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+
+
+.. _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>`_
generated by cgit v1.2.3 (git 2.39.1) at 2024-06-26 13:37:17 +0000