Composite Models and depending pars¶
from jetset.jet_model import Jet
from jetset.plot_sedfit import PlotSED
from jetset.model_manager import FitModel
Composite models allow to combine together different models, such as Jet, and templates, including additive or multiplicative models, and give to the user the possibility to define the functional form of the model composition using a very simple and intuitive form such as: .. code-block:: python
‘jet1+jet2’*Franceschini_2008
that sums two jet models SEDs, and apply to both of them the Franceschini_2008 EBL absorption.
dsad
Building composite models it is very easy. Composite models are handled by the FitModel class, as shown by the following examples.
Combine a Jet model with the EBL model (Multiplicative case)¶
We start by combining a Jet model with the EBL absorption model, i.e. a multiplicative model. First, we define our Jet model
from jetset.jet_model import Jet
my_jet=Jet(electron_distribution='lppl',name='jet_flaring')
Second, we define the EBL model, and we use in this case the Franceschini_2008 model ( read the section EBL for more info regarding the EBL models)
from jetset.template_2Dmodel import EBLAbsorptionTemplate
ebl_franceschini=EBLAbsorptionTemplate.from_name('Franceschini_2008')
Now we add the components models to the the FitModel class, using the FitModel.add_component() method
composite_model=FitModel(nu_size=500,name='EBL corrected')
composite_model.add_component(my_jet)
composite_model.add_component(ebl_franceschini)
/Users/orion/anaconda3/envs/jetset/lib/python3.8/site-packages/jetset/model_manager.py:147: UserWarning: no cosmology defined, using default FlatLambdaCDM(name="Planck13", H0=67.8 km / (Mpc s), Om0=0.307, Tcmb0=2.725 K, Neff=3.05, m_nu=[0. 0. 0.06] eV, Ob0=0.0483)
warnings.warn('no cosmology defined, using default %s'%self.cosmo)
the waring message is just telling that you are not passing any specific
cosmology model to the FitModel class, so it is using a default one
composite_model.show_pars()
| model name | name | par type | units | val | phys. bound. min | phys. bound. max | log | frozen |
|---|---|---|---|---|---|---|---|---|
| jet_flaring | R | region_size | cm | 5.000000e+15 | 1.000000e+03 | 1.000000e+30 | False | False |
| jet_flaring | R_H | region_position | cm | 1.000000e+17 | 0.000000e+00 | -- | False | True |
| jet_flaring | B | magnetic_field | gauss | 1.000000e-01 | 0.000000e+00 | -- | False | False |
| jet_flaring | NH_cold_to_rel_e | cold_p_to_rel_e_ratio | 1.000000e-01 | 0.000000e+00 | -- | False | True | |
| jet_flaring | beam_obj | beaming | lorentz-factor* | 1.000000e+01 | 1.000000e-04 | -- | False | False |
| jet_flaring | z_cosm | redshift | 1.000000e-01 | 0.000000e+00 | -- | False | False | |
| jet_flaring | gmin | low-energy-cut-off | lorentz-factor* | 2.000000e+00 | 1.000000e+00 | 1.000000e+09 | False | False |
| jet_flaring | gmax | high-energy-cut-off | lorentz-factor* | 1.000000e+06 | 1.000000e+00 | 1.000000e+15 | False | False |
| jet_flaring | N | emitters_density | 1 / cm3 | 1.000000e+02 | 0.000000e+00 | -- | False | False |
| jet_flaring | gamma0_log_parab | turn-over-energy | lorentz-factor* | 1.000000e+04 | 1.000000e+00 | 1.000000e+09 | False | False |
| jet_flaring | s | LE_spectral_slope | 2.000000e+00 | -1.000000e+01 | 1.000000e+01 | False | False | |
| jet_flaring | r | spectral_curvature | 4.000000e-01 | -1.500000e+01 | 1.500000e+01 | False | False | |
| Franceschini_2008 | z_cosm | redshift | 1.000000e+00 | 0.000000e+00 | -- | False | True |
Since, both the Jet model the EBL share the same parameter, i.e. the redshift, we link the two parameters
composite_model.link_par(par_name='z_cosm', from_model=my_jet.name, to_model='Franceschini_2008')
==> par: z_cosm from model: jet_flaring linked to same parameter in model Franceschini_2008
composite_model.show_pars()
| model name | name | par type | units | val | phys. bound. min | phys. bound. max | log | frozen |
|---|---|---|---|---|---|---|---|---|
| jet_flaring | R | region_size | cm | 5.000000e+15 | 1.000000e+03 | 1.000000e+30 | False | False |
| jet_flaring | R_H | region_position | cm | 1.000000e+17 | 0.000000e+00 | -- | False | True |
| jet_flaring | B | magnetic_field | gauss | 1.000000e-01 | 0.000000e+00 | -- | False | False |
| jet_flaring | NH_cold_to_rel_e | cold_p_to_rel_e_ratio | 1.000000e-01 | 0.000000e+00 | -- | False | True | |
| jet_flaring | beam_obj | beaming | lorentz-factor* | 1.000000e+01 | 1.000000e-04 | -- | False | False |
| jet_flaring | z_cosm(L,Franceschini_2008) | redshift | -- | -- | -- | False | True | |
| jet_flaring | gmin | low-energy-cut-off | lorentz-factor* | 2.000000e+00 | 1.000000e+00 | 1.000000e+09 | False | False |
| jet_flaring | gmax | high-energy-cut-off | lorentz-factor* | 1.000000e+06 | 1.000000e+00 | 1.000000e+15 | False | False |
| jet_flaring | N | emitters_density | 1 / cm3 | 1.000000e+02 | 0.000000e+00 | -- | False | False |
| jet_flaring | gamma0_log_parab | turn-over-energy | lorentz-factor* | 1.000000e+04 | 1.000000e+00 | 1.000000e+09 | False | False |
| jet_flaring | s | LE_spectral_slope | 2.000000e+00 | -1.000000e+01 | 1.000000e+01 | False | False | |
| jet_flaring | r | spectral_curvature | 4.000000e-01 | -1.500000e+01 | 1.500000e+01 | False | False | |
| Franceschini_2008 | z_cosm(M) | redshift | 1.000000e+00 | 0.000000e+00 | -- | False | True |
As you can see, now the paramter z_cosm in jet_flaring is the
master parameter (flagged by the M in parenthesis), and the one
belonging to the Franceschini_2008 component is the linked one
(flagged by the L in parenthesis).
Setting parameters¶
Note
with the new implementation of composite model (FitModel class) to set parameters you have to specify the model component, this is different from versions<1.2.0
These methods are alternative and equivalent ways to set a parameter in a composite model:
accessing the model component member of the
using
set_parand passing as first argument the model component nameusing
set_parand passing as first argument the model component object
#a
composite_model.Franceschini_2008.parameters.z_cosm.val=0.1
#b
composite_model.set_par('Franceschini_2008','z_cosm',0.1)
#c
composite_model.set_par(ebl_franceschini,'z_cosm',0.1)
And now, we can define the functional form of the model composition, just by writing the mathematical expression as a string, using the model names reported in the model description table, and that’s it!
composite_model.show_model_components()
--------------------------------------------------------------------------------
Composite model description
--------------------------------------------------------------------------------
name: EBL corrected
type: composite_model
components models:
-model name: jet_flaring model type: jet
-model name: Franceschini_2008 model type: table2D
--------------------------------------------------------------------------------
composite_model.composite_expr='jet_flaring*Franceschini_2008'
composite_model.jet_flaring.IC_nu_size=150
composite_model.eval()
p=composite_model.plot_model()
composite_model.save_model('composite.pkl')
cm=FitModel.load_model('composite.pkl')
==> par: z_cosm from model: jet_flaring linked to same parameter in model Franceschini_2008
Sum of two jets (steady and flaring) and application of the EBL absorption to both (Multiplicative and additive)¶
Assume that now we want to sum to jet models (a steady and flaring component) and apply to both of them the EBL absorption.
composite_model=FitModel(nu_size=500,name='EBL corrected flaring+steady')
composite_model.add_component(my_jet)
composite_model.add_component(ebl_franceschini)
/Users/orion/anaconda3/envs/jetset/lib/python3.8/site-packages/jetset/model_manager.py:147: UserWarning: no cosmology defined, using default FlatLambdaCDM(name="Planck13", H0=67.8 km / (Mpc s), Om0=0.307, Tcmb0=2.725 K, Neff=3.05, m_nu=[0. 0. 0.06] eV, Ob0=0.0483)
warnings.warn('no cosmology defined, using default %s'%self.cosmo)
steady_jet=Jet(electron_distribution='plc',name='steady_jet')
composite_model.add_component(steady_jet)
composite_model.show_model_components()
--------------------------------------------------------------------------------
Composite model description
--------------------------------------------------------------------------------
name: EBL corrected flaring+steady
type: composite_model
components models:
-model name: jet_flaring model type: jet
-model name: Franceschini_2008 model type: table2D
-model name: steady_jet model type: jet
--------------------------------------------------------------------------------
now we link the same parameter z_cosm from the steady_jet to the
same master parameter used for the EBL model, i.e. to the
jet_flaring model
composite_model.link_par(par_name='z_cosm',from_model=['steady_jet'],to_model='Franceschini_2008')
==> par: z_cosm from model: steady_jet linked to same parameter in model Franceschini_2008
composite_model.show_pars()
| model name | name | par type | units | val | phys. bound. min | phys. bound. max | log | frozen |
|---|---|---|---|---|---|---|---|---|
| jet_flaring | R | region_size | cm | 5.000000e+15 | 1.000000e+03 | 1.000000e+30 | False | False |
| jet_flaring | R_H | region_position | cm | 1.000000e+17 | 0.000000e+00 | -- | False | True |
| jet_flaring | B | magnetic_field | gauss | 1.000000e-01 | 0.000000e+00 | -- | False | False |
| jet_flaring | NH_cold_to_rel_e | cold_p_to_rel_e_ratio | 1.000000e-01 | 0.000000e+00 | -- | False | True | |
| jet_flaring | beam_obj | beaming | lorentz-factor* | 1.000000e+01 | 1.000000e-04 | -- | False | False |
| jet_flaring | z_cosm(L,Franceschini_2008) | redshift | -- | -- | -- | False | True | |
| jet_flaring | gmin | low-energy-cut-off | lorentz-factor* | 2.000000e+00 | 1.000000e+00 | 1.000000e+09 | False | False |
| jet_flaring | gmax | high-energy-cut-off | lorentz-factor* | 1.000000e+06 | 1.000000e+00 | 1.000000e+15 | False | False |
| jet_flaring | N | emitters_density | 1 / cm3 | 1.000000e+02 | 0.000000e+00 | -- | False | False |
| jet_flaring | gamma0_log_parab | turn-over-energy | lorentz-factor* | 1.000000e+04 | 1.000000e+00 | 1.000000e+09 | False | False |
| jet_flaring | s | LE_spectral_slope | 2.000000e+00 | -1.000000e+01 | 1.000000e+01 | False | False | |
| jet_flaring | r | spectral_curvature | 4.000000e-01 | -1.500000e+01 | 1.500000e+01 | False | False | |
| Franceschini_2008 | z_cosm(M) | redshift | 1.000000e-01 | 0.000000e+00 | -- | False | True | |
| steady_jet | R | region_size | cm | 5.000000e+15 | 1.000000e+03 | 1.000000e+30 | False | False |
| steady_jet | R_H | region_position | cm | 1.000000e+17 | 0.000000e+00 | -- | False | True |
| steady_jet | B | magnetic_field | gauss | 1.000000e-01 | 0.000000e+00 | -- | False | False |
| steady_jet | NH_cold_to_rel_e | cold_p_to_rel_e_ratio | 1.000000e-01 | 0.000000e+00 | -- | False | True | |
| steady_jet | beam_obj | beaming | lorentz-factor* | 1.000000e+01 | 1.000000e-04 | -- | False | False |
| steady_jet | z_cosm(L,Franceschini_2008) | redshift | -- | -- | -- | False | True | |
| steady_jet | gmin | low-energy-cut-off | lorentz-factor* | 2.000000e+00 | 1.000000e+00 | 1.000000e+09 | False | False |
| steady_jet | gmax | high-energy-cut-off | lorentz-factor* | 1.000000e+06 | 1.000000e+00 | 1.000000e+15 | False | False |
| steady_jet | N | emitters_density | 1 / cm3 | 1.000000e+02 | 0.000000e+00 | -- | False | False |
| steady_jet | gamma_cut | turn-over-energy | lorentz-factor* | 1.000000e+04 | 1.000000e+00 | 1.000000e+09 | False | False |
| steady_jet | p | LE_spectral_slope | 2.000000e+00 | -1.000000e+01 | 1.000000e+01 | False | False |
composite_model.steady_jet.IC_nu_size=150
composite_model.composite_expr='(jet_flaring + steady_jet) * Franceschini_2008'
composite_model.eval()
p=composite_model.plot_model()
p.setlim(y_max=1E-12)
composite_model.save_model('composite.pkl')
cm=FitModel.load_model('composite.pkl')
==> par: z_cosm from model: jet_flaring linked to same parameter in model Franceschini_2008
==> par: z_cosm from model: steady_jet linked to same parameter in model Franceschini_2008
cm.show_pars()
| model name | name | par type | units | val | phys. bound. min | phys. bound. max | log | frozen |
|---|---|---|---|---|---|---|---|---|
| jet_flaring | gmin | low-energy-cut-off | lorentz-factor* | 2.000000e+00 | 1.000000e+00 | 1.000000e+09 | False | False |
| jet_flaring | gmax | high-energy-cut-off | lorentz-factor* | 1.000000e+06 | 1.000000e+00 | 1.000000e+15 | False | False |
| jet_flaring | N | emitters_density | 1 / cm3 | 1.000000e+02 | 0.000000e+00 | -- | False | False |
| jet_flaring | gamma0_log_parab | turn-over-energy | lorentz-factor* | 1.000000e+04 | 1.000000e+00 | 1.000000e+09 | False | False |
| jet_flaring | s | LE_spectral_slope | 2.000000e+00 | -1.000000e+01 | 1.000000e+01 | False | False | |
| jet_flaring | r | spectral_curvature | 4.000000e-01 | -1.500000e+01 | 1.500000e+01 | False | False | |
| jet_flaring | R | region_size | cm | 5.000000e+15 | 1.000000e+03 | 1.000000e+30 | False | False |
| jet_flaring | R_H | region_position | cm | 1.000000e+17 | 0.000000e+00 | -- | False | True |
| jet_flaring | B | magnetic_field | gauss | 1.000000e-01 | 0.000000e+00 | -- | False | False |
| jet_flaring | NH_cold_to_rel_e | cold_p_to_rel_e_ratio | 1.000000e-01 | 0.000000e+00 | -- | False | True | |
| jet_flaring | beam_obj | beaming | lorentz-factor* | 1.000000e+01 | 1.000000e-04 | -- | False | False |
| jet_flaring | z_cosm(L,Franceschini_2008) | redshift | -- | -- | -- | False | True | |
| Franceschini_2008 | z_cosm(M) | redshift | 1.000000e-01 | 0.000000e+00 | -- | False | True | |
| steady_jet | gmin | low-energy-cut-off | lorentz-factor* | 2.000000e+00 | 1.000000e+00 | 1.000000e+09 | False | False |
| steady_jet | gmax | high-energy-cut-off | lorentz-factor* | 1.000000e+06 | 1.000000e+00 | 1.000000e+15 | False | False |
| steady_jet | N | emitters_density | 1 / cm3 | 1.000000e+02 | 0.000000e+00 | -- | False | False |
| steady_jet | gamma_cut | turn-over-energy | lorentz-factor* | 1.000000e+04 | 1.000000e+00 | 1.000000e+09 | False | False |
| steady_jet | p | LE_spectral_slope | 2.000000e+00 | -1.000000e+01 | 1.000000e+01 | False | False | |
| steady_jet | R | region_size | cm | 5.000000e+15 | 1.000000e+03 | 1.000000e+30 | False | False |
| steady_jet | R_H | region_position | cm | 1.000000e+17 | 0.000000e+00 | -- | False | True |
| steady_jet | B | magnetic_field | gauss | 1.000000e-01 | 0.000000e+00 | -- | False | False |
| steady_jet | NH_cold_to_rel_e | cold_p_to_rel_e_ratio | 1.000000e-01 | 0.000000e+00 | -- | False | True | |
| steady_jet | beam_obj | beaming | lorentz-factor* | 1.000000e+01 | 1.000000e-04 | -- | False | False |
| steady_jet | z_cosm(L,Franceschini_2008) | redshift | -- | -- | -- | False | True |