From e65606ae498bd611f6a994868c2a66dfbea403cd Mon Sep 17 00:00:00 2001 From: Rémi Flamary Date: Mon, 20 Apr 2020 15:19:09 +0200 Subject: big update examples --- .../plot_barycenter_lp_vs_entropic.rst | 303 +++++++++++++-------- 1 file changed, 194 insertions(+), 109 deletions(-) (limited to 'docs/source/auto_examples/plot_barycenter_lp_vs_entropic.rst') diff --git a/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.rst b/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.rst index bd1c710..5e83fbf 100644 --- a/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.rst +++ b/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.rst @@ -1,6 +1,12 @@ +.. only:: html + + .. note:: + :class: sphx-glr-download-link-note + Click :ref:`here ` to download the full example code + .. rst-class:: sphx-glr-example-title -.. _sphx_glr_auto_examples_plot_barycenter_lp_vs_entropic.py: + .. _sphx_glr_auto_examples_plot_barycenter_lp_vs_entropic.py: ================================================================================= @@ -20,8 +26,7 @@ SIAM Journal on Scientific Computing, 37(2), A1111-A1138. - -.. code-block:: python +.. code-block:: default # Author: Remi Flamary @@ -43,15 +48,13 @@ SIAM Journal on Scientific Computing, 37(2), A1111-A1138. + Gaussian Data ------------- +.. code-block:: default -.. code-block:: python - - - #%% parameters problems = [] @@ -74,7 +77,16 @@ Gaussian Data M /= M.max() - #%% plot the distributions + + + + + + + + +.. code-block:: default + pl.figure(1, figsize=(6.4, 3)) for i in range(n_distributions): @@ -82,7 +94,19 @@ Gaussian Data pl.title('Distributions') pl.tight_layout() - #%% barycenter computation + + + +.. 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]) @@ -121,62 +145,55 @@ Gaussian Data -.. 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 +.. 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:: + Out: + + .. code-block:: none - Elapsed time : 0.010712385177612305 s + 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 0.006776453137633 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 + 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. - Elapsed time : 2.883899211883545 s + Current function value: 0.041058 + Iterations: 22 + Elapsed time : 2.149055242538452 s -Dirac Data ----------- +Stair Data +---------- -.. code-block:: python +.. code-block:: default - #%% parameters a1 = 1.0 * (x > 10) * (x < 50) a2 = 1.0 * (x > 60) * (x < 80) @@ -193,7 +210,16 @@ Dirac Data M /= M.max() - #%% plot the distributions + + + + + + + + +.. code-block:: default + pl.figure(1, figsize=(6.4, 3)) for i in range(n_distributions): @@ -202,7 +228,19 @@ Dirac Data pl.tight_layout() - #%% barycenter computation + + + +.. 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]) @@ -239,7 +277,50 @@ Dirac Data pl.title('Barycenters') pl.tight_layout() - #%% parameters + + + + +.. 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) @@ -262,7 +343,16 @@ Dirac Data M /= M.max() - #%% plot the distributions + + + + + + + + +.. code-block:: default + pl.figure(1, figsize=(6.4, 3)) for i in range(n_distributions): @@ -271,7 +361,19 @@ Dirac Data pl.tight_layout() - #%% barycenter computation + + + +.. 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]) @@ -312,70 +414,45 @@ Dirac Data -.. 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 +.. 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:: + 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 + .. 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 - 0.006774675520727 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 + 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. - Elapsed time : 2.690450668334961 s + Current function value: 0.093103 + Iterations: 11 + Elapsed time : 2.1853578090667725 s -Final figure ------------- +Final figure +------------ -.. code-block:: python +.. code-block:: default - #%% plot nbm = len(problems) nbm2 = (nbm // 2) @@ -414,28 +491,36 @@ Final figure -.. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_006.png - :align: center +.. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_007.png + :class: sphx-glr-single-img + + -**Total running time of the script:** ( 0 minutes 8.892 seconds) +.. 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 + .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_barycenter_lp_vs_entropic.py ` - .. container:: sphx-glr-download + .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_barycenter_lp_vs_entropic.ipynb ` @@ -444,4 +529,4 @@ Final figure .. rst-class:: sphx-glr-signature - `Gallery generated by Sphinx-Gallery `_ + `Gallery generated by Sphinx-Gallery `_ -- cgit v1.2.3