// Copyright (C) 2008-2015 National ICT Australia (NICTA)
// 
// This Source Code Form is subject to the terms of the Mozilla Public
// License, v. 2.0. If a copy of the MPL was not distributed with this
// file, You can obtain one at http://mozilla.org/MPL/2.0/.
// -------------------------------------------------------------------
// 
// Written by Conrad Sanderson - http://conradsanderson.id.au
// Written by James Sanders
// Written by Eric Jon Sundstrom


//! \addtogroup auxlib
//! @{


//! interface functions for accessing decompositions in LAPACK and ATLAS
class auxlib
  {
  public:
  
  
  template<const uword row, const uword col>
  struct pos
    {
    static const uword n2 = row + col*2;
    static const uword n3 = row + col*3;
    static const uword n4 = row + col*4;
    };
  
  
  //
  // inv
  
  template<typename eT, typename T1>
  inline static bool inv(Mat<eT>& out, const Base<eT,T1>& X);
  
  template<typename eT>
  inline static bool inv(Mat<eT>& out, const Mat<eT>& A);
  
  template<typename eT>
  inline static bool inv_noalias_tinymat(Mat<eT>& out, const Mat<eT>& X, const uword N);
  
  template<typename eT>
  inline static bool inv_inplace_lapack(Mat<eT>& out);
  
  
  //
  // inv_tr
  
  template<typename eT, typename T1>
  inline static bool inv_tr(Mat<eT>& out, const Base<eT,T1>& X, const uword layout);
  
  
  //
  // inv_sym
  
  template<typename eT, typename T1>
  inline static bool inv_sym(Mat<eT>& out, const Base<eT,T1>& X, const uword layout);
  
  
  //
  // inv_sympd
  
  template<typename eT, typename T1>
  inline static bool inv_sympd(Mat<eT>& out, const Base<eT,T1>& X, const uword layout);
  
  
  //
  // det
  
  template<typename eT, typename T1>
  inline static eT det(const Base<eT,T1>& X);
  
  template<typename eT>
  inline static eT det_tinymat(const Mat<eT>& X, const uword N);
  
  template<typename eT>
  inline static eT det_lapack(const Mat<eT>& X, const bool make_copy);
  
  
  //
  // log_det
  
  template<typename eT, typename T1>
  inline static bool log_det(eT& out_val, typename get_pod_type<eT>::result& out_sign, const Base<eT,T1>& X);
  
  
  //
  // lu
  
  template<typename eT, typename T1>
  inline static bool lu(Mat<eT>& L, Mat<eT>& U, podarray<blas_int>& ipiv, const Base<eT,T1>& X);
  
  template<typename eT, typename T1>
  inline static bool lu(Mat<eT>& L, Mat<eT>& U, Mat<eT>& P, const Base<eT,T1>& X);
  
  template<typename eT, typename T1>
  inline static bool lu(Mat<eT>& L, Mat<eT>& U, const Base<eT,T1>& X);
  
  
  //
  // eig_gen
  
  template<typename T1>
  inline static bool eig_gen(Mat< std::complex<typename T1::pod_type> >& vals, Mat< std::complex<typename T1::pod_type> >& vecs, const uword mode, const Base<typename T1::pod_type,T1>& expr);
  
  template<typename T1>
  inline static bool eig_gen(Mat< std::complex<typename T1::pod_type> >& vals, Mat< std::complex<typename T1::pod_type> >& vecs, const uword mode, const Base< std::complex<typename T1::pod_type>, T1 >& expr);
  
  template<typename T1>
  inline static bool eig_gen_dual(Mat< std::complex<typename T1::pod_type> >& vals, Mat<typename T1::pod_type>& vecs_l, Mat<typename T1::pod_type>& vecs_r, const Base<typename T1::pod_type,T1>& expr);
  
  template<typename T1>
  inline static bool eig_gen_dual(Mat< std::complex<typename T1::pod_type> >& vals, Mat< std::complex<typename T1::pod_type> >& vecs_l, Mat< std::complex<typename T1::pod_type> >& vecs_r, const Base< std::complex<typename T1::pod_type>, T1 >& expr);
  
  
  //
  // eig_pair
  
  template<typename T1, typename T2>
  inline static bool eig_pair(Mat< std::complex<typename T1::pod_type> >& vals, Mat< std::complex<typename T1::pod_type> >& vecs, const uword mode, const Base<typename T1::pod_type,T1>& A_expr, const Base<typename T1::pod_type,T2>& B_expr);
  
  template<typename T1, typename T2>
  inline static bool eig_pair(Mat< std::complex<typename T1::pod_type> >& vals, Mat< std::complex<typename T1::pod_type> >& vecs, const uword mode, const Base< std::complex<typename T1::pod_type>, T1 >& A_expr, const Base< std::complex<typename T1::pod_type>, T2 >& B_expr);
  
  
  //
  // eig_sym
  
  template<typename eT, typename T1> 
  inline static bool eig_sym(Col<eT>& eigval, const Base<eT,T1>& X);
  
  template<typename T, typename T1> 
  inline static bool eig_sym(Col<T>& eigval, const Base<std::complex<T>,T1>& X);
  
  template<typename eT, typename T1>
  inline static bool eig_sym(Col<eT>& eigval, Mat<eT>& eigvec, const Base<eT,T1>& X);
  
  template<typename T, typename T1>
  inline static bool eig_sym(Col<T>& eigval, Mat< std::complex<T> >& eigvec, const Base<std::complex<T>,T1>& X);
  
  template<typename eT, typename T1>
  inline static bool eig_sym_dc(Col<eT>& eigval, Mat<eT>& eigvec, const Base<eT,T1>& X);
  
  template<typename T, typename T1>
  inline static bool eig_sym_dc(Col<T>& eigval, Mat< std::complex<T> >& eigvec, const Base<std::complex<T>,T1>& X);
  
  
  //
  // chol
  
  template<typename eT, typename T1>
  inline static bool chol(Mat<eT>& out, const Base<eT,T1>& X, const uword layout);
  
  
  //
  // qr
  
  template<typename eT, typename T1>
  inline static bool qr(Mat<eT>& Q, Mat<eT>& R, const Base<eT,T1>& X);
  
  template<typename eT, typename T1>
  inline static bool qr_econ(Mat<eT>& Q, Mat<eT>& R, const Base<eT,T1>& X);
  
  
  //
  // svd
  
  template<typename eT, typename T1>
  inline static bool svd(Col<eT>& S, const Base<eT,T1>& X, uword& n_rows, uword& n_cols);
  
  template<typename T, typename T1>
  inline static bool svd(Col<T>& S, const Base<std::complex<T>, T1>& X, uword& n_rows, uword& n_cols);
  
  template<typename eT, typename T1>
  inline static bool svd(Col<eT>& S, const Base<eT,T1>& X);
  
  template<typename T, typename T1>
  inline static bool svd(Col<T>& S, const Base<std::complex<T>, T1>& X);
  
  template<typename eT, typename T1>
  inline static bool svd(Mat<eT>& U, Col<eT>& S, Mat<eT>& V, const Base<eT,T1>& X);
  
  template<typename T, typename T1>
  inline static bool svd(Mat< std::complex<T> >& U, Col<T>& S, Mat< std::complex<T> >& V, const Base< std::complex<T>, T1>& X);
  
  template<typename eT, typename T1>
  inline static bool svd_econ(Mat<eT>& U, Col<eT>& S, Mat<eT>& V, const Base<eT,T1>& X, const char mode);
  
  template<typename T, typename T1>
  inline static bool svd_econ(Mat< std::complex<T> >& U, Col<T>& S, Mat< std::complex<T> >& V, const Base< std::complex<T>, T1>& X, const char mode);
  
  
  template<typename eT, typename T1>
  inline static bool svd_dc(Col<eT>& S, const Base<eT,T1>& X, uword& n_rows, uword& n_cols);
  
  template<typename T, typename T1>
  inline static bool svd_dc(Col<T>& S, const Base<std::complex<T>, T1>& X, uword& n_rows, uword& n_cols);
  
  template<typename eT, typename T1>
  inline static bool svd_dc(Col<eT>& S, const Base<eT,T1>& X);
  
  template<typename T, typename T1>
  inline static bool svd_dc(Col<T>& S, const Base<std::complex<T>, T1>& X);
  
  
  template<typename eT, typename T1>
  inline static bool svd_dc(Mat<eT>& U, Col<eT>& S, Mat<eT>& V, const Base<eT,T1>& X);
  
  template<typename T, typename T1>
  inline static bool svd_dc(Mat< std::complex<T> >& U, Col<T>& S, Mat< std::complex<T> >& V, const Base< std::complex<T>, T1>& X);
  
  template<typename eT, typename T1>
  inline static bool svd_dc_econ(Mat<eT>& U, Col<eT>& S, Mat<eT>& V, const Base<eT,T1>& X);
  
  template<typename T, typename T1>
  inline static bool svd_dc_econ(Mat< std::complex<T> >& U, Col<T>& S, Mat< std::complex<T> >& V, const Base< std::complex<T>, T1>& X);
  
  
  //
  // solve
  
  template<typename T1>
  inline static bool solve_square_fast(Mat<typename T1::elem_type>& out, Mat<typename T1::elem_type>& A, const Base<typename T1::elem_type,T1>& B_expr);
  
  template<typename T1>
  inline static bool solve_square_refine(Mat<typename T1::pod_type>& out, typename T1::pod_type& out_rcond, Mat<typename T1::pod_type>& A, const Base<typename T1::pod_type,T1>& B_expr, const bool equilibrate);
  
  template<typename T1>
  inline static bool solve_square_refine(Mat< std::complex<typename T1::pod_type> >& out, typename T1::pod_type& out_rcond, Mat< std::complex<typename T1::pod_type> >& A, const Base<std::complex<typename T1::pod_type>,T1>& B_expr, const bool equilibrate);
  
  template<typename T1>
  inline static bool solve_approx_fast(Mat<typename T1::elem_type>& out, Mat<typename T1::elem_type>& A, const Base<typename T1::elem_type,T1>& B_expr);
  
  template<typename T1>
  inline static bool solve_approx_svd(Mat<typename T1::pod_type>& out, Mat<typename T1::pod_type>& A, const Base<typename T1::pod_type,T1>& B_expr);
  
  template<typename T1>
  inline static bool solve_approx_svd(Mat< std::complex<typename T1::pod_type> >& out, Mat< std::complex<typename T1::pod_type> >& A, const Base<std::complex<typename T1::pod_type>,T1>& B_expr);
  
  template<typename T1>
  inline static bool solve_tri(Mat<typename T1::elem_type>& out, const Mat<typename T1::elem_type>& A, const Base<typename T1::elem_type,T1>& B_expr, const uword layout);
  
  
  //
  // Schur decomposition
  
  template<typename eT, typename T1>
  inline static bool schur(Mat<eT>& U, Mat<eT>& S, const Base<eT,T1>& X, const bool calc_U = true);
  
  template<typename  T, typename T1>
  inline static bool schur(Mat<std::complex<T> >& U, Mat<std::complex<T> >& S, const Base<std::complex<T>,T1>& X, const bool calc_U = true);
  
  
  //
  // syl (solution of the Sylvester equation AX + XB = C)
  
  template<typename eT>
  inline static bool syl(Mat<eT>& X, const Mat<eT>& A, const Mat<eT>& B, const Mat<eT>& C);
  
  
  //
  // QZ decomposition
  
  template<typename T, typename T1, typename T2>
  inline static bool qz(Mat<T>& A, Mat<T>& B, Mat<T>& vsl, Mat<T>& vsr, const Base<T,T1>& X_expr, const Base<T,T2>& Y_expr);
  
  template<typename T, typename T1, typename T2>
  inline static bool qz(Mat< std::complex<T> >& A, Mat< std::complex<T> >& B, Mat< std::complex<T> >& vsl, Mat< std::complex<T> >& vsr, const Base< std::complex<T>, T1 >& X_expr, const Base< std::complex<T>, T2 >& Y_expr);
  
  
  // 
  // rcond
  
  template<typename T1>
  inline static typename T1::pod_type rcond(const Base<typename T1::pod_type,T1>& A_expr);
  
  template<typename T1>
  inline static typename T1::pod_type rcond(const Base<std::complex<typename T1::pod_type>,T1>& A_expr);
  };


//! @}