Source code for gammapy.estimators.asmooth_map

# 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 WcsNDMap
from gammapy.stats import CashCountsStatistic
from gammapy.utils.array import scale_cube

__all__ = ["ASmoothMapEstimator"]


def _significance_asmooth(counts, background):
    """Significance according to formula (5) in asmooth paper."""
    return (counts - background) / np.sqrt(counts + background)


[docs]class ASmoothMapEstimator: """Adaptively smooth counts image. Achieves a roughly constant significance 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 significance of a feature in the image. Parameters ---------- scales : `~astropy.units.Quantity` Smoothing scales. kernel : `astropy.convolution.Kernel` Smoothing kernel. method : {'asmooth', 'lima'} Significance estimation method. threshold : float Significance threshold. """ def __init__(self, scales, kernel=Gaussian2DKernel, method="lima", threshold=5): self.parameters = { "kernel": kernel, "method": method, "threshold": threshold, "scales": scales, }
[docs] def kernels(self, pixel_scale): """ Ring kernels according to the specified method. Parameters ---------- pixel_scale : `~astropy.coordinates.Angle` Sky image pixel scale Returns ------- kernels : list List of `~astropy.convolution.Kernel` """ p = self.parameters scales = p["scales"].to_value("deg") / Angle(pixel_scale).deg kernels = [] for scale in scales: # .value: kernel = p["kernel"](scale, mode="oversample") # TODO: check if normalizing here makes sense kernel.normalize("peak") kernels.append(kernel) return kernels
@staticmethod def _significance_cube(cubes, method): if method in {"lima"}: scube = CashCountsStatistic( cubes["counts"], cubes["background"] ).significance elif method == "asmooth": scube = _significance_asmooth(cubes["counts"], cubes["background"]) elif method == "ts": raise NotImplementedError() else: raise ValueError( "Not a valid significance estimation method." " Choose one of the following: 'lima' or 'asmooth'" ) return scube
[docs] def run(self, dataset): """ Run adaptive smoothing on input MapDataset. The latter should have Parameters ---------- dataset : `~gammapy.cube.MapDataset` or `~gammapy.cube.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' * 'significance'. """ # Check dimensionality if len(dataset.data_shape) == 3: if dataset.data_shape[0] != 1: raise ValueError( "ASmoothMapEstimator.run() requires a dataset with 1 energy bin at most." ) counts = dataset.counts.sum_over_axes(keepdims=False) background = dataset.npred() if isinstance(dataset, MapDatasetOnOff): background += dataset.background background = background.sum_over_axes(keepdims=False) if dataset.exposure is not None: exposure = dataset.exposure.sum_over_axes(keepdims=False) else: exposure = None return self.estimate_maps(counts, background, exposure)
[docs] def estimate_maps(self, counts, background, exposure=None): """ Run adaptive smoothing on input Maps. Parameters ---------- counts : `~gammapy.maps.Map` counts map background : `~gammapy.maps.Map` estimated background counts map exposure : `~gammapy.maps.Map` exposure map. If set, it will produce a flux smoothed map. Returns ------- images : dict of `~gammapy.maps.WcsNDMap` Smoothed images; keys are: * 'counts' * 'background' * 'flux' (optional) * 'scales' * 'significance'. """ pixel_scale = counts.geom.pixel_scales.mean() kernels = self.kernels(pixel_scale) cubes = {} cubes["counts"] = scale_cube(counts.data, kernels) if background is not None: cubes["background"] = scale_cube(background.data, kernels) else: # TODO: Estimate background with asmooth method raise ValueError("Background estimation required.") if exposure is not None: flux = (counts - background) / exposure cubes["flux"] = scale_cube(flux.data, kernels) cubes["significance"] = self._significance_cube( cubes, method=self.parameters["method"] ) smoothed = self._reduce_cubes(cubes, kernels) result = {} for key in ["counts", "background", "scale", "significance"]: data = smoothed[key] # set remaining pixels with significance < threshold to mean value if key in ["counts", "background"]: mask = np.isnan(data) data[mask] = np.mean(locals()[key].data[mask]) result[key] = WcsNDMap(counts.geom, data, unit=counts.unit) else: result[key] = WcsNDMap(counts.geom, data, unit="deg") if exposure is not None: data = smoothed["flux"] mask = np.isnan(data) data[mask] = np.mean(flux.data[mask]) result["flux"] = WcsNDMap(counts.geom, data, unit=flux.unit) return result
def _reduce_cubes(self, cubes, kernels): """ Combine scale cube to image. Parameters ---------- cubes : dict Data cubes """ p = self.parameters shape = cubes["counts"].shape[:2] smoothed = {} # Init smoothed data arrays for key in ["counts", "background", "scale", "significance", "flux"]: smoothed[key] = np.tile(np.nan, shape) for idx, scale in enumerate(p["scales"]): # slice out 2D image at index idx out of cube slice_ = np.s_[:, :, idx] mask = np.isnan(smoothed["counts"]) mask = (cubes["significance"][slice_] > p["threshold"]) & mask smoothed["scale"][mask] = scale smoothed["significance"][mask] = cubes["significance"][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
[docs] @staticmethod def get_scales(n_scales, factor=np.sqrt(2), kernel=Gaussian2DKernel): """Create list of Gaussian widths.""" 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)