Depending parameters#

In the following we show how to link parameters in the same model or among different models, and how to make a paramter depending on other parameters according to a mathematical expression.

Example: linked paramters for EBL#

import warnings
warnings.filterwarnings('ignore')

import jetset
print('tested with',jetset.__version__)

tested with 1.4.0rc3

from jetset.jet_model import Jet
from jetset.template_2Dmodel import EBLAbsorptionTemplate
from jetset.model_manager import FitModel

my_jet = Jet(electron_distribution='lppl', name='jet_flaring')
my_jet.parameters.z_cosm.val = 0.01

ebl_franceschini = EBLAbsorptionTemplate.from_name('Franceschini_2008')

composite_model = FitModel(nu_size=500, name='EBL corrected')
composite_model.add_component(my_jet)
composite_model.add_component(ebl_franceschini)

composite_model.show_pars()

composite_model.link_par(par_name='z_cosm', from_model='Franceschini_2008', to_model='jet_flaring')
v=0.03001
my_jet.parameters.z_cosm.val = v
assert (composite_model.Franceschini_2008.parameters.z_cosm.val==v)
assert (composite_model.Franceschini_2008.parameters.z_cosm.linked==True)

composite_model.composite_expr = '%s*%s'%(my_jet.name,ebl_franceschini.name)
composite_model.eval()

#if plot is True:
#    composite_model.plot_model()

composite_model.save_model('ebl_jet.pkl')
new_composite_model=FitModel.load_model('ebl_jet.pkl')
new_composite_model.show_pars()
v=2.0
new_composite_model.jet_flaring.parameters.z_cosm.val=v
print('new_composite_model.Franceschini_2008.parameters.z_cosm.val',new_composite_model.Franceschini_2008.parameters.z_cosm.val,'v',v)
assert (new_composite_model.Franceschini_2008.parameters.z_cosm.val == v)
assert (new_composite_model.Franceschini_2008.parameters.z_cosm.linked == True)

Table length=14

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+00	0.000000e+00	--	False	True
jet_flaring	beam_obj	beaming		1.000000e+01	1.000000e-04	--	False	False
jet_flaring	z_cosm	redshift		1.000000e-02	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	scale_factor	scale_factor		1.000000e+00	0.000000e+00	--	False	True
Franceschini_2008	z_cosm	redshift		1.000000e+00	0.000000e+00	--	False	True

Table length=14

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+00	0.000000e+00	--	False	True
jet_flaring	beam_obj	beaming		1.000000e+01	1.000000e-04	--	False	False
jet_flaring	z_cosm(M)	redshift		3.001000e-02	0.000000e+00	--	False	False
Franceschini_2008	scale_factor	scale_factor		1.000000e+00	0.000000e+00	--	False	True
Franceschini_2008	z_cosm(L,jet_flaring)	redshift		--	--	--	False	True

new_composite_model.Franceschini_2008.parameters.z_cosm.val 2.0 v 2.0

Example: depending pars for bkn power-law emitters#

here we create a custom bkn distribution where we impose a functional dependence among the low and high-energy spectral index.

from jetset.jet_emitters import EmittersDistribution
import numpy as np

from jetset.jet_model import Jet

j = Jet(emitters_distribution='bkn')

j.parameters

Table length=12

model name	name	par type	units	val	phys. bound. min	phys. bound. max	log	frozen
jet_leptonic	R	region_size	cm	5.000000e+15	1.000000e+03	1.000000e+30	False	False
jet_leptonic	R_H	region_position	cm	1.000000e+17	0.000000e+00	--	False	True
jet_leptonic	B	magnetic_field	gauss	1.000000e-01	0.000000e+00	--	False	False
jet_leptonic	NH_cold_to_rel_e	cold_p_to_rel_e_ratio		1.000000e+00	0.000000e+00	--	False	True
jet_leptonic	beam_obj	beaming		1.000000e+01	1.000000e-04	--	False	False
jet_leptonic	z_cosm	redshift		1.000000e-01	0.000000e+00	--	False	False
jet_leptonic	gmin	low-energy-cut-off	lorentz-factor*	2.000000e+00	1.000000e+00	1.000000e+09	False	False
jet_leptonic	gmax	high-energy-cut-off	lorentz-factor*	1.000000e+06	1.000000e+00	1.000000e+15	False	False
jet_leptonic	N	emitters_density	1 / cm3	1.000000e+02	0.000000e+00	--	False	False
jet_leptonic	gamma_break	turn-over-energy	lorentz-factor*	1.000000e+04	1.000000e+00	1.000000e+09	False	False
jet_leptonic	p	LE_spectral_slope		2.500000e+00	-1.000000e+01	1.000000e+01	False	False
jet_leptonic	p_1	HE_spectral_slope		3.500000e+00	-1.000000e+01	1.000000e+01	False	False

None

the functional dependence can be provided by a python function, where the argument (p in this case) is the same name as the parameter:

def f_p(p):
    return p+1
j.make_dependent_par(par='p_1',depends_on=['p'],par_expr=f_p)
j.parameters.p.val=2
np.testing.assert_allclose(j.parameters.p_1.val, j.parameters.p.val + 1)
j.parameters

adding par: p to  p_1
==> par p_1 is depending on ['p'] according to expr:   p_1 =
def f_p(p):
    return p+1

Table length=12

model name	name	par type	units	val	phys. bound. min	phys. bound. max	log	frozen
jet_leptonic	R	region_size	cm	5.000000e+15	1.000000e+03	1.000000e+30	False	False
jet_leptonic	R_H	region_position	cm	1.000000e+17	0.000000e+00	--	False	True
jet_leptonic	B	magnetic_field	gauss	1.000000e-01	0.000000e+00	--	False	False
jet_leptonic	NH_cold_to_rel_e	cold_p_to_rel_e_ratio		1.000000e+00	0.000000e+00	--	False	True
jet_leptonic	beam_obj	beaming		1.000000e+01	1.000000e-04	--	False	False
jet_leptonic	z_cosm	redshift		1.000000e-01	0.000000e+00	--	False	False
jet_leptonic	gmin	low-energy-cut-off	lorentz-factor*	2.000000e+00	1.000000e+00	1.000000e+09	False	False
jet_leptonic	gmax	high-energy-cut-off	lorentz-factor*	1.000000e+06	1.000000e+00	1.000000e+15	False	False
jet_leptonic	N	emitters_density	1 / cm3	1.000000e+02	0.000000e+00	--	False	False
jet_leptonic	gamma_break	turn-over-energy	lorentz-factor*	1.000000e+04	1.000000e+00	1.000000e+09	False	False
jet_leptonic	p(M)	LE_spectral_slope		2.000000e+00	-1.000000e+01	1.000000e+01	False	False
jet_leptonic	*p_1(D,p)	HE_spectral_slope		3.000000e+00	-1.000000e+01	1.000000e+01	False	True

None

as you can notice, now a message is shown describing the dependence of the parameters

It is also possible to set the dependence function as a string that can be evaluated

j.make_dependent_par(par='p_1',depends_on=['p'],par_expr='p+1')
j.parameters.p.val=2
np.testing.assert_allclose(j.parameters.p_1.val, j.parameters.p.val + 1)
j.parameters

==> par p_1 is depending on ['p'] according to expr:   p_1 =
p+1

Table length=12

model name	name	par type	units	val	phys. bound. min	phys. bound. max	log	frozen
jet_leptonic	R	region_size	cm	5.000000e+15	1.000000e+03	1.000000e+30	False	False
jet_leptonic	R_H	region_position	cm	1.000000e+17	0.000000e+00	--	False	True
jet_leptonic	B	magnetic_field	gauss	1.000000e-01	0.000000e+00	--	False	False
jet_leptonic	NH_cold_to_rel_e	cold_p_to_rel_e_ratio		1.000000e+00	0.000000e+00	--	False	True
jet_leptonic	beam_obj	beaming		1.000000e+01	1.000000e-04	--	False	False
jet_leptonic	z_cosm	redshift		1.000000e-01	0.000000e+00	--	False	False
jet_leptonic	gmin	low-energy-cut-off	lorentz-factor*	2.000000e+00	1.000000e+00	1.000000e+09	False	False
jet_leptonic	gmax	high-energy-cut-off	lorentz-factor*	1.000000e+06	1.000000e+00	1.000000e+15	False	False
jet_leptonic	N	emitters_density	1 / cm3	1.000000e+02	0.000000e+00	--	False	False
jet_leptonic	gamma_break	turn-over-energy	lorentz-factor*	1.000000e+04	1.000000e+00	1.000000e+09	False	False
jet_leptonic	p(M)	LE_spectral_slope		2.000000e+00	-1.000000e+01	1.000000e+01	False	False
jet_leptonic	*p_1(D,p)	HE_spectral_slope		3.000000e+00	-1.000000e+01	1.000000e+01	False	True

None

In principle, you can use strings for short expressions, and functions for more complicated formulas.

You can print the actual expression/function for the depending parameter using the print_par_expr method:

j.parameters.p_1.par_expression_source_code

==> par p_1 is depending on ['p'] according to expr:   p_1 =
p+1

j.save_model('jet.pkl')
new_jet=Jet.load_model('jet.pkl')

new_jet.parameters.p.val=2.5
np.testing.assert_allclose(new_jet.parameters.p_1.val, new_jet.parameters.p.val + 1)
new_jet.parameters

Table length=12

model name	name	par type	units	val	phys. bound. min	phys. bound. max	log	frozen
jet_leptonic	gmin	low-energy-cut-off	lorentz-factor*	2.000000e+00	1.000000e+00	1.000000e+09	False	False
jet_leptonic	gmax	high-energy-cut-off	lorentz-factor*	1.000000e+06	1.000000e+00	1.000000e+15	False	False
jet_leptonic	N	emitters_density	1 / cm3	1.000000e+02	0.000000e+00	--	False	False
jet_leptonic	gamma_break	turn-over-energy	lorentz-factor*	1.000000e+04	1.000000e+00	1.000000e+09	False	False
jet_leptonic	p(M)	LE_spectral_slope		2.500000e+00	-1.000000e+01	1.000000e+01	False	False
jet_leptonic	*p_1(D,p)	HE_spectral_slope		3.500000e+00	-1.000000e+01	1.000000e+01	False	True
jet_leptonic	R	region_size	cm	5.000000e+15	1.000000e+03	1.000000e+30	False	False
jet_leptonic	R_H	region_position	cm	1.000000e+17	0.000000e+00	--	False	True
jet_leptonic	B	magnetic_field	gauss	1.000000e-01	0.000000e+00	--	False	False
jet_leptonic	NH_cold_to_rel_e	cold_p_to_rel_e_ratio		1.000000e+00	0.000000e+00	--	False	True
jet_leptonic	beam_obj	beaming		1.000000e+01	1.000000e-04	--	False	False
jet_leptonic	z_cosm	redshift		1.000000e-01	0.000000e+00	--	False	False

None

Example depending par: R depends on variability time scale#

jet=Jet(emitters_distribution='plc')

jet.add_user_par('t_var_day',val=1, units='d',val_min=0.001,val_max=30)


def par_func(t_var_day,beam_obj,z_cosm):
    from astropy.constants import c
    R=t_var_day*86400*beam_obj/(1+z_cosm)*c.cgs.value
    return R

jet.make_dependent_par(par='R', depends_on=['t_var_day', 'beam_obj', 'z_cosm',], par_expr=par_func)

adding par: t_var_day to  R
adding par: beam_obj to  R
adding par: z_cosm to  R
==> par R is depending on ['t_var_day', 'beam_obj', 'z_cosm'] according to expr:   R =
def par_func(t_var_day,beam_obj,z_cosm):
    from astropy.constants import c
    R=t_var_day*86400*beam_obj/(1+z_cosm)*c.cgs.value
    return R

jet.parameters

Table length=12

model name	name	par type	units	val	phys. bound. min	phys. bound. max	log	frozen
jet_leptonic	*R(D,z_cosm)	region_size	cm	2.354733e+16	1.000000e+03	1.000000e+30	False	True
jet_leptonic	R_H	region_position	cm	1.000000e+17	0.000000e+00	--	False	True
jet_leptonic	B	magnetic_field	gauss	1.000000e-01	0.000000e+00	--	False	False
jet_leptonic	NH_cold_to_rel_e	cold_p_to_rel_e_ratio		1.000000e+00	0.000000e+00	--	False	True
jet_leptonic	beam_obj(M)	beaming		1.000000e+01	1.000000e-04	--	False	False
jet_leptonic	z_cosm(M)	redshift		1.000000e-01	0.000000e+00	--	False	False
jet_leptonic	gmin	low-energy-cut-off	lorentz-factor*	2.000000e+00	1.000000e+00	1.000000e+09	False	False
jet_leptonic	gmax	high-energy-cut-off	lorentz-factor*	1.000000e+06	1.000000e+00	1.000000e+15	False	False
jet_leptonic	N	emitters_density	1 / cm3	1.000000e+02	0.000000e+00	--	False	False
jet_leptonic	gamma_cut	turn-over-energy	lorentz-factor*	1.000000e+04	1.000000e+00	1.000000e+09	False	False
jet_leptonic	p	LE_spectral_slope		2.000000e+00	-1.000000e+01	1.000000e+01	False	False
jet_leptonic	t_var_day(M)	user_defined	d	1.000000e+00	1.000000e-03	3.000000e+01	False	False

None

If you are using a jet model with BulkFactor and viewing angle

jet=Jet(emitters_distribution='plc',beaming_expr='bulk_theta')

jet.add_user_par('t_var_day',val=1, units='d',val_min=0.001,val_max=30)


def par_func(t_var_day,BulkFactor,z_cosm,theta):
    from astropy.constants import c
    beta=np.sqrt(1-(1/(BulkFactor*BulkFactor)))
    beaming_factor=1/(BulkFactor*(1-beta*np.cos(np.radians(theta))))
    R=t_var_day*86400*beaming_factor/(1+z_cosm)*c.cgs.value
    return R

jet.make_dependent_par(par='R', depends_on=['t_var_day', 'BulkFactor', 'z_cosm','theta'], par_expr=par_func)

adding par: t_var_day to  R
adding par: BulkFactor to  R
adding par: z_cosm to  R
adding par: theta to  R
==> par R is depending on ['t_var_day', 'BulkFactor', 'z_cosm', 'theta'] according to expr:   R =
def par_func(t_var_day,BulkFactor,z_cosm,theta):
    from astropy.constants import c
    beta=np.sqrt(1-(1/(BulkFactor*BulkFactor)))
    beaming_factor=1/(BulkFactor*(1-beta*np.cos(np.radians(theta))))
    R=t_var_day*86400*beaming_factor/(1+z_cosm)*c.cgs.value
    return R

jet.parameters

Table length=13

model name	name	par type	units	val	phys. bound. min	phys. bound. max	log	frozen
jet_leptonic	*R(D,theta)	region_size	cm	4.696244e+16	1.000000e+03	1.000000e+30	False	True
jet_leptonic	R_H	region_position	cm	1.000000e+17	0.000000e+00	--	False	True
jet_leptonic	B	magnetic_field	gauss	1.000000e-01	0.000000e+00	--	False	False
jet_leptonic	NH_cold_to_rel_e	cold_p_to_rel_e_ratio		1.000000e+00	0.000000e+00	--	False	True
jet_leptonic	theta(M)	jet-viewing-angle	deg	1.000000e-01	0.000000e+00	9.000000e+01	False	False
jet_leptonic	BulkFactor(M)	jet-bulk-factor	lorentz-factor*	1.000000e+01	1.000000e+00	1.000000e+05	False	False
jet_leptonic	z_cosm(M)	redshift		1.000000e-01	0.000000e+00	--	False	False
jet_leptonic	gmin	low-energy-cut-off	lorentz-factor*	2.000000e+00	1.000000e+00	1.000000e+09	False	False
jet_leptonic	gmax	high-energy-cut-off	lorentz-factor*	1.000000e+06	1.000000e+00	1.000000e+15	False	False
jet_leptonic	N	emitters_density	1 / cm3	1.000000e+02	0.000000e+00	--	False	False
jet_leptonic	gamma_cut	turn-over-energy	lorentz-factor*	1.000000e+04	1.000000e+00	1.000000e+09	False	False
jet_leptonic	p	LE_spectral_slope		2.000000e+00	-1.000000e+01	1.000000e+01	False	False
jet_leptonic	t_var_day(M)	user_defined	d	1.000000e+00	1.000000e-03	3.000000e+01	False	False

None

Example depending par: Building a Jet model with B function of R_H and R_0#

In this example we create a fuctional dependence among the paramters B, R_H introducing user custom pararameters. Wewant that the value of the mangentic field in the jet is a function or R_H, and of the initial value of B=B0 at R=R_H0, according to the expression:

\(B=B_0(R_0/R_H)^{1.1}\)

jet=Jet(emitters_distribution='plc')
fit_model_lsb=FitModel( jet=jet, name='SSC-best-fit-lsb',template=None)
fit_model_lsb.jet_leptonic.parameters.beam_obj.fit_range = [5, 50]
fit_model_lsb.jet_leptonic.parameters.R_H.val=5E17
fit_model_lsb.jet_leptonic.parameters.R_H.frozen=False
fit_model_lsb.jet_leptonic.parameters.R_H.fit_range = [1E15, 1E19]
fit_model_lsb.jet_leptonic.parameters.R.fit_range = [10 ** 15.5, 10 ** 17.5]

fit_model_lsb.jet_leptonic.add_user_par(name='B0',units='G',val=1E3,val_min=0,val_max=None)
fit_model_lsb.jet_leptonic.add_user_par(name='R0', units='cm', val=5E13, val_min=0, val_max=None)
fit_model_lsb.jet_leptonic.add_user_par(name='m_B', val=1, val_min=1, val_max=2)
fit_model_lsb.jet_leptonic.parameters.R0.frozen=True
fit_model_lsb.jet_leptonic.parameters.B0.frozen=True

def par_func(R0,B0,R_H,m_B):
    return B0*np.power((R0/R_H),m_B)

fit_model_lsb.jet_leptonic.make_dependent_par(par='B', depends_on=['B0', 'R0', 'R_H','m_B'], par_expr=par_func)

B0=fit_model_lsb.jet_leptonic.parameters.B0.val
R0 = fit_model_lsb.jet_leptonic.parameters.R0.val
R_H = fit_model_lsb.jet_leptonic.parameters.R_H.val
m_B= fit_model_lsb.jet_leptonic.parameters.m_B.val

np.testing.assert_allclose(fit_model_lsb.jet_leptonic.parameters.B.val, par_func(R0,B0,R_H,m_B))

adding par: B0 to  B
adding par: R0 to  B
adding par: R_H to  B
adding par: m_B to  B
==> par B is depending on ['B0', 'R0', 'R_H', 'm_B'] according to expr:   B =
def par_func(R0,B0,R_H,m_B):
    return B0*np.power((R0/R_H),m_B)

fit_model_lsb.jet_leptonic.parameters

Table length=14

model name	name	par type	units	val	phys. bound. min	phys. bound. max	log	frozen
jet_leptonic	R	region_size	cm	5.000000e+15	1.000000e+03	1.000000e+30	False	False
jet_leptonic	R_H(M)	region_position	cm	5.000000e+17	0.000000e+00	--	False	False
jet_leptonic	*B(D,m_B)	magnetic_field	gauss	1.000000e-01	0.000000e+00	--	False	True
jet_leptonic	NH_cold_to_rel_e	cold_p_to_rel_e_ratio		1.000000e+00	0.000000e+00	--	False	True
jet_leptonic	beam_obj	beaming		1.000000e+01	1.000000e-04	--	False	False
jet_leptonic	z_cosm	redshift		1.000000e-01	0.000000e+00	--	False	False
jet_leptonic	gmin	low-energy-cut-off	lorentz-factor*	2.000000e+00	1.000000e+00	1.000000e+09	False	False
jet_leptonic	gmax	high-energy-cut-off	lorentz-factor*	1.000000e+06	1.000000e+00	1.000000e+15	False	False
jet_leptonic	N	emitters_density	1 / cm3	1.000000e+02	0.000000e+00	--	False	False
jet_leptonic	gamma_cut	turn-over-energy	lorentz-factor*	1.000000e+04	1.000000e+00	1.000000e+09	False	False
jet_leptonic	p	LE_spectral_slope		2.000000e+00	-1.000000e+01	1.000000e+01	False	False
jet_leptonic	B0(M)	user_defined	G	1.000000e+03	0.000000e+00	--	False	True
jet_leptonic	R0(M)	user_defined	cm	5.000000e+13	0.000000e+00	--	False	True
jet_leptonic	m_B(M)	user_defined		1.000000e+00	1.000000e+00	2.000000e+00	False	False

None

fit_model_lsb.save_model('test.pkl')

fit_model_lsb=FitModel.load_model('test.pkl')

B0=fit_model_lsb.jet_leptonic.parameters.B0.val
R0 = fit_model_lsb.jet_leptonic.parameters.R0.val
R_H = fit_model_lsb.jet_leptonic.parameters.R_H.val
m_B= fit_model_lsb.jet_leptonic.parameters.m_B.val

np.testing.assert_allclose(fit_model_lsb.jet_leptonic.parameters.B.val, par_func(R0,B0,R_H,m_B))

%matplotlib inline
import matplotlib.pyplot as plt

plt.figure(dpi=150)
R_H_array=np.logspace(13,18,100)
B_array=np.zeros(R_H_array.shape)
for ID,R_H in enumerate(R_H_array):
    fit_model_lsb.jet_leptonic.parameters.R_H.val=R_H
    B_array[ID]=fit_model_lsb.jet_leptonic.parameters.B.val

plt.loglog(R_H_array,B_array)
plt.xlabel('R_H (cm)')
plt.ylabel('B (G)')

Text(0, 0.5, 'B (G)')

../../../../_images/depending_pars_33_1.png

Removing the dependenencies#

for the entire fit_model

fit_model_lsb.parameters.reset_dependencies()

or, for a specific component

fit_model_lsb.jet_leptonic.parameters.reset_dependencies()

fit_model_lsb.parameters

Table length=14

model name	name	par type	units	val	phys. bound. min	phys. bound. max	log	frozen
jet_leptonic	gmin	low-energy-cut-off	lorentz-factor*	2.000000e+00	1.000000e+00	1.000000e+09	False	False
jet_leptonic	gmax	high-energy-cut-off	lorentz-factor*	1.000000e+06	1.000000e+00	1.000000e+15	False	False
jet_leptonic	N	emitters_density	1 / cm3	1.000000e+02	0.000000e+00	--	False	False
jet_leptonic	gamma_cut	turn-over-energy	lorentz-factor*	1.000000e+04	1.000000e+00	1.000000e+09	False	False
jet_leptonic	p	LE_spectral_slope		2.000000e+00	-1.000000e+01	1.000000e+01	False	False
jet_leptonic	R	region_size	cm	5.000000e+15	1.000000e+03	1.000000e+30	False	False
jet_leptonic	R_H	region_position	cm	1.000000e+18	0.000000e+00	--	False	False
jet_leptonic	B	magnetic_field	gauss	5.000000e-02	0.000000e+00	--	False	True
jet_leptonic	NH_cold_to_rel_e	cold_p_to_rel_e_ratio		1.000000e+00	0.000000e+00	--	False	True
jet_leptonic	beam_obj	beaming		1.000000e+01	1.000000e-04	--	False	False
jet_leptonic	z_cosm	redshift		1.000000e-01	0.000000e+00	--	False	False
jet_leptonic	B0	user_defined	G	1.000000e+03	0.000000e+00	--	False	True
jet_leptonic	R0	user_defined	cm	5.000000e+13	0.000000e+00	--	False	True
jet_leptonic	m_B	user_defined		1.000000e+00	1.000000e+00	2.000000e+00	False	False

None

%matplotlib inline

plt.figure(dpi=150)
R_H_array=np.logspace(13,18,100)
B_array=np.zeros(R_H_array.shape)
for ID,R_H in enumerate(R_H_array):
    fit_model_lsb.jet_leptonic.parameters.R_H.val=R_H
    B_array[ID]=fit_model_lsb.jet_leptonic.parameters.B.val

plt.loglog(R_H_array,B_array)
plt.xlabel('R_H (cm)')
plt.ylabel('B (G)')

Text(0, 0.5, 'B (G)')

../../../../_images/depending_pars_40_1.png

Example depending par: fitting with a Jet model with depending pars#

In this example we show how to use the previous model during a Fit

from jetset.test_data_helper import  test_SEDs
from jetset.data_loader import ObsData,Data
from jetset.plot_sedfit import PlotSED
from jetset.test_data_helper import  test_SEDs

data=Data.from_file(test_SEDs[1])

sed_data=ObsData(data_table=data)
sed_data.group_data(bin_width=0.2)

sed_data.add_systematics(0.1,[10.**6,10.**29])
p=sed_data.plot_sed()

================================================================================

*  binning data  *
---> N bins= 88
---> bin_width= 0.2
================================================================================

../../../../_images/depending_pars_45_1.png

from jetset.sed_shaper import  SEDShape
my_shape=SEDShape(sed_data)
my_shape.eval_indices(minimizer='lsb',silent=True)
p=my_shape.plot_indices()

================================================================================

* evaluating spectral indices for data *
================================================================================

../../../../_images/depending_pars_46_1.png

mm,best_fit=my_shape.sync_fit(check_host_gal_template=False,
                  Ep_start=None,
                  minimizer='lsb',
                  silent=True,
                  fit_range=[10.,21.])

================================================================================

* Log-Polynomial fitting of the synchrotron component *
---> first blind fit run,  fit range: [10.0, 21.0]
---> class:  HSP

Table length=4

model name	name	val	bestfit val	err +	err -	start val	fit range min	fit range max	frozen
LogCubic	b	-1.563747e-01	-1.563747e-01	5.975434e-03	--	-1.000000e+00	-1.000000e+01	0.000000e+00	False
LogCubic	c	-1.052802e-02	-1.052802e-02	8.781942e-04	--	-1.000000e+00	-1.000000e+01	1.000000e+01	False
LogCubic	Ep	1.675324e+01	1.675324e+01	2.396636e-02	--	1.670206e+01	0.000000e+00	3.000000e+01	False
LogCubic	Sp	-9.494365e+00	-9.494365e+00	1.704982e-02	--	-1.000000e+01	-3.000000e+01	0.000000e+00	False

---> sync       nu_p=+1.675324e+01 (err=+2.396636e-02)  nuFnu_p=-9.494365e+00 (err=+1.704982e-02) curv.=-1.563747e-01 (err=+5.975434e-03)
================================================================================

my_shape.IC_fit(fit_range=[23.,29.],minimizer='minuit',silent=True)
p=my_shape.plot_shape_fit()
p.setlim(y_min=1E-15)

================================================================================

* Log-Polynomial fitting of the IC component *
---> fit range: [23.0, 29.0]
---> LogCubic fit

Table length=4

model name	name	val	bestfit val	err +	err -	start val	fit range min	fit range max	frozen
LogCubic	b	-2.274590e-01	-2.274590e-01	3.262166e-02	--	-1.000000e+00	-1.000000e+01	0.000000e+00	False
LogCubic	c	-6.259967e-02	-6.259967e-02	1.629408e-02	--	-1.000000e+00	-1.000000e+01	1.000000e+01	False
LogCubic	Ep	2.527207e+01	2.527207e+01	8.149547e-02	--	2.528644e+01	0.000000e+00	3.000000e+01	False
LogCubic	Sp	-1.014119e+01	-1.014119e+01	2.734754e-02	--	-1.000000e+01	-3.000000e+01	0.000000e+00	False

---> IC         nu_p=+2.527207e+01 (err=+8.149547e-02)  nuFnu_p=-1.014119e+01 (err=+2.734754e-02) curv.=-2.274590e-01 (err=+3.262166e-02)
================================================================================

../../../../_images/depending_pars_48_3.png

from jetset.obs_constrain import ObsConstrain
from jetset.model_manager import  FitModel
sed_obspar=ObsConstrain(beaming=25,
                        B_range=[0.001,0.1],
                        distr_e='lppl',
                        t_var_sec=3*86400,
                        nu_cut_IR=1E12,
                        SEDShape=my_shape)


prefit_jet=sed_obspar.constrain_SSC_model(electron_distribution_log_values=False,silent=True)
prefit_jet.save_model('prefit_jet.pkl')

================================================================================

*  constrains parameters from observable *

/Users/orion/miniforge3/envs/jetset/lib/python3.12/site-packages/jetset/obs_constrain.py:1514: RankWarning: Polyfit may be poorly conditioned
  p=polyfit(nu_p_IC_model_log,B_grid_log,2)

Table length=12

model name	name	par type	units	val	phys. bound. min	phys. bound. max	log	frozen
jet_leptonic	R	region_size	cm	3.452668e+16	1.000000e+03	1.000000e+30	False	False
jet_leptonic	R_H	region_position	cm	1.000000e+17	0.000000e+00	--	False	True
jet_leptonic	B	magnetic_field	gauss	5.050000e-02	0.000000e+00	--	False	False
jet_leptonic	NH_cold_to_rel_e	cold_p_to_rel_e_ratio		1.000000e+00	0.000000e+00	--	False	True
jet_leptonic	beam_obj	beaming		2.500000e+01	1.000000e-04	--	False	False
jet_leptonic	z_cosm	redshift		3.080000e-02	0.000000e+00	--	False	False
jet_leptonic	gmin	low-energy-cut-off	lorentz-factor*	4.697542e+02	1.000000e+00	1.000000e+09	False	False
jet_leptonic	gmax	high-energy-cut-off	lorentz-factor*	1.300733e+06	1.000000e+00	1.000000e+15	False	False
jet_leptonic	N	emitters_density	1 / cm3	6.119093e-01	0.000000e+00	--	False	False
jet_leptonic	gamma0_log_parab	turn-over-energy	lorentz-factor*	3.290961e+04	1.000000e+00	1.000000e+09	False	False
jet_leptonic	s	LE_spectral_slope		2.169388e+00	-1.000000e+01	1.000000e+01	False	False
jet_leptonic	r	spectral_curvature		7.818737e-01	-1.500000e+01	1.500000e+01	False	False

================================================================================

from jetset.minimizer import fit_SED,ModelMinimizer

from jetset.model_manager import  FitModel
from jetset.jet_model import Jet
prefit_jet=Jet.load_model('prefit_jet.pkl')

fit_model=FitModel( jet=prefit_jet, name='SSC-best-fit-lsb',template=None)
fit_model.parameters

Table length=12

model name	name	par type	units	val	phys. bound. min	phys. bound. max	log	frozen
jet_leptonic	gmin	low-energy-cut-off	lorentz-factor*	4.697542e+02	1.000000e+00	1.000000e+09	False	False
jet_leptonic	gmax	high-energy-cut-off	lorentz-factor*	1.300733e+06	1.000000e+00	1.000000e+15	False	False
jet_leptonic	N	emitters_density	1 / cm3	6.119093e-01	0.000000e+00	--	False	False
jet_leptonic	gamma0_log_parab	turn-over-energy	lorentz-factor*	3.290961e+04	1.000000e+00	1.000000e+09	False	False
jet_leptonic	s	LE_spectral_slope		2.169388e+00	-1.000000e+01	1.000000e+01	False	False
jet_leptonic	r	spectral_curvature		7.818737e-01	-1.500000e+01	1.500000e+01	False	False
jet_leptonic	R	region_size	cm	3.452668e+16	1.000000e+03	1.000000e+30	False	False
jet_leptonic	R_H	region_position	cm	1.000000e+17	0.000000e+00	--	False	True
jet_leptonic	B	magnetic_field	gauss	5.050000e-02	0.000000e+00	--	False	False
jet_leptonic	NH_cold_to_rel_e	cold_p_to_rel_e_ratio		1.000000e+00	0.000000e+00	--	False	True
jet_leptonic	beam_obj	beaming		2.500000e+01	1.000000e-04	--	False	False
jet_leptonic	z_cosm	redshift		3.080000e-02	0.000000e+00	--	False	False

None

fit_model.jet_leptonic.parameters.beam_obj.fit_range = [5, 50]
fit_model.jet_leptonic.parameters.R_H.val=5E17
fit_model.jet_leptonic.parameters.R_H.frozen=False
fit_model.jet_leptonic.parameters.R_H.fit_range = [1E15, 1E19]
fit_model.jet_leptonic.parameters.R.fit_range = [10 ** 15.5, 10 ** 17.5]
fit_model.jet_leptonic.parameters.gamma0_log_parab.fit_range = [1E3,1E6]
fit_model.jet_leptonic.parameters.gmin.fit_range = [10,1000]
fit_model.jet_leptonic.parameters.gmax.fit_range = [1E5,1E8]

fit_model.jet_leptonic.add_user_par(name='B0',units='G',val=1E3,val_min=0,val_max=None)
fit_model.jet_leptonic.add_user_par(name='R0', units='cm', val=5E13, val_min=0, val_max=None)
fit_model.jet_leptonic.add_user_par(name='m_B', val=1, val_min=1, val_max=2)
fit_model.jet_leptonic.parameters.R0.frozen=True
fit_model.jet_leptonic.parameters.B0.frozen=True

def par_func(R0,B0,R_H,m_B):
    return B0*np.power((R0/R_H),m_B)

fit_model.jet_leptonic.make_dependent_par(par='B', depends_on=['B0', 'R0', 'R_H','m_B'], par_expr=par_func)
fit_model.parameters

adding par: B0 to  B
adding par: R0 to  B
adding par: R_H to  B
adding par: m_B to  B
==> par B is depending on ['B0', 'R0', 'R_H', 'm_B'] according to expr:   B =
def par_func(R0,B0,R_H,m_B):
    return B0*np.power((R0/R_H),m_B)

Table length=15

model name	name	par type	units	val	phys. bound. min	phys. bound. max	log	frozen
jet_leptonic	gmin	low-energy-cut-off	lorentz-factor*	4.697542e+02	1.000000e+00	1.000000e+09	False	False
jet_leptonic	gmax	high-energy-cut-off	lorentz-factor*	1.300733e+06	1.000000e+00	1.000000e+15	False	False
jet_leptonic	N	emitters_density	1 / cm3	6.119093e-01	0.000000e+00	--	False	False
jet_leptonic	gamma0_log_parab	turn-over-energy	lorentz-factor*	3.290961e+04	1.000000e+00	1.000000e+09	False	False
jet_leptonic	s	LE_spectral_slope		2.169388e+00	-1.000000e+01	1.000000e+01	False	False
jet_leptonic	r	spectral_curvature		7.818737e-01	-1.500000e+01	1.500000e+01	False	False
jet_leptonic	R	region_size	cm	3.452668e+16	1.000000e+03	1.000000e+30	False	False
jet_leptonic	R_H(M)	region_position	cm	5.000000e+17	0.000000e+00	--	False	False
jet_leptonic	*B(D,m_B)	magnetic_field	gauss	1.000000e-01	0.000000e+00	--	False	True
jet_leptonic	NH_cold_to_rel_e	cold_p_to_rel_e_ratio		1.000000e+00	0.000000e+00	--	False	True
jet_leptonic	beam_obj	beaming		2.500000e+01	1.000000e-04	--	False	False
jet_leptonic	z_cosm	redshift		3.080000e-02	0.000000e+00	--	False	False
jet_leptonic	B0(M)	user_defined	G	1.000000e+03	0.000000e+00	--	False	True
jet_leptonic	R0(M)	user_defined	cm	5.000000e+13	0.000000e+00	--	False	True
jet_leptonic	m_B(M)	user_defined		1.000000e+00	1.000000e+00	2.000000e+00	False	False

None

%matplotlib inline

plt.figure(dpi=150)
R_H_array=np.logspace(13,18,100)
B_array=np.zeros(R_H_array.shape)
for ID,R_H in enumerate(R_H_array):
    fit_model.jet_leptonic.parameters.R_H.val=R_H
    B_array[ID]=fit_model.jet_leptonic.parameters.B.val

plt.loglog(R_H_array,B_array)
plt.xlabel('R_H (cm)')
plt.ylabel('B (G)')

Text(0, 0.5, 'B (G)')

../../../../_images/depending_pars_53_1.png

fit_model.jet_leptonic.parameters.R_H.val=5E17

fit_model.parameters

Table length=15

model name	name	par type	units	val	phys. bound. min	phys. bound. max	log	frozen
jet_leptonic	gmin	low-energy-cut-off	lorentz-factor*	4.697542e+02	1.000000e+00	1.000000e+09	False	False
jet_leptonic	gmax	high-energy-cut-off	lorentz-factor*	1.300733e+06	1.000000e+00	1.000000e+15	False	False
jet_leptonic	N	emitters_density	1 / cm3	6.119093e-01	0.000000e+00	--	False	False
jet_leptonic	gamma0_log_parab	turn-over-energy	lorentz-factor*	3.290961e+04	1.000000e+00	1.000000e+09	False	False
jet_leptonic	s	LE_spectral_slope		2.169388e+00	-1.000000e+01	1.000000e+01	False	False
jet_leptonic	r	spectral_curvature		7.818737e-01	-1.500000e+01	1.500000e+01	False	False
jet_leptonic	R	region_size	cm	3.452668e+16	1.000000e+03	1.000000e+30	False	False
jet_leptonic	R_H(M)	region_position	cm	5.000000e+17	0.000000e+00	--	False	False
jet_leptonic	*B(D,m_B)	magnetic_field	gauss	1.000000e-01	0.000000e+00	--	False	True
jet_leptonic	NH_cold_to_rel_e	cold_p_to_rel_e_ratio		1.000000e+00	0.000000e+00	--	False	True
jet_leptonic	beam_obj	beaming		2.500000e+01	1.000000e-04	--	False	False
jet_leptonic	z_cosm	redshift		3.080000e-02	0.000000e+00	--	False	False
jet_leptonic	B0(M)	user_defined	G	1.000000e+03	0.000000e+00	--	False	True
jet_leptonic	R0(M)	user_defined	cm	5.000000e+13	0.000000e+00	--	False	True
jet_leptonic	m_B(M)	user_defined		1.000000e+00	1.000000e+00	2.000000e+00	False	False

None

As a resuslt of the best fit modeling, we are able to determine the value of R_H. We now perform the fit with minuit to get a better estimate of the errors

model_minimizer_minuit=ModelMinimizer('minuit')

model_minimizer_minuit.minimizer.add_simplex=False

best_fit_minuit=model_minimizer_minuit.fit(fit_model,
                                     sed_data,
                                     1E11,
                                     1E29,
                                     fitname='SSC-best-fit-minuit',
                                     repeat=3)

filtering data in fit range = [1.000000e+11,1.000000e+29]
data length 34
================================================================================

* start fit process *
-----
fit run: 0

0it [00:00, ?it/s]

- best chisq=2.96150e+01

fit run: 1
- old chisq=2.96150e+01

0it [00:00, ?it/s]

- best chisq=1.95141e+01

fit run: 2
- old chisq=1.95141e+01

0it [00:00, ?it/s]

- best chisq=1.74806e+01

-------------------------------------------------------------------------
Fit report

Model: SSC-best-fit-minuit

Table length=15

model name	name	par type	units	val	phys. bound. min	phys. bound. max	log	frozen
jet_leptonic	gmin	low-energy-cut-off	lorentz-factor*	7.901768e+02	1.000000e+00	1.000000e+09	False	False
jet_leptonic	gmax	high-energy-cut-off	lorentz-factor*	8.159004e+05	1.000000e+00	1.000000e+15	False	False
jet_leptonic	N	emitters_density	1 / cm3	5.944310e-01	0.000000e+00	--	False	False
jet_leptonic	gamma0_log_parab	turn-over-energy	lorentz-factor*	4.368239e+04	1.000000e+00	1.000000e+09	False	False
jet_leptonic	s	LE_spectral_slope		2.245708e+00	-1.000000e+01	1.000000e+01	False	False
jet_leptonic	r	spectral_curvature		7.510777e-01	-1.500000e+01	1.500000e+01	False	False
jet_leptonic	R	region_size	cm	2.468737e+16	1.000000e+03	1.000000e+30	False	False
jet_leptonic	R_H(M)	region_position	cm	8.803240e+17	0.000000e+00	--	False	False
jet_leptonic	*B(D,m_B)	magnetic_field	gauss	5.272230e-02	0.000000e+00	--	False	True
jet_leptonic	NH_cold_to_rel_e	cold_p_to_rel_e_ratio		1.000000e+00	0.000000e+00	--	False	True
jet_leptonic	beam_obj	beaming		2.782337e+01	1.000000e-04	--	False	False
jet_leptonic	z_cosm	redshift		3.146581e-02	0.000000e+00	--	False	False
jet_leptonic	B0(M)	user_defined	G	1.000000e+03	0.000000e+00	--	False	True
jet_leptonic	R0(M)	user_defined	cm	5.000000e+13	0.000000e+00	--	False	True
jet_leptonic	m_B(M)	user_defined		1.007616e+00	1.000000e+00	2.000000e+00	False	False

converged=True
calls=3117
mesg=

Migrad
FCN = 17.48	Nfcn = 3117
EDM = 1.35 (Goal: 0.0002)	time = 4.2 sec
INVALID Minimum	ABOVE EDM threshold (goal x 10)
No parameters at limit	Below call limit
Hesse ok	Covariance FORCED pos. def.

	Name	Value	Hesse Error	Minos Error-	Minos Error+	Limit-	Limit+	Fixed
0	par_0	790.18	0.08			10	1E+03
1	par_1	0.82e6	0.04e6			1E+05	1E+08
2	par_2	594.4e-3	0.4e-3			0
3	par_3	43.68e3	0.11e3			1E+03	1E+06
4	par_4	2.246	0.005			-10	10
5	par_5	751.08e-3	0.27e-3			-15	15
6	par_6	24.687e15	0.033e15			3.16E+15	3.16E+17
7	par_7	880.3e15	1.2e15			1E+15	1E+19
8	par_8	27.82	0.10			5	50
9	par_9	31.47e-3	0.29e-3			0
10	par_10	1.00762	0.00004			1	2

dof=23
chisq=17.480625, chisq/red=0.760027 null hypothesis sig=0.785020

best fit pars

Table length=15

model name	name	val	bestfit val	err +	err -	start val	fit range min	fit range max	frozen
jet_leptonic	gmin	7.901768e+02	7.901768e+02	7.906302e-02	--	4.697542e+02	1.000000e+01	1.000000e+03	False
jet_leptonic	gmax	8.159004e+05	8.159004e+05	4.249267e+04	--	1.300733e+06	1.000000e+05	1.000000e+08	False
jet_leptonic	N	5.944310e-01	5.944310e-01	4.105893e-04	--	6.119093e-01	0.000000e+00	--	False
jet_leptonic	gamma0_log_parab	4.368239e+04	4.368239e+04	1.072635e+02	--	3.290961e+04	1.000000e+03	1.000000e+06	False
jet_leptonic	s	2.245708e+00	2.245708e+00	4.928117e-03	--	2.169388e+00	-1.000000e+01	1.000000e+01	False
jet_leptonic	r	7.510777e-01	7.510777e-01	2.653911e-04	--	7.818737e-01	-1.500000e+01	1.500000e+01	False
jet_leptonic	R	2.468737e+16	2.468737e+16	3.252909e+13	--	3.452668e+16	3.162278e+15	3.162278e+17	False
jet_leptonic	R_H(M)	8.803240e+17	8.803240e+17	1.224094e+15	--	5.000000e+17	1.000000e+15	1.000000e+19	False
jet_leptonic	*B(D,m_B)	5.272230e-02	--	--	--	1.000000e-01	0.000000e+00	--	True
jet_leptonic	NH_cold_to_rel_e	1.000000e+00	--	--	--	1.000000e+00	0.000000e+00	--	True
jet_leptonic	beam_obj	2.782337e+01	2.782337e+01	9.528700e-02	--	2.500000e+01	5.000000e+00	5.000000e+01	False
jet_leptonic	z_cosm	3.146581e-02	3.146581e-02	2.918306e-04	--	3.080000e-02	0.000000e+00	--	False
jet_leptonic	B0(M)	1.000000e+03	--	--	--	1.000000e+03	0.000000e+00	--	True
jet_leptonic	R0(M)	5.000000e+13	--	--	--	5.000000e+13	0.000000e+00	--	True
jet_leptonic	m_B(M)	1.007616e+00	1.007616e+00	4.489280e-05	--	1.000000e+00	1.000000e+00	2.000000e+00	False

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

================================================================================

fit_model.plot_model(sed_data=sed_data)

<jetset.plot_sedfit.PlotSED at 0x313473320>

../../../../_images/depending_pars_60_1.png

%matplotlib inline
plt.figure(dpi=150)
R_H_array=np.logspace(13,18,100)
B_array=np.zeros(R_H_array.shape)
for ID,R_H in enumerate(R_H_array):
    fit_model.jet_leptonic.parameters.R_H.val=R_H
    B_array[ID]=fit_model.jet_leptonic.parameters.B.val

plt.loglog(R_H_array,B_array)
plt.xlabel('R_H (cm)')
plt.ylabel('B (G)')

Text(0, 0.5, 'B (G)')

../../../../_images/depending_pars_61_1.png

fit_model.save_model('test.pkl')

from jetset.model_manager import  FitModel

new_fit_model=FitModel.load_model('test.pkl')

new_fit_model.parameters

Table length=15

model name	name	par type	units	val	phys. bound. min	phys. bound. max	log	frozen
jet_leptonic	gmin	low-energy-cut-off	lorentz-factor*	7.901768e+02	1.000000e+00	1.000000e+09	False	False
jet_leptonic	gmax	high-energy-cut-off	lorentz-factor*	8.159004e+05	1.000000e+00	1.000000e+15	False	False
jet_leptonic	N	emitters_density	1 / cm3	5.944310e-01	0.000000e+00	--	False	False
jet_leptonic	gamma0_log_parab	turn-over-energy	lorentz-factor*	4.368239e+04	1.000000e+00	1.000000e+09	False	False
jet_leptonic	s	LE_spectral_slope		2.245708e+00	-1.000000e+01	1.000000e+01	False	False
jet_leptonic	r	spectral_curvature		7.510777e-01	-1.500000e+01	1.500000e+01	False	False
jet_leptonic	R	region_size	cm	2.468737e+16	1.000000e+03	1.000000e+30	False	False
jet_leptonic	R_H(M)	region_position	cm	1.000000e+18	0.000000e+00	--	False	False
jet_leptonic	*B(D,m_B)	magnetic_field	gauss	4.636767e-02	0.000000e+00	--	False	True
jet_leptonic	NH_cold_to_rel_e	cold_p_to_rel_e_ratio		1.000000e+00	0.000000e+00	--	False	True
jet_leptonic	beam_obj	beaming		2.782337e+01	1.000000e-04	--	False	False
jet_leptonic	z_cosm	redshift		3.146581e-02	0.000000e+00	--	False	False
jet_leptonic	B0(M)	user_defined	G	1.000000e+03	0.000000e+00	--	False	True
jet_leptonic	R0(M)	user_defined	cm	5.000000e+13	0.000000e+00	--	False	True
jet_leptonic	m_B(M)	user_defined		1.007616e+00	1.000000e+00	2.000000e+00	False	False

None

Depending parameters

Contents

Depending parameters#

Example: linked paramters for EBL#

Example: depending pars for bkn power-law emitters#

Example depending par: R depends on variability time scale#

Example depending par: Building a Jet model with B function of R_H and R_0#

Removing the dependenencies#

Example depending par: fitting with a Jet model with depending pars#