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.. _sphx_glr_auto_examples_plot_OT_1D.py:
====================
1D optimal transport
====================
This example illustrates the computation of EMD and Sinkhorn transport plans
and their visualization.
.. code-block:: python
# Author: Remi Flamary <remi.flamary@unice.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)
# 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_OT_1D_001.png
:scale: 47
*
.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_002.png
:scale: 47
Solve EMD
---------
.. code-block:: python
#%% EMD
G0 = ot.emd(a, b, M)
pl.figure(3, figsize=(5, 5))
ot.plot.plot1D_mat(a, b, G0, 'OT matrix G0')
.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_005.png
:align: center
Solve Sinkhorn
--------------
.. code-block:: python
#%% Sinkhorn
lambd = 1e-3
Gs = ot.sinkhorn(a, b, M, lambd, verbose=True)
pl.figure(4, figsize=(5, 5))
ot.plot.plot1D_mat(a, b, Gs, 'OT matrix Sinkhorn')
pl.show()
.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_007.png
:align: center
.. rst-class:: sphx-glr-script-out
Out::
It. |Err
-------------------
0|8.187970e-02|
10|3.460174e-02|
20|6.633335e-03|
30|9.797798e-04|
40|1.389606e-04|
50|1.959016e-05|
60|2.759079e-06|
70|3.885166e-07|
80|5.470605e-08|
90|7.702918e-09|
100|1.084609e-09|
110|1.527180e-10|
**Total running time of the script:** ( 0 minutes 0.561 seconds)
.. only :: html
.. container:: sphx-glr-footer
.. container:: sphx-glr-download
:download:`Download Python source code: plot_OT_1D.py <plot_OT_1D.py>`
.. container:: sphx-glr-download
:download:`Download Jupyter notebook: plot_OT_1D.ipynb <plot_OT_1D.ipynb>`
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_
|
