max@0: // Copyright (C) 2009-2011 NICTA (www.nicta.com.au)
max@0: // Copyright (C) 2009-2011 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 op_var
max@0: //! @{
max@0: 
max@0: 
max@0: //! find the variance of an array
max@0: template<typename eT>
max@0: inline
max@0: eT
max@0: op_var::direct_var(const eT* const X, const uword n_elem, const uword norm_type)
max@0:   {
max@0:   arma_extra_debug_sigprint();
max@0:   
max@0:   if(n_elem >= 2)
max@0:     {
max@0:     const eT acc1 = op_mean::direct_mean(X, n_elem);
max@0:     
max@0:     eT acc2 = eT(0);
max@0:     eT acc3 = eT(0);
max@0:     
max@0:     uword i,j;
max@0:     
max@0:     for(i=0, j=1; j<n_elem; i+=2, j+=2)
max@0:       {
max@0:       const eT Xi = X[i];
max@0:       const eT Xj = X[j];
max@0:       
max@0:       const eT tmpi = acc1 - Xi;
max@0:       const eT tmpj = acc1 - Xj;
max@0:       
max@0:       acc2 += tmpi*tmpi + tmpj*tmpj;
max@0:       acc3 += tmpi      + tmpj;
max@0:       }
max@0:     
max@0:     if(i < n_elem)
max@0:       {
max@0:       const eT Xi = X[i];
max@0:       
max@0:       const eT tmpi = acc1 - Xi;
max@0:       
max@0:       acc2 += tmpi*tmpi;
max@0:       acc3 += tmpi;
max@0:       }
max@0:     
max@0:     const eT norm_val = (norm_type == 0) ? eT(n_elem-1) : eT(n_elem);
max@0:     const eT var_val  = (acc2 - acc3*acc3/eT(n_elem)) / norm_val;
max@0:     
max@0:     return arma_isfinite(var_val) ? var_val : op_var::direct_var_robust(X, n_elem, norm_type);
max@0:     }
max@0:   else
max@0:     {
max@0:     return eT(0);
max@0:     }
max@0:   }
max@0: 
max@0: 
max@0: 
max@0: //! find the variance of an array (version for complex numbers)
max@0: template<typename T>
max@0: inline
max@0: T
max@0: op_var::direct_var(const std::complex<T>* const X, const uword n_elem, const uword norm_type)
max@0:   {
max@0:   arma_extra_debug_sigprint();
max@0:   
max@0:   typedef typename std::complex<T> eT;
max@0:   
max@0:   if(n_elem >= 2)
max@0:     {
max@0:     const eT acc1 = op_mean::direct_mean(X, n_elem);
max@0:     
max@0:     T  acc2 =  T(0);
max@0:     eT acc3 = eT(0);
max@0:     
max@0:     for(uword i=0; i<n_elem; ++i)
max@0:       {
max@0:       const eT tmp = acc1 - X[i];
max@0:       
max@0:       acc2 += std::norm(tmp);
max@0:       acc3 += tmp;
max@0:       }
max@0:     
max@0:     const T norm_val = (norm_type == 0) ? T(n_elem-1) : T(n_elem);
max@0:     const T var_val  = (acc2 - std::norm(acc3)/T(n_elem)) / norm_val;
max@0:     
max@0:     return arma_isfinite(var_val) ? var_val : op_var::direct_var_robust(X, n_elem, norm_type);
max@0:     }
max@0:   else
max@0:     {
max@0:     return T(0);
max@0:     }
max@0:   }
max@0: 
max@0: 
max@0: 
max@0: //! find the variance of a subview_row
max@0: template<typename eT>
max@0: inline 
max@0: typename get_pod_type<eT>::result
max@0: op_var::direct_var(const subview_row<eT>& X, const uword norm_type)
max@0:   {
max@0:   arma_extra_debug_sigprint();
max@0:   
max@0:   const uword n_elem = X.n_elem;
max@0:   
max@0:   podarray<eT> tmp(n_elem);
max@0:   
max@0:   eT* tmp_mem = tmp.memptr();
max@0:   
max@0:   for(uword i=0; i<n_elem; ++i)
max@0:     {
max@0:     tmp_mem[i] = X[i];
max@0:     }
max@0:   
max@0:   return op_var::direct_var(tmp_mem, n_elem, norm_type);
max@0:   }
max@0: 
max@0: 
max@0: 
max@0: //! find the variance of a subview_col
max@0: template<typename eT>
max@0: inline 
max@0: typename get_pod_type<eT>::result
max@0: op_var::direct_var(const subview_col<eT>& X, const uword norm_type)
max@0:   {
max@0:   arma_extra_debug_sigprint();
max@0:   
max@0:   return op_var::direct_var(X.colptr(0), X.n_elem, norm_type);
max@0:   }
max@0: 
max@0: 
max@0: 
max@0: //! find the variance of a diagview
max@0: template<typename eT>
max@0: inline 
max@0: typename get_pod_type<eT>::result
max@0: op_var::direct_var(const diagview<eT>& X, const uword norm_type)
max@0:   {
max@0:   arma_extra_debug_sigprint();
max@0:   
max@0:   const uword n_elem = X.n_elem;
max@0:   
max@0:   podarray<eT> tmp(n_elem);
max@0:   
max@0:   eT* tmp_mem = tmp.memptr();
max@0:   
max@0:   for(uword i=0; i<n_elem; ++i)
max@0:     {
max@0:     tmp_mem[i] = X[i];
max@0:     }
max@0:   
max@0:   return op_var::direct_var(tmp_mem, n_elem, norm_type);
max@0:   }
max@0: 
max@0: 
max@0: 
max@0: //! \brief
max@0: //! For each row or for each column, find the variance.
max@0: //! The result is stored in a dense matrix that has either one column or one row.
max@0: //! The dimension, for which the variances are found, is set via the var() function.
max@0: template<typename T1>
max@0: inline
max@0: void
max@0: op_var::apply(Mat<typename T1::pod_type>& out, const mtOp<typename T1::pod_type, T1, op_var>& in)
max@0:   {
max@0:   arma_extra_debug_sigprint();
max@0:   
max@0:   typedef typename T1::elem_type  in_eT;
max@0:   typedef typename T1::pod_type  out_eT;
max@0:   
max@0:   const unwrap_check_mixed<T1> tmp(in.m, out);
max@0:   const Mat<in_eT>&        X = tmp.M;
max@0:   
max@0:   const uword norm_type = in.aux_uword_a;
max@0:   const uword dim       = in.aux_uword_b;
max@0:   
max@0:   arma_debug_check( (norm_type > 1), "var(): incorrect usage. norm_type must be 0 or 1");
max@0:   arma_debug_check( (dim > 1),       "var(): incorrect usage. dim must be 0 or 1"      );
max@0:   
max@0:   const uword X_n_rows = X.n_rows;
max@0:   const uword X_n_cols = X.n_cols;
max@0:   
max@0:   if(dim == 0)
max@0:     {
max@0:     arma_extra_debug_print("op_var::apply(), dim = 0");
max@0:     
max@0:     arma_debug_check( (X_n_rows == 0), "var(): given object has zero rows" );
max@0: 
max@0:     out.set_size(1, X_n_cols);
max@0:     
max@0:     out_eT* out_mem = out.memptr();
max@0:     
max@0:     for(uword col=0; col<X_n_cols; ++col)
max@0:       {
max@0:       out_mem[col] = op_var::direct_var( X.colptr(col), X_n_rows, norm_type );
max@0:       }
max@0:     }
max@0:   else
max@0:   if(dim == 1)
max@0:     {
max@0:     arma_extra_debug_print("op_var::apply(), dim = 1");
max@0:     
max@0:     arma_debug_check( (X_n_cols == 0), "var(): given object has zero columns" );
max@0: 
max@0:     out.set_size(X_n_rows, 1);
max@0:     
max@0:     podarray<in_eT> tmp(X_n_cols);
max@0:     
max@0:     in_eT*  tmp_mem = tmp.memptr();
max@0:     out_eT* out_mem = out.memptr();
max@0:     
max@0:     for(uword row=0; row<X_n_rows; ++row)
max@0:       {
max@0:       tmp.copy_row(X, row);
max@0:       
max@0:       out_mem[row] = op_var::direct_var( tmp_mem, X_n_cols, norm_type );
max@0:       }
max@0:     }
max@0:   }
max@0: 
max@0: 
max@0: 
max@0: //! find the variance of an array (robust but slow)
max@0: template<typename eT>
max@0: inline
max@0: eT
max@0: op_var::direct_var_robust(const eT* const X, const uword n_elem, const uword norm_type)
max@0:   {
max@0:   arma_extra_debug_sigprint();
max@0:   
max@0:   if(n_elem > 1)
max@0:     {
max@0:     eT r_mean = X[0];
max@0:     eT r_var  = eT(0);
max@0:     
max@0:     for(uword i=1; i<n_elem; ++i)
max@0:       {
max@0:       const eT tmp      = X[i] - r_mean;
max@0:       const eT i_plus_1 = eT(i+1);
max@0:       
max@0:       r_var  = eT(i-1)/eT(i) * r_var + (tmp*tmp)/i_plus_1;
max@0:       
max@0:       r_mean = r_mean + tmp/i_plus_1;
max@0:       }
max@0:     
max@0:     return (norm_type == 0) ? r_var : (eT(n_elem-1)/eT(n_elem)) * r_var;
max@0:     }
max@0:   else
max@0:     {
max@0:     return eT(0);
max@0:     }
max@0:   }
max@0: 
max@0: 
max@0: 
max@0: //! find the variance of an array (version for complex numbers) (robust but slow)
max@0: template<typename T>
max@0: inline
max@0: T
max@0: op_var::direct_var_robust(const std::complex<T>* const X, const uword n_elem, const uword norm_type)
max@0:   {
max@0:   arma_extra_debug_sigprint();
max@0:   
max@0:   typedef typename std::complex<T> eT;
max@0:   
max@0:   if(n_elem > 1)
max@0:     {
max@0:     eT r_mean = X[0];
max@0:      T r_var  = T(0);
max@0:     
max@0:     for(uword i=1; i<n_elem; ++i)
max@0:       {
max@0:       const eT tmp      = X[i] - r_mean;
max@0:       const  T i_plus_1 = T(i+1);
max@0:       
max@0:       r_var  = T(i-1)/T(i) * r_var + std::norm(tmp)/i_plus_1;
max@0:       
max@0:       r_mean = r_mean + tmp/i_plus_1;
max@0:       }
max@0:     
max@0:     return (norm_type == 0) ? r_var : (T(n_elem-1)/T(n_elem)) * r_var;
max@0:     }
max@0:   else
max@0:     {
max@0:     return T(0);
max@0:     }
max@0:   }
max@0: 
max@0: 
max@0: 
max@0: //! @}
max@0: