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luminosity_model--ECPL_2param--parameter_error_estimation.py
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luminosity_model--ECPL_2param--parameter_error_estimation.py
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from __future__ import division
from astropy.io import ascii
from astropy.table import Table
from scipy.optimize import curve_fit
from scipy.integrate import quad, simps
import debduttaS_functions as mf
import specific_functions as sf
import time, pickle, pprint
import numpy as np
import matplotlib.pyplot as plt
plt.rc('axes', linewidth = 2)
plt.rc('font', family = 'serif', serif = 'cm10')
plt.rc('text', usetex = True)
plt.rcParams['text.latex.preamble'] = [r'\boldmath']
####################################################################################################################################################
P = np.pi # Dear old pi!
CC = 0.73 # Cosmological constant.
L_norm = 1e52 # in ergs.s^{-1}.
T90_cut = 2 # in sec.
cm_per_Mpc = 3.0857 * 1e24
erg_per_keV = 1.6022 * 1e-9
logL_bin = 1.0
logL_min = -5.0
logL_max = +5.1
z_min = 1e-1
z_max = 1e+1
padding = 8 # The padding of the axes labels.
size_font = 16 # The fontsize in the images.
marker_size = 7 # The size of markers in scatter plots.
al = 0.8 # The brightness of plots.
####################################################################################################################################################
####################################################################################################################################################
constraints = 3
#~ n = 1.0
#~ n = 1.5
n = 2.0
####################################################################################################################################################
####################################################################################################################################################
k_table = ascii.read( './../../tables/k_correction.txt', format = 'fixed_width' ) ; global z_sim, dL_sim, k_Fermi, k_Swift
z_sim = k_table['z'].data
dL_sim = k_table['dL'].data
k_BATSE = k_table['k_BATSE'].data
k_Fermi = k_table['k_Fermi'].data
k_Swift = k_table['k_Swift'].data
ind_zMin = mf.nearest(z_sim, z_min)
ind_zMax = mf.nearest(z_sim, z_max)
z_sim = z_sim[ ind_zMin : ind_zMax]
dL_sim = dL_sim[ ind_zMin : ind_zMax]
k_BATSE = k_BATSE[ind_zMin : ind_zMax]
k_Fermi = k_Fermi[ind_zMin : ind_zMax]
k_Swift = k_Swift[ind_zMin : ind_zMax]
volume_tab = ascii.read( './../../tables/rho_star_dot.txt', format = 'fixed_width' ) ; global volume_term
volume_term = volume_tab['vol'].data ; volume_term = volume_term[ind_zMin : ind_zMax]
Phi_table = ascii.read( './../../tables/CSFR_delayed--n={0:.1f}.txt'.format(n), format = 'fixed_width' ) ; global Phi
Phi = Phi_table['CSFR_delayed'].data ; Phi = Phi[ind_zMin : ind_zMax]
threshold_data = ascii.read( './../../tables/thresholds.txt', format = 'fixed_width' )
L_cut__Fermi = threshold_data['L_cut__Fermi'].data ; L_cut__Fermi = L_cut__Fermi[ind_zMin : ind_zMax]
L_cut__Swift = threshold_data['L_cut__Swift'].data ; L_cut__Swift = L_cut__Swift[ind_zMin : ind_zMax]
L_cut__BATSE = threshold_data['L_cut__BATSE'].data ; L_cut__BATSE = L_cut__BATSE[ind_zMin : ind_zMax]
L_cut__ACZTI = threshold_data['L_cut__CZTI'].data ; L_cut__ACZTI = L_cut__ACZTI[ind_zMin : ind_zMax]
L_vs_z__known_short = ascii.read( './../../tables/L_vs_z__known_short.txt', format = 'fixed_width' )
L_vs_z__Fermi_short = ascii.read( './../../tables/L_vs_z__Fermi_short.txt', format = 'fixed_width' )
L_vs_z__FermE_short = ascii.read( './../../tables/L_vs_z__FermE_short.txt', format = 'fixed_width' )
L_vs_z__Swift_short = ascii.read( './../../tables/L_vs_z__Swift_short.txt', format = 'fixed_width' )
L_vs_z__other_short = ascii.read( './../../tables/L_vs_z__other_short.txt', format = 'fixed_width' )
L_vs_z__BATSE_short = ascii.read( './../../tables/L_vs_z__BATSE_short.txt', format = 'fixed_width' )
known_short_redshift = L_vs_z__known_short[ 'measured z'].data
known_short_Luminosity = L_vs_z__known_short[ 'Luminosity [erg/s]'].data
known_short_Luminosity_error = L_vs_z__known_short[ 'Luminosity_error [erg/s]'].data
Fermi_short_redshift = L_vs_z__Fermi_short[ 'pseudo z' ].data
Fermi_short_Luminosity = L_vs_z__Fermi_short[ 'Luminosity [erg/s]'].data
Fermi_short_Luminosity_error = L_vs_z__Fermi_short[ 'Luminosity_error [erg/s]'].data
FermE_short_redshift = L_vs_z__FermE_short[ 'pseudo z'].data
FermE_short_Luminosity = L_vs_z__FermE_short[ 'Luminosity [erg/s]'].data
FermE_short_Luminosity_error = L_vs_z__FermE_short[ 'Luminosity_error [erg/s]'].data
Swift_short_redshift = L_vs_z__Swift_short[ 'pseudo z' ].data
Swift_short_Luminosity = L_vs_z__Swift_short[ 'Luminosity [erg/s]'].data
Swift_short_Luminosity_error = L_vs_z__Swift_short[ 'Luminosity_error [erg/s]'].data
other_short_redshift = L_vs_z__other_short[ 'measured z'].data
other_short_Luminosity = L_vs_z__other_short[ 'Luminosity [erg/s]'].data
other_short_Luminosity_error = L_vs_z__other_short[ 'Luminosity_error [erg/s]'].data
BATSE_short_redshift = L_vs_z__BATSE_short[ 'pseudo z'].data
BATSE_short_Luminosity = L_vs_z__BATSE_short[ 'Luminosity [erg/s]'].data
BATSE_short_Luminosity_error = L_vs_z__BATSE_short[ 'Luminosity_error [erg/s]'].data
inds_to_delete = np.where(other_short_Luminosity < 1e-16 )[0]
print 'other GRBs, deleted : ', inds_to_delete.size
other_short_redshift = np.delete( other_short_redshift , inds_to_delete )
other_short_Luminosity = np.delete( other_short_Luminosity, inds_to_delete )
other_short_Luminosity_error = np.delete( other_short_Luminosity_error, inds_to_delete )
inds_to_delete = []
for j, z in enumerate( Swift_short_redshift ):
array = np.abs( z_sim - z )
ind = np.where( array == array.min() )[0]
if ( Swift_short_Luminosity[j] - L_cut__Swift[ind] ) < 0 :
inds_to_delete.append( j )
inds_to_delete = np.array( inds_to_delete )
print 'Swift GRBs, deleted : ', inds_to_delete.size, '\n'
Swift_short_redshift = np.delete( Swift_short_redshift , inds_to_delete )
Swift_short_Luminosity = np.delete( Swift_short_Luminosity , inds_to_delete )
Swift_short_Luminosity_error = np.delete( Swift_short_Luminosity_error, inds_to_delete )
inds_to_delete = np.where( Fermi_short_redshift > z_max )[0]
print 'Fermi GRBs, deleted : ', inds_to_delete.size
Fermi_short_redshift = np.delete( Fermi_short_redshift , inds_to_delete )
Fermi_short_Luminosity = np.delete( Fermi_short_Luminosity , inds_to_delete )
Fermi_short_Luminosity_error = np.delete( Fermi_short_Luminosity_error, inds_to_delete )
inds_to_delete = np.where( Swift_short_redshift > z_max )[0]
print 'Swift GRBs, deleted : ', inds_to_delete.size, '\n'
Swift_short_redshift = np.delete( Swift_short_redshift , inds_to_delete )
Swift_short_Luminosity = np.delete( Swift_short_Luminosity , inds_to_delete )
Swift_short_Luminosity_error = np.delete( Swift_short_Luminosity_error, inds_to_delete )
print 'Number of "known" GRBs : ', known_short_redshift.size
print 'Number of "Fermi" GRBs : ', Fermi_short_redshift.size
print 'Number of "FermE" GRBs : ', FermE_short_redshift.size
print 'Number of "Swift" GRBs : ', Swift_short_redshift.size
print 'Number of "other" GRBs : ', other_short_redshift.size, '\n'
Fermi_short_Luminosity = np.concatenate( [ known_short_Luminosity , Fermi_short_Luminosity , FermE_short_Luminosity ] )
Fermi_short_Luminosity_error = np.concatenate( [ known_short_Luminosity_error , Fermi_short_Luminosity_error , FermE_short_Luminosity_error ] )
N__Fermi = Fermi_short_Luminosity.size
x__Fermi_short, y__Fermi_short, y__Fermi_short_poserr, y__Fermi_short_negerr = sf.my_histogram_with_errorbars( np.log10(Fermi_short_Luminosity/L_norm), np.log10( (Fermi_short_Luminosity + Fermi_short_Luminosity_error) / L_norm ) - np.log10(Fermi_short_Luminosity/L_norm), np.log10( (Fermi_short_Luminosity + Fermi_short_Luminosity_error) / L_norm ) - np.log10(Fermi_short_Luminosity/L_norm), logL_bin*1.0, logL_min, logL_max )
y__Fermi_short_error = np.maximum(y__Fermi_short_negerr, y__Fermi_short_poserr)+1
print 'Total number, Fermi : ', N__Fermi
Swift_short_Luminosity = np.concatenate( [ other_short_Luminosity , Swift_short_Luminosity ] )
Swift_short_Luminosity_error = np.concatenate( [ other_short_Luminosity_error , Swift_short_Luminosity_error ] )
# To add artificial errors, of percentage : f
f = 45.0
Swift_short_Luminosity_error = Swift_short_Luminosity_error + (f/100)*Swift_short_Luminosity
N__Swift = Swift_short_Luminosity.size
x__Swift_short, y__Swift_short, y__Swift_short_poserr, y__Swift_short_negerr = sf.my_histogram_with_errorbars( np.log10(Swift_short_Luminosity/L_norm), np.log10( (Swift_short_Luminosity + Swift_short_Luminosity_error) / L_norm ) - np.log10(Swift_short_Luminosity/L_norm), np.log10( (Swift_short_Luminosity + Swift_short_Luminosity_error) / L_norm ) - np.log10(Swift_short_Luminosity/L_norm), logL_bin*1.0, logL_min, logL_max )
y__Swift_short_error = np.maximum(y__Swift_short_negerr, y__Swift_short_poserr)+1
print 'Total number, Swift : ', N__Swift
print 'Total number, Fermi & Swift : ', N__Fermi + N__Swift, '\n'
inds_to_delete = []
for j, z in enumerate( BATSE_short_redshift ):
array = np.abs( z_sim - z )
ind = np.where( array == array.min() )[0]
if ( BATSE_short_Luminosity[j] - L_cut__BATSE[ind] ) < 0 :
inds_to_delete.append( j )
inds_to_delete = np.array( inds_to_delete )
print 'Number of BATSE GRBs : ', BATSE_short_Luminosity.size
print 'BATSE GRBs, deleted : ', inds_to_delete.size
BATSE_short_redshift = np.delete( BATSE_short_redshift , inds_to_delete )
BATSE_short_Luminosity = np.delete( BATSE_short_Luminosity , inds_to_delete )
BATSE_short_Luminosity_error = np.delete( BATSE_short_Luminosity_error, inds_to_delete )
# To add artificial errors, of percentage : f
f = 48.0
BATSE_short_Luminosity_error = BATSE_short_Luminosity_error + (f/100)*BATSE_short_Luminosity
N__BATSE = BATSE_short_Luminosity.size
x__BATSE_short, y__BATSE_short, y__BATSE_short_poserr, y__BATSE_short_negerr = sf.my_histogram_with_errorbars( np.log10(BATSE_short_Luminosity/L_norm), np.log10( (BATSE_short_Luminosity + BATSE_short_Luminosity_error) / L_norm ) - np.log10(BATSE_short_Luminosity/L_norm), np.log10( (BATSE_short_Luminosity + BATSE_short_Luminosity_error) / L_norm ) - np.log10(BATSE_short_Luminosity/L_norm), logL_bin*1.0, logL_min, logL_max )
y__BATSE_short_error = np.maximum(y__BATSE_short_negerr, y__BATSE_short_poserr)+1
print ' Number, BATSE : ', N__BATSE
print '\n'
print 'Fermi error percentage: ', np.mean(Fermi_short_Luminosity_error/Fermi_short_Luminosity)*100
print 'Swift error percentage: ', np.mean(Swift_short_Luminosity_error/Swift_short_Luminosity)*100
print 'BATSE error percentage: ', np.mean(BATSE_short_Luminosity_error/BATSE_short_Luminosity)*100
print '\n'
Luminosity_mids = x__Fermi_short
Luminosity_mins = L_norm * ( 10 ** ( Luminosity_mids - logL_bin/2 ) )
Luminosity_maxs = L_norm * ( 10 ** ( Luminosity_mids + logL_bin/2 ) )
L_lo = Luminosity_mins.min()
L_hi = Luminosity_maxs.max()
print '\n\n'
####################################################################################################################################################
###############################################################################################################################################s
def f(x, nu):
return x**(-nu) * np.exp(-x)
def model_ECPL__Fermi( x__Fermi_short, Gamma, nu, coeff ):
CSFR = Phi * volume_term
L_b = ( L_norm * coeff ) * np.ones(z_sim.size)
den_int = dL_sim**2 * k_Fermi
den_int = den_int ** (-Gamma)
deno = simps( den_int, z_sim )
lower_limit_array = L_lo/L_b
upper_limit_array = L_hi/L_b
denominator = np.zeros(z_sim.size)
for k, z in enumerate(z_sim):
lower_limit = lower_limit_array[k]
upper_limit = upper_limit_array[k]
N = 1e10
denominator[k] = quad( f, lower_limit, N*lower_limit, args=(-Gamma+nu) )[0]
N_vs_L__model = np.zeros(Luminosity_mids.size)
for j, L1 in enumerate( Luminosity_mins ):
inds = np.where( L_cut__Fermi <= L1 )[0]
Lmin = L_cut__Fermi.copy()
Lmin[inds] = L1
L2 = Luminosity_maxs[j]
Lmax = L2 * np.ones(z_sim.size)
lower_limit_array = Lmin/L_b
upper_limit_array = Lmax/L_b
integral_over_L = np.zeros(z_sim.size)
for k, z in enumerate(z_sim):
lower_limit = lower_limit_array[k]
upper_limit = upper_limit_array[k]
integral_over_L[k] = quad( f, lower_limit, upper_limit, args=(-Gamma+nu) )[0]
integral_over_L = integral_over_L / denominator
ind = np.where( integral_over_L <= 0 )[0]
integral_over_L[ind] = 0
integrand = ( CSFR * den_int/deno ) * integral_over_L
integral = simps( integrand, z_sim )
N_vs_L__model[j] = integral
norm = np.sum(N_vs_L__model)
N_vs_L__model = N_vs_L__model / norm
return N_vs_L__model
def find_discrepancy( model, observed ):
return np.sum( ( model - observed ) ** 2 )
####################################################################################################################################################
####################################################################################################################################################
print '################################################################################'
print '\n\n'
Gamma__Fermi = 0.001
#~ ## n = 1.0
#~ Fermi__nu_array = np.array( [0.35, 0.36, 0.37, 0.56, 0.71, 0.73, 0.74, 0.75, 0.76] )
#~ Fermi__Lb_array = np.array( [5.45, 5.46, 5.47, 5.48, 5.49, 5.50, 7.42, 14.52, 14.57, 14.62, 14.63, 14.64, 14.65, 14.66, 14.67] )
#~ ## n = 1.5
#~ Fermi__nu_array = np.array( [0.25, 0.26, 0.30, 0.64, 0.66, 0.68, 0.69] )
#~ Fermi__Lb_array = np.array( [5.25, 5.26, 5.27, 6.84, 13.54, 13.56, 13.57] )
## n = 2.0
Fermi__nu_array = np.array( [0.22, 0.23, 0.60, 0.64, 0.65] )
Fermi__Lb_array = np.array( [5.08, 5.09, 6.61, 12.69, 12.70] )
Fermi__nu_size = Fermi__nu_array.size
Fermi__Lb_size = Fermi__Lb_array.size
print 'nu_array: ', Fermi__nu_array
print 'Lb_array: ', Fermi__Lb_array, '\n'
grid_of_discrepancy__Fermi = np.zeros( (Fermi__nu_size, Fermi__Lb_size ) )
grid_of_rdcdchisqrd__Fermi = grid_of_discrepancy__Fermi.copy()
print 'Grid of {0:d} (nu) X {1:d} (Lb) = {2:d}.'.format( Fermi__nu_size, Fermi__Lb_size, grid_of_rdcdchisqrd__Fermi.size), '\n'
t0 = time.time()
for cnu, nu in enumerate(Fermi__nu_array):
for cLb, coeff in enumerate(Fermi__Lb_array):
model_fit__Fermi = model_ECPL__Fermi( x__Fermi_short, Gamma__Fermi, nu, coeff ) * N__Fermi
grid_of_discrepancy__Fermi[cnu, cLb] = find_discrepancy( model_fit__Fermi, y__Fermi_short )
grid_of_rdcdchisqrd__Fermi[cnu, cLb] = mf.reduced_chisquared( model_fit__Fermi, y__Fermi_short, y__Fermi_short_error, constraints )[2]
print 'Done in {:.3f} mins.'.format( (time.time()-t0)/60.0 ), '\n\n'
output = open( './../tables/pkl/Fermi--rdcdchisqrd--1.pkl', 'wb' )
pickle.dump( grid_of_rdcdchisqrd__Fermi, output )
output.close()
output = open( './../tables/pkl/Fermi--discrepancy--1.pkl', 'wb' )
pickle.dump( grid_of_discrepancy__Fermi, output )
output.close()
ind_discrepancy_min__Fermi = np.unravel_index( grid_of_discrepancy__Fermi.argmin(), grid_of_discrepancy__Fermi.shape )
nu__Fermi = Fermi__nu_array[ind_discrepancy_min__Fermi[0]]
Lb__Fermi = Fermi__Lb_array[ind_discrepancy_min__Fermi[1]]
print 'Minimum discrepancy of {0:.3f} at nu = {1:.2f}, Lb = {2:.2f}'.format( grid_of_discrepancy__Fermi[ind_discrepancy_min__Fermi], nu__Fermi, Lb__Fermi )
print 'Reduced-chisquared of {0:.3f}.'.format( grid_of_rdcdchisqrd__Fermi[ind_discrepancy_min__Fermi]), '\n'
ind_rdcdchisqrd_min__Fermi = np.unravel_index( grid_of_rdcdchisqrd__Fermi.argmin(), grid_of_rdcdchisqrd__Fermi.shape )
nu__Fermi = Fermi__nu_array[ind_rdcdchisqrd_min__Fermi[0]]
Lb__Fermi = Fermi__Lb_array[ind_rdcdchisqrd_min__Fermi[1]]
print 'Minimum reduced-chisquared of {0:.3f} at nu = {1:.2f}, Lb = {2:.2f}'.format( grid_of_rdcdchisqrd__Fermi[ind_rdcdchisqrd_min__Fermi], nu__Fermi, Lb__Fermi )
print 'Reduced-chisquared of {0:.3f}.'.format( grid_of_rdcdchisqrd__Fermi[ind_rdcdchisqrd_min__Fermi]), '\n\n'
grid_of_chisquared__Fermi = grid_of_rdcdchisqrd__Fermi * 8
chisquared_at_solution = grid_of_chisquared__Fermi[ind_discrepancy_min__Fermi]
chisquared_for_1sigma = chisquared_at_solution + 2.30
print 'Chi-squared at 1-sigma: ', np.round(chisquared_for_1sigma, 3), '\n'
print np.round( grid_of_chisquared__Fermi[ :, ind_discrepancy_min__Fermi[1] ], 3 )
print np.round( grid_of_chisquared__Fermi[ ind_discrepancy_min__Fermi[0], : ], 3 )
print '\n\n'
print '################################################################################'