# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""Implementation of adaptive smoothing algorithms."""
import numpy as np
from astropy.convolution import Gaussian2DKernel, Tophat2DKernel
from astropy.coordinates import Angle
from gammapy.datasets import MapDatasetOnOff
from gammapy.maps import Map, Maps, WcsNDMap
from gammapy.modeling.models import PowerLawSpectralModel
from gammapy.stats import CashCountsStatistic
from gammapy.utils.array import scale_cube
from gammapy.utils.pbar import progress_bar
from ..core import Estimator
from ..utils import estimate_exposure_reco_energy
__all__ = ["ASmoothMapEstimator"]
def _sqrt_ts_asmooth(counts, background):
"""Significance according to formula (5) in asmooth paper."""
return (counts - background) / np.sqrt(counts + background)
[docs]class ASmoothMapEstimator(Estimator):
"""Adaptively smooth counts image.
Achieves a roughly constant sqrt(TS) of features across the whole image.
Algorithm based on https://ui.adsabs.harvard.edu/abs/2006MNRAS.368...65E .
The algorithm was slightly adapted to also allow Li & Ma to estimate the
sqrt(TS) of a feature in the image.
Parameters
----------
scales : `~astropy.units.Quantity`
Smoothing scales.
kernel : `astropy.convolution.Kernel`
Smoothing kernel.
spectrum : `SpectralModel`
Spectral model assumption.
method : {'lima', 'asmooth'}
Significance estimation method. Default is 'lima'.
threshold : float
Significance threshold. Default is 5.
energy_edges : list of `~astropy.units.Quantity`, optional
Edges of the target maps energy bins. The resulting bin edges won't be exactly equal to the input ones,
but rather the closest values to the energy axis edges of the parent dataset.
Default is None: apply the estimator in each energy bin of the parent dataset.
For further explanation see :ref:`estimators`.
Examples
--------
>>> import astropy.units as u
>>> import numpy as np
>>> from gammapy.estimators import ASmoothMapEstimator
>>> from gammapy.datasets import MapDataset
>>> dataset = MapDataset.read("$GAMMAPY_DATA/cta-1dc-gc/cta-1dc-gc.fits.gz")
>>> scales = u.Quantity(np.arange(0.1, 1, 0.1), unit="deg")
>>> smooth = ASmoothMapEstimator(threshold=3, scales=scales, energy_edges=[1, 10] * u.TeV)
>>> images = smooth.run(dataset)
"""
tag = "ASmoothMapEstimator"
def __init__(
self,
scales=None,
kernel=Gaussian2DKernel,
spectrum=None,
method="lima",
threshold=5,
energy_edges=None,
):
if spectrum is None:
spectrum = PowerLawSpectralModel()
self.spectrum = spectrum
if scales is None:
scales = self.get_scales(n_scales=9, kernel=kernel)
self.scales = scales
self.kernel = kernel
self.threshold = threshold
self.method = method
self.energy_edges = energy_edges
[docs] def selection_all(self):
"""Which quantities are computed."""
return
[docs] @staticmethod
def get_scales(n_scales, factor=np.sqrt(2), kernel=Gaussian2DKernel):
"""Create list of Gaussian widths.
Parameters
----------
n_scales : int
Number of scales.
factor : float
Incremental factor.
Returns
-------
scales : `~numpy.ndarray`
Scale array.
"""
if kernel == Gaussian2DKernel:
sigma_0 = 1.0 / np.sqrt(9 * np.pi)
elif kernel == Tophat2DKernel:
sigma_0 = 1.0 / np.sqrt(np.pi)
return sigma_0 * factor ** np.arange(n_scales)
[docs] def get_kernels(self, pixel_scale):
"""Get kernels according to the specified method.
Parameters
----------
pixel_scale : `~astropy.coordinates.Angle`
Sky image pixel scale.
Returns
-------
kernels : list
List of `~astropy.convolution.Kernel`.
"""
scales = self.scales.to_value("deg") / Angle(pixel_scale).deg
kernels = []
for scale in scales: # .value:
kernel = self.kernel(scale, mode="oversample")
# TODO: check if normalizing here makes sense
kernel.normalize("peak")
kernels.append(kernel)
return kernels
@staticmethod
def _sqrt_ts_cube(cubes, method):
if method in {"lima"}:
scube = CashCountsStatistic(cubes["counts"], cubes["background"]).sqrt_ts
elif method == "asmooth":
scube = _sqrt_ts_asmooth(cubes["counts"], cubes["background"])
elif method == "ts":
raise NotImplementedError()
else:
raise ValueError(
"Not a valid sqrt_ts estimation method."
" Choose one of the following: 'lima' or 'asmooth'"
)
return scube
[docs] def run(self, dataset):
"""Run adaptive smoothing on input MapDataset.
Notes
-----
The progress bar can be displayed for this function.
Parameters
----------
dataset : `~gammapy.datasets.MapDataset` or `~gammapy.datasets.MapDatasetOnOff`
The input dataset (with one bin in energy at most).
Returns
-------
images : dict of `~gammapy.maps.WcsNDMap`
Smoothed images; keys are:
* 'counts'
* 'background'
* 'flux' (optional)
* 'scales'
* 'sqrt_ts'.
"""
energy_axis = self._get_energy_axis(dataset)
results = []
for energy_min, energy_max in progress_bar(
energy_axis.iter_by_edges, desc="Energy bins"
):
dataset_sliced = dataset.slice_by_energy(
energy_min=energy_min, energy_max=energy_max, name=dataset.name
)
if dataset.models is not None:
models_sliced = dataset.models._slice_by_energy(
energy_min=energy_min,
energy_max=energy_max,
)
dataset_sliced.models = models_sliced
result = self.estimate_maps(dataset_sliced)
results.append(result)
maps = Maps()
for name in results[0].keys():
maps[name] = Map.from_stack(
maps=[_[name] for _ in results], axis_name="energy"
)
return maps
[docs] def estimate_maps(self, dataset):
"""Run adaptive smoothing on input Maps.
Parameters
----------
dataset : `MapDataset`
Dataset.
Returns
-------
images : dict of `~gammapy.maps.WcsNDMap`
Smoothed images; keys are:
* 'counts'
* 'background'
* 'flux' (optional)
* 'scales'
* 'sqrt_ts'.
"""
dataset_image = dataset.to_image(name=dataset.name)
dataset_image.models = dataset.models
# extract 2d arrays
counts = dataset_image.counts.data[0].astype(float)
background = dataset_image.npred_background().data[0]
if isinstance(dataset_image, MapDatasetOnOff):
background = dataset_image.background.data[0]
if dataset_image.exposure is not None:
exposure = estimate_exposure_reco_energy(dataset_image, self.spectrum)
else:
exposure = None
pixel_scale = dataset_image.counts.geom.pixel_scales.mean()
kernels = self.get_kernels(pixel_scale)
cubes = {}
cubes["counts"] = scale_cube(counts, kernels)
cubes["background"] = scale_cube(background, kernels)
if exposure is not None:
flux = (dataset_image.counts - background) / exposure
cubes["flux"] = scale_cube(flux.data[0], kernels)
cubes["sqrt_ts"] = self._sqrt_ts_cube(cubes, method=self.method)
smoothed = self._reduce_cubes(cubes, kernels)
result = {}
geom = dataset_image.counts.geom
for name, data in smoothed.items():
# set remaining pixels with sqrt_ts < threshold to mean value
if name in ["counts", "background"]:
mask = np.isnan(data)
data[mask] = np.mean(locals()[name][mask])
result[name] = WcsNDMap(geom, data, unit="")
else:
unit = "deg" if name == "scale" else ""
result[name] = WcsNDMap(geom, data, unit=unit)
if exposure is not None:
data = smoothed["flux"]
mask = np.isnan(data)
data[mask] = np.mean(flux.data[0][mask])
result["flux"] = WcsNDMap(geom, data, unit=flux.unit)
return result
def _reduce_cubes(self, cubes, kernels):
"""
Combine scale cube to image.
Parameters
----------
cubes : dict
Data cubes.
"""
shape = cubes["counts"].shape[:2]
smoothed = {}
# Init smoothed data arrays
for key in ["counts", "background", "scale", "sqrt_ts"]:
smoothed[key] = np.tile(np.nan, shape)
if "flux" in cubes:
smoothed["flux"] = np.tile(np.nan, shape)
for idx, scale in enumerate(self.scales):
# slice out 2D image at index idx out of cube
slice_ = np.s_[:, :, idx]
mask = np.isnan(smoothed["counts"])
mask = (cubes["sqrt_ts"][slice_] > self.threshold) & mask
smoothed["scale"][mask] = scale
smoothed["sqrt_ts"][mask] = cubes["sqrt_ts"][slice_][mask]
# renormalize smoothed data arrays
norm = kernels[idx].array.sum()
for key in ["counts", "background"]:
smoothed[key][mask] = cubes[key][slice_][mask] / norm
if "flux" in cubes:
smoothed["flux"][mask] = cubes["flux"][slice_][mask] / norm
return smoothed