def discrepancy_and_redchisqrd(A, eta):
numerator__delta_pseudo_z = numerator__delta_pseudo_GRB__first_term + eta * numerator__delta_pseudo_GRB__second_term # defined for each GRB
denominator__delta_pseudo_z = denominator__delta_pseudo_zsim__first_term + (
(eta + 2) / (1 + z_sim)) # defined for each simulated redshift
denominator__F = (1 + z_sim)**eta
F_Fermi_sim = numerator__F / denominator__F
F_Fermi_sim = F_Fermi_sim * (cm_per_Mpc**2) / L_norm
RHSs = (A / common_Fermi_flux) * (common_Epeak_in_MeV**eta)
pseudo_redshifts = np.zeros(RHSs.size)
pseudo_redshifts_error = np.zeros(RHSs.size)
for j, RHS in enumerate(RHSs):
array = np.abs(F_Fermi_sim - RHS)
ind = np.where(array == array.min())[0][0]
pseudo_redshift = z_sim[ind]
pseudo_redshift_error = numerator__delta_pseudo_z[
j] / denominator__delta_pseudo_z[ind]
pseudo_redshifts[j] = pseudo_redshift
pseudo_redshifts_error[j] = pseudo_redshift_error
discrepancy = np.sum((common_redshift - pseudo_redshifts)**2)
chisquared, dof, redchisqrd = mf.reduced_chisquared(
common_redshift, pseudo_redshifts, pseudo_redshifts_error, 2)
return pseudo_redshifts, pseudo_redshifts_error, discrepancy, chisquared, dof, redchisqrd
def discrepancy_and_redchisqrd(A, eta):
numerator__delta_pseudo_z = numerator__delta_pseudo_GRB__first_term + eta * numerator__delta_pseudo_GRB__second_term # defined for each GRB
denominator__delta_pseudo_z = denominator__delta_pseudo_zsim__first_term + (
(eta + 2) / (1 + z_sim)) # defined for each simulated redshift
denominator__F = (1 + z_sim)**eta
F_Fermi_sim = numerator__F / denominator__F
F_Fermi_sim = F_Fermi_sim * (cm_per_Mpc**2) / L_norm
RHSs = (A / common_Fermi_flux) * (common_Epeak_in_MeV**eta)
pseudo_redshifts = np.zeros(RHSs.size)
pseudo_redshifts_error = np.zeros(RHSs.size)
for j, RHS in enumerate(RHSs):
array = np.abs(F_Fermi_sim - RHS)
ind = np.where(array == array.min())[0][0]
pseudo_redshift = z_sim[ind]
pseudo_redshift_error = numerator__delta_pseudo_z[
j] / denominator__delta_pseudo_z[ind]
pseudo_redshifts[j] = pseudo_redshift
pseudo_redshifts_error[j] = pseudo_redshift_error
z_min = 1e-5
z_max = 1e1
x1, y_pseudo = mf.my_histogram_according_to_given_boundaries(
pseudo_redshifts, z_bin, z_min, z_max)
x2, y_common = mf.my_histogram_according_to_given_boundaries(
common_redshift, z_bin, z_min, z_max)
# print ( x1 - x2 == 0 ).all()
discrepancy = np.sum((y_pseudo - y_common)**2)
chisquared, dof, redchisqrd = mf.reduced_chisquared(
common_redshift, pseudo_redshifts, pseudo_redshifts_error, 2)
return pseudo_redshifts, pseudo_redshifts_error, discrepancy, chisquared, dof, redchisqrd
def plot_redshift_vs_redshift(pseudo_redshifts, pseudo_redshifts_error,
coefficient, coefficient_error, exponent,
exponent_error):
reconciled = coefficient * (pseudo_redshifts**exponent)
reconciled_error = exponent * (
pseudo_redshifts_error /
pseudo_redshifts) + coefficient_error / coefficient + np.log(
pseudo_redshifts) * exponent_error
reconciled_error = reconciled_error * reconciled
ratio = reconciled / common_redshift
ratio_error = (reconciled_error / reconciled) * ratio
print 'Ratio min and max : ', round(ratio.min(), 3), round(ratio.max(), 3)
print 'Reduced chi-squared : ', mf.reduced_chisquared(
common_redshift, reconciled, reconciled_error, 4)[2]
z_min = 1e-1
z_max = 2e1
ax = plt.subplot(111)
ax.set_xscale('log')
ax.set_yscale('log')
ax.set_xlim(z_min, z_max)
ax.set_ylim(z_min, z_max)
ax.set_ylabel(r'$ \rm{ reconciled / measured } $', fontsize=size_font)
ax.set_xlabel(r'$ \rm{ pseudo \; \, redshift } $', fontsize=size_font)
ax.errorbar(pseudo_redshifts,
ratio,
yerr=ratio_error,
fmt='.',
ms=marker_size,
color='silver',
markerfacecolor='k',
markeredgecolor='k')
ax.axhline(y=1, linestyle='dashed', color='k')
model_bin__Fermi = model_bin__Fermi * Fermi_norm
Fermi_long_total_model = Fermi_long_total_model + model_bin__Fermi
ax[j] = fig.add_subplot(z_binned__Fermi.size-1,1,j+1)
ax[j].text( -3.5, 350, r'$ z : $ ' + r'$ {0:.1f} $'.format(z) + r' $ \rm{to} $ ' + r'$ {0:.1f} $'.format(z_binned__Fermi[j+1]), fontsize = size_font, ha = 'center', va = 'center' )
ax[j].set_ylabel( r'$ \rm{ N } $', fontsize = size_font, rotation = 0, labelpad = padding+6 )
ax[j].set_ylim( 0, 400 )
ax[j].errorbar( Luminosity_mids, obsFermi_long[j], yerr = [ obsFermi_long_poserr[j], obsFermi_long_negerr[j] ], fmt = '-', color = 'k', label = r' $ \rm{ observed } $' )
ax[j].plot( Luminosity_mids, model_bin__Fermi, linestyle = '--', color = 'k', label = r' $ \rm{ model } $' )
ax[j].legend()
ltext = plt.gca().get_legend().get_texts()
plt.setp( ltext[0], fontsize = 11 )
modeled__Fermi_long[j] = model_bin__Fermi
discrepancy_over_z__Fermi[j] = find_discrepancy( model_bin__Fermi, obsFermi_long[j] )
rdcdchisqrd_over_z__Fermi[j] = mf.reduced_chisquared( model_bin__Fermi, obsFermi_long[j], obsFermi_long_error[j], 4 )[2]
# print mf.reduced_chisquared( model_bin__Fermi, obsFermi_long[j], obsFermi_long_error[j], 4 )
print 'Done in {:.3f} mins.'.format( ( time.time()-t0 )/60 )
xticklabels = ax[0].get_xticklabels() + ax[1].get_xticklabels()
plt.setp( xticklabels, visible = False )
plt.xlabel( r'$ \rm{ log } $' + r'$ ( L_{iso} / L_{0} ) $', fontsize = size_font, labelpad = padding+5 )
plt.savefig( './../plots/estimated_lumfunc_models/binned_with_z/Fermi--binned.png' )
plt.clf()
plt.close()
Fermi_long_total_data_e = np.maximum(Fermi_long_total_data_ep, Fermi_long_total_data_en)+1
print 'reduced chisquared : ', mf.reduced_chisquared( Fermi_long_total_model, Fermi_long_total_data, Fermi_long_total_data_e, 4 ), '\n\n'
ax = plt.subplot(111)
ax.set_xlabel( r'$ \rm{ log } $' + r'$ ( L_{p} / L_{0} ) $', fontsize = size_font, labelpad = padding-4 )
ax.set_ylabel( r'$ \rm{ N } $', fontsize = size_font, rotation = 0, labelpad = padding+6 )
# ax[j] = fig.add_subplot(z_binned__Fermi.size-1,1,j+1)
# ax[j].text( -3.5, 350, r'$ z : $ ' + r'$ {0:.1f} $'.format(z) + r' $ \rm{to} $ ' + r'$ {0:.1f} $'.format(z_binned__Fermi[j+1]), fontsize = size_font, ha = 'center', va = 'center' )
# ax[j].set_ylabel( r'$ \rm{ N } $', fontsize = size_font, rotation = 0, labelpad = padding+6 )
# ax[j].set_ylim( 0, 400 )
# ax[j].errorbar( Luminosity_mids, obsFermi_long[j], yerr = [ obsFermi_long_poserr[j], obsFermi_long_negerr[j] ], fmt = '-', color = 'k', label = r' $ \rm{ observed } $' )
# ax[j].plot( Luminosity_mids, model_bin__Fermi, linestyle = '--', color = 'k', label = r' $ \rm{ model } $' )
# ax[j].legend()
# ltext = plt.gca().get_legend().get_texts()
# plt.setp( ltext[0], fontsize = 11 )
modeled__Fermi_long[j] = model_bin__Fermi
discrepancy_over_z__Fermi[j] = find_discrepancy(
model_bin__Fermi, obsFermi_long[j])
rdcdchisqrd_over_z__Fermi[j] = mf.reduced_chisquared(
model_bin__Fermi, obsFermi_long[j],
obsFermi_long_error[j], 5)[2]
# print mf.reduced_chisquared( model_bin__Fermi, obsFermi_long[j], obsFermi_long_error[j], 5 )[1]
# xticklabels = ax[0].get_xticklabels() + ax[1].get_xticklabels()
# plt.setp( xticklabels, visible = False )
# plt.xlabel( r'$ \rm{ log } $' + r'$ ( L_{iso} / L_{0} ) $', fontsize = size_font, labelpad = padding+5 )
# plt.show()
grid_of_discrepancy__Fermi[c1, c2, cLb, cdel, cX] = np.sum(
discrepancy_over_z__Fermi)
grid_of_rdcdchisqrd__Fermi[c1, c2, cLb, cdel,
cX] = np.mean(
rdcdchisqrd_over_z__Fermi)
print 'Fermi done in {:.3f} hrs.'.format((time.time() - t0) / 3600), '\n'
ax[j].set_ylabel( r'$ \rm{ N } $', fontsize = size_font, rotation = 0, labelpad = padding+6 )
ax[j].set_ylim( 0, 400 )
ax[j].errorbar( Luminosity_mids, obsFermi_long_bin, yerr = [ obsFermi_long_poserr_bin, obsFermi_long_negerr_bin ], fmt = '-', color = 'k', label = r' $ \rm{ observed } $' )
ax[j].plot( Luminosity_mids, model_bin__Fermi, linestyle = '--', color = 'k', label = r' $ \rm{ model } $' )
ax[j].legend()
ltext = plt.gca().get_legend().get_texts()
plt.setp( ltext[0], fontsize = 11 )
xticklabels = ax[0].get_xticklabels() + ax[1].get_xticklabels()
plt.setp( xticklabels, visible = False )
plt.xlabel( r'$ \rm{ log } $' + r'$ ( L_{p} / L_{0} ) $', fontsize = size_font, labelpad = padding+5 )
plt.savefig( './../plots/estimated_lumfunc_models/binned_with_z/Fermi--binned.png' )
plt.clf()
plt.close()
Fermi_long_total_data_e = np.maximum(Fermi_long_total_data_ep, Fermi_long_total_data_en)+1
print 'reduced chisquared : ', mf.reduced_chisquared( Fermi_long_total_model, Fermi_long_total_data, Fermi_long_total_data_e, 5 ), '\n'
ax = plt.subplot(111)
ax.set_xlabel( r'$ \rm{ log } $' + r'$ ( L_{p} / L_{0} ) $', fontsize = size_font, labelpad = padding-4 )
ax.set_ylabel( r'$ \rm{ N } $', fontsize = size_font, rotation = 0, labelpad = padding+6 )
ax.set_ylim( 0, 700 )
ax.errorbar( Luminosity_mids, Fermi_long_total_data, yerr = [ Fermi_long_total_data_ep, Fermi_long_total_data_en ], fmt = '-', color = 'k', label = r' $ \rm{ observed } $' )
ax.plot( Luminosity_mids, Fermi_long_total_model, linestyle = '--', color = 'k', label = r' $ \rm{ model } $' )
ax.legend()
plt.savefig( './../plots/estimated_lumfunc_models/binned_with_z/Fermi--total.png' )
plt.clf()
plt.close()
print 'Swift...'
Swift_long_L = known_long_Luminosity.copy() ; Swift_long_L_error = Swift_long_Luminosity_error.copy()
return pseudo_redshifts, pseudo_redshifts_error, discrepancy, chisquared, dof, redchisqrd
print '\n\n\n\n'
against = []
for i in range(5):
if i == 0:
returned = discrepancy_and_redchisqrd(A___Yonetoku, eta_Yonetoku)
pseudo_redshifts = returned[0]
pseudo_redshifts_error = returned[1]
against.append(pseudo_redshifts)
pseudo_redshifts___Yonetoku = pseudo_redshifts
pseudo_redshifts___Yonetoku_error = pseudo_redshifts_error
print i, returned[2], mf.reduced_chisquared(common_redshift,
pseudo_redshifts,
pseudo_redshifts_error, 2)
if i == 1:
returned = discrepancy_and_redchisqrd(A___Tanbestfit, eta_Tanbestfit)
pseudo_redshifts = returned[0]
pseudo_redshifts_error = returned[1]
against.append(pseudo_redshifts)
pseudo_redshifts___Tanbestfit = pseudo_redshifts
pseudo_redshifts___Tanbestfit_error = pseudo_redshifts_error
print i, returned[2], mf.reduced_chisquared(common_redshift,
pseudo_redshifts,
pseudo_redshifts_error, 2)
if i == 2:
returned = discrepancy_and_redchisqrd(A___Tanredshift, eta_Tanredshift)