.. only:: html
.. note::
:class: sphx-glr-download-link-note
Click :ref:`here ` to download the full example code
.. rst-class:: sphx-glr-example-title
.. _sphx_glr_auto_examples_plot_OT_2D_samples.py:
====================================================
2D Optimal transport between empirical distributions
====================================================
Illustration of 2D optimal transport between discributions that are weighted
sum of diracs. The OT matrix is plotted with the samples.
.. code-block:: default
# Author: Remi Flamary
# Kilian Fatras
#
# License: MIT License
import numpy as np
import matplotlib.pylab as pl
import ot
import ot.plot
Generate data
-------------
.. code-block:: default
n = 50 # nb samples
mu_s = np.array([0, 0])
cov_s = np.array([[1, 0], [0, 1]])
mu_t = np.array([4, 4])
cov_t = np.array([[1, -.8], [-.8, 1]])
xs = ot.datasets.make_2D_samples_gauss(n, mu_s, cov_s)
xt = ot.datasets.make_2D_samples_gauss(n, mu_t, cov_t)
a, b = np.ones((n,)) / n, np.ones((n,)) / n # uniform distribution on samples
# loss matrix
M = ot.dist(xs, xt)
M /= M.max()
Plot data
---------
.. code-block:: default
pl.figure(1)
pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
pl.legend(loc=0)
pl.title('Source and target distributions')
pl.figure(2)
pl.imshow(M, interpolation='nearest')
pl.title('Cost matrix M')
.. rst-class:: sphx-glr-horizontal
*
.. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_001.png
:class: sphx-glr-multi-img
*
.. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_002.png
:class: sphx-glr-multi-img
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
Text(0.5, 1.0, 'Cost matrix M')
Compute EMD
-----------
.. code-block:: default
G0 = ot.emd(a, b, M)
pl.figure(3)
pl.imshow(G0, interpolation='nearest')
pl.title('OT matrix G0')
pl.figure(4)
ot.plot.plot2D_samples_mat(xs, xt, G0, 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.legend(loc=0)
pl.title('OT matrix with samples')
.. rst-class:: sphx-glr-horizontal
*
.. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_003.png
:class: sphx-glr-multi-img
*
.. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_004.png
:class: sphx-glr-multi-img
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
Text(0.5, 1.0, 'OT matrix with samples')
Compute Sinkhorn
----------------
.. code-block:: default
# reg term
lambd = 1e-3
Gs = ot.sinkhorn(a, b, M, lambd)
pl.figure(5)
pl.imshow(Gs, interpolation='nearest')
pl.title('OT matrix sinkhorn')
pl.figure(6)
ot.plot.plot2D_samples_mat(xs, xt, Gs, color=[.5, .5, 1])
pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
pl.legend(loc=0)
pl.title('OT matrix Sinkhorn with samples')
pl.show()
.. rst-class:: sphx-glr-horizontal
*
.. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_005.png
:class: sphx-glr-multi-img
*
.. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_006.png
:class: sphx-glr-multi-img
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
/home/rflamary/PYTHON/POT/examples/plot_OT_2D_samples.py:103: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
pl.show()
Emprirical Sinkhorn
----------------
.. code-block:: default
# reg term
lambd = 1e-3
Ges = ot.bregman.empirical_sinkhorn(xs, xt, lambd)
pl.figure(7)
pl.imshow(Ges, interpolation='nearest')
pl.title('OT matrix empirical sinkhorn')
pl.figure(8)
ot.plot.plot2D_samples_mat(xs, xt, Ges, color=[.5, .5, 1])
pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
pl.legend(loc=0)
pl.title('OT matrix Sinkhorn from samples')
pl.show()
.. rst-class:: sphx-glr-horizontal
*
.. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_007.png
:class: sphx-glr-multi-img
*
.. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_008.png
:class: sphx-glr-multi-img
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
/home/rflamary/PYTHON/POT/ot/bregman.py:363: RuntimeWarning: divide by zero encountered in true_divide
v = np.divide(b, KtransposeU)
Warning: numerical errors at iteration 0
/home/rflamary/PYTHON/POT/ot/plot.py:90: RuntimeWarning: invalid value encountered in double_scalars
if G[i, j] / mx > thr:
/home/rflamary/PYTHON/POT/examples/plot_OT_2D_samples.py:128: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
pl.show()
.. rst-class:: sphx-glr-timing
**Total running time of the script:** ( 0 minutes 2.154 seconds)
.. _sphx_glr_download_auto_examples_plot_OT_2D_samples.py:
.. only :: html
.. container:: sphx-glr-footer
:class: sphx-glr-footer-example
.. container:: sphx-glr-download sphx-glr-download-python
:download:`Download Python source code: plot_OT_2D_samples.py `
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: plot_OT_2D_samples.ipynb `
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery `_