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upper_limit_18_02.py
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import matplotlib.pyplot as plt
import numpy as np
from scipy.interpolate import interp1d
class upper_limit:
def __init__(self, likelihood, mass, scale, name="scale_scan"):
self.likelihood = likelihood
self.mass = float(mass)
self.scale = float(scale)
self.name = name
def plot(self):
fig = plt.figure()
values = self.likelihood[self.name]
likelihood_values = self.likelihood["stat_scan"]
plt.plot(values, likelihood_values, "x", label="mass = " + str(int(self.mass)))
plt.xlabel(self.name)
plt.ylabel("stat_scan")
plt.legend()
return fig
def plot_interpolate(self):
f, xnew = self.interpolate()
fig = plt.figure()
values = self.likelihood[self.name]
likelihood_values = self.likelihood["stat_scan"]
plt.plot(values, likelihood_values, "x", label="mass = " + str(int(self.mass)))
plt.plot(xnew, f(xnew), label="interpolated")
plt.xlabel(self.name)
plt.ylabel("stat_scan")
plt.legend()
return fig
def interpolate(self):
xnew = np.linspace(
self.likelihood[self.name][0], self.likelihood[self.name][-1], 3000
)
f = interp1d(
self.likelihood[self.name], self.likelihood["stat_scan"], kind="cubic"
)
return f, xnew
def parabola(self, x, x_0, sigma):
return (x - x_0) ** 2 / sigma**2
def likelihood_upper_extra(self, from_0=True):
# same as likelihood_upper but extrapolate to outer values in case it was poorly choosen
# fitting the original data:
import scipy
lik = (self.likelihood[self.name], self.likelihood["stat_scan"])
min_i = np.where(lik[1] == lik[1].min())[0][0]
sigma_estimate = np.sqrt((lik[0][0] - lik[0][min_i]) ** 2 / lik[1][0])
params = [
np.round(lik[0][min_i], int(np.abs(np.log10(lik[0][min_i])) + 2)),
sigma_estimate,
]
xnew = np.linspace(
self.likelihood[self.name][0] * 0.99,
self.likelihood[self.name][-1] * 1.01,
3000,
)
# plt.plot(xnew, self.parabola(xnew, params[0], params[1]), label = "initial guess")
ynew = self.parabola(xnew, params[0], params[1])
fit_params, pcov = scipy.optimize.curve_fit(
self.parabola, lik[0], lik[1], params
)
# str_ = "\n$\sigma $ = {:.2}".format(fit_params[1])
ynew = self.parabola(xnew, fit_params[0], fit_params[1])
i_min = np.where(ynew == ynew.min())
i_min = i_min[0]
# plt.plot(l[0], l[1], 'x', label = str_ , )
# plt.plot(xnew,ynew , label = "best fit")
# plt.legend()
# try:
if from_0 == True:
while xnew[i_min] < 0:
i_min = i_min + 1
i_u = i_min[0]
while ynew[i_u] < (ynew[i_min] + (2.71)): # 2.71/2.
i_u = i_u + 1
i_error = i_min[0]
while ynew[i_error] < (ynew[i_min] + 1.0):
i_error = i_error + 1
# print("minimum at ",xnew[i_min][0], " pm " , xnew[i_error]- xnew[i_min][0])
# print("upperlimit = ", xnew[i_u])
# print("returns tupel: minimum, 1sigma error, UL")
return xnew[i_min], xnew[i_error] - xnew[i_min], xnew[i_u]
# except:
# print("An exception occurred")
# return float("nan"), float("nan"), float("nan")
def likelihood_upper(self, from_0=True):
f, xnew = self.interpolate()
i_min = np.where(f(xnew) == f(xnew).min())
i_min = i_min[0]
# try:
if from_0 == True:
while xnew[i_min] < 0:
i_min = i_min + 1
i_u = i_min[0]
while f(xnew)[i_u] < (f(xnew)[i_min] + (2.71)): # 2.71/2.
i_u = i_u + 1
i_error = i_min[0]
while f(xnew)[i_error] < (f(xnew)[i_min] + 1.0):
i_error = i_error + 1
return xnew[i_min], xnew[i_error] - xnew[i_min], xnew[i_u]
# except:
# print("An exception occurred")
# return float("nan"), float("nan"), float("nan")
def likelihood_error(self, from_0=True):
f, xnew = self.interpolate()
i_min = np.where(f(xnew) == f(xnew).min())
i_min = i_min[0]
# try:
if from_0 == True:
while xnew[i_min] < 0:
i_min = i_min + 1
# i_u = i_min[0]
i_error = i_min[0]
while f(xnew)[i_error] < (f(xnew)[i_min] + 1.0):
i_error = i_error + 1
return xnew[i_min], xnew[i_error] - xnew[i_min]
# except:
# print("An exception occurred")
# return float('nan'), float('nan'),float('nan')
def likelihood_error_asymmetric(self):
f, xnew = self.interpolate()
i_min = np.where(f(xnew) == f(xnew).min())
i_min = i_min[0]
i_error_neg = i_min[0]
i_error_pos = i_min[0]
while f(xnew)[i_error_pos] < (f(xnew)[i_min] + 1.0):
i_error_pos = i_error_pos + 1
while f(xnew)[i_error_neg] < (f(xnew)[i_min] + 1.0):
i_error_neg = i_error_neg - 1
if i_error_neg < 0:
i_error_neg = 0
print("Caution: Neg Error not found! Set to min value!")
return (
xnew[i_min],
xnew[i_min] - xnew[i_error_neg],
xnew[i_error_pos] - xnew[i_min],
)
def plot_upper_limit(self, from_0=False):
fig, ax = plt.subplots(1, 1)
# fig.set_figheight(7)
# fig.set_figwidth(7)
values = self.likelihood[self.name]
likelihood_values = self.likelihood["stat_scan"]
plt.plot(values, likelihood_values, "o", label="mass = " + str((self.mass)))
plt.xlabel("scale")
plt.ylabel(self.name)
x_min, dx_min, x_upper = self.likelihood_upper(from_0=from_0)
if from_0 == False:
distance_ul = np.abs(x_min - x_upper)[0]
print(distance_ul)
print(dx_min)
plt.axvline(
x=x_min,
linestyle="dashed",
label="Minimum at {:.3} pm {:.3}".format(x_min[0], dx_min[0]),
)
f, xnew = self.interpolate()
values = self.likelihood[self.name]
likelihood_values = self.likelihood["stat_scan"]
plt.plot(
xnew,
f(xnew),
)
if from_0:
plt.axvline(
x=x_upper,
color="g",
linestyle="dashed",
label="Upper limit {:.3}".format(x_upper),
)
else:
plt.axvline(
x=x_upper,
color="g",
linestyle="dashed",
label="Upper limit {:.3}".format(x_upper),
)
plt.axvline(
x=distance_ul,
color="blue",
linestyle="dashed",
label="Upper limit Projected{:.3}".format(distance_ul),
)
plt.axvspan(
x_min - dx_min,
x_min + dx_min,
alpha=0.5,
color="lightblue",
label="1 sigma error",
)
plt.xlabel("Parameter of Interest")
plt.ylabel("-2 Log Likelihood")
plt.legend()
return fig, ax
def plot_upper_limit_two(self, likelihood2, mass2, likelihood_upper2):
fig = plt.figure()
# fig.set_figheight(10)
# fig.set_figwidth(10)
values = self.likelihood[self.name]
likelihood_values = np.array(self.likelihood[self.name]) + min(
self.likelihood["stat_scan"]
)
values2 = likelihood2[self.name]
likelihood_values2 = np.array(likelihood2[self.name]) + min(
likelihood2["stat_scan"]
)
plt.plot(
values,
likelihood_values,
"x",
label="mass = " + str(int(self.mass)) + " GeV",
color="b",
)
plt.plot(
values2,
likelihood_values2,
"x",
label="mass = " + str(int(mass2)) + " GeV Sim",
color="r",
)
plt.xlabel("Norm")
plt.ylabel("- 2 Log Likelihood")
x_min, dx_min, x_upper = self.likelihood_upper()
x_min2, dx_min2, x_upper2 = likelihood_upper2
# plt.xlim(-2,20)
# plt.ylim(-10,80)
print(dx_min)
plt.axvline(
x=x_upper,
color="b",
linestyle="dashed",
label="Upper limit {:.3} Fit".format(x_upper),
)
plt.axvline(
x=x_upper2,
color="r",
linestyle="dashed",
label="Upper limit {:.3} Sim".format(x_upper2),
)
plt.xlabel("scale")
plt.ylabel("likelihood")
# plt.titel("mass_DM = 2TeV")
plt.legend()
return fig