225 lines
5.6 KiB
C++
225 lines
5.6 KiB
C++
// Copyright 2008-2016 Conrad Sanderson (http://conradsanderson.id.au)
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// Copyright 2008-2016 National ICT Australia (NICTA)
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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// ------------------------------------------------------------------------
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//! \addtogroup glue_quantile
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//! @{
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template<typename eTa, typename eTb>
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inline
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void
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glue_quantile::worker(eTb* out_mem, Col<eTa>& Y, const Mat<eTb>& P)
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{
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arma_extra_debug_sigprint();
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// NOTE: assuming out_mem is an array with P.n_elem elements
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// TODO: ignore non-finite values ?
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// algorithm based on "Definition 5" in:
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// Rob J. Hyndman and Yanan Fan.
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// Sample Quantiles in Statistical Packages.
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// The American Statistician, Vol. 50, No. 4, pp. 361-365, 1996.
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// http://doi.org/10.2307/2684934
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const eTb* P_mem = P.memptr();
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const uword P_n_elem = P.n_elem;
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const eTb alpha = 0.5;
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const eTb N = eTb(Y.n_elem);
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const eTb P_min = (eTb(1) - alpha) / N;
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const eTb P_max = (N - alpha) / N;
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for(uword i=0; i < P_n_elem; ++i)
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{
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const eTb P_i = P_mem[i];
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eTb out_val = eTb(0);
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if(P_i < P_min)
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{
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out_val = (P_i < eTb(0)) ? eTb(-std::numeric_limits<eTb>::infinity()) : eTb(Y.min());
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}
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else
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if(P_i > P_max)
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{
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out_val = (P_i > eTb(1)) ? eTb( std::numeric_limits<eTb>::infinity()) : eTb(Y.max());
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}
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else
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{
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const uword k = uword(std::floor(N * P_i + alpha));
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const eTb P_k = (eTb(k) - alpha) / N;
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const eTb w = (P_i - P_k) * N;
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eTa* Y_k_ptr = Y.begin() + uword(k);
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std::nth_element( Y.begin(), Y_k_ptr, Y.end() );
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const eTa Y_k_val = (*Y_k_ptr);
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eTa* Y_km1_ptr = Y.begin() + uword(k-1);
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// std::nth_element( Y.begin(), Y_km1_ptr, Y.end() );
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std::nth_element( Y.begin(), Y_km1_ptr, Y_k_ptr );
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const eTa Y_km1_val = (*Y_km1_ptr);
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out_val = ((eTb(1) - w) * Y_km1_val) + (w * Y_k_val);
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}
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out_mem[i] = out_val;
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}
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}
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template<typename eTa, typename eTb>
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inline
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void
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glue_quantile::apply_noalias(Mat<eTb>& out, const Mat<eTa>& X, const Mat<eTb>& P, const uword dim)
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{
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arma_extra_debug_sigprint();
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arma_debug_check( ((P.is_vec() == false) && (P.is_empty() == false)), "quantile(): parameter 'P' must be a vector" );
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if(X.is_empty()) { out.reset(); return; }
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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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const uword P_n_elem = P.n_elem;
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if(dim == 0)
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{
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out.set_size(P_n_elem, X_n_cols);
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if(out.is_empty()) { return; }
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Col<eTa> Y(X_n_rows, arma_nozeros_indicator());
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if(X_n_cols == 1)
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{
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arrayops::copy(Y.memptr(), X.memptr(), X_n_rows);
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glue_quantile::worker(out.memptr(), Y, P);
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}
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else
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{
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for(uword col=0; col < X_n_cols; ++col)
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{
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arrayops::copy(Y.memptr(), X.colptr(col), X_n_rows);
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glue_quantile::worker(out.colptr(col), Y, P);
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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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out.set_size(X_n_rows, P_n_elem);
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if(out.is_empty()) { return; }
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Col<eTa> Y(X_n_cols, arma_nozeros_indicator());
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if(X_n_rows == 1)
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{
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arrayops::copy(Y.memptr(), X.memptr(), X_n_cols);
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glue_quantile::worker(out.memptr(), Y, P);
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}
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else
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{
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Col<eTb> tmp(P_n_elem, arma_nozeros_indicator());
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eTb* tmp_mem = tmp.memptr();
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for(uword row=0; row < X_n_rows; ++row)
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{
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eTa* Y_mem = Y.memptr();
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for(uword col=0; col < X_n_cols; ++col) { Y_mem[col] = X.at(row,col); }
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glue_quantile::worker(tmp_mem, Y, P);
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for(uword i=0; i < P_n_elem; ++i) { out.at(row,i) = tmp_mem[i]; }
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}
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}
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}
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}
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template<typename T1, typename T2>
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inline
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void
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glue_quantile::apply(Mat<typename T2::elem_type>& out, const mtGlue<typename T2::elem_type,T1,T2,glue_quantile>& expr)
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{
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arma_extra_debug_sigprint();
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typedef typename T2::elem_type eTb;
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const uword dim = expr.aux_uword;
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arma_debug_check( (dim > 1), "quantile(): parameter 'dim' must be 0 or 1" );
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const quasi_unwrap<T1> UA(expr.A);
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const quasi_unwrap<T2> UB(expr.B);
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if(UA.is_alias(out) || UB.is_alias(out))
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{
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Mat<eTb> tmp;
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glue_quantile::apply_noalias(tmp, UA.M, UB.M, dim);
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out.steal_mem(tmp);
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}
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else
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{
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glue_quantile::apply_noalias(out, UA.M, UB.M, dim);
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}
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}
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template<typename T1, typename T2>
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inline
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void
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glue_quantile_default::apply(Mat<typename T2::elem_type>& out, const mtGlue<typename T2::elem_type,T1,T2,glue_quantile_default>& expr)
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{
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arma_extra_debug_sigprint();
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typedef typename T2::elem_type eTb;
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const quasi_unwrap<T1> UA(expr.A);
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const quasi_unwrap<T2> UB(expr.B);
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const uword dim = (T1::is_xvec) ? uword(UA.M.is_rowvec() ? 1 : 0) : uword((T1::is_row) ? 1 : 0);
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if(UA.is_alias(out) || UB.is_alias(out))
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{
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Mat<eTb> tmp;
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glue_quantile::apply_noalias(tmp, UA.M, UB.M, dim);
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out.steal_mem(tmp);
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}
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else
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{
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glue_quantile::apply_noalias(out, UA.M, UB.M, dim);
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}
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}
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//! @}
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