307 lines
6.7 KiB
C++
307 lines
6.7 KiB
C++
// Copyright (C) 2009-2015 National ICT Australia (NICTA)
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//
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// This Source Code Form is subject to the terms of the Mozilla Public
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// License, v. 2.0. If a copy of the MPL was not distributed with this
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// file, You can obtain one at http://mozilla.org/MPL/2.0/.
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// -------------------------------------------------------------------
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//
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// Written by Conrad Sanderson - http://conradsanderson.id.au
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//! \addtogroup op_var
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//! @{
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//! \brief
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//! For each row or for each column, find the variance.
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//! The result is stored in a dense matrix that has either one column or one row.
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//! The dimension, for which the variances are found, is set via the var() function.
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template<typename T1>
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inline
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void
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op_var::apply(Mat<typename T1::pod_type>& out, const mtOp<typename T1::pod_type, T1, op_var>& in)
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{
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arma_extra_debug_sigprint();
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typedef typename T1::elem_type in_eT;
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typedef typename T1::pod_type out_eT;
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const unwrap_check_mixed<T1> tmp(in.m, out);
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const Mat<in_eT>& X = tmp.M;
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const uword norm_type = in.aux_uword_a;
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const uword dim = in.aux_uword_b;
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arma_debug_check( (norm_type > 1), "var(): parameter 'norm_type' must be 0 or 1" );
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arma_debug_check( (dim > 1), "var(): parameter 'dim' must be 0 or 1" );
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const uword X_n_rows = X.n_rows;
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const uword X_n_cols = X.n_cols;
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if(dim == 0)
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{
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arma_extra_debug_print("op_var::apply(): dim = 0");
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out.set_size((X_n_rows > 0) ? 1 : 0, X_n_cols);
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if(X_n_rows > 0)
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{
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out_eT* out_mem = out.memptr();
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for(uword col=0; col<X_n_cols; ++col)
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{
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out_mem[col] = op_var::direct_var( X.colptr(col), X_n_rows, norm_type );
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}
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}
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}
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else
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if(dim == 1)
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{
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arma_extra_debug_print("op_var::apply(): dim = 1");
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out.set_size(X_n_rows, (X_n_cols > 0) ? 1 : 0);
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if(X_n_cols > 0)
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{
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podarray<in_eT> dat(X_n_cols);
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in_eT* dat_mem = dat.memptr();
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out_eT* out_mem = out.memptr();
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for(uword row=0; row<X_n_rows; ++row)
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{
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dat.copy_row(X, row);
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out_mem[row] = op_var::direct_var( dat_mem, X_n_cols, norm_type );
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}
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}
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}
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}
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template<typename T1>
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inline
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typename T1::pod_type
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op_var::var_vec(const Base<typename T1::elem_type, T1>& X, const uword norm_type)
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{
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arma_extra_debug_sigprint();
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typedef typename T1::elem_type eT;
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arma_debug_check( (norm_type > 1), "var(): parameter 'norm_type' must be 0 or 1" );
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const Proxy<T1> P(X.get_ref());
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const podarray<eT> tmp(P);
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return op_var::direct_var(tmp.memptr(), tmp.n_elem, norm_type);
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}
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template<typename eT>
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inline
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typename get_pod_type<eT>::result
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op_var::var_vec(const subview_col<eT>& X, const uword norm_type)
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{
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arma_extra_debug_sigprint();
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arma_debug_check( (norm_type > 1), "var(): parameter 'norm_type' must be 0 or 1" );
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return op_var::direct_var(X.colptr(0), X.n_rows, norm_type);
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}
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template<typename eT>
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inline
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typename get_pod_type<eT>::result
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op_var::var_vec(const subview_row<eT>& X, const uword norm_type)
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{
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arma_extra_debug_sigprint();
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arma_debug_check( (norm_type > 1), "var(): parameter 'norm_type' must be 0 or 1" );
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const Mat<eT>& A = X.m;
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const uword start_row = X.aux_row1;
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const uword start_col = X.aux_col1;
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const uword end_col_p1 = start_col + X.n_cols;
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podarray<eT> tmp(X.n_elem);
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eT* tmp_mem = tmp.memptr();
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for(uword i=0, col=start_col; col < end_col_p1; ++col, ++i)
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{
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tmp_mem[i] = A.at(start_row, col);
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}
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return op_var::direct_var(tmp.memptr(), tmp.n_elem, norm_type);
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}
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//! find the variance of an array
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template<typename eT>
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inline
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eT
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op_var::direct_var(const eT* const X, const uword n_elem, const uword norm_type)
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{
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arma_extra_debug_sigprint();
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if(n_elem >= 2)
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{
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const eT acc1 = op_mean::direct_mean(X, n_elem);
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eT acc2 = eT(0);
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eT acc3 = eT(0);
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uword i,j;
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for(i=0, j=1; j<n_elem; i+=2, j+=2)
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{
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const eT Xi = X[i];
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const eT Xj = X[j];
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const eT tmpi = acc1 - Xi;
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const eT tmpj = acc1 - Xj;
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acc2 += tmpi*tmpi + tmpj*tmpj;
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acc3 += tmpi + tmpj;
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}
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if(i < n_elem)
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{
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const eT Xi = X[i];
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const eT tmpi = acc1 - Xi;
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acc2 += tmpi*tmpi;
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acc3 += tmpi;
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}
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const eT norm_val = (norm_type == 0) ? eT(n_elem-1) : eT(n_elem);
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const eT var_val = (acc2 - acc3*acc3/eT(n_elem)) / norm_val;
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return arma_isfinite(var_val) ? var_val : op_var::direct_var_robust(X, n_elem, norm_type);
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}
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else
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{
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return eT(0);
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}
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}
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//! find the variance of an array (robust but slow)
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template<typename eT>
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inline
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eT
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op_var::direct_var_robust(const eT* const X, const uword n_elem, const uword norm_type)
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{
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arma_extra_debug_sigprint();
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if(n_elem > 1)
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{
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eT r_mean = X[0];
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eT r_var = eT(0);
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for(uword i=1; i<n_elem; ++i)
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{
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const eT tmp = X[i] - r_mean;
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const eT i_plus_1 = eT(i+1);
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r_var = eT(i-1)/eT(i) * r_var + (tmp*tmp)/i_plus_1;
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r_mean = r_mean + tmp/i_plus_1;
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}
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return (norm_type == 0) ? r_var : (eT(n_elem-1)/eT(n_elem)) * r_var;
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}
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else
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{
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return eT(0);
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}
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}
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//! find the variance of an array (version for complex numbers)
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template<typename T>
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inline
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T
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op_var::direct_var(const std::complex<T>* const X, const uword n_elem, const uword norm_type)
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{
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arma_extra_debug_sigprint();
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typedef typename std::complex<T> eT;
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if(n_elem >= 2)
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{
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const eT acc1 = op_mean::direct_mean(X, n_elem);
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T acc2 = T(0);
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eT acc3 = eT(0);
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for(uword i=0; i<n_elem; ++i)
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{
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const eT tmp = acc1 - X[i];
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acc2 += std::norm(tmp);
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acc3 += tmp;
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}
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const T norm_val = (norm_type == 0) ? T(n_elem-1) : T(n_elem);
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const T var_val = (acc2 - std::norm(acc3)/T(n_elem)) / norm_val;
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return arma_isfinite(var_val) ? var_val : op_var::direct_var_robust(X, n_elem, norm_type);
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}
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else
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{
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return T(0);
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}
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}
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//! find the variance of an array (version for complex numbers) (robust but slow)
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template<typename T>
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inline
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T
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op_var::direct_var_robust(const std::complex<T>* const X, const uword n_elem, const uword norm_type)
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{
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arma_extra_debug_sigprint();
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typedef typename std::complex<T> eT;
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if(n_elem > 1)
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{
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eT r_mean = X[0];
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T r_var = T(0);
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for(uword i=1; i<n_elem; ++i)
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{
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const eT tmp = X[i] - r_mean;
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const T i_plus_1 = T(i+1);
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r_var = T(i-1)/T(i) * r_var + std::norm(tmp)/i_plus_1;
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r_mean = r_mean + tmp/i_plus_1;
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}
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return (norm_type == 0) ? r_var : (T(n_elem-1)/T(n_elem)) * r_var;
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}
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else
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{
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return T(0);
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}
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}
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//! @}
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