def measure_image_moments(image):
"""Compute 0th, 1st and 2nd moments of an image.
NaN values are ignored in the computation.
Parameters
----------
image :`astropy.io.fits.ImageHDU`
Image to measure on.
Returns
-------
image moments : list
List of image moments:
[A, x_cms, y_cms, x_sigma, y_sigma, sqrt(x_sigma * y_sigma)]
"""
x, y = coordinates(image, lon_sym=True)
A = image.data[np.isfinite(image.data)].sum()
# Center of mass
x_cms = (x * image.data)[np.isfinite(image.data)].sum() / A
y_cms = (y * image.data)[np.isfinite(image.data)].sum() / A
# Second moments
x_var = ((x - x_cms) ** 2 * image.data)[np.isfinite(image.data)].sum() / A
y_var = ((y - y_cms) ** 2 * image.data)[np.isfinite(image.data)].sum() / A
x_sigma = np.sqrt(x_var)
y_sigma = np.sqrt(y_var)
return A, x_cms, y_cms, x_sigma, y_sigma, np.sqrt(x_sigma * y_sigma)
def _to_image_bbox(catalog, image):
"""@todo: make the usage of bbox an option of the function
_to_image_simple, otherwise we duplicate a lot of code!
Function takes catalog and an empty image.
It returns the image of the catalog.
catalog = atpy.Table
image = kapteyn.FITSimage
@todo: This function should have NO explicit references to
morphology column names.
Do something like:
for p in morphology.morph_pars:
exec('p = {0}'.format(p))
and then
pars = [eval('[??? for x in eval('morphology.{0}_par'.format(???
"""
logging.info('Building image out of catalog.')
# Select sources in FOV
# TODO: improve this check by reading the min, max from
# the FITS header instead of finding the min of the array.
l, b = utils.coordinates(image) #, glon_sym=True)
# Get catalog columns common to all morph types
morph_type = catalog.field('morph_type')
glon = catalog.field('glon')
glat = catalog.field('glat')
S_PWN = catalog.field('S_PWN')
S_SNR = catalog.field('S_SNR')
ext_in_SNR = catalog.field('ext_in_SNR')
ext_out_SNR = catalog.field('ext_out_SNR')
ext_out_PWN = catalog.field('ext_out_PWN')
contributing = np.all([
l.min() < glon + ext_out_SNR, glon - ext_out_SNR < l.max(),
b.min() < glat + ext_out_SNR, glat - ext_out_SNR < b.max(), S_SNR > 0
],
axis=0)
# Make image, adding one source at a time
nsources = contributing.sum()
logging.info('Adding {0} sources.'.format(nsources))
logging.info('Skipping {0} sources.'.format(catalog.size - nsources))
for i in range(catalog.size):
# Skip sources that are not contributing
if not contributing[i]:
# logging.debug('Skipping source {0:6d}.'.format(i))
continue
# Make a list of parameters appropriate for the morph_type
pars = [glon[i], glat[i]]
if morph_type[i] == 'sphere2d':
pars += [S_PWN[i], ext_out_PWN[i]]
elif morph_type[i] == 'shell2d':
pars += [S_SNR[i], ext_out_SNR[i], ext_in_SNR[i]]
logging.debug('Adding source {0:6d}.'.format(i))
_add_source(image, morph_type[i], pars, l, b)
def measure_image_moments(image):
"""Compute 0th, 1st and 2nd moments of an image.
NaN values are ignored in the computation.
Parameters
----------
image :`astropy.io.fits.ImageHDU`
Image to measure on.
Returns
-------
image moments : list
List of image moments:
[A, x_cms, y_cms, x_sigma, y_sigma, sqrt(x_sigma * y_sigma)]
"""
x, y = coordinates(image, lon_sym=True)
A = image.data[np.isfinite(image.data)].sum()
# Center of mass
x_cms = (x * image.data)[np.isfinite(image.data)].sum() / A
y_cms = (y * image.data)[np.isfinite(image.data)].sum() / A
# Second moments
x_var = ((x - x_cms)**2 * image.data)[np.isfinite(image.data)].sum() / A
y_var = ((y - y_cms)**2 * image.data)[np.isfinite(image.data)].sum() / A
x_sigma = np.sqrt(x_var)
y_sigma = np.sqrt(y_var)
return A, x_cms, y_cms, x_sigma, y_sigma, np.sqrt(x_sigma * y_sigma)
def measure_containment_radius(image, glon, glat, containment_fraction=0.8):
"""Measure containment radius.
Uses `scipy.optimize.brentq`.
Parameters
----------
image : `astropy.io.fits.ImageHDU`
Image to measure on.
glon : float
Source longitude in degree.
glat : float
Source latitude in degree.
containment_fraction : float (default 0.8)
Containment fraction
Returns
-------
containment_radius : float
Containment radius (pix)
"""
from scipy.optimize import brentq
GLON, GLAT = coordinates(image, lon_sym=True)
rr = (GLON - glon)**2 + (GLAT - glat)**2
# Normalize image
image.data = image.data / image.data[np.isfinite(image.data)].sum()
def func(r):
return measure_containment_fraction(r, rr,
image.data) - containment_fraction
containment_radius = brentq(func, a=0, b=np.sqrt(rr.max()))
return containment_radius
def measure_containment_radius(image, glon, glat, containment_fraction=0.8):
"""Measure containment radius.
Uses `scipy.optimize.brentq`.
Parameters
----------
image : `astropy.io.fits.ImageHDU`
Image to measure on.
glon : float
Source longitude in degree.
glat : float
Source latitude in degree.
containment_fraction : float (default 0.8)
Containment fraction
Returns
-------
containment_radius : float
Containment radius (pix)
"""
from scipy.optimize import brentq
GLON, GLAT = coordinates(image, lon_sym=True)
rr = (GLON - glon) ** 2 + (GLAT - glat) ** 2
# Normalize image
image.data = image.data / image.data[np.isfinite(image.data)].sum()
def func(r):
return measure_containment_fraction(r, rr, image.data) - containment_fraction
containment_radius = brentq(func, a=0, b=np.sqrt(rr.max()))
return containment_radius
def _to_image_bbox(catalog, image):
"""@todo: make the usage of bbox an option of the function
_to_image_simple, otherwise we duplicate a lot of code!
Function takes catalog and an empty image.
It returns the image of the catalog.
catalog = atpy.Table
image = kapteyn.FITSimage
@todo: This function should have NO explicit references to
morphology column names.
Do something like:
for p in morphology.morph_pars:
exec('p = {0}'.format(p))
and then
pars = [eval('[??? for x in eval('morphology.{0}_par'.format(???
"""
logging.info('Building image out of catalog.')
# Select sources in FOV
# TODO: improve this check by reading the min, max from
# the FITS header instead of finding the min of the array.
l, b = utils.coordinates(image)#, glon_sym=True)
# Get catalog columns common to all morph types
morph_type = catalog.field('morph_type')
glon = catalog.field('glon')
glat = catalog.field('glat')
S_PWN = catalog.field('S_PWN')
S_SNR = catalog.field('S_SNR')
ext_in_SNR = catalog.field('ext_in_SNR')
ext_out_SNR = catalog.field('ext_out_SNR')
ext_out_PWN = catalog.field('ext_out_PWN')
contributing = np.all([l.min() < glon + ext_out_SNR, glon - ext_out_SNR < l.max(),
b.min() < glat + ext_out_SNR, glat - ext_out_SNR < b.max(), S_SNR > 0], axis=0)
# Make image, adding one source at a time
nsources = contributing.sum()
logging.info('Adding {0} sources.'.format(nsources))
logging.info('Skipping {0} sources.'.format(catalog.size - nsources))
for i in range(catalog.size):
# Skip sources that are not contributing
if not contributing[i]:
# logging.debug('Skipping source {0:6d}.'.format(i))
continue
# Make a list of parameters appropriate for the morph_type
pars = [glon[i], glat[i]]
if morph_type[i] == 'sphere2d':
pars += [S_PWN[i], ext_out_PWN[i]]
elif morph_type[i] == 'shell2d':
pars += [S_SNR[i], ext_out_SNR[i], ext_in_SNR[i]]
logging.debug('Adding source {0:6d}.'.format(i))
_add_source(image, morph_type[i], pars, l, b)
def _to_image_gaussian(catalog, image):
"""Add catalog of asymmetric Gaussian sources to an image.
@type catalog: atpy.Table
@type image: maputils.FITSimage
@return: maputils.FITSimage"""
from kapteyn.maputils import FITSimage
logging.info('Adding %d sources.' % len(catalog.data))
#
# Read catalog
#
l_center = catalog.data['glon']
b_center = catalog.data['glat']
a = catalog.data['a']
b = catalog.data['b']
theta = catalog.data['theta']
flux = catalog.data['flux']
# Compute matrix entries that describe the ellipse, as defined in
# the section "9.1.6. Ellipse parameters" in the SExtractor Manual.
# Note that clb already contains the factor of 2!
#
# Another reference giving formulas is
# http://en.wikipedia.org/wiki/Gaussian_function
cll = np.cos(theta) ** 2 / a ** 2 + np.sin(theta) ** 2 / b ** 2
cbb = np.sin(theta) ** 2 / a ** 2 + np.cos(theta) ** 2 / b ** 2
clb = 2 * np.cos(theta) * np.sin(theta) * (a ** -2 - b ** -2)
#
# Add sources to image
#
data = image.dat
header = image.hdr
for i in range(len(catalog)): # Loop sources
l, b = utils.coordinates(image)
# convert l to the range -180 to +180
l = np.where(l > 180, l - 360, l)
exponent = cll[i] * (l - l_center[i]) ** 2 + \
cbb[i] * (b - b_center[i]) ** 2 + \
clb[i] * (l - l_center[i]) * (b - b_center[i])
data += flux[i] * np.exp(-exponent)
# Return image with sources
image_out = FITSimage(externalheader=header,
externaldata=data)
return image_out
def _to_image_simple(catalog, image):
"""Add sources from a catalog to an image.
catalog = atpy.Table
image = kapteyn.maputils.FITSimage
Note: This implementation doesn't use bounding boxes and thus is slow.
You should use the faster _to_image_bbox()"""
from kapteyn.maputils import FITSimage
from morphology.shapes import morph_types
nsources = len(catalog)
data = image.dat
logging.info('Adding {0} sources.'.format(nsources))
# Get coordinate maps
l, b = utils.coordinates(image)
# Add sources to image one at a time
for i in range(nsources):
logging.debug('Adding source {0:3d} of {1:3d}.' ''.format(i, nsources))
# nans = np.isnan(data).sum()
# if nans:
# logging.debug('Image contains {0} nan entries.'.format(nans))
# Get relevant columns
morph_type = catalog[i]['morph_type']
xpos = catalog[i]['glon']
xpos = np.where(xpos > 180, xpos - 360, xpos)
ypos = catalog[i]['glat']
ampl = catalog[i]['ampl']
sigma = catalog[i]['sigma']
epsilon = catalog[i]['epsilon']
theta = catalog[i]['theta']
r_in = catalog[i]['r_in']
r_out = catalog[i]['r_out']
pars = {
'delta2d': (xpos, ypos, ampl),
'shell2d': (xpos, ypos, ampl, r_in, r_out),
'gauss2d': (xpos, ypos, ampl, sigma, epsilon, theta)
}
par = pars[morph_type]
data += morph_types[morph_type](par, l, b)
return FITSimage(externalheader=image.hdr, externaldata=data)
def _to_image_gaussian(catalog, image):
"""Add catalog of asymmetric Gaussian sources to an image.
@type catalog: atpy.Table
@type image: maputils.FITSimage
@return: maputils.FITSimage"""
from kapteyn.maputils import FITSimage
logging.info('Adding %d sources.' % len(catalog.data))
#
# Read catalog
#
l_center = catalog.data['glon']
b_center = catalog.data['glat']
a = catalog.data['a']
b = catalog.data['b']
theta = catalog.data['theta']
flux = catalog.data['flux']
# Compute matrix entries that describe the ellipse, as defined in
# the section "9.1.6. Ellipse parameters" in the SExtractor Manual.
# Note that clb already contains the factor of 2!
#
# Another reference giving formulas is
# http://en.wikipedia.org/wiki/Gaussian_function
cll = np.cos(theta)**2 / a**2 + np.sin(theta)**2 / b**2
cbb = np.sin(theta)**2 / a**2 + np.cos(theta)**2 / b**2
clb = 2 * np.cos(theta) * np.sin(theta) * (a**-2 - b**-2)
#
# Add sources to image
#
data = image.dat
header = image.hdr
for i in range(len(catalog)): # Loop sources
l, b = utils.coordinates(image)
# convert l to the range -180 to +180
l = np.where(l > 180, l - 360, l)
exponent = cll[i] * (l - l_center[i]) ** 2 + \
cbb[i] * (b - b_center[i]) ** 2 + \
clb[i] * (l - l_center[i]) * (b - b_center[i])
data += flux[i] * np.exp(-exponent)
# Return image with sources
image_out = FITSimage(externalheader=header, externaldata=data)
return image_out
def _to_image_simple(catalog, image):
"""Add sources from a catalog to an image.
catalog = atpy.Table
image = kapteyn.maputils.FITSimage
Note: This implementation doesn't use bounding boxes and thus is slow.
You should use the faster _to_image_bbox()"""
from kapteyn.maputils import FITSimage
from morphology.shapes import morph_types
nsources = len(catalog)
data = image.dat
logging.info('Adding {0} sources.'.format(nsources))
# Get coordinate maps
l, b = utils.coordinates(image)
# Add sources to image one at a time
for i in range(nsources):
logging.debug('Adding source {0:3d} of {1:3d}.'
''.format(i, nsources))
# nans = np.isnan(data).sum()
# if nans:
# logging.debug('Image contains {0} nan entries.'.format(nans))
# Get relevant columns
morph_type = catalog[i]['morph_type']
xpos = catalog[i]['glon']
xpos = np.where(xpos > 180, xpos - 360, xpos)
ypos = catalog[i]['glat']
ampl = catalog[i]['ampl']
sigma = catalog[i]['sigma']
epsilon = catalog[i]['epsilon']
theta = catalog[i]['theta']
r_in = catalog[i]['r_in']
r_out = catalog[i]['r_out']
pars = {'delta2d': (xpos, ypos, ampl),
'shell2d': (xpos, ypos, ampl, r_in, r_out),
'gauss2d': (xpos, ypos, ampl, sigma, epsilon, theta)}
par = pars[morph_type]
data += morph_types[morph_type](par, l, b)
return FITSimage(externalheader=image.hdr, externaldata=data)
def measure_containment(image, glon, glat, radius):
"""
Measure containment in a given circle around the source position.
Parameters
----------
image : `astropy.io.fits.ImageHDU`
Image to measure on.
glon : float
Source longitude in degree.
glat : float
Source latitude in degree.
radius : float
Radius of the region to measure the containment in.
"""
GLON, GLAT = coordinates(image, lon_sym=True)
rr = (GLON - glon) ** 2 + (GLAT - glat) ** 2
return measure_containment_fraction(radius, rr, image.data)
def measure_containment(image, glon, glat, radius):
"""
Measure containment in a given circle around the source position.
Parameters
----------
image : `astropy.io.fits.ImageHDU`
Image to measure on.
glon : float
Source longitude in degree.
glat : float
Source latitude in degree.
radius : float
Radius of the region to measure the containment in.
"""
GLON, GLAT = coordinates(image, lon_sym=True)
rr = (GLON - glon)**2 + (GLAT - glat)**2
return measure_containment_fraction(radius, rr, image.data)
def lookup_max(image, GLON, GLAT, theta):
"""Look up the max image values within a circle of radius theta
around lists of given positions (nan if outside)"""
from .utils import coordinates
GLON = np.asarray(GLON)
GLON = np.where(GLON > 180, GLON - 360, GLON)
GLAT = np.asarray(GLAT)
n_pos = len(GLON)
theta = np.asarray(theta) * np.ones(n_pos, dtype='float32')
ll, bb = coordinates(image)
val = np.nan * np.ones(n_pos, dtype='float32')
for ii in range(n_pos):
mask = ((GLON[ii] - ll)**2 + (GLAT[ii] - bb)**2 <= theta[ii]**2)
try:
val[ii] = image.data[mask].max()
except ValueError:
pass
return val
def lookup_max(image, GLON, GLAT, theta):
"""Look up the max image values within a circle of radius theta
around lists of given positions (nan if outside)"""
from .utils import coordinates
GLON = np.asarray(GLON)
GLON = np.where(GLON > 180, GLON - 360, GLON)
GLAT = np.asarray(GLAT)
n_pos = len(GLON)
theta = np.asarray(theta) * np.ones(n_pos, dtype='float32')
ll, bb = coordinates(image)
val = np.nan * np.ones(n_pos, dtype='float32')
for ii in range(n_pos):
mask = ((GLON[ii] - ll) ** 2 +
(GLAT[ii] - bb) ** 2 <=
theta[ii] ** 2)
try:
val[ii] = image.data[mask].max()
except ValueError:
pass
return val
def _add_source(image, morph_type, pars, l, b):
"""Adds a specified source at a given position."""
from gammapy.morphology.shapes import morph_types
# Get position and extension info
# TODO: this won't work for delta2d, which doesn't
# have a pars[3] entry!
glon, glat, ext = pars[0], pars[1], pars[3]
logging.debug('Adding source of type {0} at position '
'{1}, {2} with extension {3}'
''.format(morph_type, glon, glat, ext))
# Get indices of position
#import IPython; IPython.embed()
x_pix, y_pix = np.arange(image.header['NAXIS1']), np.arange(
image.header['NAXIS2'])
# Correct pixel numbering
x_pix = np.floor(x_pix) - 1
y_pix = np.floor(y_pix) - 1
# Get data
data = image.data
pixsize = image.header['CDELT2']
# Compute boxsize with one pixel margin
boxsize = 2 * np.floor(ext / pixsize + 2)
# Determine corner pixels
left_bottom = [y_pix, x_pix] - boxsize / 2
right_top = [y_pix, x_pix] + boxsize / 2
# Determine image boundaries
y_bound, x_bound = data.shape
# Correct Behaviour at the boundaries
if left_bottom[1] < 0 or left_bottom[0] < 0 or right_top[
1] > x_bound or right_top[0] > y_bound:
logging.debug('Source is not completely in image.')
# Get out of range coordinate map
l, b = utils.coordinates(image, x_pix, y_pix, boxsize)
# Get image of source
box_image = morph_types[morph_type](pars, l, b)
# Get slices
s_x, s_y, b_x, b_y = _get_slices(left_bottom, right_top, x_bound,
y_bound)
# For debugging
logging.debug('left_bottom: {0}'.format(left_bottom))
logging.debug('right_top: {0}'.format(right_top))
logging.debug('box_image.shape: {0}'.format(box_image.shape))
logging.debug('s_x: {0}'.format(s_x))
logging.debug('s_y: {0}'.format(s_y))
logging.debug('b_x: {0}'.format(b_x))
logging.debug('b_y: {0}'.format(b_y))
logging.debug('box_image.shape: {0}'.format(box_image[b_y, b_x].shape))
logging.debug('data.shape: {0}'.format(data[s_y, s_x].shape))
# Add box to image
data[s_y, s_x] += box_image[b_y, b_x]
else:
logging.debug('Source is completely in image.')
s_x = slice(left_bottom[1], right_top[1])
s_y = slice(left_bottom[0], right_top[0])
# Get image of source
box_image = morph_types[morph_type](pars, l[s_y, s_x], b[s_y, s_x])
# Add box to image
data[s_y, s_x] += box_image
""" Script to determine what fraction of source and diffuse flux is found in the large and small region"""
from astropy.io import fits
filename = raw_input('Image filename: ')
source = fits.open(filename)[1]
from gammapy.image.utils import coordinates, solid_angle
lats, lons = coordinates(source)
solid_angle = solid_angle(source)
region_glat_high = 5
region_glat_low = -5
region_glon_high = 100
region_glon_low = -100
mask1 = (region_glat_low < lats) & (lats < region_glat_high)
mask2 = (region_glon_low < lons) & (lons < region_glon_high)
mask = mask1 & mask2
a = source.data #/ solid_angle.value
source_flux_frac = a[mask].sum() / a.sum()
print "Total Flux in Image"
print a.sum()
print "Galactic Flux"
print a[mask].sum()
print "Source Flux Fraction"
print source_flux_frac
def _add_source(image, morph_type, pars, l, b):
"""Adds a specified source at a given position."""
from gammapy.morphology.shapes import morph_types
# Get position and extension info
# TODO: this won't work for delta2d, which doesn't
# have a pars[3] entry!
glon, glat, ext = pars[0], pars[1], pars[3]
logging.debug('Adding source of type {0} at position '
'{1}, {2} with extension {3}'
''.format(morph_type, glon, glat, ext))
# Get indices of position
#import IPython; IPython.embed()
x_pix, y_pix = np.arange(image.header['NAXIS1']), np.arange(image.header['NAXIS2'])
# Correct pixel numbering
x_pix = np.floor(x_pix) - 1
y_pix = np.floor(y_pix) - 1
# Get data
data = image.data
pixsize = image.header['CDELT2']
# Compute boxsize with one pixel margin
boxsize = 2 * np.floor(ext / pixsize + 2)
# Determine corner pixels
left_bottom = [y_pix, x_pix] - boxsize / 2
right_top = [y_pix, x_pix] + boxsize / 2
# Determine image boundaries
y_bound, x_bound = data.shape
# Correct Behaviour at the boundaries
if left_bottom[1] < 0 or left_bottom[0] < 0 or right_top[1] > x_bound or right_top[0] > y_bound:
logging.debug('Source is not completely in image.')
# Get out of range coordinate map
l, b = utils.coordinates(image, x_pix, y_pix, boxsize)
# Get image of source
box_image = morph_types[morph_type](pars, l, b)
# Get slices
s_x, s_y, b_x, b_y = _get_slices(left_bottom, right_top, x_bound, y_bound)
# For debugging
logging.debug('left_bottom: {0}'.format(left_bottom))
logging.debug('right_top: {0}'.format(right_top))
logging.debug('box_image.shape: {0}'.format(box_image.shape))
logging.debug('s_x: {0}'.format(s_x))
logging.debug('s_y: {0}'.format(s_y))
logging.debug('b_x: {0}'.format(b_x))
logging.debug('b_y: {0}'.format(b_y))
logging.debug('box_image.shape: {0}'.format(box_image[b_y, b_x].shape))
logging.debug('data.shape: {0}'.format(data[s_y, s_x].shape))
# Add box to image
data[s_y, s_x] += box_image[b_y, b_x]
else:
logging.debug('Source is completely in image.')
s_x = slice(left_bottom[1], right_top[1])
s_y = slice(left_bottom[0], right_top[0])
# Get image of source
box_image = morph_types[morph_type](pars, l[s_y, s_x], b[s_y, s_x])
# Add box to image
data[s_y, s_x] += box_image
""" Script to determine what fraction of source and diffuse flux is found in the large and small region"""
from astropy.io import fits
import numpy as np
filename = raw_input('Image filename: ')
source = fits.open(filename)[1]
from gammapy.image.utils import coordinates, solid_angle
lats, lons = coordinates(source)
solid_angle = solid_angle(source)
region_glat_high = 5
region_glat_low = -5
region_glon_high = 100
region_glon_low = -100
mask1 = (region_glat_low < lats) & (lats < region_glat_high)
mask2 = (region_glon_low < lons) & (lons < region_glon_high)
mask = mask1 & mask2
a = np.nan_to_num(source.data)
source_flux_frac = a[mask].sum()/a.sum()
print "Total Flux in Image"
print a.sum()
print "Galactic Flux"
print a[mask].sum()
print "Source Flux Fraction"
print source_flux_frac
