max@0: // Copyright (C) 2008-2010 NICTA (www.nicta.com.au)
max@0: // Copyright (C) 2008-2010 Conrad Sanderson
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 fn_trace
max@0: //! @{
max@0: 
max@0: 
max@0: //! Immediate trace (sum of diagonal elements) of a square dense matrix
max@0: template<typename T1>
max@0: inline
max@0: arma_warn_unused
max@0: typename T1::elem_type
max@0: trace(const Base<typename T1::elem_type,T1>& X)
max@0:   {
max@0:   arma_extra_debug_sigprint();
max@0:   
max@0:   typedef typename T1::elem_type eT;
max@0:   
max@0:   const Proxy<T1> A(X.get_ref());
max@0: 
max@0:   arma_debug_check( (A.get_n_rows() != A.get_n_cols()), "trace(): matrix must be square sized" );
max@0:   
max@0:   const uword N   = A.get_n_rows();
max@0:         eT  val = eT(0);
max@0:   
max@0:   for(uword i=0; i<N; ++i)
max@0:     {
max@0:     val += A.at(i,i);
max@0:     }
max@0:   
max@0:   return val;
max@0:   }
max@0: 
max@0: 
max@0: 
max@0: template<typename T1>
max@0: inline
max@0: arma_warn_unused
max@0: typename T1::elem_type
max@0: trace(const Op<T1, op_diagmat>& X)
max@0:   {
max@0:   arma_extra_debug_sigprint();
max@0:   
max@0:   typedef typename T1::elem_type eT;
max@0:   
max@0:   const diagmat_proxy<T1> A(X.m);
max@0:   
max@0:   const uword N = A.n_elem;
max@0:   
max@0:   eT val = eT(0);
max@0:   
max@0:   for(uword i=0; i<N; ++i)
max@0:     {
max@0:     val += A[i];
max@0:     }
max@0:   
max@0:   return val;
max@0:   }
max@0: 
max@0: 
max@0: //! speedup for trace(A*B), where the result of A*B is a square sized matrix
max@0: template<typename T1, typename T2>
max@0: inline
max@0: arma_warn_unused
max@0: typename T1::elem_type
max@0: trace(const Glue<T1, T2, glue_times>& X)
max@0:   {
max@0:   arma_extra_debug_sigprint();
max@0:   
max@0:   typedef typename T1::elem_type eT;
max@0:   
max@0:   const unwrap<T1> tmp1(X.A);
max@0:   const unwrap<T2> tmp2(X.B);
max@0:   
max@0:   const Mat<eT>& A = tmp1.M;
max@0:   const Mat<eT>& B = tmp2.M;
max@0:   
max@0:   arma_debug_assert_mul_size(A, B, "matrix multiply");
max@0:   
max@0:   arma_debug_check( (A.n_rows != B.n_cols), "trace(): matrix must be square sized" );
max@0:   
max@0:   const uword N1  = A.n_rows;
max@0:   const uword N2  = A.n_cols;
max@0:         eT  val = eT(0);
max@0:   
max@0:   for(uword i=0; i<N1; ++i)
max@0:     {
max@0:     const eT* B_colmem = B.colptr(i);
max@0:           eT  acc      = eT(0);
max@0:     
max@0:     for(uword j=0; j<N2; ++j)
max@0:       {
max@0:       acc += A.at(i,j) * B_colmem[j];
max@0:       }
max@0:     
max@0:     val += acc;
max@0:     }
max@0:   
max@0:   return val;
max@0:   }
max@0: 
max@0: 
max@0: 
max@0: //! @}