diff options
| author | Rémi Flamary <remi.flamary@gmail.com> | 2020-04-21 17:48:37 +0200 |
|---|---|---|
| committer | GitHub <noreply@github.com> | 2020-04-21 17:48:37 +0200 |
| commit | a303cc6b483d3cd958c399621e22e40574bcbbc8 (patch) | |
| tree | dea049cb692020462da8f00d9e117f93b839bb55 /docs/source/auto_examples/plot_barycenter_lp_vs_entropic.rst | |
| parent | 0b2d808aaebb1cab60a272ea7901d5f77df43a9f (diff) | |
[MRG] Actually run sphinx-gallery (#146)
* generate gallery
* remove mock
* add sklearn to requirermnt?txt for example
* remove latex from fgw example
* add networks for graph example
* remove all
* add requirement.txt rtd
* rtd debug
* update readme
* eradthedoc with redirection
* add conf rtd
Diffstat (limited to 'docs/source/auto_examples/plot_barycenter_lp_vs_entropic.rst')
| -rw-r--r-- | docs/source/auto_examples/plot_barycenter_lp_vs_entropic.rst | 532 |
1 files changed, 0 insertions, 532 deletions
diff --git a/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.rst b/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.rst deleted file mode 100644 index 5e83fbf..0000000 --- a/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.rst +++ /dev/null @@ -1,532 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_barycenter_lp_vs_entropic.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_barycenter_lp_vs_entropic.py: - - -================================================================================= -1D Wasserstein barycenter comparison between exact LP and entropic regularization -================================================================================= - -This example illustrates the computation of regularized Wasserstein Barycenter -as proposed in [3] and exact LP barycenters using standard LP solver. - -It reproduces approximately Figure 3.1 and 3.2 from the following paper: -Cuturi, M., & Peyré, G. (2016). A smoothed dual approach for variational -Wasserstein problems. SIAM Journal on Imaging Sciences, 9(1), 320-343. - -[3] Benamou, J. D., Carlier, G., Cuturi, M., Nenna, L., & Peyré, G. (2015). -Iterative Bregman projections for regularized transportation problems -SIAM Journal on Scientific Computing, 37(2), A1111-A1138. - - - -.. code-block:: default - - - # Author: Remi Flamary <remi.flamary@unice.fr> - # - # License: MIT License - - import numpy as np - import matplotlib.pylab as pl - import ot - # necessary for 3d plot even if not used - from mpl_toolkits.mplot3d import Axes3D # noqa - from matplotlib.collections import PolyCollection # noqa - - #import ot.lp.cvx as cvx - - - - - - - - -Gaussian Data -------------- - - -.. code-block:: default - - - problems = [] - - n = 100 # nb bins - - # bin positions - x = np.arange(n, dtype=np.float64) - - # Gaussian distributions - # Gaussian distributions - a1 = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std - a2 = ot.datasets.make_1D_gauss(n, m=60, s=8) - - # creating matrix A containing all distributions - A = np.vstack((a1, a2)).T - n_distributions = A.shape[1] - - # loss matrix + normalization - M = ot.utils.dist0(n) - M /= M.max() - - - - - - - - - - -.. code-block:: default - - - pl.figure(1, figsize=(6.4, 3)) - for i in range(n_distributions): - pl.plot(x, A[:, i]) - pl.title('Distributions') - pl.tight_layout() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_001.png - :class: sphx-glr-single-img - - - - - - -.. code-block:: default - - - alpha = 0.5 # 0<=alpha<=1 - weights = np.array([1 - alpha, alpha]) - - # l2bary - bary_l2 = A.dot(weights) - - # wasserstein - reg = 1e-3 - ot.tic() - bary_wass = ot.bregman.barycenter(A, M, reg, weights) - ot.toc() - - - ot.tic() - bary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True) - ot.toc() - - pl.figure(2) - pl.clf() - pl.subplot(2, 1, 1) - for i in range(n_distributions): - pl.plot(x, A[:, i]) - pl.title('Distributions') - - pl.subplot(2, 1, 2) - pl.plot(x, bary_l2, 'r', label='l2') - pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') - pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') - pl.legend() - pl.title('Barycenters') - pl.tight_layout() - - problems.append([A, [bary_l2, bary_wass, bary_wass2]]) - - - - -.. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_002.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - Elapsed time : 0.0049059391021728516 s - Primal Feasibility Dual Feasibility Duality Gap Step Path Parameter Objective - 1.0 1.0 1.0 - 1.0 1700.336700337 - 0.006776453137632 0.006776453137632 0.006776453137632 0.9932238647293 0.006776453137632 125.6700527543 - 0.004018712867873 0.004018712867873 0.004018712867873 0.4301142633001 0.004018712867873 12.26594150092 - 0.001172775061627 0.001172775061627 0.001172775061627 0.7599932455027 0.001172775061627 0.3378536968898 - 0.0004375137005386 0.0004375137005386 0.0004375137005386 0.6422331807989 0.0004375137005386 0.1468420566359 - 0.0002326690467339 0.0002326690467339 0.0002326690467339 0.5016999460898 0.0002326690467339 0.09381703231428 - 7.430121674299e-05 7.4301216743e-05 7.430121674299e-05 0.7035962305811 7.430121674299e-05 0.05777870257169 - 5.321227838943e-05 5.321227838945e-05 5.321227838944e-05 0.3087841864307 5.321227838944e-05 0.05266249477219 - 1.990900379216e-05 1.99090037922e-05 1.990900379216e-05 0.6520472013271 1.990900379216e-05 0.04526054405523 - 6.305442046834e-06 6.305442046856e-06 6.305442046837e-06 0.7073953304085 6.305442046837e-06 0.04237597591384 - 2.290148391591e-06 2.290148391631e-06 2.290148391602e-06 0.6941812711476 2.29014839161e-06 0.04152284932101 - 1.182864875578e-06 1.182864875548e-06 1.182864875555e-06 0.5084552046229 1.182864875567e-06 0.04129461872829 - 3.626786386894e-07 3.626786386985e-07 3.626786386845e-07 0.7101651569095 3.626786385995e-07 0.0411303244893 - 1.539754244475e-07 1.539754247164e-07 1.539754247197e-07 0.6279322077522 1.539754251915e-07 0.04108867636377 - 5.193221608537e-08 5.19322169648e-08 5.193221696942e-08 0.6843453280956 5.193221892276e-08 0.04106859618454 - 1.888205219929e-08 1.88820500654e-08 1.888205006369e-08 0.6673443828803 1.888205852187e-08 0.04106214175236 - 5.676837529301e-09 5.676842740457e-09 5.676842761502e-09 0.7281712198286 5.676877044229e-09 0.04105958648535 - 3.501170987746e-09 3.501167688027e-09 3.501167721804e-09 0.4140142115019 3.501183058995e-09 0.04105916265728 - 1.110582426269e-09 1.110580273241e-09 1.110580239523e-09 0.6999003212726 1.110624310022e-09 0.04105870073273 - 5.768753963318e-10 5.769422203363e-10 5.769421938248e-10 0.5002521235315 5.767522037401e-10 0.04105859764872 - 1.534102102874e-10 1.535920569433e-10 1.535921107494e-10 0.7516900610544 1.535251083958e-10 0.04105851678411 - 6.717475002202e-11 6.735435784522e-11 6.735430717133e-11 0.5944268235824 6.732253215483e-11 0.04105850033323 - 1.751321118837e-11 1.74043080851e-11 1.740429001123e-11 0.7566075167358 1.736956306927e-11 0.0410584908946 - Optimization terminated successfully. - Current function value: 0.041058 - Iterations: 22 - Elapsed time : 2.149055242538452 s - - - - -Stair Data ----------- - - -.. code-block:: default - - - a1 = 1.0 * (x > 10) * (x < 50) - a2 = 1.0 * (x > 60) * (x < 80) - - a1 /= a1.sum() - a2 /= a2.sum() - - # creating matrix A containing all distributions - A = np.vstack((a1, a2)).T - n_distributions = A.shape[1] - - # loss matrix + normalization - M = ot.utils.dist0(n) - M /= M.max() - - - - - - - - - - -.. code-block:: default - - - pl.figure(1, figsize=(6.4, 3)) - for i in range(n_distributions): - pl.plot(x, A[:, i]) - pl.title('Distributions') - pl.tight_layout() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_003.png - :class: sphx-glr-single-img - - - - - - -.. code-block:: default - - - alpha = 0.5 # 0<=alpha<=1 - weights = np.array([1 - alpha, alpha]) - - # l2bary - bary_l2 = A.dot(weights) - - # wasserstein - reg = 1e-3 - ot.tic() - bary_wass = ot.bregman.barycenter(A, M, reg, weights) - ot.toc() - - - ot.tic() - bary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True) - ot.toc() - - - problems.append([A, [bary_l2, bary_wass, bary_wass2]]) - - pl.figure(2) - pl.clf() - pl.subplot(2, 1, 1) - for i in range(n_distributions): - pl.plot(x, A[:, i]) - pl.title('Distributions') - - pl.subplot(2, 1, 2) - pl.plot(x, bary_l2, 'r', label='l2') - pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') - pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') - pl.legend() - pl.title('Barycenters') - pl.tight_layout() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_004.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - Elapsed time : 0.008316993713378906 s - Primal Feasibility Dual Feasibility Duality Gap Step Path Parameter Objective - 1.0 1.0 1.0 - 1.0 1700.336700337 - 0.006776466288938 0.006776466288938 0.006776466288938 0.9932238515788 0.006776466288938 125.66492558 - 0.004036918865472 0.004036918865472 0.004036918865472 0.4272973099325 0.004036918865472 12.347161701 - 0.001219232687076 0.001219232687076 0.001219232687076 0.7496986855957 0.001219232687076 0.3243835647418 - 0.0003837422984467 0.0003837422984467 0.0003837422984467 0.6926882608271 0.0003837422984467 0.1361719397498 - 0.0001070128410194 0.0001070128410194 0.0001070128410194 0.7643889137854 0.0001070128410194 0.07581952832542 - 0.0001001275033713 0.0001001275033714 0.0001001275033713 0.07058704838615 0.0001001275033713 0.07347394936346 - 4.550897507807e-05 4.550897507807e-05 4.550897507807e-05 0.576117248486 4.550897507807e-05 0.05555077655034 - 8.557124125834e-06 8.557124125853e-06 8.557124125835e-06 0.853592544106 8.557124125835e-06 0.0443981466023 - 3.611995628666e-06 3.611995628643e-06 3.611995628672e-06 0.6002277331398 3.611995628673e-06 0.0428300776216 - 7.590393750111e-07 7.590393750273e-07 7.590393750129e-07 0.8221486533655 7.590393750133e-07 0.04192322976247 - 8.299929287077e-08 8.299929283415e-08 8.299929287126e-08 0.901746793884 8.299929287181e-08 0.04170825633295 - 3.117560207452e-10 3.117560192413e-10 3.117560199213e-10 0.9970399692253 3.117560200234e-10 0.04168179329766 - 1.559774508975e-14 1.559825507727e-14 1.559755309294e-14 0.9999499686993 1.559748033629e-14 0.04168169240444 - Optimization terminated successfully. - Current function value: 0.041682 - Iterations: 13 - Elapsed time : 2.0333712100982666 s - - - - -Dirac Data ----------- - - -.. code-block:: default - - - a1 = np.zeros(n) - a2 = np.zeros(n) - - a1[10] = .25 - a1[20] = .5 - a1[30] = .25 - a2[80] = 1 - - - a1 /= a1.sum() - a2 /= a2.sum() - - # creating matrix A containing all distributions - A = np.vstack((a1, a2)).T - n_distributions = A.shape[1] - - # loss matrix + normalization - M = ot.utils.dist0(n) - M /= M.max() - - - - - - - - - - -.. code-block:: default - - - pl.figure(1, figsize=(6.4, 3)) - for i in range(n_distributions): - pl.plot(x, A[:, i]) - pl.title('Distributions') - pl.tight_layout() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_005.png - :class: sphx-glr-single-img - - - - - - -.. code-block:: default - - - alpha = 0.5 # 0<=alpha<=1 - weights = np.array([1 - alpha, alpha]) - - # l2bary - bary_l2 = A.dot(weights) - - # wasserstein - reg = 1e-3 - ot.tic() - bary_wass = ot.bregman.barycenter(A, M, reg, weights) - ot.toc() - - - ot.tic() - bary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True) - ot.toc() - - - problems.append([A, [bary_l2, bary_wass, bary_wass2]]) - - pl.figure(2) - pl.clf() - pl.subplot(2, 1, 1) - for i in range(n_distributions): - pl.plot(x, A[:, i]) - pl.title('Distributions') - - pl.subplot(2, 1, 2) - pl.plot(x, bary_l2, 'r', label='l2') - pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') - pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') - pl.legend() - pl.title('Barycenters') - pl.tight_layout() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_006.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - Elapsed time : 0.001787424087524414 s - Primal Feasibility Dual Feasibility Duality Gap Step Path Parameter Objective - 1.0 1.0 1.0 - 1.0 1700.336700337 - 0.00677467552072 0.006774675520719 0.006774675520719 0.9932256422636 0.006774675520719 125.6956034741 - 0.002048208707556 0.002048208707555 0.002048208707555 0.734309536815 0.002048208707555 5.213991622102 - 0.0002697365474791 0.0002697365474791 0.0002697365474791 0.8839403501183 0.0002697365474791 0.5059383903908 - 6.832109993919e-05 6.832109993918e-05 6.832109993918e-05 0.7601171075982 6.832109993918e-05 0.2339657807271 - 2.437682932221e-05 2.437682932221e-05 2.437682932221e-05 0.6663448297463 2.437682932221e-05 0.1471256246325 - 1.134983216308e-05 1.134983216308e-05 1.134983216308e-05 0.5553643816417 1.134983216308e-05 0.1181584941171 - 3.342312725863e-06 3.34231272585e-06 3.342312725863e-06 0.7238133571629 3.342312725863e-06 0.1006387519746 - 7.078561231536e-07 7.078561231537e-07 7.078561231535e-07 0.803314255252 7.078561231535e-07 0.09474734646268 - 1.966870949422e-07 1.966870952674e-07 1.966870952717e-07 0.7525479180433 1.966870953014e-07 0.09354342735758 - 4.199895266495e-10 4.199895367352e-10 4.19989526535e-10 0.9984019849265 4.199895265747e-10 0.09310367785861 - 2.101053559204e-14 2.100331212975e-14 2.101054034304e-14 0.9999499736903 2.101053604307e-14 0.09310274466458 - Optimization terminated successfully. - Current function value: 0.093103 - Iterations: 11 - Elapsed time : 2.1853578090667725 s - - - - -Final figure ------------- - - - -.. code-block:: default - - - nbm = len(problems) - nbm2 = (nbm // 2) - - - pl.figure(2, (20, 6)) - pl.clf() - - for i in range(nbm): - - A = problems[i][0] - bary_l2 = problems[i][1][0] - bary_wass = problems[i][1][1] - bary_wass2 = problems[i][1][2] - - pl.subplot(2, nbm, 1 + i) - for j in range(n_distributions): - pl.plot(x, A[:, j]) - if i == nbm2: - pl.title('Distributions') - pl.xticks(()) - pl.yticks(()) - - pl.subplot(2, nbm, 1 + i + nbm) - - pl.plot(x, bary_l2, 'r', label='L2 (Euclidean)') - pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') - pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') - if i == nbm - 1: - pl.legend() - if i == nbm2: - pl.title('Barycenters') - - pl.xticks(()) - pl.yticks(()) - - - -.. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_007.png - :class: sphx-glr-single-img - - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 7.697 seconds) - - -.. _sphx_glr_download_auto_examples_plot_barycenter_lp_vs_entropic.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_barycenter_lp_vs_entropic.py <plot_barycenter_lp_vs_entropic.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: plot_barycenter_lp_vs_entropic.ipynb <plot_barycenter_lp_vs_entropic.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ |