.. _model_fitting_2:

Model fitting 2: SSC + galaxy template
======================================

.. code:: ipython3

    import warnings
    warnings.filterwarnings('ignore')
    
    import matplotlib.pylab as plt
    import jetset
    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


.. code:: ipython3

    print(jetset.__version__)


.. parsed-literal::

    1.3.0rc7


.. code:: ipython3

    test_SEDs




.. parsed-literal::

    ['/Users/orion/miniforge3/envs/jetset/lib/python3.10/site-packages/jetset/test_data/SEDs_data/SED_3C345.ecsv',
     '/Users/orion/miniforge3/envs/jetset/lib/python3.10/site-packages/jetset/test_data/SEDs_data/SED_MW_Mrk421_EBL_DEABS.ecsv',
     '/Users/orion/miniforge3/envs/jetset/lib/python3.10/site-packages/jetset/test_data/SEDs_data/SED_MW_Mrk501_EBL_ABS.ecsv',
     '/Users/orion/miniforge3/envs/jetset/lib/python3.10/site-packages/jetset/test_data/SEDs_data/SED_MW_Mrk501_EBL_DEABS.ecsv']



Loading data
------------

see the :ref:`data_format` user guide for further information about loading data 

.. code:: ipython3

    data=Data.from_file(test_SEDs[3])


.. code:: ipython3

    %matplotlib inline
    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()


.. parsed-literal::

    ================================================================================
    
    ***  binning data  ***
    ---> N bins= 90
    ---> bin_widht= 0.2
    msk [False  True False  True  True  True  True  True False False False  True
     False False False False False False False False False False False False
     False  True  True  True  True  True  True False False False False False
     False False  True  True  True  True False  True  True  True  True  True
      True False  True False False False False False False False False False
     False False False False False False  True False  True False  True False
      True False  True False  True False False False False False  True  True
      True  True  True  True  True False]
    ================================================================================
    



.. image:: Jet_example_model_fit_wiht_gal_template_files/Jet_example_model_fit_wiht_gal_template_8_1.png


.. code:: ipython3

    sed_data.save('Mrk_501.pkl')

Phenomenological model constraining
-----------------------------------

see the :ref:`phenom_constr` user guide for further information about loading data 

Spectral indices
~~~~~~~~~~~~~~~~

.. code:: ipython3

    from jetset.sed_shaper import  SEDShape
    my_shape=SEDShape(sed_data)
    my_shape.eval_indices(silent=True)
    p=my_shape.plot_indices()
    p.setlim(y_min=1E-15,y_max=1E-6)


.. parsed-literal::

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



.. image:: Jet_example_model_fit_wiht_gal_template_files/Jet_example_model_fit_wiht_gal_template_13_1.png


Sed shaper
~~~~~~~~~~

.. code:: ipython3

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


.. parsed-literal::

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



.. raw:: html

    <i>Table length=6</i>
    <table id="table5736199264-56934" class="table-striped table-bordered table-condensed">
    <thead><tr><th>model name</th><th>name</th><th>val</th><th>bestfit val</th><th>err +</th><th>err -</th><th>start val</th><th>fit range min</th><th>fit range max</th><th>frozen</th></tr></thead>
    <tr><td>LogCubic</td><td>b</td><td>-6.522794e-02</td><td>-6.522794e-02</td><td>5.892905e-03</td><td>--</td><td>-4.913172e-02</td><td>-1.000000e+01</td><td>0.000000e+00</td><td>False</td></tr>
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    <tr><td>LogCubic</td><td>Ep</td><td>1.704833e+01</td><td>1.704833e+01</td><td>6.858392e-02</td><td>--</td><td>1.593204e+01</td><td>0.000000e+00</td><td>3.000000e+01</td><td>False</td></tr>
    <tr><td>LogCubic</td><td>Sp</td><td>-1.030052e+01</td><td>-1.030052e+01</td><td>1.424853e-02</td><td>--</td><td>-1.022242e+01</td><td>-3.000000e+01</td><td>0.000000e+00</td><td>False</td></tr>
    <tr><td>host_galaxy</td><td>nuFnu_p_host</td><td>-1.008538e+01</td><td>-1.008538e+01</td><td>2.900917e-02</td><td>--</td><td>-1.022242e+01</td><td>-1.222242e+01</td><td>-8.222416e+00</td><td>False</td></tr>
    <tr><td>host_galaxy</td><td>nu_scale</td><td>1.934519e-02</td><td>1.934519e-02</td><td>1.919833e-03</td><td>--</td><td>0.000000e+00</td><td>-5.000000e-01</td><td>5.000000e-01</td><td>False</td></tr>
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        var a_num = parseFloat(a);
        var b_num = parseFloat(b);
    
        if (isNaN(a_num) && isNaN(b_num))
            return ((a < b) ? -1 : ((a > b) ? 1 : 0));
        else if (!isNaN(a_num) && !isNaN(b_num))
            return ((a_num < b_num) ? -1 : ((a_num > b_num) ? 1 : 0));
        else
            return isNaN(a_num) ? -1 : 1;
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    require.config({paths: {
        datatables: 'https://cdn.datatables.net/1.10.12/js/jquery.dataTables.min'
    }});
    require(["datatables"], function(){
        console.log("$('#table5736199264-56934').dataTable()");
    
    jQuery.extend( jQuery.fn.dataTableExt.oSort, {
        "optionalnum-asc": astropy_sort_num,
        "optionalnum-desc": function (a,b) { return -astropy_sort_num(a, b); }
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        $('#table5736199264-56934').dataTable({
            order: [],
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    </script>



.. parsed-literal::

    ---> sync       nu_p=+1.704833e+01 (err=+6.858392e-02)  nuFnu_p=-1.030052e+01 (err=+1.424853e-02) curv.=-6.522794e-02 (err=+5.892905e-03)
    ================================================================================
    


.. code:: ipython3

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


.. parsed-literal::

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



.. raw:: html

    <i>Table length=4</i>
    <table id="table5736199120-910386" class="table-striped table-bordered table-condensed">
    <thead><tr><th>model name</th><th>name</th><th>val</th><th>bestfit val</th><th>err +</th><th>err -</th><th>start val</th><th>fit range min</th><th>fit range max</th><th>frozen</th></tr></thead>
    <tr><td>LogCubic</td><td>b</td><td>-1.323324e-01</td><td>-1.323324e-01</td><td>3.154579e-02</td><td>--</td><td>-1.000000e+00</td><td>-1.000000e+01</td><td>0.000000e+00</td><td>False</td></tr>
    <tr><td>LogCubic</td><td>c</td><td>-3.389147e-02</td><td>-3.389147e-02</td><td>2.022657e-02</td><td>--</td><td>-1.000000e+00</td><td>-1.000000e+01</td><td>1.000000e+01</td><td>False</td></tr>
    <tr><td>LogCubic</td><td>Ep</td><td>2.550950e+01</td><td>2.550950e+01</td><td>2.190510e-01</td><td>--</td><td>2.555059e+01</td><td>0.000000e+00</td><td>3.000000e+01</td><td>False</td></tr>
    <tr><td>LogCubic</td><td>Sp</td><td>-1.057957e+01</td><td>-1.057957e+01</td><td>4.198643e-02</td><td>--</td><td>-1.000000e+01</td><td>-3.000000e+01</td><td>0.000000e+00</td><td>False</td></tr>
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        else if (!isNaN(a_num) && !isNaN(b_num))
            return ((a_num < b_num) ? -1 : ((a_num > b_num) ? 1 : 0));
        else
            return isNaN(a_num) ? -1 : 1;
    }
    
    require.config({paths: {
        datatables: 'https://cdn.datatables.net/1.10.12/js/jquery.dataTables.min'
    }});
    require(["datatables"], function(){
        console.log("$('#table5736199120-910386').dataTable()");
    
    jQuery.extend( jQuery.fn.dataTableExt.oSort, {
        "optionalnum-asc": astropy_sort_num,
        "optionalnum-desc": function (a,b) { return -astropy_sort_num(a, b); }
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            columnDefs: [{targets: [2, 3, 4, 5, 6, 7, 8], type: "optionalnum"}]
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    });
    </script>



.. parsed-literal::

    ---> IC         nu_p=+2.550950e+01 (err=+2.190510e-01)  nuFnu_p=-1.057957e+01 (err=+4.198643e-02) curv.=-1.323324e-01 (err=+3.154579e-02)
    ================================================================================
    



.. image:: Jet_example_model_fit_wiht_gal_template_files/Jet_example_model_fit_wiht_gal_template_16_3.png


Model constraining
~~~~~~~~~~~~~~~~~~

In this step we are not fitting the model, we are just obtaining the
phenomenological ``pre_fit`` model, that will be fitted in using minuit
ore least-square bound, as shown below

.. code:: ipython3

    from jetset.obs_constrain import ObsConstrain
    from jetset.model_manager import  FitModel
    from jetset.minimizer import fit_SED
    sed_obspar=ObsConstrain(beaming=25,
                            B_range=[0.001,0.1],
                            distr_e='lppl',
                            t_var_sec=3*86400,
                            nu_cut_IR=1E11,
                            SEDShape=my_shape)
    
    
    prefit_jet=sed_obspar.constrain_SSC_model(electron_distribution_log_values=False,silent=True)
    prefit_jet.save_model('prefit_jet_gal_templ.pkl')


.. parsed-literal::

    ================================================================================
    
    ***  constrains parameters from observable ***
    
    ===> setting C threads to 12



.. raw:: html

    <i>Table length=12</i>
    <table id="table5700426032-562712" class="table-striped table-bordered table-condensed">
    <thead><tr><th>model name</th><th>name</th><th>par type</th><th>units</th><th>val</th><th>phys. bound. min</th><th>phys. bound. max</th><th>log</th><th>frozen</th></tr></thead>
    <tr><td>jet_leptonic</td><td>R</td><td>region_size</td><td>cm</td><td>1.141280e+16</td><td>1.000000e+03</td><td>1.000000e+30</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>R_H</td><td>region_position</td><td>cm</td><td>1.000000e+17</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>B</td><td>magnetic_field</td><td>gauss</td><td>5.050000e-02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>NH_cold_to_rel_e</td><td>cold_p_to_rel_e_ratio</td><td></td><td>1.000000e+00</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>beam_obj</td><td>beaming</td><td></td><td>2.500000e+01</td><td>1.000000e-04</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>z_cosm</td><td>redshift</td><td></td><td>3.360000e-02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>gmin</td><td>low-energy-cut-off</td><td>lorentz-factor*</td><td>1.487509e+02</td><td>1.000000e+00</td><td>1.000000e+09</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>gmax</td><td>high-energy-cut-off</td><td>lorentz-factor*</td><td>2.310708e+06</td><td>1.000000e+00</td><td>1.000000e+15</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>N</td><td>emitters_density</td><td>1 / cm3</td><td>2.312656e+01</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>gamma0_log_parab</td><td>turn-over-energy</td><td>lorentz-factor*</td><td>1.107634e+04</td><td>1.000000e+00</td><td>1.000000e+09</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>s</td><td>LE_spectral_slope</td><td></td><td>2.248426e+00</td><td>-1.000000e+01</td><td>1.000000e+01</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>r</td><td>spectral_curvature</td><td></td><td>3.261397e-01</td><td>-1.500000e+01</td><td>1.500000e+01</td><td>False</td><td>False</td></tr>
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        else
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        datatables: 'https://cdn.datatables.net/1.10.12/js/jquery.dataTables.min'
    }});
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        "optionalnum-asc": astropy_sort_num,
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.. parsed-literal::

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


.. code:: ipython3

    pl=prefit_jet.plot_model(sed_data=sed_data)
    pl.add_residual_plot(prefit_jet,sed_data)
    pl.setlim(y_min=1E-14,x_min=1E7,x_max=1E29)



.. image:: Jet_example_model_fit_wiht_gal_template_files/Jet_example_model_fit_wiht_gal_template_20_0.png


Model fitting procedure
-----------------------

.. note::
    Please, read the introduction and the caveat :ref:`for the frequentist model fitting <frequentist_model_fitting>` to understand the frequentist fitting workflow
    see the :ref:`composite_models` user guide for further information about the implementation of :class:`.FitModel`, in particular for parameter setting

Model fitting with LSB
~~~~~~~~~~~~~~~~~~~~~~

.. code:: ipython3

    from jetset.model_manager import  FitModel
    from jetset.jet_model import Jet
    
    jet=Jet.load_model('prefit_jet_gal_templ.pkl')
    jet.set_gamma_grid_size(200)


.. parsed-literal::

    ===> setting C threads to 12


.. code:: ipython3

    fit_model=FitModel( jet=jet, name='SSC-best-fit-lsb',template=my_shape.host_gal) 
    fit_model.show_model()


.. parsed-literal::

    
    --------------------------------------------------------------------------------
    Composite model description
    --------------------------------------------------------------------------------
    name: SSC-best-fit-lsb  
    type: composite_model  
    components models:
     -model name: jet_leptonic model type: jet
     -model name: host_galaxy model type: template
    
    --------------------------------------------------------------------------------
    individual component description
    
    --------------------------------------------------------------------------------
    model description: 
    --------------------------------------------------------------------------------
    type: Jet
    name: jet_leptonic  
    geometry: spherical  
    
    electrons distribution:
     type: lppl  
     gamma energy grid size:  201
     gmin grid : 1.487509e+02
     gmax grid : 2.310708e+06
     normalization:  True
     log-values:  False
     ratio of cold protons to relativistic electrons: 1.000000e+00
    
    radiative fields:
     seed photons grid size:  100
     IC emission grid size:  100
     source emissivity lower bound :  1.000000e-120
     spectral components:
       name:Sum, state: on
       name:Sum, hidden: False
       name:Sync, state: self-abs
       name:Sync, hidden: False
       name:SSC, state: on
       name:SSC, hidden: False
    external fields transformation method: blob
    
    SED info:
     nu grid size jetkernel: 1000
     nu size: 500
     nu mix (Hz): 1.000000e+06
     nu max (Hz): 1.000000e+30
    
    flux plot lower bound   :  1.000000e-30
    
    --------------------------------------------------------------------------------



.. raw:: html

    <i>Table length=12</i>
    <table id="table5750808368-678149" class="table-striped table-bordered table-condensed">
    <thead><tr><th>model name</th><th>name</th><th>par type</th><th>units</th><th>val</th><th>phys. bound. min</th><th>phys. bound. max</th><th>log</th><th>frozen</th></tr></thead>
    <tr><td>jet_leptonic</td><td>gmin</td><td>low-energy-cut-off</td><td>lorentz-factor*</td><td>1.487509e+02</td><td>1.000000e+00</td><td>1.000000e+09</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>gmax</td><td>high-energy-cut-off</td><td>lorentz-factor*</td><td>2.310708e+06</td><td>1.000000e+00</td><td>1.000000e+15</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>N</td><td>emitters_density</td><td>1 / cm3</td><td>2.312656e+01</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>gamma0_log_parab</td><td>turn-over-energy</td><td>lorentz-factor*</td><td>1.107634e+04</td><td>1.000000e+00</td><td>1.000000e+09</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>s</td><td>LE_spectral_slope</td><td></td><td>2.248426e+00</td><td>-1.000000e+01</td><td>1.000000e+01</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>r</td><td>spectral_curvature</td><td></td><td>3.261397e-01</td><td>-1.500000e+01</td><td>1.500000e+01</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>R</td><td>region_size</td><td>cm</td><td>1.141280e+16</td><td>1.000000e+03</td><td>1.000000e+30</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>R_H</td><td>region_position</td><td>cm</td><td>1.000000e+17</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>B</td><td>magnetic_field</td><td>gauss</td><td>5.050000e-02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>NH_cold_to_rel_e</td><td>cold_p_to_rel_e_ratio</td><td></td><td>1.000000e+00</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>beam_obj</td><td>beaming</td><td></td><td>2.500000e+01</td><td>1.000000e-04</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>z_cosm</td><td>redshift</td><td></td><td>3.360000e-02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
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    </style>
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        else if (!isNaN(a_num) && !isNaN(b_num))
            return ((a_num < b_num) ? -1 : ((a_num > b_num) ? 1 : 0));
        else
            return isNaN(a_num) ? -1 : 1;
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    require.config({paths: {
        datatables: 'https://cdn.datatables.net/1.10.12/js/jquery.dataTables.min'
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    </script>



.. parsed-literal::

    --------------------------------------------------------------------------------
    
    --------------------------------------------------------------------------------
    model description
    --------------------------------------------------------------------------------
    name: host_galaxy  
    type: template  
    
    --------------------------------------------------------------------------------



.. raw:: html

    <i>Table length=2</i>
    <table id="table5735871824-374274" class="table-striped table-bordered table-condensed">
    <thead><tr><th>model name</th><th>name</th><th>par type</th><th>units</th><th>val</th><th>phys. bound. min</th><th>phys. bound. max</th><th>log</th><th>frozen</th></tr></thead>
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.. parsed-literal::

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


.. note::
   Since the `jet_leptonic to model` has to be summed to the `host_galaxy` model, we do not need to define the functional form for the composite model, because
   the default compostion is the sum of all the components
   (see the :ref:`composite_models` user guide for further information about the new implementation of `FitModel`, in particular for parameter setting).
   Anyhow, we show here the definition of the model composition  for purpose of clarity

.. code:: ipython3

    fit_model.composite_expr='jet_leptonic + host_galaxy'

.. code:: ipython3

    fit_model.freeze('jet_leptonic','z_cosm')
    fit_model.freeze('jet_leptonic','R_H')
    fit_model.jet_leptonic.parameters.N.fit_range=[1E-5, 1E5]
    fit_model.jet_leptonic.parameters.B.fit_range=[1E-3, 1]
    
    fit_model.jet_leptonic.parameters.beam_obj.fit_range=[5., 50.]
    fit_model.jet_leptonic.parameters.R.fit_range=[1E15,1E17]
    fit_model.jet_leptonic.parameters.gmax.fit_range=[1E4,1E8]
    fit_model.host_galaxy.parameters.nuFnu_p_host.frozen=False
    fit_model.host_galaxy.parameters.nu_scale.frozen=True

.. code:: ipython3

    from jetset.minimizer import fit_SED,ModelMinimizer
    
    model_minimizer_lsb=ModelMinimizer('lsb')
    best_fit_lsb=model_minimizer_lsb.fit(fit_model,sed_data,1E11,1E29,fitname='SSC-best-fit-lsb',repeat=1)


.. parsed-literal::

    filtering data in fit range = [1.000000e+11,1.000000e+29]
    data length 31
    ================================================================================
    
    *** start fit process ***
    ----- 



.. parsed-literal::

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


.. parsed-literal::

    - best chisq=4.16923e+01
    
    -------------------------------------------------------------------------
    Fit report
    
    Model: SSC-best-fit-lsb



.. raw:: html

    <i>Table length=14</i>
    <table id="table5750808368-67023" class="table-striped table-bordered table-condensed">
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    <tr><td>jet_leptonic</td><td>r</td><td>spectral_curvature</td><td></td><td>2.813492e-01</td><td>-1.500000e+01</td><td>1.500000e+01</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>R</td><td>region_size</td><td>cm</td><td>1.141280e+16</td><td>1.000000e+03</td><td>1.000000e+30</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>R_H</td><td>region_position</td><td>cm</td><td>1.000000e+17</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
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    <tr><td>jet_leptonic</td><td>NH_cold_to_rel_e</td><td>cold_p_to_rel_e_ratio</td><td></td><td>1.000000e+00</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>beam_obj</td><td>beaming</td><td></td><td>2.575826e+01</td><td>1.000000e-04</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>z_cosm</td><td>redshift</td><td></td><td>3.360000e-02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>host_galaxy</td><td>nuFnu_p_host</td><td>nuFnu-scale</td><td>erg / (s cm2)</td><td>-1.005821e+01</td><td>-2.000000e+01</td><td>2.000000e+01</td><td>False</td><td>False</td></tr>
    <tr><td>host_galaxy</td><td>nu_scale</td><td>nu-scale</td><td>Hz</td><td>1.934519e-02</td><td>-2.000000e+00</td><td>2.000000e+00</td><td>False</td><td>True</td></tr>
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        var a_num = parseFloat(a);
        var b_num = parseFloat(b);
    
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            return ((a < b) ? -1 : ((a > b) ? 1 : 0));
        else if (!isNaN(a_num) && !isNaN(b_num))
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.. parsed-literal::

    
    converged=True
    calls=429
    mesg=



.. parsed-literal::

    '`ftol` termination condition is satisfied.'


.. parsed-literal::

    dof=21
    chisq=41.692309, chisq/red=1.985348 null hypothesis sig=0.004599
    
    best fit pars



.. raw:: html

    <i>Table length=14</i>
    <table id="table5736198832-769156" class="table-striped table-bordered table-condensed">
    <thead><tr><th>model name</th><th>name</th><th>val</th><th>bestfit val</th><th>err +</th><th>err -</th><th>start val</th><th>fit range min</th><th>fit range max</th><th>frozen</th></tr></thead>
    <tr><td>jet_leptonic</td><td>gmin</td><td>8.580927e+01</td><td>8.580927e+01</td><td>2.245405e+02</td><td>--</td><td>1.487509e+02</td><td>1.000000e+00</td><td>1.000000e+09</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>gmax</td><td>2.310708e+06</td><td>2.310708e+06</td><td>3.063708e+06</td><td>--</td><td>2.310708e+06</td><td>1.000000e+04</td><td>1.000000e+08</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>N</td><td>5.244887e+01</td><td>5.244887e+01</td><td>3.642249e+02</td><td>--</td><td>2.312656e+01</td><td>1.000000e-05</td><td>1.000000e+05</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>gamma0_log_parab</td><td>1.069947e+04</td><td>1.069947e+04</td><td>1.593138e+04</td><td>--</td><td>1.107634e+04</td><td>1.000000e+00</td><td>1.000000e+09</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>s</td><td>2.220278e+00</td><td>2.220278e+00</td><td>6.119317e-02</td><td>--</td><td>2.248426e+00</td><td>-1.000000e+01</td><td>1.000000e+01</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>r</td><td>2.813492e-01</td><td>2.813492e-01</td><td>6.199616e-02</td><td>--</td><td>3.261397e-01</td><td>-1.500000e+01</td><td>1.500000e+01</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>R</td><td>1.141280e+16</td><td>1.141280e+16</td><td>4.323108e+16</td><td>--</td><td>1.141280e+16</td><td>1.000000e+15</td><td>1.000000e+17</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>R_H</td><td>1.000000e+17</td><td>--</td><td>--</td><td>--</td><td>1.000000e+17</td><td>0.000000e+00</td><td>--</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>B</td><td>3.716188e-02</td><td>3.716188e-02</td><td>4.850783e-02</td><td>--</td><td>5.050000e-02</td><td>1.000000e-03</td><td>1.000000e+00</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>NH_cold_to_rel_e</td><td>1.000000e+00</td><td>--</td><td>--</td><td>--</td><td>1.000000e+00</td><td>0.000000e+00</td><td>--</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>beam_obj</td><td>2.575826e+01</td><td>2.575826e+01</td><td>3.748732e+01</td><td>--</td><td>2.500000e+01</td><td>5.000000e+00</td><td>5.000000e+01</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>z_cosm</td><td>3.360000e-02</td><td>--</td><td>--</td><td>--</td><td>3.360000e-02</td><td>0.000000e+00</td><td>--</td><td>True</td></tr>
    <tr><td>host_galaxy</td><td>nuFnu_p_host</td><td>-1.005821e+01</td><td>-1.005821e+01</td><td>3.476096e-02</td><td>--</td><td>-1.008538e+01</td><td>-1.222242e+01</td><td>-8.222416e+00</td><td>False</td></tr>
    <tr><td>host_galaxy</td><td>nu_scale</td><td>1.934519e-02</td><td>--</td><td>--</td><td>--</td><td>1.934519e-02</td><td>-5.000000e-01</td><td>5.000000e-01</td><td>True</td></tr>
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.. parsed-literal::

    -------------------------------------------------------------------------
    
    ================================================================================
    


.. code:: ipython3

    best_fit_lsb.save_report('SSC-best-fit-lsb.pkl')
    model_minimizer_lsb.save_model('model_minimizer_lsb.pkl')
    fit_model.save_model('fit_model_lsb.pkl')

.. code:: ipython3

    %matplotlib inline
    fit_model.set_nu_grid(1E6,1E30,200)
    fit_model.eval()
    p2=fit_model.plot_model(sed_data=sed_data)
    p2.setlim(y_min=1E-14,x_min=1E6,x_max=2E28)



.. image:: Jet_example_model_fit_wiht_gal_template_files/Jet_example_model_fit_wiht_gal_template_31_0.png


Model fitting with Minuit
~~~~~~~~~~~~~~~~~~~~~~~~~

To run the ``minuit`` minimizer we will use the best-fit results from
``lsb`` to set the boundaries for our parameters.

.. code:: ipython3

    fit_model.freeze('jet_leptonic','z_cosm')
    fit_model.freeze('jet_leptonic','R_H')
    fit_model.jet_leptonic.parameters.beam_obj.fit_range=[5., 50.]
    fit_model.jet_leptonic.parameters.R.fit_range=[10**15.5,10**17.5]
    fit_model.host_galaxy.parameters.nuFnu_p_host.frozen=False
    fit_model.host_galaxy.parameters.nu_scale.frozen=True
    fit_model.jet_leptonic.parameters.gmin.fit_range=[10,1000]
    fit_model.jet_leptonic.parameters.gmax.fit_range=[5E5,1E8]
    fit_model.jet_leptonic.parameters.gamma0_log_parab.fit_range=[1E3,5E5]
    


.. code:: ipython3

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


.. parsed-literal::

    filtering data in fit range = [1.000000e+11,1.000000e+29]
    data length 31
    ================================================================================
    
    *** start fit process ***
    ----- 
    fit run: 0



.. parsed-literal::

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


.. parsed-literal::

    ====> simplex
    ====> migrad
    - best chisq=1.04513e+01
    
    fit run: 1
    - old chisq=1.04513e+01



.. parsed-literal::

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


.. parsed-literal::

    ====> simplex
    ====> migrad
    - best chisq=1.04509e+01
    
    fit run: 2
    - old chisq=1.04509e+01



.. parsed-literal::

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


.. parsed-literal::

    ====> simplex
    ====> migrad
    - best chisq=1.04509e+01
    
    -------------------------------------------------------------------------
    Fit report
    
    Model: SSC-best-fit-minuit



.. raw:: html

    <i>Table length=14</i>
    <table id="table5754969760-923841" class="table-striped table-bordered table-condensed">
    <thead><tr><th>model name</th><th>name</th><th>par type</th><th>units</th><th>val</th><th>phys. bound. min</th><th>phys. bound. max</th><th>log</th><th>frozen</th></tr></thead>
    <tr><td>jet_leptonic</td><td>gmin</td><td>low-energy-cut-off</td><td>lorentz-factor*</td><td>5.455560e+01</td><td>1.000000e+00</td><td>1.000000e+09</td><td>False</td><td>False</td></tr>
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    <tr><td>jet_leptonic</td><td>N</td><td>emitters_density</td><td>1 / cm3</td><td>4.504764e+01</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>gamma0_log_parab</td><td>turn-over-energy</td><td>lorentz-factor*</td><td>5.386110e+03</td><td>1.000000e+00</td><td>1.000000e+09</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>s</td><td>LE_spectral_slope</td><td></td><td>2.168634e+00</td><td>-1.000000e+01</td><td>1.000000e+01</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>r</td><td>spectral_curvature</td><td></td><td>2.323139e-01</td><td>-1.500000e+01</td><td>1.500000e+01</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>R</td><td>region_size</td><td>cm</td><td>1.298307e+16</td><td>1.000000e+03</td><td>1.000000e+30</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>R_H</td><td>region_position</td><td>cm</td><td>1.000000e+17</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>B</td><td>magnetic_field</td><td>gauss</td><td>1.206137e-02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>NH_cold_to_rel_e</td><td>cold_p_to_rel_e_ratio</td><td></td><td>1.000000e+00</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>beam_obj</td><td>beaming</td><td></td><td>4.763830e+01</td><td>1.000000e-04</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>z_cosm</td><td>redshift</td><td></td><td>3.360000e-02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>host_galaxy</td><td>nuFnu_p_host</td><td>nuFnu-scale</td><td>erg / (s cm2)</td><td>-1.008451e+01</td><td>-2.000000e+01</td><td>2.000000e+01</td><td>False</td><td>False</td></tr>
    <tr><td>host_galaxy</td><td>nu_scale</td><td>nu-scale</td><td>Hz</td><td>1.934519e-02</td><td>-2.000000e+00</td><td>2.000000e+00</td><td>False</td><td>True</td></tr>
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.. parsed-literal::

    
    converged=True
    calls=1019
    mesg=



.. raw:: html

    <table>
        <tr>
            <th colspan="5" style="text-align:center" title="Minimizer"> Migrad </th>
        </tr>
        <tr>
            <td colspan="2" style="text-align:left" title="Minimum value of function"> FCN = 10.45 </td>
            <td colspan="3" style="text-align:center" title="Total number of function and (optional) gradient evaluations"> Nfcn = 1019 </td>
        </tr>
        <tr>
            <td colspan="2" style="text-align:left" title="Estimated distance to minimum and goal"> EDM = 1.19e-05 (Goal: 0.0002) </td>
            <td colspan="3" style="text-align:center" title="Total run time of algorithms"> time = 27.0 sec </td>
        </tr>
        <tr>
            <td colspan="2" style="text-align:center;background-color:#92CCA6;color:black"> Valid Minimum </td>
            <td colspan="3" style="text-align:center;background-color:#92CCA6;color:black"> No Parameters at limit </td>
        </tr>
        <tr>
            <td colspan="2" style="text-align:center;background-color:#92CCA6;color:black"> Below EDM threshold (goal x 10) </td>
            <td colspan="3" style="text-align:center;background-color:#92CCA6;color:black"> Below call limit </td>
        </tr>
        <tr>
            <td style="text-align:center;background-color:#92CCA6;color:black"> Covariance </td>
            <td style="text-align:center;background-color:#92CCA6;color:black"> Hesse ok </td>
            <td style="text-align:center;background-color:#92CCA6;color:black" title="Is covariance matrix accurate?"> Accurate </td>
            <td style="text-align:center;background-color:#92CCA6;color:black" title="Is covariance matrix positive definite?"> Pos. def. </td>
            <td style="text-align:center;background-color:#92CCA6;color:black" title="Was positive definiteness enforced by Minuit?"> Not forced </td>
        </tr>
    </table><table>
        <tr>
            <td></td>
            <th title="Variable name"> Name </th>
            <th title="Value of parameter"> Value </th>
            <th title="Hesse error"> Hesse Error </th>
            <th title="Minos lower error"> Minos Error- </th>
            <th title="Minos upper error"> Minos Error+ </th>
            <th title="Lower limit of the parameter"> Limit- </th>
            <th title="Upper limit of the parameter"> Limit+ </th>
            <th title="Is the parameter fixed in the fit"> Fixed </th>
        </tr>
        <tr>
            <th> 0 </th>
            <td> par_0 </td>
            <td> 54.56 </td>
            <td> 0.27 </td>
            <td>  </td>
            <td>  </td>
            <td> 10 </td>
            <td> 1E+03 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 1 </th>
            <td> par_1 </td>
            <td> 2.11e6 </td>
            <td> 0.17e6 </td>
            <td>  </td>
            <td>  </td>
            <td> 5E+05 </td>
            <td> 1E+08 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 2 </th>
            <td> par_2 </td>
            <td> 45.0 </td>
            <td> 0.4 </td>
            <td>  </td>
            <td>  </td>
            <td> 1E-05 </td>
            <td> 1E+05 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 3 </th>
            <td> par_3 </td>
            <td> 5.39e3 </td>
            <td> 0.08e3 </td>
            <td>  </td>
            <td>  </td>
            <td> 1E+03 </td>
            <td> 5E+05 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 4 </th>
            <td> par_4 </td>
            <td> 2.169 </td>
            <td> 0.004 </td>
            <td>  </td>
            <td>  </td>
            <td> -10 </td>
            <td> 10 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 5 </th>
            <td> par_5 </td>
            <td> 232.3e-3 </td>
            <td> 0.8e-3 </td>
            <td>  </td>
            <td>  </td>
            <td> -15 </td>
            <td> 15 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 6 </th>
            <td> par_6 </td>
            <td> 12.983e15 </td>
            <td> 0.033e15 </td>
            <td>  </td>
            <td>  </td>
            <td> 3.16E+15 </td>
            <td> 3.16E+17 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 7 </th>
            <td> par_7 </td>
            <td> 12.06e-3 </td>
            <td> 0.09e-3 </td>
            <td>  </td>
            <td>  </td>
            <td> 0.001 </td>
            <td> 1 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 8 </th>
            <td> par_8 </td>
            <td> 47.64 </td>
            <td> 0.17 </td>
            <td>  </td>
            <td>  </td>
            <td> 5 </td>
            <td> 50 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 9 </th>
            <td> par_9 </td>
            <td> -10.085 </td>
            <td> 0.020 </td>
            <td>  </td>
            <td>  </td>
            <td> -12.2 </td>
            <td> -8.22 </td>
            <td>  </td>
        </tr>
    </table>


.. parsed-literal::

    dof=21
    chisq=10.450851, chisq/red=0.497660 null hypothesis sig=0.972444
    
    best fit pars



.. raw:: html

    <i>Table length=14</i>
    <table id="table5754962608-994070" class="table-striped table-bordered table-condensed">
    <thead><tr><th>model name</th><th>name</th><th>val</th><th>bestfit val</th><th>err +</th><th>err -</th><th>start val</th><th>fit range min</th><th>fit range max</th><th>frozen</th></tr></thead>
    <tr><td>jet_leptonic</td><td>gmin</td><td>5.455560e+01</td><td>5.455560e+01</td><td>2.726560e-01</td><td>--</td><td>8.580927e+01</td><td>1.000000e+01</td><td>1.000000e+03</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>gmax</td><td>2.105148e+06</td><td>2.105148e+06</td><td>1.675281e+05</td><td>--</td><td>2.310708e+06</td><td>5.000000e+05</td><td>1.000000e+08</td><td>False</td></tr>
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    <tr><td>jet_leptonic</td><td>gamma0_log_parab</td><td>5.386110e+03</td><td>5.386110e+03</td><td>7.892077e+01</td><td>--</td><td>1.069947e+04</td><td>1.000000e+03</td><td>5.000000e+05</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>s</td><td>2.168634e+00</td><td>2.168634e+00</td><td>3.851834e-03</td><td>--</td><td>2.220278e+00</td><td>-1.000000e+01</td><td>1.000000e+01</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>r</td><td>2.323139e-01</td><td>2.323139e-01</td><td>7.857833e-04</td><td>--</td><td>2.813492e-01</td><td>-1.500000e+01</td><td>1.500000e+01</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>R</td><td>1.298307e+16</td><td>1.298307e+16</td><td>3.259461e+13</td><td>--</td><td>1.141280e+16</td><td>3.162278e+15</td><td>3.162278e+17</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>R_H</td><td>1.000000e+17</td><td>--</td><td>--</td><td>--</td><td>1.000000e+17</td><td>0.000000e+00</td><td>--</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>B</td><td>1.206137e-02</td><td>1.206137e-02</td><td>8.551352e-05</td><td>--</td><td>3.716188e-02</td><td>1.000000e-03</td><td>1.000000e+00</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>NH_cold_to_rel_e</td><td>1.000000e+00</td><td>--</td><td>--</td><td>--</td><td>1.000000e+00</td><td>0.000000e+00</td><td>--</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>beam_obj</td><td>4.763830e+01</td><td>4.763830e+01</td><td>1.659000e-01</td><td>--</td><td>2.575826e+01</td><td>5.000000e+00</td><td>5.000000e+01</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>z_cosm</td><td>3.360000e-02</td><td>--</td><td>--</td><td>--</td><td>3.360000e-02</td><td>0.000000e+00</td><td>--</td><td>True</td></tr>
    <tr><td>host_galaxy</td><td>nuFnu_p_host</td><td>-1.008451e+01</td><td>-1.008451e+01</td><td>1.998494e-02</td><td>--</td><td>-1.005821e+01</td><td>-1.222242e+01</td><td>-8.222416e+00</td><td>False</td></tr>
    <tr><td>host_galaxy</td><td>nu_scale</td><td>1.934519e-02</td><td>--</td><td>--</td><td>--</td><td>1.934519e-02</td><td>-5.000000e-01</td><td>5.000000e-01</td><td>True</td></tr>
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.. parsed-literal::

    -------------------------------------------------------------------------
    
    ================================================================================
    


for further information regardin minuit please refer to
https://iminuit.readthedocs.io/en/stable/

.. code:: ipython3

    %matplotlib inline
    fit_model.set_nu_grid(1E6,1E30,200)
    fit_model.eval()
    p2=fit_model.plot_model(sed_data=sed_data)
    p2.setlim(y_min=1E-14,x_min=1E6,x_max=2E28)



.. image:: Jet_example_model_fit_wiht_gal_template_files/Jet_example_model_fit_wiht_gal_template_37_0.png


.. code:: ipython3

    best_fit_minuit.save_report('SSC-best-fit-minuit.pkl')
    model_minimizer_minuit.save_model('model_minimizer_minuit.pkl')
    fit_model.save_model('fit_model_minuit.pkl')

Model fitting with a bkn pl
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code:: ipython3

    from jetset.obs_constrain import ObsConstrain
    from jetset.model_manager import  FitModel
    from jetset.minimizer import fit_SED
    sed_obspar=ObsConstrain(beaming=25,
                            B_range=[0.001,0.1],
                            distr_e='bkn',
                            t_var_sec=3*86400,
                            nu_cut_IR=1E11,
                            SEDShape=my_shape)
    
    
    prefit_jet=sed_obspar.constrain_SSC_model(electron_distribution_log_values=False,silent=True)
    prefit_jet.save_model('prefit_jet_bkn_gal_templ.pkl')


.. parsed-literal::

    ================================================================================
    
    ***  constrains parameters from observable ***
    
    ===> setting C threads to 12



.. raw:: html

    <i>Table length=12</i>
    <table id="table5754377248-980135" class="table-striped table-bordered table-condensed">
    <thead><tr><th>model name</th><th>name</th><th>par type</th><th>units</th><th>val</th><th>phys. bound. min</th><th>phys. bound. max</th><th>log</th><th>frozen</th></tr></thead>
    <tr><td>jet_leptonic</td><td>R</td><td>region_size</td><td>cm</td><td>1.247372e+16</td><td>1.000000e+03</td><td>1.000000e+30</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>R_H</td><td>region_position</td><td>cm</td><td>1.000000e+17</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>B</td><td>magnetic_field</td><td>gauss</td><td>2.847716e-02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>NH_cold_to_rel_e</td><td>cold_p_to_rel_e_ratio</td><td></td><td>1.000000e+00</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>beam_obj</td><td>beaming</td><td></td><td>2.500000e+01</td><td>1.000000e-04</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>z_cosm</td><td>redshift</td><td></td><td>3.360000e-02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>gmin</td><td>low-energy-cut-off</td><td>lorentz-factor*</td><td>1.980875e+02</td><td>1.000000e+00</td><td>1.000000e+09</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>gmax</td><td>high-energy-cut-off</td><td>lorentz-factor*</td><td>3.077106e+06</td><td>1.000000e+00</td><td>1.000000e+15</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>N</td><td>emitters_density</td><td>1 / cm3</td><td>1.406682e+01</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>gamma_break</td><td>turn-over-energy</td><td>lorentz-factor*</td><td>2.094216e+05</td><td>1.000000e+00</td><td>1.000000e+09</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>p</td><td>LE_spectral_slope</td><td></td><td>2.248426e+00</td><td>-1.000000e+01</td><td>1.000000e+01</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>p_1</td><td>HE_spectral_slope</td><td></td><td>3.500000e+00</td><td>-1.000000e+01</td><td>1.000000e+01</td><td>False</td><td>False</td></tr>
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.. parsed-literal::

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


.. code:: ipython3

    pl=prefit_jet.plot_model(sed_data=sed_data)
    pl.add_residual_plot(prefit_jet,sed_data)
    pl.setlim(y_min=1E-14,x_min=1E7,x_max=1E29)



.. image:: Jet_example_model_fit_wiht_gal_template_files/Jet_example_model_fit_wiht_gal_template_41_0.png


.. code:: ipython3

    jet_minuit_bkn=Jet.load_model('prefit_jet_bkn_gal_templ.pkl')
    jet_minuit_bkn.set_gamma_grid_size(200)
    
    fit_model_bkn=FitModel( jet=jet_minuit_bkn, name='SSC-best-fit-bkn-lsb',template=my_shape.host_gal) 
    
    
    fit_model_bkn.freeze('jet_leptonic','z_cosm')
    fit_model_bkn.freeze('jet_leptonic','R_H')
    fit_model_bkn.jet_leptonic.parameters.beam_obj.fit_range=[5,50]
    fit_model_bkn.jet_leptonic.parameters.R.fit_range=[10**15.5,10**17.5]
    fit_model_bkn.jet_leptonic.parameters.gmax.fit_range=[1E4,1E8]
    fit_model_bkn.host_galaxy.parameters.nuFnu_p_host.frozen=False
    fit_model_bkn.host_galaxy.parameters.nu_scale.frozen=True
    



.. parsed-literal::

    ===> setting C threads to 12


.. code:: ipython3

    model_minimizer_lsb_bkn=ModelMinimizer('lsb')
    best_fit_lsb_bkn=model_minimizer_lsb_bkn.fit(fit_model_bkn,sed_data,1E11,1E29,fitname='SSC-best-fit-lsb')



.. parsed-literal::

    filtering data in fit range = [1.000000e+11,1.000000e+29]
    data length 31
    ================================================================================
    
    *** start fit process ***
    ----- 



.. parsed-literal::

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


.. parsed-literal::

    - best chisq=2.49214e+01
    
    -------------------------------------------------------------------------
    Fit report
    
    Model: SSC-best-fit-lsb



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    <i>Table length=14</i>
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    <tr><td>jet_leptonic</td><td>R</td><td>region_size</td><td>cm</td><td>1.247372e+16</td><td>1.000000e+03</td><td>1.000000e+30</td><td>False</td><td>False</td></tr>
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    <tr><td>jet_leptonic</td><td>NH_cold_to_rel_e</td><td>cold_p_to_rel_e_ratio</td><td></td><td>1.000000e+00</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>beam_obj</td><td>beaming</td><td></td><td>4.463828e+01</td><td>1.000000e-04</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>z_cosm</td><td>redshift</td><td></td><td>3.360000e-02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
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.. parsed-literal::

    
    converged=True
    calls=482
    mesg=



.. parsed-literal::

    '`ftol` termination condition is satisfied.'


.. parsed-literal::

    dof=21
    chisq=24.921362, chisq/red=1.186732 null hypothesis sig=0.250586
    
    best fit pars



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    <tr><td>jet_leptonic</td><td>B</td><td>1.430585e-02</td><td>1.430585e-02</td><td>1.084428e-02</td><td>--</td><td>2.847716e-02</td><td>0.000000e+00</td><td>--</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>NH_cold_to_rel_e</td><td>1.000000e+00</td><td>--</td><td>--</td><td>--</td><td>1.000000e+00</td><td>0.000000e+00</td><td>--</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>beam_obj</td><td>4.463828e+01</td><td>4.463828e+01</td><td>2.806607e+01</td><td>--</td><td>2.500000e+01</td><td>5.000000e+00</td><td>5.000000e+01</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>z_cosm</td><td>3.360000e-02</td><td>--</td><td>--</td><td>--</td><td>3.360000e-02</td><td>0.000000e+00</td><td>--</td><td>True</td></tr>
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.. parsed-literal::

    -------------------------------------------------------------------------
    
    ================================================================================
    


.. code:: ipython3

    %matplotlib inline
    fit_model_bkn.set_nu_grid(1E6,1E30,200)
    fit_model_bkn.eval()
    p2=fit_model_bkn.plot_model(sed_data=sed_data)
    p2.setlim(y_min=1E-14,x_min=1E6,x_max=2E28)



.. image:: Jet_example_model_fit_wiht_gal_template_files/Jet_example_model_fit_wiht_gal_template_44_0.png


.. code:: ipython3

    
    fit_model_bkn.jet_leptonic.parameters.beam_obj.fit_range=[5,50]
    fit_model_bkn.jet_leptonic.parameters.R.fit_range=[10**15.5,10**17.5]
    fit_model_bkn.host_galaxy.parameters.nuFnu_p_host.frozen=False
    fit_model_bkn.host_galaxy.parameters.nu_scale.frozen=True
    fit_model_bkn.jet_leptonic.parameters.gmin.fit_range=[10,1000]
    fit_model_bkn.jet_leptonic.parameters.gmax.fit_range=[5E5,1E8]
    fit_model_bkn.jet_leptonic.parameters.gamma_break.fit_range=[1E3,1E6]
    fit_model_bkn.jet_leptonic.parameters.p.fit_range=[1,3]
    fit_model_bkn.jet_leptonic.parameters.p_1.fit_range=[2,5]
    
    
    model_minimizer_minuit_bkn=ModelMinimizer('minuit')
    best_fit_minuit_bkn=model_minimizer_minuit.fit(fit_model_bkn,sed_data,1E11,1E29,fitname='SSC-best-fit-minuit-bkn',repeat=3)


.. parsed-literal::

    filtering data in fit range = [1.000000e+11,1.000000e+29]
    data length 31
    ================================================================================
    
    *** start fit process ***
    ----- 
    fit run: 0



.. parsed-literal::

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


.. parsed-literal::

    ====> simplex
    ====> migrad
    - best chisq=1.34228e+01
    
    fit run: 1
    - old chisq=1.34228e+01



.. parsed-literal::

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


.. parsed-literal::

    ====> simplex
    ====> migrad
    - best chisq=1.30362e+01
    
    fit run: 2
    - old chisq=1.30362e+01



.. parsed-literal::

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


.. parsed-literal::

    ====> simplex
    ====> migrad
    - best chisq=1.30275e+01
    
    -------------------------------------------------------------------------
    Fit report
    
    Model: SSC-best-fit-minuit-bkn



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    <tr><td>jet_leptonic</td><td>R_H</td><td>region_position</td><td>cm</td><td>1.000000e+17</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
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    <tr><td>jet_leptonic</td><td>beam_obj</td><td>beaming</td><td></td><td>4.128886e+01</td><td>1.000000e-04</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>z_cosm</td><td>redshift</td><td></td><td>3.360000e-02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>host_galaxy</td><td>nuFnu_p_host</td><td>nuFnu-scale</td><td>erg / (s cm2)</td><td>-1.007170e+01</td><td>-2.000000e+01</td><td>2.000000e+01</td><td>False</td><td>False</td></tr>
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.. parsed-literal::

    
    converged=True
    calls=1353
    mesg=



.. raw:: html

    <table>
        <tr>
            <th colspan="5" style="text-align:center" title="Minimizer"> Migrad </th>
        </tr>
        <tr>
            <td colspan="2" style="text-align:left" title="Minimum value of function"> FCN = 13.03 </td>
            <td colspan="3" style="text-align:center" title="Total number of function and (optional) gradient evaluations"> Nfcn = 1353 </td>
        </tr>
        <tr>
            <td colspan="2" style="text-align:left" title="Estimated distance to minimum and goal"> EDM = 5.33e-06 (Goal: 0.0002) </td>
            <td colspan="3" style="text-align:center" title="Total run time of algorithms"> time = 27.0 sec </td>
        </tr>
        <tr>
            <td colspan="2" style="text-align:center;background-color:#92CCA6;color:black"> Valid Minimum </td>
            <td colspan="3" style="text-align:center;background-color:#92CCA6;color:black"> No Parameters at limit </td>
        </tr>
        <tr>
            <td colspan="2" style="text-align:center;background-color:#92CCA6;color:black"> Below EDM threshold (goal x 10) </td>
            <td colspan="3" style="text-align:center;background-color:#92CCA6;color:black"> Below call limit </td>
        </tr>
        <tr>
            <td style="text-align:center;background-color:#92CCA6;color:black"> Covariance </td>
            <td style="text-align:center;background-color:#92CCA6;color:black"> Hesse ok </td>
            <td style="text-align:center;background-color:#92CCA6;color:black" title="Is covariance matrix accurate?"> Accurate </td>
            <td style="text-align:center;background-color:#92CCA6;color:black" title="Is covariance matrix positive definite?"> Pos. def. </td>
            <td style="text-align:center;background-color:#92CCA6;color:black" title="Was positive definiteness enforced by Minuit?"> Not forced </td>
        </tr>
    </table><table>
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            <td></td>
            <th title="Variable name"> Name </th>
            <th title="Value of parameter"> Value </th>
            <th title="Hesse error"> Hesse Error </th>
            <th title="Minos lower error"> Minos Error- </th>
            <th title="Minos upper error"> Minos Error+ </th>
            <th title="Lower limit of the parameter"> Limit- </th>
            <th title="Upper limit of the parameter"> Limit+ </th>
            <th title="Is the parameter fixed in the fit"> Fixed </th>
        </tr>
        <tr>
            <th> 0 </th>
            <td> par_0 </td>
            <td> 134.501 </td>
            <td> 0.019 </td>
            <td>  </td>
            <td>  </td>
            <td> 10 </td>
            <td> 1E+03 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 1 </th>
            <td> par_1 </td>
            <td> 1.7737e6 </td>
            <td> 0.0011e6 </td>
            <td>  </td>
            <td>  </td>
            <td> 5E+05 </td>
            <td> 1E+08 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 2 </th>
            <td> par_2 </td>
            <td> 16.2517 </td>
            <td> 0.0009 </td>
            <td>  </td>
            <td>  </td>
            <td> 0 </td>
            <td>  </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 3 </th>
            <td> par_3 </td>
            <td> 55.312e3 </td>
            <td> 0.032e3 </td>
            <td>  </td>
            <td>  </td>
            <td> 1E+03 </td>
            <td> 1E+06 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 4 </th>
            <td> par_4 </td>
            <td> 2.248959 </td>
            <td> 0.000020 </td>
            <td>  </td>
            <td>  </td>
            <td> 1 </td>
            <td> 3 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 5 </th>
            <td> par_5 </td>
            <td> 2.95267 </td>
            <td> 0.00015 </td>
            <td>  </td>
            <td>  </td>
            <td> 2 </td>
            <td> 5 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 6 </th>
            <td> par_6 </td>
            <td> 14.65e15 </td>
            <td> 0.05e15 </td>
            <td>  </td>
            <td>  </td>
            <td> 3.16E+15 </td>
            <td> 3.16E+17 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 7 </th>
            <td> par_7 </td>
            <td> 13.494e-3 </td>
            <td> 0.010e-3 </td>
            <td>  </td>
            <td>  </td>
            <td> 0 </td>
            <td>  </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 8 </th>
            <td> par_8 </td>
            <td> 41.29 </td>
            <td> 0.11 </td>
            <td>  </td>
            <td>  </td>
            <td> 5 </td>
            <td> 50 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 9 </th>
            <td> par_9 </td>
            <td> -10.072 </td>
            <td> 0.015 </td>
            <td>  </td>
            <td>  </td>
            <td> -12.2 </td>
            <td> -8.22 </td>
            <td>  </td>
        </tr>
    </table>


.. parsed-literal::

    dof=21
    chisq=13.027500, chisq/red=0.620357 null hypothesis sig=0.907658
    
    best fit pars



.. raw:: html

    <i>Table length=14</i>
    <table id="table5756087232-84042" class="table-striped table-bordered table-condensed">
    <thead><tr><th>model name</th><th>name</th><th>val</th><th>bestfit val</th><th>err +</th><th>err -</th><th>start val</th><th>fit range min</th><th>fit range max</th><th>frozen</th></tr></thead>
    <tr><td>jet_leptonic</td><td>gmin</td><td>1.345014e+02</td><td>1.345014e+02</td><td>1.935667e-02</td><td>--</td><td>1.485242e+02</td><td>1.000000e+01</td><td>1.000000e+03</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>gmax</td><td>1.773731e+06</td><td>1.773731e+06</td><td>1.129851e+03</td><td>--</td><td>3.071765e+06</td><td>5.000000e+05</td><td>1.000000e+08</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>N</td><td>1.625170e+01</td><td>1.625170e+01</td><td>8.522217e-04</td><td>--</td><td>1.629672e+01</td><td>0.000000e+00</td><td>--</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>gamma_break</td><td>5.531173e+04</td><td>5.531173e+04</td><td>3.220423e+01</td><td>--</td><td>8.193745e+04</td><td>1.000000e+03</td><td>1.000000e+06</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>p</td><td>2.248959e+00</td><td>2.248959e+00</td><td>2.045150e-05</td><td>--</td><td>2.262508e+00</td><td>1.000000e+00</td><td>3.000000e+00</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>p_1</td><td>2.952674e+00</td><td>2.952674e+00</td><td>1.524221e-04</td><td>--</td><td>3.169331e+00</td><td>2.000000e+00</td><td>5.000000e+00</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>R</td><td>1.464854e+16</td><td>1.464854e+16</td><td>5.023364e+13</td><td>--</td><td>1.247372e+16</td><td>3.162278e+15</td><td>3.162278e+17</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>R_H</td><td>1.000000e+17</td><td>--</td><td>--</td><td>--</td><td>1.000000e+17</td><td>0.000000e+00</td><td>--</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>B</td><td>1.349383e-02</td><td>1.349383e-02</td><td>1.023312e-05</td><td>--</td><td>1.430585e-02</td><td>0.000000e+00</td><td>--</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>NH_cold_to_rel_e</td><td>1.000000e+00</td><td>--</td><td>--</td><td>--</td><td>1.000000e+00</td><td>0.000000e+00</td><td>--</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>beam_obj</td><td>4.128886e+01</td><td>4.128886e+01</td><td>1.130872e-01</td><td>--</td><td>4.463828e+01</td><td>5.000000e+00</td><td>5.000000e+01</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>z_cosm</td><td>3.360000e-02</td><td>--</td><td>--</td><td>--</td><td>3.360000e-02</td><td>0.000000e+00</td><td>--</td><td>True</td></tr>
    <tr><td>host_galaxy</td><td>nuFnu_p_host</td><td>-1.007170e+01</td><td>-1.007170e+01</td><td>1.541061e-02</td><td>--</td><td>-1.006917e+01</td><td>-1.222242e+01</td><td>-8.222416e+00</td><td>False</td></tr>
    <tr><td>host_galaxy</td><td>nu_scale</td><td>1.934519e-02</td><td>--</td><td>--</td><td>--</td><td>1.934519e-02</td><td>-5.000000e-01</td><td>5.000000e-01</td><td>True</td></tr>
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.. parsed-literal::

    -------------------------------------------------------------------------
    
    ================================================================================
    


.. code:: ipython3

    %matplotlib inline
    fit_model_bkn.set_nu_grid(1E6,1E30,200)
    fit_model_bkn.eval()
    p2=fit_model_bkn.plot_model(sed_data=sed_data)
    p2.setlim(y_min=1E-14,x_min=1E6,x_max=2E28)



.. image:: Jet_example_model_fit_wiht_gal_template_files/Jet_example_model_fit_wiht_gal_template_46_0.png


.. code:: ipython3

    %matplotlib inline
    from jetset.plot_sedfit import PlotSED
    fit_model_bkn.set_nu_grid(1E6,1E30,200)
    fit_model_bkn.eval()
    fit_model.set_nu_grid(1E6,1E30,200)
    fit_model.eval()
    
    p2=PlotSED()
    p2.add_data_plot(sed_data,fit_range=[ 1E11, 1E29])
    p2.add_model_plot(fit_model,color='black')
    p2.add_residual_plot(fit_model,sed_data,fit_range=[ 1E11, 1E29],color='black')
    p2.add_model_plot(fit_model_bkn,color='red')
    p2.add_residual_plot(fit_model_bkn,sed_data,fit_range=[ 1E11, 1E29],color='red')
    p2.setlim(y_min=1E-14,x_min=1E6,x_max=2E28)



.. image:: Jet_example_model_fit_wiht_gal_template_files/Jet_example_model_fit_wiht_gal_template_47_0.png


MCMC sampling
-------------

.. note::
    Please, read the introduction and the caveat :ref:`for the Bayesian model fitting <bayesian_model_fitting>` to understand the MCMC sampler workflow.


.. code:: ipython3

    from jetset.mcmc import McmcSampler
    from jetset.minimizer import ModelMinimizer


.. code:: ipython3

    model_minimizer_lsb = ModelMinimizer.load_model('model_minimizer_minuit.pkl')
    
    mcmc=McmcSampler(model_minimizer_lsb)


.. parsed-literal::

    ===> setting C threads to 12


.. code:: ipython3

    labels=['N','B','beam_obj','s','gamma0_log_parab']
    model_name='jet_leptonic'
    use_labels_dict={model_name:labels}
    mcmc.set_labels(use_labels_dict=use_labels_dict)

.. code:: ipython3

    mcmc.set_bounds(bound=5.0,bound_rel=True)


.. parsed-literal::

    par: N  best fit value:  45.0476406721727  mcmc bounds: [1e-05, 270.2858440330362]
    par: B  best fit value:  0.012061365634053165  mcmc bounds: [0.001, 0.07236819380431898]
    par: beam_obj  best fit value:  47.638299687949946  mcmc bounds: [5.0, 50.0]
    par: s  best fit value:  2.1686339157854624  mcmc bounds: [-8.67453566314185, 10]
    par: gamma0_log_parab  best fit value:  5386.109843065869  mcmc bounds: [1000.0, 32316.659058395213]


.. code:: ipython3

    mcmc.run_sampler(nwalkers=20, burnin=50,steps=500,progress='notebook')


.. parsed-literal::

    ===> setting C threads to 12
    mcmc run starting
    



.. parsed-literal::

      0%|          | 0/500 [00:00<?, ?it/s]


.. parsed-literal::

    mcmc run done, with 1 threads took 215.38 seconds


.. code:: ipython3

    print(mcmc.acceptance_fraction)


.. parsed-literal::

    0.4015000000000001


.. code:: ipython3

    mcmc.model.jet_leptonic.nu_min=1E6
    mcmc.model.nu_min=1E6
    p=mcmc.plot_model(sed_data=sed_data,fit_range=[1E11, 2E28],size=100)
    p.setlim(y_min=1E-14,x_min=1E6,x_max=2E28)



.. image:: Jet_example_model_fit_wiht_gal_template_files/Jet_example_model_fit_wiht_gal_template_56_0.png


.. code:: ipython3

    p=mcmc.plot_model(sed_data=sed_data,fit_range=[2E11, 2E28],quantiles=[0.05,0.95])
    p.setlim(y_min=1E-14,x_min=1E6,x_max=2E28)



.. image:: Jet_example_model_fit_wiht_gal_template_files/Jet_example_model_fit_wiht_gal_template_57_0.png


.. code:: ipython3

    mcmc.labels




.. parsed-literal::

    ['N', 'B', 'beam_obj', 's', 'gamma0_log_parab']



To have a better rendering on the scatter plot, we redefine the plot
labels

.. code:: ipython3

    mcmc.set_plot_label('N',r'$N$')
    mcmc.set_plot_label('B',r'$B$')
    mcmc.set_plot_label('beam_obj',r'$\delta$')
    mcmc.set_plot_label('s',r'$s$')
    mcmc.set_plot_label('gamma0_log_parab',r'$\gamma_0$')

the code below lets you tuning the output:

1) mpl.rcParams[‘figure.dpi’] if you increase it you get a better
   definition
2) title_fmt=“.2E” this is the format for python, 2 significant digits,
   scientific notation
3) title_kwargs=dict(fontsize=12) you can change the fontsize

.. code:: ipython3

    import matplotlib as mpl
    mpl.rcParams['figure.dpi'] = 80
    f=mcmc.corner_plot(quantiles=(0.16, 0.5, 0.84),title_kwargs=dict(fontsize=12),title_fmt=".2E",use_math_text=True)



.. image:: Jet_example_model_fit_wiht_gal_template_files/Jet_example_model_fit_wiht_gal_template_62_0.png


.. code:: ipython3

    f=mcmc.corner_plot()



.. image:: Jet_example_model_fit_wiht_gal_template_files/Jet_example_model_fit_wiht_gal_template_63_0.png


.. code:: ipython3

    f=mcmc.plot_chain(log_plot=False)



.. image:: Jet_example_model_fit_wiht_gal_template_files/Jet_example_model_fit_wiht_gal_template_64_0.png


.. note::
    from the inspection of the corneplot and of the chains, we realize that the bemaing factor distribution is trunctated, and the posterior is not distributed around the best fit value
    this suggests that we should rerun the fit changing the starting value and the boundaries according, and rerun the mcmc as well

.. code:: ipython3

    f=mcmc.plot_par('beam_obj')



.. image:: Jet_example_model_fit_wiht_gal_template_files/Jet_example_model_fit_wiht_gal_template_66_0.png


Save and reuse MCMC
-------------------

.. code:: ipython3

    mcmc.save('mcmc_sampler.pkl')

.. code:: ipython3

    from jetset.mcmc import McmcSampler
    from jetset.data_loader import ObsData
    from jetset.plot_sedfit import PlotSED
    from jetset.test_data_helper import  test_SEDs
    
    sed_data=ObsData.load('Mrk_501.pkl')
    
    ms=McmcSampler.load('mcmc_sampler.pkl')


.. parsed-literal::

    ===> setting C threads to 12
    ===> setting C threads to 12


.. code:: ipython3

    ms.model.nu_min=1E6
    ms.model.jet_leptonic.nu_min=1E6
    p=ms.plot_model(sed_data=sed_data,fit_range=[2E11, 2E28],size=100)
    p.setlim(y_min=1E-14,x_min=1E6,x_max=2E28)



.. image:: Jet_example_model_fit_wiht_gal_template_files/Jet_example_model_fit_wiht_gal_template_70_0.png


.. code:: ipython3

    p=ms.plot_model(sed_data=sed_data,fit_range=[2E11, 2E28],quantiles=[0.05,0.95])
    p.setlim(y_min=1E-14,x_min=1E6,x_max=2E28)



.. image:: Jet_example_model_fit_wiht_gal_template_files/Jet_example_model_fit_wiht_gal_template_71_0.png


.. code:: ipython3

    f=ms.plot_par('beam_obj',log_plot=False)




.. image:: Jet_example_model_fit_wiht_gal_template_files/Jet_example_model_fit_wiht_gal_template_72_0.png


.. code:: ipython3

    f=ms.plot_chain(log_plot=False)



.. image:: Jet_example_model_fit_wiht_gal_template_files/Jet_example_model_fit_wiht_gal_template_73_0.png