.. _dep_pars:

Depending parameters
====================

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

Example: linked paramters for EBL
---------------------------------

.. code:: ipython3

    import warnings
    warnings.filterwarnings('ignore')

.. code:: ipython3

    import numpy as np

.. code:: ipython3

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


.. parsed-literal::

    tested on jetset 1.3.0rc9


.. code:: ipython3

    from jetset.jet_model import Jet
    from jetset.template_2Dmodel import EBLAbsorptionTemplate
    from jetset.model_manager import FitModel
    
    my_jet = Jet(electron_distribution='lppl', name='jet_flaring')
    my_jet.parameters.z_cosm.val = 0.01
    
    ebl_franceschini = EBLAbsorptionTemplate.from_name('Franceschini_2008')
    
    composite_model = FitModel(nu_size=500, name='EBL corrected')
    composite_model.add_component(my_jet)
    composite_model.add_component(ebl_franceschini)
    
    composite_model.show_pars()
    
    composite_model.link_par(par_name='z_cosm', from_model='Franceschini_2008', to_model='jet_flaring')
    v=0.03001
    my_jet.parameters.z_cosm.val = v
    assert (composite_model.Franceschini_2008.parameters.z_cosm.val==v)
    assert (composite_model.Franceschini_2008.parameters.z_cosm.linked==True)
    
    composite_model.composite_expr = '%s*%s'%(my_jet.name,ebl_franceschini.name)
    composite_model.eval()
    
    #if plot is True:
    #    composite_model.plot_model()
    
    composite_model.save_model('ebl_jet.pkl')
    new_composite_model=FitModel.load_model('ebl_jet.pkl')
    new_composite_model.show_pars()
    v=2.0
    new_composite_model.jet_flaring.parameters.z_cosm.val=v
    print('new_composite_model.Franceschini_2008.parameters.z_cosm.val',new_composite_model.Franceschini_2008.parameters.z_cosm.val,'v',v)
    assert (new_composite_model.Franceschini_2008.parameters.z_cosm.val == v)
    assert (new_composite_model.Franceschini_2008.parameters.z_cosm.linked == True)


.. parsed-literal::

    ===> setting C threads to 12



.. raw:: html

    <i>Table length=14</i>
    <table id="table4653352032-998550" 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_flaring</td><td>R</td><td>region_size</td><td>cm</td><td>5.000000e+15</td><td>1.000000e+03</td><td>1.000000e+30</td><td>False</td><td>False</td></tr>
    <tr><td>jet_flaring</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_flaring</td><td>B</td><td>magnetic_field</td><td>gauss</td><td>1.000000e-01</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_flaring</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_flaring</td><td>beam_obj</td><td>beaming</td><td></td><td>1.000000e+01</td><td>1.000000e-04</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_flaring</td><td>z_cosm</td><td>redshift</td><td></td><td>1.000000e-02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_flaring</td><td>gmin</td><td>low-energy-cut-off</td><td>lorentz-factor*</td><td>2.000000e+00</td><td>1.000000e+00</td><td>1.000000e+09</td><td>False</td><td>False</td></tr>
    <tr><td>jet_flaring</td><td>gmax</td><td>high-energy-cut-off</td><td>lorentz-factor*</td><td>1.000000e+06</td><td>1.000000e+00</td><td>1.000000e+15</td><td>False</td><td>False</td></tr>
    <tr><td>jet_flaring</td><td>N</td><td>emitters_density</td><td>1 / cm3</td><td>1.000000e+02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_flaring</td><td>gamma0_log_parab</td><td>turn-over-energy</td><td>lorentz-factor*</td><td>1.000000e+04</td><td>1.000000e+00</td><td>1.000000e+09</td><td>False</td><td>False</td></tr>
    <tr><td>jet_flaring</td><td>s</td><td>LE_spectral_slope</td><td></td><td>2.000000e+00</td><td>-1.000000e+01</td><td>1.000000e+01</td><td>False</td><td>False</td></tr>
    <tr><td>jet_flaring</td><td>r</td><td>spectral_curvature</td><td></td><td>4.000000e-01</td><td>-1.500000e+01</td><td>1.500000e+01</td><td>False</td><td>False</td></tr>
    <tr><td>Franceschini_2008</td><td>scale_factor</td><td>scale_factor</td><td></td><td>1.000000e+00</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>Franceschini_2008</td><td>z_cosm</td><td>redshift</td><td></td><td>1.000000e+00</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("$('#table4653352032-998550').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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        $('#table4653352032-998550').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::

    adding par: z_cosm to  z_cosm
    ===> setting C threads to 12
    adding par: z_cosm to  z_cosm



.. raw:: html

    <i>Table length=14</i>
    <table id="table5768952608-924404" 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_flaring</td><td>gmin</td><td>low-energy-cut-off</td><td>lorentz-factor*</td><td>2.000000e+00</td><td>1.000000e+00</td><td>1.000000e+09</td><td>False</td><td>False</td></tr>
    <tr><td>jet_flaring</td><td>gmax</td><td>high-energy-cut-off</td><td>lorentz-factor*</td><td>1.000000e+06</td><td>1.000000e+00</td><td>1.000000e+15</td><td>False</td><td>False</td></tr>
    <tr><td>jet_flaring</td><td>N</td><td>emitters_density</td><td>1 / cm3</td><td>1.000000e+02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_flaring</td><td>gamma0_log_parab</td><td>turn-over-energy</td><td>lorentz-factor*</td><td>1.000000e+04</td><td>1.000000e+00</td><td>1.000000e+09</td><td>False</td><td>False</td></tr>
    <tr><td>jet_flaring</td><td>s</td><td>LE_spectral_slope</td><td></td><td>2.000000e+00</td><td>-1.000000e+01</td><td>1.000000e+01</td><td>False</td><td>False</td></tr>
    <tr><td>jet_flaring</td><td>r</td><td>spectral_curvature</td><td></td><td>4.000000e-01</td><td>-1.500000e+01</td><td>1.500000e+01</td><td>False</td><td>False</td></tr>
    <tr><td>jet_flaring</td><td>R</td><td>region_size</td><td>cm</td><td>5.000000e+15</td><td>1.000000e+03</td><td>1.000000e+30</td><td>False</td><td>False</td></tr>
    <tr><td>jet_flaring</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_flaring</td><td>B</td><td>magnetic_field</td><td>gauss</td><td>1.000000e-01</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_flaring</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_flaring</td><td>beam_obj</td><td>beaming</td><td></td><td>1.000000e+01</td><td>1.000000e-04</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_flaring</td><td>z_cosm(M)</td><td>redshift</td><td></td><td>3.001000e-02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>Franceschini_2008</td><td>scale_factor</td><td>scale_factor</td><td></td><td>1.000000e+00</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>Franceschini_2008</td><td>z_cosm(L,jet_flaring)</td><td>redshift</td><td></td><td>--</td><td>--</td><td>--</td><td>False</td><td>True</td></tr>
    </table><style>table.dataTable {clear: both; width: auto !important; margin: 0 !important;}
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    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;
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    require.config({paths: {
        datatables: 'https://cdn.datatables.net/1.10.12/js/jquery.dataTables.min'
    }});
    require(["datatables"], function(){
        console.log("$('#table5768952608-924404').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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        $('#table5768952608-924404').dataTable({
            order: [],
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            lengthMenu: [[10, 25, 50, 100, 500, 1000, -1], [10, 25, 50, 100, 500, 1000, 'All']],
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    </script>



.. parsed-literal::

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


Example: depending pars for bkn power-law emitters
--------------------------------------------------

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

.. code:: ipython3

    from jetset.jet_emitters import EmittersDistribution
    import numpy as np
    
    
    
    from jetset.jet_model import Jet
    
    j = Jet(emitters_distribution='bkn')
    
    
    j.parameters



.. parsed-literal::

    ===> setting C threads to 12



.. raw:: html

    <i>Table length=12</i>
    <table id="table5774552816-774334" 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>5.000000e+15</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>1.000000e-01</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>1.000000e+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>1.000000e-01</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>2.000000e+00</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>1.000000e+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>1.000000e+02</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>1.000000e+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>p</td><td>LE_spectral_slope</td><td></td><td>2.500000e+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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    require.config({paths: {
        datatables: 'https://cdn.datatables.net/1.10.12/js/jquery.dataTables.min'
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    });
    </script>





.. parsed-literal::

    None



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

.. code:: ipython3

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


.. parsed-literal::

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



.. raw:: html

    <i>Table length=12</i>
    <table id="table5774552816-123254" 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>5.000000e+15</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>1.000000e-01</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>1.000000e+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>1.000000e-01</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>2.000000e+00</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>1.000000e+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>1.000000e+02</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>1.000000e+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>p(M)</td><td>LE_spectral_slope</td><td></td><td>2.000000e+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(D,p)</td><td>HE_spectral_slope</td><td></td><td>3.000000e+00</td><td>-1.000000e+01</td><td>1.000000e+01</td><td>False</td><td>True</td></tr>
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    </script>





.. parsed-literal::

    None



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

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

.. code:: ipython3

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


.. parsed-literal::

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



.. raw:: html

    <i>Table length=12</i>
    <table id="table5774552816-995239" 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>5.000000e+15</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>1.000000e-01</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>1.000000e+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>1.000000e-01</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>2.000000e+00</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>1.000000e+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>1.000000e+02</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>1.000000e+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>p(M)</td><td>LE_spectral_slope</td><td></td><td>2.000000e+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(D,p)</td><td>HE_spectral_slope</td><td></td><td>3.000000e+00</td><td>-1.000000e+01</td><td>1.000000e+01</td><td>False</td><td>True</td></tr>
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    .paginate_button { margin-right: 5px; }
    </style>
    <script>
    
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        var a_num = parseFloat(a);
        var b_num = parseFloat(b);
    
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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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        datatables: 'https://cdn.datatables.net/1.10.12/js/jquery.dataTables.min'
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        console.log("$('#table5774552816-995239').dataTable()");
    
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        "optionalnum-asc": astropy_sort_num,
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        });
    });
    </script>





.. parsed-literal::

    None



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

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

.. code:: ipython3

    j.parameters.p_1.par_expression_source_code


.. parsed-literal::

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


.. code:: ipython3

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



.. parsed-literal::

    ===> setting C threads to 12
    adding par: p to  p_1
    ==> par p_1 is depending on ['p'] according to expr:   p_1 =
    p+1


.. code:: ipython3

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



.. raw:: html

    <i>Table length=12</i>
    <table id="table5760519520-228964" 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>2.000000e+00</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>1.000000e+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>1.000000e+02</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>1.000000e+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>p(M)</td><td>LE_spectral_slope</td><td></td><td>2.500000e+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(D,p)</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>True</td></tr>
    <tr><td>jet_leptonic</td><td>R</td><td>region_size</td><td>cm</td><td>5.000000e+15</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>1.000000e-01</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>1.000000e+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>1.000000e-01</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>
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        var a_num = parseFloat(a);
        var b_num = parseFloat(b);
    
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    jQuery.extend( jQuery.fn.dataTableExt.oSort, {
        "optionalnum-asc": astropy_sort_num,
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            columnDefs: [{targets: [4, 5, 6], type: "optionalnum"}]
        });
    });
    </script>





.. parsed-literal::

    None



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

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

:math:`B=B_0(R_0/R_H)^{1.1}`

.. code:: ipython3

    jet=Jet(emitters_distribution='plc')
    fit_model_lsb=FitModel( jet=jet, name='SSC-best-fit-lsb',template=None)
    fit_model_lsb.jet_leptonic.parameters.beam_obj.fit_range = [5, 50]
    fit_model_lsb.jet_leptonic.parameters.R_H.val=5E17
    fit_model_lsb.jet_leptonic.parameters.R_H.frozen=False
    fit_model_lsb.jet_leptonic.parameters.R_H.fit_range = [1E15, 1E19]
    fit_model_lsb.jet_leptonic.parameters.R.fit_range = [10 ** 15.5, 10 ** 17.5]
    
    fit_model_lsb.jet_leptonic.add_user_par(name='B0',units='G',val=1E3,val_min=0,val_max=None)
    fit_model_lsb.jet_leptonic.add_user_par(name='R0', units='cm', val=5E13, val_min=0, val_max=None)
    fit_model_lsb.jet_leptonic.add_user_par(name='m_B', val=1, val_min=1, val_max=2)
    fit_model_lsb.jet_leptonic.parameters.R0.frozen=True
    fit_model_lsb.jet_leptonic.parameters.B0.frozen=True
    
    def par_func(R0,B0,R_H,m_B): 
        return B0*np.power((R0/R_H),m_B)
    
    fit_model_lsb.jet_leptonic.make_dependent_par(par='B', depends_on=['B0', 'R0', 'R_H','m_B'], par_expr=par_func)
    
    B0=fit_model_lsb.jet_leptonic.parameters.B0.val
    R0 = fit_model_lsb.jet_leptonic.parameters.R0.val
    R_H = fit_model_lsb.jet_leptonic.parameters.R_H.val
    m_B= fit_model_lsb.jet_leptonic.parameters.m_B.val
    
    np.testing.assert_allclose(fit_model_lsb.jet_leptonic.parameters.B.val, par_func(R0,B0,R_H,m_B))


.. parsed-literal::

    ===> setting C threads to 12
    adding par: B0 to  B
    adding par: R0 to  B
    adding par: R_H to  B
    adding par: m_B to  B
    ==> par B is depending on ['B0', 'R0', 'R_H', 'm_B'] according to expr:   B =
    def par_func(R0,B0,R_H,m_B): 
        return B0*np.power((R0/R_H),m_B)
    


.. code:: ipython3

    
    fit_model_lsb.jet_leptonic.parameters



.. raw:: html

    <i>Table length=14</i>
    <table id="table5762997920-499120" 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>5.000000e+15</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(M)</td><td>region_position</td><td>cm</td><td>5.000000e+17</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>*B(D,m_B)</td><td>magnetic_field</td><td>gauss</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>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>1.000000e+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>1.000000e-01</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>2.000000e+00</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>1.000000e+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>1.000000e+02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>gamma_cut</td><td>turn-over-energy</td><td>lorentz-factor*</td><td>1.000000e+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>p</td><td>LE_spectral_slope</td><td></td><td>2.000000e+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>B0(M)</td><td>user_defined</td><td>G</td><td>1.000000e+03</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>R0(M)</td><td>user_defined</td><td>cm</td><td>5.000000e+13</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>m_B(M)</td><td>user_defined</td><td></td><td>1.000000e+00</td><td>1.000000e+00</td><td>2.000000e+00</td><td>False</td><td>False</td></tr>
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            return isNaN(a_num) ? -1 : 1;
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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::

    None



.. code:: ipython3

    fit_model_lsb.save_model('test.pkl')

.. code:: ipython3

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


.. parsed-literal::

    ===> setting C threads to 12
    adding par: B0 to  B
    adding par: R0 to  B
    adding par: R_H to  B
    adding par: m_B to  B
    ==> par B is depending on ['B0', 'R0', 'R_H', 'm_B'] according to expr:   B =
    def par_func(R0,B0,R_H,m_B): 
        return B0*np.power((R0/R_H),m_B)
    


.. code:: ipython3

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

.. code:: ipython3

    %matplotlib inline
    import matplotlib.pyplot as plt
    
    plt.figure(dpi=150)
    R_H_array=np.logspace(13,18,100)
    B_array=np.zeros(R_H_array.shape)
    for ID,R_H in enumerate(R_H_array):
        fit_model_lsb.jet_leptonic.parameters.R_H.val=R_H
        B_array[ID]=fit_model_lsb.jet_leptonic.parameters.B.val
    
    plt.loglog(R_H_array,B_array)
    plt.xlabel('R_H (cm)')
    plt.ylabel('B (G)')




.. parsed-literal::

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




.. image:: depending_pars_files/depending_pars_28_1.png


Removing the dependenencies
---------------------------

for the entire ``fit_model``

.. code:: ipython3

    fit_model_lsb.parameters.reset_dependencies()

or, for a specific component

.. code:: ipython3

    fit_model_lsb.jet_leptonic.parameters.reset_dependencies()

.. code:: ipython3

    fit_model_lsb.parameters



.. raw:: html

    <i>Table length=14</i>
    <table id="table5764620272-659506" 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>2.000000e+00</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>1.000000e+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>1.000000e+02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>gamma_cut</td><td>turn-over-energy</td><td>lorentz-factor*</td><td>1.000000e+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>p</td><td>LE_spectral_slope</td><td></td><td>2.000000e+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>region_size</td><td>cm</td><td>5.000000e+15</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+18</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>B</td><td>magnetic_field</td><td>gauss</td><td>5.000000e-02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</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>1.000000e+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>1.000000e-01</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>B0</td><td>user_defined</td><td>G</td><td>1.000000e+03</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>R0</td><td>user_defined</td><td>cm</td><td>5.000000e+13</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>m_B</td><td>user_defined</td><td></td><td>1.000000e+00</td><td>1.000000e+00</td><td>2.000000e+00</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);
    
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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("$('#table5764620272-659506').dataTable()");
    
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        "optionalnum-asc": astropy_sort_num,
        "optionalnum-desc": function (a,b) { return -astropy_sort_num(a, b); }
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            columnDefs: [{targets: [4, 5, 6], type: "optionalnum"}]
        });
    });
    </script>





.. parsed-literal::

    None



.. code:: ipython3

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




.. parsed-literal::

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




.. image:: depending_pars_files/depending_pars_35_1.png


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

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

.. code:: ipython3

    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

    data=Data.from_file(test_SEDs[1])

.. code:: ipython3

    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= 89
    ---> bin_widht= 0.2
    ================================================================================
    



.. image:: depending_pars_files/depending_pars_40_1.png


.. 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()



.. parsed-literal::

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



.. image:: depending_pars_files/depending_pars_41_1.png


.. 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="table5776250320-389050" 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>-1.585748e-01</td><td>-1.585748e-01</td><td>6.470535e-03</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>-1.089513e-02</td><td>-1.089513e-02</td><td>9.764985e-04</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>1.673177e+01</td><td>1.673177e+01</td><td>2.478677e-02</td><td>--</td><td>1.667298e+01</td><td>0.000000e+00</td><td>3.000000e+01</td><td>False</td></tr>
    <tr><td>LogCubic</td><td>Sp</td><td>-9.489417e+00</td><td>-9.489417e+00</td><td>1.853260e-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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    .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("$('#table5776250320-389050').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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        $('#table5776250320-389050').dataTable({
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            columnDefs: [{targets: [2, 3, 4, 5, 6, 7, 8], type: "optionalnum"}]
        });
    });
    </script>



.. parsed-literal::

    ---> sync       nu_p=+1.673177e+01 (err=+2.478677e-02)  nuFnu_p=-9.489417e+00 (err=+1.853260e-02) curv.=-1.585748e-01 (err=+6.470535e-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="table5768200784-888826" 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>-1.971111e-01</td><td>-1.971111e-01</td><td>2.679732e-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>-4.037544e-02</td><td>-4.037544e-02</td><td>2.119803e-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>2.521789e+01</td><td>2.521789e+01</td><td>1.198160e-01</td><td>--</td><td>2.529262e+01</td><td>0.000000e+00</td><td>3.000000e+01</td><td>False</td></tr>
    <tr><td>LogCubic</td><td>Sp</td><td>-1.012535e+01</td><td>-1.012535e+01</td><td>2.996508e-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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    .paginate_button { margin-right: 5px; }
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    <script>
    
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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))
            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("$('#table5768200784-888826').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=+2.521789e+01 (err=+1.198160e-01)  nuFnu_p=-1.012535e+01 (err=+2.996508e-02) curv.=-1.971111e-01 (err=+2.679732e-02)
    ================================================================================
    



.. image:: depending_pars_files/depending_pars_43_3.png


.. 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 ***
    
    ===> setting C threads to 12



.. raw:: html

    <i>Table length=12</i>
    <table id="table5767804912-618077" 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>3.460321e+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>3.080000e-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>6.545152e-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>3.333017e+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>2.183468e+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>7.928739e-01</td><td>-1.500000e+01</td><td>1.500000e+01</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))
            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("$('#table5767804912-618077').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: [4, 5, 6], type: "optionalnum"}]
        });
    });
    </script>



.. parsed-literal::

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


.. code:: ipython3

    from jetset.minimizer import fit_SED,ModelMinimizer
    
    from jetset.model_manager import  FitModel
    from jetset.jet_model import Jet
    prefit_jet=Jet.load_model('prefit_jet.pkl')


.. parsed-literal::

    ===> setting C threads to 12


.. code:: ipython3

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



.. raw:: html

    <i>Table length=12</i>
    <table id="table5784322000-284535" 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>6.545152e-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>3.333017e+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>2.183468e+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>7.928739e-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>3.460321e+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>3.080000e-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>
    
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            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("$('#table5784322000-284535').dataTable()");
    
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        "optionalnum-asc": astropy_sort_num,
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            columnDefs: [{targets: [4, 5, 6], type: "optionalnum"}]
        });
    });
    </script>





.. parsed-literal::

    None



.. code:: ipython3

    fit_model.jet_leptonic.parameters.beam_obj.fit_range = [5, 50]
    fit_model.jet_leptonic.parameters.R_H.val=5E17
    fit_model.jet_leptonic.parameters.R_H.frozen=False
    fit_model.jet_leptonic.parameters.R_H.fit_range = [1E15, 1E19]
    fit_model.jet_leptonic.parameters.R.fit_range = [10 ** 15.5, 10 ** 17.5]
    fit_model.jet_leptonic.parameters.gamma0_log_parab.fit_range = [1E3,1E6]
    fit_model.jet_leptonic.parameters.gmin.fit_range = [10,1000]
    fit_model.jet_leptonic.parameters.gmax.fit_range = [1E5,1E8]
    
    fit_model.jet_leptonic.add_user_par(name='B0',units='G',val=1E3,val_min=0,val_max=None)
    fit_model.jet_leptonic.add_user_par(name='R0', units='cm', val=5E13, val_min=0, val_max=None)
    fit_model.jet_leptonic.add_user_par(name='m_B', val=1, val_min=1, val_max=2)
    fit_model.jet_leptonic.parameters.R0.frozen=True
    fit_model.jet_leptonic.parameters.B0.frozen=True
    
    def par_func(R0,B0,R_H,m_B): 
        return B0*np.power((R0/R_H),m_B)
    
    fit_model.jet_leptonic.make_dependent_par(par='B', depends_on=['B0', 'R0', 'R_H','m_B'], par_expr=par_func)
    fit_model.parameters


.. parsed-literal::

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



.. raw:: html

    <i>Table length=15</i>
    <table id="table5784922448-254126" 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>6.545152e-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>3.333017e+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>2.183468e+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>7.928739e-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>3.460321e+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(M)</td><td>region_position</td><td>cm</td><td>5.000000e+17</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>*B(D,m_B)</td><td>magnetic_field</td><td>gauss</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>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>3.080000e-02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>B0(M)</td><td>user_defined</td><td>G</td><td>1.000000e+03</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>R0(M)</td><td>user_defined</td><td>cm</td><td>5.000000e+13</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>m_B(M)</td><td>user_defined</td><td></td><td>1.000000e+00</td><td>1.000000e+00</td><td>2.000000e+00</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>
    
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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))
            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("$('#table5784922448-254126').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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        $('#table5784922448-254126').dataTable({
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        });
    });
    </script>





.. parsed-literal::

    None



.. code:: ipython3

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




.. parsed-literal::

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




.. image:: depending_pars_files/depending_pars_48_1.png


.. code:: ipython3

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

.. code:: ipython3

    fit_model.parameters



.. raw:: html

    <i>Table length=15</i>
    <table id="table5784926384-924057" 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>6.545152e-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>3.333017e+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>2.183468e+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>7.928739e-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>3.460321e+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(M)</td><td>region_position</td><td>cm</td><td>5.000000e+17</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>*B(D,m_B)</td><td>magnetic_field</td><td>gauss</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>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>3.080000e-02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>B0(M)</td><td>user_defined</td><td>G</td><td>1.000000e+03</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>R0(M)</td><td>user_defined</td><td>cm</td><td>5.000000e+13</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>m_B(M)</td><td>user_defined</td><td></td><td>1.000000e+00</td><td>1.000000e+00</td><td>2.000000e+00</td><td>False</td><td>False</td></tr>
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    .dataTables_info, .dataTables_length, .dataTables_filter, .dataTables_paginate{
    display: inline-block; margin-right: 1em; }
    .paginate_button { margin-right: 5px; }
    </style>
    <script>
    
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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))
            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("$('#table5784926384-924057').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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        });
    });
    </script>





.. parsed-literal::

    None



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

.. code:: ipython3

    model_minimizer_minuit=ModelMinimizer('minuit')

.. code:: ipython3

    model_minimizer_minuit.minimizer.add_simplex=False

.. code:: ipython3

    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 35
    ================================================================================
    
    *** start fit process ***
    ----- 
    fit run: 0



.. parsed-literal::

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


.. parsed-literal::

    ====> migrad
    - best chisq=3.30494e+01
    
    fit run: 1
    - old chisq=3.30494e+01



.. parsed-literal::

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


.. parsed-literal::

    ====> migrad
    - best chisq=2.21161e+01
    
    fit run: 2
    - old chisq=2.21161e+01



.. parsed-literal::

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


.. parsed-literal::

    ====> migrad
    - best chisq=2.01970e+01
    
    -------------------------------------------------------------------------
    Fit report
    
    Model: SSC-best-fit-minuit



.. raw:: html

    <i>Table length=15</i>
    <table id="table5784926384-701227" 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>5.955908e+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>7.336491e+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>7.078650e-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>3.225336e+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>2.232280e+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>6.488585e-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>2.940961e+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(M)</td><td>region_position</td><td>cm</td><td>4.786191e+17</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>*B(D,m_B)</td><td>magnetic_field</td><td>gauss</td><td>4.766679e-02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</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>3.726640e+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>5.799018e-02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>B0(M)</td><td>user_defined</td><td>G</td><td>1.000000e+03</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>R0(M)</td><td>user_defined</td><td>cm</td><td>5.000000e+13</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>m_B(M)</td><td>user_defined</td><td></td><td>1.085597e+00</td><td>1.000000e+00</td><td>2.000000e+00</td><td>False</td><td>False</td></tr>
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    .dataTables_info, .dataTables_length, .dataTables_filter, .dataTables_paginate{
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    .paginate_button { margin-right: 5px; }
    </style>
    <script>
    
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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));
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            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("$('#table5784926384-701227').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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.. parsed-literal::

    
    converged=True
    calls=4803
    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 = 20.2 </td>
            <td colspan="3" style="text-align:center" title="Total number of function and (optional) gradient evaluations"> Nfcn = 4803 </td>
        </tr>
        <tr>
            <td colspan="2" style="text-align:left" title="Estimated distance to minimum and goal"> EDM = 3.32e-07 (Goal: 0.0002) </td>
            <td colspan="3" style="text-align:center" title="Total run time of algorithms"> time = 81.2 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> 595.6 </td>
            <td> 1.1 </td>
            <td>  </td>
            <td>  </td>
            <td> 10 </td>
            <td> 1E+03 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 1 </th>
            <td> par_1 </td>
            <td> 733.6e3 </td>
            <td> 0.5e3 </td>
            <td>  </td>
            <td>  </td>
            <td> 1E+05 </td>
            <td> 1E+08 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 2 </th>
            <td> par_2 </td>
            <td> 707.865e-3 </td>
            <td> 0.010e-3 </td>
            <td>  </td>
            <td>  </td>
            <td> 0 </td>
            <td>  </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 3 </th>
            <td> par_3 </td>
            <td> 32.2534e3 </td>
            <td> 0.0022e3 </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> 2.232280 </td>
            <td> 0.000023 </td>
            <td>  </td>
            <td>  </td>
            <td> -10 </td>
            <td> 10 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 5 </th>
            <td> par_5 </td>
            <td> 648.86e-3 </td>
            <td> 0.26e-3 </td>
            <td>  </td>
            <td>  </td>
            <td> -15 </td>
            <td> 15 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 6 </th>
            <td> par_6 </td>
            <td> 29.4096e15 </td>
            <td> 0.0012e15 </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> 478.619e15 </td>
            <td> 0.027e15 </td>
            <td>  </td>
            <td>  </td>
            <td> 1E+15 </td>
            <td> 1E+19 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 8 </th>
            <td> par_8 </td>
            <td> 37.26640 </td>
            <td> 0.00024 </td>
            <td>  </td>
            <td>  </td>
            <td> 5 </td>
            <td> 50 </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 9 </th>
            <td> par_9 </td>
            <td> 57.9902e-3 </td>
            <td> 0.0034e-3 </td>
            <td>  </td>
            <td>  </td>
            <td> 0 </td>
            <td>  </td>
            <td>  </td>
        </tr>
        <tr>
            <th> 10 </th>
            <td> par_10 </td>
            <td> 1.0855972 </td>
            <td> 0.0000033 </td>
            <td>  </td>
            <td>  </td>
            <td> 1 </td>
            <td> 2 </td>
            <td>  </td>
        </tr>
    </table>


.. parsed-literal::

    dof=24
    chisq=20.196967, chisq/red=0.841540 null hypothesis sig=0.685522
    
    best fit pars



.. raw:: html

    <i>Table length=15</i>
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    <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>5.955908e+02</td><td>5.955908e+02</td><td>1.099191e+00</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>7.336491e+05</td><td>7.336491e+05</td><td>5.239237e+02</td><td>--</td><td>1.373160e+06</td><td>1.000000e+05</td><td>1.000000e+08</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>N</td><td>7.078650e-01</td><td>7.078650e-01</td><td>1.030217e-05</td><td>--</td><td>6.545152e-01</td><td>0.000000e+00</td><td>--</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>gamma0_log_parab</td><td>3.225336e+04</td><td>3.225336e+04</td><td>2.156816e+00</td><td>--</td><td>3.333017e+04</td><td>1.000000e+03</td><td>1.000000e+06</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>s</td><td>2.232280e+00</td><td>2.232280e+00</td><td>2.282556e-05</td><td>--</td><td>2.183468e+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>6.488585e-01</td><td>6.488585e-01</td><td>2.582949e-04</td><td>--</td><td>7.928739e-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>2.940961e+16</td><td>2.940961e+16</td><td>1.250211e+12</td><td>--</td><td>3.460321e+16</td><td>3.162278e+15</td><td>3.162278e+17</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>R_H(M)</td><td>4.786191e+17</td><td>4.786191e+17</td><td>2.668558e+13</td><td>--</td><td>5.000000e+17</td><td>1.000000e+15</td><td>1.000000e+19</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>*B(D,m_B)</td><td>4.766679e-02</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>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>3.726640e+01</td><td>3.726640e+01</td><td>2.449689e-04</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>5.799018e-02</td><td>5.799018e-02</td><td>3.432852e-06</td><td>--</td><td>3.080000e-02</td><td>0.000000e+00</td><td>--</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>B0(M)</td><td>1.000000e+03</td><td>--</td><td>--</td><td>--</td><td>1.000000e+03</td><td>0.000000e+00</td><td>--</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>R0(M)</td><td>5.000000e+13</td><td>--</td><td>--</td><td>--</td><td>5.000000e+13</td><td>0.000000e+00</td><td>--</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>m_B(M)</td><td>1.085597e+00</td><td>1.085597e+00</td><td>3.331357e-06</td><td>--</td><td>1.000000e+00</td><td>1.000000e+00</td><td>2.000000e+00</td><td>False</td></tr>
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.. parsed-literal::

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


.. code:: ipython3

    fit_model.plot_model(sed_data=sed_data)




.. parsed-literal::

    <jetset.plot_sedfit.PlotSED at 0x158f65750>




.. image:: depending_pars_files/depending_pars_55_1.png


.. code:: ipython3

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




.. parsed-literal::

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




.. image:: depending_pars_files/depending_pars_56_1.png


.. code:: ipython3

    fit_model.save_model('test.pkl')


.. code:: ipython3

    from jetset.model_manager import  FitModel
    
    new_fit_model=FitModel.load_model('test.pkl')


.. parsed-literal::

    ===> setting C threads to 12
    adding par: B0 to  B
    adding par: R0 to  B
    adding par: R_H to  B
    adding par: m_B to  B
    ==> par B is depending on ['B0', 'R0', 'R_H', 'm_B'] according to expr:   B =
    def par_func(R0,B0,R_H,m_B): 
        return B0*np.power((R0/R_H),m_B)
    


.. code:: ipython3

    new_fit_model.parameters



.. raw:: html

    <i>Table length=15</i>
    <table id="table5760937232-329306" 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>5.955908e+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>7.336491e+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>7.078650e-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>3.225336e+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>2.232280e+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>6.488585e-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>2.940961e+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(M)</td><td>region_position</td><td>cm</td><td>1.000000e+18</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>*B(D,m_B)</td><td>magnetic_field</td><td>gauss</td><td>2.141973e-02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</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>3.726640e+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>5.799018e-02</td><td>0.000000e+00</td><td>--</td><td>False</td><td>False</td></tr>
    <tr><td>jet_leptonic</td><td>B0(M)</td><td>user_defined</td><td>G</td><td>1.000000e+03</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>R0(M)</td><td>user_defined</td><td>cm</td><td>5.000000e+13</td><td>0.000000e+00</td><td>--</td><td>False</td><td>True</td></tr>
    <tr><td>jet_leptonic</td><td>m_B(M)</td><td>user_defined</td><td></td><td>1.085597e+00</td><td>1.000000e+00</td><td>2.000000e+00</td><td>False</td><td>False</td></tr>
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.. parsed-literal::

    None