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diff --git a/docs/source/auto_examples/plot_UOT_barycenter_1D.rst b/docs/source/auto_examples/plot_UOT_barycenter_1D.rst deleted file mode 100644 index ac17587..0000000 --- a/docs/source/auto_examples/plot_UOT_barycenter_1D.rst +++ /dev/null @@ -1,261 +0,0 @@ - - -.. _sphx_glr_auto_examples_plot_UOT_barycenter_1D.py: - - -=========================================================== -1D Wasserstein barycenter demo for Unbalanced distributions -=========================================================== - -This example illustrates the computation of regularized Wassersyein Barycenter -as proposed in [10] for Unbalanced inputs. - - -[10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816. - - - - -.. code-block:: python - - - # Author: Hicham Janati <hicham.janati@inria.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 - - - - - - - -Generate data -------------- - - - -.. code-block:: python - - - # parameters - - n = 100 # nb bins - - # bin positions - x = np.arange(n, dtype=np.float64) - - # 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) - - # make unbalanced dists - a2 *= 3. - - # 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 data ---------- - - - -.. code-block:: python - - - # 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() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_001.png - :align: center - - - - -Barycenter computation ----------------------- - - - -.. code-block:: python - - - # non weighted barycenter computation - - weight = 0.5 # 0<=weight<=1 - weights = np.array([1 - weight, weight]) - - # l2bary - bary_l2 = A.dot(weights) - - # wasserstein - reg = 1e-3 - alpha = 1. - - bary_wass = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, weights) - - 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='Wasserstein') - pl.legend() - pl.title('Barycenters') - pl.tight_layout() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_003.png - :align: center - - - - -Barycentric interpolation -------------------------- - - - -.. code-block:: python - - - # barycenter interpolation - - n_weight = 11 - weight_list = np.linspace(0, 1, n_weight) - - - B_l2 = np.zeros((n, n_weight)) - - B_wass = np.copy(B_l2) - - for i in range(0, n_weight): - weight = weight_list[i] - weights = np.array([1 - weight, weight]) - B_l2[:, i] = A.dot(weights) - B_wass[:, i] = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, weights) - - - # plot interpolation - - pl.figure(3) - - cmap = pl.cm.get_cmap('viridis') - verts = [] - zs = weight_list - for i, z in enumerate(zs): - ys = B_l2[:, i] - verts.append(list(zip(x, ys))) - - ax = pl.gcf().gca(projection='3d') - - poly = PolyCollection(verts, facecolors=[cmap(a) for a in weight_list]) - poly.set_alpha(0.7) - ax.add_collection3d(poly, zs=zs, zdir='y') - ax.set_xlabel('x') - ax.set_xlim3d(0, n) - ax.set_ylabel(r'$\alpha$') - ax.set_ylim3d(0, 1) - ax.set_zlabel('') - ax.set_zlim3d(0, B_l2.max() * 1.01) - pl.title('Barycenter interpolation with l2') - pl.tight_layout() - - pl.figure(4) - cmap = pl.cm.get_cmap('viridis') - verts = [] - zs = weight_list - for i, z in enumerate(zs): - ys = B_wass[:, i] - verts.append(list(zip(x, ys))) - - ax = pl.gcf().gca(projection='3d') - - poly = PolyCollection(verts, facecolors=[cmap(a) for a in weight_list]) - poly.set_alpha(0.7) - ax.add_collection3d(poly, zs=zs, zdir='y') - ax.set_xlabel('x') - ax.set_xlim3d(0, n) - ax.set_ylabel(r'$\alpha$') - ax.set_ylim3d(0, 1) - ax.set_zlabel('') - ax.set_zlim3d(0, B_l2.max() * 1.01) - pl.title('Barycenter interpolation with Wasserstein') - pl.tight_layout() - - pl.show() - - - -.. rst-class:: sphx-glr-horizontal - - - * - - .. image:: /auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_005.png - :scale: 47 - - * - - .. image:: /auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_006.png - :scale: 47 - - - - -**Total running time of the script:** ( 0 minutes 0.344 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_UOT_barycenter_1D.py <plot_UOT_barycenter_1D.py>` - - - - .. container:: sphx-glr-download - - :download:`Download Jupyter notebook: plot_UOT_barycenter_1D.ipynb <plot_UOT_barycenter_1D.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ |