# Licensed under a 3-clause BSD style license - see LICENSE.rst
import logging
import numpy as np
import scipy.integrate
from astropy import units as u
from astropy.coordinates import Angle
from astropy.io import fits
from astropy.utils import lazyproperty
from gammapy.utils.array import array_stats_str
from gammapy.utils.energy import energy_logspace
from gammapy.utils.gauss import Gauss2DPDF
from gammapy.utils.interpolation import ScaledRegularGridInterpolator
from gammapy.utils.scripts import make_path
__all__ = ["TablePSF", "EnergyDependentTablePSF"]
log = logging.getLogger(__name__)
[docs]class TablePSF:
r"""Radially-symmetric table PSF.
Parameters
----------
rad : `~astropy.units.Quantity` with angle units
Offset wrt source position
psf_value : `~astropy.units.Quantity` with sr^-1 units
PSF value array
interp_kwargs : dict
Keyword arguments passed to `ScaledRegularGridInterpolator`
"""
def __init__(self, rad, psf_value, interp_kwargs=None):
self.rad = Angle(rad).to("rad")
self.psf_value = u.Quantity(psf_value).to("sr^-1")
self._interp_kwargs = interp_kwargs or {}
@lazyproperty
def _interpolate(self):
points = (self.rad,)
return ScaledRegularGridInterpolator(
points=points, values=self.psf_value, **self._interp_kwargs
)
@lazyproperty
def _interpolate_containment(self):
if self.rad[0] > 0:
rad = self.rad.insert(0, 0)
else:
rad = self.rad
rad_drad = 2 * np.pi * rad * self.evaluate(rad)
values = scipy.integrate.cumtrapz(
rad_drad.to_value("rad-1"), rad.to_value("rad"), initial=0
)
return ScaledRegularGridInterpolator(points=(rad,), values=values, fill_value=1)
[docs] @classmethod
def from_shape(cls, shape, width, rad):
"""Make TablePSF objects with commonly used shapes.
This function is mostly useful for examples and testing.
Parameters
----------
shape : {'disk', 'gauss'}
PSF shape.
width : `~astropy.units.Quantity` with angle units
PSF width angle (radius for disk, sigma for Gauss).
rad : `~astropy.units.Quantity` with angle units
Offset angle
Returns
-------
psf : `TablePSF`
Table PSF
Examples
--------
>>> import numpy as np
>>> from astropy.coordinates import Angle
>>> from gammapy.irf import TablePSF
>>> rad = Angle(np.linspace(0, 0.7, 100), 'deg')
>>> psf = TablePSF.from_shape(shape='gauss', width='0.2 deg', rad=rad)
"""
width = Angle(width)
rad = Angle(rad)
if shape == "disk":
amplitude = 1 / (np.pi * width.radian ** 2)
psf_value = np.where(rad < width, amplitude, 0)
elif shape == "gauss":
gauss2d_pdf = Gauss2DPDF(sigma=width.radian)
psf_value = gauss2d_pdf(rad.radian)
else:
raise ValueError(f"Invalid shape: {shape}")
psf_value = u.Quantity(psf_value, "sr^-1")
return cls(rad, psf_value)
[docs] def info(self):
"""Print basic info."""
ss = array_stats_str(self.rad.deg, "offset")
ss += f"integral = {self.integral()}\n"
for containment in [68, 80, 95]:
radius = self.containment_radius(0.01 * containment)
ss += f"containment radius {radius.deg} deg for {containment}%\n"
return ss
[docs] def evaluate(self, rad):
r"""Evaluate PSF.
The following PSF quantities are available:
* 'dp_domega': PDF per 2-dim solid angle :math:`\Omega` in sr^-1
.. math:: \frac{dP}{d\Omega}
Parameters
----------
rad : `~astropy.coordinates.Angle`
Offset wrt source position
Returns
-------
psf_value : `~astropy.units.Quantity`
PSF value
"""
rad = np.atleast_1d(u.Quantity(rad))
return self._interpolate((rad,))
[docs] def containment(self, rad_max):
"""Compute PSF containment fraction.
Parameters
----------
rad_max : `~astropy.units.Quantity`
Offset angle range
Returns
-------
integral : float
PSF integral
"""
rad = np.atleast_1d(rad_max)
return self._interpolate_containment((rad,))
[docs] def containment_radius(self, fraction):
"""Containment radius.
Parameters
----------
fraction : array_like
Containment fraction (range 0 .. 1)
Returns
-------
rad : `~astropy.coordinates.Angle`
Containment radius angle
"""
rad_max = Angle(np.linspace(0, self.rad[-1].value, 10 * len(self.rad)), "rad")
containment = self.containment(rad_max=rad_max)
if not np.allclose(containment.max(), 1, atol=0.01):
log.warn(
"PSF does not integrate to unity within a precision of 1%."
" Containment radius computation might give biased results."
)
fraction = np.atleast_1d(fraction)
fraction_idx = np.argmin(np.abs(containment - fraction[:, np.newaxis]), axis=1)
return rad_max[fraction_idx].to("deg")
[docs] def normalize(self):
"""Normalize PSF to unit integral.
Computes the total PSF integral via the :math:`dP / dr` spline
and then divides the :math:`dP / dr` array.
"""
integral = self.containment(self.rad[-1])
self.psf_value /= integral
[docs] def broaden(self, factor, normalize=True):
r"""Broaden PSF by scaling the offset array.
For a broadening factor :math:`f` and the offset
array :math:`r`, the offset array scaled
in the following way:
.. math::
r_{new} = f \times r_{old}
\frac{dP}{dr}(r_{new}) = \frac{dP}{dr}(r_{old})
Parameters
----------
factor : float
Broadening factor
normalize : bool
Normalize PSF after broadening
"""
self.rad *= factor
self._setup_interpolators()
if normalize:
self.normalize()
[docs] def plot_psf_vs_rad(self, ax=None, **kwargs):
"""Plot PSF vs radius.
Parameters
----------
ax : ``
kwargs : dict
Keyword arguments passed to `matplotlib.pyplot.plot`
"""
import matplotlib.pyplot as plt
ax = plt.gca() if ax is None else ax
ax.plot(self.rad.to_value("deg"), self.psf_value.to_value("sr-1"), **kwargs)
ax.set_yscale("log")
ax.set_xlabel("Radius (deg)")
ax.set_ylabel("PSF (sr-1)")
[docs]class EnergyDependentTablePSF:
"""Energy-dependent radially-symmetric table PSF (``gtpsf`` format).
TODO: add references and explanations.
Parameters
----------
energy : `~astropy.units.Quantity`
Energy (1-dim)
rad : `~astropy.units.Quantity` with angle units
Offset angle wrt source position (1-dim)
exposure : `~astropy.units.Quantity`
Exposure (1-dim)
psf_value : `~astropy.units.Quantity`
PSF (2-dim with axes: psf[energy_index, offset_index]
interp_kwargs : dict
Interpolation keyword arguments pass to `ScaledRegularGridInterpolator`.
"""
def __init__(self, energy, rad, exposure=None, psf_value=None, interp_kwargs=None):
self.energy = u.Quantity(energy).to("GeV")
self.rad = u.Quantity(rad).to("radian")
if exposure is None:
self.exposure = u.Quantity(np.ones(len(energy)), "cm^2 s")
else:
self.exposure = u.Quantity(exposure).to("cm^2 s")
if psf_value is None:
self.psf_value = u.Quantity(np.zeros(len(energy), len(rad)), "sr^-1")
else:
self.psf_value = u.Quantity(psf_value).to("sr^-1")
self._interp_kwargs = interp_kwargs or {}
@lazyproperty
def _interpolate(self):
points = (self.energy, self.rad)
return ScaledRegularGridInterpolator(
points=points, values=self.psf_value, **self._interp_kwargs
)
@lazyproperty
def _interpolate_containment(self):
if self.rad[0] > 0:
rad = self.rad.insert(0, 0)
else:
rad = self.rad
rad_drad = 2 * np.pi * rad * self.evaluate(energy=self.energy, rad=rad)
values = scipy.integrate.cumtrapz(
rad_drad.to_value("rad-1"), rad.to_value("rad"), initial=0, axis=1
)
points = (self.energy, rad)
return ScaledRegularGridInterpolator(points=points, values=values, fill_value=1)
def __str__(self):
ss = "EnergyDependentTablePSF\n"
ss += "-----------------------\n"
ss += "\nAxis info:\n"
ss += " " + array_stats_str(self.rad.to("deg"), "rad")
ss += " " + array_stats_str(self.energy, "energy")
ss += "\nContainment info:\n"
# Print some example containment radii
fractions = [0.68, 0.95]
energies = u.Quantity([10, 100], "GeV")
for fraction in fractions:
rads = self.containment_radius(energy=energies, fraction=fraction)
for energy, rad in zip(energies, rads):
ss += f" {100 * fraction}% containment radius at {energy:3.0f}: {rad:.2f}\n"
return ss
[docs] @classmethod
def from_fits(cls, hdu_list):
"""Create `EnergyDependentTablePSF` from ``gtpsf`` format HDU list.
Parameters
----------
hdu_list : `~astropy.io.fits.HDUList`
HDU list with ``THETA`` and ``PSF`` extensions.
"""
rad = Angle(hdu_list["THETA"].data["Theta"], "deg")
energy = u.Quantity(hdu_list["PSF"].data["Energy"], "MeV")
exposure = u.Quantity(hdu_list["PSF"].data["Exposure"], "cm^2 s")
psf_value = u.Quantity(hdu_list["PSF"].data["PSF"], "sr^-1")
return cls(energy, rad, exposure, psf_value)
[docs] def to_fits(self):
"""Convert to FITS HDU list format.
Returns
-------
hdu_list : `~astropy.io.fits.HDUList`
PSF in HDU list format.
"""
# TODO: write HEADER keywords as gtpsf
data = self.rad
theta_hdu = fits.BinTableHDU(data=data, name="Theta")
data = [self.energy, self.exposure, self.psf_value]
psf_hdu = fits.BinTableHDU(data=data, name="PSF")
hdu_list = fits.HDUList([theta_hdu, psf_hdu])
return hdu_list
[docs] @classmethod
def read(cls, filename):
"""Create `EnergyDependentTablePSF` from ``gtpsf``-format FITS file.
Parameters
----------
filename : str
File name
"""
filename = str(make_path(filename))
with fits.open(filename, memmap=False) as hdulist:
psf = cls.from_fits(hdulist)
return psf
[docs] def write(self, *args, **kwargs):
"""Write to FITS file.
Calls `~astropy.io.fits.HDUList.writeto`, forwarding all arguments.
"""
self.to_fits().writeto(*args, **kwargs)
[docs] def evaluate(self, energy=None, rad=None, method="linear"):
"""Evaluate the PSF at a given energy and offset
Parameters
----------
energy : `~astropy.units.Quantity`
Energy value
rad : `~astropy.coordinates.Angle`
Offset wrt source position
method : {"linear", "nearest"}
Linear or nearest neighbour interpolation.
Returns
-------
values : `~astropy.units.Quantity`
Interpolated value
"""
if energy is None:
energy = self.energy
if rad is None:
rad = self.rad
energy = np.atleast_1d(u.Quantity(energy))[:, np.newaxis]
rad = np.atleast_1d(u.Quantity(rad))
return self._interpolate((energy, rad), clip=True, method=method)
[docs] def table_psf_at_energy(self, energy, method="linear", **kwargs):
"""Create `~gammapy.irf.TablePSF` at one given energy.
Parameters
----------
energy : `~astropy.units.Quantity`
Energy
method : {"linear", "nearest"}
Linear or nearest neighbour interpolation.
Returns
-------
psf : `~gammapy.irf.TablePSF`
Table PSF
"""
psf_value = self.evaluate(energy=energy, method=method)[0, :]
return TablePSF(self.rad, psf_value, **kwargs)
[docs] def table_psf_in_energy_band(self, energy_band, spectrum=None, n_bins=11, **kwargs):
"""Average PSF in a given energy band.
Expected counts in sub energy bands given the given exposure
and spectrum are used as weights.
Parameters
----------
energy_band : `~astropy.units.Quantity`
Energy band
spectrum : `~gammapy.modeling.models.SpectralModel`
Spectral model used for weighting the PSF. Default is a power law
with index=2.
n_bins : int
Number of energy points in the energy band, used to compute the
weigthed PSF.
Returns
-------
psf : `TablePSF`
Table PSF
"""
from gammapy.modeling.models import PowerLawSpectralModel, TemplateSpectralModel
if spectrum is None:
spectrum = PowerLawSpectralModel()
exposure = TemplateSpectralModel(self.energy, self.exposure)
e_min, e_max = energy_band
energy = energy_logspace(emin=e_min, emax=e_max, nbins=n_bins)
weights = (spectrum * exposure)(energy)
weights /= weights.sum()
psf_value = self.evaluate(energy=energy)
psf_value_weighted = weights[:, np.newaxis] * psf_value
return TablePSF(self.rad, psf_value_weighted.sum(axis=0), **kwargs)
[docs] def containment_radius(self, energy, fraction=0.68):
"""Containment radius.
Parameters
----------
energy : `~astropy.units.Quantity`
Energy
fraction : float
Containment fraction.
Returns
-------
rad : `~astropy.units.Quantity`
Containment radius in deg
"""
# upsamle for better precision
rad_max = Angle(np.linspace(0, self.rad[-1].value, 10 * len(self.rad)), "rad")
containment = self.containment(energy=energy, rad_max=rad_max)
if not np.allclose(containment.max(axis=1), 1, atol=0.01):
log.warning(
"PSF does not integrate to unity within a precision of 1% in each energy bin."
" Containment radius computation might give biased results."
)
# find nearest containment value
fraction_idx = np.argmin(np.abs(containment - fraction), axis=1)
return rad_max[fraction_idx].to("deg")
[docs] def containment(self, energy, rad_max):
"""Compute containment of the PSF.
Parameters
----------
energy : `~astropy.units.Quantity`
Energy
rad_max : `~astropy.coordinates.Angle`
Maximum offset angle.
Returns
-------
fraction : array_like
Containment fraction (in range 0 .. 1)
"""
energy = np.atleast_1d(u.Quantity(energy))[:, np.newaxis]
rad_max = np.atleast_1d(u.Quantity(rad_max))
return self._interpolate_containment((energy, rad_max))
[docs] def info(self):
"""Print basic info"""
print(str(self))
[docs] def plot_psf_vs_rad(self, energies=None, ax=None, **kwargs):
"""Plot PSF vs radius.
Parameters
----------
energy : `~astropy.units.Quantity`
Energies where to plot the PSF.
**kwargs : dict
Keyword arguments pass to `~matplotlib.pyplot.plot`.
"""
import matplotlib.pyplot as plt
if energies is None:
energies = [100, 1000, 10000] * u.GeV
ax = plt.gca() if ax is None else ax
for energy in energies:
psf_value = np.squeeze(self.evaluate(energy=energy))
label = f"{energy:.0f}"
ax.plot(
self.rad.to_value("deg"),
psf_value.to_value("sr-1"),
label=label,
**kwargs,
)
ax.set_yscale("log")
ax.set_xlabel("Offset (deg)")
ax.set_ylabel("PSF (1 / sr)")
plt.legend()
return ax
[docs] def plot_containment_vs_energy(
self, ax=None, fractions=[0.68, 0.8, 0.95], **kwargs
):
"""Plot containment versus energy."""
import matplotlib.pyplot as plt
ax = plt.gca() if ax is None else ax
for fraction in fractions:
rad = self.containment_radius(self.energy, fraction)
label = f"{100 * fraction:.1f}% Containment"
ax.plot(self.energy.value, rad.value, label=label, **kwargs)
ax.semilogx()
ax.legend(loc="best")
ax.set_xlabel("Energy (GeV)")
ax.set_ylabel("Containment radius (deg)")
[docs] def plot_exposure_vs_energy(self):
"""Plot exposure versus energy."""
import matplotlib.pyplot as plt
plt.figure(figsize=(4, 3))
plt.plot(self.energy, self.exposure, color="black", lw=3)
plt.semilogx()
plt.xlabel("Energy (MeV)")
plt.ylabel("Exposure (cm^2 s)")
plt.xlim(1e4 / 1.3, 1.3 * 1e6)
plt.ylim(0, 1.5e11)
plt.tight_layout()
[docs] def stack(self, psf):
"""Stack two EnergyDependentTablePSF objects.s
Parameters
----------
psf : `EnergyDependentTablePSF`
PSF to stack.
Returns
-------
stacked_psf : `EnergyDependentTablePSF`
Stacked PSF.
"""
exposure = self.exposure + psf.exposure
psf_value = self.psf_value.T * self.exposure + psf.psf_value.T * psf.exposure
with np.errstate(invalid="ignore"):
# exposure can be zero
psf_value = np.nan_to_num(psf_value / exposure)
return self.__class__(
energy=self.energy, rad=self.rad, psf_value=psf_value.T, exposure=exposure
)