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+// SPDX-License-Identifier: Apache-2.0
+//
+// Copyright 2008-2016 Conrad Sanderson (http://conradsanderson.id.au)
+// Copyright 2008-2016 National ICT Australia (NICTA)
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+// ------------------------------------------------------------------------
+
+
+//! \addtogroup op_var
+//! @{
+
+
+
+template<typename T1>
+inline
+void
+op_var::apply(Mat<typename T1::pod_type>& out, const mtOp<typename T1::pod_type, T1, op_var>& in)
+ {
+ arma_extra_debug_sigprint();
+
+ typedef typename T1::pod_type out_eT;
+
+ const uword norm_type = in.aux_uword_a;
+ const uword dim = in.aux_uword_b;
+
+ arma_debug_check( (norm_type > 1), "var(): parameter 'norm_type' must be 0 or 1" );
+ arma_debug_check( (dim > 1), "var(): parameter 'dim' must be 0 or 1" );
+
+ const quasi_unwrap<T1> U(in.m);
+
+ if(U.is_alias(out))
+ {
+ Mat<out_eT> tmp;
+
+ op_var::apply_noalias(tmp, U.M, norm_type, dim);
+
+ out.steal_mem(tmp);
+ }
+ else
+ {
+ op_var::apply_noalias(out, U.M, norm_type, dim);
+ }
+ }
+
+
+
+template<typename in_eT>
+inline
+void
+op_var::apply_noalias(Mat<typename get_pod_type<in_eT>::result>& out, const Mat<in_eT>& X, const uword norm_type, const uword dim)
+ {
+ arma_extra_debug_sigprint();
+
+ typedef typename get_pod_type<in_eT>::result out_eT;
+
+ const uword X_n_rows = X.n_rows;
+ const uword X_n_cols = X.n_cols;
+
+ if(dim == 0)
+ {
+ arma_extra_debug_print("op_var::apply_noalias(): dim = 0");
+
+ out.set_size((X_n_rows > 0) ? 1 : 0, X_n_cols);
+
+ if(X_n_rows > 0)
+ {
+ out_eT* out_mem = out.memptr();
+
+ for(uword col=0; col<X_n_cols; ++col)
+ {
+ out_mem[col] = op_var::direct_var( X.colptr(col), X_n_rows, norm_type );
+ }
+ }
+ }
+ else
+ if(dim == 1)
+ {
+ arma_extra_debug_print("op_var::apply_noalias(): dim = 1");
+
+ out.set_size(X_n_rows, (X_n_cols > 0) ? 1 : 0);
+
+ if(X_n_cols > 0)
+ {
+ podarray<in_eT> dat(X_n_cols);
+
+ in_eT* dat_mem = dat.memptr();
+ out_eT* out_mem = out.memptr();
+
+ for(uword row=0; row<X_n_rows; ++row)
+ {
+ dat.copy_row(X, row);
+
+ out_mem[row] = op_var::direct_var( dat_mem, X_n_cols, norm_type );
+ }
+ }
+ }
+ }
+
+
+
+template<typename T1>
+inline
+typename T1::pod_type
+op_var::var_vec(const Base<typename T1::elem_type, T1>& X, const uword norm_type)
+ {
+ arma_extra_debug_sigprint();
+
+ arma_debug_check( (norm_type > 1), "var(): parameter 'norm_type' must be 0 or 1" );
+
+ const quasi_unwrap<T1> U(X.get_ref());
+
+ return op_var::direct_var(U.M.memptr(), U.M.n_elem, norm_type);
+ }
+
+
+
+template<typename eT>
+inline
+typename get_pod_type<eT>::result
+op_var::var_vec(const subview_col<eT>& X, const uword norm_type)
+ {
+ arma_extra_debug_sigprint();
+
+ arma_debug_check( (norm_type > 1), "var(): parameter 'norm_type' must be 0 or 1" );
+
+ return op_var::direct_var(X.colptr(0), X.n_rows, norm_type);
+ }
+
+
+
+
+template<typename eT>
+inline
+typename get_pod_type<eT>::result
+op_var::var_vec(const subview_row<eT>& X, const uword norm_type)
+ {
+ arma_extra_debug_sigprint();
+
+ arma_debug_check( (norm_type > 1), "var(): parameter 'norm_type' must be 0 or 1" );
+
+ const Mat<eT>& A = X.m;
+
+ const uword start_row = X.aux_row1;
+ const uword start_col = X.aux_col1;
+
+ const uword end_col_p1 = start_col + X.n_cols;
+
+ podarray<eT> tmp(X.n_elem);
+ eT* tmp_mem = tmp.memptr();
+
+ for(uword i=0, col=start_col; col < end_col_p1; ++col, ++i)
+ {
+ tmp_mem[i] = A.at(start_row, col);
+ }
+
+ return op_var::direct_var(tmp.memptr(), tmp.n_elem, norm_type);
+ }
+
+
+
+//! find the variance of an array
+template<typename eT>
+inline
+eT
+op_var::direct_var(const eT* const X, const uword n_elem, const uword norm_type)
+ {
+ arma_extra_debug_sigprint();
+
+ if(n_elem >= 2)
+ {
+ const eT acc1 = op_mean::direct_mean(X, n_elem);
+
+ eT acc2 = eT(0);
+ eT acc3 = eT(0);
+
+ uword i,j;
+
+ for(i=0, j=1; j<n_elem; i+=2, j+=2)
+ {
+ const eT Xi = X[i];
+ const eT Xj = X[j];
+
+ const eT tmpi = acc1 - Xi;
+ const eT tmpj = acc1 - Xj;
+
+ acc2 += tmpi*tmpi + tmpj*tmpj;
+ acc3 += tmpi + tmpj;
+ }
+
+ if(i < n_elem)
+ {
+ const eT Xi = X[i];
+
+ const eT tmpi = acc1 - Xi;
+
+ acc2 += tmpi*tmpi;
+ acc3 += tmpi;
+ }
+
+ const eT norm_val = (norm_type == 0) ? eT(n_elem-1) : eT(n_elem);
+ const eT var_val = (acc2 - acc3*acc3/eT(n_elem)) / norm_val;
+
+ return arma_isfinite(var_val) ? var_val : op_var::direct_var_robust(X, n_elem, norm_type);
+ }
+ else
+ {
+ return eT(0);
+ }
+ }
+
+
+
+//! find the variance of an array (robust but slow)
+template<typename eT>
+inline
+eT
+op_var::direct_var_robust(const eT* const X, const uword n_elem, const uword norm_type)
+ {
+ arma_extra_debug_sigprint();
+
+ if(n_elem > 1)
+ {
+ eT r_mean = X[0];
+ eT r_var = eT(0);
+
+ for(uword i=1; i<n_elem; ++i)
+ {
+ const eT tmp = X[i] - r_mean;
+ const eT i_plus_1 = eT(i+1);
+
+ r_var = eT(i-1)/eT(i) * r_var + (tmp*tmp)/i_plus_1;
+
+ r_mean = r_mean + tmp/i_plus_1;
+ }
+
+ return (norm_type == 0) ? r_var : (eT(n_elem-1)/eT(n_elem)) * r_var;
+ }
+ else
+ {
+ return eT(0);
+ }
+ }
+
+
+
+//! find the variance of an array (version for complex numbers)
+template<typename T>
+inline
+T
+op_var::direct_var(const std::complex<T>* const X, const uword n_elem, const uword norm_type)
+ {
+ arma_extra_debug_sigprint();
+
+ typedef typename std::complex<T> eT;
+
+ if(n_elem >= 2)
+ {
+ const eT acc1 = op_mean::direct_mean(X, n_elem);
+
+ T acc2 = T(0);
+ eT acc3 = eT(0);
+
+ for(uword i=0; i<n_elem; ++i)
+ {
+ const eT tmp = acc1 - X[i];
+
+ acc2 += std::norm(tmp);
+ acc3 += tmp;
+ }
+
+ const T norm_val = (norm_type == 0) ? T(n_elem-1) : T(n_elem);
+ const T var_val = (acc2 - std::norm(acc3)/T(n_elem)) / norm_val;
+
+ return arma_isfinite(var_val) ? var_val : op_var::direct_var_robust(X, n_elem, norm_type);
+ }
+ else
+ {
+ return T(0);
+ }
+ }
+
+
+
+//! find the variance of an array (version for complex numbers) (robust but slow)
+template<typename T>
+inline
+T
+op_var::direct_var_robust(const std::complex<T>* const X, const uword n_elem, const uword norm_type)
+ {
+ arma_extra_debug_sigprint();
+
+ typedef typename std::complex<T> eT;
+
+ if(n_elem > 1)
+ {
+ eT r_mean = X[0];
+ T r_var = T(0);
+
+ for(uword i=1; i<n_elem; ++i)
+ {
+ const eT tmp = X[i] - r_mean;
+ const T i_plus_1 = T(i+1);
+
+ r_var = T(i-1)/T(i) * r_var + std::norm(tmp)/i_plus_1;
+
+ r_mean = r_mean + tmp/i_plus_1;
+ }
+
+ return (norm_type == 0) ? r_var : (T(n_elem-1)/T(n_elem)) * r_var;
+ }
+ else
+ {
+ return T(0);
+ }
+ }
+
+
+
+//! @}
+