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.. only:: html
.. note::
:class: sphx-glr-download-link-note
Click :ref:`here <sphx_glr_download_auto_examples_plot_screenkhorn_1D.py>` to download the full example code
.. rst-class:: sphx-glr-example-title
.. _sphx_glr_auto_examples_plot_screenkhorn_1D.py:
===============================
1D Screened optimal transport
===============================
This example illustrates the computation of Screenkhorn:
Screening Sinkhorn Algorithm for Optimal transport.
.. code-block:: default
# Author: Mokhtar Z. Alaya <mokhtarzahdi.alaya@gmail.com>
#
# License: MIT License
import numpy as np
import matplotlib.pylab as pl
import ot.plot
from ot.datasets import make_1D_gauss as gauss
from ot.bregman import screenkhorn
Generate data
-------------
.. code-block:: default
n = 100 # nb bins
# bin positions
x = np.arange(n, dtype=np.float64)
# Gaussian distributions
a = gauss(n, m=20, s=5) # m= mean, s= std
b = gauss(n, m=60, s=10)
# loss matrix
M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))
M /= M.max()
Plot distributions and loss matrix
----------------------------------
.. code-block:: default
pl.figure(1, figsize=(6.4, 3))
pl.plot(x, a, 'b', label='Source distribution')
pl.plot(x, b, 'r', label='Target distribution')
pl.legend()
# plot distributions and loss matrix
pl.figure(2, figsize=(5, 5))
ot.plot.plot1D_mat(a, b, M, 'Cost matrix M')
.. rst-class:: sphx-glr-horizontal
*
.. image:: /auto_examples/images/sphx_glr_plot_screenkhorn_1D_001.png
:class: sphx-glr-multi-img
*
.. image:: /auto_examples/images/sphx_glr_plot_screenkhorn_1D_002.png
:class: sphx-glr-multi-img
Solve Screenkhorn
-----------------------
.. code-block:: default
# Screenkhorn
lambd = 2e-03 # entropy parameter
ns_budget = 30 # budget number of points to be keeped in the source distribution
nt_budget = 30 # budget number of points to be keeped in the target distribution
G_screen = screenkhorn(a, b, M, lambd, ns_budget, nt_budget, uniform=False, restricted=True, verbose=True)
pl.figure(4, figsize=(5, 5))
ot.plot.plot1D_mat(a, b, G_screen, 'OT matrix Screenkhorn')
pl.show()
.. image:: /auto_examples/images/sphx_glr_plot_screenkhorn_1D_003.png
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
/home/rflamary/PYTHON/POT/ot/bregman.py:2056: UserWarning: Bottleneck module is not installed. Install it from https://pypi.org/project/Bottleneck/ for better performance.
"Bottleneck module is not installed. Install it from https://pypi.org/project/Bottleneck/ for better performance.")
epsilon = 0.020986042861303855
kappa = 3.7476531411890917
Cardinality of selected points: |Isel| = 30 |Jsel| = 30
/home/rflamary/PYTHON/POT/examples/plot_screenkhorn_1D.py:68: 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 0.228 seconds)
.. _sphx_glr_download_auto_examples_plot_screenkhorn_1D.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_screenkhorn_1D.py <plot_screenkhorn_1D.py>`
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: plot_screenkhorn_1D.ipynb <plot_screenkhorn_1D.ipynb>`
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_
|
