.. 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_OT_1D.py:
====================
1D optimal transport
====================
This example illustrates the computation of EMD and Sinkhorn transport plans
and their visualization.
.. code-block:: default
# Author: Remi Flamary
#
# 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)
# 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()
.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_001.png
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
.. code-block:: default
pl.figure(2, figsize=(5, 5))
ot.plot.plot1D_mat(a, b, M, 'Cost matrix M')
.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_002.png
:class: sphx-glr-single-img
Solve EMD
---------
.. code-block:: default
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_003.png
:class: sphx-glr-single-img
Solve Sinkhorn
--------------
.. code-block:: default
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_004.png
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
It. |Err
-------------------
0|2.861463e-01|
10|1.860154e-01|
20|8.144529e-02|
30|3.130143e-02|
40|1.178815e-02|
50|4.426078e-03|
60|1.661047e-03|
70|6.233110e-04|
80|2.338932e-04|
90|8.776627e-05|
100|3.293340e-05|
110|1.235791e-05|
120|4.637176e-06|
130|1.740051e-06|
140|6.529356e-07|
150|2.450071e-07|
160|9.193632e-08|
170|3.449812e-08|
180|1.294505e-08|
190|4.857493e-09|
It. |Err
-------------------
200|1.822723e-09|
210|6.839572e-10|
/home/rflamary/PYTHON/POT/examples/plot_OT_1D.py:84: 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 0.665 seconds)
.. _sphx_glr_download_auto_examples_plot_OT_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_OT_1D.py `
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: plot_OT_1D.ipynb `
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery `_