.. _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 # # License: MIT License import matplotlib.pylab as pl import numpy as np import ot import ot.plot COMPUTE TRANSPORTATION MATRIX FOR SEMI-DUAL PROBLEM ############################################################################ .. code-block:: python print("------------SEMI-DUAL PROBLEM------------") .. rst-class:: sphx-glr-script-out Out:: ------------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:: [3.9018759 7.63059124 3.93260224 2.67274989 1.43888443 3.26904884 2.78748299] [-2.48511647 -2.43621119 -0.93585194 5.8571796 ] [[2.56614773e-02 9.96758169e-02 1.75151781e-02 4.67049862e-06] [1.21201047e-01 1.24433535e-02 1.28173754e-03 7.93100436e-03] [3.58778167e-03 7.64232233e-02 6.28459924e-02 1.45441936e-07] [2.63551754e-02 3.35577920e-02 8.25011211e-02 4.43054320e-04] [9.24518246e-03 7.03074064e-04 1.00325744e-02 1.22876312e-01] [2.03656325e-02 8.45420425e-04 1.73604569e-03 1.19910044e-01] [4.17781688e-02 2.66463708e-02 7.18353075e-02 2.59729583e-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 ############################################################################ .. code-block:: python print("------------DUAL PROBLEM------------") .. rst-class:: sphx-glr-script-out Out:: ------------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:: [ 1.29325617 5.0435082 1.30996326 0.05538236 -1.08113283 0.73711558 0.18086364] [0.08840343 0.17710082 1.68604226 8.37377551] [[2.47763879e-02 1.00144623e-01 1.77492330e-02 4.25988443e-06] [1.19568278e-01 1.27740478e-02 1.32714202e-03 7.39121816e-03] [3.41581121e-03 7.57137404e-02 6.27992039e-02 1.30808430e-07] [2.52245323e-02 3.34219732e-02 8.28754229e-02 4.00582912e-04] [9.75329554e-03 7.71824343e-04 1.11085400e-02 1.22456628e-01] [2.12304276e-02 9.17096580e-04 1.89946234e-03 1.18084973e-01] [4.04179693e-02 2.68253041e-02 7.29410047e-02 2.37369404e-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 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 22.857 seconds) .. only :: html .. container:: sphx-glr-footer .. container:: sphx-glr-download :download:`Download Python source code: plot_stochastic.py ` .. container:: sphx-glr-download :download:`Download Jupyter notebook: plot_stochastic.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_