.. note::
    :class: sphx-glr-download-link-note

    Click :ref:`here <sphx_glr_download_auto_examples_pac_plot_compare_normalizations.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_pac_plot_compare_normalizations.py:


===========================
Compare normalization types
===========================

This example illustrates the effect of the different implemented
normalizations. First, the true PAC is estimated, then this is the surrogate
distribution that is estimated (i.e the PAC that could be obtained by chance).
Finally, the true PAC is corrected by this distribution. Tensorpac includes
four types of normalization that should give similar results :

    * Substract the mean of surrogates (1)
    * Divide by the mean of surrogates (2)
    * Substract then divide by the mean of surrogates (3)
    * Substract the mean then divide by the deviation of surrogates
      (z-score, 4)


.. code-block:: default

    from textwrap import wrap

    from tensorpac import Pac
    from tensorpac.signals import pac_signals_wavelet

    import matplotlib.pyplot as plt
 






Simulate artificial coupling
##############################################################################
 first, we generate several trials that contains a coupling between a 10z
 phase and a 100hz amplitude. By default, the returned dataset is organized as
 (n_epochs, n_times) where n_times is the number of time points and n_epochs
 is the number of trials


.. code-block:: default


    f_pha = 10      # frequency phase for the coupling
    f_amp = 100     # frequency amplitude for the coupling
    n_epochs = 20   # number of trials
    n_times = 2000  # number of time points
    sf = 512.       # sampling frequency
    data, time = pac_signals_wavelet(f_pha=f_pha, f_amp=f_amp, noise=2.,
                                     n_epochs=n_epochs, n_times=n_times, sf=sf)







Extract phases and amplitudes
##############################################################################
 now we can extract all of the phases and amplitudes


.. code-block:: default


    # define the pac object
    p = Pac(f_pha='mres', f_amp='mres')
    # Now, we want to compare PAC methods, hence it's useless to systematically
    # filter the data. So we extract the phase and the amplitude only once
    phases = p.filter(sf, data, ftype='phase', n_jobs=1)
    amplitudes = p.filter(sf, data, ftype='amplitude', n_jobs=1)







Recompute PAC and surrogates and switch the normalization types
##############################################################################
 finally, we can recompute PAC and surrogates and then switch the
 normalization type. In particular this script uses the Gaussian-Copula PAC
 as the main measure and then permutes times blocks of amplitudes cut at a
 random time point


.. code-block:: default


    plt.figure(figsize=(14, 8))
    for i, k in enumerate(range(5)):
        # switch the normalization method
        p.idpac = (6, 2, k)
        print('-> Normalization using ' + p.str_norm)
        # compute pac and surrogates (n_perm)
        xpac = p.fit(phases, amplitudes, n_perm=20)
        # plot
        plt.subplot(2, 3, k + 1)
        title = '\n'.join(wrap(f"{p.str_norm} ({k})", 40))
        p.comodulogram(xpac.mean(-1), title=title, cmap='plasma', vmin=0.)

    plt.tight_layout()
    plt.show()



.. image:: /auto_examples/pac/images/sphx_glr_plot_compare_normalizations_001.png
    :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    -> Normalization using No normalization
    -> Normalization using Substract the mean of surrogates
    -> Normalization using Divide by the mean of surrogates
    -> Normalization using Substract then divide by the mean of surrogates
    -> Normalization using Substract the mean and divide by the deviation of the surrogates




.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  13.809 seconds)


.. _sphx_glr_download_auto_examples_pac_plot_compare_normalizations.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example



  .. container:: sphx-glr-download

     :download:`Download Python source code: plot_compare_normalizations.py <plot_compare_normalizations.py>`



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: plot_compare_normalizations.ipynb <plot_compare_normalizations.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_