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-
-
-.. _sphx_glr_auto_examples_plot_OT_L1_vs_L2.py:
-
-
-==========================================
-2D Optimal transport for different metrics
-==========================================
-
-2D OT on empirical distributio with different gound metric.
-
-Stole the figure idea from Fig. 1 and 2 in
-https://arxiv.org/pdf/1706.07650.pdf
-
-
-
-
-
-.. code-block:: python
-
-
- # Author: Remi Flamary <remi.flamary@unice.fr>
- #
- # License: MIT License
-
- import numpy as np
- import matplotlib.pylab as pl
- import ot
- import ot.plot
-
-
-
-
-
-
-
-Dataset 1 : uniform sampling
-----------------------------
-
-
-
-.. code-block:: python
-
-
- n = 20 # nb samples
- xs = np.zeros((n, 2))
- xs[:, 0] = np.arange(n) + 1
- xs[:, 1] = (np.arange(n) + 1) * -0.001 # to make it strictly convex...
-
- xt = np.zeros((n, 2))
- xt[:, 1] = np.arange(n) + 1
-
- a, b = ot.unif(n), ot.unif(n) # uniform distribution on samples
-
- # loss matrix
- M1 = ot.dist(xs, xt, metric='euclidean')
- M1 /= M1.max()
-
- # loss matrix
- M2 = ot.dist(xs, xt, metric='sqeuclidean')
- M2 /= M2.max()
-
- # loss matrix
- Mp = np.sqrt(ot.dist(xs, xt, metric='euclidean'))
- Mp /= Mp.max()
-
- # Data
- pl.figure(1, figsize=(7, 3))
- pl.clf()
- pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
- pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
- pl.axis('equal')
- pl.title('Source and target distributions')
-
-
- # Cost matrices
- pl.figure(2, figsize=(7, 3))
-
- pl.subplot(1, 3, 1)
- pl.imshow(M1, interpolation='nearest')
- pl.title('Euclidean cost')
-
- pl.subplot(1, 3, 2)
- pl.imshow(M2, interpolation='nearest')
- pl.title('Squared Euclidean cost')
-
- pl.subplot(1, 3, 3)
- pl.imshow(Mp, interpolation='nearest')
- pl.title('Sqrt Euclidean cost')
- pl.tight_layout()
-
-
-
-
-.. rst-class:: sphx-glr-horizontal
-
-
- *
-
- .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_001.png
- :scale: 47
-
- *
-
- .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_002.png
- :scale: 47
-
-
-
-
-Dataset 1 : Plot OT Matrices
-----------------------------
-
-
-
-.. code-block:: python
-
-
-
- #%% EMD
- G1 = ot.emd(a, b, M1)
- G2 = ot.emd(a, b, M2)
- Gp = ot.emd(a, b, Mp)
-
- # OT matrices
- pl.figure(3, figsize=(7, 3))
-
- pl.subplot(1, 3, 1)
- ot.plot.plot2D_samples_mat(xs, xt, G1, c=[.5, .5, 1])
- pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
- pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
- pl.axis('equal')
- # pl.legend(loc=0)
- pl.title('OT Euclidean')
-
- pl.subplot(1, 3, 2)
- ot.plot.plot2D_samples_mat(xs, xt, G2, c=[.5, .5, 1])
- pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
- pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
- pl.axis('equal')
- # pl.legend(loc=0)
- pl.title('OT squared Euclidean')
-
- pl.subplot(1, 3, 3)
- ot.plot.plot2D_samples_mat(xs, xt, Gp, c=[.5, .5, 1])
- pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
- pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
- pl.axis('equal')
- # pl.legend(loc=0)
- pl.title('OT sqrt Euclidean')
- pl.tight_layout()
-
- pl.show()
-
-
-
-
-
-.. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_005.png
- :align: center
-
-
-
-
-Dataset 2 : Partial circle
---------------------------
-
-
-
-.. code-block:: python
-
-
- n = 50 # nb samples
- xtot = np.zeros((n + 1, 2))
- xtot[:, 0] = np.cos(
- (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi)
- xtot[:, 1] = np.sin(
- (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi)
-
- xs = xtot[:n, :]
- xt = xtot[1:, :]
-
- a, b = ot.unif(n), ot.unif(n) # uniform distribution on samples
-
- # loss matrix
- M1 = ot.dist(xs, xt, metric='euclidean')
- M1 /= M1.max()
-
- # loss matrix
- M2 = ot.dist(xs, xt, metric='sqeuclidean')
- M2 /= M2.max()
-
- # loss matrix
- Mp = np.sqrt(ot.dist(xs, xt, metric='euclidean'))
- Mp /= Mp.max()
-
-
- # Data
- pl.figure(4, figsize=(7, 3))
- pl.clf()
- pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
- pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
- pl.axis('equal')
- pl.title('Source and traget distributions')
-
-
- # Cost matrices
- pl.figure(5, figsize=(7, 3))
-
- pl.subplot(1, 3, 1)
- pl.imshow(M1, interpolation='nearest')
- pl.title('Euclidean cost')
-
- pl.subplot(1, 3, 2)
- pl.imshow(M2, interpolation='nearest')
- pl.title('Squared Euclidean cost')
-
- pl.subplot(1, 3, 3)
- pl.imshow(Mp, interpolation='nearest')
- pl.title('Sqrt Euclidean cost')
- pl.tight_layout()
-
-
-
-
-.. rst-class:: sphx-glr-horizontal
-
-
- *
-
- .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_007.png
- :scale: 47
-
- *
-
- .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_008.png
- :scale: 47
-
-
-
-
-Dataset 2 : Plot OT Matrices
------------------------------
-
-
-
-.. code-block:: python
-
-
-
- #%% EMD
- G1 = ot.emd(a, b, M1)
- G2 = ot.emd(a, b, M2)
- Gp = ot.emd(a, b, Mp)
-
- # OT matrices
- pl.figure(6, figsize=(7, 3))
-
- pl.subplot(1, 3, 1)
- ot.plot.plot2D_samples_mat(xs, xt, G1, c=[.5, .5, 1])
- pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
- pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
- pl.axis('equal')
- # pl.legend(loc=0)
- pl.title('OT Euclidean')
-
- pl.subplot(1, 3, 2)
- ot.plot.plot2D_samples_mat(xs, xt, G2, c=[.5, .5, 1])
- pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
- pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
- pl.axis('equal')
- # pl.legend(loc=0)
- pl.title('OT squared Euclidean')
-
- pl.subplot(1, 3, 3)
- ot.plot.plot2D_samples_mat(xs, xt, Gp, c=[.5, .5, 1])
- pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
- pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
- pl.axis('equal')
- # pl.legend(loc=0)
- pl.title('OT sqrt Euclidean')
- pl.tight_layout()
-
- pl.show()
-
-
-
-.. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_011.png
- :align: center
-
-
-
-
-**Total running time of the script:** ( 0 minutes 0.958 seconds)
-
-
-
-.. only :: html
-
- .. container:: sphx-glr-footer
-
-
- .. container:: sphx-glr-download
-
- :download:`Download Python source code: plot_OT_L1_vs_L2.py <plot_OT_L1_vs_L2.py>`
-
-
-
- .. container:: sphx-glr-download
-
- :download:`Download Jupyter notebook: plot_OT_L1_vs_L2.ipynb <plot_OT_L1_vs_L2.ipynb>`
-
-
-.. only:: html
-
- .. rst-class:: sphx-glr-signature
-
- `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_
generated by cgit v1.2.3 (git 2.39.1) at 2024-04-28 04:27:19 +0000