Fourier analysis (MSAP4-01A)
============================

.. code:: ipython3

    import star_privateer as sp
    import plato_msap4_demonstrator_datasets.plato_sim_dataset as plato_sim_dataset

.. code:: ipython3

    import numpy as np
    import matplotlib.pyplot as plt
    import pandas as pd

K2: Rotation period analysis
----------------------------

.. code:: ipython3

    t, s, dt = sp.load_k2_example ()

.. code:: ipython3

    fig, ax = plt.subplots (1, 1, figsize=(8,4))
    
    ax.scatter (t[s!=0]-t[0], s[s!=0], color='black', 
                marker='o', s=1)
    
    ax.set_xlabel ('Time (day)')
    ax.set_ylabel ('Flux (ppm)')
    
    fig.tight_layout ()



.. image:: fourier_analysis_files/fourier_analysis_5_0.png


As we want to recover rotation periods below 45 days, we only consider
the section of the periodogram verifying
:math:`P < P_\mathrm{cutoff} = 45` days.

.. code:: ipython3

    pcutoff = 60

As a preprocessing step, we compute the Lomb-Scargle periodogram (in the
SAS framework, it will be directyly provided by MSAP1).

.. code:: ipython3

    p_ps, ps_object = sp.compute_lomb_scargle (t, s)
    ls = ps_object.power_standard_norm

Now we perform the periodogram analysis.

.. code:: ipython3

    cond = p_ps < pcutoff
    prot, e_p, E_p, param, h_ps = sp.compute_prot_err_gaussian_fit_chi2_distribution (p_ps[cond], ls[cond], n_profile=20, 
                                                                                         threshold=0.1, plot_procedure=False,
                                                                                         verbose=False)
    sp.plot_ls (p_ps, ls, filename='figures/fourier_k2.png', param_profile=param, 
                   logscale=False, xlim=(0.1, 5))
    IDP_SAS_PROT_FOURIER = sp.prepare_idp_fourier (param, h_ps, ls.size,
                                                      pcutoff=pcutoff, pthresh=None,
                                                      fapcutoff=1e-6)
    
    df = pd.DataFrame (data=IDP_SAS_PROT_FOURIER)
    df




.. raw:: html

    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
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        .dataframe tbody tr th {
            vertical-align: top;
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        .dataframe thead th {
            text-align: right;
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    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>0</th>
          <th>1</th>
          <th>2</th>
          <th>3</th>
          <th>4</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>2.759429</td>
          <td>0.036004</td>
          <td>0.036968</td>
          <td>0.422299</td>
          <td>1.000000e-16</td>
        </tr>
        <tr>
          <th>1</th>
          <td>1.393418</td>
          <td>0.013796</td>
          <td>0.014075</td>
          <td>0.216592</td>
          <td>1.000000e-16</td>
        </tr>
        <tr>
          <th>2</th>
          <td>0.775871</td>
          <td>0.007650</td>
          <td>0.007804</td>
          <td>0.057243</td>
          <td>1.000000e-16</td>
        </tr>
      </tbody>
    </table>
    </div>




.. image:: fourier_analysis_files/fourier_analysis_11_1.png


.. code:: ipython3

    df.to_latex (buf='data_products/idp_sas_prot_fourier_k2_211015853.tex', 
                 formatters=['{:.2f}'.format, '{:.2f}'.format, '{:.2f}'.format,
                             '{:.2f}'.format, '{:.0e}'.format],  
                 index=False, header=False)
    np.savetxt ('data_products/IDP_SAS_PROT_FOURIER_K2.dat', 
                 IDP_SAS_PROT_FOURIER)

This time, we are interested in recovering long term modulations. We
consider the section of the periodogram verifying
:math:`P > P_\mathrm{tresh} = 90` days.

PLATO: Rotation period analysis
-------------------------------

.. code:: ipython3

    filename = sp.get_target_filename (plato_sim_dataset, '040', filetype='csv')
    t, s, dt = sp.load_resource (filename)

.. code:: ipython3

    fig, ax = plt.subplots (1, 1, figsize=(8,4))
    
    ax.scatter (t[s!=0]-t[0], s[s!=0], color='black', 
                marker='o', s=1)
    
    ax.set_xlabel ('Time (day)')
    ax.set_ylabel ('Flux (ppm)')
    
    fig.tight_layout ()



.. image:: fourier_analysis_files/fourier_analysis_16_0.png


As we want to recover rotation periods below 45 days, we only consider
the section of the periodogram verifying
:math:`P < P_\mathrm{cutoff} = 60` days.

.. code:: ipython3

    pcutoff = 60

As a preprocessing step, we compute the Lomb-Scargle periodogram (in the
SAS framework, it will be directyly provided by MSAP1).

.. code:: ipython3

    p_ps, ps_object = sp.compute_lomb_scargle (t, s)
    ls = ps_object.power_standard_norm

Now we perform the periodogram analysis.

.. code:: ipython3

    cond = p_ps < pcutoff
    prot, e_p, E_p, param, h_ps = sp.compute_prot_err_gaussian_fit_chi2_distribution (p_ps[cond], ls[cond], n_profile=20, 
                                                                                         threshold=0.1,
                                                                                         verbose=False)
    sp.plot_ls (p_ps, ls, filename='figures/fourier_plato_short.png', param_profile=param, 
                   logscale=False, xlim=(1, pcutoff), ylim=(-0.01, 0.1))
    IDP_SAS_PROT_FOURIER = sp.prepare_idp_fourier (param, h_ps, ls.size,
                                                      pcutoff=pcutoff, pthresh=None,
                                                      fapcutoff=1e-6)
    df = pd.DataFrame (data=IDP_SAS_PROT_FOURIER)
    df




.. raw:: html

    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }
    
        .dataframe tbody tr th {
            vertical-align: top;
        }
    
        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>0</th>
          <th>1</th>
          <th>2</th>
          <th>3</th>
          <th>4</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>25.732016</td>
          <td>0.254994</td>
          <td>0.260150</td>
          <td>0.041200</td>
          <td>1.000000e-16</td>
        </tr>
        <tr>
          <th>1</th>
          <td>36.903489</td>
          <td>7.445647</td>
          <td>12.482641</td>
          <td>0.032378</td>
          <td>1.000000e-16</td>
        </tr>
      </tbody>
    </table>
    </div>




.. image:: fourier_analysis_files/fourier_analysis_22_1.png


.. code:: ipython3

    df.to_latex (buf='data_products/idp_sas_prot_fourier_plato_040.tex', 
                 formatters=['{:.2f}'.format, '{:.2f}'.format, '{:.2f}'.format,
                             '{:.2f}'.format, '{:.0e}'.format],  
                 index=False, header=False)
    np.savetxt ('data_products/IDP_SAS_PROT_FOURIER_PLATO.dat', 
                 IDP_SAS_PROT_FOURIER)

PLATO: Long term modulation analysis
------------------------------------

This time, we are interested in recovering long term modulations. We
consider the section of the periodogram verifying
:math:`P > P_\mathrm{tresh} = 90` days.

.. code:: ipython3

    pthresh = 60

As a preprocessing step, we compute the Lomb-Scargle periodogram (in the
SAS framework, it will be directyly provided by MSAP1).

.. code:: ipython3

    p_ps, ps_object = sp.compute_lomb_scargle (t, s)
    ls = ps_object.power_standard_norm

Now we perform the periodogram analysis.

.. code:: ipython3

    plongterm, e_p, E_p, param, h_ps = sp.compute_prot_err_gaussian_fit_chi2_distribution (p_ps[p_ps>pthresh], ls[p_ps>pthresh], 
                                                                                              n_profile=5, threshold=0.1, verbose=False)
    fig = sp.plot_ls (p_ps, ls, filename='figures/fourier_plato_long.png', param_profile=param, 
                        logscale=False, xlim=(1,8*pthresh))
    IDP_SAS_LONGTERM_MODULATION_FOURIER = sp.prepare_idp_fourier (param, h_ps, ls.size,
                                                                     pcutoff=None, pthresh=pthresh,
                                                                     fapcutoff=1e-6)
    df = pd.DataFrame (data=IDP_SAS_LONGTERM_MODULATION_FOURIER)
    df




.. raw:: html

    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }
    
        .dataframe tbody tr th {
            vertical-align: top;
        }
    
        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>0</th>
          <th>1</th>
          <th>2</th>
          <th>3</th>
          <th>4</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>347.125305</td>
          <td>31.560819</td>
          <td>38.575413</td>
          <td>0.500829</td>
          <td>1.000000e-16</td>
        </tr>
        <tr>
          <th>1</th>
          <td>701.007116</td>
          <td>64.295915</td>
          <td>78.739851</td>
          <td>0.130459</td>
          <td>1.000000e-16</td>
        </tr>
      </tbody>
    </table>
    </div>




.. image:: fourier_analysis_files/fourier_analysis_30_1.png


.. code:: ipython3

    df.to_latex (buf='data_products/idp_sas_longterm_modulation_fourier_plato_040.tex', 
                 formatters=['{:.2f}'.format, '{:.2f}'.format, '{:.2f}'.format,
                             '{:.2f}'.format, '{:.0e}'.format],  
                 index=False, header=False)
    np.savetxt ('data_products/IDP_SAS_LONGTERM_MODULATION_FOURIER_PLATO.dat', 
                 IDP_SAS_LONGTERM_MODULATION_FOURIER)