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-.. only:: html
-
- .. note::
- :class: sphx-glr-download-link-note
-
- Click :ref:`here <sphx_glr_download_auto_examples_plot_OT_1D.py>` 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 <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:: 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
-
-
- <matplotlib.legend.Legend object at 0x7f4c75f9fcc0>
-
-
-
-
-.. 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 <plot_OT_1D.py>`
-
-
-
- .. container:: sphx-glr-download sphx-glr-download-jupyter
-
- :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.github.io>`_