def _significance_cube(self, cubes):
p = self.parameters
if p['method'] == 'lima':
scube = significance(cubes['counts'], cubes['background'], method='lima')
elif p['method'] == 'simple':
scube = significance(cubes['counts'], cubes['background'], method='simple')
elif p['method'] == 'asmooth':
scube = _significance_asmooth(cubes['counts'], cubes['background'])
elif p['method'] == 'ts':
raise NotImplementedError
else:
raise ValueError("Not a valid significance estimation method."
" Choose one of the following: 'lima', 'simple',"
" 'asmooth' or 'ts'")
return scube
def cli(n_observed, mu_background, method):
"""Compute significance for a Poisson count observation.
The significance is the tail probability to observe N_OBSERVED counts
or more, given a known background level MU_BACKGROUND."""
s = significance(n_observed, mu_background, method)
print(s)
def cli(n_observed, mu_background, method):
"""Compute significance for a Poisson count observation.
The significance is the tail probability to observe N_OBSERVED counts
or more, given a known background level MU_BACKGROUND."""
s = significance(n_observed, mu_background, method)
print(s)
def info_dict(self, in_safe_energy_range=True):
"""Info dict with summary statistics, summed over energy
Parameters
----------
in_safe_energy_range : bool
Whether to sum only in the safe energy range
Returns
-------
info_dict : dict
Dictionary with summary info.
"""
info = dict()
mask = self.mask_safe if in_safe_energy_range else slice(None)
info["name"] = self.name
info["livetime"] = self.livetime.copy()
info["n_on"] = self.counts.data[mask].sum()
info["background"] = self.background.data[mask].sum()
info["excess"] = self.excess.data[mask].sum()
info["significance"] = significance(
self.counts.data[mask].sum(),
self.background.data[mask].sum(),
)
info["background_rate"] = info["background"] / info["livetime"]
info["gamma_rate"] = info["excess"] / info["livetime"]
return info
def make_significance_image():
counts_image = fits.open("counts_image.fits")[1]
bkg_image = fits.open("bkg_image.fits")[1]
counts = disk_correlate(counts_image.data, 10)
bkg = disk_correlate(bkg_image.data, 10)
s = significance(counts, bkg)
s_image = fits.ImageHDU(data=s, header=counts_image.header)
s_image.writeto("significance_image.fits", clobber=True)
def make_significance_image():
counts_image = fits.open("counts_image.fits")[1]
bkg_image = fits.open("bkg_image.fits")[1]
counts = disk_correlate(counts_image.data, 10)
bkg = disk_correlate(bkg_image.data, 10)
s = significance(counts, bkg)
s_image = fits.ImageHDU(data=s, header=counts_image.header)
s_image.writeto("significance_image.fits", clobber=True)
def compute_correlated_maps(self, kernel):
"""Compute significance image for a given kernel.
"""
self.counts_corr = convolve(self.counts, kernel)
self.background_corr = convolve(self.background, kernel)
self.significance = significance(self.counts_corr, self.background_corr)
return self
def compute_correlated_maps(self, kernel):
"""Compute significance image for a given kernel.
"""
#import IPython; IPython.embed()
self.counts_corr = convolve(self.counts, kernel)
self.background_corr = convolve(self.background, kernel)
self.significance = significance(self.counts_corr, self.background_corr)
return self
def _significance_cube(self, cubes):
p = self.parameters
if p['method'] == 'lima':
scube = significance(cubes['counts'],
cubes['background'],
method='lima')
elif p['method'] == 'simple':
scube = significance(cubes['counts'],
cubes['background'],
method='simple')
elif p['method'] == 'asmooth':
scube = _significance_asmooth(cubes['counts'], cubes['background'])
elif p['method'] == 'ts':
raise NotImplementedError
else:
raise ValueError("Not a valid significance estimation method."
" Choose one of the following: 'lima', 'simple',"
" 'asmooth' or 'ts'")
return scube
def test_significance_on_off_against_known_background():
# Check that the Li & Ma limit formula is correct
# With small alpha and high counts, the significance
# and significance_on_off should be very close
actual = significance(n_on=1300, mu_bkg=1100, method="lima")
assert_allclose(actual, 5.8600870406703329)
actual = significance_on_off(n_on=1300,
n_off=1100 / 1.0e-8,
alpha=1e-8,
method="lima")
assert_allclose(actual, 5.8600864348078519)
def _significance_cube(cubes, method):
if method in {"lima", "simple"}:
scube = significance(cubes["counts"],
cubes["background"],
method="lima")
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', 'simple',"
" 'asmooth' or 'ts'")
return scube
def residual_images(model_file, data_file, out_file, thetas, overwrite):
"""Compute source model residual images.
The input `data_file` must contain the following HDU extensions:
* 'On' -- Counts image
* 'Background' -- Background image
"""
import logging
logging.basicConfig(level=logging.DEBUG,
format='%(levelname)s - %(message)s')
import numpy as np
from astropy.io import fits
from gammapy.image import disk_correlate
from gammapy.stats import significance
logging.info('Reading {0}'.format(data_file))
hdu_list = fits.open(data_file)
header = hdu_list[0].header
counts = hdu_list['On'].data.astype(np.float64)
background = hdu_list['Background'].data.astype(np.float64)
diffuse = hdu_list['Diffuse'].data.astype(np.float64)
logging.info('Reading {0}'.format(model_file))
model = fits.getdata(model_file)
background_plus_model_diffuse = background + model + diffuse
out_hdu_list = fits.HDUList()
for theta in thetas:
logging.info('Processing theta = {0} deg'.format(theta))
theta_pix = theta / header['CDELT2']
counts_corr = disk_correlate(counts, theta_pix)
background_plus_model_corr = disk_correlate(
background_plus_model_diffuse, theta_pix)
# excess_corr = counts_corr - background_plus_model_corr
significance_corr = significance(counts_corr,
background_plus_model_corr)
name = 'RESIDUAL_SIGNIFICANCE_{0}'.format(theta)
logging.info('Appending HDU extension: {0}'.format(name))
hdu = fits.ImageHDU(significance_corr, header, name)
out_hdu_list.append(hdu)
logging.info('Writing {0}'.format(out_file))
out_hdu_list.writeto(out_file, clobber=overwrite)
def significance_image(self, radius):
"""Make the significance image from the counts and bkg images.
Parameters
----------
radius : float
Disk radius in pixels.
"""
image = SkyImage.empty_like(self.empty_image)
disk = Tophat2DKernel(radius)
disk.normalize('peak')
counts = self.images["counts"].convolve(disk.array)
bkg = self.images["bkg"].convolve(disk.array)
image.data = significance(counts.data, bkg.data)
self.images["significance"] = image
def residual_images(model_file,
data_file,
out_file,
thetas,
overwrite):
"""Compute source model residual images.
The input `data_file` must contain the following HDU extensions:
* 'On' -- Counts image
* 'Background' -- Background image
"""
import numpy as np
from astropy.io import fits
from gammapy.image import disk_correlate
from gammapy.stats import significance
log.info('Reading {0}'.format(data_file))
hdu_list = fits.open(data_file)
header = hdu_list[0].header
counts = hdu_list['On'].data.astype(np.float64)
background = hdu_list['Background'].data.astype(np.float64)
diffuse = hdu_list['Diffuse'].data.astype(np.float64)
log.info('Reading {0}'.format(model_file))
model = fits.getdata(model_file)
background_plus_model_diffuse = background + model + diffuse
out_hdu_list = fits.HDUList()
for theta in thetas:
log.info('Processing theta = {0} deg'.format(theta))
theta_pix = theta / header['CDELT2']
counts_corr = disk_correlate(counts, theta_pix)
background_plus_model_corr = disk_correlate(background_plus_model_diffuse, theta_pix)
# excess_corr = counts_corr - background_plus_model_corr
significance_corr = significance(counts_corr, background_plus_model_corr)
name = 'RESIDUAL_SIGNIFICANCE_{0}'.format(theta)
log.info('Appending HDU extension: {0}'.format(name))
hdu = fits.ImageHDU(significance_corr, header, name)
out_hdu_list.append(hdu)
log.info('Writing {0}'.format(out_file))
out_hdu_list.writeto(out_file, clobber=overwrite)
def compute_lima_image(counts, background, kernel):
"""Compute Li & Ma significance and flux images for known background.
Parameters
----------
counts : `~gammapy.maps.WcsNDMap`
Counts image
background : `~gammapy.maps.WcsNDMap`
Background image
kernel : `astropy.convolution.Kernel2D`
Convolution kernel
Returns
-------
images : dict
Dictionary containing result maps
Keys are: significance, counts, background and excess
See Also
--------
gammapy.stats.significance
"""
# Kernel is modified later make a copy here
kernel = copy.deepcopy(kernel)
kernel.normalize("peak")
# fft convolution adds numerical noise, to ensure integer results we call
# np.rint
counts_conv = np.rint(counts.convolve(kernel.array).data)
background_conv = background.convolve(kernel.array).data
excess_conv = counts_conv - background_conv
significance_conv = significance(counts_conv,
background_conv,
method="lima")
return {
"significance": counts.copy(data=significance_conv),
"counts": counts.copy(data=counts_conv),
"background": counts.copy(data=background_conv),
"excess": counts.copy(data=excess_conv),
}
from gammapy.stats import significance
from gammapy.image.utils import disk_correlate
from aplpy import FITSFigure
from npred_general import prepare_images
model, gtmodel, ratio, counts, header = prepare_images()
# Top hat correlation
correlation_radius = 3
correlated_gtmodel = disk_correlate(gtmodel, correlation_radius)
correlated_counts = disk_correlate(counts, correlation_radius)
correlated_model = disk_correlate(model, correlation_radius)
# Fermi significance
fermi_significance = np.nan_to_num(significance(correlated_counts, gtmodel,
method='lima'))
# Gammapy significance
significance = np.nan_to_num(significance(correlated_counts, correlated_model,
method='lima'))
titles = ['Gammapy Significance', 'Fermi Tools Significance']
# Plot
fig = plt.figure(figsize=(10, 5))
hdu1 = fits.ImageHDU(significance, header)
f1 = FITSFigure(hdu1, figure=fig, convention='wells', subplot=(1, 2, 1))
f1.set_tick_labels_font(size='x-small')
f1.tick_labels.set_xformat('ddd')
f1.tick_labels.set_yformat('ddd')
f1.show_colorscale(vmin=0, vmax=10, cmap='afmhot')
from gammapy.stats import significance
from gammapy.image.utils import disk_correlate
from npred_general import prepare_images
from aplpy import FITSFigure
model, gtmodel, ratio, counts, header = prepare_images()
# Top hat correlation
correlation_radius = 3
correlated_gtmodel = disk_correlate(gtmodel, correlation_radius)
correlated_counts = disk_correlate(counts, correlation_radius)
correlated_model = disk_correlate(model, correlation_radius)
# Fermi significance
fermi_significance = np.nan_to_num(significance(correlated_counts, gtmodel,
method='lima'))
# Gammapy significance
significance = np.nan_to_num(significance(correlated_counts, correlated_model,
method='lima'))
titles = ['Gammapy Significance', 'Fermi Tools Significance']
# Plot
fig = plt.figure(figsize=(10, 5))
hdu1 = fits.ImageHDU(significance, header)
f1 = FITSFigure(hdu1, figure=fig, convention='wells', subplot=(1,2,1))
f1.set_tick_labels_font(size='x-small')
f1.tick_labels.set_xformat('ddd')
f1.tick_labels.set_yformat('ddd')
f1.show_colorscale(vmin=0, vmax=10, cmap='afmhot')
"""Plot significance image with HESS and MILAGRO colormap.
"""
import numpy as np
import matplotlib.pyplot as plt
from gammapy.datasets import load_poisson_stats_image
from gammapy.image import disk_correlate
from gammapy.stats import significance
from gammapy.image import colormap_hess, colormap_milagro
from astropy.visualization.mpl_normalize import ImageNormalize
from astropy.visualization import LinearStretch
# Compute an example significance image
counts = load_poisson_stats_image()
counts = disk_correlate(counts, radius=5, mode='reflect')
background = np.median(counts) * np.ones_like(counts)
image = significance(counts, background)
# Plot with the HESS and Milagro colormap
vmin, vmax, vtransition = -5, 15, 5
plt.figure(figsize=(8, 4))
normalize = ImageNormalize(vmin=vmin, vmax=vmax, stretch=LinearStretch())
transition = normalize(vtransition)
plt.subplot(121)
cmap = colormap_hess(transition=transition)
plt.imshow(image, cmap=cmap, norm=normalize)
plt.axis('off')
plt.colorbar()
plt.title('HESS-style colormap')
from gammapy.image.utils import disk_correlate
from aplpy import FITSFigure
from npred_general import prepare_images
model, gtmodel, ratio, counts, header = prepare_images()
# Top hat correlation
correlation_radius = 3
correlated_gtmodel = disk_correlate(gtmodel, correlation_radius)
correlated_counts = disk_correlate(counts, correlation_radius)
correlated_model = disk_correlate(model, correlation_radius)
# Fermi significance
fermi_significance = np.nan_to_num(
significance(correlated_counts, gtmodel, method='lima'))
# Gammapy significance
significance = np.nan_to_num(
significance(correlated_counts, correlated_model, method='lima'))
titles = ['Gammapy Significance', 'Fermi Tools Significance']
# Plot
fig = plt.figure(figsize=(10, 5))
hdu1 = fits.ImageHDU(significance, header)
f1 = FITSFigure(hdu1, figure=fig, convention='wells', subplot=(1, 2, 1))
f1.set_tick_labels_font(size='x-small')
f1.tick_labels.set_xformat('ddd')
f1.tick_labels.set_yformat('ddd')
f1.show_colorscale(vmin=0, vmax=10, cmap='afmhot')
def test_significance(p):
s = significance(p["n_on"], p["mu_bkg"], p["method"])
assert_allclose(s, p["s"], atol=1e-5)
show_image(images['excess'], vmax=2)
# In[18]:
# Significance image
# Just for fun, let's compute it by hand ...
from astropy.convolution import Tophat2DKernel
kernel = Tophat2DKernel(4)
kernel.normalize('peak')
counts_conv = images['counts'].convolve(kernel.array)
background_conv = images['background'].convolve(kernel.array)
from gammapy.stats import significance
significance_image = SkyImage.empty_like(ref_image)
significance_image.data = significance(counts_conv.data, background_conv.data)
show_image(significance_image, vmax=8)
# ## Source Detection
#
# Use the class [TSImageEstimator](http://docs.gammapy.org/dev/api/gammapy.detect.compute_ts_image.html#gammapy.detect.TSImageEstimator.html) and [photutils.find_peaks](http://photutils.readthedocs.io/en/stable/api/photutils.find_peaks.html) to detect point-like sources on the images:
# In[19]:
# cut out smaller piece of the PSF image to save computing time
# for covenience we're "misusing" the SkyImage class represent the PSF on the sky.
kernel = images['psf'].cutout(target_position, size=1.1 * u.deg)
kernel.show()
# In[20]:
