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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 differnew file mode 100644 index 0000000..3500812 --- /dev/null +++ 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 differnew file mode 100644 index 0000000..37fef68 --- /dev/null +++ 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 differnew file mode 100644 index 0000000..88796df --- /dev/null +++ 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 differnew file mode 100644 index 0000000..22b5d0c --- /dev/null +++ b/docs/source/auto_examples/images/sphx_glr_plot_otda_linear_mapping_002.png diff --git a/docs/source/auto_examples/images/sphx_glr_plot_otda_linear_mapping_004.png b/docs/source/auto_examples/images/sphx_glr_plot_otda_linear_mapping_004.png Binary files differnew file mode 100644 index 0000000..ff10b72 --- /dev/null +++ b/docs/source/auto_examples/images/sphx_glr_plot_otda_linear_mapping_004.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 differnew file mode 100644 index 0000000..c68e95f --- /dev/null +++ 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 differnew file mode 100644 index 0000000..277950e --- /dev/null +++ b/docs/source/auto_examples/images/thumb/sphx_glr_plot_otda_linear_mapping_thumb.png diff --git a/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.ipynb b/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.ipynb new file mode 100644 index 0000000..2199162 --- /dev/null +++ b/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.ipynb @@ -0,0 +1,108 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# 1D Wasserstein barycenter comparison between exact LP and entropic regularization\n\n\nThis example illustrates the computation of regularized Wasserstein Barycenter\nas proposed in [3] and exact LP barycenters using standard LP solver.\n\nIt reproduces approximately Figure 3.1 and 3.2 from the following paper:\nCuturi, M., & Peyr\u00e9, G. (2016). A smoothed dual approach for variational\nWasserstein problems. SIAM Journal on Imaging Sciences, 9(1), 320-343.\n\n[3] Benamou, J. D., Carlier, G., Cuturi, M., Nenna, L., & Peyr\u00e9, G. (2015).\nIterative Bregman projections for regularized transportation problems\nSIAM Journal on Scientific Computing, 37(2), A1111-A1138.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Author: Remi Flamary <remi.flamary@unice.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\n# necessary for 3d plot even if not used\nfrom mpl_toolkits.mplot3d import Axes3D # noqa\nfrom matplotlib.collections import PolyCollection # noqa\n\n#import ot.lp.cvx as cvx" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Gaussian Data\n-------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% parameters\n\nproblems = []\n\nn = 100 # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\n# Gaussian distributions\na1 = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std\na2 = ot.datasets.make_1D_gauss(n, m=60, s=8)\n\n# creating matrix A containing all distributions\nA = np.vstack((a1, a2)).T\nn_distributions = A.shape[1]\n\n# loss matrix + normalization\nM = ot.utils.dist0(n)\nM /= M.max()\n\n\n#%% plot the distributions\n\npl.figure(1, figsize=(6.4, 3))\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\npl.tight_layout()\n\n#%% barycenter computation\n\nalpha = 0.5 # 0<=alpha<=1\nweights = np.array([1 - alpha, alpha])\n\n# l2bary\nbary_l2 = A.dot(weights)\n\n# wasserstein\nreg = 1e-3\not.tic()\nbary_wass = ot.bregman.barycenter(A, M, reg, weights)\not.toc()\n\n\not.tic()\nbary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True)\not.toc()\n\npl.figure(2)\npl.clf()\npl.subplot(2, 1, 1)\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\n\npl.subplot(2, 1, 2)\npl.plot(x, bary_l2, 'r', label='l2')\npl.plot(x, bary_wass, 'g', label='Reg Wasserstein')\npl.plot(x, bary_wass2, 'b', label='LP Wasserstein')\npl.legend()\npl.title('Barycenters')\npl.tight_layout()\n\nproblems.append([A, [bary_l2, bary_wass, bary_wass2]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Dirac Data\n----------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% parameters\n\na1 = 1.0 * (x > 10) * (x < 50)\na2 = 1.0 * (x > 60) * (x < 80)\n\na1 /= a1.sum()\na2 /= a2.sum()\n\n# creating matrix A containing all distributions\nA = np.vstack((a1, a2)).T\nn_distributions = A.shape[1]\n\n# loss matrix + normalization\nM = ot.utils.dist0(n)\nM /= M.max()\n\n\n#%% plot the distributions\n\npl.figure(1, figsize=(6.4, 3))\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\npl.tight_layout()\n\n\n#%% barycenter computation\n\nalpha = 0.5 # 0<=alpha<=1\nweights = np.array([1 - alpha, alpha])\n\n# l2bary\nbary_l2 = A.dot(weights)\n\n# wasserstein\nreg = 1e-3\not.tic()\nbary_wass = ot.bregman.barycenter(A, M, reg, weights)\not.toc()\n\n\not.tic()\nbary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True)\not.toc()\n\n\nproblems.append([A, [bary_l2, bary_wass, bary_wass2]])\n\npl.figure(2)\npl.clf()\npl.subplot(2, 1, 1)\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\n\npl.subplot(2, 1, 2)\npl.plot(x, bary_l2, 'r', label='l2')\npl.plot(x, bary_wass, 'g', label='Reg Wasserstein')\npl.plot(x, bary_wass2, 'b', label='LP Wasserstein')\npl.legend()\npl.title('Barycenters')\npl.tight_layout()\n\n#%% parameters\n\na1 = np.zeros(n)\na2 = np.zeros(n)\n\na1[10] = .25\na1[20] = .5\na1[30] = .25\na2[80] = 1\n\n\na1 /= a1.sum()\na2 /= a2.sum()\n\n# creating matrix A containing all distributions\nA = np.vstack((a1, a2)).T\nn_distributions = A.shape[1]\n\n# loss matrix + normalization\nM = ot.utils.dist0(n)\nM /= M.max()\n\n\n#%% plot the distributions\n\npl.figure(1, figsize=(6.4, 3))\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\npl.tight_layout()\n\n\n#%% barycenter computation\n\nalpha = 0.5 # 0<=alpha<=1\nweights = np.array([1 - alpha, alpha])\n\n# l2bary\nbary_l2 = A.dot(weights)\n\n# wasserstein\nreg = 1e-3\not.tic()\nbary_wass = ot.bregman.barycenter(A, M, reg, weights)\not.toc()\n\n\not.tic()\nbary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True)\not.toc()\n\n\nproblems.append([A, [bary_l2, bary_wass, bary_wass2]])\n\npl.figure(2)\npl.clf()\npl.subplot(2, 1, 1)\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\n\npl.subplot(2, 1, 2)\npl.plot(x, bary_l2, 'r', label='l2')\npl.plot(x, bary_wass, 'g', label='Reg Wasserstein')\npl.plot(x, bary_wass2, 'b', label='LP Wasserstein')\npl.legend()\npl.title('Barycenters')\npl.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Final figure\n------------\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% plot\n\nnbm = len(problems)\nnbm2 = (nbm // 2)\n\n\npl.figure(2, (20, 6))\npl.clf()\n\nfor i in range(nbm):\n\n A = problems[i][0]\n bary_l2 = problems[i][1][0]\n bary_wass = problems[i][1][1]\n bary_wass2 = problems[i][1][2]\n\n pl.subplot(2, nbm, 1 + i)\n for j in range(n_distributions):\n pl.plot(x, A[:, j])\n if i == nbm2:\n pl.title('Distributions')\n pl.xticks(())\n pl.yticks(())\n\n pl.subplot(2, nbm, 1 + i + nbm)\n\n pl.plot(x, bary_l2, 'r', label='L2 (Euclidean)')\n pl.plot(x, bary_wass, 'g', label='Reg Wasserstein')\n pl.plot(x, bary_wass2, 'b', label='LP Wasserstein')\n if i == nbm - 1:\n pl.legend()\n if i == nbm2:\n pl.title('Barycenters')\n\n pl.xticks(())\n pl.yticks(())" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.5" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.py b/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.py new file mode 100644 index 0000000..b82765e --- /dev/null +++ b/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.py @@ -0,0 +1,281 @@ +# -*- coding: utf-8 -*- +""" +================================================================================= +1D Wasserstein barycenter comparison between exact LP and entropic regularization +================================================================================= + +This example illustrates the computation of regularized Wasserstein Barycenter +as proposed in [3] and exact LP barycenters using standard LP solver. + +It reproduces approximately Figure 3.1 and 3.2 from the following paper: +Cuturi, M., & Peyré, G. (2016). A smoothed dual approach for variational +Wasserstein problems. SIAM Journal on Imaging Sciences, 9(1), 320-343. + +[3] Benamou, J. D., Carlier, G., Cuturi, M., Nenna, L., & Peyré, G. (2015). +Iterative Bregman projections for regularized transportation problems +SIAM Journal on Scientific Computing, 37(2), A1111-A1138. + +""" + +# Author: Remi Flamary <remi.flamary@unice.fr> +# +# License: MIT License + +import numpy as np +import matplotlib.pylab as pl +import ot +# necessary for 3d plot even if not used +from mpl_toolkits.mplot3d import Axes3D # noqa +from matplotlib.collections import PolyCollection # noqa + +#import ot.lp.cvx as cvx + +############################################################################## +# Gaussian Data +# ------------- + +#%% parameters + +problems = [] + +n = 100 # nb bins + +# bin positions +x = np.arange(n, dtype=np.float64) + +# Gaussian distributions +# Gaussian distributions +a1 = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std +a2 = ot.datasets.make_1D_gauss(n, m=60, s=8) + +# creating matrix A containing all distributions +A = np.vstack((a1, a2)).T +n_distributions = A.shape[1] + +# loss matrix + normalization +M = ot.utils.dist0(n) +M /= M.max() + + +#%% plot the distributions + +pl.figure(1, figsize=(6.4, 3)) +for i in range(n_distributions): + pl.plot(x, A[:, i]) +pl.title('Distributions') +pl.tight_layout() + +#%% barycenter computation + +alpha = 0.5 # 0<=alpha<=1 +weights = np.array([1 - alpha, alpha]) + +# l2bary +bary_l2 = A.dot(weights) + +# wasserstein +reg = 1e-3 +ot.tic() +bary_wass = ot.bregman.barycenter(A, M, reg, weights) +ot.toc() + + +ot.tic() +bary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True) +ot.toc() + +pl.figure(2) +pl.clf() +pl.subplot(2, 1, 1) +for i in range(n_distributions): + pl.plot(x, A[:, i]) +pl.title('Distributions') + +pl.subplot(2, 1, 2) +pl.plot(x, bary_l2, 'r', label='l2') +pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') +pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') +pl.legend() +pl.title('Barycenters') +pl.tight_layout() + +problems.append([A, [bary_l2, bary_wass, bary_wass2]]) + +############################################################################## +# Dirac Data +# ---------- + +#%% parameters + +a1 = 1.0 * (x > 10) * (x < 50) +a2 = 1.0 * (x > 60) * (x < 80) + +a1 /= a1.sum() +a2 /= a2.sum() + +# creating matrix A containing all distributions +A = np.vstack((a1, a2)).T +n_distributions = A.shape[1] + +# loss matrix + normalization +M = ot.utils.dist0(n) +M /= M.max() + + +#%% plot the distributions + +pl.figure(1, figsize=(6.4, 3)) +for i in range(n_distributions): + pl.plot(x, A[:, i]) +pl.title('Distributions') +pl.tight_layout() + + +#%% barycenter computation + +alpha = 0.5 # 0<=alpha<=1 +weights = np.array([1 - alpha, alpha]) + +# l2bary +bary_l2 = A.dot(weights) + +# wasserstein +reg = 1e-3 +ot.tic() +bary_wass = ot.bregman.barycenter(A, M, reg, weights) +ot.toc() + + +ot.tic() +bary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True) +ot.toc() + + +problems.append([A, [bary_l2, bary_wass, bary_wass2]]) + +pl.figure(2) +pl.clf() +pl.subplot(2, 1, 1) +for i in range(n_distributions): + pl.plot(x, A[:, i]) +pl.title('Distributions') + +pl.subplot(2, 1, 2) +pl.plot(x, bary_l2, 'r', label='l2') +pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') +pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') +pl.legend() +pl.title('Barycenters') +pl.tight_layout() + +#%% parameters + +a1 = np.zeros(n) +a2 = np.zeros(n) + +a1[10] = .25 +a1[20] = .5 +a1[30] = .25 +a2[80] = 1 + + +a1 /= a1.sum() +a2 /= a2.sum() + +# creating matrix A containing all distributions +A = np.vstack((a1, a2)).T +n_distributions = A.shape[1] + +# loss matrix + normalization +M = ot.utils.dist0(n) +M /= M.max() + + +#%% plot the distributions + +pl.figure(1, figsize=(6.4, 3)) +for i in range(n_distributions): + pl.plot(x, A[:, i]) +pl.title('Distributions') +pl.tight_layout() + + +#%% barycenter computation + +alpha = 0.5 # 0<=alpha<=1 +weights = np.array([1 - alpha, alpha]) + +# l2bary +bary_l2 = A.dot(weights) + +# wasserstein +reg = 1e-3 +ot.tic() +bary_wass = ot.bregman.barycenter(A, M, reg, weights) +ot.toc() + + +ot.tic() +bary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True) +ot.toc() + + +problems.append([A, [bary_l2, bary_wass, bary_wass2]]) + +pl.figure(2) +pl.clf() +pl.subplot(2, 1, 1) +for i in range(n_distributions): + pl.plot(x, A[:, i]) +pl.title('Distributions') + +pl.subplot(2, 1, 2) +pl.plot(x, bary_l2, 'r', label='l2') +pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') +pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') +pl.legend() +pl.title('Barycenters') +pl.tight_layout() + + +############################################################################## +# Final figure +# ------------ +# + +#%% plot + +nbm = len(problems) +nbm2 = (nbm // 2) + + +pl.figure(2, (20, 6)) +pl.clf() + +for i in range(nbm): + + A = problems[i][0] + bary_l2 = problems[i][1][0] + bary_wass = problems[i][1][1] + bary_wass2 = problems[i][1][2] + + pl.subplot(2, nbm, 1 + i) + for j in range(n_distributions): + pl.plot(x, A[:, j]) + if i == nbm2: + pl.title('Distributions') + pl.xticks(()) + pl.yticks(()) + + pl.subplot(2, nbm, 1 + i + nbm) + + pl.plot(x, bary_l2, 'r', label='L2 (Euclidean)') + pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') + pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') + if i == nbm - 1: + pl.legend() + if i == nbm2: + pl.title('Barycenters') + + pl.xticks(()) + pl.yticks(()) diff --git a/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.rst b/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.rst new file mode 100644 index 0000000..bd1c710 --- /dev/null +++ b/docs/source/auto_examples/plot_barycenter_lp_vs_entropic.rst @@ -0,0 +1,447 @@ + + +.. _sphx_glr_auto_examples_plot_barycenter_lp_vs_entropic.py: + + +================================================================================= +1D Wasserstein barycenter comparison between exact LP and entropic regularization +================================================================================= + +This example illustrates the computation of regularized Wasserstein Barycenter +as proposed in [3] and exact LP barycenters using standard LP solver. + +It reproduces approximately Figure 3.1 and 3.2 from the following paper: +Cuturi, M., & Peyré, G. (2016). A smoothed dual approach for variational +Wasserstein problems. SIAM Journal on Imaging Sciences, 9(1), 320-343. + +[3] Benamou, J. D., Carlier, G., Cuturi, M., Nenna, L., & Peyré, G. (2015). +Iterative Bregman projections for regularized transportation problems +SIAM Journal on Scientific Computing, 37(2), A1111-A1138. + + + + +.. code-block:: python + + + # Author: Remi Flamary <remi.flamary@unice.fr> + # + # License: MIT License + + import numpy as np + import matplotlib.pylab as pl + import ot + # necessary for 3d plot even if not used + from mpl_toolkits.mplot3d import Axes3D # noqa + from matplotlib.collections import PolyCollection # noqa + + #import ot.lp.cvx as cvx + + + + + + + +Gaussian Data +------------- + + + +.. code-block:: python + + + #%% parameters + + problems = [] + + n = 100 # nb bins + + # bin positions + x = np.arange(n, dtype=np.float64) + + # Gaussian distributions + # Gaussian distributions + a1 = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std + a2 = ot.datasets.make_1D_gauss(n, m=60, s=8) + + # creating matrix A containing all distributions + A = np.vstack((a1, a2)).T + n_distributions = A.shape[1] + + # loss matrix + normalization + M = ot.utils.dist0(n) + M /= M.max() + + + #%% plot the distributions + + pl.figure(1, figsize=(6.4, 3)) + for i in range(n_distributions): + pl.plot(x, A[:, i]) + pl.title('Distributions') + pl.tight_layout() + + #%% barycenter computation + + alpha = 0.5 # 0<=alpha<=1 + weights = np.array([1 - alpha, alpha]) + + # l2bary + bary_l2 = A.dot(weights) + + # wasserstein + reg = 1e-3 + ot.tic() + bary_wass = ot.bregman.barycenter(A, M, reg, weights) + ot.toc() + + + ot.tic() + bary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True) + ot.toc() + + pl.figure(2) + pl.clf() + pl.subplot(2, 1, 1) + for i in range(n_distributions): + pl.plot(x, A[:, i]) + pl.title('Distributions') + + pl.subplot(2, 1, 2) + pl.plot(x, bary_l2, 'r', label='l2') + pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') + pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') + pl.legend() + pl.title('Barycenters') + pl.tight_layout() + + problems.append([A, [bary_l2, bary_wass, bary_wass2]]) + + + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_001.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_002.png + :scale: 47 + + +.. rst-class:: sphx-glr-script-out + + Out:: + + Elapsed time : 0.010712385177612305 s + Primal Feasibility Dual Feasibility Duality Gap Step Path Parameter Objective + 1.0 1.0 1.0 - 1.0 1700.336700337 + 0.006776453137632 0.006776453137633 0.006776453137633 0.9932238647293 0.006776453137633 125.6700527543 + 0.004018712867874 0.004018712867874 0.004018712867874 0.4301142633 0.004018712867874 12.26594150093 + 0.001172775061627 0.001172775061627 0.001172775061627 0.7599932455029 0.001172775061627 0.3378536968897 + 0.0004375137005385 0.0004375137005385 0.0004375137005385 0.6422331807989 0.0004375137005385 0.1468420566358 + 0.000232669046734 0.0002326690467341 0.000232669046734 0.5016999460893 0.000232669046734 0.09381703231432 + 7.430121674303e-05 7.430121674303e-05 7.430121674303e-05 0.7035962305812 7.430121674303e-05 0.0577787025717 + 5.321227838876e-05 5.321227838875e-05 5.321227838876e-05 0.308784186441 5.321227838876e-05 0.05266249477203 + 1.990900379199e-05 1.990900379196e-05 1.990900379199e-05 0.6520472013244 1.990900379199e-05 0.04526054405519 + 6.305442046799e-06 6.30544204682e-06 6.3054420468e-06 0.7073953304075 6.305442046798e-06 0.04237597591383 + 2.290148391577e-06 2.290148391582e-06 2.290148391578e-06 0.6941812711492 2.29014839159e-06 0.041522849321 + 1.182864875387e-06 1.182864875406e-06 1.182864875427e-06 0.508455204675 1.182864875445e-06 0.04129461872827 + 3.626786381529e-07 3.626786382468e-07 3.626786382923e-07 0.7101651572101 3.62678638267e-07 0.04113032448923 + 1.539754244902e-07 1.539754249276e-07 1.539754249356e-07 0.6279322066282 1.539754253892e-07 0.04108867636379 + 5.193221323143e-08 5.193221463044e-08 5.193221462729e-08 0.6843453436759 5.193221708199e-08 0.04106859618414 + 1.888205054507e-08 1.888204779723e-08 1.88820477688e-08 0.6673444085651 1.888205650952e-08 0.041062141752 + 5.676855206925e-09 5.676854518888e-09 5.676854517651e-09 0.7281705804232 5.676885442702e-09 0.04105958648713 + 3.501157668218e-09 3.501150243546e-09 3.501150216347e-09 0.414020345194 3.501164437194e-09 0.04105916265261 + 1.110594251499e-09 1.110590786827e-09 1.11059083379e-09 0.6998954759911 1.110636623476e-09 0.04105870073485 + 5.770971626386e-10 5.772456113791e-10 5.772456200156e-10 0.4999769658132 5.77013379477e-10 0.04105859769135 + 1.535218204536e-10 1.536993317032e-10 1.536992771966e-10 0.7516471627141 1.536205005991e-10 0.04105851679958 + 6.724209350756e-11 6.739211232927e-11 6.739210470901e-11 0.5944802416166 6.735465384341e-11 0.04105850033766 + 1.743382199199e-11 1.736445896691e-11 1.736448490761e-11 0.7573407808104 1.734254328931e-11 0.04105849088824 + Optimization terminated successfully. + Elapsed time : 2.883899211883545 s + + +Dirac Data +---------- + + + +.. code-block:: python + + + #%% parameters + + a1 = 1.0 * (x > 10) * (x < 50) + a2 = 1.0 * (x > 60) * (x < 80) + + a1 /= a1.sum() + a2 /= a2.sum() + + # creating matrix A containing all distributions + A = np.vstack((a1, a2)).T + n_distributions = A.shape[1] + + # loss matrix + normalization + M = ot.utils.dist0(n) + M /= M.max() + + + #%% plot the distributions + + pl.figure(1, figsize=(6.4, 3)) + for i in range(n_distributions): + pl.plot(x, A[:, i]) + pl.title('Distributions') + pl.tight_layout() + + + #%% barycenter computation + + alpha = 0.5 # 0<=alpha<=1 + weights = np.array([1 - alpha, alpha]) + + # l2bary + bary_l2 = A.dot(weights) + + # wasserstein + reg = 1e-3 + ot.tic() + bary_wass = ot.bregman.barycenter(A, M, reg, weights) + ot.toc() + + + ot.tic() + bary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True) + ot.toc() + + + problems.append([A, [bary_l2, bary_wass, bary_wass2]]) + + pl.figure(2) + pl.clf() + pl.subplot(2, 1, 1) + for i in range(n_distributions): + pl.plot(x, A[:, i]) + pl.title('Distributions') + + pl.subplot(2, 1, 2) + pl.plot(x, bary_l2, 'r', label='l2') + pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') + pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') + pl.legend() + pl.title('Barycenters') + pl.tight_layout() + + #%% parameters + + a1 = np.zeros(n) + a2 = np.zeros(n) + + a1[10] = .25 + a1[20] = .5 + a1[30] = .25 + a2[80] = 1 + + + a1 /= a1.sum() + a2 /= a2.sum() + + # creating matrix A containing all distributions + A = np.vstack((a1, a2)).T + n_distributions = A.shape[1] + + # loss matrix + normalization + M = ot.utils.dist0(n) + M /= M.max() + + + #%% plot the distributions + + pl.figure(1, figsize=(6.4, 3)) + for i in range(n_distributions): + pl.plot(x, A[:, i]) + pl.title('Distributions') + pl.tight_layout() + + + #%% barycenter computation + + alpha = 0.5 # 0<=alpha<=1 + weights = np.array([1 - alpha, alpha]) + + # l2bary + bary_l2 = A.dot(weights) + + # wasserstein + reg = 1e-3 + ot.tic() + bary_wass = ot.bregman.barycenter(A, M, reg, weights) + ot.toc() + + + ot.tic() + bary_wass2 = ot.lp.barycenter(A, M, weights, solver='interior-point', verbose=True) + ot.toc() + + + problems.append([A, [bary_l2, bary_wass, bary_wass2]]) + + pl.figure(2) + pl.clf() + pl.subplot(2, 1, 1) + for i in range(n_distributions): + pl.plot(x, A[:, i]) + pl.title('Distributions') + + pl.subplot(2, 1, 2) + pl.plot(x, bary_l2, 'r', label='l2') + pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') + pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') + pl.legend() + pl.title('Barycenters') + pl.tight_layout() + + + + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_003.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_004.png + :scale: 47 + + +.. rst-class:: sphx-glr-script-out + + Out:: + + Elapsed time : 0.014938592910766602 s + Primal Feasibility Dual Feasibility Duality Gap Step Path Parameter Objective + 1.0 1.0 1.0 - 1.0 1700.336700337 + 0.006776466288966 0.006776466288966 0.006776466288966 0.9932238515788 0.006776466288966 125.6649255808 + 0.004036918865495 0.004036918865495 0.004036918865495 0.4272973099316 0.004036918865495 12.3471617011 + 0.00121923268707 0.00121923268707 0.00121923268707 0.749698685599 0.00121923268707 0.3243835647408 + 0.0003837422984432 0.0003837422984432 0.0003837422984432 0.6926882608284 0.0003837422984432 0.1361719397493 + 0.0001070128410183 0.0001070128410183 0.0001070128410183 0.7643889137854 0.0001070128410183 0.07581952832518 + 0.0001001275033711 0.0001001275033711 0.0001001275033711 0.07058704837812 0.0001001275033712 0.0734739493635 + 4.550897507844e-05 4.550897507841e-05 4.550897507844e-05 0.5761172484828 4.550897507845e-05 0.05555077655047 + 8.557124125522e-06 8.5571241255e-06 8.557124125522e-06 0.8535925441152 8.557124125522e-06 0.04439814660221 + 3.611995628407e-06 3.61199562841e-06 3.611995628414e-06 0.6002277331554 3.611995628415e-06 0.04283007762152 + 7.590393750365e-07 7.590393750491e-07 7.590393750378e-07 0.8221486533416 7.590393750381e-07 0.04192322976248 + 8.299929287441e-08 8.299929286079e-08 8.299929287532e-08 0.9017467938799 8.29992928758e-08 0.04170825633295 + 3.117560203449e-10 3.117560130137e-10 3.11756019954e-10 0.997039969226 3.11756019952e-10 0.04168179329766 + 1.559749653711e-14 1.558073160926e-14 1.559756940692e-14 0.9999499686183 1.559750643989e-14 0.04168169240444 + Optimization terminated successfully. + Elapsed time : 2.642659902572632 s + Elapsed time : 0.002908945083618164 s + Primal Feasibility Dual Feasibility Duality Gap Step Path Parameter Objective + 1.0 1.0 1.0 - 1.0 1700.336700337 + 0.006774675520727 0.006774675520727 0.006774675520727 0.9932256422636 0.006774675520727 125.6956034743 + 0.002048208707562 0.002048208707562 0.002048208707562 0.7343095368143 0.002048208707562 5.213991622123 + 0.000269736547478 0.0002697365474781 0.0002697365474781 0.8839403501193 0.000269736547478 0.505938390389 + 6.832109993943e-05 6.832109993944e-05 6.832109993944e-05 0.7601171075965 6.832109993943e-05 0.2339657807272 + 2.437682932219e-05 2.43768293222e-05 2.437682932219e-05 0.6663448297475 2.437682932219e-05 0.1471256246325 + 1.13498321631e-05 1.134983216308e-05 1.13498321631e-05 0.5553643816404 1.13498321631e-05 0.1181584941171 + 3.342312725885e-06 3.342312725884e-06 3.342312725885e-06 0.7238133571615 3.342312725885e-06 0.1006387519747 + 7.078561231603e-07 7.078561231509e-07 7.078561231604e-07 0.8033142552512 7.078561231603e-07 0.09474734646269 + 1.966870956916e-07 1.966870954537e-07 1.966870954468e-07 0.752547917788 1.966870954633e-07 0.09354342735766 + 4.19989524849e-10 4.199895164852e-10 4.199895238758e-10 0.9984019849375 4.19989523951e-10 0.09310367785861 + 2.101015938666e-14 2.100625691113e-14 2.101023853438e-14 0.999949974425 2.101023691864e-14 0.09310274466458 + Optimization terminated successfully. + Elapsed time : 2.690450668334961 s + + +Final figure +------------ + + + + +.. code-block:: python + + + #%% plot + + nbm = len(problems) + nbm2 = (nbm // 2) + + + pl.figure(2, (20, 6)) + pl.clf() + + for i in range(nbm): + + A = problems[i][0] + bary_l2 = problems[i][1][0] + bary_wass = problems[i][1][1] + bary_wass2 = problems[i][1][2] + + pl.subplot(2, nbm, 1 + i) + for j in range(n_distributions): + pl.plot(x, A[:, j]) + if i == nbm2: + pl.title('Distributions') + pl.xticks(()) + pl.yticks(()) + + pl.subplot(2, nbm, 1 + i + nbm) + + pl.plot(x, bary_l2, 'r', label='L2 (Euclidean)') + pl.plot(x, bary_wass, 'g', label='Reg Wasserstein') + pl.plot(x, bary_wass2, 'b', label='LP Wasserstein') + if i == nbm - 1: + pl.legend() + if i == nbm2: + pl.title('Barycenters') + + pl.xticks(()) + pl.yticks(()) + + + +.. image:: /auto_examples/images/sphx_glr_plot_barycenter_lp_vs_entropic_006.png + :align: center + + + + +**Total running time of the script:** ( 0 minutes 8.892 seconds) + + + +.. only :: html + + .. container:: sphx-glr-footer + + + .. container:: sphx-glr-download + + :download:`Download Python source code: plot_barycenter_lp_vs_entropic.py <plot_barycenter_lp_vs_entropic.py>` + + + + .. container:: sphx-glr-download + + :download:`Download Jupyter notebook: plot_barycenter_lp_vs_entropic.ipynb <plot_barycenter_lp_vs_entropic.ipynb>` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_otda_linear_mapping.ipynb b/docs/source/auto_examples/plot_otda_linear_mapping.ipynb new file mode 100644 index 0000000..027b6cb --- /dev/null +++ b/docs/source/auto_examples/plot_otda_linear_mapping.ipynb @@ -0,0 +1,180 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# Linear OT mapping estimation\n\n\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Author: Remi Flamary <remi.flamary@unice.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport pylab as pl\nimport ot" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate data\n-------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "n = 1000\nd = 2\nsigma = .1\n\n# source samples\nangles = np.random.rand(n, 1) * 2 * np.pi\nxs = np.concatenate((np.sin(angles), np.cos(angles)),\n axis=1) + sigma * np.random.randn(n, 2)\nxs[:n // 2, 1] += 2\n\n\n# target samples\nanglet = np.random.rand(n, 1) * 2 * np.pi\nxt = np.concatenate((np.sin(anglet), np.cos(anglet)),\n axis=1) + sigma * np.random.randn(n, 2)\nxt[:n // 2, 1] += 2\n\n\nA = np.array([[1.5, .7], [.7, 1.5]])\nb = np.array([[4, 2]])\nxt = xt.dot(A) + b" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot data\n---------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "pl.figure(1, (5, 5))\npl.plot(xs[:, 0], xs[:, 1], '+')\npl.plot(xt[:, 0], xt[:, 1], 'o')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Estimate linear mapping and transport\n-------------------------------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "Ae, be = ot.da.OT_mapping_linear(xs, xt)\n\nxst = xs.dot(Ae) + be" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot transported samples\n------------------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "pl.figure(1, (5, 5))\npl.clf()\npl.plot(xs[:, 0], xs[:, 1], '+')\npl.plot(xt[:, 0], xt[:, 1], 'o')\npl.plot(xst[:, 0], xst[:, 1], '+')\n\npl.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Load image data\n---------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def im2mat(I):\n \"\"\"Converts and image to matrix (one pixel per line)\"\"\"\n return I.reshape((I.shape[0] * I.shape[1], I.shape[2]))\n\n\ndef mat2im(X, shape):\n \"\"\"Converts back a matrix to an image\"\"\"\n return X.reshape(shape)\n\n\ndef minmax(I):\n return np.clip(I, 0, 1)\n\n\n# Loading images\nI1 = pl.imread('../data/ocean_day.jpg').astype(np.float64) / 256\nI2 = pl.imread('../data/ocean_sunset.jpg').astype(np.float64) / 256\n\n\nX1 = im2mat(I1)\nX2 = im2mat(I2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Estimate mapping and adapt\n----------------------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "mapping = ot.da.LinearTransport()\n\nmapping.fit(Xs=X1, Xt=X2)\n\n\nxst = mapping.transform(Xs=X1)\nxts = mapping.inverse_transform(Xt=X2)\n\nI1t = minmax(mat2im(xst, I1.shape))\nI2t = minmax(mat2im(xts, I2.shape))\n\n# %%" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot transformed images\n-----------------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "pl.figure(2, figsize=(10, 7))\n\npl.subplot(2, 2, 1)\npl.imshow(I1)\npl.axis('off')\npl.title('Im. 1')\n\npl.subplot(2, 2, 2)\npl.imshow(I2)\npl.axis('off')\npl.title('Im. 2')\n\npl.subplot(2, 2, 3)\npl.imshow(I1t)\npl.axis('off')\npl.title('Mapping Im. 1')\n\npl.subplot(2, 2, 4)\npl.imshow(I2t)\npl.axis('off')\npl.title('Inverse mapping Im. 2')" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.5" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_otda_linear_mapping.py b/docs/source/auto_examples/plot_otda_linear_mapping.py new file mode 100644 index 0000000..c65bd4f --- /dev/null +++ b/docs/source/auto_examples/plot_otda_linear_mapping.py @@ -0,0 +1,144 @@ +#!/usr/bin/env python3 +# -*- coding: utf-8 -*- +""" +============================ +Linear OT mapping estimation +============================ + + +""" + +# Author: Remi Flamary <remi.flamary@unice.fr> +# +# License: MIT License + +import numpy as np +import pylab as pl +import ot + +############################################################################## +# Generate data +# ------------- + +n = 1000 +d = 2 +sigma = .1 + +# source samples +angles = np.random.rand(n, 1) * 2 * np.pi +xs = np.concatenate((np.sin(angles), np.cos(angles)), + axis=1) + sigma * np.random.randn(n, 2) +xs[:n // 2, 1] += 2 + + +# target samples +anglet = np.random.rand(n, 1) * 2 * np.pi +xt = np.concatenate((np.sin(anglet), np.cos(anglet)), + axis=1) + sigma * np.random.randn(n, 2) +xt[:n // 2, 1] += 2 + + +A = np.array([[1.5, .7], [.7, 1.5]]) +b = np.array([[4, 2]]) +xt = xt.dot(A) + b + +############################################################################## +# Plot data +# --------- + +pl.figure(1, (5, 5)) +pl.plot(xs[:, 0], xs[:, 1], '+') +pl.plot(xt[:, 0], xt[:, 1], 'o') + + +############################################################################## +# Estimate linear mapping and transport +# ------------------------------------- + +Ae, be = ot.da.OT_mapping_linear(xs, xt) + +xst = xs.dot(Ae) + be + + +############################################################################## +# Plot transported samples +# ------------------------ + +pl.figure(1, (5, 5)) +pl.clf() +pl.plot(xs[:, 0], xs[:, 1], '+') +pl.plot(xt[:, 0], xt[:, 1], 'o') +pl.plot(xst[:, 0], xst[:, 1], '+') + +pl.show() + +############################################################################## +# Load image data +# --------------- + + +def im2mat(I): + """Converts and image to matrix (one pixel per line)""" + return I.reshape((I.shape[0] * I.shape[1], I.shape[2])) + + +def mat2im(X, shape): + """Converts back a matrix to an image""" + return X.reshape(shape) + + +def minmax(I): + return np.clip(I, 0, 1) + + +# Loading images +I1 = pl.imread('../data/ocean_day.jpg').astype(np.float64) / 256 +I2 = pl.imread('../data/ocean_sunset.jpg').astype(np.float64) / 256 + + +X1 = im2mat(I1) +X2 = im2mat(I2) + +############################################################################## +# Estimate mapping and adapt +# ---------------------------- + +mapping = ot.da.LinearTransport() + +mapping.fit(Xs=X1, Xt=X2) + + +xst = mapping.transform(Xs=X1) +xts = mapping.inverse_transform(Xt=X2) + +I1t = minmax(mat2im(xst, I1.shape)) +I2t = minmax(mat2im(xts, I2.shape)) + +# %% + + +############################################################################## +# Plot transformed images +# ----------------------- + +pl.figure(2, figsize=(10, 7)) + +pl.subplot(2, 2, 1) +pl.imshow(I1) +pl.axis('off') +pl.title('Im. 1') + +pl.subplot(2, 2, 2) +pl.imshow(I2) +pl.axis('off') +pl.title('Im. 2') + +pl.subplot(2, 2, 3) +pl.imshow(I1t) +pl.axis('off') +pl.title('Mapping Im. 1') + +pl.subplot(2, 2, 4) +pl.imshow(I2t) +pl.axis('off') +pl.title('Inverse mapping Im. 2') diff --git a/docs/source/auto_examples/plot_otda_linear_mapping.rst b/docs/source/auto_examples/plot_otda_linear_mapping.rst new file mode 100644 index 0000000..8e2e0cf --- /dev/null +++ b/docs/source/auto_examples/plot_otda_linear_mapping.rst @@ -0,0 +1,260 @@ + + +.. _sphx_glr_auto_examples_plot_otda_linear_mapping.py: + + +============================ +Linear OT mapping estimation +============================ + + + + + +.. code-block:: python + + + # Author: Remi Flamary <remi.flamary@unice.fr> + # + # License: MIT License + + import numpy as np + import pylab as pl + import ot + + + + + + + +Generate data +------------- + + + +.. code-block:: python + + + n = 1000 + d = 2 + sigma = .1 + + # source samples + angles = np.random.rand(n, 1) * 2 * np.pi + xs = np.concatenate((np.sin(angles), np.cos(angles)), + axis=1) + sigma * np.random.randn(n, 2) + xs[:n // 2, 1] += 2 + + + # target samples + anglet = np.random.rand(n, 1) * 2 * np.pi + xt = np.concatenate((np.sin(anglet), np.cos(anglet)), + axis=1) + sigma * np.random.randn(n, 2) + xt[:n // 2, 1] += 2 + + + A = np.array([[1.5, .7], [.7, 1.5]]) + b = np.array([[4, 2]]) + xt = xt.dot(A) + b + + + + + + + +Plot data +--------- + + + +.. code-block:: python + + + pl.figure(1, (5, 5)) + pl.plot(xs[:, 0], xs[:, 1], '+') + pl.plot(xt[:, 0], xt[:, 1], 'o') + + + + + +.. image:: /auto_examples/images/sphx_glr_plot_otda_linear_mapping_001.png + :align: center + + + + +Estimate linear mapping and transport +------------------------------------- + + + +.. code-block:: python + + + Ae, be = ot.da.OT_mapping_linear(xs, xt) + + xst = xs.dot(Ae) + be + + + + + + + + +Plot transported samples +------------------------ + + + +.. code-block:: python + + + pl.figure(1, (5, 5)) + pl.clf() + pl.plot(xs[:, 0], xs[:, 1], '+') + pl.plot(xt[:, 0], xt[:, 1], 'o') + pl.plot(xst[:, 0], xst[:, 1], '+') + + pl.show() + + + + +.. image:: /auto_examples/images/sphx_glr_plot_otda_linear_mapping_002.png + :align: center + + + + +Load image data +--------------- + + + +.. code-block:: python + + + + def im2mat(I): + """Converts and image to matrix (one pixel per line)""" + return I.reshape((I.shape[0] * I.shape[1], I.shape[2])) + + + def mat2im(X, shape): + """Converts back a matrix to an image""" + return X.reshape(shape) + + + def minmax(I): + return np.clip(I, 0, 1) + + + # Loading images + I1 = pl.imread('../data/ocean_day.jpg').astype(np.float64) / 256 + I2 = pl.imread('../data/ocean_sunset.jpg').astype(np.float64) / 256 + + + X1 = im2mat(I1) + X2 = im2mat(I2) + + + + + + + +Estimate mapping and adapt +---------------------------- + + + +.. code-block:: python + + + mapping = ot.da.LinearTransport() + + mapping.fit(Xs=X1, Xt=X2) + + + xst = mapping.transform(Xs=X1) + xts = mapping.inverse_transform(Xt=X2) + + I1t = minmax(mat2im(xst, I1.shape)) + I2t = minmax(mat2im(xts, I2.shape)) + + # %% + + + + + + + + +Plot transformed images +----------------------- + + + +.. code-block:: python + + + pl.figure(2, figsize=(10, 7)) + + pl.subplot(2, 2, 1) + pl.imshow(I1) + pl.axis('off') + pl.title('Im. 1') + + pl.subplot(2, 2, 2) + pl.imshow(I2) + pl.axis('off') + pl.title('Im. 2') + + pl.subplot(2, 2, 3) + pl.imshow(I1t) + pl.axis('off') + pl.title('Mapping Im. 1') + + pl.subplot(2, 2, 4) + pl.imshow(I2t) + pl.axis('off') + pl.title('Inverse mapping Im. 2') + + + +.. image:: /auto_examples/images/sphx_glr_plot_otda_linear_mapping_004.png + :align: center + + + + +**Total running time of the script:** ( 0 minutes 0.635 seconds) + + + +.. only :: html + + .. container:: sphx-glr-footer + + + .. container:: sphx-glr-download + + :download:`Download Python source code: plot_otda_linear_mapping.py <plot_otda_linear_mapping.py>` + + + + .. container:: sphx-glr-download + + :download:`Download Jupyter notebook: plot_otda_linear_mapping.ipynb <plot_otda_linear_mapping.ipynb>` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ |
