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joint_fit_dL_emax_vary.py
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joint_fit_dL_emax_vary.py
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# -*- coding: utf-8 -*-
"""
Created on Tue Nov 22 17:40:04 2022
@author: Ana
"""
import h5py
import numpy as np
import matplotlib.pyplot as plt
from scipy import interpolate
import scipy.optimize as opt
from scipy import integrate
from matplotlib import rc
from mpl_toolkits.axes_grid.inset_locator import (inset_axes, InsetPosition,mark_inset)
from tqdm import tqdm
import os
import errno
def sigmoid_2(dL, dLmid, gamma, delta, emax, alpha=2.05):
denom = 1. + (dL/dLmid) ** alpha * \
np.exp(gamma * ((dL / dLmid) - 1.) + delta * ((dL**2 / dLmid**2) - 1.))
return emax / denom
def integrand_2(dL_int, dLmid, gamma, delta, emax, alpha=2.05):
return dLpdf_interp(dL_int) * sigmoid_2(dL_int, dLmid, gamma, delta, emax, alpha)
def lam_2(dL, pdL, dLmid, gamma, delta, emax, alpha=2.05):
return pdL * sigmoid_2(dL, dLmid, gamma, delta, emax, alpha)
# in_param is a generic minimization variable, here ln(zmid)
def logL_quad_2(in_param, dL, pdL, Total_expected, gamma, delta):
dLmid, emax = np.exp(in_param[0]), np.exp(in_param[1])
quad_fun = lambda dL_int: Total_expected * integrand_2(dL_int, dLmid, gamma, delta, emax)
# it's hard to check here what is the value of new_try_z
Lambda_2 = integrate.quad(quad_fun, min(new_try_dL), max(new_try_dL))[0]
lnL = -Lambda_2 + np.sum(np.log(Total_expected * lam_2(dL, pdL, dLmid, gamma, delta, emax)))
return lnL
def logL_quad_2_global(in_param, nbin1, nbin2, dLmid_inter, emax_inter):
# in_param is a generic minimization variable, here it is a list [gamma, ln(delta)]
gamma, delta = in_param[0], np.exp(in_param[1])
lnL_global = np.zeros([nbin1, nbin2])
for i in range(0, nbin1):
for j in range(0, nbin2):
if j > i:
continue
m1inbin = (m1 >= m1_bin[i]) & (m1 < m1_bin[i+1])
m2inbin = (m2 >= m2_bin[j]) & (m2 < m2_bin[j+1])
mbin = m1inbin & m2inbin & found_any
data = dL_origin[mbin]
data_pdf = dL_pdf_origin[mbin]
if len(data) < 1:
continue
index_sorted = np.argsort(data)
dL = data[index_sorted]
pdL = data_pdf[index_sorted]
if dLmid_inter[i,j] < 0.1 * min(dL):
dLmid_inter[i,j] = min(dL)
Total_expected = NTOT * mean_mass_pdf[i,j]
quad_fun = lambda dL_int: Total_expected * integrand_2(dL_int, dLmid_inter[i,j], gamma, delta, emax_inter[i,j])
Lambda_2 = integrate.quad(quad_fun, min(new_try_dL), max(new_try_dL))[0]
#print(Lambda_2)
lnL = -Lambda_2 + np.sum(np.log(Total_expected * lam_2(dL, pdL, dLmid_inter[i,j], gamma, delta, emax_inter[i,j])))
#sigmoid_2(dL, dLmid_inter[i,j], gamma, delta)
if lnL == -np.inf:
print("epsilon gives a zero value in ", i, j, " bin because zmid is zero or almost zero")
#print(sigmoid_2(z, zmid_inter[i,j], gamma, delta))
continue
lnL_global[i,j] = lnL
#print(lnL_global)
print('\n', lnL_global.sum())
return lnL_global.sum()
# the nelder-mead algorithm has these default tolerances: xatol=1e-4, fatol=1e-4
def MLE_2(dL, pdL, dLmid_guess, emax_guess, Total_expected, gamma_new, delta_new):
res = opt.minimize(fun=lambda in_param, dL, pdL: -logL_quad_2(in_param, dL, pdL, Total_expected, gamma_new, delta_new),
x0=np.array([np.log(dLmid_guess), np.log(emax_guess)]),
args=(dL, pdL,),
method='Nelder-Mead')
dLmid_res, emax_res = np.exp(res.x)
min_likelihood = res.fun
return dLmid_res, emax_res, -min_likelihood
def MLE_2_global(nbin1, nbin2, dLmid_inter, emax_inter, gamma_guess, delta_guess):
res = opt.minimize(fun=lambda in_param: -logL_quad_2_global(in_param, nbin1, nbin2, dLmid_inter, emax_inter),
x0=np.array([gamma_guess, np.log(delta_guess)]),
args=(),
method='Nelder-Mead')
gamma, logdelta = res.x
delta = np.exp(logdelta)
min_likelihood = res.fun
return gamma, delta, -min_likelihood
try:
os.mkdir('dL_joint_fit_results_emax_vary')
except OSError as e:
if e.errno != errno.EEXIST:
raise
try:
os.mkdir('dL_joint_fit_results_emax_vary/dLmid')
except OSError as e:
if e.errno != errno.EEXIST:
raise
try:
os.mkdir('dL_joint_fit_results_emax_vary/emax')
except OSError as e:
if e.errno != errno.EEXIST:
raise
try:
os.mkdir('dL_joint_fit_results_emax_vary/maxL')
except OSError as e:
if e.errno != errno.EEXIST:
raise
try:
os.mkdir('dL_joint_fit_results_emax_vary/final_plots')
except OSError as e:
if e.errno != errno.EEXIST:
raise
# Is this needed ?
plt.close('all')
rc('text', usetex=True)
np.random.seed(42)
f = h5py.File('endo3_bbhpop-LIGO-T2100113-v12.hdf5', 'r')
NTOT = f.attrs['total_generated']
z_origin = f["injections/redshift"][:]
z_pdf_origin = f["injections/redshift_sampling_pdf"][:]
dL_origin = f["injections/distance"][:]
m1 = f["injections/mass1_source"][:]
m2 = f["injections/mass2_source"][:]
far_pbbh = f["injections/far_pycbc_bbh"][:]
far_gstlal = f["injections/far_gstlal"][:]
far_mbta = f["injections/far_mbta"][:]
far_pfull = f["injections/far_pycbc_hyperbank"][:]
mean_mass_pdf = np.loadtxt('mean_mpdf.dat')
###################################### for the dL_pdf interpolation
H0 = 67.9 #km/sMpc
c = 3e5 #km/s
omega_m = 0.3065
A = np.sqrt(omega_m*(1+z_origin)**3+1-omega_m)
dL_dif_origin = (c*(1+z_origin)/H0)*(1/A)
dL_pdf_origin = z_pdf_origin/dL_dif_origin
index_all = np.argsort(dL_origin)
all_dL = dL_origin[index_all]
dL_pdf = dL_pdf_origin[index_all]
index = np.random.choice(np.arange(len(all_dL)), 200, replace=False)
try_dL = all_dL[index]
try_dLpdf = dL_pdf[index]
index_try = np.argsort(try_dL)
try_dL_ordered = try_dL[index_try]
try_dLpdf_ordered = try_dLpdf[index_try]
new_try_dL = np.insert(try_dL_ordered, 0, 0, axis=0)
new_try_dLpdf = np.insert(try_dLpdf_ordered, 0, 0, axis=0)
dLpdf_interp = interpolate.interp1d(new_try_dL, new_try_dLpdf)
#####################################
# FAR (false alarm rate) threshold for finding an injection
thr = 1.
nbin1 = 14
nbin2 = 14
mmin = 2.
mmax = 100.
m1_bin = np.round(np.logspace(np.log10(mmin), np.log10(mmax), nbin1+1), 1)
m2_bin = np.round(np.logspace(np.log10(mmin), np.log10(mmax), nbin2+1), 1)
found_pbbh = far_pbbh <= thr
found_gstlal = far_gstlal <= thr
found_mbta = far_mbta <= thr
found_pfull = far_pfull <= thr
found_any = found_pbbh | found_gstlal | found_mbta | found_pfull
# ## descoment for a new optimization
# zmid_inter = np.loadtxt('maximization_results/zmid_2.dat')
# #zmid_old is the zmid value from the old fit to the FC data
# # -> This was a zmid value for one specific mass bin?
# zmid_old = 0.327
# H0 = 67.9 #km/sMpc
# omega_m = 0.3065
# c = 3e5 #km/s
# #A_inter = np.sqrt(omega_m*(1+zmid_inter)**3+1-omega_m)
# def fun_A(t):
# return np.sqrt(omega_m*(1+t)**3+1-omega_m)
# quad_fun_A = lambda t: 1/fun_A(t)
# dLmid_inter = np.array([[(c*(1+zmid_inter[i,j])/H0)*integrate.quad(quad_fun_A, 0, zmid_inter[i,j])[0] for j in range(nbin2)] for i in range(nbin1)])
# emax_inter = np.zeros([nbin1,nbin2])
# for i in range(nbin1):
# for j in range(nbin2):
# if dLmid_inter[i,j]!=0 :
# emax_inter[i,j] = 0.967
# # I'm not seeing why the reason to use this one value of zmid to scale some initial
# # values of gamma / delta ... it should be better to pick one mass bin where the
# # previous fit with gamma, delta works well and then scale the fitted gamma / delta
# # values with that bin's zmid. However if this works anyway maybe it doesn't matter
# dLmid_old = (c*(1+zmid_old)/H0)*integrate.quad(quad_fun_A, 0, zmid_old)[0]
# delta_new = 0.1146989
# gamma_new = -0.18395
# total_lnL = np.zeros([1])
# dif_lnL = np.zeros([1])
# all_delta = np.array([delta_new])
# all_gamma = np.array([gamma_new])
# for k in range(0,10000):
# print('\n\n')
# print(k)
# gamma_new, delta_new, maxL_global = MLE_2_global(nbin1, nbin2, dLmid_inter, emax_inter, gamma_new, delta_new)
# all_delta = np.append(all_delta, delta_new)
# all_gamma = np.append(all_gamma, gamma_new)
# maxL_inter = np.zeros([nbin1, nbin2])
# for i in range(0, nbin1):
# for j in range(0, nbin2):
# if j > i:
# continue
# print('\n\n')
# print(i, j)
# m1inbin = (m1 >= m1_bin[i]) & (m1 < m1_bin[i+1])
# m2inbin = (m2 >= m2_bin[j]) & (m2 < m2_bin[j+1])
# mbin = m1inbin & m2inbin & found_any
# data = dL_origin[mbin]
# data_pdf = dL_pdf_origin[mbin]
# if len(data) < 1:
# continue
# index3 = np.argsort(data)
# dL = data[index3]
# pdL = data_pdf[index3]
# if dLmid_inter[i,j] < 0.1 * min(dL):
# dLmid_inter[i,j] = min(dL)
# Total_expected = NTOT * mean_mass_pdf[i,j]
# dLmid_new, emax_new, maxL = MLE_2(dL, pdL, dLmid_inter[i,j], emax_inter[i,j], Total_expected, gamma_new, delta_new)
# if maxL == -np.inf:
# #just in case, but in principle this does not happen
# print("epsilon gives a zero value in ", i, j, " bin")
# maxL = 0
# dLmid_inter[i, j] = dLmid_new
# emax_inter[i, j] = emax_new
# maxL_inter[i, j] = maxL
# name = f"dL_joint_fit_results_emax_vary/dLmid/dLmid_{k}.dat"
# np.savetxt(name, dLmid_inter, fmt='%10.3f')
# name = f"dL_joint_fit_results_emax_vary/emax/emax_{k}.dat"
# np.savetxt(name, emax_inter, fmt='%10.3f')
# name = f"dL_joint_fit_results_emax_vary/maxL/maxL_{k}.dat"
# np.savetxt(name, maxL_inter, fmt='%10.3f')
# total_lnL = np.append(total_lnL, maxL_inter.sum())
# dif_lnL = np.append(dif_lnL, total_lnL[k + 1] - total_lnL[k])
# print(maxL_inter.sum())
# print(dif_lnL)
# if np.abs( total_lnL[k + 1] - total_lnL[k] ) <= 1e-2:
# break
# print(k)
# np.savetxt('dL_joint_fit_results_emax_vary/all_delta.dat', np.delete(all_delta, 0), fmt='%10.5f')
# np.savetxt('dL_joint_fit_results_emax_vary/all_gamma.dat', np.delete(all_gamma, 0), fmt='%10.5f')
# np.savetxt('dL_joint_fit_results_emax_vary/total_lnL.dat', np.delete(total_lnL, 0), fmt='%10.3f')
#%%
#compare_1 plots
#rc('text', usetex=True)
k = 10 #number of the last iteration
dLmid_plot = np.loadtxt(f'dL_joint_fit_results_emax_vary/dLmid/dLmid_{k}.dat')
gamma_plot = np.loadtxt('dL_joint_fit_results_emax_vary/all_gamma.dat')[-1]
delta_plot = np.loadtxt('dL_joint_fit_results_emax_vary/all_delta.dat')[-1]
emax_plot = np.loadtxt(f'dL_joint_fit_results_emax_vary/emax/emax_{k}.dat')
for i in range(12,13):
for j in range(12,13):
try:
data_binned = np.loadtxt(f'dL_binned/{i}{j}_data.dat')
except OSError:
continue
mid_dL=data_binned[:,0]
dL_com_1=np.linspace(0,max(mid_dL), 200)
pdL_binned=data_binned[:,1]
dLm_detections=data_binned[:,2]
nonzero = dLm_detections > 0
plt.figure()
plt.plot(mid_dL, pdL_binned, '.', label='bins over dL')
plt.errorbar(mid_dL[nonzero], pdL_binned[nonzero], yerr=pdL_binned[nonzero]/np.sqrt(dLm_detections[nonzero]), fmt="none", color="k", capsize=2, elinewidth=0.4)
plt.plot(dL_com_1, sigmoid_2(dL_com_1, dLmid_plot[i,j], gamma_plot, delta_plot, emax_plot[i,j]), '-', label='sigmoid model')
plt.xlabel(r'$dL$', fontsize=14)
plt.ylabel(r'$P_{det}(dL)$', fontsize=14)
plt.title(r'$m_1:$ %.0f-%.0f M$_{\odot}$ \& $m_2:$ %.0f-%.0f M$_{\odot}$' %(m1_bin[i], m1_bin[i+1], m2_bin[j], m2_bin[j+1]) )
plt.legend(fontsize=14)
#name=f"dL_joint_fit_results_emax_vary/final_plots/{i}_{j}.png"
name=f"dL_joint_fit_results_emax_vary/final_plots/{i}_{j}.png"
plt.savefig(name, format='png', dpi=1000)
plt.close()