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.. _sphx_glr_auto_examples_plot_compute_emd.py:
====================
1D optimal transport
====================
.. rst-class:: sphx-glr-horizontal
*
.. image:: /auto_examples/images/sphx_glr_plot_compute_emd_001.png
:scale: 47
*
.. image:: /auto_examples/images/sphx_glr_plot_compute_emd_002.png
:scale: 47
.. 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 get_1D_gauss as gauss
#%% 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 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()
#%% 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 M3
pl.figure(2)
pl.plot(d_emd, label='Euclidean EMD')
pl.plot(d_emd2, label='Squared Euclidean EMD')
pl.title('EMD distances')
pl.legend()
#%%
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()
**Total running time of the script:** ( 0 minutes 0.906 seconds)
.. 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>`
.. rst-class:: sphx-glr-signature
`Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_
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