From d54184c233cd211a693e4cdf4b25dd68b07ed00b Mon Sep 17 00:00:00 2001 From: Rémi Flamary Date: Mon, 20 Apr 2020 16:10:18 +0200 Subject: add rst file for documentation --- .../auto_examples/plot_partial_wass_and_gromov.rst | 314 +++++++++++++++++++++ docs/source/auto_examples/plot_screenkhorn_1D.rst | 178 ++++++++++++ 2 files changed, 492 insertions(+) create mode 100644 docs/source/auto_examples/plot_partial_wass_and_gromov.rst create mode 100644 docs/source/auto_examples/plot_screenkhorn_1D.rst diff --git a/docs/source/auto_examples/plot_partial_wass_and_gromov.rst b/docs/source/auto_examples/plot_partial_wass_and_gromov.rst new file mode 100644 index 0000000..7f47f83 --- /dev/null +++ b/docs/source/auto_examples/plot_partial_wass_and_gromov.rst @@ -0,0 +1,314 @@ +.. only:: html + + .. note:: + :class: sphx-glr-download-link-note + + Click :ref:`here ` 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 + # 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 ` + + + + .. container:: sphx-glr-download sphx-glr-download-jupyter + + :download:`Download Jupyter notebook: plot_partial_wass_and_gromov.ipynb ` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ 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 ` 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 + # + # 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 ` + + + + .. container:: sphx-glr-download sphx-glr-download-jupyter + + :download:`Download Jupyter notebook: plot_screenkhorn_1D.ipynb ` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ -- cgit v1.2.3