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.. _sphx_glr_auto_examples_plot_UOT_1D.py:
===============================
1D Unbalanced optimal transport
===============================
This example illustrates the computation of Unbalanced Optimal transport
using a Kullback-Leibler relaxation.
.. code-block:: python
# Author: Hicham Janati <hicham.janati@inria.fr>
#
# License: MIT License
import numpy as np
import matplotlib.pylab as pl
import ot
import ot.plot
from ot.datasets import make_1D_gauss as gauss
Generate data
-------------
.. code-block:: python
#%% parameters
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)
# make distributions unbalanced
b *= 5.
# loss matrix
M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))
M /= M.max()
Plot distributions and loss matrix
----------------------------------
.. code-block:: python
#%% plot the distributions
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_UOT_1D_001.png
:scale: 47
*
.. image:: /auto_examples/images/sphx_glr_plot_UOT_1D_002.png
:scale: 47
Solve Unbalanced Sinkhorn
--------------
.. code-block:: python
# Sinkhorn
epsilon = 0.1 # entropy parameter
alpha = 1. # Unbalanced KL relaxation parameter
Gs = ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, alpha, verbose=True)
pl.figure(4, figsize=(5, 5))
ot.plot.plot1D_mat(a, b, Gs, 'UOT matrix Sinkhorn')
pl.show()
.. image:: /auto_examples/images/sphx_glr_plot_UOT_1D_006.png
:align: center
.. rst-class:: sphx-glr-script-out
Out::
It. |Err
-------------------
0|1.838786e+00|
10|1.242379e-01|
20|2.581314e-03|
30|5.674552e-05|
40|1.252959e-06|
50|2.768136e-08|
60|6.116090e-10|
**Total running time of the script:** ( 0 minutes 0.259 seconds)
.. only :: html
.. container:: sphx-glr-footer
.. container:: sphx-glr-download
:download:`Download Python source code: plot_UOT_1D.py <plot_UOT_1D.py>`
.. container:: sphx-glr-download
:download:`Download Jupyter notebook: plot_UOT_1D.ipynb <plot_UOT_1D.ipynb>`
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_
|