def diag_size(self):
"""return the largest diagonal size"""
p1, p2, p3, p4 = self.calc_footprint()
return np.max([
angular_separation(*np.concatenate([p1, p3])),
angular_separation(*np.concatenate([p2, p4]))
])
def edge_size(self):
"""return the p1,p2 and p2,p3 size (The order is counter-clockwise starting with
the bottom left corner. p1,p2,p3,p4)"""
p1, p2, p3, p4 = self.calc_footprint()
return angular_separation(
*np.concatenate([p1, p2])), angular_separation(
*np.concatenate([p2, p3]))
def solid_angle(self):
"""Solid angle array (`~astropy.units.Quantity` in ``sr``).
The array has the same dimension as the WcsGeom object.
To return solid angles for the spatial dimensions only use::
WcsGeom.to_image().solid_angle()
"""
coord = self.get_coord(mode="edges")
lon = coord.lon * np.pi / 180.0
lat = coord.lat * np.pi / 180.0
# Compute solid angle across centres of the pixels, approximating it
# as a rectangle
# First index is "y", second index is "x"
# TODO: Calculate actual solid angle between two great circles? Here are two references
# suggesting more precise methods:
# https://mail.python.org/pipermail/astropy/2013-December/002632.html
# https://cta-redmine.irap.omp.eu/issues/1017
lon_centres = (lon[..., :-1, :-1] + lon[..., 1:, 1:]) / 2
lat_centres = (lat[..., :-1, :-1] + lat[..., 1:, 1:]) / 2
ymid_xlo = lon[..., :-1, :-1], lat_centres
ymid_xhi = lon[..., :-1, 1:], lat_centres
ylo_xmid = lon_centres, lat[..., :-1, 1:]
yhi_xmid = lon_centres, lat[..., 1:, :-1]
dx = angular_separation(*(ymid_xlo + ymid_xhi))
dy = angular_separation(*(ylo_xmid + yhi_xmid))
return u.Quantity(dx * dy, "sr", copy=False)
def read_and_update_dl2(filepath, tel_id=1, filters=['intensity > 0']):
"""
read DL2 data from lstchain file and update it to be compliant with irf Maker
"""
dl2_params_lstcam_key = 'dl2/event/telescope/parameters/LST_LSTCam' # lstchain DL2 files
data = pd.read_hdf(filepath, key=dl2_params_lstcam_key)
data = deepcopy(data.query(f'tel_id == {tel_id}'))
for filter in filters:
data = deepcopy(data.query(filter))
# angles are in degrees in protopipe
data['xi'] = pd.Series(angular_separation(
data.reco_az.values * u.rad,
data.reco_alt.values * u.rad,
data.mc_az.values * u.rad,
data.mc_alt.values * u.rad,
).to(u.deg).value,
index=data.index)
data['offset'] = pd.Series(angular_separation(
data.reco_az.values * u.rad,
data.reco_alt.values * u.rad,
data.mc_az_tel.values * u.rad,
data.mc_alt_tel.values * u.rad,
).to(u.deg).value,
index=data.index)
for key in [
'mc_alt', 'mc_az', 'reco_alt', 'reco_az', 'mc_alt_tel', 'mc_az_tel'
]:
data[key] = np.rad2deg(data[key])
return data
def solid_angle(self):
"""Solid angle array (`~astropy.units.Quantity` in ``sr``).
The array has the same dimension as the WcsGeom object.
To return solid angles for the spatial dimensions only use::
WcsGeom.to_image().solid_angle()
"""
coord = self.get_coord(mode="edges")
lon = coord.lon * np.pi / 180.0
lat = coord.lat * np.pi / 180.0
# Compute solid angle across centres of the pixels, approximating it
# as a rectangle
# First index is "y", second index is "x"
# TODO: Calculate actual solid angle between two great circles? Here are two references
# suggesting more precise methods:
# https://mail.python.org/pipermail/astropy/2013-December/002632.html
# https://cta-redmine.irap.omp.eu/issues/1017
lon_centres = (lon[..., :-1, :-1] + lon[..., 1:, 1:]) / 2
lat_centres = (lat[..., :-1, :-1] + lat[..., 1:, 1:]) / 2
ymid_xlo = lon[..., :-1, :-1], lat_centres
ymid_xhi = lon[..., :-1, 1:], lat_centres
ylo_xmid = lon_centres, lat[..., :-1, 1:]
yhi_xmid = lon_centres, lat[..., 1:, :-1]
dx = angular_separation(*(ymid_xlo + ymid_xhi))
dy = angular_separation(*(ylo_xmid + yhi_xmid))
return u.Quantity(dx * dy, "sr", copy=False)
def solid_angle(self):
"""Solid angle array (`~astropy.units.Quantity` in ``sr``).
The array has the same dimension as the WcsGeom object.
To return solid angles for the spatial dimensions only use: WcsGeom.to_image().solid_angle()
"""
# TODO: Improve by exposing a mode 'edge' for get_coord
# Note that edge is applied only to spatial coordinates in the following call
# Note also that pix_to_coord is already called in _get_pix_coords.
# This should be made more efficient.
pix = self._get_pix_coords(mode='edge')
coord = self.pix_to_coord(pix)
lon = coord[0] * np.pi / 180.
lat = coord[1] * np.pi / 180.
# Compute solid angle using the approximation that it's
# the product between angular separation of pixel corners.
# First index is "y", second index is "x"
ylo_xlo = lon[..., :-1, :-1], lat[..., :-1, :-1]
ylo_xhi = lon[..., :-1, 1:], lat[..., :-1, 1:]
yhi_xlo = lon[..., 1:, :-1], lat[..., 1:, :-1]
dx = angular_separation(*(ylo_xlo + ylo_xhi))
dy = angular_separation(*(ylo_xlo + yhi_xlo))
return u.Quantity(dx * dy, 'sr')
def coarse_quad_search(self, obsjd, quads, objects, vlim):
"""Nearest-neighbor search.
Parameters
----------
obsjd : float
Julian date.
quads : list of lists
Each item is a list of quadrant parameters:
obsjd, pid, ra_c, dec_c, ra1, ra2, ra3, ra4, dec1, dec2, dec3, dec4
where 1..4 are coordinates of the corners.
objects : list of string
Objects.
vlim : float
Limiting magnitude to consider.
Returns
-------
objects : list
Found objects.
quads : list
Nearest 4 quads for each object.
"""
import numpy as np
from astropy.coordinates.angle_utilities import angular_separation
from .exceptions import EphemerisError
(ra_c, dec_c, ra1, ra2, ra3, ra4,
dec1, dec2, dec3, dec4) = tuple(zip(*quads))[2:]
found = []
for obj in objects:
try:
ra, dec, vmag = self._get_ephemeris(obj, obsjd)
except EphemerisError as e:
self.logger.debug(str(e))
continue
# vmag greater than vlim? skip.
if vmag > vlim:
continue
# farther than 12 deg from any corner? forget it
if angular_separation(ra, dec, ra_c[0], dec_c[0]) > 0.21:
continue
# Farther than 1.5 deg from any quad? skip.
d = angular_separation(ra, dec, ra_c, dec_c)
if min(d) > 0.026:
continue
found.append((obj, [quads[i] for i in np.argsort(d)[:4]]))
return found
def evaluate(self, lon, lat, lon_0, lat_0, semi_major, e, theta, edge):
"""Evaluate the model (static function)."""
# find the foci of the ellipse
c = semi_major * e
lon_1, lat_1 = self._offset_by(lon_0, lat_0, 90 * u.deg - theta, c)
lon_2, lat_2 = self._offset_by(lon_0, lat_0, 270 * u.deg - theta, c)
sep_1 = angular_separation(lon, lat, lon_1, lat_1)
sep_2 = angular_separation(lon, lat, lon_2, lat_2)
in_ellipse = smooth_edge(sep_1 + sep_2 - 2 * semi_major, edge)
norm = SkyEllipse.compute_norm(semi_major, e)
return u.Quantity(norm * in_ellipse, "sr-1", copy=False)
def evaluate(self, lon, lat, lon_0, lat_0, semi_major, e, theta, edge):
"""Evaluate the model (static function)."""
# find the foci of the ellipse
c = semi_major * e
lon_1, lat_1 = self._offset_by(lon_0, lat_0, 90 * u.deg - theta, c)
lon_2, lat_2 = self._offset_by(lon_0, lat_0, 270 * u.deg - theta, c)
sep_1 = angular_separation(lon, lat, lon_1, lat_1)
sep_2 = angular_separation(lon, lat, lon_2, lat_2)
in_ellipse = smooth_edge(sep_1 + sep_2 - 2 * semi_major, 2 * edge)
norm = SkyEllipse.compute_norm(semi_major, e)
return u.Quantity(norm * in_ellipse, "sr-1", copy=False)
def __init__(self, ra, dec, trigger_time, ft2file, degree=2):
# Open the FT2 file and read the pointing information
with pyfits.open(ft2file) as f:
# Remember: in the FT2 all quantities (except the livetime) refer to the START time
time = f['SC_DATA'].data['START']
# Read the position of the Z-axis (the boresight) and convert it to radians
ra_scz_rad = np.deg2rad(f['SC_DATA'].data['RA_SCZ'])
dec_scz_rad = np.deg2rad(f['SC_DATA'].data['DEC_SCZ'])
# Prepare the interpolator
ang_dist_rad = angular_separation(ra_scz_rad, dec_scz_rad, np.deg2rad(ra), np.deg2rad(dec))
self._theta_interpolator_radians = scipy.interpolate.InterpolatedUnivariateSpline(time - trigger_time,
ang_dist_rad,
w=np.ones_like(ang_dist_rad),
k=2,
ext=2,
check_finite=True)
# Store the trigegr time as reference time
self._reference_time = float(trigger_time)
self._degree = int(degree)
self._scales = np.ones(self._degree+1)
self.clip_at_zero = False
def calculate_source_fov_offset(events, prefix="true"):
"""Calculate angular separation between true and pointing positions.
Parameters
----------
events : astropy.QTable
Astropy Table object containing the reconstructed events information.
prefix: str
Column prefix for az / alt, can be used to calculate reco or true
source fov offset.
Returns
-------
theta: astropy.units.Quantity
Angular separation between the true and pointing positions
in the sky.
"""
theta = angular_separation(
events[f"{prefix}_az"],
events[f"{prefix}_alt"],
events["pointing_az"],
events["pointing_alt"],
)
return theta.to(u.deg)
def compute_constraint(self, times, observer, targets):
moon = get_moon(times, observer.location, observer.pressure)
targets = [target.coord if hasattr(target, 'coord') else target
for target in targets]
moon_separation = Angle([angular_separation(moon.spherical.lon,
moon.spherical.lat,
target.spherical.lon,
target.spherical.lat)
for target in targets])
# The line below should have worked, but needs a workaround.
# TODO: once bug has been fixed, replace workaround with simpler version.
# Relevant PR: https://github.com/astropy/astropy/issues/4033
# moon_separation = Angle([moon.separation(target) for target in targets])
if self.min is None and self.max is not None:
mask = self.max > moon_separation
elif self.max is None and self.min is not None:
mask = self.min < moon_separation
elif self.min is not None and self.max is not None:
mask = ((self.min < moon_separation) &
(moon_separation < self.max))
else:
raise ValueError("No max and/or min specified in "
"MoonSeparationConstraint.")
return mask
def moon_phase_angle(time, location):
"""
Calculate lunar orbital phase [radians].
Parameters
----------
time : `~astropy.time.Time`
Time of observation
location : `~astropy.coordinates.EarthLocation`
Location of observer
Returns
-------
i : float
Phase angle of the moon [radians]
"""
# TODO: cache these sun/moon SkyCoord objects
sun = get_sun(time).transform_to(AltAz(location=location, obstime=time))
moon = get_moon(time, location)
# The line below should have worked, but needs a workaround.
# TODO: once bug has been fixed, replace workaround with simpler version.
# elongation = sun.separation(moon)
elongation = Angle(angular_separation(moon.spherical.lon,
moon.spherical.lat,
sun.spherical.lon,
sun.spherical.lat), u.deg)
return np.arctan2(sun.distance*np.sin(elongation),
moon.distance - sun.distance*np.cos(elongation))
def triangle_test(p, v):
"""Test if point p lies within the triangle with vertices v.
All points in units of raidans.
Edges and vertices are included.
Assumes points are located on the unit sphere.
http://mathworld.wolfram.com/TriangleInterior.html
"""
import numpy as np
from astropy.coordinates.angle_utilities import (
angular_separation, position_angle)
# project coordinate system about p to avoid polar and boundary issues
# Zenithal projection
th = angular_separation(p[0], p[1], v[:, 0], v[:, 1])
phi = position_angle(p[0], p[1], v[:, 0], v[:, 1])
x = np.c_[th * np.sin(phi), -th * np.cos(phi)]
a = x[1] - x[0]
b = x[2] - x[0]
#s = (np.cross(p, b) - np.cross(v[0], b)) / np.cross(a, b)
#t = -(np.cross(p, a) - np.cross(v[0], a)) / np.cross(a, b)
s = -np.cross(x[0], b) / np.cross(a, b)
t = np.cross(x[0], a) / np.cross(a, b)
return (s >= 0) * (t >= 0) * (s + t <= 1)
def compute_constraint(self, times, observer, targets):
moon = get_moon(times, observer.location, observer.pressure)
targets = [
target.coord if hasattr(target, 'coord') else target
for target in targets
]
moon_separation = Angle([
angular_separation(moon.spherical.lon, moon.spherical.lat,
target.spherical.lon, target.spherical.lat)
for target in targets
])
# The line below should have worked, but needs a workaround.
# TODO: once bug has been fixed, replace workaround with simpler version.
# Relevant PR: https://github.com/astropy/astropy/issues/4033
# moon_separation = Angle([moon.separation(target) for target in targets])
if self.min is None and self.max is not None:
mask = self.max >= moon_separation
elif self.max is None and self.min is not None:
mask = self.min <= moon_separation
elif self.min is not None and self.max is not None:
mask = ((self.min <= moon_separation) &
(moon_separation <= self.max))
else:
raise ValueError("No max and/or min specified in "
"MoonSeparationConstraint.")
return mask
def moon_phase_angle(time, location):
"""
Calculate lunar orbital phase [radians].
Parameters
----------
time : `~astropy.time.Time`
Time of observation
location : `~astropy.coordinates.EarthLocation`
Location of observer
Returns
-------
i : float
Phase angle of the moon [radians]
"""
# TODO: cache these sun/moon SkyCoord objects
sun = get_sun(time).transform_to(AltAz(location=location, obstime=time))
moon = get_moon(time, location)
# The line below should have worked, but needs a workaround.
# TODO: once bug has been fixed, replace workaround with simpler version.
# elongation = sun.separation(moon)
elongation = Angle(
angular_separation(moon.spherical.lon, moon.spherical.lat,
sun.spherical.lon, sun.spherical.lat), u.deg)
return np.arctan2(sun.distance * np.sin(elongation),
moon.distance - sun.distance * np.cos(elongation))
def calculate_theta(events, assumed_source_az, assumed_source_alt):
"""Calculate sky separation between assumed and reconstructed positions.
Parameters
----------
events : astropy.QTable
Astropy Table object containing the reconstructed events information.
assumed_source_az: astropy.units.Quantity
Assumed Azimuth angle of the source.
assumed_source_alt: astropy.units.Quantity
Assumed Altitude angle of the source.
Returns
-------
theta: astropy.units.Quantity
Angular separation between the assumed and reconstructed positions
in the sky.
"""
theta = angular_separation(
assumed_source_az,
assumed_source_alt,
events["reco_az"],
events["reco_alt"],
)
return theta.to(u.deg)
def f(params, row, col, alt, az):
print(params)
zenith_row, zenith_col, rotation = params
magic_2018.zenith_row = zenith_row + magic_2018.sensor.resolution_row / 2
magic_2018.zenith_col = zenith_col + magic_2018.sensor.resolution_col / 2
magic_2018.rotation = rotation * u.deg
magic_2018.lens.mapping = 'spline'
r, phi = magic_2018.pixel2polar(row, col)
r *= magic_2018.sensor.pixel_width.to(u.mm).value
x = np.append(0, r)
y = np.append(0, 90 - alt)
idx = np.argsort(x)
tck = splrep(x[idx],
y[idx],
t=np.linspace(np.percentile(x, 1), np.percentile(x, 99), 10))
magic_2018.lens.tck_inv = tck
coords = magic_2018.pixel2horizontal(row, col)
val = angular_separation(alt * u.deg, az * u.deg, coords.alt,
coords.az).value.mean()
return val
def evaluate(lon, lat, lon_0, lat_0, sigma):
"""Evaluate the model (static function)."""
sep = angular_separation(lon, lat, lon_0, lat_0)
a = 1.0 - np.cos(sigma)
norm = 1 / (4 * np.pi * a * (1.0 - np.exp(-1.0 / a)))
exponent = -0.5 * ((1 - np.cos(sep)) / a)
return u.Quantity(norm.value * np.exp(exponent).value, "sr-1", copy=False)
def search_for_maximum(self, ra_center, dec_center, half_side_deg, n_side, proj_name='AIT', verbose=False):
"""
:param ra_center: R.A. of the center of the map
:param dec_center: Dec of the center of the map
:param half_size_deg: half size of the side of the TS map ("radius", even though it is a square)
:param n_side: number of points on one side. So n_side = 5 means that a 5x5 map will be computed
:param stepsize: size of the step, i.e., distance between two adiancent points in the RA or Dec direction
:param proj_name: name for the projection (default: AIT). All projections supported by astropy.wcs can be used
:return: (max_ts_position, max_ts): returns a tuple of (RA, Dec) and the maximum TS found
"""
# Figure out step size
stepsize = half_side_deg / (n_side / 2.0)
# Create WCS object which will allow us to make the grid
wcs = pywcs.WCS(naxis=2)
wcs.wcs.crpix = [n_side / 2. + 0.5, n_side / 2. + 0.5]
wcs.wcs.cdelt = [-stepsize, stepsize]
wcs.wcs.crval = [float(ra_center), float(dec_center)]
wcs.wcs.ctype = ["RA---%s" % proj_name, "DEC--%s" % proj_name]
# Compute all TSs
# These two will hold maximum and position of the maximum
# Init them with worse case scenario
max_ts = 0.0
max_ts_position = (ra_center, dec_center)
ang_sep = []
for i in range(n_side):
for j in range(n_side):
this_ra, this_dec = wcs.wcs_pix2world(i, j, 0)
this_TS = self._calc_one_TS(float(this_ra), float(this_dec))
if this_TS >= max_ts:
# New maximum
max_ts = this_TS
max_ts_position = (this_ra, this_dec)
if verbose:
ang_sep.append(np.rad2deg(angular_separation(*np.deg2rad([ra_center, dec_center,
this_ra, this_dec]))))
print("(%.3f, %.3f) -> %.2f (%.3f deg away from center)" % (this_ra, this_dec,
this_TS, ang_sep[-1]))
if verbose:
print("Total number of points: %i" % len(ang_sep))
print("Minimum ang. dist: %s deg" % min(ang_sep))
print("Maximum ang. dist: %s deg" % max(ang_sep))
# Find maximum and its position
return max_ts_position, max_ts
def const_score(tb, ob, times, site):
"""
calculates a score for an OB thar represents how well it would fit here,
infinity if constraints make it unobservable
Remember: Lower numbers are better
"""
moon = astroplan.get_moon(times, site.location, site.pressure)
altaz = site.altaz(times, ob.target)
if np.any(altaz.alt < ob.constraints[1].min) or np.any(altaz.alt > ob.constraints[1].max):
return float('inf') # altitude constraint
if np.any(site.moon_illumination(times) > ob.constraints[2].max):
return float('inf') # moon illumination constraint
moon_sep = astropy.coordinates.Angle([angular_separation(moon.spherical.lon,
moon.spherical.lat,
ob.target.coord.spherical.lon,
ob.target.coord.spherical.lat)])
if np.any(moon_sep < ob.constraints[0].min):
return float('inf') # moon separation constraint
score = 0.
score += ob.priority*weights.w_priority # the marked priority
score += ob.program.rank*weights.w_rank # the rank of the program
if tb is not None:
# the time to slew
score += tb.components.get('slew_time', 0*u.second).value*weights.w_slew
# the time to change filter
score += tb.components.get('filter_change',
0*u.second).value*weights.w_filterchange
return score
def process_mc(simtelfile, dl2_file, mc_type):
"""
Process the MC simulated and reconstructed to extract the relevant
parameters to compute the sensitivity
Paramenters
---------
simtel: simtelarray file
dl2_file: `pandas.DataFrame` dl2 parameters
mc_type: 'string' type of particle
Returns
---------
gammaness: `numpy.ndarray`
angdist2: `numpy.ndarray` angular distance squared
e_reco: `numpy.ndarray` reconstructed energies
n_reco: `int` number of reconstructed events
mc_par: `dict` with simulated parameters
"""
source = SimTelFile(simtelfile)
sim_par = read_sim_par(source)
events = pd.read_hdf(dl2_file)
e_reco = 10**events.mc_energy.to_numpy() * u.GeV
gammaness = events.gammaness
#Get source position in radians
focal_length = source.telescope_descriptions[1]['camera_settings']['focal_length'] * u.m
# If the particle is a gamma ray, it returns the squared angular distance
# from the reconstructed gamma-ray position and the simulated incoming position
if mc_type=='gamma':
events = events[events.mc_type==0]
alt2 = events.mc_alt
az2 = np.arctan(np.tan(events.mc_az))
# If the particle is not a gamma-ray (diffuse protons/electrons), it returns
# the squared angular distance of the reconstructed position w.r.t. the
# center of the camera
else:
events = events[events.mc_type!=0]
alt2 = events.mc_alt_tel
az2 = np.arctan(np.tan(events.mc_az_tel))
src_pos_reco = reco_source_position_sky(events.x.values * u.m,
events.y.values * u.m,
events.disp_dx_rec.values * u.m,
events.disp_dy_rec.values * u.m,
focal_length,
events.mc_alt_tel.values * u.rad,
events.mc_az_tel.values * u.rad)
alt1 = src_pos_reco.alt.rad
az1 = np.arctan(np.tan(src_pos_reco.az.rad))
angdist2 = (angular_separation(az1, alt1, az2, alt2).to_numpy() * u.rad)**2
return gammaness, angdist2.to(u.deg**2), e_reco, sim_par
def pair_correlation(lon, lat, theta_bins):
"""Compute pair correlation function for points on the sphere.
Parameters
----------
lon, lat : array_like
Coordinate arrays
theta_bins : array_like
Array defining the ``theta`` binning.
``theta`` is the angular offset between positions.
unit : {'deg', 'rad'}
Units of input and output coordinates
Returns
-------
counts : array
Array of point separations per ``theta`` bin.
"""
# TODO: Implement speedups:
# - use radians
# - avoid processing each pair twice (distance a to b and b to a)
counts = np.zeros(shape=len(theta_bins) - 1, dtype=int)
# If there are many points this should have acceptable performance
# because the inner loop is in np.histogram, not in Python
for ii in range(len(lon)):
theta = angular_separation(lon[ii], lat[ii], lon, lat)
hist = np.histogram(theta, theta_bins)[0]
counts += hist
return counts
def minimum_separation(lon1, lat1, lon2, lat2):
"""Compute minimum distance of each (lon1, lat1) to any (lon2, lat2).
Parameters
----------
lon1, lat1 : array_like
Primary coordinates of interest
lon2, lat2 : array_like
Counterpart coordinate array
unit : {'deg', 'rad'}
Units of input and output coordinates
Returns
-------
theta_min : array
Minimum distance
"""
lon1 = np.asanyarray(lon1)
lat1 = np.asanyarray(lat1)
theta_min = np.empty_like(lon1, dtype=np.float64)
for i1 in range(lon1.size):
thetas = angular_separation(lon1[i1], lat1[i1], lon2, lat2)
theta_min[i1] = thetas.min()
return theta_min
def anglesep(lon0: float,
lat0: float,
lon1: float,
lat1: float,
deg: bool = True) -> float:
"""
inputs: DEGREES
For reference, this is from astropy astropy/coordinates/angle_utilities.py
Angular separation between two points on a sphere.
"""
if angular_separation is None:
raise ImportError('angledist requires AstroPy. Try angledis_meeus')
if deg:
lon0 = radians(lon0)
lat0 = radians(lat0)
lon1 = radians(lon1)
lat1 = radians(lat1)
sep_rad = angular_separation(lon0, lat0, lon1, lat1)
if deg:
return degrees(sep_rad)
else:
return sep_rad
def evaluate(lon, lat, lon_0, lat_0, r_0):
"""Evaluate the model (static function)."""
sep = angular_separation(lon, lat, lon_0, lat_0)
# Surface area of a spherical cap, see https://en.wikipedia.org/wiki/Spherical_cap
norm = 1.0 / (2 * np.pi * (1 - np.cos(r_0)))
return u.Quantity(norm.value * (sep <= r_0), "sr-1", copy=False)
def process_mc(dl2_file, mc_type):
"""
Process the MC simulated and reconstructed to extract the relevant
parameters to compute the sensitivity
Parameters
----------
dl2_file: dl2 file with mc parameters
events: `pandas DataFrame' dl2 events
mc_type: 'string' type of particle
Returns
-------
gammaness: `numpy.ndarray`
angdist2: `numpy.ndarray` angular distance squared
e_reco: `numpy.ndarray` reconstructed energies
n_reco: `int` number of reconstructed events
mc_par: `dict` with simulated parameters
"""
sim_par = read_sim_par(dl2_file)
events = pd.read_hdf(dl2_file, key=dl2_params_lstcam_key)
# Filters:
# TO DO: These cuts must be given in a configuration file
# By now: only cut in leakage and intensity
# we use all telescopes (number of events needs to be multiplied
# by the number of LSTs in the simulation)
filter_good_events = ((events.leakage_intensity_width_2 < 0.2)
& (events.intensity > 100))
events = events[filter_good_events]
e_reco = events.reco_energy.to_numpy() * u.TeV
e_true = events.mc_energy.to_numpy() * u.TeV
gammaness = events.gammaness
# If the particle is a gamma ray, it returns the squared angular distance
# from the reconstructed gamma-ray position and the simulated incoming position
if mc_type == 'gamma':
alt2 = events.mc_alt
az2 = events.mc_az
# If the particle is not a gamma-ray (diffuse protons/electrons), it returns
# the squared angular distance of the reconstructed position w.r.t. the
# center of the camera
else:
alt2 = events.mc_alt_tel
az2 = events.mc_az_tel
alt1 = events.reco_alt
az1 = events.reco_az
angdist2 = (angular_separation(az1, alt1, az2, alt2).to_numpy() * u.rad)**2
events['theta2'] = angdist2.to_value(u.deg**2)
return gammaness, angdist2.to(u.deg**2), e_reco, e_true, sim_par, events
def angledist(lon1, lat1, lon2, lat2):
"""
For reference, this is from astropy astropy/coordinates/angle_utilities.py
Angular separation between two points on a sphere.
"""
return degrees(
angular_separation(radians(lon1), radians(lat1), radians(lon2),
radians(lat2)))
def angledist_astropy(lon1, lat1, lon2, lat2):
"""
For reference, this is from astropy astropy/coordinates/angle_utilities.py
Angular separation between two points on a sphere.
"""
return degrees(angular_separation(radians(lon1),
radians(lat1), radians(lon2),
radians(lat2)))
def test_fk4_no_e_fk5():
lines = get_pkg_data_contents('data/fk4_no_e_fk5.csv').split('\n')
t = Table.read(lines, format='ascii', delimiter=',', guess=False)
if N_ACCURACY_TESTS >= len(t):
idxs = range(len(t))
else:
idxs = np.random.randint(len(t), size=N_ACCURACY_TESTS)
diffarcsec1 = []
diffarcsec2 = []
for i in idxs:
# Extract row
r = t[int(i)] # int here is to get around a py 3.x astropy.table bug
# FK4NoETerms to FK5
c1 = FK4NoETerms(ra=r['ra_in'] * u.deg,
dec=r['dec_in'] * u.deg,
obstime=Time(r['obstime']),
equinox=Time(r['equinox_fk4']))
c2 = c1.transform_to(FK5(equinox=Time(r['equinox_fk5'])))
# Find difference
diff = angular_separation(c2.ra.radian, c2.dec.radian,
np.radians(r['ra_fk5']),
np.radians(r['dec_fk5']))
diffarcsec1.append(np.degrees(diff) * 3600.)
# FK5 to FK4NoETerms
c1 = FK5(ra=r['ra_in'] * u.deg,
dec=r['dec_in'] * u.deg,
equinox=Time(r['equinox_fk5']))
fk4neframe = FK4NoETerms(obstime=Time(r['obstime']),
equinox=Time(r['equinox_fk4']))
c2 = c1.transform_to(fk4neframe)
# Find difference
diff = angular_separation(c2.ra.radian, c2.dec.radian,
np.radians(r['ra_fk4']),
np.radians(r['dec_fk4']))
diffarcsec2.append(np.degrees(diff) * 3600.)
np.testing.assert_array_less(diffarcsec1, TOLERANCE)
np.testing.assert_array_less(diffarcsec2, TOLERANCE)
def evaluate(lon, lat, lon_0, lat_0, r_0, eta, e, phi):
sep = angular_separation(lon, lat, lon_0, lat_0)
if isinstance(eta, u.Quantity):
eta = eta.value # gamma function does not allow quantities
minor_axis, r_eff = compute_sigma_eff(lon_0, lat_0, lon, lat, phi, r_0, e)
z = sep / r_eff
norm = 1 / (2 * np.pi * minor_axis * r_0 * eta * scipy.special.gamma(2 * eta))
return (norm * np.exp(-(z ** (1 / eta)))).to("sr-1")
def evaluate(lon, lat, lon_0, lat_0, r_0, edge):
"""Evaluate model."""
sep = angular_separation(lon, lat, lon_0, lat_0)
# Surface area of a spherical cap, see https://en.wikipedia.org/wiki/Spherical_cap
norm = 1.0 / (2 * np.pi * (1 - np.cos(r_0)))
in_disk = smooth_edge(sep - r_0, edge)
return u.Quantity(norm.value * in_disk, "sr-1", copy=False)
def fov_offset(df):
pointing_lat = (90 - df.aux_pointing_position_zd.values) * u.deg
pointing_lon = df.aux_pointing_position_az.values * u.deg
source_lat = (90 - df.source_position_zd.values) * u.deg
source_lon = df.source_position_az.values * u.deg
return angular_separation(pointing_lon, pointing_lat, source_lon,
source_lat)
def calculate_distance_to_true_source_position(df):
source_az = Angle(df.mc_az.values * u.deg).wrap_at(180 * u.deg)
source_alt = Angle(df.mc_alt.values * u.deg)
az = Angle(df.az.values * u.deg).wrap_at(180 * u.deg)
alt = Angle(df.alt.values * u.deg)
distance = angular_separation(source_az, source_alt, az, alt).to(u.deg)
return distance
def evaluate(lon, lat, lon_0, lat_0, r_0, edge):
"""Evaluate the model (static function)."""
sep = angular_separation(lon, lat, lon_0, lat_0)
# Surface area of a spherical cap, see https://en.wikipedia.org/wiki/Spherical_cap
norm = 1.0 / (2 * np.pi * (1 - np.cos(r_0)))
in_disk = smooth_edge(sep - r_0, edge)
return u.Quantity(norm.value * in_disk, "sr-1", copy=False)
def calculate_distance_to_point_source(df, source_alt, source_az):
source_az = Angle(source_az).wrap_at(180 * u.deg)
source_alt = Angle(source_alt)
az = Angle(df.az.values * u.deg).wrap_at(180 * u.deg)
alt = Angle(df.alt.values * u.deg)
distance = angular_separation(source_az, source_alt, az, alt).to(u.deg)
return distance
def evaluate(lon, lat, lon_0, lat_0, sigma):
"""Evaluate the model (static function)."""
sep = angular_separation(lon, lat, lon_0, lat_0)
a = 1.0 - np.cos(sigma)
norm = 1 / (4 * np.pi * a * (1.0 - np.exp(-1.0 / a)))
exponent = -0.5 * ((1 - np.cos(sep)) / a)
return u.Quantity(norm.value * np.exp(exponent).value,
"sr-1",
copy=False)
def test_fk4_no_e_fk5():
lines = get_pkg_data_contents('fk4_no_e_fk5.csv').split('\n')
t = Table.read(lines, format='ascii', delimiter=',', guess=False)
if N_ACCURACY_TESTS >= len(t):
idxs = range(len(t))
else:
idxs = np.random.randint(len(t), size=N_ACCURACY_TESTS)
diffarcsec1 = []
diffarcsec2 = []
for i in idxs:
# Extract row
r = t[int(i)] # int here is to get around a py 3.x astropy.table bug
# FK4NoETerms to FK5
c1 = FK4NoETerms(ra=r['ra_in']*u.deg, dec=r['dec_in']*u.deg,
obstime=Time(r['obstime'], scale='utc'),
equinox=Time(r['equinox_fk4'], scale='utc'))
c2 = c1.transform_to(FK5(equinox=Time(r['equinox_fk5'], scale='utc')))
# Find difference
diff = angular_separation(c2.ra.radian, c2.dec.radian,
np.radians(r['ra_fk5']),
np.radians(r['dec_fk5']))
diffarcsec1.append(np.degrees(diff) * 3600.)
# FK5 to FK4NoETerms
c1 = FK5(ra=r['ra_in']*u.deg, dec=r['dec_in']*u.deg,
equinox=Time(r['equinox_fk5'], scale='utc'))
fk4neframe = FK4NoETerms(obstime=Time(r['obstime'], scale='utc'),
equinox=Time(r['equinox_fk4'], scale='utc'))
c2 = c1.transform_to(fk4neframe)
# Find difference
diff = angular_separation(c2.ra.radian, c2.dec.radian,
np.radians(r['ra_fk4']),
np.radians(r['dec_fk4']))
diffarcsec2.append(np.degrees(diff) * 3600.)
np.testing.assert_array_less(diffarcsec1, TOLERANCE)
np.testing.assert_array_less(diffarcsec2, TOLERANCE)
def evaluate(lon, lat, lon_0, lat_0, r_0):
"""Evaluate the model (static function)."""
sep = angular_separation(lon, lat, lon_0, lat_0)
sep = sep.to('rad').value
r_0 = r_0.to('rad').value
norm = 1. / (2 * np.pi * (1 - np.cos(r_0)))
val = np.where(sep <= r_0, norm, 0)
return val * u.Unit('sr-1')
def solid_angle(self):
"""
Solid angle image (2-dim `~astropy.units.Quantity` in `sr`).
"""
coordinates = self.coordinates(mode='edges')
lon = coordinates.data.lon.radian
lat = coordinates.data.lat.radian
# Compute solid angle using the approximation that it's
# the product between angular separation of pixel corners.
# First index is "y", second index is "x"
ylo_xlo = lon[:-1, :-1], lat[:-1, :-1]
ylo_xhi = lon[:-1, 1:], lat[:-1, 1:]
yhi_xlo = lon[1:, :-1], lat[1:, :-1]
dx = angular_separation(*(ylo_xlo + ylo_xhi))
dy = angular_separation(*(ylo_xlo + yhi_xlo))
omega = u.Quantity(dx * dy, 'sr')
return omega
def solid_angle(self):
"""
Solid angle image (2-dim `~astropy.units.Quantity` in `sr`).
"""
coordinates = self.coordinates(mode='edges')
lon = coordinates.data.lon.radian
lat = coordinates.data.lat.radian
# Compute solid angle using the approximation that it's
# the product between angular separation of pixel corners.
# First index is "y", second index is "x"
ylo_xlo = lon[:-1, :-1], lat[:-1, :-1]
ylo_xhi = lon[:-1, 1:], lat[:-1, 1:]
yhi_xlo = lon[1:, :-1], lat[1:, :-1]
dx = angular_separation(*(ylo_xlo + ylo_xhi))
dy = angular_separation(*(ylo_xlo + yhi_xlo))
omega = u.Quantity(dx * dy, 'sr')
return omega
def _pix_cen(self):
"""
Offset of every pixel from the origin, along each direction
Returns
-------
tuple of spectral_offset, y_offset, x_offset, each 3D arrays
describing the distance from the origin
Notes
-----
These arrays are broadcast, and are not memory intensive
Each array is in the units of the corresponding wcs.cunit, but
this is implicit (e.g., they are not astropy Quantity arrays)
"""
# Start off by extracting the world coordinates of the pixels
_, lat, lon = self.world[0, :, :]
spectral, _, _ = self.world[:, 0, 0]
# Convert to radians
lon = np.radians(lon)
lat = np.radians(lat)
# Find the dx and dy arrays
from astropy.coordinates.angle_utilities import angular_separation
dx = angular_separation(lon[:, :-1], lat[:, :-1],
lon[:, 1:], lat[:, :-1])
dy = angular_separation(lon[:-1, :], lat[:-1, :],
lon[1:, :], lat[1:, :])
# Find the cumulative offset - need to add a zero at the start
x = np.zeros(self._data.shape[1:])
y = np.zeros(self._data.shape[1:])
x[:, 1:] = np.cumsum(np.degrees(dx), axis=1)
y[1:, :] = np.cumsum(np.degrees(dy), axis=0)
x = x.reshape(1, x.shape[0], x.shape[1])
y = y.reshape(1, y.shape[0], y.shape[1])
spectral = spectral.reshape(-1, 1, 1) - spectral.ravel()[0]
x, y, spectral = np.broadcast_arrays(x, y, spectral)
return spectral, y, x
def angular_separation_deg_to_arcsec(lon1, lat1, lon2, lat2):
from astropy.coordinates.angle_utilities import angular_separation
from astropy.coordinates import Angle
lon1 = np.radians(lon1)
lat1 = np.radians(lat1)
lon2 = np.radians(lon2)
lat2 = np.radians(lat2)
separation = angular_separation(lon1, lat1, lon2, lat2)
return Angle(separation, 'radian').to('arcsec').value
def test_galactic_fk4():
lines = get_pkg_data_contents('data/galactic_fk4.csv').split('\n')
t = Table.read(lines, format='ascii', delimiter=',', guess=False)
if N_ACCURACY_TESTS >= len(t):
idxs = range(len(t))
else:
idxs = np.random.randint(len(t), size=N_ACCURACY_TESTS)
diffarcsec1 = []
diffarcsec2 = []
for i in idxs:
# Extract row
r = t[int(i)] # int here is to get around a py 3.x astropy.table bug
# Galactic to FK4
c1 = Galactic(l=r['lon_in']*u.deg, b=r['lat_in']*u.deg)
c2 = c1.transform_to(FK4(equinox=Time(r['equinox_fk4'], scale='utc')))
# Find difference
diff = angular_separation(c2.ra.radian, c2.dec.radian,
np.radians(r['ra_fk4']),
np.radians(r['dec_fk4']))
diffarcsec1.append(np.degrees(diff) * 3600.)
# FK4 to Galactic
c1 = FK4(ra=r['lon_in']*u.deg, dec=r['lat_in']*u.deg,
obstime=Time(r['obstime'], scale='utc'),
equinox=Time(r['equinox_fk4'], scale='utc'))
c2 = c1.transform_to(Galactic)
# Find difference
diff = angular_separation(c2.l.radian, c2.b.radian,
np.radians(r['lon_gal']),
np.radians(r['lat_gal']))
diffarcsec2.append(np.degrees(diff) * 3600.)
np.testing.assert_array_less(diffarcsec1, TOLERANCE)
np.testing.assert_array_less(diffarcsec2, TOLERANCE)
def compute_angletosun(self, meteo):
"""
Computes the distance to the Sun
:param meteo: a Meteo object, whose time attribute has been actualized beforehand
"""
if SETTINGS["misc"]["singletargetlogs"] == "True":
logger.debug("Computing angletosun for {}...".format(self.name))
sunalt, sunaz = meteo.sunalt, meteo.sunaz
alt, az = self.altitude, self.azimuth
separation = angle_utilities.angular_separation(sunaz, sunalt, az, alt) # Warning, separation is in radian!!
angletosun = angles.Angle(separation.value, unit="radian")
self.angletosun = angletosun
def test_angsep():
"""
Tests that the angular separation object also behaves correctly.
"""
from astropy.coordinates.angle_utilities import angular_separation
# check it both works with floats in radians, Quantities, or Angles
for conv in (np.deg2rad,
lambda x: u.Quantity(x, "deg"),
lambda x: Angle(x, "deg")):
for (lon1, lat1, lon2, lat2), corrsep in zip(coords, correct_seps):
angsep = angular_separation(conv(lon1), conv(lat1),
conv(lon2), conv(lat2))
assert np.fabs(angsep - conv(corrsep)) < conv(correctness_margin)
def evaluate(lon, lat, lon_0, lat_0, radius, width):
"""Evaluate the model (static function)."""
sep = angular_separation(lon, lat, lon_0, lat_0)
radius_out = radius + width
norm = 3 / (2 * np.pi * (radius_out ** 3 - radius ** 3))
with np.errstate(invalid="ignore"):
# np.where and np.select do not work with quantities, so we use the
# workaround with indexing
value = np.sqrt(radius_out ** 2 - sep ** 2)
mask = [sep < radius]
value[mask] = (value - np.sqrt(radius ** 2 - sep ** 2))[mask]
value[sep > radius_out] = 0
return norm * value
def _compute_kernel_separations(geom, factor):
# utility function used for preparing distance to the center of the upsampled geom
# TODO : take into account non regular geometry for energy dependent PSF kernel size
if geom.is_regular is False:
raise ValueError("Non regular geometries are not supported yet.")
upsampled_image_geom = geom.to_image().upsample(factor)
# get center coordinate
center_coord = upsampled_image_geom.center_coord * u.deg
# get coordinates
map_c = upsampled_image_geom.get_coord()
# compute distances to map center
separations = angular_separation(
center_coord[0], center_coord[1], map_c.lon * u.deg, map_c.lat * u.deg
)
# Create map
kernel_map = Map.from_geom(geom=upsampled_image_geom.to_cube(axes=geom.axes))
return kernel_map, separations
def compute_angletowind(self, meteo):
"""
Computes the angle to wind
:param meteo: a Meteo object, whose time attribute has been actualized beforehand
"""
if SETTINGS["misc"]["singletargetlogs"] == "True":
logger.debug("Computing angletowind for {}...".format(self.name))
winddirection = meteo.winddirection
if winddirection < 0 or winddirection > 360:
self.angletowind = None
return
try:
winddirection = angles.Angle(winddirection, unit='degree')
self.angletowind = angle_utilities.angular_separation(winddirection, 0., self.azimuth, 0.)
self.angletowind = angles.Angle(self.angletowind, unit="radian")
except AttributeError:
logger.error("{} has no azimuth! \n Compute its azimuth first !".format(self.name))
raise AttributeError("%s has no azimuth! \n Compute its azimuth first !")
def anglesep(lon0: float, lat0: float,
lon1: float, lat1: float, deg: bool = True) -> float:
"""
Parameters
----------
lon0 : float
longitude of first point
lat0 : float
latitude of first point
lon1 : float
longitude of second point
lat1 : float
latitude of second point
deg : bool, optional
degrees input/output (False: radians in/out)
Returns
-------
sep_rad : float or numpy.ndarray of float
angular separation
For reference, this is from astropy astropy/coordinates/angle_utilities.py
Angular separation between two points on a sphere.
"""
if angular_separation is None:
raise ImportError('angledist requires AstroPy. Try angledis_meeus')
if deg:
lon0 = radians(lon0)
lat0 = radians(lat0)
lon1 = radians(lon1)
lat1 = radians(lat1)
sep_rad = angular_separation(lon0, lat0, lon1, lat1)
if deg:
return degrees(sep_rad)
else:
return sep_rad
def pair_correlation(lon, lat, theta_bins):
"""Compute pair correlation function for points on the sphere.
Parameters
----------
lon, lat : array_like
Coordinate arrays
theta_bins : array_like
Array defining the ``theta`` binning.
``theta`` is the angular offset between positions.
unit : {'deg', 'rad'}
Units of input and output coordinates
Returns
-------
counts : array
Array of point separations per ``theta`` bin.
"""
separation = angular_separation(lon[:, np.newaxis], lat[:, np.newaxis], lon, lat)
pair_correlation, _ = np.histogram(separation.ravel(), theta_bins)
return pair_correlation
def minimum_separation(lon1, lat1, lon2, lat2):
"""Compute minimum distance of each (lon1, lat1) to any (lon2, lat2).
Parameters
----------
lon1, lat1 : array_like
Primary coordinates of interest
lon2, lat2 : array_like
Counterpart coordinate array
unit : {'deg', 'rad'}
Units of input and output coordinates
Returns
-------
theta_min : array
Minimum distance
"""
lon1 = np.asanyarray(lon1)
lat1 = np.asanyarray(lat1)
separation = angular_separation(
lon1[:, np.newaxis], lat1[:, np.newaxis], lon2, lat2
)
return separation.min(axis=1)
def get_lon_lat_path(ax, transform, lon_lat):
"""
Draw a curve, taking into account discontinuities.
Parameters
----------
ax : ~matplotlib.axes.Axes
The axes in which to plot the grid
transform : transformation class
The transformation between the world and pixel coordinates
lon_lat : `~numpy.ndarray`
The longitude and latitude values along the curve, given as a (n,2)
array.
"""
# Get pixel limits
# xlim = ax.get_xlim()
# ylim = ax.get_ylim()
# Transform line to pixel coordinates
pixel = transform.transform(lon_lat)
# In some spherical projections, some parts of the curve are 'behind' or
# 'in front of' the plane of the image, so we find those by reversing the
# transformation and finding points where the result is not consistent.
lon_lat_check = transform.inverted().transform(pixel)
sep = angular_separation(np.radians(lon_lat[:, 0]),
np.radians(lon_lat[:, 1]),
np.radians(lon_lat_check[:, 0]),
np.radians(lon_lat_check[:, 1]))
sep[sep > np.pi] -= 2. * np.pi
mask = np.abs(sep > ROUND_TRIP_TOL)
# Mask values with invalid pixel positions
mask = mask | np.isnan(pixel[:, 0]) | np.isnan(pixel[:, 1])
# Mask values outside the viewport
# This has now been disabled because it assumes specifically rectangular
# axes, and also doesn't work if the coordinate direction is flipped.
# outside = ((pixel[:, 0] < xlim[0]) | (pixel[:, 0] > xlim[-1]) |
# (pixel[:, 1] < ylim[0]) | (pixel[:, 1] > ylim[-1]))
# mask[1:-1] = mask[1:-1] | (outside[2:] & outside[:-2])
# We can now start to set up the codes for the Path.
codes = np.zeros(lon_lat.shape[0], dtype=np.uint8)
codes[:] = Path.LINETO
codes[0] = Path.MOVETO
codes[mask] = Path.MOVETO
# Also need to move to point *after* a hidden value
codes[1:][mask[:-1]] = Path.MOVETO
# We now go through and search for discontinuities in the curve that would
# be due to the curve going outside the field of view, invalid WCS values,
# or due to discontinuities in the projection.
# We start off by pre-computing the step in pixel coordinates from one
# point to the next. The idea is to look for large jumps that might indicate
# discontinuities.
step = np.sqrt((pixel[1:, 0] - pixel[:-1, 0]) ** 2 +
(pixel[1:, 1] - pixel[:-1, 1]) ** 2)
# We search for discontinuities by looking for places where the step
# is larger by more than a given factor compared to the median
# discontinuous = step > DISCONT_FACTOR * np.median(step)
discontinuous = step[1:] > DISCONT_FACTOR * step[:-1]
# Skip over discontinuities
codes[2:][discontinuous] = Path.MOVETO
# The above missed the first step, so check that too
if step[0] > DISCONT_FACTOR * step[1]:
codes[1] = Path.MOVETO
# Create the path
path = Path(pixel, codes=codes)
# And add to the axes
return path
def get_lon_lat_path(lon_lat, pixel, lon_lat_check):
"""
Draw a curve, taking into account discontinuities.
Parameters
----------
lon_lat : `~numpy.ndarray`
The longitude and latitude values along the curve, given as a (n,2)
array.
pixel : `~numpy.ndarray`
The pixel coordinates corresponding to ``lon_lat``
lon_lat : `~numpy.ndarray`
The world coordinates derived from converting from ``pixel``, which is
used to ensure round-tripping.
"""
# In some spherical projections, some parts of the curve are 'behind' or
# 'in front of' the plane of the image, so we find those by reversing the
# transformation and finding points where the result is not consistent.
sep = angular_separation(np.radians(lon_lat[:, 0]),
np.radians(lon_lat[:, 1]),
np.radians(lon_lat_check[:, 0]),
np.radians(lon_lat_check[:, 1]))
sep[sep > np.pi] -= 2. * np.pi
mask = np.abs(sep > ROUND_TRIP_TOL)
# Mask values with invalid pixel positions
mask = mask | np.isnan(pixel[:, 0]) | np.isnan(pixel[:, 1])
# We can now start to set up the codes for the Path.
codes = np.zeros(lon_lat.shape[0], dtype=np.uint8)
codes[:] = Path.LINETO
codes[0] = Path.MOVETO
codes[mask] = Path.MOVETO
# Also need to move to point *after* a hidden value
codes[1:][mask[:-1]] = Path.MOVETO
# We now go through and search for discontinuities in the curve that would
# be due to the curve going outside the field of view, invalid WCS values,
# or due to discontinuities in the projection.
# We start off by pre-computing the step in pixel coordinates from one
# point to the next. The idea is to look for large jumps that might indicate
# discontinuities.
step = np.sqrt((pixel[1:, 0] - pixel[:-1, 0]) ** 2 +
(pixel[1:, 1] - pixel[:-1, 1]) ** 2)
# We search for discontinuities by looking for places where the step
# is larger by more than a given factor compared to the median
# discontinuous = step > DISCONT_FACTOR * np.median(step)
discontinuous = step[1:] > DISCONT_FACTOR * step[:-1]
# Skip over discontinuities
codes[2:][discontinuous] = Path.MOVETO
# The above missed the first step, so check that too
if step[0] > DISCONT_FACTOR * step[1]:
codes[1] = Path.MOVETO
# Create the path
path = Path(pixel, codes=codes)
return path
def _pix_size(self):
"""
Return the size of each pixel along each direction, in world units
Returns
-------
dv, dy, dx : tuple of 3D arrays
The extent of each pixel along each direction
Notes
-----
These arrays are broadcast, and are not memory intensive
Each array is in the units of the corresponding wcs.cunit, but
this is implicit (e.g., they are not astropy Quantity arrays)
"""
# First, scale along x direction
xpix = np.linspace(-0.5, self._data.shape[2] - 0.5, self._data.shape[2] + 1)
ypix = np.linspace(0., self._data.shape[1] - 1, self._data.shape[1])
xpix, ypix = np.meshgrid(xpix, ypix)
zpix = np.zeros(xpix.shape)
lon, lat, _ = self._wcs.all_pix2world(xpix, ypix, zpix, 0)
# Convert to radians
lon = np.radians(lon)
lat = np.radians(lat)
# Find the dx and dy arrays
from astropy.coordinates.angle_utilities import angular_separation
dx = angular_separation(lon[:, :-1], lat[:, :-1],
lon[:, 1:], lat[:, :-1])
# Next, scale along y direction
xpix = np.linspace(0., self._data.shape[2] - 1, self._data.shape[2])
ypix = np.linspace(-0.5,
self._data.shape[1] - 0.5,
self._data.shape[1] + 1)
xpix, ypix = np.meshgrid(xpix, ypix)
zpix = np.zeros(xpix.shape)
lon, lat, _ = self._wcs.all_pix2world(xpix, ypix, zpix, 0)
# Convert to radians
lon = np.radians(lon)
lat = np.radians(lat)
# Find the dx and dy arrays
from astropy.coordinates.angle_utilities import angular_separation
dy = angular_separation(lon[:-1, :], lat[:-1, :],
lon[1:, :], lat[1:, :])
# Next, spectral coordinates
zpix = np.linspace(-0.5, self._data.shape[0] - 0.5,
self._data.shape[0] + 1)
xpix = np.zeros(zpix.shape)
ypix = np.zeros(zpix.shape)
_, _, spectral = self._wcs.all_pix2world(xpix, ypix, zpix, 0)
dspectral = np.diff(spectral)
dx = np.abs(np.degrees(dx.reshape(1, dx.shape[0], dx.shape[1])))
dy = np.abs(np.degrees(dy.reshape(1, dy.shape[0], dy.shape[1])))
dspectral = np.abs(dspectral.reshape(-1, 1, 1))
dx, dy, dspectral = np.broadcast_arrays(dx, dy, dspectral)
return dspectral, dy, dx
def diag_size(self):
"""return the largest diagonal size"""
p1,p2,p3,p4 = self.calc_footprint()
return np.max([angular_separation(*np.concatenate([p1,p3])),
angular_separation(*np.concatenate([p2,p4]))])
# It fails for empty pixels
try:
hillas_params[tel_id] = hillas_parameters(camgeom, cleaned_image)
except:
pass
if len(hillas_params) < 2:
continue
reco_result = reco.predict(hillas_params, event.inst, point_altitude, point_azimuth)
# get angular offset between reconstructed shower direction and MC
# generated shower direction
off_angle = angular_separation(
event.mc.az,
event.mc.alt,
reco_result.az,
reco_result.alt
)
# Appending all estimated off angles
off_angles.append(off_angle.to(u.deg).value)
# calculate theta square for angles which are not nan
off_angles = np.array(off_angles)
thetasquare = off_angles[np.isfinite(off_angles)]**2
# To plot thetasquare The number of events in th data files for LSTCam is not
# significantly high to give a nice thetasquare plot for gammas One can use
# deedicated MC file for LST get nice plot
plt.figure(figsize=(10, 8))
plt.hist(thetasquare, bins=np.linspace(0, 1, 50))
# assume the location of the centroids to be the published value
# draw values from 4 normal distribution
centroid_old = [[NW_cent.ra.deg, NW_cent.dec.deg, 0.87,
SE_cent.ra.deg, SE_cent.dec.deg, 0.87]] * no
# hopefully that the arrays shape will be broadcast
N_halos = [2] * no
centroid_steps = [1. / np.sqrt(2) / 60. / 60.] * no
cent_new = map(get_new_centroids, N_halos, centroid_old, centroid_steps)
cent_new = np.array(cent_new)
[NW_ra, NW_dec, NW_z, SE_ra, SE_dec, SE_z] = cent_new.transpose()
# inputs of angular separation has to be in units of radians
ang_sep = \
ang_util.angular_separation(NW_ra / 180. * np.pi,
NW_dec / 180. * np.pi,
SE_ra / 180. * np.pi,
SE_dec / 180. * np.pi)
cosmo = FlatLambdaCDM(H0=70, Om0=0.3)
D_proj = cosmo.angular_diameter_distance(0.87) * ang_sep
###
# Debug input
###
def plot_dproj():
plt.title('D-proj')
plt.xlabel('Mpc')
plt.hist(D_proj, bins=100, normed=True, histtype='step')
plt.savefig(out_prefix + '_D_proj.png')
plt.close()
