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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>`_