def run(graph=False):
i = 1
Evalues = [233, 700, 2000, 3500]
total = len(Evalues)
for Epn in Evalues:
zenith = 0
phi = math.radians(68+zenith)
hprob = np.linspace(0.001, 0.999, 999)
loc1 = str(total) + str(2) + str(i)
loc2 = str(total) + str(2) + str(i + 1)
ax1 = plt.subplot(loc1)
ax2 = plt.subplot(loc2)
h=[]
r=[]
for p in hprob:
height = atm.runheight(p, text=False)
radius, theta = cr.run(Epn, height, math.sin(phi), text=False)
r.append(radius)
h.append(height)
ax1.plot(r, hprob, '-r')
ax2.plot(r, h, '-r')
title = "Epn = " + str(Epn)
ax1.set_title(title)
ax1.set_xlabel('Radius')
ax1.set_xlim(0, 150)
ax2.set_xlim(0, 150)
ax1.set_ylim(0, 1)
ax2.set_ylim(0, 100000)
ax2.set_xlabel('Radius')
ax1.set_ylabel('Probability')
ax2.set_ylabel('Height')
i+=2
plt.tight_layout()
plt.suptitle('Radius with Height')
plt.savefig('/d6/rstein/Hamburg-Cosmic-Rays/positioning/graphs/stats/radius.pdf')
if graph:
plt.show()
def run():
#Randomly generates a target centre of -150<x<150m and -150<y<150m
xpos = (random.random() * 300) - 150
ypos = (random.random() * 300) - 150
#Generates a random probability, and converts this to an Epn value following an E^-1.7 power series
R = random.random() * 3.01 * (10**-3)
Epn = ((1.7 * R / 321) + (2411**-1.7))**(-1 / 1.7)
#Generates a fixed charge number of Z=26
Z = 26
N = 56
energy = Epn * N
#Randomly generates a height probability, and converts this probability to a set height
hprob = random.random()
height = atm.runheight(hprob)
#Chooses a zenith angle +- 22 degrees
zenith = random.random() * 44
phi = math.radians(68 + zenith)
phi = math.radians(90)
#Randomly choose an angle NESW
epsilon = math.pi * random.random() * 2
#~ #Calculate resultant surface radius and angular width of beam
#~
#~ radius, theta = cr.run(Epn, height, math.sin(phi), text=text)
#~
#~ if text:
#~ print "Height is", height
#~ print "Theta is", math.degrees(theta)
#~ print "Phi is", math.degrees(phi)
#~ print "Epsilon is", math.degrees(epsilon)
#~ print "Radius is", radius
return xpos, ypos, epsilon, energy, Z, height, phi, N
def run():
#Randomly generates a target centre of -150<x<150m and -150<y<150m
xpos = (random.random()*300)-150
ypos = (random.random()*300)-150
#Generates a random probability, and converts this to an Epn value following an E^-1.7 power series
R = random.random()*3.01*(10**-3)
Epn = ((1.7*R/321)+(2411**-1.7))**(-1/1.7)
#Generates a fixed charge number of Z=26
Z= 26
N = 56
energy = Epn*N
#Randomly generates a height probability, and converts this probability to a set height
hprob = random.random()
height = atm.runheight(hprob)
#Chooses a zenith angle +- 22 degrees
zenith = random.random()*44
phi = math.radians(68+zenith)
phi = math.radians(90)
#Randomly choose an angle NESW
epsilon = math.pi*random.random()*2
#~ #Calculate resultant surface radius and angular width of beam
#~
#~ radius, theta = cr.run(Epn, height, math.sin(phi), text=text)
#~
#~ if text:
#~ print "Height is", height
#~ print "Theta is", math.degrees(theta)
#~ print "Phi is", math.degrees(phi)
#~ print "Epsilon is", math.degrees(epsilon)
#~ print "Radius is", radius
return xpos, ypos, epsilon, energy, Z, height, phi, N
def run(eff, rowcount, mincount=4, text=False, graph=False, output="default", layout="five", number=1, nh=1):
#Define number of bins, stepcount
bincount = 20
stepcount = 1000
lower = float(1)/float(stepcount)
upper = float(1-lower)
Rrange = np.linspace(lower, upper, stepcount)
#~ ax1 = plt.subplot(321)
#~
decaylengths = []
survivallengths = []
decayheights = []
survivalheights = []
for R in Rrange:
dl = atm.runlengths(R)
decaylengths.append(dl)
sl = atm.runlengths(1-R)
survivallengths.append(sl)
dh = atm.runheight(R)
decayheights.append(dh)
sh = atm.runheight(1-R)
survivalheights.append(sh)
#~ ax1.plot(survivallengths, Rrange, label="survived")
#~ ax1.plot(decaylengths, Rrange, label = "decayed")
#~ plt.ylabel('Fraction')
#~ plt.xlabel('Interaction Lengths', labelpad=0)
#~ plt.legend()
ax2 = plt.subplot(311)
rawheights=[]
opticallengths = []
with open('/d6/rstein/Hamburg-Cosmic-Rays/positioning/atmospheredata/atmprofile.csv', 'rb') as csvfile:
reader = csv.reader(csvfile, delimiter=',', quotechar='|')
i=0
for row in reader:
i +=1
if i > 3:
opticallengths.append(float(row[2]))
rawheights.append(float(row[0])*1000)
ax2.plot(rawheights, opticallengths, 'r', label="Sum")
plt.ylabel('Integrated Interaction Lengths')
plt.yscale('log')
plt.xlabel('Height', labelpad=0)
ax2.invert_xaxis()
ax3 = plt.subplot(312, sharex=ax2)
ax3.plot(survivalheights, Rrange, label="survived")
ax3.plot(decayheights, Rrange, label = "interacted")
plt.ylabel('Fraction')
plt.xlabel('First Interaction Height', labelpad=0)
ax3.invert_xaxis()
plt.legend(loc=2)
#Create a subplot for the fractional abundance
hrange=[]
fullcount = []
nDC = []
wnDC = []
bT = []
wbT = []
mT = []
wmT = []
emith = []
#Iterate over Energies
simset = simulationset(eff, layout, mincount=0, hmacceptance = [1,1,1,1,1,1])
simset.generate(number)
for sim in simset.simulations:
true = sim.true
height = true.height
multiplicity = int(true.truemultiplicity)
hrange.append(height)
if multiplicity == int(0):
nDC.append(height)
elif multiplicity < int(mincount):
bT.append(height)
emith.append(height)
else:
mT.append(height)
emith.append(height)
print "High Multiplicity DC emission is", float(len(mT))/float(number)
print "Low Multiplicity DC emission is", float(len(bT))/float(number)
print "Non-DC emission is", float(len(nDC))/float(number)
#Create labels for each bin
labels = ["metThreshold", "belowThreshold", "nonDC"]
hrange.sort()
hcount = len(hrange)
limits = [hrange[0], hrange[hcount - 1]]
hbins = np.linspace(limits[0], limits[1], bincount)
#~ extent = ax1.get_window_extent().transformed(figure.dpi_scale_trans.inverted())
#~ plt.savefig('decay.png', bbox_inches=extent.expanded(1.2, 1.2))
#~
#~ extent = ax2.get_window_extent().transformed(figure.dpi_scale_trans.inverted())
#~ plt.savefig('Decay Lengths.pdf', bbox_inches=extent.expanded(1.2, 1.2))
#~
#~ extent = ax3.get_window_extent().transformed(figure.dpi_scale_trans.inverted())
#~ plt.savefig('Fraction with Height.pdf', bbox_inches=extent.expanded(1.2, 1.2))
#~
#~ extent = ax4.get_window_extent().transformed(figure.dpi_scale_trans.inverted())
#~ plt.savefig('first interaction height.pdf', bbox_inches=extent.expanded(1.2, 1.2))
#~
#~ extent = ax5.get_window_extent().transformed(figure.dpi_scale_trans.inverted())
#~ plt.savefig('interaction category.pdf', bbox_inches=extent.expanded(1.2, 1.2))
ax4 = plt.subplot(313, sharex=ax2)
tweights = np.ones_like(decayheights)/len(decayheights)
#~ mcweights = np.ones_like(hrange)/len(hrange)
plt.hist([decayheights], weights=[tweights])
plt.ylabel('Fraction')
plt.xlabel('First Interaction Height', labelpad=0)
ax4.invert_xaxis()
fig = plt.gcf() # get current figure
st = fig.suptitle("Atmospheric Interaction", fontsize=20)
st.set_y(0.98)
fig.set_size_inches(10, 15)
fig.tight_layout()
fig.subplots_adjust(top=0.95)
plt.savefig('/d6/rstein/Hamburg-Cosmic-Rays/positioning/graphs/stats/generalheight.pdf')
plt.savefig('/d6/rstein/Hamburg-Cosmic-Rays/report/graphs/generalheight.png')
#Plot the unscaled histogram
ax5 = plt.subplot(211, sharex=ax2)
plt.hist([mT, bT, nDC], bins=20, log=True, histtype='bar', range=limits, label=labels)
print "Overall mean first interaction height is", np.mean(hrange)
hrange.sort()
nhrange = len(hrange)
halfin = int(nhrange/2.)
hmedian = hrange[halfin]
print "Overall median first interaction height is", hmedian
tscale = atm.runlengthswithh(hmedian)
print "Corresponding Median Interaction Lengths", tscale
texpectation = tscale/math.log(2)
print "Resultant Expectation Interaction Lengths", texpectation
emith.sort()
ehrange = len(emith)
ehalfin = int(ehrange/2.)
ehmedian = emith[ehalfin]
print "Cherenkov-Emission mean first interaction height is", np.mean(emith)
print "Cherenkov-Emission median first interaction height is", ehmedian
etscale = atm.runlengthswithh(ehmedian)
print "Corresponding Median Interaction Lengths", etscale
etexpectation = etscale/math.log(2)
print "Resultant Expectation Interaction Lengths", etexpectation
plt.xlim(limits)
plt.ylabel('Recorded Count')
plt.xlabel('First Interaction Height', labelpad=0)
plt.legend(loc=2)
ax5.invert_xaxis()
#plot the histogram scaled with E^-1.7 distribution to the second subplot
ax6 = plt.subplot(212)
if len(mT) > 0:
n, bins, _ = plt.hist([mT], bins=20, label=labels)
mid = (bins[1:] + bins[:-1])*0.5
errors = []
for count in n:
errors.append(math.sqrt(count))
plt.errorbar(mid, n, yerr=errors, fmt='kx')
nmax = np.amax(n)
uplim = nmax + 2*(math.sqrt(nmax))
plt.ylim(0, uplim)
plt.xlabel('First Interaction Height', labelpad=0)
plt.ylabel('Recorded Count')
plt.legend()
print "For Ntel > ", mincount, ", mean first interaction height is", np.mean(mT)
ax6.invert_xaxis()
title = 'Height Statistics for ' + str(nh) + " hours"
fig = plt.gcf() # get current figure
st = fig.suptitle(title, fontsize=20)
st.set_y(0.98)
fig.set_size_inches(10, 15)
fig.tight_layout()
fig.subplots_adjust(top=0.95)
#~ extent = ax1.get_window_extent().transformed(figure.dpi_scale_trans.inverted())
#~ plt.savefig('decay.png', bbox_inches=extent.expanded(1.2, 1.2))
#~
#~ extent = ax2.get_window_extent().transformed(figure.dpi_scale_trans.inverted())
#~ plt.savefig('Decay Lengths.pdf', bbox_inches=extent.expanded(1.2, 1.2))
#~
#~ extent = ax3.get_window_extent().transformed(figure.dpi_scale_trans.inverted())
#~ plt.savefig('Fraction with Height.pdf', bbox_inches=extent.expanded(1.2, 1.2))
#~
#~ extent = ax4.get_window_extent().transformed(figure.dpi_scale_trans.inverted())
#~ plt.savefig('first interaction height.pdf', bbox_inches=extent.expanded(1.2, 1.2))
#~
#~ extent = ax5.get_window_extent().transformed(figure.dpi_scale_trans.inverted())
#~ plt.savefig('interaction category.pdf', bbox_inches=extent.expanded(1.2, 1.2))
plt.savefig('/d6/rstein/Hamburg-Cosmic-Rays/report/graphs/hessheight.png')
plt.savefig('/d6/rstein/Hamburg-Cosmic-Rays/positioning/graphs/stats/Height.pdf')
if graph:
plt.show()
def run(numberofhours):
ax1 = plt.subplot(211)
category = "lst"
tradius = tr.run(category)
raweff = 0.06
selectionefficiency = 0.50
flux = 2.0 * (10**-4)
solidangle = math.radians(5)
ranges = []
lowerlim = 15
midlim = 50
upperlim = 200
lowerbincount = 20
upperbincount = 10
lowerrange = [lowerlim, midlim, lowerbincount]
ranges.append(lowerrange)
upperrange = [midlim, upperlim, upperbincount]
ranges.append(upperrange)
fullcount = []
edges = []
for i in range (0, 10):
fullcount.append([])
for i in range(0, 2):
entry = ranges[i]
lower = entry[0]
upper = entry[1]
bins = entry[2]
edge = np.linspace(lower, upper, bins)
edges.extend(edge)
telescopegap = (edge[1:] + edge[:-1])*0.5
print edge
print telescopegap
simlim = (upper + 150)
area = 4*(simlim**2)
detectedflux = flux*area*solidangle*selectionefficiency
rateperhour = detectedflux * 60 * 60
n = int(rateperhour*float(numberofhours))
print time.asctime(time.localtime()),"Cosmic Ray Iron Flux is", flux, "Simulated Area is", area, "Field of View is", solidangle, "Detected Flux is", detectedflux
print time.asctime(time.localtime()),"Rate per hour", rateperhour, "Simulated Hours", numberofhours, "Simulated Events", n
for gap in telescopegap:
specificcount = []
coordinates = []
points = np.linspace(-gap, gap, 3)
for x in points:
for y in points:
coordinates.append([x,y])
for i in range (0, n):
#Randomly generates a target centre of -150<x<150m and -150<y<150m
rayxpos = (random.random()*2 * simlim)-simlim
rayypos = (random.random()*2 * simlim)-simlim
#Generates a random probability, and converts this to an Epn value following an E^-1.7 power series
R = random.random()*0.0178
Epn = ((1.7*R/321)+(3571**-1.7))**(-1/1.7)
#Generates a fixed charge number of Z=26
Z= 26
#Randomly generates a height probability, and converts this probability to a set height
hprob = random.random()
height = atm.runheight(hprob, text=False)
#Chooses a zenith angle +- 22 degrees
zenith = random.random()*44
phi = math.radians(68+zenith)
#Randomly choose an angle NESW
epsilon = math.pi*random.random()*2
#Calculate resultant surface radius and angular width of beam
radius, theta = cr.run(Epn, height, math.sin(phi), text=False)
frac = atm.runabsorption(height)
eff = raweff*frac/math.sin(phi)
j=0
if radius > 0:
for [xpos, ypos] in coordinates:
r, dangle = ce.run(radius, theta, phi, epsilon, xpos, ypos, rayxpos, rayypos)
sigcount, bkgcount= cs.run(tradius, r, rayxpos, rayypos, xpos, ypos, Epn, Z, eff)
count = sigcount + bkgcount
recorded = random.gauss(count, math.sqrt(count))
thresholdfrac = ld.trigger()
threshold = float(bkgcount)*thresholdfrac
if float(sigcount) > float(threshold):
j+=1
if j > 0:
fullcount[j].append(gap)
plotcount = []
labels = []
edges.remove(midlim)
print edges
for i in range (0, 10):
if len(fullcount[i]) > int(0):
plotcount.append(fullcount[i])
label = str(i)
labels.append(label)
n, bins, _ = ax1.hist(plotcount, label=labels, bins=edges, stacked=True)
print n
print bins
plt.legend(loc=2)
plt.xlabel('Grid width (m)', fontsize=20, labelpad=0)
plt.ylabel('Count', fontsize=20, labelpad=0)
ax2 = plt.subplot(212)
f = 0
for label in labels:
if float(label) < float(4):
fourlim = f
if float(label) < float(5):
fivelim = f
if float(label) < float(6):
sixlim = f
f += 1
lines =[]
for i in range (0,len(n)):
if i == fourlim:
subfourline = n[i]
if i == fivelim:
subfiveline = n[i]
if i == sixlim:
subsixline = n[i]
if i == (len(n)-1):
if i > fourlim:
fourline = n[i] - subfourline
lines.append(fourline)
if i > fivelim:
fiveline = n[i] - subfiveline
lines.append(fiveline)
if i > sixlim:
sixline = n[i] - subsixline
lines.append(sixline)
linelabels = ["Detections > 3", "Detections > 4", "Detections > 5"]
mid = (bins[1:] + bins[:-1])*0.5
#~ print mid
for k in range (0, len(lines)):
line = lines[k]
label = linelabels[k]
plt.plot(mid, line, label=label)
plt.legend()
plt.xlabel('Grid width (m)', fontsize=20, labelpad=0)
plt.ylabel('Count', fontsize=20, labelpad=0)
plt.yscale('log')
ax1.tick_params(labelsize=20)
ax2.tick_params(labelsize=20)
title = "Telescope Observations for " +str(numberofhours) + " hours"
plt.suptitle(title, fontsize=20)
figure = plt.gcf() # get current figure
figure.set_size_inches(20, 15)
plt.savefig('/d6/rstein/Hamburg-Cosmic-Rays/positioning/graphs/stats/optimiselayout.pdf')
plt.savefig('/d6/rstein/Hamburg-Cosmic-Rays/report/graphs/logenergyradius.png')
def run(eff,
rowcount,
mincount=4,
text=False,
graph=False,
output="default",
layout="five",
number=1,
nh=1):
#Define number of bins, stepcount
bincount = 20
stepcount = 1000
lower = float(1) / float(stepcount)
upper = float(1 - lower)
Rrange = np.linspace(lower, upper, stepcount)
#~ ax1 = plt.subplot(321)
#~
decaylengths = []
survivallengths = []
decayheights = []
survivalheights = []
for R in Rrange:
dl = atm.runlengths(R)
decaylengths.append(dl)
sl = atm.runlengths(1 - R)
survivallengths.append(sl)
dh = atm.runheight(R)
decayheights.append(dh)
sh = atm.runheight(1 - R)
survivalheights.append(sh)
#~ ax1.plot(survivallengths, Rrange, label="survived")
#~ ax1.plot(decaylengths, Rrange, label = "decayed")
#~ plt.ylabel('Fraction')
#~ plt.xlabel('Interaction Lengths', labelpad=0)
#~ plt.legend()
ax2 = plt.subplot(311)
rawheights = []
opticallengths = []
with open(
'/d6/rstein/Hamburg-Cosmic-Rays/positioning/atmospheredata/atmprofile.csv',
'rb') as csvfile:
reader = csv.reader(csvfile, delimiter=',', quotechar='|')
i = 0
for row in reader:
i += 1
if i > 3:
opticallengths.append(float(row[2]))
rawheights.append(float(row[0]) * 1000)
ax2.plot(rawheights, opticallengths, 'r', label="Sum")
plt.ylabel('Integrated Interaction Lengths')
plt.yscale('log')
plt.xlabel('Height', labelpad=0)
ax2.invert_xaxis()
ax3 = plt.subplot(312, sharex=ax2)
ax3.plot(survivalheights, Rrange, label="survived")
ax3.plot(decayheights, Rrange, label="interacted")
plt.ylabel('Fraction')
plt.xlabel('First Interaction Height', labelpad=0)
ax3.invert_xaxis()
plt.legend(loc=2)
#Create a subplot for the fractional abundance
hrange = []
fullcount = []
nDC = []
wnDC = []
bT = []
wbT = []
mT = []
wmT = []
emith = []
#Iterate over Energies
simset = simulationset(eff,
layout,
mincount=0,
hmacceptance=[1, 1, 1, 1, 1, 1])
simset.generate(number)
for sim in simset.simulations:
true = sim.true
height = true.height
multiplicity = int(true.truemultiplicity)
hrange.append(height)
if multiplicity == int(0):
nDC.append(height)
elif multiplicity < int(mincount):
bT.append(height)
emith.append(height)
else:
mT.append(height)
emith.append(height)
print "High Multiplicity DC emission is", float(len(mT)) / float(number)
print "Low Multiplicity DC emission is", float(len(bT)) / float(number)
print "Non-DC emission is", float(len(nDC)) / float(number)
#Create labels for each bin
labels = ["metThreshold", "belowThreshold", "nonDC"]
hrange.sort()
hcount = len(hrange)
limits = [hrange[0], hrange[hcount - 1]]
hbins = np.linspace(limits[0], limits[1], bincount)
#~ extent = ax1.get_window_extent().transformed(figure.dpi_scale_trans.inverted())
#~ plt.savefig('decay.png', bbox_inches=extent.expanded(1.2, 1.2))
#~
#~ extent = ax2.get_window_extent().transformed(figure.dpi_scale_trans.inverted())
#~ plt.savefig('Decay Lengths.pdf', bbox_inches=extent.expanded(1.2, 1.2))
#~
#~ extent = ax3.get_window_extent().transformed(figure.dpi_scale_trans.inverted())
#~ plt.savefig('Fraction with Height.pdf', bbox_inches=extent.expanded(1.2, 1.2))
#~
#~ extent = ax4.get_window_extent().transformed(figure.dpi_scale_trans.inverted())
#~ plt.savefig('first interaction height.pdf', bbox_inches=extent.expanded(1.2, 1.2))
#~
#~ extent = ax5.get_window_extent().transformed(figure.dpi_scale_trans.inverted())
#~ plt.savefig('interaction category.pdf', bbox_inches=extent.expanded(1.2, 1.2))
ax4 = plt.subplot(313, sharex=ax2)
tweights = np.ones_like(decayheights) / len(decayheights)
#~ mcweights = np.ones_like(hrange)/len(hrange)
plt.hist([decayheights], weights=[tweights])
plt.ylabel('Fraction')
plt.xlabel('First Interaction Height', labelpad=0)
ax4.invert_xaxis()
fig = plt.gcf() # get current figure
st = fig.suptitle("Atmospheric Interaction", fontsize=20)
st.set_y(0.98)
fig.set_size_inches(10, 15)
fig.tight_layout()
fig.subplots_adjust(top=0.95)
plt.savefig(
'/d6/rstein/Hamburg-Cosmic-Rays/positioning/graphs/stats/generalheight.pdf'
)
plt.savefig(
'/d6/rstein/Hamburg-Cosmic-Rays/report/graphs/generalheight.png')
#Plot the unscaled histogram
ax5 = plt.subplot(211, sharex=ax2)
plt.hist([mT, bT, nDC],
bins=20,
log=True,
histtype='bar',
range=limits,
label=labels)
print "Overall mean first interaction height is", np.mean(hrange)
hrange.sort()
nhrange = len(hrange)
halfin = int(nhrange / 2.)
hmedian = hrange[halfin]
print "Overall median first interaction height is", hmedian
tscale = atm.runlengthswithh(hmedian)
print "Corresponding Median Interaction Lengths", tscale
texpectation = tscale / math.log(2)
print "Resultant Expectation Interaction Lengths", texpectation
emith.sort()
ehrange = len(emith)
ehalfin = int(ehrange / 2.)
ehmedian = emith[ehalfin]
print "Cherenkov-Emission mean first interaction height is", np.mean(emith)
print "Cherenkov-Emission median first interaction height is", ehmedian
etscale = atm.runlengthswithh(ehmedian)
print "Corresponding Median Interaction Lengths", etscale
etexpectation = etscale / math.log(2)
print "Resultant Expectation Interaction Lengths", etexpectation
plt.xlim(limits)
plt.ylabel('Recorded Count')
plt.xlabel('First Interaction Height', labelpad=0)
plt.legend(loc=2)
ax5.invert_xaxis()
#plot the histogram scaled with E^-1.7 distribution to the second subplot
ax6 = plt.subplot(212)
if len(mT) > 0:
n, bins, _ = plt.hist([mT], bins=20, label=labels)
mid = (bins[1:] + bins[:-1]) * 0.5
errors = []
for count in n:
errors.append(math.sqrt(count))
plt.errorbar(mid, n, yerr=errors, fmt='kx')
nmax = np.amax(n)
uplim = nmax + 2 * (math.sqrt(nmax))
plt.ylim(0, uplim)
plt.xlabel('First Interaction Height', labelpad=0)
plt.ylabel('Recorded Count')
plt.legend()
print "For Ntel > ", mincount, ", mean first interaction height is", np.mean(
mT)
ax6.invert_xaxis()
title = 'Height Statistics for ' + str(nh) + " hours"
fig = plt.gcf() # get current figure
st = fig.suptitle(title, fontsize=20)
st.set_y(0.98)
fig.set_size_inches(10, 15)
fig.tight_layout()
fig.subplots_adjust(top=0.95)
#~ extent = ax1.get_window_extent().transformed(figure.dpi_scale_trans.inverted())
#~ plt.savefig('decay.png', bbox_inches=extent.expanded(1.2, 1.2))
#~
#~ extent = ax2.get_window_extent().transformed(figure.dpi_scale_trans.inverted())
#~ plt.savefig('Decay Lengths.pdf', bbox_inches=extent.expanded(1.2, 1.2))
#~
#~ extent = ax3.get_window_extent().transformed(figure.dpi_scale_trans.inverted())
#~ plt.savefig('Fraction with Height.pdf', bbox_inches=extent.expanded(1.2, 1.2))
#~
#~ extent = ax4.get_window_extent().transformed(figure.dpi_scale_trans.inverted())
#~ plt.savefig('first interaction height.pdf', bbox_inches=extent.expanded(1.2, 1.2))
#~
#~ extent = ax5.get_window_extent().transformed(figure.dpi_scale_trans.inverted())
#~ plt.savefig('interaction category.pdf', bbox_inches=extent.expanded(1.2, 1.2))
plt.savefig('/d6/rstein/Hamburg-Cosmic-Rays/report/graphs/hessheight.png')
plt.savefig(
'/d6/rstein/Hamburg-Cosmic-Rays/positioning/graphs/stats/Height.pdf')
if graph:
plt.show()