# Licensed under a 3-clause BSD style license - see LICENSE.rst
import abc
import logging
import numpy as np
from astropy import units as u
from gammapy.maps import MapAxes, MapAxis
from gammapy.utils.gauss import MultiGauss2D
from gammapy.utils.interpolation import ScaledRegularGridInterpolator
from .core import PSF
__all__ = ["ParametricPSF", "EnergyDependentMultiGaussPSF", "PSFKing"]
log = logging.getLogger(__name__)
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class ParametricPSF(PSF):
"""Parametric PSF base class.
Parameters
----------
axes : list of `MapAxis` or `MapAxes`
Axes.
data : dict of `~numpy.ndarray` or `~numpy.recarray`
Data.
unit : dict of str or `~astropy.units.Unit`
Unit.
meta : dict
Metadata dictionary.
"""
@property
@abc.abstractmethod
def required_parameters(self):
return []
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@abc.abstractmethod
def evaluate_direct(self, rad, **kwargs):
pass
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@abc.abstractmethod
def evaluate_containment(self, rad, **kwargs):
pass
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def normalize(self):
"""Normalize parametric PSF."""
raise NotImplementedError
@property
def quantity(self):
"""Quantity."""
quantity = {}
for name in self.required_parameters:
quantity[name] = self.data[name] * self.unit[name]
return quantity
@property
def unit(self):
"""Map unit as a `~astropy.units.Unit`."""
return self._unit
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def to_unit(self, unit):
"""Convert IRF to unit."""
raise NotImplementedError
@property
def _interpolators(self):
interps = {}
for name in self.required_parameters:
points = [a.center for a in self.axes]
points_scale = tuple([a.interp for a in self.axes])
interps[name] = ScaledRegularGridInterpolator(
points, values=self.quantity[name], points_scale=points_scale
)
return interps
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def evaluate_parameters(self, energy_true, offset):
"""Evaluate analytic PSF parameters at a given energy and offset.
Uses nearest-neighbor interpolation.
Parameters
----------
energy_true : `~astropy.units.Quantity`
Energy value.
offset : `~astropy.coordinates.Angle`
Offset in the field of view.
Returns
-------
values : `~astropy.units.Quantity`
Interpolated value.
"""
pars = {}
for name in self.required_parameters:
value = self._interpolators[name]((energy_true, offset))
pars[name] = value
return pars
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def to_table(self, format="gadf-dl3"):
"""Convert PSF table data to table.
Parameters
----------
format : {"gadf-dl3"}
Format specification. Default is "gadf-dl3".
Returns
-------
hdu_list : `~astropy.io.fits.HDUList`
PSF in HDU list format.
"""
from gammapy.irf.io import IRF_DL3_HDU_SPECIFICATION
table = self.axes.to_table(format="gadf-dl3")
spec = IRF_DL3_HDU_SPECIFICATION[self.tag]["column_name"]
for name in self.required_parameters:
column_name = spec[name]
table[column_name] = self.data[name].T[np.newaxis]
table[column_name].unit = self.unit[name]
# Create hdu and hdu list
return table
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@classmethod
def from_table(cls, table, format="gadf-dl3"):
"""Create parametric PSF from `~astropy.table.Table`.
Parameters
----------
table : `~astropy.table.Table`
Table information.
format : {"gadf-dl3"}, optional
Format specification. Default is "gadf-dl3".
Returns
-------
psf : `~ParametricPSF`
PSF class.
"""
from gammapy.irf.io import IRF_DL3_HDU_SPECIFICATION
axes = MapAxes.from_table(table, format=format)[cls.required_axes]
dtype = {
"names": cls.required_parameters,
"formats": len(cls.required_parameters) * (np.float32,),
}
data = np.empty(axes.shape, dtype=dtype)
unit = {}
spec = IRF_DL3_HDU_SPECIFICATION[cls.tag]["column_name"]
for name in cls.required_parameters:
column = table[spec[name]]
values = column.data[0].transpose()
# This fixes some files where sigma is written as zero
if "sigma" in name:
values[values == 0] = 1.0
data[name] = values.reshape(axes.shape)
unit[name] = column.unit or ""
unit = {key: u.Unit(val) for key, val in unit.items()}
return cls(axes=axes, data=data, meta=table.meta.copy(), unit=unit)
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def to_psf3d(self, rad=None):
"""Create a PSF3D from a parametric PSF.
It will be defined on the same energy and offset values than the input PSF.
Parameters
----------
rad : `~astropy.units.Quantity`
Rad values.
Returns
-------
psf3d : `~gammapy.irf.PSF3D`
3D PSF.
"""
from gammapy.datasets.map import RAD_AXIS_DEFAULT
from gammapy.irf import PSF3D
offset_axis = self.axes["offset"]
energy_axis_true = self.axes["energy_true"]
if rad is None:
rad_axis = RAD_AXIS_DEFAULT
else:
rad_axis = MapAxis.from_edges(rad, name="rad")
axes = MapAxes([energy_axis_true, offset_axis, rad_axis])
data = self.evaluate(**axes.get_coord())
return PSF3D(axes=axes, data=data.value, unit=data.unit, meta=self.meta.copy())
def __str__(self):
str_ = f"{self.__class__.__name__}\n"
str_ += "-" * len(self.__class__.__name__) + "\n\n"
str_ += f"\taxes : {self.axes.names}\n"
str_ += f"\tshape : {self.data.shape}\n"
str_ += f"\tndim : {len(self.axes)}\n"
str_ += f"\tparameters: {self.required_parameters}\n"
return str_.expandtabs(tabsize=2)
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def containment(self, rad, **kwargs):
"""Containment of the PSF at given axes coordinates.
Parameters
----------
rad : `~astropy.units.Quantity`
Rad value.
**kwargs : dict
Other coordinates.
Returns
-------
containment : `~numpy.ndarray`
Containment.
"""
pars = self.evaluate_parameters(**kwargs)
containment = self.evaluate_containment(rad=rad, **pars)
return containment
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def evaluate(self, rad, **kwargs):
"""Evaluate the PSF model.
Parameters
----------
rad : `~astropy.coordinates.Angle`
Offset from PSF center used for evaluating the PSF on a grid.
**kwargs : dict
Other coordinates.
Returns
-------
psf_value : `~astropy.units.Quantity`
PSF value.
"""
pars = self.evaluate_parameters(**kwargs)
value = self.evaluate_direct(rad=rad, **pars)
return value
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def is_allclose(self, other, rtol_axes=1e-3, atol_axes=1e-6, **kwargs):
"""Compare two data IRFs for equivalency.
Parameters
----------
other : `gammapy.irfs.ParametricPSF`
The PSF to compare against.
rtol_axes : float, optional
Relative tolerance for the axis comparison. Default is 1e-3.
atol_axes : float, optional
Relative tolerance for the axis comparison. Default is 1e-6.
**kwargs : dict
Keywords passed to `numpy.allclose`.
Returns
-------
is_allclose : bool
Whether the IRF is all close.
"""
if not isinstance(other, self.__class__):
return TypeError(f"Cannot compare {type(self)} and {type(other)}")
data_eq = True
for key in self.quantity.keys():
if self.quantity[key].shape != other.quantity[key].shape:
return False
data_eq &= np.allclose(self.quantity[key], other.quantity[key], **kwargs)
axes_eq = self.axes.is_allclose(other.axes, rtol=rtol_axes, atol=atol_axes)
return axes_eq and data_eq
def get_sigmas_and_norms(**kwargs):
"""Convert scale and amplitude to norms."""
sigmas = u.Quantity([kwargs[f"sigma_{idx}"] for idx in [1, 2, 3]])
scale = kwargs["scale"]
ones = np.ones(scale.shape)
amplitudes = u.Quantity([ones, kwargs["ampl_2"], kwargs["ampl_3"]])
norms = 2 * scale * amplitudes * sigmas**2
return sigmas, norms
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class EnergyDependentMultiGaussPSF(ParametricPSF):
"""Triple Gauss analytical PSF depending on true energy and offset.
Parameters
----------
axes : list of `MapAxis`
Required axes are ["energy_true", "offset"].
data : `~numpy.recarray`
Data array.
meta : dict
Metadata dictionary.
Examples
--------
Plot R68 of the PSF vs. offset and true energy:
.. plot::
:include-source:
import matplotlib.pyplot as plt
from gammapy.irf import EnergyDependentMultiGaussPSF
filename = '$GAMMAPY_DATA/cta-1dc/caldb/data/cta/1dc/bcf/South_z20_50h/irf_file.fits'
psf = EnergyDependentMultiGaussPSF.read(filename, hdu='POINT SPREAD FUNCTION')
psf.plot_containment_radius(fraction=0.68)
plt.show()
"""
tag = "psf_3gauss"
required_axes = ["energy_true", "offset"]
required_parameters = ["sigma_1", "sigma_2", "sigma_3", "scale", "ampl_2", "ampl_3"]
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@staticmethod
def evaluate_containment(rad, **kwargs):
"""Containment of the PSF at given axes coordinates.
Parameters
----------
rad : `~astropy.units.Quantity`
Rad value.
**kwargs : dict
Parameters, see `required_parameters`.
Returns
-------
containment : `~numpy.ndarray`
Containment.
"""
sigmas, norms = get_sigmas_and_norms(**kwargs)
m = MultiGauss2D(sigmas=sigmas, norms=norms)
m.normalize()
containment = m.containment_fraction(rad)
return containment
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@staticmethod
def evaluate_direct(rad, **kwargs):
"""Evaluate PSF model.
Parameters
----------
rad : `~astropy.units.Quantity`
Rad value.
**kwargs : dict
Parameters, see `required_parameters`.
Returns
-------
value : `~numpy.ndarray`
PSF value.
"""
sigmas, norms = get_sigmas_and_norms(**kwargs)
m = MultiGauss2D(sigmas=sigmas, norms=norms)
m.normalize()
return m(rad)
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class PSFKing(ParametricPSF):
"""King profile analytical PSF depending on energy and offset.
This PSF parametrisation and FITS data format is described here: :ref:`gadf:psf_king`.
Parameters
----------
axes : list of `MapAxis` or `MapAxes`
Data axes, required are ["energy_true", "offset"].
meta : dict
Metadata dictionary.
"""
tag = "psf_king"
required_axes = ["energy_true", "offset"]
required_parameters = ["gamma", "sigma"]
default_interp_kwargs = dict(bounds_error=False, fill_value=None)
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@staticmethod
def evaluate_containment(rad, gamma, sigma):
"""Containment of the PSF at given axes coordinates.
Parameters
----------
rad : `~astropy.units.Quantity`
Rad value.
gamma : `~astropy.units.Quantity`
Gamma parameter.
sigma : `~astropy.units.Quantity`
Sigma parameter.
Returns
-------
containment : `~numpy.ndarray`
Containment.
"""
with np.errstate(divide="ignore", invalid="ignore"):
powterm = 1 - gamma
term = (1 + rad**2 / (2 * gamma * sigma**2)) ** powterm
containment = 1 - term
return containment
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@staticmethod
def evaluate_direct(rad, gamma, sigma):
"""Evaluate the PSF model.
Formula is given here: :ref:`gadf:psf_king`.
Parameters
----------
rad : `~astropy.coordinates.Angle`
Offset from PSF center used for evaluating the PSF on a grid.
Returns
-------
psf_value : `~astropy.units.Quantity`
PSF value.
"""
with np.errstate(divide="ignore"):
term1 = 1 / (2 * np.pi * sigma**2)
term2 = 1 - 1 / gamma
term3 = (1 + rad**2 / (2 * gamma * sigma**2)) ** (-gamma)
return term1 * term2 * term3
