armadillo_matrix: auxlib_bones.hpp Source File

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00001 // Copyright (C) 2008-2011 NICTA (www.nicta.com.au)
00002 // Copyright (C) 2008-2011 Conrad Sanderson
00003 // Copyright (C)      2009 Edmund Highcock
00004 // Copyright (C)      2011 James Sanders
00005 // 
00006 // This file is part of the Armadillo C++ library.
00007 // It is provided without any warranty of fitness
00008 // for any purpose. You can redistribute this file
00009 // and/or modify it under the terms of the GNU
00010 // Lesser General Public License (LGPL) as published
00011 // by the Free Software Foundation, either version 3
00012 // of the License or (at your option) any later version.
00013 // (see http://www.opensource.org/licenses for more info)
00014 
00015 
00018 
00019 
00021 class auxlib
00022   {
00023   public:
00024   
00025   
00026   template<const uword row, const uword col>
00027   struct pos
00028     {
00029     static const uword n2 = row + col*2;
00030     static const uword n3 = row + col*3;
00031     static const uword n4 = row + col*4;
00032     };
00033   
00034   
00035   //
00036   // inv
00037   
00038   template<typename eT, typename T1>
00039   inline static bool inv(Mat<eT>& out, const Base<eT,T1>& X, const bool slow = false);
00040   
00041   template<typename eT>
00042   inline static bool inv(Mat<eT>& out, const Mat<eT>& A, const bool slow = false);
00043   
00044   template<typename eT>
00045   inline static bool inv_noalias_tinymat(Mat<eT>& out, const Mat<eT>& X, const uword N);
00046   
00047   template<typename eT>
00048   inline static bool inv_inplace_tinymat(Mat<eT>& out, const uword N);
00049   
00050   template<typename eT>
00051   inline static bool inv_inplace_lapack(Mat<eT>& out);
00052   
00053   
00054   //
00055   // inv_tr
00056   
00057   template<typename eT, typename T1>
00058   inline static bool inv_tr(Mat<eT>& out, const Base<eT,T1>& X, const uword layout);
00059   
00060   
00061   //
00062   // inv_sym
00063   
00064   template<typename eT, typename T1>
00065   inline static bool inv_sym(Mat<eT>& out, const Base<eT,T1>& X, const uword layout);
00066   
00067   
00068   //
00069   // inv_sympd
00070   
00071   template<typename eT, typename T1>
00072   inline static bool inv_sympd(Mat<eT>& out, const Base<eT,T1>& X, const uword layout);
00073   
00074   
00075   //
00076   // det
00077   
00078   template<typename eT, typename T1>
00079   inline static eT det(const Base<eT,T1>& X, const bool slow = false);
00080   
00081   template<typename eT>
00082   inline static eT det_tinymat(const Mat<eT>& X, const uword N);
00083   
00084   template<typename eT>
00085   inline static eT det_lapack(const Mat<eT>& X, const bool make_copy);
00086   
00087   
00088   //
00089   // log_det
00090   
00091   template<typename eT, typename T1>
00092   inline static bool log_det(eT& out_val, typename get_pod_type<eT>::result& out_sign, const Base<eT,T1>& X);
00093   
00094   
00095   //
00096   // lu
00097   
00098   template<typename eT, typename T1>
00099   inline static bool lu(Mat<eT>& L, Mat<eT>& U, podarray<blas_int>& ipiv, const Base<eT,T1>& X);
00100   
00101   template<typename eT, typename T1>
00102   inline static bool lu(Mat<eT>& L, Mat<eT>& U, Mat<eT>& P, const Base<eT,T1>& X);
00103   
00104   template<typename eT, typename T1>
00105   inline static bool lu(Mat<eT>& L, Mat<eT>& U, const Base<eT,T1>& X);
00106   
00107   
00108   //
00109   // eig
00110   
00111   template<typename eT, typename T1> 
00112   inline static bool eig_sym(Col<eT>& eigval, const Base<eT,T1>& X);
00113   
00114   template<typename T, typename T1> 
00115   inline static bool eig_sym(Col<T>& eigval, const Base<std::complex<T>,T1>& X);
00116   
00117   template<typename eT, typename T1>
00118   inline static bool eig_sym(Col<eT>& eigval, Mat<eT>& eigvec, const Base<eT,T1>& X);
00119   
00120   template<typename T, typename T1>
00121   inline static bool eig_sym(Col<T>& eigval, Mat< std::complex<T> >& eigvec, const Base<std::complex<T>,T1>& X);
00122   
00123   template<typename T, typename T1>
00124   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);
00125   
00126   template<typename T, typename T1>
00127   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);
00128   
00129   
00130   //
00131   // chol
00132   
00133   template<typename eT, typename T1>
00134   inline static bool chol(Mat<eT>& out, const Base<eT,T1>& X);
00135   
00136   
00137   //
00138   // qr
00139   
00140   template<typename eT, typename T1>
00141   inline static bool qr(Mat<eT>& Q, Mat<eT>& R, const Base<eT,T1>& X);
00142   
00143   
00144   //
00145   // svd
00146   
00147   template<typename eT, typename T1>
00148   inline static bool svd(Col<eT>& S, const Base<eT,T1>& X, uword& n_rows, uword& n_cols);
00149   
00150   template<typename T, typename T1>
00151   inline static bool svd(Col<T>& S, const Base<std::complex<T>, T1>& X, uword& n_rows, uword& n_cols);
00152   
00153   template<typename eT, typename T1>
00154   inline static bool svd(Col<eT>& S, const Base<eT,T1>& X);
00155   
00156   template<typename T, typename T1>
00157   inline static bool svd(Col<T>& S, const Base<std::complex<T>, T1>& X);
00158   
00159   template<typename eT, typename T1>
00160   inline static bool svd(Mat<eT>& U, Col<eT>& S, Mat<eT>& V, const Base<eT,T1>& X);
00161   
00162   template<typename T, typename T1>
00163   inline static bool svd(Mat< std::complex<T> >& U, Col<T>& S, Mat< std::complex<T> >& V, const Base< std::complex<T>, T1>& X);
00164   
00165   template<typename eT, typename T1>
00166   inline static bool svd_econ(Mat<eT>& U, Col<eT>& S, Mat<eT>& V, const Base<eT,T1>& X, const char mode);
00167   
00168   template<typename T, typename T1>
00169   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);
00170   
00171   
00172   //
00173   // solve
00174   
00175   template<typename eT>
00176   inline static bool solve   (Mat<eT>& out, Mat<eT>& A, const Mat<eT>& B, const bool slow = false);
00177   
00178   template<typename eT>
00179   inline static bool solve_od(Mat<eT>& out, Mat<eT>& A, const Mat<eT>& B);
00180   
00181   template<typename eT>
00182   inline static bool solve_ud(Mat<eT>& out, Mat<eT>& A, const Mat<eT>& B);
00183   
00184   
00185   //
00186   // solve_tr
00187   
00188   template<typename eT>
00189   inline static bool solve_tr(Mat<eT>& out, const Mat<eT>& A, const Mat<eT>& B, const uword layout);
00190 
00191 
00192   //
00193   // Schur decomposition
00194   
00195   template<typename eT>
00196   inline static bool schur_dec(Mat<eT>& Z, Mat<eT>& T, const Mat<eT>& A);
00197   
00198   template<typename cT>
00199   inline static bool schur_dec(Mat<std::complex<cT> >& Z, Mat<std::complex<cT> >& T, const Mat<std::complex<cT> >& A);
00200   
00201   
00202   //
00203   // syl (solution of the Sylvester equation AX + XB = C)
00204   
00205   template<typename eT>
00206   inline static bool syl(Mat<eT>& X, const Mat<eT>& A, const Mat<eT>& B, const Mat<eT>& C);
00207   
00208   
00209   //
00210   // lyap (solution of the continuous Lyapunov equation AX + XA^H + Q = 0)
00211   
00212   template<typename eT>
00213   inline static bool lyap(Mat<eT>& X, const Mat<eT>& A, const Mat<eT>& Q);
00214   
00215   
00216   //
00217   // dlyap (solution of the discrete Lyapunov equation AXA^H - X + Q = 0)
00218   
00219   template<typename eT>
00220   inline static bool dlyap(Mat<eT>& X, const Mat<eT>& A, const Mat<eT>& Q);
00221   };
00222 
00223