# Licensed under a 3-clause BSD style license - see LICENSE.rst
import numpy as np
from astropy.table import Column, Table
from gammapy.maps import Map
from gammapy.modeling.models import PowerLawSpectralModel, SkyModel
from gammapy.stats import WStatCountsStatistic
from .core import Estimator
__all__ = ["SensitivityEstimator"]
[docs]class SensitivityEstimator(Estimator):
"""Estimate differential sensitivity.
This class allows to determine for each reconstructed energy bin the flux
associated to the number of gamma-ray events for which the significance is
``n_sigma``, and being larger than ``gamma_min`` and ``bkg_sys`` percent
larger than the number of background events in the ON region.
Parameters
----------
spectrum : `SpectralModel`
Spectral model assumption
n_sigma : float, optional
Minimum significance. Default is 5.
gamma_min : float, optional
Minimum number of gamma-rays. Default is 10.
bkg_syst_fraction : float, optional
Fraction of background counts above which the number of gamma-rays is. Default is 0.05
Examples
--------
For a usage example see `cta_sensitivity.html <../tutorials/cta_sensitivity.html>`__
"""
tag = "SensitivityEstimator"
def __init__(
self, spectrum=None, n_sigma=5.0, gamma_min=10, bkg_syst_fraction=0.05
):
if spectrum is None:
spectrum = PowerLawSpectralModel(index=2, amplitude="1 cm-2 s-1 TeV-1")
self.spectrum = spectrum
self.n_sigma = n_sigma
self.gamma_min = gamma_min
self.bkg_syst_fraction = bkg_syst_fraction
[docs] def estimate_min_excess(self, dataset):
"""Estimate minimum excess to reach the given significance.
Parameters
----------
dataset : `SpectrumDataset`
Spectrum dataset
Returns
-------
excess : `RegionNDMap`
Minimal excess
"""
n_off = dataset.counts_off.data
stat = WStatCountsStatistic(
n_on=dataset.alpha.data * n_off, n_off=n_off, alpha=dataset.alpha.data
)
excess_counts = stat.n_sig_matching_significance(self.n_sigma)
is_gamma_limited = excess_counts < self.gamma_min
excess_counts[is_gamma_limited] = self.gamma_min
bkg_syst_limited = (
excess_counts < self.bkg_syst_fraction * dataset.background.data
)
excess_counts[bkg_syst_limited] = (
self.bkg_syst_fraction * dataset.background.data[bkg_syst_limited]
)
excess = Map.from_geom(geom=dataset._geom, data=excess_counts)
return excess
[docs] def estimate_min_e2dnde(self, excess, dataset):
"""Estimate dnde from given min. excess
Parameters
----------
excess : `RegionNDMap`
Minimal excess
dataset : `SpectrumDataset`
Spectrum dataset
Returns
-------
e2dnde : `~astropy.units.Quantity`
Minimal differential flux.
"""
energy = dataset._geom.axes["energy"].center
dataset.models = SkyModel(spectral_model=self.spectrum)
npred = dataset.npred_signal()
phi_0 = excess / npred
dnde_model = self.spectrum(energy=energy)
dnde = phi_0.data[:, 0, 0] * dnde_model * energy ** 2
return dnde.to("erg / (cm2 s)")
def _get_criterion(self, excess, bkg):
is_gamma_limited = excess == self.gamma_min
is_bkg_syst_limited = excess == bkg * self.bkg_syst_fraction
criterion = np.chararray(excess.shape, itemsize=12)
criterion[is_gamma_limited] = "gamma"
criterion[is_bkg_syst_limited] = "bkg"
criterion[
~np.logical_or(is_gamma_limited, is_bkg_syst_limited)
] = "significance"
return criterion
[docs] def run(self, dataset):
"""Run the sensitivty estimation
Parameters
----------
dataset : `SpectrumDatasetOnOff`
Dataset to compute sensitivty for.
Returns
-------
sensitivity : `~astropy.table.Table`
Sensitivity table
"""
energy = dataset._geom.axes["energy"].center
excess = self.estimate_min_excess(dataset)
e2dnde = self.estimate_min_e2dnde(excess, dataset)
criterion = self._get_criterion(
excess.data.squeeze(), dataset.background.data.squeeze()
)
return Table(
[
Column(
data=energy,
name="energy",
format="5g",
description="Reconstructed Energy",
),
Column(
data=e2dnde,
name="e2dnde",
format="5g",
description="Energy squared times differential flux",
),
Column(
data=excess.data.squeeze(),
name="excess",
format="5g",
description="Number of excess counts in the bin",
),
Column(
data=dataset.background.data.squeeze(),
name="background",
format="5g",
description="Number of background counts in the bin",
),
Column(
data=criterion,
name="criterion",
description="Sensitivity-limiting criterion",
),
]
)