diff options
| 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 | |
| parent | b5e45bbc83fd8cd8c1634a78f2f983d1cf28af73 (diff) | |
update notebooks
22 files changed, 414 insertions, 254 deletions
@@ -25,12 +25,23 @@ It provides the following solvers: Some demonstrations (both in Python and Jupyter Notebook format) are available in the examples folder. +#### 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: +``` +@article{flamary2017pot, + title={POT Python Optimal Transport library}, + author={Flamary, R{\'e}mi and Courty, Nicolas}, + year={2017} +} +``` + ## 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: - Numpy (>=1.11) -- Scipy (>=0.17) +- Scipy (>=1.0) - Cython (>=0.23) - Matplotlib (>=1.5) @@ -156,16 +167,7 @@ This toolbox benefit a lot from open source research and we would like to thank * [Nicolas Bonneel](http://liris.cnrs.fr/~nbonneel/) ( C++ code for EMD) * [Marco Cuturi](http://marcocuturi.net/) (Sinkhorn Knopp in Matlab/Cuda) -## 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: -``` -@article{flamary2017pot, - title={POT Python Optimal Transport library}, - author={Flamary, R{\'e}mi and Courty, Nicolas}, - year={2017} -} -``` ## Contributions and code of conduct Every contribution is welcome and should respect the [contribution guidelines](CONTRIBUTING.md). Each member of the project is expected to follow the [code of conduct](CODE_OF_CONDUCT.md). diff --git a/docs/cache_nbrun b/docs/cache_nbrun index 8e58a2e..318bcf4 100644 --- a/docs/cache_nbrun +++ b/docs/cache_nbrun @@ -1 +1 @@ -{"plot_otda_mapping_colors_images.ipynb": "4f0587a00a3c082799a75a0ed36e9ce1", "plot_optim_OTreg.ipynb": "481801bb0d133ef350a65179cf8f739a", "plot_barycenter_1D.ipynb": "6063193f9ac87517acced2625edb9a54", "plot_WDA.ipynb": "27f8de4c6d7db46497076523673eedfb", "plot_otda_linear_mapping.ipynb": "23d5203f707e0156f3cf8755d96f1dc1", "plot_OT_L1_vs_L2.ipynb": "5d565b8aaf03be4309eba731127851dc", "plot_otda_color_images.ipynb": "d047d635f4987c81072383241590e21f", "plot_otda_classes.ipynb": "39087b6e98217851575f2271c22853a4", "plot_otda_d2.ipynb": "e6feae588103f2a8fab942e5f4eff483", "plot_otda_mapping.ipynb": "2f1ebbdc0f855d9e2b7adf9edec24d25", "plot_gromov.ipynb": "24f2aea489714d34779521f46d5e2c47", "plot_compute_emd.ipynb": "f5cd71cad882ec157dc8222721e9820c", "plot_OT_1D.ipynb": "b5348bdc561c07ec168a1622e5af4b93", "plot_gromov_barycenter.ipynb": "953e5047b886ec69ec621ec52f5e21d1", "plot_otda_semi_supervised.ipynb": "f6dfb02ba2bbd939408ffcd22a3b007c", "plot_OT_2D_samples.ipynb": "07dbc14859fa019a966caa79fa0825bd", "plot_barycenter_lp_vs_entropic.ipynb": "9866e6f8d1dbfcd0f2ea514dc3a330fc"}
\ No newline at end of file +{"plot_otda_mapping_colors_images.ipynb": "4f0587a00a3c082799a75a0ed36e9ce1", "plot_optim_OTreg.ipynb": "481801bb0d133ef350a65179cf8f739a", "plot_otda_color_images.ipynb": "d047d635f4987c81072383241590e21f", "plot_WDA.ipynb": "27f8de4c6d7db46497076523673eedfb", "plot_otda_linear_mapping.ipynb": "a472c767abe82020e0a58125a528785c", "plot_OT_L1_vs_L2.ipynb": "5d565b8aaf03be4309eba731127851dc", "plot_barycenter_1D.ipynb": "6063193f9ac87517acced2625edb9a54", "plot_otda_classes.ipynb": "39087b6e98217851575f2271c22853a4", "plot_otda_d2.ipynb": "e6feae588103f2a8fab942e5f4eff483", "plot_otda_mapping.ipynb": "2f1ebbdc0f855d9e2b7adf9edec24d25", "plot_gromov.ipynb": "24f2aea489714d34779521f46d5e2c47", "plot_compute_emd.ipynb": "f5cd71cad882ec157dc8222721e9820c", "plot_OT_1D.ipynb": "b5348bdc561c07ec168a1622e5af4b93", "plot_gromov_barycenter.ipynb": "953e5047b886ec69ec621ec52f5e21d1", "plot_otda_semi_supervised.ipynb": "f6dfb02ba2bbd939408ffcd22a3b007c", "plot_OT_2D_samples.ipynb": "07dbc14859fa019a966caa79fa0825bd", "plot_barycenter_lp_vs_entropic.ipynb": "51833e8c76aaedeba9599ac7a30eb357"}
\ No newline at end of file diff --git a/docs/source/auto_examples/auto_examples_jupyter.zip b/docs/source/auto_examples/auto_examples_jupyter.zip Binary files differindex bba0bee..8102274 100644 --- a/docs/source/auto_examples/auto_examples_jupyter.zip +++ b/docs/source/auto_examples/auto_examples_jupyter.zip diff --git a/docs/source/auto_examples/auto_examples_python.zip b/docs/source/auto_examples/auto_examples_python.zip Binary files differindex 8d9edce..d685070 100644 --- a/docs/source/auto_examples/auto_examples_python.zip +++ b/docs/source/auto_examples/auto_examples_python.zip diff --git a/docs/source/auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_001.png b/docs/source/auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_001.png Binary files differindex 73d1a4f..3500812 100644 --- a/docs/source/auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_001.png +++ b/docs/source/auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_001.png diff --git a/docs/source/auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_002.png b/docs/source/auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_002.png Binary files differindex 88d8203..37fef68 100644 --- a/docs/source/auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_002.png +++ b/docs/source/auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_002.png diff --git a/docs/source/auto_examples/images/sphx_glr_plot_otda_linear_mapping_001.png b/docs/source/auto_examples/images/sphx_glr_plot_otda_linear_mapping_001.png Binary files differindex 2bf9514..88796df 100644 --- a/docs/source/auto_examples/images/sphx_glr_plot_otda_linear_mapping_001.png +++ b/docs/source/auto_examples/images/sphx_glr_plot_otda_linear_mapping_001.png diff --git a/docs/source/auto_examples/images/sphx_glr_plot_otda_linear_mapping_002.png b/docs/source/auto_examples/images/sphx_glr_plot_otda_linear_mapping_002.png Binary files differindex ab574fb..22b5d0c 100644 --- a/docs/source/auto_examples/images/sphx_glr_plot_otda_linear_mapping_002.png +++ b/docs/source/auto_examples/images/sphx_glr_plot_otda_linear_mapping_002.png diff --git a/docs/source/auto_examples/images/thumb/sphx_glr_plot_barycenter_lp_vs_entropic_thumb.png b/docs/source/auto_examples/images/thumb/sphx_glr_plot_barycenter_lp_vs_entropic_thumb.png Binary files differindex b49b28b..c68e95f 100644 --- a/docs/source/auto_examples/images/thumb/sphx_glr_plot_barycenter_lp_vs_entropic_thumb.png +++ b/docs/source/auto_examples/images/thumb/sphx_glr_plot_barycenter_lp_vs_entropic_thumb.png diff --git a/docs/source/auto_examples/images/thumb/sphx_glr_plot_otda_linear_mapping_thumb.png b/docs/source/auto_examples/images/thumb/sphx_glr_plot_otda_linear_mapping_thumb.png Binary files differindex b4adccf..277950e 100644 --- a/docs/source/auto_examples/images/thumb/sphx_glr_plot_otda_linear_mapping_thumb.png +++ b/docs/source/auto_examples/images/thumb/sphx_glr_plot_otda_linear_mapping_thumb.png diff --git a/docs/source/auto_examples/index.rst b/docs/source/auto_examples/index.rst index 5bd2ce2..69fb320 100644 --- a/docs/source/auto_examples/index.rst +++ b/docs/source/auto_examples/index.rst @@ -109,7 +109,7 @@ This is a gallery of all the POT example files. .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip="@author: rflamary "> + <div class="sphx-glr-thumbcontainer" tooltip=" "> .. only:: html diff --git a/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.ipynb b/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.ipynb index 8114835..2199162 100644 --- a/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.ipynb +++ b/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.ipynb @@ -15,7 +15,7 @@ "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\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) diff --git a/docs/source/conf.py b/docs/source/conf.py index 4105d87..114245d 100644 --- a/docs/source/conf.py +++ b/docs/source/conf.py @@ -81,7 +81,7 @@ master_doc = 'index' # General information about the project. project = u'POT Python Optimal Transport' -copyright = u'2016, Rémi Flamary, Nicolas Courty' +copyright = u'2016-2018, Rémi Flamary, Nicolas Courty' author = u'Rémi Flamary, Nicolas Courty' # The version info for the project you're documenting, acts as replacement for diff --git a/examples/plot_barycenter_lp_vs_entropic.py b/examples/plot_barycenter_lp_vs_entropic.py index 2255107..b82765e 100644 --- a/examples/plot_barycenter_lp_vs_entropic.py +++ b/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/examples/plot_otda_linear_mapping.py b/examples/plot_otda_linear_mapping.py index 7a3b761..c65bd4f 100644 --- a/examples/plot_otda_linear_mapping.py +++ b/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/notebooks/plot_barycenter_lp_vs_entropic.ipynb b/notebooks/plot_barycenter_lp_vs_entropic.ipynb index e188875..9c8e83e 100644 --- a/notebooks/plot_barycenter_lp_vs_entropic.ipynb +++ b/notebooks/plot_barycenter_lp_vs_entropic.ipynb @@ -30,14 +30,43 @@ "Iterative Bregman projections for regularized transportation problems\n", "SIAM Journal on Scientific Computing, 37(2), A1111-A1138.\n", "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Author: Remi Flamary <remi.flamary@unice.fr>\n", + "#\n", + "# License: MIT License\n", "\n", + "import numpy as np\n", + "import matplotlib.pylab as pl\n", + "import ot\n", + "# necessary for 3d plot even if not used\n", + "from mpl_toolkits.mplot3d import Axes3D # noqa\n", + "from 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": 2, + "execution_count": 3, "metadata": { "collapsed": false }, @@ -46,7 +75,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Elapsed time : 0.010513782501220703 s\n", + "Elapsed time : 0.010422945022583008 s\n", "Primal Feasibility Dual Feasibility Duality Gap Step Path Parameter Objective \n", "1.0 1.0 1.0 - 1.0 1700.336700337 \n", "0.006776453137632 0.006776453137633 0.006776453137633 0.9932238647293 0.006776453137633 125.6700527543 \n", @@ -72,46 +101,12 @@ "6.724209350756e-11 6.739211232927e-11 6.739210470901e-11 0.5944802416166 6.735465384341e-11 0.04105850033766 \n", "1.743382199199e-11 1.736445896691e-11 1.736448490761e-11 0.7573407808104 1.734254328931e-11 0.04105849088824 \n", "Optimization terminated successfully.\n", - "Elapsed time : 2.89129376411438 s\n", - "Elapsed time : 0.014848947525024414 s\n", - "Primal Feasibility Dual Feasibility Duality Gap Step Path Parameter Objective \n", - "1.0 1.0 1.0 - 1.0 1700.336700337 \n", - "0.006776466288966 0.006776466288966 0.006776466288966 0.9932238515788 0.006776466288966 125.6649255808 \n", - "0.004036918865495 0.004036918865495 0.004036918865495 0.4272973099316 0.004036918865495 12.3471617011 \n", - "0.00121923268707 0.00121923268707 0.00121923268707 0.749698685599 0.00121923268707 0.3243835647408 \n", - "0.0003837422984432 0.0003837422984432 0.0003837422984432 0.6926882608284 0.0003837422984432 0.1361719397493 \n", - "0.0001070128410183 0.0001070128410183 0.0001070128410183 0.7643889137854 0.0001070128410183 0.07581952832518 \n", - "0.0001001275033711 0.0001001275033711 0.0001001275033711 0.07058704837812 0.0001001275033712 0.0734739493635 \n", - "4.550897507844e-05 4.550897507841e-05 4.550897507844e-05 0.5761172484828 4.550897507845e-05 0.05555077655047 \n", - "8.557124125522e-06 8.5571241255e-06 8.557124125522e-06 0.8535925441152 8.557124125522e-06 0.04439814660221 \n", - "3.611995628407e-06 3.61199562841e-06 3.611995628414e-06 0.6002277331554 3.611995628415e-06 0.04283007762152 \n", - "7.590393750365e-07 7.590393750491e-07 7.590393750378e-07 0.8221486533416 7.590393750381e-07 0.04192322976248 \n", - "8.299929287441e-08 8.299929286079e-08 8.299929287532e-08 0.9017467938799 8.29992928758e-08 0.04170825633295 \n", - "3.117560203449e-10 3.117560130137e-10 3.11756019954e-10 0.997039969226 3.11756019952e-10 0.04168179329766 \n", - "1.559749653711e-14 1.558073160926e-14 1.559756940692e-14 0.9999499686183 1.559750643989e-14 0.04168169240444 \n", - "Optimization terminated successfully.\n", - "Elapsed time : 2.7255496978759766 s\n", - "Elapsed time : 0.002989530563354492 s\n", - "Primal Feasibility Dual Feasibility Duality Gap Step Path Parameter Objective \n", - "1.0 1.0 1.0 - 1.0 1700.336700337 \n", - "0.006774675520727 0.006774675520727 0.006774675520727 0.9932256422636 0.006774675520727 125.6956034743 \n", - "0.002048208707562 0.002048208707562 0.002048208707562 0.7343095368143 0.002048208707562 5.213991622123 \n", - "0.000269736547478 0.0002697365474781 0.0002697365474781 0.8839403501193 0.000269736547478 0.505938390389 \n", - "6.832109993943e-05 6.832109993944e-05 6.832109993944e-05 0.7601171075965 6.832109993943e-05 0.2339657807272 \n", - "2.437682932219e-05 2.43768293222e-05 2.437682932219e-05 0.6663448297475 2.437682932219e-05 0.1471256246325 \n", - "1.13498321631e-05 1.134983216308e-05 1.13498321631e-05 0.5553643816404 1.13498321631e-05 0.1181584941171 \n", - "3.342312725885e-06 3.342312725884e-06 3.342312725885e-06 0.7238133571615 3.342312725885e-06 0.1006387519747 \n", - "7.078561231603e-07 7.078561231509e-07 7.078561231604e-07 0.8033142552512 7.078561231603e-07 0.09474734646269 \n", - "1.966870956916e-07 1.966870954537e-07 1.966870954468e-07 0.752547917788 1.966870954633e-07 0.09354342735766 \n", - "4.19989524849e-10 4.199895164852e-10 4.199895238758e-10 0.9984019849375 4.19989523951e-10 0.09310367785861 \n", - "2.101015938666e-14 2.100625691113e-14 2.101023853438e-14 0.999949974425 2.101023691864e-14 0.09310274466458 \n", - "Optimization terminated successfully.\n", - "Elapsed time : 2.594216823577881 s\n" + "Elapsed time : 2.927520990371704 s\n" ] }, { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "<Figure size 460.8x216 with 1 Axes>" ] @@ -121,9 +116,9 @@ }, { "data": { - "image/png": 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\n", 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J+gbnMrP+CqdkoF+2TK2RXp3rleNI1DlW7jl2+Y1N9oqPhR+HOsmpyb0wZGbmJqckItBqONz5E0QdgnHtIeKvzN+PyVcsQeUi0bHx/L71MB3rlslRNZWbriuNn48Xv1ozX84SdxYm3uk07bV7Fbq8k/Xdwq+9CYb+D3z8YXwX2L8ya/dn8jRLULnIgm2HORuXkO1j711OIT8fbrquNL9ujCAx0S6S5wjnTsOEPrB9DnQdBS0fyb59l6wGd/8KASXg6x6wa2H27dvkKZagcpGZf4UTVMiXpjmoeS9Jp3pliTx9jlV7j3s6FBMbDRNuh71Loden0Pju7I+hWCW4+zcoXhm+ux32/JH9MZhczxJULnE2NoHft0bSoW7ZHDmsUNtaZfD18bLefJ4WH+vcm7RvGfT+DEJu91wshcvC4F+geDB81w8OrPFcLCZXynnfdCZVC/+OJDo2gc51c1bzXpJAPx9uqFGKXzeGWzOfpyQmwM/3w47/Qbf3oW5vT0fk9PAb+DMULA7f9nbuwzImnSxB5RLT1h2kZKAvzavmvOa9JF1DynHo1DmW77befNlOFWY+Dpt+gnavQKMhno7oH0XKw8Cpzg2+3/SE43s9HZHJJSxB5QKnYuKYtzWSriHlc2TzXpJ2tctQ0Nebaets1Kpst/gdWP2l09W75aOejuZiQdc6Nam4aKfzxlm7VmkuL+d+25nzftsYQWx8Ij1Cs+D+lUxU0NeHDnXKMuuvcM7FJ3g6nPxjwySY/xqE9IO2L3o6mrSVqQN9J8CxXTBxoHO9zJhLsASVC0xbd4DKQQUJ9cDMuVeqR2h5TsU492uZbLDnD5j2IAS3hu4f5vxRxau0hh5jnCk8pj9sY/eZS7IElcMdOhXD0p1H6RFagUvMAZljtKpWkpKBvtbMlx0O/w0/3OH0kuv7Te6Zm6l+X7jpeWcOqgVveDoak4NZgsrhZqw/iCr0zOHNe0l8vL3oGlKeeVsjORUT5+lw8q7oY879Rd6+MGBy7pvlts0TEHonLHzTmSjRmFRYgsrhpq47QEjFolQtFejpUNKtR2h5YuMT+W1jhKdDyZviY50hjE4dhH7fOTWo3EbEGeGickuniXL/Ck9HZHIgS1A52I7IKDYeOEWP0AqeDuWKhF5TjMpBBa2ZLyuowszhsHcJ9PgIrmnq6Yiuno8v3P4NFCnnNFWe2OfpiEwOYwkqB5u+7gBeAt3q58ybc9MiIvQIrcDSnUc5dCrG0+HkLUs/hLXfQpsnPTtKRGYpFAR3THJqhd/1c8YQNMZlCSqHSkxUflp7gJbVSlK6sL+nw7liPUPLowo/r7VaVKbZOsuZ16l2D7jxWU9Hk3lKXQd9voTDW+HHe5wRMYzBElSOtWj7YcKOn6VvkwzMeOpBVUsF0jS4BN+v2GdDH2WGiI3Ol3f5UOg5Frzy2H/dam2h05vw929OEjYGS1A51oTl+ygZ6Ev72mU9HcpVG9C8EnuPRrNk5xFPh5K7RUXC9/3Avyj0+x58C3o6oqzR9F5nUsVlH8Garz0djckB0pWgRKSjiGwTkR0i8nQq6/1EZKK7frmIBLvL24nIahH5y/17c7L3LHDLXOc+SmfWh8rtwk+eZd6WQ9ze+Bp8fXLvb4iOdctSopAvE/60i99XLS7G6UAQfRT6f+90KMjLOv4Hrr0ZfhkOuxd7OhrjYZf99hMRb2AM0AmoDfQXkdopNhsKHFfVasAo4E13+RGgm6rWAwYD36R43wBVDXUfkRn4HHnKDyv2o0D/ppU8HUqG+Pl406dRRf635ZB1lrgaiYkw9QEIWwm3fuI07+V13j5w25dQ4lqnK/2R7Z6OyHhQen6eNwV2qOouVY0FfgB6pNimB/CV+3wK0FZERFXXqupBd/kmIEBE/DIj8LwqLiGRH1bu44YapbimRO5vyunftBIJicrElfs9HUruM+/lf6Zrr93d09Fkn4BiMGCSM/r5hNvgjDUR51fpSVAVgOTfLmHuslS3UdV44CQQlGKb3sAaVT2XbNmXbvPe/0ka4/iIyH0iskpEVh0+nPfHd5u3JZJDp84xoFllT4eSKYJLFqJ19ZJ8v2If8QmJng4n91g9Hpa878yGe/3Dno4m+xUPhv4/wOkI5/pb3FlPR2Q8IFsucIhIHZxmv/uTLR7gNv21dh8DU3uvqn6qqo1VtXGpUqWyPlgPm7B8L+WL+nNzzbxzSW5As8qEn4xhwba8/wMjU+yYC7+MgGrtoNPbOX8A2KxSsTH0+gzCVjkTMSbaD5z8Jj0J6gCQvK9zRXdZqtuIiA9QFDjqvq4I/AwMUtWdSW9Q1QPu39PAdzhNifnaniNnWLz9CP2aVsLbK+98KbWtVZoyRfz45k+bqO6ywlbDxEFQurZzb5C3j6cj8qza3aH9a7B5Gvz2lI1+ns+kJ0GtBKqLSBUR8QX6AdNTbDMdpxMEwG3AfFVVESkGzASeVtUlSRuLiI+IlHSfFwC6Ahsz9lFyv/8u2IGfjxf9mubOe5/SUsDbi4HNK7Pw78NsPHDS0+HkXIf/dq65FCoJd04Bv8KejihnuP4hp5lzxaew6G1PR2Oy0WUTlHtN6SFgNrAFmKSqm0TkFRFJunI7DggSkR3ACCCpK/pDQDXghRTdyf2A2SKyAViHUwP7LDM/WG6z/1g0P605QP+mlXLlyBGXM+j6YIr4+/DBPOuVlaqTB+DbXuDl7cw8Wzj33v+WJW55BerfAb+PhJXjPB2NySbpaj9Q1VnArBTLXkj2PAbok8r7XgNeS6PYRukPM+/774IdeInwwA3XejqULFHEvwB3t6rC+3O3s/ngKWqXL+LpkHKOM0ec5HT2BNw105ke3VzIywu6fwBnj8HMx52bluvd5umoTBbLvXeB5iFhx6OZsjqMfk2voWzRvFd7SnJXyyoU9vPhw/lWizrvzFH4qjsc3+PciFuuvqcjyrm8Czj3SFW+Hn66z+mCb/I0S1A5wMcLnL4jebX2lKRoQAHuahnMrxsj2BpxytPheF70Mfi6Oxzb6XSprtLa0xHlfL4FndHPr2kKU4Y6nSdMnmUJysMOnjjLpFX76dP4GsoXC/B0OFnu7lZVCPTz4cP5OzwdimclJacj252a07U3eTqi3MMv0JlFuGJjmHI3bE7ZZ8vkFZagPOzD+TtQhWE35u3aU5JiBX0ZfH1lZv0VzqaD+bRH38kD8GUnp9de/++csefMlfErDAOmQPmGMHkIrJ3g6YhMFrAE5UGr9x7nh5X7GNiiMhWL5/5hjdLr3tZVKVHQl2d/3khCfpuK4/A2GNfeSVJ3ToFqt3g6otzLvwgM/MlpGp02DP543+6TymMsQXlIbHwiz/70F+WK+PN4++s8HU62KlbQlxe61Wb9/hN8m59u3g1bBV90gIRYp7delTaejij38ysMd0yGOr1g7osw53kbcSIPsQTlIZ8t3sW2Q6d5pUddAv3y32gB3euXp02NUrz121YOnsgH46xtmATju4B/MRg623rrZSYfX+g9Dpre78wlNWkgxFgnnLzAEpQH7D5yhtHzttOlXjluqV3G0+F4hIgwsmddElR5YdomNK82zSTEw2/Pwk/3QoXGMPR/UKKqp6PKe7y8nBl5O/4Htv0Kn7eFI/m8I04eYAkqmyUmKs/+9Bd+Pl682C3ltFr5yzUlCjKiXQ3mbjnErxsjPB1O5ouKhG9vhT/HQLMHYNBUCMz7Ax57jAg0/5dznKOPwmc3wdaZno7KZIAlqGz25uytLNt1lOc616J0kbx7U2563d2yCvUqFOXfUzawLeK0p8PJPFtmwH+bw77l0PNj59e9dwFPR5U/VGkD9y2AElWc2YinPwLnojwdlbkKlqCy0Q8r9vHJwl3c2bwSfZvkrQFhr5aPtxefDGxEQV9v7h6/ksjTuXzm3ZhTMHWYMxts0Ypw/yIIvcPTUeU/xSo5zaktH4M1X8PYlrDvT09HZa6QJahssmTHEZ6fupHW1UvyUrc6pDE/Y75UvlgA4wY34diZWO79ejUxcQmeDunKqTodIcY0hfXfQ5snYehcKF3T05HlXz5+0O5luGsWaCJ80dGpTdkMvbmGJahssDXiFA98u5qqpQoxZkBDfLztsKdUr2JR3u8XyoawEwyfuI643DT77sF1Tvfxn+51RiEfOhduft7pXWY8r/L18K+l0OJBWDcBPmgIf46FhDhPR2Yuw74ps9j8rYe47eNlBBTwZtzgJhTxt+sQaelQpyzPda7FrxsjGDRuBcfPxHo6pEs7uBZ+GACf3gDHdkGPMXDPfKhoA/XnOH6FocNIJ1FVbORMfvhhI1g9HuLPeTo6kwbJTd17GzdurKtWrfJ0GOmiqny+eDev/7qF2uWK8NmgxvlirL3M8NOaMJ7+8S/KFfNn3ODGVCudgybuS0yE3Qvhz//C9jnOtA/NHnB+nfsX9XR0Jj1UnX+7Bf+Bg2ugSAVo8RCE9oeA4p6OLl8QkdWq2viy21mCynyRp2MYOXML09YdpHO9srzTpz4FffPfzbgZsXrvce7/ZjXn4hJ4sXsdejWogJeXB6/bnY5wmofWfO1MjRFQwklKTe+1xJRbqcKu32Hh27BvKfj4Q+0e0HAwVGrh3FtlsoQlKA84G5vAZ4t3MXbhTuISEnn45uo8dFM1z36x5mIHT5zlwe/WsHbfCepWKMJznWvT4tqg7Avg2C7Y8gts/QX2rwAUKreCRkOgVjcoYLcJ5BnhG2DNV05Hl3OnoHA5qNkFanaF4FZ2i0AmswSVjXYfOcPUtQeYuHI/Eadi6FS3LE91rElwyUKeDi3XS0xUZmw4yFu/bePAibO0rl6S2xpVpH3tsgT4emfmjpyEtH857F0Ce/6AE+44gWXrQc1uULc3lKyWefs0OU9stPODZMt02DEP4qKhQCGo1Awqt3QeZes5U36Yq5apCUpEOgKjAW/gc1X9T4r1fsDXONO4HwX6quoed90zwFAgAXhEVWenp8zU5JQEFR0bz/r9J1mz7zhzNh9i/f4TiMD11wbx2C01aBJcwtMh5jkxcQl8uWQP3yzbw8GTMRT09aZDnbK0uDaIhpWKU7VkofTVVOPPwckwOLrTSUhHt0PERji0EWLdmzkDSkBwSwhuDTU6QvHKWfrZTA4VdxZ2zoddC2DPEojc5K4QCKrmJKpSNSHoWmf4quLBzjUsu4XksjItQYmIN/A30A4IA1YC/VV1c7JthgEhqvqAiPQDblXVviJSG/geaAqUB+YCNdy3XbLM1GRlgkpMVM7FJ3I2LoGzcQmcOhvH8ehYTkTHcfj0OfYfi2b/8Wj2Ho1me2TU+WkiapUrwq0NytO9foU8PV27R6k697EkxJEYf441uw8xZ8M+lmw9SNy5aAI4R0m/RGoUh4oB8ZQLiKWUTwxF9DSBCSfxjz+Bb3Qk3mci8IpOcQ+Mb2EoUwfKhUDZEKjQyPnSsesPJqUzR50adsRfELHBaRY8ue/CbXwCoEh551GoJBQMcn7wBBR3ehL6FwHfQPAtBAUCoEBB534tbz/ntgRvP6c50csnTye69Cao9Fy5bwrsUNVdbsE/AD2A5MmkB/CS+3wK8JE4d6L2AH5Q1XPAbhHZ4ZZHOsrMVPu2b0Am9Dn/WnESTFJ+TpmnA9xHefe1CPh4CT7eXvgV8cLXxws/Hy+8EViL88g3kh2si37gaCpPkx/kFM818Z8ElPyRmACa4PxN/Od+FS+gsfsAwC/Zro+7D9cZ9eM4hTmogURqcSK0PhFanAiC2C/lOeBVjlOxxfA56IWEC95e4CXhCOHnb6RO+o4QAeHCL4w8/P1h0hSA8xXmfI35FjxHBY2gQmI45fUQJROPUvLkMUqdOEJR3UVRPUURovDiyi+lxONFAt4k4nXBQxESEVScUhOT3S2k7jn6z18gxXmryV5rGssvJUEKUPmFjVf8ea5GehJUBWB/stdhQLO0tlHVeBE5CQS5y/9M8d4K7vPLlQmAiNwH3AdQqVKldISbOv+AQMKK1nO/VAQvcf7ZRAQvL+e1twjeXs6jgLeThHy9vfAr4IWfj3c6//nyiQu+neXy684vk382Fy/3tYB4O6+THl7e//z1cn9Revs4z338//m1mfQrtECAc13ArwjnvAsScc6X47Hebi04lujYBM7GJuC9QV/DAAAgAElEQVQXl0CZuERKJCZSJ0GJS0gkUZWERKcWnajOTxfVf37EoFz09ZKbrt2arFaGM9RnO7A9lbWiCfgnRuOfeAb/BOevr8bgm+g8fDQWH407//DSeLw1AS8S8Dr/10lPqCIoXiQ431+aiJxPQ0nnpPs6lXNUUqSk1JdfmnoVILsavXN832dV/RT4FJwmvqstp3TFqpQePiXT4jI5lx9Q2X0YY3Kv9DS0HwCSj2xa0V2W6jYi4gMUxekskdZ701OmMcaYfCw9CWolUF1EqoiIL9APmJ5im+nAYPf5bcB8ddpApgP9RMRPRKoA1YEV6SzTGGNMPnbZJj73mtJDwGycLuFfqOomEXkFWKWq04FxwDduJ4hjOAkHd7tJOJ0f4oEHVTUBILUyLxfL6tWrj4jI3qv5oMmUBGw443/Y8biQHY8L2fG4kB2Pi13NMUlXC3yuulE3M4jIqvR0b8wv7HhcyI7Hhex4XMiOx8Wy8pjYzR7GGGNyJEtQxhhjcqT8mKA+9XQAOYwdjwvZ8biQHY8L2fG4WJYdk3x3DcoYY0zukB9rUMYYY3IBS1DGGGNypHyToESko4hsE5EdIvK0p+PJbiJyjYj8LiKbRWSTiDzqLi8hIv8Tke3u33w157WIeIvIWhH5xX1dRUSWu+fJRPdG8nxDRIqJyBQR2SoiW0SkRX4+R0RkuPv/ZaOIfC8i/vnpHBGRL0QkUkQ2JluW6vkgjg/c47JBRBpmdP/5IkG5U4aMAToBtYH+7lQg+Uk88Liq1gaaAw+6x+BpYJ6qVgfmua/zk0eBLclevwmMUtVqOGOjD/VIVJ4zGvhNVWsC9XGOTb48R0SkAvAI0FhV6+IMKtCP/HWOjAc6pliW1vnQCWe0oOo4A3x/nNGd54sERbIpQ1Q1Fkia3iPfUNVwVV3jPj+N88VTAec4fOVu9hXQ0zMRZj8RqQh0AT53XwtwM86UMZD/jkdRoA3OyDCoaqyqniAfnyM4o+0EuGOMFgTCyUfniKouwhkdKLm0zocewNfq+BMoJiLlMrL//JKgUpsypEIa2+Z5IhIMNACWA2VUNdxdFQGU8VBYnvA+8G8g0X0dBJxQ1Xj3dX47T6oAh4Ev3WbPz0WkEPn0HFHVA8A7wD6cxHQSWE3+Pkcg7fMh079n80uCMi4RCQR+BB5T1VPJ17kD/OaL+w5EpCsQqaqrPR1LDuIDNAQ+VtUGwBlSNOfls3OkOE6toArO3KWFuLi5K1/L6vMhvyQom94DEJECOMlpgqr+5C4+lFQNd/9Geiq+bNYS6C4ie3CafG/Guf5SzG3Ogfx3noQBYaq63H09BSdh5ddz5BZgt6oeVtU44Cec8yY/nyOQ9vmQ6d+z+SVB5fvpPdzrK+OALar6XrJVyadKGQxMy+7YPEFVn1HViqoajHM+zFfVAcDvOFPGQD46HgCqGgHsF5Hr3EVtcWYiyJfnCE7TXnMRKej+/0k6Hvn2HHGldT5MBwa5vfmaAyeTNQVelXwzkoSIdMa55pA0vcdID4eUrUSkFbAY+It/rrk8i3MdahJQCdgL3K6qKS+K5mkiciPwhKp2FZGqODWqEsBa4E5VPefJ+LKTiITidBrxBXYBd+H8kM2X54iIvAz0xekFuxa4B+e6Sr44R0Tke+BGnCk1DgEvAlNJ5Xxwk/hHOM2g0cBdqroqQ/vPLwnKGGNM7pJfmviMMcbkMpagjDHG5EiWoIwxxuRIlqCMMcbkSJagjDHG5EiWoIwxxuRIlqCMMcbkSJagjDHG5EiWoIwxxuRIlqCMMcbkSJagjDHG5EiWoIwxxuRIlqCMMcbkSJagTL4nIntE5KyIRInIcRGZKSLXXP6dOYOIvCQi33o6DmMymyUoYxzdVDUQKIcz782HV1pAsllWc5XcGrfJ+yxBGZOMqsbgTHVeG0BEuojIWhE5JSL7ReSlpG1FJFhEVESGisg+YL5b+3o4eZkiskFEbnWf1xGR/4nIMRE5JCLPusu9RORpEdkpIkdFZJKIlEixn8Eisk9EjojIc+66jjgTT/Z1a4Dr3eVFRWSciISLyAEReU1EvN11Q0RkiYiMEpGjwEsiUk1EForISbf8iVl6oI1JB0tQxiQjIgVxZlD90110BhgEFAO6AP8SkZ4p3nYDUAvoAHwF3JmsvPo4M7DOFJHCwFzgN6A8UA2Y5276MNDTLas8cBwYk2I/rYDrcKYef0FEaqnqb8DrwERVDVTV+u6243Fmga0GNADa48wGm6QZzoy5ZYCRwKvAHKA4UJGrqEEak9ksQRnjmCoiJ4CTQDvgbQBVXaCqf6lqoqpuAL7HSSLJvaSqZ1T1LDAdqCEi1d11A3GSRyzQFYhQ1XdVNUZVT6vqcne7B4DnVDXMnT78JeC2FM1vL6vqWVVdD6wH6pMKESkDdAYec+OKBEYB/ZJtdlBVP1TVeDfuOKAyUN6N7Y8rO3zGZD5LUMY4eqpqMcAfeAhYKCJlRaSZiPwuIodF5CROIimZ4r37k564TYQTgTtFxAvoD3zjrr4G2JnG/isDP4vICTdRbgEScGo4SSKSPY8GAi9RVgEgPFl5nwClU4vZ9W9AgBUisklE7k6jbGOyjSUoY5JR1QRV/QknObQCvsOpFV2jqkWBsThf5Be8LcXrr4ABOE1x0aq6zF2+H6iaxq73A51UtViyh7+qHkhP2KmUdQ4omaysIqpaJ633qGqEqt6rquWB+4H/iki1dOzbmCxjCcqYZMTRA+dazBagMHBMVWNEpClwx+XKcBNSIvAu/9SeAH4ByonIYyLiJyKFRaSZu24sMFJEKrtxlHLjSI9DQLBbY0NVw3GuJ70rIkXcDhjXikjKpsnkn7uPiFR0Xx7HSWCJ6dy/MVnCEpQxjhkiEgWcwuk0MFhVNwHDgFdE5DTwAjApneV9DdQDzt+fpKqnca5vdcNprtsO3OSuHo1TU5vj7utPnI4M6THZ/XtURNa4zwcBvsBmnIQzBacLfVqaAMvdYzAdeFRVd6Vz/8ZkCVFN2TpgjMkoERkE3KeqrTwdizG5ldWgjMlkblf1YcCnno7FmNzMEpQxmUhEOgCHca4LfefhcIzJ1ayJzxhjTI5kNShjjDE5Uq4aJLJkyZIaHBzs6TCMMcZkwOrVq4+oaqnLbZerElRwcDCrVq3ydBjGGGMyQET2pmc7a+IzxhiTI1mCMsa1fj1YBd2YnCNDCUpEOorINhHZISJPp7LeT0QmuuuXi0hwsnUhIrLMHZjyLxHxz0gsxmTEmTPQvj00bw4ff+zpaIwxkIFrUO7kZ2Nwhm4JA1aKyHRV3Zxss6HAcVWtJiL9gDdxJlbzwRkCZqCqrheRIJzh/o3xiNGjITLSSVDDhsHWrfDuu+CTq67S5k5xcXGEhYURExPj6VBMJvP396dixYoUKFDgqt6fkf9+TYEdSeN1icgPQA+csb+S9MCZ1wacscA+EhHBmTxtgzuvDap6NANxGJMhx4/DW29Bt27w88/w5JMwahTs2OG89vX1dIR5W1hYGIULFyY4OBjn68HkBarK0aNHCQsLo0qVKldVRkaa+Cpw4ZwyYe6yVLdR1XicyeCCgBqAishsEVkjIv/OQBzGZMhbb8GpU/Daa+DtDe+9B2PGwKxZ8NFHno4u74uJiSEoKMiSUx4jIgQFBWWoZuypThI+OHPtDHD/3ioibVPbUETuE5FVIrLq8OHD2RmjyQciIpzmvf79ISTkn+XDhkGHDvDqq3DU6vdZzpJT3pTRf9eMJKgDODOEJqnoLkt1G/e6U1HgKE5ta5GqHlHVaGAW0DC1najqp6raWFUblyp12fu6jLlAYiLceSfcfbdTI4qNvXD9yJEQFwf3P3GQb9Z/w7cbvmXfyX0AvPOOU7N69VUPBG6MydA1qJVAdRGpgpOI+nHxZG7TgcHAMuA2YL6qqojMBv7tjvocC9wAjMpALMakatEimDDBuY705ZdQtCg0bAgnT0LkkXgOhHlRqPn33DD9zgveF1wsmHZV23HH4PcZM6YgDz4I1at76EOYLBcYGEhUVBTr1q3jX//6F6dOncLb25vnnnuOvn37ejq8fOuqE5SqxovIQ8BswBv4QlU3icgrwCpVnQ6MA74RkR3AMZwkhqoeF5H3cJKcArNUdWYGP4sxF/niCyhSBPbuhSVLYMoUp4eed+FIDrMAr+A93DDoL9rXHc0NlZ0JZxfuXcjCvQv5ZsM3FKq4hAJ+63nqKR9++snDH8ZkuYIFC/L1119TvXp1Dh48SKNGjejQoQPFihXzdGj5k6rmmkejRo3UmPQ6eVI1IED1/vv/WRYTF6MjfhuhvITW+2893RS5Kc33b4rcpHX/W1e5+VkF1dn/i82GqPOfzZs3ezoELVSoUKrLQ0JC9O+//87maPKW1P59cSoxl/3Ot7s8TJ41aRKcPQt33eW8jk+Mp/ek3szcPpNhjYfxTvt3CCgQkOb7a5eqzYp7VvBo6Wf4bM0uOncry0+TvOjezTubPkE+9NhjsG5d5pYZGgrvv3/Fb1uxYgWxsbFce+21mRuPSTcb6sjkWV98AbVqQdOmTkvBY789xsztM/mo00eM6TLmkskpSUCBAD7t/T6vfr2IhGJb6dlTGDUKbBq1vC08PJyBAwfy5Zdf4uVlX5OeYjUokydt3QrLljn3OInA6D8/YMzKMTze4nEebPrgFZf3fLchRI59hg+f2c2IEb359Vfw83O6oJ85A5984oxCYTLoKmo6me3UqVN06dKFkSNH0tz+UT3KfhqYPGn8eOem24EDYdrWaQyfPZxba97KW+3euuoyR3V7jR7/NwFueIX1m6PZvx8KFoTt250egib3i42N5dZbb2XQoEHcdtttng4n37MEZfKc+Hj46ivo3Bli/Pcw4KcBNC7fmG97fYuXXP0p7+3lzYTe39B4wAyiHyzDtAV7mTsXOnaEX3+1Zr+8YNKkSSxatIjx48cTGhpKaGgo6zL7mphJN0tQJs+ZM8cZIWLIEOXeGfciIkzuM5mCBQpmuOxCvoX48fYfAbjvl/tQVTp1gv37YdOmDBdvPCQqKgqAO++8k7i4ONatW3f+ERoa6uHo8i9LUCbPmTzZuSH3cIXxzN01l7dueYvKxSpnWvmVilbizVveZM7OOYxfN55OnZzlv/6aabswxmAJyuQx8fEwYwa07RDNU78Pp03lNtzf+P5M388DjR+gTeU2jJgzAq+iBwkJcYZSMsZkHktQJk/54w+nZ93e8qOJTYhlXPdxGbrulBYv8eLzbp8TEx/DsJnD6NhR+eMPZ+w+Y0zmsARl8pSff4YCvgmsDhjJqze9SrUS1bJsX9WDqvPqTa8ybds0AussIj4e5s7Nst0Zk+9YgjJ5hir8PFUpUP13Qipdy2PNH8vyfQ5vPpx6pevx5dH7KFpUrZnPmExkCcrkGWvWwP59QnS1Cbzd7m28vbJ+SCJvL2/ebvc2u0/9TXDD7dbd3JhMZAnK5BnfTToLksBNHc7Q/tr22bbfDtU60P7a9mwP+oCDB2HDhmzbtckk3t7ehIaGUrduXbp168aJEycyXOaJEycICgpC3V8sy5YtQ0QICwsD4OTJk5QoUYLExMQM7yujpk6dyubNmy+73dixY/n666+zISKHJSiTZ3z1w0movIjRvf4v2/f9dru3ia7szMdhzXy5T0BAAOvWrWPjxo2UKFGCMWPGZLjMYsWKUa5cObZs2QLA0qVLadCgAUuXLgXgzz//pGnTptk61l9CQkKqy9OboB544AEGDRqU2WGlyRKUyRPmrdzP0X1laXZLOPXK1Mv2/YeUCeHu1p2Qcmv5cVpMtu/fZJ4WLVpw4MA/k4O//fbbNGnShJCQEF588cXzy1999VWuu+46WrVqRf/+/XnnnXcuKuv6668/n5CWLl3K8OHDL3jdsmVLAD777DOaNGlC/fr16d27N9HR0QBMnjyZunXrUr9+fdq0aQPApk2baNq0KaGhoYSEhLB9+3YAvv322/PL77///vPJKDAwkMcff5z69euzbNkynn76aWrXrk1ISAhPPPEES5cuZfr06Tz55JOEhoayc+dOdu7cSceOHWnUqBGtW7dm69atALz00kvnP+eNN97IU089RdOmTalRowaLFy/OvH8Elw0Wa/KEx0cvBu7gg8du9lgMr9z0Cl/X+pLVv9cnPBzKlfNYKLnWY789xrqIzB1aKLRsKO93TN8gtAkJCcybN4+hQ4cCMGfOHLZv386KFStQVbp3786iRYsICAjgxx9/ZP369cTFxdGwYUMaNWp0UXktW7Zk4cKF3HPPPezatYs+ffrwySefAE6CevrppwHo1asX9957LwDPP/8848aN4+GHH+aVV15h9uzZVKhQ4Xyz49ixY3n00UcZMGAAsbGxJCQksGXLFiZOnMiSJUsoUKAAw4YNY8KECQwaNIgzZ87QrFkz3n33XY4ePcrQoUPZunUrIsKJEycoVqwY3bt3p2vXrufHH2zbti1jx46levXqLF++nGHDhjF//vyLPl98fDwrVqxg1qxZvPzyy8zN5G6slqBMrrch4i/Wz6tF2RoHaFqngsfiqFCkAncNCOSz+V58OP4grz9T3mOxmCtz9uxZQkNDOXDgALVq1aJdu3aAk6DmzJlDgwYNAGdIpO3bt3P69Gl69OiBv78//v7+dOvWLdVyr7/+et544w12795NcHAw/v7+qCpRUVGsXr2aZs2aAbBx40aef/55Tpw4QVRUFB06dACcBDdkyBBuv/12evXqBTg1vJEjRxIWFkavXr2oXr068+bNY/Xq1TRp0uT85yldujTgXF/r3bs3AEWLFsXf35+hQ4fStWtXunbtelHMUVFRLF26lD59+pxfdu7cuVQ/X1JMjRo1Ys+ePek/4OlkCcrkev8a9QtEPMMzL0R5OhT+038Q457ZwmffqCWoq5Demk5mS7oGFR0dTYcOHRgzZgyPPPIIqsozzzzD/fdfOBrJ++mcFqR69eqcOHGCGTNm0KJFC8D5Mv/yyy8JDg4mMDAQgCFDhjB16lTq16/P+PHjWbBgAeDUlpYvX87MmTNp1KgRq1ev5o477qBZs2bMnDmTzp0788knn6CqDB48mDfeeOOiGPz9/fH2dnq0+vj4sGLFCubNm8eUKVP46KOPLqoZJSYmUqxYsXQNkuvn5wc4STA+Pj5dx+RK2DUok6utC1/P0m/aUbzcMf51T6Cnw6FEQAladgznyJaazNtw+YvOJmcpWLAgH3zwAe+++y7x8fF06NCBL7744vxgsgcOHCAyMpKWLVsyY8YMYmJiiIqK4pdffkmzzObNmzN69OjzCapFixa8//77568/AZw+fZpy5coRFxfHhAkTzi/fuXMnzZo145VXXqFUqVLs37+fXbt2UbVqVR555BF69OjBhg0baNu2LVOmTCEyMhKAY8eOsXfv3otiiYqK4uTJk3Tu3JlRo0axfv16AAoXLszp06cBKFKkCFWqVGHy5MmAM9ln0nbZLUMJSkQ6isg2EdkhIk+nst5PRCa665eLSHCK9ZVEJEpEnshIHCb/+td7syC8Ma+86EeBAp6OxvGfRxoBXjw++g9Ph2KuQoMGDQgJCeH777+nffv23HHHHbRo0YJ69epx2223cfr0aZo0aUL37t0JCQmhU6dO1KtXj6JFi6ZaXsuWLdm/fz+NGzcGnAS1a9curr/++vPbvPrqqzRr1oyWLVtSs2bN88uffPJJ6tWrR926dbn++uupX78+kyZNom7duoSGhrJx40YGDRpE7dq1ee2112jfvj0hISG0a9eO8PDwi2I5ffo0Xbt2JSQkhFatWvHee+8B0K9fP95++20aNGjAzp07mTBhAuPGjaN+/frUqVOHadOmZeYhTjfRq7yrUES8gb+BdkAYsBLor6qbk20zDAhR1QdEpB9wq6r2TbZ+CqDAclW9uAtMCo0bN9ZVq1ZdVbwm71kbvo6GDRMp7lWZyL1B+OSgButSwZEckU2sXVac0LI2XcOlbNmyhVq1ank6jCsWFRVFYGAg0dHRtGnThk8//ZSGDRt6OqwcJ7V/XxFZraqNL/fejNSgmgI7VHWXqsYCPwA9UmzTA/jKfT4FaCsi4gbYE9gN2Cw6nnDuHMyfD9u2eTqSq/bAu7MgoiGvvRSQo5ITwF13FIa9bXhmmuenMDdZ47777iM0NJSGDRvSu3dvS05ZICP/rSsA+5O9DgOapbWNqsaLyEkgSERigKdwal+XbN4TkfuA+wAqVaqUgXAN8fEwfTr8+CP88ss/Q2/Xrg29esEdd0Au+SW7NnwdKyZ0okSFo9x3V5Cnw7nIwP4BvP0G/DYjgHU91lktKg/67rvvPB1CnuepThIvAaNU9bLdrlT1U1VtrKqNS5UqlfWR5VVnzzpJqHdvmD0b+vSBqVPhww+hTBl4/XWoXx8mTfJ0pOnywH8WQEQDRr7sn+NqTwB160L1Ggl4b+nP64tf93Q4xuRKGUlQB4Brkr2u6C5LdRsR8QGKAkdxalpvicge4DHgWRF5KAOxmEs5eRI6dHBqTaNHO/Ohf/459OgBDz3kNPUdPAjNmkG/fjB2rKcjvqRVe7aw4svbKFPtIPcOKeTpcFIlAn1v9yZxTysmL/+DLYe3eDokY3KdjCSolUB1EakiIr5AP2B6im2mA4Pd57cB89XRWlWDVTUYeB94XVU/ykAsJi2HDsENN8CyZfDdd/DII6Ra5ShTxqlZde4M//oXjByZY4flvuvJbXC6Ip9/XBDvrB+w/KoNGgTeXoL37//hjT8uvj/FGHNpV52gVDUeeAiYDWwBJqnqJhF5RUS6u5uNw7nmtAMYAVzUFd1koZgYaN8etm935kHv1+/S2xcs6Mz4d+ed8PzzkAkDZma2BWv3snFqR2reuIautxTzdDiXVL06jBghJKwZxISZu9l1fJenQzImd1HVXPNo1KiRmiswfLgqqM6YcWXvS0hQ7dJF1c9PdePGrIntKgW3WK0UiNJVWyI8HUq6nD6tWq5CvErZdXrPzw94OpwcafPmzZ4OQQsVKnTRshdffFHLly+v9evX1zp16ui0adMuWJ+YmKhBQUF67NgxVVU9ePCgArp48eLz25QsWVKPHDmStcGnw++//65Lliy57HbTpk3TN954I1P3ndq/L7BK0/GdbyNJ5FVz58KoUTBsGKQy3tYleXnBuHFQpAgMGOB0Sc8BfpgeyZ5lDWnWbz6NapbxdDjpEhgIH7zvjUbU54vP/Ak7FebpkMwVGD58OOvWrWPy5MncfffdF8zdJCI0b96cZcuWARdPp7Ft2zaCgoIICsq+XqZpTaexYMGC83FdSvfu3c8PYJsTWILKi44dg8GDoWZNePvtqyujTBknSa1f7zT3eVhsLDz4cAIU283Xb+WuLtu9e0Prm8+SOO8lXpzxsafDMVehVq1a+Pj4cOTIkQuWpzadRvKElTSc0YwZM2jWrBkNGjTglltu4dChQwAsXLiQ0NBQQkNDadCgAadPnyY8PJw2bdqcn0AxaRqLOXPm0KJFCxo2bEifPn3OD78UHBzMU089RcOGDZk8eTIffPDB+ek0+vXrx549exg7diyjRo0iNDSUxYsXc/jwYXr37k2TJk1o0qQJS5YsAWD8+PE89JDTX23IkCE88sgjXH/99VStWpUpU6Zk8VG+WA7soGsyRBXuvx8iI53rTgULXn1Z3bo5Zb37LnTqBDd7biqLV988zbF95bjludHUKPuox+K4GiLw+ccB1Krjw/jXm/Ba9wjKFS7r6bBypMceg3SMUXpFQkMhnWO7pmn58uV4eXmR8laXli1b8vLLLwOwYsUKXn75ZUaPHg04CSppOKNWrVrx559/IiJ8/vnnvPXWW7z77ru88847jBkzhpYtWxIVFYW/vz+ffvopHTp04LnnniMhIYHo6GiOHDnCa6+9xty5cylUqBBvvvkm7733Hi+88AIAQUFBrFmzBoDy5cuze/du/Pz8zk+n8cADDxAYGMgTTzi3nd5xxx0MHz6cVq1asW/fPjp06HB+YsXkwsPD+eOPP9i6dSvdu3c/Px1HdrEElddMnQpTpsAbb0Bm3Nn+7rvw++9wzz2weTP4+2e8zCu0bx/8Z6Qf1JzGxyO6ZPv+M0ONGvDk8yd486WeDHxmKnM/6unpkEw6jBo1im+//ZbChQszceJE3IFwzmvSpAlr167lzJkzxMXFERgYSNWqVdmxYwdLly7l8ccfByAsLIy+ffsSHh5ObGwsVapUAZwEN2LECAYMGECvXr2oWLEiTZo04e677yYuLo6ePXsSGhrKwoUL2bx58/kaWWxs7PnBZwH69j0/ghwhISEMGDCAnj170rNn6ufZ3LlzL5hB99SpU+drZMn17NkTLy8vateufb7Wl50sQeUl587Bk086I0M8kUnj7xYqBB995PQG/OAD+Pe/M6fcKzDs4XPEJ8bT87HfqVYi5Whaucfr/1eKb2asYd7Yzsztd4JbWuXsXoiekNGaTmYbPnz4+VpHagoWLEj16tX54osvzg911Lx5c2bNmkVkZCTXXXcdAA8//DAjRoyge/fuLFiwgJdeegmAp59+mi5dujBr1ixatmzJ7NmzadOmDYsWLWLmzJkMGTKEESNGULx4cdq1a8f333+fahyFCv1zP+DMmTNZtGgRM2bMYOTIkf/f3pmHR1FlC/x3O52kIUAAgSBhl10IssoiyqKIK6Ki4IKjDIgzDriNiINPUBx1xBkEF56giIooomhcmRlRfMoiEBRlNewEAoQlkL2767w/bgWSECBk6epO39/31ddV1bfqnr51u85dzj2HX3/99ZT0lmWxYsUKPGdpcOaH0wBtUBdozBxUZWLGDNi6Ff75z+LXOpWWK67QhhZTpuh1VQHkiy/gi8RouOxp/n7jvWe/IIhxueDDeTEQk8rQWyzsAKmGEKdXr15MmzatUDiNl156iR49epzocaWnpxMfr4Npzp0798S1W7dupUOHDubcEg0AABwzSURBVIwfP55u3bqxadMmdu7cSVxcHKNGjeKPf/wjSUlJ9OjRgx9//JHk5GQAMjMz2bJlyymyWJbF7t276devH88//zzp6elkZGQUCqcBMHDgQGbMmHHiuCSxn5zAKKjKwsGD8PTTeq7IjsZZrkydqt0l2WPegcDng/v/4sdVbxM33bOTtnVDw0/gmejVujV9/zqTo/urM+IPeU6LY7DJysqiYcOGJ7b8MBQloXfv3mzbtu2EgurcuTN79uwpFE5j0qRJDB06lC5dulCnTp0T56dNm0b79u1JSEggMjKSq666iu+++46OHTvSqVMnPvjgA8aNG0fdunV56623GD58OAkJCfTs2ZNNmzadIovf7+eOO+6gQ4cOdOrUibFjx1KzZk2uu+46Fi1adMJIYvr06axevZqEhATatWvHzGD1HlMSW/Rg2cw6qDNw330iEREiFbmmZOxYEZdLZN26isujAN9+q5dxcfNQ+XnfzwHJMxCs3bdW6PuEgMjmzU5L4zzBsA7KUHGYdVDhzm+/wf/+r3ZRVJHeyJ98EmJj4cEHA+IG6cOP8yAil6uvdtGxfscKzy9QXFT/IvoN3gvAos9yHJbGYAhejIKqDDz2mF5Ua0+8Vhi1a+s8vvlG++2rQERg/sJMaP5fJl9Z+QIuPz/0XqizkdkfFPWvbDAY8jEKKtRZvlxbEjz6KARixfqYMdC0qV68W4G9qOVrjnNkXy0SLttB1wZnDbwZcnSL70bz7ptJTmrI3kPpTovjOBKkjokNZaOsz9UoqFBn4kSoV097KQ8EUVF6qG/NGr3mqoKY+NoqAF7486UVlofT/PWuC8EfzcMzv3RaFEfxeDwcOnTIKKlKhohw6NChs5qynwkVSpWia9eusnr1aqfFCB6WLIEBA7TPvQceCFy+Pp+OyOd2a1dI5Rzz4kj2Eeq03E5slWoc/r1Vud47mMjLg5jYbFTCfPZ/N4RaVWo5LZIjeL1e9uzZQ06OmY+rbHg8Hho2bEhkZGSh80qpNSJy1qERs1A3VBGBJ56A+Hg97BZI3G6YPFmH71iwAIYPL9fbP5n4OlbKeEY8nlqu9w02oqLg0v55LPnhcqYue5FnBkxxWiRHiIyMPOFZwWAoiFFQocpXX8GyZTr6rQPuhxg6VIeJf/JJvV9OC4PTstJ4/b19AIy+vfL7qxs+JJYlX8byr8R/82DPB6hTtc7ZL6oIRGDbNj2nuWsXpKXpLTdXz23WqQN160KnTtC1qzN1zhB2GAUViuT3npo1g7vvdkYGl0svDB48GObOhZEjy+W2z/3wHLnrB9G4WS5t20af/YIQ56qr9Gf2hn4898NzTB04NXCZZ2fDp59q340//FDYS0hMjFZK0dHaO/6hQyeNYqKitJIaOFCHDTa9H0MFYYwkQpFFiyApSfdeoqKck+O666B7d3jqqXKJGbX9yHamf/8Wrp2XM/TGaIr45ayUxMdDx44Qt+9uZvw0g+1Htld8pmvX6mHh88/Xw7MrVmh3Vq+9BuvWQVYWZGTAjh2webP2UuL1wt692jBm3DitrCZPhubNoW9f3UgJkrhhhkpESVbzBstmPEmIiM8n0q6dSJs2et9p/v1v7e7h5ZfLfKvhC4dL5C13Coh8/305yBYiTJggEhFhSfTf4uS2j26ruIxWrxa57jr9vKpUEbnzTpFvvtERlEvDrl0izzwj0rKlvmejRiKvvSaSk1O+chsqHZTQk4TjSudcNqOgROTdd/VjW7DAaUk0liVy6aUi9euLZGaW+jarUlYJ/6MkrkWKNG8eHLo3UPzwg36k1z8+X5iErEpZVb4ZbNp0UjHVqiUyZYrI0aPld3/LEvn6a5EePU4qqjlzSq/4DJWegCgoYBCwGUgGHivm+2jgA/v7lUBT+/wVwBrgV/uzf0nyC3sFlZcn0qKFSMeOwfXn//57XZVeeKFUl1uWJZfNuUxq3Hm3gMjbb5ezfEGO1ytywQUibdv55Lxn46TvW33Fsqyy3zgzU+Txx0UiI0Vq1NCKKT297Pc9HZYlsnixSPfuuj707i3yc+XxoWgoPypcQQERwFagORAF/AK0K5LmT8BMe38Y8IG93wloYO+3B1JKkmfYK6hZs/QjS0x0WpJTufJKkfPOEzl27JwvTdyUKPyPS85vnhY0I5eBZuFC/WiHPbZEmIR8tvmzst3wiy9EmjTRN73zTpHU1HKRs0T4/SJvvCFSp452YPzAA2XqXRsqH4FQUD2BxQWOJwATiqRZDPS0991AGvbi4AJpFHAYiD5bnmGtoHJy9NDJxRfrlmqw8dNPujo99dQ5XZbry5XWM1pL/bseFBB5//0Kki/IsSyRSy4RqVfPkgv+cZG0ebmN5Ppyz/1G6ekiI0fqZ9GuncjSpeUvbEk5dEhkzBgtS8uWIsuXOyeLIagoqYIqixVfPLC7wPEe+1yxaUTEB6QDRR3G3QQkiUixJkBKqdFKqdVKqdUHDx4sg7ghzsyZsHu3DhoYjOZt3brBDTfouFFpaSW+bOqyqWw+kIxr6dN06KCXVIUjSsGLL8KBA4ou2z5kU9omXlz24rndZOlSbRI4Z452IJyUBJc66Cqqdm1tGbhkibbw690bHn9cu9AwGEpCSbRYcRtwMzC7wPGdwMtF0vwGNCxwvBWoU+D4QvvcBSXJM2x7UEeOiNSuLXL55cHZe8pn/XodL2rs2BIl33Z4m3imeKTLfTMERBYtqmD5QoDbbhPxeESufHmUVJlSRbYd3nb2i7xekYkTRZTSc5Q//ljxgp4r6eki99yje1Ndu4okJzstkcFBCEAPKgVoVOC4oX2u2DRKKTcQCxyyjxsCi4ARIrK1DHJUfp55Bo4c0b2TYOw95dOuHYwaBa++Cr//fsakIsL9X92PK6Mhez65jy5d9JrfcOfZZ/Wn77OXUN5qjP16bH5jrnh274Z+/XTP+g9/gJ9/hgKRXIOGGjXgjTfg448hOVl7pHj/faelMgQ7JdFixW3oOaVtQDNOGklcWCTNnylsJLHA3q9pp7/xXPIMyx7Utm0iUVEid9/ttCQlIzVVpFo1kSFDzpjsow0fCY9XlYatU6VaNWPsVZAXX9QdjdoNjggj+suijafpWn72mTYbr1ZNLz8IFXbsEOnVS//IkSNFsrKclsgQYAiQmfnVwBb0MN3f7HNPAdfb+x7gQ7SZ+U9Ac/v8RCAT+LnAVu9s+YWlgho2TC+q3LPHaUlKzpQpcqbVtsdyjkn81EZSo+M34nJZ8lkZDdYqI99/L9KipSUgEnPxPDmYfvzkl16vyKOP6jLu1ElkyxbnBC0tXq9eoQwiCQmh+RsMpSYgCirQW9gpqBUr9CN64gmnJTk3MjNF4uNFunUrdr3WPZ/cI/R+XkBk2jQH5AsRsrJEbh+zR0Ck481f6JMpKSJ9+uh6ce+9ItnZzgpZVr78Us+vVq8u8uGHTktjCBBGQYU6fr9Iz54icXGlWlvkOG+9pavXO+8UOv3Rho+E6/WC3PvuC26bj2Chw8BVgitP/vXCqyL16onExITWkN7Z2LnzpBeKsWNFckthXm8IKYyCCnVefVU/njlznJakdPj9es1WnToiBw+KiMie9D1SffT1olxeufwKv3i9DssYIqTszZaIKofEHf+D7O7USltLVjZyc/WCXtD1ZudOpyUyVCAlVVDGm3kwkpKi17EMGAB33eW0NKXD5YJZs+DoUXj4YSyxGDrzcY6/M4cLWvpZ+KGrvEJIVW4OHqTB3TcwxfUgvpTeDEy4F6ttG6elKn+ionRk6IULYeNGbeX3xRdOS2VwGKOggpG//EUvZpw5M7jNys9Ghw4wfjy8/TZPvfIQy5+fSHVPFf79VTSxsU4LFwJ89x1cdBF89x3jX+xNqy4pbHz/HiZ9PtNpySqOm26CNWugUSO49lp45BGzsDeMMQoq2Fi0SG+TJkGLFk5LU3YmTuTLS+OZPG0QruNN+Ppzj4lvdzb8fv38BwyAatVg5UrUvaP59N0GuPwxPP1oPF9u+cppKSuOFi10jKo//Um71+jTR0f7NYQdRkEFE0ePwv33a3c1Dz3ktDTlwm/Hkrmx5hDYOoipl35Kr14h3CMMBDt26IW3kyfDHXfo3kTHjgC0aaN45u8WbBrMjeN+ZP2B9c7KWpF4PPDKK3rIb/NmPeT37rsno/oawoOSTFQFy1apjST8fpHrrxdxu0VWlXM8IIfYn7Ff4p+4RFRUhvRpuE4s0F62DadiWSJz52pz6+rV9f5pkl09OFNQPqn/5+FyIONAgAV1gG3bdOgOELnlFu2E1hDSYKz4QoznnpPKtDAoIzdDes7qLarpUomp5pOdm7N1HKtatfQLx3CS/ftFbr5ZP/9LLhHZvv2MyY8dE2naIkuISZWuUwdLZl4YhLLw+XT0Xrdbr7H76iunJTKUAaOgQolvv9VOVm+5pVIsDDqWc0wunXOpqKvGCojMnm1/kZwsEhsr0rlz6C8wLQ/ye021a2t3Vs8+W+JgWBs2iHiq5gmNfpQ+swbI8dzjZ7+oMrBmjUjbtnIizlVamtMSGUqBUVChQkqKXnzZpk1oLsgtQnpOuvR6o5e47u0mUR6vXH11EZ376ae62o0a5ZiMQcHWrTrII2i/dKVY2/TBB/py1Wuq9H6jt6TnVGC03GAiJ0d7V3G7RerWFZk3r1I07MIJo6BCgUOHtC+1mJhKsfjycNZh6T6ru0Q81Fxq1smSxo1F9u0rJmG+D7a//z3gMjrO8eM6DHt0tHbyOmNGse6gSsp99+midN1+nXSf1V0OZx0uR2GDnHXrToaX79NHJCnJaYkMJcQoqGDn8GGRLl300E4lGE9fl7pOWkxvIe4JdaRxy3SJjRX57bfTJPb5dOAj0HNv4YDPJ/L22yINGujffccd5eIAONue2qsemyvuh5tKi+ktZF3qunIQOETw+URef117LFFKZPRokb17nZbKcBZKqqCMmbkTHD0KAwfCr7/qNU+DBjktUZmYt24eF8++mIysPDou/Z2922vw8cdw4YWnuSAiAubOheHDtceMF14IqLwBxbLgww8hIQFGjIDzz4dly+CddyC+aADqc8fjgQULQPxRtPv+ZzKyc7h49sXMWzevHIQPASIidAyy33+HcePgzTfhggv0At9wjsBdWSiJFguWrVL0oFJStJfvyEgJ9TgT6TnpMuazMcIkpNMTo6VT11wB7Se2RHi9IrfeqnsUTz5ZpqGuoCMvT8+NJCTo39e2rciCBRX2G+fN09kMGJgt3afeLExCxnw2JnzmpfJJThYZMUIbHcXEiDzyiMiuXU5LZSgCZogvCFm8WE/qVq0qkpjotDSlxrIsmbduntSfWl/4a11JuGqFKGVJXJzIe++d4828Xv1CAZErrtABD0OZtDRtjRcfr39T69ba83gJrfPKwvTpumrFxFjSd3Si8IRbzp96vry37j2xws2IYONGkeHDtaKKiNBx1VasMMYUQYJRUMGE1yvyt7/pMfL27bWNcIiybNcy6ftmf+GuvnLexV9ItMcnbrfIww+LpJe2sW5ZIrNmiXg8IvXri/z3v+Uqc4Xj9Yp8/rleyxQVZXdlBuhFyQHuFe7YIXLttVqEJhdkSfyQl4VxTaTfW/1k2a5lAZUlKNi+XeShh0Rq1NCF0r69yNSpp7HeMQQKo6CCAcsS+eijk+s2Ro7UwfxCDL/ll8RNidLj5UHCFQ+Lq/Z2AZEaNSwZM6Yc9e26ddrcHnTI+NNaWQQB2dlaKY0apZcJgJ6oHzdO/w4Hya92+VHVQcTddLkw+C7pObO/JG5KFL9ViYZTS0J6ushrr+lQHqB7VZdfrq0ozRBgwDEKykl8Ph0pNN8Etk0bkUWLnJbqnLAsS5L2Jsn4/4yX+An9he7TRUVlCIj07uOTd9+tIF2bkSEyebJu8Solcvvt2vWT00MzPp/I6tW69X3NNXp+A7Sp+NCh+vkGYaC9bdu0NX+r1n5tjl71iNBzqsRP6C/j/zNekvYmhefw34QJJxtDoE0hH3xQr9M7csRpCSs9JVVQSqctHUqpQcBLQAQwW0SeK/J9NPA20AU4BNwqIjvs7yYAIwE/MFZEFp8tv65du8rq1atLLW+FYlmQlATvvQfz50Nqqg4ZMGmStt4KgeBHe4/vZemOpSzduZT/bFrOth86w9qRsOsSItx+brtN8eADLjp1CoAwhw7BP/4BM2ZAdrb2cD1sGAwZosN4REZWXN6ZmbBlC2zYoJ21rl4Na9dCRob+vlUr6N8fBg/Wjl2joytOlnJCBJYuhZdfsfjkE/D7XNBwJSTMpVmfVQxs34XLmlzGZU0vo0H1Bk6LGzg2b4ZPPoHFi7V1ZW6uDnHTti106QJdu+qQJ23aQN26oR3+JohQSq0Rka5nTVdaBaWUigC2AFcAe4BVwHAR2VAgzZ+ABBEZo5QaBgwRkVuVUu2A+UB3oAHwX6CViPjPlGfQKCivV3udTk7WSmnZMli+HI4c0YHXrrkGbr9dx7MJspdXtjeb3cd2s/3wTjbsSuXn5H2s33GIrbszOLovFg5eiCutA6S1wfJG0aKVj1Ej3YwYAfXrOyDwkSPaFH/+fFiyRDcEqlSBzp31y6NFC90QaNxYv0CqVdNb0QaB16sVT2YmHDsGaWl6O3AA9uyB3bth1y79THfvPnmdx6NfUF26QK9e0LcvNAjtF3hqKsybB2/O8bFhvRuUheu8rVj11kL9X6jV4DAtm3no2KoWXVrF0/y8xjSp2YRGNRpRJbKK0+JXHDk5sHKl1uSrVumGSWrqye9r1YLWraFZM2jSRG/x8RAXd3LzeJyTP4QIhILqCUwSkSvt4wkAIvJsgTSL7TTLlVJuIBWoCzxWMG3BdGfKsywKKnVnKvNmfwuc6NTrl50lIBb4LfD7dCwen18HScvL1Z/Z2ZCRCZkZcPw4HE3X1+QTFwdNmyLNmkG7dlCl6in5CyfLuWiRW/njrRQQTQSxwMLCsvT3frHw+S18fsHvF/K8Fnk+P948IdfrtzcfuXl+snL8ZGVbZGVbZByPIPOoh+xjMfgzakFGfcisB9apvZD68blc1CGKDh0UN9wAPXsGUaNx/3749lv46Sf9IklK0i+V4nC7teD5Beo/Q9vH5dJKp3Fj/fJp00a/iNq00S3pEOj9lgYR+OUXSEyEtWuFVWvzSNlZTIMq6jh4joLnKBExR/HEHiemZjbVa3ipWhWqVlVUi3ERHekmym1vkRFEul1E258REQp3hMLtVkQoFy6X0pvSn0qBQp2oa0opFIUrXsF6eKbvCp8vY+VNT4fUfbohs/8AHDygG01Hj+r3R1HckVC1KlTxgKcKREdBtEc3XCMjISpS1ye3GyLyPyN0HYxw6U+XS/8gVWDfpQBln8//wfb+ic/TFYQ642GJKHDfiAgXD0y8uRQ3KXi7kimosvzz4oECTU32ABefLo2I+JRS6cB59vkVRa4tdtWiUmo0MBqgcePGpRZ25f+t55Epw0t9/RlJBX6pmFuXBxGeTKrEZlAnNpvYxj7i6mfTuME+mjeqRtumNWnQwEVcnG4MVq8eXD2+QsTF6WG+YcP0sWXpxZi7dunt8GE9DJeRAVlZOo2y/9QeD8TE6K16dd3bqlsX6tTRXcNKqoTOhFK6c3jRRaDfWtEcPw47d+pO5M6dFpt3ppNyMJPUtFzSDkWRfqQBGQc9HEmuxoGsGLDCr9zCnogcHpgYmKyCvnaJyOvA66B7UKW9T89+CUx/bpHdKrFbAydaK/Y5dyS4I/QWGa1bPOXYfSjYmnOpU1uA+a1CLY5uWUYoF0opIlwuUBDljsDtcuF2u/BEuvFEu6kSFYknMpJqVTxER7pxu/X72OPJ/wkxQEy5/Y6gweU6ObTSrZvT0lQKqleH9u31puOZ1rK34snL022BrCzdXsj1+sjMySHX5yXH6z3Ro/f5dW8/z+vXHVpLjwz4xR4hQE4MSthHhfIpOOpQdNSnDNPoziGW7tV7vbrg/H49imNZYPlB7DT5Izx6WIWTI0DYP1xOLYBChXVKxmUWXb+6birzfUpCWRRUCtCowHFD+1xxafbYQ3yxaGOJklxbrtSLr8tfxg+pyCwMhrAjKkpvNWvmn3ED1RyUyFCZKIsvvlVAS6VUM6VUFDAMSCySJhG4y96/GVhimxgmAsOUUtFKqWZAS+CnMshiMBgMhkpGqXtQ9pzS/cBitJn5myKyXin1FNrGPRF4A3hHKZUMHEYrMex0C4ANgA/489ks+AwGg8EQXpRpHVSgUUodBHaW8TZ1gLRyEKeyYMqjMKY8CmPKozCmPE6lNGXSRETqni1RSCmo8kAptbok5o3hgimPwpjyKIwpj8KY8jiViiwTEw/KYDAYDEGJUVAGg8FgCErCUUG97rQAQYYpj8KY8iiMKY/CmPI4lQork7CbgzIYDAZDaBCOPSiDwWAwhABGQRkMBoMhKAkbBaWUGqSU2qyUSlZKPea0PIFGKdVIKfWtUmqDUmq9Umqcfb62Uuo/Sqnf7c/TO16rhCilIpRSa5VSn9vHzZRSK+168oHtJSVsUErVVEotVEptUkptVEr1DOc6opR60P6//KaUmq+U8oRTHVFKvamUOqCU+q3AuWLrg9JMt8tlnVKqc1nzDwsFZceuegW4CmgHDLdjUoUTPuBhEWkH9AD+bJfBY8A3ItIS+MY+DifGARsLHD8P/EtEWgBH0EE1w4mXgK9FpA3QEV02YVlHlFLxwFigq4i0R3vMGUZ41ZG3gEFFzp2uPlyFdlvXEh2B4rWyZh4WCgodGDFZRLaJSB7wPjDYYZkCiojsE5Eke/84+sUTjy6HuXayucANzkgYeJRSDYFrgNn2sQL6AwvtJOFWHrHApWgXZYhInogcJYzrCNodXBXb2XVVYB9hVEdE5Hu0m7qCnK4+DAbetqO6rwBqKqXOL0v+4aKgiotdVWz8qXBAKdUU6ASsBOJEZJ/9VSoQ55BYTjANeBTIjzx3HnBURHz2cbjVk2bAQWCOPew5W+lYLWFZR0QkBZgK7EIrpnRgDeFdR+D09aHc37PhoqAMNkqpasBHwAMicqzgd7an+bBYd6CUuhY4ICJrnJYliHADnYHXRKQTkEmR4bwwqyO10L2CZkADdFC1osNdYU1F14dwUVABjz8VjCilItHKaZ6IfGyf3p/fDbc/DzglX4DpDVyvlNqBHvLtj55/qWkP50D41ZM9wB4RWWkfL0QrrHCtI5cD20XkoIh4gY/R9Sac6wicvj6U+3s2XBRUSWJXVWrs+ZU3gI0i8s8CXxWM2XUX8GmgZXMCEZkgIg1FpCm6PiwRkduBb9GxyyCMygNARFKB3Uqp1vapAeiQOGFZR9BDez2UUlXt/09+eYRtHbE5XX1IBEbY1nw9gPQCQ4GlImw8SSilrkbPOeTHrnrGYZECilLqEuD/gF85OefyOHoeagHQGB3K5BYRKTopWqlRSvUFHhGRa5VSzdE9qtrAWuAOEcl1Ur5AopS6CG00EgVsA+5GN2TDso4opSYDt6KtYNcCf0TPq4RFHVFKzQf6okNq7AeeBD6hmPpgK/GX0cOgWcDdIrK6TPmHi4IyGAwGQ2gRLkN8BoPBYAgxjIIyGAwGQ1BiFJTBYDAYghKjoAwGg8EQlBgFZTAYDIagxCgog8FgMAQlRkEZDAaDISj5f6BTr9XdUiFQAAAAAElFTkSuQmCC\n", "text/plain": [ - "<Figure size 432x288 with 6 Axes>" + "<Figure size 432x288 with 2 Axes>" ] }, "metadata": {}, @@ -131,23 +126,6 @@ } ], "source": [ - "# Author: Remi Flamary <remi.flamary@unice.fr>\n", - "#\n", - "# License: MIT License\n", - "\n", - "import numpy as np\n", - "import matplotlib.pylab as pl\n", - "import ot\n", - "# necessary for 3d plot even if not used\n", - "from mpl_toolkits.mplot3d import Axes3D # noqa\n", - "from matplotlib.collections import PolyCollection # noqa\n", - "\n", - "#import ot.lp.cvx as cvx\n", - "\n", - "#\n", - "# Generate data\n", - "# -------------\n", - "\n", "#%% parameters\n", "\n", "problems = []\n", @@ -170,9 +148,6 @@ "M = ot.utils.dist0(n)\n", "M /= M.max()\n", "\n", - "#\n", - "# Plot data\n", - "# ---------\n", "\n", "#%% plot the distributions\n", "\n", @@ -182,10 +157,6 @@ "pl.title('Distributions')\n", "pl.tight_layout()\n", "\n", - "#\n", - "# Barycenter computation\n", - "# ----------------------\n", - "\n", "#%% barycenter computation\n", "\n", "alpha = 0.5 # 0<=alpha<=1\n", @@ -220,8 +191,87 @@ "pl.title('Barycenters')\n", "pl.tight_layout()\n", "\n", - "problems.append([A, [bary_l2, bary_wass, bary_wass2]])\n", - "\n", + "problems.append([A, [bary_l2, bary_wass, bary_wass2]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Dirac Data\n", + "----------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Elapsed time : 0.014856815338134766 s\n", + "Primal Feasibility Dual Feasibility Duality Gap Step Path Parameter Objective \n", + "1.0 1.0 1.0 - 1.0 1700.336700337 \n", + "0.006776466288966 0.006776466288966 0.006776466288966 0.9932238515788 0.006776466288966 125.6649255808 \n", + "0.004036918865495 0.004036918865495 0.004036918865495 0.4272973099316 0.004036918865495 12.3471617011 \n", + "0.00121923268707 0.00121923268707 0.00121923268707 0.749698685599 0.00121923268707 0.3243835647408 \n", + "0.0003837422984432 0.0003837422984432 0.0003837422984432 0.6926882608284 0.0003837422984432 0.1361719397493 \n", + "0.0001070128410183 0.0001070128410183 0.0001070128410183 0.7643889137854 0.0001070128410183 0.07581952832518 \n", + "0.0001001275033711 0.0001001275033711 0.0001001275033711 0.07058704837812 0.0001001275033712 0.0734739493635 \n", + "4.550897507844e-05 4.550897507841e-05 4.550897507844e-05 0.5761172484828 4.550897507845e-05 0.05555077655047 \n", + "8.557124125522e-06 8.5571241255e-06 8.557124125522e-06 0.8535925441152 8.557124125522e-06 0.04439814660221 \n", + "3.611995628407e-06 3.61199562841e-06 3.611995628414e-06 0.6002277331554 3.611995628415e-06 0.04283007762152 \n", + "7.590393750365e-07 7.590393750491e-07 7.590393750378e-07 0.8221486533416 7.590393750381e-07 0.04192322976248 \n", + "8.299929287441e-08 8.299929286079e-08 8.299929287532e-08 0.9017467938799 8.29992928758e-08 0.04170825633295 \n", + "3.117560203449e-10 3.117560130137e-10 3.11756019954e-10 0.997039969226 3.11756019952e-10 0.04168179329766 \n", + "1.559749653711e-14 1.558073160926e-14 1.559756940692e-14 0.9999499686183 1.559750643989e-14 0.04168169240444 \n", + "Optimization terminated successfully.\n", + "Elapsed time : 2.703077793121338 s\n", + "Elapsed time : 0.0029761791229248047 s\n", + "Primal Feasibility Dual Feasibility Duality Gap Step Path Parameter Objective \n", + "1.0 1.0 1.0 - 1.0 1700.336700337 \n", + "0.006774675520727 0.006774675520727 0.006774675520727 0.9932256422636 0.006774675520727 125.6956034743 \n", + "0.002048208707562 0.002048208707562 0.002048208707562 0.7343095368143 0.002048208707562 5.213991622123 \n", + "0.000269736547478 0.0002697365474781 0.0002697365474781 0.8839403501193 0.000269736547478 0.505938390389 \n", + "6.832109993943e-05 6.832109993944e-05 6.832109993944e-05 0.7601171075965 6.832109993943e-05 0.2339657807272 \n", + "2.437682932219e-05 2.43768293222e-05 2.437682932219e-05 0.6663448297475 2.437682932219e-05 0.1471256246325 \n", + "1.13498321631e-05 1.134983216308e-05 1.13498321631e-05 0.5553643816404 1.13498321631e-05 0.1181584941171 \n", + "3.342312725885e-06 3.342312725884e-06 3.342312725885e-06 0.7238133571615 3.342312725885e-06 0.1006387519747 \n", + "7.078561231603e-07 7.078561231509e-07 7.078561231604e-07 0.8033142552512 7.078561231603e-07 0.09474734646269 \n", + "1.966870956916e-07 1.966870954537e-07 1.966870954468e-07 0.752547917788 1.966870954633e-07 0.09354342735766 \n", + "4.19989524849e-10 4.199895164852e-10 4.199895238758e-10 0.9984019849375 4.19989523951e-10 0.09310367785861 \n", + "2.101015938666e-14 2.100625691113e-14 2.101023853438e-14 0.999949974425 2.101023691864e-14 0.09310274466458 \n", + "Optimization terminated successfully.\n", + "Elapsed time : 2.6085386276245117 s\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 460.8x216 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 2 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ "#%% parameters\n", "\n", "a1 = 1.0 * (x > 10) * (x < 50)\n", @@ -247,9 +297,6 @@ "pl.title('Distributions')\n", "pl.tight_layout()\n", "\n", - "#\n", - "# Barycenter computation\n", - "# ----------------------\n", "\n", "#%% barycenter computation\n", "\n", @@ -319,9 +366,6 @@ "pl.title('Distributions')\n", "pl.tight_layout()\n", "\n", - "#\n", - "# Barycenter computation\n", - "# ----------------------\n", "\n", "#%% barycenter computation\n", "\n", @@ -358,14 +402,38 @@ "pl.plot(x, bary_wass2, 'b', label='LP Wasserstein')\n", "pl.legend()\n", "pl.title('Barycenters')\n", - "pl.tight_layout()\n", - "\n", - "\n", - "#\n", - "# Final figure\n", - "# ------------\n", - "#\n", + "pl.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Final figure\n", + "------------\n", "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 1440x432 with 6 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ "#%% plot\n", "\n", "nbm = len(problems)\n", diff --git a/notebooks/plot_otda_linear_mapping.ipynb b/notebooks/plot_otda_linear_mapping.ipynb index 7b0e7ad..4b6713d 100644 --- a/notebooks/plot_otda_linear_mapping.ipynb +++ b/notebooks/plot_otda_linear_mapping.ipynb @@ -16,9 +16,10 @@ "metadata": {}, "source": [ "\n", - "Created on Tue Mar 20 14:31:15 2018\n", + "# Linear OT mapping estimation\n", + "\n", + "\n", "\n", - "@author: rflamary\n", "\n" ] }, @@ -30,6 +31,10 @@ }, "outputs": [], "source": [ + "# Author: Remi Flamary <remi.flamary@unice.fr>\n", + "#\n", + "# License: MIT License\n", + "\n", "import numpy as np\n", "import pylab as pl\n", "import ot" @@ -94,7 +99,7 @@ { "data": { "text/plain": [ - "[<matplotlib.lines.Line2D at 0x7fec708d6710>]" + "[<matplotlib.lines.Line2D at 0x7f3ed402e748>]" ] }, "execution_count": 4, @@ -103,7 +108,7 @@ }, { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "<Figure size 360x360 with 1 Axes>" ] @@ -158,7 +163,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "<Figure size 360x360 with 1 Axes>" ] |
