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authorRĂ©mi Flamary <remi.flamary@gmail.com>2020-04-21 17:48:37 +0200
committerGitHub <noreply@github.com>2020-04-21 17:48:37 +0200
commita303cc6b483d3cd958c399621e22e40574bcbbc8 (patch)
treedea049cb692020462da8f00d9e117f93b839bb55 /docs/source/auto_examples/plot_stochastic.rst
parent0b2d808aaebb1cab60a272ea7901d5f77df43a9f (diff)
[MRG] Actually run sphinx-gallery (#146)
* generate gallery * remove mock * add sklearn to requirermnt?txt for example * remove latex from fgw example * add networks for graph example * remove all * add requirement.txt rtd * rtd debug * update readme * eradthedoc with redirection * add conf rtd
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-.. only:: html
-
- .. note::
- :class: sphx-glr-download-link-note
-
- Click :ref:`here <sphx_glr_download_auto_examples_plot_stochastic.py>` to download the full example code
- .. rst-class:: sphx-glr-example-title
-
- .. _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:: default
-
-
- # 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:: default
-
-
- 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:: default
-
-
- 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:
-
- .. code-block:: none
-
- [[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:: default
-
-
- 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:: default
-
-
- 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:
-
- .. code-block:: none
-
- [3.89943264 7.64823414 3.9284189 2.67501041 1.42825446 3.26039819
- 2.79237712] [-2.50786905 -2.42684838 -0.93647774 5.87119517]
- [[2.50229922e-02 1.00367920e-01 1.74615056e-02 4.72486104e-06]
- [1.20583329e-01 1.27839737e-02 1.30373565e-03 8.18610462e-03]
- [3.49243139e-03 7.68200813e-02 6.25444833e-02 1.46879008e-07]
- [2.58205995e-02 3.39501207e-02 8.26360982e-02 4.50324517e-04]
- [8.94164918e-03 7.02183713e-04 9.92028326e-03 1.23293027e-01]
- [1.97360234e-02 8.46022708e-04 1.72001583e-03 1.20555081e-01]
- [4.10386980e-02 2.70289873e-02 7.21425804e-02 2.64687723e-03]]
-
-
-
-
-Compare the results with the Sinkhorn algorithm
----------------------------------------------
-
-Call the Sinkhorn algorithm from POT
-
-
-.. code-block:: default
-
-
- sinkhorn_pi = ot.sinkhorn(a, b, M, reg)
- print(sinkhorn_pi)
-
-
-
-
-
-
-.. rst-class:: sphx-glr-script-out
-
- Out:
-
- .. code-block:: none
-
- [[2.55553508e-02 9.96395661e-02 1.76579142e-02 4.31178193e-06]
- [1.21640234e-01 1.25357448e-02 1.30225079e-03 7.37891333e-03]
- [3.56123974e-03 7.61451746e-02 6.31505947e-02 1.33831455e-07]
- [2.61515201e-02 3.34246014e-02 8.28734709e-02 4.07550425e-04]
- [9.85500876e-03 7.52288523e-04 1.08262629e-02 1.21423583e-01]
- [2.16904255e-02 9.03825804e-04 1.87178504e-03 1.18391107e-01]
- [4.15462212e-02 2.65987989e-02 7.23177217e-02 2.39440105e-03]]
-
-
-
-
-PLOT TRANSPORTATION MATRIX
-#############################################################################
-
-Plot SAG results
-----------------
-
-
-.. code-block:: default
-
-
- 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_001.png
- :class: sphx-glr-single-img
-
-
-.. rst-class:: sphx-glr-script-out
-
- Out:
-
- .. code-block:: none
-
- /home/rflamary/PYTHON/POT/examples/plot_stochastic.py:119: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
- pl.show()
-
-
-
-
-Plot ASGD results
------------------
-
-
-.. code-block:: default
-
-
- 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_002.png
- :class: sphx-glr-single-img
-
-
-.. rst-class:: sphx-glr-script-out
-
- Out:
-
- .. code-block:: none
-
- /home/rflamary/PYTHON/POT/examples/plot_stochastic.py:128: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
- pl.show()
-
-
-
-
-Plot Sinkhorn results
----------------------
-
-
-.. code-block:: default
-
-
- 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_003.png
- :class: sphx-glr-single-img
-
-
-.. rst-class:: sphx-glr-script-out
-
- Out:
-
- .. code-block:: none
-
- /home/rflamary/PYTHON/POT/examples/plot_stochastic.py:137: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
- pl.show()
-
-
-
-
-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:: default
-
-
- 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:: default
-
-
- 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:
-
- .. code-block:: none
-
- [0.91421006 2.78075506 1.06828701 0.01979397 0.60914807 1.81887037
- 0.1152939 ] [0.33964624 0.47604281 1.57223631 4.93843308]
- [[2.18038772e-02 9.24355133e-02 1.08426805e-02 9.39355366e-08]
- [1.59966167e-02 1.79248770e-03 1.23251128e-04 2.47779034e-05]
- [3.44864558e-03 8.01760930e-02 4.40119061e-02 3.30922887e-09]
- [3.12954103e-02 4.34915712e-02 7.13747533e-02 1.24533534e-05]
- [6.79742497e-02 5.64192090e-03 5.37416946e-02 2.13851205e-02]
- [8.05141568e-02 3.64790957e-03 5.00040902e-03 1.12213345e-02]
- [4.86643900e-02 3.38763749e-02 6.09634969e-02 7.16139950e-05]]
-
-
-
-
-Compare the results with the Sinkhorn algorithm
----------------------------------------------
-
-Call the Sinkhorn algorithm from POT
-
-
-.. code-block:: default
-
-
- sinkhorn_pi = ot.sinkhorn(a, b, M, reg)
- print(sinkhorn_pi)
-
-
-
-
-
-.. rst-class:: sphx-glr-script-out
-
- Out:
-
- .. code-block:: none
-
- [[2.55553508e-02 9.96395661e-02 1.76579142e-02 4.31178193e-06]
- [1.21640234e-01 1.25357448e-02 1.30225079e-03 7.37891333e-03]
- [3.56123974e-03 7.61451746e-02 6.31505947e-02 1.33831455e-07]
- [2.61515201e-02 3.34246014e-02 8.28734709e-02 4.07550425e-04]
- [9.85500876e-03 7.52288523e-04 1.08262629e-02 1.21423583e-01]
- [2.16904255e-02 9.03825804e-04 1.87178504e-03 1.18391107e-01]
- [4.15462212e-02 2.65987989e-02 7.23177217e-02 2.39440105e-03]]
-
-
-
-
-Plot SGD results
------------------
-
-
-.. code-block:: default
-
-
- 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_004.png
- :class: sphx-glr-single-img
-
-
-.. rst-class:: sphx-glr-script-out
-
- Out:
-
- .. code-block:: none
-
- /home/rflamary/PYTHON/POT/examples/plot_stochastic.py:199: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
- pl.show()
-
-
-
-
-Plot Sinkhorn results
----------------------
-
-
-.. code-block:: default
-
-
- 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_005.png
- :class: sphx-glr-single-img
-
-
-.. rst-class:: sphx-glr-script-out
-
- Out:
-
- .. code-block:: none
-
- /home/rflamary/PYTHON/POT/examples/plot_stochastic.py:208: 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 8.885 seconds)
-
-
-.. _sphx_glr_download_auto_examples_plot_stochastic.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_stochastic.py <plot_stochastic.py>`
-
-
-
- .. container:: sphx-glr-download sphx-glr-download-jupyter
-
- :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.github.io>`_