def fit_origin_crosses(self):
'''calculates the origin of the gamma as the weighted average
direction of the intersections of all great circles
Returns
-------
gamma : shape (3) numpy array
direction of origin of the reconstructed shower as a 3D vector
crossings : shape (n,3) list
list of all the crossings of the `GreatCircle`s
'''
crossings = []
for perm in combinations(self.circles.values(), 2):
n1, n2 = perm[0].norm, perm[1].norm
# cross product automatically weighs in the angle between
# the two vectors: narrower angles have less impact,
# perpendicular vectors have the most
crossing = np.cross(n1, n2)
# two great circles cross each other twice (one would be
# the origin, the other one the direction of the gamma) it
# doesn't matter which we pick but it should at least be
# consistent: make sure to always take the "upper" solution
if crossing[2] < 0:
crossing *= -1
crossings.append(crossing * perm[0].weight * perm[1].weight)
# averaging over the solutions of all permutations
return linalg.normalise(np.sum(crossings,
axis=0)) * u.dimless, crossings
def __init__(self, dirs, weight=1):
'''the constructor takes two directions on the circle and creates the
normal vector belonging to that plane
Parameters
-----------
dirs : shape (2,3) ndarray
contains two 3D direction-vectors
weight : float, optional
weight of this telescope for later use during the
reconstruction
Algorithm:
----------
c : length 3 ndarray
c = (a × b) × a -> a and c form an orthogonal base for the
great circle (only orthonormal if a and b are of unit-length)
norm : length 3 ndarray
normal vector of the circle's plane,
perpendicular to a, b and c
'''
self.a = dirs[0]
self.b = dirs[1]
# a and c form an orthogonal basis for the great circle
# not really necessary since the norm can be calculated
# with a and b just as well
self.c = np.cross(np.cross(self.a, self.b), self.a)
# normal vector for the plane defined by the great circle
self.norm = linalg.normalise(np.cross(self.a, self.c))
# some weight for this circle
# (put e.g. uncertainty on the Hillas parameters
# or number of PE in here)
self.weight = weight
def fit_origin_crosses(self):
'''calculates the origin of the gamma as the weighted average
direction of the intersections of all great circles
'''
if len(self.circles) < 2:
raise TooFewTelescopesException(
"need at least two telescopes, have {}"
.format(len(self.circles)))
crossings = []
for perm in combinations(self.circles.values(), 2):
n1, n2 = perm[0].norm, perm[1].norm
# cross product automatically weighs in the angle between
# the two vectors: narrower angles have less impact,
# perpendicular vectors have the most
crossing = np.cross(n1, n2)
# two great circles cross each other twice (one would be
# the origin, the other one the direction of the gamma) it
# doesn't matter which we pick but it should at least be
# consistent: make sure to always take the "upper"
# solution
if crossing[2] < 0:
crossing *= -1
crossings.append(crossing * perm[0].weight * perm[1].weight)
# averaging over the solutions of all permutations
return linalg.normalise(np.sum(crossings, axis=0)) * u.dimless, crossings
def fit_origin_crosses(self):
'''calculates the origin of the gamma as the weighted average
direction of the intersections of all great circles
'''
if len(self.circles) < 2:
raise TooFewTelescopesException(
"need at least two telescopes, have {}".format(
len(self.circles)))
crossings = []
for perm in combinations(self.circles.values(), 2):
n1, n2 = perm[0].norm, perm[1].norm
# cross product automatically weighs in the angle between
# the two vectors: narrower angles have less impact,
# perpendicular vectors have the most
crossing = np.cross(n1, n2)
# two great circles cross each other twice (one would be
# the origin, the other one the direction of the gamma) it
# doesn't matter which we pick but it should at least be
# consistent: make sure to always take the "upper"
# solution
if crossing[2] < 0:
crossing *= -1
crossings.append(crossing * perm[0].weight * perm[1].weight)
# averaging over the solutions of all permutations
return linalg.normalise(np.sum(crossings,
axis=0)) * u.dimless, crossings
def __init__(self, dirs, weight=1):
'''the constructor takes two directions on the circle and creates the
normal vector belonging to that plane
Parameters
-----------
dirs : shape (2,3) ndarray
contains two 3D direction-vectors
weight : float, optional
weight of this telescope for later use during the
reconstruction
Algorithm:
----------
c : length 3 ndarray
c = (a × b) × a -> a and c form an orthogonal base for the
great circle (only orthonormal if a and b are of unit-length)
norm : length 3 ndarray
normal vector of the circle's plane,
perpendicular to a, b and c
'''
self.a = dirs[0]
self.b = dirs[1]
# a and c form an orthogonal basis for the great circle
# not really necessary since the norm can be calculated
# with a and b just as well
self.c = np.cross(np.cross(self.a, self.b), self.a)
# normal vector for the plane defined by the great circle
self.norm = linalg.normalise(np.cross(self.a, self.c))
# some weight for this circle
# (put e.g. uncertainty on the Hillas parameters
# or number of PE in here)
self.weight = weight
def fit_core_minimise(self, seed=(0, 0), test_function=dist_to_traces):
"""
reconstructs the shower core position from the already set up
great circles
Notes
-----
The core of the shower lies on the cross section of the great
circle with the horizontal plane. The direction of this cross
section is the cross-product of the circle's normal vector and
the horizontal plane. Here, we only care about the direction;
not the orientation...
Parameters
----------
seed : tuple
shape (2) tuple with optional starting coordinates
tuple of floats or astropy.length -- if floats, assume metres
test_function : function object, optional (default: dist_to_traces)
function to be used by the minimiser
"""
if type(seed) == u.Quantity:
unit = seed.unit
else:
unit = u.m
# the direction of the cross section of the great circle with
# the horizontal frame is the cross product of the great
# circle's normal vector with the z-axis:
# n × z = (n[1], -n[0], 0)
for circle in self.circles.values():
circle.trace = linalg.normalise(
np.array([circle.norm[1], -circle.norm[0], 0]))
# minimising the test function (note: minimize strips seed off its
# unit)
self.fit_result_core = minimize(test_function,
seed[:2],
args=(self.circles),
method='BFGS',
options={'disp': False})
if not self.fit_result_core.success:
print("fit_core: fit no success")
return np.array(self.fit_result_core.x) * unit
def fit_origin_minimise(self, seed=(0, 0, 1), test_function=neg_angle_sum):
''' Fits the origin of the gamma with a minimisation procedure this
function expects that
:func:`get_great_circles<ctapipe.reco.FitGammaHillas.get_great_circles>`
has been run already. A seed should be given otherwise it defaults to
"straight up" supperted functions to minimise are an M-estimator and the
negative sum of the angles to all normal vectors of the great
circles
Parameters
-----------
seed : length-3 array
starting point of the minimisation
test_function : function object, optional (default: neg_angle_sum)
either neg_angle_sum or MEst (or own implementation...)
neg_angle_sum seemingly superior to MEst
Returns
-------
direction : length-3 numpy array as dimensionless quantity
best fit for the origin of the gamma from
the minimisation process
'''
# using the sum of the cosines of each direction with every
# other direction as weight; don't use the product -- with many
# steep angles, the product will become too small and the
# weight (and the whole fit) useless
weights = [
np.sum([
linalg.length(np.cross(A.norm, B.norm))
for A in self.circles.values()
]) * B.weight for B in self.circles.values()
]
# minimising the test function
self.fit_result_origin = minimize(test_function,
seed,
args=(self.circles, weights),
method='BFGS',
options={'disp': False})
return np.array(linalg.normalise(self.fit_result_origin.x)) * u.dimless
def fit_core_minimise(self, seed=(0, 0), test_function=dist_to_traces):
'''reconstructs the shower core position from the already set up
great circles
Notes
-----
The core of the shower lies on the cross section of the great circle with
the horizontal plane. The direction of this cross section is the cross-product of
the circle's normal vector and the horizontal plane.
Here, we only care about the direction; not the orientation...
Parameters
----------
seed : tuple, optional (default: (0, 0))
shape (2) tuple with optional starting coordinates
tuple of floats or astropy.length -- if floats, assume metres
test_function : function object, optional (default: dist_to_traces)
function to be used by the minimiser
'''
if type(seed) == u.Quantity:
unit = seed.unit
else:
unit = u.m
# the direction of the cross section of the great circle with
# the horizontal frame is the cross product of the great
# circle's normal vector with the z-axis:
# n × z = (n[1], -n[0], 0)
for circle in self.circles.values():
circle.trace = linalg.normalise(np.array([circle.norm[1],
-circle.norm[0], 0]))
# minimising the test function (note: minimize strips seed off its
# unit)
self.fit_result_core = minimize(test_function, seed[:2],
args=(self.circles),
method='BFGS', options={'disp': False})
if not self.fit_result_core.success:
print("fit_core: fit no success")
return np.array(self.fit_result_core.x) * unit
def fit_origin_minimise(self, seed=[0, 0, 1], test_function=None):
''' fits the origin of the gamma with a minimisation procedure
this function expects that get_great_circles has been run already
a seed should be given otherwise it defaults to "straight up"
supperted functions to minimise are an M-estimator and the
negative sum of the angles to all normal vectors of the
great circles
Parameters:
-----------
seed : length-3 array
starting point of the minimisation
test_function : member function if this class
either _n_angle_sum or _MEst (or own implementation...)
defaults to _n_angle_sum if none is given
_n_angle_sum seemingly superior to _MEst
Returns:
--------
direction : length-3 numpy array as dimensionless quantity
best fit for the origin of the gamma from
the minimisation process
'''
if test_function is None: test_function = self._n_angle_sum
'''
using the sum of the cosines of each direction with
every otherdirection as weight;
don't use the product -- with many steep angles, the product will
become too small and the weight (and the whole fit) useless
'''
weights = [
np.sum([
linalg.length(np.cross(A.norm, B.norm))
for A in self.circles.values()
]) * B.weight for B in self.circles.values()
]
''' minimising the test function '''
self.fit_result_origin = minimize(test_function,
seed,
args=(self.circles, weights),
method='BFGS',
options={'disp': False})
return np.array(linalg.normalise(self.fit_result_origin.x)) * u.dimless
def fit_origin_minimise(self, seed=[0, 0, 1], test_function=None):
''' fits the origin of the gamma with a minimisation procedure
this function expects that get_great_circles has been run already
a seed should be given otherwise it defaults to "straight up"
supperted functions to minimise are an M-estimator and the
negative sum of the angles to all normal vectors of the
great circles
Parameters:
-----------
seed : length-3 array
starting point of the minimisation
test_function : member function if this class
either _n_angle_sum or _MEst (or own implementation...)
defaults to _n_angle_sum if none is given
_n_angle_sum seemingly superior to _MEst
Returns:
--------
direction : length-3 numpy array as dimensionless quantity
best fit for the origin of the gamma from
the minimisation process
'''
if test_function is None: test_function = self._n_angle_sum
'''
using the sum of the cosines of each direction with
every otherdirection as weight;
don't use the product -- with many steep angles, the product will
become too small and the weight (and the whole fit) useless
'''
weights = [np.sum([linalg.length(np.cross(A.norm, B.norm))
for A in self.circles.values()]
) * B.weight
for B in self.circles.values()]
''' minimising the test function '''
self.fit_result_origin = minimize(test_function, seed,
args=(self.circles, weights),
method='BFGS',
options={'disp': False}
)
return np.array(linalg.normalise(self.fit_result_origin.x))*u.dimless
def fit_origin_minimise(self, seed=(0, 0, 1), test_function=neg_angle_sum):
''' Fits the origin of the gamma with a minimisation procedure this
function expects that
:func:`get_great_circles<ctapipe.reco.FitGammaHillas.get_great_circles>`
has been run already. A seed should be given otherwise it defaults to
"straight up" supperted functions to minimise are an M-estimator and the
negative sum of the angles to all normal vectors of the great
circles
Parameters
-----------
seed : length-3 array
starting point of the minimisation
test_function : function object, optional (default: neg_angle_sum)
either neg_angle_sum or MEst (or own implementation...)
neg_angle_sum seemingly superior to MEst
Returns
-------
direction : length-3 numpy array as dimensionless quantity
best fit for the origin of the gamma from
the minimisation process
'''
# using the sum of the cosines of each direction with every
# other direction as weight; don't use the product -- with many
# steep angles, the product will become too small and the
# weight (and the whole fit) useless
weights = [np.sum([linalg.length(np.cross(A.norm, B.norm))
for A in self.circles.values()]
) * B.weight
for B in self.circles.values()]
# minimising the test function
self.fit_result_origin = minimize(test_function, seed,
args=(self.circles, weights),
method='BFGS',
options={'disp': False}
)
return np.array(linalg.normalise(self.fit_result_origin.x)) * u.dimless
def fit_core(self, seed=(0 * u.m, 0 * u.m), test_function=dist_to_traces):
'''reconstructs the shower core position from the already set up
great circles
.. note::
the core of the shower lies on the cross section of the
great circle with the horizontal plane the direction of this
cross section is the cross-product of the normal vectors of
the circle and the horizontal plane here we only care about
the direction; not the orientation...
Parameters
----------
seed : python tuple * astropy quantity, optional
shape (2) tuple with optional starting coordinates in
test_function : function object, optional
function to be used by the minimiser
by default uses self._dist_to_traces
'''
# the direction of the cross section of the great circle with
# the horizontal frame is the cross product of the great
# circle's normal vector with the z-axis
zdir = np.array([0, 0, 1])
for circle in self.circles.values():
circle.trace = linalg.normalise(np.cross(circle.norm, zdir))
# minimising the test function
self.fit_result_core = minimize(test_function,
seed[:2] / u.m,
args=(self.circles),
method='BFGS',
options={'disp': False})
if self.fit_result_core.success:
return np.array(self.fit_result_core.x) * u.m
else:
print("fit no success")
return np.array(self.fit_result_core.x) * u.m
return np.array([np.nan] * 3) * u.m
def fit_core(self, seed=(0*u.m, 0*u.m), test_function=dist_to_traces):
'''reconstructs the shower core position from the already set up
great circles
.. note::
the core of the shower lies on the cross section of the
great circle with the horizontal plane the direction of this
cross section is the cross-product of the normal vectors of
the circle and the horizontal plane here we only care about
the direction; not the orientation...
Parameters
----------
seed : python tuple * astropy quantity, optional
shape (2) tuple with optional starting coordinates in
test_function : function object, optional
function to be used by the minimiser
by default uses self._dist_to_traces
'''
# the direction of the cross section of the great circle with
# the horizontal frame is the cross product of the great
# circle's normal vector with the z-axis
zdir = np.array([0, 0, 1])
for circle in self.circles.values():
circle.trace = linalg.normalise(np.cross(circle.norm, zdir))
# minimising the test function
self.fit_result_core = minimize(test_function, seed[:2] / u.m,
args=(self.circles),
method='BFGS', options={'disp': False})
if self.fit_result_core.success:
return np.array(self.fit_result_core.x) * u.m
else:
print("fit no success")
return np.array(self.fit_result_core.x) * u.m
return np.array([np.nan] * 3) * u.m
90 * u.deg).to(u.deg)
length[k] = h.length
width[k] = h.width
for k, signal in { # 'p': pmt_signal_p,
'w': pmt_signal_w
}.items():
h = hillas[k]
p1_x = h.cen_x
p1_y = h.cen_y
p2_x = p1_x + h.length * np.cos(h.psi)
p2_y = p1_y + h.length * np.sin(h.psi)
T = linalg.normalise(
np.array([(p1_x - p2_x) / u.m, (p1_y - p2_y) / u.m]))
x = geom[k].pix_x
y = geom[k].pix_y
D = [p1_x - x, p1_y - y]
dl = D[0] * T[0] + D[1] * T[1]
dp = D[0] * T[1] - D[1] * T[0]
for pe, pp in zip(signal[abs(dl) > 1 * hillas[k].length],
dp[abs(dl) > 1 * hillas[k].length]):
pe_vs_dp[k].fill([np.log10(sum_p), pp], pe)
'''
do some plotting '''
def plot_perpendicular_hit_distribution(histogram_axis, image_axis, image_array, pixels_position, title):
image_array = copy.deepcopy(image_array)
###
#size_m = 0.2 # Size of the "phase space" in meter
size_m = 0.2 # Size of the "phase space" in meter
# # TODO: clean these following hard coded values for Astri
# num_pixels_x = 40
# num_pixels_y = 40
#
# x = np.linspace(-0.142555996776, 0.142555996776, num_pixels_x)
# y = np.linspace(-0.142555996776, 0.142555996776, num_pixels_y)
#
# #x = np.arange(0, np.shape(ref_image_array)[0], 1) # TODO: wrong values -10 10 21
# #y = np.arange(0, np.shape(ref_image_array)[1], 1) # TODO: wrong values (30, ...)
#
# xx, yy = np.meshgrid(x, y)
# print("delta x:", xx - pixels_position[0])
# print("delta y:", yy - pixels_position[1])
xx, yy = pixels_position[0], pixels_position[1]
# Based on Tino's evaluate_cleaning.py (l. 277)
hillas = hillas_parameters_1(xx.flatten() * u.meter, # TODO: essayer avec hillas param 2 !!!
yy.flatten() * u.meter,
image_array.flatten()) # [0]
centroid = (hillas.cen_x, hillas.cen_y)
length = hillas.length
width = hillas.width
angle = np.radians(hillas.psi) # - np.pi/2. # TODO
print("centroid:", centroid)
print("length:", length)
print("width:", width)
print("angle:", angle)
###
# p1 = center of the ellipse
p1_x = hillas.cen_x
p1_y = hillas.cen_y
#image_axis.scatter(p1_x, p1_y) # DEBUG plot
# p2 = intersection between the ellipse and the shower track
p2_x = p1_x + hillas.length * np.cos(angle) # hillas.psi + np.pi/2)
p2_y = p1_y + hillas.length * np.sin(angle) # hillas.psi + np.pi/2)
#image_axis.scatter(p2_x, p2_y) # DEBUG plot
#image_axis.plot([p1_x, p2_x], [p1_y, p2_y]) # DEBUG plot
print(p1_x, p2_x, p1_y, p2_y) # DEBUG plot
d12_x = p1_x - p2_x
d12_y = p1_y - p2_y
print(d12_x, d12_y) # DEBUG plot
# Slope of the shower track
T = linalg.normalise(np.array([d12_x.value, d12_y.value])) # why a dedicated function ? if it's what I understand, it can easily be done on the fly
#print("[p1_x-p2_x, p1_y-p2_y]:", [p1_x-p2_x, p1_y-p2_y])
#print("T:", T)
#image_axis.plot([p1_x, p1_x*T[0]], [p1_y, p1_y*T[1]], "-g", linewidth=3) # DEBUG plot
x = xx.flatten()
y = yy.flatten()
# Manhattan distance of pixels to the center of the ellipse
# Translate (center) on P1 ?
D = [p1_x.value-x, p1_y.value-y]
# Pixels in the new base
dl = D[0]*T[0] + D[1]*T[1]
dp = D[0]*T[1] - D[1]*T[0]
# nparray.ravel(): Return a flattened array.
values, bins, patches = histogram_axis.hist(dp.ravel(),
histtype='step',
bins=np.linspace(-size_m, size_m, 31)) # -10 10 21
# TODO: scatter seulement les points qui sont dans le linspace de bins defini juste au dessus, faire apparaitre chaque bin d'une couleure différente
##image_axis.scatter(dl, dp, s=10, alpha=0.5) # DEBUG plot
#image_axis.scatter(dl, dp, s=10, alpha=0.5) # DEBUG plot
#image_axis.plot(dl.reshape(40, 40).T, dp.reshape(40, 40).T) # DEBUG plot
#print(dl)
#print(dp.shape)
###
histogram_axis.set_xlim([-size_m, size_m])
histogram_axis.set_xlabel('Distance to the shower axis (m)', fontsize=14)
histogram_axis.set_ylabel('Hits', fontsize=14)
histogram_axis.set_title(title)
def plot_perpendicular_hit_distribution(histogram_axis, image_axis,
image_array, pixels_position, title):
image_array = copy.deepcopy(image_array)
###
#size_m = 0.2 # Size of the "phase space" in meter
size_m = 0.2 # Size of the "phase space" in meter
# # TODO: clean these following hard coded values for Astri
# num_pixels_x = 40
# num_pixels_y = 40
#
# x = np.linspace(-0.142555996776, 0.142555996776, num_pixels_x)
# y = np.linspace(-0.142555996776, 0.142555996776, num_pixels_y)
#
# #x = np.arange(0, np.shape(ref_image_array)[0], 1) # TODO: wrong values -10 10 21
# #y = np.arange(0, np.shape(ref_image_array)[1], 1) # TODO: wrong values (30, ...)
#
# xx, yy = np.meshgrid(x, y)
# print("delta x:", xx - pixels_position[0])
# print("delta y:", yy - pixels_position[1])
xx, yy = pixels_position[0], pixels_position[1]
# Based on Tino's evaluate_cleaning.py (l. 277)
hillas = hillas_parameters_1(
xx.flatten() * u.meter, # TODO: essayer avec hillas param 2 !!!
yy.flatten() * u.meter,
image_array.flatten()) # [0]
centroid = (hillas.x, hillas.y)
length = hillas.length
width = hillas.width
angle = np.radians(hillas.psi) # - np.pi/2. # TODO
print("centroid:", centroid)
print("length:", length)
print("width:", width)
print("angle:", angle)
###
# p1 = center of the ellipse
p1_x = hillas.x
p1_y = hillas.y
#image_axis.scatter(p1_x, p1_y) # DEBUG plot
# p2 = intersection between the ellipse and the shower track
p2_x = p1_x + hillas.length * np.cos(angle) # hillas.psi + np.pi/2)
p2_y = p1_y + hillas.length * np.sin(angle) # hillas.psi + np.pi/2)
#image_axis.scatter(p2_x, p2_y) # DEBUG plot
#image_axis.plot([p1_x, p2_x], [p1_y, p2_y]) # DEBUG plot
print(p1_x, p2_x, p1_y, p2_y) # DEBUG plot
d12_x = p1_x - p2_x
d12_y = p1_y - p2_y
print(d12_x, d12_y) # DEBUG plot
# Slope of the shower track
T = linalg.normalise(
np.array([d12_x.value, d12_y.value])
) # why a dedicated function ? if it's what I understand, it can easily be done on the fly
#print("[p1_x-p2_x, p1_y-p2_y]:", [p1_x-p2_x, p1_y-p2_y])
#print("T:", T)
#image_axis.plot([p1_x, p1_x*T[0]], [p1_y, p1_y*T[1]], "-g", linewidth=3) # DEBUG plot
x = xx.flatten()
y = yy.flatten()
# Manhattan distance of pixels to the center of the ellipse
# Translate (center) on P1 ?
D = [p1_x.value - x, p1_y.value - y]
# Pixels in the new base
dl = D[0] * T[0] + D[1] * T[1]
dp = D[0] * T[1] - D[1] * T[0]
# nparray.ravel(): Return a flattened array.
values, bins, patches = histogram_axis.hist(dp.ravel(),
histtype='step',
bins=np.linspace(
-size_m, size_m,
31)) # -10 10 21
# TODO: scatter seulement les points qui sont dans le linspace de bins defini juste au dessus, faire apparaitre chaque bin d'une couleure différente
##image_axis.scatter(dl, dp, s=10, alpha=0.5) # DEBUG plot
#image_axis.scatter(dl, dp, s=10, alpha=0.5) # DEBUG plot
#image_axis.plot(dl.reshape(40, 40).T, dp.reshape(40, 40).T) # DEBUG plot
#print(dl)
#print(dp.shape)
###
histogram_axis.set_xlim([-size_m, size_m])
histogram_axis.set_xlabel('Distance to the shower axis (m)', fontsize=14)
histogram_axis.set_ylabel('Hits', fontsize=14)
histogram_axis.set_title(title)