comparison armadillo-2.4.4/include/armadillo_bits/fn_norm.hpp @ 0:8b6102e2a9b0

Armadillo Library

+// Copyright (C) 2008-2011 NICTA (www.nicta.com.au)
+// Copyright (C) 2008-2011 Conrad Sanderson
+// 
+// This file is part of the Armadillo C++ library.
+// It is provided without any warranty of fitness
+// for any purpose. You can redistribute this file
+// and/or modify it under the terms of the GNU
+// Lesser General Public License (LGPL) as published
+// by the Free Software Foundation, either version 3
+// of the License or (at your option) any later version.
+// (see http://www.opensource.org/licenses for more info)
+
+
+//! \addtogroup fn_norm
+//! @{
+
+
+
+template<typename T1>
+arma_hot
+inline
+typename T1::pod_type
+arma_vec_norm_1(const Proxy<T1>& A)
+  {
+  arma_extra_debug_sigprint();
+  
+  typedef typename T1::pod_type T;
+
+  T acc = T(0);
+    
+  if(Proxy<T1>::prefer_at_accessor == false)
+    {
+    typename Proxy<T1>::ea_type P = A.get_ea();
+    
+    const uword N = A.get_n_elem();
+    
+    uword i,j;
+    
+    for(i=0, j=1; j<N; i+=2, j+=2)
+      {
+      acc += std::abs(P[i]);
+      acc += std::abs(P[j]);
+      }
+    
+    if(i < N)
+      {
+      acc += std::abs(P[i]);
+      }
+    }
+  else
+    {
+    const uword n_rows = A.get_n_rows();
+    const uword n_cols = A.get_n_cols();
+    
+    for(uword col=0; col<n_cols; ++col)
+      {
+      uword i,j;
+      
+      for(i=0, j=1; j<n_rows; i+=2, j+=2)
+        {
+        acc += std::abs(A.at(i,col));
+        acc += std::abs(A.at(j,col));
+        }
+      
+      if(i < n_rows)
+        {
+        acc += std::abs(A.at(i,col));
+        }
+      }
+    }
+    
+  return acc;
+  }
+
+
+
+template<typename T1>
+arma_hot
+inline
+typename T1::pod_type
+arma_vec_norm_2(const Proxy<T1>& A, const typename arma_not_cx<typename T1::elem_type>::result* junk = 0)
+  {
+  arma_extra_debug_sigprint();
+  arma_ignore(junk);
+  
+  typedef typename T1::pod_type T;
+  
+  T acc = T(0);
+  
+  if(Proxy<T1>::prefer_at_accessor == false)
+    {
+    typename Proxy<T1>::ea_type P = A.get_ea();
+    
+    const uword N = A.get_n_elem();
+    
+    uword i,j;
+    
+    for(i=0, j=1; j<N; i+=2, j+=2)
+      {
+      const T tmp_i = P[i];
+      const T tmp_j = P[j];
+      
+      acc += tmp_i * tmp_i;
+      acc += tmp_j * tmp_j;
+      }
+    
+    if(i < N)
+      {
+      const T tmp_i = P[i];
+      
+      acc += tmp_i * tmp_i;
+      }
+    }
+  else
+    {
+    const uword n_rows = A.get_n_rows();
+    const uword n_cols = A.get_n_cols();
+    
+    for(uword col=0; col<n_cols; ++col)
+      {
+      uword i,j;
+      
+      for(i=0, j=1; j<n_rows; i+=2, j+=2)
+        {
+        const T tmp_i = A.at(i,col);
+        const T tmp_j = A.at(j,col);
+        
+        acc += tmp_i * tmp_i;
+        acc += tmp_j * tmp_j;
+        }
+      
+      if(i < n_rows)
+        {
+        const T tmp_i = A.at(i,col);
+        
+        acc += tmp_i * tmp_i;
+        }
+      }
+    }
+  
+  return std::sqrt(acc);
+  }
+
+
+
+template<typename T1>
+arma_hot
+inline
+typename T1::pod_type
+arma_vec_norm_2(const Proxy<T1>& A, const typename arma_cx_only<typename T1::elem_type>::result* junk = 0)
+  {
+  arma_extra_debug_sigprint();
+  arma_ignore(junk);
+  
+  typedef typename T1::pod_type T;
+  
+  T acc = T(0);
+  
+  if(Proxy<T1>::prefer_at_accessor == false)
+    {
+    typename Proxy<T1>::ea_type P = A.get_ea();
+    
+    const uword N = A.get_n_elem();
+    
+    for(uword i=0; i<N; ++i)
+      {
+      const T tmp = std::abs(P[i]);
+      acc += tmp*tmp;
+      }
+    }
+  else
+    {
+    const uword n_rows = A.get_n_rows();
+    const uword n_cols = A.get_n_cols();
+    
+    for(uword col=0; col<n_cols; ++col)
+    for(uword row=0; row<n_rows; ++row)
+      {
+      const T tmp = std::abs(A.at(row,col));
+      acc += tmp*tmp;
+      }
+    }
+  
+  return std::sqrt(acc);
+  }
+
+
+
+template<typename T1>
+arma_hot
+inline
+typename T1::pod_type
+arma_vec_norm_k(const Proxy<T1>& A, const int k)
+  {
+  arma_extra_debug_sigprint();
+  
+  typedef typename T1::pod_type T;
+  
+  T acc = T(0);
+  
+  if(Proxy<T1>::prefer_at_accessor == false)
+    {
+    typename Proxy<T1>::ea_type P = A.get_ea();
+    
+    const uword N = A.get_n_elem();
+    
+    uword i,j;
+    
+    for(i=0, j=1; j<N; i+=2, j+=2)
+      {
+      acc += std::pow(std::abs(P[i]), k);
+      acc += std::pow(std::abs(P[j]), k);
+      }
+    
+    if(i < N)
+      {
+      acc += std::pow(std::abs(P[i]), k);
+      }
+    }
+  else
+    {
+    const uword n_rows = A.get_n_rows();
+    const uword n_cols = A.get_n_cols();
+    
+    for(uword col=0; col<n_cols; ++col)
+    for(uword row=0; row<n_rows; ++row)
+      {
+      acc += std::pow(std::abs(A.at(row,col)), k);
+      }
+    }
+  
+  return std::pow(acc, T(1)/T(k));
+  }
+
+
+
+template<typename T1>
+arma_hot
+inline
+typename T1::pod_type
+arma_vec_norm_max(const Proxy<T1>& A)
+  {
+  arma_extra_debug_sigprint();
+  
+  typedef typename T1::pod_type       T;
+  typedef typename Proxy<T1>::ea_type ea_type;
+  
+        ea_type P = A.get_ea();
+  const uword     N = A.get_n_elem();
+  
+  T max_val = (N != 1) ? priv::most_neg<T>() : std::abs(P[0]);
+  
+  uword i,j;
+  
+  for(i=0, j=1; j<N; i+=2, j+=2)
+    {
+    const T tmp_i = std::abs(P[i]);
+    const T tmp_j = std::abs(P[j]);
+    
+    if(max_val < tmp_i) { max_val = tmp_i; }
+    if(max_val < tmp_j) { max_val = tmp_j; }
+    }
+  
+  if(i < N)
+    {
+    const T tmp_i = std::abs(P[i]);
+    
+    if(max_val < tmp_i) { max_val = tmp_i; }
+    }
+  
+  return max_val;
+  }
+
+
+
+template<typename T1>
+arma_hot
+inline
+typename T1::pod_type
+arma_vec_norm_min(const Proxy<T1>& A)
+  {
+  arma_extra_debug_sigprint();
+  
+  typedef typename T1::pod_type       T;
+  typedef typename Proxy<T1>::ea_type ea_type;
+  
+        ea_type P = A.get_ea();
+  const uword     N = A.get_n_elem();
+  
+  T min_val = (N != 1) ? priv::most_pos<T>() : std::abs(P[0]);
+  
+  uword i,j;
+  
+  for(i=0, j=1; j<N; i+=2, j+=2)
+    {
+    const T tmp_i = std::abs(P[i]);
+    const T tmp_j = std::abs(P[j]);
+    
+    if(min_val > tmp_i) { min_val = tmp_i; }
+    if(min_val > tmp_j) { min_val = tmp_j; }
+    }
+  
+  if(i < N)
+    {
+    const T tmp_i = std::abs(P[i]);
+    
+    if(min_val > tmp_i) { min_val = tmp_i; }
+    }
+  
+  return min_val;
+  }
+
+
+
+template<typename T1>
+inline
+typename T1::pod_type
+arma_mat_norm_1(const Proxy<T1>& A)
+  {
+  arma_extra_debug_sigprint();
+  
+  typedef typename T1::elem_type eT;
+  typedef typename T1::pod_type   T;
+  
+  const unwrap<typename Proxy<T1>::stored_type> tmp(A.Q);
+  const Mat<eT>& X = tmp.M;
+  
+  // TODO: this can be sped up with a dedicated implementation
+  return as_scalar( max( sum(abs(X)), 1) );
+  }
+
+
+
+template<typename T1>
+inline
+typename T1::pod_type
+arma_mat_norm_2(const Proxy<T1>& A)
+  {
+  arma_extra_debug_sigprint();
+  
+  typedef typename T1::elem_type eT;
+  typedef typename T1::pod_type   T;
+  
+  const unwrap<typename Proxy<T1>::stored_type> tmp(A.Q);
+  const Mat<eT>& X = tmp.M;
+  
+  Col<T> S;
+  svd(S, X);
+  
+  return (S.n_elem > 0) ? max(S) : T(0);
+  }
+
+
+
+template<typename T1>
+inline
+typename T1::pod_type
+arma_mat_norm_inf(const Proxy<T1>& A)
+  {
+  arma_extra_debug_sigprint();
+  
+  typedef typename T1::elem_type eT;
+  typedef typename T1::pod_type   T;
+  
+  const unwrap<typename Proxy<T1>::stored_type> tmp(A.Q);
+  const Mat<eT>& X = tmp.M;
+  
+  // TODO: this can be sped up with a dedicated implementation
+  return as_scalar( max( sum(abs(X),1) ) );
+  }
+
+
+
+template<typename T1>
+inline
+arma_warn_unused
+typename T1::pod_type
+norm
+  (
+  const Base<typename T1::elem_type,T1>& X,
+  const uword k,
+  const typename arma_float_or_cx_only<typename T1::elem_type>::result* junk = 0
+  )
+  {
+  arma_extra_debug_sigprint();
+  arma_ignore(junk);
+  
+  typedef typename T1::elem_type eT;
+  typedef typename T1::pod_type   T;
+  
+  const Proxy<T1> A(X.get_ref());
+  
+  if(A.get_n_elem() == 0)
+    {
+    return T(0);
+    }
+  
+  const bool is_vec = (A.get_n_rows() == 1) || (A.get_n_cols() == 1);
+  
+  if(is_vec == true)
+    {
+    switch(k)
+      {
+      case 1:
+        return arma_vec_norm_1(A);
+        break;
+      
+      case 2:
+        return arma_vec_norm_2(A);
+        break;
+      
+      default:
+        {
+        arma_debug_check( (k == 0), "norm(): k must be greater than zero"   );
+        return arma_vec_norm_k(A, int(k));
+        }
+      }
+    }
+  else
+    {
+    switch(k)
+      {
+      case 1:
+        return arma_mat_norm_1(A);
+        break;
+      
+      case 2:
+        return arma_mat_norm_2(A);
+        break;
+      
+      default:
+        arma_stop("norm(): unsupported matrix norm type");
+        return T(0);
+      }
+    }
+  }
+
+
+
+template<typename T1>
+inline
+arma_warn_unused
+typename T1::pod_type
+norm
+  (
+  const Base<typename T1::elem_type,T1>& X,
+  const char* method,
+  const typename arma_float_or_cx_only<typename T1::elem_type>::result* junk = 0
+  )
+  {
+  arma_extra_debug_sigprint();
+  arma_ignore(junk);
+  
+  typedef typename T1::elem_type eT;
+  typedef typename T1::pod_type   T;
+  
+  const Proxy<T1> A(X.get_ref());
+  
+  if(A.get_n_elem() == 0)
+    {
+    return T(0);
+    }
+  
+  const char sig    = method[0];
+  const bool is_vec = (A.get_n_rows() == 1) || (A.get_n_cols() == 1);
+  
+  if(is_vec == true)
+    {
+    if( (sig == 'i') || (sig == 'I') || (sig == '+') )   // max norm
+      {
+      return arma_vec_norm_max(A);
+      }
+    else
+    if(sig == '-')   // min norm
+      {
+      return arma_vec_norm_min(A);
+      }
+    else
+    if( (sig == 'f') || (sig == 'F') )
+      {
+      return arma_vec_norm_2(A);
+      }
+    else
+      {
+      arma_stop("norm(): unsupported vector norm type");
+      return T(0);
+      }
+    }
+  else
+    {
+    if( (sig == 'i') || (sig == 'I') || (sig == '+') )   // inf norm
+      {
+      return arma_mat_norm_inf(A);
+      }
+    else
+    if( (sig == 'f') || (sig == 'F') )
+      {
+      return arma_vec_norm_2(A);
+      }
+    else
+      {
+      arma_stop("norm(): unsupported matrix norm type");
+      return T(0);
+      }
+    }
+  }
+
+
+
+//! @}