Chris@49: // Copyright (C) 2009-2012 NICTA (www.nicta.com.au)
Chris@49: // Copyright (C) 2009-2012 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 op_var
Chris@49: //! @{
Chris@49: 
Chris@49: 
Chris@49: //! \brief
Chris@49: //! For each row or for each column, find the variance.
Chris@49: //! The result is stored in a dense matrix that has either one column or one row.
Chris@49: //! The dimension, for which the variances are found, is set via the var() function.
Chris@49: template<typename T1>
Chris@49: inline
Chris@49: void
Chris@49: op_var::apply(Mat<typename T1::pod_type>& out, const mtOp<typename T1::pod_type, T1, op_var>& in)
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49:   
Chris@49:   typedef typename T1::elem_type  in_eT;
Chris@49:   typedef typename T1::pod_type  out_eT;
Chris@49:   
Chris@49:   const unwrap_check_mixed<T1> tmp(in.m, out);
Chris@49:   const Mat<in_eT>&        X = tmp.M;
Chris@49:   
Chris@49:   const uword norm_type = in.aux_uword_a;
Chris@49:   const uword dim       = in.aux_uword_b;
Chris@49:   
Chris@49:   arma_debug_check( (norm_type > 1), "var(): incorrect usage. norm_type must be 0 or 1");
Chris@49:   arma_debug_check( (dim > 1),       "var(): incorrect usage. dim must be 0 or 1"      );
Chris@49:   
Chris@49:   const uword X_n_rows = X.n_rows;
Chris@49:   const uword X_n_cols = X.n_cols;
Chris@49:   
Chris@49:   if(dim == 0)
Chris@49:     {
Chris@49:     arma_extra_debug_print("op_var::apply(), dim = 0");
Chris@49:     
Chris@49:     arma_debug_check( (X_n_rows == 0), "var(): given object has zero rows" );
Chris@49:     
Chris@49:     out.set_size(1, X_n_cols);
Chris@49:     
Chris@49:     out_eT* out_mem = out.memptr();
Chris@49:     
Chris@49:     for(uword col=0; col<X_n_cols; ++col)
Chris@49:       {
Chris@49:       out_mem[col] = op_var::direct_var( X.colptr(col), X_n_rows, norm_type );
Chris@49:       }
Chris@49:     }
Chris@49:   else
Chris@49:   if(dim == 1)
Chris@49:     {
Chris@49:     arma_extra_debug_print("op_var::apply(), dim = 1");
Chris@49:     
Chris@49:     arma_debug_check( (X_n_cols == 0), "var(): given object has zero columns" );
Chris@49:     
Chris@49:     out.set_size(X_n_rows, 1);
Chris@49:     
Chris@49:     podarray<in_eT> dat(X_n_cols);
Chris@49:     
Chris@49:     in_eT*  dat_mem = dat.memptr();
Chris@49:     out_eT* out_mem = out.memptr();
Chris@49:     
Chris@49:     for(uword row=0; row<X_n_rows; ++row)
Chris@49:       {
Chris@49:       dat.copy_row(X, row);
Chris@49:       
Chris@49:       out_mem[row] = op_var::direct_var( dat_mem, X_n_cols, norm_type );
Chris@49:       }
Chris@49:     }
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: template<typename T1>
Chris@49: inline
Chris@49: typename T1::pod_type
Chris@49: op_var::var_vec(const Base<typename T1::elem_type, T1>& X, const uword norm_type)
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49:   
Chris@49:   typedef typename T1::elem_type eT;
Chris@49:   
Chris@49:   arma_debug_check( (norm_type > 1), "var(): incorrect usage. norm_type must be 0 or 1");
Chris@49:   
Chris@49:   const Proxy<T1> P(X.get_ref());
Chris@49:   
Chris@49:   const podarray<eT> tmp(P);
Chris@49:   
Chris@49:   return op_var::direct_var(tmp.memptr(), tmp.n_elem, norm_type);
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: template<typename eT>
Chris@49: inline
Chris@49: typename get_pod_type<eT>::result
Chris@49: op_var::var_vec(const subview_col<eT>& X, const uword norm_type)
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49:   
Chris@49:   arma_debug_check( (norm_type > 1), "var(): incorrect usage. norm_type must be 0 or 1");
Chris@49:   
Chris@49:   return op_var::direct_var(X.colptr(0), X.n_rows, norm_type);
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: template<typename eT>
Chris@49: inline
Chris@49: typename get_pod_type<eT>::result
Chris@49: op_var::var_vec(const subview_row<eT>& X, const uword norm_type)
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49:   
Chris@49:   arma_debug_check( (norm_type > 1), "var(): incorrect usage. norm_type must be 0 or 1");
Chris@49:   
Chris@49:   const Mat<eT>& A = X.m;
Chris@49:   
Chris@49:   const uword start_row = X.aux_row1;
Chris@49:   const uword start_col = X.aux_col1;
Chris@49:   
Chris@49:   const uword end_col_p1 = start_col + X.n_cols;
Chris@49:   
Chris@49:   podarray<eT> tmp(X.n_elem);
Chris@49:   eT* tmp_mem = tmp.memptr();
Chris@49:   
Chris@49:   for(uword i=0, col=start_col; col < end_col_p1; ++col, ++i)
Chris@49:     {
Chris@49:     tmp_mem[i] = A.at(start_row, col);
Chris@49:     }
Chris@49:   
Chris@49:   return op_var::direct_var(tmp.memptr(), tmp.n_elem, norm_type);
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: //! find the variance of an array
Chris@49: template<typename eT>
Chris@49: inline
Chris@49: eT
Chris@49: op_var::direct_var(const eT* const X, const uword n_elem, const uword norm_type)
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49:   
Chris@49:   if(n_elem >= 2)
Chris@49:     {
Chris@49:     const eT acc1 = op_mean::direct_mean(X, n_elem);
Chris@49:     
Chris@49:     eT acc2 = eT(0);
Chris@49:     eT acc3 = eT(0);
Chris@49:     
Chris@49:     uword i,j;
Chris@49:     
Chris@49:     for(i=0, j=1; j<n_elem; i+=2, j+=2)
Chris@49:       {
Chris@49:       const eT Xi = X[i];
Chris@49:       const eT Xj = X[j];
Chris@49:       
Chris@49:       const eT tmpi = acc1 - Xi;
Chris@49:       const eT tmpj = acc1 - Xj;
Chris@49:       
Chris@49:       acc2 += tmpi*tmpi + tmpj*tmpj;
Chris@49:       acc3 += tmpi      + tmpj;
Chris@49:       }
Chris@49:     
Chris@49:     if(i < n_elem)
Chris@49:       {
Chris@49:       const eT Xi = X[i];
Chris@49:       
Chris@49:       const eT tmpi = acc1 - Xi;
Chris@49:       
Chris@49:       acc2 += tmpi*tmpi;
Chris@49:       acc3 += tmpi;
Chris@49:       }
Chris@49:     
Chris@49:     const eT norm_val = (norm_type == 0) ? eT(n_elem-1) : eT(n_elem);
Chris@49:     const eT var_val  = (acc2 - acc3*acc3/eT(n_elem)) / norm_val;
Chris@49:     
Chris@49:     return arma_isfinite(var_val) ? var_val : op_var::direct_var_robust(X, n_elem, norm_type);
Chris@49:     }
Chris@49:   else
Chris@49:     {
Chris@49:     return eT(0);
Chris@49:     }
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: //! find the variance of an array (robust but slow)
Chris@49: template<typename eT>
Chris@49: inline
Chris@49: eT
Chris@49: op_var::direct_var_robust(const eT* const X, const uword n_elem, const uword norm_type)
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49:   
Chris@49:   if(n_elem > 1)
Chris@49:     {
Chris@49:     eT r_mean = X[0];
Chris@49:     eT r_var  = eT(0);
Chris@49:     
Chris@49:     for(uword i=1; i<n_elem; ++i)
Chris@49:       {
Chris@49:       const eT tmp      = X[i] - r_mean;
Chris@49:       const eT i_plus_1 = eT(i+1);
Chris@49:       
Chris@49:       r_var  = eT(i-1)/eT(i) * r_var + (tmp*tmp)/i_plus_1;
Chris@49:       
Chris@49:       r_mean = r_mean + tmp/i_plus_1;
Chris@49:       }
Chris@49:     
Chris@49:     return (norm_type == 0) ? r_var : (eT(n_elem-1)/eT(n_elem)) * r_var;
Chris@49:     }
Chris@49:   else
Chris@49:     {
Chris@49:     return eT(0);
Chris@49:     }
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: //! find the variance of an array (version for complex numbers)
Chris@49: template<typename T>
Chris@49: inline
Chris@49: T
Chris@49: op_var::direct_var(const std::complex<T>* const X, const uword n_elem, const uword norm_type)
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49:   
Chris@49:   typedef typename std::complex<T> eT;
Chris@49:   
Chris@49:   if(n_elem >= 2)
Chris@49:     {
Chris@49:     const eT acc1 = op_mean::direct_mean(X, n_elem);
Chris@49:     
Chris@49:     T  acc2 =  T(0);
Chris@49:     eT acc3 = eT(0);
Chris@49:     
Chris@49:     for(uword i=0; i<n_elem; ++i)
Chris@49:       {
Chris@49:       const eT tmp = acc1 - X[i];
Chris@49:       
Chris@49:       acc2 += std::norm(tmp);
Chris@49:       acc3 += tmp;
Chris@49:       }
Chris@49:     
Chris@49:     const T norm_val = (norm_type == 0) ? T(n_elem-1) : T(n_elem);
Chris@49:     const T var_val  = (acc2 - std::norm(acc3)/T(n_elem)) / norm_val;
Chris@49:     
Chris@49:     return arma_isfinite(var_val) ? var_val : op_var::direct_var_robust(X, n_elem, norm_type);
Chris@49:     }
Chris@49:   else
Chris@49:     {
Chris@49:     return T(0);
Chris@49:     }
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: //! find the variance of an array (version for complex numbers) (robust but slow)
Chris@49: template<typename T>
Chris@49: inline
Chris@49: T
Chris@49: op_var::direct_var_robust(const std::complex<T>* const X, const uword n_elem, const uword norm_type)
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49:   
Chris@49:   typedef typename std::complex<T> eT;
Chris@49:   
Chris@49:   if(n_elem > 1)
Chris@49:     {
Chris@49:     eT r_mean = X[0];
Chris@49:      T r_var  = T(0);
Chris@49:     
Chris@49:     for(uword i=1; i<n_elem; ++i)
Chris@49:       {
Chris@49:       const eT tmp      = X[i] - r_mean;
Chris@49:       const  T i_plus_1 = T(i+1);
Chris@49:       
Chris@49:       r_var  = T(i-1)/T(i) * r_var + std::norm(tmp)/i_plus_1;
Chris@49:       
Chris@49:       r_mean = r_mean + tmp/i_plus_1;
Chris@49:       }
Chris@49:     
Chris@49:     return (norm_type == 0) ? r_var : (T(n_elem-1)/T(n_elem)) * r_var;
Chris@49:     }
Chris@49:   else
Chris@49:     {
Chris@49:     return T(0);
Chris@49:     }
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: //! @}
Chris@49: