.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/plot_stochastic.py" .. LINE NUMBERS ARE GIVEN BELOW. .. 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_stochastic.py: =================== Stochastic examples =================== This example is designed to show how to use the stochatic optimization algorithms for discrete and semi-continuous measures from the POT library. [18] Genevay, A., Cuturi, M., Peyré, G. & Bach, F. Stochastic Optimization for Large-scale Optimal Transport. Advances in Neural Information Processing Systems (2016). [19] Seguy, V., Bhushan Damodaran, B., Flamary, R., Courty, N., Rolet, A. & Blondel, M. Large-scale Optimal Transport and Mapping Estimation. International Conference on Learning Representation (2018) .. GENERATED FROM PYTHON SOURCE LINES 18-29 .. code-block:: default # Author: Kilian Fatras # # License: MIT License import matplotlib.pylab as pl import numpy as np import ot import ot.plot .. GENERATED FROM PYTHON SOURCE LINES 30-38 Compute the Transportation Matrix for the Semi-Dual Problem ----------------------------------------------------------- Discrete case ````````````` Sample two discrete measures for the discrete case and compute their cost matrix c. .. GENERATED FROM PYTHON SOURCE LINES 38-52 .. 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) .. GENERATED FROM PYTHON SOURCE LINES 53-54 Call the "SAG" method to find the transportation matrix in the discrete case .. GENERATED FROM PYTHON SOURCE LINES 54-60 .. 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 .. 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]] .. GENERATED FROM PYTHON SOURCE LINES 61-67 Semi-Continuous Case ```````````````````` Sample one general measure a, one discrete measures b for the semicontinous case, the points where source and target measures are defined and compute the cost matrix. .. GENERATED FROM PYTHON SOURCE LINES 67-82 .. 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) .. GENERATED FROM PYTHON SOURCE LINES 83-85 Call the "ASGD" method to find the transportation matrix in the semicontinous case. .. GENERATED FROM PYTHON SOURCE LINES 85-92 .. 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 .. code-block:: none [3.89210786 7.62897384 3.89245014 2.61724317 1.51339313 3.34708637 2.73931688] [-2.47771832 -2.44147638 -0.84136916 5.76056385] [[2.56007346e-02 9.81885744e-02 1.90636347e-02 4.19914973e-06] [1.21903709e-01 1.23580049e-02 1.40646856e-03 7.18896015e-03] [3.47217135e-03 7.30299279e-02 6.63549167e-02 1.26850485e-07] [2.51172810e-02 3.15791525e-02 8.57801775e-02 3.80531864e-04] [1.00343023e-02 7.53482461e-04 1.18796723e-02 1.20189686e-01] [2.21820738e-02 9.09237539e-04 2.06293608e-03 1.17702895e-01] [4.01092095e-02 2.52599884e-02 7.52407360e-02 2.24720898e-03]] .. GENERATED FROM PYTHON SOURCE LINES 93-94 Compare the results with the Sinkhorn algorithm .. GENERATED FROM PYTHON SOURCE LINES 94-99 .. code-block:: default sinkhorn_pi = ot.sinkhorn(a, b, M, reg) print(sinkhorn_pi) .. rst-class:: sphx-glr-script-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]] .. GENERATED FROM PYTHON SOURCE LINES 100-104 Plot Transportation Matrices ```````````````````````````` For SAG .. GENERATED FROM PYTHON SOURCE LINES 104-110 .. 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-sg:: /auto_examples/images/sphx_glr_plot_stochastic_001.png :alt: semi-dual : OT matrix SAG :srcset: /auto_examples/images/sphx_glr_plot_stochastic_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 111-112 For ASGD .. GENERATED FROM PYTHON SOURCE LINES 112-118 .. 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-sg:: /auto_examples/images/sphx_glr_plot_stochastic_002.png :alt: semi-dual : OT matrix ASGD :srcset: /auto_examples/images/sphx_glr_plot_stochastic_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 119-120 For Sinkhorn .. GENERATED FROM PYTHON SOURCE LINES 120-126 .. code-block:: default pl.figure(4, figsize=(5, 5)) ot.plot.plot1D_mat(a, b, sinkhorn_pi, 'OT matrix Sinkhorn') pl.show() .. image-sg:: /auto_examples/images/sphx_glr_plot_stochastic_003.png :alt: OT matrix Sinkhorn :srcset: /auto_examples/images/sphx_glr_plot_stochastic_003.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 127-135 Compute the Transportation Matrix for the Dual Problem ------------------------------------------------------ Semi-continuous case ```````````````````` Sample one general measure a, one discrete measures b for the semi-continuous case and compute the cost matrix c. .. GENERATED FROM PYTHON SOURCE LINES 135-152 .. 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) .. GENERATED FROM PYTHON SOURCE LINES 153-155 Call the "SGD" dual method to find the transportation matrix in the semi-continuous case .. GENERATED FROM PYTHON SOURCE LINES 156-163 .. 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 .. code-block:: none [0.92355578 2.77992798 1.07804471 0.02016319 0.60713159 1.81182019 0.11197572] [0.34336982 0.4710476 1.5721106 4.94609115] [[2.20907087e-02 9.28385311e-02 1.09431124e-02 9.55464538e-08] [1.60430180e-02 1.78208165e-03 1.23133751e-04 2.49477404e-05] [3.49545252e-03 8.05588419e-02 4.44378765e-02 3.36736644e-09] [3.14237585e-02 4.32908444e-02 7.13921359e-02 1.25537224e-05] [6.80903869e-02 5.60249986e-03 5.36266927e-02 2.15061075e-02] [8.02467634e-02 3.60423269e-03 4.96465510e-03 1.12281580e-02] [4.86841219e-02 3.35959147e-02 6.07539060e-02 7.19254669e-05]] .. GENERATED FROM PYTHON SOURCE LINES 164-168 Compare the results with the Sinkhorn algorithm ``````````````````````````````````````````````` Call the Sinkhorn algorithm from POT .. GENERATED FROM PYTHON SOURCE LINES 169-173 .. code-block:: default sinkhorn_pi = ot.sinkhorn(a, b, M, reg) print(sinkhorn_pi) .. rst-class:: sphx-glr-script-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]] .. GENERATED FROM PYTHON SOURCE LINES 174-178 Plot Transportation Matrices ```````````````````````````` For SGD .. GENERATED FROM PYTHON SOURCE LINES 178-184 .. 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-sg:: /auto_examples/images/sphx_glr_plot_stochastic_004.png :alt: dual : OT matrix SGD :srcset: /auto_examples/images/sphx_glr_plot_stochastic_004.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 185-186 For Sinkhorn .. GENERATED FROM PYTHON SOURCE LINES 186-190 .. code-block:: default pl.figure(4, figsize=(5, 5)) ot.plot.plot1D_mat(a, b, sinkhorn_pi, 'OT matrix Sinkhorn') pl.show() .. image-sg:: /auto_examples/images/sphx_glr_plot_stochastic_005.png :alt: OT matrix Sinkhorn :srcset: /auto_examples/images/sphx_glr_plot_stochastic_005.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 7.635 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 ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_stochastic.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_