Source code for

# 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 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 : {'asmooth', 'lima'} Significance estimation method. threshold : float Significance threshold. """ 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. 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, ) dataset_sliced.models = dataset.models 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( dataset_image.models = dataset.models # extract 2d arrays counts =[0].astype(float) background = dataset_image.npred_background().data[0] if isinstance(dataset_image, MapDatasetOnOff): background =[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([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([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