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64 files changed, 3906 insertions, 166 deletions
diff --git a/.coveragerc b/.coveragerc new file mode 100644 index 0000000..2114fb4 --- /dev/null +++ b/.coveragerc @@ -0,0 +1,6 @@ +[run] + +omit= + ot/externals/* + ot/externals/funcsigs.py + ot/gpu/* diff --git a/.travis.yml b/.travis.yml index d146395..90a0ff4 100644 --- a/.travis.yml +++ b/.travis.yml @@ -26,11 +26,11 @@ before_script: # configure a headless display to test plot generation # command to install dependencies install: - pip install -r requirements.txt - - pip install flake8 pytest + - pip install flake8 pytest pytest-cov - pip install . # command to run tests + check syntax style script: - python setup.py develop - flake8 examples/ ot/ test/ - - python -m pytest -v test/ + - python -m pytest -v test/ --cov=ot # - py.test ot test diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md index 84ef29a..54e7e42 100644 --- a/CONTRIBUTING.md +++ b/CONTRIBUTING.md @@ -17,7 +17,7 @@ GitHub, clone, and develop on a branch. Steps: a copy of the code under your GitHub user account. For more details on how to fork a repository see [this guide](https://help.github.com/articles/fork-a-repo/). -2. Clone your fork of the scikit-learn repo from your GitHub account to your local disk: +2. Clone your fork of the POT repo from your GitHub account to your local disk: ```bash $ git clone git@github.com:YourLogin/POT.git @@ -84,7 +84,7 @@ following rules before you submit a pull request: example script in the ``examples/`` folder. Have a look at other examples for reference. Examples should demonstrate why the new functionality is useful in practice and, if possible, compare it - to other methods available in scikit-learn. + to other methods available in POT. - Documentation and high-coverage tests are necessary for enhancements to be accepted. Bug-fixes or new features should be provided with @@ -145,7 +145,7 @@ following rules before submitting: See [Creating and highlighting code blocks](https://help.github.com/articles/creating-and-highlighting-code-blocks). - Please include your operating system type and version number, as well - as your Python, scikit-learn, numpy, and scipy versions. This information + as your Python, POT, numpy, and scipy versions. This information can be found by running the following code snippet: ```python @@ -165,8 +165,8 @@ following rules before submitting: New contributor tips -------------------- -A great way to start contributing to scikit-learn is to pick an item -from the list of [Easy issues](https://github.com/scikit-learn/scikit-learn/issues?labels=Easy) +A great way to start contributing to POT is to pick an item +from the list of [Easy issues](https://github.com/rflamary/POT/issues?labels=Easy) in the issue tracker. Resolving these issues allow you to start contributing to the project without much prior knowledge. Your assistance in this area will be greatly appreciated by the more @@ -201,4 +201,4 @@ method does to the data and a figure (coming from an example) illustrating it. -This Contrubution guide is strongly inpired by the one of the [scikit-learn](https://github.com/scikit-learn/scikit-learn) team. +This Contribution guide is strongly inpired by the one of the [scikit-learn](https://github.com/scikit-learn/scikit-learn) team. @@ -4,6 +4,7 @@ [](https://anaconda.org/conda-forge/pot) [](https://travis-ci.org/rflamary/POT) [](http://pot.readthedocs.io/en/latest/?badge=latest) +[](https://pepy.tech/project/pot) [](https://anaconda.org/conda-forge/pot) [](https://github.com/rflamary/POT/blob/master/LICENSE) @@ -79,7 +80,7 @@ Note that for easier access the module is name ot instead of pot. Some sub-modules require additional dependences which are discussed below -* **ot.dr** (Wasserstein dimensionality rediuction) depends on autograd and pymanopt that can be installed with: +* **ot.dr** (Wasserstein dimensionality reduction) depends on autograd and pymanopt that can be installed with: ``` pip install pymanopt autograd ``` diff --git a/RELEASES.md b/RELEASES.md index 58712c8..a617441 100644 --- a/RELEASES.md +++ b/RELEASES.md @@ -1,5 +1,64 @@ # POT Releases + +## 0.5.0 Year 2 +*Sep 2018* + +POT is 2 years old! This release brings numerous new features to the +toolbox as listed below but also several bug correction. + +Among the new features, we can highlight a [non-regularized Gromov-Wasserstein +solver](https://github.com/rflamary/POT/blob/master/notebooks/plot_gromov.ipynb), +a new [greedy variant of sinkhorn](https://pot.readthedocs.io/en/latest/all.html#ot.bregman.greenkhorn), +[non-regularized](https://pot.readthedocs.io/en/latest/all.html#ot.lp.barycenter), +[convolutional (2D)](https://github.com/rflamary/POT/blob/master/notebooks/plot_convolutional_barycenter.ipynb) +and [free support](https://github.com/rflamary/POT/blob/master/notebooks/plot_free_support_barycenter.ipynb) + Wasserstein barycenters and [smooth](https://github.com/rflamary/POT/blob/prV0.5/notebooks/plot_OT_1D_smooth.ipynb) + and [stochastic](https://pot.readthedocs.io/en/latest/all.html#ot.stochastic.sgd_entropic_regularization) +implementation of entropic OT. + +POT 0.5 also comes with a rewriting of ot.gpu using the cupy framework instead of +the unmaintained cudamat. Note that while we tried to keed changes to the +minimum, the OTDA classes were deprecated. If you are happy with the cudamat +implementation, we recommend you stay with stable release 0.4 for now. + +The code quality has also improved with 92% code coverage in tests that is now +printed to the log in the Travis builds. The documentation has also been +greatly improved with new modules and examples/notebooks. + +This new release is so full of new stuff and corrections thanks to the old +and new POT contributors (you can see the list in the [readme](https://github.com/rflamary/POT/blob/master/README.md)). + +#### Features + +* Add non regularized Gromov-Wasserstein solver (PR #41) +* Linear OT mapping between empirical distributions and 90\% test coverage (PR #42) +* Add log parameter in class EMDTransport and SinkhornLpL1Transport (PR #44) +* Add Markdown format for Pipy (PR #45) +* Test for Python 3.5 and 3.6 on Travis (PR #46) +* Non regularized Wasserstein barycenter with scipy linear solver and/or cvxopt (PR #47) +* Rename dataset functions to be more sklearn compliant (PR #49) +* Smooth and sparse Optimal transport implementation with entropic and quadratic regularization (PR #50) +* Stochastic OT in the dual and semi-dual (PR #52 and PR #62) +* Free support barycenters (PR #56) +* Speed-up Sinkhorn function (PR #57 and PR #58) +* Add convolutional Wassersein barycenters for 2D images (PR #64) +* Add Greedy Sinkhorn variant (Greenkhorn) (PR #66) +* Big ot.gpu update with cupy implementation (instead of un-maintained cudamat) (PR #67) + +#### Deprecation + +Deprecated OTDA Classes were removed from ot.da and ot.gpu for version 0.5 +(PR #48 and PR #67). The deprecation message has been for a year here since +0.4 and it is time to pull the plug. + +#### Closed issues + +* Issue #35 : remove import plot from ot/__init__.py (See PR #41) +* Issue #43 : Unusable parameter log for EMDTransport (See PR #44) +* Issue #55 : UnicodeDecodeError: 'ascii' while installing with pip + + ## 0.4 Community edition *15 Sep 2017* diff --git a/docs/cache_nbrun b/docs/cache_nbrun index 318bcf4..575adc8 100644 --- a/docs/cache_nbrun +++ b/docs/cache_nbrun @@ -1 +1 @@ -{"plot_otda_mapping_colors_images.ipynb": "4f0587a00a3c082799a75a0ed36e9ce1", "plot_optim_OTreg.ipynb": "481801bb0d133ef350a65179cf8f739a", "plot_otda_color_images.ipynb": "d047d635f4987c81072383241590e21f", "plot_WDA.ipynb": "27f8de4c6d7db46497076523673eedfb", "plot_otda_linear_mapping.ipynb": "a472c767abe82020e0a58125a528785c", "plot_OT_L1_vs_L2.ipynb": "5d565b8aaf03be4309eba731127851dc", "plot_barycenter_1D.ipynb": "6063193f9ac87517acced2625edb9a54", "plot_otda_classes.ipynb": "39087b6e98217851575f2271c22853a4", "plot_otda_d2.ipynb": "e6feae588103f2a8fab942e5f4eff483", "plot_otda_mapping.ipynb": "2f1ebbdc0f855d9e2b7adf9edec24d25", "plot_gromov.ipynb": "24f2aea489714d34779521f46d5e2c47", "plot_compute_emd.ipynb": "f5cd71cad882ec157dc8222721e9820c", "plot_OT_1D.ipynb": "b5348bdc561c07ec168a1622e5af4b93", "plot_gromov_barycenter.ipynb": "953e5047b886ec69ec621ec52f5e21d1", "plot_otda_semi_supervised.ipynb": "f6dfb02ba2bbd939408ffcd22a3b007c", "plot_OT_2D_samples.ipynb": "07dbc14859fa019a966caa79fa0825bd", "plot_barycenter_lp_vs_entropic.ipynb": "51833e8c76aaedeba9599ac7a30eb357"}
\ No newline at end of file +{"plot_otda_mapping_colors_images.ipynb": "4f0587a00a3c082799a75a0ed36e9ce1", "plot_optim_OTreg.ipynb": "481801bb0d133ef350a65179cf8f739a", "plot_barycenter_1D.ipynb": "5f6fb8aebd8e2e91ebc77c923cb112b3", "plot_stochastic.ipynb": "e2c520150378ae4635f74509f687fa01", "plot_WDA.ipynb": "27f8de4c6d7db46497076523673eedfb", "plot_otda_linear_mapping.ipynb": "a472c767abe82020e0a58125a528785c", "plot_OT_1D_smooth.ipynb": "3a059103652225a0c78ea53895cf79e5", "plot_OT_L1_vs_L2.ipynb": "5d565b8aaf03be4309eba731127851dc", "plot_otda_color_images.ipynb": "d047d635f4987c81072383241590e21f", "plot_otda_classes.ipynb": "39087b6e98217851575f2271c22853a4", "plot_otda_d2.ipynb": "e6feae588103f2a8fab942e5f4eff483", "plot_otda_mapping.ipynb": "2f1ebbdc0f855d9e2b7adf9edec24d25", "plot_gromov.ipynb": "24f2aea489714d34779521f46d5e2c47", "plot_compute_emd.ipynb": "f5cd71cad882ec157dc8222721e9820c", "plot_OT_1D.ipynb": "b5348bdc561c07ec168a1622e5af4b93", "plot_gromov_barycenter.ipynb": "953e5047b886ec69ec621ec52f5e21d1", "plot_free_support_barycenter.ipynb": "246dd2feff4b233a4f1a553c5a202fdc", "plot_convolutional_barycenter.ipynb": "a72bb3716a1baaffd81ae267a673f9b6", "plot_otda_semi_supervised.ipynb": "f6dfb02ba2bbd939408ffcd22a3b007c", "plot_OT_2D_samples.ipynb": "07dbc14859fa019a966caa79fa0825bd", "plot_barycenter_lp_vs_entropic.ipynb": "51833e8c76aaedeba9599ac7a30eb357"}
\ No newline at end of file diff --git a/docs/source/all.rst b/docs/source/all.rst index 1eaf3b1..32930fd 100644 --- a/docs/source/all.rst +++ b/docs/source/all.rst @@ -19,11 +19,6 @@ ot.bregman .. automodule:: ot.bregman :members: - -ot.smooth ------ -.. automodule:: ot.smooth - :members: ot.smooth ----- diff --git a/docs/source/auto_examples/auto_examples_jupyter.zip b/docs/source/auto_examples/auto_examples_jupyter.zip Binary files differindex 8102274..304bb06 100644 --- a/docs/source/auto_examples/auto_examples_jupyter.zip +++ b/docs/source/auto_examples/auto_examples_jupyter.zip diff --git a/docs/source/auto_examples/auto_examples_python.zip b/docs/source/auto_examples/auto_examples_python.zip Binary files differindex d685070..3be8a76 100644 --- a/docs/source/auto_examples/auto_examples_python.zip +++ b/docs/source/auto_examples/auto_examples_python.zip diff --git a/docs/source/auto_examples/images/sphx_glr_plot_OT_1D_smooth_001.png 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tooltip="Illustration of 2D Wasserstein barycenters if discributions that are weighted sum of diracs."> + +.. only:: html + + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_free_support_barycenter_thumb.png + + :ref:`sphx_glr_auto_examples_plot_free_support_barycenter.py` + +.. raw:: html + + </div> + + +.. toctree:: + :hidden: + + /auto_examples/plot_free_support_barycenter + +.. raw:: html + + <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of EMD, Sinkhorn and smooth OT plans and their visuali..."> + +.. only:: html + + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_OT_1D_smooth_thumb.png + + :ref:`sphx_glr_auto_examples_plot_OT_1D_smooth.py` + +.. raw:: html + + </div> + + +.. toctree:: + :hidden: + + /auto_examples/plot_OT_1D_smooth + +.. raw:: html + <div class="sphx-glr-thumbcontainer" tooltip="This example is designed to show how to use the Gromov-Wassertsein distance computation in POT...."> .. only:: html @@ -109,6 +149,26 @@ This is a gallery of all the POT example files. .. raw:: html + <div class="sphx-glr-thumbcontainer" tooltip="This example is designed to illustrate how the Convolutional Wasserstein Barycenter function of..."> + +.. only:: html + + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_convolutional_barycenter_thumb.png + + :ref:`sphx_glr_auto_examples_plot_convolutional_barycenter.py` + +.. raw:: html + + </div> + + +.. toctree:: + :hidden: + + /auto_examples/plot_convolutional_barycenter + +.. raw:: html + <div class="sphx-glr-thumbcontainer" tooltip=" "> .. only:: html @@ -149,13 +209,13 @@ This is a gallery of all the POT example files. .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip="This example presents a way of transferring colors between two image with Optimal Transport as ..."> + <div class="sphx-glr-thumbcontainer" tooltip="This example is designed to show how to use the stochatic optimization algorithms for descrete ..."> .. only:: html - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_otda_color_images_thumb.png + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_stochastic_thumb.png - :ref:`sphx_glr_auto_examples_plot_otda_color_images.py` + :ref:`sphx_glr_auto_examples_plot_stochastic.py` .. raw:: html @@ -165,17 +225,17 @@ This is a gallery of all the POT example files. .. toctree:: :hidden: - /auto_examples/plot_otda_color_images + /auto_examples/plot_stochastic .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip="OT for domain adaptation with image color adaptation [6] with mapping estimation [8]."> + <div class="sphx-glr-thumbcontainer" tooltip="This example presents a way of transferring colors between two image with Optimal Transport as ..."> .. only:: html - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_otda_mapping_colors_images_thumb.png + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_otda_color_images_thumb.png - :ref:`sphx_glr_auto_examples_plot_otda_mapping_colors_images.py` + :ref:`sphx_glr_auto_examples_plot_otda_color_images.py` .. raw:: html @@ -185,7 +245,7 @@ This is a gallery of all the POT example files. .. toctree:: :hidden: - /auto_examples/plot_otda_mapping_colors_images + /auto_examples/plot_otda_color_images .. raw:: html @@ -209,6 +269,26 @@ This is a gallery of all the POT example files. .. raw:: html + <div class="sphx-glr-thumbcontainer" tooltip="OT for domain adaptation with image color adaptation [6] with mapping estimation [8]."> + +.. only:: html + + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_otda_mapping_colors_images_thumb.png + + :ref:`sphx_glr_auto_examples_plot_otda_mapping_colors_images.py` + +.. raw:: html + + </div> + + +.. toctree:: + :hidden: + + /auto_examples/plot_otda_mapping_colors_images + +.. raw:: html + <div class="sphx-glr-thumbcontainer" tooltip="This example presents how to use MappingTransport to estimate at the same time both the couplin..."> .. only:: html diff --git a/docs/source/auto_examples/plot_OT_1D_smooth.ipynb b/docs/source/auto_examples/plot_OT_1D_smooth.ipynb new file mode 100644 index 0000000..d523f6a --- /dev/null +++ b/docs/source/auto_examples/plot_OT_1D_smooth.ipynb @@ -0,0 +1,144 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# 1D smooth optimal transport\n\n\nThis example illustrates the computation of EMD, Sinkhorn and smooth OT plans\nand their visualization.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Author: Remi Flamary <remi.flamary@unice.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\nimport ot.plot\nfrom ot.datasets import make_1D_gauss as gauss" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate data\n-------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% parameters\n\nn = 100 # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\na = gauss(n, m=20, s=5) # m= mean, s= std\nb = gauss(n, m=60, s=10)\n\n# loss matrix\nM = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))\nM /= M.max()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot distributions and loss matrix\n----------------------------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% plot the distributions\n\npl.figure(1, figsize=(6.4, 3))\npl.plot(x, a, 'b', label='Source distribution')\npl.plot(x, b, 'r', label='Target distribution')\npl.legend()\n\n#%% plot distributions and loss matrix\n\npl.figure(2, figsize=(5, 5))\not.plot.plot1D_mat(a, b, M, 'Cost matrix M')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Solve EMD\n---------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% EMD\n\nG0 = ot.emd(a, b, M)\n\npl.figure(3, figsize=(5, 5))\not.plot.plot1D_mat(a, b, G0, 'OT matrix G0')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Solve Sinkhorn\n--------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% Sinkhorn\n\nlambd = 2e-3\nGs = ot.sinkhorn(a, b, M, lambd, verbose=True)\n\npl.figure(4, figsize=(5, 5))\not.plot.plot1D_mat(a, b, Gs, 'OT matrix Sinkhorn')\n\npl.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Solve Smooth OT\n--------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% Smooth OT with KL regularization\n\nlambd = 2e-3\nGsm = ot.smooth.smooth_ot_dual(a, b, M, lambd, reg_type='kl')\n\npl.figure(5, figsize=(5, 5))\not.plot.plot1D_mat(a, b, Gsm, 'OT matrix Smooth OT KL reg.')\n\npl.show()\n\n\n#%% Smooth OT with KL regularization\n\nlambd = 1e-1\nGsm = ot.smooth.smooth_ot_dual(a, b, M, lambd, reg_type='l2')\n\npl.figure(6, figsize=(5, 5))\not.plot.plot1D_mat(a, b, Gsm, 'OT matrix Smooth OT l2 reg.')\n\npl.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.5" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_OT_1D_smooth.py b/docs/source/auto_examples/plot_OT_1D_smooth.py new file mode 100644 index 0000000..b690751 --- /dev/null +++ b/docs/source/auto_examples/plot_OT_1D_smooth.py @@ -0,0 +1,110 @@ +# -*- coding: utf-8 -*- +""" +=========================== +1D smooth optimal transport +=========================== + +This example illustrates the computation of EMD, Sinkhorn and smooth OT plans +and their visualization. + +""" + +# Author: Remi Flamary <remi.flamary@unice.fr> +# +# License: MIT License + +import numpy as np +import matplotlib.pylab as pl +import ot +import ot.plot +from ot.datasets import make_1D_gauss as gauss + +############################################################################## +# Generate data +# ------------- + + +#%% parameters + +n = 100 # nb bins + +# bin positions +x = np.arange(n, dtype=np.float64) + +# Gaussian distributions +a = gauss(n, m=20, s=5) # m= mean, s= std +b = gauss(n, m=60, s=10) + +# loss matrix +M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1))) +M /= M.max() + + +############################################################################## +# Plot distributions and loss matrix +# ---------------------------------- + +#%% plot the distributions + +pl.figure(1, figsize=(6.4, 3)) +pl.plot(x, a, 'b', label='Source distribution') +pl.plot(x, b, 'r', label='Target distribution') +pl.legend() + +#%% plot distributions and loss matrix + +pl.figure(2, figsize=(5, 5)) +ot.plot.plot1D_mat(a, b, M, 'Cost matrix M') + +############################################################################## +# Solve EMD +# --------- + + +#%% EMD + +G0 = ot.emd(a, b, M) + +pl.figure(3, figsize=(5, 5)) +ot.plot.plot1D_mat(a, b, G0, 'OT matrix G0') + +############################################################################## +# Solve Sinkhorn +# -------------- + + +#%% Sinkhorn + +lambd = 2e-3 +Gs = ot.sinkhorn(a, b, M, lambd, verbose=True) + +pl.figure(4, figsize=(5, 5)) +ot.plot.plot1D_mat(a, b, Gs, 'OT matrix Sinkhorn') + +pl.show() + +############################################################################## +# Solve Smooth OT +# -------------- + + +#%% Smooth OT with KL regularization + +lambd = 2e-3 +Gsm = ot.smooth.smooth_ot_dual(a, b, M, lambd, reg_type='kl') + +pl.figure(5, figsize=(5, 5)) +ot.plot.plot1D_mat(a, b, Gsm, 'OT matrix Smooth OT KL reg.') + +pl.show() + + +#%% Smooth OT with KL regularization + +lambd = 1e-1 +Gsm = ot.smooth.smooth_ot_dual(a, b, M, lambd, reg_type='l2') + +pl.figure(6, figsize=(5, 5)) +ot.plot.plot1D_mat(a, b, Gsm, 'OT matrix Smooth OT l2 reg.') + +pl.show() diff --git a/docs/source/auto_examples/plot_OT_1D_smooth.rst b/docs/source/auto_examples/plot_OT_1D_smooth.rst new file mode 100644 index 0000000..5a0ebd3 --- /dev/null +++ b/docs/source/auto_examples/plot_OT_1D_smooth.rst @@ -0,0 +1,242 @@ + + +.. _sphx_glr_auto_examples_plot_OT_1D_smooth.py: + + +=========================== +1D smooth optimal transport +=========================== + +This example illustrates the computation of EMD, Sinkhorn and smooth OT plans +and their visualization. + + + + +.. code-block:: python + + + # Author: Remi Flamary <remi.flamary@unice.fr> + # + # License: MIT License + + import numpy as np + import matplotlib.pylab as pl + import ot + import ot.plot + from ot.datasets import make_1D_gauss as gauss + + + + + + + +Generate data +------------- + + + +.. code-block:: python + + + + #%% parameters + + n = 100 # nb bins + + # bin positions + x = np.arange(n, dtype=np.float64) + + # Gaussian distributions + a = gauss(n, m=20, s=5) # m= mean, s= std + b = gauss(n, m=60, s=10) + + # loss matrix + M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1))) + M /= M.max() + + + + + + + + +Plot distributions and loss matrix +---------------------------------- + + + +.. code-block:: python + + + #%% plot the distributions + + pl.figure(1, figsize=(6.4, 3)) + pl.plot(x, a, 'b', label='Source distribution') + pl.plot(x, b, 'r', label='Target distribution') + pl.legend() + + #%% plot distributions and loss matrix + + pl.figure(2, figsize=(5, 5)) + ot.plot.plot1D_mat(a, b, M, 'Cost matrix M') + + + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_001.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_002.png + :scale: 47 + + + + +Solve EMD +--------- + + + +.. code-block:: python + + + + #%% EMD + + G0 = ot.emd(a, b, M) + + pl.figure(3, figsize=(5, 5)) + ot.plot.plot1D_mat(a, b, G0, 'OT matrix G0') + + + + +.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_005.png + :align: center + + + + +Solve Sinkhorn +-------------- + + + +.. code-block:: python + + + + #%% Sinkhorn + + lambd = 2e-3 + Gs = ot.sinkhorn(a, b, M, lambd, verbose=True) + + pl.figure(4, figsize=(5, 5)) + ot.plot.plot1D_mat(a, b, Gs, 'OT matrix Sinkhorn') + + pl.show() + + + + +.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_007.png + :align: center + + +.. rst-class:: sphx-glr-script-out + + Out:: + + It. |Err + ------------------- + 0|7.958844e-02| + 10|5.921715e-03| + 20|1.238266e-04| + 30|2.469780e-06| + 40|4.919966e-08| + 50|9.800197e-10| + + +Solve Smooth OT +-------------- + + + +.. code-block:: python + + + + #%% Smooth OT with KL regularization + + lambd = 2e-3 + Gsm = ot.smooth.smooth_ot_dual(a, b, M, lambd, reg_type='kl') + + pl.figure(5, figsize=(5, 5)) + ot.plot.plot1D_mat(a, b, Gsm, 'OT matrix Smooth OT KL reg.') + + pl.show() + + + #%% Smooth OT with KL regularization + + lambd = 1e-1 + Gsm = ot.smooth.smooth_ot_dual(a, b, M, lambd, reg_type='l2') + + pl.figure(6, figsize=(5, 5)) + ot.plot.plot1D_mat(a, b, Gsm, 'OT matrix Smooth OT l2 reg.') + + pl.show() + + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_009.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_010.png + :scale: 47 + + + + +**Total running time of the script:** ( 0 minutes 1.053 seconds) + + + +.. only :: html + + .. container:: sphx-glr-footer + + + .. container:: sphx-glr-download + + :download:`Download Python source code: plot_OT_1D_smooth.py <plot_OT_1D_smooth.py>` + + + + .. container:: sphx-glr-download + + :download:`Download Jupyter notebook: plot_OT_1D_smooth.ipynb <plot_OT_1D_smooth.ipynb>` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_barycenter_1D.ipynb b/docs/source/auto_examples/plot_barycenter_1D.ipynb index 5866088..fc60e1f 100644 --- a/docs/source/auto_examples/plot_barycenter_1D.ipynb +++ b/docs/source/auto_examples/plot_barycenter_1D.ipynb @@ -26,7 +26,79 @@ }, "outputs": [], "source": [ - "# Author: Remi Flamary <remi.flamary@unice.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\n# necessary for 3d plot even if not used\nfrom mpl_toolkits.mplot3d import Axes3D # noqa\nfrom matplotlib.collections import PolyCollection\n\n#\n# Generate data\n# -------------\n\n#%% parameters\n\nn = 100 # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\na1 = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std\na2 = ot.datasets.make_1D_gauss(n, m=60, s=8)\n\n# creating matrix A containing all distributions\nA = np.vstack((a1, a2)).T\nn_distributions = A.shape[1]\n\n# loss matrix + normalization\nM = ot.utils.dist0(n)\nM /= M.max()\n\n#\n# Plot data\n# ---------\n\n#%% plot the distributions\n\npl.figure(1, figsize=(6.4, 3))\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\npl.tight_layout()\n\n#\n# Barycenter computation\n# ----------------------\n\n#%% barycenter computation\n\nalpha = 0.2 # 0<=alpha<=1\nweights = np.array([1 - alpha, alpha])\n\n# l2bary\nbary_l2 = A.dot(weights)\n\n# wasserstein\nreg = 1e-3\nbary_wass = ot.bregman.barycenter(A, M, reg, weights)\n\npl.figure(2)\npl.clf()\npl.subplot(2, 1, 1)\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\n\npl.subplot(2, 1, 2)\npl.plot(x, bary_l2, 'r', label='l2')\npl.plot(x, bary_wass, 'g', label='Wasserstein')\npl.legend()\npl.title('Barycenters')\npl.tight_layout()\n\n#\n# Barycentric interpolation\n# -------------------------\n\n#%% barycenter interpolation\n\nn_alpha = 11\nalpha_list = np.linspace(0, 1, n_alpha)\n\n\nB_l2 = np.zeros((n, n_alpha))\n\nB_wass = np.copy(B_l2)\n\nfor i in range(0, n_alpha):\n alpha = alpha_list[i]\n weights = np.array([1 - alpha, alpha])\n B_l2[:, i] = A.dot(weights)\n B_wass[:, i] = ot.bregman.barycenter(A, M, reg, weights)\n\n#%% plot interpolation\n\npl.figure(3)\n\ncmap = pl.cm.get_cmap('viridis')\nverts = []\nzs = alpha_list\nfor i, z in enumerate(zs):\n ys = B_l2[:, i]\n verts.append(list(zip(x, ys)))\n\nax = pl.gcf().gca(projection='3d')\n\npoly = PolyCollection(verts, facecolors=[cmap(a) for a in alpha_list])\npoly.set_alpha(0.7)\nax.add_collection3d(poly, zs=zs, zdir='y')\nax.set_xlabel('x')\nax.set_xlim3d(0, n)\nax.set_ylabel('$\\\\alpha$')\nax.set_ylim3d(0, 1)\nax.set_zlabel('')\nax.set_zlim3d(0, B_l2.max() * 1.01)\npl.title('Barycenter interpolation with l2')\npl.tight_layout()\n\npl.figure(4)\ncmap = pl.cm.get_cmap('viridis')\nverts = []\nzs = alpha_list\nfor i, z in enumerate(zs):\n ys = B_wass[:, i]\n verts.append(list(zip(x, ys)))\n\nax = pl.gcf().gca(projection='3d')\n\npoly = PolyCollection(verts, facecolors=[cmap(a) for a in alpha_list])\npoly.set_alpha(0.7)\nax.add_collection3d(poly, zs=zs, zdir='y')\nax.set_xlabel('x')\nax.set_xlim3d(0, n)\nax.set_ylabel('$\\\\alpha$')\nax.set_ylim3d(0, 1)\nax.set_zlabel('')\nax.set_zlim3d(0, B_l2.max() * 1.01)\npl.title('Barycenter interpolation with Wasserstein')\npl.tight_layout()\n\npl.show()" + "# Author: Remi Flamary <remi.flamary@unice.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\n# necessary for 3d plot even if not used\nfrom mpl_toolkits.mplot3d import Axes3D # noqa\nfrom matplotlib.collections import PolyCollection" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate data\n-------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% parameters\n\nn = 100 # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\na1 = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std\na2 = ot.datasets.make_1D_gauss(n, m=60, s=8)\n\n# creating matrix A containing all distributions\nA = np.vstack((a1, a2)).T\nn_distributions = A.shape[1]\n\n# loss matrix + normalization\nM = ot.utils.dist0(n)\nM /= M.max()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot data\n---------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% plot the distributions\n\npl.figure(1, figsize=(6.4, 3))\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\npl.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Barycenter computation\n----------------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% barycenter computation\n\nalpha = 0.2 # 0<=alpha<=1\nweights = np.array([1 - alpha, alpha])\n\n# l2bary\nbary_l2 = A.dot(weights)\n\n# wasserstein\nreg = 1e-3\nbary_wass = ot.bregman.barycenter(A, M, reg, weights)\n\npl.figure(2)\npl.clf()\npl.subplot(2, 1, 1)\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\n\npl.subplot(2, 1, 2)\npl.plot(x, bary_l2, 'r', label='l2')\npl.plot(x, bary_wass, 'g', label='Wasserstein')\npl.legend()\npl.title('Barycenters')\npl.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Barycentric interpolation\n-------------------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% barycenter interpolation\n\nn_alpha = 11\nalpha_list = np.linspace(0, 1, n_alpha)\n\n\nB_l2 = np.zeros((n, n_alpha))\n\nB_wass = np.copy(B_l2)\n\nfor i in range(0, n_alpha):\n alpha = alpha_list[i]\n weights = np.array([1 - alpha, alpha])\n B_l2[:, i] = A.dot(weights)\n B_wass[:, i] = ot.bregman.barycenter(A, M, reg, weights)\n\n#%% plot interpolation\n\npl.figure(3)\n\ncmap = pl.cm.get_cmap('viridis')\nverts = []\nzs = alpha_list\nfor i, z in enumerate(zs):\n ys = B_l2[:, i]\n verts.append(list(zip(x, ys)))\n\nax = pl.gcf().gca(projection='3d')\n\npoly = PolyCollection(verts, facecolors=[cmap(a) for a in alpha_list])\npoly.set_alpha(0.7)\nax.add_collection3d(poly, zs=zs, zdir='y')\nax.set_xlabel('x')\nax.set_xlim3d(0, n)\nax.set_ylabel('$\\\\alpha$')\nax.set_ylim3d(0, 1)\nax.set_zlabel('')\nax.set_zlim3d(0, B_l2.max() * 1.01)\npl.title('Barycenter interpolation with l2')\npl.tight_layout()\n\npl.figure(4)\ncmap = pl.cm.get_cmap('viridis')\nverts = []\nzs = alpha_list\nfor i, z in enumerate(zs):\n ys = B_wass[:, i]\n verts.append(list(zip(x, ys)))\n\nax = pl.gcf().gca(projection='3d')\n\npoly = PolyCollection(verts, facecolors=[cmap(a) for a in alpha_list])\npoly.set_alpha(0.7)\nax.add_collection3d(poly, zs=zs, zdir='y')\nax.set_xlabel('x')\nax.set_xlim3d(0, n)\nax.set_ylabel('$\\\\alpha$')\nax.set_ylim3d(0, 1)\nax.set_zlabel('')\nax.set_zlim3d(0, B_l2.max() * 1.01)\npl.title('Barycenter interpolation with Wasserstein')\npl.tight_layout()\n\npl.show()" ] } ], diff --git a/docs/source/auto_examples/plot_barycenter_1D.py b/docs/source/auto_examples/plot_barycenter_1D.py index 5ed9f3f..6864301 100644 --- a/docs/source/auto_examples/plot_barycenter_1D.py +++ b/docs/source/auto_examples/plot_barycenter_1D.py @@ -25,7 +25,7 @@ import ot from mpl_toolkits.mplot3d import Axes3D # noqa from matplotlib.collections import PolyCollection -# +############################################################################## # Generate data # ------------- @@ -48,7 +48,7 @@ n_distributions = A.shape[1] M = ot.utils.dist0(n) M /= M.max() -# +############################################################################## # Plot data # --------- @@ -60,7 +60,7 @@ for i in range(n_distributions): pl.title('Distributions') pl.tight_layout() -# +############################################################################## # Barycenter computation # ---------------------- @@ -90,7 +90,7 @@ pl.legend() pl.title('Barycenters') pl.tight_layout() -# +############################################################################## # Barycentric interpolation # ------------------------- diff --git a/docs/source/auto_examples/plot_barycenter_1D.rst b/docs/source/auto_examples/plot_barycenter_1D.rst index b314dc1..66ac042 100644 --- a/docs/source/auto_examples/plot_barycenter_1D.rst +++ b/docs/source/auto_examples/plot_barycenter_1D.rst @@ -18,52 +18,34 @@ SIAM Journal on Scientific Computing, 37(2), A1111-A1138. +.. code-block:: python -.. rst-class:: sphx-glr-horizontal - - - * - .. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_001.png - :scale: 47 + # Author: Remi Flamary <remi.flamary@unice.fr> + # + # License: MIT License - * + import numpy as np + import matplotlib.pylab as pl + import ot + # necessary for 3d plot even if not used + from mpl_toolkits.mplot3d import Axes3D # noqa + from matplotlib.collections import PolyCollection - .. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_002.png - :scale: 47 - * - .. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_003.png - :scale: 47 - * - .. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_004.png - :scale: 47 +Generate data +------------- .. code-block:: python - # Author: Remi Flamary <remi.flamary@unice.fr> - # - # License: MIT License - - import numpy as np - import matplotlib.pylab as pl - import ot - # necessary for 3d plot even if not used - from mpl_toolkits.mplot3d import Axes3D # noqa - from matplotlib.collections import PolyCollection - - # - # Generate data - # ------------- - #%% parameters n = 100 # nb bins @@ -83,9 +65,19 @@ SIAM Journal on Scientific Computing, 37(2), A1111-A1138. M = ot.utils.dist0(n) M /= M.max() - # - # Plot data - # --------- + + + + + + +Plot data +--------- + + + +.. code-block:: python + #%% plot the distributions @@ -95,9 +87,22 @@ SIAM Journal on Scientific Computing, 37(2), A1111-A1138. pl.title('Distributions') pl.tight_layout() - # - # Barycenter computation - # ---------------------- + + + +.. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_001.png + :align: center + + + + +Barycenter computation +---------------------- + + + +.. code-block:: python + #%% barycenter computation @@ -125,9 +130,22 @@ SIAM Journal on Scientific Computing, 37(2), A1111-A1138. pl.title('Barycenters') pl.tight_layout() - # - # Barycentric interpolation - # ------------------------- + + + +.. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_003.png + :align: center + + + + +Barycentric interpolation +------------------------- + + + +.. code-block:: python + #%% barycenter interpolation @@ -194,7 +212,25 @@ SIAM Journal on Scientific Computing, 37(2), A1111-A1138. pl.show() -**Total running time of the script:** ( 0 minutes 0.363 seconds) + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_005.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_006.png + :scale: 47 + + + + +**Total running time of the script:** ( 0 minutes 0.413 seconds) diff --git a/docs/source/auto_examples/plot_convolutional_barycenter.ipynb b/docs/source/auto_examples/plot_convolutional_barycenter.ipynb new file mode 100644 index 0000000..4981ba3 --- /dev/null +++ b/docs/source/auto_examples/plot_convolutional_barycenter.ipynb @@ -0,0 +1,90 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# Convolutional Wasserstein Barycenter example\n\n\nThis example is designed to illustrate how the Convolutional Wasserstein Barycenter\nfunction of POT works.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Author: Nicolas Courty <ncourty@irisa.fr>\n#\n# License: MIT License\n\n\nimport numpy as np\nimport pylab as pl\nimport ot" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Data preparation\n----------------\n\nThe four distributions are constructed from 4 simple images\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "f1 = 1 - pl.imread('../data/redcross.png')[:, :, 2]\nf2 = 1 - pl.imread('../data/duck.png')[:, :, 2]\nf3 = 1 - pl.imread('../data/heart.png')[:, :, 2]\nf4 = 1 - pl.imread('../data/tooth.png')[:, :, 2]\n\nA = []\nf1 = f1 / np.sum(f1)\nf2 = f2 / np.sum(f2)\nf3 = f3 / np.sum(f3)\nf4 = f4 / np.sum(f4)\nA.append(f1)\nA.append(f2)\nA.append(f3)\nA.append(f4)\nA = np.array(A)\n\nnb_images = 5\n\n# those are the four corners coordinates that will be interpolated by bilinear\n# interpolation\nv1 = np.array((1, 0, 0, 0))\nv2 = np.array((0, 1, 0, 0))\nv3 = np.array((0, 0, 1, 0))\nv4 = np.array((0, 0, 0, 1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Barycenter computation and visualization\n----------------------------------------\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "pl.figure(figsize=(10, 10))\npl.title('Convolutional Wasserstein Barycenters in POT')\ncm = 'Blues'\n# regularization parameter\nreg = 0.004\nfor i in range(nb_images):\n for j in range(nb_images):\n pl.subplot(nb_images, nb_images, i * nb_images + j + 1)\n tx = float(i) / (nb_images - 1)\n ty = float(j) / (nb_images - 1)\n\n # weights are constructed by bilinear interpolation\n tmp1 = (1 - tx) * v1 + tx * v2\n tmp2 = (1 - tx) * v3 + tx * v4\n weights = (1 - ty) * tmp1 + ty * tmp2\n\n if i == 0 and j == 0:\n pl.imshow(f1, cmap=cm)\n pl.axis('off')\n elif i == 0 and j == (nb_images - 1):\n pl.imshow(f3, cmap=cm)\n pl.axis('off')\n elif i == (nb_images - 1) and j == 0:\n pl.imshow(f2, cmap=cm)\n pl.axis('off')\n elif i == (nb_images - 1) and j == (nb_images - 1):\n pl.imshow(f4, cmap=cm)\n pl.axis('off')\n else:\n # call to barycenter computation\n pl.imshow(ot.bregman.convolutional_barycenter2d(A, reg, weights), cmap=cm)\n pl.axis('off')\npl.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.5" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_convolutional_barycenter.py b/docs/source/auto_examples/plot_convolutional_barycenter.py new file mode 100644 index 0000000..e74db04 --- /dev/null +++ b/docs/source/auto_examples/plot_convolutional_barycenter.py @@ -0,0 +1,92 @@ + +#%% +# -*- coding: utf-8 -*- +""" +============================================ +Convolutional Wasserstein Barycenter example +============================================ + +This example is designed to illustrate how the Convolutional Wasserstein Barycenter +function of POT works. +""" + +# Author: Nicolas Courty <ncourty@irisa.fr> +# +# License: MIT License + + +import numpy as np +import pylab as pl +import ot + +############################################################################## +# Data preparation +# ---------------- +# +# The four distributions are constructed from 4 simple images + + +f1 = 1 - pl.imread('../data/redcross.png')[:, :, 2] +f2 = 1 - pl.imread('../data/duck.png')[:, :, 2] +f3 = 1 - pl.imread('../data/heart.png')[:, :, 2] +f4 = 1 - pl.imread('../data/tooth.png')[:, :, 2] + +A = [] +f1 = f1 / np.sum(f1) +f2 = f2 / np.sum(f2) +f3 = f3 / np.sum(f3) +f4 = f4 / np.sum(f4) +A.append(f1) +A.append(f2) +A.append(f3) +A.append(f4) +A = np.array(A) + +nb_images = 5 + +# those are the four corners coordinates that will be interpolated by bilinear +# interpolation +v1 = np.array((1, 0, 0, 0)) +v2 = np.array((0, 1, 0, 0)) +v3 = np.array((0, 0, 1, 0)) +v4 = np.array((0, 0, 0, 1)) + + +############################################################################## +# Barycenter computation and visualization +# ---------------------------------------- +# + +pl.figure(figsize=(10, 10)) +pl.title('Convolutional Wasserstein Barycenters in POT') +cm = 'Blues' +# regularization parameter +reg = 0.004 +for i in range(nb_images): + for j in range(nb_images): + pl.subplot(nb_images, nb_images, i * nb_images + j + 1) + tx = float(i) / (nb_images - 1) + ty = float(j) / (nb_images - 1) + + # weights are constructed by bilinear interpolation + tmp1 = (1 - tx) * v1 + tx * v2 + tmp2 = (1 - tx) * v3 + tx * v4 + weights = (1 - ty) * tmp1 + ty * tmp2 + + if i == 0 and j == 0: + pl.imshow(f1, cmap=cm) + pl.axis('off') + elif i == 0 and j == (nb_images - 1): + pl.imshow(f3, cmap=cm) + pl.axis('off') + elif i == (nb_images - 1) and j == 0: + pl.imshow(f2, cmap=cm) + pl.axis('off') + elif i == (nb_images - 1) and j == (nb_images - 1): + pl.imshow(f4, cmap=cm) + pl.axis('off') + else: + # call to barycenter computation + pl.imshow(ot.bregman.convolutional_barycenter2d(A, reg, weights), cmap=cm) + pl.axis('off') +pl.show() diff --git a/docs/source/auto_examples/plot_convolutional_barycenter.rst b/docs/source/auto_examples/plot_convolutional_barycenter.rst new file mode 100644 index 0000000..a28db2f --- /dev/null +++ b/docs/source/auto_examples/plot_convolutional_barycenter.rst @@ -0,0 +1,151 @@ + + +.. _sphx_glr_auto_examples_plot_convolutional_barycenter.py: + + +============================================ +Convolutional Wasserstein Barycenter example +============================================ + +This example is designed to illustrate how the Convolutional Wasserstein Barycenter +function of POT works. + + + +.. code-block:: python + + + # Author: Nicolas Courty <ncourty@irisa.fr> + # + # License: MIT License + + + import numpy as np + import pylab as pl + import ot + + + + + + + +Data preparation +---------------- + +The four distributions are constructed from 4 simple images + + + +.. code-block:: python + + + + f1 = 1 - pl.imread('../data/redcross.png')[:, :, 2] + f2 = 1 - pl.imread('../data/duck.png')[:, :, 2] + f3 = 1 - pl.imread('../data/heart.png')[:, :, 2] + f4 = 1 - pl.imread('../data/tooth.png')[:, :, 2] + + A = [] + f1 = f1 / np.sum(f1) + f2 = f2 / np.sum(f2) + f3 = f3 / np.sum(f3) + f4 = f4 / np.sum(f4) + A.append(f1) + A.append(f2) + A.append(f3) + A.append(f4) + A = np.array(A) + + nb_images = 5 + + # those are the four corners coordinates that will be interpolated by bilinear + # interpolation + v1 = np.array((1, 0, 0, 0)) + v2 = np.array((0, 1, 0, 0)) + v3 = np.array((0, 0, 1, 0)) + v4 = np.array((0, 0, 0, 1)) + + + + + + + + +Barycenter computation and visualization +---------------------------------------- + + + + +.. code-block:: python + + + pl.figure(figsize=(10, 10)) + pl.title('Convolutional Wasserstein Barycenters in POT') + cm = 'Blues' + # regularization parameter + reg = 0.004 + for i in range(nb_images): + for j in range(nb_images): + pl.subplot(nb_images, nb_images, i * nb_images + j + 1) + tx = float(i) / (nb_images - 1) + ty = float(j) / (nb_images - 1) + + # weights are constructed by bilinear interpolation + tmp1 = (1 - tx) * v1 + tx * v2 + tmp2 = (1 - tx) * v3 + tx * v4 + weights = (1 - ty) * tmp1 + ty * tmp2 + + if i == 0 and j == 0: + pl.imshow(f1, cmap=cm) + pl.axis('off') + elif i == 0 and j == (nb_images - 1): + pl.imshow(f3, cmap=cm) + pl.axis('off') + elif i == (nb_images - 1) and j == 0: + pl.imshow(f2, cmap=cm) + pl.axis('off') + elif i == (nb_images - 1) and j == (nb_images - 1): + pl.imshow(f4, cmap=cm) + pl.axis('off') + else: + # call to barycenter computation + pl.imshow(ot.bregman.convolutional_barycenter2d(A, reg, weights), cmap=cm) + pl.axis('off') + pl.show() + + + +.. image:: /auto_examples/images/sphx_glr_plot_convolutional_barycenter_001.png + :align: center + + + + +**Total running time of the script:** ( 1 minutes 11.608 seconds) + + + +.. only :: html + + .. container:: sphx-glr-footer + + + .. container:: sphx-glr-download + + :download:`Download Python source code: plot_convolutional_barycenter.py <plot_convolutional_barycenter.py>` + + + + .. container:: sphx-glr-download + + :download:`Download Jupyter notebook: plot_convolutional_barycenter.ipynb <plot_convolutional_barycenter.ipynb>` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_free_support_barycenter.ipynb b/docs/source/auto_examples/plot_free_support_barycenter.ipynb new file mode 100644 index 0000000..05a81c8 --- /dev/null +++ b/docs/source/auto_examples/plot_free_support_barycenter.ipynb @@ -0,0 +1,108 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# 2D free support Wasserstein barycenters of distributions\n\n\nIllustration of 2D Wasserstein barycenters if discributions that are weighted\nsum of diracs.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Author: Vivien Seguy <vivien.seguy@iip.ist.i.kyoto-u.ac.jp>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate data\n -------------\n%% parameters and data generation\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "N = 3\nd = 2\nmeasures_locations = []\nmeasures_weights = []\n\nfor i in range(N):\n\n n_i = np.random.randint(low=1, high=20) # nb samples\n\n mu_i = np.random.normal(0., 4., (d,)) # Gaussian mean\n\n A_i = np.random.rand(d, d)\n cov_i = np.dot(A_i, A_i.transpose()) # Gaussian covariance matrix\n\n x_i = ot.datasets.make_2D_samples_gauss(n_i, mu_i, cov_i) # Dirac locations\n b_i = np.random.uniform(0., 1., (n_i,))\n b_i = b_i / np.sum(b_i) # Dirac weights\n\n measures_locations.append(x_i)\n measures_weights.append(b_i)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Compute free support barycenter\n-------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "k = 10 # number of Diracs of the barycenter\nX_init = np.random.normal(0., 1., (k, d)) # initial Dirac locations\nb = np.ones((k,)) / k # weights of the barycenter (it will not be optimized, only the locations are optimized)\n\nX = ot.lp.free_support_barycenter(measures_locations, measures_weights, X_init, b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot data\n---------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "pl.figure(1)\nfor (x_i, b_i) in zip(measures_locations, measures_weights):\n color = np.random.randint(low=1, high=10 * N)\n pl.scatter(x_i[:, 0], x_i[:, 1], s=b * 1000, label='input measure')\npl.scatter(X[:, 0], X[:, 1], s=b * 1000, c='black', marker='^', label='2-Wasserstein barycenter')\npl.title('Data measures and their barycenter')\npl.legend(loc=0)\npl.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.5" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_free_support_barycenter.py b/docs/source/auto_examples/plot_free_support_barycenter.py new file mode 100644 index 0000000..b6efc59 --- /dev/null +++ b/docs/source/auto_examples/plot_free_support_barycenter.py @@ -0,0 +1,69 @@ +# -*- coding: utf-8 -*- +""" +==================================================== +2D free support Wasserstein barycenters of distributions +==================================================== + +Illustration of 2D Wasserstein barycenters if discributions that are weighted +sum of diracs. + +""" + +# Author: Vivien Seguy <vivien.seguy@iip.ist.i.kyoto-u.ac.jp> +# +# License: MIT License + +import numpy as np +import matplotlib.pylab as pl +import ot + + +############################################################################## +# Generate data +# ------------- +#%% parameters and data generation +N = 3 +d = 2 +measures_locations = [] +measures_weights = [] + +for i in range(N): + + n_i = np.random.randint(low=1, high=20) # nb samples + + mu_i = np.random.normal(0., 4., (d,)) # Gaussian mean + + A_i = np.random.rand(d, d) + cov_i = np.dot(A_i, A_i.transpose()) # Gaussian covariance matrix + + x_i = ot.datasets.make_2D_samples_gauss(n_i, mu_i, cov_i) # Dirac locations + b_i = np.random.uniform(0., 1., (n_i,)) + b_i = b_i / np.sum(b_i) # Dirac weights + + measures_locations.append(x_i) + measures_weights.append(b_i) + + +############################################################################## +# Compute free support barycenter +# ------------- + +k = 10 # number of Diracs of the barycenter +X_init = np.random.normal(0., 1., (k, d)) # initial Dirac locations +b = np.ones((k,)) / k # weights of the barycenter (it will not be optimized, only the locations are optimized) + +X = ot.lp.free_support_barycenter(measures_locations, measures_weights, X_init, b) + + +############################################################################## +# Plot data +# --------- + +pl.figure(1) +for (x_i, b_i) in zip(measures_locations, measures_weights): + color = np.random.randint(low=1, high=10 * N) + pl.scatter(x_i[:, 0], x_i[:, 1], s=b * 1000, label='input measure') +pl.scatter(X[:, 0], X[:, 1], s=b * 1000, c='black', marker='^', label='2-Wasserstein barycenter') +pl.title('Data measures and their barycenter') +pl.legend(loc=0) +pl.show() diff --git a/docs/source/auto_examples/plot_free_support_barycenter.rst b/docs/source/auto_examples/plot_free_support_barycenter.rst new file mode 100644 index 0000000..d1b3b80 --- /dev/null +++ b/docs/source/auto_examples/plot_free_support_barycenter.rst @@ -0,0 +1,140 @@ + + +.. _sphx_glr_auto_examples_plot_free_support_barycenter.py: + + +==================================================== +2D free support Wasserstein barycenters of distributions +==================================================== + +Illustration of 2D Wasserstein barycenters if discributions that are weighted +sum of diracs. + + + + +.. code-block:: python + + + # Author: Vivien Seguy <vivien.seguy@iip.ist.i.kyoto-u.ac.jp> + # + # License: MIT License + + import numpy as np + import matplotlib.pylab as pl + import ot + + + + + + + + +Generate data + ------------- +%% parameters and data generation + + + +.. code-block:: python + + N = 3 + d = 2 + measures_locations = [] + measures_weights = [] + + for i in range(N): + + n_i = np.random.randint(low=1, high=20) # nb samples + + mu_i = np.random.normal(0., 4., (d,)) # Gaussian mean + + A_i = np.random.rand(d, d) + cov_i = np.dot(A_i, A_i.transpose()) # Gaussian covariance matrix + + x_i = ot.datasets.make_2D_samples_gauss(n_i, mu_i, cov_i) # Dirac locations + b_i = np.random.uniform(0., 1., (n_i,)) + b_i = b_i / np.sum(b_i) # Dirac weights + + measures_locations.append(x_i) + measures_weights.append(b_i) + + + + + + + + +Compute free support barycenter +------------- + + + +.. code-block:: python + + + k = 10 # number of Diracs of the barycenter + X_init = np.random.normal(0., 1., (k, d)) # initial Dirac locations + b = np.ones((k,)) / k # weights of the barycenter (it will not be optimized, only the locations are optimized) + + X = ot.lp.free_support_barycenter(measures_locations, measures_weights, X_init, b) + + + + + + + + +Plot data +--------- + + + +.. code-block:: python + + + pl.figure(1) + for (x_i, b_i) in zip(measures_locations, measures_weights): + color = np.random.randint(low=1, high=10 * N) + pl.scatter(x_i[:, 0], x_i[:, 1], s=b * 1000, label='input measure') + pl.scatter(X[:, 0], X[:, 1], s=b * 1000, c='black', marker='^', label='2-Wasserstein barycenter') + pl.title('Data measures and their barycenter') + pl.legend(loc=0) + pl.show() + + + +.. image:: /auto_examples/images/sphx_glr_plot_free_support_barycenter_001.png + :align: center + + + + +**Total running time of the script:** ( 0 minutes 0.129 seconds) + + + +.. only :: html + + .. container:: sphx-glr-footer + + + .. container:: sphx-glr-download + + :download:`Download Python source code: plot_free_support_barycenter.py <plot_free_support_barycenter.py>` + + + + .. container:: sphx-glr-download + + :download:`Download Jupyter notebook: plot_free_support_barycenter.ipynb <plot_free_support_barycenter.ipynb>` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_stochastic.ipynb b/docs/source/auto_examples/plot_stochastic.ipynb new file mode 100644 index 0000000..c6f0013 --- /dev/null +++ b/docs/source/auto_examples/plot_stochastic.ipynb @@ -0,0 +1,331 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# Stochastic examples\n\n\nThis example is designed to show how to use the stochatic optimization\nalgorithms for descrete and semicontinous measures from the POT library.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Author: Kilian Fatras <kilian.fatras@gmail.com>\n#\n# License: MIT License\n\nimport matplotlib.pylab as pl\nimport numpy as np\nimport ot\nimport ot.plot" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "COMPUTE TRANSPORTATION MATRIX FOR SEMI-DUAL PROBLEM\n############################################################################\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "print(\"------------SEMI-DUAL PROBLEM------------\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "DISCRETE CASE\nSample two discrete measures for the discrete case\n---------------------------------------------\n\nDefine 2 discrete measures a and b, the points where are defined the source\nand the target measures and finally the cost matrix c.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "n_source = 7\nn_target = 4\nreg = 1\nnumItermax = 1000\n\na = ot.utils.unif(n_source)\nb = ot.utils.unif(n_target)\n\nrng = np.random.RandomState(0)\nX_source = rng.randn(n_source, 2)\nY_target = rng.randn(n_target, 2)\nM = ot.dist(X_source, Y_target)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Call the \"SAG\" method to find the transportation matrix in the discrete case\n---------------------------------------------\n\nDefine the method \"SAG\", call ot.solve_semi_dual_entropic and plot the\nresults.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "method = \"SAG\"\nsag_pi = ot.stochastic.solve_semi_dual_entropic(a, b, M, reg, method,\n numItermax)\nprint(sag_pi)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "SEMICONTINOUS CASE\nSample one general measure a, one discrete measures b for the semicontinous\ncase\n---------------------------------------------\n\nDefine one general measure a, one discrete measures b, the points where\nare defined the source and the target measures and finally the cost matrix c.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "n_source = 7\nn_target = 4\nreg = 1\nnumItermax = 1000\nlog = True\n\na = ot.utils.unif(n_source)\nb = ot.utils.unif(n_target)\n\nrng = np.random.RandomState(0)\nX_source = rng.randn(n_source, 2)\nY_target = rng.randn(n_target, 2)\nM = ot.dist(X_source, Y_target)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Call the \"ASGD\" method to find the transportation matrix in the semicontinous\ncase\n---------------------------------------------\n\nDefine the method \"ASGD\", call ot.solve_semi_dual_entropic and plot the\nresults.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "method = \"ASGD\"\nasgd_pi, log_asgd = ot.stochastic.solve_semi_dual_entropic(a, b, M, reg, method,\n numItermax, log=log)\nprint(log_asgd['alpha'], log_asgd['beta'])\nprint(asgd_pi)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Compare the results with the Sinkhorn algorithm\n---------------------------------------------\n\nCall the Sinkhorn algorithm from POT\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "sinkhorn_pi = ot.sinkhorn(a, b, M, reg)\nprint(sinkhorn_pi)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "PLOT TRANSPORTATION MATRIX\n#############################################################################\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot SAG results\n----------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "pl.figure(4, figsize=(5, 5))\not.plot.plot1D_mat(a, b, sag_pi, 'semi-dual : OT matrix SAG')\npl.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot ASGD results\n-----------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "pl.figure(4, figsize=(5, 5))\not.plot.plot1D_mat(a, b, asgd_pi, 'semi-dual : OT matrix ASGD')\npl.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot Sinkhorn results\n---------------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "pl.figure(4, figsize=(5, 5))\not.plot.plot1D_mat(a, b, sinkhorn_pi, 'OT matrix Sinkhorn')\npl.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "COMPUTE TRANSPORTATION MATRIX FOR DUAL PROBLEM\n############################################################################\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "print(\"------------DUAL PROBLEM------------\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "SEMICONTINOUS CASE\nSample one general measure a, one discrete measures b for the semicontinous\ncase\n---------------------------------------------\n\nDefine one general measure a, one discrete measures b, the points where\nare defined the source and the target measures and finally the cost matrix c.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "n_source = 7\nn_target = 4\nreg = 1\nnumItermax = 100000\nlr = 0.1\nbatch_size = 3\nlog = True\n\na = ot.utils.unif(n_source)\nb = ot.utils.unif(n_target)\n\nrng = np.random.RandomState(0)\nX_source = rng.randn(n_source, 2)\nY_target = rng.randn(n_target, 2)\nM = ot.dist(X_source, Y_target)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Call the \"SGD\" dual method to find the transportation matrix in the\nsemicontinous case\n---------------------------------------------\n\nCall ot.solve_dual_entropic and plot the results.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "sgd_dual_pi, log_sgd = ot.stochastic.solve_dual_entropic(a, b, M, reg,\n batch_size, numItermax,\n lr, log=log)\nprint(log_sgd['alpha'], log_sgd['beta'])\nprint(sgd_dual_pi)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Compare the results with the Sinkhorn algorithm\n---------------------------------------------\n\nCall the Sinkhorn algorithm from POT\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "sinkhorn_pi = ot.sinkhorn(a, b, M, reg)\nprint(sinkhorn_pi)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot SGD results\n-----------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "pl.figure(4, figsize=(5, 5))\not.plot.plot1D_mat(a, b, sgd_dual_pi, 'dual : OT matrix SGD')\npl.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot Sinkhorn results\n---------------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "pl.figure(4, figsize=(5, 5))\not.plot.plot1D_mat(a, b, sinkhorn_pi, 'OT matrix Sinkhorn')\npl.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.5" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_stochastic.py b/docs/source/auto_examples/plot_stochastic.py new file mode 100644 index 0000000..b9375d4 --- /dev/null +++ b/docs/source/auto_examples/plot_stochastic.py @@ -0,0 +1,207 @@ +""" +========================== +Stochastic examples +========================== + +This example is designed to show how to use the stochatic optimization +algorithms for descrete and semicontinous measures from the POT library. + +""" + +# 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 +############################################################################# +print("------------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. + +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. + +method = "SAG" +sag_pi = ot.stochastic.solve_semi_dual_entropic(a, b, M, reg, method, + numItermax) +print(sag_pi) + +############################################################################# +# 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. + +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. + +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) + +############################################################################# +# +# Compare the results with the Sinkhorn algorithm +# --------------------------------------------- +# +# Call the Sinkhorn algorithm from POT + +sinkhorn_pi = ot.sinkhorn(a, b, M, reg) +print(sinkhorn_pi) + + +############################################################################## +# PLOT TRANSPORTATION MATRIX +############################################################################## + +############################################################################## +# Plot SAG results +# ---------------- + +pl.figure(4, figsize=(5, 5)) +ot.plot.plot1D_mat(a, b, sag_pi, 'semi-dual : OT matrix SAG') +pl.show() + + +############################################################################## +# Plot ASGD results +# ----------------- + +pl.figure(4, figsize=(5, 5)) +ot.plot.plot1D_mat(a, b, asgd_pi, 'semi-dual : OT matrix ASGD') +pl.show() + + +############################################################################## +# Plot Sinkhorn results +# --------------------- + +pl.figure(4, figsize=(5, 5)) +ot.plot.plot1D_mat(a, b, sinkhorn_pi, 'OT matrix Sinkhorn') +pl.show() + + +############################################################################# +# COMPUTE TRANSPORTATION MATRIX FOR DUAL PROBLEM +############################################################################# +print("------------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. + +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. + +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) + +############################################################################# +# +# Compare the results with the Sinkhorn algorithm +# --------------------------------------------- +# +# Call the Sinkhorn algorithm from POT + +sinkhorn_pi = ot.sinkhorn(a, b, M, reg) +print(sinkhorn_pi) + +############################################################################## +# Plot SGD results +# ----------------- + +pl.figure(4, figsize=(5, 5)) +ot.plot.plot1D_mat(a, b, sgd_dual_pi, 'dual : OT matrix SGD') +pl.show() + + +############################################################################## +# Plot Sinkhorn results +# --------------------- + +pl.figure(4, figsize=(5, 5)) +ot.plot.plot1D_mat(a, b, sinkhorn_pi, 'OT matrix Sinkhorn') +pl.show() diff --git a/docs/source/auto_examples/plot_stochastic.rst b/docs/source/auto_examples/plot_stochastic.rst new file mode 100644 index 0000000..a49bc05 --- /dev/null +++ b/docs/source/auto_examples/plot_stochastic.rst @@ -0,0 +1,475 @@ + + +.. _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 +############################################################################ + + + +.. 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 <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>`_ diff --git a/docs/source/readme.rst b/docs/source/readme.rst index a839231..e7c2bd1 100644 --- a/docs/source/readme.rst +++ b/docs/source/readme.rst @@ -2,7 +2,7 @@ POT: Python Optimal Transport ============================= |PyPI version| |Anaconda Cloud| |Build Status| |Documentation Status| -|Anaconda downloads| |License| +|Downloads| |Anaconda downloads| |License| This open source Python library provide several solvers for optimization problems related to Optimal Transport for signal, image processing and @@ -108,7 +108,7 @@ Dependencies Some sub-modules require additional dependences which are discussed below -- **ot.dr** (Wasserstein dimensionality rediuction) depends on autograd +- **ot.dr** (Wasserstein dimensionality reduction) depends on autograd and pymanopt that can be installed with: :: @@ -374,6 +374,8 @@ Advances in Neural Information Processing Systems (NIPS) 31 :target: https://travis-ci.org/rflamary/POT .. |Documentation Status| image:: https://readthedocs.org/projects/pot/badge/?version=latest :target: http://pot.readthedocs.io/en/latest/?badge=latest +.. |Downloads| image:: https://pepy.tech/badge/pot + :target: https://pepy.tech/project/pot .. |Anaconda downloads| image:: https://anaconda.org/conda-forge/pot/badges/downloads.svg :target: https://anaconda.org/conda-forge/pot .. |License| image:: https://anaconda.org/conda-forge/pot/badges/license.svg diff --git a/examples/plot_barycenter_1D.py b/examples/plot_barycenter_1D.py index 5ed9f3f..6864301 100644 --- a/examples/plot_barycenter_1D.py +++ b/examples/plot_barycenter_1D.py @@ -25,7 +25,7 @@ import ot from mpl_toolkits.mplot3d import Axes3D # noqa from matplotlib.collections import PolyCollection -# +############################################################################## # Generate data # ------------- @@ -48,7 +48,7 @@ n_distributions = A.shape[1] M = ot.utils.dist0(n) M /= M.max() -# +############################################################################## # Plot data # --------- @@ -60,7 +60,7 @@ for i in range(n_distributions): pl.title('Distributions') pl.tight_layout() -# +############################################################################## # Barycenter computation # ---------------------- @@ -90,7 +90,7 @@ pl.legend() pl.title('Barycenters') pl.tight_layout() -# +############################################################################## # Barycentric interpolation # ------------------------- diff --git a/notebooks/plot_OT_1D_smooth.ipynb b/notebooks/plot_OT_1D_smooth.ipynb new file mode 100644 index 0000000..69e71da --- /dev/null +++ b/notebooks/plot_OT_1D_smooth.ipynb @@ -0,0 +1,302 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "# 1D smooth optimal transport\n", + "\n", + "\n", + "This example illustrates the computation of EMD, Sinkhorn and smooth OT plans\n", + "and their visualization.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Author: Remi Flamary <remi.flamary@unice.fr>\n", + "#\n", + "# License: MIT License\n", + "\n", + "import numpy as np\n", + "import matplotlib.pylab as pl\n", + "import ot\n", + "import ot.plot\n", + "from ot.datasets import make_1D_gauss as gauss" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate data\n", + "-------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% parameters\n", + "\n", + "n = 100 # nb bins\n", + "\n", + "# bin positions\n", + "x = np.arange(n, dtype=np.float64)\n", + "\n", + "# Gaussian distributions\n", + "a = gauss(n, m=20, s=5) # m= mean, s= std\n", + "b = gauss(n, m=60, s=10)\n", + "\n", + "# loss matrix\n", + "M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))\n", + "M /= M.max()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot distributions and loss matrix\n", + "----------------------------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 460.8x216 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 360x360 with 3 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#%% plot the distributions\n", + "\n", + "pl.figure(1, figsize=(6.4, 3))\n", + "pl.plot(x, a, 'b', label='Source distribution')\n", + "pl.plot(x, b, 'r', label='Target distribution')\n", + "pl.legend()\n", + "\n", + "#%% plot distributions and loss matrix\n", + "\n", + "pl.figure(2, figsize=(5, 5))\n", + "ot.plot.plot1D_mat(a, b, M, 'Cost matrix M')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Solve EMD\n", + "---------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 360x360 with 3 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#%% EMD\n", + "\n", + "G0 = ot.emd(a, b, M)\n", + "\n", + "pl.figure(3, figsize=(5, 5))\n", + "ot.plot.plot1D_mat(a, b, G0, 'OT matrix G0')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Solve Sinkhorn\n", + "--------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "It. |Err \n", + "-------------------\n", + " 0|7.958844e-02|\n", + " 10|5.921715e-03|\n", + " 20|1.238266e-04|\n", + " 30|2.469780e-06|\n", + " 40|4.919966e-08|\n", + " 50|9.800197e-10|\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 360x360 with 3 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#%% Sinkhorn\n", + "\n", + "lambd = 2e-3\n", + "Gs = ot.sinkhorn(a, b, M, lambd, verbose=True)\n", + "\n", + "pl.figure(4, figsize=(5, 5))\n", + "ot.plot.plot1D_mat(a, b, Gs, 'OT matrix Sinkhorn')\n", + "\n", + "pl.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Solve Smooth OT\n", + "--------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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ilyb/6EepI0lOCVikO9TU+Bi5224L3/1u6mjS2m03n3Lpxht99ucCpgQs0h2uv95HPbv6aujZM3U06f34xz5k5RlnFPTccUrAIl3t3Xe9zfeww+Dzn08dTXbo3x+uuAKefdansS9QSsAiXSkE7/FQVeUzBefDbBedZdIkPyl33nmwaFHqaJJQAhbpSrffDlOmwOWXw447po4muxQVwe9+519OJ5/sX1YFRglYpKssXAhnnw377ee3srkddvBeEQ8+6Mm4wCgBi3SF6mo49ljv/XDLLVBcnDqi7HXWWT4T9Fln+cSkBUQJWKQrfP/78MwzftWbmh4+WlER3HEH9O0LX/pSQU1fpAQs0tnuucfH+j31VK+CZcuGDYM774TXX4dvfKNguqYpAYt0pmefha9/Hfbd1/v8SusdcoiPFXHPPf4LogCUpA5AJG+88YbPAjxyJDzwAFRUpI4o95x/Prz1lo8VMWoUnHZa6oi6lBKwSGd4/XWv4Mz8jP6gQakjyk1mcN113oPk9NP95OXJJ6eOqsuoCUKko2bN8rP4dXXw5JM66dZRJSUwebKPH3zKKX4BS55SAhbpiIce8vZeM3jiCdh119QR5Yfych85buJE75523nlQW5s6qk6nBCzSHrW1fnXb0Uf7xQT/+hd8/OOpo8ovmSR87rlwzTVw5JE+nVMeUQIWaau5c73J4fvf936rTz0FI0akjio/FRd7b5KbbvL3efRouP/+1FF1GiVgkdZat85HNdt1Vx/H9rbb4K67oHfv1JHlv5NOghkz/Ivu//0/bx+ePTt1VB2mBCyyJatWebeo7bbzcWy/8AV49VXv76vRzbrPrrvCtGlw5ZXw9NO+fsIJ/rfIUUrAIs2pqYG//x1OPNGv0rroIthrL7+8+M471eSQSlmZ9xWePRvOOcfbiHfbDQ480Ke7X7EidYRtYqEAh4CTzY0dOzZMnz49dRjp1Nb6hRTPPOO9GR55BD74wJsXvvpV7w41ZkzqKKWpZct8FLWbb4Y33/Q24wMPhAkT/HbMGOjVq8ue3sxmhBDGtvvxSsACBZCAq6q8Olq2DN57zzv6z5sHc+Z44p01C9av932HDoVDD/W2xsMP79IPsHSSEOD55+G+++Cvf/Xpn8CbiHbayXuo7LgjVFb6lYrDhvnEqAMH+t+3nU1JSsDSKcYOHhymT5zY9U/U0v+3zPbG94ew+VJX57e1tQ1LTY0v1dWwcaMvGzb4snYtrFnj/27OiBGw886w++5eLY0b5x9Yte3mtvff93E5Zs70E6ZvvOFftlVVm+9bUgJ9+vjSsyf06OFd4MrLvcmjtNT3KS5uWLbZBq66SglYOsfYsrIwvbumSm8puWW2N77fbNOlqMhvG38Yiov9Q1Ja2vDB6dHDlz59vBmhf39fBg+GIUM88Y4Y4ftKYair818/8+f77dKl/qtoxQr/kl6zxn8FbdjQ8EVeVeVf7DU1DV/4dXU+u/Ujj3Q4AWssCHF77AH53AQhUlTkTQ/DhqWOpJ56QYiIJKIELCKSiNqABQAzWwO8kTqOLRgELE8dxBbkQoyQG3HmQow7hxD6tPfBagOWjDc6cjKhO5jZdMXYOXIhzlyJsSOPVxOEiEgiSsAiIokoAUvGTakDaAXF2HlyIc68j1En4UREElEFLCKSiBKwiEgiSsAFzsyOMLM3zGyOmX0vdTwZZjbSzJ4ws1fN7BUzOyduH2hmj5rZm/F2QBbEWmxmM81sSlzfzsymxff0bjMrSxxffzObbGavm9lrZrZPtr2PZnZe/DvPMrO7zKwiG95HM/udmS01s1mNtjX73pn73xjvS2a2xfFLlYALmJkVA9cDnwV2BY4zs2yZ1rcGOD+EsCswHjgjxvY94PEQwo7A43E9tXOA1xqtXwFcHULYAVgBfDNJVA2uBR4OIewCfAKPNWveRzMbDpwNjA0h7A4UA8eSHe/j74Ejmmxr6b37LLBjXE4Gbtzi0UMIWgp0AfYBHmm0fhFwUeq4Woj1AeAz+NV6w+K2YfgFJCnjGhE/hIcAUwDDr94qae49ThBfP+Bt4gn3Rtuz5n0EhgMLgIH4xWFTgMOz5X0EKoFZW3rvgF8DxzW3X0uLKuDClvmPn7EwbssqZlYJ7AlMA4aEEBbHu5YAQxKFlXENcAFQF9e3AlaGEGrieur3dDtgGXBLbCb5rZn1IovexxDCIuBKYD6wGFgFzCC73sfGWnrv2vx5UgKWrGZmvYF7gXNDCKsb3xe8zEjWj9LMjgaWhhBmpIqhFUqAMcCNIYQ9gXU0aW7IgvdxADAR/7LYBujF5j/7s1JH3zsl4MK2CBjZaH1E3JYVzKwUT753hBD+FDe/Z2bD4v3DgKWp4gP2A/7DzN4B/g9vhrgW6G9mmXFWUr+nC4GFIYRpcX0ynpCz6X08FHg7hLAshFAN/Al/b7PpfWyspfeuzZ8nJeDC9jywYzzbXIaf+Phz4pgAP6MM3Ay8FkK4qtFdfwYmxX9PwtuGkwghXBRCGBFCqMTfu7+HEI4HngC+GHdLHeMSYIGZ7Rw3TQBeJYveR7zpYbyZ9Yx/90yMWfM+NtHSe/dn4ITYG2I8sKpRU0XzUjW8a8mOBTgSmA28BXw/dTyN4tof/2n3EvBiXI7E21gfB94EHgMGpo41xnsQMCX+e3vgX8Ac4B6gPHFsnwSmx/fyfmBAtr2PwKXA68As4A9AeTa8j8BdeLt0Nf5r4pstvXf4Cdjr42fpZbxXx0cev0OXIpvZEfhPrmLgtyGEn7b7YCIiBabdCTj2IZ2Ndw1aiP+cPS6E8GrnhScikr86MiD7p4A5IYS5AGb2f/iZzBYT8KBBg0JlZWUHnlI6auVKn/x15MhNt8+YMWN5CGFwZv0zRV/SKE0ijTxad08L03m3X0cScHN93sY13cnMTsavCmHUqFFM18y7SV1wAVx33eYTIJvZvDQRiRSuLu8FEUK4KYQwNoQwdvDgwVt+gHSp6mooLU0dhYhAxxJwVvchleZVVUFZ0qFhRCSjIwk4a/uQSsvWr4devVJHISLQgTbgEEKNmZ0JPIJ3Q/tdCOGVTotMusTq1dC7d+ooRAQ6OC19COFB4MFOikW6wfvvw1ZbpY4ii1g8sd2B/vAi7aVLkQvMokUwdGjqKEQElIALSm0tvPMOfOxjqSNJyKzJUhSXptubLCJdQAm4gMyaBTU1sPvuqSMREehgG7Dkln/8w28PPDBtHNnEiry6DbWb3eG3IY6z3lIVrLZj6QBVwAXk9tth1103vwxZRNJQBVwgpk6F55/3y5ALmm1ac1hJCx+B4mK/rYsVbqyU69czlTGZ1ea3q0KWj6IKuABUVcFpp8GQIXDCCamjEZEMVcB5LgT4/vfhxRfh/vuhb9/UEWWXzYZjjRWyZSrg4sz2Jm3ATR5ndXWbHq9JRbxZhazKWFAFnNdC8NHPrrzSK+CJE1NHJCKNqQLOU6tWwdlnw223wRlnwP/+b+qIskTTNtq6FirRJhWvlcaPSpM25Pq24cx+tbWbHDfE9cz2UJupgFUZiyrgvHT//d7b4fbb4Yc/9BNvRfpLi2QdVcB55Lnn4Cc/gb/8BfbYwxPx3nunjirLZCpMy/T/3bQDsBXVNbtffeVbnLn1xmHLDK7cdEyJuG41Nb45thHXr1dV+3p9ZRzjyKyrMi4IqotyXG0t3Hcf7Lcf7Lsv/POfcPnlPuOFkq9IdlMFnKNeew3uvhvuuAPmzIHKSm/n/c//1HCTrVJfUTbtzxtrkkzbbX1lm9mvaNPtJV4Jh7JNK+FQXrLJ4TO9JKjx4xbFCjizHjZW+frGjb6eqZSr422mQlZFnFeUgHPI7NmedP/4Rx/XwcwvK77sMvjCF6ClawpEJDvpI5vF1q6Fp5+Gxx6DRx+Fl1/2pLv//n5i7ZhjYNiw1FHmuM0qydg7IVae9VfEZdpsM70b4t4W4vxOTSrf2l7lvl7iFXMojm3C8fmsum6T4xVtiMffUBXXYyX8od/WV8ZVfn+mN4Uq49ymBJxFqqth2jRPuI8/7pcP19T4HG777QfXXANf/CIMH546UhHpDErACS1d6gk3szz3HKxb58XUXnvB+efDoYd68u3RI3W0BaJJ23CoadpvuEmlmekNkWkTbtIvuK7MK+CaHr5fbXmT+0t9vXijH6/4Qz9+6XqvwIvXxop4zYd+u95vw4YNfvth823GqohzgxJwN9m40S8HnjrVk+3UqfD2235fcTGMHg2TJsGECXDQQTBwYNJwRaQbKAF3gbVr4aWXPOHOnOm3L73kg+KANyGMH++XB48b59WuZirOMk0qx1ATey2E4mbvz1z5ZrFttrg07hcr4tpyr4TrSmNFXOHbq/rGtuNMd+M6f1xxlX80S9ZXAFC+xv+DlK30CrdklVe+RWvW++1avw3rY2WcaSuuadqLQhVxNlEC7qD33ts00c6cCW++2fD/fOBA2HNPOOccT7bjxsGIEWljFpHsoATcShs2wKuvek+ExsuSJQ37VFZ6sj3+ePjkJ/3fI0ZoSrG8EDYd26F+DInMbWZ7rDgzVzhZfRtyT398rIjrSjIVsa9Xx19AtT3i88QC2uLDizf4R7Vstd+Wr/BeFhUr/IEVy73iLVkRK+LV6/w4mbbiDbHtWP2Ks4oScBO1tTB37uaJds6chvMvFRU+1sLhhzck2k98Avr3Txu7iOSWgk7AS5dunmhfeQXWexGBmc8gPHo0HHus344eDTvs0NA9VApMplKMk8iF0GR0s1hZFmWupKv2tuOSWHlaLHWLarxttyb2isj0E66JlXBN/9gLolfs1RDHqFhb45Xz6rV+5V3ZB/4fsWKZV9g9l/pxeyzt4/e/75Vv8cq1/jxr4m2mIo79m1URp1EQCXj9ek+sTZPt0qUN+wwe7Mn1pJMaEu1uu+nkmIh0nbxLwB984CfCXnih4Xb27IYv9IoKn5b9qKMaEu3o0T5dj0ibtdA2XJfpFVGTqXxjJRwrzqIP/Zvd6nzgjvUb40cxeIW7IY4xQayAt+rvlevgnt62W2L+fKuqvIP4klVe8S5ZGtuEF3sbca/FZfE2bl/qU6IUf+DHszWxrbhp7wn1J+4WOZuAQ4B339082c6f37DPyJEwZsymzQcf+5iaD0QkO+RMAq6r82aEp57y8RGeegoWL264f6edYJ99fPaHPff0ZdCgdPFKgWmhbbjpjBiWGVMiXsFWsTH2613rFWpp7PdbssGrhLXVvr4sPk3fMn/czgPeA2BU+Qd+RxwTZP52fgXPyyu3AWDOksEArJrvlXLvhV4p937X24x7LPG24JLlXhEXrfbbunWxX7Eq4i6VtQm4uhpmzGhIts88AytW+H3Dh/vVYuPHe4X7iU9Anz5JwxURabOsSsAh+IDit93mQy6uXu3bd9rJh1s84AAffrGyUn1rJcs1rYirYuWYaSuObcKZirh0nbfBFq+OvRdWxSvfVnsb7trVXsHOXuel7rpRvr10iB9vfO85ABzQczYAH/b3j/br2/j+T2+/EwDT3t0WgHffiZXwfH+ePgu90u652LeXLFsDqCLualtMwGY2ErgNGIKPwndTCOFaMxsI3A1UAu8AXw4hrGhPEHPnwh/+4Il37lzveXDMMfC5z/nQi0OHtueoIiLZrTUVcA1wfgjhBTPrA8wws0eBE4HHQwg/NbPvAd8DLmxrAL/4BXznO17RTpgAl1zi1a66f0leyfSWaDI2Q2bsCIvj/Vq8cq1inVeipbF3Q8UH3ma75gP/yC5937vtTN7Oe1HMH+Vtv0dv9W8AxlUsAGCP3gsBOLznXAD+PWgrAB7edjQA/1i4AwCL3/ariHq/48/TZ4H3oui52I+fqYgtVsT1vSYyo7GpH3G7bDEBhxAWA4vjv9eY2WvAcGAicFDc7VbgSdqYgG+6yZPvMcfA1Vd7rwURkULRpjZgM6sE9gSmAUNicgZYgjdRtNrbb8Opp8LYsXDnnT7ouEjBqK+IN70SzTJXzMXKMjPKWa+VXomWv+/9eHvFK95WL/Htzy3eBYBXtvf2ukNGeFvw5/q/CMCe5X78I3r6cceVPwXAtH4vAzBlm08C8OQor4iXzPXKu887mTZir4h7vOvrJcu9Ig71/YgzbcTNXFmnarhFrZ4V2cx6A/dlzgyZAAAPx0lEQVQC54YQVje+L4QQaJilpenjTjaz6WY2fdmyZfXbR4yAgw/2/rsPPti+4EVEcpmFVnw7mVkpMAV4JIRwVdz2BnBQCGGxmQ0Dngwh7PxRxxk7dmyYPn16/fqaNfCZz8Dzz/vANpMmwcSJfrWadC8zmxFCGJtZ/0zRl1S2pJDp3mNx9uVS/5Fq8Sei9YxTo/TzCrVmsN+uH+YV6pqRsf/wtt4W27tyFQCfHuG9JA7t9woAu5X5dfg949O9W+vHf3b9jgA8uvzjAMya5/2Jy97x4/ee5/v3WeSVesUSr4CLVsSKeG1mFLbMWBNVeTMW8aN193R636stVsDmc63cDLyWSb7Rn4FJ8d+TgAfa+uR9+sDDD8OFF/rYDMce6z0eTj7Z+/3W1W35GCIiuWqLFbCZ7Q88DbxMZqIsuBhvB/4jMAqYh3dD++CjjtW0Am6sthaefBJuvRXuvdcH0BkwwLuhHXig9wEeMwZKS9vy8qS1VAFnqRYq4qJyr0gzFXGIFXH14Di2xDb+M3LNCH/culH+0e0VK+K9h3oviX37eWW8Y7kPbF0cP+ILqr23xLNrvE34uSXbAbB8vveW6DXf4+gzPx53sfcPLlvqFbCtjBXxunWbz1uXoxVxV1TArekF8U+gpSee0FmBFBd7N7QJE+CGG+CBB+CJJ/xKuL/8xffp2dMvN85ckPGpT6m7mojkrqy6Ei6jd2+fVeL44319yRK/Qi4zDsSll/qXpxnsvLOP+zBmTMMYEJrQUvJGC1fU1WZ6S8T+w0WxX27ZKq88S5d5RdxrUayI53vFvHbuAACeGtE/3nqF+7GhfoJ8t37esWl4+UoARlb4j9q6IV5JzyrzSnd+L/+QVffx427sF9uI+3pK6RFHYSv+oLx+xDVijKjvcL2sTMBNDR0KX/yiLwArV8Kzz/rJu5kzPTnfdVfD/ttu25CQx4zxWSu22UaXL4tIdsmJBNxU//5w5JG+ZCxf7sk4s7zwAtx/f8OX6oABDUNS7rGH3+6+uwbxkRzTyorY4tgNJSu9x2jfpV4J91rotxvmeRvxuiHehjxvmI8R8caw4QD0HOxV69Z9/cq3fmXeq6FnqVfAW23l29+PRc2aUq+Aa3qUxFtvG+zZq5TS9/2+ohXxKrq1Teary/G24Y7IyQTcnEGDvEvbZz7TsG3NGvj3v315+WWfGv6223x7RmXlpgOzjx7tg//oZJ/khBYScmawHIuD51j8+V8cT471iQO391zotxsHeSLeMNhTwvqt+wGwaJBf+PHOwDjVUi+/0KK4JF5CXeTPX9PX7/+wLjObqDdZ1JaV06NHnDapLHMC0T9ctiqmnw89uVOAA/3kTQJuTp8+3oti//0btoUA8+ZtPj3RQw/VT2hLWRnsssvmiVkzHItIZ8rrBNwcM696Kyt9tLWMjRvhjTe8Ss4k5X/8A+64o2Gf/v292aJpU0bfvt39KkRasKWKOJ4As3jpcNEqb6LoudQH4ano500UfQZ4RbxxK69WNwz0KnbjAE8Z1bHpLlTEqZcys8zEp49zjrKxvxEsk2b8mGWlvnNJnJqmKE4wGtbFpglr0m0tTu9EXW1r34WcUXAJuCXl5Z5Q99hj0+0rVsCsWZtWy3fc0TBWMfgsyZnp6TO3Q4eqWhaRj6YEvAUDBni/4wMOaNgWAixY4NXyiy/68sILMHlywz5bb92QkD/5SdhrL0/USsrSrbY0VVKTk3YWT5CUve/VaumSON19X1+v7uelbVUc8H1jH2/rrfHdqC3b9D+41UJdHGiruncsk0O8rDrGVlzkj7GieGFubD8mxkas3utbgvOobVgJuB3MYNQoX44+umH7qlWelGfO9KQ8cyZcdVX95AcMHAjjxvkyfrxfSDJgQJrXICLpKQF3on79Nq+Wq6rg1Vdh+nSYNg2mTvXxLzJf3jvt5Ml43DjYd19vAilq9Rh1Im3UtCLOFJOZijhzJjoOpmNrM4PteNVa0cMr4fLefturt1fENb29Hbemp1e5NRX+n7iuxAiZwrY2DsFZ7BVvbUUcaKgmdlOLIVpmEJjiTCXsvSMyvSQy0zrlQ7c1JeAuVlbW0AzxrW/5ttWrPSFPnepJ+eGHvXsceHe6gw+GQw/1y7K3317NFiL5Sgk4gb594ZBDfIGGrnFPPQWPP+7LPff4fZWVDWNkHHGEmiykizSZMqm+ytys94T3J7Y1XvFmBgUqr/DbsngbenjFXNujlLryTBeJTRVVx0o3Vhgh9o6wsthPuOkD6jbdvz70HK6ElYCzQOOucSec4P+P3nijIRnfey/cfLNfHHLYYfDlL/u4yf36pY5cRDpCCTgLmfmFILvsAmec4cXI8897Iv7jH+Gvf/WmjSOO8GR8zDEaxF46WUu9J+IUSpkr7OrbikuaDBwfq9jSsjJCRewGUeIVboj9f+sbfTOFbdMKN+5vdfGy1DiBaX11HmPM1MP1lXDT15DFdLonBxQX+4m6n/8c3nkHnnvOE/OMGfC1r/ngQz/+Mbz/fupIRaQtWjUlUWf5qAHZpe3q6nzM5F/8wi+l7tEDvvEN+O53PSm3hQZkl3ZpOmB87NNLrHKtpKR+EHkyVXLJpuv1x8g8trZJP99YGYdM1R2vjAsbNx3Wsn4MiYxO7i+cZEoiyV5FRX5y7sEHG6Z0uukm2HVXuOaa+l9qIpKllIDzxO67w+9+B2++CQcdBOed5/2KX3kldWSS10Lwpa4W6moJtXGpqiJUVVG34UPq1m3wZc1aX1av8WXVaupWrSasWePL2nW+bNjgy8aNvlRXE6qrvaKorY1T3TdMGGlmvhRtujTaIWv7cioB55ltt4UpU+DOO2HuXE/CzzyTOioRaY56QeQhMzjuOB+G89BDvevan//szRUiXappe2uore9BUb+pSXtx/Xpxk3qwfmwI2/TYmfVM23BLbbzW5Hgh+9rkVAHnsZEj/eKO7bf36ZwWLUodkYg0pgSc54YMgfvu84GlTjopJ7pGSr7JtBO31F5cU02oqaauatMl044cqqp9qa7xng6xLTjU1hFq67xXRF1u/sdWAi4AO+wAl1/uXdWeeCJ1NCKSoQRcIE491YfDvOGG1JGIRC1Uxi1VyE0r5fr7M0td2GRp2lsiGykBF4iKCpg0CR54AOLMLyKSmBJwATnsMJ94dOrU1JGItEKmMm6j+n7AVgRWtHm/4CyiBFxA9tnHb//1r7RxiIhTP+AC0q+f94p4663UkYi0QTN9iz9y97qPXs8mqoALTGUlzJ+fOgoRASXggjNokIatFMkWSsAFZsAAWLEidRQiAm1IwGZWbGYzzWxKXN/OzKaZ2Rwzu9vMyrouTOksPXvChg2poxARaFsFfA7wWqP1K4CrQwg7ACuAb3ZmYNI1KiqUgEWyRasSsJmNAI4CfhvXDTgEmBx3uRX4fFcEKJ2rtBSqq1NHISLQ+gr4GuAC6qfPYytgZQghMwfIQmB4cw80s5PNbLqZTV+2bFmHgpWOKynxizFEJL0tJmAzOxpYGkKY0Z4nCCHcFEIYG0IYO3jw4PYcQjpRUVH9MKoiklhrLsTYD/gPMzsSqAD6AtcC/c2sJFbBIwCNNpsDlIBFsscWK+AQwkUhhBEhhErgWODvIYTjgSeAL8bdJgEPdFmU0mnMNCawSLboSD/gC4Fvm9kcvE345s4JSbqSErBI9mjTWBAhhCeBJ+O/5wKf6vyQpCtl6eSwIgVJV8KJiCSiBFxgVAGLZA8lYBGRRJSARUQSUQIWEUlECVhEJBElYBGRRJSARUQSUQIWEUlECVhEJBElYBGRRJSARUQSUQIWEUlECVhEJBElYBGRRJSARUQSUQIWEUlECVhEJBElYBGRRJSARUQSUQIWEUlECVhEJBElYBGRRJSARUQSUQIWEUlECVhEJBElYBGRRJSARUQSUQIWEUlECVhEJBElYBGRRFqVgM2sv5lNNrPXzew1M9vHzAaa2aNm9ma8HdDVwYqI5JPWVsDXAg+HEHYBPgG8BnwPeDyEsCPweFwXEZFW2mICNrN+wIHAzQAhhKoQwkpgInBr3O1W4PNdFaSISD5qTQW8HbAMuMXMZprZb82sFzAkhLA47rMEGNLcg83sZDObbmbTly1b1jlRi4jkgdYk4BJgDHBjCGFPYB1NmhtCCAEIzT04hHBTCGFsCGHs4MGDOxqviEjeaE0CXggsDCFMi+uT8YT8npkNA4i3S7smRBGR/LTFBBxCWAIsMLOd46YJwKvAn4FJcdsk4IEuiVBEJE+VtHK/s4A7zKwMmAv8J568/2hm3wTmAV/umhBFRPJTqxJwCOFFYGwzd03o3HBERAqHroQTEUlECVhEJBElYBGRRJSARUQSUQIWEUlECVhEJBElYBGRRJSARUQSUQIWEUlECVhEJBElYBGRRJSARUQSUQIWEUlECVhEJBElYBGRRJSARUQSUQIWEUlECVhEJBElYBGRRJSARUQSUQIWEUlECVhEJBElYBGRRJSARUQSUQIWEUlECVhEJBElYBGRRJSARUQSUQIWEUlECVhEJJFWJWAzO8/MXjGzWWZ2l5lVmNl2ZjbNzOaY2d1mVtbVwYqI5JMtJmAzGw6cDYwNIewOFAPHAlcAV4cQdgBWAN/sykBFRPJNa5sgSoAeZlYC9AQWA4cAk+P9twKf7/zwRETy1xYTcAhhEXAlMB9PvKuAGcDKEEJN3G0hMLy5x5vZyWY23cymL1u2rHOiFhHJA61pghgATAS2A7YBegFHtPYJQgg3hRDGhhDGDh48uN2Biojkm9Y0QRwKvB1CWBZCqAb+BOwH9I9NEgAjgEVdFKOISF5qTQKeD4w3s55mZsAE4FXgCeCLcZ9JwANdE6KISH5qTRvwNPxk2wvAy/ExNwEXAt82sznAVsDNXRiniEjeKdnyLhBC+BHwoyab5wKf6vSIREQKhK6EExFJRAlYRCQRJWARkUSUgEVEElECFhFJRAlYRCQRJWARkUSUgEVEElECFhFJRAlYRCQRJWARkUSUgEVEElECFhFJRAlYRCQRJWARkUSUgEWkMJj5kkWUgEVEEmnVjBgiIjkvhNQRbEYVsIhIIkrAIiKJKAGLiCSiBCwikogSsIhIIkrAIiKJKAGLiCSiBCwikogSsIhIIkrAIlIYiop9ySJKwCIiiWgsCBEpDHW1qSPYjCpgEZFElIBFRBJRAi4w48fDOeekjkJEACx04xiZZrYMmNdtTyhtsW0IYXDqIEQKSbcmYBERaaAmCBGRRJSARUQSUQIWEUlECVhEJBElYBGRRJSARUQSUQIWEUlECVhEJBElYBGRRJSARUQSUQIWEUlECVhEJBElYBGRRJSARUQSUQIWEUlECVhEJBElYBGRRJSARUQSUQIWEUlECVhEJBElYBGRRJSARUQS+f/Js7GEh8ojHQAAAABJRU5ErkJggg==\n", + "text/plain": [ + "<Figure size 360x360 with 3 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 360x360 with 3 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#%% Smooth OT with KL regularization\n", + "\n", + "lambd = 2e-3\n", + "Gsm = ot.smooth.smooth_ot_dual(a, b, M, lambd, reg_type='kl')\n", + "\n", + "pl.figure(5, figsize=(5, 5))\n", + "ot.plot.plot1D_mat(a, b, Gsm, 'OT matrix Smooth OT KL reg.')\n", + "\n", + "pl.show()\n", + "\n", + "\n", + "#%% Smooth OT with KL regularization\n", + "\n", + "lambd = 1e-1\n", + "Gsm = ot.smooth.smooth_ot_dual(a, b, M, lambd, reg_type='l2')\n", + "\n", + "pl.figure(6, figsize=(5, 5))\n", + "ot.plot.plot1D_mat(a, b, Gsm, 'OT matrix Smooth OT l2 reg.')\n", + "\n", + "pl.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.5" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/notebooks/plot_barycenter_1D.ipynb b/notebooks/plot_barycenter_1D.ipynb index 4a0956b..bd73a99 100644 --- a/notebooks/plot_barycenter_1D.ipynb +++ b/notebooks/plot_barycenter_1D.ipynb @@ -36,48 +36,7 @@ "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "<Figure size 460.8x216 with 1 Axes>" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "<Figure size 432x288 with 2 Axes>" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "<Figure size 432x288 with 1 Axes>" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "<Figure size 432x288 with 1 Axes>" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "# Author: Remi Flamary <remi.flamary@unice.fr>\n", "#\n", @@ -88,12 +47,26 @@ "import ot\n", "# necessary for 3d plot even if not used\n", "from mpl_toolkits.mplot3d import Axes3D # noqa\n", - "from matplotlib.collections import PolyCollection\n", - "\n", - "#\n", - "# Generate data\n", - "# -------------\n", - "\n", + "from matplotlib.collections import PolyCollection" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate data\n", + "-------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ "#%% parameters\n", "\n", "n = 100 # nb bins\n", @@ -111,24 +84,74 @@ "\n", "# loss matrix + normalization\n", "M = ot.utils.dist0(n)\n", - "M /= M.max()\n", - "\n", - "#\n", - "# Plot data\n", - "# ---------\n", - "\n", + "M /= M.max()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot data\n", + "---------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 460.8x216 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ "#%% plot the distributions\n", "\n", "pl.figure(1, figsize=(6.4, 3))\n", "for i in range(n_distributions):\n", " pl.plot(x, A[:, i])\n", "pl.title('Distributions')\n", - "pl.tight_layout()\n", - "\n", - "#\n", - "# Barycenter computation\n", - "# ----------------------\n", - "\n", + "pl.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Barycenter computation\n", + "----------------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 2 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ "#%% barycenter computation\n", "\n", "alpha = 0.2 # 0<=alpha<=1\n", @@ -153,12 +176,47 @@ "pl.plot(x, bary_wass, 'g', label='Wasserstein')\n", "pl.legend()\n", "pl.title('Barycenters')\n", - "pl.tight_layout()\n", - "\n", - "#\n", - "# Barycentric interpolation\n", - "# -------------------------\n", - "\n", + "pl.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Barycentric interpolation\n", + "-------------------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ "#%% barycenter interpolation\n", "\n", "n_alpha = 11\n", diff --git a/notebooks/plot_convolutional_barycenter.ipynb b/notebooks/plot_convolutional_barycenter.ipynb new file mode 100644 index 0000000..d0df486 --- /dev/null +++ b/notebooks/plot_convolutional_barycenter.ipynb @@ -0,0 +1,176 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "# Convolutional Wasserstein Barycenter example\n", + "\n", + "\n", + "This example is designed to illustrate how the Convolutional Wasserstein Barycenter\n", + "function of POT works.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Author: Nicolas Courty <ncourty@irisa.fr>\n", + "#\n", + "# License: MIT License\n", + "\n", + "\n", + "import numpy as np\n", + "import pylab as pl\n", + "import ot" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Data preparation\n", + "----------------\n", + "\n", + "The four distributions are constructed from 4 simple images\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "f1 = 1 - pl.imread('../data/redcross.png')[:, :, 2]\n", + "f2 = 1 - pl.imread('../data/duck.png')[:, :, 2]\n", + "f3 = 1 - pl.imread('../data/heart.png')[:, :, 2]\n", + "f4 = 1 - pl.imread('../data/tooth.png')[:, :, 2]\n", + "\n", + "A = []\n", + "f1 = f1 / np.sum(f1)\n", + "f2 = f2 / np.sum(f2)\n", + "f3 = f3 / np.sum(f3)\n", + "f4 = f4 / np.sum(f4)\n", + "A.append(f1)\n", + "A.append(f2)\n", + "A.append(f3)\n", + "A.append(f4)\n", + "A = np.array(A)\n", + "\n", + "nb_images = 5\n", + "\n", + "# those are the four corners coordinates that will be interpolated by bilinear\n", + "# interpolation\n", + "v1 = np.array((1, 0, 0, 0))\n", + "v2 = np.array((0, 1, 0, 0))\n", + "v3 = np.array((0, 0, 1, 0))\n", + "v4 = np.array((0, 0, 0, 1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Barycenter computation and visualization\n", + "----------------------------------------\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 720x720 with 25 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pl.figure(figsize=(10, 10))\n", + "pl.title('Convolutional Wasserstein Barycenters in POT')\n", + "cm = 'Blues'\n", + "# regularization parameter\n", + "reg = 0.004\n", + "for i in range(nb_images):\n", + " for j in range(nb_images):\n", + " pl.subplot(nb_images, nb_images, i * nb_images + j + 1)\n", + " tx = float(i) / (nb_images - 1)\n", + " ty = float(j) / (nb_images - 1)\n", + "\n", + " # weights are constructed by bilinear interpolation\n", + " tmp1 = (1 - tx) * v1 + tx * v2\n", + " tmp2 = (1 - tx) * v3 + tx * v4\n", + " weights = (1 - ty) * tmp1 + ty * tmp2\n", + "\n", + " if i == 0 and j == 0:\n", + " pl.imshow(f1, cmap=cm)\n", + " pl.axis('off')\n", + " elif i == 0 and j == (nb_images - 1):\n", + " pl.imshow(f3, cmap=cm)\n", + " pl.axis('off')\n", + " elif i == (nb_images - 1) and j == 0:\n", + " pl.imshow(f2, cmap=cm)\n", + " pl.axis('off')\n", + " elif i == (nb_images - 1) and j == (nb_images - 1):\n", + " pl.imshow(f4, cmap=cm)\n", + " pl.axis('off')\n", + " else:\n", + " # call to barycenter computation\n", + " pl.imshow(ot.bregman.convolutional_barycenter2d(A, reg, weights), cmap=cm)\n", + " pl.axis('off')\n", + "pl.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.5" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/notebooks/plot_free_support_barycenter.ipynb b/notebooks/plot_free_support_barycenter.ipynb new file mode 100644 index 0000000..b8df589 --- /dev/null +++ b/notebooks/plot_free_support_barycenter.ipynb @@ -0,0 +1,169 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "# 2D free support Wasserstein barycenters of distributions\n", + "\n", + "\n", + "Illustration of 2D Wasserstein barycenters if discributions that are weighted\n", + "sum of diracs.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Author: Vivien Seguy <vivien.seguy@iip.ist.i.kyoto-u.ac.jp>\n", + "#\n", + "# License: MIT License\n", + "\n", + "import numpy as np\n", + "import matplotlib.pylab as pl\n", + "import ot" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate data\n", + " -------------\n", + "%% parameters and data generation\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "N = 3\n", + "d = 2\n", + "measures_locations = []\n", + "measures_weights = []\n", + "\n", + "for i in range(N):\n", + "\n", + " n_i = np.random.randint(low=1, high=20) # nb samples\n", + "\n", + " mu_i = np.random.normal(0., 4., (d,)) # Gaussian mean\n", + "\n", + " A_i = np.random.rand(d, d)\n", + " cov_i = np.dot(A_i, A_i.transpose()) # Gaussian covariance matrix\n", + "\n", + " x_i = ot.datasets.make_2D_samples_gauss(n_i, mu_i, cov_i) # Dirac locations\n", + " b_i = np.random.uniform(0., 1., (n_i,))\n", + " b_i = b_i / np.sum(b_i) # Dirac weights\n", + "\n", + " measures_locations.append(x_i)\n", + " measures_weights.append(b_i)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Compute free support barycenter\n", + "-------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "k = 10 # number of Diracs of the barycenter\n", + "X_init = np.random.normal(0., 1., (k, d)) # initial Dirac locations\n", + "b = np.ones((k,)) / k # weights of the barycenter (it will not be optimized, only the locations are optimized)\n", + "\n", + "X = ot.lp.free_support_barycenter(measures_locations, measures_weights, X_init, b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot data\n", + "---------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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cB/OKQh5e2Z8T3ct1KVUj7N0AOfsq/jxnIWyomtnhmtij6Medh8k+FjxZGgyfbdgTlRgapCZid4b2T6NRnaSoxKBUjZKzByyVGMUuyoXV0yMfjw+a2KNoQ9YRXK7gB6dzC538tOtwVGJo3SCVFifUCtouNcnKyNNbRSUGpWqU5HrlL1QdqvxDkY3FD03sUSQi5Sp3+mOJ4pSou89rT0qCNcC2oW5yAud0bBK1GJSqMZr1AFsly+7WqZrJCZrYo+i0VieElNdTk6z0blM/anGcn96UGwe2IyXBWm5KbbLNQv3URGaOPwObTnVUKjiL1V2CNyH4N+FSEmtD7+ujE1MZ+pccRZ2a1aV1g9Sg7RKtVs4+tXFUY7ll8Cm8c/3pDOnUhOQEC1YRTqybzB3ntueLuwaGFKdSyuOMm6DDnyqQ3MVdk739+VENq3hreoJSdG38/SiXTV1GXpHveeTJCRZeHd2Ls04pffGRAruTvCIndZJtetKQUrHIGPjpXfjwJiBYHhW4+QdoeEpYm9QTlGJEp2Z1eX9CX26f9SM7D+ZjjMEAVotQPzWRf13Wlb7t/rhi+bdb9vPCV1v4IfMQVs8Y/QVdmnLToHac3LhO9b0QpVRpIoC4h2ZcjsBtE1Jgz9qwE3uoNLFXgU7N6rLwjgGszzrC6h2HcLkMnZun0av1Ce4DrB7Pf7GFl77+tfgsUW9Vl4/W/M6C9Xt4dXQvzjyloc9tKKWq0L5NsHY2bJwXPKmD+8SkQ9ujH5eHJvYqlN48jfTmaT6XfbM5u1RSL8lpDPl2J+PfWsniiYN0vrlS1SXvIMwaBVmrwVlUukZMQAbE/8y0SNPB2xjx3BdbAtZzAXchMT3tX6lqYs+HaefDrh/AkV+BpO7R+NToxOWDJvYYkFPoYM3O4CcoFTpcvL9qVxVEpJQqZ827cGSHu6deYQL1qu4EwHCvefpvEflZRNaKyFwRqRepwI4nOQUObNbQTlDKLQxhPE8pFXnLnqt8ES+LDeq3i2w8gTYX5vM/B9KNMV2BzcCk8EM6/tSrlYAzhNIDAA1q65WOlKpyxsDhMA5+tu4Ltqr72w0rsRtjFhpjvF3I74AW4Yd0/ElOsDL41MZBL7RSK9HKmL5tqiQmpVRZlS37IfCnJyIaSTCRHGO/BvjU30IRGS8iK0VkZXZ2dgQ3WzPcMvgUkgJcTUmAlEQrI7qHfxUWpVQFiUDT7pV5IpzUHxp3jHhIgQRN7CKySETW+/gZXqLNA4ADeMffeowxrxhjehljejVq1Mhfs+NW52ZpPH/laaQkWEkoM96ekmClfmois2/oQ2qSzlBVqlqceTskVKD0hjUJ6reFy9+MWkj+BM0SxphzAi0XkbHAMGCwqY76BDXIuZ2a8MVdA5ixfDsfrskir9BBw9pJjOnbhktOa06d5ITqDlGp49epF0LbWfDrF74viedlTYLEVDj9BuhzEyRV/RnjYdWKEZHzgaeBAcaYkMdXjqdaMUqpGuTAVnipj/8pj9Yk6DQcLp7qLjUQYaHWigl3jP0FoA7wuYisEZGpYa5PKaVi15ePBS4h4CyETR/BgV+rLiYfwhqwNcacHKlAlFIqpuUfgl/mB796kssB3/0HLpxSNXH5oGeeKqVUKA5sA2sIc9FdDvh9dfTjCUATu1JKBeNyuWvE2HNDa5+bDYXHohtTAJrYlVIqkJxsmNoXvvwbuEIs/HVsL0w9C3L3Rzc2PzSxK6WUP047vDkU9m+FohB76wDGAUd2wXv/F73YAtDErpRS/vwyH45mgcte8ee67LB3PexZF/m4gtDErpRS/ix/qWI99bIcRbDu/cjFEyJN7Eop5c/hMC9sY5yQsy8ysVSAJnallPInITm851sSIK3qC/fFTUWpAruTRZv2svNgPikJFgad2pjWDSpQkEcppSqq8yWw7Hn3GaWVYbFCtysjG1MIYj6xG2N4dck2nl20BcSd4G0WC//49Gd6tKrHc1f2oHGdMP+rKqWUL72vheUvVu651iRocxY0qLorJ3nF/FDMUws3M+XzLeQWOcktdOJ0ua/9WehwsTLzEBc+/y0HcytzDUKllAqibjMY8R8qnCoTUqFJZ7j8jaiEFUxMJ/btB3J5dck28u2+TwpwuAwHc4p4+vNfqjgypdRxI/1iaNIp9PYntIOLnoNrF1ZLyV6I8cT+5rJMXEHKCttdhjmrssgvCvGMMKVUUNOnT2fWrFnVHUbsaDcotDox1iS4dgF0uQys1Xf9hJhO7N9tO4DdGbxevNUC2/bnVEFEStV8OTk53HLLLUyYMIGCggAXlDie9L4OJFi6FGg7EGo3roKAAovpxB76NUAqe5FZpVRZzz//PE6nE7vdzssvv1zd4cSGE9pAz3GQUMt/m8RUGPJYlYUUSEwn9t5t6mOzBE/aDpeLkxrq1EelwpWTk8M//vEP8vLyyM3N5eGHH9Zeu9eQxyFjvHu4xZbyx+OJtaFucxj3KTQ8pfriKyGmE/u4fm2wBknsNoswontzaiXG/MxNpWKSw/HHFYG8vXUv7bWXYLHAuY/AXT/D4IfgtNFw+l/girfhjg3QtGt1R1gsrGueVlZFrnn66Mcbeff7HT5nxlgtwgm1Eph/21k6l12pSnj66ad5//33Wbp0Kbm5uTRr1oxjx0rXEa9Xrx67d+8mOVn/xqpblVzzVEQeFZG1nuudLhSRZuGsz5cHL+jIhAFtSUmwUivRfXFYm0VITrCQ3qwu/7vlTE3qSlVCbm4ujzzyCKtXr+brr78u11v30l57/Amrxy4idY0xRz23bwU6GWMmBHteRXrsXrmFDuav283Og3mkJNoY3LEx7ZtUzxxRpWqCJ554gr/97W/k5eXRrVs3tm3bVq637qW99tgQao893ItZHy1xNxWI2rhOapKNy3u1jNbqlTqu5Obm8vjjj5OXlwfAxo0bsVj8f4H39tpvu+22qgpRhSHsg6ci8piI7ARGAg+FH5JSKtpeeOGFUgdN7XY7hYX+C13pDJn4EnQoRkQWASf6WPSAMWZeiXaTgGRjzF/9rGc8MB6gVatWPbdv317poJVSlec9SHr06NFyy1JTU7HZfH+RP3bsGG+++SZXX311tENUfkRsKMYYc06I23wHmA/4TOzGmFeAV8A9xh7iOpVSEVa2t15S8+bNee211xDxPc24e/fu0QxNRUhYY+wicooxZovn7nDg5/BDUkpF0v79+3niiSf417/+RV5eXqmx9bKysrJwOBwMGjSoiqNUkRTuWT3/FJEOgAvYDgSdEaOUqlqPP/44U6ZMYcCAAWzYsMFvbx3cwzR33303K1eu9NtrP+447bDpI1j6HBzYAmKF1n2h763u3zG4n2L+BCWlVOVlZ2fTunVr8vPzOeWUU9izZ4/fKY1eycnJzJ8/X3vtAIXHYPqFkL0Z7CUvai2QkAJd/wzDnqmy5F4l0x2VUrHtH//4B97O265du7BYLNSuXTvo85YsWaKJHWD2WNi70cel8QzY82DtbDjhJDjz9uqIzi9N7ErVUNnZ2UydOrV4imJ+fj4dOnRg06ZNOswSiv1bYPu3ga93as+Db5+GPjdVa/31smK6CJhSqvJK9ta9srKy+OSTT6opojiz5l1w+T8eUczlgm2Lox9PBWhiV6oG+OWXX1i2bFnx/bK9da+cnBzuvvvucglf+XBkV2iJ3bggd1/046kATexK1QCjRo1ixIgRFBW5L+zuq7fupb32ENVuREgp0mKB5HpRD6ciNLErFee+/vprNm3aRF5eHm+++abf3rqX9tpD1OXPkJAUvJ3L6b4kXgzRxK5UnJs4cSK5ubnk5uby4IMP8ve//z1o0tZeewiadYdGp4IlwBwTWwr0vhYSA1wyrxroPHal4tj//vc/rrjiCvLz8wF3rZeCggKSk5P91nwBKCgooFu3bnz//fdVFWp8OrYXXj8HcvaBo8w3oIRa7hOUrpxZZTNidB67UseBsWPHFid1cJ85mpaWxvTp00lICJxsmjWL+HVxap46TWDCUvjhdfjuJcg7ABho2ME9d73L5WCxVneU5WhiVypOzZw5k4MHD5Z73OFwsHfvXsaPH18NUdVAyXXhrDvcP/Z8d0kBW2J1RxWQDsUoFacaNGjgM7EDNGrUiF27dpGYGNsJSFVMlVzzVClVPfz11r28M2TU8alG9tgdThdZh/NxugzN6qWQnBB7Y2BKhSNQb91Le+01z3F58DSvyMHUxb8yY9l2ipwuBHAZuOS05tw2+BQa19UL8ar4N2fOnIBJ3Xvt0oMHD/L2229zzTXXVFVoKkbUmMSeU+jg0peWkXkgl0KHq9SyWT/s5NP1e5h3Uz9a1o+t+aZKeb399tts27aNhx4KfOngd999F4vFgsvlKrcsJSWF++67r3iqY48ePaISq4ptNSax3//BOn7bn0ORs/zQksNlOJxXxLg3f+DzO/prZTsVcwoKCrj11lvJy8tj/PjxnHiir8sMw/bt2/n00099JnVw99YbNGjATTfdFM1wVYyrEQdPD+UWsWDDHp9J3ctlIOtQPj/uPFyFkSkVmldeeYWioiKMMTz66KN+202ePBm73e53eW5uLg899BCFhQFKzaoar0Yk9m+2ZJNgCd4LL7A7+XTd7iqISKnQFRQU8PDDD5Obm0tRURHTpk1jz5495dpt376dd955J+Cl7QCOHj3Ka6+9Fq1wVRyoEUMx+UVOXCFM7jHAsYIQynAqVYW8vXUvl8vFo48+yosvvliqnTGGq666CqfTGXSdelbp8S0i0x1F5C7gSaCRMWZ/sPaRnu74zeZs/vLOKnILA3/gk2wWbj+nPX8Z2C5i21YqHAUFBTRr1oxDhw6Vejw5OZnffvvN71i7Oj5V2QlKItISOA/YEe66KqtvuwYkWIO/FANcelrz6AekjhvGGD799NNKl8At21v38vbalaqMSIyxTwHuwZ03q4XNamHieR1ICXAiUnKChYt7NNe57CqiPvvsM4YOHcrChQsr/NySY+tlBRprV1XIGHAUun/HkbASu4gMB7KMMT+F0Ha8iKwUkZXZ2dnhbNankWe0ZsKAtiTZLNhKHEi1CKQkWBl0amP+PiI94ttVxy9jDHfddRdApS5c4a+37qW99mq0axXMvAoebQiPnQiPN4OP74SDv1V3ZCEJOsYuIosAXwN9DwD3A+cZY46ISCbQqzrG2Ev6bX8ubyz9jW+37MdpDOnN07j+rLZ0a5Gm89dVRC1YsIDLLruM3NxcUlNTmTNnDkOGDAnpuf7G1svSsfZqsOJV+Hwy2AsoNRBhSQBrIoz8L7TpVy2hhTrGXumDpyLSBfgCyPM81AL4HcgwxgT8/qjVHVW8M8aQnp7Oxo0bix9LT09n7dq1IXUg5syZw+WXX05qamrAdvn5+Tz++OPcc889YcesQrB9Obx9sbs8rz+JteHWNZ5rolatqNeKMcasAxqX2GAmIfbYlYp3n332Gdu3by/12G+//cbChQtD6rWPGDGCzZs3h7Stli1bVipGVQmLnwic1AFcDlg9HfrfXTUxVULEqjvGylCMUtHmq7fuVZFeu4ox9nz4Rwt34g6mXmu4fW30YyqjyuuxG2PaaG9dHQ989da9vL12FYcKjwW+cHVJBUeiG0uYakRJAaWqincmjK8piuCu1VKZGTIqBiTVBRP8rF4AajWIbixh0sSuVAUE6q17aa89TiUkwynnAUGG0RJqQe9rqySkytLErlQF3H333X576165ublMnDixiiJSEdV/ojvBB2JNhO4jqyaeSqoRRcCUqipXXHEFu3e7K4QeOnSI//73v6WKclmtVoYPH64XuIhXzXrA8JfgwxvdB1FdJUok25LBlgRjPoKUetUXYwg0sStVAZMnTy6+ffHFF5db7nK5yM7O5sEHH6zKsFQkpV8CTbvB8hdhwwdgz4OU+tDrWug1DlIbVneEQdXIi1krFW0///wzPXr0oKCgoNyyWrVq8eWXX3L66adXQ2SqJqvy6Y5KHU8mTZrk90pG+fn5OsauqpUmdqUq6Oeff2bBggV+L3hhjGHVqlV8//33VRyZUm6a2JWqoEmTJgWsygiQl5envXZVbfTgqVIVJCJ07NgxaLukpKQqiEap8jSxK1VBH3zwQXWHoFRAOhSjlFIHf7g5AAAeoElEQVQ1jCZ2pcLgcrmqOwSlytHErlQluVwuevbsyezZs6s7FKVK0cSuVCXNmzePDRs2cOedd/qd+qhUddDErlQluFwuJk6ciN1u58iRI8ycObO6Q1KqmCZ2pSph3rx57N27F4CcnBzuvfde7bWrmKGJXakK8vbWc3Jyih/TXruKJWEldhF5WESyRGSN52dopAJTKlaV7K17aa9dxZJI9NinGGO6e37mR2B9SsUsX711L+21q1ihQzFK+fHuu++W65n76q17aa9dxYpIJPabRWStiEwTkRP8NRKR8SKyUkRWZmdnR2CzSkXPtm3buPrqq5k0aVLxY4F6617aa1exIGhiF5FFIrLex89w4D9AO6A7sBt4yt96jDGvGGN6GWN6NWrUKGIvQKlomDx5MhaLhffee4+dO3cC7t6697J4/mivXcWCoEXAjDHnhLIiEXkV+DjsiJSqZtu2beODDz7A4XAgIvz1r39l2rRpLFy4EKfTGbRq4+HDh/n1119p3759FUWsVGlhXRpPRJoaY3Z7bt8BnG6M+b9gz9NL46lYNnLkSGbPno3D4QAgOTmZzZs307Jly2qOTB3vqurSeP8SkXUishYYBNwR5vqUqlYle+teTqeTv/71r9UYlVIVE1ZiN8ZcbYzpYozpaoy5yNt7VypeTZ48uVRSB7Db7aXG2pWKdTrdUSkPX711L+21q3iiiV0pD1+9dS/ttat4ooldKQL31r20167ihSZ2pYDHHnsMh8NBUlKS3x8RYcaMGX7PPFUqVujFrJUCxowZQ48ePYK2s9ls1KlTpwoiUqryNLErBfTv35/+/ftXdxhKRUTMJHa73c6uXbsoKCio7lCUIjk5mRYtWpCQkFDdoShVYTGT2Hft2kWdOnVo06YNIlLd4ajjmDGGAwcOsGvXLk466aTqDkepCouZg6cFBQU0aNBAk7qqdiJCgwYN9Nujilsxk9gBTeoqZuhnUcWzmBmKqYjtB3J5dck2Pvzxd3ILHaQm2RjRoxnXn9WW1g1Sqzs8pZSqVjHVYw/FV7/s4/xnljBzxU5yCh0YIKfQwcwVOzn/mSV89cu+Sq+7b9++kQvUIzMzk3fffTfi61VKKX/iKrFvP5DLjW+vJt/uxOEqXW7Y4TLk253c+PZqth/IrdT6ly1bFokwS4m3xB7ozEulVHyIq8T+6pJt2J2ugG3sThevLfmtUuuvXbs2AF9//TUDBw7ksssu49RTT2XkyJF469a3adOGe+65hy5dupCRkcHWrVsBGDt2LO+//365dd13330sWbKE7t27M2XKlFLb+/rrrxkwYADDhw+nbdu23HfffbzzzjtkZGTQpUsXfv31VwCys7O59NJL6d27N71792bp0qUArFixgj59+tCjRw/69u3LL7/8AsCGDRvIyMige/fudO3alS1btpCZmUl6enrxtp988kkefvhhAAYOHMjtt99Or169ePbZZ/1uTykVH+JqjP3DH38v11Mvy+EyzP0xi0dHpAdsF8yPP/7Ihg0baNasGf369WPp0qWceeaZAKSlpbFu3TpmzJjB7bffzscf+79w1D//+U+efPJJv21++uknNm3aRP369Wnbti3XXXcdK1as4Nlnn+X555/nmWee4bbbbuOOO+7gzDPPZMeOHQwZMoRNmzZx6qmnsmTJEmw2G4sWLeL+++9nzpw5TJ06ldtuu42RI0dSVFSE0+kMehp8UVER3oufXHXVVT63p5SKD3GV2HMLQxsmyC0KfzghIyODFi1aANC9e3cyMzOLE/uVV15Z/PuOO8K7tkjv3r1p2rQpAO3ateO8884DoEuXLnz11VcALFq0iI0bNxY/5+jRo+Tk5HDkyBHGjBnDli1bEBHsdjsAffr04bHHHmPXrl1ccsklnHLKKUHjuOKKK4pv+9ue91uIUiq2xVViT02ykRNCck9NDP9llbyupdVqLTX2XHIqnPe2zWbD5XIPE7lcLoqKiiq8HYvFUnzfYrEUb9PlcvHdd9+RnJxc6rk333wzgwYNYu7cuWRmZjJw4EDA3eM+/fTT+eSTTxg6dCgvv/wy7du3L44PKDdHOzX1j9lE/ranlIoPcTXGPqJHM2yWwPOLbRbh4h7NoxrHrFmzin/36dMHcI+9r1q1CoCPPvqouPdcp04djh07Ftb2zjvvPJ5//vni+2vWrAHgyJEjNG/ufq1vvvlm8fJt27bRtm1bbr31VoYPH87atWtp0qQJ+/bt48CBAxQWFgYcPvK3PaVUfAg7sYvILSLys4hsEJF/RSIof64/qy0J1sAhJ1gtXHdWdE8DP3ToEF27duXZZ58tPiB6/fXXs3jxYrp168by5cuLe8Bdu3bFarXSrVu3cgdPQ/Xcc8+xcuVKunbtSqdOnZg6dSoA99xzD5MmTaJHjx6lvlHMnj2b9PR0unfvzvr16xk9ejQJCQk89NBDZGRkcO6553LqqadWeHtKqfgg3tkelXqyyCDgAeACY0yhiDQ2xgSdSN6rVy/jPVDntWnTJjp27Bh0m1/9so8b316N3ekqdSDVZhESrBZeGnUagzo0rvBrCVWbNm1YuXIlDRs2jNo2VGwI9TOpVFURkVXGmF7B2oXbY/8L8E9jTCFAKEk9XIM6NGbB7WdxZUYraifZEIHaSTauzGjFgtvPimpSV0qpeBDuUcb2wFki8hhQANxtjPnBV0MRGQ+MB2jVqlVYG23dIJVHR6SHPaWxMjIzM6t8m0opVRFBE7uILAJO9LHoAc/z6wNnAL2B2SLS1vgY3zHGvAK8Au6hmHCCVkop5V/QxG6MOcffMhH5C/CBJ5GvEBEX0BDIjlyISimlKiLcMfYPgUEAItIeSAT2hxuUUkqpygt3jH0aME1E1gNFwBhfwzARd3AbLHsB1s6GohxIrA1d/wx9b4b6baO+eaWUimVh9diNMUXGmFHGmHRjzGnGmC8jFZhfWz6H//SD1TOg6Bhg3L9Xz3A/vuXzSq9ay/YqpWqCuDrzlIPbYPZosOeBy156mcvufnz2aHe7StCyvVq2V6maIL4S+7IXwGkP3MZph+UvVmr1WrZXy/YqVRPEVREw1s4u31Mvy2WHtbPggqfC2pSW7dWyvUrFq/hK7EU5kW0XgJbt1bK9SsWr+ErsibU9B0xDaBcmLdurZXuVilfxNcbe9c9gSQjcxpIAXa8I3CZMWrZXKRXL4iux970ZrEESuzUB+twU1TC0bK9SKpaFVba3ssIp28uWz91TGp320gdSLQnupP7nGXDKuRGO+A9atvf4oWV7a5bfjvzGB1s+YOexnaQlpTH0pKFknJhRamg11oVatje+xtjBnbT/stQ9pXHtrBJnnl7h7qnrmadKqRLyHflMXDyR73Z/h9PlxGHc324X/LaABikNmHrOVFrVDa/ibKyJv8QO7uR9wVNhT2msDC3bq1T8cBkX4xaM4+eDP+M0zlLL8hx5FBwrYNT8UXww/AMaptScb+HxNcaulFIh2p2zm+EfDmfDgQ3lkrqXCxfH7Md4bd1rVRxddGliV0rVOPvy9nHFx1eQeTQzaFuHy8HcLXOxBzurPY7E51CMUiouGWNYvW810zdMZ93+dQB0a9SNsZ3H0q1Rt4gdyHx65dMcLToacnuXcXGg4AAnpvq6plD8icvEvvPoTqZvnM7H2z4mz55HrYRaDGs7jDGdxtCybsvqDk8p5YPD5WDSkkks3rWYAkcBBveMvC93fMmy35dxTqtz+PuZf8ciFnYe3ck7P7/Dkl1LcBon7U9oz+hOo+nZpGfQ5H+s6BiLdizyO/zii8u4sFniMh36FHevZMmuJdy5+E4cTkfx0e1cey5zNs9h3q/zeHrA05zV4qxKrbtv374Rr/CYmZnJsmXLuOqqqyK6XqVinTGGn7J/4q2Nb7H50GYOFR4ipzAHJ6UTrsGQ78jn8+2f06hWI9IS03jpp5dKzWD5Ped3vtv9HT0b9+SZs58hyZrka5MAbD28lQRLAoXOwpBjrZ9SnwbJDSr3QmNQXI2x7zy6kzsX30mBo6D4DfdyGAcFjgLuXHwnO4/urNT6tWyvlu1VkVHkLOLmL29m/Ofj+Xz752QezeRI4ZFySb2kAmcBMzbM4D8//YdCZ2Gpv3Fv8v9h7w/cv+T+iMaabE1mXOdxcTWfPZi4SuzTN07H4QyceBxOBzM2zqjU+rVsr5btVZVT5Czik22fMG7BOEZ8OIJz/nsOy39fTr4jv3jIJRQO46DAWeB3eaGzkK93fc3OY/47b+3qtcMerAqshxUr6Q3TubzD5SHHGA/iaijm420fl+upl+UwDj7e9jEPnPFAWNvSsr1atleF5tfDv3LtZ9eS78gnz5EX9e25jIu5W+Zy62m3+lxeN7Eug1sN5rPMz4KOsw8/eTgPnvEgCcFqUMWZsBK7iMwCOnju1gMOG2O6hx2VH3n20D40ufbcsLelZXu1bK8K7kD+AcZ8OoajRUcr1DMPh8PlYMexHQHb3NnzTpb/vpwjRUdwGVe55YmWRMZ0HuP3n0O8CyuxG2OKs4GIPAUcCTuiAGol1AopaacmpAZtE4yW7dWyvSq4d39+t8LDLZFQJ7FOwOVNUpvw3rD3uOvru9h6eCtO48TpcpJiSwHgxu43MrrT6KoItVpEZIxd3Nntz8B7kVifP8PaDsMmgf8X2cTGsLbDohmGlu1VymPWL7MocoXWiQnGJjYsEjwl1bLV4vw25wdt17x2c2YOm8l7F7zHrT1u5cbuN/JQn4dYfMVixnQeU6MOlpYVqYOnZwF7jTFb/DUQkfEislJEVmZnZ1dqI2M6jcFmDZLYrbao/yfWsr0qHhhjcLpCn8tdUQ6Xg6OFoZ8EFEiSNYlWdVtxUbuLAk5lFIQTkk8g48SMkNd9ygmnMC59HBO6TeCCtheQbKv530SDlu0VkUWAr9OxHjDGzPO0+Q+w1RgTUlWucMr2+prHDu7/9jarLax57KHQsr3Hj3gs21voKOTVda8yf9t8duXswmBoXKsxV3e8mss7XB6RYUovYww93upRoROByrKIhXpJ9RjVcRQjO47EIhbGLRjHlsNbys1Dt4qV1IRU3hn6Dm3S2oQZfXyKWNleY8w5QTZkAy4BeoYeXuWd1eIsPrjwA2ZsnMHH2z4m155LakIqw9oOY3Sn0XrmqTouOVwOXlzzIm+sf6Ncot2Xt4/nf3yemb/M5O2hb0esiqGIcHrT01n2e+XO/7CJjbeGvkWnBp1KDcFM/9N03tr4FjM2ziDPnodFLLiMi2Fth3FDtxtqzGn/0RT2hTZE5HxgkjFmQKjPCetCG0pVkXj5TDpdTm796laWZS0LOB3YJjban9CeWRfOiti2f9jzAzcuujHg3HNfEiwJ9GvWj+cHP++3jcu42J27G6fLSeNajY+LIZRgqvJCG/9HlA+aKnU8ybPn8eHWD5mxcQZ7cvdgtVjp3aQ316RfQ0bT8mPL83+bzw97fgjpHI/fjv7G+v3rSW+YHrBtqHqf2JurO13NWxvfCjm5p9hSaFevHU/0fyJgO4tYaF67eSTCPO6EndiNMWMjEIdSCsjOy+bqT6/mQP6B4kTpdDpZ+vtSVu9bzSUnX8K9GfeWmtHx+rrXyXfkh7T+Qmch87bOi1hiB7j1tFvpUL8DL615iaycLBIsCdhddtrUbcOAlgNYsXsFGw9sxGA4Ke0kxqWPY0ibITXupKBYEldnnipVkxljGP/5ePbm7vXZ+8535DNn6xza1mvLnzv8ufixUGqOe7mMi/35+yMVcrEhbYYwpM0Qdh3bxZHCI9RPrk/T2u4T7+gR8c2pIOI6se/evZszzzyTpUuXcuKJekBFVa1fDv7CjI0zWLXXff5Ct0bdGN15NJ0bdC5us/nQZnbn7CbFlkK3xt0CTuVbuXclWTlZAYdUChwFTP1pKpe1vwyLWHC4HO7ee4iHyixYaJLaJLTGldCiTgta1GkRtfWr0MRVEbCyHn30UTIzM3n00UfDXtfOnTsZNGgQnTp1onPnzjz77LM+291xxx0888wzxfeHDBnCddddV3z/rrvu4umnnw47nnAdPnyYl156KaS2ffv2rdC6Bw4cSNmD37FkzZo1zJ8/P2rrN8bw+PePM2r+KD7Z9glZOVlk5WSxIHMBYz8dy4PfPsjXO7/mwrkXMmr+KO5bch+3fXUb/Wf256mVT1Hk9H1Cz9wtcylwBB+nzrXnsmH/BgBqJ9Smlq1WyLEnWhMZcfKIkNur+BS3iX337t288cYbuFwu3njjDfbs2RPW+mw2G0899RQbN27ku+++48UXXyxVL8WrX79+xeV9XS4X+/fvZ8OGDcXLly1bVuFEGQ5/ZXYrktijUa7Yn6ooC1yZxF6RuF5e+7I7CTsLSk0tdBkXBc4CPtn2Cbd/dTuZRzPJd+STY88hx55DniOP935+j2s/u9bnZdj25e0L6dR8i1g4VHgIcE85vPLUK0m0JAZ9nlWsdGzQkVPr+z85TdUMcZvYH3300eLaJ06nM+xee9OmTTnttNMAdxmAjh07kpWVVa5d3759Wb58OeAuj5uenk6dOnU4dOgQhYWFbNq0idNOO42cnBwGDx7MaaedRpcuXZg3bx4Aubm5XHDBBXTr1o309PTi8gT33XcfnTp1omvXrtx9992A/3K9Dz/8MFdffTX9+vXj6quv9lmm97777uPXX3+le/fuTJw4EYB///vf9O7dm65du/LXv/61+DWFUq64rLfeeovu3buTnp7OihUrAP9lhN98800uuugizj77bAYPHszo0aP58MMPi9c1cuRI5s2bh9Pp5O677yY9PZ2uXbsWlzVYtWoVAwYMoGfPngwZMoTdu3cD7m8O9957LxkZGbRv354lS5ZQVFTEQw89xKxZs+jevTuzZs0iNzeXa665hoyMDHr06FH8XpSNKxT5jnymrZ8WcAaIwzj8nrRT6Cxk08FNvLnxzXLLQp1f7jIu6iXVK74/quMo6ibVDXg6viC0rtOa58/2P71Q1RxxOcbu7a17C20VFRXxxhtvMHny5IiMtWdmZvLjjz9y+umnl1vWrFkzbDYbO3bsYNmyZfTp04esrCyWL19OWloaXbp0ITExEYvFwty5c6lbty779+/njDPO4KKLLmLBggU0a9aMTz75BHDXezlw4ABz587l559/RkQ4fPgwgN9yvQAbN27k22+/JSUlhVtuuaVcmd5//vOfrF+/vrjOy8KFC9myZQsrVqzAGMNFF13EN998Q//+/Uu9vkDlikvKy8tjzZo1fPPNN1xzzTWsX7/ebxlhgNWrV7N27Vrq16/P4sWLmTJlCiNGjODIkSMsW7aM6dOn88orr5CZmcmaNWuw2WwcPHgQu93OLbfcwrx582jUqBGzZs3igQceYNq0aYC7p71ixQrmz5/PI488wqJFi/jb3/7GypUreeGFFwC4//77Ofvss5k2bRqHDx8mIyODc845p1xcofhqx1cI4dUYKXQW8vbGt7mm8zVYLdbixy8+5WK+2vlV0NK3KbaUUrNa6iXX492h73LDohvYk7un3AyZZGsyd/a8k0vaXxJwjF/VHHGZ2Ev21r28vfYXX3wxrHXn5ORw6aWX8swzz1C3bl2fbbyX0Fu2bBl33nknWVlZLFu2jLS0NPr16we4x2Hvv/9+vvnmGywWC1lZWezdu5cuXbpw1113ce+99zJs2DDOOussHA4HycnJXHvttQwbNoxhw9xFzPyVzwW46KKLSElxV6oLpUzvwoULWbhwIT169Ch+nVu2bCmX2AOVKy7JW7q4f//+HD16lMOHD3Ps2DGfZYQBzj333OLkOWDAAG688Uays7OZM2cOl156afE/gwkTJmCzuT+W9evXZ/369axfv55zzz0XcL/P3jLHAJdccgkAPXv2JDMz0+f7tXDhQj766COefPJJwF3ZcseOHeXiCsWevD1+x8grIt+Rz66cXbSu27r4sYwTM2hSqwk7ju3w2+NPtiYzvuv4cr3zprWbMm/4PFbvW83/fv0fBwsO0qx2My455RLan9A+7HhVfIm7xF62t+4ViV673W7n0ksvZeTIkcUJY+fOnVx44YUATJgwgQkTJhSPs69bt4709HRatmzJU089Rd26dRk3bhwA77zzDtnZ2axatYqEhATatGlDQUEB7du3Z/Xq1cyfP58HH3yQwYMH89BDD7FixQq++OIL3n//fV544QW+/PLLgOVzS5bZ9VWmt23btqXaG2OYNGkSN9xwQ8B9EKhccUllK+OJCJMnT/ZZRrhsvACjR4/m7bffZubMmbzxxht+4zHG0Llz5+LhL3/xBorVGMOcOXPo0KFDqce///77cnEFk2pLxWqxBr2SVzAWLOXG2UWEV857hVHzR3Gk8Ei54Z4UWwrD2g7jylOv9LlOEaFnk570bFIl1T1UDIu7MXZfvXWvcMbajTFce+21dOzYkTvvvLP48ZYtW7JmzRrWrFnDhAkTAHeP/eOPP6Z+/fpYrVbq16/P4cOHWb58efGB0yNHjtC4cWMSEhL46quv2L59OwC///47tWrVYtSoUUycOJHVq1cXXzRj6NChTJkyhZ9++gkIvXyurzK9ZcsFDxkyhGnTphX3+LOysti3b1+l9hX8Ubr422+/JS0tjbS0NL9lhH0ZO3Zs8eyiTp06Ae7e88svv1ycoA8ePEiHDh3Izs4uTux2u73UwWpffL32559/vvh4wY8//ljBV/uH/i36+z3uUBF2Y/dZ8+TE1BOZO3wuN3W/iSa1miAIVrHS+8TeTBk4hclnTK7R5WZVZMRVYvfXW/fy9torM0Nm6dKlvPXWW3z55Zd0796d7t27+51Z0aVLl+Jx85KPpaWlFVd9HDlyJCtXrqRLly7MmDGjuEzuunXrig90PvLIIzz44IMcO3aMYcOG0bVrV84888zi6ZKhls/1Vaa3QYMG9OvXj/T0dCZOnMh5553HVVddRZ8+fejSpQuXXXZZWHXik5OT6dGjBxMmTOD1118H/JcR9qVJkyZ07Nix+BsOwHXXXUerVq3o2rUr3bp149133yUxMZH333+fe++9l27dutG9e/egs3gGDRrExo0biw+eTp48GbvdTteuXencuTOTJ0+u9OtuWrspGU0zwjpr0iIWBrcaTO1E31ekqpNYh7HpY1l0+SJ+Gv0Ta0avYdqQafRr3k+TugpJ2EXAKqOyRcBuvPFGXn/99YBXJ0pMTOS6664Le6xdRVdeXh5dunRh9erVpKWlVXc4Pvn7TB4pPMKVn1zJ3ty95S4yUfJiEf4uQJFqS2X2hbNpVbdV5INWNVqoRcDiqsf+0UcfBb3kXFFRUfF0NhWbFi1aRMeOHbnllltiNqkHkpaUxuxhsxnTeQx1EuuQYkshxZZCakIqozqNYv4l8+nTrA9J1iSs8sesl1q2WtRPrs+086dpUldRFVc9dqWqUiifSYfLwZ5c99Bfk1pNSLD+MUSz9dBWZm+eTeaRTGon1mboSUMZ2HIgNkvczVlQMaIqy/ZGjDFGxxBVTAi1w2Oz2PzWRjn5hJO5//T7IxmWUiGJmaGY5ORkDhw4EJEZB0qFwxjDgQMHfE4zVSoexEyPvUWLFuzatYvKXuhaqUhKTk4uPlFLqXgTM4k9ISGBk046qbrDUEqpuBczQzFKKaUiQxO7UkrVMJrYlVKqhqmWeewikg1sr/INR1ZDIPIXj6xZdB+FRvdTcLqP3FobYxoFa1Qtib0mEJGVoZwocDzTfRQa3U/B6T6qGB2KUUqpGkYTu1JK1TCa2CvvleoOIA7oPgqN7qfgdB9VgI6xK6VUDaM9dqWUqmE0sSulVA2jiT1MInKXiBgRaVjdscQiEfm3iPwsImtFZK6I1KvumGKFiJwvIr+IyFYRua+644lFItJSRL4SkY0iskFEbqvumOKBJvYwiEhL4DxgR3XHEsM+B9KNMV2BzcCkao4nJoiIFXgR+BPQCbhSRDpVb1QxyQHcZYzpBJwB3KT7KThN7OGZAtwD6BFoP4wxC40x3itbfwdoLVy3DGCrMWabMaYImAkMr+aYYo4xZrcxZrXn9jFgE9C8eqOKfZrYK0lEhgNZxpifqjuWOHIN8Gl1BxEjmgM7S9zfhSasgESkDdAD+L56I4l9MVOPPRaJyCLgRB+LHgDuxz0Mc9wLtJ+MMfM8bR7A/bX6naqMTdUMIlIbmAPcbow5Wt3xxDpN7AEYY87x9biIdAFOAn7yXKO1BbBaRDKMMXuqMMSY4G8/eYnIWGAYMNjoiRNeWUDLEvdbeB5TZYhIAu6k/o4x5oPqjice6AlKESAimUAvY4xWnytDRM4HngYGGGP0uoceImLDfTB5MO6E/gNwlTFmQ7UGFmPE3XOaDhw0xtxe3fHECx1jV9H2AlAH+FxE1ojI1OoOKBZ4DijfDHyG+4DgbE3qPvUDrgbO9nx+1ojI0OoOKtZpj10ppWoY7bErpVQNo4ldKaVqGE3sSilVw2hiV0qpGkYTu1JK1TCa2JVSqobRxK6UUjXM/wOLEmgPgpS5HgAAAABJRU5ErkJggg==\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pl.figure(1)\n", + "for (x_i, b_i) in zip(measures_locations, measures_weights):\n", + " color = np.random.randint(low=1, high=10 * N)\n", + " pl.scatter(x_i[:, 0], x_i[:, 1], s=b * 1000, label='input measure')\n", + "pl.scatter(X[:, 0], X[:, 1], s=b * 1000, c='black', marker='^', label='2-Wasserstein barycenter')\n", + "pl.title('Data measures and their barycenter')\n", + "pl.legend(loc=0)\n", + "pl.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.5" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/notebooks/plot_stochastic.ipynb b/notebooks/plot_stochastic.ipynb new file mode 100644 index 0000000..e784e11 --- /dev/null +++ b/notebooks/plot_stochastic.ipynb @@ -0,0 +1,610 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "# Stochastic examples\n", + "\n", + "\n", + "This example is designed to show how to use the stochatic optimization\n", + "algorithms for descrete and semicontinous measures from the POT library.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Author: Kilian Fatras <kilian.fatras@gmail.com>\n", + "#\n", + "# License: MIT License\n", + "\n", + "import matplotlib.pylab as pl\n", + "import numpy as np\n", + "import ot\n", + "import ot.plot" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "COMPUTE TRANSPORTATION MATRIX FOR SEMI-DUAL PROBLEM\n", + "############################################################################\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "------------SEMI-DUAL PROBLEM------------\n" + ] + } + ], + "source": [ + "print(\"------------SEMI-DUAL PROBLEM------------\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "DISCRETE CASE\n", + "Sample two discrete measures for the discrete case\n", + "---------------------------------------------\n", + "\n", + "Define 2 discrete measures a and b, the points where are defined the source\n", + "and the target measures and finally the cost matrix c.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "n_source = 7\n", + "n_target = 4\n", + "reg = 1\n", + "numItermax = 1000\n", + "\n", + "a = ot.utils.unif(n_source)\n", + "b = ot.utils.unif(n_target)\n", + "\n", + "rng = np.random.RandomState(0)\n", + "X_source = rng.randn(n_source, 2)\n", + "Y_target = rng.randn(n_target, 2)\n", + "M = ot.dist(X_source, Y_target)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Call the \"SAG\" method to find the transportation matrix in the discrete case\n", + "---------------------------------------------\n", + "\n", + "Define the method \"SAG\", call ot.solve_semi_dual_entropic and plot the\n", + "results.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[2.55553509e-02 9.96395660e-02 1.76579142e-02 4.31178196e-06]\n", + " [1.21640234e-01 1.25357448e-02 1.30225078e-03 7.37891338e-03]\n", + " [3.56123975e-03 7.61451746e-02 6.31505947e-02 1.33831456e-07]\n", + " [2.61515202e-02 3.34246014e-02 8.28734709e-02 4.07550428e-04]\n", + " [9.85500870e-03 7.52288517e-04 1.08262628e-02 1.21423583e-01]\n", + " [2.16904253e-02 9.03825797e-04 1.87178503e-03 1.18391107e-01]\n", + " [4.15462212e-02 2.65987989e-02 7.23177216e-02 2.39440107e-03]]\n" + ] + } + ], + "source": [ + "method = \"SAG\"\n", + "sag_pi = ot.stochastic.solve_semi_dual_entropic(a, b, M, reg, method,\n", + " numItermax)\n", + "print(sag_pi)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "SEMICONTINOUS CASE\n", + "Sample one general measure a, one discrete measures b for the semicontinous\n", + "case\n", + "---------------------------------------------\n", + "\n", + "Define one general measure a, one discrete measures b, the points where\n", + "are defined the source and the target measures and finally the cost matrix c.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "n_source = 7\n", + "n_target = 4\n", + "reg = 1\n", + "numItermax = 1000\n", + "log = True\n", + "\n", + "a = ot.utils.unif(n_source)\n", + "b = ot.utils.unif(n_target)\n", + "\n", + "rng = np.random.RandomState(0)\n", + "X_source = rng.randn(n_source, 2)\n", + "Y_target = rng.randn(n_target, 2)\n", + "M = ot.dist(X_source, Y_target)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Call the \"ASGD\" method to find the transportation matrix in the semicontinous\n", + "case\n", + "---------------------------------------------\n", + "\n", + "Define the method \"ASGD\", call ot.solve_semi_dual_entropic and plot the\n", + "results.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[3.75309361 7.63288278 3.76418767 2.53747778 1.70389504 3.53981297\n", + " 2.67663944] [-2.49164966 -2.25281897 -0.77666675 5.52113539]\n", + "[[2.19699465e-02 1.03185982e-01 1.76983379e-02 2.87611188e-06]\n", + " [1.20688044e-01 1.49823131e-02 1.50635578e-03 5.68043045e-03]\n", + " [3.01194583e-03 7.75764779e-02 6.22686313e-02 8.78225379e-08]\n", + " [2.28707628e-02 3.52120795e-02 8.44977549e-02 2.76545693e-04]\n", + " [1.19721129e-02 1.10087991e-03 1.53333937e-02 1.14450756e-01]\n", + " [2.65247890e-02 1.33140544e-03 2.66861405e-03 1.12332334e-01]\n", + " [3.71512413e-02 2.86513804e-02 7.53932500e-02 1.66127118e-03]]\n" + ] + } + ], + "source": [ + "method = \"ASGD\"\n", + "asgd_pi, log_asgd = ot.stochastic.solve_semi_dual_entropic(a, b, M, reg, method,\n", + " numItermax, log=log)\n", + "print(log_asgd['alpha'], log_asgd['beta'])\n", + "print(asgd_pi)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Compare the results with the Sinkhorn algorithm\n", + "---------------------------------------------\n", + "\n", + "Call the Sinkhorn algorithm from POT\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[2.55535622e-02 9.96413843e-02 1.76578860e-02 4.31043335e-06]\n", + " [1.21640742e-01 1.25369034e-02 1.30234529e-03 7.37715259e-03]\n", + " [3.56096458e-03 7.61460101e-02 6.31500344e-02 1.33788624e-07]\n", + " [2.61499607e-02 3.34255577e-02 8.28741973e-02 4.07427179e-04]\n", + " [9.85698720e-03 7.52505948e-04 1.08291770e-02 1.21418473e-01]\n", + " [2.16947591e-02 9.04086158e-04 1.87228707e-03 1.18386011e-01]\n", + " [4.15442692e-02 2.65998963e-02 7.23192701e-02 2.39370724e-03]]\n" + ] + } + ], + "source": [ + "sinkhorn_pi = ot.sinkhorn(a, b, M, reg)\n", + "print(sinkhorn_pi)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "PLOT TRANSPORTATION MATRIX\n", + "#############################################################################\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot SAG results\n", + "----------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 360x360 with 3 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pl.figure(4, figsize=(5, 5))\n", + "ot.plot.plot1D_mat(a, b, sag_pi, 'semi-dual : OT matrix SAG')\n", + "pl.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot ASGD results\n", + "-----------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "<Figure size 360x360 with 3 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pl.figure(4, figsize=(5, 5))\n", + "ot.plot.plot1D_mat(a, b, asgd_pi, 'semi-dual : OT matrix ASGD')\n", + "pl.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot Sinkhorn results\n", + "---------------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "<Figure size 360x360 with 3 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pl.figure(4, figsize=(5, 5))\n", + "ot.plot.plot1D_mat(a, b, sinkhorn_pi, 'OT matrix Sinkhorn')\n", + "pl.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "COMPUTE TRANSPORTATION MATRIX FOR DUAL PROBLEM\n", + "############################################################################\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "------------DUAL PROBLEM------------\n" + ] + } + ], + "source": [ + "print(\"------------DUAL PROBLEM------------\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "SEMICONTINOUS CASE\n", + "Sample one general measure a, one discrete measures b for the semicontinous\n", + "case\n", + "---------------------------------------------\n", + "\n", + "Define one general measure a, one discrete measures b, the points where\n", + "are defined the source and the target measures and finally the cost matrix c.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "n_source = 7\n", + "n_target = 4\n", + "reg = 1\n", + "numItermax = 100000\n", + "lr = 0.1\n", + "batch_size = 3\n", + "log = True\n", + "\n", + "a = ot.utils.unif(n_source)\n", + "b = ot.utils.unif(n_target)\n", + "\n", + "rng = np.random.RandomState(0)\n", + "X_source = rng.randn(n_source, 2)\n", + "Y_target = rng.randn(n_target, 2)\n", + "M = ot.dist(X_source, Y_target)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Call the \"SGD\" dual method to find the transportation matrix in the\n", + "semicontinous case\n", + "---------------------------------------------\n", + "\n", + "Call ot.solve_dual_entropic and plot the results.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1.67648902 5.3770004 1.70385554 0.4276547 -0.77206786 1.0474898\n", + " 0.54202203] [-0.23723788 -0.20259434 1.30855788 8.06179985]\n", + "[[2.62451875e-02 1.00499531e-01 1.78515577e-02 4.57450829e-06]\n", + " [1.20510690e-01 1.21972758e-02 1.27002374e-03 7.55197481e-03]\n", + " [3.65708350e-03 7.67963231e-02 6.38381061e-02 1.41974930e-07]\n", + " [2.64286344e-02 3.31748063e-02 8.24445965e-02 4.25479786e-04]\n", + " [9.59295422e-03 7.19190875e-04 1.03739180e-02 1.22100712e-01]\n", + " [2.09087627e-02 8.55676046e-04 1.77617241e-03 1.17896019e-01]\n", + " [4.18792948e-02 2.63326297e-02 7.17598381e-02 2.49335733e-03]]\n" + ] + } + ], + "source": [ + "sgd_dual_pi, log_sgd = ot.stochastic.solve_dual_entropic(a, b, M, reg,\n", + " batch_size, numItermax,\n", + " lr, log=log)\n", + "print(log_sgd['alpha'], log_sgd['beta'])\n", + "print(sgd_dual_pi)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Compare the results with the Sinkhorn algorithm\n", + "---------------------------------------------\n", + "\n", + "Call the Sinkhorn algorithm from POT\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[2.55535622e-02 9.96413843e-02 1.76578860e-02 4.31043335e-06]\n", + " [1.21640742e-01 1.25369034e-02 1.30234529e-03 7.37715259e-03]\n", + " [3.56096458e-03 7.61460101e-02 6.31500344e-02 1.33788624e-07]\n", + " [2.61499607e-02 3.34255577e-02 8.28741973e-02 4.07427179e-04]\n", + " [9.85698720e-03 7.52505948e-04 1.08291770e-02 1.21418473e-01]\n", + " [2.16947591e-02 9.04086158e-04 1.87228707e-03 1.18386011e-01]\n", + " [4.15442692e-02 2.65998963e-02 7.23192701e-02 2.39370724e-03]]\n" + ] + } + ], + "source": [ + "sinkhorn_pi = ot.sinkhorn(a, b, M, reg)\n", + "print(sinkhorn_pi)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot SGD results\n", + "-----------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 360x360 with 3 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pl.figure(4, figsize=(5, 5))\n", + "ot.plot.plot1D_mat(a, b, sgd_dual_pi, 'dual : OT matrix SGD')\n", + "pl.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot Sinkhorn results\n", + "---------------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 360x360 with 3 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pl.figure(4, figsize=(5, 5))\n", + "ot.plot.plot1D_mat(a, b, sinkhorn_pi, 'OT matrix Sinkhorn')\n", + "pl.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.5" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/ot/__init__.py b/ot/__init__.py index 1dde390..b27541d 100644 --- a/ot/__init__.py +++ b/ot/__init__.py @@ -29,7 +29,7 @@ from .da import sinkhorn_lpl1_mm # utils functions from .utils import dist, unif, tic, toc, toq -__version__ = "0.4.0" +__version__ = "0.5.0" __all__ = ["emd", "emd2", "sinkhorn", "sinkhorn2", "utils", 'datasets', 'bregman', 'lp', 'tic', 'toc', 'toq', 'gromov', diff --git a/ot/datasets.py b/ot/datasets.py index 362a89b..e76e75d 100644 --- a/ot/datasets.py +++ b/ot/datasets.py @@ -38,9 +38,9 @@ def make_1D_gauss(n, m, s): @deprecated() -def get_1D_gauss(n, m, sigma, random_state=None): +def get_1D_gauss(n, m, sigma): """ Deprecated see make_1D_gauss """ - return make_1D_gauss(n, m, sigma, random_state=None) + return make_1D_gauss(n, m, sigma) def make_2D_samples_gauss(n, m, sigma, random_state=None): diff --git a/ot/gpu/__init__.py b/ot/gpu/__init__.py index 0187a4f..deda6b1 100644 --- a/ot/gpu/__init__.py +++ b/ot/gpu/__init__.py @@ -9,15 +9,17 @@ By default, the functions in this module accept and return numpy arrays in order to proide drop-in replacement for the other POT function but the transfer between CPU en GPU comes with a significant overhead. -In order to get the best erformances, we recommend to given only cupy +In order to get the best erformances, we recommend to give only cupy arrays to the functions and desactivate the conversion to numpy of the result of the function with parameter ``to_numpy=False``. - - - """ +# Author: Remi Flamary <remi.flamary@unice.fr> +# Leo Gautheron <https://github.com/aje> +# +# License: MIT License + from . import bregman from . import da from .bregman import sinkhorn @@ -27,10 +29,9 @@ from . import utils from .utils import dist, to_gpu, to_np -# Author: Remi Flamary <remi.flamary@unice.fr> -# Leo Gautheron <https://github.com/aje> -# -# License: MIT License + + __all__ = ["utils", "dist", "sinkhorn", "sinkhorn_lpl1_mm", 'bregman', 'da', 'to_gpu', 'to_np'] + diff --git a/ot/gpu/da.py b/ot/gpu/da.py index 6aba29c..4a98038 100644 --- a/ot/gpu/da.py +++ b/ot/gpu/da.py @@ -10,10 +10,12 @@ Domain adaptation with optimal transport with GPU implementation # # License: MIT License + import cupy as np # np used for matrix computation import cupy as cp # cp used for cupy specific operations import numpy as npp from . import utils + from .bregman import sinkhorn @@ -131,6 +133,7 @@ def sinkhorn_lpl1_mm(a, labels_a, b, M, reg, eta=0.1, numItermax=10, # separated W = np.ones(M.shape) for (i, c) in enumerate(classes): + majs = np.sum(transp[indices_labels[i]], axis=0) majs = p * ((majs + epsilon)**(p - 1)) W[indices_labels[i]] = majs diff --git a/test/test_bregman.py b/test/test_bregman.py index b0c3358..14edaf5 100644 --- a/test/test_bregman.py +++ b/test/test_bregman.py @@ -118,12 +118,12 @@ def test_wasserstein_bary_2d(): a2 += a2.min() a2 = a2 / np.sum(a2) # creating matrix A containing all distributions - A = np.zeros((2, 100, 100)) + A = np.zeros((2, size, size)) A[0, :, :] = a1 A[1, :, :] = a2 # wasserstein - reg = 1e-3 + reg = 1e-2 bary_wass = ot.bregman.convolutional_barycenter2d(A, reg) np.testing.assert_allclose(1, np.sum(bary_wass)) diff --git a/test/test_gromov.py b/test/test_gromov.py index fb86274..305ae84 100644 --- a/test/test_gromov.py +++ b/test/test_gromov.py @@ -28,7 +28,7 @@ def test_gromov(): C1 /= C1.max()
C2 /= C2.max()
- G = ot.gromov.gromov_wasserstein(C1, C2, p, q, 'square_loss')
+ G = ot.gromov.gromov_wasserstein(C1, C2, p, q, 'square_loss', verbose=True)
# check constratints
np.testing.assert_allclose(
@@ -69,7 +69,7 @@ def test_entropic_gromov(): C2 /= C2.max()
G = ot.gromov.entropic_gromov_wasserstein(
- C1, C2, p, q, 'square_loss', epsilon=5e-4)
+ C1, C2, p, q, 'square_loss', epsilon=5e-4, verbose=True)
# check constratints
np.testing.assert_allclose(
@@ -107,7 +107,8 @@ def test_gromov_barycenter(): [ot.unif(ns), ot.unif(nt)
], ot.unif(n_samples), [.5, .5],
'square_loss', # 5e-4,
- max_iter=100, tol=1e-3)
+ max_iter=100, tol=1e-3,
+ verbose=True)
np.testing.assert_allclose(Cb.shape, (n_samples, n_samples))
Cb2 = ot.gromov.gromov_barycenters(n_samples, [C1, C2],
@@ -134,7 +135,8 @@ def test_gromov_entropic_barycenter(): [ot.unif(ns), ot.unif(nt)
], ot.unif(n_samples), [.5, .5],
'square_loss', 2e-3,
- max_iter=100, tol=1e-3)
+ max_iter=100, tol=1e-3,
+ verbose=True)
np.testing.assert_allclose(Cb.shape, (n_samples, n_samples))
Cb2 = ot.gromov.entropic_gromov_barycenters(n_samples, [C1, C2],
diff --git a/test/test_ot.py b/test/test_ot.py index 45e777a..7652394 100644 --- a/test/test_ot.py +++ b/test/test_ot.py @@ -70,7 +70,7 @@ def test_emd_empty(): def test_emd2_multi(): - n = 1000 # nb bins + n = 500 # nb bins # bin positions x = np.arange(n, dtype=np.float64) @@ -78,7 +78,7 @@ def test_emd2_multi(): # Gaussian distributions a = gauss(n, m=20, s=5) # m= mean, s= std - ls = np.arange(20, 1000, 20) + ls = np.arange(20, 500, 20) nb = len(ls) b = np.zeros((n, nb)) for i in range(nb): @@ -207,11 +207,11 @@ def test_warnings(): def test_dual_variables(): - n = 5000 # nb bins - m = 6000 # nb bins + n = 500 # nb bins + m = 600 # nb bins - mean1 = 1000 - mean2 = 1100 + mean1 = 300 + mean2 = 400 # bin positions x = np.arange(n, dtype=np.float64) diff --git a/test/test_plot.py b/test/test_plot.py index f77d879..caf84de 100644 --- a/test/test_plot.py +++ b/test/test_plot.py @@ -5,10 +5,18 @@ # License: MIT License import numpy as np -import matplotlib -matplotlib.use('Agg') +import pytest +try: # test if matplotlib is installed + import matplotlib + matplotlib.use('Agg') + nogo = False +except ImportError: + nogo = True + + +@pytest.mark.skipif(nogo, reason="Matplotlib not installed") def test_plot1D_mat(): import ot @@ -30,6 +38,7 @@ def test_plot1D_mat(): ot.plot.plot1D_mat(a, b, M, 'Cost matrix M') +@pytest.mark.skipif(nogo, reason="Matplotlib not installed") def test_plot2D_samples_mat(): import ot diff --git a/test/test_utils.py b/test/test_utils.py index b524ef6..640598d 100644 --- a/test/test_utils.py +++ b/test/test_utils.py @@ -12,7 +12,7 @@ import sys def test_parmap(): - n = 100 + n = 10 def f(i): return 1.0 * i * i |
