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Diffstat (limited to 'docs/source')
201 files changed, 661 insertions, 14863 deletions
diff --git a/docs/source/_templates/module.rst b/docs/source/_templates/module.rst new file mode 100644 index 0000000..5ad89be --- /dev/null +++ b/docs/source/_templates/module.rst @@ -0,0 +1,57 @@ +{{ fullname }} +{{ underline }} + +.. automodule:: {{ fullname }} + + {% block functions %} + {% if functions %} + + Functions + --------- + + {% for item in functions %} + + .. autofunction:: {{ item }} + + .. include:: backreferences/{{fullname}}.{{item}}.examples + + .. raw:: html + + <div class="sphx-glr-clear"></div> + + {%- endfor %} + {% endif %} + {% endblock %} + + {% block classes %} + {% if classes %} + + Classes + ------- + + {% for item in classes %} + .. autoclass:: {{ item }} + :members: + + .. include:: backreferences/{{fullname}}.{{item}}.examples + + .. raw:: html + + <div class="sphx-glr-clear"></div> + + {%- endfor %} + {% endif %} + {% endblock %} + + {% block exceptions %} + {% if exceptions %} + + Exceptions + ---------- + + .. autosummary:: + {% for item in exceptions %} + {{ item }} + {%- endfor %} + {% endif %} + {% endblock %}
\ No newline at end of file diff --git a/docs/source/all.rst b/docs/source/all.rst index c968aa1..d7b878f 100644 --- a/docs/source/all.rst +++ b/docs/source/all.rst @@ -1,88 +1,36 @@ +.. _sphx_glr_api_reference: -Python modules -============== +API and modules +=============== -ot --- +.. currentmodule:: ot -.. automodule:: ot - :members: - -ot.lp ------ -.. automodule:: ot.lp - :members: - -ot.bregman ----------- - -.. automodule:: ot.bregman - :members: - -ot.smooth ------ -.. automodule:: ot.smooth - :members: - -ot.gromov ----------- - -.. automodule:: ot.gromov - :members: - - -ot.optim --------- - -.. automodule:: ot.optim - :members: -ot.da --------- +:py:mod:`ot`: -.. automodule:: ot.da - :members: +.. autosummary:: + :toctree: gen_modules/ + :template: module.rst -ot.gpu --------- + lp + bregman + smooth + gromov + optim + da + gpu + dr + utils + datasets + plot + stochastic + unbalanced + partial -.. automodule:: ot.gpu - :members: +.. autosummary:: + :toctree: ../modules/generated/ + :template: module.rst -ot.dr --------- - -.. automodule:: ot.dr - :members: - - -ot.utils --------- - -.. automodule:: ot.utils - :members: - -ot.datasets ------------ - -.. automodule:: ot.datasets - :members: - -ot.plot -------- - -.. automodule:: ot.plot - :members: - -ot.stochastic -------------- - -.. automodule:: ot.stochastic +.. automodule:: ot :members: - -ot.unbalanced -------------- - -.. automodule:: ot.unbalanced - :members: diff --git a/docs/source/auto_examples/auto_examples_jupyter.zip b/docs/source/auto_examples/auto_examples_jupyter.zip Binary files differdeleted file mode 100644 index 901195a..0000000 --- a/docs/source/auto_examples/auto_examples_jupyter.zip +++ /dev/null diff --git a/docs/source/auto_examples/auto_examples_python.zip b/docs/source/auto_examples/auto_examples_python.zip Binary files differdeleted file mode 100644 index ded2613..0000000 --- a/docs/source/auto_examples/auto_examples_python.zip +++ /dev/null diff --git 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index 609339d..0000000 --- a/docs/source/auto_examples/images/thumb/sphx_glr_plot_stochastic_thumb.png +++ /dev/null diff --git a/docs/source/auto_examples/index.rst b/docs/source/auto_examples/index.rst deleted file mode 100644 index fe6702d..0000000 --- a/docs/source/auto_examples/index.rst +++ /dev/null @@ -1,535 +0,0 @@ -:orphan: - -POT Examples -============ - -This is a gallery of all the POT example files. - - - -.. raw:: 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="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="Illustration of 2D Wasserstein barycenters if discributions that are weighted sum of diracs."> - -.. only:: html - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_free_support_barycenter_thumb.png - - :ref:`sphx_glr_auto_examples_plot_free_support_barycenter.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_free_support_barycenter - -.. raw:: html - - <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of EMD, Sinkhorn and smooth OT plans and their visuali..."> - -.. only:: html - - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_OT_1D_smooth_thumb.png - - :ref:`sphx_glr_auto_examples_plot_OT_1D_smooth.py` - -.. raw:: html - - </div> - - -.. toctree:: - :hidden: - - /auto_examples/plot_OT_1D_smooth - -.. raw:: html - - <div class="sphx-glr-thumbcontainer" tooltip="This example is designed to show how to use the Gromov-Wassertsein distance computation in POT...."> - -.. only:: html - - .. 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="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 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="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="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 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="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 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 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 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 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 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 style='clear:both'></div> - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :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 - - :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.readthedocs.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 bd0439e..0000000 --- a/docs/source/auto_examples/plot_OT_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 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": [ - "#%% parameters\n\nn = 100 # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\na = gauss(n, m=20, s=5) # m= mean, s= std\nb = gauss(n, m=60, s=10)\n\n# loss matrix\nM = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))\nM /= M.max()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Plot distributions and loss matrix\n----------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "#%% plot the distributions\n\npl.figure(1, figsize=(6.4, 3))\npl.plot(x, a, 'b', label='Source distribution')\npl.plot(x, b, 'r', label='Target distribution')\npl.legend()\n\n#%% plot distributions and loss matrix\n\npl.figure(2, figsize=(5, 5))\not.plot.plot1D_mat(a, b, M, 'Cost matrix M')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solve EMD\n---------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "#%% EMD\n\nG0 = ot.emd(a, b, M)\n\npl.figure(3, figsize=(5, 5))\not.plot.plot1D_mat(a, b, G0, 'OT matrix G0')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solve Sinkhorn\n--------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "#%% Sinkhorn\n\nlambd = 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": "3.6.5" - } - }, - "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 b97d67c..0000000 --- a/docs/source/auto_examples/plot_OT_1D.rst +++ /dev/null @@ -1,199 +0,0 @@ - - -.. _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:: python - - - # Author: Remi Flamary <remi.flamary@unice.fr> - # - # License: MIT License - - import numpy as np - import matplotlib.pylab as pl - import ot - import ot.plot - from ot.datasets import make_1D_gauss as gauss - - - - - - - -Generate data -------------- - - - -.. code-block:: python - - - - #%% parameters - - n = 100 # nb bins - - # bin positions - x = np.arange(n, dtype=np.float64) - - # Gaussian distributions - a = gauss(n, m=20, s=5) # m= mean, s= std - b = gauss(n, m=60, s=10) - - # loss matrix - M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1))) - M /= M.max() - - - - - - - - -Plot distributions and loss matrix ----------------------------------- - - - -.. code-block:: python - - - #%% plot the distributions - - pl.figure(1, figsize=(6.4, 3)) - pl.plot(x, a, 'b', label='Source distribution') - pl.plot(x, b, 'r', label='Target distribution') - pl.legend() - - #%% plot distributions and loss matrix - - pl.figure(2, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, M, 'Cost matrix M') - - - - -.. rst-class:: sphx-glr-horizontal - - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_001.png - :scale: 47 - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_002.png - :scale: 47 - - - - -Solve EMD ---------- - - - -.. code-block:: python - - - - #%% EMD - - G0 = ot.emd(a, b, M) - - pl.figure(3, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, G0, 'OT matrix G0') - - - - -.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_005.png - :align: center - - - - -Solve Sinkhorn --------------- - - - -.. code-block:: python - - - - #%% 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() - - - -.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_007.png - :align: center - - -.. rst-class:: sphx-glr-script-out - - Out:: - - It. |Err - ------------------- - 0|8.187970e-02| - 10|3.460174e-02| - 20|6.633335e-03| - 30|9.797798e-04| - 40|1.389606e-04| - 50|1.959016e-05| - 60|2.759079e-06| - 70|3.885166e-07| - 80|5.470605e-08| - 90|7.702918e-09| - 100|1.084609e-09| - 110|1.527180e-10| - - -**Total running time of the script:** ( 0 minutes 0.561 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_OT_1D.py <plot_OT_1D.py>` - - - - .. container:: sphx-glr-download - - :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.readthedocs.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 d523f6a..0000000 --- a/docs/source/auto_examples/plot_OT_1D_smooth.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# 1D smooth optimal transport\n\n\nThis example illustrates the computation of EMD, Sinkhorn and smooth OT plans\nand their visualization.\n\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Author: Remi Flamary <remi.flamary@unice.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\nimport ot.plot\nfrom ot.datasets import make_1D_gauss as gauss" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Generate data\n-------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "#%% parameters\n\nn = 100 # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\na = gauss(n, m=20, s=5) # m= mean, s= std\nb = gauss(n, m=60, s=10)\n\n# loss matrix\nM = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))\nM /= M.max()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Plot distributions and loss matrix\n----------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "#%% plot the distributions\n\npl.figure(1, figsize=(6.4, 3))\npl.plot(x, a, 'b', label='Source distribution')\npl.plot(x, b, 'r', label='Target distribution')\npl.legend()\n\n#%% plot distributions and loss matrix\n\npl.figure(2, figsize=(5, 5))\not.plot.plot1D_mat(a, b, M, 'Cost matrix M')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solve EMD\n---------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "#%% EMD\n\nG0 = ot.emd(a, b, M)\n\npl.figure(3, figsize=(5, 5))\not.plot.plot1D_mat(a, b, G0, 'OT matrix G0')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solve Sinkhorn\n--------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "#%% Sinkhorn\n\nlambd = 2e-3\nGs = ot.sinkhorn(a, b, M, lambd, verbose=True)\n\npl.figure(4, figsize=(5, 5))\not.plot.plot1D_mat(a, b, Gs, 'OT matrix Sinkhorn')\n\npl.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solve Smooth OT\n--------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "#%% Smooth OT with KL regularization\n\nlambd = 2e-3\nGsm = ot.smooth.smooth_ot_dual(a, b, M, lambd, reg_type='kl')\n\npl.figure(5, figsize=(5, 5))\not.plot.plot1D_mat(a, b, Gsm, 'OT matrix Smooth OT KL reg.')\n\npl.show()\n\n\n#%% Smooth OT with KL regularization\n\nlambd = 1e-1\nGsm = ot.smooth.smooth_ot_dual(a, b, M, lambd, reg_type='l2')\n\npl.figure(6, figsize=(5, 5))\not.plot.plot1D_mat(a, b, Gsm, 'OT matrix Smooth OT l2 reg.')\n\npl.show()" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.5" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_OT_1D_smooth.py b/docs/source/auto_examples/plot_OT_1D_smooth.py 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 5a0ebd3..0000000 --- a/docs/source/auto_examples/plot_OT_1D_smooth.rst +++ /dev/null @@ -1,242 +0,0 @@ - - -.. _sphx_glr_auto_examples_plot_OT_1D_smooth.py: - - -=========================== -1D smooth optimal transport -=========================== - -This example illustrates the computation of EMD, Sinkhorn and smooth OT plans -and their visualization. - - - - -.. code-block:: python - - - # Author: Remi Flamary <remi.flamary@unice.fr> - # - # License: MIT License - - import numpy as np - import matplotlib.pylab as pl - import ot - import ot.plot - from ot.datasets import make_1D_gauss as gauss - - - - - - - -Generate data -------------- - - - -.. code-block:: python - - - - #%% parameters - - n = 100 # nb bins - - # bin positions - x = np.arange(n, dtype=np.float64) - - # Gaussian distributions - a = gauss(n, m=20, s=5) # m= mean, s= std - b = gauss(n, m=60, s=10) - - # loss matrix - M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1))) - M /= M.max() - - - - - - - - -Plot distributions and loss matrix ----------------------------------- - - - -.. code-block:: python - - - #%% plot the distributions - - pl.figure(1, figsize=(6.4, 3)) - pl.plot(x, a, 'b', label='Source distribution') - pl.plot(x, b, 'r', label='Target distribution') - pl.legend() - - #%% plot distributions and loss matrix - - pl.figure(2, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, M, 'Cost matrix M') - - - - -.. rst-class:: sphx-glr-horizontal - - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_001.png - :scale: 47 - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_002.png - :scale: 47 - - - - -Solve EMD ---------- - - - -.. code-block:: python - - - - #%% EMD - - G0 = ot.emd(a, b, M) - - pl.figure(3, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, G0, 'OT matrix G0') - - - - -.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_005.png - :align: center - - - - -Solve Sinkhorn --------------- - - - -.. code-block:: python - - - - #%% Sinkhorn - - lambd = 2e-3 - Gs = ot.sinkhorn(a, b, M, lambd, verbose=True) - - pl.figure(4, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, Gs, 'OT matrix Sinkhorn') - - pl.show() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_007.png - :align: center - - -.. rst-class:: sphx-glr-script-out - - Out:: - - It. |Err - ------------------- - 0|7.958844e-02| - 10|5.921715e-03| - 20|1.238266e-04| - 30|2.469780e-06| - 40|4.919966e-08| - 50|9.800197e-10| - - -Solve Smooth OT --------------- - - - -.. code-block:: python - - - - #%% Smooth OT with KL regularization - - lambd = 2e-3 - Gsm = ot.smooth.smooth_ot_dual(a, b, M, lambd, reg_type='kl') - - pl.figure(5, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, Gsm, 'OT matrix Smooth OT KL reg.') - - pl.show() - - - #%% Smooth OT with KL regularization - - lambd = 1e-1 - Gsm = ot.smooth.smooth_ot_dual(a, b, M, lambd, reg_type='l2') - - pl.figure(6, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, Gsm, 'OT matrix Smooth OT l2 reg.') - - pl.show() - - - -.. rst-class:: sphx-glr-horizontal - - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_009.png - :scale: 47 - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_010.png - :scale: 47 - - - - -**Total running time of the script:** ( 0 minutes 1.053 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_OT_1D_smooth.py <plot_OT_1D_smooth.py>` - - - - .. container:: sphx-glr-download - - :download:`Download Jupyter notebook: plot_OT_1D_smooth.ipynb <plot_OT_1D_smooth.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_OT_2D_samples.ipynb b/docs/source/auto_examples/plot_OT_2D_samples.ipynb deleted file mode 100644 index dad138b..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": [ - "#%% parameters and data generation\n\nn = 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": [ - "#%% plot samples\n\npl.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": [ - "#%% EMD\n\nG0 = 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": [ - "#%% sinkhorn\n\n# 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": [ - "#%% sinkhorn\n\n# 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": "3.6.8" - } - }, - "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 1f1d713..0000000 --- a/docs/source/auto_examples/plot_OT_2D_samples.rst +++ /dev/null @@ -1,273 +0,0 @@ - - -.. _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:: python - - - # 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:: python - - - #%% 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 ---------- - - - -.. code-block:: python - - - #%% 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') - - - - -.. rst-class:: sphx-glr-horizontal - - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_001.png - :scale: 47 - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_002.png - :scale: 47 - - - - -Compute EMD ------------ - - - -.. code-block:: python - - - #%% 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') - - - - - -.. rst-class:: sphx-glr-horizontal - - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_005.png - :scale: 47 - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_006.png - :scale: 47 - - - - -Compute Sinkhorn ----------------- - - - -.. code-block:: python - - - #%% 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() - - - - - -.. rst-class:: sphx-glr-horizontal - - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_009.png - :scale: 47 - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_010.png - :scale: 47 - - - - -Emprirical Sinkhorn ----------------- - - - -.. code-block:: python - - - #%% 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() - - - -.. rst-class:: sphx-glr-horizontal - - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_013.png - :scale: 47 - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_014.png - :scale: 47 - - -.. rst-class:: sphx-glr-script-out - - Out:: - - Warning: numerical errors at iteration 0 - - -**Total running time of the script:** ( 0 minutes 2.616 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_OT_2D_samples.py <plot_OT_2D_samples.py>` - - - - .. container:: sphx-glr-download - - :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.readthedocs.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 125d720..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": [ - "#%% EMD\nG1 = 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": [ - "#%% EMD\nG1 = 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": "3.6.5" - } - }, - "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 5db4b55..0000000 --- a/docs/source/auto_examples/plot_OT_L1_vs_L2.rst +++ /dev/null @@ -1,318 +0,0 @@ - - -.. _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:: python - - - # Author: Remi Flamary <remi.flamary@unice.fr> - # - # License: MIT License - - import numpy as np - import matplotlib.pylab as pl - import ot - import ot.plot - - - - - - - -Dataset 1 : uniform sampling ----------------------------- - - - -.. code-block:: python - - - 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 - :scale: 47 - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_002.png - :scale: 47 - - - - -Dataset 1 : Plot OT Matrices ----------------------------- - - - -.. code-block:: python - - - - #%% 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() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_005.png - :align: center - - - - -Dataset 2 : Partial circle --------------------------- - - - -.. code-block:: python - - - 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_007.png - :scale: 47 - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_008.png - :scale: 47 - - - - -Dataset 2 : Plot OT Matrices ------------------------------ - - - -.. code-block:: python - - - - #%% 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() - - - -.. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_011.png - :align: center - - - - -**Total running time of the script:** ( 0 minutes 0.958 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_OT_L1_vs_L2.py <plot_OT_L1_vs_L2.py>` - - - - .. container:: sphx-glr-download - - :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.readthedocs.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 c695306..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": [ - "#%% parameters\n\nn = 100 # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\na = gauss(n, m=20, s=5) # m= mean, s= std\nb = gauss(n, m=60, s=10)\n\n# 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": [ - "#%% plot the distributions\n\npl.figure(1, figsize=(6.4, 3))\npl.plot(x, a, 'b', label='Source distribution')\npl.plot(x, b, 'r', label='Target distribution')\npl.legend()\n\n# plot distributions and loss matrix\n\npl.figure(2, figsize=(5, 5))\not.plot.plot1D_mat(a, b, M, 'Cost matrix M')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solve 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": "3.6.8" - } - }, - "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 8e618b4..0000000 --- a/docs/source/auto_examples/plot_UOT_1D.rst +++ /dev/null @@ -1,173 +0,0 @@ - - -.. _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:: python - - - # 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:: python - - - - #%% parameters - - n = 100 # nb bins - - # bin positions - x = np.arange(n, dtype=np.float64) - - # Gaussian distributions - a = gauss(n, m=20, s=5) # m= mean, s= std - b = gauss(n, m=60, s=10) - - # 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:: python - - - #%% plot the distributions - - pl.figure(1, figsize=(6.4, 3)) - pl.plot(x, a, 'b', label='Source distribution') - pl.plot(x, b, 'r', label='Target distribution') - pl.legend() - - # plot distributions and loss matrix - - pl.figure(2, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, M, 'Cost matrix M') - - - - - -.. rst-class:: sphx-glr-horizontal - - - * - - .. image:: /auto_examples/images/sphx_glr_plot_UOT_1D_001.png - :scale: 47 - - * - - .. image:: /auto_examples/images/sphx_glr_plot_UOT_1D_002.png - :scale: 47 - - - - -Solve Unbalanced Sinkhorn --------------- - - - -.. code-block:: python - - - - # 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_006.png - :align: center - - -.. rst-class:: sphx-glr-script-out - - Out:: - - It. |Err - ------------------- - 0|1.838786e+00| - 10|1.242379e-01| - 20|2.581314e-03| - 30|5.674552e-05| - 40|1.252959e-06| - 50|2.768136e-08| - 60|6.116090e-10| - - -**Total running time of the script:** ( 0 minutes 0.259 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_UOT_1D.py <plot_UOT_1D.py>` - - - - .. container:: sphx-glr-download - - :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.readthedocs.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 e59cdc2..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)\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)\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": "3.6.8" - } - }, - "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 c8d9d3b..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) - -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) - - -# 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 ac17587..0000000 --- a/docs/source/auto_examples/plot_UOT_barycenter_1D.rst +++ /dev/null @@ -1,261 +0,0 @@ - - -.. _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:: python - - - # 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:: python - - - # 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:: python - - - # 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 - :align: center - - - - -Barycenter computation ----------------------- - - - -.. code-block:: python - - - # 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) - - 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_003.png - :align: center - - - - -Barycentric interpolation -------------------------- - - - -.. code-block:: python - - - # 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) - - - # 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_005.png - :scale: 47 - - * - - .. image:: /auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_006.png - :scale: 47 - - - - -**Total running time of the script:** ( 0 minutes 0.344 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_UOT_barycenter_1D.py <plot_UOT_barycenter_1D.py>` - - - - .. container:: sphx-glr-download - - :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.readthedocs.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 fc60e1f..0000000 --- a/docs/source/auto_examples/plot_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\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": [ - "#%% parameters\n\nn = 100 # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\na1 = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std\na2 = ot.datasets.make_1D_gauss(n, m=60, s=8)\n\n# creating matrix A containing all distributions\nA = np.vstack((a1, a2)).T\nn_distributions = A.shape[1]\n\n# loss matrix + normalization\nM = ot.utils.dist0(n)\nM /= M.max()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Plot data\n---------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "#%% plot the distributions\n\npl.figure(1, figsize=(6.4, 3))\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\npl.tight_layout()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Barycenter computation\n----------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "#%% barycenter computation\n\nalpha = 0.2 # 0<=alpha<=1\nweights = np.array([1 - alpha, alpha])\n\n# l2bary\nbary_l2 = A.dot(weights)\n\n# wasserstein\nreg = 1e-3\nbary_wass = ot.bregman.barycenter(A, M, reg, weights)\n\npl.figure(2)\npl.clf()\npl.subplot(2, 1, 1)\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\n\npl.subplot(2, 1, 2)\npl.plot(x, bary_l2, 'r', label='l2')\npl.plot(x, bary_wass, 'g', label='Wasserstein')\npl.legend()\npl.title('Barycenters')\npl.tight_layout()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Barycentric interpolation\n-------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "#%% barycenter interpolation\n\nn_alpha = 11\nalpha_list = np.linspace(0, 1, n_alpha)\n\n\nB_l2 = np.zeros((n, n_alpha))\n\nB_wass = np.copy(B_l2)\n\nfor i in range(0, n_alpha):\n alpha = alpha_list[i]\n weights = np.array([1 - alpha, alpha])\n B_l2[:, i] = A.dot(weights)\n B_wass[:, i] = ot.bregman.barycenter(A, M, reg, weights)\n\n#%% plot interpolation\n\npl.figure(3)\n\ncmap = pl.cm.get_cmap('viridis')\nverts = []\nzs = alpha_list\nfor i, z in enumerate(zs):\n ys = B_l2[:, i]\n verts.append(list(zip(x, ys)))\n\nax = pl.gcf().gca(projection='3d')\n\npoly = PolyCollection(verts, facecolors=[cmap(a) for a in alpha_list])\npoly.set_alpha(0.7)\nax.add_collection3d(poly, zs=zs, zdir='y')\nax.set_xlabel('x')\nax.set_xlim3d(0, n)\nax.set_ylabel('$\\\\alpha$')\nax.set_ylim3d(0, 1)\nax.set_zlabel('')\nax.set_zlim3d(0, B_l2.max() * 1.01)\npl.title('Barycenter interpolation with l2')\npl.tight_layout()\n\npl.figure(4)\ncmap = pl.cm.get_cmap('viridis')\nverts = []\nzs = alpha_list\nfor i, z in enumerate(zs):\n ys = B_wass[:, i]\n verts.append(list(zip(x, ys)))\n\nax = pl.gcf().gca(projection='3d')\n\npoly = PolyCollection(verts, facecolors=[cmap(a) for a in alpha_list])\npoly.set_alpha(0.7)\nax.add_collection3d(poly, zs=zs, zdir='y')\nax.set_xlabel('x')\nax.set_xlim3d(0, n)\nax.set_ylabel('$\\\\alpha$')\nax.set_ylim3d(0, 1)\nax.set_zlabel('')\nax.set_zlim3d(0, B_l2.max() * 1.01)\npl.title('Barycenter interpolation with Wasserstein')\npl.tight_layout()\n\npl.show()" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.5" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_barycenter_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 66ac042..0000000 --- a/docs/source/auto_examples/plot_barycenter_1D.rst +++ /dev/null @@ -1,257 +0,0 @@ - - -.. _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:: python - - - # Author: Remi Flamary <remi.flamary@unice.fr> - # - # License: MIT License - - import numpy as np - import matplotlib.pylab as pl - import ot - # necessary for 3d plot even if not used - from mpl_toolkits.mplot3d import Axes3D # noqa - from matplotlib.collections import PolyCollection - - - - - - - -Generate data -------------- - - - -.. code-block:: python - - - #%% 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 ---------- - - - -.. code-block:: python - - - #%% 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_barycenter_1D_001.png - :align: center - - - - -Barycenter computation ----------------------- - - - -.. code-block:: python - - - #%% 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() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_003.png - :align: center - - - - -Barycentric interpolation -------------------------- - - - -.. code-block:: python - - - #%% 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() - - - -.. rst-class:: sphx-glr-horizontal - - - * - - .. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_005.png - :scale: 47 - - * - - .. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_006.png - :scale: 47 - - - - -**Total running time of the script:** ( 0 minutes 0.413 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_barycenter_1D.py <plot_barycenter_1D.py>` - - - - .. container:: sphx-glr-download - - :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.readthedocs.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 28229b2..0000000 --- a/docs/source/auto_examples/plot_barycenter_fgw.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=================================\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\n\n#%% load libraries\nimport 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\n#%% Graph functions\n\n\ndef 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": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "#%% circular dataset\n# We build a dataset of noisy circular graphs.\n# Noise is added on the structures by random connections and on the features by gaussian noise.\n\n\nnp.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": [ - "#%% Plot graphs\n\nplt.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": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "#%% We compute the barycenter using FGW. Structure matrices are computed using the shortest_path distance in the graph\n# Features distances are the euclidean distances\nCs = [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": [ - "#%% Create the barycenter\nbary = 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)\n\n#%%\npos = 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": "3.6.8" - } - }, - "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 2c44a65..0000000 --- a/docs/source/auto_examples/plot_barycenter_fgw.rst +++ /dev/null @@ -1,268 +0,0 @@ - - -.. _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:: python - - - # 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 -------------- - - - -.. code-block:: python - - - #%% 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 ---------- - - - -.. code-block:: python - - - #%% 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() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_barycenter_fgw_001.png - :align: center - - - - -Barycenter computation ----------------------- - - - -.. code-block:: python - - - #%% 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 -------------------------- - - - -.. code-block:: python - - - #%% 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() - - - -.. image:: /auto_examples/images/sphx_glr_plot_barycenter_fgw_002.png - :align: center - - - - -**Total running time of the script:** ( 0 minutes 2.065 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_barycenter_fgw.py <plot_barycenter_fgw.py>` - - - - .. container:: sphx-glr-download - - :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.readthedocs.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 2199162..0000000 --- a/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.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 Wasserstein barycenter comparison between exact LP and entropic regularization\n\n\nThis example illustrates the computation of regularized Wasserstein Barycenter\nas proposed in [3] and exact LP barycenters using standard LP solver.\n\nIt reproduces approximately Figure 3.1 and 3.2 from the following paper:\nCuturi, M., & Peyr\u00e9, G. (2016). A smoothed dual approach for variational\nWasserstein problems. SIAM Journal on Imaging Sciences, 9(1), 320-343.\n\n[3] Benamou, J. D., Carlier, G., Cuturi, M., Nenna, L., & Peyr\u00e9, G. (2015).\nIterative Bregman projections for regularized transportation problems\nSIAM Journal on Scientific Computing, 37(2), A1111-A1138.\n\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Author: Remi Flamary <remi.flamary@unice.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\n# necessary for 3d plot even if not used\nfrom mpl_toolkits.mplot3d import Axes3D # noqa\nfrom matplotlib.collections import PolyCollection # noqa\n\n#import ot.lp.cvx as cvx" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Gaussian Data\n-------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "#%% parameters\n\nproblems = []\n\nn = 100 # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\n# Gaussian distributions\na1 = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std\na2 = ot.datasets.make_1D_gauss(n, m=60, s=8)\n\n# creating matrix A containing all distributions\nA = np.vstack((a1, a2)).T\nn_distributions = A.shape[1]\n\n# loss matrix + normalization\nM = ot.utils.dist0(n)\nM /= M.max()\n\n\n#%% plot the distributions\n\npl.figure(1, figsize=(6.4, 3))\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\npl.tight_layout()\n\n#%% barycenter computation\n\nalpha = 0.5 # 0<=alpha<=1\nweights = np.array([1 - alpha, alpha])\n\n# l2bary\nbary_l2 = A.dot(weights)\n\n# wasserstein\nreg = 1e-3\not.tic()\nbary_wass = ot.bregman.barycenter(A, M, reg, weights)\not.toc()\n\n\not.tic()\nbary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True)\not.toc()\n\npl.figure(2)\npl.clf()\npl.subplot(2, 1, 1)\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\n\npl.subplot(2, 1, 2)\npl.plot(x, bary_l2, 'r', label='l2')\npl.plot(x, bary_wass, 'g', label='Reg Wasserstein')\npl.plot(x, bary_wass2, 'b', label='LP Wasserstein')\npl.legend()\npl.title('Barycenters')\npl.tight_layout()\n\nproblems.append([A, [bary_l2, bary_wass, bary_wass2]])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Dirac Data\n----------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "#%% parameters\n\na1 = 1.0 * (x > 10) * (x < 50)\na2 = 1.0 * (x > 60) * (x < 80)\n\na1 /= a1.sum()\na2 /= a2.sum()\n\n# creating matrix A containing all distributions\nA = np.vstack((a1, a2)).T\nn_distributions = A.shape[1]\n\n# loss matrix + normalization\nM = ot.utils.dist0(n)\nM /= M.max()\n\n\n#%% plot the distributions\n\npl.figure(1, figsize=(6.4, 3))\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\npl.tight_layout()\n\n\n#%% barycenter computation\n\nalpha = 0.5 # 0<=alpha<=1\nweights = np.array([1 - alpha, alpha])\n\n# l2bary\nbary_l2 = A.dot(weights)\n\n# wasserstein\nreg = 1e-3\not.tic()\nbary_wass = ot.bregman.barycenter(A, M, reg, weights)\not.toc()\n\n\not.tic()\nbary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True)\not.toc()\n\n\nproblems.append([A, [bary_l2, bary_wass, bary_wass2]])\n\npl.figure(2)\npl.clf()\npl.subplot(2, 1, 1)\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\n\npl.subplot(2, 1, 2)\npl.plot(x, bary_l2, 'r', label='l2')\npl.plot(x, bary_wass, 'g', label='Reg Wasserstein')\npl.plot(x, bary_wass2, 'b', label='LP Wasserstein')\npl.legend()\npl.title('Barycenters')\npl.tight_layout()\n\n#%% parameters\n\na1 = np.zeros(n)\na2 = np.zeros(n)\n\na1[10] = .25\na1[20] = .5\na1[30] = .25\na2[80] = 1\n\n\na1 /= a1.sum()\na2 /= a2.sum()\n\n# creating matrix A containing all distributions\nA = np.vstack((a1, a2)).T\nn_distributions = A.shape[1]\n\n# loss matrix + normalization\nM = ot.utils.dist0(n)\nM /= M.max()\n\n\n#%% plot the distributions\n\npl.figure(1, figsize=(6.4, 3))\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\npl.tight_layout()\n\n\n#%% barycenter computation\n\nalpha = 0.5 # 0<=alpha<=1\nweights = np.array([1 - alpha, alpha])\n\n# l2bary\nbary_l2 = A.dot(weights)\n\n# wasserstein\nreg = 1e-3\not.tic()\nbary_wass = ot.bregman.barycenter(A, M, reg, weights)\not.toc()\n\n\not.tic()\nbary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True)\not.toc()\n\n\nproblems.append([A, [bary_l2, bary_wass, bary_wass2]])\n\npl.figure(2)\npl.clf()\npl.subplot(2, 1, 1)\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\n\npl.subplot(2, 1, 2)\npl.plot(x, bary_l2, 'r', label='l2')\npl.plot(x, bary_wass, 'g', label='Reg Wasserstein')\npl.plot(x, bary_wass2, 'b', label='LP Wasserstein')\npl.legend()\npl.title('Barycenters')\npl.tight_layout()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Final figure\n------------\n\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "#%% plot\n\nnbm = len(problems)\nnbm2 = (nbm // 2)\n\n\npl.figure(2, (20, 6))\npl.clf()\n\nfor i in range(nbm):\n\n A = problems[i][0]\n bary_l2 = problems[i][1][0]\n bary_wass = problems[i][1][1]\n bary_wass2 = problems[i][1][2]\n\n pl.subplot(2, nbm, 1 + i)\n for j in range(n_distributions):\n pl.plot(x, A[:, j])\n if i == nbm2:\n pl.title('Distributions')\n pl.xticks(())\n pl.yticks(())\n\n pl.subplot(2, nbm, 1 + i + nbm)\n\n pl.plot(x, bary_l2, 'r', label='L2 (Euclidean)')\n pl.plot(x, bary_wass, 'g', label='Reg Wasserstein')\n pl.plot(x, bary_wass2, 'b', label='LP Wasserstein')\n if i == nbm - 1:\n pl.legend()\n if i == nbm2:\n pl.title('Barycenters')\n\n pl.xticks(())\n pl.yticks(())" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.5" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.py b/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.py deleted file mode 100644 index b82765e..0000000 --- a/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.py +++ /dev/null @@ -1,281 +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]]) - -############################################################################## -# Dirac Data -# ---------- - -#%% parameters - -a1 = 1.0 * (x > 10) * (x < 50) -a2 = 1.0 * (x > 60) * (x < 80) - -a1 /= a1.sum() -a2 /= a2.sum() - -# creating matrix A containing all distributions -A = np.vstack((a1, a2)).T -n_distributions = A.shape[1] - -# loss matrix + normalization -M = ot.utils.dist0(n) -M /= M.max() - - -#%% plot the distributions - -pl.figure(1, figsize=(6.4, 3)) -for i in range(n_distributions): - pl.plot(x, A[:, i]) -pl.title('Distributions') -pl.tight_layout() - - -#%% barycenter computation - -alpha = 0.5 # 0<=alpha<=1 -weights = np.array([1 - alpha, alpha]) - -# l2bary -bary_l2 = A.dot(weights) - -# wasserstein -reg = 1e-3 -ot.tic() -bary_wass = ot.bregman.barycenter(A, M, reg, weights) -ot.toc() - - -ot.tic() -bary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True) -ot.toc() - - -problems.append([A, [bary_l2, bary_wass, bary_wass2]]) - -pl.figure(2) -pl.clf() -pl.subplot(2, 1, 1) -for i in range(n_distributions): - pl.plot(x, A[:, i]) -pl.title('Distributions') - -pl.subplot(2, 1, 2) -pl.plot(x, bary_l2, 'r', label='l2') -pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') -pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') -pl.legend() -pl.title('Barycenters') -pl.tight_layout() - -#%% parameters - -a1 = np.zeros(n) -a2 = np.zeros(n) - -a1[10] = .25 -a1[20] = .5 -a1[30] = .25 -a2[80] = 1 - - -a1 /= a1.sum() -a2 /= a2.sum() - -# creating matrix A containing all distributions -A = np.vstack((a1, a2)).T -n_distributions = A.shape[1] - -# loss matrix + normalization -M = ot.utils.dist0(n) -M /= M.max() - - -#%% plot the distributions - -pl.figure(1, figsize=(6.4, 3)) -for i in range(n_distributions): - pl.plot(x, A[:, i]) -pl.title('Distributions') -pl.tight_layout() - - -#%% barycenter computation - -alpha = 0.5 # 0<=alpha<=1 -weights = np.array([1 - alpha, alpha]) - -# l2bary -bary_l2 = A.dot(weights) - -# wasserstein -reg = 1e-3 -ot.tic() -bary_wass = ot.bregman.barycenter(A, M, reg, weights) -ot.toc() - - -ot.tic() -bary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True) -ot.toc() - - -problems.append([A, [bary_l2, bary_wass, bary_wass2]]) - -pl.figure(2) -pl.clf() -pl.subplot(2, 1, 1) -for i in range(n_distributions): - pl.plot(x, A[:, i]) -pl.title('Distributions') - -pl.subplot(2, 1, 2) -pl.plot(x, bary_l2, 'r', label='l2') -pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') -pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') -pl.legend() -pl.title('Barycenters') -pl.tight_layout() - - -############################################################################## -# Final figure -# ------------ -# - -#%% plot - -nbm = len(problems) -nbm2 = (nbm // 2) - - -pl.figure(2, (20, 6)) -pl.clf() - -for i in range(nbm): - - A = problems[i][0] - bary_l2 = problems[i][1][0] - bary_wass = problems[i][1][1] - bary_wass2 = problems[i][1][2] - - pl.subplot(2, nbm, 1 + i) - for j in range(n_distributions): - pl.plot(x, A[:, j]) - if i == nbm2: - pl.title('Distributions') - pl.xticks(()) - pl.yticks(()) - - pl.subplot(2, nbm, 1 + i + nbm) - - pl.plot(x, bary_l2, 'r', label='L2 (Euclidean)') - pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') - pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') - if i == nbm - 1: - pl.legend() - if i == nbm2: - pl.title('Barycenters') - - pl.xticks(()) - pl.yticks(()) diff --git a/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.rst b/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.rst deleted file mode 100644 index bd1c710..0000000 --- a/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.rst +++ /dev/null @@ -1,447 +0,0 @@ - - -.. _sphx_glr_auto_examples_plot_barycenter_lp_vs_entropic.py: - - -================================================================================= -1D Wasserstein barycenter comparison between exact LP and entropic regularization -================================================================================= - -This example illustrates the computation of regularized Wasserstein Barycenter -as proposed in [3] and exact LP barycenters using standard LP solver. - -It reproduces approximately Figure 3.1 and 3.2 from the following paper: -Cuturi, M., & Peyré, G. (2016). A smoothed dual approach for variational -Wasserstein problems. SIAM Journal on Imaging Sciences, 9(1), 320-343. - -[3] Benamou, J. D., Carlier, G., Cuturi, M., Nenna, L., & Peyré, G. (2015). -Iterative Bregman projections for regularized transportation problems -SIAM Journal on Scientific Computing, 37(2), A1111-A1138. - - - - -.. code-block:: python - - - # Author: Remi Flamary <remi.flamary@unice.fr> - # - # License: MIT License - - import numpy as np - import matplotlib.pylab as pl - import ot - # necessary for 3d plot even if not used - from mpl_toolkits.mplot3d import Axes3D # noqa - from matplotlib.collections import PolyCollection # noqa - - #import ot.lp.cvx as cvx - - - - - - - -Gaussian Data -------------- - - - -.. code-block:: python - - - #%% parameters - - problems = [] - - n = 100 # nb bins - - # bin positions - x = np.arange(n, dtype=np.float64) - - # Gaussian distributions - # Gaussian distributions - a1 = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std - a2 = ot.datasets.make_1D_gauss(n, m=60, s=8) - - # creating matrix A containing all distributions - A = np.vstack((a1, a2)).T - n_distributions = A.shape[1] - - # loss matrix + normalization - M = ot.utils.dist0(n) - M /= M.max() - - - #%% plot the distributions - - pl.figure(1, figsize=(6.4, 3)) - for i in range(n_distributions): - pl.plot(x, A[:, i]) - pl.title('Distributions') - pl.tight_layout() - - #%% barycenter computation - - alpha = 0.5 # 0<=alpha<=1 - weights = np.array([1 - alpha, alpha]) - - # l2bary - bary_l2 = A.dot(weights) - - # wasserstein - reg = 1e-3 - ot.tic() - bary_wass = ot.bregman.barycenter(A, M, reg, weights) - ot.toc() - - - ot.tic() - bary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True) - ot.toc() - - pl.figure(2) - pl.clf() - pl.subplot(2, 1, 1) - for i in range(n_distributions): - pl.plot(x, A[:, i]) - pl.title('Distributions') - - pl.subplot(2, 1, 2) - pl.plot(x, bary_l2, 'r', label='l2') - pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') - pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') - pl.legend() - pl.title('Barycenters') - pl.tight_layout() - - problems.append([A, [bary_l2, bary_wass, bary_wass2]]) - - - - -.. rst-class:: sphx-glr-horizontal - - - * - - .. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_001.png - :scale: 47 - - * - - .. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_002.png - :scale: 47 - - -.. rst-class:: sphx-glr-script-out - - Out:: - - Elapsed time : 0.010712385177612305 s - Primal Feasibility Dual Feasibility Duality Gap Step Path Parameter Objective - 1.0 1.0 1.0 - 1.0 1700.336700337 - 0.006776453137632 0.006776453137633 0.006776453137633 0.9932238647293 0.006776453137633 125.6700527543 - 0.004018712867874 0.004018712867874 0.004018712867874 0.4301142633 0.004018712867874 12.26594150093 - 0.001172775061627 0.001172775061627 0.001172775061627 0.7599932455029 0.001172775061627 0.3378536968897 - 0.0004375137005385 0.0004375137005385 0.0004375137005385 0.6422331807989 0.0004375137005385 0.1468420566358 - 0.000232669046734 0.0002326690467341 0.000232669046734 0.5016999460893 0.000232669046734 0.09381703231432 - 7.430121674303e-05 7.430121674303e-05 7.430121674303e-05 0.7035962305812 7.430121674303e-05 0.0577787025717 - 5.321227838876e-05 5.321227838875e-05 5.321227838876e-05 0.308784186441 5.321227838876e-05 0.05266249477203 - 1.990900379199e-05 1.990900379196e-05 1.990900379199e-05 0.6520472013244 1.990900379199e-05 0.04526054405519 - 6.305442046799e-06 6.30544204682e-06 6.3054420468e-06 0.7073953304075 6.305442046798e-06 0.04237597591383 - 2.290148391577e-06 2.290148391582e-06 2.290148391578e-06 0.6941812711492 2.29014839159e-06 0.041522849321 - 1.182864875387e-06 1.182864875406e-06 1.182864875427e-06 0.508455204675 1.182864875445e-06 0.04129461872827 - 3.626786381529e-07 3.626786382468e-07 3.626786382923e-07 0.7101651572101 3.62678638267e-07 0.04113032448923 - 1.539754244902e-07 1.539754249276e-07 1.539754249356e-07 0.6279322066282 1.539754253892e-07 0.04108867636379 - 5.193221323143e-08 5.193221463044e-08 5.193221462729e-08 0.6843453436759 5.193221708199e-08 0.04106859618414 - 1.888205054507e-08 1.888204779723e-08 1.88820477688e-08 0.6673444085651 1.888205650952e-08 0.041062141752 - 5.676855206925e-09 5.676854518888e-09 5.676854517651e-09 0.7281705804232 5.676885442702e-09 0.04105958648713 - 3.501157668218e-09 3.501150243546e-09 3.501150216347e-09 0.414020345194 3.501164437194e-09 0.04105916265261 - 1.110594251499e-09 1.110590786827e-09 1.11059083379e-09 0.6998954759911 1.110636623476e-09 0.04105870073485 - 5.770971626386e-10 5.772456113791e-10 5.772456200156e-10 0.4999769658132 5.77013379477e-10 0.04105859769135 - 1.535218204536e-10 1.536993317032e-10 1.536992771966e-10 0.7516471627141 1.536205005991e-10 0.04105851679958 - 6.724209350756e-11 6.739211232927e-11 6.739210470901e-11 0.5944802416166 6.735465384341e-11 0.04105850033766 - 1.743382199199e-11 1.736445896691e-11 1.736448490761e-11 0.7573407808104 1.734254328931e-11 0.04105849088824 - Optimization terminated successfully. - Elapsed time : 2.883899211883545 s - - -Dirac Data ----------- - - - -.. code-block:: python - - - #%% parameters - - a1 = 1.0 * (x > 10) * (x < 50) - a2 = 1.0 * (x > 60) * (x < 80) - - a1 /= a1.sum() - a2 /= a2.sum() - - # creating matrix A containing all distributions - A = np.vstack((a1, a2)).T - n_distributions = A.shape[1] - - # loss matrix + normalization - M = ot.utils.dist0(n) - M /= M.max() - - - #%% plot the distributions - - pl.figure(1, figsize=(6.4, 3)) - for i in range(n_distributions): - pl.plot(x, A[:, i]) - pl.title('Distributions') - pl.tight_layout() - - - #%% barycenter computation - - alpha = 0.5 # 0<=alpha<=1 - weights = np.array([1 - alpha, alpha]) - - # l2bary - bary_l2 = A.dot(weights) - - # wasserstein - reg = 1e-3 - ot.tic() - bary_wass = ot.bregman.barycenter(A, M, reg, weights) - ot.toc() - - - ot.tic() - bary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True) - ot.toc() - - - problems.append([A, [bary_l2, bary_wass, bary_wass2]]) - - pl.figure(2) - pl.clf() - pl.subplot(2, 1, 1) - for i in range(n_distributions): - pl.plot(x, A[:, i]) - pl.title('Distributions') - - pl.subplot(2, 1, 2) - pl.plot(x, bary_l2, 'r', label='l2') - pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') - pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') - pl.legend() - pl.title('Barycenters') - pl.tight_layout() - - #%% parameters - - a1 = np.zeros(n) - a2 = np.zeros(n) - - a1[10] = .25 - a1[20] = .5 - a1[30] = .25 - a2[80] = 1 - - - a1 /= a1.sum() - a2 /= a2.sum() - - # creating matrix A containing all distributions - A = np.vstack((a1, a2)).T - n_distributions = A.shape[1] - - # loss matrix + normalization - M = ot.utils.dist0(n) - M /= M.max() - - - #%% plot the distributions - - pl.figure(1, figsize=(6.4, 3)) - for i in range(n_distributions): - pl.plot(x, A[:, i]) - pl.title('Distributions') - pl.tight_layout() - - - #%% barycenter computation - - alpha = 0.5 # 0<=alpha<=1 - weights = np.array([1 - alpha, alpha]) - - # l2bary - bary_l2 = A.dot(weights) - - # wasserstein - reg = 1e-3 - ot.tic() - bary_wass = ot.bregman.barycenter(A, M, reg, weights) - ot.toc() - - - ot.tic() - bary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True) - ot.toc() - - - problems.append([A, [bary_l2, bary_wass, bary_wass2]]) - - pl.figure(2) - pl.clf() - pl.subplot(2, 1, 1) - for i in range(n_distributions): - pl.plot(x, A[:, i]) - pl.title('Distributions') - - pl.subplot(2, 1, 2) - pl.plot(x, bary_l2, 'r', label='l2') - pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') - pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') - pl.legend() - pl.title('Barycenters') - pl.tight_layout() - - - - - -.. rst-class:: sphx-glr-horizontal - - - * - - .. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_003.png - :scale: 47 - - * - - .. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_004.png - :scale: 47 - - -.. rst-class:: sphx-glr-script-out - - Out:: - - Elapsed time : 0.014938592910766602 s - Primal Feasibility Dual Feasibility Duality Gap Step Path Parameter Objective - 1.0 1.0 1.0 - 1.0 1700.336700337 - 0.006776466288966 0.006776466288966 0.006776466288966 0.9932238515788 0.006776466288966 125.6649255808 - 0.004036918865495 0.004036918865495 0.004036918865495 0.4272973099316 0.004036918865495 12.3471617011 - 0.00121923268707 0.00121923268707 0.00121923268707 0.749698685599 0.00121923268707 0.3243835647408 - 0.0003837422984432 0.0003837422984432 0.0003837422984432 0.6926882608284 0.0003837422984432 0.1361719397493 - 0.0001070128410183 0.0001070128410183 0.0001070128410183 0.7643889137854 0.0001070128410183 0.07581952832518 - 0.0001001275033711 0.0001001275033711 0.0001001275033711 0.07058704837812 0.0001001275033712 0.0734739493635 - 4.550897507844e-05 4.550897507841e-05 4.550897507844e-05 0.5761172484828 4.550897507845e-05 0.05555077655047 - 8.557124125522e-06 8.5571241255e-06 8.557124125522e-06 0.8535925441152 8.557124125522e-06 0.04439814660221 - 3.611995628407e-06 3.61199562841e-06 3.611995628414e-06 0.6002277331554 3.611995628415e-06 0.04283007762152 - 7.590393750365e-07 7.590393750491e-07 7.590393750378e-07 0.8221486533416 7.590393750381e-07 0.04192322976248 - 8.299929287441e-08 8.299929286079e-08 8.299929287532e-08 0.9017467938799 8.29992928758e-08 0.04170825633295 - 3.117560203449e-10 3.117560130137e-10 3.11756019954e-10 0.997039969226 3.11756019952e-10 0.04168179329766 - 1.559749653711e-14 1.558073160926e-14 1.559756940692e-14 0.9999499686183 1.559750643989e-14 0.04168169240444 - Optimization terminated successfully. - Elapsed time : 2.642659902572632 s - Elapsed time : 0.002908945083618164 s - Primal Feasibility Dual Feasibility Duality Gap Step Path Parameter Objective - 1.0 1.0 1.0 - 1.0 1700.336700337 - 0.006774675520727 0.006774675520727 0.006774675520727 0.9932256422636 0.006774675520727 125.6956034743 - 0.002048208707562 0.002048208707562 0.002048208707562 0.7343095368143 0.002048208707562 5.213991622123 - 0.000269736547478 0.0002697365474781 0.0002697365474781 0.8839403501193 0.000269736547478 0.505938390389 - 6.832109993943e-05 6.832109993944e-05 6.832109993944e-05 0.7601171075965 6.832109993943e-05 0.2339657807272 - 2.437682932219e-05 2.43768293222e-05 2.437682932219e-05 0.6663448297475 2.437682932219e-05 0.1471256246325 - 1.13498321631e-05 1.134983216308e-05 1.13498321631e-05 0.5553643816404 1.13498321631e-05 0.1181584941171 - 3.342312725885e-06 3.342312725884e-06 3.342312725885e-06 0.7238133571615 3.342312725885e-06 0.1006387519747 - 7.078561231603e-07 7.078561231509e-07 7.078561231604e-07 0.8033142552512 7.078561231603e-07 0.09474734646269 - 1.966870956916e-07 1.966870954537e-07 1.966870954468e-07 0.752547917788 1.966870954633e-07 0.09354342735766 - 4.19989524849e-10 4.199895164852e-10 4.199895238758e-10 0.9984019849375 4.19989523951e-10 0.09310367785861 - 2.101015938666e-14 2.100625691113e-14 2.101023853438e-14 0.999949974425 2.101023691864e-14 0.09310274466458 - Optimization terminated successfully. - Elapsed time : 2.690450668334961 s - - -Final figure ------------- - - - - -.. code-block:: python - - - #%% plot - - nbm = len(problems) - nbm2 = (nbm // 2) - - - pl.figure(2, (20, 6)) - pl.clf() - - for i in range(nbm): - - A = problems[i][0] - bary_l2 = problems[i][1][0] - bary_wass = problems[i][1][1] - bary_wass2 = problems[i][1][2] - - pl.subplot(2, nbm, 1 + i) - for j in range(n_distributions): - pl.plot(x, A[:, j]) - if i == nbm2: - pl.title('Distributions') - pl.xticks(()) - pl.yticks(()) - - pl.subplot(2, nbm, 1 + i + nbm) - - pl.plot(x, bary_l2, 'r', label='L2 (Euclidean)') - pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') - pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') - if i == nbm - 1: - pl.legend() - if i == nbm2: - pl.title('Barycenters') - - pl.xticks(()) - pl.yticks(()) - - - -.. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_006.png - :align: center - - - - -**Total running time of the script:** ( 0 minutes 8.892 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_barycenter_lp_vs_entropic.py <plot_barycenter_lp_vs_entropic.py>` - - - - .. container:: sphx-glr-download - - :download:`Download Jupyter notebook: plot_barycenter_lp_vs_entropic.ipynb <plot_barycenter_lp_vs_entropic.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_compute_emd.ipynb b/docs/source/auto_examples/plot_compute_emd.ipynb deleted file mode 100644 index 562eff8..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": [ - "#%% parameters\n\nn = 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": [ - "#%% plot the distributions\n\npl.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": [ - "#%% Compute and plot distributions and loss matrix\n\nd_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": [ - "#%%\nreg = 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": "3.6.5" - } - }, - "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 27bca2c..0000000 --- a/docs/source/auto_examples/plot_compute_emd.rst +++ /dev/null @@ -1,189 +0,0 @@ - - -.. _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:: python - - - # 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:: python - - - #%% 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 ---------- - - - -.. code-block:: python - - - #%% 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() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_compute_emd_001.png - :align: center - - - - -Compute EMD for the different losses ------------------------------------- - - - -.. code-block:: python - - - #%% 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() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_compute_emd_003.png - :align: center - - - - -Compute Sinkhorn for the different losses ------------------------------------------ - - - -.. code-block:: python - - - #%% - 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_004.png - :align: center - - - - -**Total running time of the script:** ( 0 minutes 0.446 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_compute_emd.py <plot_compute_emd.py>` - - - - .. container:: sphx-glr-download - - :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.readthedocs.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 4981ba3..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": "3.6.5" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_convolutional_barycenter.py b/docs/source/auto_examples/plot_convolutional_barycenter.py 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 a28db2f..0000000 --- a/docs/source/auto_examples/plot_convolutional_barycenter.rst +++ /dev/null @@ -1,151 +0,0 @@ - - -.. _sphx_glr_auto_examples_plot_convolutional_barycenter.py: - - -============================================ -Convolutional Wasserstein Barycenter example -============================================ - -This example is designed to illustrate how the Convolutional Wasserstein Barycenter -function of POT works. - - - -.. code-block:: python - - - # Author: Nicolas Courty <ncourty@irisa.fr> - # - # License: MIT License - - - import numpy as np - import pylab as pl - import ot - - - - - - - -Data preparation ----------------- - -The four distributions are constructed from 4 simple images - - - -.. code-block:: python - - - - f1 = 1 - pl.imread('../data/redcross.png')[:, :, 2] - f2 = 1 - pl.imread('../data/duck.png')[:, :, 2] - f3 = 1 - pl.imread('../data/heart.png')[:, :, 2] - f4 = 1 - pl.imread('../data/tooth.png')[:, :, 2] - - A = [] - f1 = f1 / np.sum(f1) - f2 = f2 / np.sum(f2) - f3 = f3 / np.sum(f3) - f4 = f4 / np.sum(f4) - A.append(f1) - A.append(f2) - A.append(f3) - A.append(f4) - A = np.array(A) - - nb_images = 5 - - # those are the four corners coordinates that will be interpolated by bilinear - # interpolation - v1 = np.array((1, 0, 0, 0)) - v2 = np.array((0, 1, 0, 0)) - v3 = np.array((0, 0, 1, 0)) - v4 = np.array((0, 0, 0, 1)) - - - - - - - - -Barycenter computation and visualization ----------------------------------------- - - - - -.. code-block:: python - - - pl.figure(figsize=(10, 10)) - pl.title('Convolutional Wasserstein Barycenters in POT') - cm = 'Blues' - # regularization parameter - reg = 0.004 - for i in range(nb_images): - for j in range(nb_images): - pl.subplot(nb_images, nb_images, i * nb_images + j + 1) - tx = float(i) / (nb_images - 1) - ty = float(j) / (nb_images - 1) - - # weights are constructed by bilinear interpolation - tmp1 = (1 - tx) * v1 + tx * v2 - tmp2 = (1 - tx) * v3 + tx * v4 - weights = (1 - ty) * tmp1 + ty * tmp2 - - if i == 0 and j == 0: - pl.imshow(f1, cmap=cm) - pl.axis('off') - elif i == 0 and j == (nb_images - 1): - pl.imshow(f3, cmap=cm) - pl.axis('off') - elif i == (nb_images - 1) and j == 0: - pl.imshow(f2, cmap=cm) - pl.axis('off') - elif i == (nb_images - 1) and j == (nb_images - 1): - pl.imshow(f4, cmap=cm) - pl.axis('off') - else: - # call to barycenter computation - pl.imshow(ot.bregman.convolutional_barycenter2d(A, reg, weights), cmap=cm) - pl.axis('off') - pl.show() - - - -.. image:: /auto_examples/images/sphx_glr_plot_convolutional_barycenter_001.png - :align: center - - - - -**Total running time of the script:** ( 1 minutes 11.608 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_convolutional_barycenter.py <plot_convolutional_barycenter.py>` - - - - .. container:: sphx-glr-download - - :download:`Download Jupyter notebook: plot_convolutional_barycenter.ipynb <plot_convolutional_barycenter.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_fgw.ipynb b/docs/source/auto_examples/plot_fgw.ipynb deleted file mode 100644 index 1b150bd..0000000 --- a/docs/source/auto_examples/plot_fgw.ipynb +++ /dev/null @@ -1,162 +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": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "#%% parameters\n# We create two 1D random measures\nn = 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": [ - "#%% plot the distributions\n\npl.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": [ - "#%% Structure matrices and across-features distance matrix\nC1 = 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": [ - "#%%\ncmap = '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": [ - "#%% Computing FGW and GW\nalpha = 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": [ - "#%% visu OT matrix\ncmap = '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": "3.6.8" - } - }, - "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 aec725d..0000000 --- a/docs/source/auto_examples/plot_fgw.rst +++ /dev/null @@ -1,297 +0,0 @@ - - -.. _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:: python - - - # 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 ---------- - - - -.. code-block:: python - - - #%% 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 ---------- - - - -.. code-block:: python - - - #%% 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() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_fgw_010.png - :align: center - - - - -Create structure matrices and across-feature distance matrix ---------- - - - -.. code-block:: python - - - #%% 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 ---------- - - - -.. code-block:: python - - - #%% - 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_011.png - :align: center - - - - -Compute FGW/GW ---------- - - - -.. code-block:: python - - - #%% 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) - - - - - -.. rst-class:: sphx-glr-script-out - - Out:: - - It. |Loss |Relative loss|Absolute loss - ------------------------------------------------ - 0|4.734462e+01|0.000000e+00|0.000000e+00 - 1|2.508258e+01|8.875498e-01|2.226204e+01 - 2|2.189329e+01|1.456747e-01|3.189297e+00 - 3|2.189329e+01|0.000000e+00|0.000000e+00 - Elapsed time : 0.0016989707946777344 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:: python - - - #%% 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() - - - -.. image:: /auto_examples/images/sphx_glr_plot_fgw_004.png - :align: center - - - - -**Total running time of the script:** ( 0 minutes 1.468 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_fgw.py <plot_fgw.py>` - - - - .. container:: sphx-glr-download - - :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.readthedocs.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 05a81c8..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 * 1000, label='input measure')\npl.scatter(X[:, 0], X[:, 1], s=b * 1000, c='black', marker='^', label='2-Wasserstein barycenter')\npl.title('Data measures and their barycenter')\npl.legend(loc=0)\npl.show()" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.5" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_free_support_barycenter.py b/docs/source/auto_examples/plot_free_support_barycenter.py deleted file mode 100644 index b6efc59..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 * 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 d1b3b80..0000000 --- a/docs/source/auto_examples/plot_free_support_barycenter.rst +++ /dev/null @@ -1,140 +0,0 @@ - - -.. _sphx_glr_auto_examples_plot_free_support_barycenter.py: - - -==================================================== -2D free support Wasserstein barycenters of distributions -==================================================== - -Illustration of 2D Wasserstein barycenters if discributions that are weighted -sum of diracs. - - - - -.. code-block:: python - - - # Author: Vivien Seguy <vivien.seguy@iip.ist.i.kyoto-u.ac.jp> - # - # License: MIT License - - import numpy as np - import matplotlib.pylab as pl - import ot - - - - - - - - -Generate data - ------------- -%% parameters and data generation - - - -.. code-block:: python - - N = 3 - d = 2 - measures_locations = [] - measures_weights = [] - - for i in range(N): - - n_i = np.random.randint(low=1, high=20) # nb samples - - mu_i = np.random.normal(0., 4., (d,)) # Gaussian mean - - A_i = np.random.rand(d, d) - cov_i = np.dot(A_i, A_i.transpose()) # Gaussian covariance matrix - - x_i = ot.datasets.make_2D_samples_gauss(n_i, mu_i, cov_i) # Dirac locations - b_i = np.random.uniform(0., 1., (n_i,)) - b_i = b_i / np.sum(b_i) # Dirac weights - - measures_locations.append(x_i) - measures_weights.append(b_i) - - - - - - - - -Compute free support barycenter -------------- - - - -.. code-block:: python - - - k = 10 # number of Diracs of the barycenter - X_init = np.random.normal(0., 1., (k, d)) # initial Dirac locations - b = np.ones((k,)) / k # weights of the barycenter (it will not be optimized, only the locations are optimized) - - X = ot.lp.free_support_barycenter(measures_locations, measures_weights, X_init, b) - - - - - - - - -Plot data ---------- - - - -.. code-block:: python - - - pl.figure(1) - for (x_i, b_i) in zip(measures_locations, measures_weights): - color = np.random.randint(low=1, high=10 * N) - pl.scatter(x_i[:, 0], x_i[:, 1], s=b * 1000, label='input measure') - pl.scatter(X[:, 0], X[:, 1], s=b * 1000, c='black', marker='^', label='2-Wasserstein barycenter') - pl.title('Data measures and their barycenter') - pl.legend(loc=0) - pl.show() - - - -.. image:: /auto_examples/images/sphx_glr_plot_free_support_barycenter_001.png - :align: center - - - - -**Total running time of the script:** ( 0 minutes 0.129 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_free_support_barycenter.py <plot_free_support_barycenter.py>` - - - - .. container:: sphx-glr-download - - :download:`Download Jupyter notebook: plot_free_support_barycenter.ipynb <plot_free_support_barycenter.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_gromov.ipynb b/docs/source/auto_examples/plot_gromov.ipynb deleted file mode 100644 index dc1f179..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": "3.6.5" - } - }, - "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 3ed4e11..0000000 --- a/docs/source/auto_examples/plot_gromov.rst +++ /dev/null @@ -1,214 +0,0 @@ - - -.. _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:: python - - - # 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:: python - - - - 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:: python - - - - 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 - :align: center - - - - -Compute distance kernels, normalize them and then display ---------------------------------------------------------- - - - -.. code-block:: python - - - - 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 - :align: center - - - - -Compute Gromov-Wasserstein plans and distance ---------------------------------------------- - - - -.. code-block:: python - - - 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 - :align: center - - -.. rst-class:: sphx-glr-script-out - - Out:: - - It. |Loss |Delta loss - -------------------------------- - 0|4.328711e-02|0.000000e+00 - 1|2.281369e-02|-8.974178e-01 - 2|1.843659e-02|-2.374139e-01 - 3|1.602820e-02|-1.502598e-01 - 4|1.353712e-02|-1.840179e-01 - 5|1.285687e-02|-5.290977e-02 - 6|1.284537e-02|-8.952931e-04 - 7|1.284525e-02|-8.989584e-06 - 8|1.284525e-02|-8.989950e-08 - 9|1.284525e-02|-8.989949e-10 - It. |Err - ------------------- - 0|7.263293e-02| - 10|1.737784e-02| - 20|7.783978e-03| - 30|3.399419e-07| - 40|3.751207e-11| - Gromov-Wasserstein distances: 0.012845252089244688 - Entropic Gromov-Wasserstein distances: 0.013543882352191079 - - -**Total running time of the script:** ( 0 minutes 1.916 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_gromov.py <plot_gromov.py>` - - - - .. container:: sphx-glr-download - - :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.readthedocs.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 4c2f28f..0000000 --- a/docs/source/auto_examples/plot_gromov_barycenter.ipynb +++ /dev/null @@ -1,126 +0,0 @@ -{ - "cells": [ - { - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ], - "cell_type": "code" - }, - { - "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": "markdown" - }, - { - "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 scipy.ndimage as spi\nimport matplotlib.pylab as pl\nfrom sklearn import manifold\nfrom sklearn.decomposition import PCA\n\nimport ot" - ], - "cell_type": "code" - }, - { - "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": "markdown" - }, - { - "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": "code" - }, - { - "metadata": {}, - "source": [ - "Data preparation\n----------------\n\nThe four distributions are constructed from 4 simple images\n\n" - ], - "cell_type": "markdown" - }, - { - "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 = spi.imread('../data/square.png').astype(np.float64)[:, :, 2] / 256\ncross = spi.imread('../data/cross.png').astype(np.float64)[:, :, 2] / 256\ntriangle = spi.imread('../data/triangle.png').astype(np.float64)[:, :, 2] / 256\nstar = spi.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": "code" - }, - { - "metadata": {}, - "source": [ - "Barycenter computation\n----------------------\n\n" - ], - "cell_type": "markdown" - }, - { - "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": "code" - }, - { - "metadata": {}, - "source": [ - "Visualization\n-------------\n\nThe PCA helps in getting consistency between the rotations\n\n" - ], - "cell_type": "markdown" - }, - { - "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')" - ], - "cell_type": "code" - } - ], - "metadata": { - "language_info": { - "name": "python", - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "nbconvert_exporter": "python", - "version": "3.5.2", - "pygments_lexer": "ipython3", - "file_extension": ".py", - "mimetype": "text/x-python" - }, - "kernelspec": { - "display_name": "Python 3", - "name": "python3", - "language": "python" - } - }, - "nbformat_minor": 0, - "nbformat": 4 -}
\ 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 58fc51a..0000000 --- a/docs/source/auto_examples/plot_gromov_barycenter.py +++ /dev/null @@ -1,248 +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 scipy.ndimage as spi
-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 = spi.imread('../data/square.png').astype(np.float64)[:, :, 2] / 256
-cross = spi.imread('../data/cross.png').astype(np.float64)[:, :, 2] / 256
-triangle = spi.imread('../data/triangle.png').astype(np.float64)[:, :, 2] / 256
-star = spi.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 531ee22..0000000 --- a/docs/source/auto_examples/plot_gromov_barycenter.rst +++ /dev/null @@ -1,329 +0,0 @@ - - -.. _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:: python - - - # Author: Erwan Vautier <erwan.vautier@gmail.com> - # Nicolas Courty <ncourty@irisa.fr> - # - # License: MIT License - - - import numpy as np - import scipy as sp - - import scipy.ndimage as spi - 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:: python - - - - 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:: python - - - - def im2mat(I): - """Converts and image to matrix (one pixel per line)""" - return I.reshape((I.shape[0] * I.shape[1], I.shape[2])) - - - square = spi.imread('../data/square.png').astype(np.float64)[:, :, 2] / 256 - cross = spi.imread('../data/cross.png').astype(np.float64)[:, :, 2] / 256 - triangle = spi.imread('../data/triangle.png').astype(np.float64)[:, :, 2] / 256 - star = spi.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:: python - - - - 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:: python - - - - 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 - :align: center - - - - -**Total running time of the script:** ( 0 minutes 5.906 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_gromov_barycenter.py <plot_gromov_barycenter.py>` - - - - .. container:: sphx-glr-download - - :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.readthedocs.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 107c299..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": [ - "#%% parameters\n\nn = 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": [ - "#%% EMD\n\nG0 = ot.emd(a, b, M)\n\npl.figure(3, figsize=(5, 5))\not.plot.plot1D_mat(a, b, G0, 'OT matrix G0')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solve EMD with Frobenius norm regularization\n--------------------------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "#%% Example with Frobenius norm regularization\n\n\ndef 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": [ - "#%% Example with entropic regularization\n\n\ndef 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": [ - "#%% Example with Frobenius norm + entropic regularization with gcg\n\n\ndef 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": "3.6.5" - } - }, - "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 844cba0..0000000 --- a/docs/source/auto_examples/plot_optim_OTreg.rst +++ /dev/null @@ -1,663 +0,0 @@ - - -.. _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:: python - - - import numpy as np - import matplotlib.pylab as pl - import ot - import ot.plot - - - - - - - -Generate data -------------- - - - -.. code-block:: python - - - #%% 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 ---------- - - - -.. code-block:: python - - - #%% EMD - - G0 = ot.emd(a, b, M) - - pl.figure(3, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, G0, 'OT matrix G0') - - - - -.. image:: /auto_examples/images/sphx_glr_plot_optim_OTreg_003.png - :align: center - - - - -Solve EMD with Frobenius norm regularization --------------------------------------------- - - - -.. code-block:: python - - - #%% 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') - - - - -.. image:: /auto_examples/images/sphx_glr_plot_optim_OTreg_004.png - :align: center - - -.. rst-class:: sphx-glr-script-out - - Out:: - - It. |Loss |Delta loss - -------------------------------- - 0|1.760578e-01|0.000000e+00 - 1|1.669467e-01|-5.457501e-02 - 2|1.665639e-01|-2.298130e-03 - 3|1.664378e-01|-7.572776e-04 - 4|1.664077e-01|-1.811855e-04 - 5|1.663912e-01|-9.936787e-05 - 6|1.663852e-01|-3.555826e-05 - 7|1.663814e-01|-2.305693e-05 - 8|1.663785e-01|-1.760450e-05 - 9|1.663767e-01|-1.078011e-05 - 10|1.663751e-01|-9.525192e-06 - 11|1.663737e-01|-8.396466e-06 - 12|1.663727e-01|-6.086938e-06 - 13|1.663720e-01|-4.042609e-06 - 14|1.663713e-01|-4.160914e-06 - 15|1.663707e-01|-3.823502e-06 - 16|1.663702e-01|-3.022440e-06 - 17|1.663697e-01|-3.181249e-06 - 18|1.663692e-01|-2.698532e-06 - 19|1.663687e-01|-3.258253e-06 - It. |Loss |Delta loss - -------------------------------- - 20|1.663682e-01|-2.741118e-06 - 21|1.663678e-01|-2.624135e-06 - 22|1.663673e-01|-2.645179e-06 - 23|1.663670e-01|-1.957237e-06 - 24|1.663666e-01|-2.261541e-06 - 25|1.663663e-01|-1.851305e-06 - 26|1.663660e-01|-1.942296e-06 - 27|1.663657e-01|-2.092896e-06 - 28|1.663653e-01|-1.924361e-06 - 29|1.663651e-01|-1.625455e-06 - 30|1.663648e-01|-1.641123e-06 - 31|1.663645e-01|-1.566666e-06 - 32|1.663643e-01|-1.338514e-06 - 33|1.663641e-01|-1.222711e-06 - 34|1.663639e-01|-1.221805e-06 - 35|1.663637e-01|-1.440781e-06 - 36|1.663634e-01|-1.520091e-06 - 37|1.663632e-01|-1.288193e-06 - 38|1.663630e-01|-1.123055e-06 - 39|1.663628e-01|-1.024487e-06 - It. |Loss |Delta loss - -------------------------------- - 40|1.663627e-01|-1.079606e-06 - 41|1.663625e-01|-1.172093e-06 - 42|1.663623e-01|-1.047880e-06 - 43|1.663621e-01|-1.010577e-06 - 44|1.663619e-01|-1.064438e-06 - 45|1.663618e-01|-9.882375e-07 - 46|1.663616e-01|-8.532647e-07 - 47|1.663615e-01|-9.930189e-07 - 48|1.663613e-01|-8.728955e-07 - 49|1.663612e-01|-9.524214e-07 - 50|1.663610e-01|-9.088418e-07 - 51|1.663609e-01|-7.639430e-07 - 52|1.663608e-01|-6.662611e-07 - 53|1.663607e-01|-7.133700e-07 - 54|1.663605e-01|-7.648141e-07 - 55|1.663604e-01|-6.557516e-07 - 56|1.663603e-01|-7.304213e-07 - 57|1.663602e-01|-6.353809e-07 - 58|1.663601e-01|-7.968279e-07 - 59|1.663600e-01|-6.367159e-07 - It. |Loss |Delta loss - -------------------------------- - 60|1.663599e-01|-5.610790e-07 - 61|1.663598e-01|-5.787466e-07 - 62|1.663596e-01|-6.937777e-07 - 63|1.663596e-01|-5.599432e-07 - 64|1.663595e-01|-5.813048e-07 - 65|1.663594e-01|-5.724600e-07 - 66|1.663593e-01|-6.081892e-07 - 67|1.663592e-01|-5.948732e-07 - 68|1.663591e-01|-4.941833e-07 - 69|1.663590e-01|-5.213739e-07 - 70|1.663589e-01|-5.127355e-07 - 71|1.663588e-01|-4.349251e-07 - 72|1.663588e-01|-5.007084e-07 - 73|1.663587e-01|-4.880265e-07 - 74|1.663586e-01|-4.931950e-07 - 75|1.663585e-01|-4.981309e-07 - 76|1.663584e-01|-3.952959e-07 - 77|1.663584e-01|-4.544857e-07 - 78|1.663583e-01|-4.237579e-07 - 79|1.663582e-01|-4.382386e-07 - It. |Loss |Delta loss - -------------------------------- - 80|1.663582e-01|-3.646051e-07 - 81|1.663581e-01|-4.197994e-07 - 82|1.663580e-01|-4.072764e-07 - 83|1.663580e-01|-3.994645e-07 - 84|1.663579e-01|-4.842721e-07 - 85|1.663578e-01|-3.276486e-07 - 86|1.663578e-01|-3.737346e-07 - 87|1.663577e-01|-4.282043e-07 - 88|1.663576e-01|-4.020937e-07 - 89|1.663576e-01|-3.431951e-07 - 90|1.663575e-01|-3.052335e-07 - 91|1.663575e-01|-3.500538e-07 - 92|1.663574e-01|-3.063176e-07 - 93|1.663573e-01|-3.576367e-07 - 94|1.663573e-01|-3.224681e-07 - 95|1.663572e-01|-3.673221e-07 - 96|1.663572e-01|-3.635561e-07 - 97|1.663571e-01|-3.527236e-07 - 98|1.663571e-01|-2.788548e-07 - 99|1.663570e-01|-2.727141e-07 - It. |Loss |Delta loss - -------------------------------- - 100|1.663570e-01|-3.127278e-07 - 101|1.663569e-01|-2.637504e-07 - 102|1.663569e-01|-2.922750e-07 - 103|1.663568e-01|-3.076454e-07 - 104|1.663568e-01|-2.911509e-07 - 105|1.663567e-01|-2.403398e-07 - 106|1.663567e-01|-2.439790e-07 - 107|1.663567e-01|-2.634542e-07 - 108|1.663566e-01|-2.452203e-07 - 109|1.663566e-01|-2.852991e-07 - 110|1.663565e-01|-2.165490e-07 - 111|1.663565e-01|-2.450250e-07 - 112|1.663564e-01|-2.685294e-07 - 113|1.663564e-01|-2.821800e-07 - 114|1.663564e-01|-2.237390e-07 - 115|1.663563e-01|-1.992842e-07 - 116|1.663563e-01|-2.166739e-07 - 117|1.663563e-01|-2.086064e-07 - 118|1.663562e-01|-2.435945e-07 - 119|1.663562e-01|-2.292497e-07 - It. |Loss |Delta loss - -------------------------------- - 120|1.663561e-01|-2.366209e-07 - 121|1.663561e-01|-2.138746e-07 - 122|1.663561e-01|-2.009637e-07 - 123|1.663560e-01|-2.386258e-07 - 124|1.663560e-01|-1.927442e-07 - 125|1.663560e-01|-2.081681e-07 - 126|1.663559e-01|-1.759123e-07 - 127|1.663559e-01|-1.890771e-07 - 128|1.663559e-01|-1.971315e-07 - 129|1.663558e-01|-2.101983e-07 - 130|1.663558e-01|-2.035645e-07 - 131|1.663558e-01|-1.984492e-07 - 132|1.663557e-01|-1.849064e-07 - 133|1.663557e-01|-1.795703e-07 - 134|1.663557e-01|-1.624087e-07 - 135|1.663557e-01|-1.689557e-07 - 136|1.663556e-01|-1.644308e-07 - 137|1.663556e-01|-1.618007e-07 - 138|1.663556e-01|-1.483013e-07 - 139|1.663555e-01|-1.708771e-07 - It. |Loss |Delta loss - -------------------------------- - 140|1.663555e-01|-2.013847e-07 - 141|1.663555e-01|-1.721217e-07 - 142|1.663554e-01|-2.027911e-07 - 143|1.663554e-01|-1.764565e-07 - 144|1.663554e-01|-1.677151e-07 - 145|1.663554e-01|-1.351982e-07 - 146|1.663553e-01|-1.423360e-07 - 147|1.663553e-01|-1.541112e-07 - 148|1.663553e-01|-1.491601e-07 - 149|1.663553e-01|-1.466407e-07 - 150|1.663552e-01|-1.801524e-07 - 151|1.663552e-01|-1.714107e-07 - 152|1.663552e-01|-1.491257e-07 - 153|1.663552e-01|-1.513799e-07 - 154|1.663551e-01|-1.354539e-07 - 155|1.663551e-01|-1.233818e-07 - 156|1.663551e-01|-1.576219e-07 - 157|1.663551e-01|-1.452791e-07 - 158|1.663550e-01|-1.262867e-07 - 159|1.663550e-01|-1.316379e-07 - It. |Loss |Delta loss - -------------------------------- - 160|1.663550e-01|-1.295447e-07 - 161|1.663550e-01|-1.283286e-07 - 162|1.663550e-01|-1.569222e-07 - 163|1.663549e-01|-1.172942e-07 - 164|1.663549e-01|-1.399809e-07 - 165|1.663549e-01|-1.229432e-07 - 166|1.663549e-01|-1.326191e-07 - 167|1.663548e-01|-1.209694e-07 - 168|1.663548e-01|-1.372136e-07 - 169|1.663548e-01|-1.338395e-07 - 170|1.663548e-01|-1.416497e-07 - 171|1.663548e-01|-1.298576e-07 - 172|1.663547e-01|-1.190590e-07 - 173|1.663547e-01|-1.167083e-07 - 174|1.663547e-01|-1.069425e-07 - 175|1.663547e-01|-1.217780e-07 - 176|1.663547e-01|-1.140754e-07 - 177|1.663546e-01|-1.160707e-07 - 178|1.663546e-01|-1.101798e-07 - 179|1.663546e-01|-1.114904e-07 - It. |Loss |Delta loss - -------------------------------- - 180|1.663546e-01|-1.064022e-07 - 181|1.663546e-01|-9.258231e-08 - 182|1.663546e-01|-1.213120e-07 - 183|1.663545e-01|-1.164296e-07 - 184|1.663545e-01|-1.188762e-07 - 185|1.663545e-01|-9.394153e-08 - 186|1.663545e-01|-1.028656e-07 - 187|1.663545e-01|-1.115348e-07 - 188|1.663544e-01|-9.768310e-08 - 189|1.663544e-01|-1.021806e-07 - 190|1.663544e-01|-1.086303e-07 - 191|1.663544e-01|-9.879008e-08 - 192|1.663544e-01|-1.050210e-07 - 193|1.663544e-01|-1.002463e-07 - 194|1.663543e-01|-1.062747e-07 - 195|1.663543e-01|-9.348538e-08 - 196|1.663543e-01|-7.992512e-08 - 197|1.663543e-01|-9.558020e-08 - 198|1.663543e-01|-9.993772e-08 - 199|1.663543e-01|-8.588499e-08 - It. |Loss |Delta loss - -------------------------------- - 200|1.663543e-01|-8.737134e-08 - - -Solve EMD with entropic regularization --------------------------------------- - - - -.. code-block:: python - - - #%% 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') - - - - -.. image:: /auto_examples/images/sphx_glr_plot_optim_OTreg_006.png - :align: center - - -.. rst-class:: sphx-glr-script-out - - Out:: - - It. |Loss |Delta loss - -------------------------------- - 0|1.692289e-01|0.000000e+00 - 1|1.617643e-01|-4.614437e-02 - 2|1.612639e-01|-3.102965e-03 - 3|1.611291e-01|-8.371098e-04 - 4|1.610468e-01|-5.110558e-04 - 5|1.610198e-01|-1.672927e-04 - 6|1.610130e-01|-4.232417e-05 - 7|1.610090e-01|-2.513455e-05 - 8|1.610002e-01|-5.443507e-05 - 9|1.609996e-01|-3.657071e-06 - 10|1.609948e-01|-2.998735e-05 - 11|1.609695e-01|-1.569217e-04 - 12|1.609533e-01|-1.010779e-04 - 13|1.609520e-01|-8.043897e-06 - 14|1.609465e-01|-3.415246e-05 - 15|1.609386e-01|-4.898605e-05 - 16|1.609324e-01|-3.837052e-05 - 17|1.609298e-01|-1.617826e-05 - 18|1.609184e-01|-7.080015e-05 - 19|1.609083e-01|-6.273206e-05 - It. |Loss |Delta loss - -------------------------------- - 20|1.608988e-01|-5.940805e-05 - 21|1.608853e-01|-8.380030e-05 - 22|1.608844e-01|-5.185045e-06 - 23|1.608824e-01|-1.279113e-05 - 24|1.608819e-01|-3.156821e-06 - 25|1.608783e-01|-2.205746e-05 - 26|1.608764e-01|-1.189894e-05 - 27|1.608755e-01|-5.474607e-06 - 28|1.608737e-01|-1.144227e-05 - 29|1.608676e-01|-3.775335e-05 - 30|1.608638e-01|-2.348020e-05 - 31|1.608627e-01|-6.863136e-06 - 32|1.608529e-01|-6.110230e-05 - 33|1.608487e-01|-2.641106e-05 - 34|1.608409e-01|-4.823638e-05 - 35|1.608373e-01|-2.256641e-05 - 36|1.608338e-01|-2.132444e-05 - 37|1.608310e-01|-1.786649e-05 - 38|1.608260e-01|-3.103848e-05 - 39|1.608206e-01|-3.321265e-05 - It. |Loss |Delta loss - -------------------------------- - 40|1.608201e-01|-3.054747e-06 - 41|1.608195e-01|-4.198335e-06 - 42|1.608193e-01|-8.458736e-07 - 43|1.608159e-01|-2.153759e-05 - 44|1.608115e-01|-2.738314e-05 - 45|1.608108e-01|-3.960032e-06 - 46|1.608081e-01|-1.675447e-05 - 47|1.608072e-01|-5.976340e-06 - 48|1.608046e-01|-1.604130e-05 - 49|1.608020e-01|-1.617036e-05 - 50|1.608014e-01|-3.957795e-06 - 51|1.608011e-01|-1.292411e-06 - 52|1.607998e-01|-8.431795e-06 - 53|1.607964e-01|-2.127054e-05 - 54|1.607947e-01|-1.021878e-05 - 55|1.607947e-01|-3.560621e-07 - 56|1.607900e-01|-2.929781e-05 - 57|1.607890e-01|-5.740229e-06 - 58|1.607858e-01|-2.039550e-05 - 59|1.607836e-01|-1.319545e-05 - It. |Loss |Delta loss - -------------------------------- - 60|1.607826e-01|-6.378947e-06 - 61|1.607808e-01|-1.145102e-05 - 62|1.607776e-01|-1.941743e-05 - 63|1.607743e-01|-2.087422e-05 - 64|1.607741e-01|-1.310249e-06 - 65|1.607738e-01|-1.682752e-06 - 66|1.607691e-01|-2.913936e-05 - 67|1.607671e-01|-1.288855e-05 - 68|1.607654e-01|-1.002448e-05 - 69|1.607641e-01|-8.209492e-06 - 70|1.607632e-01|-5.588467e-06 - 71|1.607619e-01|-8.050388e-06 - 72|1.607618e-01|-9.417493e-07 - 73|1.607598e-01|-1.210509e-05 - 74|1.607591e-01|-4.392914e-06 - 75|1.607579e-01|-7.759587e-06 - 76|1.607574e-01|-2.760280e-06 - 77|1.607556e-01|-1.146469e-05 - 78|1.607550e-01|-3.689456e-06 - 79|1.607550e-01|-4.065631e-08 - It. |Loss |Delta loss - -------------------------------- - 80|1.607539e-01|-6.555681e-06 - 81|1.607528e-01|-7.177470e-06 - 82|1.607527e-01|-5.306068e-07 - 83|1.607514e-01|-7.816045e-06 - 84|1.607511e-01|-2.301970e-06 - 85|1.607504e-01|-4.281072e-06 - 86|1.607503e-01|-7.821886e-07 - 87|1.607480e-01|-1.403013e-05 - 88|1.607480e-01|-1.169298e-08 - 89|1.607473e-01|-4.235982e-06 - 90|1.607470e-01|-1.717105e-06 - 91|1.607470e-01|-6.148402e-09 - 92|1.607462e-01|-5.396481e-06 - 93|1.607461e-01|-5.194954e-07 - 94|1.607450e-01|-6.525707e-06 - 95|1.607442e-01|-5.332060e-06 - 96|1.607439e-01|-1.682093e-06 - 97|1.607437e-01|-1.594796e-06 - 98|1.607435e-01|-7.923812e-07 - 99|1.607420e-01|-9.738552e-06 - It. |Loss |Delta loss - -------------------------------- - 100|1.607419e-01|-1.022448e-07 - 101|1.607419e-01|-4.865999e-07 - 102|1.607418e-01|-7.092012e-07 - 103|1.607408e-01|-5.861815e-06 - 104|1.607402e-01|-3.953266e-06 - 105|1.607395e-01|-3.969572e-06 - 106|1.607390e-01|-3.612075e-06 - 107|1.607377e-01|-7.683735e-06 - 108|1.607365e-01|-7.777599e-06 - 109|1.607364e-01|-2.335096e-07 - 110|1.607364e-01|-4.562036e-07 - 111|1.607360e-01|-2.089538e-06 - 112|1.607356e-01|-2.755355e-06 - 113|1.607349e-01|-4.501960e-06 - 114|1.607347e-01|-1.160544e-06 - 115|1.607346e-01|-6.289450e-07 - 116|1.607345e-01|-2.092146e-07 - 117|1.607336e-01|-5.990866e-06 - 118|1.607330e-01|-3.348498e-06 - 119|1.607328e-01|-1.256222e-06 - It. |Loss |Delta loss - -------------------------------- - 120|1.607320e-01|-5.418353e-06 - 121|1.607318e-01|-8.296189e-07 - 122|1.607311e-01|-4.381608e-06 - 123|1.607310e-01|-8.913901e-07 - 124|1.607309e-01|-3.808821e-07 - 125|1.607302e-01|-4.608994e-06 - 126|1.607294e-01|-5.063777e-06 - 127|1.607290e-01|-2.532835e-06 - 128|1.607285e-01|-2.870049e-06 - 129|1.607284e-01|-4.892812e-07 - 130|1.607281e-01|-1.760452e-06 - 131|1.607279e-01|-1.727139e-06 - 132|1.607275e-01|-2.220706e-06 - 133|1.607271e-01|-2.516930e-06 - 134|1.607269e-01|-1.201434e-06 - 135|1.607269e-01|-2.183459e-09 - 136|1.607262e-01|-4.223011e-06 - 137|1.607258e-01|-2.530202e-06 - 138|1.607258e-01|-1.857260e-07 - 139|1.607256e-01|-1.401957e-06 - It. |Loss |Delta loss - -------------------------------- - 140|1.607250e-01|-3.242751e-06 - 141|1.607247e-01|-2.308071e-06 - 142|1.607247e-01|-4.730700e-08 - 143|1.607246e-01|-4.240229e-07 - 144|1.607242e-01|-2.484810e-06 - 145|1.607238e-01|-2.539206e-06 - 146|1.607234e-01|-2.535574e-06 - 147|1.607231e-01|-1.954802e-06 - 148|1.607228e-01|-1.765447e-06 - 149|1.607228e-01|-1.620007e-08 - 150|1.607222e-01|-3.615783e-06 - 151|1.607222e-01|-8.668516e-08 - 152|1.607215e-01|-4.000673e-06 - 153|1.607213e-01|-1.774103e-06 - 154|1.607213e-01|-6.328834e-09 - 155|1.607209e-01|-2.418783e-06 - 156|1.607208e-01|-2.848492e-07 - 157|1.607207e-01|-8.836043e-07 - 158|1.607205e-01|-1.192836e-06 - 159|1.607202e-01|-1.638022e-06 - It. |Loss |Delta loss - -------------------------------- - 160|1.607202e-01|-3.670914e-08 - 161|1.607197e-01|-3.153709e-06 - 162|1.607197e-01|-2.419565e-09 - 163|1.607194e-01|-2.136882e-06 - 164|1.607194e-01|-1.173754e-09 - 165|1.607192e-01|-8.169238e-07 - 166|1.607191e-01|-9.218755e-07 - 167|1.607189e-01|-9.459255e-07 - 168|1.607187e-01|-1.294835e-06 - 169|1.607186e-01|-5.797668e-07 - 170|1.607186e-01|-4.706272e-08 - 171|1.607183e-01|-1.753383e-06 - 172|1.607183e-01|-1.681573e-07 - 173|1.607183e-01|-2.563971e-10 - - -Solve EMD with Frobenius norm + entropic regularization -------------------------------------------------------- - - - -.. code-block:: python - - - #%% 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() - - - -.. image:: /auto_examples/images/sphx_glr_plot_optim_OTreg_008.png - :align: center - - -.. rst-class:: sphx-glr-script-out - - Out:: - - It. |Loss |Delta loss - -------------------------------- - 0|1.693084e-01|0.000000e+00 - 1|1.610121e-01|-5.152589e-02 - 2|1.609378e-01|-4.622297e-04 - 3|1.609284e-01|-5.830043e-05 - 4|1.609284e-01|-1.111407e-12 - - -**Total running time of the script:** ( 0 minutes 1.990 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_optim_OTreg.py <plot_optim_OTreg.py>` - - - - .. container:: sphx-glr-download - - :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.readthedocs.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 643e760..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": "3.6.5" - } - }, - "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 c311fbd..0000000 --- a/docs/source/auto_examples/plot_otda_classes.py +++ /dev/null @@ -1,150 +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 19756ff..0000000 --- a/docs/source/auto_examples/plot_otda_classes.rst +++ /dev/null @@ -1,263 +0,0 @@ - - -.. _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:: python - - - # 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:: python - - - 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:: python - - - # 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:: - - It. |Loss |Delta loss - -------------------------------- - 0|9.566309e+00|0.000000e+00 - 1|2.169680e+00|-3.409088e+00 - 2|1.914989e+00|-1.329986e-01 - 3|1.860251e+00|-2.942498e-02 - 4|1.838073e+00|-1.206621e-02 - 5|1.827064e+00|-6.025122e-03 - 6|1.820899e+00|-3.386082e-03 - 7|1.817290e+00|-1.985705e-03 - 8|1.814644e+00|-1.458223e-03 - 9|1.812661e+00|-1.093816e-03 - 10|1.810239e+00|-1.338121e-03 - 11|1.809100e+00|-6.296940e-04 - 12|1.807939e+00|-6.420646e-04 - 13|1.806965e+00|-5.389118e-04 - 14|1.806822e+00|-7.889599e-05 - 15|1.806193e+00|-3.482356e-04 - 16|1.805735e+00|-2.536930e-04 - 17|1.805321e+00|-2.292667e-04 - 18|1.804389e+00|-5.170222e-04 - 19|1.803908e+00|-2.661907e-04 - It. |Loss |Delta loss - -------------------------------- - 20|1.803696e+00|-1.178279e-04 - - -Fig 1 : plots source and target samples ---------------------------------------- - - - -.. code-block:: python - - - 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 - :align: center - - - - -Fig 2 : plot optimal couplings and transported samples ------------------------------------------------------- - - - -.. code-block:: python - - - 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_003.png - :align: center - - - - -**Total running time of the script:** ( 0 minutes 1.423 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_otda_classes.py <plot_otda_classes.py>` - - - - .. container:: sphx-glr-download - - :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.readthedocs.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 103bdec..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\nfrom scipy import ndimage\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 = ndimage.imread('../data/ocean_day.jpg').astype(np.float64) / 256\nI2 = ndimage.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": "3.6.7" - } - }, - "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 62383a2..0000000 --- a/docs/source/auto_examples/plot_otda_color_images.py +++ /dev/null @@ -1,165 +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 -from scipy import ndimage -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 = ndimage.imread('../data/ocean_day.jpg').astype(np.float64) / 256 -I2 = ndimage.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 ab0406e..0000000 --- a/docs/source/auto_examples/plot_otda_color_images.rst +++ /dev/null @@ -1,262 +0,0 @@ - - -.. _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:: python - - - # Authors: Remi Flamary <remi.flamary@unice.fr> - # Stanislas Chambon <stan.chambon@gmail.com> - # - # License: MIT License - - import numpy as np - from scipy import ndimage - 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:: python - - - # Loading images - I1 = ndimage.imread('../data/ocean_day.jpg').astype(np.float64) / 256 - I2 = ndimage.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:: python - - - 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 - :align: center - - - - -Scatter plot of colors ----------------------- - - - -.. code-block:: python - - - 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_003.png - :align: center - - - - -Instantiate the different transport algorithms and fit them ------------------------------------------------------------ - - - -.. code-block:: python - - - # 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:: python - - - 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_005.png - :align: center - - - - -**Total running time of the script:** ( 3 minutes 55.541 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_otda_color_images.py <plot_otda_color_images.py>` - - - - .. container:: sphx-glr-download - - :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.readthedocs.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 b9002ee..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": "3.6.5" - } - }, - "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 80cc34c..0000000 --- a/docs/source/auto_examples/plot_otda_d2.rst +++ /dev/null @@ -1,269 +0,0 @@ - - -.. _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:: python - - - # 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:: python - - - 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:: python - - - # 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:: python - - - 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 - :align: center - - - - -Fig 2 : plots optimal couplings for the different methods ---------------------------------------------------------- - - - -.. code-block:: python - - 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_003.png - :align: center - - - - -Fig 3 : plot transported samples --------------------------------- - - - -.. code-block:: python - - - # 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_006.png - :align: center - - - - -**Total running time of the script:** ( 0 minutes 35.515 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_otda_d2.py <plot_otda_d2.py>` - - - - .. container:: sphx-glr-download - - :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.readthedocs.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 027b6cb..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))\n\n# %%" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Plot transformed images\n-----------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "pl.figure(2, figsize=(10, 7))\n\npl.subplot(2, 2, 1)\npl.imshow(I1)\npl.axis('off')\npl.title('Im. 1')\n\npl.subplot(2, 2, 2)\npl.imshow(I2)\npl.axis('off')\npl.title('Im. 2')\n\npl.subplot(2, 2, 3)\npl.imshow(I1t)\npl.axis('off')\npl.title('Mapping Im. 1')\n\npl.subplot(2, 2, 4)\npl.imshow(I2t)\npl.axis('off')\npl.title('Inverse mapping Im. 2')" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.5" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_otda_linear_mapping.py b/docs/source/auto_examples/plot_otda_linear_mapping.py 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 8e2e0cf..0000000 --- a/docs/source/auto_examples/plot_otda_linear_mapping.rst +++ /dev/null @@ -1,260 +0,0 @@ - - -.. _sphx_glr_auto_examples_plot_otda_linear_mapping.py: - - -============================ -Linear OT mapping estimation -============================ - - - - - -.. code-block:: python - - - # Author: Remi Flamary <remi.flamary@unice.fr> - # - # License: MIT License - - import numpy as np - import pylab as pl - import ot - - - - - - - -Generate data -------------- - - - -.. code-block:: python - - - n = 1000 - d = 2 - sigma = .1 - - # source samples - angles = np.random.rand(n, 1) * 2 * np.pi - xs = np.concatenate((np.sin(angles), np.cos(angles)), - axis=1) + sigma * np.random.randn(n, 2) - xs[:n // 2, 1] += 2 - - - # target samples - anglet = np.random.rand(n, 1) * 2 * np.pi - xt = np.concatenate((np.sin(anglet), np.cos(anglet)), - axis=1) + sigma * np.random.randn(n, 2) - xt[:n // 2, 1] += 2 - - - A = np.array([[1.5, .7], [.7, 1.5]]) - b = np.array([[4, 2]]) - xt = xt.dot(A) + b - - - - - - - -Plot data ---------- - - - -.. code-block:: python - - - pl.figure(1, (5, 5)) - pl.plot(xs[:, 0], xs[:, 1], '+') - pl.plot(xt[:, 0], xt[:, 1], 'o') - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_otda_linear_mapping_001.png - :align: center - - - - -Estimate linear mapping and transport -------------------------------------- - - - -.. code-block:: python - - - Ae, be = ot.da.OT_mapping_linear(xs, xt) - - xst = xs.dot(Ae) + be - - - - - - - - -Plot transported samples ------------------------- - - - -.. code-block:: python - - - pl.figure(1, (5, 5)) - pl.clf() - pl.plot(xs[:, 0], xs[:, 1], '+') - pl.plot(xt[:, 0], xt[:, 1], 'o') - pl.plot(xst[:, 0], xst[:, 1], '+') - - pl.show() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_otda_linear_mapping_002.png - :align: center - - - - -Load image data ---------------- - - - -.. code-block:: python - - - - def im2mat(I): - """Converts and image to matrix (one pixel per line)""" - return I.reshape((I.shape[0] * I.shape[1], I.shape[2])) - - - def mat2im(X, shape): - """Converts back a matrix to an image""" - return X.reshape(shape) - - - def minmax(I): - return np.clip(I, 0, 1) - - - # Loading images - I1 = pl.imread('../data/ocean_day.jpg').astype(np.float64) / 256 - I2 = pl.imread('../data/ocean_sunset.jpg').astype(np.float64) / 256 - - - X1 = im2mat(I1) - X2 = im2mat(I2) - - - - - - - -Estimate mapping and adapt ----------------------------- - - - -.. code-block:: python - - - mapping = ot.da.LinearTransport() - - mapping.fit(Xs=X1, Xt=X2) - - - xst = mapping.transform(Xs=X1) - xts = mapping.inverse_transform(Xt=X2) - - I1t = minmax(mat2im(xst, I1.shape)) - I2t = minmax(mat2im(xts, I2.shape)) - - # %% - - - - - - - - -Plot transformed images ------------------------ - - - -.. code-block:: python - - - pl.figure(2, figsize=(10, 7)) - - pl.subplot(2, 2, 1) - pl.imshow(I1) - pl.axis('off') - pl.title('Im. 1') - - pl.subplot(2, 2, 2) - pl.imshow(I2) - pl.axis('off') - pl.title('Im. 2') - - pl.subplot(2, 2, 3) - pl.imshow(I1t) - pl.axis('off') - pl.title('Mapping Im. 1') - - pl.subplot(2, 2, 4) - pl.imshow(I2t) - pl.axis('off') - pl.title('Inverse mapping Im. 2') - - - -.. image:: /auto_examples/images/sphx_glr_plot_otda_linear_mapping_004.png - :align: center - - - - -**Total running time of the script:** ( 0 minutes 0.635 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_otda_linear_mapping.py <plot_otda_linear_mapping.py>` - - - - .. container:: sphx-glr-download - - :download:`Download Jupyter notebook: plot_otda_linear_mapping.ipynb <plot_otda_linear_mapping.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_otda_mapping.ipynb b/docs/source/auto_examples/plot_otda_mapping.ipynb deleted file mode 100644 index 898466d..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": "3.6.5" - } - }, - "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 1d95fc6..0000000 --- a/docs/source/auto_examples/plot_otda_mapping.rst +++ /dev/null @@ -1,235 +0,0 @@ - - -.. _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:: python - - - # 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:: python - - - 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:: python - - - 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 - :align: center - - - - -Instantiate the different transport algorithms and fit them ------------------------------------------------------------ - - - -.. code-block:: python - - - # 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:: - - It. |Loss |Delta loss - -------------------------------- - 0|4.299275e+03|0.000000e+00 - 1|4.290443e+03|-2.054271e-03 - 2|4.290040e+03|-9.389994e-05 - 3|4.289876e+03|-3.830707e-05 - 4|4.289783e+03|-2.157428e-05 - 5|4.289724e+03|-1.390941e-05 - 6|4.289706e+03|-4.051054e-06 - It. |Loss |Delta loss - -------------------------------- - 0|4.326465e+02|0.000000e+00 - 1|4.282533e+02|-1.015416e-02 - 2|4.279473e+02|-7.145955e-04 - 3|4.277941e+02|-3.580104e-04 - 4|4.277069e+02|-2.039229e-04 - 5|4.276462e+02|-1.418698e-04 - 6|4.276011e+02|-1.054172e-04 - 7|4.275663e+02|-8.145802e-05 - 8|4.275405e+02|-6.028774e-05 - 9|4.275191e+02|-5.005886e-05 - 10|4.275019e+02|-4.021935e-05 - - -Plot transported samples ------------------------- - - - -.. code-block:: python - - - 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_003.png - :align: center - - - - -**Total running time of the script:** ( 0 minutes 0.795 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_otda_mapping.py <plot_otda_mapping.py>` - - - - .. container:: sphx-glr-download - - :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.readthedocs.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 baffef4..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\nfrom scipy import ndimage\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 = ndimage.imread('../data/ocean_day.jpg').astype(np.float64) / 256\nI2 = ndimage.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": "3.6.7" - } - }, - "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 a20eca8..0000000 --- a/docs/source/auto_examples/plot_otda_mapping_colors_images.py +++ /dev/null @@ -1,174 +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 -from scipy import ndimage -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 = ndimage.imread('../data/ocean_day.jpg').astype(np.float64) / 256 -I2 = ndimage.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 2afdc8a..0000000 --- a/docs/source/auto_examples/plot_otda_mapping_colors_images.rst +++ /dev/null @@ -1,310 +0,0 @@ - - -.. _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:: python - - - # Authors: Remi Flamary <remi.flamary@unice.fr> - # Stanislas Chambon <stan.chambon@gmail.com> - # - # License: MIT License - - import numpy as np - from scipy import ndimage - 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:: python - - - # Loading images - I1 = ndimage.imread('../data/ocean_day.jpg').astype(np.float64) / 256 - I2 = ndimage.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:: python - - - # 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:: - - 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:: python - - - 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 - :align: center - - - - -Plot pixel values distribution ------------------------------- - - - -.. code-block:: python - - - 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_003.png - :align: center - - - - -Plot transformed images ------------------------ - - - -.. code-block:: python - - - 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_004.png - :align: center - - - - -**Total running time of the script:** ( 3 minutes 14.206 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_otda_mapping_colors_images.py <plot_otda_mapping_colors_images.py>` - - - - .. container:: sphx-glr-download - - :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.readthedocs.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 e3192da..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": "3.6.5" - } - }, - "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 2ed7819..0000000 --- a/docs/source/auto_examples/plot_otda_semi_supervised.rst +++ /dev/null @@ -1,245 +0,0 @@ - - -.. _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:: python - - - # 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:: python - - - 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:: python - - - - # 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:: python - - - 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 - :align: center - - - - -Fig 2 : plots optimal couplings for the different methods ---------------------------------------------------------- - - - -.. code-block:: python - - - 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_003.png - :align: center - - - - -Fig 3 : plot transported samples --------------------------------- - - - -.. code-block:: python - - - # 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_006.png - :align: center - - - - -**Total running time of the script:** ( 0 minutes 0.256 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_otda_semi_supervised.py <plot_otda_semi_supervised.py>` - - - - .. container:: sphx-glr-download - - :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.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_stochastic.ipynb b/docs/source/auto_examples/plot_stochastic.ipynb deleted file mode 100644 index 7f6ff3d..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": "3.6.7" - } - }, - "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 d531045..0000000 --- a/docs/source/auto_examples/plot_stochastic.rst +++ /dev/null @@ -1,446 +0,0 @@ - - -.. _sphx_glr_auto_examples_plot_stochastic.py: - - -========================== -Stochastic examples -========================== - -This example is designed to show how to use the stochatic optimization -algorithms for descrete and semicontinous measures from the POT library. - - - - -.. code-block:: python - - - # Author: Kilian Fatras <kilian.fatras@gmail.com> - # - # License: MIT License - - import matplotlib.pylab as pl - import numpy as np - import ot - import ot.plot - - - - - - - - -COMPUTE TRANSPORTATION MATRIX FOR SEMI-DUAL PROBLEM -############################################################################ -############################################################################ - DISCRETE CASE: - - Sample two discrete measures for the discrete case - --------------------------------------------- - - Define 2 discrete measures a and b, the points where are defined the source - and the target measures and finally the cost matrix c. - - - -.. code-block:: python - - - n_source = 7 - n_target = 4 - reg = 1 - numItermax = 1000 - - a = ot.utils.unif(n_source) - b = ot.utils.unif(n_target) - - rng = np.random.RandomState(0) - X_source = rng.randn(n_source, 2) - Y_target = rng.randn(n_target, 2) - M = ot.dist(X_source, Y_target) - - - - - - - -Call the "SAG" method to find the transportation matrix in the discrete case ---------------------------------------------- - -Define the method "SAG", call ot.solve_semi_dual_entropic and plot the -results. - - - -.. code-block:: python - - - method = "SAG" - sag_pi = ot.stochastic.solve_semi_dual_entropic(a, b, M, reg, method, - numItermax) - print(sag_pi) - - - - - -.. rst-class:: sphx-glr-script-out - - Out:: - - [[2.55553509e-02 9.96395660e-02 1.76579142e-02 4.31178196e-06] - [1.21640234e-01 1.25357448e-02 1.30225078e-03 7.37891338e-03] - [3.56123975e-03 7.61451746e-02 6.31505947e-02 1.33831456e-07] - [2.61515202e-02 3.34246014e-02 8.28734709e-02 4.07550428e-04] - [9.85500870e-03 7.52288517e-04 1.08262628e-02 1.21423583e-01] - [2.16904253e-02 9.03825797e-04 1.87178503e-03 1.18391107e-01] - [4.15462212e-02 2.65987989e-02 7.23177216e-02 2.39440107e-03]] - - -SEMICONTINOUS CASE: - -Sample one general measure a, one discrete measures b for the semicontinous -case ---------------------------------------------- - -Define one general measure a, one discrete measures b, the points where -are defined the source and the target measures and finally the cost matrix c. - - - -.. code-block:: python - - - n_source = 7 - n_target = 4 - reg = 1 - numItermax = 1000 - log = True - - a = ot.utils.unif(n_source) - b = ot.utils.unif(n_target) - - rng = np.random.RandomState(0) - X_source = rng.randn(n_source, 2) - Y_target = rng.randn(n_target, 2) - M = ot.dist(X_source, Y_target) - - - - - - - -Call the "ASGD" method to find the transportation matrix in the semicontinous -case ---------------------------------------------- - -Define the method "ASGD", call ot.solve_semi_dual_entropic and plot the -results. - - - -.. code-block:: python - - - method = "ASGD" - asgd_pi, log_asgd = ot.stochastic.solve_semi_dual_entropic(a, b, M, reg, method, - numItermax, log=log) - print(log_asgd['alpha'], log_asgd['beta']) - print(asgd_pi) - - - - - -.. rst-class:: sphx-glr-script-out - - Out:: - - [3.98220325 7.76235856 3.97645524 2.72051681 1.23219313 3.07696856 - 2.84476972] [-2.65544161 -2.50838395 -0.9397765 6.10360206] - [[2.34528761e-02 1.00491956e-01 1.89058354e-02 6.47543413e-06] - [1.16616747e-01 1.32074516e-02 1.45653361e-03 1.15764107e-02] - [3.16154850e-03 7.42892944e-02 6.54061055e-02 1.94426150e-07] - [2.33152216e-02 3.27486992e-02 8.61986263e-02 5.94595747e-04] - [6.34131496e-03 5.31975896e-04 8.12724003e-03 1.27856612e-01] - [1.41744829e-02 6.49096245e-04 1.42704389e-03 1.26606520e-01] - [3.73127657e-02 2.62526499e-02 7.57727161e-02 3.51901117e-03]] - - -Compare the results with the Sinkhorn algorithm ---------------------------------------------- - -Call the Sinkhorn algorithm from POT - - - -.. code-block:: python - - - sinkhorn_pi = ot.sinkhorn(a, b, M, reg) - print(sinkhorn_pi) - - - - - - -.. rst-class:: sphx-glr-script-out - - Out:: - - [[2.55535622e-02 9.96413843e-02 1.76578860e-02 4.31043335e-06] - [1.21640742e-01 1.25369034e-02 1.30234529e-03 7.37715259e-03] - [3.56096458e-03 7.61460101e-02 6.31500344e-02 1.33788624e-07] - [2.61499607e-02 3.34255577e-02 8.28741973e-02 4.07427179e-04] - [9.85698720e-03 7.52505948e-04 1.08291770e-02 1.21418473e-01] - [2.16947591e-02 9.04086158e-04 1.87228707e-03 1.18386011e-01] - [4.15442692e-02 2.65998963e-02 7.23192701e-02 2.39370724e-03]] - - -PLOT TRANSPORTATION MATRIX -############################################################################# - - -Plot SAG results ----------------- - - - -.. code-block:: python - - - pl.figure(4, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, sag_pi, 'semi-dual : OT matrix SAG') - pl.show() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_stochastic_004.png - :align: center - - - - -Plot ASGD results ------------------ - - - -.. code-block:: python - - - pl.figure(4, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, asgd_pi, 'semi-dual : OT matrix ASGD') - pl.show() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_stochastic_005.png - :align: center - - - - -Plot Sinkhorn results ---------------------- - - - -.. code-block:: python - - - pl.figure(4, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, sinkhorn_pi, 'OT matrix Sinkhorn') - pl.show() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_stochastic_006.png - :align: center - - - - -COMPUTE TRANSPORTATION MATRIX FOR DUAL PROBLEM -############################################################################ -############################################################################ - SEMICONTINOUS CASE: - - Sample one general measure a, one discrete measures b for the semicontinous - case - --------------------------------------------- - - Define one general measure a, one discrete measures b, the points where - are defined the source and the target measures and finally the cost matrix c. - - - -.. code-block:: python - - - n_source = 7 - n_target = 4 - reg = 1 - numItermax = 100000 - lr = 0.1 - batch_size = 3 - log = True - - a = ot.utils.unif(n_source) - b = ot.utils.unif(n_target) - - rng = np.random.RandomState(0) - X_source = rng.randn(n_source, 2) - Y_target = rng.randn(n_target, 2) - M = ot.dist(X_source, Y_target) - - - - - - - -Call the "SGD" dual method to find the transportation matrix in the -semicontinous case ---------------------------------------------- - -Call ot.solve_dual_entropic and plot the results. - - - -.. code-block:: python - - - sgd_dual_pi, log_sgd = ot.stochastic.solve_dual_entropic(a, b, M, reg, - batch_size, numItermax, - lr, log=log) - print(log_sgd['alpha'], log_sgd['beta']) - print(sgd_dual_pi) - - - - - -.. rst-class:: sphx-glr-script-out - - Out:: - - [0.92449986 2.75486107 1.07923806 0.02741145 0.61355413 1.81961594 - 0.12072562] [0.33831611 0.46806842 1.5640451 4.96947652] - [[2.20001105e-02 9.26497883e-02 1.08654588e-02 9.78995555e-08] - [1.55669974e-02 1.73279561e-03 1.19120878e-04 2.49058251e-05] - [3.48198483e-03 8.04151063e-02 4.41335396e-02 3.45115752e-09] - [3.14927954e-02 4.34760520e-02 7.13338154e-02 1.29442395e-05] - [6.81836550e-02 5.62182457e-03 5.35386584e-02 2.21568095e-02] - [8.04671052e-02 3.62163462e-03 4.96331605e-03 1.15837801e-02] - [4.88644009e-02 3.37903481e-02 6.07955004e-02 7.42743505e-05]] - - -Compare the results with the Sinkhorn algorithm ---------------------------------------------- - -Call the Sinkhorn algorithm from POT - - - -.. code-block:: python - - - sinkhorn_pi = ot.sinkhorn(a, b, M, reg) - print(sinkhorn_pi) - - - - - -.. rst-class:: sphx-glr-script-out - - Out:: - - [[2.55535622e-02 9.96413843e-02 1.76578860e-02 4.31043335e-06] - [1.21640742e-01 1.25369034e-02 1.30234529e-03 7.37715259e-03] - [3.56096458e-03 7.61460101e-02 6.31500344e-02 1.33788624e-07] - [2.61499607e-02 3.34255577e-02 8.28741973e-02 4.07427179e-04] - [9.85698720e-03 7.52505948e-04 1.08291770e-02 1.21418473e-01] - [2.16947591e-02 9.04086158e-04 1.87228707e-03 1.18386011e-01] - [4.15442692e-02 2.65998963e-02 7.23192701e-02 2.39370724e-03]] - - -Plot SGD results ------------------ - - - -.. code-block:: python - - - pl.figure(4, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, sgd_dual_pi, 'dual : OT matrix SGD') - pl.show() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_stochastic_007.png - :align: center - - - - -Plot Sinkhorn results ---------------------- - - - -.. code-block:: python - - - pl.figure(4, figsize=(5, 5)) - ot.plot.plot1D_mat(a, b, sinkhorn_pi, 'OT matrix Sinkhorn') - pl.show() - - - -.. image:: /auto_examples/images/sphx_glr_plot_stochastic_008.png - :align: center - - - - -**Total running time of the script:** ( 0 minutes 20.889 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_stochastic.py <plot_stochastic.py>` - - - - .. container:: sphx-glr-download - - :download:`Download Jupyter notebook: plot_stochastic.ipynb <plot_stochastic.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/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..384bf40 100644 --- a/docs/source/conf.py +++ b/docs/source/conf.py @@ -34,7 +34,9 @@ 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 = [ 'cupy'] # 'autograd.numpy','pymanopt.manifolds','pymanopt.solvers', sys.modules.update((mod_name, Mock()) for mod_name in MOCK_MODULES) # !!!! @@ -57,6 +59,7 @@ sys.path.insert(0, os.path.abspath("../..")) # ones. extensions = [ 'sphinx.ext.autodoc', + 'sphinx.ext.autosummary', 'sphinx.ext.doctest', 'sphinx.ext.intersphinx', 'sphinx.ext.todo', @@ -65,9 +68,12 @@ extensions = [ 'sphinx.ext.ifconfig', 'sphinx.ext.viewcode', 'sphinx.ext.napoleon', - #'sphinx_gallery.gen_gallery', + 'sphinx_gallery.gen_gallery', ] +autosummary_generate = True + + napoleon_numpy_docstring = True # Add any paths that contain templates here, relative to this directory. @@ -86,7 +92,7 @@ master_doc = 'index' # General information about the project. project = u'POT Python Optimal Transport' -copyright = u'2016-2019, Rémi Flamary, Nicolas Courty' +copyright = u'2016-2020, Rémi Flamary, Nicolas Courty' author = u'Rémi Flamary, Nicolas Courty' # The version info for the project you're documenting, acts as replacement for @@ -248,17 +254,17 @@ 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 @@ -295,7 +301,7 @@ latex_documents = [ # One entry per manual page. List of tuples # (source start file, name, description, authors, manual section). man_pages = [ - (master_doc, 'pot', u'POT Python Optimal Transport library Documentation', + (master_doc, 'pot', u'POT Python Optimal Transport', [author], 1) ] @@ -309,8 +315,8 @@ man_pages = [ # (source start file, target name, title, author, # dir menu entry, description, category) texinfo_documents = [ - (master_doc, 'POT', u'POT Python Optimal Transport library Documentation', - author, 'POT', 'Python Optimal Transport librar.', + (master_doc, 'POT', u'POT Python Optimal Transport', + author, 'POT', 'Python Optimal Transport', 'Miscellaneous'), ] @@ -331,13 +337,14 @@ texinfo_documents = [ intersphinx_mapping = {'python': ('https://docs.python.org/3', None), 'numpy': ('http://docs.scipy.org/doc/numpy/', None), 'scipy': ('http://docs.scipy.org/doc/scipy/reference/', None), - 'matplotlib': ('http://matplotlib.sourceforge.net/', None)} + 'matplotlib': ('http://matplotlib.org/', None)} sphinx_gallery_conf = { - 'examples_dirs': ['../../examples','../../examples/da'], + 'examples_dirs': ['../../examples', '../../examples/da'], 'gallery_dirs': 'auto_examples', - 'backreferences_dir': '../modules/generated/', + 'backreferences_dir': 'gen_modules/backreferences', + 'inspect_global_variables' : True, + 'doc_module' : ('ot','numpy','scipy','pylab'), 'reference_url': { - 'numpy': 'http://docs.scipy.org/doc/numpy-1.9.1', - 'scipy': 'http://docs.scipy.org/doc/scipy-0.17.0/reference'} + 'ot': None} } diff --git a/docs/source/index.rst b/docs/source/index.rst index 9078d35..be01343 100644 --- a/docs/source/index.rst +++ b/docs/source/index.rst @@ -10,15 +10,17 @@ Contents -------- .. toctree:: - :maxdepth: 2 + :maxdepth: 1 self quickstart all auto_examples/index + releases .. include:: readme.rst - :start-line: 5 + :start-line: 2 + Indices and tables diff --git a/docs/source/quickstart.rst b/docs/source/quickstart.rst index 978eaff..d56f812 100644 --- a/docs/source/quickstart.rst +++ b/docs/source/quickstart.rst @@ -645,6 +645,53 @@ implemented the main function :any:`ot.barycenter_unbalanced`. - :any:`auto_examples/plot_UOT_barycenter_1D` +Partial optimal transport +^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Partial OT is a variant of the optimal transport problem when only a fixed amount of mass m +is to be transported. The partial OT metric between two histograms a and b is defined as [28]_: + +.. math:: + \gamma = \arg\min_\gamma <\gamma,M>_F + + s.t. + \gamma\geq 0 \\ + \gamma 1 \leq a\\ + \gamma^T 1 \leq b\\ + 1^T \gamma^T 1 = m \leq \min\{\|a\|_1, \|b\|_1\} + + +Interestingly the problem can be casted into a regular OT problem by adding reservoir points +in which the surplus mass is sent [29]_. We provide a solver for partial OT +in :any:`ot.partial`. The exact resolution of the problem is computed in :any:`ot.partial.partial_wasserstein` +and :any:`ot.partial.partial_wasserstein2` that return respectively the OT matrix and the value of the +linear term. The entropic solution of the problem is computed in :any:`ot.partial.entropic_partial_wasserstein` +(see [3]_). + +The partial Gromov-Wasserstein formulation of the problem + +.. math:: + GW = \min_\gamma \sum_{i,j,k,l} L(C1_{i,k},C2_{j,l})*\gamma_{i,j}*\gamma_{k,l} + + s.t. + \gamma\geq 0 \\ + \gamma 1 \leq a\\ + \gamma^T 1 \leq b\\ + 1^T \gamma^T 1 = m \leq \min\{\|a\|_1, \|b\|_1\} + +is computed in :any:`ot.partial.partial_gromov_wasserstein` and in +:any:`ot.partial.entropic_partial_gromov_wasserstein` when considering the entropic +regularization of the problem. + + +.. hint:: + + Examples of the use of :any:`ot.partial` are available in : + + - :any:`auto_examples/plot_partial` + + + Gromov-Wasserstein ^^^^^^^^^^^^^^^^^^ @@ -921,3 +968,20 @@ References .. [25] Frogner C., Zhang C., Mobahi H., Araya-Polo M., Poggio T. : Learning with a Wasserstein Loss, Advances in Neural Information Processing Systems (NIPS) 2015 + +.. [26] Alaya M. Z., Bérar M., Gasso G., Rakotomamonjy A. (2019). Screening Sinkhorn + Algorithm for Regularized Optimal Transport <https://papers.nips.cc/paper/9386-screening-sinkhorn-algorithm-for-regularized-optimal-transport>, + Advances in Neural Information Processing Systems 33 (NeurIPS). + +.. [27] Redko I., Courty N., Flamary R., Tuia D. (2019). Optimal Transport for Multi-source + Domain Adaptation under Target Shift <http://proceedings.mlr.press/v89/redko19a.html>, + Proceedings of the Twenty-Second International Conference on Artificial Intelligence + and Statistics (AISTATS) 22, 2019. + +.. [28] Caffarelli, L. A., McCann, R. J. (2020). Free boundaries in optimal transport and + Monge-Ampere obstacle problems <http://www.math.toronto.edu/~mccann/papers/annals2010.pdf>, + Annals of mathematics, 673-730. + +.. [29] Chapel, L., Alaya, M., Gasso, G. (2019). Partial Gromov-Wasserstein with + Applications on Positive-Unlabeled Learning <https://arxiv.org/abs/2002.08276>, + arXiv preprint arXiv:2002.08276. diff --git a/docs/source/readme.rst b/docs/source/readme.rst index 0871779..b8cb48c 100644 --- a/docs/source/readme.rst +++ b/docs/source/readme.rst @@ -1,57 +1,116 @@ 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: - -- 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). +Website and documentation: https://PythonOT.github.io/ + +Source Code (MIT): https://github.com/PythonOT/POT + +POT provides the following generic OT solvers (links to examples): + +- `OT Network Simplex + solver <auto_examples/plot_OT_1D.html>`__ + for the linear program/ Earth Movers Distance [1] . +- `Conditional + gradient <auto_examples/plot_optim_OTreg.html>`__ + [6] and `Generalized conditional + gradient <auto_examples/plot_optim_OTreg.html>`__ + for regularized OT [7]. +- Entropic regularization OT solver with `Sinkhorn Knopp + Algorithm <auto_examples/plot_OT_1D.html>`__ + [2] , stabilized version [9] [10], greedy Sinkhorn [22] and + `Screening Sinkhorn + [26] <auto_examples/plot_screenkhorn_1D.html>`__ + with optional GPU implementation (requires cupy). +- Bregman projections for `Wasserstein + barycenter <auto_examples/barycenters/plot_barycenter_lp_vs_entropic.html>`__ + [3], `convolutional + barycenter <auto_examples/barycenters/plot_convolutional_barycenter.html>`__ + [21] and unmixing [4]. - Sinkhorn divergence [23] and entropic regularization OT from empirical data. -- Smooth optimal transport solvers (dual and semi-dual) for KL and - squared L2 regularizations [17]. -- Non regularized Wasserstein barycenters [16] with LP solver (only - small scale). -- Bregman projections for Wasserstein barycenter [3], convolutional - barycenter [21] and unmixing [4]. -- Optimal transport for domain adaptation with group lasso - regularization [5] -- Conditional gradient [6] and Generalized conditional gradient for - regularized OT [7]. -- Linear OT [14] and Joint OT matrix and mapping estimation [8]. -- Wasserstein Discriminant Analysis [11] (requires autograd + - pymanopt). -- Gromov-Wasserstein distances and barycenters ([13] and regularized - [12]) -- Stochastic Optimization for Large-scale Optimal Transport (semi-dual - problem [18] and dual problem [19]) -- Non regularized free support Wasserstein barycenters [20]. -- Unbalanced OT with KL relaxation distance and barycenter [10, 25]. - -Some demonstrations (both in Python and Jupyter Notebook format) are -available in the examples folder. +- `Smooth optimal transport + solvers <auto_examples/plot_OT_1D_smooth.html>`__ + (dual and semi-dual) for KL and squared L2 regularizations [17]. +- Non regularized `Wasserstein barycenters + [16] <auto_examples/barycenters/plot_barycenter_lp_vs_entropic.html>`__) + with LP solver (only small scale). +- `Gromov-Wasserstein + distances <auto_examples/gromov/plot_gromov.html>`__ + and `GW + barycenters <auto_examples/gromov/plot_gromov_barycenter.html>`__ + (exact [13] and regularized [12]) +- `Fused-Gromov-Wasserstein distances + solver <auto_examples/gromov/plot_fgw.html#sphx-glr-auto-examples-plot-fgw-py>`__ + and `FGW + barycenters <auto_examples/gromov/plot_barycenter_fgw.html>`__ + [24] +- `Stochastic + solver <auto_examples/plot_stochastic.html>`__ + for Large-scale Optimal Transport (semi-dual problem [18] and dual + problem [19]) +- Non regularized `free support Wasserstein + barycenters <auto_examples/barycenters/plot_free_support_barycenter.html>`__ + [20]. +- `Unbalanced + OT <auto_examples/unbalanced-partial/plot_UOT_1D.html>`__ + with KL relaxation and + `barycenter <auto_examples/unbalanced-partial/plot_UOT_barycenter_1D.html>`__ + [10, 25]. +- `Partial Wasserstein and + Gromov-Wasserstein <auto_examples/unbalanced-partial/plot_partial_wass_and_gromov.html>`__ + (exact [29] and entropic [3] formulations). + +POT provides the following Machine Learning related solvers: + +- `Optimal transport for domain + adaptation <auto_examples/domain-adaptation/plot_otda_classes.html>`__ + with `group lasso + regularization <auto_examples/domain-adaptation/plot_otda_classes.html>`__, + `Laplacian + regularization <auto_examples/domain-adaptation/plot_otda_laplacian.html>`__ + [5] [30] and `semi supervised + setting <auto_examples/domain-adaptation/plot_otda_semi_supervised.html>`__. +- `Linear OT + mapping <auto_examples/domain-adaptation/plot_otda_linear_mapping.html>`__ + [14] and `Joint OT mapping + estimation <auto_examples/domain-adaptation/plot_otda_mapping.html>`__ + [8]. +- `Wasserstein Discriminant + Analysis <auto_examples/others/plot_WDA.html>`__ + [11] (requires autograd + pymanopt). +- `JCPOT algorithm for multi-source domain adaptation with target + shift <auto_examples/domain-adaptation/plot_otda_jcpot.html>`__ + [27]. + +Some other examples are available in the +`documentation <auto_examples/index.html>`__. Using and citing the toolbox ^^^^^^^^^^^^^^^^^^^^^^^^^^^^ If you use this toolbox in your research and find it useful, please cite -POT using the following bibtex reference: +POT using the following reference: + +:: + + Rémi Flamary and Nicolas Courty, POT Python Optimal Transport library, + Website: https://pythonot.github.io/, 2017 + +In Bibtex format: :: @misc{flamary2017pot, title={POT Python Optimal Transport library}, author={Flamary, R{'e}mi and Courty, Nicolas}, - url={https://github.com/rflamary/POT}, + url={https://pythonot.github.io/}, year={2017} } @@ -59,10 +118,10 @@ Installation ------------ The library has been tested on Linux, MacOSX and Windows. It requires a -C++ compiler for using the EMD solver and relies on the following Python -modules: +C++ compiler for building/installing the EMD solver and relies on the +following Python modules: -- Numpy (>=1.11) +- Numpy (>=1.16) - Scipy (>=1.0) - Cython (>=0.23) - Matplotlib (>=1.5) @@ -83,11 +142,11 @@ You can install the toolbox through PyPI with: pip install POT -or get the very latest version by downloading it and then running: +or get the very latest version by running: :: - python setup.py install --user # for user install (no root) + pip install -U https://github.com/PythonOT/POT/archive/master.zip # with --user for user install (no root) Anaconda installation with conda-forge ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ @@ -174,42 +233,8 @@ 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/>`__. - -Here is a list of the Python notebooks available -`here <https://github.com/rflamary/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>`__ -- `OT Ground - Loss <https://github.com/rflamary/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>`__ -- `2D optimal transport on empirical - distributions <https://github.com/rflamary/POT/blob/master/notebooks/plot_OT_2D_samples.ipynb>`__ -- `1D Wasserstein - barycenter <https://github.com/rflamary/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>`__ -- `Domain adaptation with optimal - transport <https://github.com/rflamary/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>`__ -- `OT mapping estimation for domain - adaptation <https://github.com/rflamary/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>`__ -- `Wasserstein Discriminant - Analysis <https://github.com/rflamary/POT/blob/master/notebooks/plot_WDA.ipynb>`__ -- `Gromov - Wasserstein <https://github.com/rflamary/POT/blob/master/notebooks/plot_gromov.ipynb>`__ -- `Gromov Wasserstein - Barycenter <https://github.com/rflamary/POT/blob/master/notebooks/plot_gromov_barycenter.ipynb>`__ - -You can also see the notebooks with `Jupyter -nbviewer <https://nbviewer.jupyter.org/github/rflamary/POT/tree/master/notebooks/>`__. +library. The full documentation with examples and output is available on +https://PythonOT.github.io/. Acknowledgements ---------------- @@ -221,22 +246,29 @@ This toolbox has been created and is maintained by The contributors to this library are -- `Alexandre Gramfort <http://alexandre.gramfort.net/>`__ +- `Alexandre Gramfort <http://alexandre.gramfort.net/>`__ (CI, + documentation) - `Laetitia Chapel <http://people.irisa.fr/Laetitia.Chapel/>`__ + (Partial OT) - `Michael Perrot <http://perso.univ-st-etienne.fr/pem82055/>`__ (Mapping estimation) - `Léo Gautheron <https://github.com/aje>`__ (GPU implementation) - `Nathalie Gayraud <https://www.linkedin.com/in/nathalie-t-h-gayraud/?ppe=1>`__ -- `Stanislas Chambon <https://slasnista.github.io/>`__ -- `Antoine Rolet <https://arolet.github.io/>`__ + (DA classes) +- `Stanislas Chambon <https://slasnista.github.io/>`__ (DA classes) +- `Antoine Rolet <https://arolet.github.io/>`__ (EMD solver debug) - Erwan Vautier (Gromov-Wasserstein) -- `Kilian Fatras <https://kilianfatras.github.io/>`__ +- `Kilian Fatras <https://kilianfatras.github.io/>`__ (Stochastic + solvers) - `Alain Rakotomamonjy <https://sites.google.com/site/alainrakotomamonjy/home>`__ -- `Vayer Titouan <https://tvayer.github.io/>`__ +- `Vayer Titouan <https://tvayer.github.io/>`__ (Gromov-Wasserstein -, + Fused-Gromov-Wasserstein) - `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/>`__ (Laplacian DA, JCPOT) This toolbox benefit a lot from open source research and we would like to thank the following persons for providing some code (in various @@ -387,21 +419,48 @@ and Statistics, (AISTATS) 21, 2018 graphs <http://proceedings.mlr.press/v97/titouan19a.html>`__ Proceedings of the 36th International Conference on Machine Learning (ICML). -[25] Frogner C., Zhang C., Mobahi H., Araya-Polo M., Poggio T. (2019). +[25] Frogner C., Zhang C., Mobahi H., Araya-Polo M., Poggio T. (2015). `Learning with a Wasserstein Loss <http://cbcl.mit.edu/wasserstein/>`__ Advances in Neural Information Processing Systems (NIPS). +[26] Alaya M. Z., Bérar M., Gasso G., Rakotomamonjy A. (2019). +`Screening Sinkhorn Algorithm for Regularized Optimal +Transport <https://papers.nips.cc/paper/9386-screening-sinkhorn-algorithm-for-regularized-optimal-transport>`__, +Advances in Neural Information Processing Systems 33 (NeurIPS). + +[27] Redko I., Courty N., Flamary R., Tuia D. (2019). `Optimal Transport +for Multi-source Domain Adaptation under Target +Shift <http://proceedings.mlr.press/v89/redko19a.html>`__, Proceedings +of the Twenty-Second International Conference on Artificial Intelligence +and Statistics (AISTATS) 22, 2019. + +[28] Caffarelli, L. A., McCann, R. J. (2010). `Free boundaries in +optimal transport and Monge-Ampere obstacle +problems <http://www.math.toronto.edu/~mccann/papers/annals2010.pdf>`__, +Annals of mathematics, 673-730. + +[29] Chapel, L., Alaya, M., Gasso, G. (2019). `Partial +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://github.com/PythonOT/POT/workflows/build/badge.svg + :target: https://github.com/PythonOT/POT/actions +.. |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/docs/source/releases.rst b/docs/source/releases.rst new file mode 100644 index 0000000..5a357f3 --- /dev/null +++ b/docs/source/releases.rst @@ -0,0 +1,341 @@ +Releases +======== + +0.7.0 +----- + +*May 2020* + +This is the new stable release for POT. We made a lot of changes in the +documentation and added several new features such as Partial OT, +Unbalanced and Multi Sources OT Domain Adaptation and several bug fixes. +One important change is that we have created the GitHub organization +`PythonOT <https://github.com/PythonOT>`__ that now owns the main POT +repository https://github.com/PythonOT/POT and the repository for the +new documentation is now hosted at https://PythonOT.github.io/. + +This is the first release where the Python 2.7 tests have been removed. +Most of the toolbox should still work but we do not offer support for +Python 2.7 and will close related Issues. + +A lot of changes have been done to the documentation that is now hosted +on https://PythonOT.github.io/ instead of readthedocs. It was a hard +choice but readthedocs did not allow us to run sphinx-gallery to update +our beautiful examples and it was a huge amount of work to maintain. The +documentation is now automatically compiled and updated on merge. We +also removed the notebooks from the repository for space reason and also +because they are all available in the `example +gallery <auto_examples/index.html>`__. Note +that now the output of the documentation build for each commit in the PR +is available to check that the doc builds correctly before merging which +was not possible with readthedocs. + +The CI framework has also been changed with a move from Travis to Github +Action which allows to get faster tests on Windows, MacOS and Linux. We +also now report our coverage on +`Codecov.io <https://codecov.io/gh/PythonOT/POT>`__ and we have a +reasonable 92% coverage. We also now generate wheels for a number of OS +and Python versions at each merge in the master branch. They are +available as outputs of this +`action <https://github.com/PythonOT/POT/actions?query=workflow%3A%22Build+dist+and+wheels%22>`__. +This will allow simpler multi-platform releases from now on. + +In terms of new features we now have `OTDA Classes for unbalanced +OT <https://pythonot.github.io/gen_modules/ot.da.html#ot.da.UnbalancedSinkhornTransport>`__, +a new Domain adaptation class form `multi domain problems +(JCPOT) <auto_examples/domain-adaptation/plot_otda_jcpot.html#sphx-glr-auto-examples-domain-adaptation-plot-otda-jcpot-py>`__, +and several solvers to solve the `Partial Optimal +Transport <auto_examples/unbalanced-partial/plot_partial_wass_and_gromov.html#sphx-glr-auto-examples-unbalanced-partial-plot-partial-wass-and-gromov-py>`__ +problems. + +This release is also the moment to thank all the POT contributors (old +and new) for helping making POT such a nice toolbox. A lot of changes +(also in the API) are comming for the next versions. + +Features +^^^^^^^^ + +- New documentation on https://PythonOT.github.io/ (PR #160, PR #143, + PR #144) +- Documentation build on CircleCI with sphinx-gallery (PR #145,PR #146, + #155) +- Run sphinx gallery in CI (PR #146) +- Remove notebooks from repo because available in doc (PR #156) +- Build wheels in CI (#157) +- Move from travis to GitHub Action for Windows, MacOS and Linux (PR + #148, PR #150) +- Partial Optimal Transport (PR#141 and PR #142) +- Laplace regularized OTDA (PR #140) +- Multi source DA with target shift (PR #137) +- Screenkhorn algorithm (PR #121) + +Closed issues +^^^^^^^^^^^^^ + +- Bug in Unbalanced OT example (Issue #127) +- Clean Cython output when calling setup.py clean (Issue #122) +- Various Macosx compilation problems (Issue #113, Issue #118, PR#130) +- EMD dimension mismatch (Issue #114, Fixed in PR #116) +- 2D barycenter bug for non square images (Issue #124, fixed in PR + #132) +- Bad value in EMD 1D (Issue #138, fixed in PR #139) +- Log bugs for Gromov-Wassertein solver (Issue #107, fixed in PR #108) +- Weight issues in barycenter function (PR #106) + +0.6.0 +----- + +*July 2019* + +This is the first official stable release of POT and this means a jump +to 0.6! The library has been used in the wild for a while now and we +have reached a state where a lot of fundamental OT solvers are available +and tested. It has been quite stable in the last months but kept the +beta flag in its Pypi classifiers until now. + +Note that this release will be the last one supporting officially Python +2.7 (See https://python3statement.org/ for more reasons). For next +release we will keep the travis tests for Python 2 but will make them +non necessary for merge in 2020. + +The features are never complete in a toolbox designed for solving +mathematical problems and research but with the new contributions we now +implement algorithms and solvers from 24 scientific papers (listed in +the README.md file). New features include a direct implementation of the +`empirical Sinkhorn +divergence <all.html#ot.bregman.empirical_sinkhorn_divergence>`__ +, a new efficient (Cython implementation) solver for `EMD in +1D <all.html#ot.lp.emd_1d>`__ and +corresponding `Wasserstein +1D <all.html#ot.lp.wasserstein_1d>`__. +We now also have implementations for `Unbalanced +OT <auto_examples/plot_UOT_1D.html>`__ +and a solver for `Unbalanced OT +barycenters <auto_examples/plot_UOT_barycenter_1D.html>`__. +A new variant of Gromov-Wasserstein divergence called `Fused +Gromov-Wasserstein <all.html?highlight=fused_#ot.gromov.fused_gromov_wasserstein>`__ +has been also contributed with exemples of use on `structured +data <auto_examples/plot_fgw.html>`__ +and computing `barycenters of labeld +graphs <auto_examples/plot_barycenter_fgw.html>`__. + +A lot of work has been done on the documentation with several new +examples corresponding to the new features and a lot of corrections for +the docstrings. But the most visible change is a new `quick start +guide <quickstart.html>`__ for POT +that gives several pointers about which function or classes allow to +solve which specific OT problem. When possible a link is provided to +relevant examples. + +We will also provide with this release some pre-compiled Python wheels +for Linux 64bit on github and pip. This will simplify the install +process that before required a C compiler and numpy/cython already +installed. + +Finally we would like to acknowledge and thank the numerous contributors +of POT that has helped in the past build the foundation and are still +contributing to bring new features and solvers to the library. + +Features +^^^^^^^^ + +- Add compiled manylinux 64bits wheels to pip releases (PR #91) +- Add quick start guide (PR #88) +- Make doctest work on travis (PR #90) +- Update documentation (PR #79, PR #84) +- Solver for EMD in 1D (PR #89) +- Solvers for regularized unbalanced OT (PR #87, PR#99) +- Solver for Fused Gromov-Wasserstein (PR #86) +- Add empirical Sinkhorn and empirical Sinkhorn divergences (PR #80) + +Closed issues +^^^^^^^^^^^^^ + +- Issue #59 fail when using "pip install POT" (new details in doc+ + hopefully wheels) +- Issue #85 Cannot run gpu modules +- Issue #75 Greenkhorn do not return log (solved in PR #76) +- Issue #82 Gromov-Wasserstein fails when the cost matrices are + slightly different +- Issue #72 Macosx build problem + +0.5.0 +----- + +*Sep 2018* + +POT is 2 years old! This release brings numerous new features to the +toolbox as listed below but also several bug correction. + +| Among the new features, we can highlight a `non-regularized + Gromov-Wasserstein + solver <auto_examples/plot_gromov.html>`__, + a new `greedy variant of + sinkhorn <all.html#ot.bregman.greenkhorn>`__, +| `non-regularized <all.html#ot.lp.barycenter>`__, + `convolutional + (2D) <auto_examples/plot_convolutional_barycenter.html>`__ + and `free + support <auto_examples/plot_free_support_barycenter.html>`__ + Wasserstein barycenters and + `smooth <https://github.com/rflamary/POT/blob/prV0.5/notebooks/plot_OT_1D_smooth.html>`__ + and + `stochastic <all.html#ot.stochastic.sgd_entropic_regularization>`__ + implementation of entropic OT. + +POT 0.5 also comes with a rewriting of ot.gpu using the cupy framework +instead of the unmaintained cudamat. Note that while we tried to keed +changes to the minimum, the OTDA classes were deprecated. If you are +happy with the cudamat implementation, we recommend you stay with stable +release 0.4 for now. + +The code quality has also improved with 92% code coverage in tests that +is now printed to the log in the Travis builds. The documentation has +also been greatly improved with new modules and examples/notebooks. + +This new release is so full of new stuff and corrections thanks to the +old and new POT contributors (you can see the list in the +`readme <https://github.com/rflamary/POT/blob/master/README.md>`__). + +Features +^^^^^^^^ + +- Add non regularized Gromov-Wasserstein solver (PR #41) +- Linear OT mapping between empirical distributions and 90% test + coverage (PR #42) +- Add log parameter in class EMDTransport and SinkhornLpL1Transport (PR + #44) +- Add Markdown format for Pipy (PR #45) +- Test for Python 3.5 and 3.6 on Travis (PR #46) +- Non regularized Wasserstein barycenter with scipy linear solver + and/or cvxopt (PR #47) +- Rename dataset functions to be more sklearn compliant (PR #49) +- Smooth and sparse Optimal transport implementation with entropic and + quadratic regularization (PR #50) +- Stochastic OT in the dual and semi-dual (PR #52 and PR #62) +- Free support barycenters (PR #56) +- Speed-up Sinkhorn function (PR #57 and PR #58) +- Add convolutional Wassersein barycenters for 2D images (PR #64) +- Add Greedy Sinkhorn variant (Greenkhorn) (PR #66) +- Big ot.gpu update with cupy implementation (instead of un-maintained + cudamat) (PR #67) + +Deprecation +^^^^^^^^^^^ + +Deprecated OTDA Classes were removed from ot.da and ot.gpu for version +0.5 (PR #48 and PR #67). The deprecation message has been for a year +here since 0.4 and it is time to pull the plug. + +Closed issues +^^^^^^^^^^^^^ + +- Issue #35 : remove import plot from ot/\ **init**.py (See PR #41) +- Issue #43 : Unusable parameter log for EMDTransport (See PR #44) +- Issue #55 : UnicodeDecodeError: 'ascii' while installing with pip + +0.4 +--- + +*15 Sep 2017* + +This release contains a lot of contribution from new contributors. + +Features +^^^^^^^^ + +- Automatic notebooks and doc update (PR #27) +- Add gromov Wasserstein solver and Gromov Barycenters (PR #23) +- emd and emd2 can now return dual variables and have max\_iter (PR #29 + and PR #25) +- New domain adaptation classes compatible with scikit-learn (PR #22) +- Proper tests with pytest on travis (PR #19) +- PEP 8 tests (PR #13) + +Closed issues +^^^^^^^^^^^^^ + +- emd convergence problem du to fixed max iterations (#24) +- Semi supervised DA error (#26) + +0.3.1 +----- + +*11 Jul 2017* + +- Correct bug in emd on windows + +0.3 +--- + +*7 Jul 2017* + +- emd\* and sinkhorn\* are now performed in parallel for multiple + target distributions +- emd and sinkhorn are for OT matrix computation +- emd2 and sinkhorn2 are for OT loss computation +- new notebooks for emd computation and Wasserstein Discriminant + Analysis +- relocate notebooks +- update documentation +- clean\_zeros(a,b,M) for removimg zeros in sparse distributions +- GPU implementations for sinkhorn and group lasso regularization + +V0.2 +---- + +*7 Apr 2017* + +- New dimensionality reduction method (WDA) +- Efficient method emd2 returns only tarnsport (in paralell if several + histograms given) + +0.1.11 +------ + +*5 Jan 2017* + +- Add sphinx gallery for better documentation +- Small efficiency tweak in sinkhorn +- Add simple tic() toc() functions for timing + +0.1.10 +------ + +*7 Nov 2016* \* numerical stabilization for sinkhorn (log domain and +epsilon scaling) + +0.1.9 +----- + +*4 Nov 2016* + +- Update classes and examples for domain adaptation +- Joint OT matrix and mapping estimation + +0.1.7 +----- + +*31 Oct 2016* + +- Original Domain adaptation classes + +0.1.3 +----- + +- pipy works + +First pre-release +----------------- + +*28 Oct 2016* + +It provides the following solvers: \* OT solver for the linear program/ +Earth Movers Distance. \* Entropic regularization OT solver with +Sinkhorn Knopp Algorithm. \* Bregman projections for Wasserstein +barycenter [3] and unmixing. \* Optimal transport for domain adaptation +with group lasso regularization \* Conditional gradient and Generalized +conditional gradient for regularized OT. + +Some demonstrations (both in Python and Jupyter Notebook format) are +available in the examples folder. |
