Generate mock data for a cluster
================================

In this example we generate mock data with a variety of systematic
effects including photometric redshifts, source galaxy distributions,
and shape noise. We then populate a galaxy cluster object. This
notebooks is organised as follows: - Imports and configuration setup -
Generate mock data with different source galaxy options - Generate mock
data with different field-of-view options - Generate mock data with
different galaxy cluster options (only available with the Numcosmo
and/or CCL backends). Use the ``os.environ['CLMM_MODELING_BACKEND']``
line below to select your backend.

.. code:: ipython3

    import os
    
    ## Uncomment the following line if you want to use a specific modeling backend among 'ct' (cluster-toolkit), 'ccl' (CCL) or 'nc' (Numcosmo). Default is 'ccl'
    # os.environ['CLMM_MODELING_BACKEND'] = 'nc'

.. code:: ipython3

    import numpy as np
    import matplotlib.pyplot as plt
    
    %matplotlib inline

.. code:: ipython3

    import clmm

Make sure we know which version we’re using

.. code:: ipython3

    clmm.__version__




.. parsed-literal::

    '1.12.0'



Import mock data module and setup the configuration
---------------------------------------------------

.. code:: ipython3

    from clmm.support import mock_data as mock
    from clmm import Cosmology

Mock data generation requires a defined cosmology

.. code:: ipython3

    mock_cosmo = Cosmology(H0=70.0, Omega_dm0=0.27 - 0.045, Omega_b0=0.045, Omega_k0=0.0)

Mock data generation requires some cluster information. The default is
to work with the NFW profile, using the “200,mean” mass definition. The
Numcosmo and CCL backends allow for more flexibility (see last section
of this notebook)

.. code:: ipython3

    cosmo = mock_cosmo
    cluster_id = "Awesome_cluster"
    cluster_m = 1.0e15  # M200,m
    cluster_z = 0.3
    src_z = 0.8
    concentration = 4
    ngals = 1000  # number of source galaxies
    
    # Cluster centre coordinates
    cluster_ra = 50.0
    cluster_dec = 87.0

Generate the mock catalog with different source galaxy options
--------------------------------------------------------------

-  Clean data: no noise, all galaxies at the same redshift

.. code:: ipython3

    zsrc_min = cluster_z + 0.1

.. code:: ipython3

    ideal_data = mock.generate_galaxy_catalog(
        cluster_m,
        cluster_z,
        concentration,
        cosmo,
        src_z,
        ngals=ngals,
        cluster_ra=cluster_ra,
        cluster_dec=cluster_dec,
    )

.. code:: ipython3

    # let's put all these quantities in a single dictionary to facilitate clarity
    cluster_kwargs = {
        "cluster_m": cluster_m,
        "cluster_z": cluster_z,
        "cluster_ra": cluster_ra,
        "cluster_dec": cluster_dec,
        "cluster_c": concentration,
        "cosmo": cosmo,
    }

.. code:: ipython3

    ideal_data = mock.generate_galaxy_catalog(**cluster_kwargs, zsrc=src_z, ngals=ngals)

-  Noisy data: shape noise, all galaxies at the same redshift

.. code:: ipython3

    noisy_data_src_z = mock.generate_galaxy_catalog(
        **cluster_kwargs, zsrc=src_z, shapenoise=0.05, ngals=ngals
    )

-  Noisy data: shape noise plus measurement error, all galaxies at the
   same redshift

.. code:: ipython3

    noisy_data_src_z_e_err = mock.generate_galaxy_catalog(
        **cluster_kwargs, zsrc=src_z, shapenoise=0.05, mean_e_err=0.05, ngals=ngals
    )

.. container:: alert alert-warning

   **WARNING:** Experimental feature. Uncertainties are created by
   simply drawing random numbers near the value specified by
   ``mean_e_err``. Use at your own risk. This will be improved in future
   releases.

-  Noisy data: photo-z errors (and pdfs!), all galaxies at the same
   redshift. At present, the pdfs are generated by drawing a random
   value from a Normal distribution with mean ``ztrue`` and width given
   by ``dz = (1+z)*photoz_sigma_unscaled``, and the pdf is this Normal
   distribution centered around ``z`` instead of ``ztrue``.

.. code:: ipython3

    noisy_data_photoz = mock.generate_galaxy_catalog(
        **cluster_kwargs,
        zsrc=src_z,
        shapenoise=0.05,
        photoz_sigma_unscaled=0.05,
        pz_bins=101,
        ngals=ngals
    )

In the default PDF storing (``pzpdf_type='shared_bins'``), the values of
the PDF are added to the ``pzpdf`` column and the binning scheme is
stored in the ``pzpdf_info`` attribute:

.. code:: ipython3

    noisy_data_photoz.pzpdf_info




.. parsed-literal::

    {'type': 'shared_bins',
     'zbins': array([0.        , 0.01959865, 0.0391973 , 0.05879595, 0.0783946 ,
            0.09799325, 0.1175919 , 0.13719055, 0.15678921, 0.17638786,
            0.19598651, 0.21558516, 0.23518381, 0.25478246, 0.27438111,
            0.29397976, 0.31357841, 0.33317706, 0.35277571, 0.37237436,
            0.39197301, 0.41157166, 0.43117031, 0.45076896, 0.47036762,
            0.48996627, 0.50956492, 0.52916357, 0.54876222, 0.56836087,
            0.58795952, 0.60755817, 0.62715682, 0.64675547, 0.66635412,
            0.68595277, 0.70555142, 0.72515007, 0.74474872, 0.76434737,
            0.78394603, 0.80354468, 0.82314333, 0.84274198, 0.86234063,
            0.88193928, 0.90153793, 0.92113658, 0.94073523, 0.96033388,
            0.97993253, 0.99953118, 1.01912983, 1.03872848, 1.05832713,
            1.07792578, 1.09752444, 1.11712309, 1.13672174, 1.15632039,
            1.17591904, 1.19551769, 1.21511634, 1.23471499, 1.25431364,
            1.27391229, 1.29351094, 1.31310959, 1.33270824, 1.35230689,
            1.37190554, 1.3915042 , 1.41110285, 1.4307015 , 1.45030015,
            1.4698988 , 1.48949745, 1.5090961 , 1.52869475, 1.5482934 ,
            1.56789205, 1.5874907 , 1.60708935, 1.626688  , 1.64628665,
            1.6658853 , 1.68548395, 1.70508261, 1.72468126, 1.74427991,
            1.76387856, 1.78347721, 1.80307586, 1.82267451, 1.84227316,
            1.86187181, 1.88147046, 1.90106911, 1.92066776, 1.94026641,
            1.95986506])}



.. code:: ipython3

    noisy_data_photoz[:5]




.. raw:: html

    <b>GCData</b>
    <br> <b>defined by:</b> cosmo=None
    <br> <b>with columns:</b> ra, dec, e1, e2, z, ztrue, pzpdf, id
    <br> <b>and pzpdf:</b> shared_bins [0.   0.02 0.04 0.06 0.08 ... 1.88 1.9  1.92 1.94 1.96]
    <br> 5 objects
    <br> 
    <table id="table140168562981008" class="table-striped table-bordered table-condensed">
    <thead><tr><th>ra</th><th>dec</th><th>e1</th><th>e2</th><th>z</th><th>ztrue</th><th>pzpdf</th><th>id</th></tr></thead>
    <thead><tr><th>float64</th><th>float64</th><th>float64</th><th>float64</th><th>float64</th><th>float64</th><th>float64[101]</th><th>int64</th></tr></thead>
    <tr><td>46.25728808233552</td><td>86.8922305424305</td><td>0.08236207803522719</td><td>-0.05411854076714888</td><td>0.6987103181997064</td><td>0.8</td><td>3.622089304592751e-13 .. 1.0180322952717169e-42</td><td>0</td></tr>
    <tr><td>50.07778715623189</td><td>87.10740150490655</td><td>-0.01475225297133639</td><td>0.03882800844119587</td><td>0.7392962132175859</td><td>0.8</td><td>9.870794333079776e-15 .. 5.1047370592912794e-40</td><td>1</td></tr>
    <tr><td>48.40809879885119</td><td>86.87728907171557</td><td>-1.2575884722892804e-05</td><td>0.02096267636736204</td><td>0.9009303274293756</td><td>0.8</td><td>7.709520397996465e-22 .. 3.849218150728941e-30</td><td>2</td></tr>
    <tr><td>53.014368911831866</td><td>86.9440239760556</td><td>-0.011911350886457556</td><td>-0.05893011144277411</td><td>0.8447969829350334</td><td>0.8</td><td>3.2663820149084725e-19 .. 2.0599039175494822e-33</td><td>3</td></tr>
    <tr><td>53.435230187909205</td><td>87.09017457767816</td><td>-0.01999543117339179</td><td>0.02354367773663435</td><td>0.6191383565693703</td><td>0.8</td><td>2.345198551898936e-10 .. 2.86718907682299e-48</td><td>4</td></tr>
    </table></div>



It is also possible to generate individual binning of the PDF with
``pzpdf_type='individual_bins'``. In this case, both the bin values and
the PDF are added to the ``pzpdf`` column:

.. code:: ipython3

    mock.generate_galaxy_catalog(
        **cluster_kwargs,
        zsrc=src_z,
        shapenoise=0.05,
        photoz_sigma_unscaled=0.05,
        pz_bins=101,
        ngals=ngals,
        pzpdf_type="individual_bins"
    )[:5]




.. raw:: html

    <b>GCData</b>
    <br> <b>defined by:</b> cosmo=None
    <br> <b>with columns:</b> ra, dec, e1, e2, z, ztrue, pzbins, pzpdf, id
    <br> <b>and pzpdf:</b> individual_bins
    <br> 5 objects
    <br> 
    <table id="table140168561873488" class="table-striped table-bordered table-condensed">
    <thead><tr><th>ra</th><th>dec</th><th>e1</th><th>e2</th><th>z</th><th>ztrue</th><th>pzbins</th><th>pzpdf</th><th>id</th></tr></thead>
    <thead><tr><th>float64</th><th>float64</th><th>float64</th><th>float64</th><th>float64</th><th>float64</th><th>float64[101]</th><th>float64[101]</th><th>int64</th></tr></thead>
    <tr><td>51.71809588955455</td><td>86.79418499898124</td><td>0.04517177528103273</td><td>0.007954419566760369</td><td>0.7115192931034046</td><td>0.8</td><td>0.0 .. 1.6115192931034046</td><td>1.1876947502964896e-13 .. 8.54955402967386e-22</td><td>0</td></tr>
    <tr><td>46.708001638011126</td><td>86.88819976612274</td><td>-0.012879815467979831</td><td>-0.08175448050969202</td><td>0.6945681551460963</td><td>0.8</td><td>0.0 .. 1.5945681551460964</td><td>5.172194687003747e-13 .. 8.549554029673739e-22</td><td>1</td></tr>
    <tr><td>49.39451998685305</td><td>87.20677909110817</td><td>-0.0039628583975751495</td><td>0.0174994506167209</td><td>0.8315805078776208</td><td>0.8</td><td>0.0 .. 1.731580507877621</td><td>1.2824084572051592e-18 .. 8.549554029673739e-22</td><td>2</td></tr>
    <tr><td>46.860634504940194</td><td>86.93654387908563</td><td>-0.046259792137662965</td><td>0.005322896799894367</td><td>0.6917814486066362</td><td>0.8</td><td>0.0 .. 1.5917814486066364</td><td>6.565150731239997e-13 .. 8.549554029673677e-22</td><td>3</td></tr>
    <tr><td>51.265622797606405</td><td>86.8664662837592</td><td>0.031668628429442</td><td>0.050725273846685515</td><td>0.7563730258487964</td><td>0.8</td><td>0.0 .. 1.6563730258487965</td><td>2.0400190276050062e-15 .. 8.549554029673739e-22</td><td>4</td></tr>
    </table></div>



Note that if ``pzpdf_type=None``, the pdf is not stored:

.. code:: ipython3

    mock.generate_galaxy_catalog(
        **cluster_kwargs,
        zsrc=src_z,
        shapenoise=0.05,
        photoz_sigma_unscaled=0.05,
        pz_bins=101,
        ngals=ngals,
        pzpdf_type=None
    )[:5]




.. raw:: html

    <b>GCData</b>
    <br> <b>defined by:</b> cosmo=None
    <br> <b>with columns:</b> ra, dec, e1, e2, z, ztrue, id
    <br> 5 objects
    <br> 
    <table id="table140168561983568" class="table-striped table-bordered table-condensed">
    <thead><tr><th>ra</th><th>dec</th><th>e1</th><th>e2</th><th>z</th><th>ztrue</th><th>id</th></tr></thead>
    <thead><tr><th>float64</th><th>float64</th><th>float64</th><th>float64</th><th>float64</th><th>float64</th><th>int64</th></tr></thead>
    <tr><td>49.481245279211514</td><td>86.88497246906974</td><td>-0.04639901705475107</td><td>0.016810643634124524</td><td>0.6562799312782062</td><td>0.8</td><td>0</td></tr>
    <tr><td>46.76580446202989</td><td>87.11740891509298</td><td>0.008967332934760024</td><td>-0.04736707598002053</td><td>0.7566021959253701</td><td>0.8</td><td>1</td></tr>
    <tr><td>47.67683451367938</td><td>87.09593810890625</td><td>-1.6856807502580002e-06</td><td>-0.038785443779489344</td><td>0.7427555109960904</td><td>0.8</td><td>2</td></tr>
    <tr><td>45.25894486510976</td><td>87.0819953631451</td><td>0.010890284110664075</td><td>-0.002194000734056742</td><td>0.9292500730723824</td><td>0.8</td><td>3</td></tr>
    <tr><td>53.47006170976472</td><td>86.89370333944125</td><td>-0.12053390035191411</td><td>0.06970042860558802</td><td>0.7672613734120534</td><td>0.8</td><td>4</td></tr>
    </table></div>



-  Clean data: source galaxy redshifts drawn from a redshift
   distribution instead of fixed ``src_z`` value. Options are
   ``chang13`` for Chang et al. 2013 or ``desc_srd`` for the
   distribution given in the DESC Science Requirement Document. No shape
   noise or photoz errors.

.. code:: ipython3

    ideal_with_src_dist = mock.generate_galaxy_catalog(
        **cluster_kwargs, zsrc="chang13", zsrc_min=zsrc_min, zsrc_max=7.0, ngals=ngals
    )

-  Noisy data: galaxies following redshift distribution, redshift error,
   shape noise

.. code:: ipython3

    pzbins = np.linspace(0, 10, 1001)

.. code:: ipython3

    allsystematics = mock.generate_galaxy_catalog(
        **cluster_kwargs,
        zsrc="chang13",
        zsrc_min=zsrc_min,
        photoz_sigma_unscaled=0.05,
        ngals=ngals,
        pz_bins=pzbins,
    )

.. code:: ipython3

    allsystematics2 = mock.generate_galaxy_catalog(
        **cluster_kwargs,
        zsrc="desc_srd",
        zsrc_min=zsrc_min,
        zsrc_max=7.0,
        photoz_sigma_unscaled=0.05,
        ngals=ngals,
        pz_bins=pzbins,
        shapenoise=0.05,
    )

Sanity check: checking that no galaxies were originally drawn below
zsrc_min, before photoz errors are applied (when relevant)

.. code:: ipython3

    print(
        f"""Number of galaxies below zsrc_min:
        ideal_data          : {np.sum(ideal_data['ztrue']<zsrc_min):5,}
        noisy_data_src_z    : {np.sum(noisy_data_src_z['ztrue']<zsrc_min):5,}
        noisy_data_photoz   : {np.sum(noisy_data_photoz['ztrue']<zsrc_min):5,}
        ideal_with_src_dist : {np.sum(ideal_with_src_dist['ztrue']<zsrc_min):5,}
        allsystematics      : {np.sum(allsystematics['ztrue']<zsrc_min):5,}
    """
    )


.. parsed-literal::

    Number of galaxies below zsrc_min:
        ideal_data          :     0
        noisy_data_src_z    :     0
        noisy_data_photoz   :     0
        ideal_with_src_dist :     0
        allsystematics      :     0
    


Inspect the catalog data
~~~~~~~~~~~~~~~~~~~~~~~~

-  Ideal catalog first entries: no noise on the shape measurement, all
   galaxies at z=0.8, no redshift errors (z = ztrue)

.. code:: ipython3

    for n in ideal_data.colnames:
        if n != "id":
            ideal_data[n].format = "%6.3e"
    ideal_data[0:3].show_in_notebook()




.. raw:: html

    <i>GCData length=3</i>
    <table id="table140168562672400-443876" class="table-striped table-bordered table-condensed">
    <thead><tr><th>idx</th><th>ra</th><th>dec</th><th>e1</th><th>e2</th><th>z</th><th>ztrue</th><th>id</th></tr></thead>
    <tr><td>0</td><td>5.278e+01</td><td>8.690e+01</td><td>-4.495e-03</td><td>-1.083e-02</td><td>8.000e-01</td><td>8.000e-01</td><td>0</td></tr>
    <tr><td>1</td><td>5.095e+01</td><td>8.702e+01</td><td>-2.997e-02</td><td>2.582e-02</td><td>8.000e-01</td><td>8.000e-01</td><td>1</td></tr>
    <tr><td>2</td><td>4.637e+01</td><td>8.703e+01</td><td>-1.019e-02</td><td>-3.995e-03</td><td>8.000e-01</td><td>8.000e-01</td><td>2</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("$('#table140168562672400-443876').dataTable()");
    
    jQuery.extend( jQuery.fn.dataTableExt.oSort, {
        "optionalnum-asc": astropy_sort_num,
        "optionalnum-desc": function (a,b) { return -astropy_sort_num(a, b); }
    });
    
        $('#table140168562672400-443876').dataTable({
            order: [],
            pageLength: 50,
            lengthMenu: [[10, 25, 50, 100, 500, 1000, -1], [10, 25, 50, 100, 500, 1000, 'All']],
            pagingType: "full_numbers",
            columnDefs: [{targets: [0, 1, 2, 3, 4, 5, 6, 7], type: "optionalnum"}]
        });
    });
    </script>




-  With photo-z errors

.. code:: ipython3

    for n in noisy_data_photoz.colnames:
        if n != "id":
            noisy_data_photoz[n].format = "%6.3e"
    noisy_data_photoz[0:3].show_in_notebook()




.. raw:: html

    <i>GCData length=3</i>
    <table id="table140168562672400-735054" class="table-striped table-bordered table-condensed">
    <thead><tr><th>idx</th><th>ra</th><th>dec</th><th>e1</th><th>e2</th><th>z</th><th>ztrue</th><th>pzpdf</th><th>id</th></tr></thead>
    <tr><td>0</td><td>4.626e+01</td><td>8.689e+01</td><td>8.236e-02</td><td>-5.412e-02</td><td>6.987e-01</td><td>8.000e-01</td><td>3.622e-13 .. 1.018e-42</td><td>0</td></tr>
    <tr><td>1</td><td>5.008e+01</td><td>8.711e+01</td><td>-1.475e-02</td><td>3.883e-02</td><td>7.393e-01</td><td>8.000e-01</td><td>9.871e-15 .. 5.105e-40</td><td>1</td></tr>
    <tr><td>2</td><td>4.841e+01</td><td>8.688e+01</td><td>-1.258e-05</td><td>2.096e-02</td><td>9.009e-01</td><td>8.000e-01</td><td>7.710e-22 .. 3.849e-30</td><td>2</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("$('#table140168562672400-735054').dataTable()");
    
    jQuery.extend( jQuery.fn.dataTableExt.oSort, {
        "optionalnum-asc": astropy_sort_num,
        "optionalnum-desc": function (a,b) { return -astropy_sort_num(a, b); }
    });
    
        $('#table140168562672400-735054').dataTable({
            order: [],
            pageLength: 50,
            lengthMenu: [[10, 25, 50, 100, 500, 1000, -1], [10, 25, 50, 100, 500, 1000, 'All']],
            pagingType: "full_numbers",
            columnDefs: [{targets: [0, 1, 2, 3, 4, 5, 6, 7, 8], type: "optionalnum"}]
        });
    });
    </script>




-  Histogram of the redshift distribution of background galaxies, for
   the true (originally drawn) redshift and the redshift once photoz
   errors have been added, and the stacked pdf. By construction no true
   redshift occurs below zsrc_min, but some ‘observed’ redshifts
   (i.e. including photoz errors) might be.

.. code:: ipython3

    plt.hist(
        allsystematics["z"],
        bins=50,
        alpha=0.3,
        density=True,
        label="measured z (i.e. including photoz error)",
    )
    plt.hist(allsystematics["ztrue"], bins=50, alpha=0.3, density=True, label="true z")
    stacked_pdf = np.mean(allsystematics["pzpdf"], axis=0)
    plt.plot(allsystematics.pzpdf_info["zbins"], stacked_pdf, "C3", label="stacked pdf")
    plt.axvline(zsrc_min, color="k", label="requested zmin")
    plt.xlabel("Source Redshift")
    plt.ylabel("n(z)")
    plt.legend()
    plt.xlim(0, 5)
    pass



.. image:: demo_mock_cluster_files/demo_mock_cluster_47_0.png


.. code:: ipython3

    plt.hist(allsystematics["ztrue"], bins=50, alpha=0.3, label="true z")
    plt.hist(allsystematics2["ztrue"], bins=50, alpha=0.3, label="true z");



.. image:: demo_mock_cluster_files/demo_mock_cluster_48_0.png


Populate a galaxy cluster object
--------------------------------

.. code:: ipython3

    gc_object = clmm.GalaxyCluster(cluster_id, cluster_ra, cluster_dec, cluster_z, allsystematics)

From a ``GalaxyCluster`` object that has photoz information,
``draw_gal_z_from_pdz`` allows to generate ``nobj`` random redshifts of
each galaxy in ``galcat``, from its photoz pdf, and store the result in
a new ``zcol_out`` column.

.. code:: ipython3

    z_random = gc_object.draw_gal_z_from_pdz(zcol_out="z_random", overwrite=False, nobj=1)

The plot below shows the “observed photoz pdf” (blue), centered on the
“observed z” (red), the true redshift from which the shear where
computed (green) and a random redshift (orange) computed from the pdf

.. code:: ipython3

    # p(z) for one of the galaxies in the catalog,
    galid = 0
    plt.fill(gc_object.galcat.pzpdf_info["zbins"], allsystematics["pzpdf"][galid], alpha=0.3)
    plt.plot(gc_object.galcat.pzpdf_info["zbins"], gc_object.galcat["pzpdf"][galid], label="Photoz pdf")
    
    plt.axvline(gc_object.galcat["z"][galid], label="Observed z", color="red")
    plt.axvline(gc_object.galcat["ztrue"][galid], label="True z", color="g")
    plt.axvline(gc_object.galcat["z_random"][galid], label="Random z from pdf", color="orange")
    
    plt.xlabel("Redshift")
    plt.ylabel("Photo-z Probability Distribution")
    plt.legend(loc=1)
    plt.xlim(gc_object.galcat["z"][galid] - 0.5, gc_object.galcat["z"][galid] + 0.5)




.. parsed-literal::

    (1.328538487022893, 2.328538487022893)




.. image:: demo_mock_cluster_files/demo_mock_cluster_54_1.png


Plot source galaxy ellipticities

.. code:: ipython3

    plt.scatter(gc_object.galcat["e1"], gc_object.galcat["e2"])
    
    plt.xlim(-0.2, 0.2)
    plt.ylim(-0.2, 0.2)
    plt.xlabel("Ellipticity 1", fontsize="x-large")
    plt.ylabel("Ellipticity 2", fontsize="x-large")




.. parsed-literal::

    Text(0, 0.5, 'Ellipticity 2')




.. image:: demo_mock_cluster_files/demo_mock_cluster_56_1.png


Generate the mock data catalog with different field-of-view options
-------------------------------------------------------------------

In the examples above, ``ngals=1000`` galaxies were simulated in a field
corresponding to a 8 Mpc x 8 Mpc (proper distance) square box at the
cluster redshift (this is the default). The user may however vary the
field size and/or provide a galaxy density (instead of a number of
galaxies). This is examplified below, using the ``allsystematics``
example.

-  ``ngals = 1000`` in a 4 x 4 Mpc box. Asking for the same number of
   galaxies in a smaller field of view yields high galaxy density

.. code:: ipython3

    allsystematics2 = mock.generate_galaxy_catalog(
        **cluster_kwargs,
        zsrc="chang13",
        zsrc_min=zsrc_min,
        zsrc_max=7.0,
        shapenoise=0.05,
        photoz_sigma_unscaled=0.05,
        field_size=4,
        ngals=ngals
    )

.. code:: ipython3

    plt.scatter(allsystematics["ra"], allsystematics["dec"], marker=".", label="default 8 x 8 Mpc FoV")
    plt.scatter(allsystematics2["ra"], allsystematics2["dec"], marker=".", label="user-defined FoV")
    plt.legend()




.. parsed-literal::

    <matplotlib.legend.Legend at 0x7f7b82455550>




.. image:: demo_mock_cluster_files/demo_mock_cluster_61_1.png


-  Alternatively, the user may provide a galaxy density (here ~1
   gal/arcmin2 to roughly match 1000 galaxies, given the configuration)
   and the number of galaxies to draw will automatically be adjusted to
   the box size.

.. code:: ipython3

    allsystematics3 = mock.generate_galaxy_catalog(
        **cluster_kwargs,
        zsrc="chang13",
        zsrc_min=zsrc_min,
        zsrc_max=7.0,
        shapenoise=0.05,
        photoz_sigma_unscaled=0.05,
        ngal_density=1.3,
    )
    print(f"Number of drawn galaxies = {len(allsystematics3)}")


.. parsed-literal::

    Number of drawn galaxies = 989


.. code:: ipython3

    allsystematics4 = mock.generate_galaxy_catalog(
        **cluster_kwargs,
        zsrc="desc_srd",
        zsrc_min=zsrc_min,
        zsrc_max=7.0,
        shapenoise=0.05,
        photoz_sigma_unscaled=0.05,
        ngal_density=1.3,
    )
    print(f"Number of drawn galaxies = {len(allsystematics4)}")


.. parsed-literal::

    Number of drawn galaxies = 1020


.. code:: ipython3

    plt.scatter(allsystematics["ra"], allsystematics["dec"], marker=".", label="ngals = 1000")
    plt.scatter(
        allsystematics3["ra"],
        allsystematics3["dec"],
        marker=".",
        label="ngal_density = 1 gal / arcmin2",
    )
    plt.legend()




.. parsed-literal::

    <matplotlib.legend.Legend at 0x7f7b8210a350>




.. image:: demo_mock_cluster_files/demo_mock_cluster_65_1.png


Generate mock data with different galaxy cluster options
--------------------------------------------------------

WARNING: Available options depend on the modeling backend: -
Cluster-toolkit allows for other values of the overdensity parameter,
but is retricted to working with the mean mass definition - Both CCL and
Numcosmo allow for different values of the overdensity parameter, but
work with both the mean and critical mass definition - Numcosmo further
allows for the Einasto or Burkert density profiles to be used instead of
the NFW profile

Changing the overdensity parameter (all backend) - ``delta_so`` keyword (default = 200)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code:: ipython3

    allsystematics_500mean = mock.generate_galaxy_catalog(
        **cluster_kwargs,
        zsrc="chang13",
        delta_so=500,
        zsrc_min=zsrc_min,
        zsrc_max=7.0,
        shapenoise=0.05,
        photoz_sigma_unscaled=0.05,
        ngals=ngals
    )

Using the critical mass definition (Numcosmo and CCL only) - ``massdef`` keyword (default = ‘mean’)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

WARNING: error will be raised if using the cluster-toolkit backend

.. code:: ipython3

    allsystematics_200critical = mock.generate_galaxy_catalog(
        **cluster_kwargs,
        zsrc="chang13",
        massdef="critical",
        zsrc_min=zsrc_min,
        zsrc_max=7.0,
        shapenoise=0.05,
        photoz_sigma_unscaled=0.05,
        ngals=ngals
    )

Changing the halo density profile (Numcosmo and CCL only) - ``halo_profile_model`` keyword (default = ‘nfw’)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

WARNING: error will be raised if using the cluster-toolkit or CCL
backends

.. code:: ipython3

    allsystematics_200m_einasto = mock.generate_galaxy_catalog(
        **cluster_kwargs,
        zsrc="chang13",
        halo_profile_model="einasto",
        zsrc_min=zsrc_min,
        zsrc_max=7.0,
        shapenoise=0.05,
        photoz_sigma_unscaled=0.05,
        ngals=ngals
    )