.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/others/plot_GMMOT_plan.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_others_plot_GMMOT_plan.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_others_plot_GMMOT_plan.py:


====================================================
GMM Plan 1D
====================================================

Illustration of the GMM plan for
the Mixture Wasserstein between two GMM in 1D,
as well as the two maps T_mean and T_rand.
T_mean is the barycentric projection of the GMM coupling,
and T_rand takes a random gaussian image between two components,
according to the coupling and the GMMs.
See [69] for details.
.. [69] Delon, J., & Desolneux, A. (2020). A Wasserstein-type distance in the space of Gaussian mixture models. SIAM Journal on Imaging Sciences, 13(2), 936-970.

.. GENERATED FROM PYTHON SOURCE LINES 18-32

.. code-block:: Python


    # Author: Eloi Tanguy <eloi.tanguy@u-paris>
    #         Remi Flamary <remi.flamary@polytehnique.edu>
    #         Julie Delon <julie.delon@math.cnrs.fr>
    #
    # License: MIT License

    # sphinx_gallery_thumbnail_number = 1

    import numpy as np
    from ot.plot import plot1D_mat, rescale_for_imshow_plot
    from ot.gmm import gmm_ot_plan_density, gmm_pdf, gmm_ot_apply_map
    import matplotlib.pyplot as plt








.. GENERATED FROM PYTHON SOURCE LINES 33-35

Generate GMMOT plan plot it
---------------------------

.. GENERATED FROM PYTHON SOURCE LINES 35-69

.. code-block:: Python

    ks = 2
    kt = 3
    d = 1
    eps = 0.1
    m_s = np.array([[1], [2]])
    m_t = np.array([[3], [4.2], [5]])
    C_s = np.array([[[0.05]], [[0.06]]])
    C_t = np.array([[[0.03]], [[0.07]], [[0.04]]])
    w_s = np.array([0.4, 0.6])
    w_t = np.array([0.4, 0.2, 0.4])

    n = 500
    a_x, b_x = 0, 3
    x = np.linspace(a_x, b_x, n)
    a_y, b_y = 2, 6
    y = np.linspace(a_y, b_y, n)
    plan_density = gmm_ot_plan_density(
        x[:, None], y[:, None], m_s, m_t, C_s, C_t, w_s, w_t, plan=None, atol=2e-2
    )

    a = gmm_pdf(x[:, None], m_s, C_s, w_s)
    b = gmm_pdf(y[:, None], m_t, C_t, w_t)
    plt.figure(figsize=(8, 8))
    plot1D_mat(
        a,
        b,
        plan_density,
        title="GMM OT plan",
        plot_style="xy",
        a_label="Source distribution",
        b_label="Target distribution",
    )





.. image-sg:: /auto_examples/others/images/sphx_glr_plot_GMMOT_plan_001.png
   :alt: Source distribution, Target distribution, GMM OT plan
   :srcset: /auto_examples/others/images/sphx_glr_plot_GMMOT_plan_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    (<Axes: title={'center': 'Source distribution'}>, <Axes: title={'center': 'Target distribution'}>, <Axes: title={'center': 'GMM OT plan'}>)



.. GENERATED FROM PYTHON SOURCE LINES 70-72

Generate GMMOT maps and plot them over plan
-------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 72-100

.. code-block:: Python

    plt.figure(figsize=(8, 8))
    ax_s, ax_t, ax_M = plot1D_mat(
        a,
        b,
        plan_density,
        plot_style="xy",
        title="GMM OT plan with T_mean and T_rand maps",
        a_label="Source distribution",
        b_label="Target distribution",
    )
    T_mean = gmm_ot_apply_map(x[:, None], m_s, m_t, C_s, C_t, w_s, w_t, method="bary")[:, 0]
    x_rescaled, T_mean_rescaled = rescale_for_imshow_plot(x, T_mean, n, a_y=a_y, b_y=b_y)

    ax_M.plot(
        x_rescaled, T_mean_rescaled, label="T_mean", alpha=0.5, linewidth=5, color="aqua"
    )

    T_rand = gmm_ot_apply_map(
        x[:, None], m_s, m_t, C_s, C_t, w_s, w_t, method="rand", seed=0
    )[:, 0]
    x_rescaled, T_rand_rescaled = rescale_for_imshow_plot(x, T_rand, n, a_y=a_y, b_y=b_y)

    ax_M.scatter(
        x_rescaled, T_rand_rescaled, label="T_rand", alpha=0.5, s=20, color="orange"
    )

    ax_M.legend(loc="upper left", fontsize=13)




.. image-sg:: /auto_examples/others/images/sphx_glr_plot_GMMOT_plan_002.png
   :alt: Source distribution, Target distribution, GMM OT plan with T_mean and T_rand maps
   :srcset: /auto_examples/others/images/sphx_glr_plot_GMMOT_plan_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <matplotlib.legend.Legend object at 0x7f7cfabd1d20>




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

   **Total running time of the script:** (0 minutes 0.328 seconds)


.. _sphx_glr_download_auto_examples_others_plot_GMMOT_plan.py:

.. only:: html

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

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

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

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_GMMOT_plan.zip <plot_GMMOT_plan.zip>`


.. only:: html

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

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