.. _model_fitting_1:

Model fitting 1: Only SSC
=========================

.. 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::

    1.2.2


.. code:: ipython3

    test_SEDs




.. parsed-literal::

    ['/Users/orion/anaconda3/envs/jetset/lib/python3.8/site-packages/jetset/test_data/SEDs_data/SED_3C345.ecsv',
     '/Users/orion/anaconda3/envs/jetset/lib/python3.8/site-packages/jetset/test_data/SEDs_data/SED_MW_Mrk421_EBL_DEABS.ecsv',
     '/Users/orion/anaconda3/envs/jetset/lib/python3.8/site-packages/jetset/test_data/SEDs_data/SED_MW_Mrk501_EBL_ABS.ecsv',
     '/Users/orion/anaconda3/envs/jetset/lib/python3.8/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

    print(test_SEDs[1])
    data=Data.from_file(test_SEDs[1])



.. parsed-literal::

    /Users/orion/anaconda3/envs/jetset/lib/python3.8/site-packages/jetset/test_data/SEDs_data/SED_MW_Mrk421_EBL_DEABS.ecsv


.. 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()
    #p.setlim(y_min=1E-15,x_min=1E7,x_max=1E29)


.. parsed-literal::

    ================================================================================
    
    ***  binning data  ***
    ---> N bins= 89
    ---> bin_widht= 0.2
    ================================================================================
    



.. image:: Jet_example_model_fit_files/Jet_example_model_fit_8_1.png


.. code:: ipython3

    sed_data.save('Mrk_401.pkl')

phenomenological model constraining
-----------------------------------

see the :ref:`phenom_constr` user guide for further information about phenomenological constraining 

spectral indices
~~~~~~~~~~~~~~~~

.. code:: ipython3

    from jetset.sed_shaper import  SEDShape
    my_shape=SEDShape(sed_data)
    my_shape.eval_indices(minimizer='lsb',silent=True)
    p=my_shape.plot_indices()
    p.setlim(y_min=1E-15,y_max=5E-8)


.. parsed-literal::

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



.. image:: Jet_example_model_fit_files/Jet_example_model_fit_13_1.png


sed shaper
~~~~~~~~~~

.. code:: ipython3

    mm,best_fit=my_shape.sync_fit(check_host_gal_template=False,
                      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
    
    
    



.. raw:: html

    <i>Table length=4</i>
    <table id="table140311304936464-828503" 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>-1.545300e-01</td><td>-1.545300e-01</td><td>9.534795e-03</td><td>--</td><td>-1.000000e+00</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>1.672267e+01</td><td>1.672267e+01</td><td>4.139942e-02</td><td>--</td><td>1.667039e+01</td><td>0.000000e+00</td><td>3.000000e+01</td><td>False</td></tr>
    <tr><td>LogCubic</td><td>Sp</td><td>-9.491659e+00</td><td>-9.491659e+00</td><td>2.515285e-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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    require.config({paths: {
        datatables: 'https://cdn.datatables.net/1.10.12/js/jquery.dataTables.min'
    }});
    require(["datatables"], function(){
        console.log("$('#table140311304936464-828503').dataTable()");
    
    jQuery.extend( jQuery.fn.dataTableExt.oSort, {
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.. parsed-literal::

    ---> sync       nu_p=+1.672267e+01 (err=+4.139942e-02)  nuFnu_p=-9.491659e+00 (err=+2.515285e-02) curv.=-1.545300e-01 (err=+9.534795e-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,y_max=5E-8)


.. parsed-literal::

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



.. raw:: html

    <i>Table length=4</i>
    <table id="table140311306437632-265980" 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>-2.098186e-01</td><td>-2.098186e-01</td><td>3.133032e-02</td><td>--</td><td>-1.000000e+00</td><td>-1.000000e+01</td><td>0.000000e+00</td><td>False</td></tr>
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    <tr><td>LogCubic</td><td>Sp</td><td>-1.011085e+01</td><td>-1.011085e+01</td><td>3.498963e-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
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        datatables: 'https://cdn.datatables.net/1.10.12/js/jquery.dataTables.min'
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.. parsed-literal::

    ---> IC         nu_p=+2.524926e+01 (err=+1.147759e-01)  nuFnu_p=-1.011085e+01 (err=+3.498963e-02) curv.=-2.098186e-01 (err=+3.133032e-02)
    ================================================================================
    



.. image:: Jet_example_model_fit_files/Jet_example_model_fit_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
    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')


.. parsed-literal::

    ================================================================================
    
    ***  constrains parameters from observable ***
    



.. raw:: html

    <i>Table length=12</i>
    <table id="table140311299283600-383780" 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>3.112712e+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-01</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>lorentz-factor*</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>3.080000e-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>4.697542e+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>1.373160e+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>9.060842e-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>3.188500e+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>2.181578e+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>7.726502e-01</td><td>-1.500000e+01</td><td>1.500000e+01</td><td>False</td><td>False</td></tr>
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.. parsed-literal::

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


.. code:: ipython3

    prefit_jet.eval()
    pl=prefit_jet.plot_model(sed_data=sed_data)
    pl.add_residual_plot(prefit_jet,sed_data)
    pl.setlim(y_min=1E-15,x_min=1E7,x_max=1E29)



.. image:: Jet_example_model_fit_files/Jet_example_model_fit_20_0.png


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

We remind that we can use different ``minimizers`` for the model fitting. In the following we will use the ``minuit`` minimizer and the ``lsb`` (least square bound scipy minimizer). Using ``minuit`` we notice that sometimes the fit will converge, but the quality  will not be enough (``valid==false``) to run ``minos``. Anyhow, as shown in the :ref:`MCMC sampling`, it still possible to estimate asymmetric errors by means of MCMC sampling

We freeze some parameters, and we also set some `fit_range` values. Setting fit_range can speed-up the fit convergence but should be judged by the user each time according to the physics of the particular source.

When using ``minuit`` the best strategy is to set the `fit_range` for most of the free parameters

A good strategy is to run first a `lsb` fit and then, using the same `fit_model`, run a fit with `minuit`


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

see the :ref:`composite_models` user guide for further information about the new implementation of `FitModel`, in particular for parameter setting

.. code:: ipython3

    from jetset.minimizer import fit_SED,ModelMinimizer
    
    from jetset.model_manager import  FitModel
    from jetset.jet_model import Jet


if you want to fit the ``prefit_model`` you can load the saved one (this
allows you to save time) ad pass it to the ``FitModel`` class

.. code:: ipython3

    prefit_jet=Jet.load_model('prefit_jet.pkl')
    fit_model_lsb=FitModel( jet=prefit_jet, name='SSC-best-fit-lsb',template=None) 




.. raw:: html

    <i>Table length=12</i>
    <table id="table140311299208000-830059" 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>4.697542e+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>1.373160e+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>9.060842e-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>3.188500e+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>2.181578e+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>7.726502e-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>3.112712e+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-01</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>lorentz-factor*</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>3.080000e-02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
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OR use the one generated above

.. code:: ipython3

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

.. code:: ipython3

    fit_model_lsb.show_model_components()


.. parsed-literal::

    
    --------------------------------------------------------------------------------
    Composite model description
    --------------------------------------------------------------------------------
    name: SSC-best-fit-lsb  
    type: composite_model  
    components models:
     -model name: jet_leptonic model type: jet
    
    --------------------------------------------------------------------------------


There is only one component, whit name ``jet_leptonic``, that refers to
the ``prefit_jet`` model component

We now set the gamma grid size to 200, ad we set ``composite_expr``,
anyhow, since we have only one component this step could be skipped

.. code:: ipython3

    fit_model_lsb.jet_leptonic.set_gamma_grid_size(200)
    fit_model_lsb.composite_expr='jet_leptonic'

Freezeing parameters and setting fit_range intervals
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. note::
   With the new implementation of composite model  (`FitModel` class) to set parameters you have to specify the model component, this is different from versions<1.1.2,
   and this holds also for the `freeze` method and for setting  `fit_range` intervals, and for the methods relate to parameters setting in general.
   See the :ref:`composite_models` user guide for further information about the new implementation of `FitModel`, in particular for parameter setting

These methods are alternative and equivalent ways to access a model
component for setting parameters state and values

a) passing as first argument, of the method, the model component
   ``name``

b) passing as first argument, of the method, the model component
   ``object``

c) accessing the model component member of the composite model class

.. code:: ipython3

    #a
    fit_model_lsb.freeze('jet_leptonic','z_cosm')
    fit_model_lsb.freeze('jet_leptonic','R_H')
    #b
    fit_model_lsb.freeze(prefit_jet,'R')
    #c
    fit_model_lsb.jet_leptonic.parameters.R.fit_range=[10**15.5,10**17.5]
    fit_model_lsb.jet_leptonic.parameters.beam_obj.fit_range=[5., 50.]

Building the ModelMinimizer object
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now we build a ``lsb`` model minimizer and run the fit method

.. note::
   starting from version 1.1.2 the `fit` method allows to repeat the fit process, setting the parameter `repeat`. This will provide a better fit convergence.
   Setting `repeat=3` the fit process will be repeated 3 times

.. code:: ipython3

    model_minimizer_lsb=ModelMinimizer('lsb')
    best_fit_lsb=model_minimizer_lsb.fit(fit_model_lsb,
                                         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 35
    ================================================================================
    
    *** start fit process ***
    ----- 
    fit run: 0



.. parsed-literal::

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


.. parsed-literal::

    - best chisq=5.32182e+01
    
    fit run: 1
    - old chisq=5.32182e+01



.. parsed-literal::

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


.. parsed-literal::

    - best chisq=5.22603e+01
    
    fit run: 2
    - old chisq=5.22603e+01



.. parsed-literal::

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


.. parsed-literal::

    - best chisq=5.09003e+01
    
    -------------------------------------------------------------------------
    Fit report
    
    Model: SSC-best-fit-minuit



.. raw:: html

    <i>Table length=12</i>
    <table id="table140311304108064-703865" 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>4.778915e+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>9.191687e+05</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>9.085652e-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>4.337114e+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>2.184444e+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>7.644091e-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>3.112712e+16</td><td>1.000000e+03</td><td>1.000000e+30</td><td>False</td><td>True</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>5.027056e-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-01</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>lorentz-factor*</td><td>2.334793e+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>3.080000e-02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    </table><style>table.dataTable {clear: both; width: auto !important; margin: 0 !important;}
    .dataTables_info, .dataTables_length, .dataTables_filter, .dataTables_paginate{
    display: inline-block; margin-right: 1em; }
    .paginate_button { margin-right: 5px; }
    </style>
    <script>
    
    var astropy_sort_num = function(a, b) {
        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;
    }
    
    require.config({paths: {
        datatables: 'https://cdn.datatables.net/1.10.12/js/jquery.dataTables.min'
    }});
    require(["datatables"], function(){
        console.log("$('#table140311304108064-703865').dataTable()");
    
    jQuery.extend( jQuery.fn.dataTableExt.oSort, {
        "optionalnum-asc": astropy_sort_num,
        "optionalnum-desc": function (a,b) { return -astropy_sort_num(a, b); }
    });
    
        $('#table140311304108064-703865').dataTable({
            order: [],
            pageLength: 100,
            lengthMenu: [[10, 25, 50, 100, 500, 1000, -1], [10, 25, 50, 100, 500, 1000, 'All']],
            pagingType: "full_numbers",
            columnDefs: [{targets: [4, 5, 6], type: "optionalnum"}]
        });
    });
    </script>



.. parsed-literal::

    
    converged=True
    calls=63
    mesg=



.. parsed-literal::

    'The relative error between two consecutive iterates is at most 0.000000'


.. parsed-literal::

    dof=27
    chisq=50.900346, chisq/red=1.885198 null hypothesis sig=0.003576
    
    best fit pars



.. raw:: html

    <i>Table length=12</i>
    <table id="table140311299667952-838566" 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>4.778915e+02</td><td>4.778915e+02</td><td>2.699848e+02</td><td>--</td><td>4.697542e+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>9.191687e+05</td><td>9.191687e+05</td><td>1.495007e+05</td><td>--</td><td>1.373160e+06</td><td>1.000000e+00</td><td>1.000000e+15</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>N</td><td>9.085652e-01</td><td>9.085652e-01</td><td>3.950026e-01</td><td>--</td><td>9.060842e-01</td><td>0.000000e+00</td><td>--</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>gamma0_log_parab</td><td>4.337114e+04</td><td>4.337114e+04</td><td>2.937759e+04</td><td>--</td><td>3.188500e+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>2.184444e+00</td><td>2.184444e+00</td><td>1.390250e-01</td><td>--</td><td>2.181578e+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>7.644091e-01</td><td>7.644091e-01</td><td>2.758032e-01</td><td>--</td><td>7.726502e-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>3.112712e+16</td><td>--</td><td>--</td><td>--</td><td>3.112712e+16</td><td>3.162278e+15</td><td>3.162278e+17</td><td>True</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>5.027056e-02</td><td>5.027056e-02</td><td>1.208011e-02</td><td>--</td><td>5.050000e-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-01</td><td>--</td><td>--</td><td>--</td><td>1.000000e-01</td><td>0.000000e+00</td><td>--</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>beam_obj</td><td>2.334793e+01</td><td>2.334793e+01</td><td>3.239464e+00</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>3.080000e-02</td><td>--</td><td>--</td><td>--</td><td>3.080000e-02</td><td>0.000000e+00</td><td>--</td><td>True</td></tr>
    </table><style>table.dataTable {clear: both; width: auto !important; margin: 0 !important;}
    .dataTables_info, .dataTables_length, .dataTables_filter, .dataTables_paginate{
    display: inline-block; margin-right: 1em; }
    .paginate_button { margin-right: 5px; }
    </style>
    <script>
    
    var astropy_sort_num = function(a, b) {
        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;
    }
    
    require.config({paths: {
        datatables: 'https://cdn.datatables.net/1.10.12/js/jquery.dataTables.min'
    }});
    require(["datatables"], function(){
        console.log("$('#table140311299667952-838566').dataTable()");
    
    jQuery.extend( jQuery.fn.dataTableExt.oSort, {
        "optionalnum-asc": astropy_sort_num,
        "optionalnum-desc": function (a,b) { return -astropy_sort_num(a, b); }
    });
    
        $('#table140311299667952-838566').dataTable({
            order: [],
            pageLength: 100,
            lengthMenu: [[10, 25, 50, 100, 500, 1000, -1], [10, 25, 50, 100, 500, 1000, 'All']],
            pagingType: "full_numbers",
            columnDefs: [{targets: [2, 3, 4, 5, 6, 7, 8], type: "optionalnum"}]
        });
    });
    </script>



.. parsed-literal::

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


we can obtain the best fit astropy table

.. code:: ipython3

    best_fit_lsb.bestfit_table




.. raw:: html

    <i>Table length=12</i>
    <table id="table140311298739408" 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>
    <thead><tr><th>str12</th><th>str16</th><th>float64</th><th>float64</th><th>float64</th><th>float64</th><th>float64</th><th>float64</th><th>float64</th><th>bool</th></tr></thead>
    <tr><td>jet_leptonic</td><td>gmin</td><td>4.778915e+02</td><td>4.778915e+02</td><td>2.699848e+02</td><td>--</td><td>4.697542e+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>9.191687e+05</td><td>9.191687e+05</td><td>1.495007e+05</td><td>--</td><td>1.373160e+06</td><td>1.000000e+00</td><td>1.000000e+15</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>N</td><td>9.085652e-01</td><td>9.085652e-01</td><td>3.950026e-01</td><td>--</td><td>9.060842e-01</td><td>0.000000e+00</td><td>--</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>gamma0_log_parab</td><td>4.337114e+04</td><td>4.337114e+04</td><td>2.937759e+04</td><td>--</td><td>3.188500e+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>2.184444e+00</td><td>2.184444e+00</td><td>1.390250e-01</td><td>--</td><td>2.181578e+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>7.644091e-01</td><td>7.644091e-01</td><td>2.758032e-01</td><td>--</td><td>7.726502e-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>3.112712e+16</td><td>--</td><td>--</td><td>--</td><td>3.112712e+16</td><td>3.162278e+15</td><td>3.162278e+17</td><td>True</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>5.027056e-02</td><td>5.027056e-02</td><td>1.208011e-02</td><td>--</td><td>5.050000e-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-01</td><td>--</td><td>--</td><td>--</td><td>1.000000e-01</td><td>0.000000e+00</td><td>--</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>beam_obj</td><td>2.334793e+01</td><td>2.334793e+01</td><td>3.239464e+00</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>3.080000e-02</td><td>--</td><td>--</td><td>--</td><td>3.080000e-02</td><td>0.000000e+00</td><td>--</td><td>True</td></tr>
    </table>



saving fit model, model minimizer
---------------------------------

We can save all the fit products to be used later.

.. code:: ipython3

    best_fit_lsb.mesg=None
    best_fit_lsb.save_report('SSC-best-fit-lsb.pkl')
    model_minimizer_lsb.save_model('model_minimizer_lsb.pkl')
    fit_model_lsb.save_model('fit_model_lsb.pkl')

.. code:: ipython3

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



.. image:: Jet_example_model_fit_files/Jet_example_model_fit_48_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

    from jetset.minimizer import fit_SED,ModelMinimizer
    from jetset.model_manager import  FitModel
    from jetset.jet_model import Jet
    
    jet_minuit=Jet.load_model('prefit_jet.pkl')
    jet_minuit.set_gamma_grid_size(200)
    #fit_model_minuit=fit_model_lsb
    fit_model_minuit=FitModel( jet=jet_minuit, name='SSC-best-fit-minuit',template=None) 



.. raw:: html

    <i>Table length=12</i>
    <table id="table140311304765600-182668" 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>4.697542e+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>1.373160e+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>9.060842e-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>3.188500e+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>2.181578e+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>7.726502e-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>3.112712e+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-01</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>lorentz-factor*</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>3.080000e-02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    </table><style>table.dataTable {clear: both; width: auto !important; margin: 0 !important;}
    .dataTables_info, .dataTables_length, .dataTables_filter, .dataTables_paginate{
    display: inline-block; margin-right: 1em; }
    .paginate_button { margin-right: 5px; }
    </style>
    <script>
    
    var astropy_sort_num = function(a, b) {
        var a_num = parseFloat(a);
        var b_num = parseFloat(b);
    
        if (isNaN(a_num) && isNaN(b_num))
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.. code:: ipython3

    fit_model_minuit.show_model_components()



.. parsed-literal::

    
    --------------------------------------------------------------------------------
    Composite model description
    --------------------------------------------------------------------------------
    name: SSC-best-fit-minuit  
    type: composite_model  
    components models:
     -model name: jet_leptonic model type: jet
    
    --------------------------------------------------------------------------------


.. code:: ipython3

    
    fit_model_minuit.freeze('jet_leptonic','z_cosm')
    fit_model_minuit.freeze('jet_leptonic','R_H')
    fit_model_minuit.jet_leptonic.parameters.R.fit_range=[5E15,1E17]
    fit_model_minuit.jet_leptonic.parameters.gmin.fit_range=[10,1000]
    fit_model_minuit.jet_leptonic.parameters.gmax.fit_range=[5E5,1E7]
    fit_model_minuit.jet_leptonic.parameters.gamma0_log_parab.fit_range=[1E3,1E5]
    
    fit_model_minuit.jet_leptonic.parameters.beam_obj.fit_range=[5,50]

.. code:: ipython3

    model_minimizer_minuit=ModelMinimizer('minuit')
    best_fit_minuit=model_minimizer_minuit.fit(fit_model_minuit,sed_data,10**11.,10**29.0,fitname='SSC-best-fit-minuit',repeat=2)


.. parsed-literal::

    filtering data in fit range = [1.000000e+11,1.000000e+29]
    data length 35
    ================================================================================
    
    *** start fit process ***
    ----- 
    fit run: 0



.. parsed-literal::

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


.. parsed-literal::

    - best chisq=4.33705e+01
    
    fit run: 1
    - old chisq=4.33705e+01



.. parsed-literal::

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


.. parsed-literal::

    - best chisq=3.11482e+01
    
    -------------------------------------------------------------------------
    Fit report
    
    Model: SSC-best-fit-minuit



.. raw:: html

    <i>Table length=12</i>
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    <tr><td>jet_leptonic</td><td>N</td><td>emitters_density</td><td>1 / cm3</td><td>7.917986e-01</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
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    <tr><td>jet_leptonic</td><td>s</td><td>LE_spectral_slope</td><td></td><td>2.090996e+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>6.854517e-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>3.046194e+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>5.214133e-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-01</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>lorentz-factor*</td><td>2.249661e+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>3.080000e-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=2284
    mesg=



.. raw:: html

    <table>
        <tr>
            <td colspan="2" style="text-align:left" title="Minimum value of function"> FCN = 31.15 </td>
            <td colspan="3" style="text-align:center" title="No. of function evaluations in last call and total number"> Nfcn = 2284 </td>
        </tr>
        <tr>
            <td colspan="2" style="text-align:left" title="Estimated distance to minimum and goal"> EDM = 3.17e+06 (Goal: 0.0002) </td>
            <td colspan="3" style="text-align:center" title="No. of gradient evaluations in last call and total number">  </td>
        </tr>
        <tr>
            <td style="text-align:center;background-color:#c15ef7;color:black"> INVALID Minimum </td>
            <td style="text-align:center;background-color:#92CCA6;color:black"> Valid Parameters </td>
            <td colspan="3" style="text-align:center;background-color:#FFF79A;color:black"> SOME Parameters at limit </td>
        </tr>
        <tr>
            <td colspan="2" style="text-align:center;background-color:#c15ef7;color:black"> ABOVE 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:#FFF79A;color:black" title="Is covariance matrix accurate?"> APPROXIMATE </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> 0.47e3 </td>
            <td> 0.29e3 </td>
            <td>  </td>
            <td>  </td>
            <td> 10 </td>
            <td> 1E+03 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 1 </th>
            <td> par_1 </td>
            <td> 0.9e6 </td>
            <td> 2.0e6 </td>
            <td>  </td>
            <td>  </td>
            <td> 5E+05 </td>
            <td> 1E+07 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 2 </th>
            <td> par_2 </td>
            <td> 0.8 </td>
            <td> 0.8 </td>
            <td>  </td>
            <td>  </td>
            <td> 0 </td>
            <td>  </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 3 </th>
            <td> par_3 </td>
            <td> 0.03e6 </td>
            <td> 0.04e6 </td>
            <td>  </td>
            <td>  </td>
            <td> 1E+03 </td>
            <td> 1E+05 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 4 </th>
            <td> par_4 </td>
            <td> 2 </td>
            <td> 8 </td>
            <td>  </td>
            <td>  </td>
            <td> -10 </td>
            <td> 10 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 5 </th>
            <td> par_5 </td>
            <td> 1 </td>
            <td> 12 </td>
            <td>  </td>
            <td>  </td>
            <td> -15 </td>
            <td> 15 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 6 </th>
            <td> par_6 </td>
            <td> 0.030e18 </td>
            <td> 0.035e18 </td>
            <td>  </td>
            <td>  </td>
            <td> 5E+15 </td>
            <td> 1E+17 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 7 </th>
            <td> par_7 </td>
            <td> 0.1 </td>
            <td> 0.4 </td>
            <td>  </td>
            <td>  </td>
            <td> 0 </td>
            <td>  </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 8 </th>
            <td> par_8 </td>
            <td> 22 </td>
            <td> 18 </td>
            <td>  </td>
            <td>  </td>
            <td> 5 </td>
            <td> 50 </td>
            <td>  </td>
        </tr>
    </table><table>
        <tr>
            <td></td>
            <th> par_0 </th>
            <th> par_1 </th>
            <th> par_2 </th>
            <th> par_3 </th>
            <th> par_4 </th>
            <th> par_5 </th>
            <th> par_6 </th>
            <th> par_7 </th>
            <th> par_8 </th>
        </tr>
        <tr>
            <th> par_0 </th>
            <td> 9.3e+04 </td>
            <td style="background-color:rgb(250,226,226);color:black"> 9.24e+07 <strong>(0.160)</strong> </td>
            <td style="background-color:rgb(239,239,250);color:black"> -21 <strong>(-0.083)</strong> </td>
            <td style="background-color:rgb(213,213,250);color:black"> -3.93e+06 <strong>(-0.287)</strong> </td>
            <td style="background-color:rgb(250,151,151);color:black"> 1.75e+03 <strong>(0.661)</strong> </td>
            <td style="background-color:rgb(250,220,220);color:black"> 906 <strong>(0.201)</strong> </td>
            <td style="background-color:rgb(250,229,229);color:black"> 1.8e+18 <strong>(0.141)</strong> </td>
            <td style="background-color:rgb(250,200,200);color:black"> 30.6 <strong>(0.333)</strong> </td>
            <td style="background-color:rgb(246,246,250);color:black"> -220 <strong>(-0.033)</strong> </td>
        </tr>
        <tr>
            <th> par_1 </th>
            <td style="background-color:rgb(250,226,226);color:black"> 9.24e+07 <strong>(0.160)</strong> </td>
            <td> 3.61e+12 </td>
            <td style="background-color:rgb(250,249,249);color:black"> 1.29e+04 <strong>(0.008)</strong> </td>
            <td style="background-color:rgb(250,246,246);color:black"> 2.41e+09 <strong>(0.028)</strong> </td>
            <td style="background-color:rgb(242,242,250);color:black"> -1.07e+06 <strong>(-0.065)</strong> </td>
            <td style="background-color:rgb(247,247,250);color:black"> -5.55e+05 <strong>(-0.020)</strong> </td>
            <td style="background-color:rgb(248,248,250);color:black"> -1.1e+21 <strong>(-0.014)</strong> </td>
            <td style="background-color:rgb(246,246,250);color:black"> -1.87e+04 <strong>(-0.033)</strong> </td>
            <td style="background-color:rgb(250,250,250);color:black"> 1.35e+05 <strong>(0.003)</strong> </td>
        </tr>
        <tr>
            <th> par_2 </th>
            <td style="background-color:rgb(239,239,250);color:black"> -21 <strong>(-0.083)</strong> </td>
            <td style="background-color:rgb(250,249,249);color:black"> 1.29e+04 <strong>(0.008)</strong> </td>
            <td> 0.686 </td>
            <td style="background-color:rgb(248,248,250);color:black"> -548 <strong>(-0.015)</strong> </td>
            <td style="background-color:rgb(250,245,245);color:black"> 0.244 <strong>(0.034)</strong> </td>
            <td style="background-color:rgb(250,248,248);color:black"> 0.126 <strong>(0.010)</strong> </td>
            <td style="background-color:rgb(250,249,249);color:black"> 2.5e+14 <strong>(0.007)</strong> </td>
            <td style="background-color:rgb(250,247,247);color:black"> 0.00426 <strong>(0.017)</strong> </td>
            <td style="background-color:rgb(250,250,250);color:black"> -0.0307 <strong>(-0.002)</strong> </td>
        </tr>
        <tr>
            <th> par_3 </th>
            <td style="background-color:rgb(213,213,250);color:black"> -3.93e+06 <strong>(-0.287)</strong> </td>
            <td style="background-color:rgb(250,246,246);color:black"> 2.41e+09 <strong>(0.028)</strong> </td>
            <td style="background-color:rgb(248,248,250);color:black"> -548 <strong>(-0.015)</strong> </td>
            <td> 2.02e+09 </td>
            <td style="background-color:rgb(250,232,232);color:black"> 4.56e+04 <strong>(0.117)</strong> </td>
            <td style="background-color:rgb(250,245,245);color:black"> 2.36e+04 <strong>(0.036)</strong> </td>
            <td style="background-color:rgb(250,246,246);color:black"> 4.69e+19 <strong>(0.025)</strong> </td>
            <td style="background-color:rgb(250,241,241);color:black"> 797 <strong>(0.059)</strong> </td>
            <td style="background-color:rgb(249,249,250);color:black"> -5.75e+03 <strong>(-0.006)</strong> </td>
        </tr>
        <tr>
            <th> par_4 </th>
            <td style="background-color:rgb(250,151,151);color:black"> 1.75e+03 <strong>(0.661)</strong> </td>
            <td style="background-color:rgb(242,242,250);color:black"> -1.07e+06 <strong>(-0.065)</strong> </td>
            <td style="background-color:rgb(250,245,245);color:black"> 0.244 <strong>(0.034)</strong> </td>
            <td style="background-color:rgb(250,232,232);color:black"> 4.56e+04 <strong>(0.117)</strong> </td>
            <td> 75.3 </td>
            <td style="background-color:rgb(239,239,250);color:black"> -10.5 <strong>(-0.082)</strong> </td>
            <td style="background-color:rgb(243,243,250);color:black"> -2.09e+16 <strong>(-0.058)</strong> </td>
            <td style="background-color:rgb(232,232,250);color:black"> -0.355 <strong>(-0.136)</strong> </td>
            <td style="background-color:rgb(250,248,248);color:black"> 2.56 <strong>(0.013)</strong> </td>
        </tr>
        <tr>
            <th> par_5 </th>
            <td style="background-color:rgb(250,220,220);color:black"> 906 <strong>(0.201)</strong> </td>
            <td style="background-color:rgb(247,247,250);color:black"> -5.55e+05 <strong>(-0.020)</strong> </td>
            <td style="background-color:rgb(250,248,248);color:black"> 0.126 <strong>(0.010)</strong> </td>
            <td style="background-color:rgb(250,245,245);color:black"> 2.36e+04 <strong>(0.036)</strong> </td>
            <td style="background-color:rgb(239,239,250);color:black"> -10.5 <strong>(-0.082)</strong> </td>
            <td> 219 </td>
            <td style="background-color:rgb(248,248,250);color:black"> -1.08e+16 <strong>(-0.017)</strong> </td>
            <td style="background-color:rgb(245,245,250);color:black"> -0.184 <strong>(-0.041)</strong> </td>
            <td style="background-color:rgb(250,249,249);color:black"> 1.32 <strong>(0.004)</strong> </td>
        </tr>
        <tr>
            <th> par_6 </th>
            <td style="background-color:rgb(250,229,229);color:black"> 1.8e+18 <strong>(0.141)</strong> </td>
            <td style="background-color:rgb(248,248,250);color:black"> -1.1e+21 <strong>(-0.014)</strong> </td>
            <td style="background-color:rgb(250,249,249);color:black"> 2.5e+14 <strong>(0.007)</strong> </td>
            <td style="background-color:rgb(250,246,246);color:black"> 4.69e+19 <strong>(0.025)</strong> </td>
            <td style="background-color:rgb(243,243,250);color:black"> -2.09e+16 <strong>(-0.058)</strong> </td>
            <td style="background-color:rgb(248,248,250);color:black"> -1.08e+16 <strong>(-0.017)</strong> </td>
            <td> 1.75e+33 </td>
            <td style="background-color:rgb(246,246,250);color:black"> -3.65e+14 <strong>(-0.029)</strong> </td>
            <td style="background-color:rgb(250,250,250);color:black"> 2.63e+15 <strong>(0.003)</strong> </td>
        </tr>
        <tr>
            <th> par_7 </th>
            <td style="background-color:rgb(250,200,200);color:black"> 30.6 <strong>(0.333)</strong> </td>
            <td style="background-color:rgb(246,246,250);color:black"> -1.87e+04 <strong>(-0.033)</strong> </td>
            <td style="background-color:rgb(250,247,247);color:black"> 0.00426 <strong>(0.017)</strong> </td>
            <td style="background-color:rgb(250,241,241);color:black"> 797 <strong>(0.059)</strong> </td>
            <td style="background-color:rgb(232,232,250);color:black"> -0.355 <strong>(-0.136)</strong> </td>
            <td style="background-color:rgb(245,245,250);color:black"> -0.184 <strong>(-0.041)</strong> </td>
            <td style="background-color:rgb(246,246,250);color:black"> -3.65e+14 <strong>(-0.029)</strong> </td>
            <td> 0.0905 </td>
            <td style="background-color:rgb(250,249,249);color:black"> 0.0447 <strong>(0.007)</strong> </td>
        </tr>
        <tr>
            <th> par_8 </th>
            <td style="background-color:rgb(246,246,250);color:black"> -220 <strong>(-0.033)</strong> </td>
            <td style="background-color:rgb(250,250,250);color:black"> 1.35e+05 <strong>(0.003)</strong> </td>
            <td style="background-color:rgb(250,250,250);color:black"> -0.0307 <strong>(-0.002)</strong> </td>
            <td style="background-color:rgb(249,249,250);color:black"> -5.75e+03 <strong>(-0.006)</strong> </td>
            <td style="background-color:rgb(250,248,248);color:black"> 2.56 <strong>(0.013)</strong> </td>
            <td style="background-color:rgb(250,249,249);color:black"> 1.32 <strong>(0.004)</strong> </td>
            <td style="background-color:rgb(250,250,250);color:black"> 2.63e+15 <strong>(0.003)</strong> </td>
            <td style="background-color:rgb(250,249,249);color:black"> 0.0447 <strong>(0.007)</strong> </td>
            <td> 481 </td>
        </tr>
    </table>


.. parsed-literal::

    dof=26
    chisq=31.148172, chisq/red=1.198007 null hypothesis sig=0.222797
    
    best fit pars



.. raw:: html

    <i>Table length=12</i>
    <table id="table140310801226624-471894" 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>4.688283e+02</td><td>4.688283e+02</td><td>2.858882e+02</td><td>--</td><td>4.697542e+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>9.028968e+05</td><td>9.028968e+05</td><td>1.970066e+06</td><td>--</td><td>1.373160e+06</td><td>5.000000e+05</td><td>1.000000e+07</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>N</td><td>7.917986e-01</td><td>7.917986e-01</td><td>7.826153e-01</td><td>--</td><td>9.060842e-01</td><td>0.000000e+00</td><td>--</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>gamma0_log_parab</td><td>3.238465e+04</td><td>3.238465e+04</td><td>3.814239e+04</td><td>--</td><td>3.188500e+04</td><td>1.000000e+03</td><td>1.000000e+05</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>s</td><td>2.090996e+00</td><td>2.090996e+00</td><td>7.583699e+00</td><td>--</td><td>2.181578e+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>6.854517e-01</td><td>6.854517e-01</td><td>1.250924e+01</td><td>--</td><td>7.726502e-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>3.046194e+16</td><td>3.046194e+16</td><td>3.526875e+16</td><td>--</td><td>3.112712e+16</td><td>5.000000e+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>5.214133e-02</td><td>5.214133e-02</td><td>3.594802e-01</td><td>--</td><td>5.050000e-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-01</td><td>--</td><td>--</td><td>--</td><td>1.000000e-01</td><td>0.000000e+00</td><td>--</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>beam_obj</td><td>2.249661e+01</td><td>2.249661e+01</td><td>1.845509e+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>3.080000e-02</td><td>--</td><td>--</td><td>--</td><td>3.080000e-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_minuit.eval()
    p2=fit_model_minuit.plot_model(sed_data=sed_data)
    p2.setlim(y_min=1E-13,x_min=1E6,x_max=2E28)



.. image:: Jet_example_model_fit_files/Jet_example_model_fit_55_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_minuit.save_model('fit_model_minuit.pkl')

You can obtain profile and contours, but this is typically time
consuming. In any case, better results can be achieved using the MCMC
approach (discussed in next section) For further information regardin
minuit please refer to https://iminuit.readthedocs.io

.. code-block:: python

    #migrad profile

    #access the data
    profile_migrad=model_minimizer_minuit.minimizer.mnprofile('s')

    #make the plot(no need to run the previous command)
    profile_plot_migrad=model_minimizer_minuit.minimizer.draw_mnprofile('s')

.. code-block:: python

    #migrad contour
    #access the data
    contour_migrad=model_minimizer_minuit.minimizer.contour('beam_obj','B')

    #make the plot(no need to run the previous command)
    contour_plot_migrad=model_minimizer_minuit.minimizer.draw_contour('beam_obj','B')

you can use also minos contour and profile, in this case the
computational time is even longer:

.. code-block:: python
    
   profile_migrad=model_minimizer_minuit.minimizer.mnprofile('s')
   profile_plot_migrad=model_minimizer_minuit.minimizer.draw_mnprofile('s')
        
   contour_migrad=model_minimizer_minuit.minimizer.mncontour('r','s')
   contour_plot_migrad=model_minimizer_minuit.minimizer.draw_mncontour('r','s')

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

.. code:: ipython3

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


We used a flat prior centered on the best fit value. Setting
``bound=5.0`` and ``bound_rel=True`` means that:

1) the prior interval will be defined as [best_fit_val - delta_m ,
   best_fit_val + delta_p]

2) with delta_p=delta_m=best_fit_val*bound

If we set ``bound_rel=False`` then delta_p = delta_m =
best_fit_err*bound

It is possible to define asymmetric boundaries e.g. ``bound=[2.0,5.0]``
meaning that

1) for ``bound_rel=True``

   delta_p = best_fit_val*bound[1]

   delta_m =b est_fit_val*bound[0]

2) for ``bound_rel=False``

   delta_p = best_fit_err*bound[1]

   delta_m = best_fit_err*bound[0]

In the next release a more flexible prior interface will be added,
including different type of priors

Given the large parameter space, we select a sub sample of parameters
using the ``use_labels_dict``. If we do not pass the ‘use_labels_dict’
the full set of free parameters will be used

.. code:: ipython3

    from tqdm.auto import tqdm
    
    model_minimizer_minuit = ModelMinimizer.load_model('model_minimizer_minuit.pkl')
    
    mcmc=McmcSampler(model_minimizer_minuit)
    
    labels=['N','B','beam_obj','s','gamma0_log_parab']
    model_name='jet_leptonic'
    use_labels_dict={model_name:labels}
    
    mcmc.run_sampler(nwalkers=128,burnin=10,steps=50,bound=5.0,bound_rel=True,threads=None,walker_start_bound=0.005,use_labels_dict=use_labels_dict,progress='notebook')


.. parsed-literal::

    mcmc run starting
    



.. parsed-literal::

      0%|          | 0/50 [00:00<?, ?it/s]


.. parsed-literal::

    mcmc run done, with 1 threads took 341.59 seconds


.. code:: ipython3

    print(mcmc.acceptance_fraction)


.. parsed-literal::

    0.5459375


.. code:: ipython3

    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_files/Jet_example_model_fit_67_0.png


.. code:: ipython3

    p=mcmc.plot_model(sed_data=sed_data,fit_range=[1E11, 2E27],size=100,quantiles=[0.05,0.95])
    p.setlim(y_min=1E-14,x_min=1E6,x_max=2E28)



.. image:: Jet_example_model_fit_files/Jet_example_model_fit_68_0.png


.. code:: ipython3

    f=mcmc.plot_chain('s',log_plot=False)



.. image:: Jet_example_model_fit_files/Jet_example_model_fit_69_0.png


.. code:: ipython3

    f=mcmc.corner_plot()



.. image:: Jet_example_model_fit_files/Jet_example_model_fit_70_0.png


.. code:: ipython3

    mcmc.get_par('N')




.. parsed-literal::

    (array([0.78402592, 0.79701842, 0.7860921 , ..., 0.68880801, 0.70229451,
            0.65232144]),
     0)



.. code:: ipython3

    f=mcmc.plot_par('beam_obj')



.. image:: Jet_example_model_fit_files/Jet_example_model_fit_72_0.png


.. code:: ipython3

    f=mcmc.plot_par('gamma0_log_parab',log_plot=True)



.. image:: Jet_example_model_fit_files/Jet_example_model_fit_73_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_401.pkl')
    
    ms=McmcSampler.load('mcmc_sampler.pkl')

.. code:: ipython3

    ms.model.name




.. parsed-literal::

    'SSC-best-fit-minuit'



.. code:: ipython3

    p=ms.plot_model(sed_data=sed_data,fit_range=[1E11, 2E27],size=100)
    p.setlim(y_min=1E-14,x_min=1E6,x_max=2E28)



.. image:: Jet_example_model_fit_files/Jet_example_model_fit_78_0.png


.. code:: ipython3

    p=ms.plot_model(sed_data=sed_data,fit_range=[1E11, 2E27],size=100,quantiles=[0.05,0.95])
    p.setlim(y_min=1E-14,x_min=1E6,x_max=2E28)



.. image:: Jet_example_model_fit_files/Jet_example_model_fit_79_0.png


.. code:: ipython3

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




.. image:: Jet_example_model_fit_files/Jet_example_model_fit_80_0.png


.. code:: ipython3

    f=ms.plot_par('B',log_plot=True)




.. image:: Jet_example_model_fit_files/Jet_example_model_fit_81_0.png


.. code:: ipython3

    f=ms.plot_chain('s',log_plot=False)



.. image:: Jet_example_model_fit_files/Jet_example_model_fit_82_0.png


.. code:: ipython3

    f=ms.corner_plot()



.. image:: Jet_example_model_fit_files/Jet_example_model_fit_83_0.png