Chris@49: // Copyright (C) 2008-2012 NICTA (www.nicta.com.au)
Chris@49: // Copyright (C) 2008-2012 Conrad Sanderson
Chris@49: // 
Chris@49: // This Source Code Form is subject to the terms of the Mozilla Public
Chris@49: // License, v. 2.0. If a copy of the MPL was not distributed with this
Chris@49: // file, You can obtain one at http://mozilla.org/MPL/2.0/.
Chris@49: 
Chris@49: 
Chris@49: //! \addtogroup fn_norm
Chris@49: //! @{
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: template<typename T1>
Chris@49: arma_hot
Chris@49: inline
Chris@49: typename T1::pod_type
Chris@49: arma_vec_norm_1(const Proxy<T1>& P)
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49:   
Chris@49:   typedef typename T1::pod_type T;
Chris@49:   
Chris@49:   T acc = T(0);
Chris@49:   
Chris@49:   if(Proxy<T1>::prefer_at_accessor == false)
Chris@49:     {
Chris@49:     typename Proxy<T1>::ea_type A = P.get_ea();
Chris@49:     
Chris@49:     const uword N = P.get_n_elem();
Chris@49:     
Chris@49:     T acc1 = T(0);
Chris@49:     T acc2 = T(0);
Chris@49:     
Chris@49:     uword i,j;
Chris@49:     for(i=0, j=1; j<N; i+=2, j+=2)
Chris@49:       {
Chris@49:       acc1 += std::abs(A[i]);
Chris@49:       acc2 += std::abs(A[j]);
Chris@49:       }
Chris@49:     
Chris@49:     if(i < N)
Chris@49:       {
Chris@49:       acc1 += std::abs(A[i]);
Chris@49:       }
Chris@49:     
Chris@49:     acc = acc1 + acc2;
Chris@49:     }
Chris@49:   else
Chris@49:     {
Chris@49:     const uword n_rows = P.get_n_rows();
Chris@49:     const uword n_cols = P.get_n_cols();
Chris@49:     
Chris@49:     if(n_rows == 1)
Chris@49:       {
Chris@49:       for(uword col=0; col<n_cols; ++col)
Chris@49:         {
Chris@49:         acc += std::abs(P.at(0,col));
Chris@49:         }
Chris@49:       }
Chris@49:     else
Chris@49:       {
Chris@49:       for(uword col=0; col<n_cols; ++col)
Chris@49:         {
Chris@49:         uword i,j;
Chris@49:         
Chris@49:         for(i=0, j=1; j<n_rows; i+=2, j+=2)
Chris@49:           {
Chris@49:           acc += std::abs(P.at(i,col));
Chris@49:           acc += std::abs(P.at(j,col));
Chris@49:           }
Chris@49:         
Chris@49:         if(i < n_rows)
Chris@49:           {
Chris@49:           acc += std::abs(P.at(i,col));
Chris@49:           }
Chris@49:         }
Chris@49:       }
Chris@49:     }
Chris@49:     
Chris@49:   return acc;
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: template<typename T1>
Chris@49: arma_hot
Chris@49: inline
Chris@49: typename T1::pod_type
Chris@49: arma_vec_norm_2
Chris@49:   (
Chris@49:   const Proxy<T1>& P,
Chris@49:   const typename arma_not_cx<typename T1::elem_type>::result* junk = 0
Chris@49:   )
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49:   arma_ignore(junk);
Chris@49:   
Chris@49:   typedef typename T1::pod_type T;
Chris@49:   
Chris@49:   T acc = T(0);
Chris@49:   
Chris@49:   if(Proxy<T1>::prefer_at_accessor == false)
Chris@49:     {
Chris@49:     typename Proxy<T1>::ea_type A = P.get_ea();
Chris@49:     
Chris@49:     const uword N = P.get_n_elem();
Chris@49:     
Chris@49:     T acc1 = T(0);
Chris@49:     T acc2 = T(0);
Chris@49:     
Chris@49:     uword i,j;
Chris@49:     
Chris@49:     for(i=0, j=1; j<N; i+=2, j+=2)
Chris@49:       {
Chris@49:       const T tmp_i = A[i];
Chris@49:       const T tmp_j = A[j];
Chris@49:       
Chris@49:       acc1 += tmp_i * tmp_i;
Chris@49:       acc2 += tmp_j * tmp_j;
Chris@49:       }
Chris@49:     
Chris@49:     if(i < N)
Chris@49:       {
Chris@49:       const T tmp_i = A[i];
Chris@49:       
Chris@49:       acc1 += tmp_i * tmp_i;
Chris@49:       }
Chris@49:     
Chris@49:     acc = acc1 + acc2;
Chris@49:     }
Chris@49:   else
Chris@49:     {
Chris@49:     const uword n_rows = P.get_n_rows();
Chris@49:     const uword n_cols = P.get_n_cols();
Chris@49:     
Chris@49:     if(n_rows == 1)
Chris@49:       {
Chris@49:       for(uword col=0; col<n_cols; ++col)
Chris@49:         {
Chris@49:         const T tmp = P.at(0,col);
Chris@49:         
Chris@49:         acc += tmp * tmp;
Chris@49:         }
Chris@49:       }
Chris@49:     else
Chris@49:       {
Chris@49:       for(uword col=0; col<n_cols; ++col)
Chris@49:         {
Chris@49:         uword i,j;
Chris@49:         for(i=0, j=1; j<n_rows; i+=2, j+=2)
Chris@49:           {
Chris@49:           const T tmp_i = P.at(i,col);
Chris@49:           const T tmp_j = P.at(j,col);
Chris@49:           
Chris@49:           acc += tmp_i * tmp_i;
Chris@49:           acc += tmp_j * tmp_j;
Chris@49:           }
Chris@49:         
Chris@49:         if(i < n_rows)
Chris@49:           {
Chris@49:           const T tmp_i = P.at(i,col);
Chris@49:           
Chris@49:           acc += tmp_i * tmp_i;
Chris@49:           }
Chris@49:         }
Chris@49:       }
Chris@49:     }
Chris@49:   
Chris@49:   return std::sqrt(acc);
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: template<typename T1>
Chris@49: arma_hot
Chris@49: inline
Chris@49: typename T1::pod_type
Chris@49: arma_vec_norm_2
Chris@49:   (
Chris@49:   const Proxy<T1>& P,
Chris@49:   const typename arma_cx_only<typename T1::elem_type>::result* junk = 0
Chris@49:   )
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49:   arma_ignore(junk);
Chris@49:   
Chris@49:   typedef typename T1::pod_type T;
Chris@49:   
Chris@49:   T acc = T(0);
Chris@49:   
Chris@49:   if(Proxy<T1>::prefer_at_accessor == false)
Chris@49:     {
Chris@49:     typename Proxy<T1>::ea_type A = P.get_ea();
Chris@49:     
Chris@49:     const uword N = P.get_n_elem();
Chris@49:     
Chris@49:     for(uword i=0; i<N; ++i)
Chris@49:       {
Chris@49:       const T tmp = std::abs(A[i]);
Chris@49:       acc += tmp*tmp;
Chris@49:       }
Chris@49:     }
Chris@49:   else
Chris@49:     {
Chris@49:     const uword n_rows = P.get_n_rows();
Chris@49:     const uword n_cols = P.get_n_cols();
Chris@49:     
Chris@49:     if(n_rows == 1)
Chris@49:       {
Chris@49:       for(uword col=0; col<n_cols; ++col)
Chris@49:         {
Chris@49:         const T tmp = std::abs(P.at(0,col));
Chris@49:         acc += tmp*tmp;
Chris@49:         }
Chris@49:       }
Chris@49:     else
Chris@49:       {
Chris@49:       for(uword col=0; col<n_cols; ++col)
Chris@49:       for(uword row=0; row<n_rows; ++row)
Chris@49:         {
Chris@49:         const T tmp = std::abs(P.at(row,col));
Chris@49:         acc += tmp*tmp;
Chris@49:         }
Chris@49:       }
Chris@49:     }
Chris@49:   
Chris@49:   return std::sqrt(acc);
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: template<typename T1>
Chris@49: arma_hot
Chris@49: inline
Chris@49: typename T1::pod_type
Chris@49: arma_vec_norm_k
Chris@49:   (
Chris@49:   const Proxy<T1>& P,
Chris@49:   const int k
Chris@49:   )
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49:   
Chris@49:   typedef typename T1::pod_type T;
Chris@49:   
Chris@49:   T acc = T(0);
Chris@49:   
Chris@49:   if(Proxy<T1>::prefer_at_accessor == false)
Chris@49:     {
Chris@49:     typename Proxy<T1>::ea_type A = P.get_ea();
Chris@49:     
Chris@49:     const uword N = P.get_n_elem();
Chris@49:     
Chris@49:     uword i,j;
Chris@49:     
Chris@49:     for(i=0, j=1; j<N; i+=2, j+=2)
Chris@49:       {
Chris@49:       acc += std::pow(std::abs(A[i]), k);
Chris@49:       acc += std::pow(std::abs(A[j]), k);
Chris@49:       }
Chris@49:     
Chris@49:     if(i < N)
Chris@49:       {
Chris@49:       acc += std::pow(std::abs(A[i]), k);
Chris@49:       }
Chris@49:     }
Chris@49:   else
Chris@49:     {
Chris@49:     const uword n_rows = P.get_n_rows();
Chris@49:     const uword n_cols = P.get_n_cols();
Chris@49:     
Chris@49:     if(n_rows != 1)
Chris@49:       {
Chris@49:       for(uword col=0; col < n_cols; ++col)
Chris@49:       for(uword row=0; row < n_rows; ++row)
Chris@49:         {
Chris@49:         acc += std::pow(std::abs(P.at(row,col)), k);
Chris@49:         }
Chris@49:       }
Chris@49:     else
Chris@49:       {
Chris@49:       for(uword col=0; col < n_cols; ++col)
Chris@49:         {
Chris@49:         acc += std::pow(std::abs(P.at(0,col)), k);
Chris@49:         }
Chris@49:       }
Chris@49:     }
Chris@49:   
Chris@49:   return std::pow(acc, T(1)/T(k));
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: template<typename T1>
Chris@49: arma_hot
Chris@49: inline
Chris@49: typename T1::pod_type
Chris@49: arma_vec_norm_max(const Proxy<T1>& P)
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49:   
Chris@49:   typedef typename T1::pod_type T;
Chris@49:   
Chris@49:   const uword N = P.get_n_elem();
Chris@49:   
Chris@49:   T max_val = (N != 1) ? priv::most_neg<T>() : std::abs(P[0]);
Chris@49:   
Chris@49:   if(Proxy<T1>::prefer_at_accessor == false)
Chris@49:     {
Chris@49:     typename Proxy<T1>::ea_type A = P.get_ea();
Chris@49:     
Chris@49:     uword i,j;
Chris@49:     for(i=0, j=1; j<N; i+=2, j+=2)
Chris@49:       {
Chris@49:       const T tmp_i = std::abs(A[i]);
Chris@49:       const T tmp_j = std::abs(A[j]);
Chris@49:       
Chris@49:       if(max_val < tmp_i) { max_val = tmp_i; }
Chris@49:       if(max_val < tmp_j) { max_val = tmp_j; }
Chris@49:       }
Chris@49:     
Chris@49:     if(i < N)
Chris@49:       {
Chris@49:       const T tmp_i = std::abs(A[i]);
Chris@49:       
Chris@49:       if(max_val < tmp_i) { max_val = tmp_i; }
Chris@49:       }
Chris@49:     }
Chris@49:   else
Chris@49:     {
Chris@49:     const uword n_rows = P.get_n_rows();
Chris@49:     const uword n_cols = P.get_n_cols();
Chris@49:     
Chris@49:     if(n_rows != 1)
Chris@49:       {
Chris@49:       for(uword col=0; col < n_cols; ++col)
Chris@49:       for(uword row=0; row < n_rows; ++row)
Chris@49:         {
Chris@49:         const T tmp = std::abs(P.at(row,col));
Chris@49:         
Chris@49:         if(max_val < tmp) { max_val = tmp; }
Chris@49:         }
Chris@49:       }
Chris@49:     else
Chris@49:       {
Chris@49:       for(uword col=0; col < n_cols; ++col)
Chris@49:         {
Chris@49:         const T tmp = std::abs(P.at(0,col));
Chris@49:         
Chris@49:         if(max_val < tmp) { max_val = tmp; }
Chris@49:         }
Chris@49:       }
Chris@49:     }
Chris@49:   
Chris@49:   return max_val;
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: template<typename T1>
Chris@49: arma_hot
Chris@49: inline
Chris@49: typename T1::pod_type
Chris@49: arma_vec_norm_min(const Proxy<T1>& P)
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49:   
Chris@49:   typedef typename T1::pod_type T;
Chris@49:   
Chris@49:   const uword N = P.get_n_elem();
Chris@49:   
Chris@49:   T min_val = (N != 1) ? priv::most_pos<T>() : std::abs(P[0]);
Chris@49:   
Chris@49:   if(Proxy<T1>::prefer_at_accessor == false)
Chris@49:     {
Chris@49:     typename Proxy<T1>::ea_type A = P.get_ea();
Chris@49:     
Chris@49:     uword i,j;
Chris@49:     for(i=0, j=1; j<N; i+=2, j+=2)
Chris@49:       {
Chris@49:       const T tmp_i = std::abs(A[i]);
Chris@49:       const T tmp_j = std::abs(A[j]);
Chris@49:       
Chris@49:       if(min_val > tmp_i) { min_val = tmp_i; }
Chris@49:       if(min_val > tmp_j) { min_val = tmp_j; }
Chris@49:       }
Chris@49:     
Chris@49:     if(i < N)
Chris@49:       {
Chris@49:       const T tmp_i = std::abs(A[i]);
Chris@49:       
Chris@49:       if(min_val > tmp_i) { min_val = tmp_i; }
Chris@49:       }
Chris@49:     }
Chris@49:   else
Chris@49:     {
Chris@49:     const uword n_rows = P.get_n_rows();
Chris@49:     const uword n_cols = P.get_n_cols();
Chris@49:     
Chris@49:     if(n_rows != 1)
Chris@49:       {
Chris@49:       for(uword col=0; col < n_cols; ++col)
Chris@49:       for(uword row=0; row < n_rows; ++row)
Chris@49:         {
Chris@49:         const T tmp = std::abs(P.at(row,col));
Chris@49:         
Chris@49:         if(min_val > tmp) { min_val = tmp; }
Chris@49:         }
Chris@49:       }
Chris@49:     else
Chris@49:       {
Chris@49:       for(uword col=0; col < n_cols; ++col)
Chris@49:         {
Chris@49:         const T tmp = std::abs(P.at(0,col));
Chris@49:         
Chris@49:         if(min_val > tmp) { min_val = tmp; }
Chris@49:         }
Chris@49:       }
Chris@49:     }
Chris@49:   
Chris@49:   return min_val;
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: template<typename T1>
Chris@49: inline
Chris@49: typename T1::pod_type
Chris@49: arma_mat_norm_1(const Proxy<T1>& P)
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49:   
Chris@49:   // TODO: this can be sped up with a dedicated implementation
Chris@49:   return as_scalar( max( sum(abs(P.Q), 0), 1) );
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: template<typename T1>
Chris@49: inline
Chris@49: typename T1::pod_type
Chris@49: arma_mat_norm_2(const Proxy<T1>& P)
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49:   
Chris@49:   typedef typename T1::pod_type   T;
Chris@49:   
Chris@49:   // TODO: is the SVD based approach only valid for square matrices?
Chris@49:   
Chris@49:   Col<T> S;
Chris@49:   svd(S, P.Q);
Chris@49:   
Chris@49:   return (S.n_elem > 0) ? max(S) : T(0);
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: template<typename T1>
Chris@49: inline
Chris@49: typename T1::pod_type
Chris@49: arma_mat_norm_inf(const Proxy<T1>& P)
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49:   
Chris@49:   // TODO: this can be sped up with a dedicated implementation
Chris@49:   return as_scalar( max( sum(abs(P.Q), 1), 0) );
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: template<typename T1>
Chris@49: inline
Chris@49: arma_warn_unused
Chris@49: typename enable_if2< is_arma_type<T1>::value, typename T1::pod_type >::result
Chris@49: norm
Chris@49:   (
Chris@49:   const T1& X,
Chris@49:   const uword k,
Chris@49:   const typename arma_real_or_cx_only<typename T1::elem_type>::result* junk = 0
Chris@49:   )
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49:   arma_ignore(junk);
Chris@49:   
Chris@49:   typedef typename T1::pod_type T;
Chris@49:   
Chris@49:   const Proxy<T1> P(X);
Chris@49:   
Chris@49:   if(P.get_n_elem() == 0)
Chris@49:     {
Chris@49:     return T(0);
Chris@49:     }
Chris@49:   
Chris@49:   const bool is_vec = (P.get_n_rows() == 1) || (P.get_n_cols() == 1);
Chris@49:   
Chris@49:   if(is_vec == true)
Chris@49:     {
Chris@49:     switch(k)
Chris@49:       {
Chris@49:       case 1:
Chris@49:         return arma_vec_norm_1(P);
Chris@49:         break;
Chris@49:       
Chris@49:       case 2:
Chris@49:         return arma_vec_norm_2(P);
Chris@49:         break;
Chris@49:       
Chris@49:       default:
Chris@49:         {
Chris@49:         arma_debug_check( (k == 0), "norm(): k must be greater than zero"   );
Chris@49:         return arma_vec_norm_k(P, int(k));
Chris@49:         }
Chris@49:       }
Chris@49:     }
Chris@49:   else
Chris@49:     {
Chris@49:     switch(k)
Chris@49:       {
Chris@49:       case 1:
Chris@49:         return arma_mat_norm_1(P);
Chris@49:         break;
Chris@49:       
Chris@49:       case 2:
Chris@49:         return arma_mat_norm_2(P);
Chris@49:         break;
Chris@49:       
Chris@49:       default:
Chris@49:         arma_stop("norm(): unsupported matrix norm type");
Chris@49:         return T(0);
Chris@49:       }
Chris@49:     }
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: template<typename T1>
Chris@49: inline
Chris@49: arma_warn_unused
Chris@49: typename enable_if2< is_arma_type<T1>::value, typename T1::pod_type >::result
Chris@49: norm
Chris@49:   (
Chris@49:   const T1& X,
Chris@49:   const char* method,
Chris@49:   const typename arma_real_or_cx_only<typename T1::elem_type>::result* junk = 0
Chris@49:   )
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49:   arma_ignore(junk);
Chris@49:   
Chris@49:   typedef typename T1::pod_type T;
Chris@49:   
Chris@49:   const Proxy<T1> P(X);
Chris@49:   
Chris@49:   if(P.get_n_elem() == 0)
Chris@49:     {
Chris@49:     return T(0);
Chris@49:     }
Chris@49:   
Chris@49:   const char sig    = method[0];
Chris@49:   const bool is_vec = (P.get_n_rows() == 1) || (P.get_n_cols() == 1);
Chris@49:   
Chris@49:   if(is_vec == true)
Chris@49:     {
Chris@49:     if( (sig == 'i') || (sig == 'I') || (sig == '+') )   // max norm
Chris@49:       {
Chris@49:       return arma_vec_norm_max(P);
Chris@49:       }
Chris@49:     else
Chris@49:     if(sig == '-')   // min norm
Chris@49:       {
Chris@49:       return arma_vec_norm_min(P);
Chris@49:       }
Chris@49:     else
Chris@49:     if( (sig == 'f') || (sig == 'F') )
Chris@49:       {
Chris@49:       return arma_vec_norm_2(P);
Chris@49:       }
Chris@49:     else
Chris@49:       {
Chris@49:       arma_stop("norm(): unsupported vector norm type");
Chris@49:       return T(0);
Chris@49:       }
Chris@49:     }
Chris@49:   else
Chris@49:     {
Chris@49:     if( (sig == 'i') || (sig == 'I') || (sig == '+') )   // inf norm
Chris@49:       {
Chris@49:       return arma_mat_norm_inf(P);
Chris@49:       }
Chris@49:     else
Chris@49:     if( (sig == 'f') || (sig == 'F') )
Chris@49:       {
Chris@49:       return arma_vec_norm_2(P);
Chris@49:       }
Chris@49:     else
Chris@49:       {
Chris@49:       arma_stop("norm(): unsupported matrix norm type");
Chris@49:       return T(0);
Chris@49:       }
Chris@49:     }
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: //
Chris@49: // norms for sparse matrices
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: template<typename T1>
Chris@49: inline
Chris@49: typename T1::pod_type
Chris@49: arma_mat_norm_1(const SpProxy<T1>& P)
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49:   
Chris@49:   // TODO: this can be sped up with a dedicated implementation
Chris@49:   return as_scalar( max( sum(abs(P.Q), 0), 1) );
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: // template<typename T1>
Chris@49: // inline
Chris@49: // typename T1::pod_type
Chris@49: // arma_mat_norm_2(const SpProxy<T1>& P)
Chris@49: //   {
Chris@49: //   arma_extra_debug_sigprint();
Chris@49: //   
Chris@49: //   // TODO: norm = sqrt( largest eigenvalue of (A^H)*A ), where ^H is the conjugate transpose
Chris@49: //   // TODO: can use ARPACK or directly implement the Arnoldi iteration
Chris@49: //   // http://math.stackexchange.com/questions/4368/computing-the-largest-eigenvalue-of-a-very-large-sparse-matrix
Chris@49: //   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: template<typename T1>
Chris@49: inline
Chris@49: typename T1::pod_type
Chris@49: arma_mat_norm_inf(const SpProxy<T1>& P)
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49:   
Chris@49:   // TODO: this can be sped up with a dedicated implementation
Chris@49:   return as_scalar( max( sum(abs(P.Q), 1), 0) );
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: template<typename T1>
Chris@49: inline
Chris@49: arma_warn_unused
Chris@49: typename enable_if2< is_arma_sparse_type<T1>::value, typename T1::pod_type >::result
Chris@49: norm
Chris@49:   (
Chris@49:   const T1& X,
Chris@49:   const uword k,
Chris@49:   const typename arma_real_or_cx_only<typename T1::elem_type>::result* junk = 0
Chris@49:   )
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49:   arma_ignore(junk);
Chris@49:   
Chris@49:   typedef typename T1::elem_type eT;
Chris@49:   typedef typename T1::pod_type   T;
Chris@49:   
Chris@49:   const SpProxy<T1> P(X);
Chris@49:   
Chris@49:   if(P.get_n_nonzero() == 0)
Chris@49:     {
Chris@49:     return T(0);
Chris@49:     }
Chris@49:   
Chris@49:   const bool is_vec = (P.get_n_rows() == 1) || (P.get_n_cols() == 1);
Chris@49:   
Chris@49:   if(is_vec == true)
Chris@49:     {
Chris@49:     const unwrap_spmat<typename SpProxy<T1>::stored_type> tmp(P.Q);
Chris@49:     const SpMat<eT>& A = tmp.M;
Chris@49:     
Chris@49:     // create a fake dense vector to allow reuse of code for dense vectors
Chris@49:     Col<eT> fake_vector( access::rwp(A.values), A.n_nonzero, false );
Chris@49:     
Chris@49:     const Proxy< Col<eT> > P_fake_vector(fake_vector);
Chris@49:     
Chris@49:     switch(k)
Chris@49:       {
Chris@49:       case 1:
Chris@49:         return arma_vec_norm_1(P_fake_vector);
Chris@49:         break;
Chris@49:       
Chris@49:       case 2:
Chris@49:         return arma_vec_norm_2(P_fake_vector);
Chris@49:         break;
Chris@49:       
Chris@49:       default:
Chris@49:         {
Chris@49:         arma_debug_check( (k == 0), "norm(): k must be greater than zero"   );
Chris@49:         return arma_vec_norm_k(P_fake_vector, int(k));
Chris@49:         }
Chris@49:       }
Chris@49:     }
Chris@49:   else
Chris@49:     {
Chris@49:     switch(k)
Chris@49:       {
Chris@49:       case 1:
Chris@49:         return arma_mat_norm_1(P);
Chris@49:         break;
Chris@49:       
Chris@49:       // case 2:
Chris@49:       //   return arma_mat_norm_2(P);
Chris@49:       //   break;
Chris@49:       
Chris@49:       default:
Chris@49:         arma_stop("norm(): unsupported or unimplemented norm type for sparse matrices");
Chris@49:         return T(0);
Chris@49:       }
Chris@49:     }
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: template<typename T1>
Chris@49: inline
Chris@49: arma_warn_unused
Chris@49: typename enable_if2< is_arma_sparse_type<T1>::value, typename T1::pod_type >::result
Chris@49: norm
Chris@49:   (
Chris@49:   const T1& X,
Chris@49:   const char* method,
Chris@49:   const typename arma_real_or_cx_only<typename T1::elem_type>::result* junk = 0
Chris@49:   )
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49:   arma_ignore(junk);
Chris@49:   
Chris@49:   typedef typename T1::elem_type eT;
Chris@49:   typedef typename T1::pod_type   T;
Chris@49:   
Chris@49:   const SpProxy<T1> P(X);
Chris@49:   
Chris@49:   if(P.get_n_nonzero() == 0)
Chris@49:     {
Chris@49:     return T(0);
Chris@49:     }
Chris@49:   
Chris@49:   
Chris@49:   const unwrap_spmat<typename SpProxy<T1>::stored_type> tmp(P.Q);
Chris@49:   const SpMat<eT>& A = tmp.M;
Chris@49:   
Chris@49:   // create a fake dense vector to allow reuse of code for dense vectors
Chris@49:   Col<eT> fake_vector( access::rwp(A.values), A.n_nonzero, false );
Chris@49:   
Chris@49:   const Proxy< Col<eT> > P_fake_vector(fake_vector);
Chris@49:   
Chris@49:   
Chris@49:   const char sig    = method[0];
Chris@49:   const bool is_vec = (P.get_n_rows() == 1) || (P.get_n_cols() == 1);
Chris@49:   
Chris@49:   if(is_vec == true)
Chris@49:     {
Chris@49:     if( (sig == 'i') || (sig == 'I') || (sig == '+') )   // max norm
Chris@49:       {
Chris@49:       return arma_vec_norm_max(P_fake_vector);
Chris@49:       }
Chris@49:     else
Chris@49:     if(sig == '-')   // min norm
Chris@49:       {
Chris@49:       const T val = arma_vec_norm_min(P_fake_vector);
Chris@49:       
Chris@49:       if( P.get_n_nonzero() < P.get_n_elem() )
Chris@49:         {
Chris@49:         return (std::min)(T(0), val);
Chris@49:         }
Chris@49:       else
Chris@49:         {
Chris@49:         return val;
Chris@49:         }
Chris@49:       }
Chris@49:     else
Chris@49:     if( (sig == 'f') || (sig == 'F') )
Chris@49:       {
Chris@49:       return arma_vec_norm_2(P_fake_vector);
Chris@49:       }
Chris@49:     else
Chris@49:       {
Chris@49:       arma_stop("norm(): unsupported vector norm type");
Chris@49:       return T(0);
Chris@49:       }
Chris@49:     }
Chris@49:   else
Chris@49:     {
Chris@49:     if( (sig == 'i') || (sig == 'I') || (sig == '+') )   // inf norm
Chris@49:       {
Chris@49:       return arma_mat_norm_inf(P);
Chris@49:       }
Chris@49:     else
Chris@49:     if( (sig == 'f') || (sig == 'F') )
Chris@49:       {
Chris@49:       return arma_vec_norm_2(P_fake_vector);
Chris@49:       }
Chris@49:     else
Chris@49:       {
Chris@49:       arma_stop("norm(): unsupported matrix norm type");
Chris@49:       return T(0);
Chris@49:       }
Chris@49:     }
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: //! @}