diff options
| author | Rémi Flamary <remi.flamary@gmail.com> | 2020-04-21 17:48:37 +0200 |
|---|---|---|
| committer | GitHub <noreply@github.com> | 2020-04-21 17:48:37 +0200 |
| commit | a303cc6b483d3cd958c399621e22e40574bcbbc8 (patch) | |
| tree | dea049cb692020462da8f00d9e117f93b839bb55 | |
| parent | 0b2d808aaebb1cab60a272ea7901d5f77df43a9f (diff) | |
[MRG] Actually run sphinx-gallery (#146)
* generate gallery
* remove mock
* add sklearn to requirermnt?txt for example
* remove latex from fgw example
* add networks for graph example
* remove all
* add requirement.txt rtd
* rtd debug
* update readme
* eradthedoc with redirection
* add conf rtd
262 files changed, 80 insertions, 17787 deletions
@@ -5,16 +5,18 @@ [](https://travis-ci.org/PythonOT/POT) [](https://github.com/PythonOT/POT/actions) [](https://codecov.io/gh/PythonOT/POT) -[](http://pot.readthedocs.io/en/latest/?badge=latest) [](https://pepy.tech/project/pot) [](https://anaconda.org/conda-forge/pot) [](https://github.com/PythonOT/POT/blob/master/LICENSE) +This open source Python library provide several solvers for optimization +problems related to Optimal Transport for signal, image processing and machine +learning. -This open source Python library provide several solvers for optimization problems related to Optimal Transport for signal, image processing and machine learning. +Website and documentation: [https://PythonOT.github.io/](https://PythonOT.github.io/) -It provides the following solvers: +POT 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], stabilized version [9][10] and greedy Sinkhorn [22] with optional GPU implementation (requires cupy). @@ -139,7 +141,7 @@ ba=ot.barycenter(A,M,reg) # reg is regularization parameter ### Examples and Notebooks -The examples folder contain several examples and use case for the library. The full documentation is available on [Readthedocs](http://pot.readthedocs.io/). +The examples folder contain several examples and use case for the library. The full documentation is available on [https://PythonOT.github.io/](https://PythonOT.github.io/). Here is a list of the Python notebooks available [here](https://github.com/PythonOT/POT/blob/master/notebooks/) if you want a quick look: diff --git a/docs/requirements.txt b/docs/requirements.txt index 1fe37c2..256706b 100644 --- a/docs/requirements.txt +++ b/docs/requirements.txt @@ -3,3 +3,4 @@ sphinx_rtd_theme numpydoc memory_profiler pillow +networkx diff --git a/docs/requirements_rtd.txt b/docs/requirements_rtd.txt new file mode 100644 index 0000000..e3999d6 --- /dev/null +++ b/docs/requirements_rtd.txt @@ -0,0 +1,14 @@ +sphinx_gallery +numpydoc +memory_profiler +pillow +networkx +numpy +scipy>=1.0 +cython +matplotlib +autograd +pymanopt==0.2.4; python_version <'3' +pymanopt; python_version >= '3' +cvxopt +scikit-learn
\ No newline at end of file diff --git a/docs/rtd/conf.py b/docs/rtd/conf.py new file mode 100644 index 0000000..814db75 --- /dev/null +++ b/docs/rtd/conf.py @@ -0,0 +1,6 @@ +from recommonmark.parser import CommonMarkParser + +source_parsers = {'.md': CommonMarkParser} + +source_suffix = ['.md'] +master_doc = 'index'
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html - - <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of EMD and Sinkhorn transport plans and their visualiz..."> - -.. only:: html - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_OT_1D_thumb.png - - :ref:`sphx_glr_auto_examples_plot_OT_1D.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_OT_1D - -.. raw:: html - - <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of Unbalanced Optimal transport using a Kullback-Leibl..."> - -.. only:: html - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_UOT_1D_thumb.png - - :ref:`sphx_glr_auto_examples_plot_UOT_1D.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_UOT_1D - -.. raw:: html - - <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of Screenkhorn: Screening Sinkhorn Algorithm for Optim..."> - -.. only:: html - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_screenkhorn_1D_thumb.png - - :ref:`sphx_glr_auto_examples_plot_screenkhorn_1D.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_screenkhorn_1D - -.. raw:: html - - <div class="sphx-glr-thumbcontainer" tooltip="Illustrates the use of the generic solver for regularized OT with user-designed regularization ..."> - -.. only:: html - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_optim_OTreg_thumb.png - - :ref:`sphx_glr_auto_examples_plot_optim_OTreg.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_optim_OTreg - -.. 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="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="Shows how to compute multiple EMD and Sinkhorn with two differnt ground metrics and plot their ..."> - -.. only:: html - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_compute_emd_thumb.png - - :ref:`sphx_glr_auto_examples_plot_compute_emd.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_compute_emd - -.. 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 - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_gromov_thumb.png - - :ref:`sphx_glr_auto_examples_plot_gromov.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_gromov - -.. 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 - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_otda_linear_mapping_thumb.png - - :ref:`sphx_glr_auto_examples_plot_otda_linear_mapping.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_otda_linear_mapping - -.. raw:: html - - <div class="sphx-glr-thumbcontainer" tooltip="Illustration of 2D optimal transport between discributions that are weighted sum of diracs. The..."> - -.. only:: html - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_OT_2D_samples_thumb.png - - :ref:`sphx_glr_auto_examples_plot_OT_2D_samples.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_OT_2D_samples - -.. raw:: html - - <div class="sphx-glr-thumbcontainer" tooltip="This example illustrate the use of WDA as proposed in [11]."> - -.. only:: html - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_WDA_thumb.png - - :ref:`sphx_glr_auto_examples_plot_WDA.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_WDA - -.. raw:: html - - <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_stochastic_thumb.png - - :ref:`sphx_glr_auto_examples_plot_stochastic.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_stochastic - -.. raw:: html - - <div class="sphx-glr-thumbcontainer" tooltip="This example presents a way of transferring colors between two images with Optimal Transport as..."> - -.. only:: html - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_otda_color_images_thumb.png - - :ref:`sphx_glr_auto_examples_plot_otda_color_images.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_otda_color_images - -.. raw:: html - - <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of regularized Wassersyein Barycenter as proposed in [..."> - -.. only:: html - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_barycenter_1D_thumb.png - - :ref:`sphx_glr_auto_examples_plot_barycenter_1D.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_barycenter_1D - -.. raw:: html - - <div class="sphx-glr-thumbcontainer" tooltip="This example introduces a domain adaptation in a 2D setting and OTDA approach with Laplacian re..."> - -.. only:: html - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_otda_laplacian_thumb.png - - :ref:`sphx_glr_auto_examples_plot_otda_laplacian.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_otda_laplacian - -.. 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 illustrates the computation of regularized Wassersyein Barycenter as proposed in [..."> - -.. only:: html - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_UOT_barycenter_1D_thumb.png - - :ref:`sphx_glr_auto_examples_plot_UOT_barycenter_1D.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_UOT_barycenter_1D - -.. 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 - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_otda_mapping_thumb.png - - :ref:`sphx_glr_auto_examples_plot_otda_mapping.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_otda_mapping - -.. raw:: html - - <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of FGW for 1D measures[18]."> - -.. only:: html - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_fgw_thumb.png - - :ref:`sphx_glr_auto_examples_plot_fgw.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_fgw - -.. raw:: html - - <div class="sphx-glr-thumbcontainer" tooltip="This example introduces a semi supervised domain adaptation in a 2D setting. It explicits the p..."> - -.. only:: html - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_otda_semi_supervised_thumb.png - - :ref:`sphx_glr_auto_examples_plot_otda_semi_supervised.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_otda_semi_supervised - -.. raw:: html - - <div class="sphx-glr-thumbcontainer" tooltip="This example introduces a domain adaptation in a 2D setting and the 4 OTDA approaches currently..."> - -.. only:: html - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_otda_classes_thumb.png - - :ref:`sphx_glr_auto_examples_plot_otda_classes.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_otda_classes - -.. raw:: html - - <div class="sphx-glr-thumbcontainer" tooltip="This example is designed to show how to use the Partial (Gromov-)Wassertsein distance computati..."> - -.. only:: html - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_partial_wass_and_gromov_thumb.png - - :ref:`sphx_glr_auto_examples_plot_partial_wass_and_gromov.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_partial_wass_and_gromov - -.. raw:: html - - <div class="sphx-glr-thumbcontainer" tooltip="This example introduces a domain adaptation in a 2D setting. It explicits the problem of domain..."> - -.. only:: html - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_otda_d2_thumb.png - - :ref:`sphx_glr_auto_examples_plot_otda_d2.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_otda_d2 - -.. raw:: html - - <div class="sphx-glr-thumbcontainer" tooltip="2D OT on empirical distributio with different gound metric."> - -.. only:: html - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_OT_L1_vs_L2_thumb.png - - :ref:`sphx_glr_auto_examples_plot_OT_L1_vs_L2.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_OT_L1_vs_L2 - -.. raw:: html - - <div class="sphx-glr-thumbcontainer" tooltip="This example introduces a target shift problem with two 2D source and 1 target domain."> - -.. only:: html - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_otda_jcpot_thumb.png - - :ref:`sphx_glr_auto_examples_plot_otda_jcpot.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_otda_jcpot - -.. raw:: html - - <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of regularized Wasserstein Barycenter as proposed in [..."> - -.. only:: html - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_barycenter_lp_vs_entropic_thumb.png - - :ref:`sphx_glr_auto_examples_plot_barycenter_lp_vs_entropic.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_barycenter_lp_vs_entropic - -.. raw:: html - - <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation barycenter of labeled graphs using FGW"> - -.. only:: html - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_barycenter_fgw_thumb.png - - :ref:`sphx_glr_auto_examples_plot_barycenter_fgw.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_barycenter_fgw - -.. raw:: html - - <div class="sphx-glr-thumbcontainer" tooltip="This example is designed to show how to use the Gromov-Wasserstein distance computation in POT...."> - -.. only:: html - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_gromov_barycenter_thumb.png - - :ref:`sphx_glr_auto_examples_plot_gromov_barycenter.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_gromov_barycenter -.. raw:: html - - <div class="sphx-glr-clear"></div> - - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-gallery - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download all examples in Python source code: auto_examples_python.zip <//home/rflamary/PYTHON/POT/docs/source/auto_examples/auto_examples_python.zip>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download all examples in Jupyter notebooks: auto_examples_jupyter.zip <//home/rflamary/PYTHON/POT/docs/source/auto_examples/auto_examples_jupyter.zip>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ diff --git a/docs/source/auto_examples/plot_OT_1D.ipynb b/docs/source/auto_examples/plot_OT_1D.ipynb deleted file mode 100644 index f679a30..0000000 --- a/docs/source/auto_examples/plot_OT_1D.ipynb +++ /dev/null @@ -1,137 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n# 1D optimal transport\n\n\nThis example illustrates the computation of EMD and Sinkhorn transport 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": [ - "n = 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": [ - "pl.figure(1, figsize=(6.4, 3))\npl.plot(x, a, 'b', label='Source distribution')\npl.plot(x, b, 'r', label='Target distribution')\npl.legend()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pl.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": [ - "G0 = 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": [ - "lambd = 1e-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()" - ] - } - ], - "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": "3.6.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_OT_1D.py b/docs/source/auto_examples/plot_OT_1D.py deleted file mode 100644 index f33e2a4..0000000 --- a/docs/source/auto_examples/plot_OT_1D.py +++ /dev/null @@ -1,84 +0,0 @@ -# -*- coding: utf-8 -*- -""" -==================== -1D optimal transport -==================== - -This example illustrates the computation of EMD and Sinkhorn transport 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 = 1e-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() diff --git a/docs/source/auto_examples/plot_OT_1D.rst b/docs/source/auto_examples/plot_OT_1D.rst deleted file mode 100644 index ec21845..0000000 --- a/docs/source/auto_examples/plot_OT_1D.rst +++ /dev/null @@ -1,228 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_OT_1D.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_OT_1D.py: - - -==================== -1D optimal transport -==================== - -This example illustrates the computation of EMD and Sinkhorn transport plans -and their visualization. - - - -.. code-block:: default - - - # 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:: default - - - 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:: default - - - 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() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_001.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - - <matplotlib.legend.Legend object at 0x7f4c75f9fcc0> - - - - -.. code-block:: default - - - pl.figure(2, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, M, 'Cost matrix M') - - - - -.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_002.png - :class: sphx-glr-single-img - - - - - -Solve EMD ---------- - - -.. code-block:: default - - - 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_003.png - :class: sphx-glr-single-img - - - - - -Solve Sinkhorn --------------- - - -.. code-block:: default - - - lambd = 1e-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_004.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - It. |Err - ------------------- - 0|2.861463e-01| - 10|1.860154e-01| - 20|8.144529e-02| - 30|3.130143e-02| - 40|1.178815e-02| - 50|4.426078e-03| - 60|1.661047e-03| - 70|6.233110e-04| - 80|2.338932e-04| - 90|8.776627e-05| - 100|3.293340e-05| - 110|1.235791e-05| - 120|4.637176e-06| - 130|1.740051e-06| - 140|6.529356e-07| - 150|2.450071e-07| - 160|9.193632e-08| - 170|3.449812e-08| - 180|1.294505e-08| - 190|4.857493e-09| - It. |Err - ------------------- - 200|1.822723e-09| - 210|6.839572e-10| - /home/rflamary/PYTHON/POT/examples/plot_OT_1D.py:84: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 0.665 seconds) - - -.. _sphx_glr_download_auto_examples_plot_OT_1D.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_OT_1D.py <plot_OT_1D.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: plot_OT_1D.ipynb <plot_OT_1D.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ diff --git a/docs/source/auto_examples/plot_OT_1D_smooth.ipynb b/docs/source/auto_examples/plot_OT_1D_smooth.ipynb deleted file mode 100644 index 493e6bb..0000000 --- a/docs/source/auto_examples/plot_OT_1D_smooth.ipynb +++ /dev/null @@ -1,166 +0,0 @@ -{ - "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": [ - "n = 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": [ - "pl.figure(1, figsize=(6.4, 3))\npl.plot(x, a, 'b', label='Source distribution')\npl.plot(x, b, 'r', label='Target distribution')\npl.legend()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pl.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": [ - "G0 = 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": [ - "lambd = 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": [ - "lambd = 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()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "lambd = 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": "3.6.9" - } - }, - "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 deleted file mode 100644 index b690751..0000000 --- a/docs/source/auto_examples/plot_OT_1D_smooth.py +++ /dev/null @@ -1,110 +0,0 @@ -# -*- 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 deleted file mode 100644 index de42689..0000000 --- a/docs/source/auto_examples/plot_OT_1D_smooth.rst +++ /dev/null @@ -1,282 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_OT_1D_smooth.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _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:: default - - - # 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:: default - - - 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:: default - - - 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() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_001.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - - <matplotlib.legend.Legend object at 0x7f4c738a51d0> - - - - -.. code-block:: default - - - pl.figure(2, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, M, 'Cost matrix M') - - - - -.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_002.png - :class: sphx-glr-single-img - - - - - -Solve EMD ---------- - - -.. code-block:: default - - - 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_003.png - :class: sphx-glr-single-img - - - - - -Solve Sinkhorn --------------- - - -.. code-block:: default - - - 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_004.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - It. |Err - ------------------- - 0|2.821142e-01| - 10|7.695268e-02| - 20|1.112774e-02| - 30|1.571553e-03| - 40|2.218100e-04| - 50|3.130527e-05| - 60|4.418267e-06| - 70|6.235716e-07| - 80|8.800770e-08| - 90|1.242095e-08| - 100|1.753030e-09| - 110|2.474136e-10| - /home/rflamary/PYTHON/POT/examples/plot_OT_1D_smooth.py:84: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - -Solve Smooth OT --------------- - - -.. code-block:: default - - - 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() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_005.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_OT_1D_smooth.py:99: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. code-block:: default - - - 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() - - - -.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_006.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_OT_1D_smooth.py:110: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 0.732 seconds) - - -.. _sphx_glr_download_auto_examples_plot_OT_1D_smooth.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_OT_1D_smooth.py <plot_OT_1D_smooth.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :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.github.io>`_ diff --git a/docs/source/auto_examples/plot_OT_2D_samples.ipynb b/docs/source/auto_examples/plot_OT_2D_samples.ipynb deleted file mode 100644 index ff7abde..0000000 --- a/docs/source/auto_examples/plot_OT_2D_samples.ipynb +++ /dev/null @@ -1,144 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n# 2D Optimal transport between empirical distributions\n\n\nIllustration of 2D optimal transport between discributions that are weighted\nsum of diracs. The OT matrix is plotted with the samples.\n\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Author: Remi Flamary <remi.flamary@unice.fr>\n# Kilian Fatras <kilian.fatras@irisa.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\nimport ot.plot" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Generate data\n-------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "n = 50 # nb samples\n\nmu_s = np.array([0, 0])\ncov_s = np.array([[1, 0], [0, 1]])\n\nmu_t = np.array([4, 4])\ncov_t = np.array([[1, -.8], [-.8, 1]])\n\nxs = ot.datasets.make_2D_samples_gauss(n, mu_s, cov_s)\nxt = ot.datasets.make_2D_samples_gauss(n, mu_t, cov_t)\n\na, b = np.ones((n,)) / n, np.ones((n,)) / n # uniform distribution on samples\n\n# loss matrix\nM = ot.dist(xs, xt)\nM /= M.max()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Plot data\n---------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pl.figure(1)\npl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\npl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\npl.legend(loc=0)\npl.title('Source and target distributions')\n\npl.figure(2)\npl.imshow(M, interpolation='nearest')\npl.title('Cost matrix M')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Compute EMD\n-----------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "G0 = ot.emd(a, b, M)\n\npl.figure(3)\npl.imshow(G0, interpolation='nearest')\npl.title('OT matrix G0')\n\npl.figure(4)\not.plot.plot2D_samples_mat(xs, xt, G0, c=[.5, .5, 1])\npl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\npl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\npl.legend(loc=0)\npl.title('OT matrix with samples')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Compute Sinkhorn\n----------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# reg term\nlambd = 1e-3\n\nGs = ot.sinkhorn(a, b, M, lambd)\n\npl.figure(5)\npl.imshow(Gs, interpolation='nearest')\npl.title('OT matrix sinkhorn')\n\npl.figure(6)\not.plot.plot2D_samples_mat(xs, xt, Gs, color=[.5, .5, 1])\npl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\npl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\npl.legend(loc=0)\npl.title('OT matrix Sinkhorn with samples')\n\npl.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Emprirical Sinkhorn\n----------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# reg term\nlambd = 1e-3\n\nGes = ot.bregman.empirical_sinkhorn(xs, xt, lambd)\n\npl.figure(7)\npl.imshow(Ges, interpolation='nearest')\npl.title('OT matrix empirical sinkhorn')\n\npl.figure(8)\not.plot.plot2D_samples_mat(xs, xt, Ges, color=[.5, .5, 1])\npl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\npl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\npl.legend(loc=0)\npl.title('OT matrix Sinkhorn from samples')\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": "3.6.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_OT_2D_samples.py b/docs/source/auto_examples/plot_OT_2D_samples.py deleted file mode 100644 index 63126ba..0000000 --- a/docs/source/auto_examples/plot_OT_2D_samples.py +++ /dev/null @@ -1,128 +0,0 @@ -# -*- coding: utf-8 -*- -""" -==================================================== -2D Optimal transport between empirical distributions -==================================================== - -Illustration of 2D optimal transport between discributions that are weighted -sum of diracs. The OT matrix is plotted with the samples. - -""" - -# Author: Remi Flamary <remi.flamary@unice.fr> -# Kilian Fatras <kilian.fatras@irisa.fr> -# -# License: MIT License - -import numpy as np -import matplotlib.pylab as pl -import ot -import ot.plot - -############################################################################## -# Generate data -# ------------- - -#%% parameters and data generation - -n = 50 # nb samples - -mu_s = np.array([0, 0]) -cov_s = np.array([[1, 0], [0, 1]]) - -mu_t = np.array([4, 4]) -cov_t = np.array([[1, -.8], [-.8, 1]]) - -xs = ot.datasets.make_2D_samples_gauss(n, mu_s, cov_s) -xt = ot.datasets.make_2D_samples_gauss(n, mu_t, cov_t) - -a, b = np.ones((n,)) / n, np.ones((n,)) / n # uniform distribution on samples - -# loss matrix -M = ot.dist(xs, xt) -M /= M.max() - -############################################################################## -# Plot data -# --------- - -#%% plot samples - -pl.figure(1) -pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') -pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') -pl.legend(loc=0) -pl.title('Source and target distributions') - -pl.figure(2) -pl.imshow(M, interpolation='nearest') -pl.title('Cost matrix M') - -############################################################################## -# Compute EMD -# ----------- - -#%% EMD - -G0 = ot.emd(a, b, M) - -pl.figure(3) -pl.imshow(G0, interpolation='nearest') -pl.title('OT matrix G0') - -pl.figure(4) -ot.plot.plot2D_samples_mat(xs, xt, G0, c=[.5, .5, 1]) -pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') -pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') -pl.legend(loc=0) -pl.title('OT matrix with samples') - - -############################################################################## -# Compute Sinkhorn -# ---------------- - -#%% sinkhorn - -# reg term -lambd = 1e-3 - -Gs = ot.sinkhorn(a, b, M, lambd) - -pl.figure(5) -pl.imshow(Gs, interpolation='nearest') -pl.title('OT matrix sinkhorn') - -pl.figure(6) -ot.plot.plot2D_samples_mat(xs, xt, Gs, color=[.5, .5, 1]) -pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') -pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') -pl.legend(loc=0) -pl.title('OT matrix Sinkhorn with samples') - -pl.show() - - -############################################################################## -# Emprirical Sinkhorn -# ---------------- - -#%% sinkhorn - -# reg term -lambd = 1e-3 - -Ges = ot.bregman.empirical_sinkhorn(xs, xt, lambd) - -pl.figure(7) -pl.imshow(Ges, interpolation='nearest') -pl.title('OT matrix empirical sinkhorn') - -pl.figure(8) -ot.plot.plot2D_samples_mat(xs, xt, Ges, color=[.5, .5, 1]) -pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') -pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') -pl.legend(loc=0) -pl.title('OT matrix Sinkhorn from samples') - -pl.show() diff --git a/docs/source/auto_examples/plot_OT_2D_samples.rst b/docs/source/auto_examples/plot_OT_2D_samples.rst deleted file mode 100644 index 460bb95..0000000 --- a/docs/source/auto_examples/plot_OT_2D_samples.rst +++ /dev/null @@ -1,310 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_OT_2D_samples.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_OT_2D_samples.py: - - -==================================================== -2D Optimal transport between empirical distributions -==================================================== - -Illustration of 2D optimal transport between discributions that are weighted -sum of diracs. The OT matrix is plotted with the samples. - - - -.. code-block:: default - - - # Author: Remi Flamary <remi.flamary@unice.fr> - # Kilian Fatras <kilian.fatras@irisa.fr> - # - # License: MIT License - - import numpy as np - import matplotlib.pylab as pl - import ot - import ot.plot - - - - - - - - -Generate data -------------- - - -.. code-block:: default - - - n = 50 # nb samples - - mu_s = np.array([0, 0]) - cov_s = np.array([[1, 0], [0, 1]]) - - mu_t = np.array([4, 4]) - cov_t = np.array([[1, -.8], [-.8, 1]]) - - xs = ot.datasets.make_2D_samples_gauss(n, mu_s, cov_s) - xt = ot.datasets.make_2D_samples_gauss(n, mu_t, cov_t) - - a, b = np.ones((n,)) / n, np.ones((n,)) / n # uniform distribution on samples - - # loss matrix - M = ot.dist(xs, xt) - M /= M.max() - - - - - - - - -Plot data ---------- - - -.. code-block:: default - - - pl.figure(1) - pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') - pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') - pl.legend(loc=0) - pl.title('Source and target distributions') - - pl.figure(2) - pl.imshow(M, interpolation='nearest') - pl.title('Cost matrix M') - - - - -.. rst-class:: sphx-glr-horizontal - - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_001.png - :class: sphx-glr-multi-img - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_002.png - :class: sphx-glr-multi-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - - Text(0.5, 1.0, 'Cost matrix M') - - - -Compute EMD ------------ - - -.. code-block:: default - - - G0 = ot.emd(a, b, M) - - pl.figure(3) - pl.imshow(G0, interpolation='nearest') - pl.title('OT matrix G0') - - pl.figure(4) - ot.plot.plot2D_samples_mat(xs, xt, G0, c=[.5, .5, 1]) - pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') - pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') - pl.legend(loc=0) - pl.title('OT matrix with samples') - - - - - -.. rst-class:: sphx-glr-horizontal - - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_003.png - :class: sphx-glr-multi-img - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_004.png - :class: sphx-glr-multi-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - - Text(0.5, 1.0, 'OT matrix with samples') - - - -Compute Sinkhorn ----------------- - - -.. code-block:: default - - - # reg term - lambd = 1e-3 - - Gs = ot.sinkhorn(a, b, M, lambd) - - pl.figure(5) - pl.imshow(Gs, interpolation='nearest') - pl.title('OT matrix sinkhorn') - - pl.figure(6) - ot.plot.plot2D_samples_mat(xs, xt, Gs, color=[.5, .5, 1]) - pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') - pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') - pl.legend(loc=0) - pl.title('OT matrix Sinkhorn with samples') - - pl.show() - - - - - -.. rst-class:: sphx-glr-horizontal - - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_005.png - :class: sphx-glr-multi-img - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_006.png - :class: sphx-glr-multi-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_OT_2D_samples.py:103: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - -Emprirical Sinkhorn ----------------- - - -.. code-block:: default - - - # reg term - lambd = 1e-3 - - Ges = ot.bregman.empirical_sinkhorn(xs, xt, lambd) - - pl.figure(7) - pl.imshow(Ges, interpolation='nearest') - pl.title('OT matrix empirical sinkhorn') - - pl.figure(8) - ot.plot.plot2D_samples_mat(xs, xt, Ges, color=[.5, .5, 1]) - pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') - pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') - pl.legend(loc=0) - pl.title('OT matrix Sinkhorn from samples') - - pl.show() - - - -.. rst-class:: sphx-glr-horizontal - - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_007.png - :class: sphx-glr-multi-img - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_008.png - :class: sphx-glr-multi-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/ot/bregman.py:363: RuntimeWarning: divide by zero encountered in true_divide - v = np.divide(b, KtransposeU) - Warning: numerical errors at iteration 0 - /home/rflamary/PYTHON/POT/ot/plot.py:90: RuntimeWarning: invalid value encountered in double_scalars - if G[i, j] / mx > thr: - /home/rflamary/PYTHON/POT/examples/plot_OT_2D_samples.py:128: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 2.154 seconds) - - -.. _sphx_glr_download_auto_examples_plot_OT_2D_samples.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_OT_2D_samples.py <plot_OT_2D_samples.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: plot_OT_2D_samples.ipynb <plot_OT_2D_samples.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ diff --git a/docs/source/auto_examples/plot_OT_L1_vs_L2.ipynb b/docs/source/auto_examples/plot_OT_L1_vs_L2.ipynb deleted file mode 100644 index 12a09f0..0000000 --- a/docs/source/auto_examples/plot_OT_L1_vs_L2.ipynb +++ /dev/null @@ -1,126 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n# 2D Optimal transport for different metrics\n\n\n2D OT on empirical distributio with different gound metric.\n\nStole the figure idea from Fig. 1 and 2 in\nhttps://arxiv.org/pdf/1706.07650.pdf\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 matplotlib.pylab as pl\nimport ot\nimport ot.plot" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Dataset 1 : uniform sampling\n----------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "n = 20 # nb samples\nxs = np.zeros((n, 2))\nxs[:, 0] = np.arange(n) + 1\nxs[:, 1] = (np.arange(n) + 1) * -0.001 # to make it strictly convex...\n\nxt = np.zeros((n, 2))\nxt[:, 1] = np.arange(n) + 1\n\na, b = ot.unif(n), ot.unif(n) # uniform distribution on samples\n\n# loss matrix\nM1 = ot.dist(xs, xt, metric='euclidean')\nM1 /= M1.max()\n\n# loss matrix\nM2 = ot.dist(xs, xt, metric='sqeuclidean')\nM2 /= M2.max()\n\n# loss matrix\nMp = np.sqrt(ot.dist(xs, xt, metric='euclidean'))\nMp /= Mp.max()\n\n# Data\npl.figure(1, figsize=(7, 3))\npl.clf()\npl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\npl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\npl.axis('equal')\npl.title('Source and target distributions')\n\n\n# Cost matrices\npl.figure(2, figsize=(7, 3))\n\npl.subplot(1, 3, 1)\npl.imshow(M1, interpolation='nearest')\npl.title('Euclidean cost')\n\npl.subplot(1, 3, 2)\npl.imshow(M2, interpolation='nearest')\npl.title('Squared Euclidean cost')\n\npl.subplot(1, 3, 3)\npl.imshow(Mp, interpolation='nearest')\npl.title('Sqrt Euclidean cost')\npl.tight_layout()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Dataset 1 : Plot OT Matrices\n----------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "G1 = ot.emd(a, b, M1)\nG2 = ot.emd(a, b, M2)\nGp = ot.emd(a, b, Mp)\n\n# OT matrices\npl.figure(3, figsize=(7, 3))\n\npl.subplot(1, 3, 1)\not.plot.plot2D_samples_mat(xs, xt, G1, c=[.5, .5, 1])\npl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\npl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\npl.axis('equal')\n# pl.legend(loc=0)\npl.title('OT Euclidean')\n\npl.subplot(1, 3, 2)\not.plot.plot2D_samples_mat(xs, xt, G2, c=[.5, .5, 1])\npl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\npl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\npl.axis('equal')\n# pl.legend(loc=0)\npl.title('OT squared Euclidean')\n\npl.subplot(1, 3, 3)\not.plot.plot2D_samples_mat(xs, xt, Gp, c=[.5, .5, 1])\npl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\npl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\npl.axis('equal')\n# pl.legend(loc=0)\npl.title('OT sqrt Euclidean')\npl.tight_layout()\n\npl.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Dataset 2 : Partial circle\n--------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "n = 50 # nb samples\nxtot = np.zeros((n + 1, 2))\nxtot[:, 0] = np.cos(\n (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi)\nxtot[:, 1] = np.sin(\n (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi)\n\nxs = xtot[:n, :]\nxt = xtot[1:, :]\n\na, b = ot.unif(n), ot.unif(n) # uniform distribution on samples\n\n# loss matrix\nM1 = ot.dist(xs, xt, metric='euclidean')\nM1 /= M1.max()\n\n# loss matrix\nM2 = ot.dist(xs, xt, metric='sqeuclidean')\nM2 /= M2.max()\n\n# loss matrix\nMp = np.sqrt(ot.dist(xs, xt, metric='euclidean'))\nMp /= Mp.max()\n\n\n# Data\npl.figure(4, figsize=(7, 3))\npl.clf()\npl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\npl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\npl.axis('equal')\npl.title('Source and traget distributions')\n\n\n# Cost matrices\npl.figure(5, figsize=(7, 3))\n\npl.subplot(1, 3, 1)\npl.imshow(M1, interpolation='nearest')\npl.title('Euclidean cost')\n\npl.subplot(1, 3, 2)\npl.imshow(M2, interpolation='nearest')\npl.title('Squared Euclidean cost')\n\npl.subplot(1, 3, 3)\npl.imshow(Mp, interpolation='nearest')\npl.title('Sqrt Euclidean cost')\npl.tight_layout()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Dataset 2 : Plot OT Matrices\n-----------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "G1 = ot.emd(a, b, M1)\nG2 = ot.emd(a, b, M2)\nGp = ot.emd(a, b, Mp)\n\n# OT matrices\npl.figure(6, figsize=(7, 3))\n\npl.subplot(1, 3, 1)\not.plot.plot2D_samples_mat(xs, xt, G1, c=[.5, .5, 1])\npl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\npl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\npl.axis('equal')\n# pl.legend(loc=0)\npl.title('OT Euclidean')\n\npl.subplot(1, 3, 2)\not.plot.plot2D_samples_mat(xs, xt, G2, c=[.5, .5, 1])\npl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\npl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\npl.axis('equal')\n# pl.legend(loc=0)\npl.title('OT squared Euclidean')\n\npl.subplot(1, 3, 3)\not.plot.plot2D_samples_mat(xs, xt, Gp, c=[.5, .5, 1])\npl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\npl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\npl.axis('equal')\n# pl.legend(loc=0)\npl.title('OT sqrt Euclidean')\npl.tight_layout()\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": "3.6.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_OT_L1_vs_L2.py b/docs/source/auto_examples/plot_OT_L1_vs_L2.py deleted file mode 100644 index 37b429f..0000000 --- a/docs/source/auto_examples/plot_OT_L1_vs_L2.py +++ /dev/null @@ -1,208 +0,0 @@ -# -*- coding: utf-8 -*- -""" -========================================== -2D Optimal transport for different metrics -========================================== - -2D OT on empirical distributio with different gound metric. - -Stole the figure idea from Fig. 1 and 2 in -https://arxiv.org/pdf/1706.07650.pdf - - -""" - -# Author: Remi Flamary <remi.flamary@unice.fr> -# -# License: MIT License - -import numpy as np -import matplotlib.pylab as pl -import ot -import ot.plot - -############################################################################## -# Dataset 1 : uniform sampling -# ---------------------------- - -n = 20 # nb samples -xs = np.zeros((n, 2)) -xs[:, 0] = np.arange(n) + 1 -xs[:, 1] = (np.arange(n) + 1) * -0.001 # to make it strictly convex... - -xt = np.zeros((n, 2)) -xt[:, 1] = np.arange(n) + 1 - -a, b = ot.unif(n), ot.unif(n) # uniform distribution on samples - -# loss matrix -M1 = ot.dist(xs, xt, metric='euclidean') -M1 /= M1.max() - -# loss matrix -M2 = ot.dist(xs, xt, metric='sqeuclidean') -M2 /= M2.max() - -# loss matrix -Mp = np.sqrt(ot.dist(xs, xt, metric='euclidean')) -Mp /= Mp.max() - -# Data -pl.figure(1, figsize=(7, 3)) -pl.clf() -pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') -pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') -pl.axis('equal') -pl.title('Source and target distributions') - - -# Cost matrices -pl.figure(2, figsize=(7, 3)) - -pl.subplot(1, 3, 1) -pl.imshow(M1, interpolation='nearest') -pl.title('Euclidean cost') - -pl.subplot(1, 3, 2) -pl.imshow(M2, interpolation='nearest') -pl.title('Squared Euclidean cost') - -pl.subplot(1, 3, 3) -pl.imshow(Mp, interpolation='nearest') -pl.title('Sqrt Euclidean cost') -pl.tight_layout() - -############################################################################## -# Dataset 1 : Plot OT Matrices -# ---------------------------- - - -#%% EMD -G1 = ot.emd(a, b, M1) -G2 = ot.emd(a, b, M2) -Gp = ot.emd(a, b, Mp) - -# OT matrices -pl.figure(3, figsize=(7, 3)) - -pl.subplot(1, 3, 1) -ot.plot.plot2D_samples_mat(xs, xt, G1, c=[.5, .5, 1]) -pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') -pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') -pl.axis('equal') -# pl.legend(loc=0) -pl.title('OT Euclidean') - -pl.subplot(1, 3, 2) -ot.plot.plot2D_samples_mat(xs, xt, G2, c=[.5, .5, 1]) -pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') -pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') -pl.axis('equal') -# pl.legend(loc=0) -pl.title('OT squared Euclidean') - -pl.subplot(1, 3, 3) -ot.plot.plot2D_samples_mat(xs, xt, Gp, c=[.5, .5, 1]) -pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') -pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') -pl.axis('equal') -# pl.legend(loc=0) -pl.title('OT sqrt Euclidean') -pl.tight_layout() - -pl.show() - - -############################################################################## -# Dataset 2 : Partial circle -# -------------------------- - -n = 50 # nb samples -xtot = np.zeros((n + 1, 2)) -xtot[:, 0] = np.cos( - (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi) -xtot[:, 1] = np.sin( - (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi) - -xs = xtot[:n, :] -xt = xtot[1:, :] - -a, b = ot.unif(n), ot.unif(n) # uniform distribution on samples - -# loss matrix -M1 = ot.dist(xs, xt, metric='euclidean') -M1 /= M1.max() - -# loss matrix -M2 = ot.dist(xs, xt, metric='sqeuclidean') -M2 /= M2.max() - -# loss matrix -Mp = np.sqrt(ot.dist(xs, xt, metric='euclidean')) -Mp /= Mp.max() - - -# Data -pl.figure(4, figsize=(7, 3)) -pl.clf() -pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') -pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') -pl.axis('equal') -pl.title('Source and traget distributions') - - -# Cost matrices -pl.figure(5, figsize=(7, 3)) - -pl.subplot(1, 3, 1) -pl.imshow(M1, interpolation='nearest') -pl.title('Euclidean cost') - -pl.subplot(1, 3, 2) -pl.imshow(M2, interpolation='nearest') -pl.title('Squared Euclidean cost') - -pl.subplot(1, 3, 3) -pl.imshow(Mp, interpolation='nearest') -pl.title('Sqrt Euclidean cost') -pl.tight_layout() - -############################################################################## -# Dataset 2 : Plot OT Matrices -# ----------------------------- - - -#%% EMD -G1 = ot.emd(a, b, M1) -G2 = ot.emd(a, b, M2) -Gp = ot.emd(a, b, Mp) - -# OT matrices -pl.figure(6, figsize=(7, 3)) - -pl.subplot(1, 3, 1) -ot.plot.plot2D_samples_mat(xs, xt, G1, c=[.5, .5, 1]) -pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') -pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') -pl.axis('equal') -# pl.legend(loc=0) -pl.title('OT Euclidean') - -pl.subplot(1, 3, 2) -ot.plot.plot2D_samples_mat(xs, xt, G2, c=[.5, .5, 1]) -pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') -pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') -pl.axis('equal') -# pl.legend(loc=0) -pl.title('OT squared Euclidean') - -pl.subplot(1, 3, 3) -ot.plot.plot2D_samples_mat(xs, xt, Gp, c=[.5, .5, 1]) -pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') -pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') -pl.axis('equal') -# pl.legend(loc=0) -pl.title('OT sqrt Euclidean') -pl.tight_layout() - -pl.show() diff --git a/docs/source/auto_examples/plot_OT_L1_vs_L2.rst b/docs/source/auto_examples/plot_OT_L1_vs_L2.rst deleted file mode 100644 index 16b20f9..0000000 --- a/docs/source/auto_examples/plot_OT_L1_vs_L2.rst +++ /dev/null @@ -1,343 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_OT_L1_vs_L2.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_OT_L1_vs_L2.py: - - -========================================== -2D Optimal transport for different metrics -========================================== - -2D OT on empirical distributio with different gound metric. - -Stole the figure idea from Fig. 1 and 2 in -https://arxiv.org/pdf/1706.07650.pdf - - - - -.. code-block:: default - - - # Author: Remi Flamary <remi.flamary@unice.fr> - # - # License: MIT License - - import numpy as np - import matplotlib.pylab as pl - import ot - import ot.plot - - - - - - - - -Dataset 1 : uniform sampling ----------------------------- - - -.. code-block:: default - - - n = 20 # nb samples - xs = np.zeros((n, 2)) - xs[:, 0] = np.arange(n) + 1 - xs[:, 1] = (np.arange(n) + 1) * -0.001 # to make it strictly convex... - - xt = np.zeros((n, 2)) - xt[:, 1] = np.arange(n) + 1 - - a, b = ot.unif(n), ot.unif(n) # uniform distribution on samples - - # loss matrix - M1 = ot.dist(xs, xt, metric='euclidean') - M1 /= M1.max() - - # loss matrix - M2 = ot.dist(xs, xt, metric='sqeuclidean') - M2 /= M2.max() - - # loss matrix - Mp = np.sqrt(ot.dist(xs, xt, metric='euclidean')) - Mp /= Mp.max() - - # Data - pl.figure(1, figsize=(7, 3)) - pl.clf() - pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') - pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') - pl.axis('equal') - pl.title('Source and target distributions') - - - # Cost matrices - pl.figure(2, figsize=(7, 3)) - - pl.subplot(1, 3, 1) - pl.imshow(M1, interpolation='nearest') - pl.title('Euclidean cost') - - pl.subplot(1, 3, 2) - pl.imshow(M2, interpolation='nearest') - pl.title('Squared Euclidean cost') - - pl.subplot(1, 3, 3) - pl.imshow(Mp, interpolation='nearest') - pl.title('Sqrt Euclidean cost') - pl.tight_layout() - - - - -.. rst-class:: sphx-glr-horizontal - - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_001.png - :class: sphx-glr-multi-img - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_002.png - :class: sphx-glr-multi-img - - - - - -Dataset 1 : Plot OT Matrices ----------------------------- - - -.. code-block:: default - - G1 = ot.emd(a, b, M1) - G2 = ot.emd(a, b, M2) - Gp = ot.emd(a, b, Mp) - - # OT matrices - pl.figure(3, figsize=(7, 3)) - - pl.subplot(1, 3, 1) - ot.plot.plot2D_samples_mat(xs, xt, G1, c=[.5, .5, 1]) - pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') - pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') - pl.axis('equal') - # pl.legend(loc=0) - pl.title('OT Euclidean') - - pl.subplot(1, 3, 2) - ot.plot.plot2D_samples_mat(xs, xt, G2, c=[.5, .5, 1]) - pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') - pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') - pl.axis('equal') - # pl.legend(loc=0) - pl.title('OT squared Euclidean') - - pl.subplot(1, 3, 3) - ot.plot.plot2D_samples_mat(xs, xt, Gp, c=[.5, .5, 1]) - pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') - pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') - pl.axis('equal') - # pl.legend(loc=0) - pl.title('OT sqrt Euclidean') - pl.tight_layout() - - pl.show() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_003.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_OT_L1_vs_L2.py:113: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - -Dataset 2 : Partial circle --------------------------- - - -.. code-block:: default - - - n = 50 # nb samples - xtot = np.zeros((n + 1, 2)) - xtot[:, 0] = np.cos( - (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi) - xtot[:, 1] = np.sin( - (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi) - - xs = xtot[:n, :] - xt = xtot[1:, :] - - a, b = ot.unif(n), ot.unif(n) # uniform distribution on samples - - # loss matrix - M1 = ot.dist(xs, xt, metric='euclidean') - M1 /= M1.max() - - # loss matrix - M2 = ot.dist(xs, xt, metric='sqeuclidean') - M2 /= M2.max() - - # loss matrix - Mp = np.sqrt(ot.dist(xs, xt, metric='euclidean')) - Mp /= Mp.max() - - - # Data - pl.figure(4, figsize=(7, 3)) - pl.clf() - pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') - pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') - pl.axis('equal') - pl.title('Source and traget distributions') - - - # Cost matrices - pl.figure(5, figsize=(7, 3)) - - pl.subplot(1, 3, 1) - pl.imshow(M1, interpolation='nearest') - pl.title('Euclidean cost') - - pl.subplot(1, 3, 2) - pl.imshow(M2, interpolation='nearest') - pl.title('Squared Euclidean cost') - - pl.subplot(1, 3, 3) - pl.imshow(Mp, interpolation='nearest') - pl.title('Sqrt Euclidean cost') - pl.tight_layout() - - - - -.. rst-class:: sphx-glr-horizontal - - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_004.png - :class: sphx-glr-multi-img - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_005.png - :class: sphx-glr-multi-img - - - - - -Dataset 2 : Plot OT Matrices ------------------------------ - - -.. code-block:: default - - G1 = ot.emd(a, b, M1) - G2 = ot.emd(a, b, M2) - Gp = ot.emd(a, b, Mp) - - # OT matrices - pl.figure(6, figsize=(7, 3)) - - pl.subplot(1, 3, 1) - ot.plot.plot2D_samples_mat(xs, xt, G1, c=[.5, .5, 1]) - pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') - pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') - pl.axis('equal') - # pl.legend(loc=0) - pl.title('OT Euclidean') - - pl.subplot(1, 3, 2) - ot.plot.plot2D_samples_mat(xs, xt, G2, c=[.5, .5, 1]) - pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') - pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') - pl.axis('equal') - # pl.legend(loc=0) - pl.title('OT squared Euclidean') - - pl.subplot(1, 3, 3) - ot.plot.plot2D_samples_mat(xs, xt, Gp, c=[.5, .5, 1]) - pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') - pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') - pl.axis('equal') - # pl.legend(loc=0) - pl.title('OT sqrt Euclidean') - pl.tight_layout() - - pl.show() - - - -.. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_006.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_OT_L1_vs_L2.py:208: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 1.002 seconds) - - -.. _sphx_glr_download_auto_examples_plot_OT_L1_vs_L2.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_OT_L1_vs_L2.py <plot_OT_L1_vs_L2.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: plot_OT_L1_vs_L2.ipynb <plot_OT_L1_vs_L2.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ diff --git a/docs/source/auto_examples/plot_UOT_1D.ipynb b/docs/source/auto_examples/plot_UOT_1D.ipynb deleted file mode 100644 index 640e398..0000000 --- a/docs/source/auto_examples/plot_UOT_1D.ipynb +++ /dev/null @@ -1,108 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n# 1D Unbalanced optimal transport\n\n\nThis example illustrates the computation of Unbalanced Optimal transport\nusing a Kullback-Leibler relaxation.\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Author: Hicham Janati <hicham.janati@inria.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": [ - "n = 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# make distributions unbalanced\nb *= 5.\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": [ - "pl.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 Unbalanced Sinkhorn\n--------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Sinkhorn\n\nepsilon = 0.1 # entropy parameter\nalpha = 1. # Unbalanced KL relaxation parameter\nGs = ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, alpha, verbose=True)\n\npl.figure(4, figsize=(5, 5))\not.plot.plot1D_mat(a, b, Gs, 'UOT matrix Sinkhorn')\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": "3.6.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_UOT_1D.py b/docs/source/auto_examples/plot_UOT_1D.py deleted file mode 100644 index 2ea8b05..0000000 --- a/docs/source/auto_examples/plot_UOT_1D.py +++ /dev/null @@ -1,76 +0,0 @@ -# -*- coding: utf-8 -*- -""" -=============================== -1D Unbalanced optimal transport -=============================== - -This example illustrates the computation of Unbalanced Optimal transport -using a Kullback-Leibler relaxation. -""" - -# Author: Hicham Janati <hicham.janati@inria.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) - -# make distributions unbalanced -b *= 5. - -# 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 Unbalanced Sinkhorn -# -------------- - - -# Sinkhorn - -epsilon = 0.1 # entropy parameter -alpha = 1. # Unbalanced KL relaxation parameter -Gs = ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, alpha, verbose=True) - -pl.figure(4, figsize=(5, 5)) -ot.plot.plot1D_mat(a, b, Gs, 'UOT matrix Sinkhorn') - -pl.show() diff --git a/docs/source/auto_examples/plot_UOT_1D.rst b/docs/source/auto_examples/plot_UOT_1D.rst deleted file mode 100644 index f43b0c1..0000000 --- a/docs/source/auto_examples/plot_UOT_1D.rst +++ /dev/null @@ -1,177 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_UOT_1D.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_UOT_1D.py: - - -=============================== -1D Unbalanced optimal transport -=============================== - -This example illustrates the computation of Unbalanced Optimal transport -using a Kullback-Leibler relaxation. - - -.. code-block:: default - - - # Author: Hicham Janati <hicham.janati@inria.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:: default - - - 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) - - # make distributions unbalanced - b *= 5. - - # loss matrix - M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1))) - M /= M.max() - - - - - - - - - -Plot distributions and loss matrix ----------------------------------- - - -.. code-block:: default - - - 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_UOT_1D_001.png - :class: sphx-glr-multi-img - - * - - .. image:: /auto_examples/images/sphx_glr_plot_UOT_1D_002.png - :class: sphx-glr-multi-img - - - - - -Solve Unbalanced Sinkhorn --------------- - - -.. code-block:: default - - - - # Sinkhorn - - epsilon = 0.1 # entropy parameter - alpha = 1. # Unbalanced KL relaxation parameter - Gs = ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, alpha, verbose=True) - - pl.figure(4, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, Gs, 'UOT matrix Sinkhorn') - - pl.show() - - - -.. image:: /auto_examples/images/sphx_glr_plot_UOT_1D_003.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_UOT_1D.py:76: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 0.274 seconds) - - -.. _sphx_glr_download_auto_examples_plot_UOT_1D.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_UOT_1D.py <plot_UOT_1D.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: plot_UOT_1D.ipynb <plot_UOT_1D.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ diff --git a/docs/source/auto_examples/plot_UOT_barycenter_1D.ipynb b/docs/source/auto_examples/plot_UOT_barycenter_1D.ipynb deleted file mode 100644 index 549a78b..0000000 --- a/docs/source/auto_examples/plot_UOT_barycenter_1D.ipynb +++ /dev/null @@ -1,126 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n# 1D Wasserstein barycenter demo for Unbalanced distributions\n\n\nThis example illustrates the computation of regularized Wassersyein Barycenter\nas proposed in [10] for Unbalanced inputs.\n\n\n[10] Chizat, L., Peyr\u00e9, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816.\n\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Author: Hicham Janati <hicham.janati@inria.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# make unbalanced dists\na2 *= 3.\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": [ - "# non weighted barycenter computation\n\nweight = 0.5 # 0<=weight<=1\nweights = np.array([1 - weight, weight])\n\n# l2bary\nbary_l2 = A.dot(weights)\n\n# wasserstein\nreg = 1e-3\nalpha = 1.\n\nbary_wass = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, weights=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_weight = 11\nweight_list = np.linspace(0, 1, n_weight)\n\n\nB_l2 = np.zeros((n, n_weight))\n\nB_wass = np.copy(B_l2)\n\nfor i in range(0, n_weight):\n weight = weight_list[i]\n weights = np.array([1 - weight, weight])\n B_l2[:, i] = A.dot(weights)\n B_wass[:, i] = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, weights=weights)\n\n\n# plot interpolation\n\npl.figure(3)\n\ncmap = pl.cm.get_cmap('viridis')\nverts = []\nzs = weight_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 weight_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(r'$\\alpha$')\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 = weight_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 weight_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(r'$\\alpha$')\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()" - ] - } - ], - "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": "3.6.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_UOT_barycenter_1D.py b/docs/source/auto_examples/plot_UOT_barycenter_1D.py deleted file mode 100644 index acb5892..0000000 --- a/docs/source/auto_examples/plot_UOT_barycenter_1D.py +++ /dev/null @@ -1,164 +0,0 @@ -# -*- coding: utf-8 -*- -""" -=========================================================== -1D Wasserstein barycenter demo for Unbalanced distributions -=========================================================== - -This example illustrates the computation of regularized Wassersyein Barycenter -as proposed in [10] for Unbalanced inputs. - - -[10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816. - -""" - -# Author: Hicham Janati <hicham.janati@inria.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 - -# bin positions -x = np.arange(n, dtype=np.float64) - -# 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) - -# make unbalanced dists -a2 *= 3. - -# 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 data -# --------- - -# 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 -# ---------------------- - -# non weighted barycenter computation - -weight = 0.5 # 0<=weight<=1 -weights = np.array([1 - weight, weight]) - -# l2bary -bary_l2 = A.dot(weights) - -# wasserstein -reg = 1e-3 -alpha = 1. - -bary_wass = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, weights=weights) - -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='Wasserstein') -pl.legend() -pl.title('Barycenters') -pl.tight_layout() - -############################################################################## -# Barycentric interpolation -# ------------------------- - -# barycenter interpolation - -n_weight = 11 -weight_list = np.linspace(0, 1, n_weight) - - -B_l2 = np.zeros((n, n_weight)) - -B_wass = np.copy(B_l2) - -for i in range(0, n_weight): - weight = weight_list[i] - weights = np.array([1 - weight, weight]) - B_l2[:, i] = A.dot(weights) - B_wass[:, i] = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, weights=weights) - - -# plot interpolation - -pl.figure(3) - -cmap = pl.cm.get_cmap('viridis') -verts = [] -zs = weight_list -for i, z in enumerate(zs): - ys = B_l2[:, i] - verts.append(list(zip(x, ys))) - -ax = pl.gcf().gca(projection='3d') - -poly = PolyCollection(verts, facecolors=[cmap(a) for a in weight_list]) -poly.set_alpha(0.7) -ax.add_collection3d(poly, zs=zs, zdir='y') -ax.set_xlabel('x') -ax.set_xlim3d(0, n) -ax.set_ylabel(r'$\alpha$') -ax.set_ylim3d(0, 1) -ax.set_zlabel('') -ax.set_zlim3d(0, B_l2.max() * 1.01) -pl.title('Barycenter interpolation with l2') -pl.tight_layout() - -pl.figure(4) -cmap = pl.cm.get_cmap('viridis') -verts = [] -zs = weight_list -for i, z in enumerate(zs): - ys = B_wass[:, i] - verts.append(list(zip(x, ys))) - -ax = pl.gcf().gca(projection='3d') - -poly = PolyCollection(verts, facecolors=[cmap(a) for a in weight_list]) -poly.set_alpha(0.7) -ax.add_collection3d(poly, zs=zs, zdir='y') -ax.set_xlabel('x') -ax.set_xlim3d(0, n) -ax.set_ylabel(r'$\alpha$') -ax.set_ylim3d(0, 1) -ax.set_zlabel('') -ax.set_zlim3d(0, B_l2.max() * 1.01) -pl.title('Barycenter interpolation with Wasserstein') -pl.tight_layout() - -pl.show() diff --git a/docs/source/auto_examples/plot_UOT_barycenter_1D.rst b/docs/source/auto_examples/plot_UOT_barycenter_1D.rst deleted file mode 100644 index 2688d2e..0000000 --- a/docs/source/auto_examples/plot_UOT_barycenter_1D.rst +++ /dev/null @@ -1,299 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_UOT_barycenter_1D.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_UOT_barycenter_1D.py: - - -=========================================================== -1D Wasserstein barycenter demo for Unbalanced distributions -=========================================================== - -This example illustrates the computation of regularized Wassersyein Barycenter -as proposed in [10] for Unbalanced inputs. - - -[10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816. - - - -.. code-block:: default - - - # Author: Hicham Janati <hicham.janati@inria.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 -------------- - - -.. code-block:: default - - - # parameters - - n = 100 # nb bins - - # bin positions - x = np.arange(n, dtype=np.float64) - - # 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) - - # make unbalanced dists - a2 *= 3. - - # 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 data ---------- - - -.. code-block:: default - - - # 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() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_001.png - :class: sphx-glr-single-img - - - - - -Barycenter computation ----------------------- - - -.. code-block:: default - - - # non weighted barycenter computation - - weight = 0.5 # 0<=weight<=1 - weights = np.array([1 - weight, weight]) - - # l2bary - bary_l2 = A.dot(weights) - - # wasserstein - reg = 1e-3 - alpha = 1. - - bary_wass = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, weights=weights) - - 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='Wasserstein') - pl.legend() - pl.title('Barycenters') - pl.tight_layout() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_002.png - :class: sphx-glr-single-img - - - - - -Barycentric interpolation -------------------------- - - -.. code-block:: default - - - # barycenter interpolation - - n_weight = 11 - weight_list = np.linspace(0, 1, n_weight) - - - B_l2 = np.zeros((n, n_weight)) - - B_wass = np.copy(B_l2) - - for i in range(0, n_weight): - weight = weight_list[i] - weights = np.array([1 - weight, weight]) - B_l2[:, i] = A.dot(weights) - B_wass[:, i] = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, weights=weights) - - - # plot interpolation - - pl.figure(3) - - cmap = pl.cm.get_cmap('viridis') - verts = [] - zs = weight_list - for i, z in enumerate(zs): - ys = B_l2[:, i] - verts.append(list(zip(x, ys))) - - ax = pl.gcf().gca(projection='3d') - - poly = PolyCollection(verts, facecolors=[cmap(a) for a in weight_list]) - poly.set_alpha(0.7) - ax.add_collection3d(poly, zs=zs, zdir='y') - ax.set_xlabel('x') - ax.set_xlim3d(0, n) - ax.set_ylabel(r'$\alpha$') - ax.set_ylim3d(0, 1) - ax.set_zlabel('') - ax.set_zlim3d(0, B_l2.max() * 1.01) - pl.title('Barycenter interpolation with l2') - pl.tight_layout() - - pl.figure(4) - cmap = pl.cm.get_cmap('viridis') - verts = [] - zs = weight_list - for i, z in enumerate(zs): - ys = B_wass[:, i] - verts.append(list(zip(x, ys))) - - ax = pl.gcf().gca(projection='3d') - - poly = PolyCollection(verts, facecolors=[cmap(a) for a in weight_list]) - poly.set_alpha(0.7) - ax.add_collection3d(poly, zs=zs, zdir='y') - ax.set_xlabel('x') - ax.set_xlim3d(0, n) - ax.set_ylabel(r'$\alpha$') - ax.set_ylim3d(0, 1) - ax.set_zlabel('') - ax.set_zlim3d(0, B_l2.max() * 1.01) - pl.title('Barycenter interpolation with Wasserstein') - pl.tight_layout() - - pl.show() - - - -.. rst-class:: sphx-glr-horizontal - - - * - - .. image:: /auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_003.png - :class: sphx-glr-multi-img - - * - - .. image:: /auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_004.png - :class: sphx-glr-multi-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/ot/unbalanced.py:895: RuntimeWarning: overflow encountered in true_divide - u = (A / Kv) ** fi - /home/rflamary/PYTHON/POT/ot/unbalanced.py:900: RuntimeWarning: invalid value encountered in true_divide - v = (Q / Ktu) ** fi - /home/rflamary/PYTHON/POT/ot/unbalanced.py:907: UserWarning: Numerical errors at iteration 595 - warnings.warn('Numerical errors at iteration %s' % i) - /home/rflamary/PYTHON/POT/ot/unbalanced.py:900: RuntimeWarning: overflow encountered in true_divide - v = (Q / Ktu) ** fi - /home/rflamary/PYTHON/POT/ot/unbalanced.py:907: UserWarning: Numerical errors at iteration 974 - warnings.warn('Numerical errors at iteration %s' % i) - /home/rflamary/PYTHON/POT/ot/unbalanced.py:907: UserWarning: Numerical errors at iteration 615 - warnings.warn('Numerical errors at iteration %s' % i) - /home/rflamary/PYTHON/POT/ot/unbalanced.py:907: UserWarning: Numerical errors at iteration 455 - warnings.warn('Numerical errors at iteration %s' % i) - /home/rflamary/PYTHON/POT/ot/unbalanced.py:907: UserWarning: Numerical errors at iteration 361 - warnings.warn('Numerical errors at iteration %s' % i) - /home/rflamary/PYTHON/POT/examples/plot_UOT_barycenter_1D.py:164: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 1.567 seconds) - - -.. _sphx_glr_download_auto_examples_plot_UOT_barycenter_1D.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_UOT_barycenter_1D.py <plot_UOT_barycenter_1D.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: plot_UOT_barycenter_1D.ipynb <plot_UOT_barycenter_1D.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ diff --git a/docs/source/auto_examples/plot_WDA.ipynb b/docs/source/auto_examples/plot_WDA.ipynb deleted file mode 100644 index 1661c53..0000000 --- a/docs/source/auto_examples/plot_WDA.ipynb +++ /dev/null @@ -1,144 +0,0 @@ -{ - "nbformat_minor": 0, - "nbformat": 4, - "cells": [ - { - "execution_count": null, - "cell_type": "code", - "source": [ - "%matplotlib inline" - ], - "outputs": [], - "metadata": { - "collapsed": false - } - }, - { - "source": [ - "\n# Wasserstein Discriminant Analysis\n\n\nThis example illustrate the use of WDA as proposed in [11].\n\n\n[11] Flamary, R., Cuturi, M., Courty, N., & Rakotomamonjy, A. (2016).\nWasserstein Discriminant Analysis.\n\n\n" - ], - "cell_type": "markdown", - "metadata": {} - }, - { - "execution_count": null, - "cell_type": "code", - "source": [ - "# Author: Remi Flamary <remi.flamary@unice.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\n\nfrom ot.dr import wda, fda" - ], - "outputs": [], - "metadata": { - "collapsed": false - } - }, - { - "source": [ - "Generate data\n-------------\n\n" - ], - "cell_type": "markdown", - "metadata": {} - }, - { - "execution_count": null, - "cell_type": "code", - "source": [ - "#%% parameters\n\nn = 1000 # nb samples in source and target datasets\nnz = 0.2\n\n# generate circle dataset\nt = np.random.rand(n) * 2 * np.pi\nys = np.floor((np.arange(n) * 1.0 / n * 3)) + 1\nxs = np.concatenate(\n (np.cos(t).reshape((-1, 1)), np.sin(t).reshape((-1, 1))), 1)\nxs = xs * ys.reshape(-1, 1) + nz * np.random.randn(n, 2)\n\nt = np.random.rand(n) * 2 * np.pi\nyt = np.floor((np.arange(n) * 1.0 / n * 3)) + 1\nxt = np.concatenate(\n (np.cos(t).reshape((-1, 1)), np.sin(t).reshape((-1, 1))), 1)\nxt = xt * yt.reshape(-1, 1) + nz * np.random.randn(n, 2)\n\nnbnoise = 8\n\nxs = np.hstack((xs, np.random.randn(n, nbnoise)))\nxt = np.hstack((xt, np.random.randn(n, nbnoise)))" - ], - "outputs": [], - "metadata": { - "collapsed": false - } - }, - { - "source": [ - "Plot data\n---------\n\n" - ], - "cell_type": "markdown", - "metadata": {} - }, - { - "execution_count": null, - "cell_type": "code", - "source": [ - "#%% plot samples\npl.figure(1, figsize=(6.4, 3.5))\n\npl.subplot(1, 2, 1)\npl.scatter(xt[:, 0], xt[:, 1], c=ys, marker='+', label='Source samples')\npl.legend(loc=0)\npl.title('Discriminant dimensions')\n\npl.subplot(1, 2, 2)\npl.scatter(xt[:, 2], xt[:, 3], c=ys, marker='+', label='Source samples')\npl.legend(loc=0)\npl.title('Other dimensions')\npl.tight_layout()" - ], - "outputs": [], - "metadata": { - "collapsed": false - } - }, - { - "source": [ - "Compute Fisher Discriminant Analysis\n------------------------------------\n\n" - ], - "cell_type": "markdown", - "metadata": {} - }, - { - "execution_count": null, - "cell_type": "code", - "source": [ - "#%% Compute FDA\np = 2\n\nPfda, projfda = fda(xs, ys, p)" - ], - "outputs": [], - "metadata": { - "collapsed": false - } - }, - { - "source": [ - "Compute Wasserstein Discriminant Analysis\n-----------------------------------------\n\n" - ], - "cell_type": "markdown", - "metadata": {} - }, - { - "execution_count": null, - "cell_type": "code", - "source": [ - "#%% Compute WDA\np = 2\nreg = 1e0\nk = 10\nmaxiter = 100\n\nPwda, projwda = wda(xs, ys, p, reg, k, maxiter=maxiter)" - ], - "outputs": [], - "metadata": { - "collapsed": false - } - }, - { - "source": [ - "Plot 2D projections\n-------------------\n\n" - ], - "cell_type": "markdown", - "metadata": {} - }, - { - "execution_count": null, - "cell_type": "code", - "source": [ - "#%% plot samples\n\nxsp = projfda(xs)\nxtp = projfda(xt)\n\nxspw = projwda(xs)\nxtpw = projwda(xt)\n\npl.figure(2)\n\npl.subplot(2, 2, 1)\npl.scatter(xsp[:, 0], xsp[:, 1], c=ys, marker='+', label='Projected samples')\npl.legend(loc=0)\npl.title('Projected training samples FDA')\n\npl.subplot(2, 2, 2)\npl.scatter(xtp[:, 0], xtp[:, 1], c=ys, marker='+', label='Projected samples')\npl.legend(loc=0)\npl.title('Projected test samples FDA')\n\npl.subplot(2, 2, 3)\npl.scatter(xspw[:, 0], xspw[:, 1], c=ys, marker='+', label='Projected samples')\npl.legend(loc=0)\npl.title('Projected training samples WDA')\n\npl.subplot(2, 2, 4)\npl.scatter(xtpw[:, 0], xtpw[:, 1], c=ys, marker='+', label='Projected samples')\npl.legend(loc=0)\npl.title('Projected test samples WDA')\npl.tight_layout()\n\npl.show()" - ], - "outputs": [], - "metadata": { - "collapsed": false - } - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 2", - "name": "python2", - "language": "python" - }, - "language_info": { - "mimetype": "text/x-python", - "nbconvert_exporter": "python", - "name": "python", - "file_extension": ".py", - "version": "2.7.12", - "pygments_lexer": "ipython2", - "codemirror_mode": { - "version": 2, - "name": "ipython" - } - } - } -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_WDA.py b/docs/source/auto_examples/plot_WDA.py deleted file mode 100644 index 93cc237..0000000 --- a/docs/source/auto_examples/plot_WDA.py +++ /dev/null @@ -1,127 +0,0 @@ -# -*- coding: utf-8 -*- -""" -================================= -Wasserstein Discriminant Analysis -================================= - -This example illustrate the use of WDA as proposed in [11]. - - -[11] Flamary, R., Cuturi, M., Courty, N., & Rakotomamonjy, A. (2016). -Wasserstein Discriminant Analysis. - -""" - -# Author: Remi Flamary <remi.flamary@unice.fr> -# -# License: MIT License - -import numpy as np -import matplotlib.pylab as pl - -from ot.dr import wda, fda - - -############################################################################## -# Generate data -# ------------- - -#%% parameters - -n = 1000 # nb samples in source and target datasets -nz = 0.2 - -# generate circle dataset -t = np.random.rand(n) * 2 * np.pi -ys = np.floor((np.arange(n) * 1.0 / n * 3)) + 1 -xs = np.concatenate( - (np.cos(t).reshape((-1, 1)), np.sin(t).reshape((-1, 1))), 1) -xs = xs * ys.reshape(-1, 1) + nz * np.random.randn(n, 2) - -t = np.random.rand(n) * 2 * np.pi -yt = np.floor((np.arange(n) * 1.0 / n * 3)) + 1 -xt = np.concatenate( - (np.cos(t).reshape((-1, 1)), np.sin(t).reshape((-1, 1))), 1) -xt = xt * yt.reshape(-1, 1) + nz * np.random.randn(n, 2) - -nbnoise = 8 - -xs = np.hstack((xs, np.random.randn(n, nbnoise))) -xt = np.hstack((xt, np.random.randn(n, nbnoise))) - -############################################################################## -# Plot data -# --------- - -#%% plot samples -pl.figure(1, figsize=(6.4, 3.5)) - -pl.subplot(1, 2, 1) -pl.scatter(xt[:, 0], xt[:, 1], c=ys, marker='+', label='Source samples') -pl.legend(loc=0) -pl.title('Discriminant dimensions') - -pl.subplot(1, 2, 2) -pl.scatter(xt[:, 2], xt[:, 3], c=ys, marker='+', label='Source samples') -pl.legend(loc=0) -pl.title('Other dimensions') -pl.tight_layout() - -############################################################################## -# Compute Fisher Discriminant Analysis -# ------------------------------------ - -#%% Compute FDA -p = 2 - -Pfda, projfda = fda(xs, ys, p) - -############################################################################## -# Compute Wasserstein Discriminant Analysis -# ----------------------------------------- - -#%% Compute WDA -p = 2 -reg = 1e0 -k = 10 -maxiter = 100 - -Pwda, projwda = wda(xs, ys, p, reg, k, maxiter=maxiter) - - -############################################################################## -# Plot 2D projections -# ------------------- - -#%% plot samples - -xsp = projfda(xs) -xtp = projfda(xt) - -xspw = projwda(xs) -xtpw = projwda(xt) - -pl.figure(2) - -pl.subplot(2, 2, 1) -pl.scatter(xsp[:, 0], xsp[:, 1], c=ys, marker='+', label='Projected samples') -pl.legend(loc=0) -pl.title('Projected training samples FDA') - -pl.subplot(2, 2, 2) -pl.scatter(xtp[:, 0], xtp[:, 1], c=ys, marker='+', label='Projected samples') -pl.legend(loc=0) -pl.title('Projected test samples FDA') - -pl.subplot(2, 2, 3) -pl.scatter(xspw[:, 0], xspw[:, 1], c=ys, marker='+', label='Projected samples') -pl.legend(loc=0) -pl.title('Projected training samples WDA') - -pl.subplot(2, 2, 4) -pl.scatter(xtpw[:, 0], xtpw[:, 1], c=ys, marker='+', label='Projected samples') -pl.legend(loc=0) -pl.title('Projected test samples WDA') -pl.tight_layout() - -pl.show() diff --git a/docs/source/auto_examples/plot_WDA.rst b/docs/source/auto_examples/plot_WDA.rst deleted file mode 100644 index 2d83123..0000000 --- a/docs/source/auto_examples/plot_WDA.rst +++ /dev/null @@ -1,244 +0,0 @@ - - -.. _sphx_glr_auto_examples_plot_WDA.py: - - -================================= -Wasserstein Discriminant Analysis -================================= - -This example illustrate the use of WDA as proposed in [11]. - - -[11] Flamary, R., Cuturi, M., Courty, N., & Rakotomamonjy, A. (2016). -Wasserstein Discriminant Analysis. - - - - -.. code-block:: python - - - # Author: Remi Flamary <remi.flamary@unice.fr> - # - # License: MIT License - - import numpy as np - import matplotlib.pylab as pl - - from ot.dr import wda, fda - - - - - - - - -Generate data -------------- - - - -.. code-block:: python - - - #%% parameters - - n = 1000 # nb samples in source and target datasets - nz = 0.2 - - # generate circle dataset - t = np.random.rand(n) * 2 * np.pi - ys = np.floor((np.arange(n) * 1.0 / n * 3)) + 1 - xs = np.concatenate( - (np.cos(t).reshape((-1, 1)), np.sin(t).reshape((-1, 1))), 1) - xs = xs * ys.reshape(-1, 1) + nz * np.random.randn(n, 2) - - t = np.random.rand(n) * 2 * np.pi - yt = np.floor((np.arange(n) * 1.0 / n * 3)) + 1 - xt = np.concatenate( - (np.cos(t).reshape((-1, 1)), np.sin(t).reshape((-1, 1))), 1) - xt = xt * yt.reshape(-1, 1) + nz * np.random.randn(n, 2) - - nbnoise = 8 - - xs = np.hstack((xs, np.random.randn(n, nbnoise))) - xt = np.hstack((xt, np.random.randn(n, nbnoise))) - - - - - - - -Plot data ---------- - - - -.. code-block:: python - - - #%% plot samples - pl.figure(1, figsize=(6.4, 3.5)) - - pl.subplot(1, 2, 1) - pl.scatter(xt[:, 0], xt[:, 1], c=ys, marker='+', label='Source samples') - pl.legend(loc=0) - pl.title('Discriminant dimensions') - - pl.subplot(1, 2, 2) - pl.scatter(xt[:, 2], xt[:, 3], c=ys, marker='+', label='Source samples') - pl.legend(loc=0) - pl.title('Other dimensions') - pl.tight_layout() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_WDA_001.png - :align: center - - - - -Compute Fisher Discriminant Analysis ------------------------------------- - - - -.. code-block:: python - - - #%% Compute FDA - p = 2 - - Pfda, projfda = fda(xs, ys, p) - - - - - - - -Compute Wasserstein Discriminant Analysis ------------------------------------------ - - - -.. code-block:: python - - - #%% Compute WDA - p = 2 - reg = 1e0 - k = 10 - maxiter = 100 - - Pwda, projwda = wda(xs, ys, p, reg, k, maxiter=maxiter) - - - - - - -.. rst-class:: sphx-glr-script-out - - Out:: - - Compiling cost function... - Computing gradient of cost function... - iter cost val grad. norm - 1 +9.0167295050534191e-01 2.28422652e-01 - 2 +4.8324990550878105e-01 4.89362707e-01 - 3 +3.4613154515357075e-01 2.84117562e-01 - 4 +2.5277108387195002e-01 1.24888750e-01 - 5 +2.4113858393736629e-01 8.07491482e-02 - 6 +2.3642108593032782e-01 1.67612140e-02 - 7 +2.3625721372202199e-01 7.68640008e-03 - 8 +2.3625461994913738e-01 7.42200784e-03 - 9 +2.3624493441436939e-01 6.43534105e-03 - 10 +2.3621901383686217e-01 2.17960585e-03 - 11 +2.3621854258326572e-01 2.03306749e-03 - 12 +2.3621696458678049e-01 1.37118721e-03 - 13 +2.3621569489873540e-01 2.76368907e-04 - 14 +2.3621565599232983e-01 1.41898134e-04 - 15 +2.3621564465487518e-01 5.96602069e-05 - 16 +2.3621564232556647e-01 1.08709521e-05 - 17 +2.3621564230277003e-01 9.17855656e-06 - 18 +2.3621564224857586e-01 1.73728345e-06 - 19 +2.3621564224748123e-01 1.17770019e-06 - 20 +2.3621564224658587e-01 2.16179383e-07 - Terminated - min grad norm reached after 20 iterations, 9.20 seconds. - - -Plot 2D projections -------------------- - - - -.. code-block:: python - - - #%% plot samples - - xsp = projfda(xs) - xtp = projfda(xt) - - xspw = projwda(xs) - xtpw = projwda(xt) - - pl.figure(2) - - pl.subplot(2, 2, 1) - pl.scatter(xsp[:, 0], xsp[:, 1], c=ys, marker='+', label='Projected samples') - pl.legend(loc=0) - pl.title('Projected training samples FDA') - - pl.subplot(2, 2, 2) - pl.scatter(xtp[:, 0], xtp[:, 1], c=ys, marker='+', label='Projected samples') - pl.legend(loc=0) - pl.title('Projected test samples FDA') - - pl.subplot(2, 2, 3) - pl.scatter(xspw[:, 0], xspw[:, 1], c=ys, marker='+', label='Projected samples') - pl.legend(loc=0) - pl.title('Projected training samples WDA') - - pl.subplot(2, 2, 4) - pl.scatter(xtpw[:, 0], xtpw[:, 1], c=ys, marker='+', label='Projected samples') - pl.legend(loc=0) - pl.title('Projected test samples WDA') - pl.tight_layout() - - pl.show() - - - -.. image:: /auto_examples/images/sphx_glr_plot_WDA_003.png - :align: center - - - - -**Total running time of the script:** ( 0 minutes 16.182 seconds) - - - -.. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_WDA.py <plot_WDA.py>` - - - - .. container:: sphx-glr-download - - :download:`Download Jupyter notebook: plot_WDA.ipynb <plot_WDA.ipynb>` - -.. rst-class:: sphx-glr-signature - - `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_barycenter_1D.ipynb b/docs/source/auto_examples/plot_barycenter_1D.ipynb deleted file mode 100644 index 387c41a..0000000 --- a/docs/source/auto_examples/plot_barycenter_1D.ipynb +++ /dev/null @@ -1,137 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n# 1D Wasserstein barycenter demo\n\n\nThis example illustrates the computation of regularized Wassersyein Barycenter\nas proposed in [3].\n\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" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Generate data\n-------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "n = 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": [ - "pl.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": [ - "alpha = 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": [ - "n_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)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pl.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()" - ] - } - ], - "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": "3.6.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_barycenter_1D.py b/docs/source/auto_examples/plot_barycenter_1D.py deleted file mode 100644 index 6864301..0000000 --- a/docs/source/auto_examples/plot_barycenter_1D.py +++ /dev/null @@ -1,160 +0,0 @@ -# -*- coding: utf-8 -*- -""" -============================== -1D Wasserstein barycenter demo -============================== - -This example illustrates the computation of regularized Wassersyein Barycenter -as proposed in [3]. - - -[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 - -############################################################################## -# Generate data -# ------------- - -#%% parameters - -n = 100 # nb bins - -# bin positions -x = np.arange(n, dtype=np.float64) - -# 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 data -# --------- - -#%% 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 -# ---------------------- - -#%% barycenter computation - -alpha = 0.2 # 0<=alpha<=1 -weights = np.array([1 - alpha, alpha]) - -# l2bary -bary_l2 = A.dot(weights) - -# wasserstein -reg = 1e-3 -bary_wass = ot.bregman.barycenter(A, M, reg, weights) - -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='Wasserstein') -pl.legend() -pl.title('Barycenters') -pl.tight_layout() - -############################################################################## -# Barycentric interpolation -# ------------------------- - -#%% barycenter interpolation - -n_alpha = 11 -alpha_list = np.linspace(0, 1, n_alpha) - - -B_l2 = np.zeros((n, n_alpha)) - -B_wass = np.copy(B_l2) - -for i in range(0, n_alpha): - alpha = alpha_list[i] - weights = np.array([1 - alpha, alpha]) - B_l2[:, i] = A.dot(weights) - B_wass[:, i] = ot.bregman.barycenter(A, M, reg, weights) - -#%% plot interpolation - -pl.figure(3) - -cmap = pl.cm.get_cmap('viridis') -verts = [] -zs = alpha_list -for i, z in enumerate(zs): - ys = B_l2[:, i] - verts.append(list(zip(x, ys))) - -ax = pl.gcf().gca(projection='3d') - -poly = PolyCollection(verts, facecolors=[cmap(a) for a in alpha_list]) -poly.set_alpha(0.7) -ax.add_collection3d(poly, zs=zs, zdir='y') -ax.set_xlabel('x') -ax.set_xlim3d(0, n) -ax.set_ylabel('$\\alpha$') -ax.set_ylim3d(0, 1) -ax.set_zlabel('') -ax.set_zlim3d(0, B_l2.max() * 1.01) -pl.title('Barycenter interpolation with l2') -pl.tight_layout() - -pl.figure(4) -cmap = pl.cm.get_cmap('viridis') -verts = [] -zs = alpha_list -for i, z in enumerate(zs): - ys = B_wass[:, i] - verts.append(list(zip(x, ys))) - -ax = pl.gcf().gca(projection='3d') - -poly = PolyCollection(verts, facecolors=[cmap(a) for a in alpha_list]) -poly.set_alpha(0.7) -ax.add_collection3d(poly, zs=zs, zdir='y') -ax.set_xlabel('x') -ax.set_xlim3d(0, n) -ax.set_ylabel('$\\alpha$') -ax.set_ylim3d(0, 1) -ax.set_zlabel('') -ax.set_zlim3d(0, B_l2.max() * 1.01) -pl.title('Barycenter interpolation with Wasserstein') -pl.tight_layout() - -pl.show() diff --git a/docs/source/auto_examples/plot_barycenter_1D.rst b/docs/source/auto_examples/plot_barycenter_1D.rst deleted file mode 100644 index a65ac3d..0000000 --- a/docs/source/auto_examples/plot_barycenter_1D.rst +++ /dev/null @@ -1,280 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_barycenter_1D.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_barycenter_1D.py: - - -============================== -1D Wasserstein barycenter demo -============================== - -This example illustrates the computation of regularized Wassersyein Barycenter -as proposed in [3]. - - -[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:: default - - - # 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 -------------- - - -.. code-block:: default - - - n = 100 # nb bins - - # bin positions - x = np.arange(n, dtype=np.float64) - - # 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 data ---------- - - -.. code-block:: default - - - pl.figure(1, figsize=(6.4, 3)) - for i in range(n_distributions): - pl.plot(x, A[:, i]) - pl.title('Distributions') - pl.tight_layout() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_001.png - :class: sphx-glr-single-img - - - - - -Barycenter computation ----------------------- - - -.. code-block:: default - - - alpha = 0.2 # 0<=alpha<=1 - weights = np.array([1 - alpha, alpha]) - - # l2bary - bary_l2 = A.dot(weights) - - # wasserstein - reg = 1e-3 - bary_wass = ot.bregman.barycenter(A, M, reg, weights) - - 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='Wasserstein') - pl.legend() - pl.title('Barycenters') - pl.tight_layout() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_002.png - :class: sphx-glr-single-img - - - - - -Barycentric interpolation -------------------------- - - -.. code-block:: default - - - n_alpha = 11 - alpha_list = np.linspace(0, 1, n_alpha) - - - B_l2 = np.zeros((n, n_alpha)) - - B_wass = np.copy(B_l2) - - for i in range(0, n_alpha): - alpha = alpha_list[i] - weights = np.array([1 - alpha, alpha]) - B_l2[:, i] = A.dot(weights) - B_wass[:, i] = ot.bregman.barycenter(A, M, reg, weights) - - - - - - - - - -.. code-block:: default - - - pl.figure(3) - - cmap = pl.cm.get_cmap('viridis') - verts = [] - zs = alpha_list - for i, z in enumerate(zs): - ys = B_l2[:, i] - verts.append(list(zip(x, ys))) - - ax = pl.gcf().gca(projection='3d') - - poly = PolyCollection(verts, facecolors=[cmap(a) for a in alpha_list]) - poly.set_alpha(0.7) - ax.add_collection3d(poly, zs=zs, zdir='y') - ax.set_xlabel('x') - ax.set_xlim3d(0, n) - ax.set_ylabel('$\\alpha$') - ax.set_ylim3d(0, 1) - ax.set_zlabel('') - ax.set_zlim3d(0, B_l2.max() * 1.01) - pl.title('Barycenter interpolation with l2') - pl.tight_layout() - - pl.figure(4) - cmap = pl.cm.get_cmap('viridis') - verts = [] - zs = alpha_list - for i, z in enumerate(zs): - ys = B_wass[:, i] - verts.append(list(zip(x, ys))) - - ax = pl.gcf().gca(projection='3d') - - poly = PolyCollection(verts, facecolors=[cmap(a) for a in alpha_list]) - poly.set_alpha(0.7) - ax.add_collection3d(poly, zs=zs, zdir='y') - ax.set_xlabel('x') - ax.set_xlim3d(0, n) - ax.set_ylabel('$\\alpha$') - ax.set_ylim3d(0, 1) - ax.set_zlabel('') - ax.set_zlim3d(0, B_l2.max() * 1.01) - pl.title('Barycenter interpolation with Wasserstein') - pl.tight_layout() - - pl.show() - - - -.. rst-class:: sphx-glr-horizontal - - - * - - .. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_003.png - :class: sphx-glr-multi-img - - * - - .. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_004.png - :class: sphx-glr-multi-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_barycenter_1D.py:160: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 0.769 seconds) - - -.. _sphx_glr_download_auto_examples_plot_barycenter_1D.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_barycenter_1D.py <plot_barycenter_1D.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: plot_barycenter_1D.ipynb <plot_barycenter_1D.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ diff --git a/docs/source/auto_examples/plot_barycenter_fgw.ipynb b/docs/source/auto_examples/plot_barycenter_fgw.ipynb deleted file mode 100644 index 4e4704c..0000000 --- a/docs/source/auto_examples/plot_barycenter_fgw.ipynb +++ /dev/null @@ -1,173 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n=================================\nPlot graphs' barycenter using FGW\n=================================\n\nThis example illustrates the computation barycenter of labeled graphs using FGW\n\nRequires networkx >=2\n\n.. [18] Vayer Titouan, Chapel Laetitia, Flamary R{'e}mi, Tavenard Romain\n and Courty Nicolas\n \"Optimal Transport for structured data with application on graphs\"\n International Conference on Machine Learning (ICML). 2019.\n\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Author: Titouan Vayer <titouan.vayer@irisa.fr>\n#\n# License: MIT License" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "import numpy as np\nimport matplotlib.pyplot as plt\nimport networkx as nx\nimport math\nfrom scipy.sparse.csgraph import shortest_path\nimport matplotlib.colors as mcol\nfrom matplotlib import cm\nfrom ot.gromov import fgw_barycenters" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "def find_thresh(C, inf=0.5, sup=3, step=10):\n \"\"\" Trick to find the adequate thresholds from where value of the C matrix are considered close enough to say that nodes are connected\n Tthe threshold is found by a linesearch between values \"inf\" and \"sup\" with \"step\" thresholds tested.\n The optimal threshold is the one which minimizes the reconstruction error between the shortest_path matrix coming from the thresholded adjency matrix\n and the original matrix.\n Parameters\n ----------\n C : ndarray, shape (n_nodes,n_nodes)\n The structure matrix to threshold\n inf : float\n The beginning of the linesearch\n sup : float\n The end of the linesearch\n step : integer\n Number of thresholds tested\n \"\"\"\n dist = []\n search = np.linspace(inf, sup, step)\n for thresh in search:\n Cprime = sp_to_adjency(C, 0, thresh)\n SC = shortest_path(Cprime, method='D')\n SC[SC == float('inf')] = 100\n dist.append(np.linalg.norm(SC - C))\n return search[np.argmin(dist)], dist\n\n\ndef sp_to_adjency(C, threshinf=0.2, threshsup=1.8):\n \"\"\" Thresholds the structure matrix in order to compute an adjency matrix.\n All values between threshinf and threshsup are considered representing connected nodes and set to 1. Else are set to 0\n Parameters\n ----------\n C : ndarray, shape (n_nodes,n_nodes)\n The structure matrix to threshold\n threshinf : float\n The minimum value of distance from which the new value is set to 1\n threshsup : float\n The maximum value of distance from which the new value is set to 1\n Returns\n -------\n C : ndarray, shape (n_nodes,n_nodes)\n The threshold matrix. Each element is in {0,1}\n \"\"\"\n H = np.zeros_like(C)\n np.fill_diagonal(H, np.diagonal(C))\n C = C - H\n C = np.minimum(np.maximum(C, threshinf), threshsup)\n C[C == threshsup] = 0\n C[C != 0] = 1\n\n return C\n\n\ndef build_noisy_circular_graph(N=20, mu=0, sigma=0.3, with_noise=False, structure_noise=False, p=None):\n \"\"\" Create a noisy circular graph\n \"\"\"\n g = nx.Graph()\n g.add_nodes_from(list(range(N)))\n for i in range(N):\n noise = float(np.random.normal(mu, sigma, 1))\n if with_noise:\n g.add_node(i, attr_name=math.sin((2 * i * math.pi / N)) + noise)\n else:\n g.add_node(i, attr_name=math.sin(2 * i * math.pi / N))\n g.add_edge(i, i + 1)\n if structure_noise:\n randomint = np.random.randint(0, p)\n if randomint == 0:\n if i <= N - 3:\n g.add_edge(i, i + 2)\n if i == N - 2:\n g.add_edge(i, 0)\n if i == N - 1:\n g.add_edge(i, 1)\n g.add_edge(N, 0)\n noise = float(np.random.normal(mu, sigma, 1))\n if with_noise:\n g.add_node(N, attr_name=math.sin((2 * N * math.pi / N)) + noise)\n else:\n g.add_node(N, attr_name=math.sin(2 * N * math.pi / N))\n return g\n\n\ndef graph_colors(nx_graph, vmin=0, vmax=7):\n cnorm = mcol.Normalize(vmin=vmin, vmax=vmax)\n cpick = cm.ScalarMappable(norm=cnorm, cmap='viridis')\n cpick.set_array([])\n val_map = {}\n for k, v in nx.get_node_attributes(nx_graph, 'attr_name').items():\n val_map[k] = cpick.to_rgba(v)\n colors = []\n for node in nx_graph.nodes():\n colors.append(val_map[node])\n return colors" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Generate data\n-------------\n\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We build a dataset of noisy circular graphs.\nNoise is added on the structures by random connections and on the features by gaussian noise.\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "np.random.seed(30)\nX0 = []\nfor k in range(9):\n X0.append(build_noisy_circular_graph(np.random.randint(15, 25), with_noise=True, structure_noise=True, p=3))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Plot data\n---------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "plt.figure(figsize=(8, 10))\nfor i in range(len(X0)):\n plt.subplot(3, 3, i + 1)\n g = X0[i]\n pos = nx.kamada_kawai_layout(g)\n nx.draw(g, pos=pos, node_color=graph_colors(g, vmin=-1, vmax=1), with_labels=False, node_size=100)\nplt.suptitle('Dataset of noisy graphs. Color indicates the label', fontsize=20)\nplt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Barycenter computation\n----------------------\n\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Features distances are the euclidean distances\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "Cs = [shortest_path(nx.adjacency_matrix(x)) for x in X0]\nps = [np.ones(len(x.nodes())) / len(x.nodes()) for x in X0]\nYs = [np.array([v for (k, v) in nx.get_node_attributes(x, 'attr_name').items()]).reshape(-1, 1) for x in X0]\nlambdas = np.array([np.ones(len(Ys)) / len(Ys)]).ravel()\nsizebary = 15 # we choose a barycenter with 15 nodes\n\nA, C, log = fgw_barycenters(sizebary, Ys, Cs, ps, lambdas, alpha=0.95, log=True)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Plot Barycenter\n-------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "bary = nx.from_numpy_matrix(sp_to_adjency(C, threshinf=0, threshsup=find_thresh(C, sup=100, step=100)[0]))\nfor i, v in enumerate(A.ravel()):\n bary.add_node(i, attr_name=v)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pos = nx.kamada_kawai_layout(bary)\nnx.draw(bary, pos=pos, node_color=graph_colors(bary, vmin=-1, vmax=1), with_labels=False)\nplt.suptitle('Barycenter', fontsize=20)\nplt.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": "3.6.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_barycenter_fgw.py b/docs/source/auto_examples/plot_barycenter_fgw.py deleted file mode 100644 index 77b0370..0000000 --- a/docs/source/auto_examples/plot_barycenter_fgw.py +++ /dev/null @@ -1,184 +0,0 @@ -# -*- coding: utf-8 -*- -""" -================================= -Plot graphs' barycenter using FGW -================================= - -This example illustrates the computation barycenter of labeled graphs using FGW - -Requires networkx >=2 - -.. [18] Vayer Titouan, Chapel Laetitia, Flamary R{\'e}mi, Tavenard Romain - and Courty Nicolas - "Optimal Transport for structured data with application on graphs" - International Conference on Machine Learning (ICML). 2019. - -""" - -# Author: Titouan Vayer <titouan.vayer@irisa.fr> -# -# License: MIT License - -#%% load libraries -import numpy as np -import matplotlib.pyplot as plt -import networkx as nx -import math -from scipy.sparse.csgraph import shortest_path -import matplotlib.colors as mcol -from matplotlib import cm -from ot.gromov import fgw_barycenters -#%% Graph functions - - -def find_thresh(C, inf=0.5, sup=3, step=10): - """ Trick to find the adequate thresholds from where value of the C matrix are considered close enough to say that nodes are connected - Tthe threshold is found by a linesearch between values "inf" and "sup" with "step" thresholds tested. - The optimal threshold is the one which minimizes the reconstruction error between the shortest_path matrix coming from the thresholded adjency matrix - and the original matrix. - Parameters - ---------- - C : ndarray, shape (n_nodes,n_nodes) - The structure matrix to threshold - inf : float - The beginning of the linesearch - sup : float - The end of the linesearch - step : integer - Number of thresholds tested - """ - dist = [] - search = np.linspace(inf, sup, step) - for thresh in search: - Cprime = sp_to_adjency(C, 0, thresh) - SC = shortest_path(Cprime, method='D') - SC[SC == float('inf')] = 100 - dist.append(np.linalg.norm(SC - C)) - return search[np.argmin(dist)], dist - - -def sp_to_adjency(C, threshinf=0.2, threshsup=1.8): - """ Thresholds the structure matrix in order to compute an adjency matrix. - All values between threshinf and threshsup are considered representing connected nodes and set to 1. Else are set to 0 - Parameters - ---------- - C : ndarray, shape (n_nodes,n_nodes) - The structure matrix to threshold - threshinf : float - The minimum value of distance from which the new value is set to 1 - threshsup : float - The maximum value of distance from which the new value is set to 1 - Returns - ------- - C : ndarray, shape (n_nodes,n_nodes) - The threshold matrix. Each element is in {0,1} - """ - H = np.zeros_like(C) - np.fill_diagonal(H, np.diagonal(C)) - C = C - H - C = np.minimum(np.maximum(C, threshinf), threshsup) - C[C == threshsup] = 0 - C[C != 0] = 1 - - return C - - -def build_noisy_circular_graph(N=20, mu=0, sigma=0.3, with_noise=False, structure_noise=False, p=None): - """ Create a noisy circular graph - """ - g = nx.Graph() - g.add_nodes_from(list(range(N))) - for i in range(N): - noise = float(np.random.normal(mu, sigma, 1)) - if with_noise: - g.add_node(i, attr_name=math.sin((2 * i * math.pi / N)) + noise) - else: - g.add_node(i, attr_name=math.sin(2 * i * math.pi / N)) - g.add_edge(i, i + 1) - if structure_noise: - randomint = np.random.randint(0, p) - if randomint == 0: - if i <= N - 3: - g.add_edge(i, i + 2) - if i == N - 2: - g.add_edge(i, 0) - if i == N - 1: - g.add_edge(i, 1) - g.add_edge(N, 0) - noise = float(np.random.normal(mu, sigma, 1)) - if with_noise: - g.add_node(N, attr_name=math.sin((2 * N * math.pi / N)) + noise) - else: - g.add_node(N, attr_name=math.sin(2 * N * math.pi / N)) - return g - - -def graph_colors(nx_graph, vmin=0, vmax=7): - cnorm = mcol.Normalize(vmin=vmin, vmax=vmax) - cpick = cm.ScalarMappable(norm=cnorm, cmap='viridis') - cpick.set_array([]) - val_map = {} - for k, v in nx.get_node_attributes(nx_graph, 'attr_name').items(): - val_map[k] = cpick.to_rgba(v) - colors = [] - for node in nx_graph.nodes(): - colors.append(val_map[node]) - return colors - -############################################################################## -# Generate data -# ------------- - -#%% circular dataset -# We build a dataset of noisy circular graphs. -# Noise is added on the structures by random connections and on the features by gaussian noise. - - -np.random.seed(30) -X0 = [] -for k in range(9): - X0.append(build_noisy_circular_graph(np.random.randint(15, 25), with_noise=True, structure_noise=True, p=3)) - -############################################################################## -# Plot data -# --------- - -#%% Plot graphs - -plt.figure(figsize=(8, 10)) -for i in range(len(X0)): - plt.subplot(3, 3, i + 1) - g = X0[i] - pos = nx.kamada_kawai_layout(g) - nx.draw(g, pos=pos, node_color=graph_colors(g, vmin=-1, vmax=1), with_labels=False, node_size=100) -plt.suptitle('Dataset of noisy graphs. Color indicates the label', fontsize=20) -plt.show() - -############################################################################## -# Barycenter computation -# ---------------------- - -#%% We compute the barycenter using FGW. Structure matrices are computed using the shortest_path distance in the graph -# Features distances are the euclidean distances -Cs = [shortest_path(nx.adjacency_matrix(x)) for x in X0] -ps = [np.ones(len(x.nodes())) / len(x.nodes()) for x in X0] -Ys = [np.array([v for (k, v) in nx.get_node_attributes(x, 'attr_name').items()]).reshape(-1, 1) for x in X0] -lambdas = np.array([np.ones(len(Ys)) / len(Ys)]).ravel() -sizebary = 15 # we choose a barycenter with 15 nodes - -A, C, log = fgw_barycenters(sizebary, Ys, Cs, ps, lambdas, alpha=0.95, log=True) - -############################################################################## -# Plot Barycenter -# ------------------------- - -#%% Create the barycenter -bary = nx.from_numpy_matrix(sp_to_adjency(C, threshinf=0, threshsup=find_thresh(C, sup=100, step=100)[0])) -for i, v in enumerate(A.ravel()): - bary.add_node(i, attr_name=v) - -#%% -pos = nx.kamada_kawai_layout(bary) -nx.draw(bary, pos=pos, node_color=graph_colors(bary, vmin=-1, vmax=1), with_labels=False) -plt.suptitle('Barycenter', fontsize=20) -plt.show() diff --git a/docs/source/auto_examples/plot_barycenter_fgw.rst b/docs/source/auto_examples/plot_barycenter_fgw.rst deleted file mode 100644 index ad4c275..0000000 --- a/docs/source/auto_examples/plot_barycenter_fgw.rst +++ /dev/null @@ -1,320 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_barycenter_fgw.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_barycenter_fgw.py: - - -================================= -Plot graphs' barycenter using FGW -================================= - -This example illustrates the computation barycenter of labeled graphs using FGW - -Requires networkx >=2 - -.. [18] Vayer Titouan, Chapel Laetitia, Flamary R{'e}mi, Tavenard Romain - and Courty Nicolas - "Optimal Transport for structured data with application on graphs" - International Conference on Machine Learning (ICML). 2019. - - - -.. code-block:: default - - - # Author: Titouan Vayer <titouan.vayer@irisa.fr> - # - # License: MIT License - - - - - - - - - -.. code-block:: default - - import numpy as np - import matplotlib.pyplot as plt - import networkx as nx - import math - from scipy.sparse.csgraph import shortest_path - import matplotlib.colors as mcol - from matplotlib import cm - from ot.gromov import fgw_barycenters - - - - - - - - -.. code-block:: default - - - - def find_thresh(C, inf=0.5, sup=3, step=10): - """ Trick to find the adequate thresholds from where value of the C matrix are considered close enough to say that nodes are connected - Tthe threshold is found by a linesearch between values "inf" and "sup" with "step" thresholds tested. - The optimal threshold is the one which minimizes the reconstruction error between the shortest_path matrix coming from the thresholded adjency matrix - and the original matrix. - Parameters - ---------- - C : ndarray, shape (n_nodes,n_nodes) - The structure matrix to threshold - inf : float - The beginning of the linesearch - sup : float - The end of the linesearch - step : integer - Number of thresholds tested - """ - dist = [] - search = np.linspace(inf, sup, step) - for thresh in search: - Cprime = sp_to_adjency(C, 0, thresh) - SC = shortest_path(Cprime, method='D') - SC[SC == float('inf')] = 100 - dist.append(np.linalg.norm(SC - C)) - return search[np.argmin(dist)], dist - - - def sp_to_adjency(C, threshinf=0.2, threshsup=1.8): - """ Thresholds the structure matrix in order to compute an adjency matrix. - All values between threshinf and threshsup are considered representing connected nodes and set to 1. Else are set to 0 - Parameters - ---------- - C : ndarray, shape (n_nodes,n_nodes) - The structure matrix to threshold - threshinf : float - The minimum value of distance from which the new value is set to 1 - threshsup : float - The maximum value of distance from which the new value is set to 1 - Returns - ------- - C : ndarray, shape (n_nodes,n_nodes) - The threshold matrix. Each element is in {0,1} - """ - H = np.zeros_like(C) - np.fill_diagonal(H, np.diagonal(C)) - C = C - H - C = np.minimum(np.maximum(C, threshinf), threshsup) - C[C == threshsup] = 0 - C[C != 0] = 1 - - return C - - - def build_noisy_circular_graph(N=20, mu=0, sigma=0.3, with_noise=False, structure_noise=False, p=None): - """ Create a noisy circular graph - """ - g = nx.Graph() - g.add_nodes_from(list(range(N))) - for i in range(N): - noise = float(np.random.normal(mu, sigma, 1)) - if with_noise: - g.add_node(i, attr_name=math.sin((2 * i * math.pi / N)) + noise) - else: - g.add_node(i, attr_name=math.sin(2 * i * math.pi / N)) - g.add_edge(i, i + 1) - if structure_noise: - randomint = np.random.randint(0, p) - if randomint == 0: - if i <= N - 3: - g.add_edge(i, i + 2) - if i == N - 2: - g.add_edge(i, 0) - if i == N - 1: - g.add_edge(i, 1) - g.add_edge(N, 0) - noise = float(np.random.normal(mu, sigma, 1)) - if with_noise: - g.add_node(N, attr_name=math.sin((2 * N * math.pi / N)) + noise) - else: - g.add_node(N, attr_name=math.sin(2 * N * math.pi / N)) - return g - - - def graph_colors(nx_graph, vmin=0, vmax=7): - cnorm = mcol.Normalize(vmin=vmin, vmax=vmax) - cpick = cm.ScalarMappable(norm=cnorm, cmap='viridis') - cpick.set_array([]) - val_map = {} - for k, v in nx.get_node_attributes(nx_graph, 'attr_name').items(): - val_map[k] = cpick.to_rgba(v) - colors = [] - for node in nx_graph.nodes(): - colors.append(val_map[node]) - return colors - - - - - - - - -Generate data -------------- - -We build a dataset of noisy circular graphs. -Noise is added on the structures by random connections and on the features by gaussian noise. - - -.. code-block:: default - - - - np.random.seed(30) - X0 = [] - for k in range(9): - X0.append(build_noisy_circular_graph(np.random.randint(15, 25), with_noise=True, structure_noise=True, p=3)) - - - - - - - - -Plot data ---------- - - -.. code-block:: default - - - plt.figure(figsize=(8, 10)) - for i in range(len(X0)): - plt.subplot(3, 3, i + 1) - g = X0[i] - pos = nx.kamada_kawai_layout(g) - nx.draw(g, pos=pos, node_color=graph_colors(g, vmin=-1, vmax=1), with_labels=False, node_size=100) - plt.suptitle('Dataset of noisy graphs. Color indicates the label', fontsize=20) - plt.show() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_barycenter_fgw_001.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_barycenter_fgw.py:155: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - plt.show() - - - - -Barycenter computation ----------------------- - -Features distances are the euclidean distances - - -.. code-block:: default - - Cs = [shortest_path(nx.adjacency_matrix(x)) for x in X0] - ps = [np.ones(len(x.nodes())) / len(x.nodes()) for x in X0] - Ys = [np.array([v for (k, v) in nx.get_node_attributes(x, 'attr_name').items()]).reshape(-1, 1) for x in X0] - lambdas = np.array([np.ones(len(Ys)) / len(Ys)]).ravel() - sizebary = 15 # we choose a barycenter with 15 nodes - - A, C, log = fgw_barycenters(sizebary, Ys, Cs, ps, lambdas, alpha=0.95, log=True) - - - - - - - - -Plot Barycenter -------------------------- - - -.. code-block:: default - - bary = nx.from_numpy_matrix(sp_to_adjency(C, threshinf=0, threshsup=find_thresh(C, sup=100, step=100)[0])) - for i, v in enumerate(A.ravel()): - bary.add_node(i, attr_name=v) - - - - - - - - - -.. code-block:: default - - pos = nx.kamada_kawai_layout(bary) - nx.draw(bary, pos=pos, node_color=graph_colors(bary, vmin=-1, vmax=1), with_labels=False) - plt.suptitle('Barycenter', fontsize=20) - plt.show() - - - -.. image:: /auto_examples/images/sphx_glr_plot_barycenter_fgw_002.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_barycenter_fgw.py:184: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - plt.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 1.949 seconds) - - -.. _sphx_glr_download_auto_examples_plot_barycenter_fgw.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_barycenter_fgw.py <plot_barycenter_fgw.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: plot_barycenter_fgw.ipynb <plot_barycenter_fgw.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ diff --git a/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.ipynb b/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.ipynb deleted file mode 100644 index b976aae..0000000 --- a/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.ipynb +++ /dev/null @@ -1,192 +0,0 @@ -{ - "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": [ - "problems = []\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()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pl.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": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "alpha = 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": [ - "Stair Data\n----------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "a1 = 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()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pl.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": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "alpha = 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": [ - "Dirac Data\n----------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "a1 = 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()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pl.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": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "alpha = 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": [ - "nbm = 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": "3.6.9" - } - }, - "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 deleted file mode 100644 index d7c72d0..0000000 --- a/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.py +++ /dev/null @@ -1,286 +0,0 @@ -# -*- 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]]) - -############################################################################## -# Stair 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() - - -############################################################################## -# Dirac Data -# ---------- - -#%% 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 deleted file mode 100644 index 5e83fbf..0000000 --- a/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.rst +++ /dev/null @@ -1,532 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_barycenter_lp_vs_entropic.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _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:: default - - - # 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:: default - - - 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() - - - - - - - - - - -.. code-block:: default - - - pl.figure(1, figsize=(6.4, 3)) - for i in range(n_distributions): - pl.plot(x, A[:, i]) - pl.title('Distributions') - pl.tight_layout() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_001.png - :class: sphx-glr-single-img - - - - - - -.. code-block:: default - - - 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]]) - - - - -.. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_002.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - Elapsed time : 0.0049059391021728516 s - Primal Feasibility Dual Feasibility Duality Gap Step Path Parameter Objective - 1.0 1.0 1.0 - 1.0 1700.336700337 - 0.006776453137632 0.006776453137632 0.006776453137632 0.9932238647293 0.006776453137632 125.6700527543 - 0.004018712867873 0.004018712867873 0.004018712867873 0.4301142633001 0.004018712867873 12.26594150092 - 0.001172775061627 0.001172775061627 0.001172775061627 0.7599932455027 0.001172775061627 0.3378536968898 - 0.0004375137005386 0.0004375137005386 0.0004375137005386 0.6422331807989 0.0004375137005386 0.1468420566359 - 0.0002326690467339 0.0002326690467339 0.0002326690467339 0.5016999460898 0.0002326690467339 0.09381703231428 - 7.430121674299e-05 7.4301216743e-05 7.430121674299e-05 0.7035962305811 7.430121674299e-05 0.05777870257169 - 5.321227838943e-05 5.321227838945e-05 5.321227838944e-05 0.3087841864307 5.321227838944e-05 0.05266249477219 - 1.990900379216e-05 1.99090037922e-05 1.990900379216e-05 0.6520472013271 1.990900379216e-05 0.04526054405523 - 6.305442046834e-06 6.305442046856e-06 6.305442046837e-06 0.7073953304085 6.305442046837e-06 0.04237597591384 - 2.290148391591e-06 2.290148391631e-06 2.290148391602e-06 0.6941812711476 2.29014839161e-06 0.04152284932101 - 1.182864875578e-06 1.182864875548e-06 1.182864875555e-06 0.5084552046229 1.182864875567e-06 0.04129461872829 - 3.626786386894e-07 3.626786386985e-07 3.626786386845e-07 0.7101651569095 3.626786385995e-07 0.0411303244893 - 1.539754244475e-07 1.539754247164e-07 1.539754247197e-07 0.6279322077522 1.539754251915e-07 0.04108867636377 - 5.193221608537e-08 5.19322169648e-08 5.193221696942e-08 0.6843453280956 5.193221892276e-08 0.04106859618454 - 1.888205219929e-08 1.88820500654e-08 1.888205006369e-08 0.6673443828803 1.888205852187e-08 0.04106214175236 - 5.676837529301e-09 5.676842740457e-09 5.676842761502e-09 0.7281712198286 5.676877044229e-09 0.04105958648535 - 3.501170987746e-09 3.501167688027e-09 3.501167721804e-09 0.4140142115019 3.501183058995e-09 0.04105916265728 - 1.110582426269e-09 1.110580273241e-09 1.110580239523e-09 0.6999003212726 1.110624310022e-09 0.04105870073273 - 5.768753963318e-10 5.769422203363e-10 5.769421938248e-10 0.5002521235315 5.767522037401e-10 0.04105859764872 - 1.534102102874e-10 1.535920569433e-10 1.535921107494e-10 0.7516900610544 1.535251083958e-10 0.04105851678411 - 6.717475002202e-11 6.735435784522e-11 6.735430717133e-11 0.5944268235824 6.732253215483e-11 0.04105850033323 - 1.751321118837e-11 1.74043080851e-11 1.740429001123e-11 0.7566075167358 1.736956306927e-11 0.0410584908946 - Optimization terminated successfully. - Current function value: 0.041058 - Iterations: 22 - Elapsed time : 2.149055242538452 s - - - - -Stair Data ----------- - - -.. code-block:: default - - - 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() - - - - - - - - - - -.. code-block:: default - - - pl.figure(1, figsize=(6.4, 3)) - for i in range(n_distributions): - pl.plot(x, A[:, i]) - pl.title('Distributions') - pl.tight_layout() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_003.png - :class: sphx-glr-single-img - - - - - - -.. code-block:: default - - - 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() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_004.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - Elapsed time : 0.008316993713378906 s - Primal Feasibility Dual Feasibility Duality Gap Step Path Parameter Objective - 1.0 1.0 1.0 - 1.0 1700.336700337 - 0.006776466288938 0.006776466288938 0.006776466288938 0.9932238515788 0.006776466288938 125.66492558 - 0.004036918865472 0.004036918865472 0.004036918865472 0.4272973099325 0.004036918865472 12.347161701 - 0.001219232687076 0.001219232687076 0.001219232687076 0.7496986855957 0.001219232687076 0.3243835647418 - 0.0003837422984467 0.0003837422984467 0.0003837422984467 0.6926882608271 0.0003837422984467 0.1361719397498 - 0.0001070128410194 0.0001070128410194 0.0001070128410194 0.7643889137854 0.0001070128410194 0.07581952832542 - 0.0001001275033713 0.0001001275033714 0.0001001275033713 0.07058704838615 0.0001001275033713 0.07347394936346 - 4.550897507807e-05 4.550897507807e-05 4.550897507807e-05 0.576117248486 4.550897507807e-05 0.05555077655034 - 8.557124125834e-06 8.557124125853e-06 8.557124125835e-06 0.853592544106 8.557124125835e-06 0.0443981466023 - 3.611995628666e-06 3.611995628643e-06 3.611995628672e-06 0.6002277331398 3.611995628673e-06 0.0428300776216 - 7.590393750111e-07 7.590393750273e-07 7.590393750129e-07 0.8221486533655 7.590393750133e-07 0.04192322976247 - 8.299929287077e-08 8.299929283415e-08 8.299929287126e-08 0.901746793884 8.299929287181e-08 0.04170825633295 - 3.117560207452e-10 3.117560192413e-10 3.117560199213e-10 0.9970399692253 3.117560200234e-10 0.04168179329766 - 1.559774508975e-14 1.559825507727e-14 1.559755309294e-14 0.9999499686993 1.559748033629e-14 0.04168169240444 - Optimization terminated successfully. - Current function value: 0.041682 - Iterations: 13 - Elapsed time : 2.0333712100982666 s - - - - -Dirac Data ----------- - - -.. code-block:: default - - - 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() - - - - - - - - - - -.. code-block:: default - - - pl.figure(1, figsize=(6.4, 3)) - for i in range(n_distributions): - pl.plot(x, A[:, i]) - pl.title('Distributions') - pl.tight_layout() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_005.png - :class: sphx-glr-single-img - - - - - - -.. code-block:: default - - - 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() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_006.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - Elapsed time : 0.001787424087524414 s - Primal Feasibility Dual Feasibility Duality Gap Step Path Parameter Objective - 1.0 1.0 1.0 - 1.0 1700.336700337 - 0.00677467552072 0.006774675520719 0.006774675520719 0.9932256422636 0.006774675520719 125.6956034741 - 0.002048208707556 0.002048208707555 0.002048208707555 0.734309536815 0.002048208707555 5.213991622102 - 0.0002697365474791 0.0002697365474791 0.0002697365474791 0.8839403501183 0.0002697365474791 0.5059383903908 - 6.832109993919e-05 6.832109993918e-05 6.832109993918e-05 0.7601171075982 6.832109993918e-05 0.2339657807271 - 2.437682932221e-05 2.437682932221e-05 2.437682932221e-05 0.6663448297463 2.437682932221e-05 0.1471256246325 - 1.134983216308e-05 1.134983216308e-05 1.134983216308e-05 0.5553643816417 1.134983216308e-05 0.1181584941171 - 3.342312725863e-06 3.34231272585e-06 3.342312725863e-06 0.7238133571629 3.342312725863e-06 0.1006387519746 - 7.078561231536e-07 7.078561231537e-07 7.078561231535e-07 0.803314255252 7.078561231535e-07 0.09474734646268 - 1.966870949422e-07 1.966870952674e-07 1.966870952717e-07 0.7525479180433 1.966870953014e-07 0.09354342735758 - 4.199895266495e-10 4.199895367352e-10 4.19989526535e-10 0.9984019849265 4.199895265747e-10 0.09310367785861 - 2.101053559204e-14 2.100331212975e-14 2.101054034304e-14 0.9999499736903 2.101053604307e-14 0.09310274466458 - Optimization terminated successfully. - Current function value: 0.093103 - Iterations: 11 - Elapsed time : 2.1853578090667725 s - - - - -Final figure ------------- - - - -.. code-block:: default - - - 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_007.png - :class: sphx-glr-single-img - - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 7.697 seconds) - - -.. _sphx_glr_download_auto_examples_plot_barycenter_lp_vs_entropic.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_barycenter_lp_vs_entropic.py <plot_barycenter_lp_vs_entropic.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :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.github.io>`_ diff --git a/docs/source/auto_examples/plot_compute_emd.ipynb b/docs/source/auto_examples/plot_compute_emd.ipynb deleted file mode 100644 index 24a2fff..0000000 --- a/docs/source/auto_examples/plot_compute_emd.ipynb +++ /dev/null @@ -1,126 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n# Plot multiple EMD\n\n\nShows how to compute multiple EMD and Sinkhorn with two differnt\nground metrics and plot their values for diffeent distributions.\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 matplotlib.pylab as pl\nimport ot\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": [ - "n = 100 # nb bins\nn_target = 50 # nb target distributions\n\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\nlst_m = np.linspace(20, 90, n_target)\n\n# Gaussian distributions\na = gauss(n, m=20, s=5) # m= mean, s= std\n\nB = np.zeros((n, n_target))\n\nfor i, m in enumerate(lst_m):\n B[:, i] = gauss(n, m=m, s=5)\n\n# loss matrix and normalization\nM = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)), 'euclidean')\nM /= M.max()\nM2 = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)), 'sqeuclidean')\nM2 /= M2.max()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Plot data\n---------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pl.figure(1)\npl.subplot(2, 1, 1)\npl.plot(x, a, 'b', label='Source distribution')\npl.title('Source distribution')\npl.subplot(2, 1, 2)\npl.plot(x, B, label='Target distributions')\npl.title('Target distributions')\npl.tight_layout()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Compute EMD for the different losses\n------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "d_emd = ot.emd2(a, B, M) # direct computation of EMD\nd_emd2 = ot.emd2(a, B, M2) # direct computation of EMD with loss M2\n\n\npl.figure(2)\npl.plot(d_emd, label='Euclidean EMD')\npl.plot(d_emd2, label='Squared Euclidean EMD')\npl.title('EMD distances')\npl.legend()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Compute Sinkhorn for the different losses\n-----------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "reg = 1e-2\nd_sinkhorn = ot.sinkhorn2(a, B, M, reg)\nd_sinkhorn2 = ot.sinkhorn2(a, B, M2, reg)\n\npl.figure(2)\npl.clf()\npl.plot(d_emd, label='Euclidean EMD')\npl.plot(d_emd2, label='Squared Euclidean EMD')\npl.plot(d_sinkhorn, '+', label='Euclidean Sinkhorn')\npl.plot(d_sinkhorn2, '+', label='Squared Euclidean Sinkhorn')\npl.title('EMD distances')\npl.legend()\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": "3.6.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_compute_emd.py b/docs/source/auto_examples/plot_compute_emd.py deleted file mode 100644 index 7ed2b01..0000000 --- a/docs/source/auto_examples/plot_compute_emd.py +++ /dev/null @@ -1,102 +0,0 @@ -# -*- coding: utf-8 -*- -""" -================= -Plot multiple EMD -================= - -Shows how to compute multiple EMD and Sinkhorn with two differnt -ground metrics and plot their values for diffeent distributions. - - -""" - -# Author: Remi Flamary <remi.flamary@unice.fr> -# -# License: MIT License - -import numpy as np -import matplotlib.pylab as pl -import ot -from ot.datasets import make_1D_gauss as gauss - - -############################################################################## -# Generate data -# ------------- - -#%% parameters - -n = 100 # nb bins -n_target = 50 # nb target distributions - - -# bin positions -x = np.arange(n, dtype=np.float64) - -lst_m = np.linspace(20, 90, n_target) - -# Gaussian distributions -a = gauss(n, m=20, s=5) # m= mean, s= std - -B = np.zeros((n, n_target)) - -for i, m in enumerate(lst_m): - B[:, i] = gauss(n, m=m, s=5) - -# loss matrix and normalization -M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)), 'euclidean') -M /= M.max() -M2 = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)), 'sqeuclidean') -M2 /= M2.max() - -############################################################################## -# Plot data -# --------- - -#%% plot the distributions - -pl.figure(1) -pl.subplot(2, 1, 1) -pl.plot(x, a, 'b', label='Source distribution') -pl.title('Source distribution') -pl.subplot(2, 1, 2) -pl.plot(x, B, label='Target distributions') -pl.title('Target distributions') -pl.tight_layout() - - -############################################################################## -# Compute EMD for the different losses -# ------------------------------------ - -#%% Compute and plot distributions and loss matrix - -d_emd = ot.emd2(a, B, M) # direct computation of EMD -d_emd2 = ot.emd2(a, B, M2) # direct computation of EMD with loss M2 - - -pl.figure(2) -pl.plot(d_emd, label='Euclidean EMD') -pl.plot(d_emd2, label='Squared Euclidean EMD') -pl.title('EMD distances') -pl.legend() - -############################################################################## -# Compute Sinkhorn for the different losses -# ----------------------------------------- - -#%% -reg = 1e-2 -d_sinkhorn = ot.sinkhorn2(a, B, M, reg) -d_sinkhorn2 = ot.sinkhorn2(a, B, M2, reg) - -pl.figure(2) -pl.clf() -pl.plot(d_emd, label='Euclidean EMD') -pl.plot(d_emd2, label='Squared Euclidean EMD') -pl.plot(d_sinkhorn, '+', label='Euclidean Sinkhorn') -pl.plot(d_sinkhorn2, '+', label='Squared Euclidean Sinkhorn') -pl.title('EMD distances') -pl.legend() - -pl.show() diff --git a/docs/source/auto_examples/plot_compute_emd.rst b/docs/source/auto_examples/plot_compute_emd.rst deleted file mode 100644 index e4cc143..0000000 --- a/docs/source/auto_examples/plot_compute_emd.rst +++ /dev/null @@ -1,211 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_compute_emd.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_compute_emd.py: - - -================= -Plot multiple EMD -================= - -Shows how to compute multiple EMD and Sinkhorn with two differnt -ground metrics and plot their values for diffeent distributions. - - - - -.. code-block:: default - - - # Author: Remi Flamary <remi.flamary@unice.fr> - # - # License: MIT License - - import numpy as np - import matplotlib.pylab as pl - import ot - from ot.datasets import make_1D_gauss as gauss - - - - - - - - - -Generate data -------------- - - -.. code-block:: default - - - n = 100 # nb bins - n_target = 50 # nb target distributions - - - # bin positions - x = np.arange(n, dtype=np.float64) - - lst_m = np.linspace(20, 90, n_target) - - # Gaussian distributions - a = gauss(n, m=20, s=5) # m= mean, s= std - - B = np.zeros((n, n_target)) - - for i, m in enumerate(lst_m): - B[:, i] = gauss(n, m=m, s=5) - - # loss matrix and normalization - M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)), 'euclidean') - M /= M.max() - M2 = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)), 'sqeuclidean') - M2 /= M2.max() - - - - - - - - -Plot data ---------- - - -.. code-block:: default - - - pl.figure(1) - pl.subplot(2, 1, 1) - pl.plot(x, a, 'b', label='Source distribution') - pl.title('Source distribution') - pl.subplot(2, 1, 2) - pl.plot(x, B, label='Target distributions') - pl.title('Target distributions') - pl.tight_layout() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_compute_emd_001.png - :class: sphx-glr-single-img - - - - - -Compute EMD for the different losses ------------------------------------- - - -.. code-block:: default - - - d_emd = ot.emd2(a, B, M) # direct computation of EMD - d_emd2 = ot.emd2(a, B, M2) # direct computation of EMD with loss M2 - - - pl.figure(2) - pl.plot(d_emd, label='Euclidean EMD') - pl.plot(d_emd2, label='Squared Euclidean EMD') - pl.title('EMD distances') - pl.legend() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_compute_emd_002.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - - <matplotlib.legend.Legend object at 0x7f4c7389f438> - - - -Compute Sinkhorn for the different losses ------------------------------------------ - - -.. code-block:: default - - reg = 1e-2 - d_sinkhorn = ot.sinkhorn2(a, B, M, reg) - d_sinkhorn2 = ot.sinkhorn2(a, B, M2, reg) - - pl.figure(2) - pl.clf() - pl.plot(d_emd, label='Euclidean EMD') - pl.plot(d_emd2, label='Squared Euclidean EMD') - pl.plot(d_sinkhorn, '+', label='Euclidean Sinkhorn') - pl.plot(d_sinkhorn2, '+', label='Squared Euclidean Sinkhorn') - pl.title('EMD distances') - pl.legend() - - pl.show() - - - -.. image:: /auto_examples/images/sphx_glr_plot_compute_emd_003.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_compute_emd.py:102: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 0.436 seconds) - - -.. _sphx_glr_download_auto_examples_plot_compute_emd.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_compute_emd.py <plot_compute_emd.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: plot_compute_emd.ipynb <plot_compute_emd.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ diff --git a/docs/source/auto_examples/plot_convolutional_barycenter.ipynb b/docs/source/auto_examples/plot_convolutional_barycenter.ipynb deleted file mode 100644 index f94a32e..0000000 --- a/docs/source/auto_examples/plot_convolutional_barycenter.ipynb +++ /dev/null @@ -1,90 +0,0 @@ -{ - "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": "3.6.9" - } - }, - "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 deleted file mode 100644 index e74db04..0000000 --- a/docs/source/auto_examples/plot_convolutional_barycenter.py +++ /dev/null @@ -1,92 +0,0 @@ - -#%% -# -*- 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 deleted file mode 100644 index 9c9a596..0000000 --- a/docs/source/auto_examples/plot_convolutional_barycenter.rst +++ /dev/null @@ -1,173 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_convolutional_barycenter.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _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:: default - - - # 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:: default - - - - 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:: default - - - 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 - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_convolutional_barycenter.py:92: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 34.615 seconds) - - -.. _sphx_glr_download_auto_examples_plot_convolutional_barycenter.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_convolutional_barycenter.py <plot_convolutional_barycenter.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :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.github.io>`_ diff --git a/docs/source/auto_examples/plot_fgw.ipynb b/docs/source/auto_examples/plot_fgw.ipynb deleted file mode 100644 index 20c0a3f..0000000 --- a/docs/source/auto_examples/plot_fgw.ipynb +++ /dev/null @@ -1,169 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n# Plot Fused-gromov-Wasserstein\n\n\nThis example illustrates the computation of FGW for 1D measures[18].\n\n.. [18] Vayer Titouan, Chapel Laetitia, Flamary R{'e}mi, Tavenard Romain\n and Courty Nicolas\n \"Optimal Transport for structured data with application on graphs\"\n International Conference on Machine Learning (ICML). 2019.\n\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Author: Titouan Vayer <titouan.vayer@irisa.fr>\n#\n# License: MIT License\n\nimport matplotlib.pyplot as pl\nimport numpy as np\nimport ot\nfrom ot.gromov import gromov_wasserstein, fused_gromov_wasserstein" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Generate data\n---------\n\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We create two 1D random measures\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "n = 20 # number of points in the first distribution\nn2 = 30 # number of points in the second distribution\nsig = 1 # std of first distribution\nsig2 = 0.1 # std of second distribution\n\nnp.random.seed(0)\n\nphi = np.arange(n)[:, None]\nxs = phi + sig * np.random.randn(n, 1)\nys = np.vstack((np.ones((n // 2, 1)), 0 * np.ones((n // 2, 1)))) + sig2 * np.random.randn(n, 1)\n\nphi2 = np.arange(n2)[:, None]\nxt = phi2 + sig * np.random.randn(n2, 1)\nyt = np.vstack((np.ones((n2 // 2, 1)), 0 * np.ones((n2 // 2, 1)))) + sig2 * np.random.randn(n2, 1)\nyt = yt[::-1, :]\n\np = ot.unif(n)\nq = ot.unif(n2)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Plot data\n---------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pl.close(10)\npl.figure(10, (7, 7))\n\npl.subplot(2, 1, 1)\n\npl.scatter(ys, xs, c=phi, s=70)\npl.ylabel('Feature value a', fontsize=20)\npl.title('$\\mu=\\sum_i \\delta_{x_i,a_i}$', fontsize=25, usetex=True, y=1)\npl.xticks(())\npl.yticks(())\npl.subplot(2, 1, 2)\npl.scatter(yt, xt, c=phi2, s=70)\npl.xlabel('coordinates x/y', fontsize=25)\npl.ylabel('Feature value b', fontsize=20)\npl.title('$\\\\nu=\\sum_j \\delta_{y_j,b_j}$', fontsize=25, usetex=True, y=1)\npl.yticks(())\npl.tight_layout()\npl.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create structure matrices and across-feature distance matrix\n---------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "C1 = ot.dist(xs)\nC2 = ot.dist(xt)\nM = ot.dist(ys, yt)\nw1 = ot.unif(C1.shape[0])\nw2 = ot.unif(C2.shape[0])\nGot = ot.emd([], [], M)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Plot matrices\n---------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "cmap = 'Reds'\npl.close(10)\npl.figure(10, (5, 5))\nfs = 15\nl_x = [0, 5, 10, 15]\nl_y = [0, 5, 10, 15, 20, 25]\ngs = pl.GridSpec(5, 5)\n\nax1 = pl.subplot(gs[3:, :2])\n\npl.imshow(C1, cmap=cmap, interpolation='nearest')\npl.title(\"$C_1$\", fontsize=fs)\npl.xlabel(\"$k$\", fontsize=fs)\npl.ylabel(\"$i$\", fontsize=fs)\npl.xticks(l_x)\npl.yticks(l_x)\n\nax2 = pl.subplot(gs[:3, 2:])\n\npl.imshow(C2, cmap=cmap, interpolation='nearest')\npl.title(\"$C_2$\", fontsize=fs)\npl.ylabel(\"$l$\", fontsize=fs)\n#pl.ylabel(\"$l$\",fontsize=fs)\npl.xticks(())\npl.yticks(l_y)\nax2.set_aspect('auto')\n\nax3 = pl.subplot(gs[3:, 2:], sharex=ax2, sharey=ax1)\npl.imshow(M, cmap=cmap, interpolation='nearest')\npl.yticks(l_x)\npl.xticks(l_y)\npl.ylabel(\"$i$\", fontsize=fs)\npl.title(\"$M_{AB}$\", fontsize=fs)\npl.xlabel(\"$j$\", fontsize=fs)\npl.tight_layout()\nax3.set_aspect('auto')\npl.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Compute FGW/GW\n---------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "alpha = 1e-3\n\not.tic()\nGwg, logw = fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=alpha, verbose=True, log=True)\not.toc()\n\n#%reload_ext WGW\nGg, log = gromov_wasserstein(C1, C2, p, q, loss_fun='square_loss', verbose=True, log=True)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Visualize transport matrices\n---------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "cmap = 'Blues'\nfs = 15\npl.figure(2, (13, 5))\npl.clf()\npl.subplot(1, 3, 1)\npl.imshow(Got, cmap=cmap, interpolation='nearest')\n#pl.xlabel(\"$y$\",fontsize=fs)\npl.ylabel(\"$i$\", fontsize=fs)\npl.xticks(())\n\npl.title('Wasserstein ($M$ only)')\n\npl.subplot(1, 3, 2)\npl.imshow(Gg, cmap=cmap, interpolation='nearest')\npl.title('Gromov ($C_1,C_2$ only)')\npl.xticks(())\npl.subplot(1, 3, 3)\npl.imshow(Gwg, cmap=cmap, interpolation='nearest')\npl.title('FGW ($M+C_1,C_2$)')\n\npl.xlabel(\"$j$\", fontsize=fs)\npl.ylabel(\"$i$\", fontsize=fs)\n\npl.tight_layout()\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": "3.6.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_fgw.py b/docs/source/auto_examples/plot_fgw.py deleted file mode 100644 index 43efc94..0000000 --- a/docs/source/auto_examples/plot_fgw.py +++ /dev/null @@ -1,173 +0,0 @@ -# -*- coding: utf-8 -*- -""" -============================== -Plot Fused-gromov-Wasserstein -============================== - -This example illustrates the computation of FGW for 1D measures[18]. - -.. [18] Vayer Titouan, Chapel Laetitia, Flamary R{\'e}mi, Tavenard Romain - and Courty Nicolas - "Optimal Transport for structured data with application on graphs" - International Conference on Machine Learning (ICML). 2019. - -""" - -# Author: Titouan Vayer <titouan.vayer@irisa.fr> -# -# License: MIT License - -import matplotlib.pyplot as pl -import numpy as np -import ot -from ot.gromov import gromov_wasserstein, fused_gromov_wasserstein - -############################################################################## -# Generate data -# --------- - -#%% parameters -# We create two 1D random measures -n = 20 # number of points in the first distribution -n2 = 30 # number of points in the second distribution -sig = 1 # std of first distribution -sig2 = 0.1 # std of second distribution - -np.random.seed(0) - -phi = np.arange(n)[:, None] -xs = phi + sig * np.random.randn(n, 1) -ys = np.vstack((np.ones((n // 2, 1)), 0 * np.ones((n // 2, 1)))) + sig2 * np.random.randn(n, 1) - -phi2 = np.arange(n2)[:, None] -xt = phi2 + sig * np.random.randn(n2, 1) -yt = np.vstack((np.ones((n2 // 2, 1)), 0 * np.ones((n2 // 2, 1)))) + sig2 * np.random.randn(n2, 1) -yt = yt[::-1, :] - -p = ot.unif(n) -q = ot.unif(n2) - -############################################################################## -# Plot data -# --------- - -#%% plot the distributions - -pl.close(10) -pl.figure(10, (7, 7)) - -pl.subplot(2, 1, 1) - -pl.scatter(ys, xs, c=phi, s=70) -pl.ylabel('Feature value a', fontsize=20) -pl.title('$\mu=\sum_i \delta_{x_i,a_i}$', fontsize=25, usetex=True, y=1) -pl.xticks(()) -pl.yticks(()) -pl.subplot(2, 1, 2) -pl.scatter(yt, xt, c=phi2, s=70) -pl.xlabel('coordinates x/y', fontsize=25) -pl.ylabel('Feature value b', fontsize=20) -pl.title('$\\nu=\sum_j \delta_{y_j,b_j}$', fontsize=25, usetex=True, y=1) -pl.yticks(()) -pl.tight_layout() -pl.show() - -############################################################################## -# Create structure matrices and across-feature distance matrix -# --------- - -#%% Structure matrices and across-features distance matrix -C1 = ot.dist(xs) -C2 = ot.dist(xt) -M = ot.dist(ys, yt) -w1 = ot.unif(C1.shape[0]) -w2 = ot.unif(C2.shape[0]) -Got = ot.emd([], [], M) - -############################################################################## -# Plot matrices -# --------- - -#%% -cmap = 'Reds' -pl.close(10) -pl.figure(10, (5, 5)) -fs = 15 -l_x = [0, 5, 10, 15] -l_y = [0, 5, 10, 15, 20, 25] -gs = pl.GridSpec(5, 5) - -ax1 = pl.subplot(gs[3:, :2]) - -pl.imshow(C1, cmap=cmap, interpolation='nearest') -pl.title("$C_1$", fontsize=fs) -pl.xlabel("$k$", fontsize=fs) -pl.ylabel("$i$", fontsize=fs) -pl.xticks(l_x) -pl.yticks(l_x) - -ax2 = pl.subplot(gs[:3, 2:]) - -pl.imshow(C2, cmap=cmap, interpolation='nearest') -pl.title("$C_2$", fontsize=fs) -pl.ylabel("$l$", fontsize=fs) -#pl.ylabel("$l$",fontsize=fs) -pl.xticks(()) -pl.yticks(l_y) -ax2.set_aspect('auto') - -ax3 = pl.subplot(gs[3:, 2:], sharex=ax2, sharey=ax1) -pl.imshow(M, cmap=cmap, interpolation='nearest') -pl.yticks(l_x) -pl.xticks(l_y) -pl.ylabel("$i$", fontsize=fs) -pl.title("$M_{AB}$", fontsize=fs) -pl.xlabel("$j$", fontsize=fs) -pl.tight_layout() -ax3.set_aspect('auto') -pl.show() - -############################################################################## -# Compute FGW/GW -# --------- - -#%% Computing FGW and GW -alpha = 1e-3 - -ot.tic() -Gwg, logw = fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=alpha, verbose=True, log=True) -ot.toc() - -#%reload_ext WGW -Gg, log = gromov_wasserstein(C1, C2, p, q, loss_fun='square_loss', verbose=True, log=True) - -############################################################################## -# Visualize transport matrices -# --------- - -#%% visu OT matrix -cmap = 'Blues' -fs = 15 -pl.figure(2, (13, 5)) -pl.clf() -pl.subplot(1, 3, 1) -pl.imshow(Got, cmap=cmap, interpolation='nearest') -#pl.xlabel("$y$",fontsize=fs) -pl.ylabel("$i$", fontsize=fs) -pl.xticks(()) - -pl.title('Wasserstein ($M$ only)') - -pl.subplot(1, 3, 2) -pl.imshow(Gg, cmap=cmap, interpolation='nearest') -pl.title('Gromov ($C_1,C_2$ only)') -pl.xticks(()) -pl.subplot(1, 3, 3) -pl.imshow(Gwg, cmap=cmap, interpolation='nearest') -pl.title('FGW ($M+C_1,C_2$)') - -pl.xlabel("$j$", fontsize=fs) -pl.ylabel("$i$", fontsize=fs) - -pl.tight_layout() -pl.show() diff --git a/docs/source/auto_examples/plot_fgw.rst b/docs/source/auto_examples/plot_fgw.rst deleted file mode 100644 index 1c81d10..0000000 --- a/docs/source/auto_examples/plot_fgw.rst +++ /dev/null @@ -1,329 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_fgw.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_fgw.py: - - -============================== -Plot Fused-gromov-Wasserstein -============================== - -This example illustrates the computation of FGW for 1D measures[18]. - -.. [18] Vayer Titouan, Chapel Laetitia, Flamary R{'e}mi, Tavenard Romain - and Courty Nicolas - "Optimal Transport for structured data with application on graphs" - International Conference on Machine Learning (ICML). 2019. - - - -.. code-block:: default - - - # Author: Titouan Vayer <titouan.vayer@irisa.fr> - # - # License: MIT License - - import matplotlib.pyplot as pl - import numpy as np - import ot - from ot.gromov import gromov_wasserstein, fused_gromov_wasserstein - - - - - - - - -Generate data ---------- - -We create two 1D random measures - - -.. code-block:: default - - n = 20 # number of points in the first distribution - n2 = 30 # number of points in the second distribution - sig = 1 # std of first distribution - sig2 = 0.1 # std of second distribution - - np.random.seed(0) - - phi = np.arange(n)[:, None] - xs = phi + sig * np.random.randn(n, 1) - ys = np.vstack((np.ones((n // 2, 1)), 0 * np.ones((n // 2, 1)))) + sig2 * np.random.randn(n, 1) - - phi2 = np.arange(n2)[:, None] - xt = phi2 + sig * np.random.randn(n2, 1) - yt = np.vstack((np.ones((n2 // 2, 1)), 0 * np.ones((n2 // 2, 1)))) + sig2 * np.random.randn(n2, 1) - yt = yt[::-1, :] - - p = ot.unif(n) - q = ot.unif(n2) - - - - - - - - -Plot data ---------- - - -.. code-block:: default - - - pl.close(10) - pl.figure(10, (7, 7)) - - pl.subplot(2, 1, 1) - - pl.scatter(ys, xs, c=phi, s=70) - pl.ylabel('Feature value a', fontsize=20) - pl.title('$\mu=\sum_i \delta_{x_i,a_i}$', fontsize=25, usetex=True, y=1) - pl.xticks(()) - pl.yticks(()) - pl.subplot(2, 1, 2) - pl.scatter(yt, xt, c=phi2, s=70) - pl.xlabel('coordinates x/y', fontsize=25) - pl.ylabel('Feature value b', fontsize=20) - pl.title('$\\nu=\sum_j \delta_{y_j,b_j}$', fontsize=25, usetex=True, y=1) - pl.yticks(()) - pl.tight_layout() - pl.show() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_fgw_001.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_fgw.py:73: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - -Create structure matrices and across-feature distance matrix ---------- - - -.. code-block:: default - - C1 = ot.dist(xs) - C2 = ot.dist(xt) - M = ot.dist(ys, yt) - w1 = ot.unif(C1.shape[0]) - w2 = ot.unif(C2.shape[0]) - Got = ot.emd([], [], M) - - - - - - - - -Plot matrices ---------- - - -.. code-block:: default - - cmap = 'Reds' - pl.close(10) - pl.figure(10, (5, 5)) - fs = 15 - l_x = [0, 5, 10, 15] - l_y = [0, 5, 10, 15, 20, 25] - gs = pl.GridSpec(5, 5) - - ax1 = pl.subplot(gs[3:, :2]) - - pl.imshow(C1, cmap=cmap, interpolation='nearest') - pl.title("$C_1$", fontsize=fs) - pl.xlabel("$k$", fontsize=fs) - pl.ylabel("$i$", fontsize=fs) - pl.xticks(l_x) - pl.yticks(l_x) - - ax2 = pl.subplot(gs[:3, 2:]) - - pl.imshow(C2, cmap=cmap, interpolation='nearest') - pl.title("$C_2$", fontsize=fs) - pl.ylabel("$l$", fontsize=fs) - #pl.ylabel("$l$",fontsize=fs) - pl.xticks(()) - pl.yticks(l_y) - ax2.set_aspect('auto') - - ax3 = pl.subplot(gs[3:, 2:], sharex=ax2, sharey=ax1) - pl.imshow(M, cmap=cmap, interpolation='nearest') - pl.yticks(l_x) - pl.xticks(l_y) - pl.ylabel("$i$", fontsize=fs) - pl.title("$M_{AB}$", fontsize=fs) - pl.xlabel("$j$", fontsize=fs) - pl.tight_layout() - ax3.set_aspect('auto') - pl.show() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_fgw_002.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_fgw.py:128: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - -Compute FGW/GW ---------- - - -.. code-block:: default - - alpha = 1e-3 - - ot.tic() - Gwg, logw = fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=alpha, verbose=True, log=True) - ot.toc() - - #%reload_ext WGW - Gg, log = gromov_wasserstein(C1, C2, p, q, loss_fun='square_loss', verbose=True, log=True) - - - - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - It. |Loss |Relative loss|Absolute loss - ------------------------------------------------ - 0|4.734412e+01|0.000000e+00|0.000000e+00 - 1|2.508254e+01|8.875326e-01|2.226158e+01 - 2|2.189327e+01|1.456740e-01|3.189279e+00 - 3|2.189327e+01|0.000000e+00|0.000000e+00 - Elapsed time : 0.0023026466369628906 s - It. |Loss |Relative loss|Absolute loss - ------------------------------------------------ - 0|4.683978e+04|0.000000e+00|0.000000e+00 - 1|3.860061e+04|2.134468e-01|8.239175e+03 - 2|2.182948e+04|7.682787e-01|1.677113e+04 - 3|2.182948e+04|0.000000e+00|0.000000e+00 - - - - -Visualize transport matrices ---------- - - -.. code-block:: default - - cmap = 'Blues' - fs = 15 - pl.figure(2, (13, 5)) - pl.clf() - pl.subplot(1, 3, 1) - pl.imshow(Got, cmap=cmap, interpolation='nearest') - #pl.xlabel("$y$",fontsize=fs) - pl.ylabel("$i$", fontsize=fs) - pl.xticks(()) - - pl.title('Wasserstein ($M$ only)') - - pl.subplot(1, 3, 2) - pl.imshow(Gg, cmap=cmap, interpolation='nearest') - pl.title('Gromov ($C_1,C_2$ only)') - pl.xticks(()) - pl.subplot(1, 3, 3) - pl.imshow(Gwg, cmap=cmap, interpolation='nearest') - pl.title('FGW ($M+C_1,C_2$)') - - pl.xlabel("$j$", fontsize=fs) - pl.ylabel("$i$", fontsize=fs) - - pl.tight_layout() - pl.show() - - - -.. image:: /auto_examples/images/sphx_glr_plot_fgw_003.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_fgw.py:173: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 1.184 seconds) - - -.. _sphx_glr_download_auto_examples_plot_fgw.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_fgw.py <plot_fgw.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: plot_fgw.ipynb <plot_fgw.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ diff --git a/docs/source/auto_examples/plot_free_support_barycenter.ipynb b/docs/source/auto_examples/plot_free_support_barycenter.ipynb deleted file mode 100644 index 25ce60f..0000000 --- a/docs/source/auto_examples/plot_free_support_barycenter.ipynb +++ /dev/null @@ -1,108 +0,0 @@ -{ - "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_i * 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": "3.6.9" - } - }, - "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 deleted file mode 100644 index 64b89e4..0000000 --- a/docs/source/auto_examples/plot_free_support_barycenter.py +++ /dev/null @@ -1,69 +0,0 @@ -# -*- 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_i * 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 deleted file mode 100644 index f349604..0000000 --- a/docs/source/auto_examples/plot_free_support_barycenter.rst +++ /dev/null @@ -1,162 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_free_support_barycenter.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _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:: default - - - # 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:: default - - 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:: default - - - 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:: default - - - 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_i * 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 - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_free_support_barycenter.py:69: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 0.080 seconds) - - -.. _sphx_glr_download_auto_examples_plot_free_support_barycenter.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_free_support_barycenter.py <plot_free_support_barycenter.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :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.github.io>`_ diff --git a/docs/source/auto_examples/plot_gromov.ipynb b/docs/source/auto_examples/plot_gromov.ipynb deleted file mode 100644 index e5a88e7..0000000 --- a/docs/source/auto_examples/plot_gromov.ipynb +++ /dev/null @@ -1,126 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n# Gromov-Wasserstein example\n\n\nThis example is designed to show how to use the Gromov-Wassertsein distance\ncomputation in POT.\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Author: Erwan Vautier <erwan.vautier@gmail.com>\n# Nicolas Courty <ncourty@irisa.fr>\n#\n# License: MIT License\n\nimport scipy as sp\nimport numpy as np\nimport matplotlib.pylab as pl\nfrom mpl_toolkits.mplot3d import Axes3D # noqa\nimport ot" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Sample two Gaussian distributions (2D and 3D)\n---------------------------------------------\n\nThe Gromov-Wasserstein distance allows to compute distances with samples that\ndo not belong to the same metric space. For demonstration purpose, we sample\ntwo Gaussian distributions in 2- and 3-dimensional spaces.\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "n_samples = 30 # nb samples\n\nmu_s = np.array([0, 0])\ncov_s = np.array([[1, 0], [0, 1]])\n\nmu_t = np.array([4, 4, 4])\ncov_t = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])\n\n\nxs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s)\nP = sp.linalg.sqrtm(cov_t)\nxt = np.random.randn(n_samples, 3).dot(P) + mu_t" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Plotting the distributions\n--------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "fig = pl.figure()\nax1 = fig.add_subplot(121)\nax1.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\nax2 = fig.add_subplot(122, projection='3d')\nax2.scatter(xt[:, 0], xt[:, 1], xt[:, 2], color='r')\npl.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Compute distance kernels, normalize them and then display\n---------------------------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "C1 = sp.spatial.distance.cdist(xs, xs)\nC2 = sp.spatial.distance.cdist(xt, xt)\n\nC1 /= C1.max()\nC2 /= C2.max()\n\npl.figure()\npl.subplot(121)\npl.imshow(C1)\npl.subplot(122)\npl.imshow(C2)\npl.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Compute Gromov-Wasserstein plans and distance\n---------------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "p = ot.unif(n_samples)\nq = ot.unif(n_samples)\n\ngw0, log0 = ot.gromov.gromov_wasserstein(\n C1, C2, p, q, 'square_loss', verbose=True, log=True)\n\ngw, log = ot.gromov.entropic_gromov_wasserstein(\n C1, C2, p, q, 'square_loss', epsilon=5e-4, log=True, verbose=True)\n\n\nprint('Gromov-Wasserstein distances: ' + str(log0['gw_dist']))\nprint('Entropic Gromov-Wasserstein distances: ' + str(log['gw_dist']))\n\n\npl.figure(1, (10, 5))\n\npl.subplot(1, 2, 1)\npl.imshow(gw0, cmap='jet')\npl.title('Gromov Wasserstein')\n\npl.subplot(1, 2, 2)\npl.imshow(gw, cmap='jet')\npl.title('Entropic Gromov Wasserstein')\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": "3.6.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_gromov.py b/docs/source/auto_examples/plot_gromov.py deleted file mode 100644 index deb2f86..0000000 --- a/docs/source/auto_examples/plot_gromov.py +++ /dev/null @@ -1,106 +0,0 @@ -# -*- coding: utf-8 -*-
-"""
-==========================
-Gromov-Wasserstein example
-==========================
-
-This example is designed to show how to use the Gromov-Wassertsein distance
-computation in POT.
-"""
-
-# Author: Erwan Vautier <erwan.vautier@gmail.com>
-# Nicolas Courty <ncourty@irisa.fr>
-#
-# License: MIT License
-
-import scipy as sp
-import numpy as np
-import matplotlib.pylab as pl
-from mpl_toolkits.mplot3d import Axes3D # noqa
-import ot
-
-#############################################################################
-#
-# Sample two Gaussian distributions (2D and 3D)
-# ---------------------------------------------
-#
-# The Gromov-Wasserstein distance allows to compute distances with samples that
-# do not belong to the same metric space. For demonstration purpose, we sample
-# two Gaussian distributions in 2- and 3-dimensional spaces.
-
-
-n_samples = 30 # nb samples
-
-mu_s = np.array([0, 0])
-cov_s = np.array([[1, 0], [0, 1]])
-
-mu_t = np.array([4, 4, 4])
-cov_t = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
-
-
-xs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s)
-P = sp.linalg.sqrtm(cov_t)
-xt = np.random.randn(n_samples, 3).dot(P) + mu_t
-
-#############################################################################
-#
-# Plotting the distributions
-# --------------------------
-
-
-fig = pl.figure()
-ax1 = fig.add_subplot(121)
-ax1.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
-ax2 = fig.add_subplot(122, projection='3d')
-ax2.scatter(xt[:, 0], xt[:, 1], xt[:, 2], color='r')
-pl.show()
-
-#############################################################################
-#
-# Compute distance kernels, normalize them and then display
-# ---------------------------------------------------------
-
-
-C1 = sp.spatial.distance.cdist(xs, xs)
-C2 = sp.spatial.distance.cdist(xt, xt)
-
-C1 /= C1.max()
-C2 /= C2.max()
-
-pl.figure()
-pl.subplot(121)
-pl.imshow(C1)
-pl.subplot(122)
-pl.imshow(C2)
-pl.show()
-
-#############################################################################
-#
-# Compute Gromov-Wasserstein plans and distance
-# ---------------------------------------------
-
-p = ot.unif(n_samples)
-q = ot.unif(n_samples)
-
-gw0, log0 = ot.gromov.gromov_wasserstein(
- C1, C2, p, q, 'square_loss', verbose=True, log=True)
-
-gw, log = ot.gromov.entropic_gromov_wasserstein(
- C1, C2, p, q, 'square_loss', epsilon=5e-4, log=True, verbose=True)
-
-
-print('Gromov-Wasserstein distances: ' + str(log0['gw_dist']))
-print('Entropic Gromov-Wasserstein distances: ' + str(log['gw_dist']))
-
-
-pl.figure(1, (10, 5))
-
-pl.subplot(1, 2, 1)
-pl.imshow(gw0, cmap='jet')
-pl.title('Gromov Wasserstein')
-
-pl.subplot(1, 2, 2)
-pl.imshow(gw, cmap='jet')
-pl.title('Entropic Gromov Wasserstein')
-
-pl.show()
diff --git a/docs/source/auto_examples/plot_gromov.rst b/docs/source/auto_examples/plot_gromov.rst deleted file mode 100644 index 13d0d09..0000000 --- a/docs/source/auto_examples/plot_gromov.rst +++ /dev/null @@ -1,245 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_gromov.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_gromov.py: - - -========================== -Gromov-Wasserstein example -========================== - -This example is designed to show how to use the Gromov-Wassertsein distance -computation in POT. - - -.. code-block:: default - - - # Author: Erwan Vautier <erwan.vautier@gmail.com> - # Nicolas Courty <ncourty@irisa.fr> - # - # License: MIT License - - import scipy as sp - import numpy as np - import matplotlib.pylab as pl - from mpl_toolkits.mplot3d import Axes3D # noqa - import ot - - - - - - - - -Sample two Gaussian distributions (2D and 3D) ---------------------------------------------- - -The Gromov-Wasserstein distance allows to compute distances with samples that -do not belong to the same metric space. For demonstration purpose, we sample -two Gaussian distributions in 2- and 3-dimensional spaces. - - -.. code-block:: default - - - - n_samples = 30 # nb samples - - mu_s = np.array([0, 0]) - cov_s = np.array([[1, 0], [0, 1]]) - - mu_t = np.array([4, 4, 4]) - cov_t = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]]) - - - xs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s) - P = sp.linalg.sqrtm(cov_t) - xt = np.random.randn(n_samples, 3).dot(P) + mu_t - - - - - - - - -Plotting the distributions --------------------------- - - -.. code-block:: default - - - - fig = pl.figure() - ax1 = fig.add_subplot(121) - ax1.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') - ax2 = fig.add_subplot(122, projection='3d') - ax2.scatter(xt[:, 0], xt[:, 1], xt[:, 2], color='r') - pl.show() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_gromov_001.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_gromov.py:56: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - -Compute distance kernels, normalize them and then display ---------------------------------------------------------- - - -.. code-block:: default - - - - C1 = sp.spatial.distance.cdist(xs, xs) - C2 = sp.spatial.distance.cdist(xt, xt) - - C1 /= C1.max() - C2 /= C2.max() - - pl.figure() - pl.subplot(121) - pl.imshow(C1) - pl.subplot(122) - pl.imshow(C2) - pl.show() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_gromov_002.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_gromov.py:75: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - -Compute Gromov-Wasserstein plans and distance ---------------------------------------------- - - -.. code-block:: default - - - p = ot.unif(n_samples) - q = ot.unif(n_samples) - - gw0, log0 = ot.gromov.gromov_wasserstein( - C1, C2, p, q, 'square_loss', verbose=True, log=True) - - gw, log = ot.gromov.entropic_gromov_wasserstein( - C1, C2, p, q, 'square_loss', epsilon=5e-4, log=True, verbose=True) - - - print('Gromov-Wasserstein distances: ' + str(log0['gw_dist'])) - print('Entropic Gromov-Wasserstein distances: ' + str(log['gw_dist'])) - - - pl.figure(1, (10, 5)) - - pl.subplot(1, 2, 1) - pl.imshow(gw0, cmap='jet') - pl.title('Gromov Wasserstein') - - pl.subplot(1, 2, 2) - pl.imshow(gw, cmap='jet') - pl.title('Entropic Gromov Wasserstein') - - pl.show() - - - -.. image:: /auto_examples/images/sphx_glr_plot_gromov_003.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - It. |Loss |Relative loss|Absolute loss - ------------------------------------------------ - 0|8.019265e-02|0.000000e+00|0.000000e+00 - 1|3.734805e-02|1.147171e+00|4.284460e-02 - 2|2.923853e-02|2.773572e-01|8.109516e-03 - 3|2.478957e-02|1.794691e-01|4.448961e-03 - 4|2.444720e-02|1.400444e-02|3.423693e-04 - 5|2.444720e-02|0.000000e+00|0.000000e+00 - It. |Err - ------------------- - 0|8.259147e-02| - 10|6.113732e-04| - 20|1.650651e-08| - 30|5.671192e-12| - Gromov-Wasserstein distances: 0.024447198979060496 - Entropic Gromov-Wasserstein distances: 0.02488439679981518 - /home/rflamary/PYTHON/POT/examples/plot_gromov.py:106: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 0.999 seconds) - - -.. _sphx_glr_download_auto_examples_plot_gromov.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_gromov.py <plot_gromov.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: plot_gromov.ipynb <plot_gromov.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ diff --git a/docs/source/auto_examples/plot_gromov_barycenter.ipynb b/docs/source/auto_examples/plot_gromov_barycenter.ipynb deleted file mode 100644 index 17ba374..0000000 --- a/docs/source/auto_examples/plot_gromov_barycenter.ipynb +++ /dev/null @@ -1,126 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n# Gromov-Wasserstein Barycenter example\n\n\nThis example is designed to show how to use the Gromov-Wasserstein distance\ncomputation in POT.\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Author: Erwan Vautier <erwan.vautier@gmail.com>\n# Nicolas Courty <ncourty@irisa.fr>\n#\n# License: MIT License\n\n\nimport numpy as np\nimport scipy as sp\n\nimport matplotlib.pylab as pl\nfrom sklearn import manifold\nfrom sklearn.decomposition import PCA\n\nimport ot" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Smacof MDS\n----------\n\nThis function allows to find an embedding of points given a dissimilarity matrix\nthat will be given by the output of the algorithm\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "def smacof_mds(C, dim, max_iter=3000, eps=1e-9):\n \"\"\"\n Returns an interpolated point cloud following the dissimilarity matrix C\n using SMACOF multidimensional scaling (MDS) in specific dimensionned\n target space\n\n Parameters\n ----------\n C : ndarray, shape (ns, ns)\n dissimilarity matrix\n dim : int\n dimension of the targeted space\n max_iter : int\n Maximum number of iterations of the SMACOF algorithm for a single run\n eps : float\n relative tolerance w.r.t stress to declare converge\n\n Returns\n -------\n npos : ndarray, shape (R, dim)\n Embedded coordinates of the interpolated point cloud (defined with\n one isometry)\n \"\"\"\n\n rng = np.random.RandomState(seed=3)\n\n mds = manifold.MDS(\n dim,\n max_iter=max_iter,\n eps=1e-9,\n dissimilarity='precomputed',\n n_init=1)\n pos = mds.fit(C).embedding_\n\n nmds = manifold.MDS(\n 2,\n max_iter=max_iter,\n eps=1e-9,\n dissimilarity=\"precomputed\",\n random_state=rng,\n n_init=1)\n npos = nmds.fit_transform(C, init=pos)\n\n return npos" - ] - }, - { - "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": [ - "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\nsquare = pl.imread('../data/square.png').astype(np.float64)[:, :, 2] / 256\ncross = pl.imread('../data/cross.png').astype(np.float64)[:, :, 2] / 256\ntriangle = pl.imread('../data/triangle.png').astype(np.float64)[:, :, 2] / 256\nstar = pl.imread('../data/star.png').astype(np.float64)[:, :, 2] / 256\n\nshapes = [square, cross, triangle, star]\n\nS = 4\nxs = [[] for i in range(S)]\n\n\nfor nb in range(4):\n for i in range(8):\n for j in range(8):\n if shapes[nb][i, j] < 0.95:\n xs[nb].append([j, 8 - i])\n\nxs = np.array([np.array(xs[0]), np.array(xs[1]),\n np.array(xs[2]), np.array(xs[3])])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Barycenter computation\n----------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "ns = [len(xs[s]) for s in range(S)]\nn_samples = 30\n\n\"\"\"Compute all distances matrices for the four shapes\"\"\"\nCs = [sp.spatial.distance.cdist(xs[s], xs[s]) for s in range(S)]\nCs = [cs / cs.max() for cs in Cs]\n\nps = [ot.unif(ns[s]) for s in range(S)]\np = ot.unif(n_samples)\n\n\nlambdast = [[float(i) / 3, float(3 - i) / 3] for i in [1, 2]]\n\nCt01 = [0 for i in range(2)]\nfor i in range(2):\n Ct01[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[0], Cs[1]],\n [ps[0], ps[1]\n ], p, lambdast[i], 'square_loss', # 5e-4,\n max_iter=100, tol=1e-3)\n\nCt02 = [0 for i in range(2)]\nfor i in range(2):\n Ct02[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[0], Cs[2]],\n [ps[0], ps[2]\n ], p, lambdast[i], 'square_loss', # 5e-4,\n max_iter=100, tol=1e-3)\n\nCt13 = [0 for i in range(2)]\nfor i in range(2):\n Ct13[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[1], Cs[3]],\n [ps[1], ps[3]\n ], p, lambdast[i], 'square_loss', # 5e-4,\n max_iter=100, tol=1e-3)\n\nCt23 = [0 for i in range(2)]\nfor i in range(2):\n Ct23[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[2], Cs[3]],\n [ps[2], ps[3]\n ], p, lambdast[i], 'square_loss', # 5e-4,\n max_iter=100, tol=1e-3)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Visualization\n-------------\n\nThe PCA helps in getting consistency between the rotations\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "clf = PCA(n_components=2)\nnpos = [0, 0, 0, 0]\nnpos = [smacof_mds(Cs[s], 2) for s in range(S)]\n\nnpost01 = [0, 0]\nnpost01 = [smacof_mds(Ct01[s], 2) for s in range(2)]\nnpost01 = [clf.fit_transform(npost01[s]) for s in range(2)]\n\nnpost02 = [0, 0]\nnpost02 = [smacof_mds(Ct02[s], 2) for s in range(2)]\nnpost02 = [clf.fit_transform(npost02[s]) for s in range(2)]\n\nnpost13 = [0, 0]\nnpost13 = [smacof_mds(Ct13[s], 2) for s in range(2)]\nnpost13 = [clf.fit_transform(npost13[s]) for s in range(2)]\n\nnpost23 = [0, 0]\nnpost23 = [smacof_mds(Ct23[s], 2) for s in range(2)]\nnpost23 = [clf.fit_transform(npost23[s]) for s in range(2)]\n\n\nfig = pl.figure(figsize=(10, 10))\n\nax1 = pl.subplot2grid((4, 4), (0, 0))\npl.xlim((-1, 1))\npl.ylim((-1, 1))\nax1.scatter(npos[0][:, 0], npos[0][:, 1], color='r')\n\nax2 = pl.subplot2grid((4, 4), (0, 1))\npl.xlim((-1, 1))\npl.ylim((-1, 1))\nax2.scatter(npost01[1][:, 0], npost01[1][:, 1], color='b')\n\nax3 = pl.subplot2grid((4, 4), (0, 2))\npl.xlim((-1, 1))\npl.ylim((-1, 1))\nax3.scatter(npost01[0][:, 0], npost01[0][:, 1], color='b')\n\nax4 = pl.subplot2grid((4, 4), (0, 3))\npl.xlim((-1, 1))\npl.ylim((-1, 1))\nax4.scatter(npos[1][:, 0], npos[1][:, 1], color='r')\n\nax5 = pl.subplot2grid((4, 4), (1, 0))\npl.xlim((-1, 1))\npl.ylim((-1, 1))\nax5.scatter(npost02[1][:, 0], npost02[1][:, 1], color='b')\n\nax6 = pl.subplot2grid((4, 4), (1, 3))\npl.xlim((-1, 1))\npl.ylim((-1, 1))\nax6.scatter(npost13[1][:, 0], npost13[1][:, 1], color='b')\n\nax7 = pl.subplot2grid((4, 4), (2, 0))\npl.xlim((-1, 1))\npl.ylim((-1, 1))\nax7.scatter(npost02[0][:, 0], npost02[0][:, 1], color='b')\n\nax8 = pl.subplot2grid((4, 4), (2, 3))\npl.xlim((-1, 1))\npl.ylim((-1, 1))\nax8.scatter(npost13[0][:, 0], npost13[0][:, 1], color='b')\n\nax9 = pl.subplot2grid((4, 4), (3, 0))\npl.xlim((-1, 1))\npl.ylim((-1, 1))\nax9.scatter(npos[2][:, 0], npos[2][:, 1], color='r')\n\nax10 = pl.subplot2grid((4, 4), (3, 1))\npl.xlim((-1, 1))\npl.ylim((-1, 1))\nax10.scatter(npost23[1][:, 0], npost23[1][:, 1], color='b')\n\nax11 = pl.subplot2grid((4, 4), (3, 2))\npl.xlim((-1, 1))\npl.ylim((-1, 1))\nax11.scatter(npost23[0][:, 0], npost23[0][:, 1], color='b')\n\nax12 = pl.subplot2grid((4, 4), (3, 3))\npl.xlim((-1, 1))\npl.ylim((-1, 1))\nax12.scatter(npos[3][:, 0], npos[3][:, 1], color='r')" - ] - } - ], - "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": "3.6.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_gromov_barycenter.py b/docs/source/auto_examples/plot_gromov_barycenter.py deleted file mode 100644 index 101c6c5..0000000 --- a/docs/source/auto_examples/plot_gromov_barycenter.py +++ /dev/null @@ -1,247 +0,0 @@ -# -*- coding: utf-8 -*-
-"""
-=====================================
-Gromov-Wasserstein Barycenter example
-=====================================
-
-This example is designed to show how to use the Gromov-Wasserstein distance
-computation in POT.
-"""
-
-# Author: Erwan Vautier <erwan.vautier@gmail.com>
-# Nicolas Courty <ncourty@irisa.fr>
-#
-# License: MIT License
-
-
-import numpy as np
-import scipy as sp
-
-import matplotlib.pylab as pl
-from sklearn import manifold
-from sklearn.decomposition import PCA
-
-import ot
-
-##############################################################################
-# Smacof MDS
-# ----------
-#
-# This function allows to find an embedding of points given a dissimilarity matrix
-# that will be given by the output of the algorithm
-
-
-def smacof_mds(C, dim, max_iter=3000, eps=1e-9):
- """
- Returns an interpolated point cloud following the dissimilarity matrix C
- using SMACOF multidimensional scaling (MDS) in specific dimensionned
- target space
-
- Parameters
- ----------
- C : ndarray, shape (ns, ns)
- dissimilarity matrix
- dim : int
- dimension of the targeted space
- max_iter : int
- Maximum number of iterations of the SMACOF algorithm for a single run
- eps : float
- relative tolerance w.r.t stress to declare converge
-
- Returns
- -------
- npos : ndarray, shape (R, dim)
- Embedded coordinates of the interpolated point cloud (defined with
- one isometry)
- """
-
- rng = np.random.RandomState(seed=3)
-
- mds = manifold.MDS(
- dim,
- max_iter=max_iter,
- eps=1e-9,
- dissimilarity='precomputed',
- n_init=1)
- pos = mds.fit(C).embedding_
-
- nmds = manifold.MDS(
- 2,
- max_iter=max_iter,
- eps=1e-9,
- dissimilarity="precomputed",
- random_state=rng,
- n_init=1)
- npos = nmds.fit_transform(C, init=pos)
-
- return npos
-
-
-##############################################################################
-# Data preparation
-# ----------------
-#
-# The four distributions are constructed from 4 simple images
-
-
-def im2mat(I):
- """Converts and image to matrix (one pixel per line)"""
- return I.reshape((I.shape[0] * I.shape[1], I.shape[2]))
-
-
-square = pl.imread('../data/square.png').astype(np.float64)[:, :, 2] / 256
-cross = pl.imread('../data/cross.png').astype(np.float64)[:, :, 2] / 256
-triangle = pl.imread('../data/triangle.png').astype(np.float64)[:, :, 2] / 256
-star = pl.imread('../data/star.png').astype(np.float64)[:, :, 2] / 256
-
-shapes = [square, cross, triangle, star]
-
-S = 4
-xs = [[] for i in range(S)]
-
-
-for nb in range(4):
- for i in range(8):
- for j in range(8):
- if shapes[nb][i, j] < 0.95:
- xs[nb].append([j, 8 - i])
-
-xs = np.array([np.array(xs[0]), np.array(xs[1]),
- np.array(xs[2]), np.array(xs[3])])
-
-##############################################################################
-# Barycenter computation
-# ----------------------
-
-
-ns = [len(xs[s]) for s in range(S)]
-n_samples = 30
-
-"""Compute all distances matrices for the four shapes"""
-Cs = [sp.spatial.distance.cdist(xs[s], xs[s]) for s in range(S)]
-Cs = [cs / cs.max() for cs in Cs]
-
-ps = [ot.unif(ns[s]) for s in range(S)]
-p = ot.unif(n_samples)
-
-
-lambdast = [[float(i) / 3, float(3 - i) / 3] for i in [1, 2]]
-
-Ct01 = [0 for i in range(2)]
-for i in range(2):
- Ct01[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[0], Cs[1]],
- [ps[0], ps[1]
- ], p, lambdast[i], 'square_loss', # 5e-4,
- max_iter=100, tol=1e-3)
-
-Ct02 = [0 for i in range(2)]
-for i in range(2):
- Ct02[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[0], Cs[2]],
- [ps[0], ps[2]
- ], p, lambdast[i], 'square_loss', # 5e-4,
- max_iter=100, tol=1e-3)
-
-Ct13 = [0 for i in range(2)]
-for i in range(2):
- Ct13[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[1], Cs[3]],
- [ps[1], ps[3]
- ], p, lambdast[i], 'square_loss', # 5e-4,
- max_iter=100, tol=1e-3)
-
-Ct23 = [0 for i in range(2)]
-for i in range(2):
- Ct23[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[2], Cs[3]],
- [ps[2], ps[3]
- ], p, lambdast[i], 'square_loss', # 5e-4,
- max_iter=100, tol=1e-3)
-
-
-##############################################################################
-# Visualization
-# -------------
-#
-# The PCA helps in getting consistency between the rotations
-
-
-clf = PCA(n_components=2)
-npos = [0, 0, 0, 0]
-npos = [smacof_mds(Cs[s], 2) for s in range(S)]
-
-npost01 = [0, 0]
-npost01 = [smacof_mds(Ct01[s], 2) for s in range(2)]
-npost01 = [clf.fit_transform(npost01[s]) for s in range(2)]
-
-npost02 = [0, 0]
-npost02 = [smacof_mds(Ct02[s], 2) for s in range(2)]
-npost02 = [clf.fit_transform(npost02[s]) for s in range(2)]
-
-npost13 = [0, 0]
-npost13 = [smacof_mds(Ct13[s], 2) for s in range(2)]
-npost13 = [clf.fit_transform(npost13[s]) for s in range(2)]
-
-npost23 = [0, 0]
-npost23 = [smacof_mds(Ct23[s], 2) for s in range(2)]
-npost23 = [clf.fit_transform(npost23[s]) for s in range(2)]
-
-
-fig = pl.figure(figsize=(10, 10))
-
-ax1 = pl.subplot2grid((4, 4), (0, 0))
-pl.xlim((-1, 1))
-pl.ylim((-1, 1))
-ax1.scatter(npos[0][:, 0], npos[0][:, 1], color='r')
-
-ax2 = pl.subplot2grid((4, 4), (0, 1))
-pl.xlim((-1, 1))
-pl.ylim((-1, 1))
-ax2.scatter(npost01[1][:, 0], npost01[1][:, 1], color='b')
-
-ax3 = pl.subplot2grid((4, 4), (0, 2))
-pl.xlim((-1, 1))
-pl.ylim((-1, 1))
-ax3.scatter(npost01[0][:, 0], npost01[0][:, 1], color='b')
-
-ax4 = pl.subplot2grid((4, 4), (0, 3))
-pl.xlim((-1, 1))
-pl.ylim((-1, 1))
-ax4.scatter(npos[1][:, 0], npos[1][:, 1], color='r')
-
-ax5 = pl.subplot2grid((4, 4), (1, 0))
-pl.xlim((-1, 1))
-pl.ylim((-1, 1))
-ax5.scatter(npost02[1][:, 0], npost02[1][:, 1], color='b')
-
-ax6 = pl.subplot2grid((4, 4), (1, 3))
-pl.xlim((-1, 1))
-pl.ylim((-1, 1))
-ax6.scatter(npost13[1][:, 0], npost13[1][:, 1], color='b')
-
-ax7 = pl.subplot2grid((4, 4), (2, 0))
-pl.xlim((-1, 1))
-pl.ylim((-1, 1))
-ax7.scatter(npost02[0][:, 0], npost02[0][:, 1], color='b')
-
-ax8 = pl.subplot2grid((4, 4), (2, 3))
-pl.xlim((-1, 1))
-pl.ylim((-1, 1))
-ax8.scatter(npost13[0][:, 0], npost13[0][:, 1], color='b')
-
-ax9 = pl.subplot2grid((4, 4), (3, 0))
-pl.xlim((-1, 1))
-pl.ylim((-1, 1))
-ax9.scatter(npos[2][:, 0], npos[2][:, 1], color='r')
-
-ax10 = pl.subplot2grid((4, 4), (3, 1))
-pl.xlim((-1, 1))
-pl.ylim((-1, 1))
-ax10.scatter(npost23[1][:, 0], npost23[1][:, 1], color='b')
-
-ax11 = pl.subplot2grid((4, 4), (3, 2))
-pl.xlim((-1, 1))
-pl.ylim((-1, 1))
-ax11.scatter(npost23[0][:, 0], npost23[0][:, 1], color='b')
-
-ax12 = pl.subplot2grid((4, 4), (3, 3))
-pl.xlim((-1, 1))
-pl.ylim((-1, 1))
-ax12.scatter(npos[3][:, 0], npos[3][:, 1], color='r')
diff --git a/docs/source/auto_examples/plot_gromov_barycenter.rst b/docs/source/auto_examples/plot_gromov_barycenter.rst deleted file mode 100644 index 995cca7..0000000 --- a/docs/source/auto_examples/plot_gromov_barycenter.rst +++ /dev/null @@ -1,349 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_gromov_barycenter.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_gromov_barycenter.py: - - -===================================== -Gromov-Wasserstein Barycenter example -===================================== - -This example is designed to show how to use the Gromov-Wasserstein distance -computation in POT. - - -.. code-block:: default - - - # Author: Erwan Vautier <erwan.vautier@gmail.com> - # Nicolas Courty <ncourty@irisa.fr> - # - # License: MIT License - - - import numpy as np - import scipy as sp - - import matplotlib.pylab as pl - from sklearn import manifold - from sklearn.decomposition import PCA - - import ot - - - - - - - - -Smacof MDS ----------- - -This function allows to find an embedding of points given a dissimilarity matrix -that will be given by the output of the algorithm - - -.. code-block:: default - - - - def smacof_mds(C, dim, max_iter=3000, eps=1e-9): - """ - Returns an interpolated point cloud following the dissimilarity matrix C - using SMACOF multidimensional scaling (MDS) in specific dimensionned - target space - - Parameters - ---------- - C : ndarray, shape (ns, ns) - dissimilarity matrix - dim : int - dimension of the targeted space - max_iter : int - Maximum number of iterations of the SMACOF algorithm for a single run - eps : float - relative tolerance w.r.t stress to declare converge - - Returns - ------- - npos : ndarray, shape (R, dim) - Embedded coordinates of the interpolated point cloud (defined with - one isometry) - """ - - rng = np.random.RandomState(seed=3) - - mds = manifold.MDS( - dim, - max_iter=max_iter, - eps=1e-9, - dissimilarity='precomputed', - n_init=1) - pos = mds.fit(C).embedding_ - - nmds = manifold.MDS( - 2, - max_iter=max_iter, - eps=1e-9, - dissimilarity="precomputed", - random_state=rng, - n_init=1) - npos = nmds.fit_transform(C, init=pos) - - return npos - - - - - - - - - -Data preparation ----------------- - -The four distributions are constructed from 4 simple images - - -.. code-block:: default - - - - def im2mat(I): - """Converts and image to matrix (one pixel per line)""" - return I.reshape((I.shape[0] * I.shape[1], I.shape[2])) - - - square = pl.imread('../data/square.png').astype(np.float64)[:, :, 2] / 256 - cross = pl.imread('../data/cross.png').astype(np.float64)[:, :, 2] / 256 - triangle = pl.imread('../data/triangle.png').astype(np.float64)[:, :, 2] / 256 - star = pl.imread('../data/star.png').astype(np.float64)[:, :, 2] / 256 - - shapes = [square, cross, triangle, star] - - S = 4 - xs = [[] for i in range(S)] - - - for nb in range(4): - for i in range(8): - for j in range(8): - if shapes[nb][i, j] < 0.95: - xs[nb].append([j, 8 - i]) - - xs = np.array([np.array(xs[0]), np.array(xs[1]), - np.array(xs[2]), np.array(xs[3])]) - - - - - - - - -Barycenter computation ----------------------- - - -.. code-block:: default - - - - ns = [len(xs[s]) for s in range(S)] - n_samples = 30 - - """Compute all distances matrices for the four shapes""" - Cs = [sp.spatial.distance.cdist(xs[s], xs[s]) for s in range(S)] - Cs = [cs / cs.max() for cs in Cs] - - ps = [ot.unif(ns[s]) for s in range(S)] - p = ot.unif(n_samples) - - - lambdast = [[float(i) / 3, float(3 - i) / 3] for i in [1, 2]] - - Ct01 = [0 for i in range(2)] - for i in range(2): - Ct01[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[0], Cs[1]], - [ps[0], ps[1] - ], p, lambdast[i], 'square_loss', # 5e-4, - max_iter=100, tol=1e-3) - - Ct02 = [0 for i in range(2)] - for i in range(2): - Ct02[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[0], Cs[2]], - [ps[0], ps[2] - ], p, lambdast[i], 'square_loss', # 5e-4, - max_iter=100, tol=1e-3) - - Ct13 = [0 for i in range(2)] - for i in range(2): - Ct13[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[1], Cs[3]], - [ps[1], ps[3] - ], p, lambdast[i], 'square_loss', # 5e-4, - max_iter=100, tol=1e-3) - - Ct23 = [0 for i in range(2)] - for i in range(2): - Ct23[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[2], Cs[3]], - [ps[2], ps[3] - ], p, lambdast[i], 'square_loss', # 5e-4, - max_iter=100, tol=1e-3) - - - - - - - - - -Visualization -------------- - -The PCA helps in getting consistency between the rotations - - -.. code-block:: default - - - - clf = PCA(n_components=2) - npos = [0, 0, 0, 0] - npos = [smacof_mds(Cs[s], 2) for s in range(S)] - - npost01 = [0, 0] - npost01 = [smacof_mds(Ct01[s], 2) for s in range(2)] - npost01 = [clf.fit_transform(npost01[s]) for s in range(2)] - - npost02 = [0, 0] - npost02 = [smacof_mds(Ct02[s], 2) for s in range(2)] - npost02 = [clf.fit_transform(npost02[s]) for s in range(2)] - - npost13 = [0, 0] - npost13 = [smacof_mds(Ct13[s], 2) for s in range(2)] - npost13 = [clf.fit_transform(npost13[s]) for s in range(2)] - - npost23 = [0, 0] - npost23 = [smacof_mds(Ct23[s], 2) for s in range(2)] - npost23 = [clf.fit_transform(npost23[s]) for s in range(2)] - - - fig = pl.figure(figsize=(10, 10)) - - ax1 = pl.subplot2grid((4, 4), (0, 0)) - pl.xlim((-1, 1)) - pl.ylim((-1, 1)) - ax1.scatter(npos[0][:, 0], npos[0][:, 1], color='r') - - ax2 = pl.subplot2grid((4, 4), (0, 1)) - pl.xlim((-1, 1)) - pl.ylim((-1, 1)) - ax2.scatter(npost01[1][:, 0], npost01[1][:, 1], color='b') - - ax3 = pl.subplot2grid((4, 4), (0, 2)) - pl.xlim((-1, 1)) - pl.ylim((-1, 1)) - ax3.scatter(npost01[0][:, 0], npost01[0][:, 1], color='b') - - ax4 = pl.subplot2grid((4, 4), (0, 3)) - pl.xlim((-1, 1)) - pl.ylim((-1, 1)) - ax4.scatter(npos[1][:, 0], npos[1][:, 1], color='r') - - ax5 = pl.subplot2grid((4, 4), (1, 0)) - pl.xlim((-1, 1)) - pl.ylim((-1, 1)) - ax5.scatter(npost02[1][:, 0], npost02[1][:, 1], color='b') - - ax6 = pl.subplot2grid((4, 4), (1, 3)) - pl.xlim((-1, 1)) - pl.ylim((-1, 1)) - ax6.scatter(npost13[1][:, 0], npost13[1][:, 1], color='b') - - ax7 = pl.subplot2grid((4, 4), (2, 0)) - pl.xlim((-1, 1)) - pl.ylim((-1, 1)) - ax7.scatter(npost02[0][:, 0], npost02[0][:, 1], color='b') - - ax8 = pl.subplot2grid((4, 4), (2, 3)) - pl.xlim((-1, 1)) - pl.ylim((-1, 1)) - ax8.scatter(npost13[0][:, 0], npost13[0][:, 1], color='b') - - ax9 = pl.subplot2grid((4, 4), (3, 0)) - pl.xlim((-1, 1)) - pl.ylim((-1, 1)) - ax9.scatter(npos[2][:, 0], npos[2][:, 1], color='r') - - ax10 = pl.subplot2grid((4, 4), (3, 1)) - pl.xlim((-1, 1)) - pl.ylim((-1, 1)) - ax10.scatter(npost23[1][:, 0], npost23[1][:, 1], color='b') - - ax11 = pl.subplot2grid((4, 4), (3, 2)) - pl.xlim((-1, 1)) - pl.ylim((-1, 1)) - ax11.scatter(npost23[0][:, 0], npost23[0][:, 1], color='b') - - ax12 = pl.subplot2grid((4, 4), (3, 3)) - pl.xlim((-1, 1)) - pl.ylim((-1, 1)) - ax12.scatter(npos[3][:, 0], npos[3][:, 1], color='r') - - - -.. image:: /auto_examples/images/sphx_glr_plot_gromov_barycenter_001.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - - <matplotlib.collections.PathCollection object at 0x7ff28e5d6080> - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 1.747 seconds) - - -.. _sphx_glr_download_auto_examples_plot_gromov_barycenter.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_gromov_barycenter.py <plot_gromov_barycenter.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: plot_gromov_barycenter.ipynb <plot_gromov_barycenter.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ diff --git a/docs/source/auto_examples/plot_optim_OTreg.ipynb b/docs/source/auto_examples/plot_optim_OTreg.ipynb deleted file mode 100644 index 01e0689..0000000 --- a/docs/source/auto_examples/plot_optim_OTreg.ipynb +++ /dev/null @@ -1,144 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n# Regularized OT with generic solver\n\n\nIllustrates the use of the generic solver for regularized OT with\nuser-designed regularization term. It uses Conditional gradient as in [6] and\ngeneralized Conditional Gradient as proposed in [5][7].\n\n\n[5] N. Courty; R. Flamary; D. Tuia; A. Rakotomamonjy, Optimal Transport for\nDomain Adaptation, in IEEE Transactions on Pattern Analysis and Machine\nIntelligence , vol.PP, no.99, pp.1-1.\n\n[6] Ferradans, S., Papadakis, N., Peyr\u00e9, G., & Aujol, J. F. (2014).\nRegularized discrete optimal transport. SIAM Journal on Imaging Sciences,\n7(3), 1853-1882.\n\n[7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015). Generalized\nconditional gradient: analysis of convergence and applications.\narXiv preprint arXiv:1510.06567.\n\n\n\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "import numpy as np\nimport matplotlib.pylab as pl\nimport ot\nimport ot.plot" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Generate data\n-------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "n = 100 # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\na = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std\nb = ot.datasets.make_1D_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": [ - "Solve EMD\n---------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "G0 = 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 EMD with Frobenius norm regularization\n--------------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "def f(G):\n return 0.5 * np.sum(G**2)\n\n\ndef df(G):\n return G\n\n\nreg = 1e-1\n\nGl2 = ot.optim.cg(a, b, M, reg, f, df, verbose=True)\n\npl.figure(3)\not.plot.plot1D_mat(a, b, Gl2, 'OT matrix Frob. reg')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solve EMD with entropic regularization\n--------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "def f(G):\n return np.sum(G * np.log(G))\n\n\ndef df(G):\n return np.log(G) + 1.\n\n\nreg = 1e-3\n\nGe = ot.optim.cg(a, b, M, reg, f, df, verbose=True)\n\npl.figure(4, figsize=(5, 5))\not.plot.plot1D_mat(a, b, Ge, 'OT matrix Entrop. reg')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solve EMD with Frobenius norm + entropic regularization\n-------------------------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "def f(G):\n return 0.5 * np.sum(G**2)\n\n\ndef df(G):\n return G\n\n\nreg1 = 1e-3\nreg2 = 1e-1\n\nGel2 = ot.optim.gcg(a, b, M, reg1, reg2, f, df, verbose=True)\n\npl.figure(5, figsize=(5, 5))\not.plot.plot1D_mat(a, b, Gel2, 'OT entropic + matrix Frob. reg')\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": "3.6.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_optim_OTreg.py b/docs/source/auto_examples/plot_optim_OTreg.py deleted file mode 100644 index 2c58def..0000000 --- a/docs/source/auto_examples/plot_optim_OTreg.py +++ /dev/null @@ -1,129 +0,0 @@ -# -*- coding: utf-8 -*- -""" -================================== -Regularized OT with generic solver -================================== - -Illustrates the use of the generic solver for regularized OT with -user-designed regularization term. It uses Conditional gradient as in [6] and -generalized Conditional Gradient as proposed in [5][7]. - - -[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. - -[6] Ferradans, S., Papadakis, N., Peyré, G., & Aujol, J. F. (2014). -Regularized discrete optimal transport. SIAM Journal on Imaging Sciences, -7(3), 1853-1882. - -[7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015). Generalized -conditional gradient: analysis of convergence and applications. -arXiv preprint arXiv:1510.06567. - - - -""" - -import numpy as np -import matplotlib.pylab as pl -import ot -import ot.plot - -############################################################################## -# Generate data -# ------------- - -#%% parameters - -n = 100 # nb bins - -# bin positions -x = np.arange(n, dtype=np.float64) - -# Gaussian distributions -a = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std -b = ot.datasets.make_1D_gauss(n, m=60, s=10) - -# loss matrix -M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1))) -M /= M.max() - -############################################################################## -# 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 EMD with Frobenius norm regularization -# -------------------------------------------- - -#%% Example with Frobenius norm regularization - - -def f(G): - return 0.5 * np.sum(G**2) - - -def df(G): - return G - - -reg = 1e-1 - -Gl2 = ot.optim.cg(a, b, M, reg, f, df, verbose=True) - -pl.figure(3) -ot.plot.plot1D_mat(a, b, Gl2, 'OT matrix Frob. reg') - -############################################################################## -# Solve EMD with entropic regularization -# -------------------------------------- - -#%% Example with entropic regularization - - -def f(G): - return np.sum(G * np.log(G)) - - -def df(G): - return np.log(G) + 1. - - -reg = 1e-3 - -Ge = ot.optim.cg(a, b, M, reg, f, df, verbose=True) - -pl.figure(4, figsize=(5, 5)) -ot.plot.plot1D_mat(a, b, Ge, 'OT matrix Entrop. reg') - -############################################################################## -# Solve EMD with Frobenius norm + entropic regularization -# ------------------------------------------------------- - -#%% Example with Frobenius norm + entropic regularization with gcg - - -def f(G): - return 0.5 * np.sum(G**2) - - -def df(G): - return G - - -reg1 = 1e-3 -reg2 = 1e-1 - -Gel2 = ot.optim.gcg(a, b, M, reg1, reg2, f, df, verbose=True) - -pl.figure(5, figsize=(5, 5)) -ot.plot.plot1D_mat(a, b, Gel2, 'OT entropic + matrix Frob. reg') -pl.show() diff --git a/docs/source/auto_examples/plot_optim_OTreg.rst b/docs/source/auto_examples/plot_optim_OTreg.rst deleted file mode 100644 index cd5bcf5..0000000 --- a/docs/source/auto_examples/plot_optim_OTreg.rst +++ /dev/null @@ -1,593 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_optim_OTreg.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_optim_OTreg.py: - - -================================== -Regularized OT with generic solver -================================== - -Illustrates the use of the generic solver for regularized OT with -user-designed regularization term. It uses Conditional gradient as in [6] and -generalized Conditional Gradient as proposed in [5][7]. - - -[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. - -[6] Ferradans, S., Papadakis, N., Peyré, G., & Aujol, J. F. (2014). -Regularized discrete optimal transport. SIAM Journal on Imaging Sciences, -7(3), 1853-1882. - -[7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015). Generalized -conditional gradient: analysis of convergence and applications. -arXiv preprint arXiv:1510.06567. - - - - - -.. code-block:: default - - - import numpy as np - import matplotlib.pylab as pl - import ot - import ot.plot - - - - - - - - -Generate data -------------- - - -.. code-block:: default - - - n = 100 # nb bins - - # bin positions - x = np.arange(n, dtype=np.float64) - - # Gaussian distributions - a = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std - b = ot.datasets.make_1D_gauss(n, m=60, s=10) - - # loss matrix - M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1))) - M /= M.max() - - - - - - - - -Solve EMD ---------- - - -.. code-block:: default - - - 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_optim_OTreg_001.png - :class: sphx-glr-single-img - - - - - -Solve EMD with Frobenius norm regularization --------------------------------------------- - - -.. code-block:: default - - - - def f(G): - return 0.5 * np.sum(G**2) - - - def df(G): - return G - - - reg = 1e-1 - - Gl2 = ot.optim.cg(a, b, M, reg, f, df, verbose=True) - - pl.figure(3) - ot.plot.plot1D_mat(a, b, Gl2, 'OT matrix Frob. reg') - - - - -.. image:: /auto_examples/images/sphx_glr_plot_optim_OTreg_002.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - It. |Loss |Relative loss|Absolute loss - ------------------------------------------------ - 0|1.760578e-01|0.000000e+00|0.000000e+00 - 1|1.669467e-01|5.457501e-02|9.111116e-03 - 2|1.665639e-01|2.298130e-03|3.827855e-04 - 3|1.664378e-01|7.572776e-04|1.260396e-04 - 4|1.664077e-01|1.811855e-04|3.015066e-05 - 5|1.663912e-01|9.936787e-05|1.653393e-05 - 6|1.663852e-01|3.555826e-05|5.916369e-06 - 7|1.663814e-01|2.305693e-05|3.836245e-06 - 8|1.663785e-01|1.760450e-05|2.929009e-06 - 9|1.663767e-01|1.078011e-05|1.793559e-06 - 10|1.663751e-01|9.525192e-06|1.584755e-06 - 11|1.663737e-01|8.396466e-06|1.396951e-06 - 12|1.663727e-01|6.086938e-06|1.012700e-06 - 13|1.663720e-01|4.042609e-06|6.725769e-07 - 14|1.663713e-01|4.160914e-06|6.922568e-07 - 15|1.663707e-01|3.823502e-06|6.361187e-07 - 16|1.663702e-01|3.022440e-06|5.028438e-07 - 17|1.663697e-01|3.181249e-06|5.292634e-07 - 18|1.663692e-01|2.698532e-06|4.489527e-07 - 19|1.663687e-01|3.258253e-06|5.420712e-07 - It. |Loss |Relative loss|Absolute loss - ------------------------------------------------ - 20|1.663682e-01|2.741118e-06|4.560349e-07 - 21|1.663678e-01|2.624135e-06|4.365715e-07 - 22|1.663673e-01|2.645179e-06|4.400714e-07 - 23|1.663670e-01|1.957237e-06|3.256196e-07 - 24|1.663666e-01|2.261541e-06|3.762450e-07 - 25|1.663663e-01|1.851305e-06|3.079948e-07 - 26|1.663660e-01|1.942296e-06|3.231320e-07 - 27|1.663657e-01|2.092896e-06|3.481860e-07 - 28|1.663653e-01|1.924361e-06|3.201470e-07 - 29|1.663651e-01|1.625455e-06|2.704189e-07 - 30|1.663648e-01|1.641123e-06|2.730250e-07 - 31|1.663645e-01|1.566666e-06|2.606377e-07 - 32|1.663643e-01|1.338514e-06|2.226810e-07 - 33|1.663641e-01|1.222711e-06|2.034152e-07 - 34|1.663639e-01|1.221805e-06|2.032642e-07 - 35|1.663637e-01|1.440781e-06|2.396935e-07 - 36|1.663634e-01|1.520091e-06|2.528875e-07 - 37|1.663632e-01|1.288193e-06|2.143080e-07 - 38|1.663630e-01|1.123055e-06|1.868347e-07 - 39|1.663628e-01|1.024487e-06|1.704365e-07 - It. |Loss |Relative loss|Absolute loss - ------------------------------------------------ - 40|1.663627e-01|1.079606e-06|1.796061e-07 - 41|1.663625e-01|1.172093e-06|1.949922e-07 - 42|1.663623e-01|1.047880e-06|1.743277e-07 - 43|1.663621e-01|1.010577e-06|1.681217e-07 - 44|1.663619e-01|1.064438e-06|1.770820e-07 - 45|1.663618e-01|9.882375e-07|1.644049e-07 - 46|1.663616e-01|8.532647e-07|1.419505e-07 - 47|1.663615e-01|9.930189e-07|1.652001e-07 - 48|1.663613e-01|8.728955e-07|1.452161e-07 - 49|1.663612e-01|9.524214e-07|1.584459e-07 - 50|1.663610e-01|9.088418e-07|1.511958e-07 - 51|1.663609e-01|7.639430e-07|1.270902e-07 - 52|1.663608e-01|6.662611e-07|1.108397e-07 - 53|1.663607e-01|7.133700e-07|1.186767e-07 - 54|1.663605e-01|7.648141e-07|1.272349e-07 - 55|1.663604e-01|6.557516e-07|1.090911e-07 - 56|1.663603e-01|7.304213e-07|1.215131e-07 - 57|1.663602e-01|6.353809e-07|1.057021e-07 - 58|1.663601e-01|7.968279e-07|1.325603e-07 - 59|1.663600e-01|6.367159e-07|1.059240e-07 - It. |Loss |Relative loss|Absolute loss - ------------------------------------------------ - 60|1.663599e-01|5.610790e-07|9.334102e-08 - 61|1.663598e-01|5.787466e-07|9.628015e-08 - 62|1.663596e-01|6.937777e-07|1.154166e-07 - 63|1.663596e-01|5.599432e-07|9.315190e-08 - 64|1.663595e-01|5.813048e-07|9.670555e-08 - 65|1.663594e-01|5.724600e-07|9.523409e-08 - 66|1.663593e-01|6.081892e-07|1.011779e-07 - 67|1.663592e-01|5.948732e-07|9.896260e-08 - 68|1.663591e-01|4.941833e-07|8.221188e-08 - 69|1.663590e-01|5.213739e-07|8.673523e-08 - 70|1.663589e-01|5.127355e-07|8.529811e-08 - 71|1.663588e-01|4.349251e-07|7.235363e-08 - 72|1.663588e-01|5.007084e-07|8.329722e-08 - 73|1.663587e-01|4.880265e-07|8.118744e-08 - 74|1.663586e-01|4.931950e-07|8.204723e-08 - 75|1.663585e-01|4.981309e-07|8.286832e-08 - 76|1.663584e-01|3.952959e-07|6.576082e-08 - 77|1.663584e-01|4.544857e-07|7.560750e-08 - 78|1.663583e-01|4.237579e-07|7.049564e-08 - 79|1.663582e-01|4.382386e-07|7.290460e-08 - It. |Loss |Relative loss|Absolute loss - ------------------------------------------------ - 80|1.663582e-01|3.646051e-07|6.065503e-08 - 81|1.663581e-01|4.197994e-07|6.983702e-08 - 82|1.663580e-01|4.072764e-07|6.775370e-08 - 83|1.663580e-01|3.994645e-07|6.645410e-08 - 84|1.663579e-01|4.842721e-07|8.056248e-08 - 85|1.663578e-01|3.276486e-07|5.450691e-08 - 86|1.663578e-01|3.737346e-07|6.217366e-08 - 87|1.663577e-01|4.282043e-07|7.123508e-08 - 88|1.663576e-01|4.020937e-07|6.689135e-08 - 89|1.663576e-01|3.431951e-07|5.709310e-08 - 90|1.663575e-01|3.052335e-07|5.077789e-08 - 91|1.663575e-01|3.500538e-07|5.823407e-08 - 92|1.663574e-01|3.063176e-07|5.095821e-08 - 93|1.663573e-01|3.576367e-07|5.949549e-08 - 94|1.663573e-01|3.224681e-07|5.364492e-08 - 95|1.663572e-01|3.673221e-07|6.110670e-08 - 96|1.663572e-01|3.635561e-07|6.048017e-08 - 97|1.663571e-01|3.527236e-07|5.867807e-08 - 98|1.663571e-01|2.788548e-07|4.638946e-08 - 99|1.663570e-01|2.727141e-07|4.536791e-08 - It. |Loss |Relative loss|Absolute loss - ------------------------------------------------ - 100|1.663570e-01|3.127278e-07|5.202445e-08 - 101|1.663569e-01|2.637504e-07|4.387670e-08 - 102|1.663569e-01|2.922750e-07|4.862195e-08 - 103|1.663568e-01|3.076454e-07|5.117891e-08 - 104|1.663568e-01|2.911509e-07|4.843492e-08 - 105|1.663567e-01|2.403398e-07|3.998215e-08 - 106|1.663567e-01|2.439790e-07|4.058755e-08 - 107|1.663567e-01|2.634542e-07|4.382735e-08 - 108|1.663566e-01|2.452203e-07|4.079401e-08 - 109|1.663566e-01|2.852991e-07|4.746137e-08 - 110|1.663565e-01|2.165490e-07|3.602434e-08 - 111|1.663565e-01|2.450250e-07|4.076149e-08 - 112|1.663564e-01|2.685294e-07|4.467159e-08 - 113|1.663564e-01|2.821800e-07|4.694245e-08 - 114|1.663564e-01|2.237390e-07|3.722040e-08 - 115|1.663563e-01|1.992842e-07|3.315219e-08 - 116|1.663563e-01|2.166739e-07|3.604506e-08 - 117|1.663563e-01|2.086064e-07|3.470297e-08 - 118|1.663562e-01|2.435945e-07|4.052346e-08 - 119|1.663562e-01|2.292497e-07|3.813711e-08 - It. |Loss |Relative loss|Absolute loss - ------------------------------------------------ - 120|1.663561e-01|2.366209e-07|3.936334e-08 - 121|1.663561e-01|2.138746e-07|3.557935e-08 - 122|1.663561e-01|2.009637e-07|3.343153e-08 - 123|1.663560e-01|2.386258e-07|3.969683e-08 - 124|1.663560e-01|1.927442e-07|3.206415e-08 - 125|1.663560e-01|2.081681e-07|3.463000e-08 - 126|1.663559e-01|1.759123e-07|2.926406e-08 - 127|1.663559e-01|1.890771e-07|3.145409e-08 - 128|1.663559e-01|1.971315e-07|3.279398e-08 - 129|1.663558e-01|2.101983e-07|3.496771e-08 - 130|1.663558e-01|2.035645e-07|3.386414e-08 - 131|1.663558e-01|1.984492e-07|3.301317e-08 - 132|1.663557e-01|1.849064e-07|3.076024e-08 - 133|1.663557e-01|1.795703e-07|2.987255e-08 - 134|1.663557e-01|1.624087e-07|2.701762e-08 - 135|1.663557e-01|1.689557e-07|2.810673e-08 - 136|1.663556e-01|1.644308e-07|2.735399e-08 - 137|1.663556e-01|1.618007e-07|2.691644e-08 - 138|1.663556e-01|1.483013e-07|2.467075e-08 - 139|1.663555e-01|1.708771e-07|2.842636e-08 - It. |Loss |Relative loss|Absolute loss - ------------------------------------------------ - 140|1.663555e-01|2.013847e-07|3.350146e-08 - 141|1.663555e-01|1.721217e-07|2.863339e-08 - 142|1.663554e-01|2.027911e-07|3.373540e-08 - 143|1.663554e-01|1.764565e-07|2.935449e-08 - 144|1.663554e-01|1.677151e-07|2.790030e-08 - 145|1.663554e-01|1.351982e-07|2.249094e-08 - 146|1.663553e-01|1.423360e-07|2.367836e-08 - 147|1.663553e-01|1.541112e-07|2.563722e-08 - 148|1.663553e-01|1.491601e-07|2.481358e-08 - 149|1.663553e-01|1.466407e-07|2.439446e-08 - 150|1.663552e-01|1.801524e-07|2.996929e-08 - 151|1.663552e-01|1.714107e-07|2.851507e-08 - 152|1.663552e-01|1.491257e-07|2.480784e-08 - 153|1.663552e-01|1.513799e-07|2.518282e-08 - 154|1.663551e-01|1.354539e-07|2.253345e-08 - 155|1.663551e-01|1.233818e-07|2.052519e-08 - 156|1.663551e-01|1.576219e-07|2.622121e-08 - 157|1.663551e-01|1.452791e-07|2.416792e-08 - 158|1.663550e-01|1.262867e-07|2.100843e-08 - 159|1.663550e-01|1.316379e-07|2.189863e-08 - It. |Loss |Relative loss|Absolute loss - ------------------------------------------------ - 160|1.663550e-01|1.295447e-07|2.155041e-08 - 161|1.663550e-01|1.283286e-07|2.134810e-08 - 162|1.663550e-01|1.569222e-07|2.610479e-08 - 163|1.663549e-01|1.172942e-07|1.951247e-08 - 164|1.663549e-01|1.399809e-07|2.328651e-08 - 165|1.663549e-01|1.229432e-07|2.045221e-08 - 166|1.663549e-01|1.326191e-07|2.206184e-08 - 167|1.663548e-01|1.209694e-07|2.012384e-08 - 168|1.663548e-01|1.372136e-07|2.282614e-08 - 169|1.663548e-01|1.338395e-07|2.226484e-08 - 170|1.663548e-01|1.416497e-07|2.356410e-08 - 171|1.663548e-01|1.298576e-07|2.160242e-08 - 172|1.663547e-01|1.190590e-07|1.980603e-08 - 173|1.663547e-01|1.167083e-07|1.941497e-08 - 174|1.663547e-01|1.069425e-07|1.779038e-08 - 175|1.663547e-01|1.217780e-07|2.025834e-08 - 176|1.663547e-01|1.140754e-07|1.897697e-08 - 177|1.663546e-01|1.160707e-07|1.930890e-08 - 178|1.663546e-01|1.101798e-07|1.832892e-08 - 179|1.663546e-01|1.114904e-07|1.854694e-08 - It. |Loss |Relative loss|Absolute loss - ------------------------------------------------ - 180|1.663546e-01|1.064022e-07|1.770049e-08 - 181|1.663546e-01|9.258231e-08|1.540149e-08 - 182|1.663546e-01|1.213120e-07|2.018080e-08 - 183|1.663545e-01|1.164296e-07|1.936859e-08 - 184|1.663545e-01|1.188762e-07|1.977559e-08 - 185|1.663545e-01|9.394153e-08|1.562760e-08 - 186|1.663545e-01|1.028656e-07|1.711216e-08 - 187|1.663545e-01|1.115348e-07|1.855431e-08 - 188|1.663544e-01|9.768310e-08|1.625002e-08 - 189|1.663544e-01|1.021806e-07|1.699820e-08 - 190|1.663544e-01|1.086303e-07|1.807113e-08 - 191|1.663544e-01|9.879008e-08|1.643416e-08 - 192|1.663544e-01|1.050210e-07|1.747071e-08 - 193|1.663544e-01|1.002463e-07|1.667641e-08 - 194|1.663543e-01|1.062747e-07|1.767925e-08 - 195|1.663543e-01|9.348538e-08|1.555170e-08 - 196|1.663543e-01|7.992512e-08|1.329589e-08 - 197|1.663543e-01|9.558020e-08|1.590018e-08 - 198|1.663543e-01|9.993772e-08|1.662507e-08 - 199|1.663543e-01|8.588499e-08|1.428734e-08 - It. |Loss |Relative loss|Absolute loss - ------------------------------------------------ - 200|1.663543e-01|8.737134e-08|1.453459e-08 - - - - -Solve EMD with entropic regularization --------------------------------------- - - -.. code-block:: default - - - - def f(G): - return np.sum(G * np.log(G)) - - - def df(G): - return np.log(G) + 1. - - - reg = 1e-3 - - Ge = ot.optim.cg(a, b, M, reg, f, df, verbose=True) - - pl.figure(4, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, Ge, 'OT matrix Entrop. reg') - - - - -.. image:: /auto_examples/images/sphx_glr_plot_optim_OTreg_003.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - It. |Loss |Relative loss|Absolute loss - ------------------------------------------------ - 0|1.692289e-01|0.000000e+00|0.000000e+00 - 1|1.617643e-01|4.614437e-02|7.464513e-03 - 2|1.612639e-01|3.102965e-03|5.003963e-04 - 3|1.611291e-01|8.371098e-04|1.348827e-04 - 4|1.610468e-01|5.110558e-04|8.230389e-05 - 5|1.610198e-01|1.672927e-04|2.693743e-05 - 6|1.610130e-01|4.232417e-05|6.814742e-06 - 7|1.610090e-01|2.513455e-05|4.046887e-06 - 8|1.610002e-01|5.443507e-05|8.764057e-06 - 9|1.609996e-01|3.657071e-06|5.887869e-07 - 10|1.609948e-01|2.998735e-05|4.827807e-06 - 11|1.609695e-01|1.569217e-04|2.525962e-05 - 12|1.609533e-01|1.010779e-04|1.626881e-05 - 13|1.609520e-01|8.043897e-06|1.294681e-06 - 14|1.609465e-01|3.415246e-05|5.496718e-06 - 15|1.609386e-01|4.898605e-05|7.883745e-06 - 16|1.609324e-01|3.837052e-05|6.175060e-06 - 17|1.609298e-01|1.617826e-05|2.603564e-06 - 18|1.609184e-01|7.080015e-05|1.139305e-05 - 19|1.609083e-01|6.273206e-05|1.009411e-05 - It. |Loss |Relative loss|Absolute loss - ------------------------------------------------ - 20|1.608988e-01|5.940805e-05|9.558681e-06 - 21|1.608853e-01|8.380030e-05|1.348223e-05 - 22|1.608844e-01|5.185045e-06|8.341930e-07 - 23|1.608824e-01|1.279113e-05|2.057868e-06 - 24|1.608819e-01|3.156821e-06|5.078753e-07 - 25|1.608783e-01|2.205746e-05|3.548567e-06 - 26|1.608764e-01|1.189894e-05|1.914259e-06 - 27|1.608755e-01|5.474607e-06|8.807303e-07 - 28|1.608737e-01|1.144227e-05|1.840760e-06 - 29|1.608676e-01|3.775335e-05|6.073291e-06 - 30|1.608638e-01|2.348020e-05|3.777116e-06 - 31|1.608627e-01|6.863136e-06|1.104023e-06 - 32|1.608529e-01|6.110230e-05|9.828482e-06 - 33|1.608487e-01|2.641106e-05|4.248184e-06 - 34|1.608409e-01|4.823638e-05|7.758383e-06 - 35|1.608373e-01|2.256641e-05|3.629519e-06 - 36|1.608338e-01|2.132444e-05|3.429691e-06 - 37|1.608310e-01|1.786649e-05|2.873484e-06 - 38|1.608260e-01|3.103848e-05|4.991794e-06 - 39|1.608206e-01|3.321265e-05|5.341279e-06 - It. |Loss |Relative loss|Absolute loss - ------------------------------------------------ - 40|1.608201e-01|3.054747e-06|4.912648e-07 - 41|1.608195e-01|4.198335e-06|6.751739e-07 - 42|1.608193e-01|8.458736e-07|1.360328e-07 - 43|1.608159e-01|2.153759e-05|3.463587e-06 - 44|1.608115e-01|2.738314e-05|4.403523e-06 - 45|1.608108e-01|3.960032e-06|6.368161e-07 - 46|1.608081e-01|1.675447e-05|2.694254e-06 - 47|1.608072e-01|5.976340e-06|9.610383e-07 - 48|1.608046e-01|1.604130e-05|2.579515e-06 - 49|1.608020e-01|1.617036e-05|2.600226e-06 - 50|1.608014e-01|3.957795e-06|6.364188e-07 - 51|1.608011e-01|1.292411e-06|2.078211e-07 - 52|1.607998e-01|8.431795e-06|1.355831e-06 - 53|1.607964e-01|2.127054e-05|3.420225e-06 - 54|1.607947e-01|1.021878e-05|1.643126e-06 - 55|1.607947e-01|3.560621e-07|5.725288e-08 - 56|1.607900e-01|2.929781e-05|4.710793e-06 - 57|1.607890e-01|5.740229e-06|9.229659e-07 - 58|1.607858e-01|2.039550e-05|3.279306e-06 - 59|1.607836e-01|1.319545e-05|2.121612e-06 - It. |Loss |Relative loss|Absolute loss - ------------------------------------------------ - 60|1.607826e-01|6.378947e-06|1.025624e-06 - 61|1.607808e-01|1.145102e-05|1.841105e-06 - 62|1.607776e-01|1.941743e-05|3.121889e-06 - 63|1.607743e-01|2.087422e-05|3.356037e-06 - 64|1.607741e-01|1.310249e-06|2.106541e-07 - 65|1.607738e-01|1.682752e-06|2.705425e-07 - 66|1.607691e-01|2.913936e-05|4.684709e-06 - 67|1.607671e-01|1.288855e-05|2.072055e-06 - 68|1.607654e-01|1.002448e-05|1.611590e-06 - 69|1.607641e-01|8.209492e-06|1.319792e-06 - 70|1.607632e-01|5.588467e-06|8.984199e-07 - 71|1.607619e-01|8.050388e-06|1.294196e-06 - 72|1.607618e-01|9.417493e-07|1.513973e-07 - 73|1.607598e-01|1.210509e-05|1.946012e-06 - 74|1.607591e-01|4.392914e-06|7.062009e-07 - 75|1.607579e-01|7.759587e-06|1.247415e-06 - 76|1.607574e-01|2.760280e-06|4.437356e-07 - 77|1.607556e-01|1.146469e-05|1.843012e-06 - 78|1.607550e-01|3.689456e-06|5.930984e-07 - 79|1.607550e-01|4.065631e-08|6.535705e-09 - It. |Loss |Relative loss|Absolute loss - ------------------------------------------------ - 80|1.607539e-01|6.555681e-06|1.053852e-06 - 81|1.607528e-01|7.177470e-06|1.153798e-06 - 82|1.607527e-01|5.306068e-07|8.529648e-08 - 83|1.607514e-01|7.816045e-06|1.256440e-06 - 84|1.607511e-01|2.301970e-06|3.700442e-07 - 85|1.607504e-01|4.281072e-06|6.881840e-07 - 86|1.607503e-01|7.821886e-07|1.257370e-07 - 87|1.607480e-01|1.403013e-05|2.255315e-06 - 88|1.607480e-01|1.169298e-08|1.879624e-09 - 89|1.607473e-01|4.235982e-06|6.809227e-07 - 90|1.607470e-01|1.717105e-06|2.760195e-07 - 91|1.607470e-01|6.148402e-09|9.883374e-10 - - - - -Solve EMD with Frobenius norm + entropic regularization -------------------------------------------------------- - - -.. code-block:: default - - - - def f(G): - return 0.5 * np.sum(G**2) - - - def df(G): - return G - - - reg1 = 1e-3 - reg2 = 1e-1 - - Gel2 = ot.optim.gcg(a, b, M, reg1, reg2, f, df, verbose=True) - - pl.figure(5, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, Gel2, 'OT entropic + matrix Frob. reg') - pl.show() - - - -.. image:: /auto_examples/images/sphx_glr_plot_optim_OTreg_004.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - It. |Loss |Relative loss|Absolute loss - ------------------------------------------------ - 0|1.693084e-01|0.000000e+00|0.000000e+00 - 1|1.610202e-01|5.147342e-02|8.288260e-03 - 2|1.609508e-01|4.309685e-04|6.936474e-05 - 3|1.609484e-01|1.524885e-05|2.454278e-06 - 4|1.609477e-01|3.863641e-06|6.218444e-07 - 5|1.609475e-01|1.433633e-06|2.307397e-07 - 6|1.609474e-01|6.332412e-07|1.019185e-07 - 7|1.609474e-01|2.950826e-07|4.749276e-08 - 8|1.609473e-01|1.508393e-07|2.427718e-08 - 9|1.609473e-01|7.859971e-08|1.265041e-08 - 10|1.609473e-01|4.337432e-08|6.980981e-09 - /home/rflamary/PYTHON/POT/examples/plot_optim_OTreg.py:129: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 0.985 seconds) - - -.. _sphx_glr_download_auto_examples_plot_optim_OTreg.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_optim_OTreg.py <plot_optim_OTreg.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: plot_optim_OTreg.ipynb <plot_optim_OTreg.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ diff --git a/docs/source/auto_examples/plot_otda_classes.ipynb b/docs/source/auto_examples/plot_otda_classes.ipynb deleted file mode 100644 index 283d227..0000000 --- a/docs/source/auto_examples/plot_otda_classes.ipynb +++ /dev/null @@ -1,126 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n# OT for domain adaptation\n\n\nThis example introduces a domain adaptation in a 2D setting and the 4 OTDA\napproaches currently supported in POT.\n\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Authors: Remi Flamary <remi.flamary@unice.fr>\n# Stanislas Chambon <stan.chambon@gmail.com>\n#\n# License: MIT License\n\nimport matplotlib.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_source_samples = 150\nn_target_samples = 150\n\nXs, ys = ot.datasets.make_data_classif('3gauss', n_source_samples)\nXt, yt = ot.datasets.make_data_classif('3gauss2', n_target_samples)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Instantiate the different transport algorithms and fit them\n-----------------------------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# EMD Transport\not_emd = ot.da.EMDTransport()\not_emd.fit(Xs=Xs, Xt=Xt)\n\n# Sinkhorn Transport\not_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1)\not_sinkhorn.fit(Xs=Xs, Xt=Xt)\n\n# Sinkhorn Transport with Group lasso regularization\not_lpl1 = ot.da.SinkhornLpl1Transport(reg_e=1e-1, reg_cl=1e0)\not_lpl1.fit(Xs=Xs, ys=ys, Xt=Xt)\n\n# Sinkhorn Transport with Group lasso regularization l1l2\not_l1l2 = ot.da.SinkhornL1l2Transport(reg_e=1e-1, reg_cl=2e0, max_iter=20,\n verbose=True)\not_l1l2.fit(Xs=Xs, ys=ys, Xt=Xt)\n\n# transport source samples onto target samples\ntransp_Xs_emd = ot_emd.transform(Xs=Xs)\ntransp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=Xs)\ntransp_Xs_lpl1 = ot_lpl1.transform(Xs=Xs)\ntransp_Xs_l1l2 = ot_l1l2.transform(Xs=Xs)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Fig 1 : plots source and target samples\n---------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pl.figure(1, figsize=(10, 5))\npl.subplot(1, 2, 1)\npl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')\npl.xticks([])\npl.yticks([])\npl.legend(loc=0)\npl.title('Source samples')\n\npl.subplot(1, 2, 2)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')\npl.xticks([])\npl.yticks([])\npl.legend(loc=0)\npl.title('Target samples')\npl.tight_layout()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Fig 2 : plot optimal couplings and transported samples\n------------------------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "param_img = {'interpolation': 'nearest'}\n\npl.figure(2, figsize=(15, 8))\npl.subplot(2, 4, 1)\npl.imshow(ot_emd.coupling_, **param_img)\npl.xticks([])\npl.yticks([])\npl.title('Optimal coupling\\nEMDTransport')\n\npl.subplot(2, 4, 2)\npl.imshow(ot_sinkhorn.coupling_, **param_img)\npl.xticks([])\npl.yticks([])\npl.title('Optimal coupling\\nSinkhornTransport')\n\npl.subplot(2, 4, 3)\npl.imshow(ot_lpl1.coupling_, **param_img)\npl.xticks([])\npl.yticks([])\npl.title('Optimal coupling\\nSinkhornLpl1Transport')\n\npl.subplot(2, 4, 4)\npl.imshow(ot_l1l2.coupling_, **param_img)\npl.xticks([])\npl.yticks([])\npl.title('Optimal coupling\\nSinkhornL1l2Transport')\n\npl.subplot(2, 4, 5)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=0.3)\npl.scatter(transp_Xs_emd[:, 0], transp_Xs_emd[:, 1], c=ys,\n marker='+', label='Transp samples', s=30)\npl.xticks([])\npl.yticks([])\npl.title('Transported samples\\nEmdTransport')\npl.legend(loc=\"lower left\")\n\npl.subplot(2, 4, 6)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=0.3)\npl.scatter(transp_Xs_sinkhorn[:, 0], transp_Xs_sinkhorn[:, 1], c=ys,\n marker='+', label='Transp samples', s=30)\npl.xticks([])\npl.yticks([])\npl.title('Transported samples\\nSinkhornTransport')\n\npl.subplot(2, 4, 7)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=0.3)\npl.scatter(transp_Xs_lpl1[:, 0], transp_Xs_lpl1[:, 1], c=ys,\n marker='+', label='Transp samples', s=30)\npl.xticks([])\npl.yticks([])\npl.title('Transported samples\\nSinkhornLpl1Transport')\n\npl.subplot(2, 4, 8)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=0.3)\npl.scatter(transp_Xs_l1l2[:, 0], transp_Xs_l1l2[:, 1], c=ys,\n marker='+', label='Transp samples', s=30)\npl.xticks([])\npl.yticks([])\npl.title('Transported samples\\nSinkhornL1l2Transport')\npl.tight_layout()\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": "3.6.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_otda_classes.py b/docs/source/auto_examples/plot_otda_classes.py deleted file mode 100644 index f028022..0000000 --- a/docs/source/auto_examples/plot_otda_classes.py +++ /dev/null @@ -1,149 +0,0 @@ -# -*- coding: utf-8 -*- -""" -======================== -OT for domain adaptation -======================== - -This example introduces a domain adaptation in a 2D setting and the 4 OTDA -approaches currently supported in POT. - -""" - -# Authors: Remi Flamary <remi.flamary@unice.fr> -# Stanislas Chambon <stan.chambon@gmail.com> -# -# License: MIT License - -import matplotlib.pylab as pl -import ot - -############################################################################## -# Generate data -# ------------- - -n_source_samples = 150 -n_target_samples = 150 - -Xs, ys = ot.datasets.make_data_classif('3gauss', n_source_samples) -Xt, yt = ot.datasets.make_data_classif('3gauss2', n_target_samples) - - -############################################################################## -# Instantiate the different transport algorithms and fit them -# ----------------------------------------------------------- - -# EMD Transport -ot_emd = ot.da.EMDTransport() -ot_emd.fit(Xs=Xs, Xt=Xt) - -# Sinkhorn Transport -ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1) -ot_sinkhorn.fit(Xs=Xs, Xt=Xt) - -# Sinkhorn Transport with Group lasso regularization -ot_lpl1 = ot.da.SinkhornLpl1Transport(reg_e=1e-1, reg_cl=1e0) -ot_lpl1.fit(Xs=Xs, ys=ys, Xt=Xt) - -# Sinkhorn Transport with Group lasso regularization l1l2 -ot_l1l2 = ot.da.SinkhornL1l2Transport(reg_e=1e-1, reg_cl=2e0, max_iter=20, - verbose=True) -ot_l1l2.fit(Xs=Xs, ys=ys, Xt=Xt) - -# transport source samples onto target samples -transp_Xs_emd = ot_emd.transform(Xs=Xs) -transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=Xs) -transp_Xs_lpl1 = ot_lpl1.transform(Xs=Xs) -transp_Xs_l1l2 = ot_l1l2.transform(Xs=Xs) - - -############################################################################## -# Fig 1 : plots source and target samples -# --------------------------------------- - -pl.figure(1, figsize=(10, 5)) -pl.subplot(1, 2, 1) -pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') -pl.xticks([]) -pl.yticks([]) -pl.legend(loc=0) -pl.title('Source samples') - -pl.subplot(1, 2, 2) -pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') -pl.xticks([]) -pl.yticks([]) -pl.legend(loc=0) -pl.title('Target samples') -pl.tight_layout() - - -############################################################################## -# Fig 2 : plot optimal couplings and transported samples -# ------------------------------------------------------ - -param_img = {'interpolation': 'nearest'} - -pl.figure(2, figsize=(15, 8)) -pl.subplot(2, 4, 1) -pl.imshow(ot_emd.coupling_, **param_img) -pl.xticks([]) -pl.yticks([]) -pl.title('Optimal coupling\nEMDTransport') - -pl.subplot(2, 4, 2) -pl.imshow(ot_sinkhorn.coupling_, **param_img) -pl.xticks([]) -pl.yticks([]) -pl.title('Optimal coupling\nSinkhornTransport') - -pl.subplot(2, 4, 3) -pl.imshow(ot_lpl1.coupling_, **param_img) -pl.xticks([]) -pl.yticks([]) -pl.title('Optimal coupling\nSinkhornLpl1Transport') - -pl.subplot(2, 4, 4) -pl.imshow(ot_l1l2.coupling_, **param_img) -pl.xticks([]) -pl.yticks([]) -pl.title('Optimal coupling\nSinkhornL1l2Transport') - -pl.subplot(2, 4, 5) -pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=0.3) -pl.scatter(transp_Xs_emd[:, 0], transp_Xs_emd[:, 1], c=ys, - marker='+', label='Transp samples', s=30) -pl.xticks([]) -pl.yticks([]) -pl.title('Transported samples\nEmdTransport') -pl.legend(loc="lower left") - -pl.subplot(2, 4, 6) -pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=0.3) -pl.scatter(transp_Xs_sinkhorn[:, 0], transp_Xs_sinkhorn[:, 1], c=ys, - marker='+', label='Transp samples', s=30) -pl.xticks([]) -pl.yticks([]) -pl.title('Transported samples\nSinkhornTransport') - -pl.subplot(2, 4, 7) -pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=0.3) -pl.scatter(transp_Xs_lpl1[:, 0], transp_Xs_lpl1[:, 1], c=ys, - marker='+', label='Transp samples', s=30) -pl.xticks([]) -pl.yticks([]) -pl.title('Transported samples\nSinkhornLpl1Transport') - -pl.subplot(2, 4, 8) -pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=0.3) -pl.scatter(transp_Xs_l1l2[:, 0], transp_Xs_l1l2[:, 1], c=ys, - marker='+', label='Transp samples', s=30) -pl.xticks([]) -pl.yticks([]) -pl.title('Transported samples\nSinkhornL1l2Transport') -pl.tight_layout() - -pl.show() diff --git a/docs/source/auto_examples/plot_otda_classes.rst b/docs/source/auto_examples/plot_otda_classes.rst deleted file mode 100644 index 9cf31ee..0000000 --- a/docs/source/auto_examples/plot_otda_classes.rst +++ /dev/null @@ -1,287 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_otda_classes.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_otda_classes.py: - - -======================== -OT for domain adaptation -======================== - -This example introduces a domain adaptation in a 2D setting and the 4 OTDA -approaches currently supported in POT. - - - -.. code-block:: default - - - # Authors: Remi Flamary <remi.flamary@unice.fr> - # Stanislas Chambon <stan.chambon@gmail.com> - # - # License: MIT License - - import matplotlib.pylab as pl - import ot - - - - - - - - -Generate data -------------- - - -.. code-block:: default - - - n_source_samples = 150 - n_target_samples = 150 - - Xs, ys = ot.datasets.make_data_classif('3gauss', n_source_samples) - Xt, yt = ot.datasets.make_data_classif('3gauss2', n_target_samples) - - - - - - - - - -Instantiate the different transport algorithms and fit them ------------------------------------------------------------ - - -.. code-block:: default - - - # EMD Transport - ot_emd = ot.da.EMDTransport() - ot_emd.fit(Xs=Xs, Xt=Xt) - - # Sinkhorn Transport - ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1) - ot_sinkhorn.fit(Xs=Xs, Xt=Xt) - - # Sinkhorn Transport with Group lasso regularization - ot_lpl1 = ot.da.SinkhornLpl1Transport(reg_e=1e-1, reg_cl=1e0) - ot_lpl1.fit(Xs=Xs, ys=ys, Xt=Xt) - - # Sinkhorn Transport with Group lasso regularization l1l2 - ot_l1l2 = ot.da.SinkhornL1l2Transport(reg_e=1e-1, reg_cl=2e0, max_iter=20, - verbose=True) - ot_l1l2.fit(Xs=Xs, ys=ys, Xt=Xt) - - # transport source samples onto target samples - transp_Xs_emd = ot_emd.transform(Xs=Xs) - transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=Xs) - transp_Xs_lpl1 = ot_lpl1.transform(Xs=Xs) - transp_Xs_l1l2 = ot_l1l2.transform(Xs=Xs) - - - - - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - It. |Loss |Relative loss|Absolute loss - ------------------------------------------------ - 0|9.484039e+00|0.000000e+00|0.000000e+00 - 1|1.976107e+00|3.799355e+00|7.507932e+00 - 2|1.749871e+00|1.292876e-01|2.262365e-01 - 3|1.692667e+00|3.379504e-02|5.720374e-02 - 4|1.676256e+00|9.790077e-03|1.641068e-02 - 5|1.667458e+00|5.276422e-03|8.798212e-03 - 6|1.661775e+00|3.419693e-03|5.682762e-03 - 7|1.658009e+00|2.271789e-03|3.766646e-03 - 8|1.655167e+00|1.716870e-03|2.841707e-03 - 9|1.651825e+00|2.023380e-03|3.342270e-03 - 10|1.649431e+00|1.451076e-03|2.393450e-03 - 11|1.648649e+00|4.742894e-04|7.819369e-04 - 12|1.647901e+00|4.538219e-04|7.478538e-04 - 13|1.647356e+00|3.313134e-04|5.457909e-04 - 14|1.646923e+00|2.627246e-04|4.326871e-04 - 15|1.646038e+00|5.375014e-04|8.847478e-04 - 16|1.645629e+00|2.483240e-04|4.086492e-04 - 17|1.645616e+00|8.248172e-06|1.357332e-05 - 18|1.645377e+00|1.452648e-04|2.390153e-04 - 19|1.644745e+00|3.838976e-04|6.314139e-04 - It. |Loss |Relative loss|Absolute loss - ------------------------------------------------ - 20|1.644164e+00|3.538439e-04|5.817773e-04 - - - - -Fig 1 : plots source and target samples ---------------------------------------- - - -.. code-block:: default - - - pl.figure(1, figsize=(10, 5)) - pl.subplot(1, 2, 1) - pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') - pl.xticks([]) - pl.yticks([]) - pl.legend(loc=0) - pl.title('Source samples') - - pl.subplot(1, 2, 2) - pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') - pl.xticks([]) - pl.yticks([]) - pl.legend(loc=0) - pl.title('Target samples') - pl.tight_layout() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_otda_classes_001.png - :class: sphx-glr-single-img - - - - - -Fig 2 : plot optimal couplings and transported samples ------------------------------------------------------- - - -.. code-block:: default - - - param_img = {'interpolation': 'nearest'} - - pl.figure(2, figsize=(15, 8)) - pl.subplot(2, 4, 1) - pl.imshow(ot_emd.coupling_, **param_img) - pl.xticks([]) - pl.yticks([]) - pl.title('Optimal coupling\nEMDTransport') - - pl.subplot(2, 4, 2) - pl.imshow(ot_sinkhorn.coupling_, **param_img) - pl.xticks([]) - pl.yticks([]) - pl.title('Optimal coupling\nSinkhornTransport') - - pl.subplot(2, 4, 3) - pl.imshow(ot_lpl1.coupling_, **param_img) - pl.xticks([]) - pl.yticks([]) - pl.title('Optimal coupling\nSinkhornLpl1Transport') - - pl.subplot(2, 4, 4) - pl.imshow(ot_l1l2.coupling_, **param_img) - pl.xticks([]) - pl.yticks([]) - pl.title('Optimal coupling\nSinkhornL1l2Transport') - - pl.subplot(2, 4, 5) - pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=0.3) - pl.scatter(transp_Xs_emd[:, 0], transp_Xs_emd[:, 1], c=ys, - marker='+', label='Transp samples', s=30) - pl.xticks([]) - pl.yticks([]) - pl.title('Transported samples\nEmdTransport') - pl.legend(loc="lower left") - - pl.subplot(2, 4, 6) - pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=0.3) - pl.scatter(transp_Xs_sinkhorn[:, 0], transp_Xs_sinkhorn[:, 1], c=ys, - marker='+', label='Transp samples', s=30) - pl.xticks([]) - pl.yticks([]) - pl.title('Transported samples\nSinkhornTransport') - - pl.subplot(2, 4, 7) - pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=0.3) - pl.scatter(transp_Xs_lpl1[:, 0], transp_Xs_lpl1[:, 1], c=ys, - marker='+', label='Transp samples', s=30) - pl.xticks([]) - pl.yticks([]) - pl.title('Transported samples\nSinkhornLpl1Transport') - - pl.subplot(2, 4, 8) - pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=0.3) - pl.scatter(transp_Xs_l1l2[:, 0], transp_Xs_l1l2[:, 1], c=ys, - marker='+', label='Transp samples', s=30) - pl.xticks([]) - pl.yticks([]) - pl.title('Transported samples\nSinkhornL1l2Transport') - pl.tight_layout() - - pl.show() - - - -.. image:: /auto_examples/images/sphx_glr_plot_otda_classes_002.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_otda_classes.py:149: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 2.083 seconds) - - -.. _sphx_glr_download_auto_examples_plot_otda_classes.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_otda_classes.py <plot_otda_classes.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: plot_otda_classes.ipynb <plot_otda_classes.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ diff --git a/docs/source/auto_examples/plot_otda_color_images.ipynb b/docs/source/auto_examples/plot_otda_color_images.ipynb deleted file mode 100644 index c2afd41..0000000 --- a/docs/source/auto_examples/plot_otda_color_images.ipynb +++ /dev/null @@ -1,144 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n# OT for image color adaptation\n\n\nThis example presents a way of transferring colors between two images\nwith Optimal Transport as introduced in [6]\n\n[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014).\nRegularized discrete optimal transport.\nSIAM Journal on Imaging Sciences, 7(3), 1853-1882.\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Authors: Remi Flamary <remi.flamary@unice.fr>\n# Stanislas Chambon <stan.chambon@gmail.com>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\n\n\nr = np.random.RandomState(42)\n\n\ndef im2mat(I):\n \"\"\"Converts an 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)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Generate data\n-------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# 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\nX1 = im2mat(I1)\nX2 = im2mat(I2)\n\n# training samples\nnb = 1000\nidx1 = r.randint(X1.shape[0], size=(nb,))\nidx2 = r.randint(X2.shape[0], size=(nb,))\n\nXs = X1[idx1, :]\nXt = X2[idx2, :]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Plot original image\n-------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pl.figure(1, figsize=(6.4, 3))\n\npl.subplot(1, 2, 1)\npl.imshow(I1)\npl.axis('off')\npl.title('Image 1')\n\npl.subplot(1, 2, 2)\npl.imshow(I2)\npl.axis('off')\npl.title('Image 2')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Scatter plot of colors\n----------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pl.figure(2, figsize=(6.4, 3))\n\npl.subplot(1, 2, 1)\npl.scatter(Xs[:, 0], Xs[:, 2], c=Xs)\npl.axis([0, 1, 0, 1])\npl.xlabel('Red')\npl.ylabel('Blue')\npl.title('Image 1')\n\npl.subplot(1, 2, 2)\npl.scatter(Xt[:, 0], Xt[:, 2], c=Xt)\npl.axis([0, 1, 0, 1])\npl.xlabel('Red')\npl.ylabel('Blue')\npl.title('Image 2')\npl.tight_layout()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Instantiate the different transport algorithms and fit them\n-----------------------------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# EMDTransport\not_emd = ot.da.EMDTransport()\not_emd.fit(Xs=Xs, Xt=Xt)\n\n# SinkhornTransport\not_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1)\not_sinkhorn.fit(Xs=Xs, Xt=Xt)\n\n# prediction between images (using out of sample prediction as in [6])\ntransp_Xs_emd = ot_emd.transform(Xs=X1)\ntransp_Xt_emd = ot_emd.inverse_transform(Xt=X2)\n\ntransp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=X1)\ntransp_Xt_sinkhorn = ot_sinkhorn.inverse_transform(Xt=X2)\n\nI1t = minmax(mat2im(transp_Xs_emd, I1.shape))\nI2t = minmax(mat2im(transp_Xt_emd, I2.shape))\n\nI1te = minmax(mat2im(transp_Xs_sinkhorn, I1.shape))\nI2te = minmax(mat2im(transp_Xt_sinkhorn, I2.shape))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Plot new images\n---------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pl.figure(3, figsize=(8, 4))\n\npl.subplot(2, 3, 1)\npl.imshow(I1)\npl.axis('off')\npl.title('Image 1')\n\npl.subplot(2, 3, 2)\npl.imshow(I1t)\npl.axis('off')\npl.title('Image 1 Adapt')\n\npl.subplot(2, 3, 3)\npl.imshow(I1te)\npl.axis('off')\npl.title('Image 1 Adapt (reg)')\n\npl.subplot(2, 3, 4)\npl.imshow(I2)\npl.axis('off')\npl.title('Image 2')\n\npl.subplot(2, 3, 5)\npl.imshow(I2t)\npl.axis('off')\npl.title('Image 2 Adapt')\n\npl.subplot(2, 3, 6)\npl.imshow(I2te)\npl.axis('off')\npl.title('Image 2 Adapt (reg)')\npl.tight_layout()\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": "3.6.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_otda_color_images.py b/docs/source/auto_examples/plot_otda_color_images.py deleted file mode 100644 index d9cbd2b..0000000 --- a/docs/source/auto_examples/plot_otda_color_images.py +++ /dev/null @@ -1,164 +0,0 @@ -# -*- coding: utf-8 -*- -""" -============================= -OT for image color adaptation -============================= - -This example presents a way of transferring colors between two images -with Optimal Transport as introduced in [6] - -[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014). -Regularized discrete optimal transport. -SIAM Journal on Imaging Sciences, 7(3), 1853-1882. -""" - -# Authors: Remi Flamary <remi.flamary@unice.fr> -# Stanislas Chambon <stan.chambon@gmail.com> -# -# License: MIT License - -import numpy as np -import matplotlib.pylab as pl -import ot - - -r = np.random.RandomState(42) - - -def im2mat(I): - """Converts an 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) - - -############################################################################## -# Generate data -# ------------- - -# 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) - -# training samples -nb = 1000 -idx1 = r.randint(X1.shape[0], size=(nb,)) -idx2 = r.randint(X2.shape[0], size=(nb,)) - -Xs = X1[idx1, :] -Xt = X2[idx2, :] - - -############################################################################## -# Plot original image -# ------------------- - -pl.figure(1, figsize=(6.4, 3)) - -pl.subplot(1, 2, 1) -pl.imshow(I1) -pl.axis('off') -pl.title('Image 1') - -pl.subplot(1, 2, 2) -pl.imshow(I2) -pl.axis('off') -pl.title('Image 2') - - -############################################################################## -# Scatter plot of colors -# ---------------------- - -pl.figure(2, figsize=(6.4, 3)) - -pl.subplot(1, 2, 1) -pl.scatter(Xs[:, 0], Xs[:, 2], c=Xs) -pl.axis([0, 1, 0, 1]) -pl.xlabel('Red') -pl.ylabel('Blue') -pl.title('Image 1') - -pl.subplot(1, 2, 2) -pl.scatter(Xt[:, 0], Xt[:, 2], c=Xt) -pl.axis([0, 1, 0, 1]) -pl.xlabel('Red') -pl.ylabel('Blue') -pl.title('Image 2') -pl.tight_layout() - - -############################################################################## -# Instantiate the different transport algorithms and fit them -# ----------------------------------------------------------- - -# EMDTransport -ot_emd = ot.da.EMDTransport() -ot_emd.fit(Xs=Xs, Xt=Xt) - -# SinkhornTransport -ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1) -ot_sinkhorn.fit(Xs=Xs, Xt=Xt) - -# prediction between images (using out of sample prediction as in [6]) -transp_Xs_emd = ot_emd.transform(Xs=X1) -transp_Xt_emd = ot_emd.inverse_transform(Xt=X2) - -transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=X1) -transp_Xt_sinkhorn = ot_sinkhorn.inverse_transform(Xt=X2) - -I1t = minmax(mat2im(transp_Xs_emd, I1.shape)) -I2t = minmax(mat2im(transp_Xt_emd, I2.shape)) - -I1te = minmax(mat2im(transp_Xs_sinkhorn, I1.shape)) -I2te = minmax(mat2im(transp_Xt_sinkhorn, I2.shape)) - - -############################################################################## -# Plot new images -# --------------- - -pl.figure(3, figsize=(8, 4)) - -pl.subplot(2, 3, 1) -pl.imshow(I1) -pl.axis('off') -pl.title('Image 1') - -pl.subplot(2, 3, 2) -pl.imshow(I1t) -pl.axis('off') -pl.title('Image 1 Adapt') - -pl.subplot(2, 3, 3) -pl.imshow(I1te) -pl.axis('off') -pl.title('Image 1 Adapt (reg)') - -pl.subplot(2, 3, 4) -pl.imshow(I2) -pl.axis('off') -pl.title('Image 2') - -pl.subplot(2, 3, 5) -pl.imshow(I2t) -pl.axis('off') -pl.title('Image 2 Adapt') - -pl.subplot(2, 3, 6) -pl.imshow(I2te) -pl.axis('off') -pl.title('Image 2 Adapt (reg)') -pl.tight_layout() - -pl.show() diff --git a/docs/source/auto_examples/plot_otda_color_images.rst b/docs/source/auto_examples/plot_otda_color_images.rst deleted file mode 100644 index a5b0d53..0000000 --- a/docs/source/auto_examples/plot_otda_color_images.rst +++ /dev/null @@ -1,291 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_otda_color_images.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_otda_color_images.py: - - -============================= -OT for image color adaptation -============================= - -This example presents a way of transferring colors between two images -with Optimal Transport as introduced in [6] - -[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014). -Regularized discrete optimal transport. -SIAM Journal on Imaging Sciences, 7(3), 1853-1882. - - -.. code-block:: default - - - # Authors: Remi Flamary <remi.flamary@unice.fr> - # Stanislas Chambon <stan.chambon@gmail.com> - # - # License: MIT License - - import numpy as np - import matplotlib.pylab as pl - import ot - - - r = np.random.RandomState(42) - - - def im2mat(I): - """Converts an 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) - - - - - - - - - -Generate data -------------- - - -.. code-block:: default - - - # 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) - - # training samples - nb = 1000 - idx1 = r.randint(X1.shape[0], size=(nb,)) - idx2 = r.randint(X2.shape[0], size=(nb,)) - - Xs = X1[idx1, :] - Xt = X2[idx2, :] - - - - - - - - - -Plot original image -------------------- - - -.. code-block:: default - - - pl.figure(1, figsize=(6.4, 3)) - - pl.subplot(1, 2, 1) - pl.imshow(I1) - pl.axis('off') - pl.title('Image 1') - - pl.subplot(1, 2, 2) - pl.imshow(I2) - pl.axis('off') - pl.title('Image 2') - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_otda_color_images_001.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - - Text(0.5, 1.0, 'Image 2') - - - -Scatter plot of colors ----------------------- - - -.. code-block:: default - - - pl.figure(2, figsize=(6.4, 3)) - - pl.subplot(1, 2, 1) - pl.scatter(Xs[:, 0], Xs[:, 2], c=Xs) - pl.axis([0, 1, 0, 1]) - pl.xlabel('Red') - pl.ylabel('Blue') - pl.title('Image 1') - - pl.subplot(1, 2, 2) - pl.scatter(Xt[:, 0], Xt[:, 2], c=Xt) - pl.axis([0, 1, 0, 1]) - pl.xlabel('Red') - pl.ylabel('Blue') - pl.title('Image 2') - pl.tight_layout() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_otda_color_images_002.png - :class: sphx-glr-single-img - - - - - -Instantiate the different transport algorithms and fit them ------------------------------------------------------------ - - -.. code-block:: default - - - # EMDTransport - ot_emd = ot.da.EMDTransport() - ot_emd.fit(Xs=Xs, Xt=Xt) - - # SinkhornTransport - ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1) - ot_sinkhorn.fit(Xs=Xs, Xt=Xt) - - # prediction between images (using out of sample prediction as in [6]) - transp_Xs_emd = ot_emd.transform(Xs=X1) - transp_Xt_emd = ot_emd.inverse_transform(Xt=X2) - - transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=X1) - transp_Xt_sinkhorn = ot_sinkhorn.inverse_transform(Xt=X2) - - I1t = minmax(mat2im(transp_Xs_emd, I1.shape)) - I2t = minmax(mat2im(transp_Xt_emd, I2.shape)) - - I1te = minmax(mat2im(transp_Xs_sinkhorn, I1.shape)) - I2te = minmax(mat2im(transp_Xt_sinkhorn, I2.shape)) - - - - - - - - - -Plot new images ---------------- - - -.. code-block:: default - - - pl.figure(3, figsize=(8, 4)) - - pl.subplot(2, 3, 1) - pl.imshow(I1) - pl.axis('off') - pl.title('Image 1') - - pl.subplot(2, 3, 2) - pl.imshow(I1t) - pl.axis('off') - pl.title('Image 1 Adapt') - - pl.subplot(2, 3, 3) - pl.imshow(I1te) - pl.axis('off') - pl.title('Image 1 Adapt (reg)') - - pl.subplot(2, 3, 4) - pl.imshow(I2) - pl.axis('off') - pl.title('Image 2') - - pl.subplot(2, 3, 5) - pl.imshow(I2t) - pl.axis('off') - pl.title('Image 2 Adapt') - - pl.subplot(2, 3, 6) - pl.imshow(I2te) - pl.axis('off') - pl.title('Image 2 Adapt (reg)') - pl.tight_layout() - - pl.show() - - - -.. image:: /auto_examples/images/sphx_glr_plot_otda_color_images_003.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_otda_color_images.py:164: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 2 minutes 28.821 seconds) - - -.. _sphx_glr_download_auto_examples_plot_otda_color_images.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_otda_color_images.py <plot_otda_color_images.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: plot_otda_color_images.ipynb <plot_otda_color_images.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ diff --git a/docs/source/auto_examples/plot_otda_d2.ipynb b/docs/source/auto_examples/plot_otda_d2.ipynb deleted file mode 100644 index a2a7839..0000000 --- a/docs/source/auto_examples/plot_otda_d2.ipynb +++ /dev/null @@ -1,144 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n# OT for domain adaptation on empirical distributions\n\n\nThis example introduces a domain adaptation in a 2D setting. It explicits\nthe problem of domain adaptation and introduces some optimal transport\napproaches to solve it.\n\nQuantities such as optimal couplings, greater coupling coefficients and\ntransported samples are represented in order to give a visual understanding\nof what the transport methods are doing.\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Authors: Remi Flamary <remi.flamary@unice.fr>\n# Stanislas Chambon <stan.chambon@gmail.com>\n#\n# License: MIT License\n\nimport matplotlib.pylab as pl\nimport ot\nimport ot.plot" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "generate data\n-------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "n_samples_source = 150\nn_samples_target = 150\n\nXs, ys = ot.datasets.make_data_classif('3gauss', n_samples_source)\nXt, yt = ot.datasets.make_data_classif('3gauss2', n_samples_target)\n\n# Cost matrix\nM = ot.dist(Xs, Xt, metric='sqeuclidean')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Instantiate the different transport algorithms and fit them\n-----------------------------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# EMD Transport\not_emd = ot.da.EMDTransport()\not_emd.fit(Xs=Xs, Xt=Xt)\n\n# Sinkhorn Transport\not_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1)\not_sinkhorn.fit(Xs=Xs, Xt=Xt)\n\n# Sinkhorn Transport with Group lasso regularization\not_lpl1 = ot.da.SinkhornLpl1Transport(reg_e=1e-1, reg_cl=1e0)\not_lpl1.fit(Xs=Xs, ys=ys, Xt=Xt)\n\n# transport source samples onto target samples\ntransp_Xs_emd = ot_emd.transform(Xs=Xs)\ntransp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=Xs)\ntransp_Xs_lpl1 = ot_lpl1.transform(Xs=Xs)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Fig 1 : plots source and target samples + matrix of pairwise distance\n---------------------------------------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pl.figure(1, figsize=(10, 10))\npl.subplot(2, 2, 1)\npl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')\npl.xticks([])\npl.yticks([])\npl.legend(loc=0)\npl.title('Source samples')\n\npl.subplot(2, 2, 2)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')\npl.xticks([])\npl.yticks([])\npl.legend(loc=0)\npl.title('Target samples')\n\npl.subplot(2, 2, 3)\npl.imshow(M, interpolation='nearest')\npl.xticks([])\npl.yticks([])\npl.title('Matrix of pairwise distances')\npl.tight_layout()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Fig 2 : plots optimal couplings for the different methods\n---------------------------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pl.figure(2, figsize=(10, 6))\n\npl.subplot(2, 3, 1)\npl.imshow(ot_emd.coupling_, interpolation='nearest')\npl.xticks([])\npl.yticks([])\npl.title('Optimal coupling\\nEMDTransport')\n\npl.subplot(2, 3, 2)\npl.imshow(ot_sinkhorn.coupling_, interpolation='nearest')\npl.xticks([])\npl.yticks([])\npl.title('Optimal coupling\\nSinkhornTransport')\n\npl.subplot(2, 3, 3)\npl.imshow(ot_lpl1.coupling_, interpolation='nearest')\npl.xticks([])\npl.yticks([])\npl.title('Optimal coupling\\nSinkhornLpl1Transport')\n\npl.subplot(2, 3, 4)\not.plot.plot2D_samples_mat(Xs, Xt, ot_emd.coupling_, c=[.5, .5, 1])\npl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')\npl.xticks([])\npl.yticks([])\npl.title('Main coupling coefficients\\nEMDTransport')\n\npl.subplot(2, 3, 5)\not.plot.plot2D_samples_mat(Xs, Xt, ot_sinkhorn.coupling_, c=[.5, .5, 1])\npl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')\npl.xticks([])\npl.yticks([])\npl.title('Main coupling coefficients\\nSinkhornTransport')\n\npl.subplot(2, 3, 6)\not.plot.plot2D_samples_mat(Xs, Xt, ot_lpl1.coupling_, c=[.5, .5, 1])\npl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')\npl.xticks([])\npl.yticks([])\npl.title('Main coupling coefficients\\nSinkhornLpl1Transport')\npl.tight_layout()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Fig 3 : plot transported samples\n--------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# display transported samples\npl.figure(4, figsize=(10, 4))\npl.subplot(1, 3, 1)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=0.5)\npl.scatter(transp_Xs_emd[:, 0], transp_Xs_emd[:, 1], c=ys,\n marker='+', label='Transp samples', s=30)\npl.title('Transported samples\\nEmdTransport')\npl.legend(loc=0)\npl.xticks([])\npl.yticks([])\n\npl.subplot(1, 3, 2)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=0.5)\npl.scatter(transp_Xs_sinkhorn[:, 0], transp_Xs_sinkhorn[:, 1], c=ys,\n marker='+', label='Transp samples', s=30)\npl.title('Transported samples\\nSinkhornTransport')\npl.xticks([])\npl.yticks([])\n\npl.subplot(1, 3, 3)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=0.5)\npl.scatter(transp_Xs_lpl1[:, 0], transp_Xs_lpl1[:, 1], c=ys,\n marker='+', label='Transp samples', s=30)\npl.title('Transported samples\\nSinkhornLpl1Transport')\npl.xticks([])\npl.yticks([])\n\npl.tight_layout()\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": "3.6.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_otda_d2.py b/docs/source/auto_examples/plot_otda_d2.py deleted file mode 100644 index cf22c2f..0000000 --- a/docs/source/auto_examples/plot_otda_d2.py +++ /dev/null @@ -1,172 +0,0 @@ -# -*- coding: utf-8 -*- -""" -=================================================== -OT for domain adaptation on empirical distributions -=================================================== - -This example introduces a domain adaptation in a 2D setting. It explicits -the problem of domain adaptation and introduces some optimal transport -approaches to solve it. - -Quantities such as optimal couplings, greater coupling coefficients and -transported samples are represented in order to give a visual understanding -of what the transport methods are doing. -""" - -# Authors: Remi Flamary <remi.flamary@unice.fr> -# Stanislas Chambon <stan.chambon@gmail.com> -# -# License: MIT License - -import matplotlib.pylab as pl -import ot -import ot.plot - -############################################################################## -# generate data -# ------------- - -n_samples_source = 150 -n_samples_target = 150 - -Xs, ys = ot.datasets.make_data_classif('3gauss', n_samples_source) -Xt, yt = ot.datasets.make_data_classif('3gauss2', n_samples_target) - -# Cost matrix -M = ot.dist(Xs, Xt, metric='sqeuclidean') - - -############################################################################## -# Instantiate the different transport algorithms and fit them -# ----------------------------------------------------------- - -# EMD Transport -ot_emd = ot.da.EMDTransport() -ot_emd.fit(Xs=Xs, Xt=Xt) - -# Sinkhorn Transport -ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1) -ot_sinkhorn.fit(Xs=Xs, Xt=Xt) - -# Sinkhorn Transport with Group lasso regularization -ot_lpl1 = ot.da.SinkhornLpl1Transport(reg_e=1e-1, reg_cl=1e0) -ot_lpl1.fit(Xs=Xs, ys=ys, Xt=Xt) - -# transport source samples onto target samples -transp_Xs_emd = ot_emd.transform(Xs=Xs) -transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=Xs) -transp_Xs_lpl1 = ot_lpl1.transform(Xs=Xs) - - -############################################################################## -# Fig 1 : plots source and target samples + matrix of pairwise distance -# --------------------------------------------------------------------- - -pl.figure(1, figsize=(10, 10)) -pl.subplot(2, 2, 1) -pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') -pl.xticks([]) -pl.yticks([]) -pl.legend(loc=0) -pl.title('Source samples') - -pl.subplot(2, 2, 2) -pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') -pl.xticks([]) -pl.yticks([]) -pl.legend(loc=0) -pl.title('Target samples') - -pl.subplot(2, 2, 3) -pl.imshow(M, interpolation='nearest') -pl.xticks([]) -pl.yticks([]) -pl.title('Matrix of pairwise distances') -pl.tight_layout() - - -############################################################################## -# Fig 2 : plots optimal couplings for the different methods -# --------------------------------------------------------- -pl.figure(2, figsize=(10, 6)) - -pl.subplot(2, 3, 1) -pl.imshow(ot_emd.coupling_, interpolation='nearest') -pl.xticks([]) -pl.yticks([]) -pl.title('Optimal coupling\nEMDTransport') - -pl.subplot(2, 3, 2) -pl.imshow(ot_sinkhorn.coupling_, interpolation='nearest') -pl.xticks([]) -pl.yticks([]) -pl.title('Optimal coupling\nSinkhornTransport') - -pl.subplot(2, 3, 3) -pl.imshow(ot_lpl1.coupling_, interpolation='nearest') -pl.xticks([]) -pl.yticks([]) -pl.title('Optimal coupling\nSinkhornLpl1Transport') - -pl.subplot(2, 3, 4) -ot.plot.plot2D_samples_mat(Xs, Xt, ot_emd.coupling_, c=[.5, .5, 1]) -pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') -pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') -pl.xticks([]) -pl.yticks([]) -pl.title('Main coupling coefficients\nEMDTransport') - -pl.subplot(2, 3, 5) -ot.plot.plot2D_samples_mat(Xs, Xt, ot_sinkhorn.coupling_, c=[.5, .5, 1]) -pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') -pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') -pl.xticks([]) -pl.yticks([]) -pl.title('Main coupling coefficients\nSinkhornTransport') - -pl.subplot(2, 3, 6) -ot.plot.plot2D_samples_mat(Xs, Xt, ot_lpl1.coupling_, c=[.5, .5, 1]) -pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') -pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') -pl.xticks([]) -pl.yticks([]) -pl.title('Main coupling coefficients\nSinkhornLpl1Transport') -pl.tight_layout() - - -############################################################################## -# Fig 3 : plot transported samples -# -------------------------------- - -# display transported samples -pl.figure(4, figsize=(10, 4)) -pl.subplot(1, 3, 1) -pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=0.5) -pl.scatter(transp_Xs_emd[:, 0], transp_Xs_emd[:, 1], c=ys, - marker='+', label='Transp samples', s=30) -pl.title('Transported samples\nEmdTransport') -pl.legend(loc=0) -pl.xticks([]) -pl.yticks([]) - -pl.subplot(1, 3, 2) -pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=0.5) -pl.scatter(transp_Xs_sinkhorn[:, 0], transp_Xs_sinkhorn[:, 1], c=ys, - marker='+', label='Transp samples', s=30) -pl.title('Transported samples\nSinkhornTransport') -pl.xticks([]) -pl.yticks([]) - -pl.subplot(1, 3, 3) -pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=0.5) -pl.scatter(transp_Xs_lpl1[:, 0], transp_Xs_lpl1[:, 1], c=ys, - marker='+', label='Transp samples', s=30) -pl.title('Transported samples\nSinkhornLpl1Transport') -pl.xticks([]) -pl.yticks([]) - -pl.tight_layout() -pl.show() diff --git a/docs/source/auto_examples/plot_otda_d2.rst b/docs/source/auto_examples/plot_otda_d2.rst deleted file mode 100644 index 6d8e429..0000000 --- a/docs/source/auto_examples/plot_otda_d2.rst +++ /dev/null @@ -1,291 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_otda_d2.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_otda_d2.py: - - -=================================================== -OT for domain adaptation on empirical distributions -=================================================== - -This example introduces a domain adaptation in a 2D setting. It explicits -the problem of domain adaptation and introduces some optimal transport -approaches to solve it. - -Quantities such as optimal couplings, greater coupling coefficients and -transported samples are represented in order to give a visual understanding -of what the transport methods are doing. - - -.. code-block:: default - - - # Authors: Remi Flamary <remi.flamary@unice.fr> - # Stanislas Chambon <stan.chambon@gmail.com> - # - # License: MIT License - - import matplotlib.pylab as pl - import ot - import ot.plot - - - - - - - - -generate data -------------- - - -.. code-block:: default - - - n_samples_source = 150 - n_samples_target = 150 - - Xs, ys = ot.datasets.make_data_classif('3gauss', n_samples_source) - Xt, yt = ot.datasets.make_data_classif('3gauss2', n_samples_target) - - # Cost matrix - M = ot.dist(Xs, Xt, metric='sqeuclidean') - - - - - - - - - -Instantiate the different transport algorithms and fit them ------------------------------------------------------------ - - -.. code-block:: default - - - # EMD Transport - ot_emd = ot.da.EMDTransport() - ot_emd.fit(Xs=Xs, Xt=Xt) - - # Sinkhorn Transport - ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1) - ot_sinkhorn.fit(Xs=Xs, Xt=Xt) - - # Sinkhorn Transport with Group lasso regularization - ot_lpl1 = ot.da.SinkhornLpl1Transport(reg_e=1e-1, reg_cl=1e0) - ot_lpl1.fit(Xs=Xs, ys=ys, Xt=Xt) - - # transport source samples onto target samples - transp_Xs_emd = ot_emd.transform(Xs=Xs) - transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=Xs) - transp_Xs_lpl1 = ot_lpl1.transform(Xs=Xs) - - - - - - - - - -Fig 1 : plots source and target samples + matrix of pairwise distance ---------------------------------------------------------------------- - - -.. code-block:: default - - - pl.figure(1, figsize=(10, 10)) - pl.subplot(2, 2, 1) - pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') - pl.xticks([]) - pl.yticks([]) - pl.legend(loc=0) - pl.title('Source samples') - - pl.subplot(2, 2, 2) - pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') - pl.xticks([]) - pl.yticks([]) - pl.legend(loc=0) - pl.title('Target samples') - - pl.subplot(2, 2, 3) - pl.imshow(M, interpolation='nearest') - pl.xticks([]) - pl.yticks([]) - pl.title('Matrix of pairwise distances') - pl.tight_layout() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_otda_d2_001.png - :class: sphx-glr-single-img - - - - - -Fig 2 : plots optimal couplings for the different methods ---------------------------------------------------------- - - -.. code-block:: default - - pl.figure(2, figsize=(10, 6)) - - pl.subplot(2, 3, 1) - pl.imshow(ot_emd.coupling_, interpolation='nearest') - pl.xticks([]) - pl.yticks([]) - pl.title('Optimal coupling\nEMDTransport') - - pl.subplot(2, 3, 2) - pl.imshow(ot_sinkhorn.coupling_, interpolation='nearest') - pl.xticks([]) - pl.yticks([]) - pl.title('Optimal coupling\nSinkhornTransport') - - pl.subplot(2, 3, 3) - pl.imshow(ot_lpl1.coupling_, interpolation='nearest') - pl.xticks([]) - pl.yticks([]) - pl.title('Optimal coupling\nSinkhornLpl1Transport') - - pl.subplot(2, 3, 4) - ot.plot.plot2D_samples_mat(Xs, Xt, ot_emd.coupling_, c=[.5, .5, 1]) - pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') - pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') - pl.xticks([]) - pl.yticks([]) - pl.title('Main coupling coefficients\nEMDTransport') - - pl.subplot(2, 3, 5) - ot.plot.plot2D_samples_mat(Xs, Xt, ot_sinkhorn.coupling_, c=[.5, .5, 1]) - pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') - pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') - pl.xticks([]) - pl.yticks([]) - pl.title('Main coupling coefficients\nSinkhornTransport') - - pl.subplot(2, 3, 6) - ot.plot.plot2D_samples_mat(Xs, Xt, ot_lpl1.coupling_, c=[.5, .5, 1]) - pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') - pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') - pl.xticks([]) - pl.yticks([]) - pl.title('Main coupling coefficients\nSinkhornLpl1Transport') - pl.tight_layout() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_otda_d2_002.png - :class: sphx-glr-single-img - - - - - -Fig 3 : plot transported samples --------------------------------- - - -.. code-block:: default - - - # display transported samples - pl.figure(4, figsize=(10, 4)) - pl.subplot(1, 3, 1) - pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=0.5) - pl.scatter(transp_Xs_emd[:, 0], transp_Xs_emd[:, 1], c=ys, - marker='+', label='Transp samples', s=30) - pl.title('Transported samples\nEmdTransport') - pl.legend(loc=0) - pl.xticks([]) - pl.yticks([]) - - pl.subplot(1, 3, 2) - pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=0.5) - pl.scatter(transp_Xs_sinkhorn[:, 0], transp_Xs_sinkhorn[:, 1], c=ys, - marker='+', label='Transp samples', s=30) - pl.title('Transported samples\nSinkhornTransport') - pl.xticks([]) - pl.yticks([]) - - pl.subplot(1, 3, 3) - pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=0.5) - pl.scatter(transp_Xs_lpl1[:, 0], transp_Xs_lpl1[:, 1], c=ys, - marker='+', label='Transp samples', s=30) - pl.title('Transported samples\nSinkhornLpl1Transport') - pl.xticks([]) - pl.yticks([]) - - pl.tight_layout() - pl.show() - - - -.. image:: /auto_examples/images/sphx_glr_plot_otda_d2_003.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_otda_d2.py:172: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 21.323 seconds) - - -.. _sphx_glr_download_auto_examples_plot_otda_d2.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_otda_d2.py <plot_otda_d2.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: plot_otda_d2.ipynb <plot_otda_d2.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ diff --git a/docs/source/auto_examples/plot_otda_jcpot.ipynb b/docs/source/auto_examples/plot_otda_jcpot.ipynb deleted file mode 100644 index a81d47a..0000000 --- a/docs/source/auto_examples/plot_otda_jcpot.ipynb +++ /dev/null @@ -1,173 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n# OT for multi-source target shift\n\n\nThis example introduces a target shift problem with two 2D source and 1 target domain.\n\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Authors: Remi Flamary <remi.flamary@unice.fr>\n# Ievgen Redko <ievgen.redko@univ-st-etienne.fr>\n#\n# License: MIT License\n\nimport pylab as pl\nimport numpy as np\nimport ot\nfrom ot.datasets import make_data_classif" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Generate data\n-------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "n = 50\nsigma = 0.3\nnp.random.seed(1985)\n\np1 = .2\ndec1 = [0, 2]\n\np2 = .9\ndec2 = [0, -2]\n\npt = .4\ndect = [4, 0]\n\nxs1, ys1 = make_data_classif('2gauss_prop', n, nz=sigma, p=p1, bias=dec1)\nxs2, ys2 = make_data_classif('2gauss_prop', n + 1, nz=sigma, p=p2, bias=dec2)\nxt, yt = make_data_classif('2gauss_prop', n, nz=sigma, p=pt, bias=dect)\n\nall_Xr = [xs1, xs2]\nall_Yr = [ys1, ys2]" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "da = 1.5\n\n\ndef plot_ax(dec, name):\n pl.plot([dec[0], dec[0]], [dec[1] - da, dec[1] + da], 'k', alpha=0.5)\n pl.plot([dec[0] - da, dec[0] + da], [dec[1], dec[1]], 'k', alpha=0.5)\n pl.text(dec[0] - .5, dec[1] + 2, name)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Fig 1 : plots source and target samples\n---------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pl.figure(1)\npl.clf()\nplot_ax(dec1, 'Source 1')\nplot_ax(dec2, 'Source 2')\nplot_ax(dect, 'Target')\npl.scatter(xs1[:, 0], xs1[:, 1], c=ys1, s=35, marker='x', cmap='Set1', vmax=9,\n label='Source 1 ({:1.2f}, {:1.2f})'.format(1 - p1, p1))\npl.scatter(xs2[:, 0], xs2[:, 1], c=ys2, s=35, marker='+', cmap='Set1', vmax=9,\n label='Source 2 ({:1.2f}, {:1.2f})'.format(1 - p2, p2))\npl.scatter(xt[:, 0], xt[:, 1], c=yt, s=35, marker='o', cmap='Set1', vmax=9,\n label='Target ({:1.2f}, {:1.2f})'.format(1 - pt, pt))\npl.title('Data')\n\npl.legend()\npl.axis('equal')\npl.axis('off')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Instantiate Sinkhorn transport algorithm and fit them for all source domains\n----------------------------------------------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1, metric='sqeuclidean')\n\n\ndef print_G(G, xs, ys, xt):\n for i in range(G.shape[0]):\n for j in range(G.shape[1]):\n if G[i, j] > 5e-4:\n if ys[i]:\n c = 'b'\n else:\n c = 'r'\n pl.plot([xs[i, 0], xt[j, 0]], [xs[i, 1], xt[j, 1]], c, alpha=.2)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Fig 2 : plot optimal couplings and transported samples\n------------------------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pl.figure(2)\npl.clf()\nplot_ax(dec1, 'Source 1')\nplot_ax(dec2, 'Source 2')\nplot_ax(dect, 'Target')\nprint_G(ot_sinkhorn.fit(Xs=xs1, Xt=xt).coupling_, xs1, ys1, xt)\nprint_G(ot_sinkhorn.fit(Xs=xs2, Xt=xt).coupling_, xs2, ys2, xt)\npl.scatter(xs1[:, 0], xs1[:, 1], c=ys1, s=35, marker='x', cmap='Set1', vmax=9)\npl.scatter(xs2[:, 0], xs2[:, 1], c=ys2, s=35, marker='+', cmap='Set1', vmax=9)\npl.scatter(xt[:, 0], xt[:, 1], c=yt, s=35, marker='o', cmap='Set1', vmax=9)\n\npl.plot([], [], 'r', alpha=.2, label='Mass from Class 1')\npl.plot([], [], 'b', alpha=.2, label='Mass from Class 2')\n\npl.title('Independent OT')\n\npl.legend()\npl.axis('equal')\npl.axis('off')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Instantiate JCPOT adaptation algorithm and fit it\n----------------------------------------------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "otda = ot.da.JCPOTTransport(reg_e=1, max_iter=1000, metric='sqeuclidean', tol=1e-9, verbose=True, log=True)\notda.fit(all_Xr, all_Yr, xt)\n\nws1 = otda.proportions_.dot(otda.log_['D2'][0])\nws2 = otda.proportions_.dot(otda.log_['D2'][1])\n\npl.figure(3)\npl.clf()\nplot_ax(dec1, 'Source 1')\nplot_ax(dec2, 'Source 2')\nplot_ax(dect, 'Target')\nprint_G(ot.bregman.sinkhorn(ws1, [], otda.log_['M'][0], reg=1e-1), xs1, ys1, xt)\nprint_G(ot.bregman.sinkhorn(ws2, [], otda.log_['M'][1], reg=1e-1), xs2, ys2, xt)\npl.scatter(xs1[:, 0], xs1[:, 1], c=ys1, s=35, marker='x', cmap='Set1', vmax=9)\npl.scatter(xs2[:, 0], xs2[:, 1], c=ys2, s=35, marker='+', cmap='Set1', vmax=9)\npl.scatter(xt[:, 0], xt[:, 1], c=yt, s=35, marker='o', cmap='Set1', vmax=9)\n\npl.plot([], [], 'r', alpha=.2, label='Mass from Class 1')\npl.plot([], [], 'b', alpha=.2, label='Mass from Class 2')\n\npl.title('OT with prop estimation ({:1.3f},{:1.3f})'.format(otda.proportions_[0], otda.proportions_[1]))\n\npl.legend()\npl.axis('equal')\npl.axis('off')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Run oracle transport algorithm with known proportions\n----------------------------------------------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "h_res = np.array([1 - pt, pt])\n\nws1 = h_res.dot(otda.log_['D2'][0])\nws2 = h_res.dot(otda.log_['D2'][1])\n\npl.figure(4)\npl.clf()\nplot_ax(dec1, 'Source 1')\nplot_ax(dec2, 'Source 2')\nplot_ax(dect, 'Target')\nprint_G(ot.bregman.sinkhorn(ws1, [], otda.log_['M'][0], reg=1e-1), xs1, ys1, xt)\nprint_G(ot.bregman.sinkhorn(ws2, [], otda.log_['M'][1], reg=1e-1), xs2, ys2, xt)\npl.scatter(xs1[:, 0], xs1[:, 1], c=ys1, s=35, marker='x', cmap='Set1', vmax=9)\npl.scatter(xs2[:, 0], xs2[:, 1], c=ys2, s=35, marker='+', cmap='Set1', vmax=9)\npl.scatter(xt[:, 0], xt[:, 1], c=yt, s=35, marker='o', cmap='Set1', vmax=9)\n\npl.plot([], [], 'r', alpha=.2, label='Mass from Class 1')\npl.plot([], [], 'b', alpha=.2, label='Mass from Class 2')\n\npl.title('OT with known proportion ({:1.1f},{:1.1f})'.format(h_res[0], h_res[1]))\n\npl.legend()\npl.axis('equal')\npl.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": "3.6.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_otda_jcpot.py b/docs/source/auto_examples/plot_otda_jcpot.py deleted file mode 100644 index c495690..0000000 --- a/docs/source/auto_examples/plot_otda_jcpot.py +++ /dev/null @@ -1,171 +0,0 @@ -# -*- coding: utf-8 -*- -""" -======================== -OT for multi-source target shift -======================== - -This example introduces a target shift problem with two 2D source and 1 target domain. - -""" - -# Authors: Remi Flamary <remi.flamary@unice.fr> -# Ievgen Redko <ievgen.redko@univ-st-etienne.fr> -# -# License: MIT License - -import pylab as pl -import numpy as np -import ot -from ot.datasets import make_data_classif - -############################################################################## -# Generate data -# ------------- -n = 50 -sigma = 0.3 -np.random.seed(1985) - -p1 = .2 -dec1 = [0, 2] - -p2 = .9 -dec2 = [0, -2] - -pt = .4 -dect = [4, 0] - -xs1, ys1 = make_data_classif('2gauss_prop', n, nz=sigma, p=p1, bias=dec1) -xs2, ys2 = make_data_classif('2gauss_prop', n + 1, nz=sigma, p=p2, bias=dec2) -xt, yt = make_data_classif('2gauss_prop', n, nz=sigma, p=pt, bias=dect) - -all_Xr = [xs1, xs2] -all_Yr = [ys1, ys2] -# %% - -da = 1.5 - - -def plot_ax(dec, name): - pl.plot([dec[0], dec[0]], [dec[1] - da, dec[1] + da], 'k', alpha=0.5) - pl.plot([dec[0] - da, dec[0] + da], [dec[1], dec[1]], 'k', alpha=0.5) - pl.text(dec[0] - .5, dec[1] + 2, name) - - -############################################################################## -# Fig 1 : plots source and target samples -# --------------------------------------- - -pl.figure(1) -pl.clf() -plot_ax(dec1, 'Source 1') -plot_ax(dec2, 'Source 2') -plot_ax(dect, 'Target') -pl.scatter(xs1[:, 0], xs1[:, 1], c=ys1, s=35, marker='x', cmap='Set1', vmax=9, - label='Source 1 ({:1.2f}, {:1.2f})'.format(1 - p1, p1)) -pl.scatter(xs2[:, 0], xs2[:, 1], c=ys2, s=35, marker='+', cmap='Set1', vmax=9, - label='Source 2 ({:1.2f}, {:1.2f})'.format(1 - p2, p2)) -pl.scatter(xt[:, 0], xt[:, 1], c=yt, s=35, marker='o', cmap='Set1', vmax=9, - label='Target ({:1.2f}, {:1.2f})'.format(1 - pt, pt)) -pl.title('Data') - -pl.legend() -pl.axis('equal') -pl.axis('off') - -############################################################################## -# Instantiate Sinkhorn transport algorithm and fit them for all source domains -# ---------------------------------------------------------------------------- -ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1, metric='sqeuclidean') - - -def print_G(G, xs, ys, xt): - for i in range(G.shape[0]): - for j in range(G.shape[1]): - if G[i, j] > 5e-4: - if ys[i]: - c = 'b' - else: - c = 'r' - pl.plot([xs[i, 0], xt[j, 0]], [xs[i, 1], xt[j, 1]], c, alpha=.2) - - -############################################################################## -# Fig 2 : plot optimal couplings and transported samples -# ------------------------------------------------------ -pl.figure(2) -pl.clf() -plot_ax(dec1, 'Source 1') -plot_ax(dec2, 'Source 2') -plot_ax(dect, 'Target') -print_G(ot_sinkhorn.fit(Xs=xs1, Xt=xt).coupling_, xs1, ys1, xt) -print_G(ot_sinkhorn.fit(Xs=xs2, Xt=xt).coupling_, xs2, ys2, xt) -pl.scatter(xs1[:, 0], xs1[:, 1], c=ys1, s=35, marker='x', cmap='Set1', vmax=9) -pl.scatter(xs2[:, 0], xs2[:, 1], c=ys2, s=35, marker='+', cmap='Set1', vmax=9) -pl.scatter(xt[:, 0], xt[:, 1], c=yt, s=35, marker='o', cmap='Set1', vmax=9) - -pl.plot([], [], 'r', alpha=.2, label='Mass from Class 1') -pl.plot([], [], 'b', alpha=.2, label='Mass from Class 2') - -pl.title('Independent OT') - -pl.legend() -pl.axis('equal') -pl.axis('off') - -############################################################################## -# Instantiate JCPOT adaptation algorithm and fit it -# ---------------------------------------------------------------------------- -otda = ot.da.JCPOTTransport(reg_e=1, max_iter=1000, metric='sqeuclidean', tol=1e-9, verbose=True, log=True) -otda.fit(all_Xr, all_Yr, xt) - -ws1 = otda.proportions_.dot(otda.log_['D2'][0]) -ws2 = otda.proportions_.dot(otda.log_['D2'][1]) - -pl.figure(3) -pl.clf() -plot_ax(dec1, 'Source 1') -plot_ax(dec2, 'Source 2') -plot_ax(dect, 'Target') -print_G(ot.bregman.sinkhorn(ws1, [], otda.log_['M'][0], reg=1e-1), xs1, ys1, xt) -print_G(ot.bregman.sinkhorn(ws2, [], otda.log_['M'][1], reg=1e-1), xs2, ys2, xt) -pl.scatter(xs1[:, 0], xs1[:, 1], c=ys1, s=35, marker='x', cmap='Set1', vmax=9) -pl.scatter(xs2[:, 0], xs2[:, 1], c=ys2, s=35, marker='+', cmap='Set1', vmax=9) -pl.scatter(xt[:, 0], xt[:, 1], c=yt, s=35, marker='o', cmap='Set1', vmax=9) - -pl.plot([], [], 'r', alpha=.2, label='Mass from Class 1') -pl.plot([], [], 'b', alpha=.2, label='Mass from Class 2') - -pl.title('OT with prop estimation ({:1.3f},{:1.3f})'.format(otda.proportions_[0], otda.proportions_[1])) - -pl.legend() -pl.axis('equal') -pl.axis('off') - -############################################################################## -# Run oracle transport algorithm with known proportions -# ---------------------------------------------------------------------------- -h_res = np.array([1 - pt, pt]) - -ws1 = h_res.dot(otda.log_['D2'][0]) -ws2 = h_res.dot(otda.log_['D2'][1]) - -pl.figure(4) -pl.clf() -plot_ax(dec1, 'Source 1') -plot_ax(dec2, 'Source 2') -plot_ax(dect, 'Target') -print_G(ot.bregman.sinkhorn(ws1, [], otda.log_['M'][0], reg=1e-1), xs1, ys1, xt) -print_G(ot.bregman.sinkhorn(ws2, [], otda.log_['M'][1], reg=1e-1), xs2, ys2, xt) -pl.scatter(xs1[:, 0], xs1[:, 1], c=ys1, s=35, marker='x', cmap='Set1', vmax=9) -pl.scatter(xs2[:, 0], xs2[:, 1], c=ys2, s=35, marker='+', cmap='Set1', vmax=9) -pl.scatter(xt[:, 0], xt[:, 1], c=yt, s=35, marker='o', cmap='Set1', vmax=9) - -pl.plot([], [], 'r', alpha=.2, label='Mass from Class 1') -pl.plot([], [], 'b', alpha=.2, label='Mass from Class 2') - -pl.title('OT with known proportion ({:1.1f},{:1.1f})'.format(h_res[0], h_res[1])) - -pl.legend() -pl.axis('equal') -pl.axis('off') -pl.show() diff --git a/docs/source/auto_examples/plot_otda_jcpot.rst b/docs/source/auto_examples/plot_otda_jcpot.rst deleted file mode 100644 index 3433190..0000000 --- a/docs/source/auto_examples/plot_otda_jcpot.rst +++ /dev/null @@ -1,336 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_otda_jcpot.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_otda_jcpot.py: - - -======================== -OT for multi-source target shift -======================== - -This example introduces a target shift problem with two 2D source and 1 target domain. - - - -.. code-block:: default - - - # Authors: Remi Flamary <remi.flamary@unice.fr> - # Ievgen Redko <ievgen.redko@univ-st-etienne.fr> - # - # License: MIT License - - import pylab as pl - import numpy as np - import ot - from ot.datasets import make_data_classif - - - - - - - - -Generate data -------------- - - -.. code-block:: default - - n = 50 - sigma = 0.3 - np.random.seed(1985) - - p1 = .2 - dec1 = [0, 2] - - p2 = .9 - dec2 = [0, -2] - - pt = .4 - dect = [4, 0] - - xs1, ys1 = make_data_classif('2gauss_prop', n, nz=sigma, p=p1, bias=dec1) - xs2, ys2 = make_data_classif('2gauss_prop', n + 1, nz=sigma, p=p2, bias=dec2) - xt, yt = make_data_classif('2gauss_prop', n, nz=sigma, p=pt, bias=dect) - - all_Xr = [xs1, xs2] - all_Yr = [ys1, ys2] - - - - - - - - -.. code-block:: default - - - da = 1.5 - - - def plot_ax(dec, name): - pl.plot([dec[0], dec[0]], [dec[1] - da, dec[1] + da], 'k', alpha=0.5) - pl.plot([dec[0] - da, dec[0] + da], [dec[1], dec[1]], 'k', alpha=0.5) - pl.text(dec[0] - .5, dec[1] + 2, name) - - - - - - - - - -Fig 1 : plots source and target samples ---------------------------------------- - - -.. code-block:: default - - - pl.figure(1) - pl.clf() - plot_ax(dec1, 'Source 1') - plot_ax(dec2, 'Source 2') - plot_ax(dect, 'Target') - pl.scatter(xs1[:, 0], xs1[:, 1], c=ys1, s=35, marker='x', cmap='Set1', vmax=9, - label='Source 1 ({:1.2f}, {:1.2f})'.format(1 - p1, p1)) - pl.scatter(xs2[:, 0], xs2[:, 1], c=ys2, s=35, marker='+', cmap='Set1', vmax=9, - label='Source 2 ({:1.2f}, {:1.2f})'.format(1 - p2, p2)) - pl.scatter(xt[:, 0], xt[:, 1], c=yt, s=35, marker='o', cmap='Set1', vmax=9, - label='Target ({:1.2f}, {:1.2f})'.format(1 - pt, pt)) - pl.title('Data') - - pl.legend() - pl.axis('equal') - pl.axis('off') - - - - -.. image:: /auto_examples/images/sphx_glr_plot_otda_jcpot_001.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - - (-1.85, 5.85, -4.1171725099266725, 4.197384527473105) - - - -Instantiate Sinkhorn transport algorithm and fit them for all source domains ----------------------------------------------------------------------------- - - -.. code-block:: default - - ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1, metric='sqeuclidean') - - - def print_G(G, xs, ys, xt): - for i in range(G.shape[0]): - for j in range(G.shape[1]): - if G[i, j] > 5e-4: - if ys[i]: - c = 'b' - else: - c = 'r' - pl.plot([xs[i, 0], xt[j, 0]], [xs[i, 1], xt[j, 1]], c, alpha=.2) - - - - - - - - - -Fig 2 : plot optimal couplings and transported samples ------------------------------------------------------- - - -.. code-block:: default - - pl.figure(2) - pl.clf() - plot_ax(dec1, 'Source 1') - plot_ax(dec2, 'Source 2') - plot_ax(dect, 'Target') - print_G(ot_sinkhorn.fit(Xs=xs1, Xt=xt).coupling_, xs1, ys1, xt) - print_G(ot_sinkhorn.fit(Xs=xs2, Xt=xt).coupling_, xs2, ys2, xt) - pl.scatter(xs1[:, 0], xs1[:, 1], c=ys1, s=35, marker='x', cmap='Set1', vmax=9) - pl.scatter(xs2[:, 0], xs2[:, 1], c=ys2, s=35, marker='+', cmap='Set1', vmax=9) - pl.scatter(xt[:, 0], xt[:, 1], c=yt, s=35, marker='o', cmap='Set1', vmax=9) - - pl.plot([], [], 'r', alpha=.2, label='Mass from Class 1') - pl.plot([], [], 'b', alpha=.2, label='Mass from Class 2') - - pl.title('Independent OT') - - pl.legend() - pl.axis('equal') - pl.axis('off') - - - - -.. image:: /auto_examples/images/sphx_glr_plot_otda_jcpot_002.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - - (-1.85, 5.85, -4.11901398007908, 4.201462272227509) - - - -Instantiate JCPOT adaptation algorithm and fit it ----------------------------------------------------------------------------- - - -.. code-block:: default - - otda = ot.da.JCPOTTransport(reg_e=1, max_iter=1000, metric='sqeuclidean', tol=1e-9, verbose=True, log=True) - otda.fit(all_Xr, all_Yr, xt) - - ws1 = otda.proportions_.dot(otda.log_['D2'][0]) - ws2 = otda.proportions_.dot(otda.log_['D2'][1]) - - pl.figure(3) - pl.clf() - plot_ax(dec1, 'Source 1') - plot_ax(dec2, 'Source 2') - plot_ax(dect, 'Target') - print_G(ot.bregman.sinkhorn(ws1, [], otda.log_['M'][0], reg=1e-1), xs1, ys1, xt) - print_G(ot.bregman.sinkhorn(ws2, [], otda.log_['M'][1], reg=1e-1), xs2, ys2, xt) - pl.scatter(xs1[:, 0], xs1[:, 1], c=ys1, s=35, marker='x', cmap='Set1', vmax=9) - pl.scatter(xs2[:, 0], xs2[:, 1], c=ys2, s=35, marker='+', cmap='Set1', vmax=9) - pl.scatter(xt[:, 0], xt[:, 1], c=yt, s=35, marker='o', cmap='Set1', vmax=9) - - pl.plot([], [], 'r', alpha=.2, label='Mass from Class 1') - pl.plot([], [], 'b', alpha=.2, label='Mass from Class 2') - - pl.title('OT with prop estimation ({:1.3f},{:1.3f})'.format(otda.proportions_[0], otda.proportions_[1])) - - pl.legend() - pl.axis('equal') - pl.axis('off') - - - - -.. image:: /auto_examples/images/sphx_glr_plot_otda_jcpot_003.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - - (-1.85, 5.85, -4.11901398007908, 4.201462272227509) - - - -Run oracle transport algorithm with known proportions ----------------------------------------------------------------------------- - - -.. code-block:: default - - h_res = np.array([1 - pt, pt]) - - ws1 = h_res.dot(otda.log_['D2'][0]) - ws2 = h_res.dot(otda.log_['D2'][1]) - - pl.figure(4) - pl.clf() - plot_ax(dec1, 'Source 1') - plot_ax(dec2, 'Source 2') - plot_ax(dect, 'Target') - print_G(ot.bregman.sinkhorn(ws1, [], otda.log_['M'][0], reg=1e-1), xs1, ys1, xt) - print_G(ot.bregman.sinkhorn(ws2, [], otda.log_['M'][1], reg=1e-1), xs2, ys2, xt) - pl.scatter(xs1[:, 0], xs1[:, 1], c=ys1, s=35, marker='x', cmap='Set1', vmax=9) - pl.scatter(xs2[:, 0], xs2[:, 1], c=ys2, s=35, marker='+', cmap='Set1', vmax=9) - pl.scatter(xt[:, 0], xt[:, 1], c=yt, s=35, marker='o', cmap='Set1', vmax=9) - - pl.plot([], [], 'r', alpha=.2, label='Mass from Class 1') - pl.plot([], [], 'b', alpha=.2, label='Mass from Class 2') - - pl.title('OT with known proportion ({:1.1f},{:1.1f})'.format(h_res[0], h_res[1])) - - pl.legend() - pl.axis('equal') - pl.axis('off') - pl.show() - - - -.. image:: /auto_examples/images/sphx_glr_plot_otda_jcpot_004.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_otda_jcpot.py:171: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 4.725 seconds) - - -.. _sphx_glr_download_auto_examples_plot_otda_jcpot.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_otda_jcpot.py <plot_otda_jcpot.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: plot_otda_jcpot.ipynb <plot_otda_jcpot.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ diff --git a/docs/source/auto_examples/plot_otda_laplacian.ipynb b/docs/source/auto_examples/plot_otda_laplacian.ipynb deleted file mode 100644 index c1e9efe..0000000 --- a/docs/source/auto_examples/plot_otda_laplacian.ipynb +++ /dev/null @@ -1,126 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n# OT with Laplacian regularization for domain adaptation\n\n\nThis example introduces a domain adaptation in a 2D setting and OTDA\napproach with Laplacian regularization.\n\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Authors: Ievgen Redko <ievgen.redko@univ-st-etienne.fr>\n\n# License: MIT License\n\nimport matplotlib.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_source_samples = 150\nn_target_samples = 150\n\nXs, ys = ot.datasets.make_data_classif('3gauss', n_source_samples)\nXt, yt = ot.datasets.make_data_classif('3gauss2', n_target_samples)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Instantiate the different transport algorithms and fit them\n-----------------------------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# EMD Transport\not_emd = ot.da.EMDTransport()\not_emd.fit(Xs=Xs, Xt=Xt)\n\n# Sinkhorn Transport\not_sinkhorn = ot.da.SinkhornTransport(reg_e=.01)\not_sinkhorn.fit(Xs=Xs, Xt=Xt)\n\n# EMD Transport with Laplacian regularization\not_emd_laplace = ot.da.EMDLaplaceTransport(reg_lap=100, reg_src=1)\not_emd_laplace.fit(Xs=Xs, Xt=Xt)\n\n# transport source samples onto target samples\ntransp_Xs_emd = ot_emd.transform(Xs=Xs)\ntransp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=Xs)\ntransp_Xs_emd_laplace = ot_emd_laplace.transform(Xs=Xs)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Fig 1 : plots source and target samples\n---------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pl.figure(1, figsize=(10, 5))\npl.subplot(1, 2, 1)\npl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')\npl.xticks([])\npl.yticks([])\npl.legend(loc=0)\npl.title('Source samples')\n\npl.subplot(1, 2, 2)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')\npl.xticks([])\npl.yticks([])\npl.legend(loc=0)\npl.title('Target samples')\npl.tight_layout()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Fig 2 : plot optimal couplings and transported samples\n------------------------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "param_img = {'interpolation': 'nearest'}\n\npl.figure(2, figsize=(15, 8))\npl.subplot(2, 3, 1)\npl.imshow(ot_emd.coupling_, **param_img)\npl.xticks([])\npl.yticks([])\npl.title('Optimal coupling\\nEMDTransport')\n\npl.figure(2, figsize=(15, 8))\npl.subplot(2, 3, 2)\npl.imshow(ot_sinkhorn.coupling_, **param_img)\npl.xticks([])\npl.yticks([])\npl.title('Optimal coupling\\nSinkhornTransport')\n\npl.subplot(2, 3, 3)\npl.imshow(ot_emd_laplace.coupling_, **param_img)\npl.xticks([])\npl.yticks([])\npl.title('Optimal coupling\\nEMDLaplaceTransport')\n\npl.subplot(2, 3, 4)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=0.3)\npl.scatter(transp_Xs_emd[:, 0], transp_Xs_emd[:, 1], c=ys,\n marker='+', label='Transp samples', s=30)\npl.xticks([])\npl.yticks([])\npl.title('Transported samples\\nEmdTransport')\npl.legend(loc=\"lower left\")\n\npl.subplot(2, 3, 5)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=0.3)\npl.scatter(transp_Xs_sinkhorn[:, 0], transp_Xs_sinkhorn[:, 1], c=ys,\n marker='+', label='Transp samples', s=30)\npl.xticks([])\npl.yticks([])\npl.title('Transported samples\\nSinkhornTransport')\n\npl.subplot(2, 3, 6)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=0.3)\npl.scatter(transp_Xs_emd_laplace[:, 0], transp_Xs_emd_laplace[:, 1], c=ys,\n marker='+', label='Transp samples', s=30)\npl.xticks([])\npl.yticks([])\npl.title('Transported samples\\nEMDLaplaceTransport')\npl.tight_layout()\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": "3.6.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_otda_laplacian.py b/docs/source/auto_examples/plot_otda_laplacian.py deleted file mode 100644 index 67c8f67..0000000 --- a/docs/source/auto_examples/plot_otda_laplacian.py +++ /dev/null @@ -1,127 +0,0 @@ -# -*- coding: utf-8 -*- -""" -====================================================== -OT with Laplacian regularization for domain adaptation -====================================================== - -This example introduces a domain adaptation in a 2D setting and OTDA -approach with Laplacian regularization. - -""" - -# Authors: Ievgen Redko <ievgen.redko@univ-st-etienne.fr> - -# License: MIT License - -import matplotlib.pylab as pl -import ot - -############################################################################## -# Generate data -# ------------- - -n_source_samples = 150 -n_target_samples = 150 - -Xs, ys = ot.datasets.make_data_classif('3gauss', n_source_samples) -Xt, yt = ot.datasets.make_data_classif('3gauss2', n_target_samples) - - -############################################################################## -# Instantiate the different transport algorithms and fit them -# ----------------------------------------------------------- - -# EMD Transport -ot_emd = ot.da.EMDTransport() -ot_emd.fit(Xs=Xs, Xt=Xt) - -# Sinkhorn Transport -ot_sinkhorn = ot.da.SinkhornTransport(reg_e=.01) -ot_sinkhorn.fit(Xs=Xs, Xt=Xt) - -# EMD Transport with Laplacian regularization -ot_emd_laplace = ot.da.EMDLaplaceTransport(reg_lap=100, reg_src=1) -ot_emd_laplace.fit(Xs=Xs, Xt=Xt) - -# transport source samples onto target samples -transp_Xs_emd = ot_emd.transform(Xs=Xs) -transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=Xs) -transp_Xs_emd_laplace = ot_emd_laplace.transform(Xs=Xs) - -############################################################################## -# Fig 1 : plots source and target samples -# --------------------------------------- - -pl.figure(1, figsize=(10, 5)) -pl.subplot(1, 2, 1) -pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') -pl.xticks([]) -pl.yticks([]) -pl.legend(loc=0) -pl.title('Source samples') - -pl.subplot(1, 2, 2) -pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') -pl.xticks([]) -pl.yticks([]) -pl.legend(loc=0) -pl.title('Target samples') -pl.tight_layout() - - -############################################################################## -# Fig 2 : plot optimal couplings and transported samples -# ------------------------------------------------------ - -param_img = {'interpolation': 'nearest'} - -pl.figure(2, figsize=(15, 8)) -pl.subplot(2, 3, 1) -pl.imshow(ot_emd.coupling_, **param_img) -pl.xticks([]) -pl.yticks([]) -pl.title('Optimal coupling\nEMDTransport') - -pl.figure(2, figsize=(15, 8)) -pl.subplot(2, 3, 2) -pl.imshow(ot_sinkhorn.coupling_, **param_img) -pl.xticks([]) -pl.yticks([]) -pl.title('Optimal coupling\nSinkhornTransport') - -pl.subplot(2, 3, 3) -pl.imshow(ot_emd_laplace.coupling_, **param_img) -pl.xticks([]) -pl.yticks([]) -pl.title('Optimal coupling\nEMDLaplaceTransport') - -pl.subplot(2, 3, 4) -pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=0.3) -pl.scatter(transp_Xs_emd[:, 0], transp_Xs_emd[:, 1], c=ys, - marker='+', label='Transp samples', s=30) -pl.xticks([]) -pl.yticks([]) -pl.title('Transported samples\nEmdTransport') -pl.legend(loc="lower left") - -pl.subplot(2, 3, 5) -pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=0.3) -pl.scatter(transp_Xs_sinkhorn[:, 0], transp_Xs_sinkhorn[:, 1], c=ys, - marker='+', label='Transp samples', s=30) -pl.xticks([]) -pl.yticks([]) -pl.title('Transported samples\nSinkhornTransport') - -pl.subplot(2, 3, 6) -pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=0.3) -pl.scatter(transp_Xs_emd_laplace[:, 0], transp_Xs_emd_laplace[:, 1], c=ys, - marker='+', label='Transp samples', s=30) -pl.xticks([]) -pl.yticks([]) -pl.title('Transported samples\nEMDLaplaceTransport') -pl.tight_layout() - -pl.show() diff --git a/docs/source/auto_examples/plot_otda_laplacian.rst b/docs/source/auto_examples/plot_otda_laplacian.rst deleted file mode 100644 index 12cd7b9..0000000 --- a/docs/source/auto_examples/plot_otda_laplacian.rst +++ /dev/null @@ -1,233 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_otda_laplacian.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_otda_laplacian.py: - - -====================================================== -OT with Laplacian regularization for domain adaptation -====================================================== - -This example introduces a domain adaptation in a 2D setting and OTDA -approach with Laplacian regularization. - - - -.. code-block:: default - - - # Authors: Ievgen Redko <ievgen.redko@univ-st-etienne.fr> - - # License: MIT License - - import matplotlib.pylab as pl - import ot - - - - - - - - -Generate data -------------- - - -.. code-block:: default - - - n_source_samples = 150 - n_target_samples = 150 - - Xs, ys = ot.datasets.make_data_classif('3gauss', n_source_samples) - Xt, yt = ot.datasets.make_data_classif('3gauss2', n_target_samples) - - - - - - - - - -Instantiate the different transport algorithms and fit them ------------------------------------------------------------ - - -.. code-block:: default - - - # EMD Transport - ot_emd = ot.da.EMDTransport() - ot_emd.fit(Xs=Xs, Xt=Xt) - - # Sinkhorn Transport - ot_sinkhorn = ot.da.SinkhornTransport(reg_e=.01) - ot_sinkhorn.fit(Xs=Xs, Xt=Xt) - - # EMD Transport with Laplacian regularization - ot_emd_laplace = ot.da.EMDLaplaceTransport(reg_lap=100, reg_src=1) - ot_emd_laplace.fit(Xs=Xs, Xt=Xt) - - # transport source samples onto target samples - transp_Xs_emd = ot_emd.transform(Xs=Xs) - transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=Xs) - transp_Xs_emd_laplace = ot_emd_laplace.transform(Xs=Xs) - - - - - - - - -Fig 1 : plots source and target samples ---------------------------------------- - - -.. code-block:: default - - - pl.figure(1, figsize=(10, 5)) - pl.subplot(1, 2, 1) - pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') - pl.xticks([]) - pl.yticks([]) - pl.legend(loc=0) - pl.title('Source samples') - - pl.subplot(1, 2, 2) - pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') - pl.xticks([]) - pl.yticks([]) - pl.legend(loc=0) - pl.title('Target samples') - pl.tight_layout() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_otda_laplacian_001.png - :class: sphx-glr-single-img - - - - - -Fig 2 : plot optimal couplings and transported samples ------------------------------------------------------- - - -.. code-block:: default - - - param_img = {'interpolation': 'nearest'} - - pl.figure(2, figsize=(15, 8)) - pl.subplot(2, 3, 1) - pl.imshow(ot_emd.coupling_, **param_img) - pl.xticks([]) - pl.yticks([]) - pl.title('Optimal coupling\nEMDTransport') - - pl.figure(2, figsize=(15, 8)) - pl.subplot(2, 3, 2) - pl.imshow(ot_sinkhorn.coupling_, **param_img) - pl.xticks([]) - pl.yticks([]) - pl.title('Optimal coupling\nSinkhornTransport') - - pl.subplot(2, 3, 3) - pl.imshow(ot_emd_laplace.coupling_, **param_img) - pl.xticks([]) - pl.yticks([]) - pl.title('Optimal coupling\nEMDLaplaceTransport') - - pl.subplot(2, 3, 4) - pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=0.3) - pl.scatter(transp_Xs_emd[:, 0], transp_Xs_emd[:, 1], c=ys, - marker='+', label='Transp samples', s=30) - pl.xticks([]) - pl.yticks([]) - pl.title('Transported samples\nEmdTransport') - pl.legend(loc="lower left") - - pl.subplot(2, 3, 5) - pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=0.3) - pl.scatter(transp_Xs_sinkhorn[:, 0], transp_Xs_sinkhorn[:, 1], c=ys, - marker='+', label='Transp samples', s=30) - pl.xticks([]) - pl.yticks([]) - pl.title('Transported samples\nSinkhornTransport') - - pl.subplot(2, 3, 6) - pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=0.3) - pl.scatter(transp_Xs_emd_laplace[:, 0], transp_Xs_emd_laplace[:, 1], c=ys, - marker='+', label='Transp samples', s=30) - pl.xticks([]) - pl.yticks([]) - pl.title('Transported samples\nEMDLaplaceTransport') - pl.tight_layout() - - pl.show() - - - -.. image:: /auto_examples/images/sphx_glr_plot_otda_laplacian_002.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_otda_laplacian.py:127: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 1.195 seconds) - - -.. _sphx_glr_download_auto_examples_plot_otda_laplacian.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_otda_laplacian.py <plot_otda_laplacian.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: plot_otda_laplacian.ipynb <plot_otda_laplacian.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ diff --git a/docs/source/auto_examples/plot_otda_linear_mapping.ipynb b/docs/source/auto_examples/plot_otda_linear_mapping.ipynb deleted file mode 100644 index 96eccbe..0000000 --- a/docs/source/auto_examples/plot_otda_linear_mapping.ipynb +++ /dev/null @@ -1,180 +0,0 @@ -{ - "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))" - ] - }, - { - "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": "3.6.9" - } - }, - "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 deleted file mode 100644 index c65bd4f..0000000 --- a/docs/source/auto_examples/plot_otda_linear_mapping.py +++ /dev/null @@ -1,144 +0,0 @@ -#!/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 deleted file mode 100644 index 63848d2..0000000 --- a/docs/source/auto_examples/plot_otda_linear_mapping.rst +++ /dev/null @@ -1,295 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_otda_linear_mapping.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_otda_linear_mapping.py: - - -============================ -Linear OT mapping estimation -============================ - - - - -.. code-block:: default - - - # Author: Remi Flamary <remi.flamary@unice.fr> - # - # License: MIT License - - import numpy as np - import pylab as pl - import ot - - - - - - - - -Generate data -------------- - - -.. code-block:: default - - - 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:: default - - - 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 - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - - [<matplotlib.lines.Line2D object at 0x7f4c73a37320>] - - - -Estimate linear mapping and transport -------------------------------------- - - -.. code-block:: default - - - Ae, be = ot.da.OT_mapping_linear(xs, xt) - - xst = xs.dot(Ae) + be - - - - - - - - - -Plot transported samples ------------------------- - - -.. code-block:: default - - - 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 - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_otda_linear_mapping.py:73: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - -Load image data ---------------- - - -.. code-block:: default - - - - 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:: default - - - 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:: default - - - 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_003.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - - Text(0.5, 1.0, 'Inverse mapping Im. 2') - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 0.787 seconds) - - -.. _sphx_glr_download_auto_examples_plot_otda_linear_mapping.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_otda_linear_mapping.py <plot_otda_linear_mapping.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :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.github.io>`_ diff --git a/docs/source/auto_examples/plot_otda_mapping.ipynb b/docs/source/auto_examples/plot_otda_mapping.ipynb deleted file mode 100644 index ac02255..0000000 --- a/docs/source/auto_examples/plot_otda_mapping.ipynb +++ /dev/null @@ -1,126 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n# OT mapping estimation for domain adaptation\n\n\nThis example presents how to use MappingTransport to estimate at the same\ntime both the coupling transport and approximate the transport map with either\na linear or a kernelized mapping as introduced in [8].\n\n[8] M. Perrot, N. Courty, R. Flamary, A. Habrard,\n \"Mapping estimation for discrete optimal transport\",\n Neural Information Processing Systems (NIPS), 2016.\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Authors: Remi Flamary <remi.flamary@unice.fr>\n# Stanislas Chambon <stan.chambon@gmail.com>\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\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "n_source_samples = 100\nn_target_samples = 100\ntheta = 2 * np.pi / 20\nnoise_level = 0.1\n\nXs, ys = ot.datasets.make_data_classif(\n 'gaussrot', n_source_samples, nz=noise_level)\nXs_new, _ = ot.datasets.make_data_classif(\n 'gaussrot', n_source_samples, nz=noise_level)\nXt, yt = ot.datasets.make_data_classif(\n 'gaussrot', n_target_samples, theta=theta, nz=noise_level)\n\n# one of the target mode changes its variance (no linear mapping)\nXt[yt == 2] *= 3\nXt = Xt + 4" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Plot data\n---------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pl.figure(1, (10, 5))\npl.clf()\npl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')\npl.legend(loc=0)\npl.title('Source and target distributions')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Instantiate the different transport algorithms and fit them\n-----------------------------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# MappingTransport with linear kernel\not_mapping_linear = ot.da.MappingTransport(\n kernel=\"linear\", mu=1e0, eta=1e-8, bias=True,\n max_iter=20, verbose=True)\n\not_mapping_linear.fit(Xs=Xs, Xt=Xt)\n\n# for original source samples, transform applies barycentric mapping\ntransp_Xs_linear = ot_mapping_linear.transform(Xs=Xs)\n\n# for out of source samples, transform applies the linear mapping\ntransp_Xs_linear_new = ot_mapping_linear.transform(Xs=Xs_new)\n\n\n# MappingTransport with gaussian kernel\not_mapping_gaussian = ot.da.MappingTransport(\n kernel=\"gaussian\", eta=1e-5, mu=1e-1, bias=True, sigma=1,\n max_iter=10, verbose=True)\not_mapping_gaussian.fit(Xs=Xs, Xt=Xt)\n\n# for original source samples, transform applies barycentric mapping\ntransp_Xs_gaussian = ot_mapping_gaussian.transform(Xs=Xs)\n\n# for out of source samples, transform applies the gaussian mapping\ntransp_Xs_gaussian_new = ot_mapping_gaussian.transform(Xs=Xs_new)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Plot transported samples\n------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pl.figure(2)\npl.clf()\npl.subplot(2, 2, 1)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=.2)\npl.scatter(transp_Xs_linear[:, 0], transp_Xs_linear[:, 1], c=ys, marker='+',\n label='Mapped source samples')\npl.title(\"Bary. mapping (linear)\")\npl.legend(loc=0)\n\npl.subplot(2, 2, 2)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=.2)\npl.scatter(transp_Xs_linear_new[:, 0], transp_Xs_linear_new[:, 1],\n c=ys, marker='+', label='Learned mapping')\npl.title(\"Estim. mapping (linear)\")\n\npl.subplot(2, 2, 3)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=.2)\npl.scatter(transp_Xs_gaussian[:, 0], transp_Xs_gaussian[:, 1], c=ys,\n marker='+', label='barycentric mapping')\npl.title(\"Bary. mapping (kernel)\")\n\npl.subplot(2, 2, 4)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=.2)\npl.scatter(transp_Xs_gaussian_new[:, 0], transp_Xs_gaussian_new[:, 1], c=ys,\n marker='+', label='Learned mapping')\npl.title(\"Estim. mapping (kernel)\")\npl.tight_layout()\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": "3.6.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_otda_mapping.py b/docs/source/auto_examples/plot_otda_mapping.py deleted file mode 100644 index 5880adf..0000000 --- a/docs/source/auto_examples/plot_otda_mapping.py +++ /dev/null @@ -1,125 +0,0 @@ -# -*- coding: utf-8 -*- -""" -=========================================== -OT mapping estimation for domain adaptation -=========================================== - -This example presents how to use MappingTransport to estimate at the same -time both the coupling transport and approximate the transport map with either -a linear or a kernelized mapping as introduced in [8]. - -[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, - "Mapping estimation for discrete optimal transport", - Neural Information Processing Systems (NIPS), 2016. -""" - -# Authors: Remi Flamary <remi.flamary@unice.fr> -# Stanislas Chambon <stan.chambon@gmail.com> -# -# License: MIT License - -import numpy as np -import matplotlib.pylab as pl -import ot - - -############################################################################## -# Generate data -# ------------- - -n_source_samples = 100 -n_target_samples = 100 -theta = 2 * np.pi / 20 -noise_level = 0.1 - -Xs, ys = ot.datasets.make_data_classif( - 'gaussrot', n_source_samples, nz=noise_level) -Xs_new, _ = ot.datasets.make_data_classif( - 'gaussrot', n_source_samples, nz=noise_level) -Xt, yt = ot.datasets.make_data_classif( - 'gaussrot', n_target_samples, theta=theta, nz=noise_level) - -# one of the target mode changes its variance (no linear mapping) -Xt[yt == 2] *= 3 -Xt = Xt + 4 - -############################################################################## -# Plot data -# --------- - -pl.figure(1, (10, 5)) -pl.clf() -pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') -pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') -pl.legend(loc=0) -pl.title('Source and target distributions') - - -############################################################################## -# Instantiate the different transport algorithms and fit them -# ----------------------------------------------------------- - -# MappingTransport with linear kernel -ot_mapping_linear = ot.da.MappingTransport( - kernel="linear", mu=1e0, eta=1e-8, bias=True, - max_iter=20, verbose=True) - -ot_mapping_linear.fit(Xs=Xs, Xt=Xt) - -# for original source samples, transform applies barycentric mapping -transp_Xs_linear = ot_mapping_linear.transform(Xs=Xs) - -# for out of source samples, transform applies the linear mapping -transp_Xs_linear_new = ot_mapping_linear.transform(Xs=Xs_new) - - -# MappingTransport with gaussian kernel -ot_mapping_gaussian = ot.da.MappingTransport( - kernel="gaussian", eta=1e-5, mu=1e-1, bias=True, sigma=1, - max_iter=10, verbose=True) -ot_mapping_gaussian.fit(Xs=Xs, Xt=Xt) - -# for original source samples, transform applies barycentric mapping -transp_Xs_gaussian = ot_mapping_gaussian.transform(Xs=Xs) - -# for out of source samples, transform applies the gaussian mapping -transp_Xs_gaussian_new = ot_mapping_gaussian.transform(Xs=Xs_new) - - -############################################################################## -# Plot transported samples -# ------------------------ - -pl.figure(2) -pl.clf() -pl.subplot(2, 2, 1) -pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=.2) -pl.scatter(transp_Xs_linear[:, 0], transp_Xs_linear[:, 1], c=ys, marker='+', - label='Mapped source samples') -pl.title("Bary. mapping (linear)") -pl.legend(loc=0) - -pl.subplot(2, 2, 2) -pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=.2) -pl.scatter(transp_Xs_linear_new[:, 0], transp_Xs_linear_new[:, 1], - c=ys, marker='+', label='Learned mapping') -pl.title("Estim. mapping (linear)") - -pl.subplot(2, 2, 3) -pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=.2) -pl.scatter(transp_Xs_gaussian[:, 0], transp_Xs_gaussian[:, 1], c=ys, - marker='+', label='barycentric mapping') -pl.title("Bary. mapping (kernel)") - -pl.subplot(2, 2, 4) -pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=.2) -pl.scatter(transp_Xs_gaussian_new[:, 0], transp_Xs_gaussian_new[:, 1], c=ys, - marker='+', label='Learned mapping') -pl.title("Estim. mapping (kernel)") -pl.tight_layout() - -pl.show() diff --git a/docs/source/auto_examples/plot_otda_mapping.rst b/docs/source/auto_examples/plot_otda_mapping.rst deleted file mode 100644 index 99787f7..0000000 --- a/docs/source/auto_examples/plot_otda_mapping.rst +++ /dev/null @@ -1,268 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_otda_mapping.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_otda_mapping.py: - - -=========================================== -OT mapping estimation for domain adaptation -=========================================== - -This example presents how to use MappingTransport to estimate at the same -time both the coupling transport and approximate the transport map with either -a linear or a kernelized mapping as introduced in [8]. - -[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, - "Mapping estimation for discrete optimal transport", - Neural Information Processing Systems (NIPS), 2016. - - -.. code-block:: default - - - # Authors: Remi Flamary <remi.flamary@unice.fr> - # Stanislas Chambon <stan.chambon@gmail.com> - # - # License: MIT License - - import numpy as np - import matplotlib.pylab as pl - import ot - - - - - - - - - -Generate data -------------- - - -.. code-block:: default - - - n_source_samples = 100 - n_target_samples = 100 - theta = 2 * np.pi / 20 - noise_level = 0.1 - - Xs, ys = ot.datasets.make_data_classif( - 'gaussrot', n_source_samples, nz=noise_level) - Xs_new, _ = ot.datasets.make_data_classif( - 'gaussrot', n_source_samples, nz=noise_level) - Xt, yt = ot.datasets.make_data_classif( - 'gaussrot', n_target_samples, theta=theta, nz=noise_level) - - # one of the target mode changes its variance (no linear mapping) - Xt[yt == 2] *= 3 - Xt = Xt + 4 - - - - - - - - -Plot data ---------- - - -.. code-block:: default - - - pl.figure(1, (10, 5)) - pl.clf() - pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') - pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') - pl.legend(loc=0) - pl.title('Source and target distributions') - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_otda_mapping_001.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - - Text(0.5, 1.0, 'Source and target distributions') - - - -Instantiate the different transport algorithms and fit them ------------------------------------------------------------ - - -.. code-block:: default - - - # MappingTransport with linear kernel - ot_mapping_linear = ot.da.MappingTransport( - kernel="linear", mu=1e0, eta=1e-8, bias=True, - max_iter=20, verbose=True) - - ot_mapping_linear.fit(Xs=Xs, Xt=Xt) - - # for original source samples, transform applies barycentric mapping - transp_Xs_linear = ot_mapping_linear.transform(Xs=Xs) - - # for out of source samples, transform applies the linear mapping - transp_Xs_linear_new = ot_mapping_linear.transform(Xs=Xs_new) - - - # MappingTransport with gaussian kernel - ot_mapping_gaussian = ot.da.MappingTransport( - kernel="gaussian", eta=1e-5, mu=1e-1, bias=True, sigma=1, - max_iter=10, verbose=True) - ot_mapping_gaussian.fit(Xs=Xs, Xt=Xt) - - # for original source samples, transform applies barycentric mapping - transp_Xs_gaussian = ot_mapping_gaussian.transform(Xs=Xs) - - # for out of source samples, transform applies the gaussian mapping - transp_Xs_gaussian_new = ot_mapping_gaussian.transform(Xs=Xs_new) - - - - - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - It. |Loss |Delta loss - -------------------------------- - 0|4.212661e+03|0.000000e+00 - 1|4.198567e+03|-3.345626e-03 - 2|4.198198e+03|-8.797101e-05 - 3|4.198027e+03|-4.059527e-05 - 4|4.197928e+03|-2.355659e-05 - 5|4.197886e+03|-1.002352e-05 - 6|4.197853e+03|-7.873125e-06 - It. |Loss |Delta loss - -------------------------------- - 0|4.231694e+02|0.000000e+00 - 1|4.185911e+02|-1.081889e-02 - 2|4.182717e+02|-7.631953e-04 - 3|4.181271e+02|-3.455908e-04 - 4|4.180328e+02|-2.255461e-04 - 5|4.179645e+02|-1.634435e-04 - 6|4.179136e+02|-1.216359e-04 - 7|4.178752e+02|-9.198108e-05 - 8|4.178465e+02|-6.870868e-05 - 9|4.178243e+02|-5.321390e-05 - 10|4.178054e+02|-4.521725e-05 - - - - -Plot transported samples ------------------------- - - -.. code-block:: default - - - pl.figure(2) - pl.clf() - pl.subplot(2, 2, 1) - pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=.2) - pl.scatter(transp_Xs_linear[:, 0], transp_Xs_linear[:, 1], c=ys, marker='+', - label='Mapped source samples') - pl.title("Bary. mapping (linear)") - pl.legend(loc=0) - - pl.subplot(2, 2, 2) - pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=.2) - pl.scatter(transp_Xs_linear_new[:, 0], transp_Xs_linear_new[:, 1], - c=ys, marker='+', label='Learned mapping') - pl.title("Estim. mapping (linear)") - - pl.subplot(2, 2, 3) - pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=.2) - pl.scatter(transp_Xs_gaussian[:, 0], transp_Xs_gaussian[:, 1], c=ys, - marker='+', label='barycentric mapping') - pl.title("Bary. mapping (kernel)") - - pl.subplot(2, 2, 4) - pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=.2) - pl.scatter(transp_Xs_gaussian_new[:, 0], transp_Xs_gaussian_new[:, 1], c=ys, - marker='+', label='Learned mapping') - pl.title("Estim. mapping (kernel)") - pl.tight_layout() - - pl.show() - - - -.. image:: /auto_examples/images/sphx_glr_plot_otda_mapping_002.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_otda_mapping.py:125: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 0.843 seconds) - - -.. _sphx_glr_download_auto_examples_plot_otda_mapping.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_otda_mapping.py <plot_otda_mapping.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: plot_otda_mapping.ipynb <plot_otda_mapping.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ diff --git a/docs/source/auto_examples/plot_otda_mapping_colors_images.ipynb b/docs/source/auto_examples/plot_otda_mapping_colors_images.ipynb deleted file mode 100644 index de46629..0000000 --- a/docs/source/auto_examples/plot_otda_mapping_colors_images.ipynb +++ /dev/null @@ -1,144 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n# OT for image color adaptation with mapping estimation\n\n\nOT for domain adaptation with image color adaptation [6] with mapping\nestimation [8].\n\n[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014). Regularized\n discrete optimal transport. SIAM Journal on Imaging Sciences, 7(3),\n 1853-1882.\n[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, \"Mapping estimation for\n discrete optimal transport\", Neural Information Processing Systems (NIPS),\n 2016.\n\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Authors: Remi Flamary <remi.flamary@unice.fr>\n# Stanislas Chambon <stan.chambon@gmail.com>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\n\nr = np.random.RandomState(42)\n\n\ndef 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)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Generate data\n-------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# 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)\n\n# training samples\nnb = 1000\nidx1 = r.randint(X1.shape[0], size=(nb,))\nidx2 = r.randint(X2.shape[0], size=(nb,))\n\nXs = X1[idx1, :]\nXt = X2[idx2, :]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Domain adaptation for pixel distribution transfer\n-------------------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# EMDTransport\not_emd = ot.da.EMDTransport()\not_emd.fit(Xs=Xs, Xt=Xt)\ntransp_Xs_emd = ot_emd.transform(Xs=X1)\nImage_emd = minmax(mat2im(transp_Xs_emd, I1.shape))\n\n# SinkhornTransport\not_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1)\not_sinkhorn.fit(Xs=Xs, Xt=Xt)\ntransp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=X1)\nImage_sinkhorn = minmax(mat2im(transp_Xs_sinkhorn, I1.shape))\n\not_mapping_linear = ot.da.MappingTransport(\n mu=1e0, eta=1e-8, bias=True, max_iter=20, verbose=True)\not_mapping_linear.fit(Xs=Xs, Xt=Xt)\n\nX1tl = ot_mapping_linear.transform(Xs=X1)\nImage_mapping_linear = minmax(mat2im(X1tl, I1.shape))\n\not_mapping_gaussian = ot.da.MappingTransport(\n mu=1e0, eta=1e-2, sigma=1, bias=False, max_iter=10, verbose=True)\not_mapping_gaussian.fit(Xs=Xs, Xt=Xt)\n\nX1tn = ot_mapping_gaussian.transform(Xs=X1) # use the estimated mapping\nImage_mapping_gaussian = minmax(mat2im(X1tn, I1.shape))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Plot original images\n--------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pl.figure(1, figsize=(6.4, 3))\npl.subplot(1, 2, 1)\npl.imshow(I1)\npl.axis('off')\npl.title('Image 1')\n\npl.subplot(1, 2, 2)\npl.imshow(I2)\npl.axis('off')\npl.title('Image 2')\npl.tight_layout()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Plot pixel values distribution\n------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pl.figure(2, figsize=(6.4, 5))\n\npl.subplot(1, 2, 1)\npl.scatter(Xs[:, 0], Xs[:, 2], c=Xs)\npl.axis([0, 1, 0, 1])\npl.xlabel('Red')\npl.ylabel('Blue')\npl.title('Image 1')\n\npl.subplot(1, 2, 2)\npl.scatter(Xt[:, 0], Xt[:, 2], c=Xt)\npl.axis([0, 1, 0, 1])\npl.xlabel('Red')\npl.ylabel('Blue')\npl.title('Image 2')\npl.tight_layout()" - ] - }, - { - "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, 5))\n\npl.subplot(2, 3, 1)\npl.imshow(I1)\npl.axis('off')\npl.title('Im. 1')\n\npl.subplot(2, 3, 4)\npl.imshow(I2)\npl.axis('off')\npl.title('Im. 2')\n\npl.subplot(2, 3, 2)\npl.imshow(Image_emd)\npl.axis('off')\npl.title('EmdTransport')\n\npl.subplot(2, 3, 5)\npl.imshow(Image_sinkhorn)\npl.axis('off')\npl.title('SinkhornTransport')\n\npl.subplot(2, 3, 3)\npl.imshow(Image_mapping_linear)\npl.axis('off')\npl.title('MappingTransport (linear)')\n\npl.subplot(2, 3, 6)\npl.imshow(Image_mapping_gaussian)\npl.axis('off')\npl.title('MappingTransport (gaussian)')\npl.tight_layout()\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": "3.6.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_otda_mapping_colors_images.py b/docs/source/auto_examples/plot_otda_mapping_colors_images.py deleted file mode 100644 index bc9afba..0000000 --- a/docs/source/auto_examples/plot_otda_mapping_colors_images.py +++ /dev/null @@ -1,173 +0,0 @@ -# -*- coding: utf-8 -*- -""" -===================================================== -OT for image color adaptation with mapping estimation -===================================================== - -OT for domain adaptation with image color adaptation [6] with mapping -estimation [8]. - -[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014). Regularized - discrete optimal transport. SIAM Journal on Imaging Sciences, 7(3), - 1853-1882. -[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, "Mapping estimation for - discrete optimal transport", Neural Information Processing Systems (NIPS), - 2016. - -""" - -# Authors: Remi Flamary <remi.flamary@unice.fr> -# Stanislas Chambon <stan.chambon@gmail.com> -# -# License: MIT License - -import numpy as np -import matplotlib.pylab as pl -import ot - -r = np.random.RandomState(42) - - -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) - - -############################################################################## -# Generate data -# ------------- - -# 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) - -# training samples -nb = 1000 -idx1 = r.randint(X1.shape[0], size=(nb,)) -idx2 = r.randint(X2.shape[0], size=(nb,)) - -Xs = X1[idx1, :] -Xt = X2[idx2, :] - - -############################################################################## -# Domain adaptation for pixel distribution transfer -# ------------------------------------------------- - -# EMDTransport -ot_emd = ot.da.EMDTransport() -ot_emd.fit(Xs=Xs, Xt=Xt) -transp_Xs_emd = ot_emd.transform(Xs=X1) -Image_emd = minmax(mat2im(transp_Xs_emd, I1.shape)) - -# SinkhornTransport -ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1) -ot_sinkhorn.fit(Xs=Xs, Xt=Xt) -transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=X1) -Image_sinkhorn = minmax(mat2im(transp_Xs_sinkhorn, I1.shape)) - -ot_mapping_linear = ot.da.MappingTransport( - mu=1e0, eta=1e-8, bias=True, max_iter=20, verbose=True) -ot_mapping_linear.fit(Xs=Xs, Xt=Xt) - -X1tl = ot_mapping_linear.transform(Xs=X1) -Image_mapping_linear = minmax(mat2im(X1tl, I1.shape)) - -ot_mapping_gaussian = ot.da.MappingTransport( - mu=1e0, eta=1e-2, sigma=1, bias=False, max_iter=10, verbose=True) -ot_mapping_gaussian.fit(Xs=Xs, Xt=Xt) - -X1tn = ot_mapping_gaussian.transform(Xs=X1) # use the estimated mapping -Image_mapping_gaussian = minmax(mat2im(X1tn, I1.shape)) - - -############################################################################## -# Plot original images -# -------------------- - -pl.figure(1, figsize=(6.4, 3)) -pl.subplot(1, 2, 1) -pl.imshow(I1) -pl.axis('off') -pl.title('Image 1') - -pl.subplot(1, 2, 2) -pl.imshow(I2) -pl.axis('off') -pl.title('Image 2') -pl.tight_layout() - - -############################################################################## -# Plot pixel values distribution -# ------------------------------ - -pl.figure(2, figsize=(6.4, 5)) - -pl.subplot(1, 2, 1) -pl.scatter(Xs[:, 0], Xs[:, 2], c=Xs) -pl.axis([0, 1, 0, 1]) -pl.xlabel('Red') -pl.ylabel('Blue') -pl.title('Image 1') - -pl.subplot(1, 2, 2) -pl.scatter(Xt[:, 0], Xt[:, 2], c=Xt) -pl.axis([0, 1, 0, 1]) -pl.xlabel('Red') -pl.ylabel('Blue') -pl.title('Image 2') -pl.tight_layout() - - -############################################################################## -# Plot transformed images -# ----------------------- - -pl.figure(2, figsize=(10, 5)) - -pl.subplot(2, 3, 1) -pl.imshow(I1) -pl.axis('off') -pl.title('Im. 1') - -pl.subplot(2, 3, 4) -pl.imshow(I2) -pl.axis('off') -pl.title('Im. 2') - -pl.subplot(2, 3, 2) -pl.imshow(Image_emd) -pl.axis('off') -pl.title('EmdTransport') - -pl.subplot(2, 3, 5) -pl.imshow(Image_sinkhorn) -pl.axis('off') -pl.title('SinkhornTransport') - -pl.subplot(2, 3, 3) -pl.imshow(Image_mapping_linear) -pl.axis('off') -pl.title('MappingTransport (linear)') - -pl.subplot(2, 3, 6) -pl.imshow(Image_mapping_gaussian) -pl.axis('off') -pl.title('MappingTransport (gaussian)') -pl.tight_layout() - -pl.show() diff --git a/docs/source/auto_examples/plot_otda_mapping_colors_images.rst b/docs/source/auto_examples/plot_otda_mapping_colors_images.rst deleted file mode 100644 index 26664e3..0000000 --- a/docs/source/auto_examples/plot_otda_mapping_colors_images.rst +++ /dev/null @@ -1,334 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_otda_mapping_colors_images.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_otda_mapping_colors_images.py: - - -===================================================== -OT for image color adaptation with mapping estimation -===================================================== - -OT for domain adaptation with image color adaptation [6] with mapping -estimation [8]. - -[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014). Regularized - discrete optimal transport. SIAM Journal on Imaging Sciences, 7(3), - 1853-1882. -[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, "Mapping estimation for - discrete optimal transport", Neural Information Processing Systems (NIPS), - 2016. - - - -.. code-block:: default - - - # Authors: Remi Flamary <remi.flamary@unice.fr> - # Stanislas Chambon <stan.chambon@gmail.com> - # - # License: MIT License - - import numpy as np - import matplotlib.pylab as pl - import ot - - r = np.random.RandomState(42) - - - 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) - - - - - - - - - -Generate data -------------- - - -.. code-block:: default - - - # 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) - - # training samples - nb = 1000 - idx1 = r.randint(X1.shape[0], size=(nb,)) - idx2 = r.randint(X2.shape[0], size=(nb,)) - - Xs = X1[idx1, :] - Xt = X2[idx2, :] - - - - - - - - - -Domain adaptation for pixel distribution transfer -------------------------------------------------- - - -.. code-block:: default - - - # EMDTransport - ot_emd = ot.da.EMDTransport() - ot_emd.fit(Xs=Xs, Xt=Xt) - transp_Xs_emd = ot_emd.transform(Xs=X1) - Image_emd = minmax(mat2im(transp_Xs_emd, I1.shape)) - - # SinkhornTransport - ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1) - ot_sinkhorn.fit(Xs=Xs, Xt=Xt) - transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=X1) - Image_sinkhorn = minmax(mat2im(transp_Xs_sinkhorn, I1.shape)) - - ot_mapping_linear = ot.da.MappingTransport( - mu=1e0, eta=1e-8, bias=True, max_iter=20, verbose=True) - ot_mapping_linear.fit(Xs=Xs, Xt=Xt) - - X1tl = ot_mapping_linear.transform(Xs=X1) - Image_mapping_linear = minmax(mat2im(X1tl, I1.shape)) - - ot_mapping_gaussian = ot.da.MappingTransport( - mu=1e0, eta=1e-2, sigma=1, bias=False, max_iter=10, verbose=True) - ot_mapping_gaussian.fit(Xs=Xs, Xt=Xt) - - X1tn = ot_mapping_gaussian.transform(Xs=X1) # use the estimated mapping - Image_mapping_gaussian = minmax(mat2im(X1tn, I1.shape)) - - - - - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - It. |Loss |Delta loss - -------------------------------- - 0|3.680534e+02|0.000000e+00 - 1|3.592501e+02|-2.391854e-02 - 2|3.590682e+02|-5.061555e-04 - 3|3.589745e+02|-2.610227e-04 - 4|3.589167e+02|-1.611644e-04 - 5|3.588768e+02|-1.109242e-04 - 6|3.588482e+02|-7.972733e-05 - 7|3.588261e+02|-6.166174e-05 - 8|3.588086e+02|-4.871697e-05 - 9|3.587946e+02|-3.919056e-05 - 10|3.587830e+02|-3.228124e-05 - 11|3.587731e+02|-2.744744e-05 - 12|3.587648e+02|-2.334451e-05 - 13|3.587576e+02|-1.995629e-05 - 14|3.587513e+02|-1.761058e-05 - 15|3.587457e+02|-1.542568e-05 - 16|3.587408e+02|-1.366315e-05 - 17|3.587365e+02|-1.221732e-05 - 18|3.587325e+02|-1.102488e-05 - 19|3.587303e+02|-6.062107e-06 - It. |Loss |Delta loss - -------------------------------- - 0|3.784871e+02|0.000000e+00 - 1|3.646491e+02|-3.656142e-02 - 2|3.642975e+02|-9.642655e-04 - 3|3.641626e+02|-3.702413e-04 - 4|3.640888e+02|-2.026301e-04 - 5|3.640419e+02|-1.289607e-04 - 6|3.640097e+02|-8.831646e-05 - 7|3.639861e+02|-6.487612e-05 - 8|3.639679e+02|-4.994063e-05 - 9|3.639536e+02|-3.941436e-05 - 10|3.639419e+02|-3.209753e-05 - - - - -Plot original images --------------------- - - -.. code-block:: default - - - pl.figure(1, figsize=(6.4, 3)) - pl.subplot(1, 2, 1) - pl.imshow(I1) - pl.axis('off') - pl.title('Image 1') - - pl.subplot(1, 2, 2) - pl.imshow(I2) - pl.axis('off') - pl.title('Image 2') - pl.tight_layout() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_otda_mapping_colors_images_001.png - :class: sphx-glr-single-img - - - - - -Plot pixel values distribution ------------------------------- - - -.. code-block:: default - - - pl.figure(2, figsize=(6.4, 5)) - - pl.subplot(1, 2, 1) - pl.scatter(Xs[:, 0], Xs[:, 2], c=Xs) - pl.axis([0, 1, 0, 1]) - pl.xlabel('Red') - pl.ylabel('Blue') - pl.title('Image 1') - - pl.subplot(1, 2, 2) - pl.scatter(Xt[:, 0], Xt[:, 2], c=Xt) - pl.axis([0, 1, 0, 1]) - pl.xlabel('Red') - pl.ylabel('Blue') - pl.title('Image 2') - pl.tight_layout() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_otda_mapping_colors_images_002.png - :class: sphx-glr-single-img - - - - - -Plot transformed images ------------------------ - - -.. code-block:: default - - - pl.figure(2, figsize=(10, 5)) - - pl.subplot(2, 3, 1) - pl.imshow(I1) - pl.axis('off') - pl.title('Im. 1') - - pl.subplot(2, 3, 4) - pl.imshow(I2) - pl.axis('off') - pl.title('Im. 2') - - pl.subplot(2, 3, 2) - pl.imshow(Image_emd) - pl.axis('off') - pl.title('EmdTransport') - - pl.subplot(2, 3, 5) - pl.imshow(Image_sinkhorn) - pl.axis('off') - pl.title('SinkhornTransport') - - pl.subplot(2, 3, 3) - pl.imshow(Image_mapping_linear) - pl.axis('off') - pl.title('MappingTransport (linear)') - - pl.subplot(2, 3, 6) - pl.imshow(Image_mapping_gaussian) - pl.axis('off') - pl.title('MappingTransport (gaussian)') - pl.tight_layout() - - pl.show() - - - -.. image:: /auto_examples/images/sphx_glr_plot_otda_mapping_colors_images_003.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_otda_mapping_colors_images.py:173: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 2 minutes 24.007 seconds) - - -.. _sphx_glr_download_auto_examples_plot_otda_mapping_colors_images.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_otda_mapping_colors_images.py <plot_otda_mapping_colors_images.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: plot_otda_mapping_colors_images.ipynb <plot_otda_mapping_colors_images.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ diff --git a/docs/source/auto_examples/plot_otda_semi_supervised.ipynb b/docs/source/auto_examples/plot_otda_semi_supervised.ipynb deleted file mode 100644 index d2157fb..0000000 --- a/docs/source/auto_examples/plot_otda_semi_supervised.ipynb +++ /dev/null @@ -1,144 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n# OTDA unsupervised vs semi-supervised setting\n\n\nThis example introduces a semi supervised domain adaptation in a 2D setting.\nIt explicits the problem of semi supervised domain adaptation and introduces\nsome optimal transport approaches to solve it.\n\nQuantities such as optimal couplings, greater coupling coefficients and\ntransported samples are represented in order to give a visual understanding\nof what the transport methods are doing.\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Authors: Remi Flamary <remi.flamary@unice.fr>\n# Stanislas Chambon <stan.chambon@gmail.com>\n#\n# License: MIT License\n\nimport matplotlib.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_samples_source = 150\nn_samples_target = 150\n\nXs, ys = ot.datasets.make_data_classif('3gauss', n_samples_source)\nXt, yt = ot.datasets.make_data_classif('3gauss2', n_samples_target)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Transport source samples onto target samples\n--------------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# unsupervised domain adaptation\not_sinkhorn_un = ot.da.SinkhornTransport(reg_e=1e-1)\not_sinkhorn_un.fit(Xs=Xs, Xt=Xt)\ntransp_Xs_sinkhorn_un = ot_sinkhorn_un.transform(Xs=Xs)\n\n# semi-supervised domain adaptation\not_sinkhorn_semi = ot.da.SinkhornTransport(reg_e=1e-1)\not_sinkhorn_semi.fit(Xs=Xs, Xt=Xt, ys=ys, yt=yt)\ntransp_Xs_sinkhorn_semi = ot_sinkhorn_semi.transform(Xs=Xs)\n\n# semi supervised DA uses available labaled target samples to modify the cost\n# matrix involved in the OT problem. The cost of transporting a source sample\n# of class A onto a target sample of class B != A is set to infinite, or a\n# very large value\n\n# note that in the present case we consider that all the target samples are\n# labeled. For daily applications, some target sample might not have labels,\n# in this case the element of yt corresponding to these samples should be\n# filled with -1.\n\n# Warning: we recall that -1 cannot be used as a class label" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Fig 1 : plots source and target samples + matrix of pairwise distance\n---------------------------------------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pl.figure(1, figsize=(10, 10))\npl.subplot(2, 2, 1)\npl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')\npl.xticks([])\npl.yticks([])\npl.legend(loc=0)\npl.title('Source samples')\n\npl.subplot(2, 2, 2)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')\npl.xticks([])\npl.yticks([])\npl.legend(loc=0)\npl.title('Target samples')\n\npl.subplot(2, 2, 3)\npl.imshow(ot_sinkhorn_un.cost_, interpolation='nearest')\npl.xticks([])\npl.yticks([])\npl.title('Cost matrix - unsupervised DA')\n\npl.subplot(2, 2, 4)\npl.imshow(ot_sinkhorn_semi.cost_, interpolation='nearest')\npl.xticks([])\npl.yticks([])\npl.title('Cost matrix - semisupervised DA')\n\npl.tight_layout()\n\n# the optimal coupling in the semi-supervised DA case will exhibit \" shape\n# similar\" to the cost matrix, (block diagonal matrix)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Fig 2 : plots optimal couplings for the different methods\n---------------------------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pl.figure(2, figsize=(8, 4))\n\npl.subplot(1, 2, 1)\npl.imshow(ot_sinkhorn_un.coupling_, interpolation='nearest')\npl.xticks([])\npl.yticks([])\npl.title('Optimal coupling\\nUnsupervised DA')\n\npl.subplot(1, 2, 2)\npl.imshow(ot_sinkhorn_semi.coupling_, interpolation='nearest')\npl.xticks([])\npl.yticks([])\npl.title('Optimal coupling\\nSemi-supervised DA')\n\npl.tight_layout()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Fig 3 : plot transported samples\n--------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# display transported samples\npl.figure(4, figsize=(8, 4))\npl.subplot(1, 2, 1)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=0.5)\npl.scatter(transp_Xs_sinkhorn_un[:, 0], transp_Xs_sinkhorn_un[:, 1], c=ys,\n marker='+', label='Transp samples', s=30)\npl.title('Transported samples\\nEmdTransport')\npl.legend(loc=0)\npl.xticks([])\npl.yticks([])\n\npl.subplot(1, 2, 2)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=0.5)\npl.scatter(transp_Xs_sinkhorn_semi[:, 0], transp_Xs_sinkhorn_semi[:, 1], c=ys,\n marker='+', label='Transp samples', s=30)\npl.title('Transported samples\\nSinkhornTransport')\npl.xticks([])\npl.yticks([])\n\npl.tight_layout()\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": "3.6.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_otda_semi_supervised.py b/docs/source/auto_examples/plot_otda_semi_supervised.py deleted file mode 100644 index 8a67720..0000000 --- a/docs/source/auto_examples/plot_otda_semi_supervised.py +++ /dev/null @@ -1,148 +0,0 @@ -# -*- coding: utf-8 -*- -""" -============================================ -OTDA unsupervised vs semi-supervised setting -============================================ - -This example introduces a semi supervised domain adaptation in a 2D setting. -It explicits the problem of semi supervised domain adaptation and introduces -some optimal transport approaches to solve it. - -Quantities such as optimal couplings, greater coupling coefficients and -transported samples are represented in order to give a visual understanding -of what the transport methods are doing. -""" - -# Authors: Remi Flamary <remi.flamary@unice.fr> -# Stanislas Chambon <stan.chambon@gmail.com> -# -# License: MIT License - -import matplotlib.pylab as pl -import ot - - -############################################################################## -# Generate data -# ------------- - -n_samples_source = 150 -n_samples_target = 150 - -Xs, ys = ot.datasets.make_data_classif('3gauss', n_samples_source) -Xt, yt = ot.datasets.make_data_classif('3gauss2', n_samples_target) - - -############################################################################## -# Transport source samples onto target samples -# -------------------------------------------- - - -# unsupervised domain adaptation -ot_sinkhorn_un = ot.da.SinkhornTransport(reg_e=1e-1) -ot_sinkhorn_un.fit(Xs=Xs, Xt=Xt) -transp_Xs_sinkhorn_un = ot_sinkhorn_un.transform(Xs=Xs) - -# semi-supervised domain adaptation -ot_sinkhorn_semi = ot.da.SinkhornTransport(reg_e=1e-1) -ot_sinkhorn_semi.fit(Xs=Xs, Xt=Xt, ys=ys, yt=yt) -transp_Xs_sinkhorn_semi = ot_sinkhorn_semi.transform(Xs=Xs) - -# semi supervised DA uses available labaled target samples to modify the cost -# matrix involved in the OT problem. The cost of transporting a source sample -# of class A onto a target sample of class B != A is set to infinite, or a -# very large value - -# note that in the present case we consider that all the target samples are -# labeled. For daily applications, some target sample might not have labels, -# in this case the element of yt corresponding to these samples should be -# filled with -1. - -# Warning: we recall that -1 cannot be used as a class label - - -############################################################################## -# Fig 1 : plots source and target samples + matrix of pairwise distance -# --------------------------------------------------------------------- - -pl.figure(1, figsize=(10, 10)) -pl.subplot(2, 2, 1) -pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') -pl.xticks([]) -pl.yticks([]) -pl.legend(loc=0) -pl.title('Source samples') - -pl.subplot(2, 2, 2) -pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') -pl.xticks([]) -pl.yticks([]) -pl.legend(loc=0) -pl.title('Target samples') - -pl.subplot(2, 2, 3) -pl.imshow(ot_sinkhorn_un.cost_, interpolation='nearest') -pl.xticks([]) -pl.yticks([]) -pl.title('Cost matrix - unsupervised DA') - -pl.subplot(2, 2, 4) -pl.imshow(ot_sinkhorn_semi.cost_, interpolation='nearest') -pl.xticks([]) -pl.yticks([]) -pl.title('Cost matrix - semisupervised DA') - -pl.tight_layout() - -# the optimal coupling in the semi-supervised DA case will exhibit " shape -# similar" to the cost matrix, (block diagonal matrix) - - -############################################################################## -# Fig 2 : plots optimal couplings for the different methods -# --------------------------------------------------------- - -pl.figure(2, figsize=(8, 4)) - -pl.subplot(1, 2, 1) -pl.imshow(ot_sinkhorn_un.coupling_, interpolation='nearest') -pl.xticks([]) -pl.yticks([]) -pl.title('Optimal coupling\nUnsupervised DA') - -pl.subplot(1, 2, 2) -pl.imshow(ot_sinkhorn_semi.coupling_, interpolation='nearest') -pl.xticks([]) -pl.yticks([]) -pl.title('Optimal coupling\nSemi-supervised DA') - -pl.tight_layout() - - -############################################################################## -# Fig 3 : plot transported samples -# -------------------------------- - -# display transported samples -pl.figure(4, figsize=(8, 4)) -pl.subplot(1, 2, 1) -pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=0.5) -pl.scatter(transp_Xs_sinkhorn_un[:, 0], transp_Xs_sinkhorn_un[:, 1], c=ys, - marker='+', label='Transp samples', s=30) -pl.title('Transported samples\nEmdTransport') -pl.legend(loc=0) -pl.xticks([]) -pl.yticks([]) - -pl.subplot(1, 2, 2) -pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=0.5) -pl.scatter(transp_Xs_sinkhorn_semi[:, 0], transp_Xs_sinkhorn_semi[:, 1], c=ys, - marker='+', label='Transp samples', s=30) -pl.title('Transported samples\nSinkhornTransport') -pl.xticks([]) -pl.yticks([]) - -pl.tight_layout() -pl.show() diff --git a/docs/source/auto_examples/plot_otda_semi_supervised.rst b/docs/source/auto_examples/plot_otda_semi_supervised.rst deleted file mode 100644 index 4a355e7..0000000 --- a/docs/source/auto_examples/plot_otda_semi_supervised.rst +++ /dev/null @@ -1,267 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_otda_semi_supervised.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_otda_semi_supervised.py: - - -============================================ -OTDA unsupervised vs semi-supervised setting -============================================ - -This example introduces a semi supervised domain adaptation in a 2D setting. -It explicits the problem of semi supervised domain adaptation and introduces -some optimal transport approaches to solve it. - -Quantities such as optimal couplings, greater coupling coefficients and -transported samples are represented in order to give a visual understanding -of what the transport methods are doing. - - -.. code-block:: default - - - # Authors: Remi Flamary <remi.flamary@unice.fr> - # Stanislas Chambon <stan.chambon@gmail.com> - # - # License: MIT License - - import matplotlib.pylab as pl - import ot - - - - - - - - - -Generate data -------------- - - -.. code-block:: default - - - n_samples_source = 150 - n_samples_target = 150 - - Xs, ys = ot.datasets.make_data_classif('3gauss', n_samples_source) - Xt, yt = ot.datasets.make_data_classif('3gauss2', n_samples_target) - - - - - - - - - -Transport source samples onto target samples --------------------------------------------- - - -.. code-block:: default - - - - # unsupervised domain adaptation - ot_sinkhorn_un = ot.da.SinkhornTransport(reg_e=1e-1) - ot_sinkhorn_un.fit(Xs=Xs, Xt=Xt) - transp_Xs_sinkhorn_un = ot_sinkhorn_un.transform(Xs=Xs) - - # semi-supervised domain adaptation - ot_sinkhorn_semi = ot.da.SinkhornTransport(reg_e=1e-1) - ot_sinkhorn_semi.fit(Xs=Xs, Xt=Xt, ys=ys, yt=yt) - transp_Xs_sinkhorn_semi = ot_sinkhorn_semi.transform(Xs=Xs) - - # semi supervised DA uses available labaled target samples to modify the cost - # matrix involved in the OT problem. The cost of transporting a source sample - # of class A onto a target sample of class B != A is set to infinite, or a - # very large value - - # note that in the present case we consider that all the target samples are - # labeled. For daily applications, some target sample might not have labels, - # in this case the element of yt corresponding to these samples should be - # filled with -1. - - # Warning: we recall that -1 cannot be used as a class label - - - - - - - - - -Fig 1 : plots source and target samples + matrix of pairwise distance ---------------------------------------------------------------------- - - -.. code-block:: default - - - pl.figure(1, figsize=(10, 10)) - pl.subplot(2, 2, 1) - pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') - pl.xticks([]) - pl.yticks([]) - pl.legend(loc=0) - pl.title('Source samples') - - pl.subplot(2, 2, 2) - pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') - pl.xticks([]) - pl.yticks([]) - pl.legend(loc=0) - pl.title('Target samples') - - pl.subplot(2, 2, 3) - pl.imshow(ot_sinkhorn_un.cost_, interpolation='nearest') - pl.xticks([]) - pl.yticks([]) - pl.title('Cost matrix - unsupervised DA') - - pl.subplot(2, 2, 4) - pl.imshow(ot_sinkhorn_semi.cost_, interpolation='nearest') - pl.xticks([]) - pl.yticks([]) - pl.title('Cost matrix - semisupervised DA') - - pl.tight_layout() - - # the optimal coupling in the semi-supervised DA case will exhibit " shape - # similar" to the cost matrix, (block diagonal matrix) - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_otda_semi_supervised_001.png - :class: sphx-glr-single-img - - - - - -Fig 2 : plots optimal couplings for the different methods ---------------------------------------------------------- - - -.. code-block:: default - - - pl.figure(2, figsize=(8, 4)) - - pl.subplot(1, 2, 1) - pl.imshow(ot_sinkhorn_un.coupling_, interpolation='nearest') - pl.xticks([]) - pl.yticks([]) - pl.title('Optimal coupling\nUnsupervised DA') - - pl.subplot(1, 2, 2) - pl.imshow(ot_sinkhorn_semi.coupling_, interpolation='nearest') - pl.xticks([]) - pl.yticks([]) - pl.title('Optimal coupling\nSemi-supervised DA') - - pl.tight_layout() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_otda_semi_supervised_002.png - :class: sphx-glr-single-img - - - - - -Fig 3 : plot transported samples --------------------------------- - - -.. code-block:: default - - - # display transported samples - pl.figure(4, figsize=(8, 4)) - pl.subplot(1, 2, 1) - pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=0.5) - pl.scatter(transp_Xs_sinkhorn_un[:, 0], transp_Xs_sinkhorn_un[:, 1], c=ys, - marker='+', label='Transp samples', s=30) - pl.title('Transported samples\nEmdTransport') - pl.legend(loc=0) - pl.xticks([]) - pl.yticks([]) - - pl.subplot(1, 2, 2) - pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', - label='Target samples', alpha=0.5) - pl.scatter(transp_Xs_sinkhorn_semi[:, 0], transp_Xs_sinkhorn_semi[:, 1], c=ys, - marker='+', label='Transp samples', s=30) - pl.title('Transported samples\nSinkhornTransport') - pl.xticks([]) - pl.yticks([]) - - pl.tight_layout() - pl.show() - - - -.. image:: /auto_examples/images/sphx_glr_plot_otda_semi_supervised_003.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_otda_semi_supervised.py:148: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 0.660 seconds) - - -.. _sphx_glr_download_auto_examples_plot_otda_semi_supervised.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_otda_semi_supervised.py <plot_otda_semi_supervised.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: plot_otda_semi_supervised.ipynb <plot_otda_semi_supervised.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ diff --git a/docs/source/auto_examples/plot_partial_wass_and_gromov.ipynb b/docs/source/auto_examples/plot_partial_wass_and_gromov.ipynb deleted file mode 100644 index 539d575..0000000 --- a/docs/source/auto_examples/plot_partial_wass_and_gromov.ipynb +++ /dev/null @@ -1,126 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n# Partial Wasserstein and Gromov-Wasserstein example\n\n\nThis example is designed to show how to use the Partial (Gromov-)Wassertsein\ndistance computation in POT.\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Author: Laetitia Chapel <laetitia.chapel@irisa.fr>\n# License: MIT License\n\n# necessary for 3d plot even if not used\nfrom mpl_toolkits.mplot3d import Axes3D # noqa\nimport scipy as sp\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Sample two 2D Gaussian distributions and plot them\n--------------------------------------------------\n\nFor demonstration purpose, we sample two Gaussian distributions in 2-d\nspaces and add some random noise.\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "n_samples = 20 # nb samples (gaussian)\nn_noise = 20 # nb of samples (noise)\n\nmu = np.array([0, 0])\ncov = np.array([[1, 0], [0, 2]])\n\nxs = ot.datasets.make_2D_samples_gauss(n_samples, mu, cov)\nxs = np.append(xs, (np.random.rand(n_noise, 2) + 1) * 4).reshape((-1, 2))\nxt = ot.datasets.make_2D_samples_gauss(n_samples, mu, cov)\nxt = np.append(xt, (np.random.rand(n_noise, 2) + 1) * -3).reshape((-1, 2))\n\nM = sp.spatial.distance.cdist(xs, xt)\n\nfig = pl.figure()\nax1 = fig.add_subplot(131)\nax1.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\nax2 = fig.add_subplot(132)\nax2.scatter(xt[:, 0], xt[:, 1], color='r')\nax3 = fig.add_subplot(133)\nax3.imshow(M)\npl.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Compute partial Wasserstein plans and distance\n----------------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "p = ot.unif(n_samples + n_noise)\nq = ot.unif(n_samples + n_noise)\n\nw0, log0 = ot.partial.partial_wasserstein(p, q, M, m=0.5, log=True)\nw, log = ot.partial.entropic_partial_wasserstein(p, q, M, reg=0.1, m=0.5,\n log=True)\n\nprint('Partial Wasserstein distance (m = 0.5): ' + str(log0['partial_w_dist']))\nprint('Entropic partial Wasserstein distance (m = 0.5): ' +\n str(log['partial_w_dist']))\n\npl.figure(1, (10, 5))\npl.subplot(1, 2, 1)\npl.imshow(w0, cmap='jet')\npl.title('Partial Wasserstein')\npl.subplot(1, 2, 2)\npl.imshow(w, cmap='jet')\npl.title('Entropic partial Wasserstein')\npl.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Sample one 2D and 3D Gaussian distributions and plot them\n---------------------------------------------------------\n\nThe Gromov-Wasserstein distance allows to compute distances with samples that\ndo not belong to the same metric space. For demonstration purpose, we sample\ntwo Gaussian distributions in 2- and 3-dimensional spaces.\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "n_samples = 20 # nb samples\nn_noise = 10 # nb of samples (noise)\n\np = ot.unif(n_samples + n_noise)\nq = ot.unif(n_samples + n_noise)\n\nmu_s = np.array([0, 0])\ncov_s = np.array([[1, 0], [0, 1]])\n\nmu_t = np.array([0, 0, 0])\ncov_t = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])\n\n\nxs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s)\nxs = np.concatenate((xs, ((np.random.rand(n_noise, 2) + 1) * 4)), axis=0)\nP = sp.linalg.sqrtm(cov_t)\nxt = np.random.randn(n_samples, 3).dot(P) + mu_t\nxt = np.concatenate((xt, ((np.random.rand(n_noise, 3) + 1) * 10)), axis=0)\n\nfig = pl.figure()\nax1 = fig.add_subplot(121)\nax1.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\nax2 = fig.add_subplot(122, projection='3d')\nax2.scatter(xt[:, 0], xt[:, 1], xt[:, 2], color='r')\npl.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Compute partial Gromov-Wasserstein plans and distance\n-----------------------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "C1 = sp.spatial.distance.cdist(xs, xs)\nC2 = sp.spatial.distance.cdist(xt, xt)\n\n# transport 100% of the mass\nprint('-----m = 1')\nm = 1\nres0, log0 = ot.partial.partial_gromov_wasserstein(C1, C2, p, q, m=m, log=True)\nres, log = ot.partial.entropic_partial_gromov_wasserstein(C1, C2, p, q, 10,\n m=m, log=True)\n\nprint('Wasserstein distance (m = 1): ' + str(log0['partial_gw_dist']))\nprint('Entropic Wasserstein distance (m = 1): ' + str(log['partial_gw_dist']))\n\npl.figure(1, (10, 5))\npl.title(\"mass to be transported m = 1\")\npl.subplot(1, 2, 1)\npl.imshow(res0, cmap='jet')\npl.title('Wasserstein')\npl.subplot(1, 2, 2)\npl.imshow(res, cmap='jet')\npl.title('Entropic Wasserstein')\npl.show()\n\n# transport 2/3 of the mass\nprint('-----m = 2/3')\nm = 2 / 3\nres0, log0 = ot.partial.partial_gromov_wasserstein(C1, C2, p, q, m=m, log=True)\nres, log = ot.partial.entropic_partial_gromov_wasserstein(C1, C2, p, q, 10,\n m=m, log=True)\n\nprint('Partial Wasserstein distance (m = 2/3): ' +\n str(log0['partial_gw_dist']))\nprint('Entropic partial Wasserstein distance (m = 2/3): ' +\n str(log['partial_gw_dist']))\n\npl.figure(1, (10, 5))\npl.title(\"mass to be transported m = 2/3\")\npl.subplot(1, 2, 1)\npl.imshow(res0, cmap='jet')\npl.title('Partial Wasserstein')\npl.subplot(1, 2, 2)\npl.imshow(res, cmap='jet')\npl.title('Entropic partial Wasserstein')\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": "3.6.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_partial_wass_and_gromov.py b/docs/source/auto_examples/plot_partial_wass_and_gromov.py deleted file mode 100644 index 9f95a70..0000000 --- a/docs/source/auto_examples/plot_partial_wass_and_gromov.py +++ /dev/null @@ -1,163 +0,0 @@ -# -*- coding: utf-8 -*-
-"""
-==================================================
-Partial Wasserstein and Gromov-Wasserstein example
-==================================================
-
-This example is designed to show how to use the Partial (Gromov-)Wassertsein
-distance computation in POT.
-"""
-
-# Author: Laetitia Chapel <laetitia.chapel@irisa.fr>
-# License: MIT License
-
-# necessary for 3d plot even if not used
-from mpl_toolkits.mplot3d import Axes3D # noqa
-import scipy as sp
-import numpy as np
-import matplotlib.pylab as pl
-import ot
-
-
-#############################################################################
-#
-# Sample two 2D Gaussian distributions and plot them
-# --------------------------------------------------
-#
-# For demonstration purpose, we sample two Gaussian distributions in 2-d
-# spaces and add some random noise.
-
-
-n_samples = 20 # nb samples (gaussian)
-n_noise = 20 # nb of samples (noise)
-
-mu = np.array([0, 0])
-cov = np.array([[1, 0], [0, 2]])
-
-xs = ot.datasets.make_2D_samples_gauss(n_samples, mu, cov)
-xs = np.append(xs, (np.random.rand(n_noise, 2) + 1) * 4).reshape((-1, 2))
-xt = ot.datasets.make_2D_samples_gauss(n_samples, mu, cov)
-xt = np.append(xt, (np.random.rand(n_noise, 2) + 1) * -3).reshape((-1, 2))
-
-M = sp.spatial.distance.cdist(xs, xt)
-
-fig = pl.figure()
-ax1 = fig.add_subplot(131)
-ax1.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
-ax2 = fig.add_subplot(132)
-ax2.scatter(xt[:, 0], xt[:, 1], color='r')
-ax3 = fig.add_subplot(133)
-ax3.imshow(M)
-pl.show()
-
-#############################################################################
-#
-# Compute partial Wasserstein plans and distance
-# ----------------------------------------------
-
-p = ot.unif(n_samples + n_noise)
-q = ot.unif(n_samples + n_noise)
-
-w0, log0 = ot.partial.partial_wasserstein(p, q, M, m=0.5, log=True)
-w, log = ot.partial.entropic_partial_wasserstein(p, q, M, reg=0.1, m=0.5,
- log=True)
-
-print('Partial Wasserstein distance (m = 0.5): ' + str(log0['partial_w_dist']))
-print('Entropic partial Wasserstein distance (m = 0.5): ' +
- str(log['partial_w_dist']))
-
-pl.figure(1, (10, 5))
-pl.subplot(1, 2, 1)
-pl.imshow(w0, cmap='jet')
-pl.title('Partial Wasserstein')
-pl.subplot(1, 2, 2)
-pl.imshow(w, cmap='jet')
-pl.title('Entropic partial Wasserstein')
-pl.show()
-
-
-#############################################################################
-#
-# Sample one 2D and 3D Gaussian distributions and plot them
-# ---------------------------------------------------------
-#
-# The Gromov-Wasserstein distance allows to compute distances with samples that
-# do not belong to the same metric space. For demonstration purpose, we sample
-# two Gaussian distributions in 2- and 3-dimensional spaces.
-
-n_samples = 20 # nb samples
-n_noise = 10 # nb of samples (noise)
-
-p = ot.unif(n_samples + n_noise)
-q = ot.unif(n_samples + n_noise)
-
-mu_s = np.array([0, 0])
-cov_s = np.array([[1, 0], [0, 1]])
-
-mu_t = np.array([0, 0, 0])
-cov_t = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
-
-
-xs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s)
-xs = np.concatenate((xs, ((np.random.rand(n_noise, 2) + 1) * 4)), axis=0)
-P = sp.linalg.sqrtm(cov_t)
-xt = np.random.randn(n_samples, 3).dot(P) + mu_t
-xt = np.concatenate((xt, ((np.random.rand(n_noise, 3) + 1) * 10)), axis=0)
-
-fig = pl.figure()
-ax1 = fig.add_subplot(121)
-ax1.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
-ax2 = fig.add_subplot(122, projection='3d')
-ax2.scatter(xt[:, 0], xt[:, 1], xt[:, 2], color='r')
-pl.show()
-
-
-#############################################################################
-#
-# Compute partial Gromov-Wasserstein plans and distance
-# -----------------------------------------------------
-
-C1 = sp.spatial.distance.cdist(xs, xs)
-C2 = sp.spatial.distance.cdist(xt, xt)
-
-# transport 100% of the mass
-print('-----m = 1')
-m = 1
-res0, log0 = ot.partial.partial_gromov_wasserstein(C1, C2, p, q, m=m, log=True)
-res, log = ot.partial.entropic_partial_gromov_wasserstein(C1, C2, p, q, 10,
- m=m, log=True)
-
-print('Wasserstein distance (m = 1): ' + str(log0['partial_gw_dist']))
-print('Entropic Wasserstein distance (m = 1): ' + str(log['partial_gw_dist']))
-
-pl.figure(1, (10, 5))
-pl.title("mass to be transported m = 1")
-pl.subplot(1, 2, 1)
-pl.imshow(res0, cmap='jet')
-pl.title('Wasserstein')
-pl.subplot(1, 2, 2)
-pl.imshow(res, cmap='jet')
-pl.title('Entropic Wasserstein')
-pl.show()
-
-# transport 2/3 of the mass
-print('-----m = 2/3')
-m = 2 / 3
-res0, log0 = ot.partial.partial_gromov_wasserstein(C1, C2, p, q, m=m, log=True)
-res, log = ot.partial.entropic_partial_gromov_wasserstein(C1, C2, p, q, 10,
- m=m, log=True)
-
-print('Partial Wasserstein distance (m = 2/3): ' +
- str(log0['partial_gw_dist']))
-print('Entropic partial Wasserstein distance (m = 2/3): ' +
- str(log['partial_gw_dist']))
-
-pl.figure(1, (10, 5))
-pl.title("mass to be transported m = 2/3")
-pl.subplot(1, 2, 1)
-pl.imshow(res0, cmap='jet')
-pl.title('Partial Wasserstein')
-pl.subplot(1, 2, 2)
-pl.imshow(res, cmap='jet')
-pl.title('Entropic partial Wasserstein')
-pl.show()
diff --git a/docs/source/auto_examples/plot_partial_wass_and_gromov.rst b/docs/source/auto_examples/plot_partial_wass_and_gromov.rst deleted file mode 100644 index 2d51210..0000000 --- a/docs/source/auto_examples/plot_partial_wass_and_gromov.rst +++ /dev/null @@ -1,312 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_partial_wass_and_gromov.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_partial_wass_and_gromov.py: - - -================================================== -Partial Wasserstein and Gromov-Wasserstein example -================================================== - -This example is designed to show how to use the Partial (Gromov-)Wassertsein -distance computation in POT. - - -.. code-block:: default - - - # Author: Laetitia Chapel <laetitia.chapel@irisa.fr> - # License: MIT License - - # necessary for 3d plot even if not used - from mpl_toolkits.mplot3d import Axes3D # noqa - import scipy as sp - import numpy as np - import matplotlib.pylab as pl - import ot - - - - - - - - - -Sample two 2D Gaussian distributions and plot them --------------------------------------------------- - -For demonstration purpose, we sample two Gaussian distributions in 2-d -spaces and add some random noise. - - -.. code-block:: default - - - - n_samples = 20 # nb samples (gaussian) - n_noise = 20 # nb of samples (noise) - - mu = np.array([0, 0]) - cov = np.array([[1, 0], [0, 2]]) - - xs = ot.datasets.make_2D_samples_gauss(n_samples, mu, cov) - xs = np.append(xs, (np.random.rand(n_noise, 2) + 1) * 4).reshape((-1, 2)) - xt = ot.datasets.make_2D_samples_gauss(n_samples, mu, cov) - xt = np.append(xt, (np.random.rand(n_noise, 2) + 1) * -3).reshape((-1, 2)) - - M = sp.spatial.distance.cdist(xs, xt) - - fig = pl.figure() - ax1 = fig.add_subplot(131) - ax1.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') - ax2 = fig.add_subplot(132) - ax2.scatter(xt[:, 0], xt[:, 1], color='r') - ax3 = fig.add_subplot(133) - ax3.imshow(M) - pl.show() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_partial_wass_and_gromov_001.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:51: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - -Compute partial Wasserstein plans and distance ----------------------------------------------- - - -.. code-block:: default - - - p = ot.unif(n_samples + n_noise) - q = ot.unif(n_samples + n_noise) - - w0, log0 = ot.partial.partial_wasserstein(p, q, M, m=0.5, log=True) - w, log = ot.partial.entropic_partial_wasserstein(p, q, M, reg=0.1, m=0.5, - log=True) - - print('Partial Wasserstein distance (m = 0.5): ' + str(log0['partial_w_dist'])) - print('Entropic partial Wasserstein distance (m = 0.5): ' + - str(log['partial_w_dist'])) - - pl.figure(1, (10, 5)) - pl.subplot(1, 2, 1) - pl.imshow(w0, cmap='jet') - pl.title('Partial Wasserstein') - pl.subplot(1, 2, 2) - pl.imshow(w, cmap='jet') - pl.title('Entropic partial Wasserstein') - pl.show() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_partial_wass_and_gromov_002.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - Partial Wasserstein distance (m = 0.5): 0.507323938973194 - Entropic partial Wasserstein distance (m = 0.5): 0.5205305886057896 - /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:76: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - -Sample one 2D and 3D Gaussian distributions and plot them ---------------------------------------------------------- - -The Gromov-Wasserstein distance allows to compute distances with samples that -do not belong to the same metric space. For demonstration purpose, we sample -two Gaussian distributions in 2- and 3-dimensional spaces. - - -.. code-block:: default - - - n_samples = 20 # nb samples - n_noise = 10 # nb of samples (noise) - - p = ot.unif(n_samples + n_noise) - q = ot.unif(n_samples + n_noise) - - mu_s = np.array([0, 0]) - cov_s = np.array([[1, 0], [0, 1]]) - - mu_t = np.array([0, 0, 0]) - cov_t = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]]) - - - xs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s) - xs = np.concatenate((xs, ((np.random.rand(n_noise, 2) + 1) * 4)), axis=0) - P = sp.linalg.sqrtm(cov_t) - xt = np.random.randn(n_samples, 3).dot(P) + mu_t - xt = np.concatenate((xt, ((np.random.rand(n_noise, 3) + 1) * 10)), axis=0) - - fig = pl.figure() - ax1 = fig.add_subplot(121) - ax1.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') - ax2 = fig.add_subplot(122, projection='3d') - ax2.scatter(xt[:, 0], xt[:, 1], xt[:, 2], color='r') - pl.show() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_partial_wass_and_gromov_003.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:112: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - -Compute partial Gromov-Wasserstein plans and distance ------------------------------------------------------ - - -.. code-block:: default - - - C1 = sp.spatial.distance.cdist(xs, xs) - C2 = sp.spatial.distance.cdist(xt, xt) - - # transport 100% of the mass - print('-----m = 1') - m = 1 - res0, log0 = ot.partial.partial_gromov_wasserstein(C1, C2, p, q, m=m, log=True) - res, log = ot.partial.entropic_partial_gromov_wasserstein(C1, C2, p, q, 10, - m=m, log=True) - - print('Wasserstein distance (m = 1): ' + str(log0['partial_gw_dist'])) - print('Entropic Wasserstein distance (m = 1): ' + str(log['partial_gw_dist'])) - - pl.figure(1, (10, 5)) - pl.title("mass to be transported m = 1") - pl.subplot(1, 2, 1) - pl.imshow(res0, cmap='jet') - pl.title('Wasserstein') - pl.subplot(1, 2, 2) - pl.imshow(res, cmap='jet') - pl.title('Entropic Wasserstein') - pl.show() - - # transport 2/3 of the mass - print('-----m = 2/3') - m = 2 / 3 - res0, log0 = ot.partial.partial_gromov_wasserstein(C1, C2, p, q, m=m, log=True) - res, log = ot.partial.entropic_partial_gromov_wasserstein(C1, C2, p, q, 10, - m=m, log=True) - - print('Partial Wasserstein distance (m = 2/3): ' + - str(log0['partial_gw_dist'])) - print('Entropic partial Wasserstein distance (m = 2/3): ' + - str(log['partial_gw_dist'])) - - pl.figure(1, (10, 5)) - pl.title("mass to be transported m = 2/3") - pl.subplot(1, 2, 1) - pl.imshow(res0, cmap='jet') - pl.title('Partial Wasserstein') - pl.subplot(1, 2, 2) - pl.imshow(res, cmap='jet') - pl.title('Entropic partial Wasserstein') - pl.show() - - - -.. image:: /auto_examples/images/sphx_glr_plot_partial_wass_and_gromov_004.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - -----m = 1 - Wasserstein distance (m = 1): 63.65368600872179 - Entropic Wasserstein distance (m = 1): 65.23659085946916 - /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:141: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - -----m = 2/3 - Partial Wasserstein distance (m = 2/3): 0.23235485397666825 - Entropic partial Wasserstein distance (m = 2/3): 1.4645434781619244 - /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:157: MatplotlibDeprecationWarning: Adding an axes using the same arguments as a previous axes currently reuses the earlier instance. In a future version, a new instance will always be created and returned. Meanwhile, this warning can be suppressed, and the future behavior ensured, by passing a unique label to each axes instance. - pl.subplot(1, 2, 1) - /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:160: MatplotlibDeprecationWarning: Adding an axes using the same arguments as a previous axes currently reuses the earlier instance. In a future version, a new instance will always be created and returned. Meanwhile, this warning can be suppressed, and the future behavior ensured, by passing a unique label to each axes instance. - pl.subplot(1, 2, 2) - /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:163: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 1.543 seconds) - - -.. _sphx_glr_download_auto_examples_plot_partial_wass_and_gromov.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_partial_wass_and_gromov.py <plot_partial_wass_and_gromov.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: plot_partial_wass_and_gromov.ipynb <plot_partial_wass_and_gromov.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ diff --git a/docs/source/auto_examples/plot_screenkhorn_1D.ipynb b/docs/source/auto_examples/plot_screenkhorn_1D.ipynb deleted file mode 100644 index 1c27d3b..0000000 --- a/docs/source/auto_examples/plot_screenkhorn_1D.ipynb +++ /dev/null @@ -1,108 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n# 1D Screened optimal transport\n\n\nThis example illustrates the computation of Screenkhorn:\nScreening Sinkhorn Algorithm for Optimal transport.\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Author: Mokhtar Z. Alaya <mokhtarzahdi.alaya@gmail.com>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot.plot\nfrom ot.datasets import make_1D_gauss as gauss\nfrom ot.bregman import screenkhorn" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Generate data\n-------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "n = 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": [ - "pl.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 Screenkhorn\n-----------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Screenkhorn\nlambd = 2e-03 # entropy parameter\nns_budget = 30 # budget number of points to be keeped in the source distribution\nnt_budget = 30 # budget number of points to be keeped in the target distribution\n\nG_screen = screenkhorn(a, b, M, lambd, ns_budget, nt_budget, uniform=False, restricted=True, verbose=True)\npl.figure(4, figsize=(5, 5))\not.plot.plot1D_mat(a, b, G_screen, 'OT matrix Screenkhorn')\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": "3.6.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_screenkhorn_1D.py b/docs/source/auto_examples/plot_screenkhorn_1D.py deleted file mode 100644 index 840ead8..0000000 --- a/docs/source/auto_examples/plot_screenkhorn_1D.py +++ /dev/null @@ -1,68 +0,0 @@ -# -*- coding: utf-8 -*- -""" -=============================== -1D Screened optimal transport -=============================== - -This example illustrates the computation of Screenkhorn: -Screening Sinkhorn Algorithm for Optimal transport. -""" - -# Author: Mokhtar Z. Alaya <mokhtarzahdi.alaya@gmail.com> -# -# License: MIT License - -import numpy as np -import matplotlib.pylab as pl -import ot.plot -from ot.datasets import make_1D_gauss as gauss -from ot.bregman import screenkhorn - -############################################################################## -# 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 Screenkhorn -# ----------------------- - -# Screenkhorn -lambd = 2e-03 # entropy parameter -ns_budget = 30 # budget number of points to be keeped in the source distribution -nt_budget = 30 # budget number of points to be keeped in the target distribution - -G_screen = screenkhorn(a, b, M, lambd, ns_budget, nt_budget, uniform=False, restricted=True, verbose=True) -pl.figure(4, figsize=(5, 5)) -ot.plot.plot1D_mat(a, b, G_screen, 'OT matrix Screenkhorn') -pl.show() diff --git a/docs/source/auto_examples/plot_screenkhorn_1D.rst b/docs/source/auto_examples/plot_screenkhorn_1D.rst deleted file mode 100644 index 039479e..0000000 --- a/docs/source/auto_examples/plot_screenkhorn_1D.rst +++ /dev/null @@ -1,178 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_screenkhorn_1D.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_screenkhorn_1D.py: - - -=============================== -1D Screened optimal transport -=============================== - -This example illustrates the computation of Screenkhorn: -Screening Sinkhorn Algorithm for Optimal transport. - - -.. code-block:: default - - - # Author: Mokhtar Z. Alaya <mokhtarzahdi.alaya@gmail.com> - # - # License: MIT License - - import numpy as np - import matplotlib.pylab as pl - import ot.plot - from ot.datasets import make_1D_gauss as gauss - from ot.bregman import screenkhorn - - - - - - - - -Generate data -------------- - - -.. code-block:: default - - - 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:: default - - - 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_screenkhorn_1D_001.png - :class: sphx-glr-multi-img - - * - - .. image:: /auto_examples/images/sphx_glr_plot_screenkhorn_1D_002.png - :class: sphx-glr-multi-img - - - - - -Solve Screenkhorn ------------------------ - - -.. code-block:: default - - - # Screenkhorn - lambd = 2e-03 # entropy parameter - ns_budget = 30 # budget number of points to be keeped in the source distribution - nt_budget = 30 # budget number of points to be keeped in the target distribution - - G_screen = screenkhorn(a, b, M, lambd, ns_budget, nt_budget, uniform=False, restricted=True, verbose=True) - pl.figure(4, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, G_screen, 'OT matrix Screenkhorn') - pl.show() - - - -.. image:: /auto_examples/images/sphx_glr_plot_screenkhorn_1D_003.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/ot/bregman.py:2056: UserWarning: Bottleneck module is not installed. Install it from https://pypi.org/project/Bottleneck/ for better performance. - "Bottleneck module is not installed. Install it from https://pypi.org/project/Bottleneck/ for better performance.") - epsilon = 0.020986042861303855 - - kappa = 3.7476531411890917 - - Cardinality of selected points: |Isel| = 30 |Jsel| = 30 - - /home/rflamary/PYTHON/POT/examples/plot_screenkhorn_1D.py:68: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 0.228 seconds) - - -.. _sphx_glr_download_auto_examples_plot_screenkhorn_1D.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_screenkhorn_1D.py <plot_screenkhorn_1D.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: plot_screenkhorn_1D.ipynb <plot_screenkhorn_1D.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ diff --git a/docs/source/auto_examples/plot_stochastic.ipynb b/docs/source/auto_examples/plot_stochastic.ipynb deleted file mode 100644 index c29f75a..0000000 --- a/docs/source/auto_examples/plot_stochastic.ipynb +++ /dev/null @@ -1,295 +0,0 @@ -{ - "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 DISCRETE CASE:\n\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": 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:\n\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 SEMICONTINOUS CASE:\n\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": 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": "3.6.9" - } - }, - "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 deleted file mode 100644 index 742f8d9..0000000 --- a/docs/source/auto_examples/plot_stochastic.py +++ /dev/null @@ -1,208 +0,0 @@ -""" -========================== -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 -############################################################################# -############################################################################# -# 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 -############################################################################# -############################################################################# -# 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 deleted file mode 100644 index 63fc74f..0000000 --- a/docs/source/auto_examples/plot_stochastic.rst +++ /dev/null @@ -1,518 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_stochastic.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_stochastic.py: - - -========================== -Stochastic examples -========================== - -This example is designed to show how to use the stochatic optimization -algorithms for descrete and semicontinous measures from the POT library. - - - -.. code-block:: default - - - # Author: Kilian Fatras <kilian.fatras@gmail.com> - # - # License: MIT License - - import matplotlib.pylab as pl - import numpy as np - import ot - import ot.plot - - - - - - - - - -COMPUTE TRANSPORTATION MATRIX FOR SEMI-DUAL PROBLEM -############################################################################ -############################################################################ - DISCRETE CASE: - - Sample two discrete measures for the discrete case - --------------------------------------------- - - Define 2 discrete measures a and b, the points where are defined the source - and the target measures and finally the cost matrix c. - - -.. code-block:: default - - - n_source = 7 - n_target = 4 - reg = 1 - numItermax = 1000 - - a = ot.utils.unif(n_source) - b = ot.utils.unif(n_target) - - rng = np.random.RandomState(0) - X_source = rng.randn(n_source, 2) - Y_target = rng.randn(n_target, 2) - M = ot.dist(X_source, Y_target) - - - - - - - - -Call the "SAG" method to find the transportation matrix in the discrete case ---------------------------------------------- - -Define the method "SAG", call ot.solve_semi_dual_entropic and plot the -results. - - -.. code-block:: default - - - method = "SAG" - sag_pi = ot.stochastic.solve_semi_dual_entropic(a, b, M, reg, method, - numItermax) - print(sag_pi) - - - - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - [[2.55553509e-02 9.96395660e-02 1.76579142e-02 4.31178196e-06] - [1.21640234e-01 1.25357448e-02 1.30225078e-03 7.37891338e-03] - [3.56123975e-03 7.61451746e-02 6.31505947e-02 1.33831456e-07] - [2.61515202e-02 3.34246014e-02 8.28734709e-02 4.07550428e-04] - [9.85500870e-03 7.52288517e-04 1.08262628e-02 1.21423583e-01] - [2.16904253e-02 9.03825797e-04 1.87178503e-03 1.18391107e-01] - [4.15462212e-02 2.65987989e-02 7.23177216e-02 2.39440107e-03]] - - - - -SEMICONTINOUS CASE: - -Sample one general measure a, one discrete measures b for the semicontinous -case ---------------------------------------------- - -Define one general measure a, one discrete measures b, the points where -are defined the source and the target measures and finally the cost matrix c. - - -.. code-block:: default - - - n_source = 7 - n_target = 4 - reg = 1 - numItermax = 1000 - log = True - - a = ot.utils.unif(n_source) - b = ot.utils.unif(n_target) - - rng = np.random.RandomState(0) - X_source = rng.randn(n_source, 2) - Y_target = rng.randn(n_target, 2) - M = ot.dist(X_source, Y_target) - - - - - - - - -Call the "ASGD" method to find the transportation matrix in the semicontinous -case ---------------------------------------------- - -Define the method "ASGD", call ot.solve_semi_dual_entropic and plot the -results. - - -.. code-block:: default - - - method = "ASGD" - asgd_pi, log_asgd = ot.stochastic.solve_semi_dual_entropic(a, b, M, reg, method, - numItermax, log=log) - print(log_asgd['alpha'], log_asgd['beta']) - print(asgd_pi) - - - - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - [3.89943264 7.64823414 3.9284189 2.67501041 1.42825446 3.26039819 - 2.79237712] [-2.50786905 -2.42684838 -0.93647774 5.87119517] - [[2.50229922e-02 1.00367920e-01 1.74615056e-02 4.72486104e-06] - [1.20583329e-01 1.27839737e-02 1.30373565e-03 8.18610462e-03] - [3.49243139e-03 7.68200813e-02 6.25444833e-02 1.46879008e-07] - [2.58205995e-02 3.39501207e-02 8.26360982e-02 4.50324517e-04] - [8.94164918e-03 7.02183713e-04 9.92028326e-03 1.23293027e-01] - [1.97360234e-02 8.46022708e-04 1.72001583e-03 1.20555081e-01] - [4.10386980e-02 2.70289873e-02 7.21425804e-02 2.64687723e-03]] - - - - -Compare the results with the Sinkhorn algorithm ---------------------------------------------- - -Call the Sinkhorn algorithm from POT - - -.. code-block:: default - - - sinkhorn_pi = ot.sinkhorn(a, b, M, reg) - print(sinkhorn_pi) - - - - - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - [[2.55553508e-02 9.96395661e-02 1.76579142e-02 4.31178193e-06] - [1.21640234e-01 1.25357448e-02 1.30225079e-03 7.37891333e-03] - [3.56123974e-03 7.61451746e-02 6.31505947e-02 1.33831455e-07] - [2.61515201e-02 3.34246014e-02 8.28734709e-02 4.07550425e-04] - [9.85500876e-03 7.52288523e-04 1.08262629e-02 1.21423583e-01] - [2.16904255e-02 9.03825804e-04 1.87178504e-03 1.18391107e-01] - [4.15462212e-02 2.65987989e-02 7.23177217e-02 2.39440105e-03]] - - - - -PLOT TRANSPORTATION MATRIX -############################################################################# - -Plot SAG results ----------------- - - -.. code-block:: default - - - pl.figure(4, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, sag_pi, 'semi-dual : OT matrix SAG') - pl.show() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_stochastic_001.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_stochastic.py:119: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - -Plot ASGD results ------------------ - - -.. code-block:: default - - - pl.figure(4, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, asgd_pi, 'semi-dual : OT matrix ASGD') - pl.show() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_stochastic_002.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_stochastic.py:128: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - -Plot Sinkhorn results ---------------------- - - -.. code-block:: default - - - pl.figure(4, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, sinkhorn_pi, 'OT matrix Sinkhorn') - pl.show() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_stochastic_003.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_stochastic.py:137: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - -COMPUTE TRANSPORTATION MATRIX FOR DUAL PROBLEM -############################################################################ -############################################################################ - SEMICONTINOUS CASE: - - Sample one general measure a, one discrete measures b for the semicontinous - case - --------------------------------------------- - - Define one general measure a, one discrete measures b, the points where - are defined the source and the target measures and finally the cost matrix c. - - -.. code-block:: default - - - n_source = 7 - n_target = 4 - reg = 1 - numItermax = 100000 - lr = 0.1 - batch_size = 3 - log = True - - a = ot.utils.unif(n_source) - b = ot.utils.unif(n_target) - - rng = np.random.RandomState(0) - X_source = rng.randn(n_source, 2) - Y_target = rng.randn(n_target, 2) - M = ot.dist(X_source, Y_target) - - - - - - - - -Call the "SGD" dual method to find the transportation matrix in the -semicontinous case ---------------------------------------------- - -Call ot.solve_dual_entropic and plot the results. - - -.. code-block:: default - - - sgd_dual_pi, log_sgd = ot.stochastic.solve_dual_entropic(a, b, M, reg, - batch_size, numItermax, - lr, log=log) - print(log_sgd['alpha'], log_sgd['beta']) - print(sgd_dual_pi) - - - - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - [0.91421006 2.78075506 1.06828701 0.01979397 0.60914807 1.81887037 - 0.1152939 ] [0.33964624 0.47604281 1.57223631 4.93843308] - [[2.18038772e-02 9.24355133e-02 1.08426805e-02 9.39355366e-08] - [1.59966167e-02 1.79248770e-03 1.23251128e-04 2.47779034e-05] - [3.44864558e-03 8.01760930e-02 4.40119061e-02 3.30922887e-09] - [3.12954103e-02 4.34915712e-02 7.13747533e-02 1.24533534e-05] - [6.79742497e-02 5.64192090e-03 5.37416946e-02 2.13851205e-02] - [8.05141568e-02 3.64790957e-03 5.00040902e-03 1.12213345e-02] - [4.86643900e-02 3.38763749e-02 6.09634969e-02 7.16139950e-05]] - - - - -Compare the results with the Sinkhorn algorithm ---------------------------------------------- - -Call the Sinkhorn algorithm from POT - - -.. code-block:: default - - - sinkhorn_pi = ot.sinkhorn(a, b, M, reg) - print(sinkhorn_pi) - - - - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - [[2.55553508e-02 9.96395661e-02 1.76579142e-02 4.31178193e-06] - [1.21640234e-01 1.25357448e-02 1.30225079e-03 7.37891333e-03] - [3.56123974e-03 7.61451746e-02 6.31505947e-02 1.33831455e-07] - [2.61515201e-02 3.34246014e-02 8.28734709e-02 4.07550425e-04] - [9.85500876e-03 7.52288523e-04 1.08262629e-02 1.21423583e-01] - [2.16904255e-02 9.03825804e-04 1.87178504e-03 1.18391107e-01] - [4.15462212e-02 2.65987989e-02 7.23177217e-02 2.39440105e-03]] - - - - -Plot SGD results ------------------ - - -.. code-block:: default - - - pl.figure(4, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, sgd_dual_pi, 'dual : OT matrix SGD') - pl.show() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_stochastic_004.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_stochastic.py:199: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - -Plot Sinkhorn results ---------------------- - - -.. code-block:: default - - - pl.figure(4, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, sinkhorn_pi, 'OT matrix Sinkhorn') - pl.show() - - - -.. image:: /auto_examples/images/sphx_glr_plot_stochastic_005.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_stochastic.py:208: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 8.885 seconds) - - -.. _sphx_glr_download_auto_examples_plot_stochastic.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_stochastic.py <plot_stochastic.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: plot_stochastic.ipynb <plot_stochastic.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ diff --git a/docs/source/auto_examples/searchindex b/docs/source/auto_examples/searchindex Binary files differdeleted file mode 100644 index 2cad500..0000000 --- a/docs/source/auto_examples/searchindex +++ /dev/null diff --git a/docs/source/conf.py b/docs/source/conf.py index d29b829..880c71d 100644 --- a/docs/source/conf.py +++ b/docs/source/conf.py @@ -34,9 +34,11 @@ class Mock(MagicMock): @classmethod def __getattr__(cls, name): return MagicMock() -MOCK_MODULES = ['ot.lp.emd_wrap','autograd','pymanopt','cupy','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) +#sys.modules.update((mod_name, Mock()) for mod_name in MOCK_MODULES) # !!!! # If extensions (or modules to document with autodoc) are in another directory, @@ -65,7 +67,7 @@ extensions = [ 'sphinx.ext.ifconfig', 'sphinx.ext.viewcode', 'sphinx.ext.napoleon', - #'sphinx_gallery.gen_gallery', + 'sphinx_gallery.gen_gallery', ] napoleon_numpy_docstring = True @@ -248,17 +250,17 @@ htmlhelp_basename = 'POTdoc' # -- Options for LaTeX output --------------------------------------------- latex_elements = { -# The paper size ('letterpaper' or 'a4paper'). -#'papersize': 'letterpaper', + # The paper size ('letterpaper' or 'a4paper'). + #'papersize': 'letterpaper', -# The font size ('10pt', '11pt' or '12pt'). -#'pointsize': '10pt', + # The font size ('10pt', '11pt' or '12pt'). + #'pointsize': '10pt', -# Additional stuff for the LaTeX preamble. -#'preamble': '', + # Additional stuff for the LaTeX preamble. + #'preamble': '', -# Latex figure (float) alignment -#'figure_align': 'htbp', + # Latex figure (float) alignment + #'figure_align': 'htbp', } # Grouping the document tree into LaTeX files. List of tuples @@ -334,7 +336,7 @@ intersphinx_mapping = {'python': ('https://docs.python.org/3', None), 'matplotlib': ('http://matplotlib.sourceforge.net/', None)} sphinx_gallery_conf = { - 'examples_dirs': ['../../examples','../../examples/da'], + 'examples_dirs': ['../../examples', '../../examples/da'], 'gallery_dirs': 'auto_examples', 'backreferences_dir': '../modules/generated/', 'reference_url': { diff --git a/docs/source/index.md b/docs/source/index.md new file mode 100644 index 0000000..9acdcf3 --- /dev/null +++ b/docs/source/index.md @@ -0,0 +1 @@ +<meta http-equiv="refresh" content="0; URL=https://PythonOT.github.io">`
\ No newline at end of file diff --git a/docs/source/readme.rst b/docs/source/readme.rst index 4f6af01..279e5da 100644 --- a/docs/source/readme.rst +++ b/docs/source/readme.rst @@ -1,14 +1,16 @@ POT: Python Optimal Transport ============================= -|PyPI version| |Anaconda Cloud| |Build Status| |Documentation Status| +|PyPI version| |Anaconda Cloud| |Build Status| |Codecov Status| |Downloads| |Anaconda downloads| |License| This open source Python library provide several solvers for optimization problems related to Optimal Transport for signal, image processing and machine learning. -It provides the following solvers: +Website and documentation: https://PythonOT.github.io/ + +POT provides the following solvers: - OT Network Flow solver for the linear program/ Earth Movers Distance [1]. @@ -24,7 +26,7 @@ It provides the following solvers: - Bregman projections for Wasserstein barycenter [3], convolutional barycenter [21] and unmixing [4]. - Optimal transport for domain adaptation with group lasso - regularization [5] + regularization and Laplacian regularization [5][30] - Conditional gradient [6] and Generalized conditional gradient for regularized OT [7]. - Linear OT [14] and Joint OT matrix and mapping estimation [8]. @@ -180,45 +182,45 @@ Examples and Notebooks The examples folder contain several examples and use case for the library. The full documentation is available on -`Readthedocs <http://pot.readthedocs.io/>`__. +https://PythonOT.github.io/. Here is a list of the Python notebooks available -`here <https://github.com/rflamary/POT/blob/master/notebooks/>`__ if you +`here <https://github.com/PythonOT/POT/blob/master/notebooks/>`__ if you want a quick look: - `1D optimal - transport <https://github.com/rflamary/POT/blob/master/notebooks/plot_OT_1D.ipynb>`__ + transport <https://github.com/PythonOT/POT/blob/master/notebooks/plot_OT_1D.ipynb>`__ - `OT Ground - Loss <https://github.com/rflamary/POT/blob/master/notebooks/plot_OT_L1_vs_L2.ipynb>`__ + Loss <https://github.com/PythonOT/POT/blob/master/notebooks/plot_OT_L1_vs_L2.ipynb>`__ - `Multiple EMD - computation <https://github.com/rflamary/POT/blob/master/notebooks/plot_compute_emd.ipynb>`__ + computation <https://github.com/PythonOT/POT/blob/master/notebooks/plot_compute_emd.ipynb>`__ - `2D optimal transport on empirical - distributions <https://github.com/rflamary/POT/blob/master/notebooks/plot_OT_2D_samples.ipynb>`__ + distributions <https://github.com/PythonOT/POT/blob/master/notebooks/plot_OT_2D_samples.ipynb>`__ - `1D Wasserstein - barycenter <https://github.com/rflamary/POT/blob/master/notebooks/plot_barycenter_1D.ipynb>`__ + barycenter <https://github.com/PythonOT/POT/blob/master/notebooks/plot_barycenter_1D.ipynb>`__ - `OT with user provided - regularization <https://github.com/rflamary/POT/blob/master/notebooks/plot_optim_OTreg.ipynb>`__ + regularization <https://github.com/PythonOT/POT/blob/master/notebooks/plot_optim_OTreg.ipynb>`__ - `Domain adaptation with optimal - transport <https://github.com/rflamary/POT/blob/master/notebooks/plot_otda_d2.ipynb>`__ + transport <https://github.com/PythonOT/POT/blob/master/notebooks/plot_otda_d2.ipynb>`__ - `Color transfer in - images <https://github.com/rflamary/POT/blob/master/notebooks/plot_otda_color_images.ipynb>`__ + images <https://github.com/PythonOT/POT/blob/master/notebooks/plot_otda_color_images.ipynb>`__ - `OT mapping estimation for domain - adaptation <https://github.com/rflamary/POT/blob/master/notebooks/plot_otda_mapping.ipynb>`__ + adaptation <https://github.com/PythonOT/POT/blob/master/notebooks/plot_otda_mapping.ipynb>`__ - `OT mapping estimation for color transfer in - images <https://github.com/rflamary/POT/blob/master/notebooks/plot_otda_mapping_colors_images.ipynb>`__ + images <https://github.com/PythonOT/POT/blob/master/notebooks/plot_otda_mapping_colors_images.ipynb>`__ - `Wasserstein Discriminant - Analysis <https://github.com/rflamary/POT/blob/master/notebooks/plot_WDA.ipynb>`__ + Analysis <https://github.com/PythonOT/POT/blob/master/notebooks/plot_WDA.ipynb>`__ - `Gromov - Wasserstein <https://github.com/rflamary/POT/blob/master/notebooks/plot_gromov.ipynb>`__ + Wasserstein <https://github.com/PythonOT/POT/blob/master/notebooks/plot_gromov.ipynb>`__ - `Gromov Wasserstein - Barycenter <https://github.com/rflamary/POT/blob/master/notebooks/plot_gromov_barycenter.ipynb>`__ + Barycenter <https://github.com/PythonOT/POT/blob/master/notebooks/plot_gromov_barycenter.ipynb>`__ - `Fused Gromov - Wasserstein <https://github.com/rflamary/POT/blob/master/notebooks/plot_fgw.ipynb>`__ + Wasserstein <https://github.com/PythonOT/POT/blob/master/notebooks/plot_fgw.ipynb>`__ - `Fused Gromov Wasserstein - Barycenter <https://github.com/rflamary/POT/blob/master/notebooks/plot_barycenter_fgw.ipynb>`__ + Barycenter <https://github.com/PythonOT/POT/blob/master/notebooks/plot_barycenter_fgw.ipynb>`__ You can also see the notebooks with `Jupyter -nbviewer <https://nbviewer.jupyter.org/github/rflamary/POT/tree/master/notebooks/>`__. +nbviewer <https://nbviewer.jupyter.org/github/PythonOT/POT/tree/master/notebooks/>`__. Acknowledgements ---------------- @@ -247,6 +249,7 @@ The contributors to this library are - `Hicham Janati <https://hichamjanati.github.io/>`__ (Unbalanced OT) - `Romain Tavenard <https://rtavenar.github.io/>`__ (1d Wasserstein) - `Mokhtar Z. Alaya <http://mzalaya.github.io/>`__ (Screenkhorn) +- `Ievgen Redko <https://ievred.github.io/>`__ This toolbox benefit a lot from open source research and we would like to thank the following persons for providing some code (in various @@ -422,17 +425,23 @@ Gromov-Wasserstein with Applications on Positive-Unlabeled Learning <https://arxiv.org/abs/2002.08276>`__, arXiv preprint arXiv:2002.08276. +[30] Flamary R., Courty N., Tuia D., Rakotomamonjy A. (2014). `Optimal +transport with Laplacian regularization: Applications to domain +adaptation and shape +matching <https://remi.flamary.com/biblio/flamary2014optlaplace.pdf>`__, +NIPS Workshop on Optimal Transport and Machine Learning OTML, 2014. + .. |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 :target: https://anaconda.org/conda-forge/pot -.. |Build Status| image:: https://travis-ci.org/rflamary/POT.svg?branch=master - :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 +.. |Build Status| image:: https://travis-ci.org/PythonOT/POT.svg?branch=master + :target: https://travis-ci.org/PythonOT/POT +.. |Codecov Status| image:: https://codecov.io/gh/PythonOT/POT/branch/master/graph/badge.svg + :target: https://codecov.io/gh/PythonOT/POT .. |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 - :target: https://github.com/rflamary/POT/blob/master/LICENSE + :target: https://github.com/PythonOT/POT/blob/master/LICENSE diff --git a/examples/plot_fgw.py b/examples/plot_fgw.py index 43efc94..cfdc33b 100644 --- a/examples/plot_fgw.py +++ b/examples/plot_fgw.py @@ -60,14 +60,14 @@ pl.subplot(2, 1, 1) pl.scatter(ys, xs, c=phi, s=70) pl.ylabel('Feature value a', fontsize=20) -pl.title('$\mu=\sum_i \delta_{x_i,a_i}$', fontsize=25, usetex=True, y=1) +pl.title('$\mu=\sum_i \delta_{x_i,a_i}$', fontsize=25, y=1) pl.xticks(()) pl.yticks(()) pl.subplot(2, 1, 2) pl.scatter(yt, xt, c=phi2, s=70) pl.xlabel('coordinates x/y', fontsize=25) pl.ylabel('Feature value b', fontsize=20) -pl.title('$\\nu=\sum_j \delta_{y_j,b_j}$', fontsize=25, usetex=True, y=1) +pl.title('$\\nu=\sum_j \delta_{y_j,b_j}$', fontsize=25, y=1) pl.yticks(()) pl.tight_layout() pl.show() diff --git a/requirements.txt b/requirements.txt index c08822e..bee22f7 100644 --- a/requirements.txt +++ b/requirements.txt @@ -2,9 +2,9 @@ numpy scipy>=1.0 cython matplotlib -sphinx-gallery autograd pymanopt==0.2.4; python_version <'3' pymanopt; python_version >= '3' cvxopt +scikit-learn pytest
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