def fitSkewedGaussianAndComputeMaxLLH(self, n, bins, nbins, fileName, number,
latex=False, string=' ', plotFigures=False):
# Read data from file
data = np.loadtxt(fileName)
bestFits = data[:, 1]
lowLimit = data[:, 2]
highLimit = data[:, 3]
# Compute estimates
best = bestFits[number]
lower = bestFits[number] - lowLimit[number]
upper = highLimit[number] - bestFits[number]
# Initialise maximum likelihood parameters
llhood = Stats()
llhood.best = -1000
llhood.minus = 0
llhood.plus = 0
# Fit skewed Gaussian distribution to the result
# Note that the number of bins is one larger than the number of results, so we need to remove the last bin
# Find approximate position of the maximum and the width of the curve to easy the fitting process
curveInfo = (np.max(bins), np.argmax(n[1:-10]), 0, 0, 1)
skewFits, skewCovar = opt.curve_fit(self.skewGaussian, bins[1:-10], n[1:-10], p0=curveInfo)
ySkew = self.skewGaussian(bins, skewFits[0], skewFits[1], skewFits[2], skewFits[3], skewFits[4])
# Determine maximum likelihood and its uncertainties based on skewed Gaussian fit
llhood.likeLimits1D(ySkew, bins, 1)
## OUTPUT
# Plot if wanted
if (plotFigures == True):
plt.plot(bins, ySkew, 'k--', linewidth=2, label="Skewed Gaussian fit")
plt.legend(loc="center right", bbox_to_anchor=(1.018, 1.07), ncol=2)
# End if-statement
# Print distribution properties to screen
if (latex==False):
# Print in readable format
print "~" * 60, "\n"
print "\tstackResults"
print "\tMaximum likelihood: tau0 =", llhood.best
print "\tDifference to lower limit:", llhood.minus
print "\tDifference to upper limit:", llhood.plus
if (number != None):
print "\tJavelin best fit value:", best
print "\tDifference to Javelin lower limit:", lower
print "\tDifference to Javelin upper limit:", upper
# End if-statement
print "\n", "~" * 60
else:
# Print in LaTeX format
print(' ', string, '& $',round(llhood.best,1),'_{-',
round(llhood.minus,1),'}^{+',round(llhood.plus,1),'} $ & $',
round(best,1),'_{-',round(lower,1),'}^{+', round(upper,1),'} $ \\')
# End if-statement
# Decide what output to give from function
if (number != None):
return np.array([llhood.best, llhood.minus, llhood.plus, best, lower, upper])
else:
return np.array([llhood.best, llhood.minus, llhood.plus, -1000, 0, 0 ])
def testingTFimpact():
# These are the data we'll be using
folder = '/Users/uqnsomme/Documents/Obelix/FakeAGN/TFs/'
names = ['0Phi', '001Phi', '010Phi', '025Phi', '01TH', 'Gamma', 'Gauss', 'Sphere']
nn = len(names)
maxLag = 1000.0
# Initialisation
bins = np.arange(0.0, maxLag, 10) # Grid/x-axis for histograms
binssmall = np.arange(0.0, maxLag) # Grid/x-axis for accurate median calculation
est = np.zeros((nn, 1000)) # Array to hold all the time lag estimates from Javelin
n = np.zeros((nn, 99)) # y-axis for hisograms
nsmall = np.zeros((nn, 999)) # y-axis for accurate median calculation
# We'll be making the same kind of plot for all of the TFs
for i in range(nn):
print 'About to start reading ' + names[i]
# Import data
lagMatrName = folder + 'TFs' + names[i] + '.dat'
lagMatr = np.loadtxt(lagMatrName) # Load in results file
true = lagMatr[:, 0] # Time lag, as created by me
est[i,:] = lagMatr[:, 1] # Estimates found by Javelin
# Depending on what physical scenario we're considering, choose appropriate axes and labels for figure
if (i==0):
maxN = 4e-2
ymal = 1e-2
ymil = 5e-3
else:
maxN = 1e-2
ymal = 2e-3
ymil = 1e-3
# End if-statement
# Calculate histograms to do some maths
n[i,:], _ = np.histogram(est, bins=bins, normed=True)
nsmall[i,:], _ = np.histogram(est, bins=binssmall, normed=True)
# Fit skewed Gaussian distribution to the result to later calculate median
skewFits, skewCovar = opt.curve_fit(Stacking.skewGaussian, bins[0:-1], n[i,:], p0=(1./np.std(n[i,:]), np.argmax(n[i,:]), 0, 0, 1))
ySkew = Stacking.skewGaussian(binssmall, skewFits[0], skewFits[1], skewFits[2], skewFits[3], skewFits[4])
# Determine maximum likelihood and its uncertainties
llhood = Stats()
llhood.best = -1000
llhood.minus = 0
llhood.plus = 0
llhood.likeLimits1D(ySkew, binssmall, 1)
# Determine median and error estimates
median, minus, plus = Stats.getMedianEstimates(binssmall, nsmall[i,:])
# Print distribution properties to screen
print "=" * 60, "\n"
print "\tMaximum likelihood: tau0 =", llhood.best
print "\tDifference to lower limit:", llhood.minus
print "\tDifference to upper limit:", llhood.plus
print "\tMedian:", median
print "\tMedian lower:", minus
print "\tMedian upper:", plus
print "\n", "=" * 60
# Create figure showing the distribution of estimates for a particular TF
fig = plt.figure(figsize=(6,10))
plt.hist(est, bins=bins, normed=True, label='JAVELIN estimates')
plt.plot(binssmall, ySkew, linewidth=2, label="Best skewed Gaussian fit")
plt.plot([true[i], true[i]], [0, maxN], linewidth=2, label='True lag')
# Specify figure properties
plt.axis([0, maxLag, 0, maxN])
plt.xlabel('Time lag [days]', fontsize='large')
plt.ylabel('Number of instances', fontsize='large')
plt.legend()
ax = plt.axes()
ax.xaxis.set_major_locator(tck.MultipleLocator(200))
ax.xaxis.set_minor_locator(tck.MultipleLocator(100))
ax.yaxis.set_major_locator(tck.MultipleLocator(ymal))
ax.yaxis.set_minor_locator(tck.MultipleLocator(ymil))
ax.set_aspect(maxLag/maxN)
plt.savefig(folder+names[i]+'.png', dpi=500, bbox_inches='tight')
# End for-loop
# Create plot showing the different estimate distributions for all of the TFs
fig = plt.figure(figsize=(6,10))
plt.hist(est[4,:], bins=bins, normed=True, histtype='step', color='darkblue', label=r'$\mathrm{Face-on\ ring}$')
plt.hist(est[7,:], bins=bins, normed=True, histtype='step', color='paleturquoise', label=r'$\mathrm{Sphere}$')
plt.hist(est[1,:], bins=bins, normed=True, histtype='step', color='mediumorchid', label=r'$\phi=\pi/100$')
plt.hist(est[2,:], bins=bins, normed=True, histtype='step', color='darkgreen', label=r'$\phi=\pi/10$')
plt.hist(est[3,:], bins=bins, normed=True, histtype='step', color='black', label=r'$\phi=\pi/4$')
plt.hist(est[5,:], bins=bins, normed=True, histtype='step', color='olivedrab', label=r'$\mathrm{Gamma}$')
plt.hist(est[4,:], bins=bins, normed=True, histtype='step', color='pink', label=r'$\mathrm{Gauss}$')
plt.plot([true[i], true[i]], [0, maxN], 'r', label=r'$\mathrm{True\ lag}$')
# Specify figure properties
plt.axis([0, maxLag, 0, 0.009])
plt.xlabel(r'$\mathrm{Time\ lag\ [days]}$', fontsize='large')
plt.ylabel(r'$N_{norm}$', fontsize='large')
plt.legend()
ax = plt.axes()
ax.xaxis.set_major_locator(tck.MultipleLocator(200))
ax.xaxis.set_minor_locator(tck.MultipleLocator(100))
ax.yaxis.set_major_locator(tck.MultipleLocator(0.001))
ax.yaxis.set_minor_locator(tck.MultipleLocator(0.0005))
ax.set_aspect(maxLag/maxN)
plt.savefig('/Users/uqnsomme/Documents/ManyHists.png', dpi=500, bbox_inches='tight')
