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101 files changed, 7974 insertions, 730 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/.github/ISSUE_TEMPLATE/bug_report.md b/.github/ISSUE_TEMPLATE/bug_report.md new file mode 100644 index 0000000..7f8acda --- /dev/null +++ b/.github/ISSUE_TEMPLATE/bug_report.md @@ -0,0 +1,36 @@ +--- +name: Bug report +about: Create a report to help us improve POT + +--- + +**Describe the bug** +A clear and concise description of what the bug is. + +**To Reproduce** +Steps to reproduce the behavior: +1 ... +2. + +**Expected behavior** +A clear and concise description of what you expected to happen. + +**Screenshots** +If applicable, add screenshots to help explain your problem. + +**Desktop (please complete the following information):** + - OS: [e.g. MacOSX, Windows, Ubuntu] + - Python version [2.7,3.6] +- How was POT installed [source, pip, conda] + +Output of the following code snippet: +```python +import platform; print(platform.platform()) +import sys; print("Python", sys.version) +import numpy; print("NumPy", numpy.__version__) +import scipy; print("SciPy", scipy.__version__) +import ot; print("POT", ot.__version__) +``` + +**Additional context** +Add any other context about the problem here. 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. @@ -1,6 +1,7 @@ PYTHON=python3 +branch := $(shell git symbolic-ref --short -q HEAD) help : @echo "The following make targets are available:" @@ -57,6 +58,16 @@ rdoc : notebook : ipython notebook --matplotlib=inline --notebook-dir=notebooks/ +bench : + @git stash >/dev/null 2>&1 + @echo 'Branch master' + @git checkout master >/dev/null 2>&1 + python3 $(script) + @echo 'Branch $(branch)' + @git checkout $(branch) >/dev/null 2>&1 + python3 $(script) + @git stash apply >/dev/null 2>&1 + autopep8 : autopep8 -ir test ot examples --jobs -1 @@ -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) @@ -14,10 +15,10 @@ This open source Python library provide several solvers for optimization problem It provides the following solvers: * OT Network Flow solver for the linear program/ Earth Movers Distance [1]. -* Entropic regularization OT solver with Sinkhorn Knopp Algorithm [2] and stabilized version [9][10] with optional GPU implementation (requires cudamat). +* Entropic regularization OT solver with Sinkhorn Knopp Algorithm [2] and stabilized version [9][10] and greedy SInkhorn [22] with optional GPU implementation (requires cupy). * Smooth optimal transport solvers (dual and semi-dual) for KL and squared L2 regularizations [17]. * Non regularized Wasserstein barycenters [16] with LP solver (only small scale). -* Bregman projections for Wasserstein barycenter [3] and unmixing [4]. +* Bregman projections for Wasserstein barycenter [3], convolutional barycenter [21] and unmixing [4]. * Optimal transport for domain adaptation with group lasso regularization [5] * Conditional gradient [6] and Generalized conditional gradient for regularized OT [7]. * Linear OT [14] and Joint OT matrix and mapping estimation [8]. @@ -79,16 +80,12 @@ 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 ``` -* **ot.gpu** (GPU accelerated OT) depends on cudamat that have to be installed with: -``` -git clone https://github.com/cudamat/cudamat.git -cd cudamat -python setup.py install --user # for user install (no root) -``` +* **ot.gpu** (GPU accelerated OT) depends on cupy that have to be installed following instructions on [this page](https://docs-cupy.chainer.org/en/stable/install.html). + obviously you need CUDA installed and a compatible GPU. @@ -165,6 +162,7 @@ The contributors to this library are: * [Antoine Rolet](https://arolet.github.io/) * Erwan Vautier (Gromov-Wasserstein) * [Kilian Fatras](https://kilianfatras.github.io/) +* [Alain Rakotomamonjy](https://sites.google.com/site/alainrakotomamonjy/home) This toolbox benefit a lot from open source research and we would like to thank the following persons for providing some code (in various languages): @@ -228,3 +226,7 @@ You can also post bug reports and feature requests in Github issues. Make sure t [19] Seguy, V., Bhushan Damodaran, B., Flamary, R., Courty, N., Rolet, A.& Blondel, M. [Large-scale Optimal Transport and Mapping Estimation](https://arxiv.org/pdf/1711.02283.pdf). International Conference on Learning Representation (2018) [20] Cuturi, M. and Doucet, A. (2014) [Fast Computation of Wasserstein Barycenters](http://proceedings.mlr.press/v32/cuturi14.html). International Conference in Machine Learning + +[21] Solomon, J., De Goes, F., Peyré, G., Cuturi, M., Butscher, A., Nguyen, A. & Guibas, L. (2015). [Convolutional wasserstein distances: Efficient optimal transportation on geometric domains](https://dl.acm.org/citation.cfm?id=2766963). ACM Transactions on Graphics (TOG), 34(4), 66. + +[22] J. Altschuler, J.Weed, P. Rigollet, (2017) [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://papers.nips.cc/paper/6792-near-linear-time-approximation-algorithms-for-optimal-transport-via-sinkhorn-iteration.pdf), Advances in Neural Information Processing Systems (NIPS) 31 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/data/duck.png b/data/duck.png Binary files differnew file mode 100644 index 0000000..9181697 --- /dev/null +++ b/data/duck.png diff --git a/data/heart.png b/data/heart.png Binary files differnew file mode 100644 index 0000000..44a6385 --- /dev/null +++ b/data/heart.png diff --git a/data/redcross.png b/data/redcross.png Binary files differnew file mode 100644 index 0000000..8d0a6fa --- /dev/null +++ b/data/redcross.png diff --git a/data/tooth.png b/data/tooth.png Binary files differnew file mode 100644 index 0000000..cd92c9d --- /dev/null +++ b/data/tooth.png 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 9459023..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 ----- @@ -48,6 +43,12 @@ ot.da .. automodule:: ot.da :members: + +ot.gpu +-------- + +.. automodule:: ot.gpu + :members: ot.dr -------- 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 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b/docs/source/auto_examples/images/thumb/sphx_glr_plot_stochastic_thumb.png diff --git a/docs/source/auto_examples/index.rst b/docs/source/auto_examples/index.rst index 69fb320..259fca1 100644 --- a/docs/source/auto_examples/index.rst +++ b/docs/source/auto_examples/index.rst @@ -49,6 +49,46 @@ This is a gallery of all the POT example files. .. raw:: html + <div class="sphx-glr-thumbcontainer" 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_barycenter_lp_vs_entropic.ipynb b/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.ipynb new file mode 100644 index 0000000..2199162 --- /dev/null +++ b/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.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# 1D Wasserstein barycenter comparison between exact LP and entropic regularization\n\n\nThis example illustrates the computation of regularized Wasserstein Barycenter\nas proposed in [3] and exact LP barycenters using standard LP solver.\n\nIt reproduces approximately Figure 3.1 and 3.2 from the following paper:\nCuturi, M., & Peyr\u00e9, G. (2016). A smoothed dual approach for variational\nWasserstein problems. SIAM Journal on Imaging Sciences, 9(1), 320-343.\n\n[3] Benamou, J. D., Carlier, G., Cuturi, M., Nenna, L., & Peyr\u00e9, G. (2015).\nIterative Bregman projections for regularized transportation problems\nSIAM Journal on Scientific Computing, 37(2), A1111-A1138.\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\n# necessary for 3d plot even if not used\nfrom mpl_toolkits.mplot3d import Axes3D # noqa\nfrom matplotlib.collections import PolyCollection # noqa\n\n#import ot.lp.cvx as cvx" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Gaussian Data\n-------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% parameters\n\nproblems = []\n\nn = 100 # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\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 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#%% barycenter computation\n\nalpha = 0.5 # 0<=alpha<=1\nweights = np.array([1 - alpha, alpha])\n\n# l2bary\nbary_l2 = A.dot(weights)\n\n# wasserstein\nreg = 1e-3\not.tic()\nbary_wass = ot.bregman.barycenter(A, M, reg, weights)\not.toc()\n\n\not.tic()\nbary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True)\not.toc()\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='Reg Wasserstein')\npl.plot(x, bary_wass2, 'b', label='LP Wasserstein')\npl.legend()\npl.title('Barycenters')\npl.tight_layout()\n\nproblems.append([A, [bary_l2, bary_wass, bary_wass2]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Dirac Data\n----------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% parameters\n\na1 = 1.0 * (x > 10) * (x < 50)\na2 = 1.0 * (x > 60) * (x < 80)\n\na1 /= a1.sum()\na2 /= a2.sum()\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 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\nalpha = 0.5 # 0<=alpha<=1\nweights = np.array([1 - alpha, alpha])\n\n# l2bary\nbary_l2 = A.dot(weights)\n\n# wasserstein\nreg = 1e-3\not.tic()\nbary_wass = ot.bregman.barycenter(A, M, reg, weights)\not.toc()\n\n\not.tic()\nbary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True)\not.toc()\n\n\nproblems.append([A, [bary_l2, bary_wass, bary_wass2]])\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='Reg Wasserstein')\npl.plot(x, bary_wass2, 'b', label='LP Wasserstein')\npl.legend()\npl.title('Barycenters')\npl.tight_layout()\n\n#%% parameters\n\na1 = np.zeros(n)\na2 = np.zeros(n)\n\na1[10] = .25\na1[20] = .5\na1[30] = .25\na2[80] = 1\n\n\na1 /= a1.sum()\na2 /= a2.sum()\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 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\nalpha = 0.5 # 0<=alpha<=1\nweights = np.array([1 - alpha, alpha])\n\n# l2bary\nbary_l2 = A.dot(weights)\n\n# wasserstein\nreg = 1e-3\not.tic()\nbary_wass = ot.bregman.barycenter(A, M, reg, weights)\not.toc()\n\n\not.tic()\nbary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True)\not.toc()\n\n\nproblems.append([A, [bary_l2, bary_wass, bary_wass2]])\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='Reg Wasserstein')\npl.plot(x, bary_wass2, 'b', label='LP Wasserstein')\npl.legend()\npl.title('Barycenters')\npl.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Final figure\n------------\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% plot\n\nnbm = len(problems)\nnbm2 = (nbm // 2)\n\n\npl.figure(2, (20, 6))\npl.clf()\n\nfor i in range(nbm):\n\n A = problems[i][0]\n bary_l2 = problems[i][1][0]\n bary_wass = problems[i][1][1]\n bary_wass2 = problems[i][1][2]\n\n pl.subplot(2, nbm, 1 + i)\n for j in range(n_distributions):\n pl.plot(x, A[:, j])\n if i == nbm2:\n pl.title('Distributions')\n pl.xticks(())\n pl.yticks(())\n\n pl.subplot(2, nbm, 1 + i + nbm)\n\n pl.plot(x, bary_l2, 'r', label='L2 (Euclidean)')\n pl.plot(x, bary_wass, 'g', label='Reg Wasserstein')\n pl.plot(x, bary_wass2, 'b', label='LP Wasserstein')\n if i == nbm - 1:\n pl.legend()\n if i == nbm2:\n pl.title('Barycenters')\n\n pl.xticks(())\n pl.yticks(())" + ] + } + ], + "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_barycenter_lp_vs_entropic.py b/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.py new file mode 100644 index 0000000..b82765e --- /dev/null +++ b/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.py @@ -0,0 +1,281 @@ +# -*- coding: utf-8 -*- +""" +================================================================================= +1D Wasserstein barycenter comparison between exact LP and entropic regularization +================================================================================= + +This example illustrates the computation of regularized Wasserstein Barycenter +as proposed in [3] and exact LP barycenters using standard LP solver. + +It reproduces approximately Figure 3.1 and 3.2 from the following paper: +Cuturi, M., & Peyré, G. (2016). A smoothed dual approach for variational +Wasserstein problems. SIAM Journal on Imaging Sciences, 9(1), 320-343. + +[3] Benamou, J. D., Carlier, G., Cuturi, M., Nenna, L., & Peyré, G. (2015). +Iterative Bregman projections for regularized transportation problems +SIAM Journal on Scientific Computing, 37(2), A1111-A1138. + +""" + +# 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 # noqa + +#import ot.lp.cvx as cvx + +############################################################################## +# Gaussian Data +# ------------- + +#%% parameters + +problems = [] + +n = 100 # nb bins + +# bin positions +x = np.arange(n, dtype=np.float64) + +# Gaussian distributions +# Gaussian distributions +a1 = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std +a2 = ot.datasets.make_1D_gauss(n, m=60, s=8) + +# creating matrix A containing all distributions +A = np.vstack((a1, a2)).T +n_distributions = A.shape[1] + +# loss matrix + normalization +M = ot.utils.dist0(n) +M /= M.max() + + +#%% plot the distributions + +pl.figure(1, figsize=(6.4, 3)) +for i in range(n_distributions): + pl.plot(x, A[:, i]) +pl.title('Distributions') +pl.tight_layout() + +#%% barycenter computation + +alpha = 0.5 # 0<=alpha<=1 +weights = np.array([1 - alpha, alpha]) + +# l2bary +bary_l2 = A.dot(weights) + +# wasserstein +reg = 1e-3 +ot.tic() +bary_wass = ot.bregman.barycenter(A, M, reg, weights) +ot.toc() + + +ot.tic() +bary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True) +ot.toc() + +pl.figure(2) +pl.clf() +pl.subplot(2, 1, 1) +for i in range(n_distributions): + pl.plot(x, A[:, i]) +pl.title('Distributions') + +pl.subplot(2, 1, 2) +pl.plot(x, bary_l2, 'r', label='l2') +pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') +pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') +pl.legend() +pl.title('Barycenters') +pl.tight_layout() + +problems.append([A, [bary_l2, bary_wass, bary_wass2]]) + +############################################################################## +# Dirac Data +# ---------- + +#%% parameters + +a1 = 1.0 * (x > 10) * (x < 50) +a2 = 1.0 * (x > 60) * (x < 80) + +a1 /= a1.sum() +a2 /= a2.sum() + +# creating matrix A containing all distributions +A = np.vstack((a1, a2)).T +n_distributions = A.shape[1] + +# loss matrix + normalization +M = ot.utils.dist0(n) +M /= M.max() + + +#%% plot the distributions + +pl.figure(1, figsize=(6.4, 3)) +for i in range(n_distributions): + pl.plot(x, A[:, i]) +pl.title('Distributions') +pl.tight_layout() + + +#%% barycenter computation + +alpha = 0.5 # 0<=alpha<=1 +weights = np.array([1 - alpha, alpha]) + +# l2bary +bary_l2 = A.dot(weights) + +# wasserstein +reg = 1e-3 +ot.tic() +bary_wass = ot.bregman.barycenter(A, M, reg, weights) +ot.toc() + + +ot.tic() +bary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True) +ot.toc() + + +problems.append([A, [bary_l2, bary_wass, bary_wass2]]) + +pl.figure(2) +pl.clf() +pl.subplot(2, 1, 1) +for i in range(n_distributions): + pl.plot(x, A[:, i]) +pl.title('Distributions') + +pl.subplot(2, 1, 2) +pl.plot(x, bary_l2, 'r', label='l2') +pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') +pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') +pl.legend() +pl.title('Barycenters') +pl.tight_layout() + +#%% parameters + +a1 = np.zeros(n) +a2 = np.zeros(n) + +a1[10] = .25 +a1[20] = .5 +a1[30] = .25 +a2[80] = 1 + + +a1 /= a1.sum() +a2 /= a2.sum() + +# creating matrix A containing all distributions +A = np.vstack((a1, a2)).T +n_distributions = A.shape[1] + +# loss matrix + normalization +M = ot.utils.dist0(n) +M /= M.max() + + +#%% plot the distributions + +pl.figure(1, figsize=(6.4, 3)) +for i in range(n_distributions): + pl.plot(x, A[:, i]) +pl.title('Distributions') +pl.tight_layout() + + +#%% barycenter computation + +alpha = 0.5 # 0<=alpha<=1 +weights = np.array([1 - alpha, alpha]) + +# l2bary +bary_l2 = A.dot(weights) + +# wasserstein +reg = 1e-3 +ot.tic() +bary_wass = ot.bregman.barycenter(A, M, reg, weights) +ot.toc() + + +ot.tic() +bary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True) +ot.toc() + + +problems.append([A, [bary_l2, bary_wass, bary_wass2]]) + +pl.figure(2) +pl.clf() +pl.subplot(2, 1, 1) +for i in range(n_distributions): + pl.plot(x, A[:, i]) +pl.title('Distributions') + +pl.subplot(2, 1, 2) +pl.plot(x, bary_l2, 'r', label='l2') +pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') +pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') +pl.legend() +pl.title('Barycenters') +pl.tight_layout() + + +############################################################################## +# Final figure +# ------------ +# + +#%% plot + +nbm = len(problems) +nbm2 = (nbm // 2) + + +pl.figure(2, (20, 6)) +pl.clf() + +for i in range(nbm): + + A = problems[i][0] + bary_l2 = problems[i][1][0] + bary_wass = problems[i][1][1] + bary_wass2 = problems[i][1][2] + + pl.subplot(2, nbm, 1 + i) + for j in range(n_distributions): + pl.plot(x, A[:, j]) + if i == nbm2: + pl.title('Distributions') + pl.xticks(()) + pl.yticks(()) + + pl.subplot(2, nbm, 1 + i + nbm) + + pl.plot(x, bary_l2, 'r', label='L2 (Euclidean)') + pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') + pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') + if i == nbm - 1: + pl.legend() + if i == nbm2: + pl.title('Barycenters') + + pl.xticks(()) + pl.yticks(()) diff --git a/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.rst b/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.rst new file mode 100644 index 0000000..bd1c710 --- /dev/null +++ b/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.rst @@ -0,0 +1,447 @@ + + +.. _sphx_glr_auto_examples_plot_barycenter_lp_vs_entropic.py: + + +================================================================================= +1D Wasserstein barycenter comparison between exact LP and entropic regularization +================================================================================= + +This example illustrates the computation of regularized Wasserstein Barycenter +as proposed in [3] and exact LP barycenters using standard LP solver. + +It reproduces approximately Figure 3.1 and 3.2 from the following paper: +Cuturi, M., & Peyré, G. (2016). A smoothed dual approach for variational +Wasserstein problems. SIAM Journal on Imaging Sciences, 9(1), 320-343. + +[3] Benamou, J. D., Carlier, G., Cuturi, M., Nenna, L., & Peyré, G. (2015). +Iterative Bregman projections for regularized transportation problems +SIAM Journal on Scientific Computing, 37(2), A1111-A1138. + + + + +.. 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 # noqa + + #import ot.lp.cvx as cvx + + + + + + + +Gaussian Data +------------- + + + +.. code-block:: python + + + #%% parameters + + problems = [] + + n = 100 # nb bins + + # bin positions + x = np.arange(n, dtype=np.float64) + + # Gaussian distributions + # Gaussian distributions + a1 = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std + a2 = ot.datasets.make_1D_gauss(n, m=60, s=8) + + # creating matrix A containing all distributions + A = np.vstack((a1, a2)).T + n_distributions = A.shape[1] + + # loss matrix + normalization + M = ot.utils.dist0(n) + M /= M.max() + + + #%% plot the distributions + + pl.figure(1, figsize=(6.4, 3)) + for i in range(n_distributions): + pl.plot(x, A[:, i]) + pl.title('Distributions') + pl.tight_layout() + + #%% barycenter computation + + alpha = 0.5 # 0<=alpha<=1 + weights = np.array([1 - alpha, alpha]) + + # l2bary + bary_l2 = A.dot(weights) + + # wasserstein + reg = 1e-3 + ot.tic() + bary_wass = ot.bregman.barycenter(A, M, reg, weights) + ot.toc() + + + ot.tic() + bary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True) + ot.toc() + + pl.figure(2) + pl.clf() + pl.subplot(2, 1, 1) + for i in range(n_distributions): + pl.plot(x, A[:, i]) + pl.title('Distributions') + + pl.subplot(2, 1, 2) + pl.plot(x, bary_l2, 'r', label='l2') + pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') + pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') + pl.legend() + pl.title('Barycenters') + pl.tight_layout() + + problems.append([A, [bary_l2, bary_wass, bary_wass2]]) + + + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_001.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_002.png + :scale: 47 + + +.. rst-class:: sphx-glr-script-out + + Out:: + + Elapsed time : 0.010712385177612305 s + Primal Feasibility Dual Feasibility Duality Gap Step Path Parameter Objective + 1.0 1.0 1.0 - 1.0 1700.336700337 + 0.006776453137632 0.006776453137633 0.006776453137633 0.9932238647293 0.006776453137633 125.6700527543 + 0.004018712867874 0.004018712867874 0.004018712867874 0.4301142633 0.004018712867874 12.26594150093 + 0.001172775061627 0.001172775061627 0.001172775061627 0.7599932455029 0.001172775061627 0.3378536968897 + 0.0004375137005385 0.0004375137005385 0.0004375137005385 0.6422331807989 0.0004375137005385 0.1468420566358 + 0.000232669046734 0.0002326690467341 0.000232669046734 0.5016999460893 0.000232669046734 0.09381703231432 + 7.430121674303e-05 7.430121674303e-05 7.430121674303e-05 0.7035962305812 7.430121674303e-05 0.0577787025717 + 5.321227838876e-05 5.321227838875e-05 5.321227838876e-05 0.308784186441 5.321227838876e-05 0.05266249477203 + 1.990900379199e-05 1.990900379196e-05 1.990900379199e-05 0.6520472013244 1.990900379199e-05 0.04526054405519 + 6.305442046799e-06 6.30544204682e-06 6.3054420468e-06 0.7073953304075 6.305442046798e-06 0.04237597591383 + 2.290148391577e-06 2.290148391582e-06 2.290148391578e-06 0.6941812711492 2.29014839159e-06 0.041522849321 + 1.182864875387e-06 1.182864875406e-06 1.182864875427e-06 0.508455204675 1.182864875445e-06 0.04129461872827 + 3.626786381529e-07 3.626786382468e-07 3.626786382923e-07 0.7101651572101 3.62678638267e-07 0.04113032448923 + 1.539754244902e-07 1.539754249276e-07 1.539754249356e-07 0.6279322066282 1.539754253892e-07 0.04108867636379 + 5.193221323143e-08 5.193221463044e-08 5.193221462729e-08 0.6843453436759 5.193221708199e-08 0.04106859618414 + 1.888205054507e-08 1.888204779723e-08 1.88820477688e-08 0.6673444085651 1.888205650952e-08 0.041062141752 + 5.676855206925e-09 5.676854518888e-09 5.676854517651e-09 0.7281705804232 5.676885442702e-09 0.04105958648713 + 3.501157668218e-09 3.501150243546e-09 3.501150216347e-09 0.414020345194 3.501164437194e-09 0.04105916265261 + 1.110594251499e-09 1.110590786827e-09 1.11059083379e-09 0.6998954759911 1.110636623476e-09 0.04105870073485 + 5.770971626386e-10 5.772456113791e-10 5.772456200156e-10 0.4999769658132 5.77013379477e-10 0.04105859769135 + 1.535218204536e-10 1.536993317032e-10 1.536992771966e-10 0.7516471627141 1.536205005991e-10 0.04105851679958 + 6.724209350756e-11 6.739211232927e-11 6.739210470901e-11 0.5944802416166 6.735465384341e-11 0.04105850033766 + 1.743382199199e-11 1.736445896691e-11 1.736448490761e-11 0.7573407808104 1.734254328931e-11 0.04105849088824 + Optimization terminated successfully. + Elapsed time : 2.883899211883545 s + + +Dirac Data +---------- + + + +.. code-block:: python + + + #%% parameters + + a1 = 1.0 * (x > 10) * (x < 50) + a2 = 1.0 * (x > 60) * (x < 80) + + a1 /= a1.sum() + a2 /= a2.sum() + + # creating matrix A containing all distributions + A = np.vstack((a1, a2)).T + n_distributions = A.shape[1] + + # loss matrix + normalization + M = ot.utils.dist0(n) + M /= M.max() + + + #%% plot the distributions + + pl.figure(1, figsize=(6.4, 3)) + for i in range(n_distributions): + pl.plot(x, A[:, i]) + pl.title('Distributions') + pl.tight_layout() + + + #%% barycenter computation + + alpha = 0.5 # 0<=alpha<=1 + weights = np.array([1 - alpha, alpha]) + + # l2bary + bary_l2 = A.dot(weights) + + # wasserstein + reg = 1e-3 + ot.tic() + bary_wass = ot.bregman.barycenter(A, M, reg, weights) + ot.toc() + + + ot.tic() + bary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True) + ot.toc() + + + problems.append([A, [bary_l2, bary_wass, bary_wass2]]) + + pl.figure(2) + pl.clf() + pl.subplot(2, 1, 1) + for i in range(n_distributions): + pl.plot(x, A[:, i]) + pl.title('Distributions') + + pl.subplot(2, 1, 2) + pl.plot(x, bary_l2, 'r', label='l2') + pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') + pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') + pl.legend() + pl.title('Barycenters') + pl.tight_layout() + + #%% parameters + + a1 = np.zeros(n) + a2 = np.zeros(n) + + a1[10] = .25 + a1[20] = .5 + a1[30] = .25 + a2[80] = 1 + + + a1 /= a1.sum() + a2 /= a2.sum() + + # creating matrix A containing all distributions + A = np.vstack((a1, a2)).T + n_distributions = A.shape[1] + + # loss matrix + normalization + M = ot.utils.dist0(n) + M /= M.max() + + + #%% plot the distributions + + pl.figure(1, figsize=(6.4, 3)) + for i in range(n_distributions): + pl.plot(x, A[:, i]) + pl.title('Distributions') + pl.tight_layout() + + + #%% barycenter computation + + alpha = 0.5 # 0<=alpha<=1 + weights = np.array([1 - alpha, alpha]) + + # l2bary + bary_l2 = A.dot(weights) + + # wasserstein + reg = 1e-3 + ot.tic() + bary_wass = ot.bregman.barycenter(A, M, reg, weights) + ot.toc() + + + ot.tic() + bary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True) + ot.toc() + + + problems.append([A, [bary_l2, bary_wass, bary_wass2]]) + + pl.figure(2) + pl.clf() + pl.subplot(2, 1, 1) + for i in range(n_distributions): + pl.plot(x, A[:, i]) + pl.title('Distributions') + + pl.subplot(2, 1, 2) + pl.plot(x, bary_l2, 'r', label='l2') + pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') + pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') + pl.legend() + pl.title('Barycenters') + pl.tight_layout() + + + + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_003.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_004.png + :scale: 47 + + +.. rst-class:: sphx-glr-script-out + + Out:: + + Elapsed time : 0.014938592910766602 s + Primal Feasibility Dual Feasibility Duality Gap Step Path Parameter Objective + 1.0 1.0 1.0 - 1.0 1700.336700337 + 0.006776466288966 0.006776466288966 0.006776466288966 0.9932238515788 0.006776466288966 125.6649255808 + 0.004036918865495 0.004036918865495 0.004036918865495 0.4272973099316 0.004036918865495 12.3471617011 + 0.00121923268707 0.00121923268707 0.00121923268707 0.749698685599 0.00121923268707 0.3243835647408 + 0.0003837422984432 0.0003837422984432 0.0003837422984432 0.6926882608284 0.0003837422984432 0.1361719397493 + 0.0001070128410183 0.0001070128410183 0.0001070128410183 0.7643889137854 0.0001070128410183 0.07581952832518 + 0.0001001275033711 0.0001001275033711 0.0001001275033711 0.07058704837812 0.0001001275033712 0.0734739493635 + 4.550897507844e-05 4.550897507841e-05 4.550897507844e-05 0.5761172484828 4.550897507845e-05 0.05555077655047 + 8.557124125522e-06 8.5571241255e-06 8.557124125522e-06 0.8535925441152 8.557124125522e-06 0.04439814660221 + 3.611995628407e-06 3.61199562841e-06 3.611995628414e-06 0.6002277331554 3.611995628415e-06 0.04283007762152 + 7.590393750365e-07 7.590393750491e-07 7.590393750378e-07 0.8221486533416 7.590393750381e-07 0.04192322976248 + 8.299929287441e-08 8.299929286079e-08 8.299929287532e-08 0.9017467938799 8.29992928758e-08 0.04170825633295 + 3.117560203449e-10 3.117560130137e-10 3.11756019954e-10 0.997039969226 3.11756019952e-10 0.04168179329766 + 1.559749653711e-14 1.558073160926e-14 1.559756940692e-14 0.9999499686183 1.559750643989e-14 0.04168169240444 + Optimization terminated successfully. + Elapsed time : 2.642659902572632 s + Elapsed time : 0.002908945083618164 s + Primal Feasibility Dual Feasibility Duality Gap Step Path Parameter Objective + 1.0 1.0 1.0 - 1.0 1700.336700337 + 0.006774675520727 0.006774675520727 0.006774675520727 0.9932256422636 0.006774675520727 125.6956034743 + 0.002048208707562 0.002048208707562 0.002048208707562 0.7343095368143 0.002048208707562 5.213991622123 + 0.000269736547478 0.0002697365474781 0.0002697365474781 0.8839403501193 0.000269736547478 0.505938390389 + 6.832109993943e-05 6.832109993944e-05 6.832109993944e-05 0.7601171075965 6.832109993943e-05 0.2339657807272 + 2.437682932219e-05 2.43768293222e-05 2.437682932219e-05 0.6663448297475 2.437682932219e-05 0.1471256246325 + 1.13498321631e-05 1.134983216308e-05 1.13498321631e-05 0.5553643816404 1.13498321631e-05 0.1181584941171 + 3.342312725885e-06 3.342312725884e-06 3.342312725885e-06 0.7238133571615 3.342312725885e-06 0.1006387519747 + 7.078561231603e-07 7.078561231509e-07 7.078561231604e-07 0.8033142552512 7.078561231603e-07 0.09474734646269 + 1.966870956916e-07 1.966870954537e-07 1.966870954468e-07 0.752547917788 1.966870954633e-07 0.09354342735766 + 4.19989524849e-10 4.199895164852e-10 4.199895238758e-10 0.9984019849375 4.19989523951e-10 0.09310367785861 + 2.101015938666e-14 2.100625691113e-14 2.101023853438e-14 0.999949974425 2.101023691864e-14 0.09310274466458 + Optimization terminated successfully. + Elapsed time : 2.690450668334961 s + + +Final figure +------------ + + + + +.. code-block:: python + + + #%% plot + + nbm = len(problems) + nbm2 = (nbm // 2) + + + pl.figure(2, (20, 6)) + pl.clf() + + for i in range(nbm): + + A = problems[i][0] + bary_l2 = problems[i][1][0] + bary_wass = problems[i][1][1] + bary_wass2 = problems[i][1][2] + + pl.subplot(2, nbm, 1 + i) + for j in range(n_distributions): + pl.plot(x, A[:, j]) + if i == nbm2: + pl.title('Distributions') + pl.xticks(()) + pl.yticks(()) + + pl.subplot(2, nbm, 1 + i + nbm) + + pl.plot(x, bary_l2, 'r', label='L2 (Euclidean)') + pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') + pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') + if i == nbm - 1: + pl.legend() + if i == nbm2: + pl.title('Barycenters') + + pl.xticks(()) + pl.yticks(()) + + + +.. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_006.png + :align: center + + + + +**Total running time of the script:** ( 0 minutes 8.892 seconds) + + + +.. only :: html + + .. container:: sphx-glr-footer + + + .. container:: sphx-glr-download + + :download:`Download Python source code: plot_barycenter_lp_vs_entropic.py <plot_barycenter_lp_vs_entropic.py>` + + + + .. container:: sphx-glr-download + + :download:`Download Jupyter notebook: plot_barycenter_lp_vs_entropic.ipynb <plot_barycenter_lp_vs_entropic.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_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_otda_linear_mapping.ipynb b/docs/source/auto_examples/plot_otda_linear_mapping.ipynb new file mode 100644 index 0000000..027b6cb --- /dev/null +++ b/docs/source/auto_examples/plot_otda_linear_mapping.ipynb @@ -0,0 +1,180 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# Linear OT mapping estimation\n\n\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 pylab as pl\nimport ot" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate data\n-------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "n = 1000\nd = 2\nsigma = .1\n\n# source samples\nangles = np.random.rand(n, 1) * 2 * np.pi\nxs = np.concatenate((np.sin(angles), np.cos(angles)),\n axis=1) + sigma * np.random.randn(n, 2)\nxs[:n // 2, 1] += 2\n\n\n# target samples\nanglet = np.random.rand(n, 1) * 2 * np.pi\nxt = np.concatenate((np.sin(anglet), np.cos(anglet)),\n axis=1) + sigma * np.random.randn(n, 2)\nxt[:n // 2, 1] += 2\n\n\nA = np.array([[1.5, .7], [.7, 1.5]])\nb = np.array([[4, 2]])\nxt = xt.dot(A) + 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, (5, 5))\npl.plot(xs[:, 0], xs[:, 1], '+')\npl.plot(xt[:, 0], xt[:, 1], 'o')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Estimate linear mapping and transport\n-------------------------------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "Ae, be = ot.da.OT_mapping_linear(xs, xt)\n\nxst = xs.dot(Ae) + be" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot transported samples\n------------------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "pl.figure(1, (5, 5))\npl.clf()\npl.plot(xs[:, 0], xs[:, 1], '+')\npl.plot(xt[:, 0], xt[:, 1], 'o')\npl.plot(xst[:, 0], xst[:, 1], '+')\n\npl.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Load image data\n---------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def im2mat(I):\n \"\"\"Converts and image to matrix (one pixel per line)\"\"\"\n return I.reshape((I.shape[0] * I.shape[1], I.shape[2]))\n\n\ndef mat2im(X, shape):\n \"\"\"Converts back a matrix to an image\"\"\"\n return X.reshape(shape)\n\n\ndef minmax(I):\n return np.clip(I, 0, 1)\n\n\n# Loading images\nI1 = pl.imread('../data/ocean_day.jpg').astype(np.float64) / 256\nI2 = pl.imread('../data/ocean_sunset.jpg').astype(np.float64) / 256\n\n\nX1 = im2mat(I1)\nX2 = im2mat(I2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Estimate mapping and adapt\n----------------------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "mapping = ot.da.LinearTransport()\n\nmapping.fit(Xs=X1, Xt=X2)\n\n\nxst = mapping.transform(Xs=X1)\nxts = mapping.inverse_transform(Xt=X2)\n\nI1t = minmax(mat2im(xst, I1.shape))\nI2t = minmax(mat2im(xts, I2.shape))\n\n# %%" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot transformed images\n-----------------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "pl.figure(2, figsize=(10, 7))\n\npl.subplot(2, 2, 1)\npl.imshow(I1)\npl.axis('off')\npl.title('Im. 1')\n\npl.subplot(2, 2, 2)\npl.imshow(I2)\npl.axis('off')\npl.title('Im. 2')\n\npl.subplot(2, 2, 3)\npl.imshow(I1t)\npl.axis('off')\npl.title('Mapping Im. 1')\n\npl.subplot(2, 2, 4)\npl.imshow(I2t)\npl.axis('off')\npl.title('Inverse mapping Im. 2')" + ] + } + ], + "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_otda_linear_mapping.py b/docs/source/auto_examples/plot_otda_linear_mapping.py new file mode 100644 index 0000000..c65bd4f --- /dev/null +++ b/docs/source/auto_examples/plot_otda_linear_mapping.py @@ -0,0 +1,144 @@ +#!/usr/bin/env python3 +# -*- coding: utf-8 -*- +""" +============================ +Linear OT mapping estimation +============================ + + +""" + +# Author: Remi Flamary <remi.flamary@unice.fr> +# +# License: MIT License + +import numpy as np +import pylab as pl +import ot + +############################################################################## +# Generate data +# ------------- + +n = 1000 +d = 2 +sigma = .1 + +# source samples +angles = np.random.rand(n, 1) * 2 * np.pi +xs = np.concatenate((np.sin(angles), np.cos(angles)), + axis=1) + sigma * np.random.randn(n, 2) +xs[:n // 2, 1] += 2 + + +# target samples +anglet = np.random.rand(n, 1) * 2 * np.pi +xt = np.concatenate((np.sin(anglet), np.cos(anglet)), + axis=1) + sigma * np.random.randn(n, 2) +xt[:n // 2, 1] += 2 + + +A = np.array([[1.5, .7], [.7, 1.5]]) +b = np.array([[4, 2]]) +xt = xt.dot(A) + b + +############################################################################## +# Plot data +# --------- + +pl.figure(1, (5, 5)) +pl.plot(xs[:, 0], xs[:, 1], '+') +pl.plot(xt[:, 0], xt[:, 1], 'o') + + +############################################################################## +# Estimate linear mapping and transport +# ------------------------------------- + +Ae, be = ot.da.OT_mapping_linear(xs, xt) + +xst = xs.dot(Ae) + be + + +############################################################################## +# Plot transported samples +# ------------------------ + +pl.figure(1, (5, 5)) +pl.clf() +pl.plot(xs[:, 0], xs[:, 1], '+') +pl.plot(xt[:, 0], xt[:, 1], 'o') +pl.plot(xst[:, 0], xst[:, 1], '+') + +pl.show() + +############################################################################## +# Load image data +# --------------- + + +def im2mat(I): + """Converts and image to matrix (one pixel per line)""" + return I.reshape((I.shape[0] * I.shape[1], I.shape[2])) + + +def mat2im(X, shape): + """Converts back a matrix to an image""" + return X.reshape(shape) + + +def minmax(I): + return np.clip(I, 0, 1) + + +# Loading images +I1 = pl.imread('../data/ocean_day.jpg').astype(np.float64) / 256 +I2 = pl.imread('../data/ocean_sunset.jpg').astype(np.float64) / 256 + + +X1 = im2mat(I1) +X2 = im2mat(I2) + +############################################################################## +# Estimate mapping and adapt +# ---------------------------- + +mapping = ot.da.LinearTransport() + +mapping.fit(Xs=X1, Xt=X2) + + +xst = mapping.transform(Xs=X1) +xts = mapping.inverse_transform(Xt=X2) + +I1t = minmax(mat2im(xst, I1.shape)) +I2t = minmax(mat2im(xts, I2.shape)) + +# %% + + +############################################################################## +# Plot transformed images +# ----------------------- + +pl.figure(2, figsize=(10, 7)) + +pl.subplot(2, 2, 1) +pl.imshow(I1) +pl.axis('off') +pl.title('Im. 1') + +pl.subplot(2, 2, 2) +pl.imshow(I2) +pl.axis('off') +pl.title('Im. 2') + +pl.subplot(2, 2, 3) +pl.imshow(I1t) +pl.axis('off') +pl.title('Mapping Im. 1') + +pl.subplot(2, 2, 4) +pl.imshow(I2t) +pl.axis('off') +pl.title('Inverse mapping Im. 2') diff --git a/docs/source/auto_examples/plot_otda_linear_mapping.rst b/docs/source/auto_examples/plot_otda_linear_mapping.rst new file mode 100644 index 0000000..8e2e0cf --- /dev/null +++ b/docs/source/auto_examples/plot_otda_linear_mapping.rst @@ -0,0 +1,260 @@ + + +.. _sphx_glr_auto_examples_plot_otda_linear_mapping.py: + + +============================ +Linear OT mapping estimation +============================ + + + + + +.. code-block:: python + + + # Author: Remi Flamary <remi.flamary@unice.fr> + # + # License: MIT License + + import numpy as np + import pylab as pl + import ot + + + + + + + +Generate data +------------- + + + +.. code-block:: python + + + n = 1000 + d = 2 + sigma = .1 + + # source samples + angles = np.random.rand(n, 1) * 2 * np.pi + xs = np.concatenate((np.sin(angles), np.cos(angles)), + axis=1) + sigma * np.random.randn(n, 2) + xs[:n // 2, 1] += 2 + + + # target samples + anglet = np.random.rand(n, 1) * 2 * np.pi + xt = np.concatenate((np.sin(anglet), np.cos(anglet)), + axis=1) + sigma * np.random.randn(n, 2) + xt[:n // 2, 1] += 2 + + + A = np.array([[1.5, .7], [.7, 1.5]]) + b = np.array([[4, 2]]) + xt = xt.dot(A) + b + + + + + + + +Plot data +--------- + + + +.. code-block:: python + + + pl.figure(1, (5, 5)) + pl.plot(xs[:, 0], xs[:, 1], '+') + pl.plot(xt[:, 0], xt[:, 1], 'o') + + + + + +.. image:: /auto_examples/images/sphx_glr_plot_otda_linear_mapping_001.png + :align: center + + + + +Estimate linear mapping and transport +------------------------------------- + + + +.. code-block:: python + + + Ae, be = ot.da.OT_mapping_linear(xs, xt) + + xst = xs.dot(Ae) + be + + + + + + + + +Plot transported samples +------------------------ + + + +.. code-block:: python + + + pl.figure(1, (5, 5)) + pl.clf() + pl.plot(xs[:, 0], xs[:, 1], '+') + pl.plot(xt[:, 0], xt[:, 1], 'o') + pl.plot(xst[:, 0], xst[:, 1], '+') + + pl.show() + + + + +.. image:: /auto_examples/images/sphx_glr_plot_otda_linear_mapping_002.png + :align: center + + + + +Load image data +--------------- + + + +.. code-block:: python + + + + def im2mat(I): + """Converts and image to matrix (one pixel per line)""" + return I.reshape((I.shape[0] * I.shape[1], I.shape[2])) + + + def mat2im(X, shape): + """Converts back a matrix to an image""" + return X.reshape(shape) + + + def minmax(I): + return np.clip(I, 0, 1) + + + # Loading images + I1 = pl.imread('../data/ocean_day.jpg').astype(np.float64) / 256 + I2 = pl.imread('../data/ocean_sunset.jpg').astype(np.float64) / 256 + + + X1 = im2mat(I1) + X2 = im2mat(I2) + + + + + + + +Estimate mapping and adapt +---------------------------- + + + +.. code-block:: python + + + mapping = ot.da.LinearTransport() + + mapping.fit(Xs=X1, Xt=X2) + + + xst = mapping.transform(Xs=X1) + xts = mapping.inverse_transform(Xt=X2) + + I1t = minmax(mat2im(xst, I1.shape)) + I2t = minmax(mat2im(xts, I2.shape)) + + # %% + + + + + + + + +Plot transformed images +----------------------- + + + +.. code-block:: python + + + pl.figure(2, figsize=(10, 7)) + + pl.subplot(2, 2, 1) + pl.imshow(I1) + pl.axis('off') + pl.title('Im. 1') + + pl.subplot(2, 2, 2) + pl.imshow(I2) + pl.axis('off') + pl.title('Im. 2') + + pl.subplot(2, 2, 3) + pl.imshow(I1t) + pl.axis('off') + pl.title('Mapping Im. 1') + + pl.subplot(2, 2, 4) + pl.imshow(I2t) + pl.axis('off') + pl.title('Inverse mapping Im. 2') + + + +.. image:: /auto_examples/images/sphx_glr_plot_otda_linear_mapping_004.png + :align: center + + + + +**Total running time of the script:** ( 0 minutes 0.635 seconds) + + + +.. only :: html + + .. container:: sphx-glr-footer + + + .. container:: sphx-glr-download + + :download:`Download Python source code: plot_otda_linear_mapping.py <plot_otda_linear_mapping.py>` + + + + .. container:: sphx-glr-download + + :download:`Download Jupyter notebook: plot_otda_linear_mapping.ipynb <plot_otda_linear_mapping.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/conf.py b/docs/source/conf.py index 114245d..433eca6 100644 --- a/docs/source/conf.py +++ b/docs/source/conf.py @@ -31,7 +31,7 @@ class Mock(MagicMock): @classmethod def __getattr__(cls, name): return MagicMock() -MOCK_MODULES = ['ot.lp.emd_wrap','autograd','pymanopt','cudamat','autograd.numpy','pymanopt.manifolds','pymanopt.solvers'] +MOCK_MODULES = ['ot.lp.emd_wrap','autograd','pymanopt','cupy','autograd.numpy','pymanopt.manifolds','pymanopt.solvers'] # 'autograd.numpy','pymanopt.manifolds','pymanopt.solvers', sys.modules.update((mod_name, Mock()) for mod_name in MOCK_MODULES) # !!!! diff --git a/docs/source/readme.rst b/docs/source/readme.rst index 5d37f64..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 @@ -13,13 +13,14 @@ It provides the following solvers: - OT Network Flow solver for the linear program/ Earth Movers Distance [1]. - Entropic regularization OT solver with Sinkhorn Knopp Algorithm [2] - and stabilized version [9][10] with optional GPU implementation - (requires cudamat). + and stabilized version [9][10] and greedy SInkhorn [22] with optional + GPU implementation (requires cudamat). - Smooth optimal transport solvers (dual and semi-dual) for KL and squared L2 regularizations [17]. - Non regularized Wasserstein barycenters [16] with LP solver (only small scale). -- Bregman projections for Wasserstein barycenter [3] and unmixing [4]. +- Bregman projections for Wasserstein barycenter [3], convolutional + barycenter [21] and unmixing [4]. - Optimal transport for domain adaptation with group lasso regularization [5] - Conditional gradient [6] and Generalized conditional gradient for @@ -29,6 +30,9 @@ It provides the following solvers: pymanopt). - Gromov-Wasserstein distances and barycenters ([13] and regularized [12]) +- Stochastic Optimization for Large-scale Optimal Transport (semi-dual + problem [18] and dual problem [19]) +- Non regularized free support Wasserstein barycenters [20]. Some demonstrations (both in Python and Jupyter Notebook format) are available in the examples folder. @@ -104,7 +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: :: @@ -219,6 +223,9 @@ The contributors to this library are: - `Stanislas Chambon <https://slasnista.github.io/>`__ - `Antoine Rolet <https://arolet.github.io/>`__ - Erwan Vautier (Gromov-Wasserstein) +- `Kilian Fatras <https://kilianfatras.github.io/>`__ +- `Alain + Rakotomamonjy <https://sites.google.com/site/alainrakotomamonjy/home>`__ This toolbox benefit a lot from open source research and we would like to thank the following persons for providing some code (in various @@ -334,6 +341,31 @@ Optimal Transport <https://arxiv.org/abs/1710.06276>`__. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics (AISTATS). +[18] Genevay, A., Cuturi, M., Peyré, G. & Bach, F. (2016) `Stochastic +Optimization for Large-scale Optimal +Transport <https://arxiv.org/abs/1605.08527>`__. Advances in Neural +Information Processing Systems (2016). + +[19] Seguy, V., Bhushan Damodaran, B., Flamary, R., Courty, N., Rolet, +A.& Blondel, M. `Large-scale Optimal Transport and Mapping +Estimation <https://arxiv.org/pdf/1711.02283.pdf>`__. International +Conference on Learning Representation (2018) + +[20] Cuturi, M. and Doucet, A. (2014) `Fast Computation of Wasserstein +Barycenters <http://proceedings.mlr.press/v32/cuturi14.html>`__. +International Conference in Machine Learning + +[21] Solomon, J., De Goes, F., Peyré, G., Cuturi, M., Butscher, A., +Nguyen, A. & Guibas, L. (2015). `Convolutional wasserstein distances: +Efficient optimal transportation on geometric +domains <https://dl.acm.org/citation.cfm?id=2766963>`__. ACM +Transactions on Graphics (TOG), 34(4), 66. + +[22] J. Altschuler, J.Weed, P. Rigollet, (2017) `Near-linear time +approximation algorithms for optimal transport via Sinkhorn +iteration <https://papers.nips.cc/paper/6792-near-linear-time-approximation-algorithms-for-optimal-transport-via-sinkhorn-iteration.pdf>`__, +Advances in Neural Information Processing Systems (NIPS) 31 + .. |PyPI version| image:: https://badge.fury.io/py/POT.svg :target: https://badge.fury.io/py/POT .. |Anaconda Cloud| image:: https://anaconda.org/conda-forge/pot/badges/version.svg @@ -342,6 +374,8 @@ Statistics (AISTATS). :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_OT_1D_smooth.py b/examples/plot_OT_1D_smooth.py new file mode 100644 index 0000000..b690751 --- /dev/null +++ b/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/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/examples/plot_convolutional_barycenter.py b/examples/plot_convolutional_barycenter.py new file mode 100644 index 0000000..e74db04 --- /dev/null +++ b/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/examples/plot_free_support_barycenter.py b/examples/plot_free_support_barycenter.py new file mode 100644 index 0000000..b6efc59 --- /dev/null +++ b/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/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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YDUGItNWMGf4tfk0NvPCCvnRrq6IimDjR1w8+80w/gCVHKYBF2uLJJ3281wyefx522SV2Rbmha1dfOW7cOJ+edtFFUF0du6p2pwAWaY3qaj+67dhj/WCCf/4T/u3fYleVW9IQvvBCuPFGOPpoP51TDlEAi2yuuXN9yOGKK3ze6osvwrBhsavKTYWFPpvk9tv9fR45Eh59NHZV7UYBLNJSa9b4qma77OLr2N5zD9x/P/ToEbuy3Hf66TBtmn/Q/ed/+vjw7Nmxq2ozBbBIc1au9GlR22zj69h+7Wvw7rs+31erm3WeXXaBKVPguuvgpZf89imn+L9FllIAizSmqgr+/nc49VQ/Suuyy2Cvvfzw4vvu05BDLMXFPld49my44AIfI951VzjwQD/d/YoVsSvcLBbycAk42djo0aPD1KlTY5cRT3W1H0jxyis+m+Hpp+Gzz3x44Zvf9OlQo0bFrlIaWr7cV1G78054/30fMz7wQBg71q9HjYLu3Tvs5c1sWghhdKufrwAWyIMArqjw7mj5cli61Cf6z5sHc+Z48M6YAWvX+raDBsGhh/pY4xFHdOgPsLSTEOD11+GRR+Cvf/XTP4EPEe24o89Q2WEHKCvzIxUHD/YTo/br5/++rRxKUgBLuxg9YECYOm5cx79QU//f0vvrPx7CxpeaGr+urq67VFX5pbIS1q/3y7p1flm9GsrL/c+NGTYMdtoJRozwbmnMGP+B1dhudvv0U1+XY/p0/8J01iz/sK2o2HjboiLo2dMvpaXQrZtPgeva1Yc8unTxbQoL6y5DhsD11yuApX2MLi4OUzvrVOlNhVt6f/3HzTa8FBT4df0fhsJC/yHp0qXuB6dbN7/07OnDCH36+GXAABg40IN32DDfVvJDTY3/9vPxx369bJn/VrRihX9Il5f7b0Hr1tV9kFdU+Ad7VVXdB35NjZ/d+umn2xzAWgtC3G67QS4PQYgUFPjQw+DBsSuppVkQIiKRKIBFRCLRGLAAYGblwKzYdTSjP/BJ7CKakQ01QnbUmQ017hRC6NnaJ2sMWFKz2vJlQmcws6mqsX1kQ53ZUmNbnq8hCBGRSBTAIiKRKIAldXvsAlpANbafbKgz52vUl3AiIpGoAxYRiUQBLCISiQI4z5nZkWY2y8zmmNmPYteTMrPhZva8mb1rZu+Y2QXJ/f3M7Bkzez+57psBtRaa2XQzm5Tc3sbMpiTv6QNmVhy5vj5mNtHM3jOzmWa2T6a9j2Z2UfLvPMPM7jezkkx4H83sD2a2zMxm1Luv0ffO3P8m9b5lZs2uX6oAzmNmVgjcAhwF7AKcZGaZclrfKuDiEMIuwN7AuUltPwKeCyHsADyX3I7tAmBmvdvXADeEELYHVgCnRamqzk3AUyGEnYHd8Voz5n00s6HA+cDoEMIIoBA4kcx4H/8IHNngvqbeu6OAHZLLGcBtze49hKBLnl6AfYCn692+DLgsdl1N1PoYcBh+tN7g5L7B+AEkMesalvwQHgJMAgw/equosfc4Qn29gQ9JvnCvd3/GvI/AUGA+0A8/OGwScESmvI9AGTCjufcO+B1wUmPbNXVRB5zf0v/4qQXJfRnFzMqAPYEpwMAQwuLkoSXAwEhlpW4ELgFqkttbAJ+HEKqS27Hf022A5cBdyTDJHWbWnQx6H0MIC4HrgI+BxcBKYBqZ9T7W19R7t9k/TwpgyWhm1gN4GLgwhLCq/mPB24xo8yjN7FhgWQhhWqwaWqAIGAXcFkLYE1hDg+GGDHgf+wLj8A+LIUB3Nv61PyO19b1TAOe3hcDwereHJfdlBDPrgofvhBDCn5O7l5rZ4OTxwcCyWPUB+wH/YWYfAf+HD0PcBPQxs3Sdldjv6QJgQQhhSnJ7Ih7ImfQ+Hgp8GEJYHkKoBP6Mv7eZ9D7W19R7t9k/Twrg/PY6sEPybXMx/sXH45FrAvwbZeBOYGYI4fp6Dz0OjE/+PB4fG44ihHBZCGFYCKEMf+/+HkI4GXgeOD7ZLHaNS4D5ZrZTctdY4F0y6H3Ehx72NrPS5N89rTFj3scGmnrvHgdOSWZD7A2srDdU0bhYA++6ZMYFOBqYDXwAXBG7nnp17Y//avcW8GZyORofY30OeB94FugXu9ak3oOAScmftwX+CcwBHgK6Rq5tD2Bq8l4+CvTNtPcRuAp4D5gB/AnomgnvI3A/Pi5dif82cVpT7x3+Bewtyc/S2/isjk3uv02HIpvZkfivXIXAHSGEX7Z6ZyIieabVAZzMIZ2NTw1agP86e1II4d32K09EJHe1ZUH2LwNzQghzAczs//BvMpsM4P79+4eysrI2vKS01eef+8lfhw/f8P5p06Z9EkIYkN4+rODrWqVJpJ5nah5q4nTerdeWAG5sztuYhhuZ2Rn4USFstdVWTNWZd6O65BK4+eaNT4BsZvPiVCSSvzp8FkQI4fYQwugQwugBAwY0/wTpUJWV0KVL7CpEBNoWwBk9h1QaV1EBxVGXhhGRVFsCOGPnkErT1q6F7t1jVyEi0IYx4BBClZl9D3gan4b2hxDCO+1WmXSIVaugR4/YVYgItPG09CGEJ4An2qkW6QSffgpbbBG7ChEBHYqcdxYuhEGDYlchIqAAzivV1fDRR7DddrEricisdReRDqAAziMzZkBVFYwYEbsSEYE2jgFLdvnHP/z6wAPj1hFFU12stbAHafj0UNPgtg4clM2nDjiP3Hsv7LLLxochi0gc6oDzxOTJ8PrrfhiysFHnawXW6P0UNGh9a9JOt9Cvkk441DTogNUhSwuoA84DFRVw9tkwcCCcckrsakQkpQ44x4UAV1wBb74Jjz4KvXrFriiStANNx4LTDrWJjtfS7QoKNnxeEyzdf03SEVfXbPA6tR2yOmOpRx1wDgvBVz+77jrvgMeNi12RiNSnDjhHrVwJ558P99wD554L//u/sSvKEA074YbSTrXQNtjOCpMx3/S6YMPHG+7fqqv9ZtIJ1932a9LbDTtjdcR5RR1wDnr0UZ/tcO+98JOf+BdvBfqXFsk46oBzyGuvwS9+AX/5C+y2mwfxl74Uu6oMVdtppmO0/gllBcntkHS+6fZpx1uYbFeU/Oik14WNf8JZOhZcVeX7Ta5rb1c2uF+dcV5RX5TlqqvhkUdgv/1g333h5Zfh6qv9jBcKX5HMpg44S82cCQ88ABMmwJw5UFbm47zf/raWm9wsTXXCJGO1yRhvSMZwrLBBJ5p0vqE4Oc1Il6INtq9tcdJJF+kYcNL5Fqyv9O0rKvz+9ev9dlOdcfr8jeqXbKQAziKzZ3voPvigr+tg5ocV//zn8LWv1f02LCLZQT+yGWz1anjpJXj2WXjmGXj7bQ/d/ff3L9aOOw4GD45dZY5oohNOx2rTseDafjOdHdHgUy8U+fNqSrwjrin2WROhS4Mj75IxXqvw1yv4IumI165PbiedcHJd2xlXJB1z2iGnHbHGirOSAjiDVFbClCkeuM8954cPV1X5Odz22w9uvBGOPx6GDo1dqYi0BwVwRMuWeeCml9degzVrvLnaay+4+GI49FAP327dYlebJ9IOMiRjrqHxeb4N1R45V+Qdr3X1DjjtfKtK/f6qkqRDLtpwvwVVvt+iL0r9eq2/ftFq73gLVn+RXK/z/a5Lrtf72HHtGHLDsWJ1xBlNAdxJ1q/3w4EnT/awnTwZPvzQHysshJEjYfx4GDsWDjoI+vWLWq6IdAIFcAdYvRreessDd/p0v37rLV8UB3wIYe+9/fDgMWO829WZijNU0kHWdpTp/NyaDdd+qD0CLnlaQdIRFyRjwpR4B5x2vhU9/Lq6myX3p6/n2xVW+B1Fa7sC0LXcO+Piz33st8vKpCNe5Z1wweq1/vS0M07HkNP5xppXnJEUwG20dOmGQTt9Orz/ft3/7379YM894YILPGzHjIFhw+LWLCKZQQHcQuvWwbvv+kyE+pclS+q2KSvzsD35ZNhjD//zsGE6pVhOaDg2nN6/vkFHmc5uSDrjooadZkExANVd/UevMpmzXdnTr6u6+/Y1yZITljTeRV/4HV3K/brrCt9Pt8/8V6eun/pYcZfPvBMuWLXGy1qbdsbeMWv2RGZRADdQXQ1z524ctHPm1P22WVLiay0ccURd0O6+O/TpE7d2EckueR3Ay5ZtHLTvvANJ04CZn0F45Eg48US/HjkStt++blEsyVM1G86SSMdc0yPdLJ0/nFwXpUe+VSUtb02JP8/8R7Cm2PdTmXwXUN3Lty/s4dfVhb7fiir/j1e+2mdZdFnht0uW+35Kl/mYcbfl3lJ3/cTHhAs/W+2vl44Vp51xOq9YHXEUeRHAa9d6sDYM22XL6rYZMMDD9fTT64J211315ZiIdJycC+DPPvMvwt54o+569uy6D/SSEj8t+zHH1AXtyJF+uh6RzdZwbDg5so0G6/5a0mkWJms/dFvfI7ntn/CFld7RWnIE3tpkPnHo7h1wv17esW7Z3TvZomRweGWFTxBfuso73qXLfH8li32MuHSx77fH4uT+5T4WXPip78dWJZ3x2mT2RDJVJx0rVkfcsbI2gEOARYs2DtuPP67bZvhwGDVqw+GD7bbT8IGIZIasCeCaGh9GePFFXx/hxRdh8eK6x3fcEfbZx8/+sOeefunfP169kqcazBuuHRuu3HBM2JJOs+s6vy5a6x1xl7U+Nly4zn8011T67eVJA9q92Lcf2XcRAFv1+wCAgsHeqS4s6wvA258PAeCDJQMAWDXfO+XuC/x1eizy26WLvXMu+sQ74YKkI65Zk44RqyPuSBkbwJWVMG1aXdi+8gqsWOGPDR3qR4vtvbd3uLvvDj17Ri1XRGSzZVQAh+ALit9zjy+5uGqV37/jjr7c4gEH+PKLZWWaWysZbqM1JZLOcV1yXeljwZascla0zq97lCed8Cq/7rrKx3DLV3nHOnfNIADWbp3Mghjo+9+v5/sAHFA6G4Dj+vg42+wh/uXGS9vtBMCUxVsBsPij3v5683xsuMcC77S7L2rQEa8sB9QRd5RmA9jMhgP3AAPx+ee3hxBuMrN+wANAGfARcEIIYUVripg7F/70Jw/euXN95sFxx8FXvuJLLw4a1Jq9iohktpZ0wFXAxSGEN8ysJzDNzJ4BTgWeCyH80sx+BPwIuHRzC/j1r+EHP/COduxYuPJK73Y1/UtySjo2XLXhkWh1Y8JJR5ys5VCyxq+7rPSOtOQzXwui/FP/kf3s0y0BeHQbf3z+1j72e/QWbwGwX7ePABjRYwEAR3afB8CbW/jRQk8PHwnA89vuAMDiD/35PT/y1+k53+cTly7yH8S0I7akI66dNZGuOaF5xK3SbACHEBYDi5M/l5vZTGAoMA44KNnsbuAFNjOAb7/dw/e44+CGG3zWgohIvtisMWAzKwP2BKYAA5NwBliCD1G02IcfwllnwejRcN99vui4SN5obrZEcrsg6YRLVyZjwp95x1u63MeEy5d6xzp18Y4AvLud/xhOHTYHgGP7vAnAl7quBODw0srk9ssAHNH7bQAmDdkDgBe23h6AJR8kY8QfeQfcMxkjLk3mExd+4p2wrUznEW/iyDp1w01q8VmRzawH8DBwYQhhVf3HQgiBeuuTNHjeGWY21cymLl++vPb+YcPg4IN9/u4TT7SueBGRbGahBZ9OZtYFmAQ8HUK4PrlvFnBQCGGxmQ0GXggh7LSp/YwePTpMnTq19nZ5ORx2GLz+ui9sM348jBvnR6tJ5zKzaSGE0entwwq+rrYlhnR6j6VnYU7OsFHiY7JWmpwapbd3wlUD/HrNEH+8fLhvv3prH4vts41/L37wUJ8lkXa8e3T9HIBS8+2XVnvn/cq6MgCe+HQ3AKbN81kTBR/66/bwoWR6LvDtS5Z651v4aTI2XJ50xOnqaxUVOXN2jmdqHmr3uVfNdsDm51q5E5iZhm/icWB88ufxwGOb++I9e8JTT8Gll/raDCee6DMezjjD5/2mq4+JiOSiZjtgM9sfeAl4m/SUsXA5Pg78ILAVMA+fhvbZpvbVsAOur7oaXngB7r4bHn7YF9Dp29enoR14oM8BHjUKunTZnL+etJQ64AzVsCPu4l/bWPKlSUF3HwMOSUdcOcDHitcO3rAjXrOV/+h2L/Ox4DGD/Zj9A3rPAmDH4qUAdEnWmJiHDyNoAAAN7UlEQVRf5efEeqXcZ0m8vHRbAJbM2wKA0nleR8/5yX4X+dhv16XJbInPk454zZqNz86RpR1xR3TALZkF8TJ1Z1ppaGx7FVJY6NPQxo6FW2+Fxx6D55/3I+H+8hffprTUDzdOD8j48pc1XU1EsleLxoDby6Y64E1ZssSPkEvXgfjXv/zD0wx22snXfRg1qm4NCJ3QcvOpA84SLe2Ie3knnI4Rrx3kHfHqoUlHPDT55x3usyy2G+RfkI/s42tMDO3qY8c1wV/n4/X+Q/X2Cl9j4qPF3gkXpkfQzfe6ei7yLrfbknqrrjVccS1L5w5H6YAzwaBBcPzxfgH4/HN49VX/8m76dA/n+++v237rresCedQoP2vFkCE6fFlEMktWBHBDffrA0Uf7JfXJJx7G6eWNN+DRR+s+VPv2rVuScrfd/HrECC3iI1mmifWHa8/1lqzVYMnaDUXJkWu9lnlH3H2hX38xwDvX1YN9dsO8wVsDMGvwUN9uSz+n3MBe/vzexd69divysd4BW/j9y5OmpryLd9jV3ZJz3ZV6J15a2oXiT5LufEV6Vo7kfHXJOhi160tk6dhwW2RlADemf3+f0nbYYXX3lZf7cMW//uWzLN56y9ebKC+v26asbMOF2UeO9MV/9GWfZIVmAjk9oMOS0CtMvhzrkRzA0W2RB/L6/h7E6wZ4JKzd0g/EmD+gFwBz+/r+C3okC8sXJYdSJwFc3dNvr6tKTtFU4EMX1V2KKe3qfy7p6j9UBSuSxefLvSaSoQnycKGfnAngxvTs6bMo9t+/7r4QYN68jU9P9OSTkHxJS3Ex7LzzxsGsMxyLSHvK6QBujJl3vWVlvtpaav16mDXLu+Q0lP/xD5gwoW6bPn182KLhUEavXp39txBpQhPLYIYGp0aytenp670jLl2WdMS9kkOP+/nt9Vt4t7qun395t75vMsSQDN2FEn+99CwzaX9SnRxMtb6PYSGJmQK/s7jIO+Ki5EkFRf54WJMMTVhuTFtribwL4KZ07eqButtuG96/YgXMmLFhtzxhQt1axeBnSU5PT59eDxqkbllENk0B3Iy+fX3e8QEH1N0XAsyf793ym2/65Y03YOLEum223LIukPfYA/bay4NaoSydqrmOOPkiLP3SzpIvSIo/8zHhLkuSL9N6+e3K3t7FVvTx6Fjf07vZKt+M6uJ0mpxfFVRDdfJ9SkWP5LDq6g1X3ioqTKbUJePGte10Mn5NYwv81P+7ZTEFcCuYwVZb+eXYY+vuX7nSQ3n6dA/l6dPh+utrT35Av34wZoxf9t7bDyTp2zfO30FE4lMAt6PevTfulisq4N13YepUmDIFJk/29S/SD+8dd/QwHjMG9t3Xh0AKWrxGnchmatgRp81kgwXiSRbTSWdPFKzwrrWkm3fCXXskJ/ns4R1xVQ9vc6tKvXutKvH/xDVFdb/yFVQlS3AmDW5Nif+hpsqnsBUktdU+I/11Mf2BSGZJkC7hmQNjwwrgDlZcXDcM8d3v+n2rVnkgT57sofzUUz49Dnw63cEHw6GH+mHZ226rYQuRXKUAjqBXLzjkEL9A3dS4F1+E557zy0MP+WNlZXVrZBx5pIYspIM0OGVSbZfZcD5xMmfXypM5vV29e+2aLJdZXOodcU1JcXJdRCj2DjYUbNhJWGUyHp3cHbokrXHyXGuqs03H9NLSa9KuPvvGhhXAGaD+1LhTTvH/P7Nm1YXxww/DnXf6wSGHHw4nnODrJvfuHbtyEWkLBXAGMvMDQXbeGc4915uR11/3IH7wQfjrX31o48gjPYyPO06L2Es7a2r2RFUyjzgdj03HiosaLApU7B1yYXExITkCjmThoJDOcki/60gaV2u4AHg6OyLZd22Xnjxc20+n84VrGuwwCzphfd2TBQoL/Yu6X/0KPvoIXnvNg3naNPjWt3zxoZ/9DD79NHalIrI5smI5SmlcTY2vmfzrX/uh1N26wXe+Az/8oYfy5tBylNIqDZfHTMd501MpFRXVLplJ2iUXbXg77XQ3Up10smmHm45Pp7crG9yfjlt30JhwlFMSSeYqKPAv5554ou6UTrffDrvsAjfeWPv/UUQylAI4R4wYAX/4A7z/Phx0EFx0kc8rfued2JVJTgvBLzXVUFNNqKryS0UFoaKCmnVfULN6jV/KV/tlVblfVq6iZuUqQnpZvcYva9b65Ysv/FJZSais9I64ugZqgl8SZoaZeRduBViBeSee3MYsY+dyKoBzzNZbw6RJcN99MHeuh/Arr8SuSkQao1kQOcgMTjrJl+E89FCfuvb44z5cIdIp6s2iCOlE33SMtsF4ce3tdCw4PfKtua614dhuOv7c1NBbur8Mmh2hDjiHDR/uB3dsu62fzmnhwtgViUh9CuAcN3AgPPKIr3d8+ukZ9eEv+SIdJ244XlydXKoqCVWV1FQkly/WU/PFesL65FJRueElHWdOn19dQ2hkbLhWOhacgTKzKmlX228PV1/tU9Wefz52NSKSUgDnibPO8uUwb701diUiiSY646Y65NrblVUbXqqrN7zUhLq5wODzgUO9o+wyaFaEAjhPlJTA+PHw2GOQnPlFRCJTAOeRww/3g4gmT45diUgLNNMh13a2zV2a2m8GUADnkX328et//jNuHSLiNA84j/Tu7bMiPvggdiUi7SBDuti2UAecZ8rK4OOPY1chIqAAzjv9+2vZSpFMoQDOM337wooVsasQEdiMADazQjObbmaTktvbmNkUM5tjZg+YWXHHlSntpbQU1q2LXYWIwOZ1wBcAM+vdvga4IYSwPbACOK09C5OOUVKiABbJFC0KYDMbBhwD3JHcNuAQYGKyyd3AVzuiQGlfXbpsdFJZEYmkpR3wjcAl1J7tji2Az0MIyblAWAAMbeyJZnaGmU01s6nLly9vU7HSdkVFtWd0EZHImg1gMzsWWBZCmNaaFwgh3B5CGB1CGD1gwIDW7ELaUUGBn0tOROJryYEY+wH/YWZHAyVAL+AmoI+ZFSVd8DBAq81mAQWwSOZotgMOIVwWQhgWQigDTgT+HkI4GXgeOD7ZbDzwWIdVKe3GLCcOIBLJCW2ZB3wp8H0zm4OPCd/ZPiVJR1IAi2SOzVoLIoTwAvBC8ue5wJfbvyTpSBmyDKqIoCPhRESiUQDnGXXAIplDASwiEokCWEQkEgWwiEgkCmARkUgUwCIikSiARUQiUQCLiESiABYRiUQBLCISiQJYRCQSBbCISCQKYBGRSBTAIiKRKIBFRCJRAIuIRKIAFhGJRAEsIhKJAlhEJBIFsIhIJApgEZFIFMAiIpEogEVEIlEAi4hEogAWEYlEASwiEokCWEQkEgWwiEgkCmARkUgUwCIikbQogM2sj5lNNLP3zGymme1jZv3M7Bkzez+57tvRxYqI5JKWdsA3AU+FEHYGdgdmAj8Cngsh7AA8l9wWEZEWajaAzaw3cCBwJ0AIoSKE8DkwDrg72exu4KsdVaSISC5qSQe8DbAcuMvMppvZHWbWHRgYQlicbLMEGNjYk83sDDObamZTly9f3j5Vi4jkgJYEcBEwCrgthLAnsIYGww0hhACExp4cQrg9hDA6hDB6wIABba1XRCRntCSAFwALQghTktsT8UBeamaDAZLrZR1ToohIbmo2gEMIS4D5ZrZTctdY4F3gcWB8ct944LEOqVBEJEcVtXC784AJZlYMzAW+jYf3g2Z2GjAPOKFjShQRyU0tCuAQwpvA6EYeGtu+5YiI5A8dCSciEokCWEQkEgWwiEgkCmARkUgUwCIikSiARUQiUQCLiESiABYRiUQBLCISiQJYRCQSBbCISCQKYBGRSBTAIiKRKIBFRCJRAIuIRKIAFhGJRAEsIhKJAlhEJBIFsIhIJApgEZFIFMAiIpEogEVEIlEAi4hEogAWEYlEASwiEokCWEQkEgWwiEgkCmARkUgUwCIikSiARUQiaVEAm9lFZvaOmc0ws/vNrMTMtjGzKWY2x8weMLPiji5WRCSXNBvAZjYUOB8YHUIYARQCJwLXADeEELYHVgCndWShIiK5pqVDEEVANzMrAkqBxcAhwMTk8buBr7Z/eSIiuavZAA4hLASuAz7Gg3clMA34PIRQlWy2ABja2PPN7Awzm2pmU5cvX94+VYuI5ICWDEH0BcYB2wBDgO7AkS19gRDC7SGE0SGE0QMGDGh1oSIiuaYlQxCHAh+GEJaHECqBPwP7AX2SIQmAYcDCDqpRRCQntSSAPwb2NrNSMzNgLPAu8DxwfLLNeOCxjilRRCQ3tWQMeAr+ZdsbwNvJc24HLgW+b2ZzgC2AOzuwThGRnFPU/CYQQvgp8NMGd88FvtzuFYmI5AkdCSciEokCWEQkEgWwiEgkCmARkUgUwCIikSiARUQiUQCLiESiABYRiUQBLCISiQJYRCQSBbCISCQKYBGRSBTAIiKRKIBFRCJRAIuIRKIAFhGJRAEsIhKJAlhEJBIFsIhIJApgEZFIFMAiIpEogEVEIlEAi4hEogAWEYlEASwiEokCWEQkEgWwiEgkCmARkUgUwCIikSiARUQiUQCLiESiABYRiUQBnGf23hsuuCB2FSICYCGEznsxs+XAvE57QdkcW4cQBsQuQiSfdGoAi4hIHQ1BiIhEogAWEYlEASwiEokCWEQkEgWwiEgkCmARkUgUwCIikSiARUQiUQCLiESiABYRiUQBLCISiQJYRCQSBbCISCQKYBGRSBTAIiKRKIBFRCJRAIuIRKIAFhGJRAEsIhKJAlhEJBIFsIhIJApgEZFI/j/fTeIW/P11/gAAAABJRU5ErkJggg==\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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\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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ZuXYvtSqHlsrSGoXVL7o+h06ksmz74YILm9KVkQb/G+Ekp053we0zSjY5ZROB7o/AkKlwYj98cDXsW1vy7ZhyxRKUHzmVlsEPmw7Sp01dnzpTueKCOoQGBfCtdfP5lvTTMHGI07V31d/gmn95flh4sytgxHcQFAYfXwO7lnm2PVOmWYLyI/N/Pcjp9MxSn3uvIJVCg7jigjp8u24fWVl2kdwnpB6Hz26GzXPg2teg24Ol13at5nDnt1ChBoyLg60/ll7bpkyxBOVHZqzdS81KIXT2oe69bH2j63HgeCrxO454OxSTdgo+uwV2LIQbx0LsnaUfQ7VGcOcsqN4YJtwC238p/RiM37ME5SdOp2Xyw6YD9G5TzyenFerZqi4hQQE2ms/bMtKce5N2LoKb3oe2t3gvlir1YPg3UD0KJgyE3Su8F4vxS773TWfy9ONvBziVlkm/Nr7VvZetcmgQl7Wszbfr9lo3n7dkZcK0eyDhO7judWhzk7cjckb4DZ0GFavD+Juc+7CMKSRLUH7iq1V7qFU5hEua+l73XrZr29Zn/7FUlmyz0XylThVmPAbrp8JVL0DH270d0e+qRsDQL50bfD+9Ho7s8HZExk9YgvIDx1LSmbvpANe2jfDJ7r1sV7WuS8WQQL5aZbNWlbqf/wXLP3KGend7yNvR/FHNZs6ZVPopZ/DGabtWaQrmu9925oxZ6/aRlpFFXIwH7l8pQRVDguh9UT1mrt1Lakamt8MpP9ZMgnl/h7YDoedfvR1N/upeBLd+Boe3wsShzvUyY87BEpQf+GrVbhrXrEiMF1bOPV9xMREcS3Hu1zKlYPsv8NX9ENUD+r/p+7OKN+kBcWOcJTymP2Bz95lzsgTl4/YfS2HhliTiYhpwjjUgfUb35rWoVTnEuvlKw8Hf4IvbnFFyt37qP2sztbsVrnjGWYNq/v/zdjTGh1mC8nFfr96DKlzv49172YICA7i2bQRzNx3gWEq6t8Mpu04ddu4vCgyBwZP9b5XbSx+HmCHw40vOQonG5MESlI/7ctVu2kaG07R2ZW+HUmhxMRGkZWQxa90+b4dSNmWkOVMYHdsDAyc4Z1D+RsSZ4aJxN6eLctdSb0dkfJAlKB+WcOAE63YfIy6mgbdDOS8xDavRuGZF6+bzBFWY8QjsWABxb0HDzt6OqOiCQuCWT6Fqfaer8uhOb0dkfIwlKB82fdVuAgSua+ebN+fmR0SIi2nAwi1J7D+W4u1wypaFb8LK8XDpE96dJaKkVKoJt01yzgonDHTmEDTGZQnKR2VlKVNX7qZb81rUqRLm7XDO2/UxEajCtJV2FlViNs101nVqHQeXj/Z2NCWn9gVw80dwcBP870/OjBjGYAnKZ/20+SCJR05za6dirHjqRU1rV6ZzVA0+X7rTpj4qCfvWOV/eETFw/bsQUMb+6zbvCX1fgt9mOUnYGCxB+azPluykVuUQrm5dz9uhFNngSxqxI+kUC7Yc8nYo/u3EAfh8IISFw8DPIaSityPyjM53OYsqLnoLVozzdjTGBxQqQYlIHxH5VUQSROSpPPaHishEd/8SEYlyt18lIstFZK3788ocx8x361zlPuqU1C/l7/Ymn2buxv3cEtuQkCD//RuiT5t61KgUwmeL7eJ3kaWnOAMITiXBoM+dAQVlWZ9/QrMr4ZtHYNvP3o7GeFmB334iEgiMAfoCrYFBItI6V7ERwBFVbQ68Brzkbj8EXKeq0cBw4NNcxw1W1Rj3caAYv0eZ8sXSXSgwqHMjb4dSLKFBgdzcMZLvNu63wRJFkZUFX46ExGVww3tO915ZFxgEAz6CGs2cofSHNns7IuNFhfnzvDOQoKpbVTUN+AKIy1UmDvjEfT4F6CkioqorVXWPu309UEFEQksi8LIqPTOLL5bt5LKWtWlYw/+7cgZ1bkRmljJx2S5vh+J/5j7/+3Ltrft7O5rSU6EaDJ7kzH7+2QA4aV3E5VVhElQDIOe3S6K7Lc8yqpoBJAM1c5W5CVihqqk5tn3kdu/9RfKZx0dE7haReBGJP3iw7M/vNnfjAfYfS2XwxY29HUqJiKpViR4tavH50p1kZGZ5Oxz/sfxjWPC6sxpu1we8HU3pqx4Fg76A4/uc62/pp70dkfGCUrnAISIX4XT73ZNj82C366+H+xia17GqOlZVY1U1tnbt2p4P1ss+W7KDiPAwrryw7FySG3xxY/YmpzD/17L/B0aJSPgevnkUml8FfV/x/QlgPSUyFm58HxLjnYUYs+wPnPKmMAlqN5BzrHOkuy3PMiISBIQDSe7rSGAaMExVt2QfoKq73Z/HgQk4XYnl2vZDJ/l58yEGdm5EYEDZ+VLq2aoOdauG8uliW6iuQInLYeIwqNPauTcoMMjbEXlX6/5w9d9hw1cw60mb/bycKUyCWga0EJEmIhICDASm5yozHWcQBMAAYJ6qqohUA2YAT6nqguzCIhIkIrXc58HAtcC64v0q/u/t+QmEBgUwsLN/3vuUn+DAAIZe0pgffzvIut3J3g7Hdx38zbnmUqkWDJkCoVW8HZFv6DrK6eZcOhZ+esXb0ZhSVGCCcq8pjQJmAxuBSaq6XkReEJHsK7cfADVFJAF4FMgeij4KaA48m2s4eSgwW0TWAKtwzsDeL8lfzN/sOnyKqSt2M6hzI7+cOaIgw7pGUTUsiDfm2qisPCXvhvE3QkCgs/JsFf+9/80jer0A7W6DH/4Byz7wdjSmlBSq/0BVZwIzc217NsfzFODmPI77O/D3fKrtWPgwy7635ycQIMLIy5p5OxSPqBoWzJ3dm/D695vZsOcYrSOqejsk33HykJOcTh+FO2Y4y6ObswUEQP834PRhmPGYc9Ny9ABvR2U8zH/vAi1DEo+cYsryRAZ2bki98LJ39pTtjm5NqBIaxJvz7CzqjJNJ8El/OLLduRG3fjtvR+S7AoOde6Qad4WpdztD8E2ZZgnKB7wz3xk7UlbPnrKFVwjmjm5RfLtuH5v2HfN2ON536jCM6w+HtzhDqpv08HZEvi+kojP7ecPOMGWEM3jClFmWoLxsz9HTTIrfxc2xDYmoVsHb4Xjcnd2bUDk0iDfnJXg7FO/KTk6HNjtnTs2u8HZE/iO0srOKcGQsTLkTNuQes2XKCktQXvbmvARU4b7Ly/bZU7ZqFUMY3rUxM9fuZf2ecjqiL3k3fNTXGbU3aIIz95w5P6FVYPAUiOgAk2+HlZ95OyLjAZagvGj5jiN8sWwnQ7s0JrK6/09rVFh39WhKjYohjJ62jszythTHwV/hg6udJDVkCjTv5e2I/FdYVRg61eka/eo++OV1u0+qjLEE5SVpGVmMnrqW+lXDeOzqC7wdTqmqVjGEZ69rzepdRxlfnm7eTYyHD3tDZpozWq/Jpd6OyP+FVoHbJsNFN8L3f4U5z9iME2WIJSgvef/nrfy6/zgvxLWhcmj5my2gf7sILm1Zm5dnbWLP0XIwz9qaSfDxNRBWDUbMttF6JSkoBG76ADrf46wlNWkopNggnLLAEpQXbDt0kv/M3cw10fXp1bqut8PxChHhH9e3IVOVZ79aj5bVrpnMDJg1GqbeBQ1iYcR3UKOpt6MqewICnBV5+/wTfv0W/tsTDpXzgThlgCWoUpaVpYyeupbQoAD+el3uZbXKl4Y1KvLoVS35fuN+vl23z9vhlLwTB2D8DbB4DFw8EoZ9CZXL/oTHXiMCl9zrvM+nkuD9K2DTDG9HZYrBElQpe2n2JhZtTeLpfq2oU7Xs3pRbWHd2a0J0g3D+b8oaft133NvhlJyNX8Pbl8DOJXD9O85f94HB3o6qfGhyKdw9H2o0cVYjnv4gpJ7wdlSmCCxBlaIvlu7kvR+3MuSSRtzaqWxNCFtUQYEBvDe0IxVDArnz42UcOO7nK++mHIMv73NWgw2PhHt+gpjbvB1V+VOtkdOd2u1hWDEO3u0GOxd7OypznixBlZIFCYd45st19GhRi+euu4h81mcslyKqVeCD4Z04fDKNu8YtJyU909shnT9VZyDEmM6w+nO49AkY8T3UudDbkZVfQaFw1fNwx0zQLPiwj3M2ZSv0+g1LUKVg075jjBy/nKa1KzFmcAeCAu1tzy06MpzXB8awJvEoj0xcRbo/rb67Z5UzfHzqXc4s5CO+hyufcUaXGe9r3BXuXQhd7odVn8EbHWDxu5CZ7u3ITAHsm9LD5m3az4B3FlEhOJAPhneiaphdh8hP74vq8XS/Vny7bh/DPljKkZNp3g7p3PashC8Gw9jL4PBWiBsDf5oHkTZRv88JrQK9/+EkqsiOzuKHb3aE5R9DRqq3ozP5EH8a3hsbG6vx8fHeDqNQVJX//ryNF7/dSOv6VXl/WGy5mGuvJExdkchT/1tL/WphfDA8luZ1fGjhvqws2PYjLH4bNs9xln24eKTz13lYuLejM4Wh6vzbzf8n7FkBVRtAl1EQMwgqVPd2dOWCiCxX1dgCy1mCKnkHjqfwjxkb+WrVHvpF1+NfN7ejYkj5uxm3OJbvOMI9ny4nNT2Tv/a/iBvbNyAgwIvX7Y7vc7qHVoxzlsaoUMNJSp3vssTkr1Rh6w/w4yuwcyEEhUHrOOgwHBp1ce6tMh5hCcoLTqdl8v7PW3n3xy2kZ2bxwJUtGHVFc+9+sfqxPUdPc/+EFazceZQ2DarydL/WdGlWs/QCOLwVNn4Dm76BXUsBhcbdoePt0Oo6CLbbBMqMvWtgxSfOQJfUY1ClPlx4DVx4LUR1t1sESpglqFK07dBJvly5m4nLdrHvWAp929TjyT4XElWrkrdD83tZWcrXa/bw8qxf2X30ND1a1GJAx0iubl2PCiGBJdmQk5B2LYEdC2D7L3DUnSewXjRceB20uQlqNS+5No3vSTvl/EGycTokzIX0UxBcCRpdDI27OY960c6SH6bISjRBiUgf4D9AIPBfVf1nrv2hwDicZdyTgFtVdbu778/ACCATeFBVZxemzrz4SoI6lZbB6l3JrNh5hDkb9rN611FEoGuzmjzcqyWdomp4O8QyJyU9k48WbOfTRdvZk5xCxZBAel9Ujy7NatKhUXWa1qpUuDPVjFRIToSkLU5CStoM+9bB/nWQ5t7MWaEGRHWDqB7Qsg9Ub+zR3834qPTTsGUebJ0P2xfAgfXuDoGazZ1EVftCqNnMmb6qepRzDctuISlQiSUoEQkEfgOuAhKBZcAgVd2Qo8x9QFtVHSkiA4EbVPVWEWkNfA50BiKA74GW7mHnrDMvnkxQWVlKakYWp9MzOZ2eybHT6Rw5lcbRU+kcPJ7KrsOn2HXkFDuSTrH5wIkzy0S0ql+VG9pH0L9dgzK9XLtXqTr3sWSmk5WRyopt+5mzZicLNu0hPfUUFUilVmgWLatDZIUM6ldIo3ZQClX1OJUzkwnLOErIqQMEntxHwKlc98CEVIG6F0H9tlCvLTTo6Hzp2PUHk9vJJOcMe99a2LfG6RZM3nl2maAKUDXCeVSqBRVrOn/wVKjujCQMqwohlSGkEgRXgOCKzv1agaHObQmBoU53YkBQmU50hU1Qhbly3xlIUNWtbsVfAHFAzmQSBzznPp8CvCXOnahxwBeqmgpsE5EEtz4KUWeJ2rl5DfLZzWdeK06Cyc7PufN0BfcR4b4WgaAAISgwgNCqAYQEBRAaFEAgAitxHuVGjjfrD3/gaB5Pc77JuZ5r1u8JKOcjKxM00/mZ9fv9KgFArPsAIDRH00fch+ukhnKEKuzRyhzQ6uzTduzT6uyjJrskgt0B9TmWVo2gPQHIXiEwAAJkL8LeMzdSZ39HiIBw9hdGGf7+MPmqgPMV5nyNhVRMpYHuo0HWXiJ0P7WykqiVfJjaRw8RrlsJ12NU5QQBnP+llAwCyCSQLALOeihCFoKKU2tWjruF1P2M/v4TyPW51RyvNZ/t55IpwTR+dt15/z5FUZgE1QDYleN1InBxfmVUNUNEkoGa7vbFuY5t4D4vqE4ARORu4G6ARo0aFSLcvIVVqExieLT7pSIEiPPPJiIEBDivA0UIDHAewYFOEgoJDCA0OIDQoMBC/vOVE2d9O0vB+85sk9+LS4D7WkACndfZj4DA338GuH9RBgY5z4PCfv9rM/uv0OAKznWB0KqkBlZkX2oIR9IC3bPgNE6lZXI6LZPQ9EzqpmdRIyttLOCIAAAgAElEQVSLizKV9MwsslTJzHLOorPU+dNF9fc/YlD+8PXiT9dujafV5STt2AxszmOvaCZhWacIyzpJWKbzM0RTCMlyHkGaRpCmn3kEaAaBmkkAmQSc+emkJ1QRlAAyne8vzULOpKHsz6T7Oo/PqORKSXlvPzcNCKa0Or19fuyzqo4FxoLTxVfUeupENqXOI1NKLC7ju0KBxu7DGOO/CtPRvhvIObNppLstzzIiEgSE4wyWyO/YwtRpjDGmHCtMgloGtBCRJiISAgwEpucqMx0Y7j4fAMxTpw9kOjBQREJFpAnQAlhayDqNMcaUYwV28bnXlEYBs3GGhH+oqutF5AUgXlWnAx8An7qDIA7jJBzccpNwBj9kAPeraiZAXnUWFMvy5csPiciOovyiOdQCbDrj39n7cTZ7P85m78fZ7P34o6K8J4XqgferG3VLgojEF2Z4Y3lh78fZ7P04m70fZ7P34488+Z7YzR7GGGN8kiUoY4wxPqk8Jqix3g7Ax9j7cTZ7P85m78fZ7P34I4+9J+XuGpQxxhj/UB7PoIwxxvgBS1DGGGN8UrlJUCLSR0R+FZEEEXnK2/GUNhFpKCI/iMgGEVkvIg+522uIyHcistn9Wa7WvBaRQBFZKSLfuK+biMgS93My0b2RvNwQkWoiMkVENonIRhHpUp4/IyLyiPv/ZZ2IfC4iYeXpMyIiH4rIARFZl2Nbnp8Hcbzhvi9rRKRDcdsvFwnKXTJkDNAXaA0McpcCKU8ygMdUtTVwCXC/+x48BcxV1RbAXPd1efIQsDHH65eA11S1Oc7c6CO8EpX3/AeYpaoXAu1w3pty+RkRkQbAg0CsqrbBmVRgIOXrM/Ix0CfXtvw+D31xZgtqgTPB9zvFbbxcJChyLBmiqmlA9vIe5Yaq7lXVFe7z4zhfPA1w3odP3GKfANd7J8LSJyKRwDXAf93XAlyJs2QMlL/3Ixy4FGdmGFQ1TVWPUo4/Iziz7VRw5xitCOylHH1GVPUnnNmBcsrv8xAHjFPHYqCaiNQvTvvlJUHltWRIg3zKlnkiEgW0B5YAdVV1r7trH1DXS2F5w+vA/wFZ7uuawFFVzXBfl7fPSRPgIPCR2+35XxGpRDn9jKjqbuBfwE6cxJQMLKd8f0Yg/89DiX/PlpcEZVwiUhn4H/Cwqh7Luc+d4Ldc3HcgItcCB1R1ubdj8SFBQAfgHVVtD5wkV3deOfuMVMc5K2iCs3ZpJf7Y3VWuefrzUF4SlC3vAYhIME5y+kxVp7qb92efhrs/D3grvlLWDegvIttxunyvxLn+Us3tzoHy9zlJBBJVdYn7egpOwiqvn5FewDZVPaiq6cBUnM9Nef6MQP6fhxL/ni0vCarcL+/hXl/5ANioqq/m2JVzqZThwFelHZs3qOqfVTVSVaNwPg/zVHUw8APOkjFQjt4PAFXdB+wSkQvcTT1xViIol58RnK69S0Skovv/J/v9KLefEVd+n4fpwDB3NN8lQHKOrsAiKTczSYhIP5xrDtnLe/zDyyGVKhHpDvwMrOX3ay6jca5DTQIaATuAW1Q190XRMk1ELgceV9VrRaQpzhlVDWAlMERVU70ZX2kSkRicQSMhwFbgDpw/ZMvlZ0REngduxRkFuxL4E851lXLxGRGRz4HLcZbU2A/8FfiSPD4PbhJ/C6cb9BRwh6rGF6v98pKgjDHG+Jfy0sVnjDHGz1iCMsYY45MsQRljjPFJlqCMMcb4JEtQxhhjfJIlKGOMMT7JEpQxxhifZAnKGGOMT7IEZYwxxidZgjLGGOOTLEEZY4zxSZagjDHG+CRLUMYYY3ySJShT7onIdhE5LSInROSIiMwQkYYFH+kbROQ5ERnv7TiMKWmWoIxxXKeqlYH6OOvevHm+FeRYZdWv+GvcpuyzBGVMDqqagrPUeWsAEblGRFaKyDER2SUiz2WXFZEoEVERGSEiO4F57tnXAznrFJE1InKD+/wiEflORA6LyH4RGe1uDxCRp0Rki4gkicgkEamRq53hIrJTRA6JyNPuvj44C0/e6p4Brna3h4vIByKyV0R2i8jfRSTQ3Xe7iCwQkddEJAl4TkSai8iPIpLs1j/Ro2+0MYVgCcqYHESkIs4KqovdTSeBYUA14BrgXhG5PtdhlwGtgN7AJ8CQHPW1w1mBdYaIVAG+B2YBEUBzYK5b9AHgereuCOAIMCZXO92BC3CWHn9WRFqp6izgRWCiqlZW1XZu2Y9xVoFtDrQHrsZZDTbbxTgr5tYF/gH8DZgDVAciKcIZpDElzRKUMY4vReQokAxcBbwCoKrzVXWtqmap6hrgc5wkktNzqnpSVU8D04GWItLC3TcUJ3mkAdcC+1T136qaoqrHVXWJW24k8LSqJrrLhz8HDMjV/fa8qp5W1dXAaqAdeRCRukA/4GE3rgPAa8DAHMX2qOqbqprhxp0ONAYi3Nh+Ob+3z5iSZwnKGMf1qloNCANGAT+KSD0RuVhEfhCRgyKSjJNIauU6dlf2E7eLcCIwREQCgEHAp+7uhsCWfNpvDEwTkaNuotwIZOKc4WTbl+P5KaDyOeoKBvbmqO89oE5eMbv+DxBgqYisF5E786nbmFJjCcqYHFQ1U1Wn4iSH7sAEnLOihqoaDryL80V+1mG5Xn8CDMbpijulqovc7buApvk0vQvoq6rVcjzCVHV3YcLOo65UoFaOuqqq6kX5HaOq+1T1LlWNAO4B3haR5oVo2xiPsQRlTA7iiMO5FrMRqAIcVtUUEekM3FZQHW5CygL+ze9nTwDfAPVF5GERCRWRKiJysbvvXeAfItLYjaO2G0dh7Aei3DM2VHUvzvWkf4tIVXcARjMRyd01mfP3vllEIt2XR3ASWFYh2zfGIyxBGeP4WkROAMdwBg0MV9X1wH3ACyJyHHgWmFTI+sYB0cCZ+5NU9TjO9a3rcLrrNgNXuLv/g3OmNsdtazHOQIbCmOz+TBKRFe7zYUAIsAEn4UzBGUKfn07AEvc9mA48pKpbC9m+MR4hqrl7B4wxxSUiw4C7VbW7t2Mxxl/ZGZQxJcwdqn4fMNbbsRjjzyxBGVOCRKQ3cBDnutAEL4djjF+zLj5jjDE+yc6gjDHG+CS/miSyVq1aGhUV5e0wjDHGFMPy5csPqWrtgsr5VYKKiooiPj7e22EYY4wpBhHZUZhy1sVnjDHGJ1mCMqVux9EdfLjyQ5btXkZmVqa3wzHG+Ci/6uIzJejYMfjiC2jWDK68EiT39HIlKyMrg29++4axy8cyK2EW6k4FFx4azuVRl/NA5wfo2bSnR2MwxvgXS1DlTXIyvPkmvPoqHDnibOvaFZ59Fq6+2iOJ6kTaCfp+1pdfdv5CRJUInrn0GW5qdRMbD21k3rZ5fJvwLb3H92bsdWO5s71Nom1KTnp6OomJiaSkpHg7lHIpLCyMyMhIgoODi3S8Jajy5KefIC4Ojh6F666Dp56CNWvgxRehTx/o1QtmzICQkBJr8mTaSa6ZcA2Ldi3ig/4fMKzdMIICnI9du3rtGNhmIMdTjzNg8gBGTB/BnuN7eLrH04iHz+hM+ZCYmEiVKlWIioqyz1QpU1WSkpJITEykSZMmRaqjWNegRKSPiPwqIgki8lQe+0NFZKK7f4mIROXY11ZEFrlrz6wVkbDixGIKcOQI3HYb1K4Ny5fD9OnOmdPIkZCQ4JxRff+9cyZVQk6nnybuizh+2fkL428cz53t7zyTnHKqElqFrwd9zdC2Q/nLD3/h/pn3YzeQm5KQkpJCzZo1LTl5gYhQs2bNYp29FvkMSkQCcZakvgpIBJaJyHRV3ZCj2AjgiKo2F5GBwEvAre4qoeOBoaq6WkRq4qzoaTzlvvtg/35YtAg6dDh7X0gIPPIIbNwIL78M/frBpZcWq7mMrAxunHQj87bN45PrP2Fgm4HnLB8SGMIn139CnUp1+Peif9Ohfgf+1OFP5zzGmMKw5OQ9xX3vi3MG1RlIUNWt7nLWXwC516+Jw1m8DZzp/nuKE/HVwBp36WpUNUlVbTiXp0yY4AyIeO45iI3Nv9yrrzqDJoYNc65VFcMbS95gVsIs3rnmHYa2G1qoY0SEl696mSuiruCR2Y+w7ci2YsVgjPFvxUlQDTh72ehEd1ueZVQ1A0gGagItARWR2SKyQkT+L79GRORuEYkXkfiDBw8WI9xyaudO5+ypa1d48slzl61cGT79FBIT4YEHitzktiPb+MsPf+G6ltdxd8e7z+vYAAngo7iPEIQ7vrqDLLU184x/q1y5MgCrVq2iS5cuXHTRRbRt25aJEyd6OTLf5637oIJwltMe7P68QUTyHGOsqmNVNVZVY2vXLnBmDJPbyJGQmekknqBC9Ohecgk8/bRTfubM825OVbl3xr0ESABj+o0p0il+42qNeb3P6/y440feWPLGeR9vjC+qWLEi48aNY/369cyaNYuHH36Yo0ePejssn1acBLUbaJjjdaS7Lc8y7nWncCAJ52zrJ1U9pKqngJlArgsjpthWrYJvv4XRo6Fp08If98wz0LixM7rvPE1YO4HZW2bz4pUv0jC8YcEH5OOOmDu4tuW1/Hnun9l0aFOR6zHGV7Rs2ZIWLVoAEBERQZ06dbBeoXMrzjDzZUALEWmCk4gGArflKjMdGA4sAgYA81RVRWQ28H/uwm5pwGXAa8WIxeTlX/9yuu3uvff8jgsOdgZNPPywM6iiS5dCHZZ0KomHZz/MxQ0u5r5O9xUh4N+JCO9f9z6txrTiie+e4OtBXxerPmN4+GHnj7aSFBMDr79+3octXbqUtLQ0mjVrVrLxlDFFPoNyrymNAmYDG4FJqrpeRF4Qkf5usQ+AmiKSADwKPOUeewR4FSfJrQJWqOqMov8a5g927XIGRtx1F1Srdv7HjxgB1as7Sa6Q/jr/rxxNOcr7171PYEDg+beZS73K9Xii6xN889s3LE5cXOz6jPEFe/fuZejQoXz00UcEBNhsc+ekqn7z6Nixo5pCevRR1cBA1R07il7H6NGqIqqbNxdYdFfyLg35W4jeNf2uoreXh+Opx7XOK3X0yk+uLNF6TfmwYcMGb4eglSpVOvM8OTlZ27dvr5MnT/ZiRKUrr38DIF4L8Z1v6bssOnoUxo6FW2+FRo2KXs+oUU5336uvFlj0pV9eIkuzGN1jdNHby0PlkMqM7j6aedvmMW/bvBKt25jSlJaWxg033MCwYcMYMGCAt8PxC5agyqKxY+HECXjiieLVU78+DB0KH30E57iYu/vYbsauGMvt7W4nqlpU8drMwz2x9xBZNZKn5z1tM0wYvzVp0iR++uknPv74Y2JiYoiJiWFVSV8TK2MsQZU1aWnwn/848+rFxBS/vsceg5QUGDMm3yIvLfDM2VO2sKAwnr30WRYnLuab377xSBvGeMqJEycAGDJkCOnp6axaterMI6Yk/o+WYZagypqvv4Y9e+DRR0umvlatnKmPxo517qfKZc/xPYxd7pw9NaletAkhC+P2mNtpVr0Zz85/1s6ijCknLEGVNePGQUSEs3RGSbnzTti7F+bO/cOul355iUzN9NjZU7bgwGBG9xjNqn2r+GH7Dx5tyxjjGyxBlSUHDzqzPwweDIHFH+Z9xrXXOkPVx407a3PSqSTGrhjL0LZDPXr2lO226NuoU6kOry4qeNCGMcb/WYIqS774AjIynMleS1JoqDMicNo0OH78zOaxy8eSkpHCY10eK9n28hEWFMb9ne5nxuYZNruEMeWAJaiyZNw4aN8e2rQp+bqHDYNTp2DqVADSM9MZs2wMvZr24qI6F5V8e/kYGTuS0MBQXl98/nfvG2P8iyWosmLjRoiPL/mzp2xdujhLcbjdfFM3TmX38d08dPFDnmkvH3Uq1WFo26GMWz2OQ6cOlWrbxpjSZQmqrPj0U+e606BBnqlfxEl+P/wAO3fy+pLXaV6jOf1a9PNMe+fw8CUPczrjNO/Fv1fqbRtzPh555BFezzFXX+/evfnTn35fiPOxxx7j1ULcCO9JR48e5e233y5U2a5du3o4mrNZgioLsrKcBNWnD9St67l2hgwBVZZ++k8WJy7mwc4PEiCl/xG6qM5F9G7Wm7eWvUVqRmqpt29MYXXr1o2FCxcCkJWVxaFDh1i/fv2Z/QsXLiy1L/2MjIw8t59Pgsr+XUqLJaiyYP58Z5FBT3XvZWvaFHr04D9bPqNqaFVuj7nds+2dw6NdHmXfiX1M3jDZazEYU5CuXbuyaNEiANavX0+bNm2oUqUKR44cITU1lY0bN9K6dWt69uxJhw4diI6O5quvvgLg5MmTXHPNNbRr1442bdqcWeDwqaeeonXr1rRt25bHH38cgIMHD3LTTTfRqVMnOnXqxIIFCwB47rnnGDp0KN26dWPo0KGsX7+ezp07ExMTQ9u2bdm8eTNPPfUUW7ZsISYmhifc2WdeeeUVOnXqRNu2bfnrX/965vfJXnxx/vz5XH755QwYMIALL7yQwYMHe+T+xOIst2F8xfjxULUqXHedx5vac9t1TNrzM6MiBlEltIrH28tPr6a9aFGjBe/Ev8OQtkO8FofxHw/PephV+0p2aqGYejG83if/ATsREREEBQWxc+dOFi5cSJcuXdi9ezeLFi0iPDyc6OhoKlasyLRp06hatSqHDh3ikksuoX///syaNYuIiAhmzHAWekhOTiYpKYlp06axadMmROTMgocPPfQQjzzyCN27d2fnzp307t2bjRs3ArBhwwZ++eUXKlSowAMPPMBDDz3E4MGDSUtLIzMzk3/+85+sW7fuzLRLc+bMYfPmzSxduhRVpX///vz0009ceumlZ/1uK1euZP369URERNCtWzcWLFhA9+7dS/T9tTMof5eW5gz/vv56qFDB482NbXyIzAAYtdF7yQmcpeHvjb2XhbsWsnrfaq/GYsy5dO3alYULF55JUF26dDnzulu3bqgqo0ePpm3btvTq1Yvdu3ezf/9+oqOj+e6773jyySf5+eefCQ8PJzw8nLCwMEaMGMHUqVOpWLEiAN9//z2jRo0iJiaG/v37c+zYsTNTLPXv358K7ndDly5dePHFF3nppZfYsWPHme05zZkzhzlz5tC+fXs6dOjApk2b2Lx58x/Kde7cmcjISAICAoiJiWH79u0l/t7ZGZS/+/57Z/byW27xeFMZWRm8v3E8vZNr0eyr7+BFdQZPeMnwmOGMnjead+Lf4d1r3/VaHMY/nOtMx5Oyr0OtXbuWNm3a0LBhQ/79739TtWpV7rjjDj777DMOHjzI8uXLCQ4OJioqipSUFFq2bMmKFSuYOXMmzzzzDD179uTZZ59l6dKlzJ07lylTpvDWW28xb948srKyWLx4MWFhYX9ov1KlSmee33bbbVx88cXMmDGDfv368d5779E012rbqsqf//xn7rnnnnP+XqGhoWeeBwYG5nuNqzjsDMrfTZoE4eFw1VUeb+qb375hz/E9jGw+CLZtg+XLPd7mudSoUIOBbQYyfs14jqUe82osxuSna9eufPPNN9SoUYPAwEBq1KjB0aNHWbRoEV27diU5OZk6deoQHBzMDz/8wI4dOwDYs2cPFStWZMiQITzxxBOsWLGCEydOkJycTL9+/XjttddYvdrpPbj66qt58803z7SZ3yzpW7dupWnTpjz44IPExcWxZs0aqlSpwvEcN+D37t2bDz/88MwZ2O7duzlw4ICn3p5zsgTlz9LS4Msvne69kBCPN/dO/DtEVo3kmlufgaAgmOz9AQr3xd7HyfSTfLr6U2+HYkyeoqOjz1xbyrktPDycWrVqMXjwYOLj44mOjmbcuHFceOGFAKxdu/bMgIbnn3+eZ555huPHj3PttdfStm1bunfvfmaI+htvvEF8fDxt27aldevWvPtu3j0KkyZNok2bNsTExLBu3TqGDRtGzZo16datG23atOGJJ57g6quv5rbbbqNLly5ER0czYMCAsxJYaRJ/mhk6NjZW4+PjvR2G75gxw5knb8YMZ8ZxD9pyeAvN32zO85c/z7OXPeu0t3EjbN3q1W4+gNixsaRkpLD23rWIl2MxvmXjxo20atXK22GUa3n9G4jIclWNLejYYp1BiUgfEflVRBJE5Kk89oeKyER3/xIRicq1v5GInBCRx4sTR7k1ebIziWuvXh5v6r3l7xEogYxoP8LZcPPNsH2717v5AO6NvZf1B9fz886fvR2KMaYEFTlBiUggMAboC7QGBolI61zFRgBHVLU58BrwUq79rwLfFjWGci01tdS691IzUvlw5YfEXRhHg6oNnI3XX+8sBz9pkkfbLoxB0YMIDw3nnfh3vB2KMaYEFecMqjOQoKpbVTUN+AKIy1UmDvjEfT4F6CluH4yIXA9sA9Zjzt9330FysnMm42FTNkwh6XQSIzuO/H1j9erOwIxJk8DL3cQVgysyvN1w/rfhfxw46Z2LucZ3+dNljLKmuO99cRJUA2BXjteJ7rY8y6hqBpAM1BSRysCTwPMFNSIid4tIvIjEHzx4sBjhljGl2L337vJ3aV6jOT2b9jx7x803w44dziS1XnZP7D2kZ6Xz8aqPvR2K8SFhYWEkJSVZkvICVSUpKSnPoe+F5a37oJ4DXlPVEwVd1FbVscBYcAZJeD40P5CaCl99BTfc4PHuvXUH1vHLzl945apX/jjvXlzc7918nTp5NI6CtK7dmh6NejB2+Vge7/q4V+YINL4nMjKSxMRE7I9b7wgLCyMyMrLIxxcnQe0GGuZ4Heluy6tMoogEAeFAEnAxMEBEXgaqAVkikqKqbxUjnvKjFLv33ot/j5DAkLzn3cvu5ps8GV5+2euj+UbGjmTw1MHM3TqXq5p5/r4w4/uCg4Np0sTzqz0bzyjOn5nLgBYi0kREQoCBwPRcZaYDw93nA4B56uihqlGqGgW8Drxoyek8TJpUKt17J9NOMm7NOG5ufTO1KtbKu9AttzjdfMuWeTSWwrip1U3UrFCT95bbMhzGlAVFTlDuNaVRwGxgIzBJVdeLyAsi0t8t9gHONacE4FHgD0PRzXkqxe69L9Z9wbHUY4yMHZl/oexuPh+4aTc0KJQ7Yu7gy01fsvf4Xm+HY4wpJrtR1998/TX07w8zZ0Lfvh5tqtP7nTidfrrgG2CvvRbWrXOmP/JyN9/mpM20fKslf7/i7zx96dNejcUYk7dSuVHXeMHkyc61n549Cy5bDPF74onfE8/I2JEFz86QPZrPB7r5WtRsQc8mPRm7YiyZWZneDscYUwyWoPxJdvdeKdyc+178e1QMrsjQtkMLLpxzNJ8PGBk7kp3JO5m5eaa3QzHGFIMlKH8yZw4cO+bxpTWSU5KZsG4Cg9oMIjwsvOADqlWDq6+GKVO8ftMuQNwFcURUiWDMsjHeDsUYUwyWoPxJKXXvfbzqY06ln+Le2HsLf5APjeYLDgzmno73MHvLbDYn/XGhNWOMf7AE5S9ydu8FB3usmSzN4q1lb9ElsgsdIzoW/sD+/X2qm++uDncRFBBk8/MZ48csQfmLUurem7NlDgmHExjVedT5HVitGvTu7ZzlZWV5JrjzUL9KfQa0HsCHKz/kZNpJb4djjCkCS1D+YsIEqFkTrrzSo828ufRN6lWux4DWA87/4FtvhZ07YeHCkg+sCO7vdD/JqclMWDvB26EYY4rAEpQ/OHbMWVrj1ls9Onov4XAC327+lns63kNIYBHauf56qFgRPvus5IMrgm4Nu9G2blvGLBtjk4Ua44csQfmDadMgJQWGDPFoM28ve5vAgEDu7nh30SqoXNmZ4WLiRGc5ei8TEUZ1GsXq/atZuMs3zuqMMYVnCcofjB8PTZvCJZd4rIkTaSf4cOWHDGg9gIgqEUWvaMgQOHIEvvWNdShvi76NamHVeH3J694OxRhznixB+bo9e2DuXOeL34PTCI1fM57k1GQe6PxA8Srq1Qvq1HGSqg+oFFKJkR1HMnXjVLYc3uLtcIwx58ESlK/7/HPn5tfBgz3WRGZWJq8uepWO9TvSJbJL8SoLCoJBg5w5A48eLZkAi+mBix8gUAJ5fbGdRRnjTyxB+brx46FzZ2jZ0mNNfLnpSzYf3syT3Z4seN69whg82Llv63//K35dJSCiSgSD2w7mw1UfknQqydvhGGMKyRKUL1u/Hlat8ujgCFXlpQUv0ax6M25sdWPJVBob6yRUH+nmA3isy2OcSj/Fu/HvejsUY0whWYLyZZ99BoGBzvByD5m/fT7L9izj8a6PExgQWDKVijhJdf58574oH9CmThv6NO/Dm0vfJCUjxdvhGGMKwRKUr8rIgE8/dWZnqFPHY828vPBl6lSqw/B2wwsufD6yr5mNG1ey9RbD410eZ//J/Xy2xjfu0zLGnJslKF/1zTeQmAh33eWxJlbvW82shFk82PlBKgRXKNnKmzZ1RvS9/z5k+sa6TFc2uZL29drzr0X/srWijPEDlqB81TvvQGSks1qth7y88GUqh1Tmvk73eaaBe+91uvhm+sa6TCLCn7v/mU2HNjFx/URvh2OMKUCxEpSI9BGRX0UkQUSeymN/qIhMdPcvEZEod/tVIrJcRNa6Pz07wZy/SUhwJoe9+25n2LYH/HroVyaum8jdHe6meoXqHmmD/v0hIgLeftsz9RfBTa1vom3dtjw3/zkysjK8HY4x5hyKnKBEJBAYA/QFWgODRKR1rmIjgCOq2hx4DXjJ3X4IuE5Vo4HhwKdFjaNMevddJzH96U8ea+IvP/yFsKAwnuz+pMfaICjI6aKcPRu2bvVcO+chQAJ4/vLn2Xx4M+PX+M4oQ2PMHxXnDKozkKCqW1U1DfgCiMtVJg74xH0+BegpIqKqK1V1j7t9PVBBREKLEUvZcfo0fPSRM/Fq/foeaWLF3hVM3jCZRy55hDqVPDcAA3ASVEAAvPeeZ9s5D3EXxNGhfgde+PEF0jPTvR2OMSYfxUlQDYBdOV4nutvyLKOqGUAyUDNXmZuAFaqamlcjInK3iMSLSPzBgweLEa6fmDwZDmiATV4AABPLSURBVB92rt94yNPznqZGhRo83vVxj7VxRoMGEBcHH3zgTHjrA0SEFy5/gW1Ht/Hxqo+9HY4xJh9eHSQhIhfhdPvdk18ZVR2rqrGqGlu7du3SC85b3nkHLrgArrjCI9X/tOMnZiX8//bOPbqq4t7jn985OXmSxCDIO7wM1wqLIkEeBcQCVqC14q3ysLYK0pda1F610F4pgrfK9YFe6aWLohVua5VaH4iIokBBCI8ElYYgD0UkGJKAQB7kfX73j9mHJBAhknOyTzjzWWvWOXvv2bN/mcyZ78zsmd+sYsbQGSTHJofkGWfwi1/A0aPw8svN87xGMC5tHIM6DWLu+rlUVDfYNrJYLC7TFIE6BHSpc9zZOddgHBGJApKBo85xZ+BV4Meqar14AmRmwubNpkIPgWNYVWXmezPpmNjx6++Y2xRGjoS0NHjmGeNXMAwQEeZ+ey4Hiw6yYOsCt82xWCwN0BSB2gakiUh3EYkGJgHLT4uzHDMJAuBGYI2qqohcBLwJzFDVjU2w4cJi7lyzdfptt4Uk+eW7l7Pp4CZmXTUr+OuezobHA7/6FWzdCu++23zPPQeje4xmXNo4HvrnQ3xR/MW5b7BYLM3KeQuU807pLuBtYBewTFV3isgcEfm+E+1Z4GIR2Qf8CghMRb8LuBSYJSIfOiHEb+vDnO3bYflyU5EnB3/orbSylOmrptO7bW+mXjE16OmfkylToEsXmD07rHpRT495moqaCu5ffb/b5lgsltOQlrQV9oABAzQzM9NtM0LD+PHwz3/CZ5+FRKDuf+d+Hs94nPenvM/Q1KFBT79RLFwId9xh1nhdc407NjTAg2se5OEND7Pu1nWM6DbCbXMslgseEclS1QHnimc9SYQDH3wAr78est7TR4c/Yv7m+Uy7Ypp74gQwdarxjhFGvSiAmcNn0jW5K3e9dZeddm6xhBFWoMKBhx4y756mTw960n718/M3f07ruNbMu2beuW8IJTEx8JvfwKZNZpfgMCHeF8/8a+eTXZBtJ0xYLGGEFSi3CfSe7r03JL2nRVmL2Jy7mSe+8wSt41oHPf2vTZj2osZfNp5xaeP47ZrfklOY47Y5FosFK1DuogozZhhhCkHvaVfhLu575z5GdR/FLX1Dt+nh1yLQi9q40UwKCRNEhMXXLSYhOoHJ/5hs94yyWMIAK1Bu8te/mgkDgenlQaS0spSb/n4T8b54loxfEpyt3IPFtGnQty/ceScUFbltzSk6JHZgyfgl7MjfwQOrH3DbHIsl4rEC5RaFhXDPPTBkiJnZFkRUlTtW3kFOYQ4v/OAFOiWd7oHKZXw+s09UXh7MnOm2NfUYlzaOewbdwzNbn2HFnhVum2OxRDSh2cvBcm7uvdf0Hv70J7OtexB57oPnWPrRUmaPmM3oHqODmnbQGDgQ7r4b5s+Hm2+GoS7OLjyNR0c/yroD65jy+hS2TttK95TubpsUOoqKYP9+OHwY8vOhoABKSozfxPJys9lkTAzExkJcHFx8MbRrZ0LnziZ4bDvXEhrsOig3eOstGDcOZs0yM/iCyKaDmxi1dBTDUoex6oer8HqCK35BpaQE+vQxFd+HH5qKMEzYfWQ3Q54dQpv4Nrw/9f3Qe30PNWVlsGOHmZSzfTvk5MDevUaQGiIgSh4PVFQYsfL7z4wXGwuXXgq9ekG/fnDFFdC/v/HEH07DypaworHroKxANTdHj5ofcHx80CvlrC+yGLl0JO0S2rWcSnXVKhg7Fh54AOa5PA3+NDYd3MTopaPpfUlv1vx4DYkxiW6b1HiOHIH16+H9903Yvt30hgBSUkzDoFcv4yOxZ08jKIGeUatWDYtLZaVJNz/f9LgOHDAit3cvfPyx+QzQuTMMG2bC8OHmebanZXGwAhWOVFQYDwpbthivEYMHBy3p7IJsRjw/gsToRDZM2UCX5C7nvilc+NnPYNEisw9WiPwQni9v7nmT61+8nm93/zZv3vwm0d5ot01qmLIyI0jvvmvChx+a87GxZjh16FC48krTOEpNDU3vprgYPvoIsrIgI8MI4yHHf3TbtjBqlAnXXmvcXlkiFitQ4YYq/OhHZubeCy/A5MlBS3r3kd2MeH4EXo+X9betp2frnkFLu1moqjJDnuvWmd13R45026J6LPlwCbe9fhtjLx3LSze+FD49qU8+gZUrzZDxunVGpKKjjRiNGmXyMT3dnHMDVfj8c2Pbe+8Z4czLM9d694YxY8z/fdgw92y0uEJjBQpVbTEhPT1dWyyzZqmC6sMPBzXZt/a+pRc9epG2/e+2mlOQE9S0m5Xjx1V791ZNTlbdudNta85gUeYi9T7k1b4L++qB4wfcMaKyUnXtWtX77lO97DJTnkA1LU11+nTVlStVS0vdsa0x+P2q2dmqjz+uOmqUqs9n7E9KUr3xRtXnn1fNz3fbSkszAGRqI+p810Xn64QWKVB+v+r8+Sarp041x0FJ1q+PbHhEZbZo34V99ZMvPwlKuq7y2Weq7durpqaq5oSf2L6z7x1NeiRJ2z3WTrfkbmmeh+bnqy5ZojphghFvUI2OVr3mGtWnnlLdu7d57AgFxcWqr72m+pOfqHbsaP42EdVBg1TnzFHNylKtqXHbSksIsAIVDpSXq95+u8nmG25QragISrJ5xXn6g5d+oMxGJ/59opZUlAQl3bAgK0v1kktUExNV33jDbWvOYGfBTu32VDf1zfHp79b+TsuryoP7gKoq1Y0bVR98UHXAAFNhgxHu229XfeUV1aKi4D4zHPD7zf9+zhwjUIG/u1071VtvVX3xRdXCQrettAQJK1Buc/iw6tChJov/8z+D0hKsrK7U+RnzNemRJPXN8eljGx9Tf5B6ZGHF55+r9u9vKqnf/z5ovc5gUVhaqJNfnqzMRr+x4Bu64cCG80/M7ze9xT/8QXX8eDPcBaoej+qQIabC3rYt8noShw+bnuOkSaopKbW9q/R01RkzVFevDu/hTMtZsQLlFlVVqn/8o+kFxMWZll9Tk6yp0mXZy7TP//ZRZqNj/jJGdx/ZHQRjw5jSUlM5gepVV6lu3eq2RWewcs9K7Tq/qzIbveHFGzTjYMa5b6qsNILz9NOqN91kykngXVK3bma4a9ky1aNHQ/8HtBSqq1UzMoxYDx+uGhVl8svnM43AmTNNb9v2sFoMjRUoO4svWKjCihXw61/Drl1mZtKCBfDNb553kgWlBSzevpiFmQvJLcqlZ0pPnrz2Sa7rdV14+dYLFapm+vmsWWZB6cSJxm9hWprblp2itLKUeRvnsWDrAo6VH2N46nCmD5rOuLRxxOODPXvMGqSsrNpQVmZu7tIFrr7ahBEjoEcPu7i1MRQXmy1b1q2DtWtNnlZXm2tpabXT6dPTzeLhIPu5tDSdZplmLiJjgKcBL7BYVR897XoMsBRIB44CE1X1M+faTOB2oAaYrqpvn+t5YSlQu3bVTh3fv98sfpw3D66//mtXNn71k1OYw4o9K3hjzxtkHMxAUUb3GM0vB/6S76Z9N7w9Q4SK4mJ47DF44gk4edKsH7v5ZpgwwSwsdZuiIko+3sGzWX/iyYLX+ZwTxFULY/fBv+9UrjoAXariTGU5cCB861vGB6NdCxQcTp6EzEyz9iojwwhWbm7t9U6dzELh3r1rFyenpZnzdvGwK4RcoETEC+wBrgFygW3AZFXNqRPnDqCvqv5cRCYBN6jqRBG5HPgbMBDoCLwL9FLVmrM901WBUoVjx8zak23bYPNmE/buNYV89Gi45RaYNMk4Qz0LfvWTV5zHp8c+5dNjn5JdkE1mXiZZX2RRXFkMQP8O/bmu13VM6D2By9te3hx/YfiTlwdLl5rGwI4dpgFw2WWmxTxwoKmAunQxXgya6qGjqgpOnDCeP44erfWgkJdnwqFDZo3PgQNw/Pip26o9sP7KS/hH/zhebXuEPE8pAJ0SOzG482D6te9HWus00i5Oo2dKT5JikiKjN9zc5Oebnuu//gXZ2Sbs2mVcNgXw+Ux56drVfHboUBvatoU2bUxo3Tqs3HBdCDSHQA0BZqvqtc7xTABVfaROnLedOBkiEgUcBtoCM+rGrRvvbM9sikCVHM1jy+o/Q40f1G/8itXUmKGB6hq0ugoqytGKCrSiHEpK0aIiKC5Cjx3DX3AYf1kZCtR4oCYlGX+vXlT3+QZVA9OpapVAlb+K8upyyqrKKK8up6SyhOLKYooqijhefpyC0gIKTxZSUFpAZU3lKduivdH0a9+P9A7pXNnxSr7T8zvh54E83Ni5E159FbZuNSE/v/71Nm3MPltJSZCYaBaCer0miJj/e02NEaKystpQUmKEKTAM1xBt2kDHjqZiS001nz171roNio8HTENke952Mg5mkJGbwebczew/vr9eUvG+eNq3ak/7Vu1JiU0hOTaZ5JhkEqMTifPFEe+LJy4qDp/XR7Q3Gp/HR5QnCq/Hi1e8eD1ePOI5FQQ5JXiB74JzXEcIA+cawwUjoH6/aWgcOmR6WPmOg9z8AjOE/OWXte6gTifaBwmtICHB+I4MhNhYU7ZiYkyIijLC5/OZ71FREOUFbxR4PeBxyqDHY8rh6Z8NBiDw/wqcq3OqgYPzGypu5D0ej5erx9/z9dOv96jQC9SNwBhVneYc/wgYpKp31YmT7cTJdY4/AQYBs4HNqvoX5/yzwFuq+nIDz/kp8FOA1NTU9AMHDpyXvTs3vUaf1Tec173nS4IvgcSYRJJikkiOSeaShEtOha7JXenZuic9UnrQNbkrPu/Ze12Ws6BqKpw9e+DgQRO++MJ46i4uNp9VVbWipFqn8ogyFU18vPlMSDDCFhC3Nm2MB++6Xryb4PXgZNVJ9n25j71H97L/+H4Olxw+FY6VH+NE+QlOVJyguKKYipqKIGaSxRIcYqqhfG7T5i40VqDCfrsNVV0ELALTgzrfdLr1Hsb6oj+alorHA+IxLZoon2nh+HxIbBzExCC+aMQZmw60NL0e76kWaaDlGvj0eXz4vD58Hh9xvjhio2KJ9kbjETu+3SyImCGaFvBOJ94XT992fenbru854/rVT1lVGWXVZVTVVFHlr6KyppJqfzU1/hpqtIZqf7WZ8YRS469BMT+RwLlAAzRwPnCtsdS9z9JIVJ2RmWqoMSM0VFfXjtoEGkl+ZyRH/aA43wNzOp1zgeNAunWf0dD3ho6DTHP2qJsiUIeAujVCZ+dcQ3FynSG+ZMxkicbcG1QSktswfMzPQvkIiyWoeMRDQnQCCdEJbptisbhCU5r424A0EekuItHAJGD5aXGWA7c6328E1jhz4JcDk0QkRkS6A2nA1ibYYrFYLJYLjPPuQalqtYjcBbyNmWb+nKruFJE5mEVYy4Fngf8TkX3AlxgRw4m3DMgBqoE7zzWDz2KxWCyRRYtaqCsihcD5zZKopQ1wJAjmXCjY/KiPzY/62Pyoj82PMzmfPOmqqm3PFalFCVQwEJHMxsweiRRsftTH5kd9bH7Ux+bHmYQyT+w0M4vFYrGEJVagLBaLxRKWRKJALXLbgDDD5kd9bH7Ux+ZHfWx+nEnI8iTi3kFZLBaLpWUQiT0oi8VisbQArEBZLBaLJSyJGIESkTEisltE9onIDLftaW5EpIuIrBWRHBHZKSJ3O+dbi8hqEdnrfKa4bWtzIiJeEflARFY4x91FZItTTl5yvKREDCJykYi8LCIfi8guERkSyWVERO51fi/ZIvI3EYmNpDIiIs+JSIHj+DtwrsHyIIb/cfJlh4j0b+rzI0KgnL2r/gCMBS4HJjt7UkUS1cB/qOrlwGDgTicPZgDvqWoa8J5zHEncDeyqczwPmK+qlwLHMJtqRhJPA6tU9TLgm5i8icgyIiKdgOnAAFXtg/GYM4nIKiPPA2NOO/dV5WEsxm1dGmYHioVNfXhECBRmY8R9qvqpqlYCLwLXu2xTs6Kqeaq63flejKl4OmHyYYkTbQkw3h0Lmx8R6Qx8F1jsHAswEghs+xJp+ZEMXIVxUYaqVqrqcSK4jGDcwcU5zq7jgTwiqIyo6nqMm7q6fFV5uB5YqobNwEUi0qEpz48UgeoEHKxznOuci0hEpBtwBbAFaKeqec6lw0AY7KHebDwFPAD4neOLgeOqWu0cR1o56Q4UAn92hj0Xi0gCEVpGVPUQ8DjwOUaYTgBZRHYZga8uD0GvZyNFoCwOItIK+Adwj6oW1b3meJqPiHUHIvI9oEBVs9y2JYyIAvoDC1X1CqCU04bzIqyMpGB6Bd2BjkACZw53RTShLg+RIlDNvv9UOCIiPow4/VVVX3FO5we64c5ngVv2NTNDge+LyGeYId+RmPcvFznDORB55SQXyFXVLc7xyxjBitQyMhrYr6qFqloFvIIpN5FcRuCry0PQ69lIEajG7F11QeO8X3kW2KWqT9a5VHfPrluB15vbNjdQ1Zmq2llVu2HKwxpV/SGwFrN3GURQfgCo6mHgoIj8m3NqFGZLnIgsI5ihvcEiEu/8fgL5EbFlxOGrysNy4MfObL7BwIk6Q4HnRcR4khCRcZh3DoG9q/7LZZOaFREZBmwA/kXtO5ffYN5DLQNSMVuZTFDV01+KXtCIyNXAfar6PRHpgelRtQY+AG5R1Qo37WtORKQfZtJINPApMAXTkI3IMiIiDwETMbNgPwCmYd6rREQZEZG/AVdjttTIB34HvEYD5cER8QWYYdCTwBRVzWzS8yNFoCwWi8XSsoiUIT6LxWKxtDCsQFksFoslLLECZbFYLJawxAqUxWKxWMISK1AWi8ViCUusQFksFoslLLECZbFYLJaw5P8B8+yyfxkpn3sAAAAASUVORK5CYII=\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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FjY2N+MxnPoN//ud/xuWXXx6zjdtuuw0tLS1YuHAhVq5ciY0bN0bc/7WvfQ3Hjx9HRUUFbrjhhpjnP/DAA1i/fj3WrFmD1atX4/zzz4+pm0qVkpISnH/++ejs7ERRURGA8MVLS0sL6urqFJ+jdCzTZenSpaitrUV9fX2EeFxwwQVwOp3YtGmT9Ngf/ehH2L9/P8rLy3HNNdfgs5/9rHRfIBDAvffei5qaGtTX12NiYgI//elPAQCvvvoqOjs7YTQaceedd+K5556DwWBAc3MzduzYgZ/85Ceora1Fc3MzHnnkkbiCK4oifvGLX6CxsRFVVVXYtWsXfvOb3wAAPvnJT6KzsxP19fWoqakBAPzbv/0bFi9ejI0bN6KsrAyXX365WvtUADDRaaUkqOM2ZpmnnnoKv/3tb6VUoUpinnzySfzud79Tj5eKSmGRUs55divqVNLC6/Xi17/+Nf7+7/9+tnelYCCEIBgMQhRFaDQasCwLlmVzuhamoqIyO6gpvnOE1157DbW1tViwYAFuueWW2d6dWUcURXg8Hvj9fgSDQfj9fng8HrhcLhw7dgxOpxMejwehUAiEEAiCEGNCUVFRKWzUFJ/KOQOtjQiFQhBFEe+//z42bdoEnuchiqIUNe3btw8bNmyIqKdgGCZcV8Gy4DguItqiEZcadamozBhqik9lbkDO9FajQgRAEhSGYaToiOO4mPuitwOEa5qi+/QxDKMoXqpwqajMHqpAqRQsNDUnCIIUIckFQxRFnDx5EpOTk9JtBoMBgUAA4+PjKCkpQXFxsWQvpo9REhwqgoIgSPZjCsdxEX9U4VJRmRlUgVIpOKgw8TwvpefkguDxeGA2m+Hz+VBRUYGOjg6IoghCCPx+Pw4ePAifzwebzQav1wtRFKHX6yXBKikpQUlJiRRxAYgrOHLhovtCYVlWiraocKkGDRWV3KEKlErBQAgBz/MRYkCjHwCYnp6GyWRCKBRCW1sbpqenUV9fL6XrWJZFcXExtFqt1IqIbtfv98Pr9cLj8WB4eBherxeCIECn00WIFn0+JZFwUQehknBFR1yqcKmopI8qUCqzDhUmKjRyYSKEwG63w2w2g2VZtLe3S0WiPT09EduIJwAMw8BgMMBgMEgFuvQ5wWAQHo8HHo8HY2Nj8Hg84HkeWq02QrRKSkqkoli6zXjCBYRnUYVCIQCAw+EAy7KorKxUhUtFJQ1UgVKZNWjqTC5M9GRNCMHExATMZjOKi4uxbNmyiKauuYBhGOh0Ouh0OlRVVUXcR4XL6/XCarXCYrEgFApBo9FERFxUuKLXt+Si4/f7JcGlwqXkLFQSLlW8VOYzqkCpzDjUkScIAoBIYRJFEaOjo+jv70dFRQXWrl0Lg8Ew4/tYVFSEoqIiVFZWRtzO87wUcdntdgwODiIQCIBl2ZiIS6/XRwiW6ixUUUkPVaBUZoToGiYgUpgEQcDQ0BCGhoZQW1uLrq4uaXRDpq+Xj5O4RqNBeXk5ysvLI24XBEFa45qensbIyIgUORFCoNfrodFoJOFSnYUqKslRBUolrySqYQKAUCiEgYEBjI2NobGxERdeeGHEXKRUth8NTZ3N5Mma4ziUlpbGpCFFUYTZbAbP83C73RgfH4fP5wMQtsRHGzTkppBMnYXqOpfKXEEVKJW8ILeKHz16FKtWrYo44fr9flgsFthsNixatAgbN26MsH2nAo1Ook++VKAKAZZlJadgQ0ODdLsoilJ7Jo/Hg8nJSfh8vghLvFy4UrXE0yg1GAyqwqVyzqMKlEpOUaphcrlcMTVMLpcLra2tWLp0aUTUkA4Mw0S0OJLfXigCFQ9qiS8uLkZtba10O7XEU4OGw+GIsMRH13LJo810nIVutxt+vx91dXWqcKkULKpAqeSEZDVMTqcTJpMJwWAQbW1t6OzszPokGC+Vdy4IVDzklng50Zb40dFReL3elC3x8r+BsEvR6/UCUJ2FKoWLKlAqWZGsholGAD09PWhvb49xxWVDPCE6lwUqHpla4qMjLmqJV+rQQVGdhSqFgipQKhmRrIbJarXCbDZDr9dDp9Ohq6sr5/tA16CimYsClYh4lvhQKCQ5C202m2SJ5zgODMOA4zjYbDYUFxfHWOLlf8tJ1VlIRUwVLpVsUAVKJWWSWcVFUcTY2BgsFgsqKiqwevVqFBcX47333svL/iSKoFQArVYb1xI/MDAAj8eDqakpDA8PS5Z4g8EQYdCQW+IB1VmoMrOoAqWSlGRW8VzXMKUKNUlQ4Yy+XUUZjuOkuqzm5mbpdkEQ4PP5pMGP0ZZ4+TpXOpZ41VmokimqQKnEJdm4C1rDNDo6isbGRlxwwQURjVYp+axLGh8fx+joKERRlJxxXq8XdrsdVVVVEakrlbMofR4cx8FoNMJoNEbcLooifD6flC60Wq3wer0ghCjWcqVqiQcinYVAuG8h3Z5Go4lIR6qf4/xDFSiVGJKNuwgEArBYLJicnERzczO6u7sT1jCxLAtRFNOuc4qHKIoYHh6GzWaDRqPBeeedJ4mg1+vFqVOn4HK5YLPZpNRVdP+8+S5c6VwwyNs4xbPEezweOBwOeDweiKKYkiVe/jfFbrdLEZ78+0cfqzoL5xeqQKlIJLOKe71emM1mOJ1OtLS0YMmSJSnVMOVKoARBwODgIIaHh7FgwQLU1NSgtbUVOp0OwWBQ6uZgMBjQ3NyMkpIS6Xnx2hDNV+GiVvJskFvia2pqIrYdCASkYz46OgqPxwNBECIs8fSPPOqm35PofVOdhfMTVaBUQAiBx+ORfuhKNUxmsxl+vx9tbW1YuXJlWj/8bNeEeJ6XUokNDQ1SO6SjR48qbjfaPBGvDdF8Fq58toJiGAZ6vR56vT7CEk/XomjENTExAY/HE2GJd7lccLlc0Ol0SbvEy7ebqrNQXec6t1AFah4jt4ofP34cbW1tKCsrk+6nc5gAZFXDRCOodAkGg+jv78fExASamppi2iFlWwc1n4VrpnsVAuHPJZkl3ul0wul0wmq1SlFx9BpX9DFXnYVzF1Wg5iFK4y44jpMcV/IapiVLlkSIViakK1CBQABmsxl2ux2LFi1Cd3e3YjoqX4W6qQrX6OgofD7fOSlcsyFQiaCWeJ1Oh9bWVqmTBs/z0jGPtsRTNyE95gaDIWXhUp2F5waqQM0TktUwsSyL8fFxHD9+HGVlZVINUy6IV1Abjc/ng9lsxtTUVEp9+ma6k0Qi4fL5fHC73XA6nTHCxfM89Ho9KioqCka4Ck2gKISQiChZo9GgrKws5iIp2hI/NjYGv98PADG1XAaDIWVLPBDrLKT3BQIBVFRUSKKlOgvzjypQc5xUapiGh4cxNjaGqqoqnHfeedDr9Tndh2QRlMfjgclkgsfjQVtbG1asWJHSD18ufNFXzjPZSSKRPdvr9WJgYAA+nw+9vb3w+/2SuaCkpARGoxHFxcUxV//5plAFShCElPYrmSWernOla4mX/02h7lCz2YwVK1ZE3Kc6C/OLKlBzlGRW8VAohMHBQYyMjKChoQELFy6UrvBzTTyBcrlc6OvrQzAYRHt7O6qrq3NiviiUVkcsy8JoNKKsrAwcx0njNqhweTyeiIiLYZiYVGG+hKtQBYrWs2WK3BIvJ9oSb7fb4fV6IyzxcuGKtsRTd6Fc0FRnYf5RBWqOoSRM8h+8vIapqalJqmEymUx5674QLSRTU1PS67W3t8c0P01nu+diLz4qXPEiLnnaKl/CVagClQv7uxLJLPG02e7IyIhkiS8qKpIEK95YF/nf0e9DdRZmjypQc4RUapgsFou0vhNdw8RxnGSayDUsy0IQBNjtdphMJnAch46OjpgecekiF6Logs5CFqh4zKRwFapAATPbS1Fuia+urpZuj7bE2+12uN1u7Nu3T7LER483UZ2FuUcVqHOcROMugHAazWQySTVM8dZ3MrWCp7J/Pp8Pp06dQmlpKZYtWxZjMsgUeQul2VyDyjfpCBc1CiQTrkIWqEIg2hJfVFQEr9eL1tZWSbi8Xi9sNhsGBgYULfElJSXQ6XSqszALVIE6R0k07gII9zQzmUwghEg1TIm+0BzHIRAI5Gz/CCEYHx+HxWKBKIpobm5GS0tLzrYPqOM2shEur9eLQCCgClWKCIIgrUtptVpUVFSgoqIi4jFyS7zD4YixxMujrnQs8XTb0c5CatCQr3HRP3MFVaDOIZJZxQkhmJychNlsRlFRUVo1TLmKoOQjNyorK7F27VqMjY1FTHjNFYVukpgtkgkXHWw4MjKCwcFBAMkjrvmOIAhJT/yJLPHRpph0LPHyvylyg4bf78fJkyexatUq6bEPP/wwHnnkkezedAGgCtQ5ADU+OJ1OqYBRLkyiKErRSmlpKTo7O2NcTMnIdg2KNnAdGBhATU1NxMiNbFsdxYMKER2HTtcB5rtAxUMuXHa7HY2NjSgrK4uwZkeP2aDFsEajUXE+1HyB5/mM6wLj1c8ls8TL17gSWeJpFEyL7QHgb3/7W4bvtLBQBaqAkY+7EAQBhw4dQnd3d0wN0+DgIKqrq7OqYco0gopu4Ko0ciNf61tA2BE4ODgIhmHA87z0Iy0uLpZcWPmI3s515Kk9uTW7rq5Oeoz8BOp2uxXnQ8nruHIhXIV6YZGt/V2JRJZ4+XgTuSVer9fHpAt5npfSjwzDwOfzzcg8tplAFagCJJFVnJ6IBwYGpBqmeHOY0iHdCIrnefT392N0dBQLFy6UGrgqQV18uYIQgtHRUZjNZhQXF2PdunXSonEoFILZbAbP87BarbBYLAiFQkm7aM83Ull7incCTUW44qWsst2n2UIQhJyNi0kGdWcWFxfHtcR7PB4MDw/D6/UiGAxCFEX09PTg448/hlarTcuI9Oqrr+LOO++EIAi4/fbbce+990bcHwgEcNttt+Hjjz9GdXU1tm/fLplFbr/9duzfvx88z+O2227DD37wg5wdB0AVqIIimVVcFEWcPn0aVqsVCxcuxMaNG+OKQrqkGuVEN3BNNguKbjt6gTcTRFHE6Ogo+vv7UVVVhZaWFskmTGtNtFqtNO21sbExYr/pD3t8fBwejwc8z0tRljwayNUxLWSyEYNUhIt2K09HuPIRpeSKmRSoeMSzxFutVjgcDtTU1MDhcGDPnj04duwY1q1bh8rKSqxevRr/+Z//qfh5C4KAb3/723jjjTfQ1NSEDRs24Prrr8fKlSulxzz++OOorKxEb28vnnvuOdxzzz3Yvn07nn/+eQQCARw5cgRerxcrV67EF7/4RbS2tubsPc/9X+I5QDKrOK1h8nq9KCkpweLFi3P+Q04WQfn9flgslqQNXJXINsUniiJGRkYwMDCA6upqaX1rZGQkrvMwOlWk1EWbrl1FX5EKghDRXYAK12yfoHJJPqKVbIUr2pJdSBSCQMWD9nqsrKzEt771LXR1dWH79u347W9/C5vNBpPJFPe47tu3D4sXL0Z7ezsA4Oabb8aOHTsiBGrHjh146KGHAAA33ngjvvOd70jfH3qh5/P5UFRUlHVj6WhUgZpFklnFXS4XzGYzvF4v2tra4HA40NjYmJcfcTwRoQ1cp6en0draimXLlqX9+qk2i41Gbryoq6vD+vXrI9aTsu0kwTAMdDoddDpdzNwieSplcHAwYg2AihZdAyjUq/5EzGQ6LVXhGhsbg8vlwocffphVqjAfFLJAyS3wQHhdllrgq6urI6KtaIaHh9Hc3Cz9u6mpCXv37o37GI1Gg/LycthsNtx4443YsWMHGhoa4PV68R//8R8Zd4WJhypQs4DSuAv5yULeCqitrQ1VVVVgGAZmszmno9PlREdQ8gau7e3tKTdwVSJdF5/c/BHPeEG3m486qETdBWg/N7fbjcnJScl1pWTTLnThmu1oJVq4aEPdzs7OrFKF+aCQBSoUCkWI//T0dEyNVj7Yt28fOI7DyMgIHA4HNm/ejMsvv1yKxnKBKlAzRDo1TFqtVrEVEBWRfPxQaASVbQPXRNtOhtwRWF9fn9B4Qbc7k4W68fq5iaIIv98Pt9sdc0KlLiuDwYDy8vKCqS8qREMCXYNKFnF5vV643e4ZFa5CFqjoCCodgVq4cKFUCwcAQ0NDWLhwoeJjmpqawPM8pqenUV1djW3btuHTn/40tFot6urqcNFFF+G1HJk3AAAgAElEQVSjjz5SBepcItm4C0KIVNhaWlqKlStXxhRYUvLZL4+O2j59+nRW03OVSCZQPM9HdFZPJkyUQmkWKx+eJ4cWxg4ODsLv96Ovr09xwKHRaJzx9ZdCFqh4yIWrtrY24nnyyJbWEwGQRmzQlGymwpWvJra5IBQKxQjUsmXLUnruhg0b0NPTA7PZjIULF+K5557Dtm3bIh5z/fXX4/e//z26u7vxwgsv4JOf/CQYhsGiRYuwc+dO3HrrrfB4PPjggw9w11135fS9qQKVJ5KNu6DrK4ODgynPYcq1QBFCpAauGo0GOp0OXV1dOds+JZ5AUbt8KlZ1JQq9kwQtjC0tLY0Yt5FopLx8fUupCWmuUOrOPdtk6uKTXyDEEy55ISyAiLVE+txCFaBkZBNBaTQa/OpXv8KVV14JQRDw1a9+FZ2dnXjwwQexfv16XH/99fja176GW2+9FYsXL0ZVVRWee+45AMC3v/1tfOUrX0FnZycIIfjKV76CNWvW5PS9qQKVY5KNu6DRAk1jRS/8JyJXAkXTiSaTCQaDAStWrIDRaMR7772X9baViBaoUCiEgYEBjI2NoampCRs3bswofVIoEVS6xOssIO/lFt2EVC5auSo+nisCFY90hUvewUFeCFvowqUUQaWzBnX11Vfj6quvjrjtxz/+sfT/er0ezz//fMzzjEaj4u25RBWoHJGshkleP5RpDRPHcTGD0dLdx/HxcZjNZpSWluZ0rHsi6FpRKBSCxWLBxMQEmpub07KqK3GuClQ84vVy43k+In1Fi481Gk2McKVafHwupvhyRTzhoh0cqHDJTTB+vx8mk6kghUveSQKYOZPETKAKVJZQYfJ6vTh16hTWrFkT8cX1+XywWCxwOBxp1w9Fo9FoMoqg5AWulZWVeRnrngie5+F0OrFv376sj4EcuRDN5XEb1NobbZoJhUKSMSNe8TH9E30xVIjHZ7YLdeUdHKIjrg8//BClpaUxwlUIEVf0+tj09HRO15BnE1WgMiS6hkmj0UhD5ADA7XbDZDJJM2SWL1+e9RVruik+URQxNDSEwcHBmAauMwGd3mu1WsGybM6EiTLfx21otVpUVlYmLD4eHR2VJsTKi4+paaeQnGmzLVDxEEURWq0WtbW1KUdcsylcTqdTjaDmI9QqrlTDRBfsaQ2TIAhoa2vLiU2bkqpA8TyPoaGhhA1c45GL1I/f74fZbIbD4UBraytaWlpw5MiRnP9AC90kMRukWnwcCARw6NChiOJjuWlgNoSiUAUqnsU8XsQ128IVCoXUZrHziVSs4jabDR6PB2azGe3t7Xm5gkm2BiU3HzQ2NqbtiqNmhkyvqmmefmpqCm1tbVLUKD9uuYQKEc/zGB0dhV6vh9FonNcCFY/o4uPx8XGsX78+pvjYZrNFnEzla1z5Loo91wQqHukIl8/ngyiKGQtX9Jyqufa9VwUqAfJxF9SWGy1M1HRgNBqh1+tx3nnn5W1/NBqNYu85uQGjubk5Y1dcpoXAPp8PJpMJTqdTcax8vsZtCIIAl8uFvXv3oqamRmoNFQgEpNeTn2ALKZ1VKCQrPqbCFV18nI/hhqIoFmSj3lwV6SYTLlqATC8SqHDR4200GmEwGCL2JdpiLn+tuUDhfRsKgFRqmGjz0srKSqxbtw4GgwHvvfdeXt1R0Sm+bBq4KpGukHi9XphMJrjdbrS3t2PlypWK7z3XEQ0d9TEyMgKWZbFx48aIlOv09DSGh4dRXV0tNYH1eDxSOouKFv3BF+JV+2yTyKIdPU5eqfiYDjdM57dQiLVZQP67SCQaryG3w0fPhaLmF3q+4jgOfr9/zqT3AFWgIkhmFZfXMC1YsCCmhinbFFkyqEB5vV6YzWY4nc6MG7gm2n4yPB6P1BWhvb0dnZ2dCV8/VycdeWFvU1MTzj//fJw+fRoajQaiKEY4+liWRVVVVcw6jFIvPQARV6mZnFznC/HGyScrPpYf23jFx4Vm2qDMVpujeNGt/Htss9ng9/tx4MAB/OIXv4DD4YDb7ca2bdvQ2dmJZcuWJXTsZjoL6g9/+EPESPnDhw9j//79WLduXU6PgSpQSD7ugqbQxsfHE9YwaTQaaaprPggGg7BarVIqLV7EkinJIii3242+vj74/X50dHTk1ACSiGhhoilMv9+flkkiUTqLnlydTqd0cuU4LqJNjtFoVKfzxiFe8bEgCBERgLz4OLprxlxZg8o38u8xHfW+ePFiPP3009i5cyceffRRDA0N4bXXXsPg4CDefPPNnM+C+tKXvoQvfelLAIAjR47ghhtuyLk4AfNcoJKNu5C70Zqbm7Fp06aEPyAqULkOsZ1OJ0wmE3w+H/R6PTZs2JAXYYgXQdEGsqFQCO3t7VJ39XwTT5gouSrUTRQVyM0D/f39MdN56Qm2ENdOCgGO4xIWH9NODhaLRTrONputoCYfF5pAyZEX6XIch/LycixduhT/9E//lPS52c6Cojz77LO4+eabc/iuzjIvf1XJxl243W6YzWa43e4IN1oyqEDliqmpKfT19QEA2tvbodfrceLEibyJQ3QE5XQ60dfXB0EQJGGaCaJ79MUzfeS7k0S8k6u8QHZsbAxut1uqM5JHW4XUbaDQUCo+Pn36NKqrq8GybEbFx/niXBEoIHIWVDKymQUlz0Bs374dO3bsyOZtxGXeCFSycRdAuALbZDJJkUK6KaxcCFR0A9fFixdLP+JQKJRTAYyGZVkIgoDp6Wn09fWBEIKOjo4ZK/pLVZjk+xtPiPJpt41XIEvrjNxut7SgTb93er0eGo0mp663uYYgCCgqKkJpaWnMsZVfFMQrPs7X5GNBEGY9iotHdMZmptsc7d27F8XFxVi1alVetj/nBYrWMNntdimFE20Vp4LAcVxWNUzZNHMlhMBqtcJsNkc0cM3V9lMhGAyip6cHer1ecR5VvpCP20hFmCiF1Isv0ZBDs9ksnWCjXW/R61vzWbjiufgYhkFRUZGi6UVefDw0NBTh1sxV8XGhR1CZDivMZhYU5bnnnsMXv/jFLN9FfOa0QAmCgFAoBEIIjh49iu7u7pgaJovFguLiYkVBSJdMIih5LVVZWVnCBq6Zjk5Pht1uR19fHwKBABoaGtDR0ZHz11BC7orMpKt5ok4ShQI9uRoMBmncBnDW9eZ2u+FwODA0NIRAICBFWfL1rUK9es816c5cSmXyMXW6RXdySGc+VKELlPz7MVOzoIDwBcUf//hHvPPOO7l7Q1HMaYGi0C8gPaHRGqaKigqsXbsWBoMhJ6+TjkDNdgNXGjn29fWhqKgIy5cvh91uz+sPkS6uRkdM3d3d82rcBpB45IZ8Mq/b7ZbWYKI7lxfqSTNTcuXiS2TPpp0c0ik+LnSBku/bTM2CAoDdu3ejubk5pxN0Y/Yxb1suAFiWjbiaNpvNGBkZQW1tbV4ap9KGsYkQBEEaVFhbW5vWPKhcQNsy9fX1wWAwREzwnZ6ezlsKkWVZhEIhDA8Pp53Ki0e8DubngkDFQ6PRoKKiIuIkI28A63a7IwqPM4kICpV828wTdSv3+Xxwu92KxcdutxtGoxFarbbg6uOUIqiZmAUFAJdeeik++OCDNPc4Pea0QAHhdZWBgQHJDZRuf7p0SBRByaOG+vr6tBq45gL5kEK6qCnPXQNnRSTXCIKAQCCAffv25USYknEuC5QSiRrA+v3+iIhLHhHII65CO7EqMVt1UPJiYjk0DXvixAmpjiu6+Hi21w/n8iwoYI4LFCEEBw4cQGNjI2pra9HQ0JBXa6qSQGXbwFWJdNopUfOFyWSC0WhMusaVy555giBgYGBAaknU1dWVs3RqIuaaQMVDnspSakfkdrsjujrQ4lg6biMYDBZU4XGhFerSNKxWq0V7e7t0QSkvPpavH8qPr7xrRj6JbhY7l2ZBAXNcoGifNkIInE5nXi3aQKRABYNBaRZSNg1co6FOvmQiF22+SGWtLVcuQUEQJPMDFeXDhw/P2BXmfBGoeMQrPKaDNV0uFwRBwLFjxyIKj+UR12wUHhfilF8gdg0qleLjycnJnEw+TgX5MZtLs6CAOS5QcrRabV7SV3Jot/ETJ07A4XCgpaUFixcvzulVYTKBIoRgbGwMZrMZFRUVaZkvaB1UplBhonZVebSYr47mhBBMTEzAZDKBYRjJUhwKhQp6cXs2oCPlS0pKMDY2JnXel69vyWuMZmNOVCEKVKruwkSTj+nxlRcfa7XaGOHK9sJgLs2CAuaBQNGraa1Wm9cIyuv1oq+vD1NTU2hqasrJBF0l4kU5oihibGwMFosFVVVVOP/889N2BXIcl5GIREdMSr0K41nCM4WuqXm9XkxMTKCzsxMApC7bwWAQBw4ckIwE0R3MC/FEOFNERypFRUUoKipSLDym61vUqg1A0Zgxn49nMrRaraLxJZXi40SOzejPcS5mDea8QFE0Gk1eIig62t3n86G1tRUulyui3iXXRAuU3DZfXV2dlTsx3RSfUiov3hVgLiMom82G3t5eFBcXw2AwYNWqVVKHEJ1Oh8rKSkxMTEgD+eTW4vHxccmhJT/JzqdGsKmk0uQ1RtGNdenxjHa8pdq1XCVx8XEwGJSEK3pUjPwYa7XauC3A5grzRqC0Wi08Hk/Otkf71PE8H9FAlfbOyxd0nUsURQwPD2NgYCBndvVURUQuTA0NDSkZP3IhUHa7Hb29vdDpdJIL8b333ot5XLT9XMlanKgRrFy05mK9UTZrPXIhqqurk26XFx7Lu5bTwmN5Kmu+FB5ngtyxmaj42G63w+12w+/348iRI9i7dy8YhpEyRamkCjMdtQGEx2vccccdcDqdYFkWH374YV7qOOe8QNEfYq4auTocDphMJgDhBq4z7ZhhWRajo6M4fvw46urqcmpXTxZBZSJM8v3OVKCmpqbQ29sLjUYTUbclJ/qEmyzdEW+hO97V61xKE+bDjBCv8Jiuvyg1f41urFuIFEraTKn42OVyYXBwEK2trbBYLHj77bcxPj6OjRs3AgCWL1+Op556SnH9LJtRGzzPY+vWrXj66aexdu1a2Gy2vF10zHmBomRjkpD369NqtViyZEnMiS3fCIKAoaEhjIyMoLq6Oi91VPFEhL720NBQ2sIk33a6P/bp6Wn09vaCYRgsXbp0Ro55vLQLLeSkJ9p00oSFcpKjzKRbTqvVorLMgWrjaTB1IQjchRCZmogLgcHBQWke15EjRwqq8LiQjTbUaFFcXIzrrrsOS5cuxfT0NLZv345QKASLxRL32GUzauP111/HmjVrsHbtWgCIiPRyzZwXKPpDzESgUmngGu95uZwiSwt8Gxoa0NLSAoPBkJcrlmiByoUwxdt2IlwuF3p6ekAIiejmng65PAHL04RyUk0T5sO9mA0zJlAkBA3/EjhhN4CwSHPCW+A1V4HRXR6RxhJFER9//DE6OjoUWxFFF8bqdLoZeQ+FLlDRRbr0t0IvpOORzaiN06dPg2EYXHnllbBarbj55ptTmj+VCXNeoCjppPioVdtisSRt4BrvdbIVEPnoCbkBYWBgIG/tiGiKL5fCRElFoNxuN3p7exEKhbB48eKU06c0QpGfeGciakk1TehwOCTXYSGkCTMRqLSfQwg0/PPghH1RdwjQ8C+BMGUQuQukW+m493itiOSFx8PDwxGFsfL1rVwbXc4lgUpnFlS2r7tnzx58+OGHKC4uxmWXXYauri5cdtllOX+tOS9Q8ggqmUDJHXFVVVUZNXDNVqB4nkd/fz/GxsYU2wJxHJe3ei5RFBEMBvHBBx+gvr4+p22hEtnMPR6PNEqeNqVMZ7uFRnSacHBwEBzHoaKiIuM0YS5JR2yCwgSsgR3w8ifAsaWoKvoUyrUXJX0+J+xSEKezaEPbEWQWgLAtABJ3kUhUeBw9lVcpgi0uLs74e3wuCdRMjdpoamrCJZdcIq2FXX311di/f78qUNmQqLtALhu4ZmrGCIVC6O/vx/j4eMLOE6k0pE0XecRECMlLv0KlCIrWjnm9XnR0dKQ9IBI4N0ZuAJmnCeXRQa5OlKkKlE+wYMj7XyAk/H3mRScm/H9CQBhCnf4LcbfBiEPQ8MkmrArQhv6EYNF3gTOfYbprTfEKY+UR7MjISEzhMT2mqRQe08iuEOF5PuICOh2BymbUxpVXXol///d/h9frRVFREXbt2oXvfve7OX1vlHkjUErko4FrugIVDAbR39+PiYkJLFq0CN3d3Ql/NLkcWiiKIoaGhjA4OChFTPv27ctLmxu5QPl8PphMJrhcLnR0dKCmpiZjQYl34VFoxoR4ZOomTLVINiD6YPEdg09wYaF+CWq0C1MSqJDowKj3cUmc5EyH9kLPLUJ50abYJxICDf8n0DWnRDBkAKx4ECJ3Xk778MUzulCbttvtloq8AcQ4NOWNdaPHWRQSShFUqrOgshm1UVlZie9973vYsGEDGIbB1VdfjWuuuSYv73HOC5SS/Zim0cbHx2Na8mQLx3EpCVQwGITZbIbNZktJmOTbz1aglIQp373XWJZFIBDA8ePHMT09jfb2dqxcuTLrSIcKVKFFTNmSzE0YPZ1XKU1oD41hl/0F8CScEu7xHsQK4wVYRFYnPF6EiBj1PQGeuOM+xhrYgWLNUmjZmojbWfEjsKI55fep4V9EkF01I6M2lGZEJRq1Qbub064ahVZ4nG0n82xGbWzduhVbt25Nc4/TZ84LlByGYXDq1CnYbDY0NzenLArpoNFoEgpIIBCA2WyG3W5Ha2srlixZktY+ZCNQsyFMQPg9j42Nwe12Y/ny5VixYkXOfuhUoKKPYSGdSDKFEAJHyAVrcBqLDHUwcLqU04RuYQqm0vdBNCI0Gg4cp4GG43DCvQ+ChkDP1MZ5VcAZ2ge/MBj3fgAQSRAT/j9jYfE3ZDscgoZ/Ma33yBA7WPEARHF5wY3aoNGr3+/HiRMnpMLj6ELu2WisC8z9URvAPBAohmHg9/thNpvh8XhQX1+fF2GixEvx0X1wOBxoa2vDsmXLMjqJZiJQ0cKULJWZq4hEHiVWVlaisrIS9fX1WW9XDk0dRqdhzpUUXzwIIXht8kPsnz4NACjm9Ph07QVYblwU89joNKFIBLxhewaGkA48z4PnBYRCPgiCAEKAj5g3scxzCaqsVbHTY4kfk4GXU9pHD38CfmEIeq4pvB/C+2CIM+33quH3QBSXFtyojbKyMrhcLpSVlUkGAnnjV3rRFd0/jxoz8p0aVAVqDkAIwfHjx9HY2IhQKISampq8/hCie/75fD6YzWZMT0+jra0t6yay6QiUXJgWLFiQ0hpbvBN+OtAiwYmJCbS0tGDJkiWwWq1wuVwZbzMe1CRBa2Zot+5CYNTngp7TpC2WhBC8Yt2Hg84e6Tav4Mefx97BbQuvQJMhfvQDAH2+w3DydjAMC622CJEfeThdNSaeQqOrJSalxZbvA6+zQ8NpwKTwO3EE/4YGw98BhAcn7EzrfVIYMgCWDIBlC6+bhCAIEYapeI1flQqP892BRGnc+1yaBQXMA4FiGAZdXV3hdInDMSMjN3w+H7xeL0wmE9xuN9ra2nKW1krFhJGJMFGoAGYiUHKLfPS6Wj7GbdATw8GDB1FWVga9Xo+RkRG43W54vV4cOXJEMhREL37nE14U8dLwCewcD/dlrBI1+LuFa1J+/knPQIQ4nYXgxYn38LXmq1HEKn+eAdGH4+73E2ydAcuy8OgmYWzSoL1oNYDwidjltmIw8DH4YAg+wSetC3Gc5kyaMJwqlB9Dd+gQgkUT0MMEhkyl/B6j0eEDsOzlGT8/X/A8n3SOWqL+efJGxUqFx1S8Mik8jk5tz7VZUMA8ECg5MzETiud5jI2NwWazob29HZ2dnTk9KSaKoOQNZNMVJkomQkKLikdGRuKu7eVaoGjjWL/fj1WrVqGyshKhUEh63b1796K9vT2m67a8uJP+iV5DCPA8Ttgm0VFZhdIMyg2e6z+EfbazazjDATeeHTuOf2xogJZNLPwhkcebk/vj3u8IufC27RCuqF2veP8J914ExUBK+3nM/T7qqsIpQ47jIOqPQMdw0OFsBEpEEbxA04T+M2lCIomVRsNhgryJdr0ppdeMh449Ao69JKtt5INssgmJGhXT1k7RE3nlZQW0Y3mqzLVZUMA8ESi6kJ6rhrFK0LEbLpcLer0eXV1deblaV9pmLoSJkk4KUT6gsKmpCd3d3XF/zLkSqOnpafT09IDjOKxcuRImk0mxmJplWRQXF8d03abFnXT0Rl9fX0SNzCAfxJ/7LSAMA2NREb64chXW1NbFbD8eJ53WCHGimH3TeGXkNK5vWpHw+e85jsHJJ+66f8DZg4sqO1GiibyyD4g+mH1HUtxTBpPBEUyFrKjQ1kIkIUwFd8c+imWhZWPThIIgQhB48DwPW+A1VPkIWDDgNGEzBqfRgOO4NNLpPEqKegEsT/HxM0Mq06vTJV5jXfl3k7ZYix5sSP+OPq7n+pprPOaFQFHyEUG5XC709fUhGAyio6MDOp1OanCab+TClKvO5qkICU0hDgwMxB1QqLTdbH5EbrcbPT09EEURS5YskYoz5XVQR4cncHLMhsV1YWu2ktlDqbiT1sgM2Cbxx5NH4Q0EIQgCphngP999B3/fuRrtNbVJW+kEBB7bLYfi3r97woRLF7ShTKvcncQvBLFv6mTSYyEQAR9Nn8aW6rURt5t9R8Er1C1FI/8YTL7DOF97GVyhjxPayiNhzkRQHIqKdGDFSXDaCpSypRAEATzPIxgMQuB5iISAZWKFS6n8o6ToGIBrU9yHmUEQhBkzb6RSeExr4gRBQCAQgMlkwuDgIIxGIxiGSfm8k+moDYvFghUrVkj1Vhs3bsRjjz2WmwOgwLwQKHm7I1qcly3yeVAdHR1SvUogEMhbrzwKIQSDg4M5FSZKOinEVISJkkj4QrwA65QHDdWlMT8wr9crpfKWLFkSswhMTRK7Tlvw14+PgwDYax7C8hIO56coiAzDQKfX469Dg+B0OpSeSZMQQiDwAl4ZHsTnCaRWOnRUBP1DOxK8a+2HLRj/+xUUBbw+2osbF61SvP+Qqw8hktoF1P7p0+iuXCmtRYlEQJ/3YErPBQjoYe73ncCqkosxFXonxedGEwTgxpQAlHFl0Gg0Md8JURQh8AJ4gUfI74fA8yAAOJYNC5dGEx7Ix5kB4gKYUsVXmg0KodWRUk2c3+/H8ePHUVZWhlOnTuHVV19Ff38/1q9fj2XLlmHVqlX4/ve/r/j7zGbUBgB0dHTg4MFUv2vZMS8EipKLFN/09DT6+vpACFGcB5VqoW4mUIHweDzw+/0zNnJDFEWMjo7CYrFIgqjRaOCY8qKqMrWvULyWRB8eH8Sf3z4MUQQu7erApzcuk0oD+vr64HK5sHjx4rhtkBiGwZDDiR37T4YjgzMP+XDUgS0TdixtSOx4oxyaGMeQO9IizTAMNFoNxvkQ7MZibFy6NMKxReuOvF4vRELwv/4B+CCcOelyYBlW2h/Ku1YLLqvvQGVRZHpOJCI+mjqV0r4CgE8M4IjLjK7ypQCAIX8PvEKqEdBZeBKCybcHrDiS9nMBgCV2AARu0Q2e8NAwsd8HlmXBFrHQQvZdJYAgChD4cJowGAiAEILx8T/CTzZFdMuYzUnHhSBQSlBre01NDb7xjW/g+uuvx3e+8x289NJL6OnpwfHjx+PudzajNmaaeSFQ2YzcoExNTUnTchONgMhlKyIKbWLb39+Puro6GI1GdHR0pJ16GOybQGlFMSqq448Mke8/IUQSpurqamzYsAFFRUWYnvZhx4sfwmy2Yssly7D54qXguMT7oiR8tmkP/vedY6A3v/1xH0BEtFWxsNvt6OjoSNptgmEYvH4itnMBIcCzHx7F/ddugSbJcSKE4M3+xN0PXjH14cKGhXEdW4fsIwieHgbLE4RCIfh8PhBRPGPVJuBYDjzHgWg0+GByAFc1Rrak6fUOY5pPT2COuEySQJl9R1N/IgHkytnn3YMlGQ1DFQHiOLNJApfgQqUmRZszg7NpwjN7w3EcllQ5YQ8ulNoRyaNWubllJuqMgMIVqHg1UFqtFitXrowQm2iyGbUBAGazGeeddx7Kysrw8MMPY/Pmzbl8axHMC4GiZCJQDocDfX194R9PCoMKc7n29P9+9yZ6D5tQtqgYF/2fCySBcDgcaefGhy2T+MP/fRMCL2D9lmW48qYNio9jWRaCIGBsbAwmkwlVVVXo6uqKcAe98OePMDAQ/rK+9fZJ8LyIyy+L/4Og25ULFCEEz795GMFQWAxFIsLn9eKvOz/GXV+4GN3d3Skdy2GnF6fH7bGRJANMewM4NDiGrpbGhNvom3Kg3zmd8DF2vw8nbJNYWaMcke22WqDRcNBoOMh9VKJI4PV6pXUuXhDwsnM/mmxBlJaWSlHCR1Onk77XaEb8k7CHXNCxBBPBxJ0f5EReBwuYDA2jpciAojQveBjiAnD2YswpOlGJzOpwwprJgMMAykoZlJVFfmbyqHVoaEjqTUiNMKn2JkyXfLdgypREs6DySUNDAwYGBlBdXY2PP/4YN9xwA44dO5a3YaLzSqDSSfHZ7Xb09fVBq9Vi2bJlMY6bfCKKIg68ewivb9uJIq0OxUPFuPqmSinVQaOcVNN77mkf/vibt8CfEYMP3z6FVetbsbAt8mRL6zZGRkZQU1OD888/P8Yh198/KYkTZe8+E7o3dqCkJL7FNVqg+sccMI/YQUi4F5o/EIDBYEB5SSVOj3qwYklqJ5m9Q1aQOI1JCQje6RnA+YsaEp603hqwpPRa7w4PKgrUuN+NHtek4nNYlpFMAXo9XdsCsKACBlIUThkPW3AwdBJgAI1Uc6QBp+HAJjnZHndZUFWU2PUXy9k1KJ44QYgIG8+jIc1UGnMmeqJ4RA8EIoBjMog4CDkT0xGw4jGI3MaIu5P1JlTqo5erNGEhts3KZhZUNqM2aAYBALq6utDR0YHTp09j/XrlsodsmRcCRbLjlYQAACAASURBVL9gydJvdLR7X18fdDpdyhN0420r3S82TeVZzBa8/9QBVJRXSNX8bzy9C1964HMpvY9ojuwzweOOrI15868HcOtdn5JccJOTk1IKs6mpScpPR/POntgC0mCQx553e3DlFcqL/0Csi++jE4Pw+bzw+fzQG/SorKiUjteHxwdx2YYlMBoS13S4fAH0O1zQKAg1c+Z0N2ifhsU2hbYa5St7byiEY5PWhK9DOWq1wuH3ozJKtPfbh1N6vrRvDHDIM4mtbedhwYIFsE2dQMVkOUSRSC64QMAP3num5ojlwGk4SbxYlpME5qjLjEWG1PZfCV4Mi4wtlK5ABQFECiMBgUt0oYJLv1iURlAAwAlHYgRKCXmdkbyUQN6bUD4narbShPkgmzZH2YzasFqtqKqqAsdxMJlM6OnpiXuuyAXzQqAo8QSDnqBNJhMMBgM6OzuzapeTbrsg+RpTbW0tFpQ2wmvfG9FqpveABaZD/Whf25K2QB37yBJz20DvBE4fHkRNUwl6e3tRXFyMNWvWwG63x932+Pg0enrHFe/78CMzNnUvRmmp8mIGPSaiKKJ/YBA7PzgKVqNFZWUFGCYyhRLiRbxz0IyruhPXxBwcHA2f2JQCKObs7e+cHogrUIcmxiGkuPgrguCDkSFc1b5Yuo0Qgv329A0GBx0juGnRaug4DY65LADC0RbLaqDVnv1ZEhL+fvA8L1mLBVEAAwYaDQcnNw2WuFCh08Ycx3iQM2tQBEEIJNzZwCkICIpiymm+cPQUe9xcQmYCdTaCAljxFEACAJNZ0WmyESZut1tqR0QIgcFgiBCumeo4kg3ZzILKZtTG7t278eCDD0Kr1YJlWTz22GNpDRhNl3khUImEyWq1wmQywWg0pjXaPRE0lZhMoKKFia4x7dy2R/Hxu1/4AO1rW9JKVVpHpzE25Ii5PRQK4i9P78RVt56HVatWSYI8NTUVd53u2PH4J+JQSMDH+/tx6Zb482gCgQA++OADTHpZlJSWhV1ucfj45BCuvHAZWDb+iWJ//ygAnE3xRT2U3n5sZAL+EA+9NvbrfmBiLO72lTgwPhYhUCM+J8b96fcYDIoCTjitaC4pwWjAFvdxDANwHAuOi4xuxDMW+GneiglfAGzAL7W+0ZyJtrgz7YliDgzC0T0vRrYmsvM86lOKoggYorxm5xbdEImY8LNV3iKkCArgwYonIXJrEzwjfTJJEwaDQTgcjrS7OuSbbGZBAZmP2vjc5z6Hz33ucxnscWbMC4GSwzAMBEGQIqaysjKsXbs2ab+tdKACEq/tCLVt9/f3o6amRhImiulQv+LzBk4MwT3lSSuCOvZRpDuNdmNmWQYsU4K2RYsjosVE244XPVGOHx+OESh6EUA7NmzcuBHPvHYw6QnM5QnAMmpH+8JqxfsdHh9MVnv8qa6ykzIvijgxasV5ixoiHuMJBXHKFl8clBj1uGH1elF75kImk+iJcnRqDC6SWYqJZRgwGg14MQg3o0F5eTEAcibaEiAIPALeIEQx/FnKWxPR9DMfJTJTvID6FPSJIR6EU3yxiBDhET0o5dJbs41OibPi8ZwLlBKJ0oROpxNTU1MFmSacD53MgXkmUISEc/x79+5FRUUF1q1bl1NhosSLcKKFSWm0vM/tx0if8lU9IcDJvb2oXGxMWaBO7B8AAPB8WJgAJqL/3IkDA7jwk2fb78QrqHW5/RgZSdwMdHzCCavVhdra8MnJZrOht7cXJSUlWLduHQ4cOACW08A0bE9p34/2jcUVqIMDo9L/E0IgknAaTMNpzgYMsgzUkaGJGIE6NDEBMYXJr9Ecto7jspa2cHrPkY1AjcPLZt7ZJEh8ECHCLQABQYSOY8GyHIqKOACy79WZ7z0v8AgGQwgGgwDrB6vzgGFYMAzAMCymhLOdHxLBIPH3wC260xYoeYoPAFjxRPgLP0upNtqz0WAwYOnSpdLthZImVAVqjjEyMgKLxQJRFNHZ2ZnXtvTRUYhcmKqrqxWFiWI5MoBESyIn3j+Nzcs2pCRQbqcP4yP2M8JEzgxXi0xTnNjfHyFQ8SKo3t6JpK8HAMeOD2Pd2nr09PSgqKgoIn0IAOYRO3ghtZ58R/pGcd1m5TqoE6NnjQHBQBBerxcaLjwskoCAiOErcm2RFhpOgxOjVgR5AUWas1e7h62JI8J4HJ4IC9So3wVbIF0H3VmmQj70uZ0o12V2Be4Tzr62LSSgMV4t2plWQ5xGA50uvNZFODcIGx4FIooEIhEg8ATDU1OoOFNorNFowHGaM2lW+hkIQJKZT27RnbZJKDLFBzDECYYMgTDNcZ+Tb5RqoOKlCWnz10RuwlymCVWBmmOEQiF0dXWht7c373UNNIJKR5gofXHSexTLsUFc6F0H1pj4Pbjdbrz1+l643W6UlJTE/WEMmScxbfegvCosIvEiqGTpPQDgBR5vvX0QZaVLsXz5ckVrfs9g6o4zpycAy6gDbY2Ri7AhXkDfhB1+nx8+rw9arRaVlZURLkGXywWWY8OOOH8ATpeA/931LtY018NoNEJXbMDpNNN7FPP0FJyBAI5NZSZwFI/gA+/nMxIoQgC/eFag7EEejfpUT34EIlxgEO7dJp2DOSBUpEWxNvz9DQVD8Al+iKIAhgmvbem0Hmi5sEkjZmnrDEESRJAEoUvH5BAVQQHhNJ/AFpZAKcEwjNSBPFU3obz5ayZpQiWBmmuzoIB5IlAMw6C1tVXqaJ7vkRscx8FqtaK3tzdlYaIMnUqcMhJFgv4jw1h8QYvi/R6PB319ffD7/SCBopSuqk4c6MfGM4W2ShGUKBL09cWPoOgPUSQijCVGNDUtjls31jOoXC8UjyO9oxECRQjBvpM9sE7aUFRUBEOxASzDRjSNBcKfuVarjfgR+wxlqK2thdvtxr7eXkw67CAk/J41Gu5MQ1NN+AImwcU/AXDEOoGj7iwFivfBI/JoL0/frRY4k96jOEICBELApRC1iPCBQACD2IscBy+gTaeDTqeBvOKYkPDaFktGIQqidKwZJvwf+hmEbwRcogs6NvX3FR1BAQAnHIeguTLlbeSabLtIKLkJaassKlzy4YbyouNkacLoQv25OAsKmCcCBZztep3PmVC0NdDAwABKSkrSEiYAEHgBkymsz5j296P1/MjCOq/Xi76+Pni9Xska+tSe11N63ZMHBiSBUoqgJidd8Ptjj5koilJnZXmUduLkKOrqYivLfUEeo5PpOd5O9E/genSCECKtaR2e9KC8ohwsy8Lv8ysW6jIKCtMz4UBF91pUVlbiI58H5RUVZ9Znzsw8CvHw+/wQRREMy5ypO9KcqUHiIk6gh6zjsAix7shU4UURPjEIiICfF6HXpBfV+4XI1KIIYDokoKoo+U+aMPE/g4Aowi8SGLjI48cwLIq0PBgxAODMSfvMYSdEhEhEEJFItzl4B4wao9TBPFm6jxAS85kxZGBWm8fmo82RvFVWKmlCuhYmFy76O5Mf07k4CwqYRwJFycdMqOiedR0dHVIonw62YQeEFNZnRk6PI+APu6h8Pp80h6qjowM1NTVhpyIvYHQgNTPCsGUSfm8Q+uIixQhqaDjyRCyKIrxeL0KhkGKVPu3RF82o3ZfS/sixT3thHhzF5NgQdDod1qxZg91vfwyW9YcfwABSICFrFiuvg6J4gkEMT7nQVFmGE7YzkRzDhO3YGi4iYojowO0LghfOuuE0nAZ7/QMw1rJJexDGwyOcPRaOAI8GTerflej0nrSdlASKQGQ8SODex5TAw8Ap7E/0xFwaMDEsIk7jJJzmE4mIQIAHf8ZIELbAy8ZusFxkpBqzTwSseBoi15XkPeWHmezDl2qakM6I8vl86O3txcjICDQaTVrLFpmO2qAMDAxg5cqVeOihh/CP//iPWb/3RMwbgZI3jKVjl7MlWphozzqr1ZrRa4wPpLY+Iwoihk+PguUYTE9Po729Paap6tiQQ2ptlPx9AAN9E1i6ukkxgho6U0dFr/KCwSCKi4vjdtkYGLQjGORRFHWyHJ/yI3z1ndriOS+EB7i9+/Fx/J/LLkBpaSlcvgCGpyIX6ZPVQck5PWZDiaEIo57EjVmVO3DTTg8CJn1O+B0EOi481C/ixMtxSc1nHsEv/f9UQEBDGnXhQeKPSO9RHCl83gJxI6zo8XdwmhfQEKNPJPWR7mc8FYJWOOvmI4AoCuClThkBCKIYbhKr0YCIIkKhEDQcF1Ggzoon5oVAxUMpTSgIAj766CNUVVVh7969ePHFF9Hf34+uri4sXrwYq1evxve//33FQZ7ZjtoAgO9973u46qqr8vvGzzBvBIqi1WrhdCZ2ISVDLkxKzVQzjdIm+pMLlCiEe9f1HDBh7UWrsGLFCsX0ybA5vfY3llNjWLq6STGCGhwMj5QInOmXl2wxVhBEDAzYsHjxgojbrc4AiKY4qTwJoiClDo0lJYC+QlrT6pmINDYopfIS3X563AZDWYZOKuqG4zQIBAhKNTpUVBjO1h7xPII+n3T86NqWIER2FREJgVc423pqKiCk5XpTip4AwCOISbtB8CmIzLQgxNjNGXgRr/bp/7P3rjGSnfd55+89l7p0Vd/mQg45HIqXGVISSYkSNRK1iRebtRHb8FpZOwbixHFsGLaBBQw4BhZWEHgDJUEQBfAXB04+Jd7Y3oUsbbKwI2CjFROvbVmmREm2LGkoitNzn+6ZnulrXc85720/vOecOnXtqq4eklL7kYYz6K46tzr1Pud/e55x6JuHEuD5PiXf74u4s9EPmSSuG1OrPNryfR/P/ws6wd9iYWHYRfZB451AUKNgjMm7CX/qp36KH//xH+djH/sYX/ziF10K/BvfGJu9mcdqQwjB7//+7/Pkk0/OpbQzC44dQc2T4juImObdx72b47vKbJpWS5KESqVCe7PLmTNnxm9rfcqn3RTX33SzV8UISmvNlSvX+M6bN6lUKjN1CV25er+PoGKp2G1LlpfGz7YYa+i02wOpQ8GV29sYY/E8wdX7A3WfEam8ST+/trVL+cR8t31XS7S1tCLFQ7hrVip5UOoRn7XkunpaJ0gpiaMIz/eQnkFbnTugKmNpScNi6eDF0Nrh+lMRu1LzcHncQm7Qpkl/LnQY2lpa2rBUaMmfOnoqoGUOtg8RQhAEAcLzqNXTRc+6e0ErhdIt7q5/hd2GI7rBtu0H6RWltX5bvajGYZySue/7PPvssxMVJeax2qhUKvyrf/WveOWVV/j1X//1Iz6r0Tg2BDWPJ9S0xJThsJ5Qm9eHO+UcMXVJkl70Yq3l/o0dZKIIx9Qc7h0wVDv0+vU92s2I2mIFay03b97k1q1bGFtjZXVlbEQyDtcGIrhbm3tgRy+N1ho63S5xHBdSh71XdSLJ+v19zj28wrX7/XU1gZioZj4IZQxfX9+EOcZRWspFEp1YoY3FH1HQEYLcfiN7+qyUyxhruBvtYJVTfci64e7stQgWy7mS+TiJJ2ljNOPvrd1E83B59Mlp2xx7rQaxp1WBoDSMkTaahNjGJDahJGZc5AV4wsMrlQiBZ59W6OBi3pTTarXY2dnh5s2bJElCGIZDDsdHEfm8UyOot2sG6hOf+AS/8iu/cmgB7cPg2BBUhlkIylrL3bt3uXbt2lTElOEwEVTUjtjf7j1xWuNSeX1ptZRkBa7j7/Z3NnjyhcdHHvf9O7M/8V7/zh1WHinRbreJ45gPf/jDfOnL12YmJ4A7d/dpt+PcguPW5p47fGtz7rE4HbSoG+XnOG5fa7e3OLVaY313oANtTKQ0bjuJ1tzf63L69OFTFC3l0nPWQjuSLC1MuQAL8PCIGdZp7KQzSXGcoLVz6B2lYj4uvZdhV45PFyrjSGYaitpXOm8aEbYBI2pe06Ct25RmaAAZBc98G83fxPM8FhcXh0YYBtUd2u021tr8YSf7Uy6XZxoefqcSlJTy0F5Q81htfPnLX+Y//sf/yK/+6q+yt7eH53lUKhV+6Zd+6WhObASODUFlN+Y05HFYYspwGIK6f8ul94rElKfVRnyprLVc/9bNkQS1t91CJrNEcJY4Tvj/PvclfuAnPsDCwgIXLlwA4M4hiC7DtWv3ef75xwDn/4QQqUqGM+/rdLuUy+WRiuaDuHxrizOPLE8dAeB2M4S2lHTmGDPQ1tJRvfe3IzU9QQGxlSg7/Nm0lSUsl/o8o0apmLf9Xaxn8vSgcDpF+XYSa+kay4I/eM9olC2m3CYv1E2tUdYSCDHk+zQLWqZ1sInhAR+pZ66D7YAYLeQ8St3BpN+jVqvF/v4+6+vrxHFMEAR9Q7L1en0sCb1TCUprfWgvqHmsNr7whS/kr/nEJz5BvV5/oOQEx4igMgz6EhVRJKbV1dWZiWmafYzD1voO3U6HKIomEhOQ//z6t26P/PX9qdN72dBghyAIMNEK7373u/mzP/uz/BV3Nw/fUHLt+hbPP/+YSxne3UUASRITRRFhyQ0RT6t6ffPuLmubw0O+Y1N8Yy5dWyYksUobF2YvundU0re3djTbg0hbRSN/biw0E81K2X0lR6mYS5PQTXaw1kslilyK0Kavz3T1duKEhYUyxYugbIPpYqceGkpzMtRAZ6b3FdE27QMbQCwHNYhYPPMdjP+BqfebyQzVajUefrhXC5VS0mq1aLfb3Llzh1arhTGGarXaF21VKpV3LEGNiqDeCquNtwPHhqAmfkEGiGmUk+yDgjGGW7du8doXv4q1lpWVlb4220lYv3wHGUvCgZrDNPUnKR0xeZ7H0tISvu/T2O3S2OstRkmi2Nk5vNbcrVuuXrTT6LDbaJNIiQWWl5fxvNm++FIZvnF9hHLDRMWH4QW5nbhjiCJFrTZ76qkl+zvZokSjjcGf8jMrtpcPYj/uEdQoRKYDWeTU9xuLta6WZy3c70TUkyitg7muQ+PvjhTRnYR9rTgVHD6CBtBourbLwpjoxx3PsMzRIFy7+fQENQ6ZLFax4Wec5UYUOQuT5eXlnLiKxPB2YTCCmrUGdVirjSKyLr8Hjbf/ar9NyCKczc1Nrl69+rYQ0/r6Ojdv3uTMmTOcrJ3ibm26wdoMWhtuv3lnKM13f2N8QVspSbvVRgjBYr2OP/CFW7/qmhustdy715g5Eixi816Dzc0t/vgr3yTqdimFIdWFhZnJKTueK+tbLJ4YoT5v3R+t0ideMboGlWiNtK6W0u3IwxGU6ncmtkA70iwtHExQ2hoiM75Vez+enJYdX38SaQTlrmtXwPKyq7FprZAqQpomWJsLEWf6esITY+t1e0pBaT6CAhdFLXjjCWqUzNEgPPPGA1M3H2e58Rd/8Rc8/PDDxHHM5uZmbhlTqVT6UoTVavUtbYGXUg6ZFc7iBfXdhGNJUJ7n5UaBD5KYRqU2MgHZ69ev89BDD/HhD3+YMAz5o/tfHrOViTtg/fLdYYIaUTfSyg29Wiy1+rCqeYbbV++zdM51Ic6T3ssm4L/0pW8SLK6wtNSh1WrCIQkvUopWFA8RlMD5e+3u7eKJ/iFjz/fwhJe2MQvahdpTtzt7HUoaTWyGSaQTSZYWDm4LnBQ9gUvxjdPTU1Yh7XRzSNK6mah64BMEIdbbx5jeV10pmUt/GWXS+5S+upYQHl2TkBhNac61t23anOb0+BdMEUE5dfN1rHhsvoOZAcYYVldX+9J81rr6aVHdodPp9CmXZ38/qBb1eSOo7yYcG4LKvpCbm5t5m+qDjJiyRolMN2tQdWLQpHDn7mxPqhnx3X6zX1xWK812gVhyIVdjJqqaZ7h9bYvn33USYwybm7O3Fg/q89XqD3O9mXXeiUO4Lzl0E0nUkX2kr6Si2WpijHGp0Wxht9DpOgFOKSXdbhdjDdtSorVGeIJuV2K0xRtqJhiPrL18EO14ujpUZ0z9KYOhvw5VxKTZp1HYk5p62iY+aEwIAuF5eH20YF09y1q0MWA1nojZSXweCuO0vtUTg50FHdNBW40vRkfO00RQkKmbv7UENRgZCSGoVqtUq1VOnTqV/7woSbS9vc2NGzdIkoRyuTzUAj9vtDVPDeq7DceGoKy1fPWrX6Ver3Py5EmeeOKJB5rOC4Igf9LJ0ojjOgKjdkSnOZs0Uka462/e6Vu097bbaG0wRtNud1BKpUOvIdOsLHdv7fC8PTVzBNUng1RboFxy53jz1ja3VTc9Zg4dQXUSiVYGGWv8ULho0FgWqgvESYzv+73oSYDv+XkbbIbN7W086yIGpQ337+9QqfRUzINMpmjMDFJbjiaobqzHzkP10K8eMQ7j6lAHtZcPYk9qHquCsTHGTiZGhyxyItU4NwhradgyDwmnq2d1QS0+TQ3mKcIDaoEd0xlrYjitioavL6GDvznFuRwdpm1Ln6RcnrXAb287RRZgqAW+VCpNva/j4gUFx4ighBC89NJLeJ7Ht7/97SMXjB2E7/tsbm6ysbHB8vLyxGht9xCRCilBtfY77N9vsPKQm4PY3Nih1WohZcLCQo3Fxf6h14OgtWHvfgetNffuHUxQWYF5nAzS9RvbRKsuxdZrM58dnUQClt3tBqUFkStNaKWJkzELf2FfUhukNQjPxQ2eD0FYZWm56kRhlSKKI7Ryc0TDFhxibARlcUO7i9Xx0WlsFXqKWaJRdShtFYk9mNz6tqOcXJEa2SI+RUqNBATsmxAhPDyPXMQcSx5t9VtvCPrb33vbm+iyO0WKD95+dfNZUVQuP3my5wydiS23Wi12d3e5detW38BxMVU4qovwuHhBwTEiKHBRjTHmgXpCWWvZ2tpie3sbrfVUtvI7h5g1EvT8j26/eYfa6gLXr1/ntT/7ZjrrUWPmXEyK7bttdnfbIy02iuh2u3S73Yn6fK1OjC5bKvVSejSzM5TUmm6cuLmgJOThswUDwwlSR8UGj7YaPpduRyJOLhCEAUFY+CpYpweoVM+CI9KSSMcuYkjTXcUn3k40maA6ZjqCGVWH6s6Y3gNQFtpa4x9gzz4aFnAPcIn16FqPBVEg16xeVby/0vk25847HG3tm31Oc8otrAORwrQpPtdu/m2M/+FDnNM7B57n5ZFTEVm01W63WV9fz1PzxWirVqsNEdT3qhcUHDOCyvAgPKGstezs7LC2tpZ3A505c+ZAcoLDRVAiXYCtMXz9i99gX2zz+OOPc3r1EW5XDj+3ArB9pzkxeorjmE6nkw7Zrk5MTUSxxLQdQSFmq0FZLFE3YqfZQgj3uamkfwvTqly0k+HoJ4rU6PSScBGw7/csOJKoQ9CVA3WaXuSw34o4UQ/GyhR1TcwIf8AhGKCVaJYLab5Z03sZtpM2p0uzS26Bi1Yz7OuQBe8AghXuP3lNbyDaklbSiJp42l2ETPk98AOMnV6lwtevvyUENU/36mExzcDxxsYGnU6HP//zP+fy5cvcueNS/IOdfeNwWKuN1157jV/8xV8E3LX5xCc+wY/92I8d7QUYgWNJUEftCZURU7lc5vnnn6dWq3HlypWp97E7Y4MEuEUxiiKklNy7Uefv/q9/G9/3+aN7b8y8rUFsbTTZHEFQmRNoGIb9TQkT0E0UtmVYfjglk6m++DYnwVKpRFCp4Em3iMlEo6QmCAudVeMMCws/7oyIoIy1xLGmUjn4a9BScd8MUpFrrDFE0hBFMUan3ke+MzkMgoDESKTVeNMwFC7NlxGUtnrm9F6GXRlxemwj2fjPTtB/rfZUyCPh4Y6hL9oqw0qwkiuYa6VIZIJMEkz6s5y4RvlFkbWbKxAPduka1SDxdmDUwPFrr73G+973PoQQ3Lp1i+3tbX7oh36IdrvNU089xb/7d/+uj+QyzGO18fzzz/PVr36VIAi4c+cO73//+/nRH/3RBz4XdqwIqigYG0XTFI4nY29vj8uXLxOGIe9973v7QvZZSHDv/gwRVNrmGscxYejUGDpbkXMz9WFnirrRQYg6kls3esrqUkra7Ta+76dDttN/ceNEYlWajpyCnxLpSDBTUfY8n/vb/XWUqCOpL6cENS7FV4AyhniMeG/UlQcSlB2QNxpENljthRUWF4M0RZiqcStFM+mg0b3ZI5E2F4wh+P2CTFVXH6wIPhqGfakxlonmhMNQDOru7evwSEaQWqbFCU7kCuZBEFAGkiBAaU2lXEFphVaKTpK4jktII60s4jJ45grGf7BzP+9UFYks4g/DkA9+8IN84AMf4LOf/Sxf/OIXMcZw/fr1sbp881htLCz05tiiKJpJ03AeHCuCyjBvim9/f5+1tTWEELz73e8eEq8EZqpz7d+fglRsf1RRqVQJAmfuprXh7rV7nH78NM39+c0YhRCsX91Gl0Pa7XSod3Fx5i+s0galLWiLljo1vx3NJkop2u0WQgiWFhfx/ezWtHST/uvoCMqlM6aROmpP+By6XcnK6uQ0bFvJscddRCdW1CpBmiJ0MkWlcon7poFv/VQCy6QRRH9zgZdq6nnCo5H0/Ji6U1hWjIK1CmMFbR2wGAw8KE04FcFwpKQRtIzPon+YdGEPbdPGWDMkb5Utup7vUfJLMMIvSimV+0Vtrf9ndro/2NcFV61Wj3TRfKcSlNa67wExiqK8K9jzvJx8RmEeq41Tp07x5S9/mZ/7uZ/jxo0b/O7v/u5boqpxrAiqGEEdJsXXbDa5fPky1lrOnz8/UUE4CIKpXHWttezfb056Qa6XF4YBy8sreL5HN7XRznD7O3fwK7PrBo6CMZaNG/epnV2iXju8vEtUIJa4LfEXBAy49WbmhEYbavUa4cAAcaxcC3ffdjsFwpkQQWXENUkctjuuDlVAe0z33tDrIsXpgVtCW0tkZX6sQnjDKUJrscam7e8Ki+XuboN6WRB73Vxjb/qmF4tJ03QNNYKgxmI4esqwp8O5Ccpg6JgOdb+/OcBZsIw+t2K0lWFpucVJc55WOne0ublJt9vF9/28A25xcZFarXboe/edSlDjvKDeCnzkIx/h0qVLfPvb3+ZnfuZn+OEf/uEHrrxzrAgqw6xdfK1Wi7W1NaSUnD9/fqqWzmlTgOP7+QAAIABJREFUfK3dNkqN/uLLtObjUmtLeIUvTDYHlWFj7S6Lj5wctZmpkc1OdbsRKrKsLM/XGRQlvfOP2wm1hUrOJc6csIOUSZ854SA6yfDnFHcV1th8XmlsDSrFpAhKKYNShjAcvxg11XT1l048THYdHXGQQaAQAjHQXCD9EO03sQaMUblLyXAr9yilew1p40FDhZxlunS2mOCYu6tKnCvNnxZvmuYQQR1weYYg2Gehcp/qwrs4fbqnUKFStZRWq8Xdu3dptVporUcKwR4UbX03EdS0HXzzWG0U8Z73vId6vc63vvUtPvShD81xNgfjWBHUrKaF7XabtbU14jjOlX2nxbQEtb81nN5Tac1HCOd/M6iXB+5cirI+G1fucurZc0OvmwbW9tx6FxZqJIlBddt9JHAYRHE/QdUfcmaI7Y7zm1qoVqnXV5m0Og2m99zxWuJIUVkIx3fxpZGVtpZYT/4coq4aS1DKGKID3p9BG0ssNZWCiWRLHS7l2pSGajVO1RfSY7M9tYd+JXORpwmFENhCk0NTBVPWoRRMMEJsGh9lBYGYr7utZVpDJG6xU6vaZ/D1N1Heu/p+lqWkihHFoBDsnTt3iKII3/f7SGvQduOdTFBFNZhZIqh5rDauXbvGuXPnCIKAGzdu8MYbb/DEE08c5amNxLEiqAwHOd52Oh2uXLlCp9PJiWnW/Pa0rrp7haaGjJgQwn1hJqQnBiOo7Tt7bN6aTWw2H7KNIqoLVVZXnMXH3l4HayxJJ6FcP3zasC+C6iTEcUKcONfc1ZXJ7ekZRhEUuDRfZSE8MMXXSRXUJ+4jkiwujT7PccO549COegRlrD1Qf28c9mLJqpH9AdJYJXOXIjTWYI3BiiR9jWvrb0iflQPazUfVngZfsa8DTgbzjWckNiGxCWVRuN5TDuoW4Zm/BPsjB3ZujBOCVUrlCg9F241s5khrnT8MvFUNAdNAqX6zy1m8oOax2vjTP/1TPvnJTxKGIZ7n8W//7b/tk3p6UDiWBDXuhut2u1y5coVWq8XTTz/NqVOnDn1zTh1B3W/0hFytdXnzA/TyYJigANbfvDPdwVlLN4rodrtUKhVWBmaZEukWs7gZHZqgtLHINHVpjEFL5QhvocxCdYL1QgHGGiI5+hpGnQTo346UEk94Tq4oXfLGyRMV0e2O/5xacrb26k6sOJkOT3V0PJvBYgGJVXSVx0J40IxQSlrpmmVshLUeGWtbC/vSpyac/UY2i2atST9zgZt7OngWaU+FcxMUuDRf2evdV9MP6vYg7H2EvY0Vh8saBEHAyspK3+KeyXVlda1Op8Pu7m5uclgcln27oqtREdRbYbXx0z/90/z0T//0IY54PhwrghpHNlEUcfXqVfb393nqqad47rnn5n5qmoagut0ur3/9DZrNphNynUH9eBRB3bm2yeIjk55qip2A451sZWKwWOJWBByuABsnEmsNSmnXFhuECDvb7dZN1NjlvdgoYa1ld3fXLRrWpWcsFizsa+lSlQPSO0UkscIYOzxgaw8TQfUEbdv68B2Vxio6yTQE1fcubNaQkcVQAlqmQhi687DWoIzOU4RY8P0I0tRdHp+NuFa7R9Ru3jRNTtG7T621Uw9cF+Hrv0B5hyOoURBC5DNHSilOnjzJ2bNnc5PDVquVKzyMspSfRU/vsBiMoL6XdfjgmBFUEdmg6/Xr19nZ2eGpp57iPe95z5HdYJNSfHEcc+XKFfb390EKd4PN+gQ5oGtnlKGx3R5DUCM6AcfMMrmpdA0W4ubhhjO11uzsNXKx3OyayrYkmMGDaVx6D0BJQ9xNiJKus0VYWe1bXKWUtDtd4qSXqsl+6Xn9TQYWNw+1MHBsXS1RM6gcAEhtkcoQBj6tA9TLx0FbR8xt6XOK6btNe+TUj5YK8vqR6yLUhTb+CGF7WVKTXacCEWXpwhifyHpUxWzXZBAd00FaSSjCfF+HUeXyzF+A/dH5GXMEMkk0GG1yeJCeXjHaOsqBX6VU30zS97IXFBwzgsoWyiRJiOOYr371qzz11FM8++yzR/7kM2p7SZJw7do1tre3c0L8+qe/c6gvmCuG9xgqSRRRY1gSJxuyLTrnToKUOt+q7CQYbfCmtEYvWm1Y4Q95TsUdSdUenL7MMKqDz8GilWZ3u8HJh5dp6ZabMTIFIrIQWzNkjthrMrCu2w0Awd5emyCw+AUFg+aM6b0M7VgRComZIm02Cto6UupIf4aIxWLGEBS4ZonVcPD32qlGiF7klO/L9rojbfZvC1txwNlSNFIQdhY0dZMTwYl0V4er8wi7i7DXseLJwx3EBCilJrZQH6Sn12q1uHXrlqspQ5/B4TxeUX8VQX0Pw1rL2toam5ublEol3v/+91Or1R74fpVSXL9+nc3NTd71rndx4cKFdGjT9jVJzAIh+mUZZKKQUYJKJEEpzFtugZmsqpOk/4k9bsVUlycPshatNrKW8Z317aHXqVhj9LSLth1JUFq79JTv+wRemSAIsFiajSZ+4BP4LrUaJ/GAYE+/4rZDTzBOKovSmjhOFQyEYNdEGMyQMOxB6EQKPzgcuVlrcmIzlinrUGBtwqQJ3D0ZDhCURUxqPxf96T7h3sKeLXOWqJcizH6fDhlP6xnVNE1OcCI7+MPyHL7+Cso7eoI6rNTROD29TqdDs9nMvaKklJRKpZm9ouatQX234VgRlBAunfbUU0/x+uuvP3DLDWst165dy6ezP/rRj/bdgN1WRBIfrujs2swLBJW2dHf2WlDxpzYoHEQcq77GuLgZjSUoS9YF2G+1YazNGy36jhlIOhqmcAZIlEYV2uiNMWnrr5efU9SVYGFlZQWtNVEU0ew2c0JpxDEam6s0DNc5erklmViq+XyMQBpFst+BAWFYCu3c4+aQWpHCrx4uvacGUnrT1aEM5gC33Ybqvw9c196MEZ6Apgkwnt9rN8/+slkXYS9fmM9rjfCMapt2bmJ4mCaJDL7+c1TwP4M4WvfaQdfaeTAq2hrnFZV1HS4uLubvKX6Hj5MXFBwzggI4ffo01tpDq0lMA2MMt2/fzuXyP/rRj45MrTW2JihIHATR31+dxBKtFLub2zzy7Lmxg68HIY+g0gU5bo5eaKO0C7BcLrOyutK3+MfjmhsEyGhK99k0erLGoFJ5l0GyjVN1caVVrt93YvUEwhMoYzBb9/FSNW0XuWVRVM8uI1NoMMYJx5bLAWBoyiRdXL1h1YfCHFK6wb45pE4iWTCW2R/ALcb2X59p6lAHkRNApH0i7VHxDcJTMENtq/8IBXs65FSQ7jMLmITAxy++8EDPqH21z4nwxKGbJNIzwzN/ifEvHvL9o6GUeqBiseO8orTWebR1//59rl27hlIqd+Ztt9skSZJLO30ve0HBVAYA31vIUhAPwhPKWsv6+jqvvvoqcRyzsrLCuXPnxtZ9ptLgO2ifxtButWk22wjPw9dQKpU5bHEgTlTfW+NWf6oqSRJ2d3fRWrOyssLCwsLQ4hIl4xc/2ZluYWx2I5SSGGMIU6fbQRhj2d7ao9vt5k+c2WBxW0pHGp5rOw/DgDAMCYIw7dazGKNRSqKURGtFo9FNG1uEU4/I0qiFPwLwhHDCpWFIEIaurV0IZxCoFYmWRB2dpyOnbTTPmiOK6EgfM2kDVo9tjhjEvgoBiSfmu+931BRRuQDhOX09P/Cd51YQ4Kf1TGMNW9F99vb2UErlppda6wPFfwfh6y8f/KIZkaWR32r4vs/i4iKPPvoozzzzDB/84Ae5ePEizz77LMvLyyiluHXrFr/xG7/Byy+/zPr6Op/61Kf4whe+4JquJuBzn/sczz77LOfPn+eTn/zk0O/jOObv/J2/w/nz5/nIRz7C9evXAXjllVd46aWXeOGFF3jppZf4wz/8wwdx6iNx7Agqw1F6QllruXv3Lq+++iqtVouLFy9y4cKFA6O0vXkIKn2K393bc4uACPA8j6hxeC8ol3boP14dK7R0Yp17e3vEcczy8jK1Wm182/7YtKVARXqi147WmkZjn2Y3wvcDN6w8uB9rc6VwYf2RzR+tEf5P4DaVkVYQpKQVhnieTxxrojhir7HPbreNUmooUioewxBp+T6+H2A9sDrIRwGy9KSUEq00Ro++BsoO3yvGQleO+5pa9JQyRuDmoSbWnabErgonk+Y4pHNYnu+uvwo1taUavucRhAFGazrtNnv7e+zv79NutYiiCCXlxHvGM2sIc+/Q5zMK7yQlCSEElUqFU6dOEYYhL7zwAv/wH/5DXnnllTyy+sxnPsPHPvYxrl69OnIbmdXGf/kv/4XXX3+dT33qU7z++ut9rylabfzKr/wKH//4xwE4deoUn/3sZ/nmN7/Jb//2b7+l81DHLsVXjKDi+JAeNyky99wrV66wtLQ0ZOt+0CzU/mFSfKndRiZEe2J1FaOdOjaAiiUqTgjKs+fks/ZyQc9Y0FrLzt1tSktl6ot1Av/gW2ZSBGW0QcWacMDiwmnztZFSUl2oYUU0IgZ055k93YaeN2RgmGEcQY2CwD3tK2Wp1+o0VEzQjnspKmux2chAIZ2X/dsdmiMrZRVYkAnU0hRR1qbt+VmnocmVCtwmBVYYLAYGajUA7cSnVhquF1krc829g2FoqAOisSmh8GjogJWpRWhHw2JpmAYBPuVSqe8BwOYPIZoojtHtNhYXYWQ+W34QOIkkAb7+E5T3E3OeWQ/vJIIah3q9jhCCn//5nz+wiWceq40PfOAD+Wuee+65PNrNVNQfJI4dQWUIw5BW67BeOz2Twkqlwvve976+2YQMBxLUvdl8oIp2GysrK+ztOaPDZNCOotGhPt6pbiziuHisFqVS8VPJ1Hpf1lriMeoP+X7aSU5QmdxSFEcsLCxQq9dpRfFQlieLQgZrUX3K5tn2lUaa2ZW3M+HYhoxyYdZ80fTTYn6RtIquup6ra0mrQYDWrq4lhE2tM0hniwTC84fqWrFJ8n9nvRvZktNOMmWIYgSnMVMZGVpcM4RFW0FTlVn054+itlRpboIC2Nf7aTdf/wIrhMhTqDmsU79XSpFIie5GqX2HwPP/kB31ErX66am64Q7CdwNBZZimw3Req40M/+k//Sc++MEPviXkBMeQoOa13Njf3+fy5cv4vj9kUjiIo4qgMlXz3MQv/eJkKSQZ9+/DEdTsnT1xIrHY/Ole+B6B56EmSAENIkoUE7Ixbj+dhPrJKlFKuJVyhdXUoddaS7uQIsybJIQgHJHuU9IMOezOKk9URLub0Biz8Lt+ijSCKvzcZsdpdZ+Ab9xRBCWL53tuHqswY1R8t8kbFgS5sIftvbAjBVGsCLxek4EVB6lUWHrk1MOurBwJQe3oEtZ25p6R7douCcl0JVNBmkb1+xZIk5pDhvI1btx4Pu+Gq9Vqfd1ws3blvZM0+GC49b3oBfVW4NKlS3z84x/n85///Fu2z2NHUBlmbZJoNpusra1hjOGZZ55haWlpqn1MJKgDalB9quYj6iyZmkQygqBmhrW0W12kVPi+hxAefvpliFvx1KKZ4+tPPXSaEd6uya3jvfQ8TFrP6SQyN6oD+tQoRu6z6LALNGdI7w1irxVhF2bLg7kUoYcxKp9vs9ailEe5arEWZOrIO2hOaAUoU7hmBWLq7UCQEFIJTBq9RVhrCq8ThYjLFv4MY1dWOHcEa5q0Hg0TsOzPH0W1vBYP8dDBLxwDz/PwSiXOlF/nxJkfBxGitfMZazabbG5ucuXKlT7rjYy4yuXyO46IxmEeL6h5rTZu377Nj/3Yj/E7v/M7PP3000dwNtPh2BLUtE0SnU6HtbU1oijiwoULM7V0TiIomSha+6OJZFrx2ExNQibDBDW9CrMlimK6nQ5JognDAIHIa1oARmpUrAgrB3dvdSfUn9zC7QjvkfopgtDPiQncAqu0ptnpYq1TdZiKFAsOu9baif5PB6HZjhALYmb1HWMtypiUONI5NeXj+xlR+KlIa88yQ2mFFhIjioOqmYBrARZacchSqYMlAqELZDQbYhPQNQH1Oc0HwaX5joKg2mK00+6sEHYfX7+KDv57fN81zxQfJIvWG41Gg/X1deI4JgiCvkjrrRjePwzmmYGax2pjb2+PH/mRH+GTn/wkf+2v/bUjPaeDcOwIalpPqCiKuHLlCs1mk/Pnz3Py5MmZn7QmueqOmoEy6VOf1noq8dhMTWIwglKJRMWSsDL5/UmaOgzDgKWlZe5v3R+7KMeteCqCGhlBWafS4EgTfD9AxRov8Ppe0+l22e90Xbv8DDWEYh2qdUDH1yRYC7HUlLUPvhi5/I+6PhaIdZIrhGf3iVakIrS99xbrWsY3KGMRtjfTlkkKQX82s5X4KJuk7SuD12Zy1DSIPVWhHrTHn9CU2JIlnix1pvCamgyDoWEarPjzD5z6+r+i/Y+CGL5Xx1lvSClpNpt98kTtdpvXX3997MDs24F5Iqh5rDZ+8zd/k7W1Nf7ZP/tnufL55z//+b5r+KBw7AgqQ5aKGUSSJFy9epXd3V2eeuop3vve9x46BRAEwVjB2GJ6zxpDu9NBJpJabcEN2U6xz0xNYjCCAhdFjSMopSStVr8+XxRNToslzQhOja+3Qc+wrwdbkCZybfBSuoU8aseUa6kiRGb9Ua3ilyp4yWwpyiTqqZE35ujMlKk2n0ksfnVUD+EwBRjj5p20MK5RYnCbMZRHCHFYQJr0WEX+n94/C6k+iyXRhlhaygGFdF62t/6h7eGj7f/dnqxyttzKd1HY/ZDiwyQoPHb10Vhw7Kgdlr3ludNtwjbw9RfQwf849XvCMOyTJzLG8LWvfY1z587RarX6BmYrlUpOWIuLi1O58x4VBglqFi8oOLzVxq/92q/xa7/2a4c44vlx7Ahq3M0kpeT69evcu3ePJ5988kgEZCel+Hbv7WONyVs2FxYWqNdqM0m+CCHSWZ1hoo0abRYf6r95XV6+hTV2qGgcD0RhbsnrTfgPDuyOQlToJjRao43G93zCMCNKi+85lfe9+w1MKDHWOr+dxUWCIGCztTfl2fdgrROirdRK8xFU2vlnE2AEqRQ/mayrUHge1hdgh5NuApCJoFzt/3wsIG3CxBHevKHC5E3/HVmmEnbTVCH0GiCKNajim0dJO0FTlUkIKHturCAXHba4Y5qBtO7J8pEQVNd26dgONTF/ei1Qn0f7F0EsHur9mczR4uIii4uLPPLII4BLEUZRlMsTbW5u0u128+HaB+0XddxkjuAYEtQglFLcvHmTO3fu8Pjjjw/p5c2DcQRljOHK61fY3dujWqm4utYhFc0H03sZio0SxqQzRkpRH5M6HCSood+3ogPrWt1Ypgu3KrSD9z/de76PsAIda/wgYKFUQqdELZVyKT5S/bai+OgBiLoSUxboGe0xMmhr0WlEbeLxxGHTdCW4z9cKiLUcSQUWSxK7GS8hUnt2BMrqXLF8+F2k7DMcr7VkiRNEBfLotQX2SMv2PVgMRlvuNT7bySqPVLogDI7oNEIYBGZ60sJ5REkrCA9rBV9425baolY6ivpPRKD+Myr8qUO9e1yLuRCCarVKtVrl9OnT+c8zd95msznSLyojr8MqmBf381cEdUxgjEFKyZe+9CUee+wxXn755SN/6vF9v4+grLVsbGxw/fp19u41XGv1HGQohBhqMc8QNTqYdOFPUpv1+mKdcY/C8ajmhkKngNUW2Uko1Ua3gEkp2d1rptJEYYFweyuQtaC1xFoIAp+Fco2gVOi+i2KCVF/PGCdFNKjh5nlerp/Xd75tSVQ95CIJJIW5KSudhbooFFcsqRFiOiScPcRk80uDyEjBGrDaw0u/adomadfebHUjgI4M0QaG3U9EH2kVY7lsrMqm0VYWDW0nJR6pxLh6lgXC3pEIR1hgEELnpOW2mpJ4wdbkbhxwthT3mhwOmXhomRaRiah4420upoWvv4L2P4z1Lsz83llnoEa58xb9onZ2dnIF80z5oahgPu1DmFKqj+S+172g4JgS1O3bt7lx4wZCCF588cWJs0zzIIugrLXcu3ePK1eucPLkSS5evMgbn70xFzkBrv14DEHJKGZ78z71lUVWVw6K0CxxNJCmGfH6qBkNEVTWzmutxeARBH2DPPk/tdYYm9WiXKda3E4ISr1cWitOAEdE/euDTYUaDEbrXtdfTlqCqCOJpxSiHTp7C6pIULgoyq+65Joxbr+e7+OHYb7+amumithkAl4A2kqkVem1LV7frDHiANKy0JYllsrTtNGnFClsLsaai17gTAzbsabs9xo73B8PZ0PiU4ij+iMtDEKY/Lg31QKPBjGa4QeKWX2j7ql7PF56fLoXH4BQ/p8kpV8FMTxEPwlHMaQ7ScE8a8i4f/8+nU4nf20xTThq/6PMCv8qgvoehLWWD3/4w0NaVEeNIAiIoojXXnuNWq3WJ4U0lw5fCoEYapAoKi6URUi1evCXU0o9VMfKEnPFdSVuxnDG/dtaS7vt9OpqtRrGCsxuzODi6qSJ0lpUEPZtMW4n1FYHCWrMmQoQwgev4OJUUMtOpCJuA6FXcMz1JvNyisToIUqwMZhyr84UFIiJ9CwjM13tJYnBq8ZoO661W8BQVDg63deMpyUoW3AI6SfEbFf7tsajQZReR5PqDqZirWLAeTgnraAYE4PQRBgaCFaDDpA43hqh+j6WtAqn3TRNOqbDgjcbqYyCsHuE8jPI8GdmSqE/KBWJooJ5UZ0h825rtVrcuXOHVquFMabPUn5xcREp5V+l+L7XIYTg8ccfzy03jlrRPEOj0eDNN98kjmM++MEP9s1WyETR2ht2v50VQmQ+UGKk4kLU6LB05sSB24nGRR7W9n2x41aExdLtFBo76nUslt1GlyI59UkT9aX8eojbvWufaE2iZpvNyRc6z0Mqha8FourlKUJrFRnNCm/Ax6lwiokZPn8Vafy6GDsknORpuvFwdSFDHBsCo2csM2bFnv43daSHc8HVLm03IoKzKakNEtMgtpIyj5Qzd9zJzsPuVhAMR1suRbihFlgKHwWrQUQIESOI8IiAOCdaY1PfKF2kOScbJdIU4abc5InSE0fSHeeZr+Prx2fq6nurZY4yhZhiy3hmAtpqtdjf32d9fZ39/X2azSZRFHHp0iW2t7enntn63Oc+xy//8i+jtebnf/7n+Uf/6B/1/T6OY/7BP/gHfO1rX+PkyZN8+tOf5oknnmB7e5uf+Imf4Ctf+Qo/+7M/y2/+5m8e6bkfhGNHUEAuqfMgPKHa7TaXL19GKcWFCxe4dOnS0E20tzmDBt8k2Ezg1RHJ4GI6raJEPKVpYtSM2N3aoVKr5h5Q2dNxN5aAwFqDUs6RNgjCiYtM0knyWk/rgDb3ybAuRRd7eIt+mvYr/DZNDzp1ikyBwS2yaqCXLtPCExb8VIi0z7rdgrI6b0kfjnl6tvO9RgOBlh7BCMHXWaGtR0dWqJfTbQkLuMjHWO1IWYCYwqigq33a2qcejDCX7CPynvNwrz5o8rk2ITy2jaQdBtSCEKhjqfWuq7WOtIgRIiUtP4L8M9GptqET2m3QYFNushqsOFsT3z9UE1GGQP1nrDiB8V+c6vXvBB2+TKqpVqvx8MMPA/CNb3yDJ554glu3brGxscGbb77J3//7f59qtcoLL7zAP/7H/zgXgy0iUzJ/5ZVXeOyxx7h48SIf+9jH+oRii0rmv/d7v8fHP/5xPv3pT1OpVPjn//yf861vfYtvfetbb9n5ZziWBJXhKD2hioO9Fy5c6DMhG8RR+EBprWnst7DGuPTTqJpRoz2VokQ0WH+CvpXXFKKzSlBlobrgnnoLc2SdboJSEotrgBBTqAJYC0lXUq6VaEbztIenJBPbkeebLaJAXttyChaGROnCyFFGXO5NJoGg2u/Eq9AkVvWR0DRtDir2j4SgABpJQD1P8wmwHloZhAgJ/Er62TlVC5s2O1hG+yzdT8rUg2nnzkbVB3vkf73d4Vx6SEEQEPgBfuAsSIRYwNqFvu5ARIwxHZRpUQ0tEAGOpHbZpWZqiK7s65rMtnmQ/NUgQvm7SHyM/8KBr30nENQoZDWo5557jn/6T/8pf/qnf8qf/MmfYK3l0qVLfTbzRcyjZF6r1fjrf/2vs7a29sDPbxSOJUFNqyYxDaSUXL16le3tbZ5++umRg72Di+buLCrmA7DG0G63kVIh8HMV7VEw2pC0I8r10Zbt6RZHtphn0ZGUEtK0oRCCuNVvAW+tpdFs0Y3jfBh3FkSthKAa0B5bfzoYMpNlMhaUhfDghUsIR2xAXmwTwsv6sF07eUdjAxcNCs/DYEisShsO+jv8RkZOBejYw9bnCgRyNCM/3VYq7GusM03su/Y+QvgICuoHIq0xpYRlMWwlZR6vdvDnOK6s1tcUUK7VqHgeWju/rjiOUaoN1o0YhGGQWmYEKO3TaftUKg+jRSm9kAohIiwRu0GVs9WH8MVOHmkppUhSkWFr7bD9xtj7TxPK/x3J38P4H5p4Pkdp936UGCTOrCtQCMGHPjT+nI5KyfztwDvvU3gLMY8nlFKKGzducPfuXd71rnfxzDPPjCQK3/eHbvjdw6T40px0sfZz/87BQ61RozORoKQ0fbp7blcWbVwqLAhCJ+aa/i9pxJBqTHa7XWcoh1+YeZoNcSvBLvkzNFv3Y7CTzsZ2lMrNEJQxxNoRc7GdPGMQAQgJfuCDtSRWIQdqVfnnLcRY0spmiqz2sNpDBPNHUcoKGhEsBArf8/DDab/GXh5J9o7U0NI1TpcTjI0wtouZ0qF3ENbCrTjhmYUqQeDci4u/1Fo7x+EkoRm3wFqCMECnIx+BHyC8EEuIpc6egYD/gSXvRYRdJ/DuEpTWKZkNPO6CNWPsNzyCwHfpwSDAz5XkDaH8P9BmHRX8CIjR101r/ZaqhE+L4oPuYeW8vttwrAnqMBGUMYbbt29z69Ytzp49e+Bgb9ZqXiSonTu70+/Q9gwKKwNDvUms8if+cejut1l+dHy6sVh/yqw2jLFpQ4F7Mi5uH6pEAAAgAElEQVRGBHErIoqiXOp/dXWVja0Ghx1+iVox3c7hH9+TQXKNDbbee8ocGqBNW967Jh2unRDSWA1aGqSvsNj8c7bZhrJ/F2zdB0nL/T8lPVmhXEo75tIUnMFMmSTsnYC1sB8FLK8O9lkeBh4bkcejleWcqC0qJStHWNpGWDvs0TUK96XkEV1icTBFJgR+4COlRErJ4mKdUlhK08e9aCtrrMlSeffN/02ldo5q+CzKXEBam3bAKzw28fwN/GCDCuv4dgNsjLEGpRRaKTpxjDaulT7wM9J6hUCvoUt/F+s9OnQO79QU3yhMk+acV8n87cSxJKjDeEJZa7lz5w7Xrl3j4Ycf5iMf+chUaYBRahJTEVQ6M9Fut3ODwsG5KRmrAxeNqDG5W7DbdQSltUYbg+97hKHvZn+MRRQGVq2xRO2IuBOxvJouaNZ5KPUKHLMtmFoZOq0Ywtlnwqy1ffNL4CIo0idN10XXI1htnC6gAuwBc2HZ+3RkYKBRqkhs2b8nkZYjK5CRoFoDT/j4uKf67B3GOkddM460bO+4hBC0VQlt1Iih3dnR1oYdqTlZCtJzCvBFHV8U5wMNxkZo2+2RF9HIJ/mr3Yj31foHUJ3+Yyu1WFnNf+f5PiXfp1Qa9ndSWtHptnh9/9cRe3+bxerZfFaoVqshxOMYew6Vp2ot2C0CsYEf3KFk16mwgbANd6+kpBVFEVp9E2sv0ZQfIhF/g1r9TC4I+04kqMEywSxeUPMomb/dOJYElWGaJonM1n1tbY2VlRUuXrw4k2TJIEEZY9i9OznFN86gsAijjevgOwBxsztkdNaDpdXqkkiJ73m51YbFplbaBm0MVpu8TuN5HiQ9ko8ShTbZk3xxyHTK6XhjsBGIQxBUPEqIV/fqUNm8jzU2n2cSno82LiLC9ghiLNHHAmoHxw7TkFaSuIFoP+i1amfeUL5I54wKw7QGjU3TWCZ16s0eFoyFRhywWj2aLtTb3SQnqNHw8MQCXt/Qq8HYxEVZRDlxtbRmU0rOlEpYa2i3O2itWKwv4k/xUJf5O4X0vmfBqS+wan+ObksMzQotLS1Rq9WcvmR4BmMfRpn3u8/eWjzRxLMb+OU7hKV1SnYdjy2wlrp+HaXeYKf1Xt64+SzduIaUMleaWVxcfEd4Rg2S5lulZA7wxBNP0Gg0SJKE3//93+fzn/98X4PFg8SxJKhpmyR2d3e5fPky1WqVF198kWp1UrPBaAwSVGOriRoz76NTTS8hBIuLk7/MQ8oPY2CtJW52qS73hwFSSlrNFt0oyRsgsjoTkJOR1RoQeIHvKMhaWttNbKpG04o1RutUO2/U3M24xd29Tirtmrdm1PU01o61dbeRq0O5p2add5VJa4iyulOefusdS4+0CoSVCMcGh4hUhkgLgdEh5bLrILS5h1Sq9OANzBml3Xm+F1IK3AUvpgYbEZyoHhxFT4NdqWlIzVI4S+Tg4YkKnqgUFhKLtQmbSnFCnaXduEp9pURYl0z70DIKyu6z6/0Wjz3yizz2mFscMzmhZrPJ7u4uN2/eJEkSKpVKHmktLi7ihytYVpD2PSS5RFOEsHcIvA2C0gZnKus8eur/wYgnuHzjBOHCQzSbTTY2NojjmDAM+9QejsJWfqbzn1OH77BK5gDXr1+f7WCPEMeSoDKME3NtNpu8+eabeJ53oK37rPvYGdHYUPSBck+BB1f54+70tbNov50TVGaGCBCWKgR+3E9M+TGZPOXne8WajgAJK6srrh14Y9s97euiWZ9HJkE0nrTcPI22FmI989KVNTiMgo0Mquran30/QHiCWKs+vb1RGKwZuSO1eNLHVjIx2fnoQEaChZp1M1bFY8ZFei5iMthU2SMjrSzF4+OR+cJrXWJRnKIcaqRJkDZ2f0wyW10rxdVOzPuXqnNGCwJjfFqtLm/4Xf7WU/8b5VIFZRpE+jaxvk2kbxHrdRKzPdOWldnnZus3OFP9eyyVPtAnJzSoON5sNmk2m9y9e5dut0sYhn2kVaksIMR5lHlqoK51D2u/yJnVrxOGiwhvCeM9TixP00odere3t3Nb+aLSwziJoqPAPF5Q3804lgSVfQEHv4iZe24cx1y4cOFIZEQGCWq7UH+y6RNgMqMPFEAyZQQFrg6VKZor7aSJwjBke7s1TEypAoSzyRh9eyTtBKOMU/KWZuBL2Rvm1CNIK1N0AEGSpeiUxSqDGKXjN4K6lDG9usMArLXYrkac8AiCEG0MsZK5UvmsEAi8RBAuuHM09NQQDMYNmM5ABkoKtLZDs0QCwBNY7c4hCFzbuLVOZUEXJIPyBhZPsNGWPHuiSskrk4Wh1oKyCdImSNMjrb6B4xHYk7qvFjUrMvUDKROnMBLEvN59lQ+U/gaBt0Tdey/1sJca0rZLrNdzwor0bRJ9d+L1NDZho/MfaKlv8nDlb+N7/ZmBouJ40VAv08BrNpvcuHGDdrs9pIFXKpVYu9Yhit7Do8F7McIDYxFmh0BcZ2WxzOpyGeE9AtTRxs+tNwbTjkUynFfFHOb3gvpuxbEkqEHEccyVK1doNBqHds8dh8E61/bGLlibt2hXq1VWV2fzgQIONBgsorm1T2Vvj4VajXqpnjcPdAtRmEnrNE4qKTwgG2OJmxHxyOGZcWKvTiHcaNcWbq2bX7Kkpx5pqHv5NgrvLNSKXGqvq4bJ2WYnlRaeTGKIQ31oYirCdC122UUwHlndqBcB2ZS0tDUpgU3uzEu6UB0IynX+YOBsSrIrIIQA3y9oOdB3LTcaHVZtRCV0LdXZn9BLazh+Pb8+Tqy2n7Q0/VHl1XbMauinDxHTImvo6VCtVqjVVsg+wzfbf04tWOKZ2ktD7/JFlYXgPAvB+fxnxkpivZETVqxvE5t1zIA9SSP5Gm15iZOVH2Sl9H14B8wWlEolTp482deZprXO7d+vXr3K3t4epVKJ5eVl7t27l9e1/OAhrD2NMcbp5RrAdrFWU6+FLNZXeeTMSTwvxFhBt9vtSztm80r9EdxsRofH0WoDjjlBSSmJooivfe1rPPXUU7znPe858mJoJhgLbmG5/p0b7O7uDrWMzwRjSaZQ7jZao7XB15rFhTpBOUxr9q4bLIqc9YVOIzw3nT/dIUSNiGZ52hx8WlPxe6WcWCn3dJq2TZu2xJZ7Eju5UGlfrcgSKd07B3oLdo70d7pj0UtH81laAzYBMaZpSiDwhehL21lcnclY40ZiC6QVR4JKzckEFf2lwiA88Po7kQtBb7LWpxuUObHgo5QmSWI6nTYmHWINs1mgICDwQgJCqr6LOqwFg+qlB01CZGJudyWPL0z31G+MzuumK8vLIxX6v77/R4SizJMLzx+4PU+EVIN3UQ3elf/MWkNi7hVShO5vbbvc6/4BO9F/Y6X8fayUPkrgTZ/28n2fUqnE1tYWlUqF7/u+7yMIgqnqWmGYXUObCy1r7fQZyyWfyqkTPHT6FJ7nZvziOM49ozKjwyAI+iK4Wq02tq71VwR1zHDt2jU2NjYIgoCXXnrpgQ3mZRHUvXv3WFtbY2t9Z2TL+CxIYtW/KGctdilyoVYhCEvOI7yz32axnH15Bd1uTJLIfBq/b1h1CnT3u3SWDpe6sNYis/Re2oItEhDpFzBTKB+01YiNRhu3sDsHW+uk6EQvNZiRlhdbZq9sjYfpWrzy9NsTOC0/X3i5lkNOWsZSNgJFTGwUfjBrxNKP9XbC2cU6lUoAuPs4m/fKhlhVp+vsTjy/L9LyvICKH1Ch150XG3hh8SU80WFXbrIr79FSuwMxoU3T0wm1Wj0d1B4NC7y29/8Smy7vrl+c+fyE8Cj7Zyj7Z4APpednUXa3QFo3udH6EmX/ERbDD1APX8AX45uarLW5UekzzzzTJxM0a10rI5gsKspU3N1wsov2A99ndWWFE6urjoSEcI1KKWndunUrrw0P1rVGzVIeBy8oOMYEVS6Xefnll/nGN76BHtWufETodrvcuXMHKSXPP/cC/zV6dW4fqKjbS+8JyPkpm/UQoqdo7mCJ9lssPrSCtZZut83WVgvhefgzElOG9l4Hu1jUQ5t+O4nOoqACtAVpEaVUusnz8rSWsYauVE4xwvYiJpG2aGft5MX2Bl8LSiLEeDZ3y3VRzOGgI4NvxVwRtgDXvm8M8Z7l3EMnKVfKJEYRm4TYSPe3ljPVtbSxrLcS3rXUe8gSwmkiBoFPkbSMcUOsKpsHMtopL4RO5y4InBTRqzs3+JlzP0iQNshIk7Cn7rMrN1nfu8bNnSt4C376FD/dNfnLxp+wr7Z4aen7Cbz56jJCCEJxgtA7wWL4vvznyjSJ9Tr7yZcQBATeIoFYoeI/hkiVIxqNBm+88QYnTpzg4sWLBzY2zFPXcvNaws0VOtXivvVmaXGR5aWlfJQk81fLLOWvXLni5KxSXTwhBEmS/FUN6nsZQgjOnj2bFqNHd/LNi1arxeXLl/NZihdeeIGNK3cPEn6YCt1OQZ4pfWLLbuJ+Ec3eTFJ3r00Udel2I6qVChDgeYfXIUwShRdrqIT0zz/19lxssM6QCbSORKSh1E/eyhgilc4tpbNW/Z2Bqe9R3/hVGpVFlrDuF9Xo0lpRWi9K/57mI7EarAQxx7pqrEWnDxCxDQhLJSfA64dU/N5RWuvsPDLCioxMSWt8k8N6K+HReolwwgOHK2d5+H6Jcrl3IjobjFWKdifGaMO+2OO39xN+6OTFfM5o0ZzkzpVtTtjzfPTZHyEsB+zLLXblPfbUPfe3vD/Gzt7heud1tpM7vLT8AzxcPhpjwiICb5HAezc13p3/zNiY2NzFaMHNG+s0Gh3e/Z7nWFo8PWFLB2NSXavZbE6e1woCip5ZOm36yYioXq9z5swZN+phLW+88QalUonr16/zT/7JP+H27du8+uqr/PEf/zEvvvgi3//9399nQ1/EYa02AP7lv/yX/Pt//+/xfZ9//a//NT/4gz841zWbFceSoIA8FD9qT6goilhbW6PdbnPhwgUWFha4dOkSAPdubh3NPtpZBOWK5cpolybqi8x6FGGMobm9zwmpWFlZxhiI4sML1mrt8u6iIxGV0Rp8IiOOfBTW/bc7ylo+PzENS2E+H5SY1Iah0AAx7M4qilzVG7y1oNsKXbZ9BoZeOhwbFgabTCHCyqKtkYKvHYNXmr2N2AJaKyfqGgQunWdht5VwennY3lwIKPshZT+ENPVmLUiriHVKWCl5mbRLUhvLjUbM+ZXZ7dJ9z8Mvlfq6zYyx3FDb/HlrjSd2TrC7u4uUktXVVR566KF8NuhE6QwnSmd677OGptphV95jV26yJ++xq+4hTS/qb6pd/mj7/+KxygWeX/zvWA4frCCpJ8q0diusra1x9uxZnj3/GKDRtouzJcn0CUUeZR0Wvu8PeTtNO69VKpX6SAvIoy1rLSdPnuTJJ5/klVde4Wd/9mf55V/+ZdrtNl//+tdZX18fSVDzWG28/vrr/N7v/R6XLl1iY2ODH/iBH+DNN998a72y3rI9vUNxVJ5QUkquXbvG1tYWTz/9NM899xxCiDydArB5/f7c+9FKkyQqb4BAuPx2L22YEZNw5KVV2lXn4xsnFtppd+c6BplGQKYrJ8yv9izGSY8oURnhFEmroOPQscRx7MpL6QuyLj5E//bG7LIXtQlApsoXgiEDw1GkxUjS6kVbxW6+aWAZtIv3+rh1qxFxcqk8Vf1JCCiJgJIX5DPNrp1cE6XpwUY3QdYDwmD++9nzBKVSyFflFZrdBh85+17OnTuXL7S3b9+m1WoBUKvVWFpayusxy+EplsNTPMF70+O0tPQee/J+j7TkJrejy9yOLnO28jRPL7yfM+UnjrxJKY5j3nzzTYwxvPjii7mjNQT4A8ufIwc3mO4wehxlVhxmXisjrnK5zO3bt2m325TLZbTWJEnCt7/9bZ544gkef/xxfviHf3jsvuex2viDP/gDfvInf5JyucyTTz7J+fPnee211/joRz861/WYBceeoOb1hDLGcPPmTdbX13n88cd5+eWX+yKZTM0cjiCCspbGXguZSDzfIyyFaOUaJoQTaQMGUn4F8urutagu12i1D++9ZC2oVKDVduWQRtg4SK2JU2LL59Dy34p0cYBAgQqFiwwyYjpsyc4CscVb8AcMDNOnVGuxepTrbpG0IDPsMxZWqSAqgq6WdLUa0gLMkKfzRtjFZ1DKsNuKObk4e9QD7uMOhU/oVVnENQRU9DL/y4WL3I/3uBPvcDfa5k68Q1PN5uBsjKXdbmOM5s264MnViKfCkJWVlb7ahzEmT2ndvXuXy5cv96W0ssV2sbTKYrDKueozQLpAm3behHGl8w2+3foyJ0pneKxygZPhI0zjKTYO1lo2Nja4efMm58+fH5v+KqJnbd+/nVH3+LT3/aR9HVTXunLlCru7u7nrwr/5N/+Gs2fP8lu/9Vu88MILY/2fipjHamN9fZ2XX365773r6+uHPufD4NgSVFHu6DCWG0Xx2DNnzvDyyy+PDH2LN/E8EVSmz9dpJm6ANhPb9Dy0NmitCqku15nnBT5FGujut9HazEVQiSw8nRsLkYLq5BkUqTWRnPxUL9Jmh1IMfkkgvAA8r5d2M7MNxGawXQML/Z9L3soO+Xrk6tdmAmm5v2Xb8NhqL32jrHFkpSSRVnRUQiQTLPTSeROwtR9xon50Wm/r3X3+5O5NPnbuvVyoP5b/vK0iNuMd7sQ73Im2uRvvsCebQ++3FqLYqefXFhYoleoIAf9t62vciXf4nx5+mZLX+7w9z2NpaYmlpaVcIdtaR27NZpOtrS2uXbuGlJJqtdpHWpVyjUcrT/No5el8e7Hpsivvca17ibJXJRRlqn6dur8y9TVqt9u88cYb1Ot1Ll68OJe306R99jXrHBFKpRKrq6vs7e0hpeTixYssLCywtrbGpz71KT7zmc8QhiGXL1/mF37hF/gX/+JfjHTR/V7BsSWoDEEQ5O2d0+Cw4rGtvTbtxuyptUF9vub2TkpOmRSOR+AJNwCbC6J66eCtI60sKujuNmk2uyMVqKeBMRap+gv1piPxxxCUtZZY6V5L+QGw1kBHEa4uFDoQC7NFg7WiKUjLRqOfgAfhGgK9kaRVtIrf31csLnpUqqX/v703D4+qsPe4P2e2TCaTDQiEJBAIWQg7SRBcqliv2tqW9rpi9WKrtmoXUNsqXlu1rVpRX62V1qVatbZqfWvfarmorVq1bhDABVmyEALZ98y+neX9Y3IOZ7KQyR7gfJ4nDySZZM5MZs7v/LbvNzr1ZjaTbEnAabERCAQIKQoJySlIZoGgJPYErsiAMkvhiEyXN8yU5NFbc/hnUyV5yVNYlHakN5RksZNnySIv6Yi9REAK0RLq0gJWnaeFw64mLBYLaalpmHoNXOz1HKQh2MZXpq+K+T290UsA6Uta6gJrd3c3dXV1hEIhEhIStKCVkpKC3W4nMyE35vdF5DBeqVtTgRcEExbBirlXv0iWZQ4ePEhHRwdFRUVjKgUUd5l3iJmWy+Vi//79zJgxg7KyMkwmE5999hkbNmzg3HPP5ZlnniEhIQFRFKmsrBw0MxyJ1UY8PzvWCEM8WY2GLuWkQN0R6erqoqmpKS51XpfLRWVlJQkJCeTn5+NwOAb9GYAPPviAzKRsnv3FX+M+PlmS8fm8SJLUs2diQRJlavY30XsAQhIlTGahx5it15tBLWUpUckcy+xMJMGM6hJr6jN0oP/Z2D94MBTpUS4/guCwYsmJHXeVe5ZPw5IcVzBUesZv1VKkkJOokz0a/GcHC1qmqRZMjtFp7CoKpKbaSEmJ9i4lKSpGK0syVpsVh8OBxdz3uk9SZAKSSFCK9GRcIuEeA0SL2URhTgrmURQfTTRbub74NLIdg5+kRVHUlFTyCvPx2yJa0GoOdtIW7u7znBYmzeL0qUvJtA9eZhoIRYn2HD0eD263G4/Ho/Vh9JmWOl6tR1YkZGR6rCLp6uqmsrKSmZkzmT179rgKuR6NeAOUJEnU1NTgcrkoLi4mKSmJUCjEvffey9tvv80jjzzCsmXLhnz/oihSWFjIm2++SXZ2NitWrOC5555j4cKF2m1++9vfsnv3bh599FFeeOEF/va3v/Hiiy+yZ88evvnNb7J9+3YaGxs566yzqKqqGq0hibii9gmfQcUzxefz+aiqqkKSJIqKikhJSRnSfQiCQH1lY1y3jerzBQiHo8656gKxoij4PEH1N6LIMqIUtSO3WC0Dvwl0vRRZMCF6Q1jTU3qClowoRU/oR9S0dUFLF7siEann5A9q5FIA/GGkcARFXVDs+YjrsaqBqWfvScMvQUp8JxhBELD0GnDoHbQIAPFdS8Rxf+D1Rpg+PRkFBZ83mn07EhORZBm/z9+TyQpRySGLBYvFitlsxmmx4bToxrt71NUDUoQk0UFqipXWYF99xOEQkCI8vP8Dri8+jczE/qXiFUWhpaWFgwcPMnv2bM0VeiowK/FIXyQii7SFu2kOdvb0tTqp9jdQ6atjriOLsrRC8pOyeyxD4kcQBOx2O3a7PSYTUPswbrebtrY2/H4/ZrNZC1jquLbFFH3vVlVVEgwGWbpkqeY4MBblt+EQz/13dXVRUVFBVlYWpaWlCILAzp07ueGGGzj//PN59913j7oIfTRGYrWxcOFCLr74YhYsWIDFYuG3v/3tuPtknbAZlOr3EgwG2bNnD6WlfbXC9Bp9BQUFw3aYLC8vZ/+rtdR8enjgGymxzrm932gALfVduLv9SKIEREeWh/IGDIVEcNix50zv+00FLWgpcmzQUhQIho9SppuZjJwYte7WxsKPhjrJJwyw+JpoxjRjeIMD/SEIkF0whTDRhd+AGCEoigPadQyGAqSkWEi0M6CKgurqqn5I6sWETsVBn2mZTQI3rzqVaQ4H9X4Xdb5u6vwuDvu6aQ54hh20Uqx2vluwkjnO9Jiv+3w+KioqsNvt5OfnD1nQVFIk2sMumoKdNIc6cUd8pFmdzHXMZI4jE6tpdK99RVHUhgfcbjc+n09z583IyCAnJydqrTHACVQfsEY64DBaiKKoraQsWLCAxMREAoEAd999N9u3b+exxx4bN9+lCSCuP8AJH6AkSaK8vDxmWkUURQ4ePEhbWxt5eXnMmDFjRC/oXbt28dr/8x8i/ennKbHOuQ7HESdS/d9GVhSq9zQgiVHjsqGWMBRZwR8II5hNOApnx/d4FBAliWBY1O00qaO3aP83pSdiznBqPyT3lNqi/8YGrai6+SCKDAIIsxxDll86GtNmOkmdGptGibJMQBQJitGgFYgMHrRUGSmbzcK8/GlRZYg4URQZUZSIiJHYoGW2YLFayE5O5X9POx17r4AXlkQaAm7qfGrg6qbR7xlUnVzFIpj55txlrJiao/VpOjs7KSwsHFU1AlmR6Qi76Qi7sZrMJJhsJJisTLElDzm7OhqBQID9+/djtVqZOXMmgUAAt9utLcWqe0Xqx3Czj7Gko6ODqqoqZs2aRVZWFoIg8MEHH3DTTTdx+eWXs379+hENdxwDGAHqaKgBCqI9olNOOQVZlqmrq6Ouro7Zs2eTk5MzKrXs/7zxPv/8zX/6+DyJPVpcZrM5Riiy998kEAjgcfnobg30664bD+GwSKQnC3LMy8ZkH/yKWRRlQhGxn4xInyUpYDVjzk3T9or6G8kVxR7nXZMQLQPKR88JhIwEhKTRe4MmJFrIzksfNDBLclQtPdAraEXHxqUeNYaoqO706U7S0oZuYqlHfW6iHxHmJybxXxkztFKWWs7q/TqMyBKNfreWZdX5umkMuKNyUAOQb0tlsd9CQU7uqL22B0NRFDxiIPq8CWbMPRcnVmFo2T+gvT/708/T30adIFT7WqIYtZjRlwhHwwJjOERLklWEQiGKi4ux2+34fD5+/vOfs2fPHh577DEKCwsn5NjGGaMHdTT0bw51ZLympoYZM2awatWqUb166azrjgk6kiTh83pRFCWmLNE7MIVCYfwBP/aEBATZEn9w6r0IqxBjDy/6g9iOEqBkWSEckbR9p77ol2aFqMV6REaxmHpkbhRtlFudhDObzVitJvSyD30yLX3Q8oowigEqFBAJBUTsjqNfTZtNAk6bDWfPCUyRFTw+L75wGCHRQbhHFzAiS3R0+ElOTsBsHv6JXhAErFZrz1V+Ig2AJ2MqBWlTNI03r9erLXuqQcvpdJLrTCdXV7oTZZkmNdPyd3PY102D301IjODzetkleKhNSeUsYSrTZBHHCPXw4n18KdbYzDUq9CpxZG25R5rqKJl1vPp5JpNJC0RZWVna/akLxp2dnRw6dEhTctBPEI61tXtbWxvV1dXMmTOHzMzohOU777zDLbfcwne+8x0eeuihce/xTHZO2AxK6SmtdXR0sGvXLrKzs5k3b96YqJo/ecefqNlxGKvV2lM7F0lyJmHryaj0fwNBEAhHIvh9PiwWS8+koMDB/U2arP9QCQTCSNIRwTpTsoOErOmo7rGKovSoHhwJFEPFnOHElK5mE9GxbFmSdFOFSkyGpX7EEhu0rLlJhGQ57qGLwUhKSSBzdvyjx2pP0JHoIMEe+7pQM615WVPIyHBy2O2i3e8fleMEuGLxUk7KOjLSK0lSTFagqjjos4Lejq6yLHPwUC37Gg9jy5xGt1mm3t9NvT8qc3XStNmcmpFLjiN1UvRk+jsXiaJITU0NHo+H+fPnj8jduvd9qUoO6nMaDAax2WwxE4T6kvtwCYfDVFRUoCgK8+fPx2az4Xa7+elPf8rhw4d5/PHHNe27EwijxHc0ZFnmww8/xGKx4PV6OeWUU8ak5KEoCndd/iBdLd1IkkRiogO7/chknooqi6TuZCUlJWlZnLvLT0tDV99fHgeRiEQ41Kv3ZTGRVDAbuUfdWuopuQ03AMKRcXO1z6LKK+mFa7W9Ilmd9IsNWtHpwSOv2ymzUknOcBAWJQIRkWA4WnILRsRhB63ZhVOxDqKnJ0ZEvD4vVkt0bPxovTCLycSPzj2FzFtTGqYAACAASURBVNRk/JEIh90u6twuDrvd1LldtA0zaJkEgYuKF3D6rNwBb6M33FN7MIAWqDo6OsjMzGTu3Lkxr21ZUWgNerXSYFiWmJrgoCBlGrlJ6SOy/hhN2traqKquYlbOLLKzs2MCxVgF1N5j736/H4vFEpNpORyOuM4ViqLQ2tpKTU0N8+bNY/r06SiKwhtvvMHPfvYz1q9fz5VXXjlpRuLHGSNADUZ3dzeJiYns2LGDxYsXj3r2pCgKn+/cy+9/9CcsViupuvF0/fOuliBEUcSRdCSzUqmvaSPgj99BV0USZYIDWMMn5mVhTox9vIpCT6CSkeSenaJ4Xx8CkJsW1Qa0mOOUqVF04pjqfR0JWnanjaz5GX1+l4KiBa1AOEJwCEErdWoi02YOMHYtK3h9PY32JCdmS3zlluy0FK4/exWWfsoz/kiEOrdbF7iGFrRW587hG4VFWE3xHUsgEGDfvn0Eg0GSk5MJBALa4IBaHuxv2k1RFFqDPtpDPhLNVuxmCwlmC2k2e4wR43gQCoWoqKgAoKioqM/7cqDX5FgFrUgkEhO0VFsN/SBG7+w1FAqxf/9+zGYzRUVFWK1Wurq6uOWWW+jq6uKRRx4hJyfnKPd63GMEqMEIh8MoisKnn37KvHnzRq18ANEpncrKSg7vaOKTV/dq+mSxgSl6QgmFgtrOU+83WcAfpr5m6BJJoihFx8oH+IvZpqdhy0jv/5s61KCllv76C1pqYDFnJmNOTSTO195A9xgTtNLnJmGymjCbzbq9IstRglaEQFgkEBEJ9RO0BJPA7IIpWKxm/Q8TCAYIBaO7Z7aEofdmzpw/lzXL5g9+Q44ErTqPqydwuWk9iprJTKeT/1m0hNzUgSfuFEWhvr6e+vp67WpdRdXLU0+wHo8nZtpNDVq9+67RAYcQZsGkuQabBAFLP4Mwo4GiKDQ0NFBXVxe3fp7+Z/WMdclS7FF46V1yTUpKQlEUXC4XBQUFzJgxA0VR+L//+z9++ctfctNNN3HZZZeNetZ05ZVXsmXLFqZPn87nn3/e5/uKorBhwwa2bt2Kw+Hg6aefpqSkZFSPYYgYAWow1AC1Z88esrOzR2Xk1uPxaJL0hYWFPP/Lv1Ozu1ZTI7ZYrVjMlqg1dyCAPSFB23lS0f9JGmvbh5Q9RXtrImLk6CPIpkQbjrzhyZYoPaVBUYqW8xR13Nxpw5w1uvIyKdOTmJKTgtij/CFGRERJ1IRwLT2LsP1lbQpRqSW1NBgtD0ZwptmZnh3NZiORCD5vdMQ/0ZE4ohPbZauWUDZneM+pPxKh3hPNtAYKWqUzZ/KVeQXMSIq9kHK5XFRUVJCenk5eXl5cjXZ12k0ftKKqJUkxQav3iLa6BC309C+1MYcRBgSv18v+/ftJTk5m3rx5oz5i3bucPhb4fD727t2rCcG+/vrrmjSRyWTitttu46yzziI9ffALw6Hy7rvv4nQ6WbduXb8BauvWrTz88MNs3bqVbdu2sWHDhj6iseOMMcU3GKPpCRUMBqmqqiIQCFBYWEhqairuTg/1FY2ahH5EFAn4/UQiEW16S+096Y0G1feP1x3A7wtpqg36ZUNda0fLNkRJjmrGxXEZIQfCyKLUIyg7dBRZxmISSEhMIOrmC7KokJxkJ9yzO9VbFmk4eDv8pM1M7tG9s6jmsCgomlxVKBTC54ugQE/QskYDl9WC3RL9UC891EzrjLmzqG1upEUKY0tLRRmFk9YL2z7HmWBj/syhG+E5rFYKp0ylcMqRZfCAGKHe7eaw+0jguvP9/7BgWgan5cwiPzWN2poa/H4/CxYsGFIFQF+iUlF9i9xuN62trZqbq16ZPCUlpd+gNdyym14/b/78+UNWaYmX3ruFo7m4q2avDQ0N2vi7ajKYmJjIFVdcQUZGBh988AGbN2/mmWeeITd34N7icDj99NOpra0d8Psvv/wy69atQxAEVq1aRXd3N01NTZpW4mTlhA5QKiPxhFKnjNrb28nPz2fatKj5miRJ7PuwMubFHw6FEASB9PR0TCZTjPV29P6FqE231YpJMNHe5EI16FMNKhRFQZaihn6yrCBL8uDKDQMgef2Y0vrvx/SLgmbjYTabY4YHonsuAg5JYUZmGihR36hgWCQYipbdgmFxyIMYsqTg7QyQkpEU83UBYeCgFREJhYL4fGJs0LJG7cylcIhPdlXx/Yu+wLRp0xBlmWaXl/pOF4c7XTR0uWns9iDK8S3CqkiKzB/e+5jLVi1h6azMwX9gEBItVgqmTKWgV9Cqc7n57HAtW8vLycuaSWFONhb7yJU39L5F+hHt/pTJ1aClBq7+9ooGq86oEj+ZmZmaMOpYc+QicHSyKL/fz759+zTldLPZTHNzMzfeeCNJSUm89dZb2jlh3bp1o3Kfw6E/242GhgYjQE1m1BfpcDyhZFmmvr6euro6Zs2axapVqxAEQTuBA+z8525kRcHv9WrlE/3V55H9lyiKohARRcRIhMb6TgK+sE6NPCruKggCZouAWa89p+sRyVL0//FkUaLHjzXOACVLUVtqs9mM+ShTbd42D8mZKSCA1WrGajWTnKRFEMKiRDAU6Qlc0SGHwQKsp9VL8rTBx31jghb2nrtUNDtzv68nezUJtElW3v+sltWlVpxOJznpKeSkp7BqXvRNLMoyzd0eDne6qO9yU9fpotnlHTRoRSSJZ97/hPOWFHBWcd6ol5OkYAhPbS2LkpL4+jnnYrVaCYoiTV4PJkEgwWLBZjKTaLWQaBm5gsJAyuRqptXR0RETtPQLxgMtw+qXVZcuXdqnxD3eDOdvpCgKhw8fprm5maKiItLS0pBlmT//+c/85je/4c4772TNmjWTYnz/WOaEDlAq6n5SPKijowcOHCAjI4OVK1diNps1CRyIvuAPfFrLoYqotbPD4cBms8Vh+SBgtVjobvMhhhWsNit6NXJZ7Al+OgsNwRTVy7P0mvJSp/HULEuSlT5BS/IFBi1vRG07JMwmU9SHahCCriBiSMSS0M9tBbBZzdisZrRCjgLhiBSdxgtFR8mPSCtFiYQk/N1BktKHfiJTlz9DoTAms4kpyVMQTAKSKPLe7nqmJpmwEr046T3pljMllZwpOu8nSaKx20t9l4u6Tjd1XS6au7191BsUFP7vs0r2NbVz6UmLmJYcm/0NB1V+q7u7u49gsd1iYW5abF8jLEn4IxFMQnS4AQHMqhDwCBEEgaSkJJKSkvrYabjdbrq6urRl2MTExJieVnd3NwcPHmTu3LmahNhk0caLF6/Xy759+0hPT2fFihWYTCYaGhrYsGEDmZmZvPvuu2PSZxoJk8E6Yzic0AFKn0HFU+Lr6uqisrKSpKQkSkpKSEhIiA4LqK62goAkybS0NPPKH7ZiMplIS4vfaE2MSLQ0dOH36gwFdWrkR3yK1Ek3GVmM7hcJApoauSBELc1N/QUtSY6dyvMFsDj7Sn0rPYFJDZrxD+YpeFvdpM2K04ZBAJvNjM1mJtWpPr6oMaKaYQVDIq4mD45U+5D0+RQl2lOJRCIkOZ1YdRmFpef/22u8XPvfq0iwmrWpLL2duT4jcDqdzJ6ayuypR4JWRJJo6vZS1+mirstFfaebJpcHWVGoaetk06vvcfK8WZy1II/UxKGX4RRFoa2tjQMHDjBr1izy8/Pjej3ZzGZsvYYlVMUO1RxSZTSCgyAIOBwOHA6HppKgLsO63W7a29vZs2cPiqKQkpKCz+ejra1NU3CIh4kOZLIsc+jQIdra2rR+mSzLPPXUUzz++ONs2rSJc889d1IG2zVr1rB582bWrl3Ltm3bSE1NnfTlPTjBA5TKYEMSPp+PyspKZFlm4cKFJCUlaYEJjji0tre3c+DAAUS3gqc+gM1qQ4xIKApYrOY+BnAQfdOFAhE8rgCuTl9ce0dHVBhMsUFLjno+SUo0W4qWBY+4wfYJWoqCw6SQMj2VUChCIBghFIog9WRqUbX0IT2VAHia3KRmpw9b7FUQIMFmIcFmIVUt1Smwcn4uU2Ym09DqoqHNRXOnd4CelkIwFCLgD5CYaCcpKYmBImxbl48/bt3JVWtOIjU1NcbkTr8IW1dXpxlHqplWamoqSUlJ/Qathi4PDV1uDne6ONDWyUdb6lmSM4NV82YxL2NwTUCI9jcqKiqw2WyUlpaOWD+u9yI0HLnY6S39NVpBKyEhgUAggMvlYunSpaSlpcUoONTX18cYF6qZlt1un1Qneo/Hw759+5g2bZrWL6utreWHP/whhYWFvPfeezEDJ+PNpZdeyttvv017ezs5OTn8/Oc/185p1157Leeddx5bt27VfOyeeuqpCTvWoXBCj5mrU2DqiWD58uUx3w+Hw1RXV2t2G1OmTEGW5Zg3tSAIuN1uqqqqSEhIIC8vj+d/8XeaDrRov0eRFUKhCGJYIhKRiIREwqEIkhgd0x6JgsPRUE0KVZ8mFLSApQUti5l5py9BMAnRnaxgELMlAVkWCIUiBIMRwmFpyHYPGUUzcGaM7hs2yZHAD773Rez2aPYTESWaOjw0tLqob4sGrcbWbjxeLxazhaQkR5wLwzAvZyqXnbucxISj9230kkOqeoM6EXdUcdeeoFXX6cITDJHmsDPV6WDutHRslt6ZrkxtbS1tbW0UFhaOe7lotAKUqp83derUPmoWve8vFAppI+9ut5tgMEhCQkLM8zpY0BoLDyhZlqmpqaGrq4vi4mKcTieSJPHEE0/wzDPP8OCDD7J69epJFUyPEYw9qMFQFc3D4TCffvopK1asAKInodraWpqbm5k7d66WCqsDEOoJPhgMUl1dTSgUoqCggJSUFMpf/YTX//DvuO47FIgQDIS1fyNH81waJdSgpfa1UGBq0UwS0pOw2RL6dS9VZCU62BCMlttCwQjhyNFLognJdrKWjv6m/JLFOfz31/suGGoXEx4fKVNn0uUXaWhzUd/qor3bF9ek4/T0JNadV8bU1KG5G/b2KlKDlnpiHUgeJySKtLp9mE0mbBYzVrMJv9vNoYM1ZGZmTipn2N4cLYipDr0j1c/rHbQCgQA2my0maCUmjmx37Wh0d3ezf/9+Zs6MuvQKgkBVVRXr16+npKSEO++8syc7NxgGRoAaDDVAKYrCRx99xKpVq2hoaODQoUNkZWWRm5uLIAg9wwbRRri6t1RbW0tnZyd5eXlMmzYt+uLdWcP/e98/kAdUAT86kijHBKxQIIwoDu93xYMiK4iSSOIUJ1lL5iKKEpKkjrvrjPUsZnq/nmRJjg419JQFg8EIETE2wM5cko09ZfQntC48v4yFC6Jj0LIs09DQQH19fUzjXU8wHKGx3aOVButbXXS4+pcbslnNfPnkIlYujNMzawDUoKVmWj6fT3OF1Wda6n0Eg0EqKyuJSBLz8gtwJCZG+4o9Qw7HyhW6qtg9a1Zf/bzRIBwOa8+pqpWnt4hXLwZGcr+SJFFdXY3X66W4uBiHw4Eoivz2t7/lr3/9K7/5zW849dRTR/FRnZAYAWowVEVzQLNVTk9P1zbZewcmVYqlvr5eMxpTr3Aryg/w/z24FXGQzGKoiBGJYCBMMBAh5A8TDIRHXBJUFEXLBi1mCyaziXmnL8bcM6WnKNHR7EiPR5EkRlXJrT3Lr6qFeW8kSe7JsiKEghFMiTamFE0f9ZNUot3GVd8+DZMpQmVlpVZCGopVgT8YobE9Gqwa2tw0tLro8gS072dlpHDOykIKZ00btePXa7q53W7NyhyiAWru3Ln9ntRVuabeRzGZgtZg+nljid4iXn1eVYFXNXD1Vxnoj87OTiorK8nOziYnJwdBENi7dy8bNmzgC1/4AnfccQf2Udg5MzAC1KAoikJ7ezuVlZV0d3dzyimnkJiYqA1AmExHNMfa2tqoqakhIyOD3NxcTYqlo7GTd178iL3vV4zbMUfCEqFA+EjgCkTiE3XtmeKSJRmzJdaVN6Mghym5/VjBaz8afU4ikSMW5iaTScuyrJb+/arOu3wVCamJNDZ209jUTVOTi0Bw6MK3emRJRhAinPNfc1i2bGGPJcnI8QXCNLQdybIa2twkJlhZuXAWS/Jn4ojD5HEoqCUkp9OJw+HA6/VqJ1d9ptVfRjAe0j3xMBL9vLFkoIsB/ci7vlcoiqKmBFNcXExiYiKRSIQHH3yQrVu38rvf/Y6ysrIJflTHFUaAGgxRFNmxYwd5eXns2bOHk046KeaNHwlGaG1uY//nFcghheSEVMwmM2JYpKvFRVNNCy21QxdyHW0URSEcEqNlQX+0PBgORmL+WLIU3dMymU09Bnuxrw+r3cbcUxcO6WSnyLKWZYkREUmWMfXsS6lyQ9Oz0rhq43maqZ+iKHR1+WlsigasxsZo0BqspxX9YVVcN4QjycGsnGlc/s1VOJ1jd0Xr8YdoaHXR1BENVs7EBLIyUpiSMvygGA6HtUXV+fPn9wmwkUhEO7GqJ1e1jDXU3stYjmaPtX7eaKMGLTVwqarkVqsVj8dDdnY22dnZ2O12Pv30UzZs2MCXv/xlbr311jFz4H3ttdfYsGEDkiRx9dVXs3HjxpjvHz58mCuuuILu7qhdzz333MN55503JscyzhgBKh6CwSAAO3fuxGKxkJaWRmpqKiaTiZqaGiRJoqCgIDq9I0q0Hm6nsbqZxuoWGqubaavvmJTPiiwrhIIR/N6oXbwYkVEk+owZ68laPJfkGSObGJNlKSbTkmWZsi/mcdKZ87WTa28tN1lW6Ojw0tDYTVNP4GpudiNKR3pa4VAYv99Pgiqu2/MwUpMTWbv2JDJnjK5I7UAoioLbF8IfCmOzWLBaTFjMJhITrIMGAn22kZeXx/Tp8Zc/++u9qOZ6R5tyG4tMS5IkDh48SGdn55jq5401kUiEffv2EQqFmDJlCm1tbVx33XXIsozb7ebaa6/lG9/4BgsXLhyTACVJEoWFhfzrX/8iJyeHFStW8Pzzz7NgwQLtNt/97ndZvnw51113HXv37uW88847qubeMYQhFjsYzc3NbNmyhZKSEhYuXEgwGKS+vl4LTHa7nSlTotbb6iLizLwZzMybQek50d8RCoRprmml8cCRoOVqc0/sA6OnJCeFMNsUcuZOx2KxIEkyoWCEoD/cUyKMIOqs4LsOt444QJlM5p7F2yM9iAMfd7JgeZhwuF17bh0OB6mpqVq5JSMj+rFsaVRqSJJk2to81Bxs4dNPq+jqNmGzpfYJsC5PgD889R6rz5jPypPmjsh+PR4EQSDVaSdVl7UpikI4Imkivuq/Zl0J1ePxsH//flJTU1mxYsWQsw2bzca0adM0XTeIDVpNTU3alNtgQUt/3OpjijfTUns0M2fOHDf9vLFAVYPRXyh0dXXhdDr5+te/zurVq/n000956KGHOPXUU/nOd74z6sewfft28vPzycvLA2Dt2rW8/PLLMQFKXWOBqGq9qpF4onBCZ1AtLS08+eST7Ny5k4qKCiRJwu/3c+2113LRRReRkZGhlQNcLpd21aqeWNUTQG98Lj+N1c00VDfT1BO0At7guDymqE5agHA4FJfEkihKR6YG/RFySgvAOnINt95My0zh2z/5ElabRRMgVZ9X1Z+od9+ltraWrq4uCgoKSE9PJxKRaGlxa6XBxqZu2tu92o5W5vRUVp9RRGFh30m+8UbdPZNEiZqa6Mh1b4misUAdzVY/1H0ifdDqz3dssEwrEokOpITDYebPnz/h+nnDJRwOs3//fgRBoKioCJvNRiAQ4K677mLHjh08+uijMQFiLPnrX//Ka6+9xhNPPAHAs88+y7Zt29i8ebN2m6amJs455xy6urrw+Xy88cYblJaWjsvxjTFGiS9e3nnnHTZs2MB5553HsmXL+OSTTygvL6e5uZm8vDxKS0spLS3V5I08Hg8ulwu32x3th+iUnQeyI+huddFY1RO0DrTQdKB1VCf+osuOYfwBv+YxNZyT9Kz5WXz9+q/QXNdJ0+FOGg910Hy4k9AAzrxDoXBxNv995Wn9OtWqpnoul4uWlhZcLhc2m42pU6dqFwT9LcCGQiJNza6eXlY0aFmtZkqW57J4UTaJiWPTOxgMRVFoaWnh4MGD5ObmHlVWZqyDqSo3pF+CtdvtfZZg+0NRFJqbm6mtrR1wjP9YQP841GEORVH48MMPuemmm7j88stZv379uPbR4glQDzzwAIqi8KMf/YgPP/yQq666is8///yYzVx1GAEqXmpra3E4HDEupBA9aVZVVbF9+3a2b9/Ozp07CQQCLFiwgNLSUsrKyli0aBGyLGsBy+12I0lSjBxOcnJynxeUJMm013X0ZFnNNFS30FbXjjKMEfJIJKLt2fR3Eh8qF9z4FYpPLtQ+VxSFzlY3jYc6aTrcQdOhDlrqu4a1o7WwLJc1607p9ySnmj06HA7mzZuH2Wzuo9qgTmKpQau/CTe/P0xzs4vmFjcJCRaSk+1kTHOSnj4+S5U+n4/9+/fjcDjIz8/vc8Gip7/331gHAL1yg/oRCoWw2+0xF1qyLLNv3z7sdjsFBQUDPo6J1sgbjGAwyL59+0hISNAeh9fr5ec//zn79u3jscceo6CgYNyP68MPP+SOO+7g9ddfB+BXv/oVALfccot2m4ULF/Laa69pVhl5eXl89NFHfc5VxyBGgBoLwuEwn332Gdu2bWP79u3s3r0bq9XK8uXLKSkpoaysjHnz5hEMBrWgpfaw9CfW/vYyIqEIzQfbtPJgY3Uz3S2uAY9FkiR8Pj+KIpOUlDRqV3+pGSlc++srsNoG/n2SKNHW7KLpUAdNPYGrrckV145W/sIs1qw7Bbsjmt1EIhEOHDiA1+ulsLDwqGUw/fiwWna1Wq19yq69n1uvN0ggEMFqNWOxmDGbBez2wQcbhoJ+eKCoqChG12+4jNc4uV7Y1eVy0dbWRjAYJCUlhalTp2qv3aH4Pk100NLvLRYUFDB16lQUReGdd97hlltu4ZprruHaa6+dsGxEFEUKCwt58803yc7OZsWKFTz33HMsXLhQu82Xv/xlLrnkEr71rW+xb98+zjrrLBoaGib8uR0FjAA1HiiKgsfjYefOnWzbto3y8nKqqqqYNm2aVhosKytj+vTpMSdWn88Xc2JNTU3ttzfgdwdiBjAaq5vxufxD6jMNh5O/XsZZl39hSD8TCYu01HfRdLiDxp7A1dnm6fe2UzKS+erlq8AWoq6ujjlz5pCZmTmsx6EOC6gXBPq+i/r89l4cVRSFSJ/BBqFfQd94UBXH9Queo4mapfR+v472/aj28VOnTmXOnDkxgxhut1uz0NBnWgMFrd4utmNxvAMRCATYt2+flsVaLBbcbjc//elPqaur47HHHmPOnDnjcixHY+vWrVx//fVIksSVV17Jrbfeym233UZZWRlr1qxh7969fOc739GEiu+9917OOeeciT7s0cAIUBOFWu/evn27FrRUXT81YJWUlGC322P6WcFgUHvzqyfW3oaGTU1N7P1kP+aQlYhbormmlaYDrURCI+8R9eaSjV+noDRvRL8j6A9Hy4KH1fJgJ+5uP2Ikgtfno7h0Fmu+eTpTp4/emHjvEpbL5dJOrPpMq79eYX8c7aQaCASoqKjAbDZTWFg4rgoKo1la0+vnFRcXD6gxp/d9Uj96O+z299yqPwtjnwnW1dXR2NhIUVER6enpKIrCv/71L2677TY2bNjAt7/97eOhh3OsYwSoyYQsy1RXV2ulQX0/Sy0NLlq0CEALWC6XS3PitdlsdHZ2kpaWxrx582KuWmVZpr2+k8YDLTRWRbOs1sPtw9YEVLEnJXD1pstIG8Udo1AoxGef7KG5rgu7KYXOFi8t9V3kFs5g6cnzyC0Ymyb8QCfWpKSkmF5h7zLpQO8PRVE4dOgQLS0tFBYWMmVKnP5XkxBVP2/27NlkZWUN+fnXO+yqVQL1udUPYhytFzca+Hw+9u3bR2pqKnl5eZjNZjo7O7nllltwuVw88sgjx4RJ3wmCEaAmO/p+Vnl5Obt378ZiscT0s0wmE//4xz84+eSTSUpK0haL1Te96knUp58VFmmpbdPKgo3VLXQ2dQ35GFMzUvifOy4ibfrIxqNlWdYssufNm6cJ7ELPlGOHl6bDnfjcQZJTE3GmJjIjJ/2ofbCRoh93Vz9kWY4ZcHE6nX00/jo6OqisrGTGjBnMmTMHk8k06QcF+iMUCrF//35MJtOoZ3/6oKV+iKKoXRCo+2/xDJAM9ryqr62Wlhbmz59PamoqiqKwZcsW7rzzTjZu3Mill15qZE2TCyNAHWvo+1n/+c9/eOGFF2hra2PZsmUsXbqU0tJSVqxYwfTp07WRbFWyRRXHVEtY/Q0KBLxBmmqOZFkN1c34uvtX9daTMi2Zb/70fKZlDy9L6OjooKqqiunTp5ObmxuXqKssy7g6fJhMAharGbPFjNkan+38SFDH3fWqDRB11nU4HHR2diIIQp9doN4n0/EoZw0XRVGor6/XhgemTZs2buU3/QWBx+PRKgR6NfKhDPuoRoJ6z6m2tjZ+8pOfoCgKmzdvZsaMGWP2mAyGjRGgjlUkSeKMM87gkksu4ZprrqGjo0MbdS8vL6epqSmmn7V8+XISExNjhjDUXRd90OrdzFYUBU+HV9vNaqhqpulAM+F+dp4sNgtfuvqLLF29IO6TWCAQoLKyEkEQKCwsHLEKtCRF1eVVZ1j9cMNYovZnmpubSUpKQhTFGOHR1NTUAQVd9YMNkyFYeb1erQymjvKrTEQWKMtyn0xLluU+mVbvoCXLMgcPHqSjo4Pi4mKSk5NRFIWXXnqJ++67j9tuu40LL7xwUjznBv1iBKhjGVEUB7yS7K+f5ff7++xnATGDAqIoahJDas+ldzajKArtDZ00Vbdoo+4ttW1aP2vu4tl88fLTmJk38FWpavjY3t6uORGPFWM9IaZOtU2ZMiXG0kMUxZiTqjqVOVgW2/uYx/LY9YxEP2+sJwd7I8tyn0xLX3o1mUzU19fHmDo2Nzdz44034nQ6+fWvfx0jCTXaZB9KQgAAGEtJREFUDCbwCvDiiy9yxx13IAgCS5cu5bnnnhuz4zlGMQLUiUQ4HGb37t0x+1kWi4Vly5Zp/ayCgoKYXRePx4OiKDGZQH+LvmJEpPVQe4x8U9r0FErPXUresjkxSuWtra3U1NRo49YTXfcfbvYSiUSorq7G7/czf/78uJxTe49kBwKBGJkhdZVgtI4xXvT6ebNmzRrR36S/YDUemZcq4FpTU4PH48Fms7Fr1y7eeecd0tPT+fDDD/nVr3415llTPAKvVVVVXHzxxbz11lukp6fT2tp6PCzWjjZGgDqR6b2ftWPHDs3cT93PUvtZPp9P62epag36TKA/2aSgL0TzwRa6W92kTE0Gi0Kbu5XkVCf5+fljZk8wXOI9iaqj/IcOHRrRbpaKekGgV2yId49Iz3D3w6qqqsZcP288FnW7urqoqKggKyuLWbNmIQgCBw4c4Oabb0YURbKysti3bx+yLPPoo4+OmV5dPOoPN910E4WFhVx99dVjcgzHCYaa+YmMIAikpKRw5plncuaZZwJH9OHU/aynnnqKxsbGPvtZDodD62c1NzdrmYB+qdielMCcRbOJRCLU1NTgdrvJnTWblJRUBEVAkuQxVxYfCvFYYagSRU6nk7KyslEZi7bb7djtdu0KWj/u3tnZSW1tbcy4u/oxUHk3nsCl150bqq3HcBjoGHqrpQ9026MhiiLV1dX4fD6WLl2qGYo+9dRTPP7449x3332cc8452u8NhUIjfDRHp6GhQZMdAsjJyWHbtm0xt6msrATg1FNPRZIk7rjjDr70pS+N6XEdr5xQASqe2vHxjCAIZGZmsmbNGtasWQPE9rP++c9/cvfdd8f0s0pLS1m+fDkQ7Wd1d3dz+PBhwuEwJpOJYDBIVlYWy5Yt6/eELolSz8kq+vkRw8TJgyiK1NTU4HK5YqSWxqJ0pdq2OBwOMjMztftRey6tra1UV1fH9FzUQQGz2RxzPPogoOL3+6moqMBut49akB0OvZ83NUgNJVCp05+zZs2iqKgIQRCora3lhz/8IUVFRbz//vskJyfH/Mx4LkoPhOrO+/bbb1NfX8/pp5/O7t27SUtLm+hDO+Y4YQKUJEl8//vfj6kdr1mzZtyk9Scr6g5MYWEh//M//wPE9rOefvppPvvss5j9LIvFwt/+9jduu+02srKy8Pl8fPzxxyiKgtPp1DItp9PZR7lcEiXCwXDMOLY1DrO/sUDfM5s1axYFBQUTchyCIOB0OnE6nZrfj37cvbGxMWbcXQ1aTqdT6yfJssyhQ4dobm7WFBTUx6jex0QT7zFEIhHNcXjZsmXY7XYkSeL3v/89zz77LA888ACrV6+ekMeUnZ1NXV2d9nl9fX2f5d+cnBxWrlyJ1Wpl7ty5FBYWUlVVxYoVK8b7cI95TpgeVDy1Y4P+UftZb775JnfffTfNzc2aNba+n5WZmamdVF0uV0w/Sy0N9tfPioRF1BRLzVqsCWN75e/3+9m/f7+mcD3Untl4T7ZB9CKrt7q7yWQiISEBt9tNRkYGBQUF/U5m9j7WybpYrKpa6Pt/lZWVbNiwgZKSEu666y4cDseEHV88Aq+vvfYazz//PM888wzt7e0sX76cTz75hKlTp07YcU9CjB6Unnhqxwb9o/azXn75ZTZu3Mj5558PENPPevrpp2lqamLOnDkx/aykpCRNb7C1tVWzbT+akCvQR1tQMAlYRmFJVz8CX1RUNOyyy0B9l7E86ZvNZtLS0rRjFkWRyspK3G43M2bMIBgMsn37dm3cXf2IxxtsojOtcDhMRUUFiqJQWlqKzWZDFEU2b97MSy+9xG9+8xtOPfXUCTk2PRaLhc2bN3PuuedqAq8LFy6MEXg999xz+ec//8mCBQswm83cd999RnAaJidMBhWPOZjByJBlmQMHDmij7jt27MDn88XsZy1ZsgSI3c8Kh8MxFvD9DQkoioIYFo9YvitKtJ/Vj/nhQLS3t1NdXT0q49YTjWpZ3p9+3mDj7gMZFPa3UzbWQVdfZp03b542TLJ3717Wr1/PGWecwe233z7iJW+DSYeRQemJp3ZsMDJMJhMFBQUUFBRw+eWXA7H9rGeeeYbPPvsMs9nM8uXLWb58OWVlZSxdulRTH9cPCej7LcnJyX3KfpIkR8uDEC0RClFZpD4j8cEgFRUVCIKg9TQmkpEsF6uPxWQyaZlGb2w2G9OmTYtZVtWPu9fX18c97t77eIdzzAOhagFaLBZtoCMcDvPggw/y6quv8rvf/Y6ysrJRuS+DY5MTJoOKp3ZsMPYoioLX643xz6qsrGTKlCl9+ln6/SyPx4PJZIrpZ/UnLySJkmaaKMsy9XV1tHW0aYZ1xyqqfl5DQwP5+fkjVkpQDQr1TtDxjLuPhgqGftdM1QIE+PTTT9mwYQPnnXce//u//zvpdukMRhVjUbc3/ZmDGUw8+v0sVW+wsbGR3NzcmH6W0+ns46Zrs9n6yAtBdLGzsrKSjIwMsrOyMZmOlAIFgVHpZ40XR9PPG00GU3fXj7sP9PN6+gtcgUCA/fv3azbyFouFUCjEpk2bePfdd3n00Ue1MrDBcY0RoCYbdXV1rFu3jpaWFgRB4Lvf/S4bNmygs7OTSy65hNraWubMmcOLL76ojQmfqPTuZ+3cuROfz0dxcXFMP0sQhD5uupIkYTKZmDt3LhkZGf0aE4oRSd/OmpT7WXr9vOLiYpxO54SIufbOZGHgcfeB0GeAev+s8vJybrzxRi666CJ+9KMfTdjelsG4YwSoyUZTUxNNTU2UlJTg8XgoLS3l73//O08//TRTpkxh48aN3HPPPXR1dbFp06aJPtxJRyQSidEb/OyzzzCZTCxfvpxly5ZRU1NDe3s7t9xyi2bx7Xa7kSQpxuMpOTm5zwlVURQkUYr5mtnSt581XqhLqnppn8nCQOPu+tKg3qPM7/ezb98+nM6oDJbZbMbv93P33Xezc+dOHn30UYqLiyf4URmMM0aAmux8/etf5wc/+AE/+MEPePvtt5k5cyZNTU2sXr2aioqKiT68SY/az3r++ef51a9+xdSpU5EkidTUVEpLSykpKdH6WYFAICYLEASB5ORkrTTYn+mjJMkoclTFXf2eyWwa02ARDoeprKwkEomMWD9vPHed+lN3t1gsCIJAMBhk7ty5zJw5E0EQ+OCDD7jppptYt24d69evH7OSpUq8CjIvvfQSF154IeXl5cZwxthjBKjJTG1tLaeffjqff/45s2fPpru7G4ieVNLT07XPDY5OIBDgsssu4xe/+AWLFi3SxpbV/azy8nIaGhr67GclJyfH9LNUuwy93mBCQkK/Qxi9Gcqo+0DoBwdGWz9PH6jGK2h5vV727NlDYmIiSUlJlJeXc9ddd2Gz2QgEAtx8882sWbNmzCdp41Efh6jx4Ve+8hXC4TCbN28elQDlcrloaWmhsLBwxL/rOMQYM5+seL1eLrjgAn7961/38eUZDwO+44nExET+9re/aZ8LgsCMGTP42te+xte+9jUgtp/1xhtvcM899+D1emP6WcuWLcNsNmtZVmNjI8FgUBvFVgPXQHqDegSTMKQdK1XVIjExcUz08/Svp/GwxTh06BBtbW0UFxeTkpKCoijU1dXhdDq59NJLKS4uZufOnVx99dWsW7eOSy+9dMyOZ/v27eTn55OXlwfA2rVrefnll/sEqJ/97GfcfPPN3HfffaNyvzt27OC5555j/vz5FBYWTlrljsmOEaDGmUgkwgUXXMBll12mKTLMmDGDpqYmrcRneMeMLv3tZ+n7WX/84x9j+lmqf9bixYuJRCK4XC46OjqoqanRLMrVgJWcnNwng+rTzxIETKa+Fx7qyby1tXVEqhaTBdV+PSMjg7KyMkwmEy6Xi5/97GfU19fzyiuvkJubC0TL2+NBPAoyu3btoq6ujq985SsjDlDt7e184xvfYNq0aezcuZO1a9cCk0ML8VjECFDjiKIoXHXVVRQXF3PjjTdqX1+zZg3PPPMMGzdu5Jlnnhm3N++JjNVqpaSkhJKSEq677rqY/azt27ezadMmKioqSE9P77Ofpdpl9BZxVZ2Kk5KS+g9aktrPgu7ubqqqqsjIyGDFihXHtKqFLMvU1NTQ1dXFggULcDqdKIrC66+/zu23387111/Pt771rUn5GGVZ5sYbb+Tpp58eld934MABzj77bG6//Xa+973vceDAAe1+JuPjn+wYPahx5L333uMLX/gCixcv1l6sd999NytXruTiiy/m8OHD5Obm8uKLL46pTbpBfAzWz1IHMVJSUvB6vVp5UB0Q6M/+Xe9vVFRU1Ef49Fg7iXV3d1NRUaHZrwuCQGdnJxs3bsTtdvPII49MqGLLYCLRLpeLefPm4XQ6AWhubmbKlCm88sorw+pD3X333ezevZvnn3+eQCBASUkJL730klZSNEp9GsaQhEH8SJJEWVkZ2dnZbNmyhYMHD7J27Vo6OjooLS3l2WefNTb7OZIt6PUGe/ezlixZgtlsjtEbDAaDCIJAKBQiMzOTOXPmDGj/3lsKaTKe0CRJorq6WnvsDocDRVHYsmULd955Jxs3buTSSy+d8IA7VAWZ1atXc//99w97SOLjjz/m8ccfZ/369RQXF7NkyRLsdjunnXYad91115i5Gh+DGEMSBvHz0EMPUVxcjNvtBuDmm2/mhhtuYO3atVx77bU8+eSTXHfddRN8lBOPyWQiPz+f/Px8LrvsMqBvP2v37t2a7l9paSnZ2dk8+uij3HjjjeTn5+P3+9m9e7cmLaQXye1tSghHgtZ4Djscjc7OTiorK8nOzqawsBBBEGhra+PHP/4xgiDwxhtvMGPGjAk7Pj3xqI+PJg6Hg8TERP7zn/8AcPbZZ1NSUsIXv/hFIzgNAyODMqC+vp4rrriCW2+9lQceeIB//OMfZGRk0NzcjMVi6VMmMTg6aj9r+/btPPzww7z33nsUFRVhsVi00mBZWRlZWVlaP8vlcuHxeFAURVNpUPtZ/S0V92Y8ApbqFBsIBCguLtbs11966SXuv/9+br/9di644IJJmfGNJ3/5y194/fXX+cc//sH999/PFVdcARjlvV4YGZRBfFx//fXce++9WsO/o6ODtLQ0TSg0JyeHhoaGiTzEYwp1CXjXrl0UFxfz3HPPkZiYSGtrK+Xl5Wzbto1nn32W+vp6cnNzKSsri+lnqdJChw4dijF9VDOtgfydxtJEsb29naqqKnJzc5k/fz6CINDc3MwNN9xASkoK//73v0csYHu8cMkll/C1r32Ne++9V3tOjOA0PIwAdYKzZcsWpk+fTmlpKW+//fZEH85xhVryUpkxYwZf/epX+epXvwrE9rPefPNNNm3ahNfrZf78+VqWtXTpUsxms7ZU3NzcrPk76ZeKbTZbv6VBleGeHCORCBUVFUiSRElJCQkJCciyzJ///Gc2b97MXXfdxVe/+lXj5NsLh8OBw+FAkqR+y7YG8WEEqBOc999/n1deeYWtW7dqnkEbNmygu7sbURSxWCyGd9YwGeykNFA/6/PPP2fbtm38+c9/5ic/+Qkmk0nrZ5WVlbFo0SJNWqi7u5vDhw8TDoc1qwxVb7C3VQYcuZKPx0FXNUXUK1vU19ezfv16cnJyePfdd4/53a2xZqxlnI53jB6Ugcbbb7/N/fffz5YtW7jooou44IILtCGJJUuW8L3vfW+iD/GEo/d+Vnl5ORUVFaSlpWkBS+1n9fZ3Uk0f1UwrHtVxiOoB7t+/H0EQKCoqwmazIcsyTz/9NL///e+59957Oeecc4yswGAkGGPmBkNDH6BqampYu3YtnZ2dLF++nD/96U/9jkUbjD+KotDW1hazn6XvZ5WUlFBaWkpqaiper1cbwtD3s9QPvemjoig0NzdTW1tLfn4+GRkZABw8eJAf/vCHFBcXc88995CcnDyRD9/g+MAIUAbHNt3d3Vx99dV8/vnnCILAH/7wB4qKigzvrH7Q97PKy8vZsWMHHo+nTz/LYrHg8Xi0TMvv95OQkIDD4aC7u5ukpCTmz5+P1WpFkiQef/xx/vSnP/Hggw9yxhlnjHnWNJjy+AMPPMATTzyBxWIhIyODP/zhD5p8ksExhRGgDI5trrjiCr7whS9w9dVXEw6HNQ8hwzsrPvT9rPLycj755BNMJhNLly7VglZBQQFPPvkk+fn5ZGZmEg6Huf3224lEInR0dLBo0SIefvjhcdlrikd5/N///jcrV67E4XDwyCOP8Pbbb/OXv/xlzI/NYNQxApTBsYvL5dJMCPVX7UVFRYZ31jDR97PKy8v597//zUcffURBQQErV65k5cqVLF26lJdffpmtW7dy1lln4XK52LlzJ1arlbfeemtMM6jBZIl68/HHH/ODH/yA999/f8yOyWDMMPagDI5dDh48SEZGBt/+9rf59NNPKS0t5aGHHqKlpYWZM2cCkJmZSUtLywQf6bGDup+1evVqRFHkhRde4OWXX6aoqEjrZ23atIni4mLefPNN7Ha79rOSJI15eS8e5XE9Tz75JF/+8pfH9JgMJhYjQBlMSkRRZNeuXTz88MOsXLmSDRs2cM8998TcZrLq1B0LnHTSSbz33nua/I66n/XLX/6y39tPtnHpP/3pT+zYsYN33nlnog/FYAw5tqSTDU4YcnJyyMnJYeXKlQBceOGF7Nq1S/POAgzvrBGgKlJMJrKzs6mrq9M+H2j/7o033uCuu+7ilVdeMSZLj3OMAGUwKcnMzGTWrFlaf+nNN99kwYIFmncWYHhnHWesWLGCqqoqDh48SDgc5oUXXugj5vrxxx9zzTXX8MorrxgXJycAxpCEwaTlk08+0Sb48vLyeOqpp5Bl2fDOOo7ZunUr119/vaY8fuutt8Yoj//Xf/0Xu3fv1vqQs2fP5pVXXpngozYYBsYUn8HYUF5ezlVXXcX27duRJImTTjqJv/zlLyxatGiiD21cePDBB3niiScQBIHFixfz1FNP0dTUZPhnGRjEjxGgDMaOn/70pwSDQQKBADk5OQOOAh9vNDQ0cNppp7F3714SExO5+OKLOe+889i6dSvnn3++Jg21dOlSwz/LwGBg4gpQRg/KYFjcdttt/Otf/2LHjh3cdNNNE30444ooigQCAURRxO/3M3PmTN566y0uvPBCILpg/Pe//32Cj9LA4NjHCFAGw6KjowOv14vH4yEYDE704Ywb2dnZ/PjHP2b27NnMnDmT1NRUSktLDf8sA4MxwAhQBsPimmuu4Ze//CWXXXYZN99880QfzrjR1dXFyy+/zMGDB2lsbMTn8/Haa69N9GEZGByXGIu6BkPmj3/8I1arlW9+85tIksQpp5zCW2+9xRe/+MWJPrQx54033mDu3Lma0vf555/P+++/b/hnGRiMAUYGZTBk1q1bx0svvQREFQa2bdt2QgQniI41f/TRR/j9fhRF0fazzjzzTP76178CJ85+1muvvUZRURH5+fl9VD4AQqEQl1xyCfn5+axcuZLa2trxP0iDYxojQBkYDIGVK1dy4YUXUlJSwuLFi5Flme9+97ts2rSJBx54gPz8fDo6Orjqqqsm+lDHFEmS+P73v8+rr77K3r17ef7559m7d2/MbZ588knS09Oprq7mhhtuOKFKwQajgzFmbmBgMGTiUR4/99xzueOOOzj55JMRRZHMzEza2toM/UQDMMbMDQxODK688kqmT58esyjd2dnJ2WefTUFBAWeffTZdXV1A1HJj/fr15Ofns2TJEnbt2jWs++xPebz35KL+NhaLhdTUVDo6OoZ1fwYnJkaAMjA4xvnWt77VZ5Lwnnvu4ayzzqKqqoqzzjpL6xG9+uqrVFVVUVVVxeOPP24sExtMaoZa4jMwMJiECIIwB9iiKMqins8rgNWKojQJgjATeFtRlCJBEB7r+f/zvW83xPs7GbhDUZRzez6/BUBRlF/pbvN6z20+FATBAjQDGYpx0jGIEyODMjA4PpmhCzrNgOrZng3U6W5X3/O1oVIOFAiCMFcQBBuwFuit2voKcEXP/y8E3jKCk8FQMPagDAyOcxRFUQRBGNXAoCiKKAjCD4DXATPwB0VR9giC8Atgh6IorwBPAs8KglANdBINYgYGcWMEKAOD45MWQRBm6kp8rT1fbwBm6W6X0/O1IaMoylZga6+v3ab7fxC4aDi/28AAjBKfgcHxir68dgXwsu7r64QoqwDXUPtPBgbjhTEkYWBwjCMIwvPAamAa0ALcDvwdeBGYDRwCLlYUpVOILiFtBr4E+IFvK4qyYyKO28BgMIwAZWBgYGAwKTFKfAYGBgYGkxIjQBkYGBgYTEqMAGVgYGBgMCkxApSBgYGBwaTk/wd1sUcynvMIGwAAAABJRU5ErkJggg==\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_barycenter_lp_vs_entropic.ipynb b/notebooks/plot_barycenter_lp_vs_entropic.ipynb new file mode 100644 index 0000000..9c8e83e --- /dev/null +++ b/notebooks/plot_barycenter_lp_vs_entropic.ipynb @@ -0,0 +1,497 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "# 1D Wasserstein barycenter comparison between exact LP and entropic regularization\n", + "\n", + "\n", + "This example illustrates the computation of regularized Wasserstein Barycenter\n", + "as proposed in [3] and exact LP barycenters using standard LP solver.\n", + "\n", + "It reproduces approximately Figure 3.1 and 3.2 from the following paper:\n", + "Cuturi, M., & Peyré, G. (2016). A smoothed dual approach for variational\n", + "Wasserstein problems. SIAM Journal on Imaging Sciences, 9(1), 320-343.\n", + "\n", + "[3] Benamou, J. D., Carlier, G., Cuturi, M., Nenna, L., & Peyré, G. (2015).\n", + "Iterative Bregman projections for regularized transportation problems\n", + "SIAM Journal on Scientific Computing, 37(2), A1111-A1138.\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", + "# necessary for 3d plot even if not used\n", + "from mpl_toolkits.mplot3d import Axes3D # noqa\n", + "from matplotlib.collections import PolyCollection # noqa\n", + "\n", + "#import ot.lp.cvx as cvx" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Gaussian Data\n", + "-------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Elapsed time : 0.010422945022583008 s\n", + "Primal Feasibility Dual Feasibility Duality Gap Step Path Parameter Objective \n", + "1.0 1.0 1.0 - 1.0 1700.336700337 \n", + "0.006776453137632 0.006776453137633 0.006776453137633 0.9932238647293 0.006776453137633 125.6700527543 \n", + "0.004018712867874 0.004018712867874 0.004018712867874 0.4301142633 0.004018712867874 12.26594150093 \n", + "0.001172775061627 0.001172775061627 0.001172775061627 0.7599932455029 0.001172775061627 0.3378536968897 \n", + "0.0004375137005385 0.0004375137005385 0.0004375137005385 0.6422331807989 0.0004375137005385 0.1468420566358 \n", + "0.000232669046734 0.0002326690467341 0.000232669046734 0.5016999460893 0.000232669046734 0.09381703231432 \n", + "7.430121674303e-05 7.430121674303e-05 7.430121674303e-05 0.7035962305812 7.430121674303e-05 0.0577787025717 \n", + "5.321227838876e-05 5.321227838875e-05 5.321227838876e-05 0.308784186441 5.321227838876e-05 0.05266249477203 \n", + "1.990900379199e-05 1.990900379196e-05 1.990900379199e-05 0.6520472013244 1.990900379199e-05 0.04526054405519 \n", + "6.305442046799e-06 6.30544204682e-06 6.3054420468e-06 0.7073953304075 6.305442046798e-06 0.04237597591383 \n", + "2.290148391577e-06 2.290148391582e-06 2.290148391578e-06 0.6941812711492 2.29014839159e-06 0.041522849321 \n", + "1.182864875387e-06 1.182864875406e-06 1.182864875427e-06 0.508455204675 1.182864875445e-06 0.04129461872827 \n", + "3.626786381529e-07 3.626786382468e-07 3.626786382923e-07 0.7101651572101 3.62678638267e-07 0.04113032448923 \n", + "1.539754244902e-07 1.539754249276e-07 1.539754249356e-07 0.6279322066282 1.539754253892e-07 0.04108867636379 \n", + "5.193221323143e-08 5.193221463044e-08 5.193221462729e-08 0.6843453436759 5.193221708199e-08 0.04106859618414 \n", + "1.888205054507e-08 1.888204779723e-08 1.88820477688e-08 0.6673444085651 1.888205650952e-08 0.041062141752 \n", + "5.676855206925e-09 5.676854518888e-09 5.676854517651e-09 0.7281705804232 5.676885442702e-09 0.04105958648713 \n", + "3.501157668218e-09 3.501150243546e-09 3.501150216347e-09 0.414020345194 3.501164437194e-09 0.04105916265261 \n", + "1.110594251499e-09 1.110590786827e-09 1.11059083379e-09 0.6998954759911 1.110636623476e-09 0.04105870073485 \n", + "5.770971626386e-10 5.772456113791e-10 5.772456200156e-10 0.4999769658132 5.77013379477e-10 0.04105859769135 \n", + "1.535218204536e-10 1.536993317032e-10 1.536992771966e-10 0.7516471627141 1.536205005991e-10 0.04105851679958 \n", + "6.724209350756e-11 6.739211232927e-11 6.739210470901e-11 0.5944802416166 6.735465384341e-11 0.04105850033766 \n", + "1.743382199199e-11 1.736445896691e-11 1.736448490761e-11 0.7573407808104 1.734254328931e-11 0.04105849088824 \n", + "Optimization terminated successfully.\n", + "Elapsed time : 2.927520990371704 s\n" + ] + }, + { + "data": { + "image/png": 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1RpNiiFpTUkG028XoAUlOhwLAMYOTEbHGTWpSjCCNtbD4j7D4cfDWQVQc9BsHx1wMdRVWgtz0DmAgYySc9WsYfiY4NK5Wqc5oUgxRq4srGDMwiWhPcNSAJ8ZGkZeZoDPbRAqfD9a+Ah89ANV7YeyFcNJt0Hc0uNxfPbahBrZ9BB/eD3+/1CoxnvUb6DfGkdCVOpLg+ERVXeJt9rGupNLxQfttjbc72xijK2aENW8DvD4b/vUDSBwA310Alz4H/cd9PSECxCTAmFlw01I4+0HYvQKePAU2/LPXQ1eqM5oUQ9DWAzXUNTUHXVKckJXCwdpGSsrrnA5F9ZSGavj7t2DDGzDjPrj+I8ie5t9rPdFw/E3wo1UwcBL84zpY/lTPxqtUF2lSDEH/XRkj+JIi6IoZYau2DOacBzs+hVl/hpNuBddRfITEp8PV/4QRZ8M7P4OFD4LWLqggoUkxBK0priC5TxS56XFOh/IVI/snEuNxabtiOKophWfOhgMb4fKXYOKV3TtfdBxc9hJMuBL+/RAsuCswcSrVTdrRJgStLq5gfFaKYytjdCTK7WLcoGQtKYYbbyO89h2oLLFKeDknBOa8bg/MegJiEuE/T0D6MJgyOzDnVuooaUkxxNQ2eNmyv5oJg51ZVLgz4wensH5PJU3NPqdDUYFgDMy/DYqWWAksUAmxhQic/VsYfha8e7tVNauUgzQphpj1uyvxGYJmJpu2JmSnUN/kY8t+XTEjLCz7P1g5B076GRxzSc9cw+WGi5+CtKFWibR8Z89cRyk/aFIMMWtKgmsmm7Za5mLVKtQwsH0RvHcHjDwXTru7Z68VmwxXvALGBy9fYfVyVcoBmhRDzOriCrLS+pCeEON0KO3KSutDWny0drYJdTUHYO53IWMEXPTk0fUy7ar0YdZ4x9LN8M5tPX89pdqhSTHErCmuDNpSIlgrZowfrJ1tQpox8NZPrJloLn3O6gjTW4adBiffZs2Ws/Ht3ruuUjZNiiHkQHU9uyvqgm7Qflvjs1LYeqCGmgav06Goo7H2Vdj8Dsy4B/qO6v3rn3SbNYn42z+xxkYq1Ys0KYaQNcXWIr7BnhQnZKVgDKzTRYdDT+VumH87ZB8P025yJgZPNFz4V6ivhLd/qgP7Va/SpBhC1hRX4HYJYwcG53CMFuO1s01oMgbm3Qy+Jrjgz+3PY9pb+o2FU++EjfNg/evOxaEijl9JUURmishmESkUkTva2R8jIq/a+5eKSG6b/dkiUiMi2nreDWtKKhjZL5E+0Q5+WPkhNT6anPQ47WwTalY8Z62JeNavrOERTjvhxzB4ijUVXPV+p6NREaLTpCgibuAJ4BxgDHCFiLRd82U2UG6MyQMeAx5us/9R4N3uhxu5fD7D6uKKoB2f2NYEe8UMFSJqy+DD+yD3JMgPklll3B644C/QdBg+uMfpaFSE8KekOBUoNMZsN8Y0Aq8As9ocMwuYYz+eC8wQew4yEbkA2AFsCEzIkWnHwVqq671fjgMMduMHp7Cvqp59lfVOh6L88eF91oLB3/hDcC0AnDEcpt9idf7ZudjpaFQE8CcpDgKKWz0vsbe1e4wxxgtUAukikgD8HPjlkS4gIjeISIGIFJSWlvobe0RZXRScK2N0pCXOlskGVBArXgarXoTjfwiZI52O5utOvBWSs63p5pqbnI5Ghbme7mhzP/CYMabmSAcZY540xuQbY/IzMzN7OKTQtKakgvhoN3l9E5wOxS9jBybhcYlWoQY7X7PVZpc4EE6+3elo2hcdB+c8BAe+gGVPOh2NCnP+rJKxG8hq9Xywva29Y0pExAMkAweB44BLROR3QArgE5F6Y8yfuh15hFlZVM6xg1Nwu4KoausIYqPcjBmYxMpd5U6Hoo6k4BnYt9YepB/EX7hGnmtNGr7wQRh3MST2dzoiFab8KSkuB4aLyBARiQYuB+a1OWYecI39+BLgY2M5yRiTa4zJBf4X+K0mxK6rbfCycW81+bmpTofSJZNzUllTUqErZgSrmlL4+Fcw9FQYc4HT0RyZCMx8CJob4P0enodVRbROk6LdRngzsADYCLxmjNkgIg+IyPn2YU9jtSEWArcCXxu2oY7emuIKmn2GSTmhlxTrm3x8safK6VBUexb91upcc84jwdW5piPpw6xON+v+AcXLnY5GhSm/Fhk2xswH5rfZdm+rx/XApZ2c4/6jiE8BK+wqyEnZoZcUwYo/VDoIRYwDm6xxiVO+B5kjnI7Gf9N/AiufhwW/gNnvh0YyVyFFZ7QJAQW7yhnRL4HkPlFOh9IlA5L7MCilz5dJXQWRD+6B6EQ45edOR9I1MQlw+t1Qsgy++JfT0agwpEkxyPl8hpVF5UzOSXM6lKMyKSeVgl2HMDp/ZfDYthC2vm+tRhGf7nQ0XTfhSug3Dj64D7wNTkejwowmxSC39UAN1fXeL6siQ01+Tir7qxrYXVHndCgKrCEY798NKTlw3I1OR3N0XG5rKrqKXTpEQwWcJsUg11L1mB+iSbF1u6IKAqtfgv3r4Yz7wROcC1X7ZdjpkHcm/PsRqD3odDQqjGhSDHIrdpWTbk+wHYpG9U8kLtqt4xWDQWMtfPwbGDwVxl7odDTdd9avoLEaPvmd05GoMKJJMcit2HWIyTmpSIj2svO4XUzISqFAk6LzPv8z1OyDs34dHr02+46GiVfD8qfh0A6no1FhQpNiECuraWDnwcMh257YIj8nlY17q6ht8DodSuSqLYPFj8Oob0L2cU5HEzin3gkuD3z8a6cjUWFCk2IQ+7I9McRmsmlrUk4qPqOLDjvqk99DUy3MuM/pSAIraQAcfxOsnwt7VjsdjQoDmhSD2Mpd5US7XYwdmOx0KN0yMTsVEe1s45jynbD8KauqMZQG6vtr+i3QJw0+vN/pSFQY0KQYxAp2lXPM4GRio9xOh9ItyX2iGNE3UdsVnfLxr60qxlPvdDqSnhGbDCf/D2xfCNs+djoaFeI0KQapBm8z60oqQ749scWknFRW7SrH59NB/L1q7xprrtDjb7KqGsPVlNmQkm2VFn06Ab06epoUg9T63ZU0NvtCbr7TjuTnpFLd4GXLgWqnQ4ksH94PfVKtKsZw5omB0++xvgRseMPpaFQI06QYpJbtsKoaw6Wk2NJZaPmOQw5HEkG22dWJJ91mVTGGu3GXQL9jrOWwvI1OR6NClCbFILVkWxkj+iWQmRjCs460kp0Wx8DkWBYX6uwjvcLns0qJydkw9XtOR9M7XC44836rY9GKZ52ORoUoTYpBqMHbzPKdhzhhWIbToQSMiHBCXgafbz9Is7Yr9rwNb8De1XD6XaE9nVtXDZsBQ06Gfz8M9bqOp+o6TYpBaOWuCuqbfEzPC5+kCDA9L53KuiZddLineRutKsR+4+CYIy5zGn5ErHldDx+Ez//kdDQqBGlSDEJLtpXhEjhuaGguF9WRlpLvkm1lDkcS5lY8Z1UhnnG/taJEpBk02ZrbdcmfoHq/09GoEKNJMQgtLizj2MEpJMWG1qLCnemXFEte3wQWb9N2xR7TUG1VHeaeBHlnOB2Nc06/B5obrPdCqS7QpBhkquubWFNSyfS8EFz81Q/Th6WzfMchGr06lqxHLPl/cLgMzvxleEz6fbTSh8Hk66xSc9lWp6NRIUSTYpBZtuMQzT7D9DDqZNPaCXkZ1DU1s6pIZ7cJuKo9sPiPVtXhoMlOR+O8U26HqD46/ZvqEk2KQWZx4UFiPC4mhcn4xLamDU3HJWgVak9Y+BswzVZbooKEvnDiT2DT27BzsdPRqBChSTHILNlWRn5uasjPd9qR5D5RHDMomSWF2tkmoPatg1UvwdQbIDXX6WiCx7QfQtIgeP8unf5N+UWTYhApq2lg077qsBqf2J4T8jJYXVyh6ysGijHw/t3QJwVOvs3paIJLdJzV6WbPKlj/utPRqBCgSTGILLGrFMNtfGJb04dl4PUZlumUb4FR+BFsXwSn/Nya51R91bGXQf9j4KNfQlO909GoIKdJMYgsKSwjMdbDMYPCe57K/NxUoj0uFmsVavc1e61SYuoQyJ/tdDTByeWCs34DlcWw9K9OR6OCnCbFILJ4WxnThqbjdoV3V/rYKDeTs1O1s00grJwDpRutIRieaKejCV5DT4HhZ8Mnv9cB/eqINCkGiV0Hayk+VMf0YeE5PrGt6XnpbNxbRWl1g9OhhK7Dh6zp3HJPgtHnOx1N8Dv7N+Cth48ecDoSFcT8SooiMlNENotIoYjc0c7+GBF51d6/VERy7e1nisgKEVln/z49sOGHjw++sL69zhjdz+FIesfpo6y/86ON+q39qC38jTXp9TkPR/ZAfX9lDIdpP4DVL0JJgdPRqCDVaVIUETfwBHAOMAa4QkTGtDlsNlBujMkDHgNa5lYqA84zxhwDXAO8EKjAw8176/cxekASWWlxTofSK0YPSCQrrQ/vbdjndCihad86KHgGplwP/cY6HU3oOOV2SOgH8/9Hh2iodvlTUpwKFBpjthtjGoFXgFltjpkFzLEfzwVmiIgYY1YZY/bY2zcAfUQkgtax8U9pdQMrisqZOba/06H0GhFh5tj+LCk8SHV9k9PhhBZjYP7tEJsCp93pdDShJSYRznwA9qyE1S85HY0KQv4kxUFAcavnJfa2do8xxniBSqBt49jFwEpjjDYitfHBF/sxBs4eFxlVpy3OHtufxmYfCzeXOh1KaFn/OhQtgRn36hCMo3HsZTB4qjX9W12F09GoINMrHW1EZCxWleqNHey/QUQKRKSgtDTyPiAXbNhHTnocI/slOh1Kr5qUnUpGQgwLtArVfw3V8P49MGA8TPqO09GEJhE49xFrzcVFDzodjQoy/iTF3UBWq+eD7W3tHiMiHiAZOGg/Hwz8E/iOMWZbexcwxjxpjMk3xuRnZmZ27S8IcVX1TSzZVsbZY/sjEdZZwuUSzhzTj0WbDlDf1Ox0OKHhowegei+c+4fIXCsxUAZOgCmzYenfoGSF09GoIOJPUlwODBeRISISDVwOzGtzzDysjjQAlwAfG2OMiKQA7wB3GGN0Rt52LNx0gKZmw9kR1J7Y2sxx/altbNaB/P4oXgbL/g+mfg+ypjgdTeibcS8k9od5P4JmbddWlk6Tot1GeDOwANgIvGaM2SAiD4hIy+Cop4F0ESkEbgVahm3cDOQB94rIavunb8D/ihC2YMM++ibGMDErxelQHHH80HQSYz1ahdoZbyPM+zEkDbQ+zFX3xSbDub+HAxtgyR+djkYFCY8/Bxlj5gPz22y7t9XjeuDSdl73a+DX3YwxbNU3NbNwUykXTRqEK8xnselItMfF6aP68sEX+/E2+/C4dT6Jdi1+3Jq55opXrR6UKjBGf9Oa+GDRwzDmAmtxYhXR9BPIQZ9uLaOuqZmZ4yKz6rTFzLH9KT/cxPKduvBwu8q2wie/sxYPHjnT6WjCz7mPgCcW3rrFGu6iIpomRQct2LCPpFgP04ZGxtRuHTllZCYxHpdWobbH1wxv3mytID/z4c6PV12X2N+aO3bnp7DiWaejUQ7TpOiQusZm3t+wjzNG9yMqwqsM46I9nDwik3fW7aWpWWcZ+YrPHoXi/8A5j0BiZI1j7VWTroGhp8GCu6Cs0OlolIMi+9PYQW+v3UNVvZdvTcnq/OAIcFl+FqXVDToXamu7V8Cih2DcxXDst5yOJry5XHDBX8ATA29cr71RI5gmRYe8tLSIvL4JHDckzelQgsJpo/oyMDmWl5YWOR1KcGiogde/Bwn94RuP6oTfvSFpAJz3R9izSgf1RzBNig5Yv7uS1cUVXHlcdsQN2O+I2yVcMTWbT7eWsbOs1ulwnLfgF3BoO1z0N+gTmcN1HDHmfJh4FXz6KOxa4nQ0ygGaFB3w92VFxEa5uGjiYKdDCSqXTcnC7RJeXhbhpcUv5lmLB0+/BXJPdDqayDPzYUjNhTdutNasVBFFk2Ivq2nw8uaq3Zx37ECS46KcDieo9E2K5awx/XitoJgGb4RO+3ZgE/zrBzBwEpx2l9PRRKaYBLj4aWs6vddnWz2AVcTQpNjL/rlqN7WNzVw5LcfpUILSlcflUH64iXfXReDwjLoKeOXb1vCLy14ET7TTEUWuwZPhG3+AbR/DR790OhrVizQp9iJjDC/9ZxfnNdk3AAAPLUlEQVRjByYxfnCy0+EEpROGpZObHsdLS3c5HUrv8vngjRugYhd863lIbrs6m+p1k6+B/O9aswmtf93paFQv0aTYi1YWVbBpXzVXHpejHWw64HIJ3z4um+U7y9m8r9rpcHrPot/C1gUw8yHIOcHpaFSLmQ9D1jRrAoV965yORvUCTYq96JnPdhAf7eb8CQOdDiWoXTI5i2iPi6c/2+50KL1j9cvwySMw8WqYcr3T0ajWPNFWyT02GV6+AipLnI5I9TBNir1kVVE576zby+yThpIQ49c87BErLT6aq47LYe6KErbsD/PS4qb58OYPYcgpVhuW1iAEn8R+8O1XrTbfFy6E2oNOR6R6kCbFXmCM4cH5m8hIiOaGk4c6HU5I+NHpecTHeHjo3U1Oh9JzdnwK/7jWWvD28pes2VRUcBowHr79ClQUwUsXQ0OYf1mLYJoUe8GHGw+wbOchbjljhJYS/ZQaH80PT8vj400HWLItDBcg3r3Sqo5LGwJXztXloEJB7olw6RzYu9b6t2uqdzoi1QM0KfYwb7OPh97dyNDMeC7XeU675NoTchmYHMtD727C5wujJX1KCuDFiyAuFa7+J8TpVH8hY+RMuPCv1ooar1xhTcenwoomxR72akEx20pr+fnMURG/GkZXxUa5ue3skawtqeSttXucDicwtn4Ac86D2BT4zjxI0k5XIefYb8GsJ2D7Inj+fG1jDDP6Kd2Dahu8PPbBVvJzUjlrjC77czQumDCI0QOSeGTB5tCf5Wbta/Dy5ZCeB7Pft6pOVWiaeBVc9hLs3wDPnA0VxU5HpAJEk2IPeuCtLyiraeDOc0fruMSj5HIJd507mpLyOh5+d7PT4RwdY+Czx+CN70H28XDtO5DQ1+moVHeNOteq/q45AE+fZa2uoUKeJsUe8uryIl4tKObm0/KYnJPqdDgh7cThGVx7Qi7PLN7B26FWjXr4kNUp48P7YeyFVqea2CSno1KBknMCXDcfxGUlxmX/Z30JUiFLk2IPWFdSyT1vbuCk4Rn89MwRTocTFn5x7mgmZadw+9y1FB4Ike7wJSvgb6dA4YfWzCiXPAtRsU5HpQKt/zi48RNrrOn822Dud6G+yumo1FHSpBhgFYcb+cFLK8iIj+bxyyfidmm1aSBEe1z8+crJ9Ilyc+MLK6hp8DodUse8DbDoYautCeC7C2Da93VgfjiLT4dvvwYz7oMv3oS/nWx1xFEhR5NiADU1+/jJq6vZX1XPE1dOIi1eVzkIpP7Jsfy/Kyayo6yW2+euoTkYh2lsXwR/OcGay3T0eXDjv60VF1T4c7ngpFvh2ret58/Pgtevh+r9zsalukSTYoBU1Tdx3bPLWbS5lPvPH8vEbG1H7Akn5GVwxzmjmL9uHze+UMDhxiApMR7cBnNnWx+Evma46g249FkdgxiJck6Am/4Dp9xhlRr/NAU+fwKa6pyOTPlBTJA1Cufn55uCggKnw+iS3RV1XPfsMraX1vLQxcdyyeTBTocU9l74fCf3zdvA2IHJPH1tPn0THWqrK9sKn/we1r0G7miYfguceKu2HSpLWSG8+z/WuozxfWH6j63lqKLjnY4s4ojICmNMfqfHaVLsnnUllcyes5y6pmb+etVkpudlOB1SxPho435u/vsq0uKjefrafEb176Venb5m2L4QVsyBjW9ZiwJPmQ3H/8iaPFqptnYuhk9+Z1Wvx6XD5GutsY5pOhdyb9Gk2MNKqxv43w+38MryYvonxfLsdVMY0U/nr+xt60oq+e6c5ZTXNnL18TncMmM4KXE90JZrDJRtgXVzYfXfoaoE+qRZC9EefzPE65ch5YfiZfDpH2Dr+2B8kHMiTLwSRp4DfbTJpSdpUuwhtQ1enluyk78s2kZ9UzNXTbM+iFO1U41jSqsbePSDLby6vIiEGA8/njGcq6blEBvl7t6JG2qgeKn1AbblPSjfCQjkzbC+5Y88V1e2UEenao/15WrVi1C+A8QN2dNgxNmQdwZkjrY67qiACWhSFJGZwOOAG3jKGPNQm/0xwPPAZOAgcJkxZqe9705gNtAM/NgYs+BI1wrGpFjf1My/t5Ty1po9fLTxAHVNzZw5ph93njOKoZkJToenbJv3VfPb+Rv595ZS4qPdnDmmH+eNH8hJwzOJ9nTyAdN42CoJHtgIuwusb/T7N4BpBk8sDD0Vhp9lfaPX+UpVoBhjTRC/5T3YsgD2r7O2xyRbvZYHT7WWFsscBSk5mii7IWBJUUTcwBbgTKAEWA5cYYz5otUxNwHHGmO+LyKXAxcaYy4TkTHAy8BUYCDwITDCGNPhJJZOJ8X6pmZ2V9SxcW8V63ZXsq6kkrUlldQ0eEmLj+bcY/pz0aTBTNLepUFr6faD/Gv1buav20dlXRNJsS6mD/QwOdPLMckNDImtIbVpP1HVJdb6eAcLoXwXYP9fiE6AQZMhaypkTbN6E0bHOfo3qQhRWQI7PrG+lJUshwNfWNWsAJ4+kDkCUnMhOQtSsiF5MCT0s6rv4zO1A88RBDIpHg/cb4w5235+J4Ax5sFWxyywj/lcRDzAPiATuKP1sa2P6+h6gUqKyz/8B95mLz4fNBtDs8/gbfbR1Gxo9PpobPZR1+jlcKOPw41eKuuaOHS4kZr6/3bxd7uErLQ4hmTEMSk7jTEDEnFHwje1LlWptzn2K681bbaZdh4b6z99y2Ofz37us0ppvmbwea3nzU3ga7J+NzdBcwN4G63fTfXQVGuV+JoOQ0MVpq4S7+EK3I1VuPB9LfIKEilz9+VgzGAO9hlKRcJQDqcMpy5xCNFRUcR4XER73HjcgscluO0flwguARGhZTh+y+OW8flf/uYIA/Z1LL/qhLupmvjKQuIrtxJfWUhcZSF9akuIObwHd3PD145vdsfgjUrCG52INyqJZk+c/dMHnycOnysan9v+cUVjXFEY8eBzeTAuD0bcIG6MuOzHgsEF4sKIAGJv++/jlhvZIK3u6bY391efmy5MZDFs8pkkJHW/EOJvUvRnxdtBQOsp4EuA4zo6xhjjFZFKIN3e/p82rx3UTrA3ADcAZGdn+xFS50Z/+iMS5CjGBbVtGqyyf7YHICgVWK4oq03PHW31AI2Ks0p0UfGQOADJGElUbDLEJkN8Jo2xaRQ3xLP1cDw7mlIpqhH2VNRTfriRqromqiq8VBc20dS8zem/TKk2htg/Z9rPDRlUMUAOki6VZEgV6VSR5q0iseEwSVJHErXESylxNNCHBuKkgWiaiKGJaJpwS3D1J+nIzv4fkZDUaS4LmKBYBt4Y8yTwJFglxUCcs/zSuVQY35ff7t0iRLldRHsEj9uFJxJKfN3ShWLM1w5tteHLb4Sti1CtHouLr3zjdLmtbSJW5wOXx97mBrfHSoTuKOt3F/8No4Fh9s+ReJutmoSGJh8NXh9en8+qafBZNQ7GgM+ufWhhDBi7ZNxSGD7SjRxsHdxU+Kq3f8rb7vB5EZ8X8TVZv41VI2M9tmprxPgAH+LzYd3Rxt5u/vucll+taoFaka/d612797OzR3bp+O7yJynuBlovGT/Y3tbeMSV29WkyVocbf17bI7LGndgbl1FhyON24XG76ImRHUqp4ObPV+3lwHARGSIi0cDlwLw2x8wDrrEfXwJ8bKyvwvOAy0UkRkSGAMOBZYEJXSmllAqsTkuKdhvhzcACrCEZzxhjNojIA0CBMWYe8DTwgogUAoewEif2ca8BXwBe4IdH6nmqlFJKOUkH7yullAp7/vY+1d4mSimllE2TolJKKWULuupTESkFdgXodBlAWYDOFc70ffKfvlf+0/fKP/o++a8771WOMSazs4OCLikGkogU+FOHHOn0ffKfvlf+0/fKP/o++a833iutPlVKKaVsmhSVUkopW7gnxSedDiBE6PvkP32v/KfvlX/0ffJfj79XYd2mqJRSSnVFuJcUlVJKKb9pUlRKKaVsYZkURWSmiGwWkUIRucPpeIKJiGSJyEIR+UJENojILfb2NBH5QES22r+7v6pnGBARt4isEpG37edDRGSpfW+9ak+SH/FEJEVE5orIJhHZKCLH6z3VPhH5qf1/b72IvCwisXpfWUTkGRE5ICLrW21r9z4Syx/t92ytiEwKRAxhlxRFxA08AZwDjAGuEJExzkYVVLzAz4wxY4BpwA/t9+cO4CNjzHDgI/u5gluAja2ePww8ZozJw1qibrYjUQWfx4H3jDGjgPFY75neU22IyCDgx0C+MWYc1iILl6P3VYvngJlttnV0H52DtfLScKxF6v8SiADCLikCU4FCY8x2Y0wj8Aowy+GYgoYxZq8xZqX9uBrrw2sQ1ns0xz5sDnCBMxEGDxEZDHwDeMp+LsDpwFz7EH2fABFJBk7GWi0HY0yjMaYCvac64gH62GvPxgF70fsKAGPMJ1grLbXW0X00C3jeWP4DpIjIgO7GEI5JcRBQ3Op5ib1NtSEiucBEYCnQzxiz1961D+jnUFjB5H+B2wGf/TwdqDDGeO3nem9ZhgClwLN2VfNTIhKP3lNfY4zZDfweKMJKhpXACvS+OpKO7qMe+awPx6So/CAiCcDrwE+MMVWt99kLREf0WB0R+SZwwBizwulYQoAHmAT8xRgzEailTVWp3lMWuz1sFtYXiYFAPF+vLlQd6I37KByT4m4gq9XzwfY2ZRORKKyE+JIx5g178/6Wqgf79wGn4gsS04HzRWQnVhX86VjtZil2tRfovdWiBCgxxiy1n8/FSpJ6T33dGcAOY0ypMaYJeAPrXtP7qmMd3Uc98lkfjklxOTDc7s0VjdWIPc/hmIKG3S72NLDRGPNoq13zgGvsx9cAb/Z2bMHEGHOnMWawMSYX6x762BhzJbAQuMQ+LOLfJwBjzD6gWERG2ptmAF+g91R7ioBpIhJn/19sea/0vupYR/fRPOA7di/UaUBlq2rWoxaWM9qIyLlY7UFu4BljzG8cDiloiMiJwKfAOv7bVvYLrHbF14BsrKW7vmWMadvgHZFE5FTgNmPMN0VkKFbJMQ1YBVxljGlwMr5gICITsDokRQPbgeuwvnTrPdWGiPwSuAyrJ/gq4HqstrCIv69E5GXgVKwlovYD9wH/op37yP5S8Ses6ufDwHXGmIJuxxCOSVEppZQ6GuFYfaqUUkodFU2KSimllE2TolJKKWXTpKiUUkrZNCkqpZRSNk2KSimllE2TolJKKWX7/0J1xNhklKqsAAAAAElFTkSuQmCC\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" + } + ], + "source": [ + "#%% parameters\n", + "\n", + "problems = []\n", + "\n", + "n = 100 # nb bins\n", + "\n", + "# bin positions\n", + "x = np.arange(n, dtype=np.float64)\n", + "\n", + "# Gaussian distributions\n", + "# Gaussian distributions\n", + "a1 = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std\n", + "a2 = ot.datasets.make_1D_gauss(n, m=60, s=8)\n", + "\n", + "# creating matrix A containing all distributions\n", + "A = np.vstack((a1, a2)).T\n", + "n_distributions = A.shape[1]\n", + "\n", + "# loss matrix + normalization\n", + "M = ot.utils.dist0(n)\n", + "M /= M.max()\n", + "\n", + "\n", + "#%% 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", + "#%% barycenter computation\n", + "\n", + "alpha = 0.5 # 0<=alpha<=1\n", + "weights = np.array([1 - alpha, alpha])\n", + "\n", + "# l2bary\n", + "bary_l2 = A.dot(weights)\n", + "\n", + "# wasserstein\n", + "reg = 1e-3\n", + "ot.tic()\n", + "bary_wass = ot.bregman.barycenter(A, M, reg, weights)\n", + "ot.toc()\n", + "\n", + "\n", + "ot.tic()\n", + "bary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True)\n", + "ot.toc()\n", + "\n", + "pl.figure(2)\n", + "pl.clf()\n", + "pl.subplot(2, 1, 1)\n", + "for i in range(n_distributions):\n", + " pl.plot(x, A[:, i])\n", + "pl.title('Distributions')\n", + "\n", + "pl.subplot(2, 1, 2)\n", + "pl.plot(x, bary_l2, 'r', label='l2')\n", + "pl.plot(x, bary_wass, 'g', label='Reg Wasserstein')\n", + "pl.plot(x, bary_wass2, 'b', label='LP Wasserstein')\n", + "pl.legend()\n", + "pl.title('Barycenters')\n", + "pl.tight_layout()\n", + "\n", + "problems.append([A, [bary_l2, bary_wass, bary_wass2]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Dirac Data\n", + "----------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Elapsed time : 0.014856815338134766 s\n", + "Primal Feasibility Dual Feasibility Duality Gap Step Path Parameter Objective \n", + "1.0 1.0 1.0 - 1.0 1700.336700337 \n", + "0.006776466288966 0.006776466288966 0.006776466288966 0.9932238515788 0.006776466288966 125.6649255808 \n", + "0.004036918865495 0.004036918865495 0.004036918865495 0.4272973099316 0.004036918865495 12.3471617011 \n", + "0.00121923268707 0.00121923268707 0.00121923268707 0.749698685599 0.00121923268707 0.3243835647408 \n", + "0.0003837422984432 0.0003837422984432 0.0003837422984432 0.6926882608284 0.0003837422984432 0.1361719397493 \n", + "0.0001070128410183 0.0001070128410183 0.0001070128410183 0.7643889137854 0.0001070128410183 0.07581952832518 \n", + "0.0001001275033711 0.0001001275033711 0.0001001275033711 0.07058704837812 0.0001001275033712 0.0734739493635 \n", + "4.550897507844e-05 4.550897507841e-05 4.550897507844e-05 0.5761172484828 4.550897507845e-05 0.05555077655047 \n", + "8.557124125522e-06 8.5571241255e-06 8.557124125522e-06 0.8535925441152 8.557124125522e-06 0.04439814660221 \n", + "3.611995628407e-06 3.61199562841e-06 3.611995628414e-06 0.6002277331554 3.611995628415e-06 0.04283007762152 \n", + "7.590393750365e-07 7.590393750491e-07 7.590393750378e-07 0.8221486533416 7.590393750381e-07 0.04192322976248 \n", + "8.299929287441e-08 8.299929286079e-08 8.299929287532e-08 0.9017467938799 8.29992928758e-08 0.04170825633295 \n", + "3.117560203449e-10 3.117560130137e-10 3.11756019954e-10 0.997039969226 3.11756019952e-10 0.04168179329766 \n", + "1.559749653711e-14 1.558073160926e-14 1.559756940692e-14 0.9999499686183 1.559750643989e-14 0.04168169240444 \n", + "Optimization terminated successfully.\n", + "Elapsed time : 2.703077793121338 s\n", + "Elapsed time : 0.0029761791229248047 s\n", + "Primal Feasibility Dual Feasibility Duality Gap Step Path Parameter Objective \n", + "1.0 1.0 1.0 - 1.0 1700.336700337 \n", + "0.006774675520727 0.006774675520727 0.006774675520727 0.9932256422636 0.006774675520727 125.6956034743 \n", + "0.002048208707562 0.002048208707562 0.002048208707562 0.7343095368143 0.002048208707562 5.213991622123 \n", + "0.000269736547478 0.0002697365474781 0.0002697365474781 0.8839403501193 0.000269736547478 0.505938390389 \n", + "6.832109993943e-05 6.832109993944e-05 6.832109993944e-05 0.7601171075965 6.832109993943e-05 0.2339657807272 \n", + "2.437682932219e-05 2.43768293222e-05 2.437682932219e-05 0.6663448297475 2.437682932219e-05 0.1471256246325 \n", + "1.13498321631e-05 1.134983216308e-05 1.13498321631e-05 0.5553643816404 1.13498321631e-05 0.1181584941171 \n", + "3.342312725885e-06 3.342312725884e-06 3.342312725885e-06 0.7238133571615 3.342312725885e-06 0.1006387519747 \n", + "7.078561231603e-07 7.078561231509e-07 7.078561231604e-07 0.8033142552512 7.078561231603e-07 0.09474734646269 \n", + "1.966870956916e-07 1.966870954537e-07 1.966870954468e-07 0.752547917788 1.966870954633e-07 0.09354342735766 \n", + "4.19989524849e-10 4.199895164852e-10 4.199895238758e-10 0.9984019849375 4.19989523951e-10 0.09310367785861 \n", + "2.101015938666e-14 2.100625691113e-14 2.101023853438e-14 0.999949974425 2.101023691864e-14 0.09310274466458 \n", + "Optimization terminated successfully.\n", + "Elapsed time : 2.6085386276245117 s\n" + ] + }, + { + "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" + } + ], + "source": [ + "#%% parameters\n", + "\n", + "a1 = 1.0 * (x > 10) * (x < 50)\n", + "a2 = 1.0 * (x > 60) * (x < 80)\n", + "\n", + "a1 /= a1.sum()\n", + "a2 /= a2.sum()\n", + "\n", + "# creating matrix A containing all distributions\n", + "A = np.vstack((a1, a2)).T\n", + "n_distributions = A.shape[1]\n", + "\n", + "# loss matrix + normalization\n", + "M = ot.utils.dist0(n)\n", + "M /= M.max()\n", + "\n", + "\n", + "#%% 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", + "alpha = 0.5 # 0<=alpha<=1\n", + "weights = np.array([1 - alpha, alpha])\n", + "\n", + "# l2bary\n", + "bary_l2 = A.dot(weights)\n", + "\n", + "# wasserstein\n", + "reg = 1e-3\n", + "ot.tic()\n", + "bary_wass = ot.bregman.barycenter(A, M, reg, weights)\n", + "ot.toc()\n", + "\n", + "\n", + "ot.tic()\n", + "bary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True)\n", + "ot.toc()\n", + "\n", + "\n", + "problems.append([A, [bary_l2, bary_wass, bary_wass2]])\n", + "\n", + "pl.figure(2)\n", + "pl.clf()\n", + "pl.subplot(2, 1, 1)\n", + "for i in range(n_distributions):\n", + " pl.plot(x, A[:, i])\n", + "pl.title('Distributions')\n", + "\n", + "pl.subplot(2, 1, 2)\n", + "pl.plot(x, bary_l2, 'r', label='l2')\n", + "pl.plot(x, bary_wass, 'g', label='Reg Wasserstein')\n", + "pl.plot(x, bary_wass2, 'b', label='LP Wasserstein')\n", + "pl.legend()\n", + "pl.title('Barycenters')\n", + "pl.tight_layout()\n", + "\n", + "#%% parameters\n", + "\n", + "a1 = np.zeros(n)\n", + "a2 = np.zeros(n)\n", + "\n", + "a1[10] = .25\n", + "a1[20] = .5\n", + "a1[30] = .25\n", + "a2[80] = 1\n", + "\n", + "\n", + "a1 /= a1.sum()\n", + "a2 /= a2.sum()\n", + "\n", + "# creating matrix A containing all distributions\n", + "A = np.vstack((a1, a2)).T\n", + "n_distributions = A.shape[1]\n", + "\n", + "# loss matrix + normalization\n", + "M = ot.utils.dist0(n)\n", + "M /= M.max()\n", + "\n", + "\n", + "#%% 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", + "alpha = 0.5 # 0<=alpha<=1\n", + "weights = np.array([1 - alpha, alpha])\n", + "\n", + "# l2bary\n", + "bary_l2 = A.dot(weights)\n", + "\n", + "# wasserstein\n", + "reg = 1e-3\n", + "ot.tic()\n", + "bary_wass = ot.bregman.barycenter(A, M, reg, weights)\n", + "ot.toc()\n", + "\n", + "\n", + "ot.tic()\n", + "bary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True)\n", + "ot.toc()\n", + "\n", + "\n", + "problems.append([A, [bary_l2, bary_wass, bary_wass2]])\n", + "\n", + "pl.figure(2)\n", + "pl.clf()\n", + "pl.subplot(2, 1, 1)\n", + "for i in range(n_distributions):\n", + " pl.plot(x, A[:, i])\n", + "pl.title('Distributions')\n", + "\n", + "pl.subplot(2, 1, 2)\n", + "pl.plot(x, bary_l2, 'r', label='l2')\n", + "pl.plot(x, bary_wass, 'g', label='Reg Wasserstein')\n", + "pl.plot(x, bary_wass2, 'b', label='LP Wasserstein')\n", + "pl.legend()\n", + "pl.title('Barycenters')\n", + "pl.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Final figure\n", + "------------\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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dkIuISD/eNBNHif90KYlzEOt2tRBLJDM6D8c1e8II1m7fRzyRzPi5REREJAu6txgPaiWOthgXEZEBJFOtxarE8YySOAfhVsbMynAljnuOzniSDQ2tGT+XiIiIZEEy4EmckNqpRERkAG9qp9KakS4lcQ5iTX0z0UiIw6rLM36u7uHGmosjIiISDGqnEhGRQqd2Ks8piXMQq+ubmTm+kkg481+m6WMriIZDSuKIiIgERaG0U+mCXERE+pNQO5XXlMTph7WW1duaMz7U2BWNhDh8XIWGG4uIiARF4CtxUskpJXFERKQ/2p3Kc0ri9GN7cwd72rqyMtTY5e5QZa3N2jlFREQkQ9zkRmC3GHeTOLogFxGRfvRO4riDjmXYlMTph1sRk61KHHDm4jS2xti1rzNr55QhshYa18FrD8GeTc7fRURE+lIw7VRK4oiISD/ctbBIlTheifgdQK5ykzgzs5nESZ3rlfpmakaUZO28MghbnofHvw9bnoX23fufL6+BKcfDaZ+H8XP9i09ERHJPIuZU4RjjdySZ4VYY6a6qiIj0x92pMeoONlYSJ11K4vRjdX0zU8eUUVGcvS+RmzBava2ZM46sydp55SA6W+Dhb8CzN0NFDcx8B0w+FsYcDrvWQF0tvP4Q/OJ0OOk/4NRroEgJOBERwblwDWoVDkAoBCasC3IREemfthj3nJI4/VhTn72hxq6q0iImjyrVDlW5Yvsq+N17oWkLHPshOOurUFy5//3TTnKeb9sN//iSU6mz+j547x9gzHT/4hYRkdyQCHgSB5yWKiVxRESkP29qp1ISJ12aidOHls44GxvbmJXlJA44LVVrlMTx3861cPs7wSbgAw/COd87MIHTU9louOAmuPwep9Xq/8535uWIiEhhS8SCuzOVKxzVBbmIiPSvuxJH7VReURKnD2tTSZSjsrgzlWv2xBFsaGilLab+ct80roPbz4dQBK68H6acMLiPm/5vcPlfILbP+fjmbZmNU0REcltBJHGKlMQREZH+uWuE2qk8oyROH9x2pmxuL+6aPWEE1sLa7fuyfm4BmrY6lTTJOFxx39DboibMg8vugdZG5zhtuwf+GBERCaZE3LkhEGThIt1VFRGR/nW3U6UqcZJK4qRLSZw+rN7WzMiyIsb7sEPUrB7DjSXLkgn489XQsddpjaqZObzjTF4I77sL9m6Cez+ubchFRAqVKnFERKTQuYn+UERz1DyiJE4f3KHGxoctQSePKqWyJKK5OH54/AbY9AS843swYX56x5p6Ipz1NXj1b/D8LV5EJyIi+aYgkjhR3VUVEZH+JbuctcIYCCnx7wUlcXqJJ5Ks3b4v6ztTuYwxzJ4wQjtUZduW5+DRb8Pci2H+Jd4c8/iPwoyz4KEvw47V3hxTRETyh3anEhGRQpfo2n9DQy24nlASp5cNDa10xpO+zMNxzZ44grX1+0gk1YaTFR1N8KcPQtVkOOf7TpbYC6EQLLnJ2dXqTx+ErnZvjisiIvkhWQBJnFBEd1VFRKR/idj++XDa0dATSuL04udQY9fsCSNo70qwsbHVtxgKyr++AU11cOEtUFLl7bEramDJz2HnanjiRm+PLSIiua3n3cegUiWOiIgcTM/WYs1R84SSOL2s3tZMNBxi+tgK32JwE0gabpwF9Suh9lY49kNwyHGZOcfhZ8Gci+CJH8Du9Zk5h4iI5J5ELPiVOLqrKiIiB5OIq53KY0ri9LK6vpnDx1VQFPbvSzOjpoJIyGi4caZZC3/7LygdDWd8MbPneus3nR9aD/53Zs8jIiK5IxFzhjgGWVjtVCIichA9b2ioetMTSuL0YK1l9bZm34Yau4ojYWbUVGi4caat+D1secbZRap0VGbPNWICnHYNvPYgvPpgZs8lIiK5oefdx6DSBbmIiBxM7yROMu5vPAGgJE4Pu/Z10tga83Uejmv2xBFqp8qkjib457UwaREseF92znn8R6H6CHjw89DVkZ1zioiIfwqlnUpbjIuISH+SPW5ohCJK/HtASZweXnGHGvtciePGsHNfJw0tnX6HEkxP/ABad8I7vuvsIpUNkahzvj0b4bmbs3NOERHxT89hjkGlIZUiInIwaqfynJI4PbgzaGblSCUOoLk4mbBvOzxzE8y9GCYdk91zH3Y6zDjL2amqoym75xYRkexKxoNfiRPSkEqRTHjw5XqaO5QglQA4YHeqqNNqLGlREqeH1duamTyqlBEl/l9wudVAaqnKgMe+65R+Z3qYcX/OvBba98BTP/bn/CIikh2F0k6lShwRTzW2dPKRO1/g3pe2+R2KSPoSXfuH/Gt3Kk9E/A4gl6yu93+osWtkWZSJVSW8oiSOt3avh+W3wTFXwOjD/Ilhwnw46gJ4+mdw3NVQUeNPHCLSLZ5I8pm7VrCjWfOqgmDepCq+fO5sv8NQO5WIDMu+jnjqT/3fkgBIdEG03HlbSRxPqBInpaUzzoaGVo6aWOV3KN1mT6zilW1qufHUI992MsGnXuNvHGd8GeId8Pj3/Y1DRADY3tzB/Su20djSScigRx4/tu5p545nNvn9LeXoefcxqHRBLuK51piTxGnrTPgciYgH3tROpeRkulSJk/LK1iashbmTc6MSB2DupCr+tXYHLZ1xKor1T5W27S/Dqj/CSf/hbPntp+oZcPRl8PytcMLHYNRUf+MRKXBtMedC+dNnHcF58yf6HI2k44dLX+fGpa+RSFrCIeNvMIkutVOJyJC1p9Ykd20SyWs918JwkXY09IAqcVJWbXUqXuZMyp1KnHmTq7DWSTCJBx67HqIVThInF5z2eTDGGXIsIr5yL5TLi8M+RyLpcv8N22I+D060toDaqVSJI+Kl1u4kjgbASgD0nA+nYfieUBIn5eWtTYwfUUJNZYnfoXRzE0qrlMRJ3841sPpeOP7DUDba72gcVZPg6MvhxTuhqc7vaEQKWlunc6FcFlXVY75z/w19v4OdTAC2AJI4Ud1VFfFYu9tO5ffPMREvJLvUTuUxJXFSVm5tYu7k3KnCARhbWcz4ESVK4njhse9BUTks/rjfkRzo5M84fz75Q3/jEClw7l3PciVx8l5Z1KnEae30+Q62e6cxHPDvqVAR2GQqaSUiXmjtVCWOBEjvdipV4qRNSRz2DzWem0OtVK65k6uUxEnXrtfg5T/BcR/KnSoc18hDYMGlsPz/oLne72hECpZ7oVwaVTtVvnOTOL7fwXarUwJfiZO6MNdFuYhn2ro0E0cCJBHrscW4KnG8oCQOPYYa52ISZ1IVGxpatcVgOh7/PkRKYPEn/Y6kbyd/FpJxeOpHfkciUrA0Eyc4yotzpJ0qUShJnNTnp4tyEc+onUoCJdGznapI64UHlMQhN4cau+ZOSg033tbsdyj5afd6Z0eqYz8IFWP9jqZvow+F+ZdA7a+hZaff0YgUpFbNxAmM7nYqv9sQ3MqUUMC/p7orcXRRLuIVtVNJoKidynNK4uAkcSZUlTC2stjvUN7ETSy9rJaq4XniB84F9Ik5WoXjOuVzkOiEZ37mdyQiBcm921mmdqq81z3YuFOVOFmhdioRz7WrnUqCpOfuVO4wfGv9jSnPKYkDrKpryslWKnCGG0+oKmFlnZI4Q9a8DV76LRx9GVSO9zuagxszHWYvgedugfa9fkcjUnBaY3Gi4RBFYS2L+S53KnEKJYnjtlMpiSPiFbc6VEkcyXvW9tqdKpXMSarKLB0Ff7W6r6OL9Tk61Ng1Z1KVKnGG4+mfOjtmnPQpvyMZnJM/A7F98Pwv/Y5EpOC0xxKUaR5OILgzcdr9/uWne3eqIn/jyDT3wlwX5CKecX9+qZ1K8p67NrhrYUjVm14o+CSOO2tmTo5tL97TvElVrNdw46Fp2+3MmJl7EYya5nc0gzNhHhz+VnjmJoi1+R2NSEFp7Uxoe/GAyJ1KnAJJ4rgzf3RBLuIZ9+dXR1eSRFJtJ5LHutfC6IF/as1IS8EncVal2pRyuhJnsjsXR8ONB+3Zm6Gr1aluyScnfxbaGuGF2/2ORKSgtMXimocTEMWRECGTAzNxuu8+qp1KRIamZxuVOx9HJC91D/nvMdgYIKEqs3QoibO1iYlVJVRX5N5QY9dcDTcems598OzP4chzoGaW39EMzdTFMOVEeOrHENcFsUi2tMYSSuIEhDGG8mhElTjZ0p3E0QW5iFd6JnHaOvV/S/JYolc7lYbhe0JJnK1NzM3hViqA6opiJlaVsFJJnMFZfht07IVTPut3JMNzymehuQ5W3eV3JCIFoz0W1/biAVJWHM6hmThBr8TRBbmI1w5I4vj9s0wkHWqnyoiCTuLsaY2xoaGVeZNH+h3KgOZNHslLW/b4HUbui3fCUz+BQ0+FyYv8jmZ4ZpwF4+c626MntXCLZENrZ4JyDTYODKcSx+8kTmqOXSjolThK4oh4rS0Wpzji/Jrme1WhSDp6V6V2J3E06zUdBZ3EeWGzkxRZNHWUz5EMbNG0UWzZ3c7O5g6/Q8ltL/0WWrY7s2XylTFO/I2vw5r7/Y5GpCC0qRInUEqjYf9bELq3GA96EkcX5CJea4slGFvpjHrwvapQJB3da2HvLca1ZqSjoJM4tZv2EAkZ5h+S+5U4C1OJptpNqsbpVyIOT/4QJh4Nh53udzTpmf1OGD0dnrgBrHYlEMk0zcQJltyaiVMg7VS6IBfxTFtnvHtep+9VhSLpSPa6oaEtxj1R0Emc5Rv3cNSkKkqKcv/C/aiJVRRHQtRuVBKnX6v/Ans2wCmfc6pZ8lkoDCd/GupXwLp/+R2NSOC1xxKqxAmQ3JiJUyCVOLogF/GUtZa2rkR3Eqfd74S0SDr6nYmjxH86CjaJE4snWVG3Ny9aqQCikRDzDxnJ8k27/Q4lN1kLT9wI1Uc6u1IFwbxLoHIiPH6j35GIBJq1ltZYXDNxAiQnZuL0vvsYVLogF/FUZzyJtTC20vm/pcHGktd6z4frnqOmNSMdBZvEeXlbE53xZN4kccCZ3fPKtmb/7y7motcfgh0vw8mfgVBAvq0jUTjxk7DpCdj8rN/RiARWR5dzwaxKnODIjZk4BdZOpUocEU+0pn52qZ1KAqHfwcZaM9IRkN92h255qi1p4bT8SeIsnDqKeNLy0pa9foeSW6yFZddD1RSYe5Hf0Xhr4ZVQNgYe+67fkYgEljs7RZU4wVEeDfv/i0/vYY5BpUocEU+5lTdqp5JA6G+wsdaMtBRuEmfTHqaMLqOmssTvUAbNHW7s7qolKesfga21cMpngle2Hi2HxR+HN/4JW1/wOxqRQHKrG0vzYD6aDE5ZccT/qlX3LmMo4BVeqsQR8ZSbxBld7vzS29qpShzJY73nw2nN8ERBJnGstdRu2pNXrVQAI8uizKipoHaj5uIcYNl3YcQkWPA+vyPJjGOvgpKR8Nj3/I5EJJD2V+IE/JftAlIeDRNLJInFk/4FUTCVOLqrKuKlttSaVFEcobQoTHuXkjiSx/prp9KOhmkpyCTO5t1tNLR05lUrlWvR1FEs37SHZFLbTgOw8QnY/BSc9B8QKfY7mswoGQEnfBRe/Stsf9nvaEQCx73LqS3Gg6M0Nd/I12qcgkni6IJcxEtuJU5pNExZNNw9I0ckLyV7t1OpBdcLBZnEcbfpXphnlTjgxNzcEeeNXS1+h5Ibll0P5TVwzBV+R5JZx38YopWajSOSAW2qxAmc8lRCrtXPWRLd7VQBTw5qi3ERT7lJnPJohLLisP+toSLp6H1Dw20x1pqRlsJM4mzaQ2VJhCNqKv0OZcgWTRsN7E9EFbQtz8GGZXDSp6Co1O9oMqt0FBx/Nay+F3au9TsakUBp00ycwClLJeR83Zo3EXMuWo3xL4ZsUDuViKfcGwul0TBlRRF/k9Ei6eo9H067U3miIJM4yzft5pgpowiF8u/CatqYMsaUR6ndpLk4PPItKKuGRR/wO5LsOOHjzqDjZd/xOxKRQFElTvC4lThtfv7yk4wHv5UKnCRVqEgX5CIe6a7EKQ5TVhz2Nxktkq7umTi926mUnExHwSVxdu3r5LUdLRx36Gi/QxkWYwzHHTqaZ9Y1Ym0Bz8XZ8DisfxRO+ayT2CgE5WOc2Tiv3APbV/kdjUhguDNxyjUTJzBK3XYqP3d1ScSCt2Nif8JRVeKIeMSdgVMH1vnaAAAgAElEQVRWFKEsqiSO5Dk3WdOdxFE7lRcKLonzxBu7ADj18LE+RzJ8pxw+lm1NHawr1Lk41sLD34TKibDog35Hk12LPwElVfDwt/yORCQw3GqNMlXiBEZ51G2n8nkmTqhQkjgRJXFEPNLeY7BxaVFESRzJb/3tTqUkTloKLomz7NVdjCmPctTEEX6HMmynHlENwKOv7vI5Ep+8sRS2PAOn/icUlfgdTXaVjoQTPwWv/R3qav2ORiQQNBMneMqL3XYqn3enKoR2KkhV4uiCXMQLrbEERWFDNBKivDjsbzJaJF39JnGU+E9HQSVxkknL4683cMrh1Xk5D8c1eVQZ08eW89jrDX6Hkn3WwsPfgJFT4OjL/Y7GH8d/BMrGONVIIpK2tliCkqIQ4TxeF+RAZTlRidNVWO1U2mJcAqipvYuP/WY5u/Z1Zu2c7bF4988wP9qp/udva3jstQK9USzeS/ZqpwqFwYS0ZqSpoJI4r2xrprE1xmlH5m8rlevUI8by7PpGOroKrMRyzf1QvwJO+wJECuQOZ2/FFXDyZ2H9I85sIBFJS2tnvLv9RoKhLGdm4hTIOhUu0l1VCaQXN+/hb6u28/zG7G0o0hZLdP8MK4tGsrrFeCJpueXx9fx1ZX3WzikBl4g5SZtQj2pnDcNPW0ElcR573ckqn5LH83Bcpx0xls54kmc3FNAuVfEYLP0qVB8J897jdzT+OvaDMGISPPRlSCb9jkYkr7XFEpQVq5UqSFSJk2W6IJeAamiJpf7MXiXOgUmcMK2xeNY2M9ndGiNps/v5SsD1NR9Ow/DTVlBJnGWv7mLOpBFUVxT7HUrajj90DNFIqLDKHWtvhd3r4a3f3D/ZvFAVlcKZX4X6l2DVXX5HI5LX2mJxyooK/GdKwEQjIYrCxt+ZOMkCSuLoglwCyk1mNGSxnartgHaqCNZCZzw7N+y6P18lccQrfc2HU/Vm2gomibOvo4sXNu/J612peiqNhjn+0NGFk8Rp2w2PfgcOOx0Of4vf0eSGuRfDxKPhX9dBrM3vaETylipxgqks6vOuLmqnEsl7bvJmV0v2Ks1aYwlKe1TiwP5txzOtsbvySJV14pG+qlI1DD9tBZPEeWpdI/Gk5dQjgpHEAael6vWdLWzb2+53KJn32Pegowne+i0wGj4KQCjkfD2at8IzP/U7GpG8pZk4wVQWDWftF58+JboKaItxtVNJMDW2Ot/XjVmsTGmPJShPJW/cZE62EtI9K3Gy1cIlAdfXDQ0l/tNWMEmcZa/toqI4wjFTRvkdimfchFTgq3F2r4fnfgFHXwbj5/gdTW6ZdhLMPBcevxH27fA7GpG81HP+gASHH7u6HCARUzuVSJ7zo72otUc7VXn3fK/sJnE640la/EyCS3D0WYmjxH+6CiKJY63lsdd2sXi6M0cmKA6vqWD8iBKWBTmJYy38/fMQKYZ/+7Lf0eSmt1zn/CD851f8jkQkL7XFEpQXqxInaMqLIzkw2LiQ2ql0QS7B424tns32ovZeg40he0Pad/VIVqmlSjzR1w2NcFRbjKcpOBmNg1hR10TdnnbeMmuc36F4yhjDWbNreOTVncHNlq++F15/CM74ElSO9zua3DRmOpz8aVj5B1j/qN/RiOSdtli8u2RdgsPZ1cXPSpwCG2ysC3IJID92p2rtjPeRxMlSJc6+/YkbDTcWTyT7uKERUjtVugoiifOXF7cSjYR429zgJQGWLJhER1eSh17Z7nco3utocqpwxs+D4672O5rcdsrnYNSh8MBnoavD72hE8kpr5/75AxIczmBjPytxCqidShfkEkCJpGV3ayfFkRBtsUTWfp60dyUoK96/OxVkt52qONW1kM0duSTA+poPp+rNtAU+iRNPJHlg5TbOnFnDiJLgXUwtnDqKyaNKuefFrX6H4r2HvwktO+C8H2hL8YEUlcK5N8DudfDEjX5HI5I3kknrXDBrsHHglEXDtHX6PRNH7VQi+WpPW4ykhSPGVQIHVqlkSiyepCthKStKVeIUZ7edqqGlc//nq0oc8UJ/7VRaM9IS+CTOE2800NASY8nRk/wOJSOMMSxZMIkn32hg574AVWBsXQ7P/RKOuwomLfQ7mvww/d9gzkXwxA3Q8Lrf0YjkhfYu55f8cm0xHjjlfm8xnowXTiWOBhtLALlJjCPHO0mNXVlIarSnfmbtr8TJbjtVY0uMw8dVYEx2t1WXAOtrPly4CBIBHQWSJYFP4vzlxa2MKIlw+pHB2Vq8tyVHTyRp4f4V9X6H4o1YG/z5w1A5QcOMh+rs/4GiMvjz1bqgFhmE1tTdzVJV4gROWXG4+9/XF4lYgW0xrjVHgsWtvJk5PnuVKW1dzs+s/TNxstdOZa2lsbWTcSNKGFUWVSWOeEO7U2VEoJM4rZ1x/vHKDs6ZN5HiSHDvss6oqWTOpBHc+1JAWqr++RVofB0uuAlKqvyOJr9UjoPzfgjbXoBl1/sdjUjOc9ttNBMneNwtxq21/gSgdiqRvOYmMWaOH3HA3zOpNbUmvWmwcRY2MGlq76IrYamuKKa6IqqZOOINtVNlRKCTOP9cvYP2rgRLFkz0O5SMW7JgEivrmnhjZ4vfoaTntYfg+Vtg8SfgsNP9jiY/HbUEFrwPHv8ebH7G72hEcppbqaGZOMFTFo2QSFo640l/AkgUWjuVLsglWNykzRHjK5y/Z2EmTnc7VWpNKgqHKAob2royX4njfr7VFVGqK4pViSPe6OuGRrjIaTmWYQt0EueeF7cysaqEY6eN9juUjDt//kRChvyuxmnZBfd+DGqOgjOv9Tua/Pa270DVIU5bVUez39GI5Cz3glkzcYLHra5q92suTkFV4kR1QS6B09ASoyhsGFtRTFVpEY2tWajEiR3YTuW8HclKJc6uVJLKqcQpprFViVnxQF/z4ZT4T1tgkzibG9t4/PVdLDl6EqGQ8TucjKsZUcJJM6r5Y20dnXEfBzkOV6IL/vQBJ+Fw4S8hUux3RPmtZAS865fQtAX+8lFI+nQnWiTHtcYOLF2X4HAHg/oyF8daSPYxByCoQhFdkEvgNLR0Mqa8GGOM016UzcHGByRxwlmZibO/EsdJ4qidSjzR13y4kFpw0xXYJM5Ny9YRCYW48sRpfoeSNVefehjbmzv48wt5WI3zjy/Bhsec7cTHHeV3NMEw5Xh46zdh7QPwmObjiPTFvbupdqrgyfauLgdwh/wWShLHvavq1/whkQxoaOmkutKppnOSGpn/pbOvFt/sJ3GiVFdGaY0l/KtklODor51Kw/DTEsgkTn1TO3cv38LFiyYzbkSJ3+Fkzckzqpk/uYqbHl1HPJFHlRcv3A7P3QwnfBwWvNfvaILlhI/B/PfCo9+G1ff5HY1IznErccqVxAkc99+0NQttCG+SdJM4BdROBZDUL3wSHA0tnVRXOJXh1ZXZmRHT1mclToS2LFQUNrR0Eg4ZRpVFuz9vzcWRtPU1Hy4cVRInTYFM4vzisfUkLXzktOl+h5JVxhg+8W+Hs3l3G/ev3OZ3OIOz6Sl44LNw2Bnwluv8jiZ4jIFzb4RJi+Cej0D9Sr8jEskp7e5dT83ECZwyP2fiuGXiBZPESV2gqzxeAqRhX6w7mTG2ophd2UjidPY1EyfcfcMhkxpbYowujxIKOXOAgKx8zhJwqsTJiMAlcRpaOvndc5tZsmASh4wu8zucrDtzZg0zx1fy00fWkUzmeFnz1uXwm3fDqKlw8a8hrDvhGVFUApf8BkpHwR0XwM61fkckkjM0Eye4yrtn4vjYThUqkHVNSRwJGGstja09KnEqouzriNOR4V2i3F2o3J9f4KxP2UhGH1B55FbiaC6OpCvRx3y4sGbipCtwSZxbn9hAZzzJx84orCocVyhk+PgZM3hjZwv/eGW73+H0b/squONdUDYarrjPSTBI5lSOhyvvg1AYbn8nNK7zOyKRnNDWGccYKIkoiRM0pd0zcXxopyq4SpzU56k7qxIQTe1ddCUs1RXO9/aYVFIj0zs2tXUmMAaKI/t/RSuLRrIyoH1XS6zH5+v82dCiX7QlTYmYdqfKgEAlcbbtbeeOpzfxjrkTmD62wu9wfPOOuRM4rLqcG/75Wm7uVLVzDdy+BKLlcOX9UDXJ74gKw5jpTsIs2QX/dz7s3uB3RCK+a40lKCsKF8QuhoVm/0wcPwcbF0oSJ3WBnlQSR4LBnQUztjK7lSltsQTl0QjG7F+TslaJs6+zu41qfxJHlTiSpmRXH+1UUbAJ7Z6bhsAkcay1fP5PK0layzVnH+l3OL4KhwxfOXc2r+9s4QdLX/c7nAOtfxRuPdspMb/yfqeVSrKnZiZc/heItcAtZ0Fdrd8RifiqLZbo3opagsWdc+RPJU6B7U4VUjuVBMuu1E5UPdupIPNJjbZYvLuK0FUWDWd8QLu1NrUbl/P5FkfCjCiJKIkj6UkmIRnvY4vx1HWXEv/DFpgkzp3Pbubx1xv44jtmMXVMud/h+O6MmTVccuwh3LxsHcs37fE7HMcLd8CdFzqVNx/6p1MZItk3YR58aCkUV8Bt58Dqe/2OSMQ3bbG45uEEVFmRn1uMu+1UBZLEUTuVBMz+7bZ7VeJkPImToLx3Eqc4QnuGZ/G0dMbpjCe7k1WQvR25JMCS/dzQ6F4zlPgfrkAkcTY2tPI/f13DKYdX877jp/gdTs748rmzmTiylP/84wp/7kS6utrhb9fAfZ+AQ0+FDzwII/Xv5Kvqw+FD/4IJ8+GuK+Bf39DFtxSk1s4EZdpePJAi4RDRSCgrsyTepOC2GFcljgRLY3cSx/k/7LZVZXpGTFssQWmvNamsKExXwhKLZ671xP283GSV+7Zm4kha+psPp8R/2vI+idPRleCzd71EJGy4/qJ5B/SQFrqK4gjfvWg+Gxpa+cYDa7DWh92q6lfAL06H526G4z8K770LSqqyH4e8WXm1MyPn6Mvg8e857VW7XvM7KpGsaovF33TXU4KjPBqmzdeZOKrEEclHDS0xQgZGlTnf2yVFYSqKM99e1Fd1qNvym8m5OL0rj8DZVl2VOJKW/ubDdSf+tWYMV14ncTq6Elx1ey0vbtnLt981lwlVpX6HlHMWTx/DR0+fzu+e28y3/prFRE7nPqe645dnQvteuOzP8PbvFM4Fbb4oKoF3/hTefQfs3Qw3nwqPf9+pnhIpAJqJE2xl0Yi/7VS95wAElS7IJWAaWjoZXV58wND76opoVipx3pTEcXfa68pcVaFbeTSmZztVRVRbjEt6upM4va6zVL2Ztry9cm2POQmcJ9c18L8XzuPceRP9DilnXXP2kbTHEtzyxAYS1nLtubMzV7GUTMCLd8DD34LWnTD3Ynj79c5W4pK7Zp8PhxwHf/0c/Os6qP01nHktzLkIQnmd6xU5qLZYnAlVJX6HIRlSXhzWFuPZoAtyCZiGls4D5sNAqr0o47tTxRk3oviA59wkTiZ32tuVSk6N7dVO1dwRpzOeoDiiilUZhgHbqbRmDFdeJnHqm9r59O9f4rmNu/nuRfO5aOFkv0PKacYYvnrebELG8KsnN9DaGeer5x1FuZd3nzua4MU74dmfOxUdhxwPl/4OJi/y7hySWZXj4ZLfwIbH4B9fgj9fBcuuhxM+AvMvdbaEFwmY1s7Em3YCkeAojUZo9aUSJ5U4KpgkTurz1E4jEhC7WmLdc3Bc1RXFrNvVktHzuluM9+TObctoO9W+ToyB0eUHDjYGaGyJMXGkuh1kGPqbD+cm/pM+zmzNc3mVxEkmLXc+u4nrH3yVeDLJje9ewJKjJ/kdVl4wxvCVc2dRGg3xs0fX8eQbjXxzyRzOmFkz/IMmupxf+F+5x3nEWmDKiXD2t2HmOaD5RPnp0FPh6mXwyp/h6Z/sr86ZcxEcdQFMPRFC+qVXgsGZiZNXS6EMgTMTx89KnAL53gqpnUqCpWFfJ4dVH3jzakxFlGc3ZH53qr62GAcyOqS9oaWTUWVRIuH91ddjyvdvq64kjgxLf/PhQqreTFdeXF10dCV48OXt/PrJDayoa+KUw6v51pK5TBlT5ndoecUYw3+dPZN/m1nDF/60in+/7XnOmlXDZSdM5ZTDxxIODSLpsmcjbHgcNj4Or/8T2ndDtBJmnQ/HXw0Tj8745yFZEArB3ItgzoWw5TlnMPVLv4XaW6FiHMw4C6adAoeeAlWqhJP85czEUVIyqMqiEfa2+TDjS+1UInnLWttvO9Weti66EkmKwplpNW+Lxd9UKe8mcTI92PhNn29ldrZVlwDrbz6c2qnSlrNJnG1721m+aQ9Pr2/kgRXbaO6IM2V0GTe8ez4XHD1Ju1ClYeHU0TzwqZP5xbL1/PqpjSxds5NJI0s5d/4Ejps2moVTRjLSNsHu9bB7A+xaC9tXOY/Wnc5Bysc6v8gftQSmn+kMyJXgMQamHO88Yq3w+kPwyl/g1b/BS79xXlM5EcbPdR7VR8Dow2D0oVA2RtVYktPiiSSd8aQqcQLMv5k4hbbFuC7IJThaOuN0xpMH7NQE+5Mau1tjjBvh/XVvImnp6EpSWtS7EsdZozJbiRN70+frzsdp2Kf/1zJM/c7EUfVmujJ+5drVFWP7tq3ErSWeTJJIWDrjzoVzRyzBvs4umtvjNLXHqG/uYNueDur2tHVPfy8pCnP+kdW8c8EUFk4ZRcgYaNmZ6bAzpJ+doQ7YMcr283zqfdbu/9MmU4+ebyec/sJk3BkynIilHl3OjkPxTuhqozjWyifDLXx00V7q6+vZtXM75ulGxj6zh1L2gtm/UCRMmKaKGbSMOZH2mfNom7AYO3YmxUVhIqEQ4T1xIqFWQsYQCjkVPwbn93eDOeD3+AN+pdfv93kmDFPe7jxsksiuNRRteYKiHSuJ7HqZ8BtLMXb/XSIbKSFZNpZk+TiSZdUkS0ZiS0aRLK7EFpVjo+XYolIIl2AjxdhwFEJF2HCRk7E3YWwonGrdCoFxHtaY1NsG55vI9EoW9fyG6+f5nnq8JhKJMrJ6vAdfKxmKWGcHzXuy/3O9rTPBWPYyxu6BfTuyfn7JvBqzl+KOXTRs35zV8xbv2U4l0NCRJLmvI6vn9kO4wzIG2Ld7O51Z/lpnW1FxGVWjqv0Oo+B0tLXQ0rw7K+fatredsexlUqT5gLVhUqSJsexl48YNhGu8nxPYHnPWpGoOXJMqupx4mndtpWF7ZhI58eZ6Zk6sOuC81TjxNGzfTMP2LO1uK4ES2VXHSGBvDGI91sKiGIwCmhq20hUN3ppRUlZJxYhRGT2HGcqW04sWLbK1tbVDOsHW9WuYdPsJQ41LsqWo3Nk5qmQkidLR7A6NZkvXCNZ1VrG2YwwvtY5kZesounK3aEtyRDExJptdTDU7mGp2MN7spsbspYa9jDb7qDItjKSVMpO7ZblrimYz60tPD+tjjTHLrbUFP8l7OOvEK0/9jaMeujRDEYn455iOn7ObEX6HkXHj2M2zJZ/wO4ysqK08k0Wf+/OwPlbrxPDWCIDn//JTjn3pixmISEQy7cLOr7LcHtn993lmHfcVf8XHiDLr6QlXsPjDPx7Wxw52ncj4b+Yjq8fx4rxrCYUMYWMIGYiEQxSFDEXhEKXRMKVFYUqKwgxmJEve67e9ZJDVA6ZH5YEJp/4MHfgIO1UMhCLO2+Go8ygqgUgJFJVCtMLZbajHgNowMDb1OKbHKbsSSZrbu9jb3kVzexcdXUk64gk6u5IkraUrkSSRtCQtJK3FWusUB3FgMZHtUWU0hNyh5LFWYEPq4TI2QSTeRlGilXCik3Cyk3Cik5DtIpRMPWwCYxOEbBysxZDEWOcB1nnb+Q7D9FfJdsA5+/uGO/D56MgJw/5cZfhqps3m2dlf9uXckZBhzqQqiiOZmW8g/mrujLO2fh9DuWHllfbisXx23IlZP69flu24kZLORr/DyLiy8Uf4HUJBGjf7JJ6NZW+diEZCzJtcRbjHNXnSwqqte+noSmbsvJGQ4ahJVZT0WpPWbt9HU3vmWk+MMcycUMmIXvN4NjS0sjPD26pLsHVFynnX+LO5INTje8vO5on6CEXxVv8Cy6BRhx0z8IvSlPFKHBGRQqA7rA6tEyIifdM6oTVCRORgBrtO6NajiIiIiIiIiEgeUBJHRERERERERCQPKIkjIiIiIiIiIpIHlMQREREREREREckDQxpsbIzZBWzKXDgiInlrqrV2rN9B+E3rhIhIvwp+ndAaISJyUINaJ4aUxBEREREREREREX+onUpEREREREREJA8oiSMiIiIiIiIikgeUxBERERERERERyQNK4oiIiIiIiIiI5AElcURERERERERE8oCSOCIiIiIiIiIieUBJHBERERERERGRPKAkjoiIiIiIiIhIHlASR0REREREREQkDyiJIyIiIiIiIiKSB5TEERERERERERHJA0riiIiIiIiIiIjkASVxRERERERERETygJI4IiIi4gljzEZjTLsxpsUYs8cY81djzCF+xzVYxpivGWPu9DsOERERkf4oiSMiIiJeOs9aWwFMAHYAPx7qAYwxEc+jyoJ8jVtERETyh5I4IiIi4jlrbQdwNzAbwBhzjjHmRWNMszFmizHma+5rjTHTjDHWGPNBY8xm4OFUFc8nex7TGLPSGHNB6u2jjDH/NMbsNsbsMMZ8MfV8yBjzBWPMOmNMozHmLmPM6F7nudIYs9kY02CM+VLqfW8Dvgi8J1VJtCL1fJUx5lZjTL0xZqsx5pvGmHDqfe83xjxpjLnRGNMIfM0YM8MYs8wY05Q6/h8y+oUWERGRgqIkjoiIiHjOGFMGvAd4JvVUK3AFMBI4B/ioMWZJrw87DZgFnA38H3BZj+PNByYBfzXGVAJLgQeBicAM4F+pl34SWJI61kRgD/DTXuc5GTgSOBO41hgzy1r7IPA/wB+stRXW2vmp194GxFPnOBp4K/ChHsc6HlgPjAO+BXwDeAgYBUxmGJVIIiIiIv1REkdERES89BdjzF6gCXgL8F0Aa+2j1tpV1tqktXYl8DucREtPX7PWtlpr24H7gCOMMYen3nc5ToIlBpwLbLfWft9a22Gt3WetfTb1uo8AX7LW1llrO4GvARf1anX6urW23Vq7AlgBzKcPxphxwDuAT6fi2gncCFzS42XbrLU/ttbGU3F3AVOBianYnhjal09ERESkf0riiIiIiJeWWGtHAiXAJ4BlxpjxxpjjjTGPGGN2GWOacJIt1b0+dov7Rqod6w/AZcaYEHApcEfq3YcA6/o5/1TgHmPM3lQyaQ2QwKmUcW3v8XYbUHGQYxUB9T2OdzNQ01fMKdcABnjOGPOKMeYD/RxbREREZMiUxBERERHPWWsT1to/4yRQTgZ+i1Ndc4i1tgr4OU6y44AP6/X3/wPeh9P21GatfTr1/BbgsH5OvQV4u7V2ZI9HibV262DC7uNYnUB1j2ONsNYe1d/HWGu3W2uvstZOBD4M/MwYM2MQ5xYREREZkJI4IiIi4jnjeCfObJg1QCWw21rbYYw5DnjvQMdIJW2SwPfZX4UD8AAwwRjzaWNMsTGm0hhzfOp9Pwe+ZYyZmopjbCqOwdgBTEtV/mCtrceZb/N9Y8yI1NDk6caY3m1gPT/vi40xk1N/3YOT5EkO8vwiIiIiB6UkjoiIiHjpfmNMC9CMM+j3SmvtK8DHgOuMMfuAa4G7Bnm824G5wJ3uE9bafTjzds7DaY16HTgj9e4f4lT8PJQ61zM4w4cH44+pPxuNMS+k3r4CiAKrcZIyd+Nsn96fY4FnU1+D+4D/sNauH+T5RURERA7KWNu7clhEREQkNxhjrgCuttae7HcsIiIiIn5TJY6IiIjkpNQ25R8DfuF3LCIiIiK5QEkcERERyTnGmLOBXThzan7rczgiIiIiOUHtVCIiIiIiIiIieUCVOCIiIiIiIiIieUBJHBERERERERGRPBAZyourq6vttGnTMhSKiEj+Wr58eYO1dqzfcfhN64SISN+0TmiNEBE5mMGuE0NK4kybNo3a2trhRyUiElDGmE1+x5ALtE6IiPRN64TWCBGRgxnsOqF2KhERERERERGRPKAkjoiIiIiIiIhIHlASR0REREREREQkDwxpJo6IiIiIiIhXurq6qKuro6Ojw+9QxGMlJSVMnjyZoqIiv0MRCRQlcSRtP/kJ3Hkn/OtfUF7udzQiIpILvvpV2LkTbrrJ70hEJJfV1dVRWVnJtGnTMMb4HY54xFpLY2MjdXV1HHrooX6H06/vfhdefRVuucXvSAJu61Y46yx48EGYOtXvaPKe2qkkbbfcAs8+C1/8ot+RiIhIrvjHP5xrNRGRg+no6GDMmDFK4ASMMYYxY8bkfIXV00/DsmV+R1EAXn0V1q51HpI2JXEkLVu2wIoVMHEi/OhH8NhjfkckIiK5YNs22L4drPU7EhHJdUrgBFM+/LvGYs5DMsz9IuuL7QklcSQtf/2r8+d998H06fDv/w6trf7GJCIi/komob4eOjqgqcnvaERERPrW1eU8JMPcL7K+2J5QEkfS8sADTvLmmGPgV7+C9evhv//b76hERMRPu3ZBPO68vX27v7GIiAykoqLiTc/dcMMNzJ49m3nz5nHmmWeyadOmPj+2vb2d0047jUQiwcaNGyktLWXBggXdj9tvvz2tmLZt28ZFF13U52tOP/10amtrh3X8/qxatYr3v//9nh4zl6kSJ0tUieMpJXFk2NranGHG554LxsCpp8JHPgI/+xns3u13dCIi4pdt2/a/rSSOiOSjo48+mtraWlauXMlFF13ENddc0+frfvWrX/Gud72LcDgMwPTp03nppZe6H1dccUVacUycOJG77747rWMMxdy5c6mrq2Pz5s1ZO6eflMTJEiVxPKUkjgzbww87pfLnnrv/uQ98ABIJp0JHREQKU88kTn29f3GIiAzXGWecQVlZGQAnnHACdXV1fb7uN7/5De985zsHPF7Pap+77767u9plx44dXHDBBcyfP5/58+fz1FNPHeqDEB8AACAASURBVPBxGzduZM6cOYBT9XPJJZcwa9YsLrjgAtrb27tf99BDD7F48WKOOeYYLr74YlpaWgC47rrrOPbYY5kzZw5XX301NjWo7PTTT+fzn/88xx13HEcccQSPP/5497HOO+88fv/73w/4OQWB2qmyRO1UntIW4zJsDzwAFRVOBY5r0SKYNAnuuQfSvPEgIiJ5auvW/W+rEkdEBu3Tn4aXXvL2mAsWwA9+kNYhbr31Vt7+9re/6flYLMb69euZNm1a93Pr1q1jwYIF3X//8Y9/zCmnnNLvsT/1qU9x2mmncc8995BIJLqTL3256aabKCsrY82aNaxcuZJjjjkGgIaGBr75zW+ydOlSysvL+d///V9uuOEGrr32Wj7xiU9w7bXXAnD55ZfzwAMPcN555wEQj8d57rnn+Nvf/sbXv/51li5dCsCiRYv4zne+02/1UZCoEidLVInjKSVx5KC6upz/a+XlBz5vrZPEOftsiEb3P28MLFnizMdpa4PUDQwRESkg27Y560FRUeYqcX71K2cb8z/8ITPHFxEBuPPOO6mtrWVZH/tQNzQ0MHLkyAOec9upBuvhhx/unpsTDoepqqrq97WPPfYYn/rUpwCYN28e8+bNA+CZZ55h9erVnHTSSYCTXFq8eDEAjzzyCNdffz1tbW3s3r2bo446qjuJ8653vQuAhQsXsnHjxu7z1NTUsK1nSWWAxWLOMP5EAlIdcZIJSuJ4SkkcOahrroGbb4YvfAH+8z/3J2VWrHDutL717TFueeF2tjRt4f0L3s+how7lggvgpz91Lq4vuMDf+EVEJPu2boWaGigpyVwlzn33wf33O9eDPW8m9LRunXNT/8ILMxODiHgszYoZry1dupRvfetbLFu2jOLi4je9v7S0lI6OjkEdq+d224P9mMGy1vKWt7yF3/3udwc839HRwcc+9jFqa2s55JBD+NrXvnbAud3PKRwOE3en0ac+rrS01NMYc1XP3EKBfMr+UBLHU5qJIwf1z39CJAJf/SrMmgXXXgtXXQXvuzwOJskXNs7nqvuv4rrHrmPGj2dw4V0XUjr9eUaNgr/8xe/oRUTED9u2wcSJMGHC8JI4P/gBXHrpwV+zbp1z97THzeM3uf56eM97dM0oIkP34osv8uEPf5j77ruPmpqaPl8zatQoEonEoJIy48aNY82aNSSTSe65557u588880xuuukmABKJBE1NTf0e49RTT+W3v/0tAC+//DIrV64EnJk9Tz75JG+88QYAra2tvPbaa91xVVdX09LSMugBya+99lr3HJ6g06iWLNEX2lNK4ki/mpth9Wr43Odg2TIYPRq+8Q24/37LprbVcNp1nDZnJo9e+ShbPrOFa068hkc2PMIZd57M4jMbuP9+/T8VEQm61IzMA7hJnPHjh9dOde+98Kc/7d+mvK9zrl/vvL1uXf/HWbvWKZE/WKJn40a4886hxygiwdHW1sbkyZO7HzfccAP/9V//RUtLCxdffDELFizg/PPP7/Nj3/rWt/LEE090/92dieM+fvSjHwHwne98h3PPPZcTTzyRCRMmdL/+hz/8IY888ghz585l4cKFrF69ut84P/rRj9LS0sKsWbO49tprWbhwIQBjx47ltttu49JLL2XevHksXryYtWvXMnLkSK666irmzJnD2WefzbHHHjuor8cjjzzCOeecM6jX5jsViGSJvtCeMravq69+LFq0yNbW1mYwHMklDz8MZ54Jf/87vO1tzkVzRwd85l8f4eblN3PPe+5hycwlB3xMY1sjC3+xkJYVb6Hxtl+ydKlzDJGgM8Yst9Yu8jsOv2mdKDzve59zTfbHP+5/rqbGaacNh53nd+0a2jEnTnSSP6++Ckcc8eb319c7rwH48Y/hE5/o+zjjxsHOnc4Mt/5+H/nkJ+EnP4G9e+EgoygyavVq+PjHnTh7z6CT4NA60fcasWbNGmbNmuVTROl74YUXuPHGG/l/9u47LKoz/f/4e+ggKAr2rkEUkaKxgJpoir1FY2JioiambXrvuZJN2c3vm2w0Mdm0NdUU1xprYtS1YldQ7F00FkRRQKTN+f3xeKgDzMDMnBm4X9fFNUw752HQmcPn3M/9/Pjjj0YPxS5ycnK48cYbWbduHV5e1e+84eq/35AQuHBBTQPWP1eEA7z5Jrz9NrzyCvzjH0aPxmVZ+zkhlTiiXJs2qcsePdSlyQT/3f89X277kpd7v1wmwAEICQhhzh1zyGg5Gw+fq8yda3biiIUQQjhTVpaqmFm5sqgiJzdXhTZ6Jc7587adeLt8uah6Z98+y48pXn1TXiXOxYsqwAE4eLD8/e3YUfG+QFWVHj1a/v3VNX8+rFpVccWQEMI1de3alf79+1NQUGD0UOzixIkTvP/++3YJcNyBFIg4ibzQdiUhjijXpk0QFqamUQEknUnikcWP0L9Nf9656Z1yn9etWTc+G/UB5nZL+WFmJleuOGnAQgghnOrPPyEnR53F1Hvf6JfNm6sQB4rCFGscOFD0fWUhTmBg0bSq0vbvL/r+WpuIMsxm1agfYO/e8sc0ZQpEREAFrSqqRR+DHNsK4Z7uv/9+PGvI0kZhYWH069fP6GE4jbRqcRJ5oe1KQhxhkaapEKdnz6Lbnlj6BMF+wfx6+694eVSczk+OnczA8fvITKvL355Jd/BohRBCGGHhwqLvd+1Sl6dOqUu9sTHY1txYD188PMoPVg4fVvf37Vt+JY4eADVoUH4lzqFDkJmpvq8oxFm6VE0n1sMWe5MQRwghnE/TpEDEaeSFtisJcYRFKSnqoFsPcVYfW83aE2t5re9rNKpjuUN/cSaTiW+fmoRnr8/44atgVq928ICFEEI4ldkMixfDLbeo68nJ6vKvv9SlPp0KbGtuvH+/Cmh69aq4EqdlS7Vq4pEjlpsr79sH3t5w003lhzj6VCo/v/JDnOxsSEhQ3ycmlj/uK1dgxYry76/oefr4cnJsf74QQoiqKSgoORVYOJCEOHYlIY6wSO+Ho4c47659l8Z1GjM5drLV22ga1JTJLxyGBge5d2J+4dlOIYQQ7m/LFjh7FiZNUmGNXomjhzjFp1PZWonTti1ER6sgxlJAc/gwtG+vvrKzLYdE+/fDddepoOf4ccvHjTt2qKBnwIDyQ5z164ueW1GI8/rrKtAqb+pWeXbvVoEYyLGtEEI4U/GZPTLLx8H0F1g+6OxCQhxh0aZN4OurDqI3ntzI8iPLeT7+efy9/W3azms3P43nbQ+ScsKDMWPgvvvghhtgzBjLB+ZCCCHcw8KFavWpwYOhS5eiSpxTp1QwEhKiVocC2ytxwsOhY0e1YpSlfjrFQxz9emn79qlthIWpkMRSY+IdO6BzZ/VZd+SI5UqYlSvBywvi48sPcdLT4euv1ferVln1YxYqPkVLjm2FMIanpycxMTFERkYyfPhw0tOr3wogPT2dkJAQ9JWAN2zYgMlk4uTJkwBcunSJBg0aYDYbvwjI/PnzK1zaXPfFF1/www8/OGFEzlH8PVfefx1Mf4ElLbMLCXGERZs2QWws+PjAu2veJcQ/hEeuf8Tm7bSq14r7RoTh2edfLFsGy5bByZMwd646gyuEEMI9LVwIvXurnjORkaqipKBAVeI0baqmRPn4qDDH2kocs1k1Ng4PVxU0ULZC5vJlteJVRSFOXp6qiAkPVyEOlJ1SpWkqxImNVfsymy1Pu1q5Uq3S2Lev+hktHeh/9ZXqrRMQgM3ThyXEEcJ4/v7+JCYmkpycTIMGDfjss8+qvc3g4GCaNm3K3mtvYgkJCcTGxpJwbX7mxo0b6dGjBx4ezvtzrLwVtKwNcR555BEmTJhg72EZRkIcJ5LpVHYlIY4oIy8Ptm1TU6l2nN7B4oOLeabXMwT6BFZpe6/0fQXt5ld4auGLnDpVdLbSis8KIYQQLuj4cdi5E4YPV9cjI9W0pqNHVSVO8+ZFj23a1PoQ5+RJtR29EgfK9sXRA5v27aFVKxUWlQ5xjh6F/PyiShwoG9CcPq2WQo+JKT8wunRJTRu76Sb1uNzcsuPJzYWPP4abb4ahQ1Ulji2VpklJRatASk8cIYwXFxfHKb1DO/DBBx/QvXt3oqKiePPNNwtvf+eddwgPD6dPnz7cddddfPjhh2W2FR8fXxjaJCQk8Mwzz5S43rt3bwC+/vprunfvTnR0NGPGjOHKtaVdZ82aRWRkJNHR0dxwww0A7N69mx49ehATE0NUVBQHr725zZgxo/D2hx9+uDCwCQwM5LnnniM6OpoNGzbw8ssvExERQVRUFM8//zwJCQksWLCAF154gZiYGA4fPszhw4cZNGgQ3bp1o2/fvuy79sb31ltvFf6c/fr146WXXqJHjx506NCBtWvX2u+X4CQS4jiRhDh2JSGOKCM5WR1E9+wJ/9rwL+r61uWxHo9VeXvt6rdjfNTdfL3zMzJyMgoPliXEEUII97RokbrUQ5wuXdTlrl2qEqdZs6LHNmli/XQqPSAJD1dBUJ06FYc4Pj4qyCm9zLj+nI4dVUASHFw2xNGbGsfGQocOYDKVDXHWrFEVOjffrEIcKDul6tdf1c/8/PPQr58KoopP3bpwQVXq5OeX/Xk1TYVh11+vrsuxrRDGKigoYMWKFYwYMQKAZcuWcfDgQTZv3kxiYiLbtm1jzZo1bNmyhTlz5pCUlMTSpUvZunWrxe317t27MLQ5cuQIY8eOLXxsQkIC8fHxAIwePZotW7aQlJREp06dmD59OgBvv/02f/zxB0lJSSxYsABQU5qeeuopEhMT2bp1Ky1atGDv3r3MnDmT9evXk5iYiKenJz/99BMAWVlZ9OzZs3Db8+bNY/fu3ezcuZPXX3+d+Ph4RowYwQcffEBiYiLt27fnoYceYtq0aWzbto0PP/yQRx991OLPl5+fz+bNm5k6dSp///vf7fRbcB7pieNEssS4XVW8TrSolfSmxhExGUyeO5dJMZMI9guu1jb/dv3f+HHnj8zeM5tJMfdRr17Fy7kKIYRwXcuWqabB4eHqekSECkGSk1WgceutRY9t0gTWrSu7jYycDJLOJnE8/TjZ+dlk52Wz8vfOwE2sv/INe7flENLydpZvzuXHpJV4mDzw9PBkwfpOQDQ7c+dxeE8BQU1uYEuyJ3P2rMJkMgEwf00Y0IUDLOTk3lxCW/RnfWIec/YUDWT2H+FAJEd953PmaB6hzQbzx8Y0OiRvoMBcQIFWwIxfu+HtG84u72/ZeTEXb9+HmL4kifNha/Dz8sPP05+33xtNh07+DBjgzd69av+rVkG7dmo/b74Jn36qTlxMnVryNTh+XFX7dO+uXlMJcURt9/TvT5N4poIO4lUQ0ySGqYOmVviY7OxsYmJiOHXqFJ06deLWa29iy5YtY9myZcTGxgKQmZnJwYMHycjIYOTIkfj5+eHn58dwPdEuJT4+nn/+858cPXqUNm3a4Ofnh6ZpZGZmsm3bNnpeW0EkOTmZ119/nfT0dDIzMxk4cCCgQqBJkyZxxx13MHr0aEBVCr333nucPHmS0aNHExYWxooVK9i2bRvdu3cv/HkaNVKryXp6ejJmzBgA6tWrh5+fH5MnT2bYsGEMGzaszJgzMzNJSEhg7NixhbfllFMmqI+pW7duHDt2rMLX2BVJJY4TSSWOXUmII8rYsgVCQ2Fr9iyy87OZEF39ua+9WvQirEEYP+z8gfti7yMiQipxhBDCXaWlqQoYXZ06KrTYuFH1rCk9ner0aVV1kpmbwfvr3mf23tkcTDuIRql5R+umgc/1vL55MpgA7yDY05cJ84t9Dq39AgKaMel39ccDeV/AodHcPuv2oses/A/UaciE39XZdEwzYG98yccsnw0NfJm49DZ13X8xqdubkTDnrqLHrEiEZqt4cvlD6npoN9ZsymbNsufU9UO3woH7YOQkQj74jbgW8QQ3mM/q1d7cf7/qk/PDD1C/vppyFR2tGvzr9H44PXqoS5lOJYQx9J44V65cYeDAgXz22Wc8+eSTaJrGK6+8wsMPP1zi8VNLJ7LlCAsLIz09nYULFxIXFweowOPbb7+lTZs2BAaqVgWTJk1i/vz5REdH891337HqWof0L774gk2bNrF48WK6devGtm3buPvuu+nZsyeLFy9myJAhfPnll2iaxsSJE/nnP/9ZZgx+fn54enoC4OXlxebNm1mxYgWzZ8/m008/ZeXKlSUebzabCQ4OJrGi5fiu8fX1BVRQlG+p3NDFSYjjRBLi2JWEOKKMpCRVNv7Dzu/pENKBns17VnubJpOJCdETeON/b3As/RidOrVh8WI7DFYIIYTT5eZC3bolb4uMhD//VN+Xnk6VkwNfrZ/J3zc9w+nM0wy+bjD3dLmHrk27cl2D6wjwDsDf25+xa+qRHmnizxdTyTfn8698fz58tx5J9x/CL6AAs2bmvhUtuNLRg5/+tgtN0/gmP5Sp2xqyfvwuAoPUKi8TF7fHK0pj+iMqJfk8ozFfTWnE5vt24eOrgqPB34TTuU82//qbWhv9wzNN+PW7Bmx9eA8+3p6kn/eh51ttePGNSzzz3Gk8TZ68mFKXeXN8OPZiOjkFVxkzrC77G+Xy5ou9Sb7gx7x980hv/Btzl/bn/zIL+O3nRly+rJodv/02PPKIqlq6dvKdpCRVwdStW9HrKkRtVlnFjKMFBATwySefMGrUKB599FEGDhzIG2+8wfjx4wkMDOTUqVN4e3vTu3dvHn74YV555RXy8/NZtGgRDz30kMVt9urVi48//pjvvvsOUJU0r7/+OkOGDCl8TEZGBk2bNiUvL4+ffvqJ5teS8MOHD9OzZ0969uzJ0qVLSUlJ4dKlS7Rr144nn3ySEydOsHPnTgYMGMDIkSN55plnaNSoERcuXCAjI4PWrVuXGEtmZiZXrlxhyJAh9O7dm3bXSgaDgoLIyMgAoG7durRt25ZZs2YxduxYNE1j586dREdH2/vlNpxMp3IiWWLcrqQnjiihoECtvtG6wyXWHF/DxOiJheXp1XVv1L0AzNg5g4gItTpVWppdNi2EEMKJcnLg2gnYQl26wLVenCUqcRo3VqHJI7++SYu6Ldg4eSNLxi/hjRvfoG+ToQQXhNOyXktCA0I5fNCbzp28CA0IpUlgE3pG1wOg4Hx7OoR0oGNoR86kBBLZMYDIRpF0adyFPjFNAfDPiCSqcRRRjaM4cbgO3aICC6/3jmmM2WwiIEs9p6VvF06d8KFfr3pENookslEkfbqFknPVg4ArnegQ0oGjiW0AGD20Hk0Cm9CwTkN6Xu/LpXQTl87V4+T+xqxf7c8Lz/nwePyDfDHsCw48foCb+nuSmRpC+LsDmTIth+hotbLVzJnqdbntNkhJUa9NUpKalla/vroux7ZCGC82NpaoqCh++eUXBgwYwN13301cXBxdunTh9ttvJyMjg+7duzNixAiioqIYPHgwXbp0oV69eha317t3b1JSUrj+WvOruLg4jhw5UtgPB1ST5J49e9K7d2866l3dgRdeeIEuXboQGRlJfHw80dHR/Pe//yUyMpKYmBiSk5OZMGECERERvPvuuwwYMICoqChuvfVWTltoRpaRkcGwYcOIioqiT58+fPTRRwCMGzeODz74gNjYWA4fPsxPP/3E9OnTiY6OpnPnzvz222/2fIldhlTiOJEsMW5fmqZZ/dWtWzdN1Gz79mkaaNptL8/TTG+ZtOPpx+26/X7f9dPCPgnTFi0ya6Bpa9fadfNCGAbYqtnwflpTv+RzonYID9e0O+4oeduvv6rPD9C0vXuLbn/2i4UaaNo9H07XCswFJZ5zxx2aFhqqaSdPalpmpnru228X3b9rl7rtp5/U9ZwcTfPw0LQ33ih6zI4d6jGzZqnrqanq+kcfFT1m40Z122+/qeurVqnrS5YUPWbdOnXbokWalpenadHRmtaihfpet2GDesz8+Zp2552aVreupqWnl3wd9DH79PhWA0379N95Je6rW1fTOnfWtIsXNa19e027/Xa1D9C0d96p6FUX7k4+Jyx/RuzZs6cKr6bxMjIyNE3TtKysLK1bt27atm3bDB6Ra3Ll3++aNUWfW599ZvRoarioKPVCd+pk9EhcmrWfE1KJI0rYuVNdbsn/lv5t+9OqXquKn2CjidETOXjhIDn11bIg0txYCCHcT3mVODp9OtXe1L18tucNAAY1nYSHqeiwIy8Pli6F8+dh/PiSK1PpwsLUEuL6fcePq9Wi2rcveozeQFhftar4ylTFtwNw6JC6XLNGXV7rVQqUXGb8s89UlczUqeBVbOJ5VJQaz9y5MGuWmh5V+uR7RASEhEDu5kngc5lDzYtWbImMhPnz4cABtRz54cOqT46Xl9qu9MQRwn089NBDxMTE0LVrV8aMGUPXrl2NHpKwkVTiOJH0xLErCXFECbt2gYeHxknfP5gYPdHu2x/TaQwB3gH8cf5rAgKkubEQQrgjSyFOWBh4e0NgoOqXczX/KuPmjKNOyGUAzp4pecixaRNkZMDtt6ueMY88om4vHuL4+qqQRg9m9KBGD25A7Ss0tGiZcUshToMG6uvgQVi8WPWnueUW1a+n+GMaNYKVK+GNN2DQILi28EqhgAC1HPkPP4CnJzz1VNnXxsMDbrxRfd/51m1M3fEuy48sL7y/f3/1/GurDqO3mfDxkWNbIdzJzz//TGJiIvv27eOVV14xejiiCqQnjhNJTxy7khBHlLBzJ9RtfoaAAE9Gdxpd+RNsFOQbxOhOo/nv3l8J72iWShwhhHBDlkIcb29VzaJX4by16i12nt3JD+Om4esLZ86UfPwff6jA4+uvYdIk2LpV3a5Xzeg6dlQhz5dfqtWvoGQljn49ORmmTYN331WrZbUqVUh63XXw++8qNIqOhjlzyv5cHTuq6qDcXLUtSy3hYmLU5b33lmzgXNyAAepn+/69XnQK7cS98+4lIyej8P5x42DKFBVA6StTSYgjhBDOJZU4TiQ9cexKQhxRws6dGtkNNjOswzACfQIdso87O99J+tV0GrQ8I5U4QgjhhiyFOABPPAF/+5uqwvly25fc2flOhnYYQpMmZUOcZcvUKk3BwfDppyoAuu46Ve1S3EMPQVCQqtT5+9/B318tW15c+/aqsuXJJ9V98+apSpniwsLg2DFo21aFOaVX14KiKVWvvqrGYkmPHiqgef75cl8eJk+G/fuhW7Q/Xw77kjOZZ5izt2Rq9PTTcOECNG6srvv4yHQqIYRwJglxnEimU9mVLDEuCmVkwNGjJrhpM6PCRzlsPze3vZk63nXIqLeFlJSRZGSoA3QhhBDuITfXcojzwAPqctbuhaRfTWdy7GRABSvFF0pJS4MtW+DNN9X1OnVUtU16etltDh8Ow4aplRPnzVP9ZkpXyDzwgJrGdd990KuX5TEPGKCm8C5cqKZfWXL77ZCaCi++WP7P/uijMHhwyelapXl5FYVAfVr1IaxBGN8nfc+kmEklHlc8aPL1lWNbIYRwJplO5UQyncquJMQRhZKT1aVnkz0MCavgCLaa/L39GXTdIFYe/A0Yyb590L27w3YnhBDCjsxmdSzm41P+Y75P+p7mQc25qe1NALRpoypvLl5Uy2kvX67WAxkwoOg5DRuqL0tMJtUUODLS8v39+6uvikyYoL4qcsst6qsivr4VBzilmUwmJkRP4I3/vcGx9GO0CW5j8XEynUoIIZxLKnGcSKZT2ZVMpxKFkpI0AOK7B1LPr14lj66eUR1HcTFwHSDNjYUQwp3ox2GWKnEAzmae5fdDv3Nv1L14eqhSk5deUlU2b6iFqli2TE2jqi0B/j1R9wAwY+eMch8jIY4QxgkMLNtC4K233qJ58+bExMQQGRnJggULStyvaRqhoaFcvHgRgNOnT2MymVi3bl3hYxo2bEhaWppjB2+FVatWkaB3U6/AggULeP/9950wItcgIY4TFZ9OpWnGjqUGkBBHFFqz+SL4XmJcfLzD9zU0bCgeDY7j6Z0vzY2FEMKN6H1bygtxft71MwVaAROii8peYmLgscfg889h+3bV1Pjmm0su312TtQluQ782/fgh6Qe0cg5efX2lJ44QruaZZ54hMTGRWbNmcf/992M2mwvvM5lM9OrViw0bNgCQkJBAbGxsYViyf/9+QkJCCAkJcdp4CwoKLN5ubYgzYsQIXn75ZXsPy2XpuYLJJCGOQ2maeoFNJvV9Of9OhfUkxBGFNmzLhEa7GNlxhMP3Vd+/Pv3b98Ur9IhU4gghhBupLMT5Pul7ujfrTqeGnUrc/vbbqhfN2LFw6hQMHOjggbqYidETOXjhIBtPbrR4v1TiCOG6OnXqhJeXF+fPny9xe3x8fGE4kpCQwDPPPFMi1OnduzcACxcupGfPnsTGxnLLLbdw9uxZAFavXk1MTAwxMTHExsaSkZHB6dOnueGGGworgNauXQvAsmXLiIuLo2vXrowdO5bMzEwA2rRpw0svvUTXrl2ZNWsWn3zyCREREURFRTFu3DiOHTvGF198wZQpU4iJiWHt2rWkpqYyZswYunfvTvfu3Vm/fj0A3333HY8//jgAkyZN4sknnyQ+Pp527doxe/ZsB7/KzqfP7KlTR2b5OJQe2tSpoy7lw67aJMQRgApFUw7Wp1H7MzSv29wp+xzVcRQ59RNJ2iX/kYUQwl1UFOIknUki6WwSE6MnlrkvOBg++ACOHFHXi/fDqQ3GdBpDgHcA3yd9b/F+CXGEcF2bNm3Cw8ODhqUad/Xu3bswxNm8eTO33XYbKSkpgApx4q9Vt/fp04eNGzeyY8cOxo0bx//93/8B8OGHH/LZZ5+RmJjI2rVr8ff35+eff2bgwIEkJiaSlJRETEwM58+f591332X58uVs376d66+/no8++qhwHCEhIWzfvp1x48bx/vvvs2PHDnbu3MkXX3xBmzZteOSRRwqrivr27ctTTz3FM888w5YtW5gzZw4P6F3pSzl9+jTr1q1j0aJFNbJCR3/PDQyU91+HKv5C0Y2boAAAIABJREFUgyRmdlBLCplFZTbvOU1BdlN6dXXMsuKWjAwfyRMNp5OyZixXrpRdVlYIIYTrqagnzo87f8Tbw5txkeMsPvfee+Gbb1R/nNatHThIFxTkG8ToTqOZuXsmUwdNxc/Lr8T9ssS4EPD005CYaN9txsTA1KlVe+6UKVOYMWMGQUFBzJw5E1OppfG6d+/Ojh07yMrKIi8vj8DAQNq1a8ehQ4dISEjgueeeA+DkyZPceeednD59mtzcXNq2bQuoEOjZZ59l/PjxjB49mhYtWtC9e3fuv/9+8vLyGDVqFDExMaxevZo9e/YUVvbk5uYSFxdXOI4777yz8PuoqCjGjx/PqFGjGDXK8mqzy5cvZ0+xUvjLly8XVvYUN2rUKDw8PIiIiCisHqpJJMRxEv3FlUocu5FKHAHA98u2A3BHfxuW3KimlvVa0j4iA00zFa6MJYQQwrXpQYOl1amWHlrKze1uJiTAcg8IkwmWLIFVqxw3Plc2NmIs6VfT2Xxqc5n7ZIlxIVyPXr2ydu1a+vbtW+b+gIAAwsLC+Oabb+jatSsAvXr1YsmSJZw7d47w8HAAnnjiCR5//HF27drFl19+ydWrVwF4+eWX+c9//kN2dja9e/dm37593HDDDaxZs4bmzZszadIkfvhB9dK69dZbSUxMJDExkT179jB9+vTCcdTR/zgGFi9ezGOPPcb27dvp3r07+fn5ZcZtNpvZuHFj4fZOnTplsbmzb7G0vrx+Xu5Mf8/195f3X4eSEMfupBJHALB8wzkAhvZx7qnRETe0ZsrnsGbjZXr0qOvUfQshhLBdedOp0q+msyd1D3dF3lXh8wMCam/lZXxLNbUiISWBG1rfUOI+mU4lRNUrZowUHx/P1KlTeeuttwCIi4vjnnvuoVevXoWVO5cuXaJ5c9Wu4Pvvi6ZUHj58mC5dutClSxe2bNnCvn378Pf3p0WLFjz44IPk5OSwfft2XnvtNR577DEOHTrEddddR1ZWFqdOnaJDhw4lxmI2m0lJSaF///706dOHX3/9lczMTIKCgrh8+XLh4wYMGMC0adN44YUXAEhMTCQmJsaRL5NLystT770+PjLDx6H0F1cPCuXDrtqkEkeQnZfN4d31qds4jeBgU+VPsKO7+/YG33SWrjvt1P0KIYSomvJCHL1hrx5UiLJCA0IJDwknIaXsKjES4ghhnCtXrtCiRYvCr+L9ZirTu3dvjhw5Uji9qWvXrpw8ebKwHw6o5crHjh1Lt27dCA0NLbx96tSpREZGEhUVhbe3N4MHD2bVqlVER0cTGxvLzJkzeeqpp2jYsCHfffcdd911F1FRUcTFxbFv374yYykoKOCee+6hS5cuxMbG8uSTTxIcHMzw4cOZN29eYWPjTz75hK1btxIVFUVERARffPFFNV4995WbWxTiyPuvA0lPHLuTShzB8oOrMR/uT9yIDKfvu2uzWLybb2BnUsPKHyyEEMJw5YU4CSkJeJg86NG8h/MH5UbiW8az8MBCNE0r0V9DlhgXwjjFlw631dixY0tMNfL19SWn1H/mkSNHMnLkyDLPnTZtWpnbJk6cyMSJZZvD33TTTWzZsqXM7ceOHSv83tvbm3Xr1pV5TIcOHdi5c2eJ22bOnFnmcZMmTWLSpEmAWqmqOEs9c9xdbi54e6svCXEcSKZT2Z1U4gi+W7wPcuox8fZGTt+3h8mD6yIyOX+sGbl5BU7fvxBCCNtUFOJEN44m0Md5DfLdUVyLOM5fOc+hC4dK3C5ngoUQwrlkOpWTFF/LHeTDzg4kxBH8709fTJ75DBlooUulE9zQIxhyA5m/YZch+xdCCGE9S6tT5Zvz2XRqk0ylskLxvjjFSYgjhBDOJdOpnESmU9mdhDi13KELh7i4qxfto85Sr54xYxh3i1oR678rDhgzACGEEFaztDpV8rlkMnMzJcSxQqeGnajnW89iiCPTqYQQwnkkxHGS0iGOvNjVJiFOLffrhtVwJpZRw/wMG0Nc13qYPPNJ2JJl2BiEEEJYx9J0qg0pGwA1VUhUzMPkQVzLOBJOlgxxZIlxUZvVxOWrhev/XqUnjpNITxy7kxCnlvvvgksAjB8dYtgYfH2hUZvznD7YmNSsVMPGIYQQonKWQpyEkwk0CWxCm+A2hozJ3cS3iGf3ud1cunqp8DY5EyxqKz8/P9LS0lz+D35hG03TSEtLw8/PuBPFlZGeOE4iPXHsTlanqsWy87LZndCKOg0uER1t0Fyqa7rFerHk9xiWHV7G+Kjxho5FCCFE+SyGOCkJxLeML7HakihfXMs4NDQ2ndrEgPYDgKI/Isxm8JBTbKIWadGiBSdPniQ1VU7k1TR+fn60aNHC6GGUS6ZTOYn0xLE7CXEcYf9+lTS68JsWwMrDazAfupn4oRmYTMaGODfHNWDJbA/mbl0vIY4QQriw0iHOmcwzHLl4hEevf9S4QbmZHs174GHyICEloTDE0V/PvLyyK38JUZN5e3vTtm1bo4chaiEJcZxEplPZnYQ49nTiBLz8Mvzyi3o3eOYZePVVqFvX6JFZ9P3ifXB1IBPHBBg9FGJj1WnH5RtSMd9nxsMkpyGFEMIVlV6dSu+HI02Ny7FnDzz+eImD1rpAl17+JMz9GF5fDoDPqXHA4+TeeCu+XtnGjNVWvr7w739DeLjRIxFCCJvl5RX1xJHiEAeS6VR2JyGOvXz0Ebz2mvr+1Vfh1Cn4f/8PvvkGpk+H4cONHZ8FK//0xeRRwNDBxp/yi45Wl5ePtWXH6R10a9bN2AEJIYSwqPTqVBtObsDH04euTbsaNyhXtno1/O9/0LdviSW94jOCmdHoDAV+vnhiKrwr1zcIvN2gN8jVq7ByJaxbJyGOEMIt5eaqGT5SieNgsjqV3UmIYw/r18Nzz8GwYfDZZ9Cqlbr9iSdg8mS49141xapxY2PHWUzKpRTSdvSmXdRpgoONn/bVoAE0b1nAqTOqL46EOEII4ZpycsBkAq9rRxCbT20mtkksvl7GnxBwSdnXqmoWLoR6RVOXeyX9wOfzJ7L/l2lENIzA9yvgYcj5ZS40M2aoNjl3Th3XZLtJ1ZAQQpQi06mcRHri2J3MWamuvDz429+gZUs1jUoPcAC6dYOZM9UBzvPPGzdGC35YsRnOdeGOsa7zT6BbrCe+53ux7Mgyo4cihBCiHDk5ahaNyaRWH0k+l0xU4yijh+W69JDD37/EzV0adQFg97ndQFGRjtv8IaH/PBLiCCHcVOklxmWBNAeRnjh25zp/wburTz6BXbvUpZ4uFhceDi++CDNmqHJqF/HrrHwAHpvQ1OCRFImNhdxzbVi3by+ZuZlGD0cIIYQFeogDkHollbTsNCIaRhg7KFeWna2Wm/L2LnFzx9COmDCxO1VCHCGEMELxJcYBCgqMHU+NJT1x7E5CnOo4eRLefBOGDoWRI8t/3KuvQtu28OijLvGPtsBcwN7VETTqeIAWLVxnOdjhw0Eze5C/exirj602ejhCCCEsKB7i6FUknRt2NnBELi47WwUepZZf9/f2p139dmVCHL3nkMvz8lJfEuIIIdxU8elU+nXhADKdyu4kxKmOZ58FsxmmTStzcFaCvz98+ins2wdTpjhvfOX4LWEPBae7MGB4htFDKaFrV2h/nRmPPXex7LBMqRJCCFeUm1ssxLkWQHRuJCFOufQQx4LOjTqzJ3UPUPSautUfEf7+EuIIIdyWhDhOItOp7E5CnKo6ehRmz1bLiLdtW/njhwyBQYPg448NTx+//PE8AM9Obm3oOEozmWDcnR6Yj/RjSeI2o4cjhBDCgpycogPe3ed2E+wXTNNA15ma63IqCnEaduZA2gFyC3Ld848ICXGEEG6seE8c/bpwAP2F1T8L5YWuNglxqmr6dJU6PPyw9c959FE4fRoWL3bcuKyQ8EczAtruJDY81NBxWDJuHKB5cmhdFCcunTB6OEIIIUopMZ0qdTcRDSMwVVSNWttVEuLkm/M5mHZQQhwhhHCy0j1xZJaPg+TlFS1rKUuB2YWEOFWRlwfffAODB5dcjaoygwdD8+bw1VeOG1sldu7NJPN4OD1vTTFsDBWJjIT24Vdh9538efhPo4cjhBCiFD3E0TSN3am7pR9OZSqZTgUqDNODMbfpiQMS4ggh3JpMp3IS/YU2mdSlpGXVJiFOVSxerCpqHnrItud5ecHkyfD773D8uGPGVokp36jw5oF76huyf2vce5cvnOjL/C1bjB6KEEKIUvQQ51zWOS5kX5AQpzIVhDjhIeF4mDzYk7rHPf+IkBBHCOHGJMRxEn3eGkgljp1IiFMVX30FzZqpPje2mjxZXU6fbt8xWWnJ/DqYmm9jTFw3Q/ZvjXHjTKB5sHJRAwrMstafEEK4Ej3EkabGVqogxCm+QpVb/hEhIY4Qwk1pmioIKd4TRwpEHESftwbqxXarDzrXJCGOrY4fV5U0kyeryhpbtWqlplVNnw75+fYfXwUOHoRzh1rR4cZt+Hr5OnXftggPh9YdL3Jlxwi2n95u9HCEEEIUUxjiyPLi1qkgxAH1+u0+t9v9lhgHCXGEEG5L/zNMKnGcQC95AqnEsRMJcWylV9DoFTVV8dBD8NdfsGSJfcZkpS+/TwfUClCubsJ4bzjVixkrZJUqIYRwJfqx2J7UPQT7BdMksInRQ3JtVoQ4By8cxOSlDmrd6thWQhwhhJvS32slxHGC0tOppOSp2lz/r3lXYjbDt9/CwIHQuhrLcw8dCk2bOn1K1S+/mKHVGu6Ii3fqfqvi8YcCMXnlMuu7xkYPRQghRDHFp1N1bthZVqaqTGUhTiO1QtWprKOAm/0RISGOEMJN6e+1ssS4ExSvxJHpVHYhIY4ttmyBkyfh7rurtx0vL7jjDvjjD8jMtM/YKpGcDH8daUBw9z/oFNrJKfusjkaNoHP/ZE6vv5WUc5eNHo4QQohrVIgjK1NZrZIQJ6JhBABHLu8D3OzYVkIcIYSb0otBZIlxJyjeE0emU9mFhDi2mDtXBTDDhlV/W2PGqCPhpUurvy0r/PyLGUwFDB6e5TZnTR9/XIPcQN7+2JiVvIQQQpSVkwNmj2y1MpU0Na5cJSFOx9COeJg8OHRJ9RiSnjhCCOF4Mp3KiaQnjt1JiGMtTVMhzs03Q307LM8dH6/KTebMqf62KqFp8MOMXGi7glHXu/5UKt19Q7vg0XITs75rhNls9GiEEEKAChmyzBcAaWpslUpCHD8vP9rXb8/+9F2Amx3bSogjhHBTEuI4kfTEsTsJcayVnAyHDsHo0fbZnqcnjBoFixfD1av22WY5tm6FUyf8oMuv3Nz2Zofuy558PH2IGr6WS381Ztkyo0cjhBACVIhzueA8UDQVSJSjoEAdvFYQ4oDqi7P34k7Azf6IkBBHCMf5/HM4d87oUbiFNWtg5UrbnqPnCNVZYjw52Snn492fLDFudxLiWGvuXDCZYORI+21z9GjVE2f5cvtt04KZM8HkmUds/2OEBIQ4dF/2NuEuf6hzhv/30RWjhyKEEAJ17JWed476fvVlZarK6CdpKglxIkIjOHRxP56emvtNpyookLOqQtjbmTPw6KPqIF5U6q234NVXbXuOPSpxPvkEHn7YtufUSjKdyu4kxLHW3LnQpw80tuNqSf37Q716atsOtHpNPlrLBIZ26e3Q/TjCkI63QNfprF7uT3q60aMRQojaTdNUJc6F3NNENIxwmx5rhtGrVKyoxCnQCvDx0dzr2Fb/uaQaRwj7yshQl05aAMXdZWTY/lLZI8Spyn5rJZlOZXcS4ljj0CHYudN+U6l0Pj4wfDj89hvk59t329eYzarUj0ZJDGg/wCH7cKQOIR1oGH4YTTOxd6/RoxFCiNotP18FORfyTtMxtKPRw3F9VoY44SHhAHh450uII4QoSgYkIbBKZqYxIU5mpjqx4aA/42oOqcSxOwlxrDFvnrq87Tb7b3v0aLhwQU3mdIDjx+Fqthe+zQ7Rq0Uvh+zDkUwmEzf1UOX6u5LlHVIIIYykT/XJMqfRIaSDsYNxB1aGOPprafLMc69jWwlxhHCMrKySl6JCWVm2v1T26IkjvyYrSU8cu5MQxxpz50K3btC6tf23PXAgBAQ4rCvWzp0aAD1i/fH29HbIPhxtTNz14HWFFZvPGD0UIYSo1Qr7tXjmFFaPiApYGeIE+QbRNLApmudV9+uJAxLiCGFvUoljEyMrcYpfinJIJY7dSYhTmbNnYeNG+zY0Li4gAAYMgIULVY26na3clArA7f3ct+x9YNgt0HA/W5Mk5hZCCCMVBgxeOVKJYw0rQxyA8NBwCjyy3evYVkIcIRxDSjxskpWl+sgXFFj/HHuEOPJrspL0xLE7CXEqs3Spuhw2zHH7GDoUUlKuNa+xrzVb0iD4KLdF32L3bTtLXd+6NGpznpTDQUYPRQghajX9ANfklU/7Bu2NHYw7sCHE6dCgA3lkSYgjhJASDxvk5RV9NtkSpujPKT6dSipxHKR4JY5Mp7ILCXEqs3gxNGsGMTGO28eQIUX7srODe/0IanGclvVa2n3bzhTbxZe8C83Yf+ovo4cihBC1ll6J0zCoLj6ePsYOxh3YEuKEdKDAlE3GFTc6uJUQRwjHkBIPqxV/iWx5ufRiEB8f8PQEk0l64jhM8Z44Mp3KLiTEqUheHixbpkIWRy6j2qwZxMbaPcRJy8gg63QLOkea7bpdIwyOU/2Ifli52eCRCCFE7aWHOM0bhBo7EHdh43QqvHJId6e/BiTEEcIxpMTDalUNcYpPpzKZqpYtSIhjJemJY3cS4lRk/Xq4fFlNd3K0oUMhIQEuXrTbJmf8bwuYvbklrondtmmUQXGtAPhjY4rBIxFCiNor+6o6KdCyfiODR+ImbKzEwTOXS1euOnhQdiQhjhCOIemA1YrnXLZkXsVDHP3SlmyhoED14bF1v7WS9MSxOwlxKrJ4sfoHd/PNjt/X0KFgNsMff9htk7+tOQLAbTeE2W2bRmnf3oSHVx67kvPJLZD0VgghjHDq4nkAWoe4/8kBp7AhxGkb3BaTZx4ZV9xoeSoJcYRwDAlxrFbd6VR6tuDtbVu2UNX91kqllxjPy3PIgj61iYQ4FVm8GG68EYKc0FC3e3cIDbXblCpN09i64yomz3wiI9xzafHivLygZbsr5J65joSUBKOHI4QQtdLhcycBaNewucEjcRM2hDjent74+3uSle1GZyglxBHCMWQ6ldWMqsSp6n5rHU0r2xMHpBqnmiTEKc/Ro7B3r3OmUoHqqDV4sFoNy5b18cqRfC6ZjJQ2NGtzufD/irvrFh0AqREsPbjU6KGoqikhhKhljl84DUD7hi0MHombsCHEAQjy9yU7p/rHAE4jIY4QjiGVOFazR08c/dKWEEcqcaxUuuRJQhy7kBCnPHpFjLNCHFANlNPSYHP1m/cuPbQUzkVyfYyfHQbmGqIjvSG9LYv2rHTujvVpbpMnQ9++qhG1lxe0aAH9+sHDD8OqVVIWKISo8Y6nnQGgeXBDg0fiJvRww8+6z+J6Af7k5GiYNTc5USAhjhCOoZd2XL1ql5O7NZlU4rg4Sy908dtFlUiIU57FiyEsTH05y8CBqiLHDlOq5iethEtt6NE1wA4Dcw0REYDmwZ69+RxPP+74HWZlwQcfqH8DgwbBvHmqff2gQfDKK6pXUn4+/Por9O8PnTvDtGlFy7cIIUQNc/JiKgB+fg5csbEmyc4GX1/wsO5wq35gAFq+DycunXDwwOzE11d9LkqII4R9SZmH1aQnjosrvpY7FL3gEuJUi4Q4lly5oiornFmFA1C/PsTHVzvEOX/lPBu3q0i4Sxd7DMw1dOp07ZvUCH7b/5tjd7ZmDURHw4svQvPm8PPPcPq0uv2bb+C99+D772HdOjhzBr79FgID4cknoVs32LrVseMTQggD6I2NfX0NHoi7yM62eioVQEhQIBT4cCDtgAMHZUcmk6oykhBHCPuSMg+rVacSx8NDnT8HqcRxGKnEcQgJcSxZuVKVLzo7xAG1z8REOHWqyptYdGAR2tkIACIj7TUw44WFqTfa0KwbHRfiZGerIObGG9X0qP/9TwU3d91V/l8t/v4waZKaBrdoEaSnQ69e8OqrMt9TCFFj5OTncP5yBiAhjtVsDHFCg+pCgQ/7z+934KDszN9fQhwh7E3KPKxWnZ44xfuGSk8cB9FfVOmJY1cS4liyeLGqqujb1/n71oOjpVVv3jt/33wC0+MIDNRo3dpO43IBPj4qyGmQ2YfVx1ZzIfuCfXeQlqamSE2bpoKcnTtVzxtbDB0KyckwcSL8858wbBhkZNh3nEIIYYDDFw+j5auDMAlxrGRjiFMvIAAKfN2nEgckxBHCETIzoU6dou9FubKyiooCbZ1O5V1sAd+qTqeqU0dCnArJdCqHkBCnNE1TIc4ttxhzlNq5M7RqVeUpVVfyrrDs8DICzt5ETIzJ2mn4biMiAq6ebkuBVsDiA/ZZjh1Qq5HFx8P27TB7Nnz8cdGHp62Cg2H6dDXtasUKVdVz+rT9xiqEEAY4kHYACtTnooQ4VrIxxPHzM2Eq8GN/mlTiCFGrZWVB48ZF34ty6XlXUJDt06mqU4mj76txY8nZKiTTqRyihv2JbwfJyZCSYsxUKlBR8tCh8OefVWqQ++fhP8lOD+LcwdYMGuSA8RksIgJOHvOjqV87+02p2rUL4uIgNRWWL4cxY+yz3fvuU9OrDhxQ2z982D7bFUIIA+w/vx8K1MFX8QNfUQEbQxwfH6DAWypxhKjtMjOLQhxJCCqUlaVCHFsrYuw1napxY8nZKlTedCoJcapFQpzS9AqYIUOMG8OQIerdYM0am586f/98/I+NKdxMTdO7N5jNJmKynuf3Q7+TnVfNA8dDh+DWW1WznfXroU8f+wxUN2gQrF6tPoBvvRX++su+2xdCCCc5kHaAOh4hgIQ4VqtCiKOZPTl+8WT1P9+cRUIcIezLbFaLrEgljlUyM1UXjMBAYypxGjaUnK1C5VXiSE+capEQp7TFiyE2Fpo1M24MN92kJnYuWWLT0/LN+Szcv5CGpybStCnExDhofAa66SaoWxcK9gwnKy+LFUdXVH1jp06paXP5+aoCp3D5Kzvr1k31OEpNVUFOWppj9iOEEA60P20/9b2b4O1t9YrZIjsbAgKsfnjhNLUCbw5eOOiYMdlbQICEOELYU3a2au8glThWqWoljj164gQEqGlckrNVQHriOIQchhV38SIkJBhfwhIQAP3729wXJyElgbTMS5xPjmXIEDUzq6bx8VG9gretak6QV31+21fFKVVpaSpQuXABfv/dcQGOrnt3WLhQTakaPFiaHQsh3IqmaexO3U197ybSD8cWV67YPp0KoMCHPal7HDMme/P3Vz+nEMI+is/TKX5dWGRkJU5V9lvrSE8ch5AQp7g//lAljEb1wylu6FA4eFB9Wem3fb/h/deNXMnwMTyHcqTbboO0NBPX5z/NggMLKDAX2LaBvDy4/XY4cgQWLIDrr3fMQEvr1w/++1/Ytg3uvVf9WxNCCDdwJvMM6VfTqefVSEIcW1SlJw5gMvu5V4gjlThC2I+EODYxsidOVfZb68gS4w4hIU5xixdDaCj06GH0SIqqgaysxjFrZmbtmUWrc4/g7a1mCdVUgwapknO/g+M4l3WONcdt6B2kafDEE7BqFfznP7YvIV5dI0bAlCnw22/wxhvO3bcQQlSRHigEeYZIiGOLKoY4ret0YHfqbgcNys4kxBHCvvSyjtDQkteFRa5QiZOVJedmyyWVOA7hZfQAXEZ+vupbMniwanJrtLZt1RSfRYvg6acrfXhCSgIpl1NosfcW+vZVfWNqqsBAGDAAEtdeR0CnOvyS/Av92/a37sn//jd8+SW89BLcc49jB1qeJ55Qq6D94x9qSfm77zZmHEKIIjk5KtSV5uMW7Y7IgF5Q5/cN+GT1hNZ2bgJvb927w+zZRo/C5hBHD8jCgjuzJ3W1gwZlZxLiCGFfellHUJCUeVhBr4jx93d+Txy9EgfU26D+vShGeuI4hIQ4uvXrVZ+UESOMHkmRkSPhww9Vr5769St86C+7fsE3M4yTh4J5+hEnjc9At90GCxd6MMjnKWbv+ZxPh3yKj2cly6X873/w1FMwfDi8955zBmqJyQSffgr798P990N4uGp+LIQwTkoKbNwIN96oQnRRwp6QBOoXZOHRoCW+eKku864qMRHmzVOnRY3uwFzFSpy2QeGsTPkPuQW5lX+2GU1CHCHsSy8nCQxUqYBU4lQoK0u9VLaGOPaYTqVX4ujXJcSxQJYYdwgJcXTz56tTYIMGGT2SIqNGwfvvqylVFVSN5JvzmbVnFpGX32Mbxvdldobhw9Wxed0jk7jY5B8sO7yMYR2Glf+EU6dg3DgIC4MZM4yvtvLxgTlzVHhz++2qT06DBsaOSYjaTF817sUXa8ebqI12f9uXzjQiJ7onvkeBb781ekjlmzIFnn0WLl+G4GDjxqFpVQ9x6oZToBVwIO0AkY0iHTRAO5EQRwj70pOIOnWK5uqIcmVmFlXiZGaqt15rFnfJzS25eGBVplM1bFgU3GRmQqNGto29VpAlxh1CeuKA+t8+f75qJBMUZPRoinTvrpY6nz+/woetOLKC1Cup5CePpE0b6NjROcMzUmgo3HAD7FrTnvp+9fkl+ZfyH5yXpwKcrCwVnLjKXLPQUJg1SwVMEybIZFohjHThgrqUMLUMTdPYfW43EaER5OTg+j1x9N+h/js1Sk6OuqzCdKqWddoDuEdzY39/dZBeYOMiA0IIy/TKG32ujlTilMtsVovj6S+VpsHVq9Y9Ny+vbCVOdaZTSdZWjtLTqaQSxy4kxAFISoJjx1Tliyvx8FBTqpYurfAs18/JPxN4/gaSEhrx4IM1c2lxS+68E/bu8aDTkc/4bd9vXMkrZ4nTV1+Fdevg668hIsK5g6xMjx7qrPHixfD//p/RoxGi9tIrcUJCjB2HCzoTQg8YAAAgAElEQVSXdY6LVy8S0dBNQhz9d6j/To2if25XoRKnqX8bPEwe7hPigPV/OQkhKqanAcW75gqLrlw79C8+rcnazCs313JPHE2z7vnFGxvbst9ap3QljvTEsQsJcUBVuphMrtUPR3fbbeodavlyi3dn52Uzb+88Qrb9i3r14LHHnDw+Az34oPqVbfzPOLKS+7Fw/8KyD5o/X/UVeuwxuOsu5w/SGo8+qiqFXn9d9e0RQjifVOKUS18lqXOjzu4R4rhKJU41QhyT2Zd29du5xwpV+s8nU6qEsA+pxLFa8ZlntlbEWOqJA9ZX40gljpWkJ45DSIgD6g/93r1dcyLjjTdCvXrlTqlacnAJGaeac2JjNx5/XD20tvD0hJ9/hq5dwTT7v3y+YHPJBxw/DvfdB9dfD//6lzGDtIbJpKqEwsJg/Hg4d87oEQlR+6Slqf+LRvZQcVF6NUhEw4gyB70uqQZU4uTkqNfbrSpxJMQRwj6kJ47ViveArkoljqUQx5psQdPKNjaWrK0c0hPHISTEOXpUTadytalUOh8fGDoUFixQy6CX8nPyz/ht+Dv+/latRF7j1KkDCxeaCKx/ldXvP8eJ1GtnXvU+OGYz/Pqr6586DgyEmTPVmWPpjyOE8124oAIco5ueu6A9qXsI9gumaWBTqcSxRRVCHP21zc2Fzg07cyDtALkFLn62UkIcIewrM1Md/3t7SyVOJapTiWNpiXH99spkZ6sgRypxrCBLjDuEhDh6hYurhjigplSdPw8JCSVuPpN5ht827CIncQwPP2wiNNSg8RmsSRP46PMLkNGM1z7bom587TW1XPDXX0P79sYO0FrR0fDxx/DHH/DBB0aPRojaJS1N+uGUY3fqbiIaRmAymdwjxKlfX126cSVObq6qxMk353PowiEHDM6OJMQRNdm5c9C3L6SkOG+feokHqITA2enAhAkwe7Zz91lFRlXiVGe/tU7p6VSenqrvq4Q41SIhzvz50KWLa/+hP3CgOmqeN6/Ezd8lfkfB2mfx8jLx/PMGjc1F3D/qOnxC/mLerAC0xYtVCPLII3DHHUYPzTYPPaTG/NprZUI7IYQDpaVJP5xy7EndQ0SoagrvFiGOl5eaW1wDQhxwgxWqJMQRNdnWrWpxjA0bnLdPvdkKOH86VX4+zJgBS5Y4b5/V4IieONZkC9XZb62Tm6tCm+KVzrau5y7KqN0hzl9/wdq1MHq00SOpWFAQDBiglqO+Ns3GrJn5fOUCTEn3c/99HjRrZvAYDebhATcPTyVrbxyLn38SoqLgo4+MHpbtTCb46ito3VpNBzN6OoAQtcWFC1KJY8G5rHOcv3Kezo06A24S4oD6XRr9/lmN6VQ5OdAxtCMmTOw+5+LNjSXEETXZ2bMlL51BX/YIiipxrF0yqbpSU9W+nPnzVkPphbyK31YZS0uM67fbsl8JcSpR+oUG29dzF2XU7hDn55/VG9Xddxs9ksqNHw+nTsHq1QCsOLKCE7+PwaR58dJLBo/NRbz1aDvQvHjbf5jqL2PDgbNLqVdPjf/MGdWY2Vkf3ELUZlKJY1HxpsbgRiFOgwZuX4kT4B1A2/pt2XNeKnGEMIwRIU7pShxNc97/LyN+3moovZBX8dsqY2mJcf12W/br5aU+F2U6VTksrYjg7S2VONVUu0OcGTOgRw/o0MHokVRu+HBVkTNjBgDTVv0CWx9h3DiNtm0NHpuL6LHwAxoE7WTr+XFcaO2CK43Z4vrr1ZSwBQvgk0+MHo0QNZ9U4likhzidG6pKHLdYnQrcthKndDl/54adZTqVEEZyhUoc/TZncLMQp6qVOGazmjlW3elU+j5lEbEKlE7LQKZT2UHtDXF27VKrUt1zj9EjsU5AAIwZA7Nncyb1KIt+bAd5dXjtVVlJBYAVK+Ddd7m34w60lDimLl1g9Iiq78knYcQIeOEF2LLF6NEIUXPl58OlS1KJY8Huc7up61uXZkFqzq5U4tigmkuMg6qA2n9+P3kFLlx2LiGOqMlcoRJHv80Zzp0runSDSvCqVuIUXzBJ0zQKzAVVamys71MWEauApbM/Mp2q2mpviPPTT6rB0rhxRo/EevfeC5cv88UP76Jteoxbh2YQEWH0oFzAqVNw113QsSPPfD8WgC++u4TmBh8+FTKZ4NtvoWlTGDvW+LPKQtRUFy+qS6nEKSM5NblwZSr9zKVbhDhuWolTfIlxUJU4eeY8Dl44aOfB2ZGEOKImKx5qOEtmZsl0QL/NGfSwKjdXndxwccUbDHt7qy9r8i49P8glk37f96PjZx05c+VEifus3a9+KZU45SivJ45U4lRL7QxxzGYV4gwaBA0bGj0a6914I7ktmzFlUTO4Wp9//j3I6BEZLy9PBXFXrsCcObTuFECH2DOkbriVPw8vN3p01deggWpo/ddfMHFiYWNrIYQd6RUbUolTQr45n61/baV7s+5AUXWIW4Q4DRpAejoUFBg3hiqEOKV7Mlzf7HoANp3cZM+R2ZeEOKImM6oSp/R0KmclBMV/TjeYUpWZCX5+RQsfBQZal3fp77HTtn7EppObSL+aztPLHytxX2X71fdny35rJemJ4xC1M8RZswZOnnSfqVQ6T09+uDuGy9sfJLbHGbp1M3pALuDVV9XSj199BZ06AfDEAyFwPoJXvv/N4MHZSY8eaqWtRYvg//7P6NEIUfPoFRtSiVPCrrO7uJJ3hbgWcYCbhTghIWoqQHq6cWOoQohjMpU8tg0PDSfYL5gNJ524vLGtJMQRNVnxEMdZFd7FK3H0lMDZlTilv3dRxWeegfUVMeuObAYgR8tg1aRVbHlwCw2D6gGwZF/lJ4GlEscG0hPHIWpniPPjj+pNccQIo0dikwJzAW9daACXW/FSZJLRwzHevHnw4Yfwt7+VWGFs0gRv/IOusn1eXzakuPCBry0eewzuuANeew1WrjR6NELULFKJY5EeHMS1dMMQR/9dGtkXJztbLVvi5WXT03x9i15rD5MHvVr0khBHCCPk58P586ovZXa2c4IUTTO+EicgoOh7F1e8BzRYVxGTV5DH44ueBeD1/i/Sq0Uv2gS3YfptnwMwZf1n/JXxV6X7hZJZm1TilEN64jhE7QtxMjNh9mzVJFh/k3ITc/fO5dSGIQR6X2TUjrfcouGYw+zeDRMmQPfuMGVKibsCA+GhBz1g7xjemP+1QQO0M5MJ/vMfCA9XYc6xY0aPSIiaQypxLEpISaBpYFNa12sNFJ00c5vVqcDYvjjZ2TZV4ehKn6CMbxHP7nO7uXTVRftTeHioQUuII2qa8+fVsXaXLuq6M0KN3FwVHhlZiePMn7eaqlKJ813id6RcPA1As+CithoNAlWbioI8E++ve7/S/fr4FBWYSCVOBSz1xJHpVNVW+0Kc776Dy5fhkUeMHolNNE3j7T8+xbRvNJPiU/DdsRE2uPCZOUe6cAFGjlQfbPPmWTwt/OxTPnjgwYpfO7Hr7C4DBukAQUEwf776cB81Sj4thLAXqcSxaMPJDcS1jMNkMgFSiWMzO4U4cS3j0NDYdMrF++JIiCNqGj3EiIoqed2RSq9dbUQlTkSECmfdJMQpXYlT0UuVk5/DO2veISpU9XqztMR4v5YD+XLbl6RcSrHbfms1mU7lELUrxDGb4ZNPoGdP6NXL6NHY5I/Df5C8IhIt35f7/xEGwcEwdarRw3K+ggK1EtWJEzBnDjRvbvFhrVrBiNvyYPuDvLN8isXHuKUOHeDXX2HnTpg8uXZXYwlhLxcuqK6I9eoZPRKXcTbzLEcuHinshwNuFuK4eSWO/loD9GjeAxMm154eLCGOqImMCHEszdMpfrsjmc2QmqpWRW3Y0C1CnOLtg6Dypb6n75hOyuUUHol9ErAc4gxvPwZN0/jH2n/Ybb+1WnnTqSTEqZbaFeIsXQoHD8LTTxs9EptomsZbq97Ce+fDRMeYiY33h4ceUiHG8eNGD8+5nnsOli2Dzz+H+PgKH/rS875wNZjZP9dhT+oeJw3QCQYNgvffh5kz4e23jR6NEO4vLQ3q11fTFgVQ1A8nvmXR+6xbhThuXInj61vy2Laub126NO5CwskEOw7OziTEETWRHmI4c3qRkZU4Fy6ok6WNG6svNwhxbKmIuZp/lffWvkefVn24vrE6QWEpxKnnE8oDXR9g+o7pHEs/ZtN+5dyqBeUtMS49caqldoU4U6eqyo0xY4weiU1+3vUzm7Zlk3cyivvvu/Yre+wx9QfHZ58ZOzhnmjoVPv4YnnlGVaFUolcv6NYjD9Omp3l66bNoNemd9YUX1JLjb70F339v9GiEcG8XLkg/nFI2pGzA28Obrk27Ft7mViFOcLD6jHTTSpzSJyjjWsSx8eRGzJrZToOzMwlxRE2khxiRkSWvO1LpZY+8vNSbgjNCHP3na9wYGjVyixDHloqYL7d+yV8Zf/F2v7fJy1MnbYrP8tG/z82FV/u+iofJg3dWv2P1fvPzpbjEIlli3CFqT4iTnAzLl8Pjj5edl+fCMnMzeXH5izQ6+DI+Phrjx1+7o1UrFUZ9/XXtqN+bMweefVb9zB9+aPXTXnjWG3Nae/78w4NFBxY5cIBOZjKpZdVvuQUeeAD+/NPoEQnhvtLSpB9OKRtObqBr0674efkV3uZWIY6Hh6qucsNKnPJCnMs5l123qlRCHFETnT2r3vAaNFBBvzOnU9m65JI9FA9xalglzumM07y56k1uaXcL/dv2t9ioX/8+Nxda1G3Bo90f5dvEb9l4cqNV+9VvF6VITxyHqD0hzscfq4OMBx80eiQ2eX/d+/x1NpvMjXcwZoyp5Mnip5+G9HT44QfDxucU69bB+PGqtObHH9XBuZVGj4amTTXqJL7Ms8ueJSc/p/InuQsfH7XSWqdOKtxKTDR6REK4J6nEKSG3IJctf20p0Q8HikIct1idCtTv1A0rcYovMa7Tl3l32b44EuKImujcOVWRYjKpUOPcOcfvs3Qljv69MytxGjVy3s9bTdZW4jy+9HFyCnL495B/A5ZXWywe4gD8vd/faV63OQ8seIDcgpKBg6X96reLUmSJcYeoHSHOiRPqj/9773WrA/WjF4/yYcKHdDn6H65kefLqq6Ue0KsX9OgBH3xQ9oivpti0CYYMgdatYcECmw+Ivb3h4YdNZO25gUMHNT7Z9ImDBmqQevVgyRI1deDWW1XFmRDCNlKJU0LSmSSu5l8t0Q8Hig5s3aISB9TvtIZU4oQ1CCPEP6SwV5HLkRBH1ERnz6owA5xXmVK6sTEYV4lz5YpLpxKaZnmJ8by8ku+hc/fOZe7eubx141uEhYQBRfmBpRBHvy/IN4jPh37O7tTdZZYct7Rf/XZRSnk9caQSp1pqR4jz6qsqRX/tNaNHYjVN03jq96fwyGnA8WWjGD26aEpuIZMJ3nsPjh2DadOMGKZjbd8OAweqMwIrV0JoaJU289BDakpxu8Mf8Paatzlx6YSdB2qwFi3U6+PtraZX7d9v9IiEcC9SiVOCHhTo1R86t5pOBW5biWPp2NZkMhHXMo6EFBdtbiwhjqiJjAhxSjc2BudW4nh5qamo+s/twlOqcnJUH+aKpjWlX03n8SWPE9Mkhmfjni18nP4eW15PHN2wDsMYFzmOd9e8W2I6a2am5f26cOZlHEvTqaQnTrXV/BBnyxb46SfVDLdVK6NHY7Uvt33JwgMLufHsLC5f8uCNN8p54C23wNCh8M47alnAmiIxUVWWBAergKKcpcSt0bSpmm10fv0ItNz/3959x0dVpQ0c/92ZTBpJIISAFCEUEZQiEoqAC4qKLKBIURYQbK+suoJrQXT3/bCLr7hYVlhRFAFFaUFQUWkiUlxpBg0BqYHQMYb0nszMff84GciESWV6ni+f+WTanXvuMHPPnec+5zmhjP98PGar2YmN9QLt2qn3Sdfh9tvh6FFPt0gI31BcrI66JBPnkh1ndtAiogUtIlrY3e9zQRwfzcRxNJwKVF2cI2lHSMv34DZVRII4wh/VxUycxo1V2QIfCOLYAjXFhnSeWvsUQ5cNZe3JlQDM37mUJ9c+Sd9FfUnJS2HBsAWYjJcDCY6GUxkMYDReGVuYc/ccwoPCGbRkEA+veZg5u+aQkV3EvvQdjIgbwbjPx/FbUZJdm0QZMsW4S/h3EEfX1ZTUjRvDtGmebk21Hfj9AH/d+FcGNhvO7lV9GDYMbrqpkgXeeEPtNf75T7e10aW2bYP+/SE0VAUmnBB8+8tfIDvLyAPWNfxw+gde3f6qExrqZTp0gM2bVdpiv34QH+/pFgnh/WyZGpKJA6gpWDce38iAmAFXPOZzQRw/ysQBuC3mNgDvLNIvQRzhb6xWVROmbBAnJ8f1n3NPZuKU317w6iBOcmnNnld2TWPBLws4nXWabefXAjBt/QyW7V9GdGg0C+9ZSPdm3e2WdTScyna7fKmWxvUas3LUSm6MvpH1x9bzzMZnyM/T+DltO4cuHmLt0bX8z8Y/AXD4/Bnnb6ivkynGXcK/gzhffgk//AAzZkBEhKdbUy0FJQWMWTWGiKAIep37hIwMreIsHJuOHeHPf4b334dDh9zSTpf5/HM1hKp5c9ixA9q0ccrL9u0LXbtC/Je9Gd/5QWZsn8EPp35wymt7lU6dVCHoevXgtttk1iohqmLL1JBMHAC+PvI1mYWZPNjlwSse87kgTsOGkJ3tuQNFJwdxerfoTdvItizet9gJjXMyCeIIf5OersbquDuokZurUkLK7mgrmzfbmcpnHtnu80IXci5wz+KxAPS/LpZjTx8j8YlEVo77CICvRm4h48UMtj60lYdueuiK5R0Np7LddrT/HdhmIBvGb+C353/j1NMXwBrIP+58gUNPHSJ5SjKTeqs+c8pXf2Pv+b1O206/IFOMu4T/BnHy8uCFF+CGG+DRRz3dmmrRdZ3J6yfza+qv/KXBOt6YGc6wYdCjRzUWnj5d7eSnTFFnD3yNrsPs2TB6NNx8swpEXHut015e02DyZEhMhDYHPqRNZBvGfT6OlFzv7JyuSvv28OOPKgA2ZAgsWuTpFgnhvSQTx87ifYtpHt6cga0HXvGYT85OBZCR4Zn1OzmIo2kaE7pOYMvJLZzKPOWEBjqRBHGEvylb5BdUVn/Z+13FNne1pl2+r6J5s52tbBAnOvryfV4mtziXIcuGkJGtdpTP9n+clvVV1n5EuPppW9/QDK3se1iOo+FUtttVxRbCtWvUOiKMAESGRPLyHZMBCNOaMHT5UE5mnqzJJvm3iqYYt1jURdSKfwZxdB2eeAJOnIB331VFunzA9K3TWfDLAsaGfcjMp7vTuXMNZg+PjoZZs1TmxaxZLm2n0+Xmwtixqm7RPffAd9+55Kz4Qw/B+PEwY3oQY4o3kVaQxqAlg8gszHT6ujyuWbPLw9IefRQmTfLfGcyEuBqSiXNJSm4KG5I2ML7LeIwG4xWP++TsVOCZujhms7o4sSYOwISuEwD4NPHTq2md89mCOLru6ZYI4RzlgzjuzMQpWw8H3JOJo+v2QRyTSe1DvSyIY7aaeWDVAySmJDL9ljeA2k31fTVBHEdli2zXJ3V+joKSAv649I9kFHjoBII3sVpVoMbRGw0ypOoq+GcQZ9EiNaX49OkwYICnW1Mtb+98m1e2v8LQ4Jmsmf4obdvCxo2qrm+1TZoEY8bA3/+ufsD7gkOH1FTpK1fCa6/B6tWqFo4LGAzqozFoEMycGsPUqB84mHqQocuGkl+S75J1elSDBrBhA7z0EsyfD7feqmYyE0JcJpk4lyzdvxSLbmFi14kOH/e54VS2/1NP1MWxZaU4MRMHIKZBDP1b9eeTfZ+ge1PAJCRE/QiU9HjhLzwVxLFl4pRly8Rx5Xc+K0t9f23bCe4r5lwDk9dPZt2xdbw35D06RfYCKp+dqiI1qYlTnqOyRbbr4do1fDnmS5LSkxixcgQlljoepKjsjS77uKgx/wviJCaqKrZ33KGCGT5g4c8LeXb9C9x4eCkb/3caTZtqbNpUixm1NU39WL/uOhXM8bIdrx2zWWUMdeum2rlxoyo+bXDtR9JkglWroHt3eG3KzTyQFc+OUz8xcuVICkr8MBXcaISZM1WtoSNHVM2c997zzSF3QriCZOJcsnjfYno060HH6I4OHy8qUrtoH0lu9WwmjouCOAATu07kWPqxS1PBewXbdsqQKuEvPDWcqqJMHLPZtUHS8ttru+5FvyUW/bKIefHzmNpnKo93f7zSjJjqZuLUZuZrR+sNDFSH3Lm5MCBmAAvvWcjWk1uZumlq5S/m7yp7o8s+LmrMv4I458/DqFEQGQlLlqhvkxezWC1M+24ajy16g4ilv/LrirEMH66xc6eaFrtWwsPhs89URH3ECPXX2yQkQJ8+KmgzZAgcOKCCbm4SFgbr1qmMnCVvdaHFivNs2JrBrR/dytnss25rh1vddx/s368qPD/1FAwcCIcPe7pVQnheero6mCh/5rOOSfgtgcSUxAqzcEAFcXwmCwd8NhOnsuFUAKNuGEWoKZTFCV5U4FiCOMLf/P67ilhHRqrbwcFQv76635UqysSxPeYqFQVxXL291RR/Pp4n1z7JHW3uYObAmUDlGTFVvVUVxRaqM5zK0Xo1zb500YNdH2Ryz8nM3j2b5fuXV/6C/qyycWtlHxc15j9BnORkNVzkwgUVxCi7E/JCmYWZDFs+jFnvnyJgwT5MWe2Ji1OjimqcgVOerZjOnj1qhiIv2QFz+jRMnKgKFycnQ1ycSovxwP9Vo0Zq8rLPPwdrXhTawp3sXzGa7vN6sePMDre3xy1atlTDqxYuhJ9/Vlk5TzzhVWdZhHC7tDSVsVFJAcS6YHHCYkwGE2M6janwOT4XxPHxTJyKRk6EB4UzouMI4n6N854MUgniCH+TkqKyb8pmiLsjMyUvz3Emju0xV/HiTJyL+RcZuXIkTcKasHzk8ks12642Eycg4MoBALWtiWO7XXa9b971Jv1a9uOxrx9jf8r+yl/UX1UVxJHhVLXmH0GcgwehXz/IzITNm1W2gRf76shXdJ3bgw1zB8Pq5fSKDSIxUeP++524klGj4OuvVbZFv36erYVy/LiaGqp9exW4eeEFOHYM7r/foz+cNE0lqBw8CBMnahRveZHs+WvoP/tBXt78MnnFbpgJwN00DR55BJKSVABnwQJo1w6mToWzfpqFJERl0tPrfD2chN8SmBc/j1E3jCIqtOL3wueCOBER6ijdxzJxAgNVAKeySTsev/lxsoqyeGnzS7VsoJNJEEf4m7JFfm3cEdRwNJzKlvLhyuLGthO+5YM42dlQWOi69VYhtziXEXEjSMlNYfX9q2kUevlMty2mVfbtCg5Wh7rVqYnjaKbFmtTEcRTEKbtek9HEylEriQiK4N4V93Im60zlL+yPqqqJI5k4tebbQRxdV1kFffuq69u2Qc+enm5VhZLSkxi2fBj3zn2e1Pc+Q9/1NM88A1u2qMmEnO7uu9VMT6mpKvtl/nz31UIxm1WdmxEjVI2e999XM1AdPapq4dSoYrNrRUTARx/B0qUQkNodwweJvDb3HB3mdmT1wdXeVTzSWaKj4Z13VARr6FB46y1o3RrGjYPt26Vmjqg70tLqdBAnuyib0Z+NplFoI+bcPafS5xYX+9D04qCO5Bs29MlMHKh8SNWtrW5lSq8pzNk9h9UHV9eigU4mQRzhb2yZOGW5KxOn/HAqd2XiGAz2/aG7ijlXILsom7uX3M2OMztYPHwxsc1i7R7Py1Nx+rL9UvlhTRVxNOs1VK8mjqPhVLbb5dfbNLwpa8asIa0gjf4f9697U49LTRyX8d0gzuHDauapxx6DLl3gxx/V8BAvo+s6205uY0TcCNr/pwPfLu1IwPxfCc7sSlwcvP22452I0/TpA7t2QdeuavaqPn1g507XVLgvLlaBtClToEULFUTatk3NjnTqlJoaqmVL56/XScaOhYRfNHp2qwdfLiZzwXJGzX+OTvM68UH8B/45g9V118Hy5Spb6umnVfZW//4qoDNtGuzeXfnpYCF8XXp6nS1qrOs6j331GMkZyawYtYLoetGVPt/nMnFA/d/6WCaO7T2u6tj29Ttfp2fznjzy1SMcTz9e4/U4lQRxhL/xpkyc6o4RuhopKarWQNl6oh4M4mQWZnLXp3ex+9xulo9czgOdHrjiOba3qnxSf3VmZK/opIQzh1PZ9Gzek80TNpNRmEH/j/t7fn/tTlITx2V8K4hjtcL69XDvvXDjjWomqgULVCpL69aebt0lVt3KrrO7eHnzy9wwtxMDXnuWDQt60uiTMxSvfZ277jBx4ICTh09V5vrr4fvv1bTryckqkNOli8q+OH269gGdrCz1uq+/DsOGqYPlAQNU1k3fvmq68HPn4NVXr6JSs3u1baviTnPnAmf6EPhBEucXzebPs76n2WvtmfDFBFYdXEVOUY6nm+pcMTHw73+r4uBLlqjv15tvqunfGzeGP/0J5s2DvXtl/KrwL3U0E8eqW5n14yw+O/gZMwfOpF/LflUu45NBnKgon83EqerYNtAYSNyoOIyakdGfjeb3PA/Wv5MgjvAnuu44iNO4MWRkuPaHpycLGzvaXttjbqLrOt8c/YaeH/bk5ws/s2r0KkbfONrhcx29VVC9TBxnDKeqTiaOTWyzWL6f8D15xXn0Xtib+XvnY7aaK1+RP5Apxl3GuycKtVhU0OG//4WtW1W9m7Nn1U5l6lR45hmPFzDOL8nnRMYJjqQeY1viCX78JZ1DBzUKzsfAxaEEpL0E+eEUajrdbtF4YzpMmOCBUjCaBuPHwz33qMyLjz+G559Xl2uugdhY9cO9SRM11CY8XHViuq4OytLS1OXcOVVP5fhxOFNmbGe7dmrDBg1SxZQjIty8gc5jMKgJnIYO1fjXvwL44os7YO+d5HxpZlmTA3x6zS4MzV6kTWsD3a9vwh86t6ZbTFvaNWxHo9BGaL5cIDUsTA2pGjcOLl6ETZvUsKU6f0kAAAiUSURBVLiNG2HFCvWc4GC44QZ16dhRRb5atVKXxo29flY4IezUsUwcXddZn7Selze/zL6UfQzvMJzn+zxfrWV9MojTsKF9X+UubgjiAMQ0iOGT+z5h+IrhtJnThmdveZbnbnmO+sH1a7zeqyJBHOFPsrLUF9BRJg6o+jEtWjh/vRaLqj/jqUycirbXDUGcYksxu87uYsa2GWxO3kz7qPZsGL+B21vfXuEyjpKWoPqZOLUdTpWbq34rlO8P69VT58Yr0q1pN7Y/vJ1J30xi0jeTeGfPO7xy2yvc2eZO6gU62BB/IMOpXMblQZzstCzWx20DHbBaVDaNxaJqppSUQFGxOjIsLICcHMjOgewstcP4LQUspVHKsHD0zoPh8VsgtocaBJmYAWTYrc9aJqtER790zWpVt3WrjlVXz7NYrVitOmaLFbPVgtliocRsoajYSlGJhfxCM3kFZvILLOQVFpOTX0xugZmsHDOZWVZyczTy0xpCelvIGATm0EvrjogspHMnI12GmujdGwYP1oiuPFPdPSIi1LCqSZPUkLRNmyA+Hn76Sc1cZK4iKty4sQrY3HabyvCJjYXu3f3yTHarVir5ZO5cjR07YO3aAH6K78KePZ3I3RtAEpAExAGEpkLDJEyNvicssoD6kRYaNoSw4EDqBQcRFhxESFAAocEmQoMCCAoyEhyoLqYAIwEGjQCjEYNBw2gwYNA0DAYNDUDTMJQGhjRNswsAlj7jyutln3M1QaXom2H8zTBuGlxMhWNJcDwJTp+B3Wdhfblq+5qmPmMR9SE8DOqFQmg9CA6BkGDV4wUGqp13gKn0b4AK/BgNYCj9qxnAoKnX0wyqt9RKX1/TAK3cRpZrg6Pr1dAwKow776s6I0E412+nU9j2bYL7V2w2Q2h7KGgE3x1x//prSXfYz6n7dXSsuhWLbqHYUkxBSQH5JfmcyznH8fTjHE47zMmMZJpHtGBmj9cY1G4Qifuql5SbluaDQZyoKNXHJbj583Wk9PN0FcOpEhKql0TUgqGs/sNx3v3pXV6J+4q3v9hCpyadaBfZjjaRbYgIiiAkIIQQUwhGgxGDZsCAwa5vsO8/atFnnM2AqK7qe5S6sebL+5Dm1zak36Aenm5GnXP812Tidx51z8ouXlSf5+z69n1Dej11/6JvoVlz56+3qEi9fkY9+/Wmpqv7txyDHBd9v9JDofH19ustLi5dbxJQvfXa9Um2f7q6brZaKNFLKNHNZJfkkVacRXpxFgdzkknIPkyhpYj6pnBejJnNyKiBmPaYSNhTcd984VhzwowGSLD/XIRp7UhJ1kiIq3jCjt+TmhKoB0LCYbv7A/NjyL4YQkLcyQqXPZUQTVhofbR99sfAYcUtyfg9nIS4ExUuC0b+E/IhmxvuZvbRZdy37x8Ytf+jU0RbOke0IzowkqjABtQ3hRFoMGHSAjAZAtBQx/9a6T8bDS8/cXzqpPoMHc23/2wdzlX3f7MPDrkwOOkh13Voxs39Ort0HVpNirbGxsbq8fHxNVrB9nW76T+kV03b5fU0o5nA0ELqR+VzbUwx7a8LoHfXBnTrEkzHjk6YJtwTdF3N8JWaejnMrGnqiLJRI4iMlCwL1Nt05oy6nDpl5ZcjaRw4ks/xJI3fztajICsUc2HND9yF54U33Un2+VtqtaymaXt1XY+t+pn+rTb9xJxXV/HM30e5qEXCmQYPhnXrPN2KGvjb32DmTM+sW9NUf1rDkxxff62SZoV3anX9Gk4evrdWy0o/Ubs+AuDxCYv48NNHXNAi4cvu5Fu+ZZDdfcP5gjUMr3LZHuxhD/a/UR9lAYt4tMplW3OCE7S1u+953uAtqpfZKvxbr1s+YdeOCbVatrr9hMszcTp0bcO0vy6zP7NuNKoz7gYDBJaejQ8MBFOgU8YZGQxXvoaGhqH0TL4ty8FoUNHMgAADRoO6BAUEEBxkJNhkIizURHhoEOEhQTQICyEk2EBgoBpxEhQUgKaFAQ4GY/oqTVOBmshIT7fEq2maqs/csiX07WtgLFemWBUVqXhYSYk62Z9bUEROQSE5+UVkFxRSVGyhsNhMQZFZZYJZrJSYrVh1HatVZYnB5ewxdd0+06wsuzPz3jyZlsUMZov6W1JSmplXmp2n65ez9XRAt14e0me7DaXXL2fZ2Sm78bV4H5o1Da36ScLp7h56E9NSPvXMyo1GiGkFRu8eXVwZu4wKTcOAAYNmwGQ0ERIQTFBAMFEhUYSYrj64HOtrPz9ffBF69fLMjHvXXFOrLNXBg1Vi7NWOTLJaLaTmXyS/JJ8iSxGF5kKsuvXSxcZpMzCeOwt5fjgBQDkdr687wy+9ycMTuhLVwI39RKBJpWRrZTIVdR1On1KjCFyloj7pwnnIcWHGgoY6sA0Ktr//YiqkZzhcpLovq2mlv7c0IwEYCNCMhBqCaGCsR5ghGINW+xKt3dvq0OgLu/veSw/moWO7q1y2c8ssaGq/7L+yAhl2uOplOzTPgRb2y/49z8StB3ah1zI7Rtd18vUiMs155FgLMOsWzFgx6xaV4aSDtTYHt54WFKg+W+7+LnlQ754uGG5ZjsszcYQQoi6QM6yK9BNCCOGY9BPSRwghRGWq20/41uxUQgghhBBCCCGEEHWUBHGEEEIIIYQQQgghfIAEcYQQQgghhBBCCCF8gARxhBBCCCGEEEIIIXxAjQoba5qWCpxyXXOEEMJntdJ1/cqpyuoY6SeEEKJCdb6fkD5CCCEqVa1+okZBHCGEEEIIIYQQQgjhGTKcSgghhBBCCCGEEMIHSBBHCCGEEEIIIYQQwgdIEEcIIYQQQgghhBDCB0gQRwghhBBCCCGEEMIHSBBHCCGEEEIIIYQQwgdIEEcIIYQQQgghhBDCB0gQRwghhBBCCCGEEMIHSBBHCCGEEEIIIYQQwgdIEEcIIYQQQgghhBDCB/w/GyUG8mwJ/CMAAAAASUVORK5CYII=\n", + "text/plain": [ + "<Figure size 1440x432 with 6 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#%% plot\n", + "\n", + "nbm = len(problems)\n", + "nbm2 = (nbm // 2)\n", + "\n", + "\n", + "pl.figure(2, (20, 6))\n", + "pl.clf()\n", + "\n", + "for i in range(nbm):\n", + "\n", + " A = problems[i][0]\n", + " bary_l2 = problems[i][1][0]\n", + " bary_wass = problems[i][1][1]\n", + " bary_wass2 = problems[i][1][2]\n", + "\n", + " pl.subplot(2, nbm, 1 + i)\n", + " for j in range(n_distributions):\n", + " pl.plot(x, A[:, j])\n", + " if i == nbm2:\n", + " pl.title('Distributions')\n", + " pl.xticks(())\n", + " pl.yticks(())\n", + "\n", + " pl.subplot(2, nbm, 1 + i + nbm)\n", + "\n", + " pl.plot(x, bary_l2, 'r', label='L2 (Euclidean)')\n", + " pl.plot(x, bary_wass, 'g', label='Reg Wasserstein')\n", + " pl.plot(x, bary_wass2, 'b', label='LP Wasserstein')\n", + " if i == nbm - 1:\n", + " pl.legend()\n", + " if i == nbm2:\n", + " pl.title('Barycenters')\n", + "\n", + " pl.xticks(())\n", + " pl.yticks(())" + ] + } + ], + "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_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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\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_otda_linear_mapping.ipynb b/notebooks/plot_otda_linear_mapping.ipynb new file mode 100644 index 0000000..4b6713d --- /dev/null +++ b/notebooks/plot_otda_linear_mapping.ipynb @@ -0,0 +1,339 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "# Linear OT mapping estimation\n", + "\n", + "\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 pylab as pl\n", + "import ot" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate data\n", + "-------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "n = 1000\n", + "d = 2\n", + "sigma = .1\n", + "\n", + "# source samples\n", + "angles = np.random.rand(n, 1) * 2 * np.pi\n", + "xs = np.concatenate((np.sin(angles), np.cos(angles)),\n", + " axis=1) + sigma * np.random.randn(n, 2)\n", + "xs[:n // 2, 1] += 2\n", + "\n", + "\n", + "# target samples\n", + "anglet = np.random.rand(n, 1) * 2 * np.pi\n", + "xt = np.concatenate((np.sin(anglet), np.cos(anglet)),\n", + " axis=1) + sigma * np.random.randn(n, 2)\n", + "xt[:n // 2, 1] += 2\n", + "\n", + "\n", + "A = np.array([[1.5, .7], [.7, 1.5]])\n", + "b = np.array([[4, 2]])\n", + "xt = xt.dot(A) + b" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot data\n", + "---------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[<matplotlib.lines.Line2D at 0x7f3ed402e748>]" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 360x360 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pl.figure(1, (5, 5))\n", + "pl.plot(xs[:, 0], xs[:, 1], '+')\n", + "pl.plot(xt[:, 0], xt[:, 1], 'o')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Estimate linear mapping and transport\n", + "-------------------------------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "Ae, be = ot.da.OT_mapping_linear(xs, xt)\n", + "\n", + "xst = xs.dot(Ae) + be" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot transported samples\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 360x360 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pl.figure(1, (5, 5))\n", + "pl.clf()\n", + "pl.plot(xs[:, 0], xs[:, 1], '+')\n", + "pl.plot(xt[:, 0], xt[:, 1], 'o')\n", + "pl.plot(xst[:, 0], xst[:, 1], '+')\n", + "\n", + "pl.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Load image data\n", + "---------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def im2mat(I):\n", + " \"\"\"Converts and image to matrix (one pixel per line)\"\"\"\n", + " return I.reshape((I.shape[0] * I.shape[1], I.shape[2]))\n", + "\n", + "\n", + "def mat2im(X, shape):\n", + " \"\"\"Converts back a matrix to an image\"\"\"\n", + " return X.reshape(shape)\n", + "\n", + "\n", + "def minmax(I):\n", + " return np.clip(I, 0, 1)\n", + "\n", + "\n", + "# Loading images\n", + "I1 = pl.imread('../data/ocean_day.jpg').astype(np.float64) / 256\n", + "I2 = pl.imread('../data/ocean_sunset.jpg').astype(np.float64) / 256\n", + "\n", + "\n", + "X1 = im2mat(I1)\n", + "X2 = im2mat(I2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Estimate mapping and adapt\n", + "----------------------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "mapping = ot.da.LinearTransport()\n", + "\n", + "mapping.fit(Xs=X1, Xt=X2)\n", + "\n", + "\n", + "xst = mapping.transform(Xs=X1)\n", + "xts = mapping.inverse_transform(Xt=X2)\n", + "\n", + "I1t = minmax(mat2im(xst, I1.shape))\n", + "I2t = minmax(mat2im(xts, I2.shape))\n", + "\n", + "# %%" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot transformed images\n", + "-----------------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5,1,'Inverse mapping Im. 2')" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 720x504 with 4 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pl.figure(2, figsize=(10, 7))\n", + "\n", + "pl.subplot(2, 2, 1)\n", + "pl.imshow(I1)\n", + "pl.axis('off')\n", + "pl.title('Im. 1')\n", + "\n", + "pl.subplot(2, 2, 2)\n", + "pl.imshow(I2)\n", + "pl.axis('off')\n", + "pl.title('Im. 2')\n", + "\n", + "pl.subplot(2, 2, 3)\n", + "pl.imshow(I1t)\n", + "pl.axis('off')\n", + "pl.title('Mapping Im. 1')\n", + "\n", + "pl.subplot(2, 2, 4)\n", + "pl.imshow(I2t)\n", + "pl.axis('off')\n", + "pl.title('Inverse mapping Im. 2')" + ] + } + ], + "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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+ "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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+ "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..b74b924 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__ = "0.5.1" __all__ = ["emd", "emd2", "sinkhorn", "sinkhorn2", "utils", 'datasets', 'bregman', 'lp', 'tic', 'toc', 'toq', 'gromov', diff --git a/ot/bregman.py b/ot/bregman.py index b017c1a..d1057ff 100644 --- a/ot/bregman.py +++ b/ot/bregman.py @@ -47,7 +47,7 @@ def sinkhorn(a, b, M, reg, method='sinkhorn', numItermax=1000, reg : float Regularization term >0 method : str - method used for the solver either 'sinkhorn', 'sinkhorn_stabilized' or + method used for the solver either 'sinkhorn', 'greenkhorn', 'sinkhorn_stabilized' or 'sinkhorn_epsilon_scaling', see those function for specific parameters numItermax : int, optional Max number of iterations @@ -103,6 +103,10 @@ def sinkhorn(a, b, M, reg, method='sinkhorn', numItermax=1000, def sink(): return sinkhorn_knopp(a, b, M, reg, numItermax=numItermax, stopThr=stopThr, verbose=verbose, log=log, **kwargs) + elif method.lower() == 'greenkhorn': + def sink(): + return greenkhorn(a, b, M, reg, numItermax=numItermax, + stopThr=stopThr, verbose=verbose, log=log) elif method.lower() == 'sinkhorn_stabilized': def sink(): return sinkhorn_stabilized(a, b, M, reg, numItermax=numItermax, @@ -197,6 +201,8 @@ def sinkhorn2(a, b, M, reg, method='sinkhorn', numItermax=1000, .. [10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816. + [21] Altschuler J., Weed J., Rigollet P. : Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration, Advances in Neural Information Processing Systems (NIPS) 31, 2017 + See Also @@ -204,6 +210,7 @@ def sinkhorn2(a, b, M, reg, method='sinkhorn', numItermax=1000, ot.lp.emd : Unregularized OT ot.optim.cg : General regularized OT ot.bregman.sinkhorn_knopp : Classic Sinkhorn [2] + ot.bregman.greenkhorn : Greenkhorn [21] ot.bregman.sinkhorn_stabilized: Stabilized sinkhorn [9][10] ot.bregman.sinkhorn_epsilon_scaling: Sinkhorn with epslilon scaling [9][10] @@ -344,8 +351,13 @@ def sinkhorn_knopp(a, b, M, reg, numItermax=1000, # print(reg) - K = np.exp(-M / reg) + # Next 3 lines equivalent to K= np.exp(-M/reg), but faster to compute + K = np.empty(M.shape, dtype=M.dtype) + np.divide(M, -reg, out=K) + np.exp(K, out=K) + # print(np.min(K)) + tmp2 = np.empty(b.shape, dtype=M.dtype) Kp = (1 / a).reshape(-1, 1) * K cpt = 0 @@ -353,6 +365,7 @@ def sinkhorn_knopp(a, b, M, reg, numItermax=1000, while (err > stopThr and cpt < numItermax): uprev = u vprev = v + KtransposeU = np.dot(K.T, u) v = np.divide(b, KtransposeU) u = 1. / np.dot(Kp, v) @@ -373,8 +386,9 @@ def sinkhorn_knopp(a, b, M, reg, numItermax=1000, err = np.sum((u - uprev)**2) / np.sum((u)**2) + \ np.sum((v - vprev)**2) / np.sum((v)**2) else: - transp = u.reshape(-1, 1) * (K * v) - err = np.linalg.norm((np.sum(transp, axis=0) - b))**2 + # compute right marginal tmp2= (diag(u)Kdiag(v))^T1 + np.einsum('i,ij,j->j', u, K, v, out=tmp2) + err = np.linalg.norm(tmp2 - b)**2 # violation of marginal if log: log['err'].append(err) @@ -389,10 +403,7 @@ def sinkhorn_knopp(a, b, M, reg, numItermax=1000, log['v'] = v if nbb: # return only loss - res = np.zeros((nbb)) - for i in range(nbb): - res[i] = np.sum( - u[:, i].reshape((-1, 1)) * K * v[:, i].reshape((1, -1)) * M) + res = np.einsum('ik,ij,jk,ij->k', u, K, v, M) if log: return res, log else: @@ -406,6 +417,148 @@ def sinkhorn_knopp(a, b, M, reg, numItermax=1000, return u.reshape((-1, 1)) * K * v.reshape((1, -1)) +def greenkhorn(a, b, M, reg, numItermax=10000, stopThr=1e-9, verbose=False, log=False): + """ + Solve the entropic regularization optimal transport problem and return the OT matrix + + The algorithm used is based on the paper + + Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration + by Jason Altschuler, Jonathan Weed, Philippe Rigollet + appeared at NIPS 2017 + + which is a stochastic version of the Sinkhorn-Knopp algorithm [2]. + + The function solves the following optimization problem: + + .. math:: + \gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma) + + s.t. \gamma 1 = a + + \gamma^T 1= b + + \gamma\geq 0 + where : + + - M is the (ns,nt) metric cost matrix + - :math:`\Omega` is the entropic regularization term :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})` + - a and b are source and target weights (sum to 1) + + + + Parameters + ---------- + a : np.ndarray (ns,) + samples weights in the source domain + b : np.ndarray (nt,) or np.ndarray (nt,nbb) + samples in the target domain, compute sinkhorn with multiple targets + and fixed M if b is a matrix (return OT loss + dual variables in log) + M : np.ndarray (ns,nt) + loss matrix + reg : float + Regularization term >0 + numItermax : int, optional + Max number of iterations + stopThr : float, optional + Stop threshol on error (>0) + log : bool, optional + record log if True + + + Returns + ------- + gamma : (ns x nt) ndarray + Optimal transportation matrix for the given parameters + log : dict + log dictionary return only if log==True in parameters + + Examples + -------- + + >>> import ot + >>> a=[.5,.5] + >>> b=[.5,.5] + >>> M=[[0.,1.],[1.,0.]] + >>> ot.bregman.greenkhorn(a,b,M,1) + array([[ 0.36552929, 0.13447071], + [ 0.13447071, 0.36552929]]) + + + References + ---------- + + .. [2] M. Cuturi, Sinkhorn Distances : Lightspeed Computation of Optimal Transport, Advances in Neural Information Processing Systems (NIPS) 26, 2013 + [22] J. Altschuler, J.Weed, P. Rigollet : Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration, Advances in Neural Information Processing Systems (NIPS) 31, 2017 + + + See Also + -------- + ot.lp.emd : Unregularized OT + ot.optim.cg : General regularized OT + + """ + + n = a.shape[0] + m = b.shape[0] + + # Next 3 lines equivalent to K= np.exp(-M/reg), but faster to compute + K = np.empty_like(M) + np.divide(M, -reg, out=K) + np.exp(K, out=K) + + u = np.full(n, 1. / n) + v = np.full(m, 1. / m) + G = u[:, np.newaxis] * K * v[np.newaxis, :] + + viol = G.sum(1) - a + viol_2 = G.sum(0) - b + stopThr_val = 1 + if log: + log['u'] = u + log['v'] = v + + for i in range(numItermax): + i_1 = np.argmax(np.abs(viol)) + i_2 = np.argmax(np.abs(viol_2)) + m_viol_1 = np.abs(viol[i_1]) + m_viol_2 = np.abs(viol_2[i_2]) + stopThr_val = np.maximum(m_viol_1, m_viol_2) + + if m_viol_1 > m_viol_2: + old_u = u[i_1] + u[i_1] = a[i_1] / (K[i_1, :].dot(v)) + G[i_1, :] = u[i_1] * K[i_1, :] * v + + viol[i_1] = u[i_1] * K[i_1, :].dot(v) - a[i_1] + viol_2 += (K[i_1, :].T * (u[i_1] - old_u) * v) + + else: + old_v = v[i_2] + v[i_2] = b[i_2] / (K[:, i_2].T.dot(u)) + G[:, i_2] = u * K[:, i_2] * v[i_2] + #aviol = (G@one_m - a) + #aviol_2 = (G.T@one_n - b) + viol += (-old_v + v[i_2]) * K[:, i_2] * u + viol_2[i_2] = v[i_2] * K[:, i_2].dot(u) - b[i_2] + + #print('b',np.max(abs(aviol -viol)),np.max(abs(aviol_2 - viol_2))) + + if stopThr_val <= stopThr: + break + else: + print('Warning: Algorithm did not converge') + + if log: + log['u'] = u + log['v'] = v + + if log: + return G, log + else: + return G + + def sinkhorn_stabilized(a, b, M, reg, numItermax=1000, tau=1e3, stopThr=1e-9, warmstart=None, verbose=False, print_period=20, log=False, **kwargs): """ @@ -915,6 +1068,116 @@ def barycenter(A, M, reg, weights=None, numItermax=1000, return geometricBar(weights, UKv) +def convolutional_barycenter2d(A, reg, weights=None, numItermax=10000, stopThr=1e-9, stabThr=1e-30, verbose=False, log=False): + """Compute the entropic regularized wasserstein barycenter of distributions A + where A is a collection of 2D images. + + The function solves the following optimization problem: + + .. math:: + \mathbf{a} = arg\min_\mathbf{a} \sum_i W_{reg}(\mathbf{a},\mathbf{a}_i) + + where : + + - :math:`W_{reg}(\cdot,\cdot)` is the entropic regularized Wasserstein distance (see ot.bregman.sinkhorn) + - :math:`\mathbf{a}_i` are training distributions (2D images) in the mast two dimensions of matrix :math:`\mathbf{A}` + - reg is the regularization strength scalar value + + The algorithm used for solving the problem is the Sinkhorn-Knopp matrix scaling algorithm as proposed in [21]_ + + Parameters + ---------- + A : np.ndarray (n,w,h) + n distributions (2D images) of size w x h + reg : float + Regularization term >0 + weights : np.ndarray (n,) + Weights of each image on the simplex (barycentric coodinates) + numItermax : int, optional + Max number of iterations + stopThr : float, optional + Stop threshol on error (>0) + stabThr : float, optional + Stabilization threshold to avoid numerical precision issue + verbose : bool, optional + Print information along iterations + log : bool, optional + record log if True + + + Returns + ------- + a : (w,h) ndarray + 2D Wasserstein barycenter + log : dict + log dictionary return only if log==True in parameters + + + References + ---------- + + .. [21] Solomon, J., De Goes, F., Peyré, G., Cuturi, M., Butscher, A., Nguyen, A. & Guibas, L. (2015). + Convolutional wasserstein distances: Efficient optimal transportation on geometric domains + ACM Transactions on Graphics (TOG), 34(4), 66 + + + """ + + if weights is None: + weights = np.ones(A.shape[0]) / A.shape[0] + else: + assert(len(weights) == A.shape[0]) + + if log: + log = {'err': []} + + b = np.zeros_like(A[0, :, :]) + U = np.ones_like(A) + KV = np.ones_like(A) + + cpt = 0 + err = 1 + + # build the convolution operator + t = np.linspace(0, 1, A.shape[1]) + [Y, X] = np.meshgrid(t, t) + xi1 = np.exp(-(X - Y)**2 / reg) + + def K(x): + return np.dot(np.dot(xi1, x), xi1) + + while (err > stopThr and cpt < numItermax): + + bold = b + cpt = cpt + 1 + + b = np.zeros_like(A[0, :, :]) + for r in range(A.shape[0]): + KV[r, :, :] = K(A[r, :, :] / np.maximum(stabThr, K(U[r, :, :]))) + b += weights[r] * np.log(np.maximum(stabThr, U[r, :, :] * KV[r, :, :])) + b = np.exp(b) + for r in range(A.shape[0]): + U[r, :, :] = b / np.maximum(stabThr, KV[r, :, :]) + + if cpt % 10 == 1: + err = np.sum(np.abs(bold - b)) + # log and verbose print + if log: + log['err'].append(err) + + if verbose: + if cpt % 200 == 0: + print('{:5s}|{:12s}'.format('It.', 'Err') + '\n' + '-' * 19) + print('{:5d}|{:8e}|'.format(cpt, err)) + + if log: + log['niter'] = cpt + log['U'] = U + return b, log + else: + return b + + def unmix(a, D, M, M0, h0, reg, reg0, alpha, numItermax=1000, stopThr=1e-3, verbose=False, log=False): """ @@ -15,7 +15,7 @@ import scipy.linalg as linalg from .bregman import sinkhorn from .lp import emd from .utils import unif, dist, kernel, cost_normalization -from .utils import check_params, deprecated, BaseEstimator +from .utils import check_params, BaseEstimator from .optim import cg from .optim import gcg @@ -740,288 +740,6 @@ def OT_mapping_linear(xs, xt, reg=1e-6, ws=None, return A, b -@deprecated("The class OTDA is deprecated in 0.3.1 and will be " - "removed in 0.5" - "\n\tfor standard transport use class EMDTransport instead.") -class OTDA(object): - - """Class for domain adaptation with optimal transport as proposed in [5] - - - References - ---------- - - .. [5] N. Courty; R. Flamary; D. Tuia; A. Rakotomamonjy, - "Optimal Transport for Domain Adaptation," in IEEE Transactions on - Pattern Analysis and Machine Intelligence , vol.PP, no.99, pp.1-1 - - """ - - def __init__(self, metric='sqeuclidean', norm=None): - """ Class initialization""" - self.xs = 0 - self.xt = 0 - self.G = 0 - self.metric = metric - self.norm = norm - self.computed = False - - def fit(self, xs, xt, ws=None, wt=None, max_iter=100000): - """Fit domain adaptation between samples is xs and xt - (with optional weights)""" - self.xs = xs - self.xt = xt - - if wt is None: - wt = unif(xt.shape[0]) - if ws is None: - ws = unif(xs.shape[0]) - - self.ws = ws - self.wt = wt - - self.M = dist(xs, xt, metric=self.metric) - self.M = cost_normalization(self.M, self.norm) - self.G = emd(ws, wt, self.M, max_iter) - self.computed = True - - def interp(self, direction=1): - """Barycentric interpolation for the source (1) or target (-1) samples - - This Barycentric interpolation solves for each source (resp target) - sample xs (resp xt) the following optimization problem: - - .. math:: - arg\min_x \sum_i \gamma_{k,i} c(x,x_i^t) - - where k is the index of the sample in xs - - For the moment only squared euclidean distance is provided but more - metric could be used in the future. - - """ - if direction > 0: # >0 then source to target - G = self.G - w = self.ws.reshape((self.xs.shape[0], 1)) - x = self.xt - else: - G = self.G.T - w = self.wt.reshape((self.xt.shape[0], 1)) - x = self.xs - - if self.computed: - if self.metric == 'sqeuclidean': - return np.dot(G / w, x) # weighted mean - else: - print( - "Warning, metric not handled yet, using weighted average") - return np.dot(G / w, x) # weighted mean - return None - else: - print("Warning, model not fitted yet, returning None") - return None - - def predict(self, x, direction=1): - """ Out of sample mapping using the formulation from [6] - - For each sample x to map, it finds the nearest source sample xs and - map the samle x to the position xst+(x-xs) wher xst is the barycentric - interpolation of source sample xs. - - References - ---------- - - .. [6] Ferradans, S., Papadakis, N., Peyré, G., & Aujol, J. F. (2014). - Regularized discrete optimal transport. SIAM Journal on Imaging - Sciences, 7(3), 1853-1882. - - """ - if direction > 0: # >0 then source to target - xf = self.xt - x0 = self.xs - else: - xf = self.xs - x0 = self.xt - - D0 = dist(x, x0) # dist netween new samples an source - idx = np.argmin(D0, 1) # closest one - xf = self.interp(direction) # interp the source samples - # aply the delta to the interpolation - return xf[idx, :] + x - x0[idx, :] - - -@deprecated("The class OTDA_sinkhorn is deprecated in 0.3.1 and will be" - " removed in 0.5 \nUse class SinkhornTransport instead.") -class OTDA_sinkhorn(OTDA): - - """Class for domain adaptation with optimal transport with entropic - regularization - - - """ - - def fit(self, xs, xt, reg=1, ws=None, wt=None, **kwargs): - """Fit regularized domain adaptation between samples is xs and xt - (with optional weights)""" - self.xs = xs - self.xt = xt - - if wt is None: - wt = unif(xt.shape[0]) - if ws is None: - ws = unif(xs.shape[0]) - - self.ws = ws - self.wt = wt - - self.M = dist(xs, xt, metric=self.metric) - self.M = cost_normalization(self.M, self.norm) - self.G = sinkhorn(ws, wt, self.M, reg, **kwargs) - self.computed = True - - -@deprecated("The class OTDA_lpl1 is deprecated in 0.3.1 and will be" - " removed in 0.5 \nUse class SinkhornLpl1Transport instead.") -class OTDA_lpl1(OTDA): - - """Class for domain adaptation with optimal transport with entropic and - group regularization""" - - def fit(self, xs, ys, xt, reg=1, eta=1, ws=None, wt=None, **kwargs): - """Fit regularized domain adaptation between samples is xs and xt - (with optional weights), See ot.da.sinkhorn_lpl1_mm for fit - parameters""" - self.xs = xs - self.xt = xt - - if wt is None: - wt = unif(xt.shape[0]) - if ws is None: - ws = unif(xs.shape[0]) - - self.ws = ws - self.wt = wt - - self.M = dist(xs, xt, metric=self.metric) - self.M = cost_normalization(self.M, self.norm) - self.G = sinkhorn_lpl1_mm(ws, ys, wt, self.M, reg, eta, **kwargs) - self.computed = True - - -@deprecated("The class OTDA_l1L2 is deprecated in 0.3.1 and will be" - " removed in 0.5 \nUse class SinkhornL1l2Transport instead.") -class OTDA_l1l2(OTDA): - - """Class for domain adaptation with optimal transport with entropic - and group lasso regularization""" - - def fit(self, xs, ys, xt, reg=1, eta=1, ws=None, wt=None, **kwargs): - """Fit regularized domain adaptation between samples is xs and xt - (with optional weights), See ot.da.sinkhorn_lpl1_gl for fit - parameters""" - self.xs = xs - self.xt = xt - - if wt is None: - wt = unif(xt.shape[0]) - if ws is None: - ws = unif(xs.shape[0]) - - self.ws = ws - self.wt = wt - - self.M = dist(xs, xt, metric=self.metric) - self.M = cost_normalization(self.M, self.norm) - self.G = sinkhorn_l1l2_gl(ws, ys, wt, self.M, reg, eta, **kwargs) - self.computed = True - - -@deprecated("The class OTDA_mapping_linear is deprecated in 0.3.1 and will be" - " removed in 0.5 \nUse class MappingTransport instead.") -class OTDA_mapping_linear(OTDA): - - """Class for optimal transport with joint linear mapping estimation as in - [8] - """ - - def __init__(self): - """ Class initialization""" - - self.xs = 0 - self.xt = 0 - self.G = 0 - self.L = 0 - self.bias = False - self.computed = False - self.metric = 'sqeuclidean' - - def fit(self, xs, xt, mu=1, eta=1, bias=False, **kwargs): - """ Fit domain adaptation between samples is xs and xt (with optional - weights)""" - self.xs = xs - self.xt = xt - self.bias = bias - - self.ws = unif(xs.shape[0]) - self.wt = unif(xt.shape[0]) - - self.G, self.L = joint_OT_mapping_linear( - xs, xt, mu=mu, eta=eta, bias=bias, **kwargs) - self.computed = True - - def mapping(self): - return lambda x: self.predict(x) - - def predict(self, x): - """ Out of sample mapping estimated during the call to fit""" - if self.computed: - if self.bias: - x = np.hstack((x, np.ones((x.shape[0], 1)))) - return x.dot(self.L) # aply the delta to the interpolation - else: - print("Warning, model not fitted yet, returning None") - return None - - -@deprecated("The class OTDA_mapping_kernel is deprecated in 0.3.1 and will be" - " removed in 0.5 \nUse class MappingTransport instead.") -class OTDA_mapping_kernel(OTDA_mapping_linear): - - """Class for optimal transport with joint nonlinear mapping - estimation as in [8]""" - - def fit(self, xs, xt, mu=1, eta=1, bias=False, kerneltype='gaussian', - sigma=1, **kwargs): - """ Fit domain adaptation between samples is xs and xt """ - self.xs = xs - self.xt = xt - self.bias = bias - - self.ws = unif(xs.shape[0]) - self.wt = unif(xt.shape[0]) - self.kernel = kerneltype - self.sigma = sigma - self.kwargs = kwargs - - self.G, self.L = joint_OT_mapping_kernel( - xs, xt, mu=mu, eta=eta, bias=bias, **kwargs) - self.computed = True - - def predict(self, x): - """ Out of sample mapping estimated during the call to fit""" - - if self.computed: - K = kernel( - x, self.xs, method=self.kernel, sigma=self.sigma, - **self.kwargs) - if self.bias: - K = np.hstack((K, np.ones((x.shape[0], 1)))) - return K.dot(self.L) - else: - print("Warning, model not fitted yet, returning None") - return None - - def distribution_estimation_uniform(X): """estimates a uniform distribution from an array of samples X 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 a2fdd3d..deda6b1 100644 --- a/ot/gpu/__init__.py +++ b/ot/gpu/__init__.py @@ -1,12 +1,37 @@ # -*- coding: utf-8 -*- +""" -from . import bregman -from . import da -from .bregman import sinkhorn +This module provides GPU implementation for several OT solvers and utility +functions. The GPU backend in handled by `cupy +<https://cupy.chainer.org/>`_. + +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 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 -__all__ = ["bregman", "da", "sinkhorn"] +from . import bregman +from . import da +from .bregman import sinkhorn +from .da import sinkhorn_lpl1_mm + +from . import utils +from .utils import dist, to_gpu, to_np + + + + + +__all__ = ["utils", "dist", "sinkhorn", + "sinkhorn_lpl1_mm", 'bregman', 'da', 'to_gpu', 'to_np'] + diff --git a/ot/gpu/bregman.py b/ot/gpu/bregman.py index 47939c4..978b307 100644 --- a/ot/gpu/bregman.py +++ b/ot/gpu/bregman.py @@ -8,14 +8,18 @@ Bregman projections for regularized OT with GPU # # License: MIT License -import numpy as np -import cudamat +import cupy as np # np used for matrix computation +import cupy as cp # cp used for cupy specific operations +from . import utils -def sinkhorn(a, b, M_GPU, reg, numItermax=1000, stopThr=1e-9, verbose=False, - log=False, returnAsGPU=False): - r""" - Solve the entropic regularization optimal transport problem on GPU +def sinkhorn_knopp(a, b, M, reg, numItermax=1000, stopThr=1e-9, + verbose=False, log=False, to_numpy=True, **kwargs): + """ + Solve the entropic regularization optimal transport on GPU + + If the input matrix are in numpy format, they will be uploaded to the + GPU first which can incur significant time overhead. The function solves the following optimization problem: @@ -40,9 +44,10 @@ def sinkhorn(a, b, M_GPU, reg, numItermax=1000, stopThr=1e-9, verbose=False, ---------- a : np.ndarray (ns,) samples weights in the source domain - b : np.ndarray (nt,) - samples in the target domain - M_GPU : cudamat.CUDAMatrix (ns,nt) + b : np.ndarray (nt,) or np.ndarray (nt,nbb) + samples in the target domain, compute sinkhorn with multiple targets + and fixed M if b is a matrix (return OT loss + dual variables in log) + M : np.ndarray (ns,nt) loss matrix reg : float Regularization term >0 @@ -54,8 +59,9 @@ def sinkhorn(a, b, M_GPU, reg, numItermax=1000, stopThr=1e-9, verbose=False, Print information along iterations log : bool, optional record log if True - returnAsGPU : bool, optional - return the OT matrix as a cudamat.CUDAMatrix + to_numpy : boolean, optional (default True) + If true convert back the GPU array result to numpy format. + Returns ------- @@ -88,60 +94,78 @@ def sinkhorn(a, b, M_GPU, reg, numItermax=1000, stopThr=1e-9, verbose=False, ot.optim.cg : General regularized OT """ + + a = cp.asarray(a) + b = cp.asarray(b) + M = cp.asarray(M) + + if len(a) == 0: + a = np.ones((M.shape[0],)) / M.shape[0] + if len(b) == 0: + b = np.ones((M.shape[1],)) / M.shape[1] + # init data Nini = len(a) Nfin = len(b) + if len(b.shape) > 1: + nbb = b.shape[1] + else: + nbb = 0 + if log: log = {'err': []} # we assume that no distances are null except those of the diagonal of # distances - u = (np.ones(Nini) / Nini).reshape((Nini, 1)) - u_GPU = cudamat.CUDAMatrix(u) - a_GPU = cudamat.CUDAMatrix(a.reshape((Nini, 1))) - ones_GPU = cudamat.empty(u_GPU.shape).assign(1) - v = (np.ones(Nfin) / Nfin).reshape((Nfin, 1)) - v_GPU = cudamat.CUDAMatrix(v) - b_GPU = cudamat.CUDAMatrix(b.reshape((Nfin, 1))) - - M_GPU.divide(-reg) + if nbb: + u = np.ones((Nini, nbb)) / Nini + v = np.ones((Nfin, nbb)) / Nfin + else: + u = np.ones(Nini) / Nini + v = np.ones(Nfin) / Nfin - K_GPU = cudamat.exp(M_GPU) + # print(reg) - ones_GPU.divide(a_GPU, target=a_GPU) - Kp_GPU = cudamat.empty(K_GPU.shape) - K_GPU.mult_by_col(a_GPU, target=Kp_GPU) + # Next 3 lines equivalent to K= np.exp(-M/reg), but faster to compute + K = np.empty(M.shape, dtype=M.dtype) + np.divide(M, -reg, out=K) + np.exp(K, out=K) - tmp_GPU = cudamat.empty(K_GPU.shape) + # print(np.min(K)) + tmp2 = np.empty(b.shape, dtype=M.dtype) + Kp = (1 / a).reshape(-1, 1) * K cpt = 0 err = 1 while (err > stopThr and cpt < numItermax): - uprev_GPU = u_GPU.copy() - vprev_GPU = v_GPU.copy() + uprev = u + vprev = v - KtransposeU_GPU = K_GPU.transpose().dot(u_GPU) - b_GPU.divide(KtransposeU_GPU, target=v_GPU) - ones_GPU.divide(Kp_GPU.dot(v_GPU), target=u_GPU) + KtransposeU = np.dot(K.T, u) + v = np.divide(b, KtransposeU) + u = 1. / np.dot(Kp, v) - if (np.any(KtransposeU_GPU.asarray() == 0) or - not u_GPU.allfinite() or not v_GPU.allfinite()): + if (np.any(KtransposeU == 0) or + np.any(np.isnan(u)) or np.any(np.isnan(v)) or + np.any(np.isinf(u)) or np.any(np.isinf(v))): # we have reached the machine precision # come back to previous solution and quit loop print('Warning: numerical errors at iteration', cpt) - u_GPU = uprev_GPU.copy() - v_GPU = vprev_GPU.copy() + u = uprev + v = vprev break if cpt % 10 == 0: # we can speed up the process by checking for the error only all # the 10th iterations - K_GPU.mult_by_col(u_GPU, target=tmp_GPU) - tmp_GPU.mult_by_row(v_GPU.transpose(), target=tmp_GPU) - - bcopy_GPU = b_GPU.copy().transpose() - bcopy_GPU.add_sums(tmp_GPU, axis=0, beta=-1) - err = bcopy_GPU.euclid_norm()**2 + if nbb: + err = np.sum((u - uprev)**2) / np.sum((u)**2) + \ + np.sum((v - vprev)**2) / np.sum((v)**2) + else: + # compute right marginal tmp2= (diag(u)Kdiag(v))^T1 + tmp2 = np.sum(u[:, None] * K * v[None, :], 0) + #tmp2=np.einsum('i,ij,j->j', u, K, v) + err = np.linalg.norm(tmp2 - b)**2 # violation of marginal if log: log['err'].append(err) @@ -150,20 +174,32 @@ def sinkhorn(a, b, M_GPU, reg, numItermax=1000, stopThr=1e-9, verbose=False, print( '{:5s}|{:12s}'.format('It.', 'Err') + '\n' + '-' * 19) print('{:5d}|{:8e}|'.format(cpt, err)) - cpt += 1 - if log: - log['u'] = u_GPU.asarray() - log['v'] = v_GPU.asarray() - - K_GPU.mult_by_col(u_GPU, target=K_GPU) - K_GPU.mult_by_row(v_GPU.transpose(), target=K_GPU) - - if returnAsGPU: - res = K_GPU - else: - res = K_GPU.asarray() - + cpt = cpt + 1 if log: - return res, log - else: - return res + log['u'] = u + log['v'] = v + + if nbb: # return only loss + #res = np.einsum('ik,ij,jk,ij->k', u, K, v, M) (explodes cupy memory) + res = np.empty(nbb) + for i in range(nbb): + res[i] = np.sum(u[:, None, i] * (K * M) * v[None, :, i]) + if to_numpy: + res = utils.to_np(res) + if log: + return res, log + else: + return res + + else: # return OT matrix + res = u.reshape((-1, 1)) * K * v.reshape((1, -1)) + if to_numpy: + res = utils.to_np(res) + if log: + return res, log + else: + return res + + +# define sinkhorn as sinkhorn_knopp +sinkhorn = sinkhorn_knopp diff --git a/ot/gpu/da.py b/ot/gpu/da.py index 71a485a..4a98038 100644 --- a/ot/gpu/da.py +++ b/ot/gpu/da.py @@ -11,80 +11,30 @@ Domain adaptation with optimal transport with GPU implementation # License: MIT License -import numpy as np -from ..utils import unif -from ..da import OTDA +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 -import cudamat -def pairwiseEuclideanGPU(a, b, returnAsGPU=False, squared=False): +def sinkhorn_lpl1_mm(a, labels_a, b, M, reg, eta=0.1, numItermax=10, + numInnerItermax=200, stopInnerThr=1e-9, verbose=False, + log=False, to_numpy=True): """ - Compute the pairwise euclidean distance between matrices a and b. - - - Parameters - ---------- - a : np.ndarray (n, f) - first matrice - b : np.ndarray (m, f) - second matrice - returnAsGPU : boolean, optional (default False) - if True, returns cudamat matrix still on GPU, else return np.ndarray - squared : boolean, optional (default False) - if True, return squared euclidean distance matrice + Solve the entropic regularization optimal transport problem with nonconvex + group lasso regularization on GPU + If the input matrix are in numpy format, they will be uploaded to the + GPU first which can incur significant time overhead. - Returns - ------- - c : (n x m) np.ndarray or cudamat.CUDAMatrix - pairwise euclidean distance distance matrix - """ - # a is shape (n, f) and b shape (m, f). Return matrix c of shape (n, m). - # First compute in c_GPU the squared euclidean distance. And return its - # square root. At each cell [i,j] of c, we want to have - # sum{k in range(f)} ( (a[i,k] - b[j,k])^2 ). We know that - # (a-b)^2 = a^2 -2ab +b^2. Thus we want to have in each cell of c: - # sum{k in range(f)} ( a[i,k]^2 -2a[i,k]b[j,k] +b[j,k]^2). - - a_GPU = cudamat.CUDAMatrix(a) - b_GPU = cudamat.CUDAMatrix(b) - - # Multiply a by b transpose to obtain in each cell [i,j] of c the - # value sum{k in range(f)} ( a[i,k]b[j,k] ) - c_GPU = cudamat.dot(a_GPU, b_GPU.transpose()) - # multiply by -2 to have sum{k in range(f)} ( -2a[i,k]b[j,k] ) - c_GPU.mult(-2) - - # Compute the vectors of the sum of squared elements. - a_GPU = cudamat.pow(a_GPU, 2).sum(axis=1) - b_GPU = cudamat.pow(b_GPU, 2).sum(axis=1) - - # Add the vectors in each columns (respectivly rows) of c. - # sum{k in range(f)} ( a[i,k]^2 -2a[i,k]b[j,k] ) - c_GPU.add_col_vec(a_GPU) - # sum{k in range(f)} ( a[i,k]^2 -2a[i,k]b[j,k] +b[j,k]^2) - c_GPU.add_row_vec(b_GPU.transpose()) - - if not squared: - c_GPU = cudamat.sqrt(c_GPU) - - if returnAsGPU: - return c_GPU - else: - return c_GPU.asarray() - - -def sinkhorn_lpl1_mm(a, labels_a, b, M_GPU, reg, eta=0.1, numItermax=10, - numInnerItermax=200, stopInnerThr=1e-9, - verbose=False, log=False): - """ - Solve the entropic regularization optimal transport problem with nonconvex group lasso regularization The function solves the following optimization problem: .. math:: - \gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega_e(\gamma)+ \eta \Omega_g(\gamma) + \gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega_e(\gamma) + + \eta \Omega_g(\gamma) s.t. \gamma 1 = a @@ -94,11 +44,16 @@ def sinkhorn_lpl1_mm(a, labels_a, b, M_GPU, reg, eta=0.1, numItermax=10, where : - M is the (ns,nt) metric cost matrix - - :math:`\Omega_e` is the entropic regularization term :math:`\Omega_e(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})` - - :math:`\Omega_g` is the group lasso regulaization term :math:`\Omega_g(\gamma)=\sum_{i,c} \|\gamma_{i,\mathcal{I}_c}\|^{1/2}_1` where :math:`\mathcal{I}_c` are the index of samples from class c in the source domain. + - :math:`\Omega_e` is the entropic regularization term + :math:`\Omega_e(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})` + - :math:`\Omega_g` is the group lasso regulaization term + :math:`\Omega_g(\gamma)=\sum_{i,c} \|\gamma_{i,\mathcal{I}_c}\|^{1/2}_1` + where :math:`\mathcal{I}_c` are the index of samples from class c + in the source domain. - a and b are source and target weights (sum to 1) - The algorithm used for solving the problem is the generalised conditional gradient as proposed in [5]_ [7]_ + The algorithm used for solving the problem is the generalised conditional + gradient as proposed in [5]_ [7]_ Parameters @@ -109,7 +64,7 @@ def sinkhorn_lpl1_mm(a, labels_a, b, M_GPU, reg, eta=0.1, numItermax=10, labels of samples in the source domain b : np.ndarray (nt,) samples weights in the target domain - M_GPU : cudamat.CUDAMatrix (ns,nt) + M : np.ndarray (ns,nt) loss matrix reg : float Regularization term for entropic regularization >0 @@ -125,6 +80,8 @@ def sinkhorn_lpl1_mm(a, labels_a, b, M_GPU, reg, eta=0.1, numItermax=10, Print information along iterations log : bool, optional record log if True + to_numpy : boolean, optional (default True) + If true convert back the GPU array result to numpy format. Returns @@ -138,8 +95,13 @@ def sinkhorn_lpl1_mm(a, labels_a, b, M_GPU, reg, eta=0.1, numItermax=10, References ---------- - .. [5] N. Courty; R. Flamary; D. Tuia; A. Rakotomamonjy, "Optimal Transport for Domain Adaptation," in IEEE Transactions on Pattern Analysis and Machine Intelligence , vol.PP, no.99, pp.1-1 - .. [7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015). Generalized conditional gradient: analysis of convergence and applications. arXiv preprint arXiv:1510.06567. + .. [5] N. Courty; R. Flamary; D. Tuia; A. Rakotomamonjy, + "Optimal Transport for Domain Adaptation," in IEEE + Transactions on Pattern Analysis and Machine Intelligence , + vol.PP, no.99, pp.1-1 + .. [7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015). + Generalized conditional gradient: analysis of convergence + and applications. arXiv preprint arXiv:1510.06567. See Also -------- @@ -148,108 +110,35 @@ def sinkhorn_lpl1_mm(a, labels_a, b, M_GPU, reg, eta=0.1, numItermax=10, ot.optim.cg : General regularized OT """ + + a, labels_a, b, M = utils.to_gpu(a, labels_a, b, M) + p = 0.5 epsilon = 1e-3 - Nfin = len(b) indices_labels = [] - classes = np.unique(labels_a) + labels_a2 = cp.asnumpy(labels_a) + classes = npp.unique(labels_a2) for c in classes: - idxc, = np.where(labels_a == c) - indices_labels.append(cudamat.CUDAMatrix(idxc.reshape(1, -1))) + idxc, = utils.to_gpu(npp.where(labels_a2 == c)) + indices_labels.append(idxc) - Mreg_GPU = cudamat.empty(M_GPU.shape) - W_GPU = cudamat.empty(M_GPU.shape).assign(0) + W = np.zeros(M.shape) for cpt in range(numItermax): - Mreg_GPU.assign(M_GPU) - Mreg_GPU.add_mult(W_GPU, eta) - transp_GPU = sinkhorn(a, b, Mreg_GPU, reg, numItermax=numInnerItermax, - stopThr=stopInnerThr, returnAsGPU=True) + Mreg = M + eta * W + transp = sinkhorn(a, b, Mreg, reg, numItermax=numInnerItermax, + stopThr=stopInnerThr, to_numpy=False) # the transport has been computed. Check if classes are really # separated - W_GPU.assign(1) - W_GPU = W_GPU.transpose() + W = np.ones(M.shape) for (i, c) in enumerate(classes): - (_, nbRow) = indices_labels[i].shape - tmpC_GPU = cudamat.empty((Nfin, nbRow)).assign(0) - transp_GPU.transpose().select_columns(indices_labels[i], tmpC_GPU) - majs_GPU = tmpC_GPU.sum(axis=1).add(epsilon) - cudamat.pow(majs_GPU, (p - 1)) - majs_GPU.mult(p) - - tmpC_GPU.assign(0) - tmpC_GPU.add_col_vec(majs_GPU) - W_GPU.set_selected_columns(indices_labels[i], tmpC_GPU) - - W_GPU = W_GPU.transpose() - - return transp_GPU.asarray() + majs = np.sum(transp[indices_labels[i]], axis=0) + majs = p * ((majs + epsilon)**(p - 1)) + W[indices_labels[i]] = majs -class OTDA_GPU(OTDA): - - def normalizeM(self, norm): - if norm == "median": - self.M_GPU.divide(float(np.median(self.M_GPU.asarray()))) - elif norm == "max": - self.M_GPU.divide(float(np.max(self.M_GPU.asarray()))) - elif norm == "log": - self.M_GPU.add(1) - cudamat.log(self.M_GPU) - elif norm == "loglog": - self.M_GPU.add(1) - cudamat.log(self.M_GPU) - self.M_GPU.add(1) - cudamat.log(self.M_GPU) - - -class OTDA_sinkhorn(OTDA_GPU): - - def fit(self, xs, xt, reg=1, ws=None, wt=None, norm=None, **kwargs): - cudamat.init() - xs = np.asarray(xs, dtype=np.float64) - xt = np.asarray(xt, dtype=np.float64) - - self.xs = xs - self.xt = xt - - if wt is None: - wt = unif(xt.shape[0]) - if ws is None: - ws = unif(xs.shape[0]) - - self.ws = ws - self.wt = wt - - self.M_GPU = pairwiseEuclideanGPU(xs, xt, returnAsGPU=True, - squared=True) - self.normalizeM(norm) - self.G = sinkhorn(ws, wt, self.M_GPU, reg, **kwargs) - self.computed = True - - -class OTDA_lpl1(OTDA_GPU): - - def fit(self, xs, ys, xt, reg=1, eta=1, ws=None, wt=None, norm=None, - **kwargs): - cudamat.init() - xs = np.asarray(xs, dtype=np.float64) - xt = np.asarray(xt, dtype=np.float64) - - self.xs = xs - self.xt = xt - - if wt is None: - wt = unif(xt.shape[0]) - if ws is None: - ws = unif(xs.shape[0]) - - self.ws = ws - self.wt = wt - - self.M_GPU = pairwiseEuclideanGPU(xs, xt, returnAsGPU=True, - squared=True) - self.normalizeM(norm) - self.G = sinkhorn_lpl1_mm(ws, ys, wt, self.M_GPU, reg, eta, **kwargs) - self.computed = True + if to_numpy: + return utils.to_np(transp) + else: + return transp diff --git a/ot/gpu/utils.py b/ot/gpu/utils.py new file mode 100644 index 0000000..41e168a --- /dev/null +++ b/ot/gpu/utils.py @@ -0,0 +1,101 @@ +# -*- coding: utf-8 -*- +""" +Utility functions for GPU +""" + +# Author: Remi Flamary <remi.flamary@unice.fr> +# Nicolas Courty <ncourty@irisa.fr> +# Leo Gautheron <https://github.com/aje> +# +# License: MIT License + +import cupy as np # np used for matrix computation +import cupy as cp # cp used for cupy specific operations + + +def euclidean_distances(a, b, squared=False, to_numpy=True): + """ + Compute the pairwise euclidean distance between matrices a and b. + + If the input matrix are in numpy format, they will be uploaded to the + GPU first which can incur significant time overhead. + + Parameters + ---------- + a : np.ndarray (n, f) + first matrix + b : np.ndarray (m, f) + second matrix + to_numpy : boolean, optional (default True) + If true convert back the GPU array result to numpy format. + squared : boolean, optional (default False) + if True, return squared euclidean distance matrix + + Returns + ------- + c : (n x m) np.ndarray or cupy.ndarray + pairwise euclidean distance distance matrix + """ + + a, b = to_gpu(a, b) + + a2 = np.sum(np.square(a), 1) + b2 = np.sum(np.square(b), 1) + + c = -2 * np.dot(a, b.T) + c += a2[:, None] + c += b2[None, :] + + if not squared: + np.sqrt(c, out=c) + if to_numpy: + return to_np(c) + else: + return c + + +def dist(x1, x2=None, metric='sqeuclidean', to_numpy=True): + """Compute distance between samples in x1 and x2 on gpu + + Parameters + ---------- + + x1 : np.array (n1,d) + matrix with n1 samples of size d + x2 : np.array (n2,d), optional + matrix with n2 samples of size d (if None then x2=x1) + metric : str + Metric from 'sqeuclidean', 'euclidean', + + + Returns + ------- + + M : np.array (n1,n2) + distance matrix computed with given metric + + """ + if x2 is None: + x2 = x1 + if metric == "sqeuclidean": + return euclidean_distances(x1, x2, squared=True, to_numpy=to_numpy) + elif metric == "euclidean": + return euclidean_distances(x1, x2, squared=False, to_numpy=to_numpy) + else: + raise NotImplementedError + + +def to_gpu(*args): + """ Upload numpy arrays to GPU and return them""" + if len(args) > 1: + return (cp.asarray(x) for x in args) + else: + return cp.asarray(args[0]) + + +def to_np(*args): + """ convert GPU arras to numpy and return them""" + if len(args) > 1: + return (cp.asnumpy(x) for x in args) + else: + return cp.asnumpy(args[0]) diff --git a/ot/lp/__init__.py b/ot/lp/__init__.py index 5dda82a..02cbd8c 100644 --- a/ot/lp/__init__.py +++ b/ot/lp/__init__.py @@ -17,6 +17,9 @@ from .import cvx from .emd_wrap import emd_c, check_result from ..utils import parmap from .cvx import barycenter +from ..utils import dist + +__all__=['emd', 'emd2', 'barycenter', 'free_support_barycenter', 'cvx'] def emd(a, b, M, numItermax=100000, log=False): @@ -214,3 +217,95 @@ def emd2(a, b, M, processes=multiprocessing.cpu_count(), res = parmap(f, [b[:, i] for i in range(nb)], processes) return res + + + +def free_support_barycenter(measures_locations, measures_weights, X_init, b=None, weights=None, numItermax=100, stopThr=1e-7, verbose=False, log=None): + """ + Solves the free support (locations of the barycenters are optimized, not the weights) Wasserstein barycenter problem (i.e. the weighted Frechet mean for the 2-Wasserstein distance) + + The function solves the Wasserstein barycenter problem when the barycenter measure is constrained to be supported on k atoms. + This problem is considered in [1] (Algorithm 2). There are two differences with the following codes: + - we do not optimize over the weights + - we do not do line search for the locations updates, we use i.e. theta = 1 in [1] (Algorithm 2). This can be seen as a discrete implementation of the fixed-point algorithm of [2] proposed in the continuous setting. + + Parameters + ---------- + measures_locations : list of (k_i,d) np.ndarray + The discrete support of a measure supported on k_i locations of a d-dimensional space (k_i can be different for each element of the list) + measures_weights : list of (k_i,) np.ndarray + Numpy arrays where each numpy array has k_i non-negatives values summing to one representing the weights of each discrete input measure + + X_init : (k,d) np.ndarray + Initialization of the support locations (on k atoms) of the barycenter + b : (k,) np.ndarray + Initialization of the weights of the barycenter (non-negatives, sum to 1) + weights : (k,) np.ndarray + Initialization of the coefficients of the barycenter (non-negatives, sum to 1) + + numItermax : int, optional + Max number of iterations + stopThr : float, optional + Stop threshol on error (>0) + verbose : bool, optional + Print information along iterations + log : bool, optional + record log if True + + Returns + ------- + X : (k,d) np.ndarray + Support locations (on k atoms) of the barycenter + + References + ---------- + + .. [1] Cuturi, Marco, and Arnaud Doucet. "Fast computation of Wasserstein barycenters." International Conference on Machine Learning. 2014. + + .. [2] Álvarez-Esteban, Pedro C., et al. "A fixed-point approach to barycenters in Wasserstein space." Journal of Mathematical Analysis and Applications 441.2 (2016): 744-762. + + """ + + iter_count = 0 + + N = len(measures_locations) + k = X_init.shape[0] + d = X_init.shape[1] + if b is None: + b = np.ones((k,))/k + if weights is None: + weights = np.ones((N,)) / N + + X = X_init + + log_dict = {} + displacement_square_norms = [] + + displacement_square_norm = stopThr + 1. + + while ( displacement_square_norm > stopThr and iter_count < numItermax ): + + T_sum = np.zeros((k, d)) + + for (measure_locations_i, measure_weights_i, weight_i) in zip(measures_locations, measures_weights, weights.tolist()): + + M_i = dist(X, measure_locations_i) + T_i = emd(b, measure_weights_i, M_i) + T_sum = T_sum + weight_i * np.reshape(1. / b, (-1, 1)) * np.matmul(T_i, measure_locations_i) + + displacement_square_norm = np.sum(np.square(T_sum-X)) + if log: + displacement_square_norms.append(displacement_square_norm) + + X = T_sum + + if verbose: + print('iteration %d, displacement_square_norm=%f\n', iter_count, displacement_square_norm) + + iter_count += 1 + + if log: + log_dict['displacement_square_norms'] = displacement_square_norms + return X, log_dict + else: + return X
\ No newline at end of file diff --git a/ot/lp/cvx.py b/ot/lp/cvx.py index c8c75bc..8e763be 100644 --- a/ot/lp/cvx.py +++ b/ot/lp/cvx.py @@ -11,6 +11,7 @@ import numpy as np import scipy as sp import scipy.sparse as sps + try: import cvxopt from cvxopt import solvers, matrix, spmatrix @@ -26,7 +27,7 @@ def scipy_sparse_to_spmatrix(A): def barycenter(A, M, weights=None, verbose=False, log=False, solver='interior-point'): - """Compute the entropic regularized wasserstein barycenter of distributions A + """Compute the Wasserstein barycenter of distributions A The function solves the following optimization problem [16]: diff --git a/ot/smooth.py b/ot/smooth.py new file mode 100644 index 0000000..5a8e4b5 --- /dev/null +++ b/ot/smooth.py @@ -0,0 +1,600 @@ +#Copyright (c) 2018, Mathieu Blondel +#All rights reserved. +# +#Redistribution and use in source and binary forms, with or without +#modification, are permitted provided that the following conditions are met: +# +#1. Redistributions of source code must retain the above copyright notice, this +#list of conditions and the following disclaimer. +# +#2. Redistributions in binary form must reproduce the above copyright notice, +#this list of conditions and the following disclaimer in the documentation and/or +#other materials provided with the distribution. +# +#THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND +#ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED +#WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. +#IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, +#INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT +#NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, +#OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF +#LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR +#OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF +#THE POSSIBILITY OF SUCH DAMAGE. + +# Author: Mathieu Blondel +# Remi Flamary <remi.flamary@unice.fr> + +""" +Implementation of +Smooth and Sparse Optimal Transport. +Mathieu Blondel, Vivien Seguy, Antoine Rolet. +In Proc. of AISTATS 2018. +https://arxiv.org/abs/1710.06276 + +[17] Blondel, M., Seguy, V., & Rolet, A. (2018). Smooth and Sparse Optimal +Transport. Proceedings of the Twenty-First International Conference on +Artificial Intelligence and Statistics (AISTATS). + +Original code from https://github.com/mblondel/smooth-ot/ + +""" + +import numpy as np +from scipy.optimize import minimize + + +def projection_simplex(V, z=1, axis=None): + """ Projection of x onto the simplex, scaled by z + + P(x; z) = argmin_{y >= 0, sum(y) = z} ||y - x||^2 + z: float or array + If array, len(z) must be compatible with V + axis: None or int + - axis=None: project V by P(V.ravel(); z) + - axis=1: project each V[i] by P(V[i]; z[i]) + - axis=0: project each V[:, j] by P(V[:, j]; z[j]) + """ + if axis == 1: + n_features = V.shape[1] + U = np.sort(V, axis=1)[:, ::-1] + z = np.ones(len(V)) * z + cssv = np.cumsum(U, axis=1) - z[:, np.newaxis] + ind = np.arange(n_features) + 1 + cond = U - cssv / ind > 0 + rho = np.count_nonzero(cond, axis=1) + theta = cssv[np.arange(len(V)), rho - 1] / rho + return np.maximum(V - theta[:, np.newaxis], 0) + + elif axis == 0: + return projection_simplex(V.T, z, axis=1).T + + else: + V = V.ravel().reshape(1, -1) + return projection_simplex(V, z, axis=1).ravel() + + +class Regularization(object): + """Base class for Regularization objects + + Notes + ----- + This class is not intended for direct use but as aparent for true + regularizatiojn implementation. + """ + + def __init__(self, gamma=1.0): + """ + + Parameters + ---------- + gamma: float + Regularization parameter. + We recover unregularized OT when gamma -> 0. + + """ + self.gamma = gamma + + def delta_Omega(X): + """ + Compute delta_Omega(X[:, j]) for each X[:, j]. + delta_Omega(x) = sup_{y >= 0} y^T x - Omega(y). + + Parameters + ---------- + X: array, shape = len(a) x len(b) + Input array. + + Returns + ------- + v: array, len(b) + Values: v[j] = delta_Omega(X[:, j]) + G: array, len(a) x len(b) + Gradients: G[:, j] = nabla delta_Omega(X[:, j]) + """ + raise NotImplementedError + + def max_Omega(X, b): + """ + Compute max_Omega_j(X[:, j]) for each X[:, j]. + max_Omega_j(x) = sup_{y >= 0, sum(y) = 1} y^T x - Omega(b[j] y) / b[j]. + + Parameters + ---------- + X: array, shape = len(a) x len(b) + Input array. + + Returns + ------- + v: array, len(b) + Values: v[j] = max_Omega_j(X[:, j]) + G: array, len(a) x len(b) + Gradients: G[:, j] = nabla max_Omega_j(X[:, j]) + """ + raise NotImplementedError + + def Omega(T): + """ + Compute regularization term. + + Parameters + ---------- + T: array, shape = len(a) x len(b) + Input array. + + Returns + ------- + value: float + Regularization term. + """ + raise NotImplementedError + + +class NegEntropy(Regularization): + """ NegEntropy regularization """ + + def delta_Omega(self, X): + G = np.exp(X / self.gamma - 1) + val = self.gamma * np.sum(G, axis=0) + return val, G + + def max_Omega(self, X, b): + max_X = np.max(X, axis=0) / self.gamma + exp_X = np.exp(X / self.gamma - max_X) + val = self.gamma * (np.log(np.sum(exp_X, axis=0)) + max_X) + val -= self.gamma * np.log(b) + G = exp_X / np.sum(exp_X, axis=0) + return val, G + + def Omega(self, T): + return self.gamma * np.sum(T * np.log(T)) + + +class SquaredL2(Regularization): + """ Squared L2 regularization """ + + def delta_Omega(self, X): + max_X = np.maximum(X, 0) + val = np.sum(max_X ** 2, axis=0) / (2 * self.gamma) + G = max_X / self.gamma + return val, G + + def max_Omega(self, X, b): + G = projection_simplex(X / (b * self.gamma), axis=0) + val = np.sum(X * G, axis=0) + val -= 0.5 * self.gamma * b * np.sum(G * G, axis=0) + return val, G + + def Omega(self, T): + return 0.5 * self.gamma * np.sum(T ** 2) + + +def dual_obj_grad(alpha, beta, a, b, C, regul): + """ + Compute objective value and gradients of dual objective. + + Parameters + ---------- + alpha: array, shape = len(a) + beta: array, shape = len(b) + Current iterate of dual potentials. + a: array, shape = len(a) + b: array, shape = len(b) + Input histograms (should be non-negative and sum to 1). + C: array, shape = len(a) x len(b) + Ground cost matrix. + regul: Regularization object + Should implement a delta_Omega(X) method. + + Returns + ------- + obj: float + Objective value (higher is better). + grad_alpha: array, shape = len(a) + Gradient w.r.t. alpha. + grad_beta: array, shape = len(b) + Gradient w.r.t. beta. + """ + obj = np.dot(alpha, a) + np.dot(beta, b) + grad_alpha = a.copy() + grad_beta = b.copy() + + # X[:, j] = alpha + beta[j] - C[:, j] + X = alpha[:, np.newaxis] + beta - C + + # val.shape = len(b) + # G.shape = len(a) x len(b) + val, G = regul.delta_Omega(X) + + obj -= np.sum(val) + grad_alpha -= G.sum(axis=1) + grad_beta -= G.sum(axis=0) + + return obj, grad_alpha, grad_beta + + +def solve_dual(a, b, C, regul, method="L-BFGS-B", tol=1e-3, max_iter=500, + verbose=False): + """ + Solve the "smoothed" dual objective. + + Parameters + ---------- + a: array, shape = len(a) + b: array, shape = len(b) + Input histograms (should be non-negative and sum to 1). + C: array, shape = len(a) x len(b) + Ground cost matrix. + regul: Regularization object + Should implement a delta_Omega(X) method. + method: str + Solver to be used (passed to `scipy.optimize.minimize`). + tol: float + Tolerance parameter. + max_iter: int + Maximum number of iterations. + + Returns + ------- + alpha: array, shape = len(a) + beta: array, shape = len(b) + Dual potentials. + """ + + def _func(params): + # Unpack alpha and beta. + alpha = params[:len(a)] + beta = params[len(a):] + + obj, grad_alpha, grad_beta = dual_obj_grad(alpha, beta, a, b, C, regul) + + # Pack grad_alpha and grad_beta. + grad = np.concatenate((grad_alpha, grad_beta)) + + # We need to maximize the dual. + return -obj, -grad + + # Unfortunately, `minimize` only supports functions whose argument is a + # vector. So, we need to concatenate alpha and beta. + alpha_init = np.zeros(len(a)) + beta_init = np.zeros(len(b)) + params_init = np.concatenate((alpha_init, beta_init)) + + res = minimize(_func, params_init, method=method, jac=True, + tol=tol, options=dict(maxiter=max_iter, disp=verbose)) + + alpha = res.x[:len(a)] + beta = res.x[len(a):] + + return alpha, beta, res + + +def semi_dual_obj_grad(alpha, a, b, C, regul): + """ + Compute objective value and gradient of semi-dual objective. + + Parameters + ---------- + alpha: array, shape = len(a) + Current iterate of semi-dual potentials. + a: array, shape = len(a) + b: array, shape = len(b) + Input histograms (should be non-negative and sum to 1). + C: array, shape = len(a) x len(b) + Ground cost matrix. + regul: Regularization object + Should implement a max_Omega(X) method. + + Returns + ------- + obj: float + Objective value (higher is better). + grad: array, shape = len(a) + Gradient w.r.t. alpha. + """ + obj = np.dot(alpha, a) + grad = a.copy() + + # X[:, j] = alpha - C[:, j] + X = alpha[:, np.newaxis] - C + + # val.shape = len(b) + # G.shape = len(a) x len(b) + val, G = regul.max_Omega(X, b) + + obj -= np.dot(b, val) + grad -= np.dot(G, b) + + return obj, grad + + +def solve_semi_dual(a, b, C, regul, method="L-BFGS-B", tol=1e-3, max_iter=500, + verbose=False): + """ + Solve the "smoothed" semi-dual objective. + + Parameters + ---------- + a: array, shape = len(a) + b: array, shape = len(b) + Input histograms (should be non-negative and sum to 1). + C: array, shape = len(a) x len(b) + Ground cost matrix. + regul: Regularization object + Should implement a max_Omega(X) method. + method: str + Solver to be used (passed to `scipy.optimize.minimize`). + tol: float + Tolerance parameter. + max_iter: int + Maximum number of iterations. + + Returns + ------- + alpha: array, shape = len(a) + Semi-dual potentials. + """ + + def _func(alpha): + obj, grad = semi_dual_obj_grad(alpha, a, b, C, regul) + # We need to maximize the semi-dual. + return -obj, -grad + + alpha_init = np.zeros(len(a)) + + res = minimize(_func, alpha_init, method=method, jac=True, + tol=tol, options=dict(maxiter=max_iter, disp=verbose)) + + return res.x, res + + +def get_plan_from_dual(alpha, beta, C, regul): + """ + Retrieve optimal transportation plan from optimal dual potentials. + + Parameters + ---------- + alpha: array, shape = len(a) + beta: array, shape = len(b) + Optimal dual potentials. + C: array, shape = len(a) x len(b) + Ground cost matrix. + regul: Regularization object + Should implement a delta_Omega(X) method. + + Returns + ------- + T: array, shape = len(a) x len(b) + Optimal transportation plan. + """ + X = alpha[:, np.newaxis] + beta - C + return regul.delta_Omega(X)[1] + + +def get_plan_from_semi_dual(alpha, b, C, regul): + """ + Retrieve optimal transportation plan from optimal semi-dual potentials. + + Parameters + ---------- + alpha: array, shape = len(a) + Optimal semi-dual potentials. + b: array, shape = len(b) + Second input histogram (should be non-negative and sum to 1). + C: array, shape = len(a) x len(b) + Ground cost matrix. + regul: Regularization object + Should implement a delta_Omega(X) method. + + Returns + ------- + T: array, shape = len(a) x len(b) + Optimal transportation plan. + """ + X = alpha[:, np.newaxis] - C + return regul.max_Omega(X, b)[1] * b + + +def smooth_ot_dual(a, b, M, reg, reg_type='l2', method="L-BFGS-B", stopThr=1e-9, + numItermax=500, verbose=False, log=False): + r""" + Solve the regularized OT problem in the dual and return the OT matrix + + The function solves the smooth relaxed dual formulation (7) in [17]_ : + + .. math:: + \max_{\alpha,\beta}\quad a^T\alpha+b^T\beta-\sum_j\delta_\Omega(\alpha+\beta_j-\mathbf{m}_j) + + where : + + - :math:`\mathbf{m}_j` is the jth column of the cost matrix + - :math:`\delta_\Omega` is the convex conjugate of the regularization term :math:`\Omega` + - a and b are source and target weights (sum to 1) + + The OT matrix can is reconstructed from the gradient of :math:`\delta_\Omega` + (See [17]_ Proposition 1). + The optimization algorithm is using gradient decent (L-BFGS by default). + + + Parameters + ---------- + a : np.ndarray (ns,) + samples weights in the source domain + b : np.ndarray (nt,) or np.ndarray (nt,nbb) + samples in the target domain, compute sinkhorn with multiple targets + and fixed M if b is a matrix (return OT loss + dual variables in log) + M : np.ndarray (ns,nt) + loss matrix + reg : float + Regularization term >0 + reg_type : str + Regularization type, can be the following (default ='l2'): + - 'kl' : Kullback Leibler (~ Neg-entropy used in sinkhorn [2]_) + - 'l2' : Squared Euclidean regularization + method : str + Solver to use for scipy.optimize.minimize + numItermax : int, optional + Max number of iterations + stopThr : float, optional + Stop threshol on error (>0) + verbose : bool, optional + Print information along iterations + log : bool, optional + record log if True + + + Returns + ------- + gamma : (ns x nt) ndarray + Optimal transportation matrix for the given parameters + log : dict + log dictionary return only if log==True in parameters + + + References + ---------- + + .. [2] M. Cuturi, Sinkhorn Distances : Lightspeed Computation of Optimal Transport, Advances in Neural Information Processing Systems (NIPS) 26, 2013 + + .. [17] Blondel, M., Seguy, V., & Rolet, A. (2018). Smooth and Sparse Optimal Transport. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics (AISTATS). + + See Also + -------- + ot.lp.emd : Unregularized OT + ot.sinhorn : Entropic regularized OT + ot.optim.cg : General regularized OT + + """ + + if reg_type.lower() in ['l2', 'squaredl2']: + regul = SquaredL2(gamma=reg) + elif reg_type.lower() in ['entropic', 'negentropy', 'kl']: + regul = NegEntropy(gamma=reg) + else: + raise NotImplementedError('Unknown regularization') + + # solve dual + alpha, beta, res = solve_dual(a, b, M, regul, max_iter=numItermax, + tol=stopThr, verbose=verbose) + + # reconstruct transport matrix + G = get_plan_from_dual(alpha, beta, M, regul) + + if log: + log = {'alpha': alpha, 'beta': beta, 'res': res} + return G, log + else: + return G + + +def smooth_ot_semi_dual(a, b, M, reg, reg_type='l2', method="L-BFGS-B", stopThr=1e-9, + numItermax=500, verbose=False, log=False): + r""" + Solve the regularized OT problem in the semi-dual and return the OT matrix + + The function solves the smooth relaxed dual formulation (10) in [17]_ : + + .. math:: + \max_{\alpha}\quad a^T\alpha-OT_\Omega^*(\alpha,b) + + where : + + .. math:: + OT_\Omega^*(\alpha,b)=\sum_j b_j + + - :math:`\mathbf{m}_j` is the jth column of the cost matrix + - :math:`OT_\Omega^*(\alpha,b)` is defined in Eq. (9) in [17] + - a and b are source and target weights (sum to 1) + + The OT matrix can is reconstructed using [17]_ Proposition 2. + The optimization algorithm is using gradient decent (L-BFGS by default). + + + Parameters + ---------- + a : np.ndarray (ns,) + samples weights in the source domain + b : np.ndarray (nt,) or np.ndarray (nt,nbb) + samples in the target domain, compute sinkhorn with multiple targets + and fixed M if b is a matrix (return OT loss + dual variables in log) + M : np.ndarray (ns,nt) + loss matrix + reg : float + Regularization term >0 + reg_type : str + Regularization type, can be the following (default ='l2'): + - 'kl' : Kullback Leibler (~ Neg-entropy used in sinkhorn [2]_) + - 'l2' : Squared Euclidean regularization + method : str + Solver to use for scipy.optimize.minimize + numItermax : int, optional + Max number of iterations + stopThr : float, optional + Stop threshol on error (>0) + verbose : bool, optional + Print information along iterations + log : bool, optional + record log if True + + + Returns + ------- + gamma : (ns x nt) ndarray + Optimal transportation matrix for the given parameters + log : dict + log dictionary return only if log==True in parameters + + + References + ---------- + + .. [2] M. Cuturi, Sinkhorn Distances : Lightspeed Computation of Optimal Transport, Advances in Neural Information Processing Systems (NIPS) 26, 2013 + + .. [17] Blondel, M., Seguy, V., & Rolet, A. (2018). Smooth and Sparse Optimal Transport. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics (AISTATS). + + See Also + -------- + ot.lp.emd : Unregularized OT + ot.sinhorn : Entropic regularized OT + ot.optim.cg : General regularized OT + + """ + if reg_type.lower() in ['l2', 'squaredl2']: + regul = SquaredL2(gamma=reg) + elif reg_type.lower() in ['entropic', 'negentropy', 'kl']: + regul = NegEntropy(gamma=reg) + else: + raise NotImplementedError('Unknown regularization') + + # solve dual + alpha, res = solve_semi_dual(a, b, M, regul, max_iter=numItermax, + tol=stopThr, verbose=verbose) + + # reconstruct transport matrix + G = get_plan_from_semi_dual(alpha, b, M, regul) + + if log: + log = {'alpha': alpha, 'res': res} + return G, log + else: + return G diff --git a/ot/utils.py b/ot/utils.py index 7dac283..bb21b38 100644 --- a/ot/utils.py +++ b/ot/utils.py @@ -77,6 +77,34 @@ def clean_zeros(a, b, M): return a2, b2, M2 +def euclidean_distances(X, Y, squared=False): + """ + Considering the rows of X (and Y=X) as vectors, compute the + distance matrix between each pair of vectors. + Parameters + ---------- + X : {array-like}, shape (n_samples_1, n_features) + Y : {array-like}, shape (n_samples_2, n_features) + squared : boolean, optional + Return squared Euclidean distances. + Returns + ------- + distances : {array}, shape (n_samples_1, n_samples_2) + """ + XX = np.einsum('ij,ij->i', X, X)[:, np.newaxis] + YY = np.einsum('ij,ij->i', Y, Y)[np.newaxis, :] + distances = np.dot(X, Y.T) + distances *= -2 + distances += XX + distances += YY + np.maximum(distances, 0, out=distances) + if X is Y: + # Ensure that distances between vectors and themselves are set to 0.0. + # This may not be the case due to floating point rounding errors. + distances.flat[::distances.shape[0] + 1] = 0.0 + return distances if squared else np.sqrt(distances, out=distances) + + def dist(x1, x2=None, metric='sqeuclidean'): """Compute distance between samples in x1 and x2 using function scipy.spatial.distance.cdist @@ -104,7 +132,8 @@ def dist(x1, x2=None, metric='sqeuclidean'): """ if x2 is None: x2 = x1 - + if metric == "sqeuclidean": + return euclidean_distances(x1, x2, squared=True) return cdist(x1, x2, metric=metric) @@ -55,7 +55,7 @@ setup(name='POT', 'Operating System :: MacOS', 'Operating System :: POSIX', 'Programming Language :: Python', - 'Topic :: Utilities' + 'Topic :: Utilities', 'Programming Language :: Python :: 2', 'Programming Language :: Python :: 2.7', 'Programming Language :: Python :: 3', diff --git a/test/test_bregman.py b/test/test_bregman.py index c8e9179..14edaf5 100644 --- a/test/test_bregman.py +++ b/test/test_bregman.py @@ -71,11 +71,14 @@ def test_sinkhorn_variants(): Ges = ot.sinkhorn( u, u, M, 1, method='sinkhorn_epsilon_scaling', stopThr=1e-10) Gerr = ot.sinkhorn(u, u, M, 1, method='do_not_exists', stopThr=1e-10) + G_green = ot.sinkhorn(u, u, M, 1, method='greenkhorn', stopThr=1e-10) # check values np.testing.assert_allclose(G0, Gs, atol=1e-05) np.testing.assert_allclose(G0, Ges, atol=1e-05) np.testing.assert_allclose(G0, Gerr) + np.testing.assert_allclose(G0, G_green, atol=1e-5) + print(G0, G_green) def test_bary(): @@ -105,6 +108,30 @@ def test_bary(): ot.bregman.barycenter(A, M, reg, log=True, verbose=True) +def test_wasserstein_bary_2d(): + + size = 100 # size of a square image + a1 = np.random.randn(size, size) + a1 += a1.min() + a1 = a1 / np.sum(a1) + a2 = np.random.randn(size, size) + a2 += a2.min() + a2 = a2 / np.sum(a2) + # creating matrix A containing all distributions + A = np.zeros((2, size, size)) + A[0, :, :] = a1 + A[1, :, :] = a2 + + # wasserstein + reg = 1e-2 + bary_wass = ot.bregman.convolutional_barycenter2d(A, reg) + + np.testing.assert_allclose(1, np.sum(bary_wass)) + + # help in checking if log and verbose do not bug the function + ot.bregman.convolutional_barycenter2d(A, reg, log=True, verbose=True) + + def test_unmix(): n_bins = 50 # nb bins diff --git a/test/test_gpu.py b/test/test_gpu.py index 1e97c45..6b7fdd4 100644 --- a/test/test_gpu.py +++ b/test/test_gpu.py @@ -6,7 +6,6 @@ import numpy as np import ot -import time import pytest try: # test if cudamat installed @@ -17,63 +16,81 @@ except ImportError: @pytest.mark.skipif(nogpu, reason="No GPU available") -def test_gpu_sinkhorn(): +def test_gpu_dist(): rng = np.random.RandomState(0) - def describe_res(r): - print("min:{:.3E}, max::{:.3E}, mean::{:.3E}, std::{:.3E}".format( - np.min(r), np.max(r), np.mean(r), np.std(r))) - for n_samples in [50, 100, 500, 1000]: print(n_samples) a = rng.rand(n_samples // 4, 100) b = rng.rand(n_samples, 100) - time1 = time.time() - transport = ot.da.OTDA_sinkhorn() - transport.fit(a, b) - G1 = transport.G - time2 = time.time() - transport = ot.gpu.da.OTDA_sinkhorn() - transport.fit(a, b) - G2 = transport.G - time3 = time.time() - print("Normal sinkhorn, time: {:6.2f} sec ".format(time2 - time1)) - describe_res(G1) - print(" GPU sinkhorn, time: {:6.2f} sec ".format(time3 - time2)) - describe_res(G2) - - np.testing.assert_allclose(G1, G2, rtol=1e-5, atol=1e-5) + + M = ot.dist(a.copy(), b.copy()) + M2 = ot.gpu.dist(a.copy(), b.copy()) + + np.testing.assert_allclose(M, M2, rtol=1e-10) + + M2 = ot.gpu.dist(a.copy(), b.copy(), metric='euclidean', to_numpy=False) + + # check raise not implemented wrong metric + with pytest.raises(NotImplementedError): + M2 = ot.gpu.dist(a.copy(), b.copy(), metric='cityblock', to_numpy=False) @pytest.mark.skipif(nogpu, reason="No GPU available") -def test_gpu_sinkhorn_lpl1(): +def test_gpu_sinkhorn(): rng = np.random.RandomState(0) - def describe_res(r): - print("min:{:.3E}, max:{:.3E}, mean:{:.3E}, std:{:.3E}" - .format(np.min(r), np.max(r), np.mean(r), np.std(r))) + for n_samples in [50, 100, 500, 1000]: + a = rng.rand(n_samples // 4, 100) + b = rng.rand(n_samples, 100) + + wa = ot.unif(n_samples // 4) + wb = ot.unif(n_samples) + + wb2 = np.random.rand(n_samples, 20) + wb2 /= wb2.sum(0, keepdims=True) + + M = ot.dist(a.copy(), b.copy()) + M2 = ot.gpu.dist(a.copy(), b.copy(), to_numpy=False) + + reg = 1 + + G = ot.sinkhorn(wa, wb, M, reg) + G1 = ot.gpu.sinkhorn(wa, wb, M, reg) + + np.testing.assert_allclose(G1, G, rtol=1e-10) + + # run all on gpu + ot.gpu.sinkhorn(wa, wb, M2, reg, to_numpy=False, log=True) + + # run sinkhorn for multiple targets + ot.gpu.sinkhorn(wa, wb2, M2, reg, to_numpy=False, log=True) + + +@pytest.mark.skipif(nogpu, reason="No GPU available") +def test_gpu_sinkhorn_lpl1(): + + rng = np.random.RandomState(0) for n_samples in [50, 100, 500]: print(n_samples) a = rng.rand(n_samples // 4, 100) labels_a = np.random.randint(10, size=(n_samples // 4)) b = rng.rand(n_samples, 100) - time1 = time.time() - transport = ot.da.OTDA_lpl1() - transport.fit(a, labels_a, b) - G1 = transport.G - time2 = time.time() - transport = ot.gpu.da.OTDA_lpl1() - transport.fit(a, labels_a, b) - G2 = transport.G - time3 = time.time() - print("Normal sinkhorn lpl1, time: {:6.2f} sec ".format( - time2 - time1)) - describe_res(G1) - print(" GPU sinkhorn lpl1, time: {:6.2f} sec ".format( - time3 - time2)) - describe_res(G2) - - np.testing.assert_allclose(G1, G2, rtol=1e-3, atol=1e-3) + + wa = ot.unif(n_samples // 4) + wb = ot.unif(n_samples) + + M = ot.dist(a.copy(), b.copy()) + M2 = ot.gpu.dist(a.copy(), b.copy(), to_numpy=False) + + reg = 1 + + G = ot.da.sinkhorn_lpl1_mm(wa, labels_a, wb, M, reg) + G1 = ot.gpu.da.sinkhorn_lpl1_mm(wa, labels_a, wb, M, reg) + + np.testing.assert_allclose(G1, G, rtol=1e-10) + + ot.gpu.da.sinkhorn_lpl1_mm(wa, labels_a, wb, M2, reg, to_numpy=False, log=True) 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 399e549..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): @@ -135,6 +135,21 @@ def test_lp_barycenter(): np.testing.assert_allclose(bary.sum(), 1) +def test_free_support_barycenter(): + + measures_locations = [np.array([-1.]).reshape((1, 1)), np.array([1.]).reshape((1, 1))] + measures_weights = [np.array([1.]), np.array([1.])] + + X_init = np.array([-12.]).reshape((1, 1)) + + # obvious barycenter location between two diracs + bar_locations = np.array([0.]).reshape((1, 1)) + + X = ot.lp.free_support_barycenter(measures_locations, measures_weights, X_init) + + np.testing.assert_allclose(X, bar_locations, rtol=1e-5, atol=1e-7) + + @pytest.mark.skipif(not ot.lp.cvx.cvxopt, reason="No cvxopt available") def test_lp_barycenter_cvxopt(): @@ -192,11 +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_smooth.py b/test/test_smooth.py new file mode 100644 index 0000000..2afa4f8 --- /dev/null +++ b/test/test_smooth.py @@ -0,0 +1,79 @@ +"""Tests for ot.smooth model """ + +# Author: Remi Flamary <remi.flamary@unice.fr> +# +# License: MIT License + +import numpy as np +import ot +import pytest + + +def test_smooth_ot_dual(): + + # get data + n = 100 + rng = np.random.RandomState(0) + + x = rng.randn(n, 2) + u = ot.utils.unif(n) + + M = ot.dist(x, x) + + with pytest.raises(NotImplementedError): + Gl2, log = ot.smooth.smooth_ot_dual(u, u, M, 1, reg_type='none') + + Gl2, log = ot.smooth.smooth_ot_dual(u, u, M, 1, reg_type='l2', log=True, stopThr=1e-10) + + # check constratints + np.testing.assert_allclose( + u, Gl2.sum(1), atol=1e-05) # cf convergence sinkhorn + np.testing.assert_allclose( + u, Gl2.sum(0), atol=1e-05) # cf convergence sinkhorn + + # kl regyularisation + G = ot.smooth.smooth_ot_dual(u, u, M, 1, reg_type='kl', stopThr=1e-10) + + # check constratints + np.testing.assert_allclose( + u, G.sum(1), atol=1e-05) # cf convergence sinkhorn + np.testing.assert_allclose( + u, G.sum(0), atol=1e-05) # cf convergence sinkhorn + + G2 = ot.sinkhorn(u, u, M, 1, stopThr=1e-10) + np.testing.assert_allclose(G, G2, atol=1e-05) + + +def test_smooth_ot_semi_dual(): + + # get data + n = 100 + rng = np.random.RandomState(0) + + x = rng.randn(n, 2) + u = ot.utils.unif(n) + + M = ot.dist(x, x) + + with pytest.raises(NotImplementedError): + Gl2, log = ot.smooth.smooth_ot_semi_dual(u, u, M, 1, reg_type='none') + + Gl2, log = ot.smooth.smooth_ot_semi_dual(u, u, M, 1, reg_type='l2', log=True, stopThr=1e-10) + + # check constratints + np.testing.assert_allclose( + u, Gl2.sum(1), atol=1e-05) # cf convergence sinkhorn + np.testing.assert_allclose( + u, Gl2.sum(0), atol=1e-05) # cf convergence sinkhorn + + # kl regyularisation + G = ot.smooth.smooth_ot_semi_dual(u, u, M, 1, reg_type='kl', stopThr=1e-10) + + # check constratints + np.testing.assert_allclose( + u, G.sum(1), atol=1e-05) # cf convergence sinkhorn + np.testing.assert_allclose( + u, G.sum(0), atol=1e-05) # cf convergence sinkhorn + + G2 = ot.sinkhorn(u, u, M, 1, stopThr=1e-10) + np.testing.assert_allclose(G, G2, atol=1e-05) diff --git a/test/test_stochastic.py b/test/test_stochastic.py index 0128317..f0f3fc8 100644 --- a/test/test_stochastic.py +++ b/test/test_stochastic.py @@ -32,7 +32,7 @@ def test_stochastic_sag(): # test sag n = 15 reg = 1 - numItermax = 300000 + numItermax = 30000 rng = np.random.RandomState(0) x = rng.randn(n, 2) @@ -62,7 +62,7 @@ def test_stochastic_asgd(): # test asgd n = 15 reg = 1 - numItermax = 300000 + numItermax = 100000 rng = np.random.RandomState(0) x = rng.randn(n, 2) @@ -92,7 +92,7 @@ def test_sag_asgd_sinkhorn(): # test all algorithms n = 15 reg = 1 - nb_iter = 300000 + nb_iter = 100000 rng = np.random.RandomState(0) x = rng.randn(n, 2) @@ -167,7 +167,7 @@ def test_dual_sgd_sinkhorn(): # test all dual algorithms n = 10 reg = 1 - nb_iter = 150000 + nb_iter = 15000 batch_size = 10 rng = np.random.RandomState(0) 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 |
