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

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_barycenters_plot_gaussian_barycenter.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_barycenters_plot_gaussian_barycenter.py:


========================================================
Gaussian Bures-Wasserstein barycenters
========================================================

Illustration of Gaussian Bures-Wasserstein barycenters.

.. GENERATED FROM PYTHON SOURCE LINES 10-16

.. code-block:: Python


    # Authors: Rémi Flamary <remi.flamary@polytechnique.edu>
    #
    # License: MIT License

    # sphinx_gallery_thumbnail_number = 2







.. GENERATED FROM PYTHON SOURCE LINES 17-24

.. code-block:: Python

    from matplotlib import colors
    from matplotlib.patches import Ellipse
    import numpy as np
    import matplotlib.pylab as pl
    import ot









.. GENERATED FROM PYTHON SOURCE LINES 25-27

Define Gaussian Covariances and distributions
---------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 27-42

.. code-block:: Python


    C1 = np.array([[0.5, -0.4], [-0.4, 0.5]])
    C2 = np.array([[1, 0.3], [0.3, 1]])
    C3 = np.array([[1.5, 0], [0, 0.5]])
    C4 = np.array([[0.5, 0], [0, 1.5]])

    C = np.stack((C1, C2, C3, C4))

    m1 = np.array([0, 0])
    m2 = np.array([0, 4])
    m3 = np.array([4, 0])
    m4 = np.array([4, 4])

    m = np.stack((m1, m2, m3, m4))








.. GENERATED FROM PYTHON SOURCE LINES 43-45

Plot the distributions
----------------------

.. GENERATED FROM PYTHON SOURCE LINES 45-89

.. code-block:: Python



    def draw_cov(mu, C, color=None, label=None, nstd=1):

        def eigsorted(cov):
            vals, vecs = np.linalg.eigh(cov)
            order = vals.argsort()[::-1]
            return vals[order], vecs[:, order]

        vals, vecs = eigsorted(C)
        theta = np.degrees(np.arctan2(*vecs[:, 0][::-1]))
        w, h = 2 * nstd * np.sqrt(vals)
        ell = Ellipse(xy=(mu[0], mu[1]),
                      width=w, height=h, alpha=0.5,
                      angle=theta, facecolor=color, edgecolor=color, label=label, fill=True)
        pl.gca().add_artist(ell)
        #pl.scatter(mu[0],mu[1],color=color, marker='x')


    axis = [-1.5, 5.5, -1.5, 5.5]

    pl.figure(1, (8, 2))
    pl.clf()

    pl.subplot(1, 4, 1)
    draw_cov(m1, C1, color='C0')
    pl.axis(axis)
    pl.title('$\mathcal{N}(m_1,\Sigma_1)$')

    pl.subplot(1, 4, 2)
    draw_cov(m2, C2, color='C1')
    pl.axis(axis)
    pl.title('$\mathcal{N}(m_2,\Sigma_2)$')

    pl.subplot(1, 4, 3)
    draw_cov(m3, C3, color='C2')
    pl.axis(axis)
    pl.title('$\mathcal{N}(m_3,\Sigma_3)$')

    pl.subplot(1, 4, 4)
    draw_cov(m4, C4, color='C3')
    pl.axis(axis)
    pl.title('$\mathcal{N}(m_4,\Sigma_4)$')




.. image-sg:: /auto_examples/barycenters/images/sphx_glr_plot_gaussian_barycenter_001.png
   :alt: $\mathcal{N}(m_1,\Sigma_1)$, $\mathcal{N}(m_2,\Sigma_2)$, $\mathcal{N}(m_3,\Sigma_3)$, $\mathcal{N}(m_4,\Sigma_4)$
   :srcset: /auto_examples/barycenters/images/sphx_glr_plot_gaussian_barycenter_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    Text(0.5, 1.0, '$\\mathcal{N}(m_4,\\Sigma_4)$')



.. GENERATED FROM PYTHON SOURCE LINES 90-92

Compute Bures-Wasserstein barycenters and plot them
-------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 92-128

.. code-block:: Python


    # basis for bilinear interpolation
    v1 = np.array((1, 0, 0, 0))
    v2 = np.array((0, 1, 0, 0))
    v3 = np.array((0, 0, 1, 0))
    v4 = np.array((0, 0, 0, 1))


    colors = np.stack((colors.to_rgb('C0'),
                       colors.to_rgb('C1'),
                       colors.to_rgb('C2'),
                       colors.to_rgb('C3')))

    pl.figure(2, (8, 8))

    nb_interp = 6

    for i in range(nb_interp):
        for j in range(nb_interp):
            tx = float(i) / (nb_interp - 1)
            ty = float(j) / (nb_interp - 1)

            # weights are constructed by bilinear interpolation
            tmp1 = (1 - tx) * v1 + tx * v2
            tmp2 = (1 - tx) * v3 + tx * v4
            weights = (1 - ty) * tmp1 + ty * tmp2

            color = np.dot(colors.T, weights)

            mb, Cb = ot.gaussian.bures_wasserstein_barycenter(m, C, weights)

            draw_cov(mb, Cb, color=color, label=None, nstd=0.3)

    pl.axis(axis)
    pl.axis('off')
    pl.tight_layout()



.. image-sg:: /auto_examples/barycenters/images/sphx_glr_plot_gaussian_barycenter_002.png
   :alt: plot gaussian barycenter
   :srcset: /auto_examples/barycenters/images/sphx_glr_plot_gaussian_barycenter_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.378 seconds)


.. _sphx_glr_download_auto_examples_barycenters_plot_gaussian_barycenter.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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