.. 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_UOT_1D.py:
===============================
1D Unbalanced optimal transport
===============================
This example illustrates the computation of Unbalanced Optimal transport
using a Kullback-Leibler relaxation.
.. code-block:: default
# Author: Hicham Janati
#
# 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:: 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)
# 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:: 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_UOT_1D_001.png
:class: sphx-glr-multi-img
*
.. image:: /auto_examples/images/sphx_glr_plot_UOT_1D_002.png
:class: sphx-glr-multi-img
Solve Unbalanced Sinkhorn
--------------
.. code-block:: default
# 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_003.png
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
/home/rflamary/PYTHON/POT/examples/plot_UOT_1D.py:76: 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 0.274 seconds)
.. _sphx_glr_download_auto_examples_plot_UOT_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_UOT_1D.py `
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: plot_UOT_1D.ipynb `
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery `_