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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>`_