def log_prob_non_detected_galaxies(self, x):
# controllo finitezza e theta(M-Mth)
self.omega.h = x['h']
self.omega.om = x['om']
self.omega.ol = x['ol']
zgal = x['zgal']
mgal = x['mgal']
logP = 0.0
DL = lal.LuminosityDistance(self.omega, zgal)
Mth = Mthreshold(DL)
Mabsi = mabs(mgal, DL)
if Mthreshold(DL) > Mabsi:
return -np.inf
else:
# compute the allowed volume for the source
gDL = 33.4
gdDL = 3.34
V = (4. / 3.) * np.pi * (gDL - gdDL)**3
# find the number density of galaxies from the low end of the Schecter
# distribution
n0 = 1. / normalise(self.omega, Mmax=Mth)
K = np.int(V * n0) - len(self.catalog)
if K <= 0.0:
# no galaxies are missing
return -np.inf
logP += np.log(Schechter(Mabsi, self.omega))
logP += np.log(lal.ComovingVolumeElement(zgal, self.omega))
# norm = np.log(dblquad(normalise_integrand, self.bounds[0][0], self.bounds[0][1],
# lambda x: mabs(mgal,lal.LuminosityDistance(self.omega, self.bounds[4][0])),
# lambda x: mabs(mgal,lal.LuminosityDistance(self.omega, self.bounds[4][0])),
# args = (self.omega, 1, ))[0])
# since for alpha < 0.0 the Schecter distribution diverges, approximate the integral with the
# maximum of the integral
norm = K * (np.log(
Schechter(
mabs(self.bounds[4][1],
lal.LuminosityDistance(
self.omega, self.bounds[0][1])), self.omega)) +
np.log(
lal.ComovingVolumeElement(self.bounds[0][1],
self.omega)))
return K * (logP - norm)
def log_prior(self, x):
# controllo finitezza e theta(M-Mth)
if not(np.isfinite(super(completeness, self).log_prior(x))):
return -np.inf
else:
self.omega.h = x['h']
self.omega.om = x['om']
self.omega.ol = x['ol']
zgw = x['z']
logP = 0.0
for zi,mi in zip(self.catalog['z'],self.catalog['Bmag']):
DL = lal.LuminosityDistance(self.omega, zi)
Mabsi = mabs(mi,DL)
if Mthreshold(DL) < Mabsi:
return -np.inf
else:
# Update parametri cosmologici con simulazione
# Calcolo prior. Ciascuna coordinata è pesata con le probabilità
# delle coordinate ('banane') GW, così come z.
# Temporaneamente, è assunta gaussiana intorno a un evento.
logP += np.log(Schechter(Mabsi, self.omega))
#log_P_RA = np.log(gaussian(x['ra'],Gal.ra.rad,Gal.ra.rad/100.))
#log_P_DEC = np.log(gaussian(x['dec'],Gal.dec.rad,Gal.dec.rad/100.))
logP += np.log(lal.ComovingVolumeElement(zi, self.omega))
return logP
def log_prior(self, x):
if not (np.isfinite(super(completeness, self).log_prior(x))):
return -np.inf
else:
self.omega.h = x['h']
self.omega.om = x['om']
self.omega.ol = x['ol']
logP = np.log(lal.ComovingVolumeElement(x['redshift'], self.omega))
return logP
def log_prob_detected_galaxies(self, x):
# controllo finitezza e theta(M-Mth)
self.omega.h = x['h']
self.omega.om = x['om']
self.omega.ol = x['ol']
zgw = x['zgw']
logP = 0.0
Vmax = lal.ComovingVolume(self.omega, self.bounds[0][1])
for zi, mi in zip(self.catalog['z'], self.catalog['Bmag']):
DL = lal.LuminosityDistance(self.omega, zi)
Mabsi = mabs(mi, DL)
if Mthreshold(DL) < Mabsi:
return -np.inf
else:
logP += np.log(Schechter(Mabsi, self.omega))
logP += np.log(
lal.ComovingVolumeElement(zi, self.omega) / Vmax)
return logP
def log_prob_detected_galaxies(self, x):
# controllo finitezza e theta(M-Mth)
if not (np.isfinite(super(completeness, self).log_prior(x))):
return -np.inf
else:
self.omega.h = x['h']
self.omega.om = x['om']
self.omega.ol = x['ol']
zgw = x['zgw']
logP = 0.0
for zi, mi in zip(self.catalog['z'], self.catalog['Bmag']):
DL = lal.LuminosityDistance(self.omega, zi)
Mabsi = mabs(mi, DL)
if Mthreshold(DL) < Mabsi:
return -np.inf
else:
logP += np.log(Schechter(Mabsi, self.omega))
logP += np.log(lal.ComovingVolumeElement(zi, self.omega))
return logP
def log_prob_non_detected_galaxies(self, x):
# controllo finitezza e theta(M-Mth)
if not (np.isfinite(super(completeness, self).log_prior(x))):
return -np.inf
else:
self.omega.h = x['h']
self.omega.om = x['om']
self.omega.ol = x['ol']
zgal = x['zgal']
mgal = x['mgal']
logP = 0.0
K = 38
DL = lal.LuminosityDistance(self.omega, zgal)
Mabsi = mabs(mgal, DL)
if Mthreshold(DL) > Mabsi:
print(Mthreshold(DL), Mabsi)
return -np.inf
else:
logP += np.log(Schechter(Mabsi, self.omega))
logP += np.log(lal.ComovingVolumeElement(zgal, self.omega))
return K * logP
def log_prior(self, x):
# controllo finitezza e theta(M-Mth)
if not (np.isfinite(super(completeness, self).log_prior(x))):
return -np.inf
else:
if x['M'] > Mthreshold(x['z'], self.omega):
return -np.inf
else:
# Update parametri cosmologici con simulazione
self.omega.h = x['h']
self.omega.om = x['om']
self.omega.ol = x['ol']
# Calcolo prior. Ciascuna coordinata è pesata con le probabilità
# delle coordinate ('banane') GW, così come z.
# Temporaneamente, è assunta gaussiana intorno a un evento.
log_P_Z = np.log(gaussian(x['z'], Gal.z, Gal.z / 10.0))
log_P_S = np.log(Schechter(x['M'], self.omega))
log_P_RA = np.log(
gaussian(x['ra'], Gal.ra.rad, Gal.ra.rad / 100.))
log_P_DEC = np.log(
gaussian(x['dec'], Gal.dec.rad, Gal.dec.rad / 100.))
log_P_ComVol = np.log(
lal.ComovingVolumeElement(x['z'], self.omega))
return log_P_S + log_P_Z + log_P_ComVol + log_P_RA + log_P_DEC
def normalise_integrand(M, z, omega, K):
PS = Schechter(M, omega)
PV = lal.ComovingVolumeElement(z, omega)
# print(" ==== integrand ===",PS,PV,K,PS*PV,(PS*PV)**K)
return (PS * PV)**K