# Licensed under a 3-clause BSD style license - see LICENSE.rst
from __future__ import absolute_import, division, print_function, unicode_literals
import logging
import numpy as np
from astropy.table import Table
from astropy.units import Quantity
from astropy.coordinates import Angle
from astropy.io import fits
from ..utils.scripts import make_path
from ..utils.array import array_stats_str
from ..utils.energy import Energy, EnergyBounds
from . import EnergyDependentTablePSF
__all__ = ["PSFKing"]
log = logging.getLogger(__name__)
[docs]class PSFKing(object):
"""King profile analytical PSF depending on energy and offset.
This PSF parametrisation and FITS data format is described here: :ref:`gadf:psf_king`.
Parameters
----------
energy_lo : `~astropy.units.Quantity`
Lower energy boundary of the energy bin.
energy_hi : `~astropy.units.Quantity`
Upper energy boundary of the energy bin.
offset : `~astropy.coordinates.Angle`
Offset nodes (1D)
gamma : `~numpy.ndarray`
PSF parameter (2D)
sigma : `~astropy.coordinates.Angle`
PSF parameter (2D)
"""
def __init__(
self,
energy_lo,
energy_hi,
offset,
gamma,
sigma,
energy_thresh_lo=Quantity(0.1, "TeV"),
energy_thresh_hi=Quantity(100, "TeV"),
):
self.energy_lo = energy_lo.to("TeV")
self.energy_hi = energy_hi.to("TeV")
self.offset = Angle(offset)
ebounds = EnergyBounds.from_lower_and_upper_bounds(energy_lo, energy_hi)
self.energy = ebounds.log_centers
self.gamma = np.asanyarray(gamma)
self.sigma = Angle(sigma)
self.energy_thresh_lo = Quantity(energy_thresh_lo).to("TeV")
self.energy_thresh_hi = Quantity(energy_thresh_hi).to("TeV")
[docs] def info(self):
"""Print some basic info.
"""
ss = "\nSummary PSFKing info\n"
ss += "---------------------\n"
ss += array_stats_str(self.offset, "offset")
ss += array_stats_str(self.energy, "energy")
ss += array_stats_str(self.gamma, "gamma")
ss += array_stats_str(self.sigma, "sigma")
# TODO: should quote containment values also
return ss
[docs] @classmethod
def read(cls, filename, hdu=1):
"""Create `PSFKing` from FITS file.
Parameters
----------
filename : str
File name
"""
filename = str(make_path(filename))
# TODO: implement it so that HDUCLASS is used
# http://gamma-astro-data-formats.readthedocs.io/en/latest/data_storage/hdu_index/index.html
table = Table.read(filename, hdu=hdu)
return cls.from_table(table)
# hdu_list = fits.open(filename)
# hdu = hdu_list[hdu]
# return cls.from_fits(hdu)
[docs] @classmethod
def from_table(cls, table):
"""Create `PSFKing` from `~astropy.table.Table`.
Parameters
----------
table : `~astropy.table.Table`
Table King PSF info.
"""
offset_lo = table["THETA_LO"].quantity[0]
offset_hi = table["THETA_HI"].quantity[0]
offset = (offset_hi + offset_lo) / 2
offset = Angle(offset, unit=table["THETA_LO"].unit)
energy_lo = table["ENERG_LO"].quantity[0]
energy_hi = table["ENERG_HI"].quantity[0]
gamma = table["GAMMA"].quantity[0]
sigma = table["SIGMA"].quantity[0]
opts = {}
try:
opts["energy_thresh_lo"] = Quantity(table.meta["LO_THRES"], "TeV")
opts["energy_thresh_hi"] = Quantity(table.meta["HI_THRES"], "TeV")
except KeyError:
pass
return cls(energy_lo, energy_hi, offset, gamma, sigma, **opts)
[docs] def to_fits(self):
"""
Convert PSF table data to FITS HDU list.
Returns
-------
hdu_list : `~astropy.io.fits.HDUList`
PSF in HDU list format.
"""
# Set up data
names = ["ENERG_LO", "ENERG_HI", "THETA_LO", "THETA_HI", "SIGMA", "GAMMA"]
units = ["TeV", "TeV", "deg", "deg", "deg", ""]
data = [
self.energy_lo,
self.energy_hi,
self.offset,
self.offset,
self.sigma,
self.gamma,
]
table = Table()
for name_, data_, unit_ in zip(names, data, units):
table[name_] = [data_]
table[name_].unit = unit_
hdu = fits.BinTableHDU(table)
hdu.header["LO_THRES"] = self.energy_thresh_lo.value
hdu.header["HI_THRES"] = self.energy_thresh_hi.value
return fits.HDUList([fits.PrimaryHDU(), hdu])
[docs] def write(self, filename, *args, **kwargs):
"""Write PSF to FITS file.
Calls `~astropy.io.fits.HDUList.writeto`, forwarding all arguments.
"""
self.to_fits().writeto(filename, *args, **kwargs)
[docs] @staticmethod
def evaluate_direct(r, gamma, sigma):
"""Evaluate the PSF model.
Formula is given here: :ref:`gadf:psf_king`.
Parameters
----------
r : `~astropy.coordinates.Angle`
Offset from PSF center used for evaluating the PSF on a grid
gamma : `~astropy.units.Quantity`
model parameter, no unit
sigma : `~astropy.coordinates.Angle`
model parameter
Returns
-------
psf_value : `~astropy.units.Quantity`
PSF value
"""
r2 = r * r
sigma2 = sigma * sigma
with np.errstate(divide="ignore"):
term1 = 1 / (2 * np.pi * sigma2)
term2 = 1 - 1 / gamma
term3 = (1 + r2 / (2 * gamma * sigma2)) ** (-gamma)
return term1 * term2 * term3
[docs] def evaluate(self, energy=None, offset=None):
"""Evaluate analytic PSF parameters at a given energy and offset.
Uses nearest-neighbor interpolation.
Parameters
----------
energy : `~astropy.units.Quantity`
energy value
offset : `~astropy.coordinates.Angle`
Offset in the field of view
Returns
-------
values : `~astropy.units.Quantity`
Interpolated value
"""
param = dict()
energy = Energy(energy)
offset = Angle(offset)
# Find nearest energy value
i = np.argmin(np.abs(self.energy - energy))
j = np.argmin(np.abs(self.offset - offset))
# TODO: Use some kind of interpolation to get PSF
# parameters for every energy and theta
# Select correct gauss parameters for given energy and theta
sigma = self.sigma[j][i]
gamma = self.gamma[j][i]
param["sigma"] = sigma
param["gamma"] = gamma
return param
[docs] def to_energy_dependent_table_psf(self, theta=None, rad=None, exposure=None):
"""Convert to energy-dependent table PSF.
Parameters
----------
theta : `~astropy.coordinates.Angle`
Offset in the field of view. Default theta = 0 deg
rad : `~astropy.coordinates.Angle`
Offset from PSF center used for evaluating the PSF on a grid.
Default offset = [0, 0.005, ..., 1.495, 1.5] deg.
exposure : `~astropy.units.Quantity`
Energy dependent exposure. Should be in units equivalent to 'cm^2 s'.
Default exposure = 1.
Returns
-------
table_psf : `~gammapy.irf.EnergyDependentTablePSF`
Energy-dependent PSF
"""
# self.energy is already the logcenter
energies = self.energy
# Defaults
theta = theta if theta is not None else Angle(0, "deg")
rad = rad if rad is not None else Angle(np.arange(0, 1.5, 0.005), "deg")
psf_value = Quantity(np.empty((len(energies), len(rad))), "deg^-2")
for i, energy in enumerate(energies):
param_king = self.evaluate(energy, theta)
val = self.evaluate_direct(rad, param_king["gamma"], param_king["sigma"])
psf_value[i] = Quantity(val, "deg^-2")
return EnergyDependentTablePSF(
energy=energies, rad=rad, exposure=exposure, psf_value=psf_value
)