.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_custom_density.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_examples_plot_custom_density.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_plot_custom_density.py:


==================================
Using a custom density with Picard
==================================

This example shows how to use custom densities using Picard

.. GENERATED FROM PYTHON SOURCE LINES 9-20

.. code-block:: default


    # Author: Pierre Ablin <pierre.ablin@inria.fr>
    #         Alexandre Gramfort <alexandre.gramfort@inria.fr>
    # License: BSD 3 clause

    import numpy as np
    import matplotlib.pyplot as plt
    from picard import picard, permute

    print(__doc__)








.. GENERATED FROM PYTHON SOURCE LINES 21-22

Build a custom density where the score function is x + tanh(x)

.. GENERATED FROM PYTHON SOURCE LINES 22-35

.. code-block:: default



    class CustomDensity(object):
        def log_lik(self, Y):
            return Y ** 2 / 2 + np.log(np.cosh(Y))

        def score_and_der(self, Y):
            tanhY = np.tanh(Y)
            return Y + tanhY, 2 - tanhY ** 2


    custom_density = CustomDensity()








.. GENERATED FROM PYTHON SOURCE LINES 36-37

Plot the corresponding functions

.. GENERATED FROM PYTHON SOURCE LINES 37-51

.. code-block:: default


    x = np.linspace(-2, 2, 100)
    log_likelihood = custom_density.log_lik(x)
    psi, psi_der = custom_density.score_and_der(x)

    names = ['log-likelihood', 'score', 'score derivative']

    plt.figure()
    for values, name in zip([log_likelihood, psi, psi_der], names):
        plt.plot(x, values, label=name)
    plt.legend()
    plt.title("Custom density")
    plt.show()




.. image-sg:: /auto_examples/images/sphx_glr_plot_custom_density_001.png
   :alt: Custom density
   :srcset: /auto_examples/images/sphx_glr_plot_custom_density_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 52-53

Run Picard on toy dataset using this density

.. GENERATED FROM PYTHON SOURCE LINES 53-65

.. code-block:: default


    rng = np.random.RandomState(0)
    N, T = 5, 1000
    S = rng.laplace(size=(N, T))
    A = rng.randn(N, N)
    X = np.dot(A, S)
    K, W, Y = picard(X, fun=custom_density, random_state=0)
    plt.figure()
    plt.imshow(permute(W.dot(K).dot(A)), interpolation='nearest')
    plt.title('Product between the estimated unmixing matrix and the mixing'
              'matrix')
    plt.show()



.. image-sg:: /auto_examples/images/sphx_glr_plot_custom_density_002.png
   :alt: Product between the estimated unmixing matrix and the mixingmatrix
   :srcset: /auto_examples/images/sphx_glr_plot_custom_density_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  0.264 seconds)


.. _sphx_glr_download_auto_examples_plot_custom_density.py:

.. only:: html

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


    .. container:: sphx-glr-download sphx-glr-download-python

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

    .. container:: sphx-glr-download sphx-glr-download-jupyter

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


.. only:: html

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

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