FLUX Light-Curve example (GRB)
We provide a companion notebook (``speclc_grbdc3_prep.ipynb``) that downloads the files and prepares them for analysis. The notebook creates in the working directory the following files:
orientation file (DC3_final_530km_3_month_with_slew_1sbins_GalacticEarth_SAA.fits)
binned data (tsel_binned_data_local_grbdc3.hdf5, tsel_binned_data_local_galbk.hdf5,tsel_binned_data_galbk_grbdc3.hdf5)
corresponding yaml file with binning info (bin_grbdc3.yaml, bin_galbk.yaml, bin_galbk_grbdc3.yaml)
detector response (ResponseContinuum.o3.e100_10000.b10log.s10396905069491.m2284.filtered.nonsparse.binnedimaging.imagingresponse.h5)
The binned data are simulations of GRB 081207680 and Galactic photon background produced for Data Challenge 3. In the data preparation, the background file is cut in time 100s before and after the GRB time window (t_start=1836496300.0, t_stop=1836496388.1, duration=88s) to ensure enough statistics.
This notebook slices a COSI dataset into time bins, ensuring that a minimum signal-to-noise of 10 is reached in each bin. Perform a fit with 3ML in each of them. It finally examines the time series of flux and fitted spectral parameters. It saves: a txt file of the raw lightcurves (lc.dat); a plot at each iteration of the fit (fit_i.pdf); a txt file (spec_lc.dat) including the mid-point of each time bin with errors, the total counts, the fluxes with asymmetric errors, the fitted parameters with symmetric errors; two plots (raw_flux_counts_lc.pdf, specpars_bk_lc.pdf) of the final time series.
[1]:
from cosipy import BinnedData
from cosipy.spacecraftfile import SpacecraftHistory
from cosipy.response.FullDetectorResponse import FullDetectorResponse
from cosipy.util import fetch_wasabi_file
from cosipy.statistics import PoissonLikelihood
from cosipy.background_estimation import FreeNormBinnedBackground
from cosipy.interfaces import ThreeMLPluginInterface
from cosipy.response import BinnedThreeMLModelFolding, BinnedInstrumentResponse, BinnedThreeMLPointSourceResponse
from cosipy.data_io import EmCDSBinnedData
from scoords import SpacecraftFrame
from astropy.time import Time, TimeDelta
import astropy.units as u
from astropy.coordinates import SkyCoord
from astropy.stats import poisson_conf_interval
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
from threeML import *
from threeML import Band, PointSource, Model, JointLikelihood, DataList
from cosipy import Band_Eflux
from astromodels import Parameter
from pathlib import Path
from cosipy.pipeline.src.plotting import *
import os
import subprocess
/home/sciaccaluga/Softwares/anaconda3/envs/cosi2/lib/python3.10/site-packages/astromodels/utils/file_utils.py:8: UserWarning: pkg_resources is deprecated as an API. See https://setuptools.pypa.io/en/latest/pkg_resources.html. The pkg_resources package is slated for removal as early as 2025-11-30. Refrain from using this package or pin to Setuptools<81.
import pkg_resources
15:54:37 WARNING The naima package is not available. Models that depend on it will not be functions.py:47 available
WARNING The GSL library or the pygsl wrapper cannot be loaded. Models that depend on it functions.py:68 will not be available.
WARNING The ebltable package is not available. Models that depend on it will not be absorption.py:33 available
15:54:38 INFO Starting 3ML! __init__.py:39
WARNING WARNINGs here are NOT errors __init__.py:40
WARNING but are inform you about optional packages that can be installed __init__.py:41
WARNING to disable these messages, turn off start_warning in your config file __init__.py:44
15:54:38 WARNING ROOT minimizer not available minimization.py:1345
WARNING Multinest minimizer not available minimization.py:1357
WARNING PyGMO is not available minimization.py:1369
WARNING The cthreeML package is not installed. You will not be able to use plugins which __init__.py:94 require the C/C++ interface (currently HAWC)
WARNING Could not import plugin HAWCLike.py. Do you have the relative instrument __init__.py:144 software installed and configured?
WARNING Could not import plugin FermiLATLike.py. Do you have the relative instrument __init__.py:144 software installed and configured?
WARNING No fermitools installed lat_transient_builder.py:44
WARNING Env. variable OMP_NUM_THREADS is not set. Please set it to 1 for optimal __init__.py:387 performances in 3ML
WARNING Env. variable MKL_NUM_THREADS is not set. Please set it to 1 for optimal __init__.py:387 performances in 3ML
15:54:39 WARNING Env. variable NUMEXPR_NUM_THREADS is not set. Please set it to 1 for optimal __init__.py:387 performances in 3ML
[1]:
'/home/sciaccaluga'
A function to create time slices with a minimum signal-to-noise.
In this ways the binning in time is coarser in the weak tails of the light-curve and finer around the peak. The function returns the edges of the time slices.
[2]:
def make_minsn_tslices(yaml_path, hdf5_path, min_sn):
#
data = BinnedData(yaml_path)
data.load_binned_data_from_hdf5(hdf5_path)
#
tstart=np.min(data.binned_data.axes['Time'].edges.value)
tstop=np.max(data.binned_data.axes['Time'].edges.value)
max_slices=data.binned_data.axes['Time'].nbins
step=(tstop-tstart)/max_slices
tmins = np.array([], dtype=float)
tmaxs = np.array([], dtype=float)
#
tmax=tstart
for i in range (max_slices):
#
tmin=tmax
tmax_i=tstart+(i+1)*step
#
sou_min = np.where(data.binned_data.axes['Time'].edges.value >= tmin)[0][0]
sou_max = np.where(data.binned_data.axes['Time'].edges.value <= tmax_i)[0][-1]
data_sliced=data.binned_data.slice[{'Time':slice(sou_min,sou_max)}].project('Em')
#
#
signal=np.sum(data_sliced.to_dense(copy=False).contents)
noise=np.sqrt(signal)
if signal == 0:
raise ValueError("Process halted: Bin with 0 counts. Consider a larger min_sn")
#
#
sn=signal/noise
if (sn >= min_sn and tmax_i<tstop):
tmins = np.append(tmins, tmin)
tmax=tmax_i
tmaxs = np.append(tmaxs, tmax)
elif(tmax_i>=tstop):
tmaxs[-1] = tmax_i
return(tmins, tmaxs)
Download and read in binned data
Run speclc_grbdc3_prep.ipynb to obtain the data to run this tutorial, if you haven’t yet. Products will be saved in the current directory.
Define the path to the directory containing the data, detector response, orientation file, and yaml files if they have already been downloaded, or the directory to download the files into. Define a directory where you want to save the outputs. Default is current directory.
[4]:
indir=str(".")
data_path = Path(indir)
odir= str(".")
Create BinnedData objects for the GRB only, GRB+background, and background only. The GRB only simulation is not used for the spectral fit, but can be used to compare the fitted spectrum to the source simulation
[5]:
grb = BinnedData(data_path / "bin_grbdc3.yaml")
grb_bkg = BinnedData(data_path / "bin_galbk_grbdc3.yaml")
bkg = BinnedData(data_path / "bin_galbk.yaml")
Load binned .hdf5 files
[6]:
grb.load_binned_data_from_hdf5(binned_data=data_path / "tsel_binned_data_local_grbdc3.hdf5")
grb_bkg.load_binned_data_from_hdf5(binned_data=data_path / "tsel_binned_data_local_galbk_grbdc3.hdf5")
bkg.load_binned_data_from_hdf5(binned_data=data_path / "tsel_binned_data_local_galbk.hdf5")
Define the path to the detector response
[7]:
dr = FullDetectorResponse.open(data_path / "ResponseContinuum.o3.e100_10000.b10log.s10396905069491.m2284.filtered.nonsparse.binnedimaging.imagingresponse.h5")
ori = SpacecraftHistory.open(data_path/"DC3_final_530km_3_month_with_slew_1sbins_GalacticEarth_SAA.fits")
Define the model to be fitted and initialize the parameters of the fits to something reasonable. In this example, for better results, we keep the indices and the pivot energy frozen. Hence, the free parameters are the normalization and the background parameter.
[8]:
#Model to be fitted
# # Setting parameters to something reasonable helps the fitting to converge\n",
beta = -2.09
l = 177.42
b = -9.41
alpha = -0.58
xp = 298.1 * u.keV
piv = 500. * u.keV
K = 0.1 / u.cm / u.cm / u.s / u.keV
spectrum = Band()
spectrum.beta.min_value = -15.0
spectrum.alpha.value = alpha
spectrum.alpha.free=False
spectrum.beta.value = beta
spectrum.beta.free=False
spectrum.xp.value = xp.value
spectrum.xp.free=False
spectrum.K.value = K.value
spectrum.piv.value = piv.value
spectrum.xp.unit = xp.unit
spectrum.K.unit = K.unit
spectrum.piv.unit = piv.unit
spectrum
[8]:
- description: Band model from Band et al., 1993, parametrized with the peak energy
- formula: $K \begin{cases} \left(\frac{x}{piv}\right)^{\alpha} \exp \left(-\frac{(2+\alpha) x}{x_{p}}\right) & x \leq (\alpha-\beta) \frac{x_{p}}{(\alpha+2)} \\ \left(\frac{x}{piv}\right)^{\beta} \exp (\beta-\alpha)\left[\frac{(\alpha-\beta) x_{p}}{piv(2+\alpha)}\right]^{\alpha-\beta} &x>(\alpha-\beta) \frac{x_{p}}{(\alpha+2)} \end{cases} $
- parameters:
- K:
- value: 0.1
- desc: Differential flux at the pivot energy
- min_value: 1e-50
- max_value: None
- unit: keV-1 s-1 cm-2
- is_normalization: True
- delta: 1e-05
- free: True
- alpha:
- value: -0.58
- desc: low-energy photon index
- min_value: -1.5
- max_value: 3.0
- unit:
- is_normalization: False
- delta: 0.1
- free: False
- xp:
- value: 298.09999999999997
- desc: peak in the x * x * N (nuFnu if x is a energy)
- min_value: 10.0
- max_value: None
- unit: keV
- is_normalization: False
- delta: 50.0
- free: False
- beta:
- value: -2.09
- desc: high-energy photon index
- min_value: -15.0
- max_value: -1.6
- unit:
- is_normalization: False
- delta: 0.2
- free: False
- piv:
- value: 500.0
- desc: pivot energy
- min_value: None
- max_value: None
- unit: keV
- is_normalization: False
- delta: 10.0
- free: False
- K:
Move to the product directory.
[9]:
os.chdir(odir)
Find time window of the GRB data and make a raw lightcurve to be plotted as a comparison.
[10]:
grb_bkg.get_raw_lightcurve(binned_data=data_path / "tsel_binned_data_local_grbdc3.hdf5", output_name="lc")
time, rate = np.loadtxt("lc.dat", skiprows=1, unpack=True)
grb_bkg.binned_data.project('Time').plot()
[10]:
(<Axes: xlabel='Time [s]'>, <ErrorbarContainer object of 3 artists>)
Now we use the make_minsn_tslices function to create N time slices with a minimum signal to noise of 10. You can customize the requirement of a minimum signal to noise to create less or more bins. We used them to slice the data in time.
[11]:
min_sn=10
yaml_path=data_path / "bin_galbk_grbdc3.yaml"
hdf5_path=data_path / "tsel_binned_data_local_galbk_grbdc3.hdf5"
tmins,tmaxs=make_minsn_tslices(yaml_path,hdf5_path,min_sn)
len(tmins)
[11]:
4
Now we used them to slice the data in time. We perform N spectral fits to determine fluxes and spectral parameters as a function of time. We save all the time series in a text file.
[13]:
#
#Initialize empty vectors that will be filled at each step.
#
tmins_lc=np.array([])
tmaxs_lc=np.array([])
tmeds_lc=np.array([])
e_tmeds_lc=np.array([])
#
cts_lc=np.array([])
fls=np.array([])
e_low_fls=np.array([])
e_hi_fls=np.array([])
#
pars_bk=np.array([])
epars_bk=np.array([])
#
par_epar=np.array([])
#
# sc orientation for background
tmin_bk = Time(bkg.tmin, format='unix')
tmax_bk = Time(bkg.tmax, format='unix')
sc_orientation_bk = ori.select_interval(tmin_bk, tmax_bk)
for i in range(len(tmaxs)):
#
#Slice the orientation file into the time interval
#
ori_min = Time(tmins[i],format = 'unix')
ori_max = Time(tmaxs[i],format = 'unix')
sc_orientation = ori.select_interval(ori_min, ori_max)
#
#
#Find the index of time axes corresponding to the limits of the tmins[i],tmaxs[i].
#These are used to slice the data in time in the fit setup.
#
#
sou_min = np.where(grb_bkg.binned_data.axes['Time'].edges.value >= tmins[i])[0][0]
sou_max = np.where(grb_bkg.binned_data.axes['Time'].edges.value <= tmaxs[i])[0][-1]
#
#Save the time bin edges and middle points for plotting later.
#
tmin_lc=grb_bkg.binned_data.axes['Time'].edges.value[sou_min]
tmins_lc=np.append(tmins_lc,tmin_lc)
#
tmax_lc=grb_bkg.binned_data.axes['Time'].edges.value[sou_max]
tmaxs_lc=np.append(tmaxs_lc,tmax_lc)
#
dt=(tmax_lc-tmin_lc) #total duration of the time bin
tmed_lc=tmin_lc+0.5*dt#midpoint of time bins
tmeds_lc=np.append(tmeds_lc,tmed_lc)#midpoints of the time bin
hdt=dt/2 #half duration of the time bin i.e symmetric error for t_med
e_tmeds_lc=np.append(e_tmeds_lc,hdt)#half duration of the time bin i.e symmetric error for t_med
data = EmCDSBinnedData(grb_bkg.binned_data.slice[{'Time':slice(sou_min,sou_max)}].project('Em', 'Phi', 'PsiChi'))
bkg_wrap = FreeNormBinnedBackground({'bkg_gal': bkg.binned_data.project('Em', 'Phi', 'PsiChi')},
sc_history = sc_orientation_bk,
copy = False)
instrument_response = BinnedInstrumentResponse(dr, data)
psr = BinnedThreeMLPointSourceResponse(data = data,
instrument_response = instrument_response,
sc_history=sc_orientation,
energy_axis = dr.axes['Ei'],
polarization_axis = dr.axes['Pol'] if 'Pol' in dr.axes.labels else None,
nside = 2*data.axes['PsiChi'].nside)
response = BinnedThreeMLModelFolding(data = data, point_source_response = psr)
like_fun = PoissonLikelihood(data, response, bkg_wrap)
cosi = ThreeMLPluginInterface('cosi',
like_fun,
response,
bkg_wrap)
cosi.bkg_parameter["bkg_gal"] = Parameter('bkg_gal', # background parameter
1, # initial value of parameter
min_value=0, # minimum value of parameter
max_value= 20, # maximum value of parameter
delta=0.05, # initial step used by fitting engine
unit = u.Hz
)
source = PointSource("source", # Name of source (arbitrary, but needs to be unique)
l = l, # Longitude (deg)
b = b, # Latitude (deg)
spectral_shape = spectrum) # Spectral model
model = Model(source) # Model with single source. If we had multiple sources, we would do Model(source1, source2, ...)
# Optional: if you want to call get_log_like manually, then you also need to set the model manually
# 3ML does this internally during the fit though
cosi.set_model(model)
plugins = DataList(cosi) # If we had multiple instruments, we would do e.g. DataList(cosi, lat, hawc, ...)
#
like = JointLikelihood(model, plugins, verbose = False)
like.fit()
results = like.results
#
#
#Obtain counts in time slices:
#
cts=np.sum(grb_bkg.binned_data.slice[{'Time':slice(sou_min,sou_max)}])
cts_lc=np.append(cts_lc,cts)
#
#Obtain parameters:
#
#bk
#
par_bk=results.get_variates("bkg_gal").median
pars_bk=np.append(pars_bk,par_bk)
epar_bk=results.get_variates("bkg_gal").std
epars_bk=np.append(epars_bk,epar_bk)
#
#These are dictionaries of parameters values and errors.
#
par_bf= {par.name:results.get_variates(par.path).median
for par in results.optimized_model["source"].parameters.values()
if par.free}
#
epar_bf= {par.name:results.get_variates(par.path).std
for par in results.optimized_model["source"].parameters.values()
if par.free}
#
par_list = list(par_bf.keys()) #This is a list of the parameter names.
for j in range(len(par_list)):
par_epar=np.append(par_epar,par_bf[par_list[j]])
par_epar=np.append(par_epar,epar_bf[par_list[j]])
#
#Obtain fluxes:
#Here I use the 3ML method to ge integrated flux in an energy range.
#I use the energy range from the data 100--10000 keV
#
threeML_config.point_source.integrate_flux_method = "trapz"
result_fl=results.get_flux(
ene_min=100. * u.keV,
ene_max= 10000.* u.keV,
confidence_level=0.95,
sum_sources=True,
flux_unit="1/(cm2 s)"
)
#
fl=result_fl["flux"].values[0].value
fls=np.append(fls,fl)
e_low_fl=np.abs(result_fl["low bound"].values[0].value-fl)
e_low_fls=np.append(e_low_fls, e_low_fl)
e_hi_fl=result_fl["hi bound"].values[0].value-fl
e_hi_fls=np.append(e_hi_fls, e_hi_fl)
#
#
#Save a plot of the current fit.
#
sliced_data=grb_bkg.binned_data.slice[{'Time':slice(sou_min,sou_max)}]
expectation = response.expectation()
bkg_expectation = bkg_wrap.expectation()
cts_exp=expectation.project('Em').to_dense(copy=False).contents + bkg_expectation.project('Em').to_dense(copy=False).contents
plot_filename=str("fit_"+str(i)+".pdf")
plot_fit(sliced_data, cts_exp, plot_filename)
#
#Save lc in in a text file:
#
lc=np.vstack((tmeds_lc,e_tmeds_lc,cts_lc,fls,e_low_fls,e_hi_fls,pars_bk,epars_bk)).T
nbins=len(tmeds_lc)
npars=2*len(par_list)
lc_par=par_epar.reshape(nbins,npars)
lc_all=np.hstack((lc,lc_par))
fl_list=['t','e_t','cts','fl','e+_fl','e-_fl','bk','e_bk']
par_list = list(par_bf.keys())
header=fl_list+par_list
np.savetxt("spec_lc.dat", lc_all, delimiter=" ",header=str(header))
16:03:59 INFO set the minimizer to minuit joint_likelihood.py:1046
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WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
16:04:01 WARNING 50.86000000000001 percent of samples have been thrown away because they analysis_results.py:1739 failed the constraints on the parameters. This results might not be suitable for error propagation. Enlarge the boundaries until you loose less than 1 percent of the samples.
Best fit values:
| result | unit | |
|---|---|---|
| parameter | ||
| source.spectrum.main.Band.K | (2.88 -0.28 +0.31) x 10^-4 | 1 / (keV s cm2) |
| bkg_gal | (0 +/- 6) x 10^-8 | Hz |
Correlation matrix:
| 1.00 | 0.00 |
| 0.00 | 1.00 |
Values of -log(likelihood) at the minimum:
| -log(likelihood) | |
|---|---|
| cosi | 698.1705378204011 |
| total | 698.1705378204011 |
Values of statistical measures:
| statistical measures | |
|---|---|
| AIC | 1400.3411277248138 |
| BIC | 1421.03622005641 |
WARNING RuntimeWarning: divide by zero encountered in divide
WARNING RuntimeWarning: invalid value encountered in divide
16:04:09 INFO set the minimizer to minuit joint_likelihood.py:1046
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
16:04:11 WARNING 28.28 percent of samples have been thrown away because they failed the analysis_results.py:1739 constraints on the parameters. This results might not be suitable for error propagation. Enlarge the boundaries until you loose less than 1 percent of the samples.
Best fit values:
| result | unit | |
|---|---|---|
| parameter | ||
| source.spectrum.main.Band.K | (6.2 -0.6 +0.7) x 10^-4 | 1 / (keV s cm2) |
| bkg_gal | (2.0 +/- 3.5) x 10^-3 | Hz |
Correlation matrix:
| 1.00 | -0.04 |
| -0.04 | 1.00 |
Values of -log(likelihood) at the minimum:
| -log(likelihood) | |
|---|---|
| cosi | 725.5474532335722 |
| total | 725.5474532335722 |
Values of statistical measures:
| statistical measures | |
|---|---|
| AIC | 1455.094958551156 |
| BIC | 1475.7900508827522 |
WARNING RuntimeWarning: divide by zero encountered in divide
WARNING RuntimeWarning: invalid value encountered in divide
16:04:19 INFO set the minimizer to minuit joint_likelihood.py:1046
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
16:04:21 WARNING 49.64 percent of samples have been thrown away because they failed the analysis_results.py:1739 constraints on the parameters. This results might not be suitable for error propagation. Enlarge the boundaries until you loose less than 1 percent of the samples.
Best fit values:
| result | unit | |
|---|---|---|
| parameter | ||
| source.spectrum.main.Band.K | (7.5 -0.7 +0.8) x 10^-4 | 1 / (keV s cm2) |
| bkg_gal | (0 +/- 5) x 10^-5 | Hz |
Correlation matrix:
| 1.00 | 0.01 |
| 0.01 | 1.00 |
Values of -log(likelihood) at the minimum:
| -log(likelihood) | |
|---|---|
| cosi | 745.4151714817089 |
| total | 745.4151714817089 |
Values of statistical measures:
| statistical measures | |
|---|---|
| AIC | 1494.8303950474292 |
| BIC | 1515.5254873790254 |
WARNING RuntimeWarning: divide by zero encountered in divide
WARNING RuntimeWarning: invalid value encountered in divide
16:04:28 INFO set the minimizer to minuit joint_likelihood.py:1046
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: divide by zero encountered in log
WARNING RuntimeWarning: invalid value encountered in multiply
WARNING RuntimeWarning: invalid value encountered in multiply
16:04:30 WARNING 50.36000000000001 percent of samples have been thrown away because they analysis_results.py:1739 failed the constraints on the parameters. This results might not be suitable for error propagation. Enlarge the boundaries until you loose less than 1 percent of the samples.
Best fit values:
| result | unit | |
|---|---|---|
| parameter | ||
| source.spectrum.main.Band.K | (2.43 -0.20 +0.22) x 10^-4 | 1 / (keV s cm2) |
| bkg_gal | (0.0 +/- 2.8) x 10^-6 | Hz |
Correlation matrix:
| 1.00 | 0.00 |
| 0.00 | 1.00 |
Values of -log(likelihood) at the minimum:
| -log(likelihood) | |
|---|---|
| cosi | 936.034617074883 |
| total | 936.034617074883 |
Values of statistical measures:
| statistical measures | |
|---|---|
| AIC | 1876.0692862337776 |
| BIC | 1896.7643785653738 |
WARNING RuntimeWarning: divide by zero encountered in divide
WARNING RuntimeWarning: invalid value encountered in divide
Plotting the time series.
Now we plot the time-series of fluxes, counts and fitted parameters. We convert the time in mjd for plotting. We use the raw lightcurve and the average flux injected as comparison. We plot the counts in each time bins to check that the fits had a reasonable statistics. In the future, we may be able to compute a goodness of fit in each time bin with 3ML.
[14]:
time_mjd=Time(time,format='unix').mjd
tmeds_mjd=Time(tmeds_lc, format='unix').mjd
e_tmeds_mjd=TimeDelta(e_tmeds_lc, format='sec').to('day').value
cm = 1/2.54
fig, axs = plt.subplots(3, 1, sharex=True, figsize=(21*cm, 29.7*cm))
#
# Raw Lightcurve
axs[0].scatter (time_mjd, rate)
axs[0].set_title('Raw lightcurve')
axs[0].set_ylabel('Rate (cts/s)')
#
# Flux Lightcurve
axs[1].errorbar(tmeds_mjd, fls, xerr=e_tmeds_mjd, yerr=[e_low_fls,e_hi_fls],fmt='o', capsize=1)
axs[1].set_title('Flux[0.1-10 MeV] LightCurve')
axs[1].set_ylabel('Flux (Photons/s/cm2)')
#
#Counts in log scale. To check that the fits have reasonable statistics.
axs[2].set_yscale('log')
axs[2].step(tmeds_mjd, cts_lc, where='mid',color='purple')
axs[2].errorbar (tmeds_mjd, cts_lc,xerr=e_tmeds_mjd,fmt='o', capsize=1)
axs[2].set_title('Counts')
axs[2].set_xlabel('Time (MJD)')
axs[2].axhline(y=100, color='red', linestyle='--')
#
#
# Adjust spacing between subplots
plt.tight_layout()
plt.savefig("raw_flux_counts_lc.pdf", dpi=300)
[15]:
#
#Plot the free parameters as a function of time.
#
npar=len(par_list)
cm = 1/2.54
fig, axs = plt.subplots(npar+1, 1, sharex=True, figsize=(21*cm, 29.7*cm))
h=np.arange(0, 2*npar, 2)
for i in range(npar):
axs[i].errorbar(tmeds_mjd, lc_par[:,h[i]], xerr=e_tmeds_mjd, yerr=lc_par[:,h[i]+1], fmt='o', capsize=5)
axs[i].set_ylabel(par_list[i])
axs[npar].errorbar(tmeds_mjd, pars_bk, xerr=e_tmeds_mjd, yerr=epars_bk, fmt='o')
axs[npar].set_title('Bakground COSI')
axs[npar].set_xlabel('Time (MJD)')
axs[npar].set_ylabel('Bk parameter')
# Adjust spacing between subplots
plt.tight_layout()
plt.savefig("specpars_bk_lc.pdf", dpi=300)
