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author | Gard Spreemann <gspr@nonempty.org> | 2020-01-20 14:07:53 +0100 |
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committer | Gard Spreemann <gspr@nonempty.org> | 2020-01-20 14:07:53 +0100 |
commit | bdfb24ff37ea777d6e266b145047cd4e281ebac3 (patch) | |
tree | 00cbac5f3dc25a4ee76164828abd72c1cbab37cc /docs/source/auto_examples/plot_UOT_barycenter_1D.rst | |
parent | abc441b00f0fe2fa4ef0efc4e1aa67b27cca9a13 (diff) | |
parent | 5e70a77fbb2feec513f21c9ef65dcc535329ace6 (diff) |
Merge tag '0.6.0' into debian/sid
Diffstat (limited to 'docs/source/auto_examples/plot_UOT_barycenter_1D.rst')
-rw-r--r-- | docs/source/auto_examples/plot_UOT_barycenter_1D.rst | 261 |
1 files changed, 261 insertions, 0 deletions
diff --git a/docs/source/auto_examples/plot_UOT_barycenter_1D.rst b/docs/source/auto_examples/plot_UOT_barycenter_1D.rst new file mode 100644 index 0000000..ac17587 --- /dev/null +++ b/docs/source/auto_examples/plot_UOT_barycenter_1D.rst @@ -0,0 +1,261 @@ + + +.. _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>`_ |