Chris@49: // Copyright (C) 2012 Ryan Curtin
Chris@49: // Copyright (C) 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 spop_var
Chris@49: //! @{
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: template<typename T1>
Chris@49: inline
Chris@49: void
Chris@49: spop_var::apply(SpMat<typename T1::pod_type>& out, const mtSpOp<typename T1::pod_type, T1, spop_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 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:   SpProxy<T1> p(in.m);
Chris@49:   
Chris@49:   if(p.is_alias(out) == false)
Chris@49:     {
Chris@49:     spop_var::apply_noalias(out, p, norm_type, dim);
Chris@49:     }
Chris@49:   else
Chris@49:     {
Chris@49:     SpMat<out_eT> tmp;
Chris@49:     
Chris@49:     spop_var::apply_noalias(tmp, p, norm_type, dim);
Chris@49:     
Chris@49:     out.steal_mem(tmp);
Chris@49:     }
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: template<typename T1>
Chris@49: inline
Chris@49: void
Chris@49: spop_var::apply_noalias
Chris@49:   (
Chris@49:         SpMat<typename T1::pod_type>& out_ref,
Chris@49:   const SpProxy<T1>&                  p,
Chris@49:   const uword                         norm_type,
Chris@49:   const uword                         dim
Chris@49:   )
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 uword p_n_rows = p.get_n_rows();
Chris@49:   const uword p_n_cols = p.get_n_cols();
Chris@49: 
Chris@49:   if(dim == 0)
Chris@49:     {
Chris@49:     arma_extra_debug_print("spop_var::apply(), dim = 0");
Chris@49: 
Chris@49:     arma_debug_check((p_n_rows == 0), "var(): given object has zero rows");
Chris@49: 
Chris@49:     out_ref.set_size(1, p_n_cols);
Chris@49: 
Chris@49:     for(uword col = 0; col < p_n_cols; ++col)
Chris@49:       {
Chris@49:       if(SpProxy<T1>::must_use_iterator == true)
Chris@49:         {
Chris@49:         // We must use an iterator; we can't access memory directly.
Chris@49:         typename SpProxy<T1>::const_iterator_type it  = p.begin_col(col);
Chris@49:         typename SpProxy<T1>::const_iterator_type end = p.begin_col(col + 1);
Chris@49:         
Chris@49:         const uword n_zero = p.get_n_rows() - (end.pos() - it.pos());
Chris@49:         
Chris@49:         // in_eT is used just to get the specialization right (complex / noncomplex)
Chris@49:         out_ref.at(col) = spop_var::iterator_var(it, end, n_zero, norm_type, in_eT(0));
Chris@49:         }
Chris@49:       else
Chris@49:         {
Chris@49:         // We can use direct memory access to calculate the variance.
Chris@49:         out_ref.at(col) = spop_var::direct_var
Chris@49:           (
Chris@49:           &p.get_values()[p.get_col_ptrs()[col]],
Chris@49:           p.get_col_ptrs()[col + 1] - p.get_col_ptrs()[col],
Chris@49:           p.get_n_rows(),
Chris@49:           norm_type
Chris@49:           );
Chris@49:         }
Chris@49:       }
Chris@49:     }
Chris@49:   else if(dim == 1)
Chris@49:     {
Chris@49:     arma_extra_debug_print("spop_var::apply_noalias(), dim = 1");
Chris@49:     
Chris@49:     arma_debug_check((p_n_cols == 0), "var(): given object has zero columns");
Chris@49:     
Chris@49:     out_ref.set_size(p_n_rows, 1);
Chris@49:     
Chris@49:     for(uword row = 0; row < p_n_rows; ++row)
Chris@49:       {
Chris@49:       // We have to use an iterator here regardless of whether or not we can
Chris@49:       // directly access memory.
Chris@49:       typename SpProxy<T1>::const_row_iterator_type it  = p.begin_row(row);
Chris@49:       typename SpProxy<T1>::const_row_iterator_type end = p.end_row(row);
Chris@49:       
Chris@49:       const uword n_zero = p.get_n_cols() - (end.pos() - it.pos());
Chris@49:       
Chris@49:       out_ref.at(row) = spop_var::iterator_var(it, end, n_zero, norm_type, in_eT(0));
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: spop_var::var_vec
Chris@49:   (
Chris@49:   const T1& X,
Chris@49:   const uword norm_type
Chris@49:   )
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:   // conditionally unwrap it into a temporary and then directly operate.
Chris@49:   
Chris@49:   const unwrap_spmat<T1> tmp(X);
Chris@49:   
Chris@49:   return direct_var(tmp.M.values, tmp.M.n_nonzero, tmp.M.n_elem, norm_type);
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: template<typename eT>
Chris@49: inline
Chris@49: eT
Chris@49: spop_var::direct_var
Chris@49:   (
Chris@49:   const eT* const X,
Chris@49:   const uword length,
Chris@49:   const uword N,
Chris@49:   const uword norm_type
Chris@49:   )
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49: 
Chris@49:   if(length >= 2 && N >= 2)
Chris@49:     {
Chris@49:     const eT acc1 = spop_mean::direct_mean(X, length, N);
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 < length; 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 < length)
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:     // Now add in all zero elements.
Chris@49:     acc2 += (N - length) * (acc1 * acc1);
Chris@49:     acc3 += (N - length) * acc1;
Chris@49: 
Chris@49:     const eT norm_val = (norm_type == 0) ? eT(N - 1) : eT(N);
Chris@49:     const eT var_val  = (acc2 - (acc3 * acc3) / eT(N)) / norm_val;
Chris@49: 
Chris@49:     return var_val;
Chris@49:     }
Chris@49:   else if(length == 1 && N > 1) // if N == 1, then variance is zero.
Chris@49:     {
Chris@49:     const eT mean = X[0] / eT(N);
Chris@49:     const eT val = mean - X[0];
Chris@49: 
Chris@49:     const eT acc2 = (val * val) + (N - length) * (mean * mean);
Chris@49:     const eT acc3 = val + (N - length) * mean;
Chris@49: 
Chris@49:     const eT norm_val = (norm_type == 0) ? eT(N - 1) : eT(N);
Chris@49:     const eT var_val  = (acc2 - (acc3 * acc3) / eT(N)) / norm_val;
Chris@49: 
Chris@49:     return var_val;
Chris@49:     }
Chris@49:   else
Chris@49:     {
Chris@49:     return eT(0);
Chris@49:     }
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: template<typename T>
Chris@49: inline
Chris@49: T
Chris@49: spop_var::direct_var
Chris@49:   (
Chris@49:   const std::complex<T>* const X,
Chris@49:   const uword length,
Chris@49:   const uword N,
Chris@49:   const uword norm_type
Chris@49:   )
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49: 
Chris@49:   typedef typename std::complex<T> eT;
Chris@49: 
Chris@49:   if(length >= 2 && N >= 2)
Chris@49:     {
Chris@49:     const eT acc1 = spop_mean::direct_mean(X, length, N);
Chris@49: 
Chris@49:      T acc2 =  T(0);
Chris@49:     eT acc3 = eT(0);
Chris@49: 
Chris@49:     for (uword i = 0; i < length; ++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:     // Add zero elements to sums
Chris@49:     acc2 += std::norm(acc1) * T(N - length);
Chris@49:     acc3 += acc1 * T(N - length);
Chris@49: 
Chris@49:     const T norm_val = (norm_type == 0) ? T(N - 1) : T(N);
Chris@49:     const T var_val  = (acc2 - std::norm(acc3) / T(N)) / norm_val;
Chris@49: 
Chris@49:     return var_val;
Chris@49:     }
Chris@49:   else if(length == 1 && N > 1) // if N == 1, then variance is zero.
Chris@49:     {
Chris@49:     const eT mean = X[0] / T(N);
Chris@49:     const eT val = mean - X[0];
Chris@49: 
Chris@49:     const T acc2 = std::norm(val) + (N - length) * std::norm(mean);
Chris@49:     const eT acc3 = val + T(N - length) * mean;
Chris@49: 
Chris@49:     const T norm_val = (norm_type == 0) ? T(N - 1) : T(N);
Chris@49:     const T var_val  = (acc2 - std::norm(acc3) / T(N)) / norm_val;
Chris@49: 
Chris@49:     return var_val;
Chris@49:     }
Chris@49:   else
Chris@49:     {
Chris@49:     return T(0); // All elements are zero
Chris@49:     }
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: template<typename T1, typename eT>
Chris@49: inline
Chris@49: eT
Chris@49: spop_var::iterator_var
Chris@49:   (
Chris@49:   T1& it,
Chris@49:   const T1& end,
Chris@49:   const uword n_zero,
Chris@49:   const uword norm_type,
Chris@49:   const eT junk1,
Chris@49:   const typename arma_not_cx<eT>::result* junk2
Chris@49:   )
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49:   arma_ignore(junk1);
Chris@49:   arma_ignore(junk2);
Chris@49: 
Chris@49:   T1 new_it(it); // for mean
Chris@49:   // T1 backup_it(it); // in case we have to call robust iterator_var
Chris@49:   eT mean = spop_mean::iterator_mean(new_it, end, n_zero, eT(0));
Chris@49: 
Chris@49:   eT acc2 = eT(0);
Chris@49:   eT acc3 = eT(0);
Chris@49: 
Chris@49:   const uword it_begin_pos = it.pos();
Chris@49: 
Chris@49:   while (it != end)
Chris@49:     {
Chris@49:     const eT tmp = mean - (*it);
Chris@49: 
Chris@49:     acc2 += (tmp * tmp);
Chris@49:     acc3 += (tmp);
Chris@49: 
Chris@49:     ++it;
Chris@49:     }
Chris@49: 
Chris@49:   const uword n_nonzero = (it.pos() - it_begin_pos);
Chris@49:   if (n_nonzero == 0)
Chris@49:     {
Chris@49:     return eT(0);
Chris@49:     }
Chris@49: 
Chris@49:   if (n_nonzero + n_zero == 1)
Chris@49:     {
Chris@49:     return eT(0); // only one element
Chris@49:     }
Chris@49: 
Chris@49:   // Add in entries for zeros.
Chris@49:   acc2 += eT(n_zero) * (mean * mean);
Chris@49:   acc3 += eT(n_zero) * mean;
Chris@49: 
Chris@49:   const eT norm_val = (norm_type == 0) ? eT(n_zero + n_nonzero - 1) : eT(n_zero + n_nonzero);
Chris@49:   const eT var_val  = (acc2 - (acc3 * acc3) / eT(n_nonzero + n_zero)) / norm_val;
Chris@49: 
Chris@49:   return var_val;
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: template<typename T1, typename eT>
Chris@49: inline
Chris@49: typename get_pod_type<eT>::result
Chris@49: spop_var::iterator_var
Chris@49:   (
Chris@49:   T1& it,
Chris@49:   const T1& end,
Chris@49:   const uword n_zero,
Chris@49:   const uword norm_type,
Chris@49:   const eT junk1,
Chris@49:   const typename arma_cx_only<eT>::result* junk2
Chris@49:   )
Chris@49:   {
Chris@49:   arma_extra_debug_sigprint();
Chris@49:   arma_ignore(junk1);
Chris@49:   arma_ignore(junk2);
Chris@49: 
Chris@49:   typedef typename get_pod_type<eT>::result T;
Chris@49: 
Chris@49:   T1 new_it(it); // for mean
Chris@49:   // T1 backup_it(it); // in case we have to call robust iterator_var
Chris@49:   eT mean = spop_mean::iterator_mean(new_it, end, n_zero, eT(0));
Chris@49: 
Chris@49:    T acc2 =  T(0);
Chris@49:   eT acc3 = eT(0);
Chris@49: 
Chris@49:   const uword it_begin_pos = it.pos();
Chris@49: 
Chris@49:   while (it != end)
Chris@49:     {
Chris@49:     eT tmp = mean - (*it);
Chris@49: 
Chris@49:     acc2 += std::norm(tmp);
Chris@49:     acc3 += (tmp);
Chris@49: 
Chris@49:     ++it;
Chris@49:     }
Chris@49: 
Chris@49:   const uword n_nonzero = (it.pos() - it_begin_pos);
Chris@49:   if (n_nonzero == 0)
Chris@49:     {
Chris@49:     return T(0);
Chris@49:     }
Chris@49: 
Chris@49:   if (n_nonzero + n_zero == 1)
Chris@49:     {
Chris@49:     return T(0); // only one element
Chris@49:     }
Chris@49: 
Chris@49:   // Add in entries for zero elements.
Chris@49:   acc2 += T(n_zero) * std::norm(mean);
Chris@49:   acc3 += T(n_zero) * mean;
Chris@49: 
Chris@49:   const T norm_val = (norm_type == 0) ? T(n_zero + n_nonzero - 1) : T(n_zero + n_nonzero);
Chris@49:   const T var_val  = (acc2 - std::norm(acc3) / T(n_nonzero + n_zero)) / norm_val;
Chris@49: 
Chris@49:   return var_val;
Chris@49:   }
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: //! @}