Source code for gammapy.cube.psf_kernel

# Licensed under a 3-clause BSD style license - see LICENSE.rst
from __future__ import absolute_import, division, print_function, unicode_literals
import numpy as np
from astropy.coordinates import Angle
from astropy.coordinates.angle_utilities import angular_separation
import astropy.units as u
from ..utils.gauss import Gauss2DPDF
from ..maps import Map, WcsGeom
from ..irf import TablePSF
from ..spectrum.models import PowerLaw

__all__ = ["PSFKernel"]


def _make_kernel_geom(geom, max_radius):
    # Create a new geom object with an odd number of pixel and a maximum size
    # This is useful for PSF kernel creation.
    center = geom.center_coord[:2]
    binsz = Angle(np.abs(geom.wcs.wcs.cdelt[0]), "deg")
    max_radius = Angle(max_radius)
    npix = 2 * int(max_radius.deg / binsz.deg) + 1
    return WcsGeom.create(
        skydir=center,
        binsz=binsz,
        npix=npix,
        proj=geom.projection,
        coordsys=geom.coordsys,
        axes=geom.axes,
    )


def _compute_kernel_separations(geom, factor):
    # utility function used for preparing distance to the center of the upsampled geom
    # TODO : take into account non regular geometry for energy dependent PSF kernel size
    if geom.is_regular is False:
        raise ValueError("Non regular geometries are not supported yet.")

    upsampled_image_geom = geom.to_image().upsample(factor)
    # get center coordinate
    center_coord = upsampled_image_geom.center_coord * u.deg
    # get coordinates
    map_c = upsampled_image_geom.get_coord()
    # compute distances to map center
    separations = angular_separation(
        center_coord[0], center_coord[1], map_c.lon * u.deg, map_c.lat * u.deg
    )

    # Create map
    kernel_map = Map.from_geom(geom=upsampled_image_geom.to_cube(axes=geom.axes))
    return kernel_map, separations


def table_psf_to_kernel_map(table_psf, geom, factor=4):
    """Compute a PSF kernel on a given MapGeom.

    If the MapGeom is not an image, the same kernel will be present on all axes.

    The PSF is estimated by oversampling defined by a given factor.
    The PSF kernel is normalized

    Parameters
    ----------
    table_psf : `~gammapy.irf.TablePSF`
        the input table PSF
    geom : `~gammapy.maps.MapGeom`
        the target geometry. The PSF kernel will be centered on the spatial center.
    factor : int
        the oversample factor to compute the PSF
    """
    # prepare map and compute distances to map center
    kernel_map, rads = _compute_kernel_separations(geom, factor)

    vals = table_psf.evaluate(rad=rads).value
    norm = vals.sum()

    for img, idx in kernel_map.iter_by_image():
        img += vals.reshape(img.shape) / norm

    return kernel_map.downsample(factor, preserve_counts=True)


def energy_dependent_table_psf_to_kernel_map(table_psf, geom, factor=4):
    """Compute an energy dependent PSF kernel on a given MapGeom.

    The PSF is estimated by oversampling defined by a given factor.

    Parameters
    ----------
    table_psf : `~gammapy.irf.EnergyDependentTablePSF`
        the input table PSF
    geom : `~gammapy.maps.MapGeom`
        the target geometry.
        The PSF kernel will be centered on the spatial centre.
        the geometry axes should contain an "energy" axis.
        The kernel will be duplicated along other axes.
    factor : int
        the oversample factor to compute the PSF
    """
    energy_axis = geom.get_axis_by_name("energy")
    energy_idx = geom.axes.index(energy_axis)
    energy_unit = u.Unit(energy_axis.unit)

    # prepare map and compute distances to map center
    kernel_map, rads = _compute_kernel_separations(geom, factor)

    # loop over images
    for img, idx in kernel_map.iter_by_image():
        # TODO: this is super complex. Find or invent a better way!
        energy = energy_axis.center[idx[energy_idx]] * energy_unit
        vals = table_psf.evaluate(energy=energy, rad=rads).reshape(img.shape)
        img += vals.value / vals.sum().value

    return kernel_map.downsample(factor, preserve_counts=True)


[docs]class PSFKernel(object): """PSF kernel for `~gammapy.maps.Map`. This is a container class to store a PSF kernel that can be used to convolve `~gammapy.maps.WcsNDMap` objects. It is usually computed from an `~gammapy.irf.EnergyDependentTablePSF`. Parameters ---------- psf_kernel_map : `~gammapy.maps.Map` PSF kernel stored in a Map Examples -------- :: import numpy as np from gammapy.maps import Map, WcsGeom, MapAxis from gammapy.irf import EnergyDependentMultiGaussPSF from gammapy.cube import PSFKernel from astropy import units as u # Define energy axis energy_axis = MapAxis.from_edges(np.logspace(-1., 1., 4), unit='TeV', name='energy') # Create WcsGeom and map geom = WcsGeom.create(binsz=0.02*u.deg, width=2.0*u.deg, axes=[energy_axis]) some_map = Map.from_geom(geom) # Fill map at two positions some_map.fill_by_coord([[0.2,0.4],[-0.1,0.6],[0.5,3.6]]) # Extract EnergyDependentTablePSF from CTA 1DC IRF filename = '$GAMMAPY_DATA/cta-1dc/caldb/data/cta/1dc/bcf/South_z20_50h/irf_file.fits' psf = EnergyDependentMultiGaussPSF.read(filename, hdu='POINT SPREAD FUNCTION') table_psf = psf.to_energy_dependent_table_psf(theta=0.5*u.deg) psf_kernel = PSFKernel.from_table_psf(table_psf,geom, max_radius=1*u.deg) # Do the convolution some_map_convolved = some_map.convolve(psf_kernel) some_map_convolved.get_image_by_coord(dict(energy=0.6*u.TeV)).plot() """ def __init__(self, psf_kernel_map): self._psf_kernel_map = psf_kernel_map @property def data(self): """Access the PSFKernel numpy array""" return self._psf_kernel_map.data @property def psf_kernel_map(self): """The map object holding the kernel (`~gammapy.maps.Map`)""" return self._psf_kernel_map
[docs] @classmethod def read(cls, *args, **kwargs): """Read kernel Map from file.""" psf_kernel_map = Map.read(*args, **kwargs) return cls(psf_kernel_map)
[docs] @classmethod def from_table_psf(cls, table_psf, geom, max_radius=None, factor=4): """Create a PSF kernel from a TablePSF or an EnergyDependentTablePSF on a given MapGeom. If the MapGeom is not an image, the same kernel will be present on all axes. The PSF is estimated by oversampling defined by a given factor. Parameters ---------- table_psf : `~gammapy.irf.TablePSF` or `~gammapy.irf.EnergyDependentTablePSF` the input table PSF geom : `~gammapy.maps.WcsGeom` the target geometry. The PSF kernel will be centered on the central pixel. The geometry axes should contain an axis with name "energy" max_radius : `~astropy.coordinates.Angle` the maximum radius of the PSF kernel. factor : int the oversample factor to compute the PSF Returns ------- kernel : `~gammapy.cube.PSFKernel` the kernel Map with reduced geometry according to the max_radius """ # TODO : use PSF containment radius if max_radius is None if max_radius is not None: geom = _make_kernel_geom(geom, max_radius) if isinstance(table_psf, TablePSF): return cls(table_psf_to_kernel_map(table_psf, geom, factor)) else: return cls( energy_dependent_table_psf_to_kernel_map(table_psf, geom, factor) )
[docs] @classmethod def from_gauss( cls, geom, sigma, max_radius=None, containment_fraction=0.99, factor=4 ): """Create Gaussian PSF. This is used for testing and examples. The map geometry parameters (pixel size, energy bins) are taken from ``geom``. The Gaussian width ``sigma`` is a scalar, TODO : support array input if it should vary along the energy axis. Parameters ---------- geom : `~gammapy.maps.WcsGeom` Map geometry sigma : `~astropy.coordinates.Angle` Gaussian width. max_radius : `~astropy.coordinates.Angle` Desired kernel map size. factor : int Oversample factor to compute the PSF Returns ------- kernel : `~gammapy.cube.PSFKernel` the kernel Map with reduced geometry according to the max_radius """ sigma = Angle(sigma) if max_radius is None: max_radius = ( Gauss2DPDF(sigma.deg).containment_radius( containment_fraction=containment_fraction ) * u.deg ) max_radius = Angle(max_radius) # Create a new geom according to given input geom = _make_kernel_geom(geom, max_radius) rad = Angle(np.linspace(0.0, max_radius.deg, 200), "deg") table_psf = TablePSF.from_shape(shape="gauss", width=sigma, rad=rad) return cls(table_psf_to_kernel_map(table_psf, geom, factor))
[docs] def write(self, *args, **kwargs): """Write the Map object which contains the PSF kernel to file.""" self.psf_kernel_map.write(*args, **kwargs)
[docs] def make_image(self, exposures, spectrum=None): """ Make a 2D PSF from a PSF kernel The PSF Kernel is first weighed with a spectrum and an array of exposures. The PSF is also normalised after summation. Parameters ---------- exposures : `~numpy.ndarray` An array of exposures for the same true energies as the PSF kernel spectrum : `~gammapy.spectrum.models.SpectralModel` Spectral model to compute the weights. Default is power-law with spectral index of 2. Returns ------- psf2D : `~gammapy.maps.Map` Weighted 2D psf """ if spectrum is None: spectrum = PowerLaw(index=2.0) energy_axis = self.psf_kernel_map.geom.get_axis_by_name("energy") energy_center = energy_axis.center * energy_axis.unit energy_edges = energy_axis.edges * energy_axis.unit energy_width = np.diff(energy_edges) weights = spectrum(energy_center) * energy_width * exposures weights /= weights.sum() psf_weighted = self.psf_kernel_map.copy() for img, idx in psf_weighted.iter_by_image(): img *= weights[idx].value psf2D = psf_weighted.sum_over_axes() psf2D.data = psf2D.data / psf2D.data.sum() return PSFKernel(psf2D)