.. 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_smooth.py:
===========================
1D smooth optimal transport
===========================
This example illustrates the computation of EMD, Sinkhorn and smooth OT 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_smooth_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_smooth_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_smooth_003.png
:class: sphx-glr-single-img
Solve Sinkhorn
--------------
.. code-block:: default
lambd = 2e-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_smooth_004.png
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
It. |Err
-------------------
0|2.821142e-01|
10|7.695268e-02|
20|1.112774e-02|
30|1.571553e-03|
40|2.218100e-04|
50|3.130527e-05|
60|4.418267e-06|
70|6.235716e-07|
80|8.800770e-08|
90|1.242095e-08|
100|1.753030e-09|
110|2.474136e-10|
/home/rflamary/PYTHON/POT/examples/plot_OT_1D_smooth.py:84: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
pl.show()
Solve Smooth OT
--------------
.. code-block:: default
lambd = 2e-3
Gsm = ot.smooth.smooth_ot_dual(a, b, M, lambd, reg_type='kl')
pl.figure(5, figsize=(5, 5))
ot.plot.plot1D_mat(a, b, Gsm, 'OT matrix Smooth OT KL reg.')
pl.show()
.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_005.png
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
/home/rflamary/PYTHON/POT/examples/plot_OT_1D_smooth.py:99: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
pl.show()
.. code-block:: default
lambd = 1e-1
Gsm = ot.smooth.smooth_ot_dual(a, b, M, lambd, reg_type='l2')
pl.figure(6, figsize=(5, 5))
ot.plot.plot1D_mat(a, b, Gsm, 'OT matrix Smooth OT l2 reg.')
pl.show()
.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_006.png
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
/home/rflamary/PYTHON/POT/examples/plot_OT_1D_smooth.py:110: 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 0.732 seconds)
.. _sphx_glr_download_auto_examples_plot_OT_1D_smooth.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_smooth.py `
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: plot_OT_1D_smooth.ipynb `
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery `_