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+
+
+.. _sphx_glr_auto_examples_plot_compute_emd.py:
+
+
+=================
+Plot multiple EMD
+=================
+
+Shows how to compute multiple EMD and Sinkhorn with two differnt
+ground metrics and plot their values for diffeent distributions.
+
+
+
+
+
+.. code-block:: python
+
+
+    # Author: Remi Flamary <remi.flamary@unice.fr>
+    #
+    # License: MIT License
+
+    import numpy as np
+    import matplotlib.pylab as pl
+    import ot
+    from ot.datasets import make_1D_gauss as gauss
+
+
+
+
+
+
+
+
+Generate data
+-------------
+
+
+
+.. code-block:: python
+
+
+    #%% parameters
+
+    n = 100  # nb bins
+    n_target = 50  # nb target distributions
+
+
+    # bin positions
+    x = np.arange(n, dtype=np.float64)
+
+    lst_m = np.linspace(20, 90, n_target)
+
+    # Gaussian distributions
+    a = gauss(n, m=20, s=5)  # m= mean, s= std
+
+    B = np.zeros((n, n_target))
+
+    for i, m in enumerate(lst_m):
+        B[:, i] = gauss(n, m=m, s=5)
+
+    # loss matrix and normalization
+    M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)), 'euclidean')
+    M /= M.max()
+    M2 = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)), 'sqeuclidean')
+    M2 /= M2.max()
+
+
+
+
+
+
+
+Plot data
+---------
+
+
+
+.. code-block:: python
+
+
+    #%% plot the distributions
+
+    pl.figure(1)
+    pl.subplot(2, 1, 1)
+    pl.plot(x, a, 'b', label='Source distribution')
+    pl.title('Source distribution')
+    pl.subplot(2, 1, 2)
+    pl.plot(x, B, label='Target distributions')
+    pl.title('Target distributions')
+    pl.tight_layout()
+
+
+
+
+
+.. image:: /auto_examples/images/sphx_glr_plot_compute_emd_001.png
+    :align: center
+
+
+
+
+Compute EMD for the different losses
+------------------------------------
+
+
+
+.. code-block:: python
+
+
+    #%% Compute and plot distributions and loss matrix
+
+    d_emd = ot.emd2(a, B, M)  # direct computation of EMD
+    d_emd2 = ot.emd2(a, B, M2)  # direct computation of EMD with loss M2
+
+
+    pl.figure(2)
+    pl.plot(d_emd, label='Euclidean EMD')
+    pl.plot(d_emd2, label='Squared Euclidean EMD')
+    pl.title('EMD distances')
+    pl.legend()
+
+
+
+
+.. image:: /auto_examples/images/sphx_glr_plot_compute_emd_003.png
+    :align: center
+
+
+
+
+Compute Sinkhorn for the different losses
+-----------------------------------------
+
+
+
+.. code-block:: python
+
+
+    #%%
+    reg = 1e-2
+    d_sinkhorn = ot.sinkhorn2(a, B, M, reg)
+    d_sinkhorn2 = ot.sinkhorn2(a, B, M2, reg)
+
+    pl.figure(2)
+    pl.clf()
+    pl.plot(d_emd, label='Euclidean EMD')
+    pl.plot(d_emd2, label='Squared Euclidean EMD')
+    pl.plot(d_sinkhorn, '+', label='Euclidean Sinkhorn')
+    pl.plot(d_sinkhorn2, '+', label='Squared Euclidean Sinkhorn')
+    pl.title('EMD distances')
+    pl.legend()
+
+    pl.show()
+
+
+
+.. image:: /auto_examples/images/sphx_glr_plot_compute_emd_004.png
+    :align: center
+
+
+
+
+**Total running time of the script:** ( 0 minutes  0.446 seconds)
+
+
+
+.. only :: html
+
+ .. container:: sphx-glr-footer
+
+
+  .. container:: sphx-glr-download
+
+     :download:`Download Python source code: plot_compute_emd.py <plot_compute_emd.py>`
+
+
+
+  .. container:: sphx-glr-download
+
+     :download:`Download Jupyter notebook: plot_compute_emd.ipynb <plot_compute_emd.ipynb>`
+
+
+.. only:: html
+
+ .. rst-class:: sphx-glr-signature
+
+    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_