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.. _sphx_glr_auto_examples_plot_OT_1D.py:
====================
1D optimal transport
====================
@author: rflamary
.. 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
*
.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_003.png
:scale: 47
*
.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_004.png
:scale: 47
.. code-block:: python
import numpy as np
import matplotlib.pylab as pl
import ot
from ot.datasets import get_1D_gauss as gauss
#%% 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 the distributions
pl.figure(1)
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)
ot.plot.plot1D_mat(a,b,M,'Cost matrix M')
#%% EMD
G0=ot.emd(a,b,M)
pl.figure(3)
ot.plot.plot1D_mat(a,b,G0,'OT matrix G0')
#%% Sinkhorn
lambd=1e-3
Gs=ot.sinkhorn(a,b,M,lambd)
pl.figure(4)
ot.plot.plot1D_mat(a,b,Gs,'OT matrix Sinkhorn')
**Total running time of the script:** ( 0 minutes 0.597 seconds)
.. 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>`
.. rst-class:: sphx-glr-signature
`Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_
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