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+
+
+.. _sphx_glr_auto_examples_plot_free_support_barycenter.py:
+
+
+====================================================
+2D free support Wasserstein barycenters of distributions
+====================================================
+
+Illustration of 2D Wasserstein barycenters if discributions that are weighted
+sum of diracs.
+
+
+
+
+.. code-block:: python
+
+
+    # Author: Vivien Seguy <vivien.seguy@iip.ist.i.kyoto-u.ac.jp>
+    #
+    # License: MIT License
+
+    import numpy as np
+    import matplotlib.pylab as pl
+    import ot
+
+
+
+
+
+
+
+
+Generate data
+ -------------
+%% parameters and data generation
+
+
+
+.. code-block:: python
+
+    N = 3
+    d = 2
+    measures_locations = []
+    measures_weights = []
+
+    for i in range(N):
+
+        n_i = np.random.randint(low=1, high=20)  # nb samples
+
+        mu_i = np.random.normal(0., 4., (d,))  # Gaussian mean
+
+        A_i = np.random.rand(d, d)
+        cov_i = np.dot(A_i, A_i.transpose())  # Gaussian covariance matrix
+
+        x_i = ot.datasets.make_2D_samples_gauss(n_i, mu_i, cov_i)  # Dirac locations
+        b_i = np.random.uniform(0., 1., (n_i,))
+        b_i = b_i / np.sum(b_i)  # Dirac weights
+
+        measures_locations.append(x_i)
+        measures_weights.append(b_i)
+
+
+
+
+
+
+
+
+Compute free support barycenter
+-------------
+
+
+
+.. code-block:: python
+
+
+    k = 10  # number of Diracs of the barycenter
+    X_init = np.random.normal(0., 1., (k, d))  # initial Dirac locations
+    b = np.ones((k,)) / k  # weights of the barycenter (it will not be optimized, only the locations are optimized)
+
+    X = ot.lp.free_support_barycenter(measures_locations, measures_weights, X_init, b)
+
+
+
+
+
+
+
+
+Plot data
+---------
+
+
+
+.. code-block:: python
+
+
+    pl.figure(1)
+    for (x_i, b_i) in zip(measures_locations, measures_weights):
+        color = np.random.randint(low=1, high=10 * N)
+        pl.scatter(x_i[:, 0], x_i[:, 1], s=b * 1000, label='input measure')
+    pl.scatter(X[:, 0], X[:, 1], s=b * 1000, c='black', marker='^', label='2-Wasserstein barycenter')
+    pl.title('Data measures and their barycenter')
+    pl.legend(loc=0)
+    pl.show()
+
+
+
+.. image:: /auto_examples/images/sphx_glr_plot_free_support_barycenter_001.png
+    :align: center
+
+
+
+
+**Total running time of the script:** ( 0 minutes  0.129 seconds)
+
+
+
+.. only :: html
+
+ .. container:: sphx-glr-footer
+
+
+  .. container:: sphx-glr-download
+
+     :download:`Download Python source code: plot_free_support_barycenter.py <plot_free_support_barycenter.py>`
+
+
+
+  .. container:: sphx-glr-download
+
+     :download:`Download Jupyter notebook: plot_free_support_barycenter.ipynb <plot_free_support_barycenter.ipynb>`
+
+
+.. only:: html
+
+ .. rst-class:: sphx-glr-signature
+
+    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_