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| author | Rémi Flamary <remi.flamary@gmail.com> | 2018-05-30 10:34:48 +0200 |
|---|---|---|
| committer | Rémi Flamary <remi.flamary@gmail.com> | 2018-05-30 10:34:48 +0200 |
| commit | 2b375f263ef88100b0321c8ef1b3605dfbb95b3d (patch) | |
| tree | a2ae2e21bf7fac9fe2fa368782d7df5ea9974342 /docs/source/auto_examples | |
| parent | b5e45bbc83fd8cd8c1634a78f2f983d1cf28af73 (diff) | |
update notebooks
Diffstat (limited to 'docs/source/auto_examples')
15 files changed, 228 insertions, 138 deletions
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(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\n\n" + "\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" ] }, { @@ -26,7 +26,61 @@ }, "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\n\n#\n# Generate data\n# -------------\n\n#%% 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 data\n# ---------\n\n#%% plot the distributions\n\npl.figure(1, figsize=(6.4, 3))\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\npl.tight_layout()\n\n#\n# Barycenter computation\n# ----------------------\n\n#%% barycenter computation\n\nalpha = 0.5 # 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]])\n\n#%% 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# ----------------------\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# ----------------------\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\n#\n# Final figure\n# ------------\n#\n\n#%% 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(())" + "# 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(())" ] } ], diff --git a/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.py b/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.py index 2255107..b82765e 100644 --- a/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.py +++ b/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.py @@ -15,8 +15,6 @@ Wasserstein problems. SIAM Journal on Imaging Sciences, 9(1), 320-343. Iterative Bregman projections for regularized transportation problems SIAM Journal on Scientific Computing, 37(2), A1111-A1138. - - """ # Author: Remi Flamary <remi.flamary@unice.fr> @@ -32,8 +30,8 @@ from matplotlib.collections import PolyCollection # noqa #import ot.lp.cvx as cvx -# -# Generate data +############################################################################## +# Gaussian Data # ------------- #%% parameters @@ -58,9 +56,6 @@ n_distributions = A.shape[1] M = ot.utils.dist0(n) M /= M.max() -# -# Plot data -# --------- #%% plot the distributions @@ -70,10 +65,6 @@ for i in range(n_distributions): pl.title('Distributions') pl.tight_layout() -# -# Barycenter computation -# ---------------------- - #%% barycenter computation alpha = 0.5 # 0<=alpha<=1 @@ -110,6 +101,10 @@ pl.tight_layout() problems.append([A, [bary_l2, bary_wass, bary_wass2]]) +############################################################################## +# Dirac Data +# ---------- + #%% parameters a1 = 1.0 * (x > 10) * (x < 50) @@ -135,9 +130,6 @@ for i in range(n_distributions): pl.title('Distributions') pl.tight_layout() -# -# Barycenter computation -# ---------------------- #%% barycenter computation @@ -207,9 +199,6 @@ for i in range(n_distributions): pl.title('Distributions') pl.tight_layout() -# -# Barycenter computation -# ---------------------- #%% barycenter computation @@ -249,7 +238,7 @@ pl.title('Barycenters') pl.tight_layout() -# +############################################################################## # Final figure # ------------ # 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 e8c15df..bd1c710 100644 --- a/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.rst +++ b/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.rst @@ -21,95 +21,6 @@ SIAM Journal on Scientific Computing, 37(2), A1111-A1138. - - - -.. 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 : 0.010588884353637695 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 : 2.8747198581695557 s - Elapsed time : 0.014937639236450195 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 : 2.6253304481506348 s - Elapsed time : 0.002875089645385742 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 : 3.587958335876465 s - - - - -| - - .. code-block:: python @@ -126,9 +37,19 @@ SIAM Journal on Scientific Computing, 37(2), A1111-A1138. #import ot.lp.cvx as cvx - # - # Generate data - # ------------- + + + + + + +Gaussian Data +------------- + + + +.. code-block:: python + #%% parameters @@ -152,9 +73,6 @@ SIAM Journal on Scientific Computing, 37(2), A1111-A1138. M = ot.utils.dist0(n) M /= M.max() - # - # Plot data - # --------- #%% plot the distributions @@ -164,10 +82,6 @@ SIAM Journal on Scientific Computing, 37(2), A1111-A1138. pl.title('Distributions') pl.tight_layout() - # - # Barycenter computation - # ---------------------- - #%% barycenter computation alpha = 0.5 # 0<=alpha<=1 @@ -204,6 +118,64 @@ SIAM Journal on Scientific Computing, 37(2), A1111-A1138. 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) @@ -229,9 +201,6 @@ SIAM Journal on Scientific Computing, 37(2), A1111-A1138. pl.title('Distributions') pl.tight_layout() - # - # Barycenter computation - # ---------------------- #%% barycenter computation @@ -301,9 +270,6 @@ SIAM Journal on Scientific Computing, 37(2), A1111-A1138. pl.title('Distributions') pl.tight_layout() - # - # Barycenter computation - # ---------------------- #%% barycenter computation @@ -343,10 +309,71 @@ SIAM Journal on Scientific Computing, 37(2), A1111-A1138. pl.tight_layout() - # - # Final figure - # ------------ - # + + + +.. 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 @@ -385,7 +412,15 @@ SIAM Journal on Scientific Computing, 37(2), A1111-A1138. pl.xticks(()) pl.yticks(()) -**Total running time of the script:** ( 0 minutes 9.816 seconds) + + +.. 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) diff --git a/docs/source/auto_examples/plot_otda_linear_mapping.ipynb b/docs/source/auto_examples/plot_otda_linear_mapping.ipynb index e43bee7..027b6cb 100644 --- a/docs/source/auto_examples/plot_otda_linear_mapping.ipynb +++ b/docs/source/auto_examples/plot_otda_linear_mapping.ipynb @@ -15,7 +15,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "\nCreated on Tue Mar 20 14:31:15 2018\n\n@author: rflamary\n\n" + "\n# Linear OT mapping estimation\n\n\n\n\n" ] }, { @@ -26,7 +26,7 @@ }, "outputs": [], "source": [ - "import numpy as np\nimport pylab as pl\nimport ot" + "# Author: Remi Flamary <remi.flamary@unice.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport pylab as pl\nimport ot" ] }, { diff --git a/docs/source/auto_examples/plot_otda_linear_mapping.py b/docs/source/auto_examples/plot_otda_linear_mapping.py index 7a3b761..c65bd4f 100644 --- a/docs/source/auto_examples/plot_otda_linear_mapping.py +++ b/docs/source/auto_examples/plot_otda_linear_mapping.py @@ -1,11 +1,17 @@ #!/usr/bin/env python3 # -*- coding: utf-8 -*- """ -Created on Tue Mar 20 14:31:15 2018 +============================ +Linear OT mapping estimation +============================ + -@author: rflamary """ +# Author: Remi Flamary <remi.flamary@unice.fr> +# +# License: MIT License + import numpy as np import pylab as pl import ot diff --git a/docs/source/auto_examples/plot_otda_linear_mapping.rst b/docs/source/auto_examples/plot_otda_linear_mapping.rst index 1321732..8e2e0cf 100644 --- a/docs/source/auto_examples/plot_otda_linear_mapping.rst +++ b/docs/source/auto_examples/plot_otda_linear_mapping.rst @@ -3,15 +3,21 @@ .. _sphx_glr_auto_examples_plot_otda_linear_mapping.py: -Created on Tue Mar 20 14:31:15 2018 +============================ +Linear OT mapping estimation +============================ + -@author: rflamary .. code-block:: python + # Author: Remi Flamary <remi.flamary@unice.fr> + # + # License: MIT License + import numpy as np import pylab as pl import ot @@ -227,7 +233,7 @@ Plot transformed images -**Total running time of the script:** ( 0 minutes 0.563 seconds) +**Total running time of the script:** ( 0 minutes 0.635 seconds) |
