Notebook .. _composite_models:

Composite Models¶

In [1]:

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. Building composite models it is very easy. Composite models are handled by the :class:`.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

In [2]:

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 :ref:`ebl_model` for more info regarding the EBL models)

In [3]:

from jetset.template_2Dmodel import EBLAbsorptionTemplate
ebl_franceschini=EBLAbsorptionTemplate.from_name('Franceschini_2008')

Now we add the components models to the the :class:`.FitModel` class, using the :class:`.FitModel.add_component()` method

In [4]:

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/python3.7/site-packages/jetset-1.1.2-py3.7-macosx-10.9-x86_64.egg/jetset/model_manager.py:160: 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

In [5]:

composite_model.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                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 gamma0_log_parab    turn-over-energy lorentz-factor* 1.000000e+04     1.000000e+00     1.000000e+09 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               G 1.000000e-01     0.000000e+00               -- False  False
      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
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

In [6]:

composite_model.link_par(par_name='z_cosm',model_name_list=['jet_flaring'],root_model_name='Franceschini_2008')

In [7]:

composite_model.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                           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            gamma0_log_parab    turn-over-energy lorentz-factor* 1.000000e+04     1.000000e+00     1.000000e+09 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               G 1.000000e-01     0.000000e+00               -- False  False
      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(R)            redshift                 1.000000e+00     0.000000e+00               -- False   True

As you can see, now the paramter z_cosm in Franceschini_2008 is the root parameter (flagged by the R in parenthesis), and the one belonging to the jet_flaring 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:

a) accessing the model component member of the

b) using set_par and passing as first argument the model component name

c) using set_par and passing as first argument the model component object

In [8]:

#a
composite_model.jet_flaring.parameters.z_cosm.val=0.1
#b
composite_model.set_par('jet_flaring','z_cosm',0.1)
#c
composite_model.set_par(my_jet,'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!

In [10]:

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

-------------------------------------------------------------------------------------------------------------------

In [11]:

composite_model.composite_expr='jet_flaring*Franceschini_2008'

In [12]:

composite_model.jet_flaring.IC_nu_size=150
composite_model.eval()
p=composite_model.plot_model()
p.rescale(y_max=-12)

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.

In [13]:

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/python3.7/site-packages/jetset-1.1.2-py3.7-macosx-10.9-x86_64.egg/jetset/model_manager.py:160: 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)

In [14]:

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

-------------------------------------------------------------------------------------------------------------------

In [15]:

composite_model.link_par(par_name='z_cosm',model_name_list=['steady_jet'],root_model_name='Franceschini_2008') 

In [16]:

composite_model.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                           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            gamma0_log_parab    turn-over-energy lorentz-factor* 1.000000e+04     1.000000e+00     1.000000e+09 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               G 1.000000e-01     0.000000e+00               -- False  False
      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(R)            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                           p   LE_spectral_slope                 2.000000e+00    -1.000000e+01     1.000000e+01 False  False
       steady_jet                   gamma_cut    turn-over-energy lorentz-factor* 1.000000e+04     1.000000e+00     1.000000e+09 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               G 1.000000e-01     0.000000e+00               -- False  False
       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

In [17]:

composite_model.steady_jet.IC_nu_size=150

In [18]:

composite_model.composite_expr='(jet_flaring + steady_jet) * Franceschini_2008'

In [19]:

composite_model.eval()
p=composite_model.plot_model()
p.rescale(y_max=-12)