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.. _sphx_glr_auto_examples_plot_OT_L1_vs_L2.py:
==========================================
2D Optimal transport for different metrics
==========================================
Stole the figure idea from Fig. 1 and 2 in
https://arxiv.org/pdf/1706.07650.pdf
.. rst-class:: sphx-glr-horizontal
*
.. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_001.png
:scale: 47
*
.. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_002.png
:scale: 47
*
.. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_003.png
:scale: 47
*
.. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_004.png
:scale: 47
*
.. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_005.png
:scale: 47
*
.. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_006.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
#%% parameters and data generation
for data in range(2):
if data:
n = 20 # nb samples
xs = np.zeros((n, 2))
xs[:, 0] = np.arange(n) + 1
xs[:, 1] = (np.arange(n) + 1) * -0.001 # to make it strictly convex...
xt = np.zeros((n, 2))
xt[:, 1] = np.arange(n) + 1
else:
n = 50 # nb samples
xtot = np.zeros((n + 1, 2))
xtot[:, 0] = np.cos(
(np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi)
xtot[:, 1] = np.sin(
(np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi)
xs = xtot[:n, :]
xt = xtot[1:, :]
a, b = ot.unif(n), ot.unif(n) # uniform distribution on samples
# loss matrix
M1 = ot.dist(xs, xt, metric='euclidean')
M1 /= M1.max()
# loss matrix
M2 = ot.dist(xs, xt, metric='sqeuclidean')
M2 /= M2.max()
# loss matrix
Mp = np.sqrt(ot.dist(xs, xt, metric='euclidean'))
Mp /= Mp.max()
#%% plot samples
pl.figure(1 + 3 * data, figsize=(7, 3))
pl.clf()
pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
pl.axis('equal')
pl.title('Source and traget distributions')
pl.figure(2 + 3 * data, figsize=(7, 3))
pl.subplot(1, 3, 1)
pl.imshow(M1, interpolation='nearest')
pl.title('Euclidean cost')
pl.subplot(1, 3, 2)
pl.imshow(M2, interpolation='nearest')
pl.title('Squared Euclidean cost')
pl.subplot(1, 3, 3)
pl.imshow(Mp, interpolation='nearest')
pl.title('Sqrt Euclidean cost')
pl.tight_layout()
#%% EMD
G1 = ot.emd(a, b, M1)
G2 = ot.emd(a, b, M2)
Gp = ot.emd(a, b, Mp)
pl.figure(3 + 3 * data, figsize=(7, 3))
pl.subplot(1, 3, 1)
ot.plot.plot2D_samples_mat(xs, xt, G1, c=[.5, .5, 1])
pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
pl.axis('equal')
# pl.legend(loc=0)
pl.title('OT Euclidean')
pl.subplot(1, 3, 2)
ot.plot.plot2D_samples_mat(xs, xt, G2, c=[.5, .5, 1])
pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
pl.axis('equal')
# pl.legend(loc=0)
pl.title('OT squared Euclidean')
pl.subplot(1, 3, 3)
ot.plot.plot2D_samples_mat(xs, xt, Gp, c=[.5, .5, 1])
pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
pl.axis('equal')
# pl.legend(loc=0)
pl.title('OT sqrt Euclidean')
pl.tight_layout()
pl.show()
**Total running time of the script:** ( 0 minutes 1.906 seconds)
.. container:: sphx-glr-footer
.. container:: sphx-glr-download
:download:`Download Python source code: plot_OT_L1_vs_L2.py <plot_OT_L1_vs_L2.py>`
.. container:: sphx-glr-download
:download:`Download Jupyter notebook: plot_OT_L1_vs_L2.ipynb <plot_OT_L1_vs_L2.ipynb>`
.. rst-class:: sphx-glr-signature
`Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_
|
