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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 glue_quantile
//! @{
template<typename eTa, typename eTb>
inline
void
glue_quantile::worker(eTb* out_mem, Col<eTa>& Y, const Mat<eTb>& P)
{
arma_extra_debug_sigprint();
// NOTE: assuming out_mem is an array with P.n_elem elements
// TODO: ignore non-finite values ?
// algorithm based on "Definition 5" in:
// Rob J. Hyndman and Yanan Fan.
// Sample Quantiles in Statistical Packages.
// The American Statistician, Vol. 50, No. 4, pp. 361-365, 1996.
// http://doi.org/10.2307/2684934
const eTb* P_mem = P.memptr();
const uword P_n_elem = P.n_elem;
const eTb alpha = 0.5;
const eTb N = eTb(Y.n_elem);
const eTb P_min = (eTb(1) - alpha) / N;
const eTb P_max = (N - alpha) / N;
for(uword i=0; i < P_n_elem; ++i)
{
const eTb P_i = P_mem[i];
eTb out_val = eTb(0);
if(P_i < P_min)
{
out_val = (P_i < eTb(0)) ? eTb(-std::numeric_limits<eTb>::infinity()) : eTb(Y.min());
}
else
if(P_i > P_max)
{
out_val = (P_i > eTb(1)) ? eTb( std::numeric_limits<eTb>::infinity()) : eTb(Y.max());
}
else
{
const uword k = uword(std::floor(N * P_i + alpha));
const eTb P_k = (eTb(k) - alpha) / N;
const eTb w = (P_i - P_k) * N;
eTa* Y_k_ptr = Y.begin() + uword(k);
std::nth_element( Y.begin(), Y_k_ptr, Y.end() );
const eTa Y_k_val = (*Y_k_ptr);
eTa* Y_km1_ptr = Y.begin() + uword(k-1);
// std::nth_element( Y.begin(), Y_km1_ptr, Y.end() );
std::nth_element( Y.begin(), Y_km1_ptr, Y_k_ptr );
const eTa Y_km1_val = (*Y_km1_ptr);
out_val = ((eTb(1) - w) * Y_km1_val) + (w * Y_k_val);
}
out_mem[i] = out_val;
}
}
template<typename eTa, typename eTb>
inline
void
glue_quantile::apply_noalias(Mat<eTb>& out, const Mat<eTa>& X, const Mat<eTb>& P, const uword dim)
{
arma_extra_debug_sigprint();
arma_debug_check( ((P.is_vec() == false) && (P.is_empty() == false)), "quantile(): parameter 'P' must be a vector" );
if(X.is_empty()) { out.reset(); return; }
const uword X_n_rows = X.n_rows;
const uword X_n_cols = X.n_cols;
const uword P_n_elem = P.n_elem;
if(dim == 0)
{
out.set_size(P_n_elem, X_n_cols);
if(out.is_empty()) { return; }
Col<eTa> Y(X_n_rows, arma_nozeros_indicator());
if(X_n_cols == 1)
{
arrayops::copy(Y.memptr(), X.memptr(), X_n_rows);
glue_quantile::worker(out.memptr(), Y, P);
}
else
{
for(uword col=0; col < X_n_cols; ++col)
{
arrayops::copy(Y.memptr(), X.colptr(col), X_n_rows);
glue_quantile::worker(out.colptr(col), Y, P);
}
}
}
else
if(dim == 1)
{
out.set_size(X_n_rows, P_n_elem);
if(out.is_empty()) { return; }
Col<eTa> Y(X_n_cols, arma_nozeros_indicator());
if(X_n_rows == 1)
{
arrayops::copy(Y.memptr(), X.memptr(), X_n_cols);
glue_quantile::worker(out.memptr(), Y, P);
}
else
{
Col<eTb> tmp(P_n_elem, arma_nozeros_indicator());
eTb* tmp_mem = tmp.memptr();
for(uword row=0; row < X_n_rows; ++row)
{
eTa* Y_mem = Y.memptr();
for(uword col=0; col < X_n_cols; ++col) { Y_mem[col] = X.at(row,col); }
glue_quantile::worker(tmp_mem, Y, P);
for(uword i=0; i < P_n_elem; ++i) { out.at(row,i) = tmp_mem[i]; }
}
}
}
}
template<typename T1, typename T2>
inline
void
glue_quantile::apply(Mat<typename T2::elem_type>& out, const mtGlue<typename T2::elem_type,T1,T2,glue_quantile>& expr)
{
arma_extra_debug_sigprint();
typedef typename T2::elem_type eTb;
const uword dim = expr.aux_uword;
arma_debug_check( (dim > 1), "quantile(): parameter 'dim' must be 0 or 1" );
const quasi_unwrap<T1> UA(expr.A);
const quasi_unwrap<T2> UB(expr.B);
arma_debug_check((UA.M.internal_has_nan() || UB.M.internal_has_nan()), "quantile(): detected NaN");
if(UA.is_alias(out) || UB.is_alias(out))
{
Mat<eTb> tmp;
glue_quantile::apply_noalias(tmp, UA.M, UB.M, dim);
out.steal_mem(tmp);
}
else
{
glue_quantile::apply_noalias(out, UA.M, UB.M, dim);
}
}
template<typename T1, typename T2>
inline
void
glue_quantile_default::apply(Mat<typename T2::elem_type>& out, const mtGlue<typename T2::elem_type,T1,T2,glue_quantile_default>& expr)
{
arma_extra_debug_sigprint();
typedef typename T2::elem_type eTb;
const quasi_unwrap<T1> UA(expr.A);
const quasi_unwrap<T2> UB(expr.B);
const uword dim = (T1::is_xvec) ? uword(UA.M.is_rowvec() ? 1 : 0) : uword((T1::is_row) ? 1 : 0);
arma_debug_check((UA.M.internal_has_nan() || UB.M.internal_has_nan()), "quantile(): detected NaN");
if(UA.is_alias(out) || UB.is_alias(out))
{
Mat<eTb> tmp;
glue_quantile::apply_noalias(tmp, UA.M, UB.M, dim);
out.steal_mem(tmp);
}
else
{
glue_quantile::apply_noalias(out, UA.M, UB.M, dim);
}
}
//! @}
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