.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/barycenters/plot_barycenter_1D.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_barycenters_plot_barycenter_1D.py: ============================== 1D Wasserstein barycenter demo ============================== This example illustrates the computation of regularized Wasserstein Barycenter as proposed in [3]. [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. .. GENERATED FROM PYTHON SOURCE LINES 16-30 .. code-block:: Python # Author: Remi Flamary # # License: MIT License # sphinx_gallery_thumbnail_number = 1 import numpy as np import matplotlib.pyplot as plt import ot # necessary for 3d plot even if not used from mpl_toolkits.mplot3d import Axes3D # noqa from matplotlib.collections import PolyCollection .. GENERATED FROM PYTHON SOURCE LINES 31-33 Generate data ------------- .. GENERATED FROM PYTHON SOURCE LINES 35-53 .. code-block:: Python 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) # 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() .. GENERATED FROM PYTHON SOURCE LINES 54-56 Barycenter computation ---------------------- .. GENERATED FROM PYTHON SOURCE LINES 58-80 .. code-block:: Python alpha = 0.2 # 0<=alpha<=1 weights = np.array([1 - alpha, alpha]) # l2bary bary_l2 = A.dot(weights) # wasserstein reg = 1e-3 bary_wass = ot.bregman.barycenter(A, M, reg, weights) f, (ax1, ax2) = plt.subplots(2, 1, tight_layout=True, num=1) ax1.plot(x, A, color="black") ax1.set_title('Distributions') ax2.plot(x, bary_l2, 'r', label='l2') ax2.plot(x, bary_wass, 'g', label='Wasserstein') ax2.set_title('Barycenters') plt.legend() plt.show() .. image-sg:: /auto_examples/barycenters/images/sphx_glr_plot_barycenter_1D_001.png :alt: Distributions, Barycenters :srcset: /auto_examples/barycenters/images/sphx_glr_plot_barycenter_1D_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 81-83 Barycentric interpolation ------------------------- .. GENERATED FROM PYTHON SOURCE LINES 85-100 .. code-block:: Python n_alpha = 11 alpha_list = np.linspace(0, 1, n_alpha) B_l2 = np.zeros((n, n_alpha)) B_wass = np.copy(B_l2) for i in range(n_alpha): alpha = alpha_list[i] weights = np.array([1 - alpha, alpha]) B_l2[:, i] = A.dot(weights) B_wass[:, i] = ot.bregman.barycenter(A, M, reg, weights) .. GENERATED FROM PYTHON SOURCE LINES 101-147 .. code-block:: Python plt.figure(2) cmap = plt.cm.get_cmap('viridis') verts = [] zs = alpha_list for i, z in enumerate(zs): ys = B_l2[:, i] verts.append(list(zip(x, ys))) ax = plt.gcf().add_subplot(projection='3d') poly = PolyCollection(verts, facecolors=[cmap(a) for a in alpha_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('$\\alpha$') ax.set_ylim3d(0, 1) ax.set_zlabel('') ax.set_zlim3d(0, B_l2.max() * 1.01) plt.title('Barycenter interpolation with l2') plt.tight_layout() plt.figure(3) cmap = plt.cm.get_cmap('viridis') verts = [] zs = alpha_list for i, z in enumerate(zs): ys = B_wass[:, i] verts.append(list(zip(x, ys))) ax = plt.gcf().add_subplot(projection='3d') poly = PolyCollection(verts, facecolors=[cmap(a) for a in alpha_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('$\\alpha$') ax.set_ylim3d(0, 1) ax.set_zlabel('') ax.set_zlim3d(0, B_l2.max() * 1.01) plt.title('Barycenter interpolation with Wasserstein') plt.tight_layout() plt.show() .. rst-class:: sphx-glr-horizontal * .. image-sg:: /auto_examples/barycenters/images/sphx_glr_plot_barycenter_1D_002.png :alt: Barycenter interpolation with l2 :srcset: /auto_examples/barycenters/images/sphx_glr_plot_barycenter_1D_002.png :class: sphx-glr-multi-img * .. image-sg:: /auto_examples/barycenters/images/sphx_glr_plot_barycenter_1D_003.png :alt: Barycenter interpolation with Wasserstein :srcset: /auto_examples/barycenters/images/sphx_glr_plot_barycenter_1D_003.png :class: sphx-glr-multi-img .. rst-class:: sphx-glr-script-out .. code-block:: none /home/circleci/project/examples/barycenters/plot_barycenter_1D.py:103: MatplotlibDeprecationWarning: The get_cmap function was deprecated in Matplotlib 3.7 and will be removed two minor releases later. Use ``matplotlib.colormaps[name]`` or ``matplotlib.colormaps.get_cmap(obj)`` instead. cmap = plt.cm.get_cmap('viridis') /home/circleci/project/examples/barycenters/plot_barycenter_1D.py:125: MatplotlibDeprecationWarning: The get_cmap function was deprecated in Matplotlib 3.7 and will be removed two minor releases later. Use ``matplotlib.colormaps[name]`` or ``matplotlib.colormaps.get_cmap(obj)`` instead. cmap = plt.cm.get_cmap('viridis') .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.703 seconds) .. _sphx_glr_download_auto_examples_barycenters_plot_barycenter_1D.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_barycenter_1D.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_barycenter_1D.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_