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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>`_