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Thibault Hallouin authoreddcb0ddf0
// Copyright (c) 2023, INRAE.// Distributed under the terms of the GPL-3 Licence.// The full licence is in the file LICENCE, distributed with this software.#ifndef EVALHYD_DETERMINIST_EVENTS_HPP#define EVALHYD_DETERMINIST_EVENTS_HPP#include <xtensor/xtensor.hpp>#include <xtensor/xview.hpp>#include <xtensor/xmasked_view.hpp>#include <xtensor/xmath.hpp>namespace evalhyd{ namespace determinist { namespace elements { // Contingency table: // // OBS // Y N // +-----+-----+ a: hits // Y | a | b | b: false alarms // PRD +-----+-----+ c: misses // N | c | d | d: correct rejections // +-----+-----+ // /// Determine observed realisation of threshold(s) exceedance. /// /// \param q_obs /// Streamflow observations. /// shape: (1, time) /// \param q_thr /// Streamflow exceedance threshold(s). /// shape: (series, thresholds) /// \param is_high_flow_event /// Whether events correspond to being above the threshold(s). /// \return /// Event observed outcome. /// shape: (series, thresholds, time) template<class XD2> inline xt::xtensor<double, 3> calc_obs_event( const XD2& q_obs, const XD2& q_thr, bool is_high_flow_event ) { if (is_high_flow_event) { // observations above threshold(s) return xt::view(q_obs, xt::all(), xt::newaxis(), xt::all()) >= xt::view(q_thr, xt::all(), xt::all(), xt::newaxis()); } else { // observations below threshold(s) return xt::view(q_obs, xt::all(), xt::newaxis(), xt::all()) <= xt::view(q_thr, xt::all(), xt::all(), xt::newaxis()); } } /// Determine predicted realisation of threshold(s) exceedance. /// /// \param q_prd /// Streamflow predictions. /// shape: (series, time) /// \param q_thr7172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140
/// Streamflow exceedance threshold(s).
/// shape: (series, thresholds)
/// \param is_high_flow_event
/// Whether events correspond to being above the threshold(s).
/// \return
/// Event predicted outcome.
/// shape: (series, thresholds, time)
template<class XD2>
inline xt::xtensor<double, 3> calc_prd_event(
const XD2& q_prd,
const XD2& q_thr,
bool is_high_flow_event
)
{
if (is_high_flow_event)
{
// observations above threshold(s)
return xt::view(q_prd, xt::all(), xt::newaxis(), xt::all())
>= xt::view(q_thr, xt::all(), xt::all(), xt::newaxis());
}
else
{
// observations below threshold(s)
return xt::view(q_prd, xt::all(), xt::newaxis(), xt::all())
<= xt::view(q_thr, xt::all(), xt::all(), xt::newaxis());
}
}
/// Determine hits ('a' in contingency table).
///
/// \param obs_event
/// Observed event outcome.
/// shape: (series, thresholds, time)
/// \param prd_event
/// Predicted event outcome.
/// shape: (series, thresholds, time)
/// \return
/// Hits.
/// shape: (series, thresholds, time)
inline xt::xtensor<double, 3> calc_ct_a(
const xt::xtensor<double, 3>& obs_event,
const xt::xtensor<double, 3>& prd_event
)
{
return xt::equal(obs_event, 1.) && xt::equal(prd_event, 1.);
}
/// Determine false alarms ('b' in contingency table).
///
/// \param obs_event
/// Observed event outcome.
/// shape: (series, thresholds, time)
/// \param prd_event
/// Predicted event outcome.
/// shape: (series, thresholds, time)
/// \return
/// False alarms.
/// shape: (series, thresholds, time)
inline xt::xtensor<double, 3> calc_ct_b(
const xt::xtensor<double, 3>& obs_event,
const xt::xtensor<double, 3>& prd_event
)
{
return xt::equal(obs_event, 0.) && xt::equal(prd_event, 1.);
}
/// Determine misses ('c' in contingency table).
///
/// \param obs_event
/// Observed event outcome.
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/// shape: (series, thresholds, time)
/// \param prd_event
/// Predicted event outcome.
/// shape: (series, thresholds, time)
/// \return
/// Misses.
/// shape: (series, thresholds, time)
inline xt::xtensor<double, 3> calc_ct_c(
const xt::xtensor<double, 3>& obs_event,
const xt::xtensor<double, 3>& prd_event
)
{
return xt::equal(obs_event, 1.) && xt::equal(prd_event, 0.);
}
/// Determine correct rejections ('d' in contingency table).
///
/// \param obs_event
/// Observed event outcome.
/// shape: (series, thresholds, time)
/// \param prd_event
/// Predicted event outcome.
/// shape: (series, thresholds, time)
/// \return
/// Correct rejections.
/// shape: (series, thresholds, time)
inline xt::xtensor<double, 3> calc_ct_d(
const xt::xtensor<double, 3>& obs_event,
const xt::xtensor<double, 3>& prd_event
)
{
return xt::equal(obs_event, 0.) && xt::equal(prd_event, 0.);
}
}
namespace metrics
{
/// Compute the cells of the contingency table (CONT_TBL),
/// i.e. 'hits', 'false alarms', 'misses', 'correct rejections',
/// in this order.
///
/// \param q_thr
/// Streamflow exceedance threshold(s).
/// shape: (series, thresholds)
/// \param ct_a
/// Hits for each time step.
/// shape: (series, thresholds, time)
/// \param ct_b
/// False alarms for each time step.
/// shape: (series, thresholds, time)
/// \param ct_c
/// Misses for each time step.
/// shape: (series, thresholds, time)
/// \param ct_d
/// Correct rejections for each time step.
/// shape: (series, thresholds, time)
/// \param t_msk
/// Temporal subsets of the whole record.
/// shape: (series, subsets, time)
/// \param b_exp
/// Boostrap samples.
/// shape: (samples, time slice)
/// \param n_srs
/// Number of prediction series.
/// \param n_thr
/// Number of thresholds.
/// \param n_msk
/// Number of temporal subsets.
/// \param n_exp
/// Number of bootstrap samples.
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/// \return
/// Contingency tables.
/// shape: (series, subsets, samples, thresholds, cells)
template<class XD2>
inline xt::xtensor<double, 5> calc_CONT_TBL(
const XD2& q_thr,
const xt::xtensor<double, 3>& ct_a,
const xt::xtensor<double, 3>& ct_b,
const xt::xtensor<double, 3>& ct_c,
const xt::xtensor<double, 3>& ct_d,
const xt::xtensor<bool, 3>& t_msk,
const std::vector<xt::xkeep_slice<int>>& b_exp,
std::size_t n_srs,
std::size_t n_thr,
std::size_t n_msk,
std::size_t n_exp
)
{
// initialise output variable
xt::xtensor<double, 5> CONT_TBL =
xt::zeros<double>({n_srs, n_msk, n_exp,
n_thr, std::size_t {4}});
// compute variable one mask at a time to minimise memory imprint
for (std::size_t m = 0; m < n_msk; m++)
{
std::size_t i = 0;
for (auto cell: {ct_a, ct_b, ct_c, ct_d})
{
// apply the mask
// (using NaN workaround until reducers work on masked_view)
auto cell_masked = xt::where(
xt::view(t_msk, xt::all(), m, xt::newaxis(), xt::all()),
cell,
NAN
);
// compute variable one sample at a time
for (std::size_t e = 0; e < n_exp; e++)
{
// apply the bootstrap sampling
auto cell_masked_sampled =
xt::view(cell_masked, xt::all(), xt::all(),
b_exp[e]);
// calculate the mean over the time steps
xt::view(CONT_TBL, xt::all(), m, e, xt::all(), i) =
xt::nansum(cell_masked_sampled, -1);
}
i++;
}
}
// assign NaN where thresholds were not provided (i.e. set as NaN)
xt::masked_view(
CONT_TBL,
xt::isnan(xt::view(q_thr, xt::all(), xt::newaxis(),
xt::newaxis(), xt::all(),
xt::newaxis()))
) = NAN;
return CONT_TBL;
}
}
}
}
#endif //EVALHYD_DETERMINIST_EVENTS_HPP