# Remove any existing result files
list = [glob.glob("*.fits"), glob.glob("*.log"), glob.glob("*.xml")]
for files in list:
for file in files:
os.remove(file)
# Setup single observation survey
#obs = survey_single()
obs = survey_gplane()
# Add background model
obs = add_background_model(obs)
# Simulate events
print("Simulate events")
obs = obsutils.sim(obs)
# Make counts map
print("Make counts map")
cntmap = obsutils.cntmap(obs)
# Fit observations
print("Fit observations")
like = obsutils.fit(obs)
#print like.opt()
#print like.obs().models()
# Make model map
print("Make model map (this step will take some time)")
modmap = obsutils.modmap(obs)
def trial(self, seed):
"""
Create the pull for a single trial.
Parameters:
seed - Random number generator seed
"""
# Write header
if self.logExplicit():
self.log.header2("Trial "+str(seed+1))
# Simulate events
obs = obsutils.sim(self.obs, \
nbins=self.m_enumbins, \
seed=seed, \
binsz=self.m_binsz, \
npix=self.m_npix, \
log=self.m_log, debug=self.m_debug)
# Determine number of events in simulation
nevents = 0.0
for run in obs:
nevents += run.events().number()
# Write simulation results
if self.logExplicit():
self.log.header3("Simulation")
self.log.parformat("Number of simulated events")
self.log(nevents)
self.log("\n")
# Fit model
like = obsutils.fit(obs, log=self.m_log, debug=self.m_debug)
# Store results
logL = like.opt().value()
npred = like.obs().npred()
models = like.obs().models()
# Write result header
if self.logExplicit():
self.log.header3("Pulls")
# Gather results
colnames = []
values = {}
for i in range(models.size()):
model = models[i]
model_name = model.name()
for k in range(model.size()):
par = model[k]
if par.is_free():
# Set parameter name
name = model_name+"_"+par.name()
# Append parameter, Pull_parameter and Unc_parameter
colnames.append(name)
colnames.append("Pull_"+name)
colnames.append("Unc_"+name)
# Compute pull
fitted_value = par.value()
real_value = self.model[i][k].value()
error = par.error()
if error != 0.0:
pull = (fitted_value - real_value) / error
else:
pull = 99.0
# Store results
values[name] = fitted_value
values["Pull_"+name] = pull
values["Unc_"+name] = error
# Write result
if self.logExplicit():
self.log.parformat(name)
self.log(pull)
self.log(" (")
self.log(fitted_value)
self.log(" +/- ")
self.log(error)
self.log(")\n")
# Bundle together results
result = {'colnames': colnames, 'values': values}
# Return
return result
def trial(self, seed):
"""
Create the TS for a single trial.
Parameters:
seed - Random number generator seed
"""
# Write header
if self.logExplicit():
self.log.header2("Trial "+str(seed+1))
# Simulate events
sim = obsutils.sim(self.obs, \
nbins=self.m_enumbins, \
seed=seed, \
binsz=self.m_binsz, \
npix=self.m_npix, \
log=self.m_log, debug=self.m_debug)
# Determine number of events in simulation
nevents = 0.0
for run in sim:
nevents += run.events().number()
# Write simulation results
if self.logExplicit():
self.log.header3("Simulation")
self.log.parformat("Number of simulated events")
self.log(nevents)
self.log("\n")
# Fit background only
sim.models(self.bkg_model)
like_bgm = obsutils.fit(sim, log=self.m_log, debug=self.m_debug)
result_bgm = like_bgm.obs().models()
LogL_bgm = like_bgm.opt().value()
npred_bgm = like_bgm.obs().npred()
# Write background fit results
if self.logExplicit():
self.log.header3("Background model fit")
self.log.parformat("log likelihood")
self.log(LogL_bgm)
self.log("\n")
self.log.parformat("Number of predicted events")
self.log(npred_bgm)
self.log("\n")
for model in result_bgm:
self.log.parformat("Model")
self.log(model.name())
self.log("\n")
for par in model:
self.log(str(par)+"\n")
# Fit background and test source
sim.models(self.full_model)
like_all = obsutils.fit(sim, log=self.m_log, debug=self.m_debug)
result_all = like_all.obs().models()
LogL_all = like_all.opt().value()
npred_all = like_all.obs().npred()
ts = 2.0*(LogL_bgm-LogL_all)
# Write background and test source fit results
if self.logExplicit():
self.log.header3("Background and test source model fit")
self.log.parformat("Test statistics")
self.log(ts)
self.log("\n")
self.log.parformat("log likelihood")
self.log(LogL_all)
self.log("\n")
self.log.parformat("Number of predicted events")
self.log(npred_all)
self.log("\n")
for model in result_all:
self.log.parformat("Model")
self.log(model.name())
self.log("\n")
for par in model:
self.log(str(par)+"\n")
# Write result
elif self.logTerse():
self.log.parformat("Trial "+str(seed))
self.log("TS=")
self.log(ts)
self.log(" Prefactor=")
self.log(result_all["Test"]["Prefactor"].value())
self.log("+/-")
self.log(result_all["Test"]["Prefactor"].error())
self.log("\n")
# Initialise results
colnames = []
values = {}
# Set TS value
colnames.append("TS")
values["TS"] = ts
# Set logL for background fit
colnames.append("LogL_bgm")
values["LogL_bgm"] = LogL_bgm
# Set logL for full fit
colnames.append("LogL_all")
values["LogL_all"] = LogL_all
# Set Nevents
colnames.append("Nevents")
values["Nevents"] = nevents
# Set Npred for background fit
colnames.append("Npred_bkg")
values["Npred_bkg"] = npred_bgm
# Set Npred for full fit
colnames.append("Npred_all")
values["Npred_all"] = npred_all
# Gather free full fit parameters
for i in range(result_all.size()):
model = result_all[i]
model_name = model.name()
for k in range(model.size()):
par = model[k]
if par.isfree():
# Set parameter name
name = model_name+"_"+par.name()
# Append value
colnames.append(name)
values[name] = par.value()
# Append error
name = "Unc_"+name
colnames.append(name)
values[name] = par.error()
# Bundle together results
result = {'colnames': colnames, 'values': values}
# Return
return result
def set_src_model(self, l, b, flux=1.0, index=-2.48, \
type="point", fitpos=False, fitidx=False):
"""
Returns a single source with Crab-like spectrum. The source flux
can be scaled in Crab units. The Crab spectrum is based on MAGIC
observations (Albert et al. 2008, ApJ, 674, 1037).
Parameters:
l - Galactic longitude of source location [deg]
b - Galactic latitude of source location [deg]
Keywords:
flux - Source flux [Crabs]
index - Spectral index
type - Source type ("point", "gauss", "disk", "shell")
fitpos - Fit position and size? (default: False)
fitidx - Fit index? (default: False)
"""
# Set source location
location = GSkyDir()
location.lb_deg(l, b)
# Set source spectrum
spectrum = GModelSpectralPlaw(flux*5.7e-16, index, GEnergy(0.3, "TeV")
if fitidx:
spectrum["Index"].free()
else:
spectrum["Index"].fix()
# Set source
if type == "point":
spatial = GModelSpatialPointSource(location)
if fitpos:
spatial["RA"].free()
spatial["DEC"].free()
else:
spatial["RA"].fix()
spatial["DEC"].fix()
elif type == "gauss":
spatial = GModelSpatialRadialGauss(location, self.m_radius)
if fitpos:
spatial["RA"].free()
spatial["DEC"].free()
spatial["Sigma"].free()
else:
spatial["RA"].fix()
spatial["DEC"].fix()
spatial["Sigma"].fix()
elif type == "disk":
spatial = GModelSpatialRadialDisk(location, self.m_radius)
if fitpos:
spatial["RA"].free()
spatial["DEC"].free()
spatial["Radius"].free()
else:
spatial["RA"].fix()
spatial["DEC"].fix()
spatial["Radius"].fix()
elif type == "shell":
spatial = GModelSpatialRadialShell(location, self.m_radius, self.m_width)
if fitpos:
spatial["RA"].free()
spatial["DEC"].free()
spatial["Radius"].free()
spatial["Width"].free()
else:
spatial["RA"].fix()
spatial["DEC"].fix()
spatial["Radius"].fix()
spatial["Width"].fix()
else:
self.log("ERROR: Unknown source type '"+type+"'.\n")
return None
source = GModelSky(spatial, spectrum)
# Set source name
source.name("Test")
# Return source
return source
def get_sensitivity(self, obs, bkg_model, full_model):
"""
Determine sensitivity for a given observations.
Parameters:
obs - Observation container
bkg_model - Background model
full_model - Source model
"""
# Set TeV->erg conversion factor
tev2erg = 1.6021764
# Determine energy boundaries from first observation in
# the container
for run in obs:
emin = run.events().ebounds().emin()
emax = run.events().ebounds().emax()
loge = math.log10(math.sqrt(emin.TeV()*emax.TeV()))
erg_mean = math.pow(10.0, loge) * tev2erg
erg_width = (emax.TeV()-emin.TeV()) * tev2erg
break
# Write header
if self.logTerse():
self.log("\n")
self.log.header2("Energies: "+str(emin)+" - "+str(emax))
# Initialise loop
flux_value = []
pflux_value = []
eflux_value = []
diffSens_value = []
iter = 0
test_flux = 0.1 # This is the initial test flux in Crab units
# Loop until we break
while True:
# Update iteration counter
iter += 1
# Write header
if self.logExplicit():
self.log.header2("Iteration "+str(iter))
# Set test flux
full_model["Test"]['Prefactor'].value(test_flux)
obs.models(full_model)
# Simulate events
sim = obsutils.sim(obs, nbins=self.m_nbins, seed=iter, \
binsz=self.m_binsz, npix=self.m_npix, \
log=self.m_log, debug=self.m_debug)
# Determine number of events in simulation
nevents = 0.0
for run in sim:
nevents += run.events().number()
# Write simulation results
if self.logExplicit():
self.log.header3("Simulation")
self.log.parformat("Number of simulated events")
self.log(nevents)
self.log("\n")
# Fit background only
sim.models(bkg_model)
like = obsutils.fit(sim, log=self.m_log, debug=self.m_debug)
result_bgm = like.obs().models().copy()
LogL_bgm = like.opt().value()
npred_bgm = like.obs().npred()
# Assess quality based on a comparison between Npred and Nevents
quality_bgm = npred_bgm-nevents
# Write background fit results
if self.logExplicit():
self.log.header3("Background model fit")
self.log.parformat("log likelihood")
self.log(LogL_bgm)
self.log("\n")
self.log.parformat("Number of predicted events")
self.log(npred_bgm)
self.log("\n")
self.log.parformat("Fit quality")
self.log(quality_bgm)
self.log("\n")
# Start over if the fit quality was bad
if abs(quality_bgm) > 3.0:
if self.logExplicit():
self.log("Fit quality outside required range. Start over.\n")
continue
# Write model fit results
if self.logExplicit():
for model in result_bgm:
self.log.parformat("Model")
self.log(model.name())
self.log("\n")
for par in model:
self.log(str(par)+"\n")
# Fit background and test source
sim.models(full_model)
like = obsutils.fit(sim, log=self.m_log, debug=self.m_debug)
result_all = like.obs().models().copy()
LogL_all = like.opt().value()
npred_all = like.obs().npred()
ts = 2.0*(LogL_bgm-LogL_all)
# Assess quality based on a comparison between Npred and Nevents
quality_all = npred_all-nevents
# Write background and test source fit results
if self.logExplicit():
self.log.header3("Background and test source model fit")
self.log.parformat("Test statistics")
self.log(ts)
self.log("\n")
self.log.parformat("log likelihood")
self.log(LogL_all)
self.log("\n")
self.log.parformat("Number of predicted events")
self.log(npred_all)
self.log("\n")
self.log.parformat("Fit quality")
self.log(quality_all)
self.log("\n")
#
for model in result_all:
self.log.parformat("Model")
self.log(model.name())
self.log("\n")
for par in model:
self.log(str(par)+"\n")
# Start over if the fit quality was bad
if abs(quality_all) > 3.0:
if self.logExplicit():
self.log("Fit quality outside required range. Start over.\n")
continue
# Start over if TS was non-positive
if ts <= 0.0:
if self.logExplicit():
self.log("Non positive TS. Start over.\n")
continue
# Get fitted Crab, photon and energy fluxes
cflux = result_all["Test"]['Prefactor'].value()
cflux_err = result_all["Test"]['Prefactor'].error()
pflux = result_all["Test"].spectral().flux(emin, emax)
eflux = result_all["Test"].spectral().eflux(emin, emax)
# Compute differential sensitivity
diffSens = pflux / erg_width * erg_mean*erg_mean
# Compute flux correction factor based on average TS
correct = 1.0
if self.m_use_ts:
if ts > 0:
correct = math.sqrt(self.m_ts_thres/ts)
else:
if cflux > 0 and cflux_err > 0:
correct = math.sqrt(self.m_ts_thres)/(cflux/cflux_err)
# Compute extrapolated fluxes
flux = correct * cflux
pflux = correct * pflux
eflux = correct * eflux
diffSens = correct * diffSens
flux_value.append(flux)
pflux_value.append(pflux)
eflux_value.append(eflux)
diffSens_value.append(diffSens)
# Write background and test source fit results
if self.logExplicit():
self.log.parformat("Photon flux")
self.log(pflux)
self.log(" ph/cm2/s\n")
self.log.parformat("Energy flux")
self.log(eflux)
self.log(" erg/cm2/s\n")
self.log.parformat("Crab flux")
self.log(cflux*1000.0)
self.log(" mCrab\n")
self.log.parformat("Differential sensitivity")
self.log(diffSens)
self.log(" erg/cm2/s\n")
for model in result_all:
self.log.parformat("Model")
self.log(model.name())
self.log("\n")
for par in model:
self.log(str(par)+"\n")
elif self.logTerse():
self.log.parformat("Iteration "+str(iter))
self.log("TS=")
self.log(ts)
self.log(" ")
self.log("corr=")
self.log(correct)
self.log(" ")
self.log(pflux)
self.log(" ph/cm2/s = ")
self.log(eflux)
self.log(" erg/cm2/s = ")
self.log(cflux*1000.0)
self.log(" mCrab = ")
self.log(diffSens)
self.log(" erg/cm2/s\n")
# Compute sliding average of extrapolated fitted prefactor,
# photon and energy flux. This damps out fluctuations and
# improves convergence
flux = 0.0
pflux = 0.0
eflux = 0.0
diffSens = 0.0
num = 0.0
for k in range(self.m_num_avg):
inx = len(flux_value) - k - 1
if inx >= 0:
flux += flux_value[inx]
pflux += pflux_value[inx]
eflux += eflux_value[inx]
diffSens += diffSens_value[inx]
num += 1.0
flux /= num
pflux /= num
eflux /= num
diffSens /= num
# Compare average flux to last average
if iter > self.m_num_avg:
if test_flux > 0:
ratio = flux/test_flux
# We have 2 convergence criteria:
# 1. The average flux does not change
# 2. The flux correction factor is small
if ratio >= 0.99 and ratio <= 1.01 and \
correct >= 0.9 and correct <= 1.1:
if self.logTerse():
self.log(" Converged ("+str(ratio)+")\n")
break
else:
if self.logTerse():
self.log(" Flux is zero.\n")
break
# Use average for next iteration
test_flux = flux
# Exit loop if number of trials exhausted
if (iter >= self.m_max_iter):
if self.logTerse():
self.log(" Test ended after "+str(self.m_max_iter)+" iterations.\n")
break
# Write fit results
if self.logTerse():
self.log.header3("Fit results")
self.log.parformat("Test statistics")
self.log(ts)
self.log("\n")
self.log.parformat("Photon flux")
self.log(pflux)
self.log(" ph/cm2/s\n")
self.log.parformat("Energy flux")
self.log(eflux)
self.log(" erg/cm2/s\n")
self.log.parformat("Crab flux")
self.log(cflux*1000.0)
self.log(" mCrab\n")
self.log.parformat("Differential sensitivity")
self.log(diffSens)
self.log(" erg/cm2/s\n")
self.log.parformat("Number of simulated events")
self.log(nevents)
self.log("\n")
self.log.header3("Background and test source model fitting")
self.log.parformat("log likelihood")
self.log(LogL_all)
self.log("\n")
self.log.parformat("Number of predicted events")
self.log(npred_all)
self.log("\n")
for model in result_all:
self.log.parformat("Model")
self.log(model.name())
self.log("\n")
for par in model:
self.log(str(par)+"\n")
self.log.header3("Background model fit")
self.log.parformat("log likelihood")
self.log(LogL_bgm)
self.log("\n")
self.log.parformat("Number of predicted events")
self.log(npred_bgm)
self.log("\n")
for model in result_bgm:
self.log.parformat("Model")
self.log(model.name())
self.log("\n")
for par in model:
self.log(str(par)+"\n")
# Store result
result = {'loge': loge, 'emin': emin.TeV(), 'emax': emax.TeV(), \
'crab': flux, 'pflux': pflux, 'eflux': eflux, \
'diffSens': diffSens}
# Return result
return result
# ======================== #
# Main routine entry point #
# ======================== #
if __name__ == '__main__':
"""
CTA ctlike-based sensitivity estimator.
"""
# Create instance of application
app = cssens(sys.argv)
# Run application
app.execute()
# Remove any existing result files
list = [glob.glob("*.fits"), glob.glob("*.log"), glob.glob("*.xml")]
for files in list:
for file in files:
os.remove(file)
# Setup single observation survey
#obs = survey_single()
obs = survey_gplane()
# Add background model
obs = add_background_model(obs)
# Simulate events
print("Simulate events")
obs = obsutils.sim(obs)
# Make counts map
print("Make counts map")
cntmap = obsutils.cntmap(obs)
# Fit observations
print("Fit observatins")
like = obsutils.fit(obs)
#print like.opt()
#print like.obs().models()
# Make model map
print("Make model map (this step will take some time)")
modmap = obsutils.modmap(obs)
def trial(self, seed):
"""
Create the pull for a single trial.
Parameters:
seed - Random number generator seed
"""
# Write header
if self.logExplicit():
self.log.header2("Trial " + str(seed + 1))
# Simulate events
obs = obsutils.sim(self.obs, \
nbins=self.m_enumbins, \
seed=seed, \
binsz=self.m_binsz, \
npix=self.m_npix, \
log=self.m_log, debug=self.m_debug)
# Determine number of events in simulation
nevents = 0.0
for run in obs:
nevents += run.events().number()
# Write simulation results
if self.logExplicit():
self.log.header3("Simulation")
self.log.parformat("Number of simulated events")
self.log(nevents)
self.log("\n")
# Fit model
like = obsutils.fit(obs, log=self.m_log, debug=self.m_debug)
# Store results
logL = like.opt().value()
npred = like.obs().npred()
models = like.obs().models()
# Write result header
if self.logExplicit():
self.log.header3("Pulls")
# Gather results
colnames = []
values = {}
for i in range(models.size()):
model = models[i]
model_name = model.name()
for k in range(model.size()):
par = model[k]
if par.isfree():
# Set parameter name
name = model_name + "_" + par.name()
# Append parameter, Pull_parameter and Unc_parameter
colnames.append(name)
colnames.append("Pull_" + name)
colnames.append("Unc_" + name)
# Compute pull
fitted_value = par.value()
real_value = self.model[i][k].value()
error = par.error()
if error != 0.0:
pull = (fitted_value - real_value) / error
else:
pull = 99.0
# Store results
values[name] = fitted_value
values["Pull_" + name] = pull
values["Unc_" + name] = error
# Write result
if self.logExplicit():
self.log.parformat(name)
self.log(pull)
self.log(" (")
self.log(fitted_value)
self.log(" +/- ")
self.log(error)
self.log(")\n")
# Bundle together results
result = {'colnames': colnames, 'values': values}
# Return
return result
def get_sensitivity(self, obs, bkg_model, full_model):
"""
Determine sensitivity for a given observations.
Parameters:
obs - Observation container
bkg_model - Background model
full_model - Source model
"""
# Set TeV->erg conversion factor
tev2erg = 1.6021764
# Determine energy boundaries from first observation in
# the container
for run in obs:
emin = run.events().ebounds().emin()
emax = run.events().ebounds().emax()
loge = math.log10(math.sqrt(emin.TeV()*emax.TeV()))
erg_mean = math.pow(10.0, loge) * tev2erg
erg_width = (emax.TeV()-emin.TeV()) * tev2erg
break
# Write header
if self.logTerse():
self.log("\n")
self.log.header2("Energies: "+str(emin)+" - "+str(emax))
# Initialise loop
flux_value = []
pflux_value = []
eflux_value = []
diffSens_value = []
iter = 0
test_flux = 0.1 # This is the initial test flux in Crab units
# Loop until we break
while True:
# Update iteration counter
iter += 1
# Write header
if self.logExplicit():
self.log.header2("Iteration "+str(iter))
# Set test flux
full_model["Test"]['Prefactor'].value(test_flux)
obs.models(full_model)
# Simulate events
sim = obsutils.sim(obs, nbins=self.m_nbins, seed=iter, \
binsz=self.m_binsz, npix=self.m_npix, \
log=self.m_log, debug=self.m_debug)
# Determine number of events in simulation
nevents = 0.0
for run in sim:
nevents += run.events().number()
# Write simulation results
if self.logExplicit():
self.log.header3("Simulation")
self.log.parformat("Number of simulated events")
self.log(nevents)
self.log("\n")
# Fit background only
sim.models(bkg_model)
like = obsutils.fit(sim, log=self.m_log, debug=self.m_debug)
result_bgm = like.obs().models().copy()
LogL_bgm = like.opt().value()
npred_bgm = like.obs().npred()
# Assess quality based on a comparison between Npred and Nevents
quality_bgm = npred_bgm-nevents
# Write background fit results
if self.logExplicit():
self.log.header3("Background model fit")
self.log.parformat("log likelihood")
self.log(LogL_bgm)
self.log("\n")
self.log.parformat("Number of predicted events")
self.log(npred_bgm)
self.log("\n")
self.log.parformat("Fit quality")
self.log(quality_bgm)
self.log("\n")
# Start over if the fit quality was bad
if abs(quality_bgm) > 3.0:
if self.logExplicit():
self.log("Fit quality outside required range. Start over.\n")
continue
# Write model fit results
if self.logExplicit():
for model in result_bgm:
self.log.parformat("Model")
self.log(model.name())
self.log("\n")
for par in model:
self.log(str(par)+"\n")
# Fit background and test source
sim.models(full_model)
like = obsutils.fit(sim, log=self.m_log, debug=self.m_debug)
result_all = like.obs().models().copy()
LogL_all = like.opt().value()
npred_all = like.obs().npred()
ts = 2.0*(LogL_bgm-LogL_all)
# Assess quality based on a comparison between Npred and Nevents
quality_all = npred_all-nevents
# Write background and test source fit results
if self.logExplicit():
self.log.header3("Background and test source model fit")
self.log.parformat("Test statistics")
self.log(ts)
self.log("\n")
self.log.parformat("log likelihood")
self.log(LogL_all)
self.log("\n")
self.log.parformat("Number of predicted events")
self.log(npred_all)
self.log("\n")
self.log.parformat("Fit quality")
self.log(quality_all)
self.log("\n")
#
for model in result_all:
self.log.parformat("Model")
self.log(model.name())
self.log("\n")
for par in model:
self.log(str(par)+"\n")
# Start over if the fit quality was bad
if abs(quality_all) > 3.0:
if self.logExplicit():
self.log("Fit quality outside required range. Start over.\n")
continue
# Start over if TS was non-positive
if ts <= 0.0:
if self.logExplicit():
self.log("Non positive TS. Start over.\n")
continue
# Get fitted Crab, photon and energy fluxes
cflux = result_all["Test"]['Prefactor'].value()
cflux_err = result_all["Test"]['Prefactor'].error()
pflux = result_all["Test"].spectral().flux(emin, emax)
eflux = result_all["Test"].spectral().eflux(emin, emax)
# Compute differential sensitivity
diffSens = pflux / erg_width * erg_mean*erg_mean
# Compute flux correction factor based on average TS
correct = 1.0
if self.m_use_ts:
if ts > 0:
correct = math.sqrt(self.m_ts_thres/ts)
else:
if cflux > 0 and cflux_err > 0:
correct = math.sqrt(self.m_ts_thres)/(cflux/cflux_err)
# Compute extrapolated fluxes
flux = correct * cflux
pflux = correct * pflux
eflux = correct * eflux
diffSens = correct * diffSens
flux_value.append(flux)
pflux_value.append(pflux)
eflux_value.append(eflux)
diffSens_value.append(diffSens)
# Write background and test source fit results
if self.logExplicit():
self.log.parformat("Photon flux")
self.log(pflux)
self.log(" ph/cm2/s\n")
self.log.parformat("Energy flux")
self.log(eflux)
self.log(" erg/cm2/s\n")
self.log.parformat("Crab flux")
self.log(cflux*1000.0)
self.log(" mCrab\n")
self.log.parformat("Differential sensitivity")
self.log(diffSens)
self.log(" erg/cm2/s\n")
for model in result_all:
self.log.parformat("Model")
self.log(model.name())
self.log("\n")
for par in model:
self.log(str(par)+"\n")
elif self.logTerse():
self.log.parformat("Iteration "+str(iter))
self.log("TS=")
self.log(ts)
self.log(" ")
self.log("corr=")
self.log(correct)
self.log(" ")
self.log(pflux)
self.log(" ph/cm2/s = ")
self.log(eflux)
self.log(" erg/cm2/s = ")
self.log(cflux*1000.0)
self.log(" mCrab = ")
self.log(diffSens)
self.log(" erg/cm2/s\n")
# Compute sliding average of extrapolated fitted prefactor,
# photon and energy flux. This damps out fluctuations and
# improves convergence
flux = 0.0
pflux = 0.0
eflux = 0.0
diffSens = 0.0
num = 0.0
for k in range(self.m_num_avg):
inx = len(flux_value) - k - 1
if inx >= 0:
flux += flux_value[inx]
pflux += pflux_value[inx]
eflux += eflux_value[inx]
diffSens += diffSens_value[inx]
num += 1.0
flux /= num
pflux /= num
eflux /= num
diffSens /= num
# Compare average flux to last average
if iter > self.m_num_avg:
if test_flux > 0:
ratio = flux/test_flux
# We have 2 convergence criteria:
# 1. The average flux does not change
# 2. The flux correction factor is small
if ratio >= 0.99 and ratio <= 1.01 and \
correct >= 0.9 and correct <= 1.1:
if self.logTerse():
self.log(" Converged ("+str(ratio)+")\n")
break
else:
if self.logTerse():
self.log(" Flux is zero.\n")
break
# Use average for next iteration
test_flux = flux
# Exit loop if number of trials exhausted
if (iter >= self.m_max_iter):
if self.logTerse():
self.log(" Test ended after "+str(self.m_max_iter)+" iterations.\n")
break
# Write fit results
if self.logTerse():
self.log.header3("Fit results")
self.log.parformat("Test statistics")
self.log(ts)
self.log("\n")
self.log.parformat("Photon flux")
self.log(pflux)
self.log(" ph/cm2/s\n")
self.log.parformat("Energy flux")
self.log(eflux)
self.log(" erg/cm2/s\n")
self.log.parformat("Crab flux")
self.log(cflux*1000.0)
self.log(" mCrab\n")
self.log.parformat("Differential sensitivity")
self.log(diffSens)
self.log(" erg/cm2/s\n")
self.log.parformat("Number of simulated events")
self.log(nevents)
self.log("\n")
self.log.header3("Background and test source model fitting")
self.log.parformat("log likelihood")
self.log(LogL_all)
self.log("\n")
self.log.parformat("Number of predicted events")
self.log(npred_all)
self.log("\n")
for model in result_all:
self.log.parformat("Model")
self.log(model.name())
self.log("\n")
for par in model:
self.log(str(par)+"\n")
self.log.header3("Background model fit")
self.log.parformat("log likelihood")
self.log(LogL_bgm)
self.log("\n")
self.log.parformat("Number of predicted events")
self.log(npred_bgm)
self.log("\n")
for model in result_bgm:
self.log.parformat("Model")
self.log(model.name())
self.log("\n")
for par in model:
self.log(str(par)+"\n")
# Store result
result = {'loge': loge, 'emin': emin.TeV(), 'emax': emax.TeV(), \
'crab': flux, 'pflux': pflux, 'eflux': eflux, \
'diffSens': diffSens}
# Return result
return result
def trial(self, seed):
"""
Create the TS for a single trial.
Parameters:
seed - Random number generator seed
"""
# Write header
if self.logExplicit():
self.log.header2("Trial " + str(seed + 1))
# Simulate events
sim = obsutils.sim(self.obs, \
nbins=self.m_enumbins, \
seed=seed, \
binsz=self.m_binsz, \
npix=self.m_npix, \
log=self.m_log, debug=self.m_debug)
# Determine number of events in simulation
nevents = 0.0
for run in sim:
nevents += run.events().number()
# Write simulation results
if self.logExplicit():
self.log.header3("Simulation")
self.log.parformat("Number of simulated events")
self.log(nevents)
self.log("\n")
# Fit background only
sim.models(self.bkg_model)
like_bgm = obsutils.fit(sim, log=self.m_log, debug=self.m_debug)
result_bgm = like_bgm.obs().models()
LogL_bgm = like_bgm.opt().value()
npred_bgm = like_bgm.obs().npred()
# Write background fit results
if self.logExplicit():
self.log.header3("Background model fit")
self.log.parformat("log likelihood")
self.log(LogL_bgm)
self.log("\n")
self.log.parformat("Number of predicted events")
self.log(npred_bgm)
self.log("\n")
for model in result_bgm:
self.log.parformat("Model")
self.log(model.name())
self.log("\n")
for par in model:
self.log(str(par) + "\n")
# Fit background and test source
sim.models(self.full_model)
like_all = obsutils.fit(sim, log=self.m_log, debug=self.m_debug)
result_all = like_all.obs().models()
LogL_all = like_all.opt().value()
npred_all = like_all.obs().npred()
ts = 2.0 * (LogL_bgm - LogL_all)
# Write background and test source fit results
if self.logExplicit():
self.log.header3("Background and test source model fit")
self.log.parformat("Test statistics")
self.log(ts)
self.log("\n")
self.log.parformat("log likelihood")
self.log(LogL_all)
self.log("\n")
self.log.parformat("Number of predicted events")
self.log(npred_all)
self.log("\n")
for model in result_all:
self.log.parformat("Model")
self.log(model.name())
self.log("\n")
for par in model:
self.log(str(par) + "\n")
# Write result
elif self.logTerse():
self.log.parformat("Trial " + str(seed))
self.log("TS=")
self.log(ts)
self.log(" Prefactor=")
self.log(result_all["Test"]["Prefactor"].value())
self.log("+/-")
self.log(result_all["Test"]["Prefactor"].error())
self.log("\n")
# Initialise results
colnames = []
values = {}
# Set TS value
colnames.append("TS")
values["TS"] = ts
# Set logL for background fit
colnames.append("LogL_bgm")
values["LogL_bgm"] = LogL_bgm
# Set logL for full fit
colnames.append("LogL_all")
values["LogL_all"] = LogL_all
# Set Nevents
colnames.append("Nevents")
values["Nevents"] = nevents
# Set Npred for background fit
colnames.append("Npred_bkg")
values["Npred_bkg"] = npred_bgm
# Set Npred for full fit
colnames.append("Npred_all")
values["Npred_all"] = npred_all
# Gather free full fit parameters
for i in range(result_all.size()):
model = result_all[i]
model_name = model.name()
for k in range(model.size()):
par = model[k]
if par.isfree():
# Set parameter name
name = model_name + "_" + par.name()
# Append value
colnames.append(name)
values[name] = par.value()
# Append error
name = "Unc_" + name
colnames.append(name)
values[name] = par.error()
# Bundle together results
result = {'colnames': colnames, 'values': values}
# Return
return result
def get_sensitivity(self, obs, bkg_model, full_model):
"""
Determine sensitivity for a given observations.
Parameters:
obs - Observation container
bkg_model - Background model
full_model - Source model
"""
# Set TeV->erg conversion factor
tev2erg = 1.6021764
# Determine energy boundaries from first observation in
# the container
for run in obs:
emin = run.events().ebounds().emin()
emax = run.events().ebounds().emax()
loge = math.log10(math.sqrt(emin.TeV() * emax.TeV()))
erg_mean = math.pow(10.0, loge) * tev2erg
erg_width = (emax.TeV() - emin.TeV()) * tev2erg
break
# Write header
if self.logTerse():
self.log("\n")
self.log.header2("Energies: " + str(emin) + " - " + str(emax))
# Initialise loop
flux_value = []
pflux_value = []
eflux_value = []
diffSens_value = []
iter = 0
test_flux = 0.1 # This is the initial test flux in Crab units
# Loop until we break
while True:
# Update iteration counter
iter += 1
# Write header
if self.logExplicit():
self.log.header2("Iteration " + str(iter))
# Set test flux
full_model["Test"]['Prefactor'].value(test_flux)
obs.models(full_model)
# Simulate events
sim = obsutils.sim(obs, nbins=self.m_nbins, seed=iter, \
binsz=self.m_binsz, npix=self.m_npix, \
log=self.m_log, debug=self.m_debug)
# Determine number of events in simulation
nevents = 0.0
for run in sim:
nevents += run.events().number()
# Write simulation results
if self.logExplicit():
self.log.header3("Simulation")
self.log.parformat("Number of simulated events")
self.log(nevents)
self.log("\n")
# Fit background only
sim.models(bkg_model)
like = obsutils.fit(sim, log=self.m_log, debug=self.m_debug)
result_bgm = like.obs().models().copy()
LogL_bgm = like.opt().value()
npred_bgm = like.obs().npred()
# Assess quality based on a comparison between Npred and Nevents
quality_bgm = npred_bgm - nevents
# Write background fit results
if self.logExplicit():
self.log.header3("Background model fit")
self.log.parformat("log likelihood")
self.log(LogL_bgm)
self.log("\n")
self.log.parformat("Number of predicted events")
self.log(npred_bgm)
self.log("\n")
self.log.parformat("Fit quality")
self.log(quality_bgm)
self.log("\n")
# Start over if the fit quality was bad
if abs(quality_bgm) > 3.0:
if self.logExplicit():
self.log(
"Fit quality outside required range. Start over.\n")
continue
# Write model fit results
if self.logExplicit():
for model in result_bgm:
self.log.parformat("Model")
self.log(model.name())
self.log("\n")
for par in model:
self.log(str(par) + "\n")
# Fit background and test source
sim.models(full_model)
like = obsutils.fit(sim, log=self.m_log, debug=self.m_debug)
result_all = like.obs().models().copy()
LogL_all = like.opt().value()
npred_all = like.obs().npred()
ts = 2.0 * (LogL_bgm - LogL_all)
# Assess quality based on a comparison between Npred and Nevents
quality_all = npred_all - nevents
# Write background and test source fit results
if self.logExplicit():
self.log.header3("Background and test source model fit")
self.log.parformat("Test statistics")
self.log(ts)
self.log("\n")
self.log.parformat("log likelihood")
self.log(LogL_all)
self.log("\n")
self.log.parformat("Number of predicted events")
self.log(npred_all)
self.log("\n")
self.log.parformat("Fit quality")
self.log(quality_all)
self.log("\n")
#
for model in result_all:
self.log.parformat("Model")
self.log(model.name())
self.log("\n")
for par in model:
self.log(str(par) + "\n")
# Start over if the fit quality was bad
if abs(quality_all) > 3.0:
if self.logExplicit():
self.log(
"Fit quality outside required range. Start over.\n")
continue
# Start over if TS was non-positive
if ts <= 0.0:
if self.logExplicit():
self.log("Non positive TS. Start over.\n")
continue
# Get fitted Crab, photon and energy fluxes
cflux = result_all["Test"]['Prefactor'].value()
cflux_err = result_all["Test"]['Prefactor'].error()
pflux = result_all["Test"].spectral().flux(emin, emax)
eflux = result_all["Test"].spectral().eflux(emin, emax)
# Compute differential sensitivity
diffSens = pflux / erg_width * erg_mean * erg_mean
# Compute flux correction factor based on average TS
correct = 1.0
if self.m_use_ts:
if ts > 0:
correct = math.sqrt(self.m_ts_thres / ts)
else:
if cflux > 0 and cflux_err > 0:
correct = math.sqrt(self.m_ts_thres) / (cflux / cflux_err)
# Compute extrapolated fluxes
flux = correct * cflux
pflux = correct * pflux
eflux = correct * eflux
diffSens = correct * diffSens
flux_value.append(flux)
pflux_value.append(pflux)
eflux_value.append(eflux)
diffSens_value.append(diffSens)
# Write background and test source fit results
if self.logExplicit():
self.log.parformat("Photon flux")
self.log(pflux)
self.log(" ph/cm2/s\n")
self.log.parformat("Energy flux")
self.log(eflux)
self.log(" erg/cm2/s\n")
self.log.parformat("Crab flux")
self.log(cflux * 1000.0)
self.log(" mCrab\n")
self.log.parformat("Differential sensitivity")
self.log(diffSens)
self.log(" erg/cm2/s\n")
for model in result_all:
self.log.parformat("Model")
self.log(model.name())
self.log("\n")
for par in model:
self.log(str(par) + "\n")
elif self.logTerse():
self.log.parformat("Iteration " + str(iter))
self.log("TS=")
self.log(ts)
self.log(" ")
self.log("corr=")
self.log(correct)
self.log(" ")
self.log(pflux)
self.log(" ph/cm2/s = ")
self.log(eflux)
self.log(" erg/cm2/s = ")
self.log(cflux * 1000.0)
self.log(" mCrab = ")
self.log(diffSens)
self.log(" erg/cm2/s\n")
# Compute sliding average of extrapolated fitted prefactor,
# photon and energy flux. This damps out fluctuations and
# improves convergence
flux = 0.0
pflux = 0.0
eflux = 0.0
diffSens = 0.0
num = 0.0
for k in range(self.m_num_avg):
inx = len(flux_value) - k - 1
if inx >= 0:
flux += flux_value[inx]
pflux += pflux_value[inx]
eflux += eflux_value[inx]
diffSens += diffSens_value[inx]
num += 1.0
flux /= num
pflux /= num
eflux /= num
diffSens /= num
# Compare average flux to last average
if iter > self.m_num_avg:
if test_flux > 0:
ratio = flux / test_flux
# We have 2 convergence criteria:
# 1. The average flux does not change
# 2. The flux correction factor is small
if ratio >= 0.99 and ratio <= 1.01 and \
correct >= 0.9 and correct <= 1.1:
if self.logTerse():
self.log(" Converged (" + str(ratio) + ")\n")
break
else:
if self.logTerse():
self.log(" Flux is zero.\n")
break
# Use average for next iteration
test_flux = flux
# Exit loop if number of trials exhausted
if (iter >= self.m_max_iter):
if self.logTerse():
self.log(" Test ended after " + str(self.m_max_iter) +
" iterations.\n")
break
# Write fit results
if self.logTerse():
self.log.header3("Fit results")
self.log.parformat("Test statistics")
self.log(ts)
self.log("\n")
self.log.parformat("Photon flux")
self.log(pflux)
self.log(" ph/cm2/s\n")
self.log.parformat("Energy flux")
self.log(eflux)
self.log(" erg/cm2/s\n")
self.log.parformat("Crab flux")
self.log(cflux * 1000.0)
self.log(" mCrab\n")
self.log.parformat("Differential sensitivity")
self.log(diffSens)
self.log(" erg/cm2/s\n")
self.log.parformat("Number of simulated events")
self.log(nevents)
self.log("\n")
self.log.header3("Background and test source model fitting")
self.log.parformat("log likelihood")
self.log(LogL_all)
self.log("\n")
self.log.parformat("Number of predicted events")
self.log(npred_all)
self.log("\n")
for model in result_all:
self.log.parformat("Model")
self.log(model.name())
self.log("\n")
for par in model:
self.log(str(par) + "\n")
self.log.header3("Background model fit")
self.log.parformat("log likelihood")
self.log(LogL_bgm)
self.log("\n")
self.log.parformat("Number of predicted events")
self.log(npred_bgm)
self.log("\n")
for model in result_bgm:
self.log.parformat("Model")
self.log(model.name())
self.log("\n")
for par in model:
self.log(str(par) + "\n")
# Store result
result = {'loge': loge, 'emin': emin.TeV(), 'emax': emax.TeV(), \
'crab': flux, 'pflux': pflux, 'eflux': eflux, \
'diffSens': diffSens}
# Return result
return result