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authorRémi Flamary <remi.flamary@gmail.com>2020-04-20 16:10:18 +0200
committerRémi Flamary <remi.flamary@gmail.com>2020-04-20 16:10:18 +0200
commitd54184c233cd211a693e4cdf4b25dd68b07ed00b (patch)
treeadca9f61de213d0277524029ef6b333efe32755e /docs
parent6ac8d405f16832e671c432d7b03ce3da38f8fedc (diff)
add rst file for documentation
Diffstat (limited to 'docs')
-rw-r--r--docs/source/auto_examples/plot_partial_wass_and_gromov.rst314
-rw-r--r--docs/source/auto_examples/plot_screenkhorn_1D.rst178
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diff --git a/docs/source/auto_examples/plot_partial_wass_and_gromov.rst b/docs/source/auto_examples/plot_partial_wass_and_gromov.rst
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+.. only:: html
+
+ .. note::
+ :class: sphx-glr-download-link-note
+
+ Click :ref:`here <sphx_glr_download_auto_examples_plot_partial_wass_and_gromov.py>` to download the full example code
+ .. rst-class:: sphx-glr-example-title
+
+ .. _sphx_glr_auto_examples_plot_partial_wass_and_gromov.py:
+
+
+==========================
+Partial Wasserstein and Gromov-Wasserstein example
+==========================
+
+This example is designed to show how to use the Partial (Gromov-)Wassertsein
+distance computation in POT.
+
+
+.. code-block:: default
+
+
+ # Author: Laetitia Chapel <laetitia.chapel@irisa.fr>
+ # License: MIT License
+
+ # necessary for 3d plot even if not used
+ from mpl_toolkits.mplot3d import Axes3D # noqa
+ import scipy as sp
+ import numpy as np
+ import matplotlib.pylab as pl
+ import ot
+
+
+
+
+
+
+
+
+
+Sample two 2D Gaussian distributions and plot them
+--------------------------------------------------
+
+For demonstration purpose, we sample two Gaussian distributions in 2-d
+spaces and add some random noise.
+
+
+.. code-block:: default
+
+
+
+ n_samples = 20 # nb samples (gaussian)
+ n_noise = 20 # nb of samples (noise)
+
+ mu = np.array([0, 0])
+ cov = np.array([[1, 0], [0, 2]])
+
+ xs = ot.datasets.make_2D_samples_gauss(n_samples, mu, cov)
+ xs = np.append(xs, (np.random.rand(n_noise, 2) + 1) * 4).reshape((-1, 2))
+ xt = ot.datasets.make_2D_samples_gauss(n_samples, mu, cov)
+ xt = np.append(xt, (np.random.rand(n_noise, 2) + 1) * -3).reshape((-1, 2))
+
+ M = sp.spatial.distance.cdist(xs, xt)
+
+ fig = pl.figure()
+ ax1 = fig.add_subplot(131)
+ ax1.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+ ax2 = fig.add_subplot(132)
+ ax2.scatter(xt[:, 0], xt[:, 1], color='r')
+ ax3 = fig.add_subplot(133)
+ ax3.imshow(M)
+ pl.show()
+
+
+
+
+.. image:: /auto_examples/images/sphx_glr_plot_partial_wass_and_gromov_001.png
+ :class: sphx-glr-single-img
+
+
+.. rst-class:: sphx-glr-script-out
+
+ Out:
+
+ .. code-block:: none
+
+ /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:51: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
+ pl.show()
+
+
+
+
+Compute partial Wasserstein plans and distance,
+by transporting 50% of the mass
+----------------------------------------------
+
+
+.. code-block:: default
+
+
+ p = ot.unif(n_samples + n_noise)
+ q = ot.unif(n_samples + n_noise)
+
+ w0, log0 = ot.partial.partial_wasserstein(p, q, M, m=0.5, log=True)
+ w, log = ot.partial.entropic_partial_wasserstein(p, q, M, reg=0.1, m=0.5,
+ log=True)
+
+ print('Partial Wasserstein distance (m = 0.5): ' + str(log0['partial_w_dist']))
+ print('Entropic partial Wasserstein distance (m = 0.5): ' +
+ str(log['partial_w_dist']))
+
+ pl.figure(1, (10, 5))
+ pl.subplot(1, 2, 1)
+ pl.imshow(w0, cmap='jet')
+ pl.title('Partial Wasserstein')
+ pl.subplot(1, 2, 2)
+ pl.imshow(w, cmap='jet')
+ pl.title('Entropic partial Wasserstein')
+ pl.show()
+
+
+
+
+
+.. image:: /auto_examples/images/sphx_glr_plot_partial_wass_and_gromov_002.png
+ :class: sphx-glr-single-img
+
+
+.. rst-class:: sphx-glr-script-out
+
+ Out:
+
+ .. code-block:: none
+
+ Partial Wasserstein distance (m = 0.5): 0.29721185147886475
+ Entropic partial Wasserstein distance (m = 0.5): 0.31204119793315976
+ /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:77: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
+ pl.show()
+
+
+
+
+Sample one 2D and 3D Gaussian distributions and plot them
+---------------------------------------------------------
+
+The Gromov-Wasserstein distance allows to compute distances with samples that
+do not belong to the same metric space. For demonstration purpose, we sample
+two Gaussian distributions in 2- and 3-dimensional spaces.
+
+
+.. code-block:: default
+
+
+ n_samples = 20 # nb samples
+ n_noise = 10 # nb of samples (noise)
+
+ p = ot.unif(n_samples + n_noise)
+ q = ot.unif(n_samples + n_noise)
+
+ mu_s = np.array([0, 0])
+ cov_s = np.array([[1, 0], [0, 1]])
+
+ mu_t = np.array([0, 0, 0])
+ cov_t = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
+
+
+ xs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s)
+ xs = np.concatenate((xs, ((np.random.rand(n_noise, 2) + 1) * 4)), axis=0)
+ P = sp.linalg.sqrtm(cov_t)
+ xt = np.random.randn(n_samples, 3).dot(P) + mu_t
+ xt = np.concatenate((xt, ((np.random.rand(n_noise, 3) + 1) * 10)), axis=0)
+
+ fig = pl.figure()
+ ax1 = fig.add_subplot(121)
+ ax1.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+ ax2 = fig.add_subplot(122, projection='3d')
+ ax2.scatter(xt[:, 0], xt[:, 1], xt[:, 2], color='r')
+ pl.show()
+
+
+
+
+
+.. image:: /auto_examples/images/sphx_glr_plot_partial_wass_and_gromov_003.png
+ :class: sphx-glr-single-img
+
+
+.. rst-class:: sphx-glr-script-out
+
+ Out:
+
+ .. code-block:: none
+
+ /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:113: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
+ pl.show()
+
+
+
+
+Compute partial Gromov-Wasserstein plans and distance,
+by transporting 100% and 2/3 of the mass
+-----------------------------------------------------
+
+
+.. code-block:: default
+
+
+ C1 = sp.spatial.distance.cdist(xs, xs)
+ C2 = sp.spatial.distance.cdist(xt, xt)
+
+ print('-----m = 1')
+ m = 1
+ res0, log0 = ot.partial.partial_gromov_wasserstein(C1, C2, p, q, m=m,
+ log=True)
+ res, log = ot.partial.entropic_partial_gromov_wasserstein(C1, C2, p, q, 10,
+ m=m, log=True)
+
+ print('Partial Wasserstein distance (m = 1): ' + str(log0['partial_gw_dist']))
+ print('Entropic partial Wasserstein distance (m = 1): ' +
+ str(log['partial_gw_dist']))
+
+ pl.figure(1, (10, 5))
+ pl.title("mass to be transported m = 1")
+ pl.subplot(1, 2, 1)
+ pl.imshow(res0, cmap='jet')
+ pl.title('Partial Wasserstein')
+ pl.subplot(1, 2, 2)
+ pl.imshow(res, cmap='jet')
+ pl.title('Entropic partial Wasserstein')
+ pl.show()
+
+ print('-----m = 2/3')
+ m = 2 / 3
+ res0, log0 = ot.partial.partial_gromov_wasserstein(C1, C2, p, q, m=m, log=True)
+ res, log = ot.partial.entropic_partial_gromov_wasserstein(C1, C2, p, q, 10,
+ m=m, log=True)
+
+ print('Partial Wasserstein distance (m = 2/3): ' +
+ str(log0['partial_gw_dist']))
+ print('Entropic partial Wasserstein distance (m = 2/3): ' +
+ str(log['partial_gw_dist']))
+
+ pl.figure(1, (10, 5))
+ pl.title("mass to be transported m = 2/3")
+ pl.subplot(1, 2, 1)
+ pl.imshow(res0, cmap='jet')
+ pl.title('Partial Wasserstein')
+ pl.subplot(1, 2, 2)
+ pl.imshow(res, cmap='jet')
+ pl.title('Entropic partial Wasserstein')
+ pl.show()
+
+
+
+.. image:: /auto_examples/images/sphx_glr_plot_partial_wass_and_gromov_004.png
+ :class: sphx-glr-single-img
+
+
+.. rst-class:: sphx-glr-script-out
+
+ Out:
+
+ .. code-block:: none
+
+ -----m = 1
+ Partial Wasserstein distance (m = 1): 56.18870587756925
+ Entropic partial Wasserstein distance (m = 1): 57.63642536818668
+ /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:144: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
+ pl.show()
+ -----m = 2/3
+ Partial Wasserstein distance (m = 2/3): 0.18550643334550976
+ Entropic partial Wasserstein distance (m = 2/3): 1.0781947761552997
+ /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:159: MatplotlibDeprecationWarning: Adding an axes using the same arguments as a previous axes currently reuses the earlier instance. In a future version, a new instance will always be created and returned. Meanwhile, this warning can be suppressed, and the future behavior ensured, by passing a unique label to each axes instance.
+ pl.subplot(1, 2, 1)
+ /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:162: MatplotlibDeprecationWarning: Adding an axes using the same arguments as a previous axes currently reuses the earlier instance. In a future version, a new instance will always be created and returned. Meanwhile, this warning can be suppressed, and the future behavior ensured, by passing a unique label to each axes instance.
+ pl.subplot(1, 2, 2)
+ /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:165: 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 1.656 seconds)
+
+
+.. _sphx_glr_download_auto_examples_plot_partial_wass_and_gromov.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_partial_wass_and_gromov.py <plot_partial_wass_and_gromov.py>`
+
+
+
+ .. container:: sphx-glr-download sphx-glr-download-jupyter
+
+ :download:`Download Jupyter notebook: plot_partial_wass_and_gromov.ipynb <plot_partial_wass_and_gromov.ipynb>`
+
+
+.. only:: html
+
+ .. rst-class:: sphx-glr-signature
+
+ `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_
diff --git a/docs/source/auto_examples/plot_screenkhorn_1D.rst b/docs/source/auto_examples/plot_screenkhorn_1D.rst
new file mode 100644
index 0000000..039479e
--- /dev/null
+++ b/docs/source/auto_examples/plot_screenkhorn_1D.rst
@@ -0,0 +1,178 @@
+.. only:: html
+
+ .. note::
+ :class: sphx-glr-download-link-note
+
+ Click :ref:`here <sphx_glr_download_auto_examples_plot_screenkhorn_1D.py>` to download the full example code
+ .. rst-class:: sphx-glr-example-title
+
+ .. _sphx_glr_auto_examples_plot_screenkhorn_1D.py:
+
+
+===============================
+1D Screened optimal transport
+===============================
+
+This example illustrates the computation of Screenkhorn:
+Screening Sinkhorn Algorithm for Optimal transport.
+
+
+.. code-block:: default
+
+
+ # Author: Mokhtar Z. Alaya <mokhtarzahdi.alaya@gmail.com>
+ #
+ # License: MIT License
+
+ import numpy as np
+ import matplotlib.pylab as pl
+ import ot.plot
+ from ot.datasets import make_1D_gauss as gauss
+ from ot.bregman import screenkhorn
+
+
+
+
+
+
+
+
+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()
+
+ # plot distributions and loss matrix
+
+ pl.figure(2, figsize=(5, 5))
+ ot.plot.plot1D_mat(a, b, M, 'Cost matrix M')
+
+
+
+
+.. rst-class:: sphx-glr-horizontal
+
+
+ *
+
+ .. image:: /auto_examples/images/sphx_glr_plot_screenkhorn_1D_001.png
+ :class: sphx-glr-multi-img
+
+ *
+
+ .. image:: /auto_examples/images/sphx_glr_plot_screenkhorn_1D_002.png
+ :class: sphx-glr-multi-img
+
+
+
+
+
+Solve Screenkhorn
+-----------------------
+
+
+.. code-block:: default
+
+
+ # Screenkhorn
+ lambd = 2e-03 # entropy parameter
+ ns_budget = 30 # budget number of points to be keeped in the source distribution
+ nt_budget = 30 # budget number of points to be keeped in the target distribution
+
+ G_screen = screenkhorn(a, b, M, lambd, ns_budget, nt_budget, uniform=False, restricted=True, verbose=True)
+ pl.figure(4, figsize=(5, 5))
+ ot.plot.plot1D_mat(a, b, G_screen, 'OT matrix Screenkhorn')
+ pl.show()
+
+
+
+.. image:: /auto_examples/images/sphx_glr_plot_screenkhorn_1D_003.png
+ :class: sphx-glr-single-img
+
+
+.. rst-class:: sphx-glr-script-out
+
+ Out:
+
+ .. code-block:: none
+
+ /home/rflamary/PYTHON/POT/ot/bregman.py:2056: UserWarning: Bottleneck module is not installed. Install it from https://pypi.org/project/Bottleneck/ for better performance.
+ "Bottleneck module is not installed. Install it from https://pypi.org/project/Bottleneck/ for better performance.")
+ epsilon = 0.020986042861303855
+
+ kappa = 3.7476531411890917
+
+ Cardinality of selected points: |Isel| = 30 |Jsel| = 30
+
+ /home/rflamary/PYTHON/POT/examples/plot_screenkhorn_1D.py:68: 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 0.228 seconds)
+
+
+.. _sphx_glr_download_auto_examples_plot_screenkhorn_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_screenkhorn_1D.py <plot_screenkhorn_1D.py>`
+
+
+
+ .. container:: sphx-glr-download sphx-glr-download-jupyter
+
+ :download:`Download Jupyter notebook: plot_screenkhorn_1D.ipynb <plot_screenkhorn_1D.ipynb>`
+
+
+.. only:: html
+
+ .. rst-class:: sphx-glr-signature
+
+ `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_