max@0: // Copyright (C) 2008-2011 NICTA (www.nicta.com.au)
max@0: // Copyright (C) 2008-2011 Conrad Sanderson
max@0: // Copyright (C)      2009 Edmund Highcock
max@0: // Copyright (C)      2011 James Sanders
max@0: // 
max@0: // This file is part of the Armadillo C++ library.
max@0: // It is provided without any warranty of fitness
max@0: // for any purpose. You can redistribute this file
max@0: // and/or modify it under the terms of the GNU
max@0: // Lesser General Public License (LGPL) as published
max@0: // by the Free Software Foundation, either version 3
max@0: // of the License or (at your option) any later version.
max@0: // (see http://www.opensource.org/licenses for more info)
max@0: 
max@0: 
max@0: //! \addtogroup auxlib
max@0: //! @{
max@0: 
max@0: 
max@0: //! wrapper for accessing external functions defined in ATLAS, LAPACK or BLAS libraries
max@0: class auxlib
max@0:   {
max@0:   public:
max@0:   
max@0:   
max@0:   template<const uword row, const uword col>
max@0:   struct pos
max@0:     {
max@0:     static const uword n2 = row + col*2;
max@0:     static const uword n3 = row + col*3;
max@0:     static const uword n4 = row + col*4;
max@0:     };
max@0:   
max@0:   
max@0:   //
max@0:   // inv
max@0:   
max@0:   template<typename eT, typename T1>
max@0:   inline static bool inv(Mat<eT>& out, const Base<eT,T1>& X, const bool slow = false);
max@0:   
max@0:   template<typename eT>
max@0:   inline static bool inv(Mat<eT>& out, const Mat<eT>& A, const bool slow = false);
max@0:   
max@0:   template<typename eT>
max@0:   inline static bool inv_noalias_tinymat(Mat<eT>& out, const Mat<eT>& X, const uword N);
max@0:   
max@0:   template<typename eT>
max@0:   inline static bool inv_inplace_tinymat(Mat<eT>& out, const uword N);
max@0:   
max@0:   template<typename eT>
max@0:   inline static bool inv_inplace_lapack(Mat<eT>& out);
max@0:   
max@0:   
max@0:   //
max@0:   // inv_tr
max@0:   
max@0:   template<typename eT, typename T1>
max@0:   inline static bool inv_tr(Mat<eT>& out, const Base<eT,T1>& X, const uword layout);
max@0:   
max@0:   
max@0:   //
max@0:   // inv_sym
max@0:   
max@0:   template<typename eT, typename T1>
max@0:   inline static bool inv_sym(Mat<eT>& out, const Base<eT,T1>& X, const uword layout);
max@0:   
max@0:   
max@0:   //
max@0:   // inv_sympd
max@0:   
max@0:   template<typename eT, typename T1>
max@0:   inline static bool inv_sympd(Mat<eT>& out, const Base<eT,T1>& X, const uword layout);
max@0:   
max@0:   
max@0:   //
max@0:   // det
max@0:   
max@0:   template<typename eT, typename T1>
max@0:   inline static eT det(const Base<eT,T1>& X, const bool slow = false);
max@0:   
max@0:   template<typename eT>
max@0:   inline static eT det_tinymat(const Mat<eT>& X, const uword N);
max@0:   
max@0:   template<typename eT>
max@0:   inline static eT det_lapack(const Mat<eT>& X, const bool make_copy);
max@0:   
max@0:   
max@0:   //
max@0:   // log_det
max@0:   
max@0:   template<typename eT, typename T1>
max@0:   inline static bool log_det(eT& out_val, typename get_pod_type<eT>::result& out_sign, const Base<eT,T1>& X);
max@0:   
max@0:   
max@0:   //
max@0:   // lu
max@0:   
max@0:   template<typename eT, typename T1>
max@0:   inline static bool lu(Mat<eT>& L, Mat<eT>& U, podarray<blas_int>& ipiv, const Base<eT,T1>& X);
max@0:   
max@0:   template<typename eT, typename T1>
max@0:   inline static bool lu(Mat<eT>& L, Mat<eT>& U, Mat<eT>& P, const Base<eT,T1>& X);
max@0:   
max@0:   template<typename eT, typename T1>
max@0:   inline static bool lu(Mat<eT>& L, Mat<eT>& U, const Base<eT,T1>& X);
max@0:   
max@0:   
max@0:   //
max@0:   // eig
max@0:   
max@0:   template<typename eT, typename T1> 
max@0:   inline static bool eig_sym(Col<eT>& eigval, const Base<eT,T1>& X);
max@0:   
max@0:   template<typename T, typename T1> 
max@0:   inline static bool eig_sym(Col<T>& eigval, const Base<std::complex<T>,T1>& X);
max@0:   
max@0:   template<typename eT, typename T1>
max@0:   inline static bool eig_sym(Col<eT>& eigval, Mat<eT>& eigvec, const Base<eT,T1>& X);
max@0:   
max@0:   template<typename T, typename T1>
max@0:   inline static bool eig_sym(Col<T>& eigval, Mat< std::complex<T> >& eigvec, const Base<std::complex<T>,T1>& X);
max@0:   
max@0:   template<typename T, typename T1>
max@0:   inline static bool eig_gen(Col< std::complex<T> >& eigval, Mat<T>& l_eigvec, Mat<T>& r_eigvec, const Base<T,T1>& X, const char side);
max@0:   
max@0:   template<typename T, typename T1>
max@0:   inline static bool eig_gen(Col< std::complex<T> >& eigval, Mat< std::complex<T> >& l_eigvec, Mat< std::complex<T> >& r_eigvec, const Base< std::complex<T>, T1 >& X, const char side);
max@0:   
max@0:   
max@0:   //
max@0:   // chol
max@0:   
max@0:   template<typename eT, typename T1>
max@0:   inline static bool chol(Mat<eT>& out, const Base<eT,T1>& X);
max@0:   
max@0:   
max@0:   //
max@0:   // qr
max@0:   
max@0:   template<typename eT, typename T1>
max@0:   inline static bool qr(Mat<eT>& Q, Mat<eT>& R, const Base<eT,T1>& X);
max@0:   
max@0:   
max@0:   //
max@0:   // svd
max@0:   
max@0:   template<typename eT, typename T1>
max@0:   inline static bool svd(Col<eT>& S, const Base<eT,T1>& X, uword& n_rows, uword& n_cols);
max@0:   
max@0:   template<typename T, typename T1>
max@0:   inline static bool svd(Col<T>& S, const Base<std::complex<T>, T1>& X, uword& n_rows, uword& n_cols);
max@0:   
max@0:   template<typename eT, typename T1>
max@0:   inline static bool svd(Col<eT>& S, const Base<eT,T1>& X);
max@0:   
max@0:   template<typename T, typename T1>
max@0:   inline static bool svd(Col<T>& S, const Base<std::complex<T>, T1>& X);
max@0:   
max@0:   template<typename eT, typename T1>
max@0:   inline static bool svd(Mat<eT>& U, Col<eT>& S, Mat<eT>& V, const Base<eT,T1>& X);
max@0:   
max@0:   template<typename T, typename T1>
max@0:   inline static bool svd(Mat< std::complex<T> >& U, Col<T>& S, Mat< std::complex<T> >& V, const Base< std::complex<T>, T1>& X);
max@0:   
max@0:   template<typename eT, typename T1>
max@0:   inline static bool svd_econ(Mat<eT>& U, Col<eT>& S, Mat<eT>& V, const Base<eT,T1>& X, const char mode);
max@0:   
max@0:   template<typename T, typename T1>
max@0:   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);
max@0:   
max@0:   
max@0:   //
max@0:   // solve
max@0:   
max@0:   template<typename eT>
max@0:   inline static bool solve   (Mat<eT>& out, Mat<eT>& A, const Mat<eT>& B, const bool slow = false);
max@0:   
max@0:   template<typename eT>
max@0:   inline static bool solve_od(Mat<eT>& out, Mat<eT>& A, const Mat<eT>& B);
max@0:   
max@0:   template<typename eT>
max@0:   inline static bool solve_ud(Mat<eT>& out, Mat<eT>& A, const Mat<eT>& B);
max@0:   
max@0:   
max@0:   //
max@0:   // solve_tr
max@0:   
max@0:   template<typename eT>
max@0:   inline static bool solve_tr(Mat<eT>& out, const Mat<eT>& A, const Mat<eT>& B, const uword layout);
max@0: 
max@0: 
max@0:   //
max@0:   // Schur decomposition
max@0:   
max@0:   template<typename eT>
max@0:   inline static bool schur_dec(Mat<eT>& Z, Mat<eT>& T, const Mat<eT>& A);
max@0:   
max@0:   template<typename cT>
max@0:   inline static bool schur_dec(Mat<std::complex<cT> >& Z, Mat<std::complex<cT> >& T, const Mat<std::complex<cT> >& A);
max@0:   
max@0:   
max@0:   //
max@0:   // syl (solution of the Sylvester equation AX + XB = C)
max@0:   
max@0:   template<typename eT>
max@0:   inline static bool syl(Mat<eT>& X, const Mat<eT>& A, const Mat<eT>& B, const Mat<eT>& C);
max@0:   
max@0:   
max@0:   //
max@0:   // lyap (solution of the continuous Lyapunov equation AX + XA^H + Q = 0)
max@0:   
max@0:   template<typename eT>
max@0:   inline static bool lyap(Mat<eT>& X, const Mat<eT>& A, const Mat<eT>& Q);
max@0:   
max@0:   
max@0:   //
max@0:   // dlyap (solution of the discrete Lyapunov equation AXA^H - X + Q = 0)
max@0:   
max@0:   template<typename eT>
max@0:   inline static bool dlyap(Mat<eT>& X, const Mat<eT>& A, const Mat<eT>& Q);
max@0:   };
max@0: 
max@0: 
max@0: //! @}