# Licensed under a 3-clause BSD style license - see LICENSE.rst
import numpy as np
import scipy.ndimage
from astropy import units as u
from astropy.coordinates import SkyCoord
from astropy.table import Table
from gammapy.datasets import SpectrumDataset, SpectrumDatasetOnOff
from gammapy.datasets.map import MapEvaluator
from gammapy.maps import MapAxis, TimeMapAxis, WcsNDMap
from gammapy.modeling.models import (
ConstantFluxSpatialModel,
PowerLawSpectralModel,
SkyModel,
)
from gammapy.stats import compute_flux_doubling, compute_fpp, compute_fvar
from .map.core import FluxMaps
__all__ = [
"estimate_exposure_reco_energy",
"find_peaks",
"find_peaks_in_flux_map",
"resample_energy_edges",
"get_rebinned_axis",
"compute_lightcurve_fvar",
"compute_lightcurve_fpp",
"compute_lightcurve_doublingtime",
]
[docs]
def find_peaks(image, threshold, min_distance=1):
"""Find local peaks in an image.
This is a very simple peak finder, that finds local peaks
(i.e. maxima) in images above a given ``threshold`` within
a given ``min_distance`` around each given pixel.
If you get multiple spurious detections near a peak, usually
it's best to smooth the image a bit, or to compute it using
a different method in the first place to result in a smooth image.
You can also increase the ``min_distance`` parameter.
The output table contains one row per peak and the following columns:
- ``x`` and ``y`` are the pixel coordinates (first pixel at zero).
- ``ra`` and ``dec`` are the RA / DEC sky coordinates (ICRS frame).
- ``value`` is the pixel value.
It is sorted by peak value, starting with the highest value.
If there are no pixel values above the threshold, an empty table is returned.
There are more featureful peak finding and source detection methods
e.g. in the ``photutils`` or ``scikit-image`` Python packages.
Parameters
----------
image : `~gammapy.maps.WcsNDMap`
Image like Map.
threshold : float or array-like
The data value or pixel-wise data values to be used for the
detection threshold. A 2D ``threshold`` must have the same
shape as the map ``data``.
min_distance : int or `~astropy.units.Quantity`
Minimum distance between peaks. An integer value is interpreted
as pixels. Default is 1.
Returns
-------
output : `~astropy.table.Table`
Table with parameters of detected peaks.
Examples
--------
>>> import astropy.units as u
>>> from gammapy.datasets import MapDataset
>>> from gammapy.estimators import ExcessMapEstimator
>>> from gammapy.estimators.utils import find_peaks
>>>
>>> dataset = MapDataset.read("$GAMMAPY_DATA/cta-1dc-gc/cta-1dc-gc.fits.gz")
>>> estimator = ExcessMapEstimator(
... correlation_radius="0.1 deg", energy_edges=[0.1, 10] * u.TeV
... )
>>> maps = estimator.run(dataset)
>>> # Find the peaks which are above 5 sigma
>>> sources = find_peaks(maps["sqrt_ts"], threshold=5, min_distance="0.25 deg")
>>> print(sources)
value x y ra dec
deg deg
------ --- --- --------- ---------
32.191 161 118 266.41924 -28.98772
18.7 125 124 266.80571 -28.14079
9.4498 257 122 264.86178 -30.97529
9.3784 204 103 266.14201 -30.10041
5.3493 282 150 263.78083 -31.12704
"""
# Input validation
if not isinstance(image, WcsNDMap):
raise TypeError("find_peaks only supports WcsNDMap")
if not image.geom.is_flat:
raise ValueError(
"find_peaks only supports flat Maps, with no spatial axes of length 1."
)
if isinstance(min_distance, (str, u.Quantity)):
min_distance = np.mean(u.Quantity(min_distance) / image.geom.pixel_scales)
min_distance = np.round(min_distance).to_value("")
size = 2 * min_distance + 1
# Remove non-finite values to avoid warnings or spurious detection
data = image.sum_over_axes(keepdims=False).data
data[~np.isfinite(data)] = np.nanmin(data)
# Handle edge case of constant data; treat as no peak
if np.all(data == data.flat[0]):
return Table()
# Run peak finder
data_max = scipy.ndimage.maximum_filter(data, size=size, mode="constant")
mask = (data == data_max) & (data > threshold)
y, x = mask.nonzero()
value = data[y, x]
# Make and return results table
if len(value) == 0:
return Table()
coord = SkyCoord.from_pixel(x, y, wcs=image.geom.wcs).icrs
table = Table()
table["value"] = value * image.unit
table["x"] = x
table["y"] = y
table["ra"] = coord.ra
table["dec"] = coord.dec
table["ra"].format = ".5f"
table["dec"].format = ".5f"
table["value"].format = ".5g"
table.sort("value")
table.reverse()
return table
[docs]
def find_peaks_in_flux_map(maps, threshold, min_distance=1):
"""Find local test statistic peaks for a given Map.
Utilises the `~gammapy.estimators.utils.find_peaks` function to find various parameters from FluxMaps.
Parameters
----------
maps : `~gammapy.estimators.FluxMaps`
Input flux map object.
threshold : float or array-like
The test statistic data value or pixel-wise test statistic data values to be used for the
detection threshold. A 2D ``threshold`` must have the same.
shape as the map ``data``.
min_distance : int or `~astropy.units.Quantity`
Minimum distance between peaks. An integer value is interpreted
as pixels. Default is 1.
Returns
-------
output : `~astropy.table.Table`
Table with parameters of detected peaks.
Examples
--------
>>> import astropy.units as u
>>> from gammapy.datasets import MapDataset
>>> from gammapy.estimators import ExcessMapEstimator
>>> from gammapy.estimators.utils import find_peaks_in_flux_map
>>>
>>> dataset = MapDataset.read("$GAMMAPY_DATA/cta-1dc-gc/cta-1dc-gc.fits.gz")
>>> estimator = ExcessMapEstimator(
... correlation_radius="0.1 deg", energy_edges=[0.1, 10]*u.TeV
... )
>>> maps = estimator.run(dataset)
>>> # Find the peaks which are above 5 sigma
>>> sources = find_peaks_in_flux_map(maps, threshold=5, min_distance=0.1*u.deg)
>>> print(sources[:4])
x y ra dec ... norm norm_err flux flux_err
deg deg ... 1 / (s cm2) 1 / (s cm2)
--- --- --------- --------- ... ------- -------- ----------- -----------
158 135 266.05019 -28.70181 ... 0.28551 0.06450 2.827e-12 6.385e-13
92 133 267.07022 -27.31834 ... 0.37058 0.08342 3.669e-12 8.259e-13
176 134 265.80492 -29.09805 ... 0.30561 0.06549 3.025e-12 6.484e-13
282 150 263.78083 -31.12704 ... 0.55027 0.12611 5.448e-12 1.249e-12
"""
quantity_for_peaks = maps["sqrt_ts"]
if not isinstance(maps, FluxMaps):
raise TypeError(
f"find_peaks_in_flux_map expects FluxMaps input. Got {type(maps)} instead."
)
if not quantity_for_peaks.geom.is_flat:
raise ValueError(
"find_peaks_in_flux_map only supports flat Maps, with energy axis of length 1."
)
table = find_peaks(quantity_for_peaks, threshold, min_distance)
if len(table) == 0:
return Table()
x = np.array(table["x"])
y = np.array(table["y"])
table.remove_column("value")
for name in maps.available_quantities:
values = maps[name].quantity
peaks = values[0, y, x]
table[name] = peaks
flux_data = maps["flux"].quantity
table["flux"] = flux_data[0, y, x]
flux_err_data = maps["flux_err"].quantity
table["flux_err"] = flux_err_data[0, y, x]
for column in table.colnames:
if column.startswith(("flux", "flux_err")):
table[column].format = ".3e"
elif column.startswith(
(
"npred",
"npred_excess",
"counts",
"sqrt_ts",
"norm",
"ts",
"norm_err",
"stat",
"stat_null",
)
):
table[column].format = ".5f"
table.reverse()
return table
[docs]
def estimate_exposure_reco_energy(dataset, spectral_model=None, normalize=True):
"""Estimate an exposure map in reconstructed energy.
Parameters
----------
dataset : `~gammapy.datasets.MapDataset` or `~gammapy.datasets.MapDatasetOnOff`
The input dataset.
spectral_model : `~gammapy.modeling.models.SpectralModel`, optional
Assumed spectral shape. If None, a Power Law of index 2 is assumed. Default is None.
normalize : bool
Normalize the exposure to the total integrated flux of the spectral model.
When not normalized it directly gives the predicted counts from the spectral
model. Default is True.
Returns
-------
exposure : `~gammapy.maps.Map`
Exposure map in reconstructed energy.
"""
if spectral_model is None:
spectral_model = PowerLawSpectralModel()
model = SkyModel(
spatial_model=ConstantFluxSpatialModel(), spectral_model=spectral_model
)
energy_axis = dataset._geom.axes["energy"]
if dataset.edisp is not None:
edisp = dataset.edisp.get_edisp_kernel(position=None, energy_axis=energy_axis)
else:
edisp = None
eval = MapEvaluator(model=model, exposure=dataset.exposure, edisp=edisp)
reco_exposure = eval.compute_npred()
if normalize:
ref_flux = spectral_model.integral(
energy_axis.edges[:-1], energy_axis.edges[1:]
)
reco_exposure = reco_exposure / ref_flux[:, np.newaxis, np.newaxis]
return reco_exposure
def _satisfies_conditions(info_dict, conditions):
satisfies = True
for key in conditions.keys():
satisfies &= info_dict[key.strip("_min")] > conditions[key]
return satisfies
[docs]
def resample_energy_edges(dataset, conditions={}):
"""Return energy edges that satisfy given condition on the per bin statistics.
Parameters
----------
dataset : `~gammapy.datasets.SpectrumDataset` or `~gammapy.datasets.SpectrumDatasetOnOff`
The input dataset.
conditions : dict
Keyword arguments containing the per-bin conditions used to resample the axis.
Available options are: 'counts_min', 'background_min', 'excess_min', 'sqrt_ts_min',
'npred_min', 'npred_background_min', 'npred_signal_min'. Default is {}.
Returns
-------
energy_edges : list of `~astropy.units.Quantity`
Energy edges for the resampled energy axis.
Examples
--------
>>> from gammapy.datasets import Datasets, SpectrumDatasetOnOff
>>> from gammapy.estimators.utils import resample_energy_edges
>>>
>>> datasets = Datasets()
>>>
>>> for obs_id in [23523, 23526]:
... dataset = SpectrumDatasetOnOff.read(
... f"$GAMMAPY_DATA/joint-crab/spectra/hess/pha_obs{obs_id}.fits"
... )
... datasets.append(dataset)
>>>
>>> spectrum_dataset = Datasets(datasets).stack_reduce()
>>> # Resample the energy edges so the minimum sqrt_ts is 2
>>> resampled_energy_edges = resample_energy_edges(
... spectrum_dataset,
... conditions={"sqrt_ts_min": 2}
... )
"""
if not isinstance(dataset, (SpectrumDataset, SpectrumDatasetOnOff)):
raise NotImplementedError(
"This method is currently supported for spectral datasets only."
)
available_conditions = [
"counts_min",
"background_min",
"excess_min",
"sqrt_ts_min",
"npred_min",
"npred_background_min",
"npred_signal_min",
]
for key in conditions.keys():
if key not in available_conditions:
raise ValueError(
f"Unrecognized option {key}. The available methods are: {available_conditions}."
)
axis = dataset.counts.geom.axes["energy"]
energy_min_all, energy_max_all = dataset.energy_range_total
energy_edges = [energy_max_all]
while energy_edges[-1] > energy_min_all:
for energy_min in reversed(axis.edges_min):
if energy_min >= energy_edges[-1]:
continue
elif len(energy_edges) == 1 and energy_min == energy_min_all:
raise ValueError("The given conditions cannot be met.")
sliced = dataset.slice_by_energy(
energy_min=energy_min, energy_max=energy_edges[-1]
)
with np.errstate(invalid="ignore"):
info = sliced.info_dict()
if _satisfies_conditions(info, conditions):
energy_edges.append(energy_min)
break
return u.Quantity(energy_edges[::-1])
[docs]
def compute_lightcurve_fvar(lightcurve, flux_quantity="flux"):
r"""Compute the fractional excess variance of the input lightcurve.
Internally calls the `~gammapy.stats.compute_fvar` function.
Parameters
----------
lightcurve : `~gammapy.estimators.FluxPoints`
The lightcurve object.
flux_quantity : str
Flux quantity to use for calculation. Should be 'dnde', 'flux', 'e2dnde' or 'eflux'. Default is 'flux'.
Returns
-------
fvar : `~astropy.table.Table`
Table of fractional excess variance and associated error for each energy bin of the lightcurve.
"""
flux = getattr(lightcurve, flux_quantity)
flux_err = getattr(lightcurve, flux_quantity + "_err")
time_id = flux.geom.axes.index_data("time")
fvar, fvar_err = compute_fvar(flux.data, flux_err.data, axis=time_id)
significance = fvar / fvar_err
energies = lightcurve.geom.axes["energy"].edges
table = Table(
[energies[:-1], energies[1:], fvar, fvar_err, significance],
names=("min_energy", "max_energy", "fvar", "fvar_err", "significance"),
meta=lightcurve.meta,
)
return table
[docs]
def compute_lightcurve_fpp(lightcurve, flux_quantity="flux"):
r"""Compute the point-to-point excess variance of the input lightcurve.
Internally calls the `~gammapy.stats.compute_fpp` function
Parameters
----------
lightcurve : `~gammapy.estimators.FluxPoints`
The lightcurve object.
flux_quantity : str
Flux quantity to use for calculation. Should be 'dnde', 'flux', 'e2dnde' or 'eflux'. Default is 'flux'.
Returns
-------
table : `~astropy.table.Table`
Table of point-to-point excess variance and associated error for each energy bin of the lightcurve.
"""
flux = getattr(lightcurve, flux_quantity)
flux_err = getattr(lightcurve, flux_quantity + "_err")
time_id = flux.geom.axes.index_data("time")
fpp, fpp_err = compute_fpp(flux.data, flux_err.data, axis=time_id)
significance = fpp / fpp_err
energies = lightcurve.geom.axes["energy"].edges
table = Table(
[energies[:-1], energies[1:], fpp, fpp_err, significance],
names=("min_energy", "max_energy", "fpp", "fpp_err", "significance"),
meta=dict(quantity=flux_quantity),
)
return table
[docs]
def compute_lightcurve_doublingtime(lightcurve, flux_quantity="flux"):
r"""Compute the minimum characteristic flux doubling and halving time for the input lightcurve.
Internally calls the `~gammapy.stats.compute_flux_doubling` function.
The characteristic doubling time is estimated to obtain the
minimum variability timescale for the light curves in which
rapid variations are clearly evident: for example it is useful in AGN flaring episodes.
This quantity, especially for AGN flares, is often expressed
as the pair of doubling time and halving time, or the minimum characteristic time
for the rising and falling components respectively.
Parameters
----------
lightcurve : `~gammapy.estimators.FluxPoints`
The lightcurve object.
axis_name : str
Name of the axis over which to compute the flux doubling.
flux_quantity : str
Flux quantity to use for calculation. Should be 'dnde', 'flux', 'e2dnde' or 'eflux'.
Default is 'flux'.
Returns
-------
table : `~astropy.table.Table`
Table of flux doubling/halving and associated error for each energy bin of the lightcurve
with axis coordinates at which they were found.
References
----------
..[Brown2013] "Locating the γ-ray emission region
of the flat spectrum radio quasar PKS 1510−089", Brown et al. (2013)
https://academic.oup.com/mnras/article/431/1/824/1054498
"""
flux = getattr(lightcurve, flux_quantity)
flux_err = getattr(lightcurve, flux_quantity + "_err")
coords = lightcurve.geom.axes["time"].center
axis = flux.geom.axes.index_data("time")
doubling_dict = compute_flux_doubling(flux.data, flux_err.data, coords, axis=axis)
energies = lightcurve.geom.axes["energy"].edges
table = Table(
[
energies[:-1],
energies[1:],
doubling_dict["doubling"],
doubling_dict["doubling_err"],
lightcurve.geom.axes["time"].reference_time
+ doubling_dict["doubling_coord"],
doubling_dict["halving"],
doubling_dict["halving_err"],
lightcurve.geom.axes["time"].reference_time
+ doubling_dict["halving_coord"],
],
names=(
"min_energy",
"max_energy",
"doublingtime",
"doubling_err",
"doubling_coord",
"halvingtime",
"halving_err",
"halving_coord",
),
meta=dict(flux_quantity=flux_quantity),
)
return table
def get_edges_fixed_bins(fluxpoint, group_size, axis_name="energy"):
"""Rebin the flux point to combine value adjacent bins.
Parameters
----------
fluxpoint : `~gammapy.estimators.FluxPoints`
The flux points object to rebin.
group_size : int
Number of bins to combine.
axis_name : str, optional
The axis name to combine along. Default is 'energy'.
Returns
-------
edges_min : `~astropy.units.Quantity` or `~astropy.time.Time`
Minimum bin edge for the new axis.
edges_max : `~astropy.units.Quantity` or `~astropy.time.Time`
Maximum bin edge for the new axis.
"""
ax = fluxpoint.geom.axes[axis_name]
nbin = ax.nbin
if not isinstance(group_size, int):
raise ValueError("Only integer number of bins can be combined")
idx = np.arange(0, nbin, group_size)
if idx[-1] < nbin:
idx = np.append(idx, nbin)
edges_min = ax.edges_min[idx[:-1]]
edges_max = ax.edges_max[idx[1:] - 1]
return edges_min, edges_max
def get_edges_min_ts(fluxpoint, ts_threshold, axis_name="energy"):
"""Rebin the flux point to combine adjacent bins until a minimum TS is obtained.
Note that to convert TS to significance, it is necessary to take the number
of degrees of freedom into account.
Parameters
----------
fluxpoint : `~gammapy.estimators.FluxPoints`
The flux points object to rebin.
ts_threshold : float
The minimum significance desired.
axis_name : str, optional
The axis name to combine along. Default is 'energy'.
Returns
-------
edges_min : `~astropy.units.Quantity` or `~astropy.time.Time`
Minimum bin edge for the new axis.
edges_max : `~astropy.units.Quantity` or `~astropy.time.Time`
Maximum bin edge for the new axis.
"""
ax = fluxpoint.geom.axes[axis_name]
nbin = ax.nbin
e_min, e_max = ax.edges_min[0], ax.edges_max[0]
edges_min = np.zeros(nbin) * e_min.unit
edges_max = np.zeros(nbin) * e_max.unit
i, i1 = 0, 0
while e_max < ax.edges_max[-1]:
ts = fluxpoint.ts.data[i]
e_min = ax.edges_min[i]
while ts < ts_threshold and i < ax.nbin - 1:
i = i + 1
ts = ts + fluxpoint.ts.data[i]
e_max = ax.edges_max[i]
i = i + 1
edges_min[i1] = e_min
edges_max[i1] = e_max
i1 = i1 + 1
edges_max = edges_max[:i1]
edges_min = edges_min[:i1]
return edges_min, edges_max
RESAMPLE_METHODS = {
"fixed-bins": get_edges_fixed_bins,
"min-ts": get_edges_min_ts,
}
[docs]
def get_rebinned_axis(fluxpoint, axis_name="energy", method=None, **kwargs):
"""Get the rebinned axis for resampling the flux point object along the mentioned axis.
Parameters
----------
fluxpoint : `~gammapy.estimators.FluxPoints`
The flux point object to rebin.
axis_name : str, optional
The axis name to combine along. Default is 'energy'.
method : str
The method to resample the axis. Supported options are
'fixed_bins' and 'min-ts'.
kwargs : dict
Keywords passed to `get_edges_fixed_bins` or `get_edges_min_ts`.
If method is 'fixed-bins', keyword should be `group_size`.
If method is 'min-ts', keyword should be `ts_threshold`.
Returns
-------
axis_new : `~gammapy.maps.MapAxis` or `~gammapy.maps.TimeMapAxis`
The new axis.
Examples
--------
>>> from gammapy.estimators.utils import get_rebinned_axis
>>> from gammapy.estimators import FluxPoints
>>>
>>> # Rebin lightcurve axis
>>> lc_1d = FluxPoints.read(
... "$GAMMAPY_DATA/estimators/pks2155_hess_lc/pks2155_hess_lc.fits",
... format="lightcurve",
... )
>>> # Rebin axis by combining adjacent bins as per the group_size
>>> new_axis = get_rebinned_axis(
... lc_1d, method="fixed-bins", group_size=2, axis_name="time"
... )
>>>
>>> # Rebin HESS flux points axis
>>> fp = FluxPoints.read(
... "$GAMMAPY_DATA/estimators/crab_hess_fp/crab_hess_fp.fits"
... )
>>> # Rebin according to a minimum significance
>>> axis_new = get_rebinned_axis(
... fp, method='min-ts', ts_threshold=4, axis_name='energy'
... )
"""
# TODO: Make fixed_bins and fixed_edges work for multidimensions
if not fluxpoint.geom.axes.is_unidimensional:
raise ValueError(
"Rebinning is supported only for Unidimensional FluxPoints \n "
"Please use `iter_by_axis` to create Unidimensional FluxPoints"
)
if method not in RESAMPLE_METHODS.keys():
raise ValueError("Incorrect option. Choose from", RESAMPLE_METHODS.keys())
edges_min, edges_max = RESAMPLE_METHODS[method](
fluxpoint=fluxpoint, axis_name=axis_name, **kwargs
)
ax = fluxpoint.geom.axes[axis_name]
if isinstance(ax, TimeMapAxis):
axis_new = TimeMapAxis.from_time_edges(
time_min=edges_min + ax.reference_time,
time_max=edges_max + ax.reference_time,
)
else:
edges = np.append(edges_min, edges_max[-1])
axis_new = MapAxis.from_edges(edges, name=axis_name, interp=ax.interp)
return axis_new
