprecated 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);
  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);
  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);
  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);
  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);
  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);
  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 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);
  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);
  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);
  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;

  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);

  arma_deprecated 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;

  inline eT min(uword& index_of_min_val) const;
  inline eT max(uword& index_of_max_val) const;

  inline eT min(uword& row_of_min_val, uword& col_of_min_val) const;
  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);

  arma_deprecated inline bool quiet_save(const std::string name,
                                         const file_type type = arma_binary) const;
  arma_deprecated inline bool quiet_save(const hdf5_name& spec,
                                         const file_type type = hdf5_binary) const;
  arma_deprecated inline bool quiet_save(const csv_name& spec,
                                         const file_type type = csv_ascii) const;
  arma_deprecated inline bool quiet_save(std::ostream& os,
                                         const file_type type = arma_binary) const;

  arma_deprecated inline bool quiet_load(const std::string name,
                                         const file_type type = auto_detect);
  arma_deprecated inline bool quiet_load(const hdf5_name& spec,
                                         const file_type type = hdf5_binary);
  arma_deprecated inline bool quiet_load(const csv_name& spec,
                                         const file_type type = csv_ascii);
  arma_deprecated 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 <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);

  friend class Cube<eT>;
  friend class subview_cube<eT>;
  friend class glue_join;
  friend class op_strans;
  friend class op_htrans;
  friend class op_resize;
  friend class op_mean;
  friend class op_max;
  friend class 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:
  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 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;

  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_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);
};

//! @}
