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diff --git a/docs/source/auto_examples/plot_stochastic.rst b/docs/source/auto_examples/plot_stochastic.rst deleted file mode 100644 index d531045..0000000 --- a/docs/source/auto_examples/plot_stochastic.rst +++ /dev/null @@ -1,446 +0,0 @@ - - -.. _sphx_glr_auto_examples_plot_stochastic.py: - - -========================== -Stochastic examples -========================== - -This example is designed to show how to use the stochatic optimization -algorithms for descrete and semicontinous measures from the POT library. - - - - -.. code-block:: python - - - # Author: Kilian Fatras <kilian.fatras@gmail.com> - # - # License: MIT License - - import matplotlib.pylab as pl - import numpy as np - import ot - import ot.plot - - - - - - - - -COMPUTE TRANSPORTATION MATRIX FOR SEMI-DUAL PROBLEM -############################################################################ -############################################################################ - DISCRETE CASE: - - Sample two discrete measures for the discrete case - --------------------------------------------- - - Define 2 discrete measures a and b, the points where are defined the source - and the target measures and finally the cost matrix c. - - - -.. code-block:: python - - - n_source = 7 - n_target = 4 - reg = 1 - numItermax = 1000 - - a = ot.utils.unif(n_source) - b = ot.utils.unif(n_target) - - rng = np.random.RandomState(0) - X_source = rng.randn(n_source, 2) - Y_target = rng.randn(n_target, 2) - M = ot.dist(X_source, Y_target) - - - - - - - -Call the "SAG" method to find the transportation matrix in the discrete case ---------------------------------------------- - -Define the method "SAG", call ot.solve_semi_dual_entropic and plot the -results. - - - -.. code-block:: python - - - method = "SAG" - sag_pi = ot.stochastic.solve_semi_dual_entropic(a, b, M, reg, method, - numItermax) - print(sag_pi) - - - - - -.. rst-class:: sphx-glr-script-out - - Out:: - - [[2.55553509e-02 9.96395660e-02 1.76579142e-02 4.31178196e-06] - [1.21640234e-01 1.25357448e-02 1.30225078e-03 7.37891338e-03] - [3.56123975e-03 7.61451746e-02 6.31505947e-02 1.33831456e-07] - [2.61515202e-02 3.34246014e-02 8.28734709e-02 4.07550428e-04] - [9.85500870e-03 7.52288517e-04 1.08262628e-02 1.21423583e-01] - [2.16904253e-02 9.03825797e-04 1.87178503e-03 1.18391107e-01] - [4.15462212e-02 2.65987989e-02 7.23177216e-02 2.39440107e-03]] - - -SEMICONTINOUS CASE: - -Sample one general measure a, one discrete measures b for the semicontinous -case ---------------------------------------------- - -Define one general measure a, one discrete measures b, the points where -are defined the source and the target measures and finally the cost matrix c. - - - -.. code-block:: python - - - n_source = 7 - n_target = 4 - reg = 1 - numItermax = 1000 - log = True - - a = ot.utils.unif(n_source) - b = ot.utils.unif(n_target) - - rng = np.random.RandomState(0) - X_source = rng.randn(n_source, 2) - Y_target = rng.randn(n_target, 2) - M = ot.dist(X_source, Y_target) - - - - - - - -Call the "ASGD" method to find the transportation matrix in the semicontinous -case ---------------------------------------------- - -Define the method "ASGD", call ot.solve_semi_dual_entropic and plot the -results. - - - -.. code-block:: python - - - method = "ASGD" - asgd_pi, log_asgd = ot.stochastic.solve_semi_dual_entropic(a, b, M, reg, method, - numItermax, log=log) - print(log_asgd['alpha'], log_asgd['beta']) - print(asgd_pi) - - - - - -.. rst-class:: sphx-glr-script-out - - Out:: - - [3.98220325 7.76235856 3.97645524 2.72051681 1.23219313 3.07696856 - 2.84476972] [-2.65544161 -2.50838395 -0.9397765 6.10360206] - [[2.34528761e-02 1.00491956e-01 1.89058354e-02 6.47543413e-06] - [1.16616747e-01 1.32074516e-02 1.45653361e-03 1.15764107e-02] - [3.16154850e-03 7.42892944e-02 6.54061055e-02 1.94426150e-07] - [2.33152216e-02 3.27486992e-02 8.61986263e-02 5.94595747e-04] - [6.34131496e-03 5.31975896e-04 8.12724003e-03 1.27856612e-01] - [1.41744829e-02 6.49096245e-04 1.42704389e-03 1.26606520e-01] - [3.73127657e-02 2.62526499e-02 7.57727161e-02 3.51901117e-03]] - - -Compare the results with the Sinkhorn algorithm ---------------------------------------------- - -Call the Sinkhorn algorithm from POT - - - -.. code-block:: python - - - sinkhorn_pi = ot.sinkhorn(a, b, M, reg) - print(sinkhorn_pi) - - - - - - -.. rst-class:: sphx-glr-script-out - - Out:: - - [[2.55535622e-02 9.96413843e-02 1.76578860e-02 4.31043335e-06] - [1.21640742e-01 1.25369034e-02 1.30234529e-03 7.37715259e-03] - [3.56096458e-03 7.61460101e-02 6.31500344e-02 1.33788624e-07] - [2.61499607e-02 3.34255577e-02 8.28741973e-02 4.07427179e-04] - [9.85698720e-03 7.52505948e-04 1.08291770e-02 1.21418473e-01] - [2.16947591e-02 9.04086158e-04 1.87228707e-03 1.18386011e-01] - [4.15442692e-02 2.65998963e-02 7.23192701e-02 2.39370724e-03]] - - -PLOT TRANSPORTATION MATRIX -############################################################################# - - -Plot SAG results ----------------- - - - -.. code-block:: python - - - pl.figure(4, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, sag_pi, 'semi-dual : OT matrix SAG') - pl.show() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_stochastic_004.png - :align: center - - - - -Plot ASGD results ------------------ - - - -.. code-block:: python - - - pl.figure(4, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, asgd_pi, 'semi-dual : OT matrix ASGD') - pl.show() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_stochastic_005.png - :align: center - - - - -Plot Sinkhorn results ---------------------- - - - -.. code-block:: python - - - pl.figure(4, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, sinkhorn_pi, 'OT matrix Sinkhorn') - pl.show() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_stochastic_006.png - :align: center - - - - -COMPUTE TRANSPORTATION MATRIX FOR DUAL PROBLEM -############################################################################ -############################################################################ - SEMICONTINOUS CASE: - - Sample one general measure a, one discrete measures b for the semicontinous - case - --------------------------------------------- - - Define one general measure a, one discrete measures b, the points where - are defined the source and the target measures and finally the cost matrix c. - - - -.. code-block:: python - - - n_source = 7 - n_target = 4 - reg = 1 - numItermax = 100000 - lr = 0.1 - batch_size = 3 - log = True - - a = ot.utils.unif(n_source) - b = ot.utils.unif(n_target) - - rng = np.random.RandomState(0) - X_source = rng.randn(n_source, 2) - Y_target = rng.randn(n_target, 2) - M = ot.dist(X_source, Y_target) - - - - - - - -Call the "SGD" dual method to find the transportation matrix in the -semicontinous case ---------------------------------------------- - -Call ot.solve_dual_entropic and plot the results. - - - -.. code-block:: python - - - sgd_dual_pi, log_sgd = ot.stochastic.solve_dual_entropic(a, b, M, reg, - batch_size, numItermax, - lr, log=log) - print(log_sgd['alpha'], log_sgd['beta']) - print(sgd_dual_pi) - - - - - -.. rst-class:: sphx-glr-script-out - - Out:: - - [0.92449986 2.75486107 1.07923806 0.02741145 0.61355413 1.81961594 - 0.12072562] [0.33831611 0.46806842 1.5640451 4.96947652] - [[2.20001105e-02 9.26497883e-02 1.08654588e-02 9.78995555e-08] - [1.55669974e-02 1.73279561e-03 1.19120878e-04 2.49058251e-05] - [3.48198483e-03 8.04151063e-02 4.41335396e-02 3.45115752e-09] - [3.14927954e-02 4.34760520e-02 7.13338154e-02 1.29442395e-05] - [6.81836550e-02 5.62182457e-03 5.35386584e-02 2.21568095e-02] - [8.04671052e-02 3.62163462e-03 4.96331605e-03 1.15837801e-02] - [4.88644009e-02 3.37903481e-02 6.07955004e-02 7.42743505e-05]] - - -Compare the results with the Sinkhorn algorithm ---------------------------------------------- - -Call the Sinkhorn algorithm from POT - - - -.. code-block:: python - - - sinkhorn_pi = ot.sinkhorn(a, b, M, reg) - print(sinkhorn_pi) - - - - - -.. rst-class:: sphx-glr-script-out - - Out:: - - [[2.55535622e-02 9.96413843e-02 1.76578860e-02 4.31043335e-06] - [1.21640742e-01 1.25369034e-02 1.30234529e-03 7.37715259e-03] - [3.56096458e-03 7.61460101e-02 6.31500344e-02 1.33788624e-07] - [2.61499607e-02 3.34255577e-02 8.28741973e-02 4.07427179e-04] - [9.85698720e-03 7.52505948e-04 1.08291770e-02 1.21418473e-01] - [2.16947591e-02 9.04086158e-04 1.87228707e-03 1.18386011e-01] - [4.15442692e-02 2.65998963e-02 7.23192701e-02 2.39370724e-03]] - - -Plot SGD results ------------------ - - - -.. code-block:: python - - - pl.figure(4, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, sgd_dual_pi, 'dual : OT matrix SGD') - pl.show() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_stochastic_007.png - :align: center - - - - -Plot Sinkhorn results ---------------------- - - - -.. code-block:: python - - - pl.figure(4, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, sinkhorn_pi, 'OT matrix Sinkhorn') - pl.show() - - - -.. image:: /auto_examples/images/sphx_glr_plot_stochastic_008.png - :align: center - - - - -**Total running time of the script:** ( 0 minutes 20.889 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_stochastic.py <plot_stochastic.py>` - - - - .. container:: sphx-glr-download - - :download:`Download Jupyter notebook: plot_stochastic.ipynb <plot_stochastic.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ |