.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/sliced-wasserstein/plot_variance_ssw.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_sliced-wasserstein_plot_variance_ssw.py: ==================================================== Spherical Sliced Wasserstein on distributions in S^2 ==================================================== This example illustrates the computation of the spherical sliced Wasserstein discrepancy as proposed in [46]. [46] Bonet, C., Berg, P., Courty, N., Septier, F., Drumetz, L., & Pham, M. T. (2023). 'Spherical Sliced-Wasserstein". International Conference on Learning Representations. .. GENERATED FROM PYTHON SOURCE LINES 13-25 .. code-block:: Python # Author: Clément Bonet # # License: MIT License # sphinx_gallery_thumbnail_number = 2 import matplotlib.pylab as pl import numpy as np import ot .. GENERATED FROM PYTHON SOURCE LINES 26-28 Generate data ------------- .. GENERATED FROM PYTHON SOURCE LINES 30-41 .. code-block:: Python n = 200 # nb samples xs = np.random.randn(n, 3) xt = np.random.randn(n, 3) xs = xs / np.sqrt(np.sum(xs**2, -1, keepdims=True)) xt = xt / np.sqrt(np.sum(xt**2, -1, keepdims=True)) a, b = np.ones((n,)) / n, np.ones((n,)) / n # uniform distribution on samples .. GENERATED FROM PYTHON SOURCE LINES 42-44 Plot data --------- .. GENERATED FROM PYTHON SOURCE LINES 46-80 .. code-block:: Python fig = pl.figure(figsize=(10, 10)) ax = pl.axes(projection='3d') ax.grid(False) u, v = np.mgrid[0:2 * np.pi:30j, 0:np.pi:30j] x = np.cos(u) * np.sin(v) y = np.sin(u) * np.sin(v) z = np.cos(v) ax.plot_surface(x, y, z, color="gray", alpha=0.03) ax.plot_wireframe(x, y, z, linewidth=1, alpha=0.25, color="gray") ax.scatter(xs[:, 0], xs[:, 1], xs[:, 2], label="Source") ax.scatter(xt[:, 0], xt[:, 1], xt[:, 2], label="Target") fs = 10 # Labels ax.set_xlabel('x', fontsize=fs) ax.set_ylabel('y', fontsize=fs) ax.set_zlabel('z', fontsize=fs) ax.view_init(20, 120) ax.set_xlim(-1.5, 1.5) ax.set_ylim(-1.5, 1.5) ax.set_zlim(-1.5, 1.5) # Ticks ax.set_xticks([-1, 0, 1]) ax.set_yticks([-1, 0, 1]) ax.set_zticks([-1, 0, 1]) pl.legend(loc=0) pl.title("Source and Target distribution") .. image-sg:: /auto_examples/sliced-wasserstein/images/sphx_glr_plot_variance_ssw_001.png :alt: Source and Target distribution :srcset: /auto_examples/sliced-wasserstein/images/sphx_glr_plot_variance_ssw_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none Text(0.5, 1.0, 'Source and Target distribution') .. GENERATED FROM PYTHON SOURCE LINES 81-83 Spherical Sliced Wasserstein for different seeds and number of projections -------------------------------------------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 83-88 .. code-block:: Python n_seed = 20 n_projections_arr = np.logspace(0, 3, 10, dtype=int) res = np.empty((n_seed, 10)) .. GENERATED FROM PYTHON SOURCE LINES 89-96 .. code-block:: Python for seed in range(n_seed): for i, n_projections in enumerate(n_projections_arr): res[seed, i] = ot.sliced_wasserstein_sphere(xs, xt, a, b, n_projections, seed=seed, p=1) res_mean = np.mean(res, axis=0) res_std = np.std(res, axis=0) .. GENERATED FROM PYTHON SOURCE LINES 97-99 Plot Spherical Sliced Wasserstein --------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 99-112 .. code-block:: Python pl.figure(2) pl.plot(n_projections_arr, res_mean, label=r"$SSW_1$") pl.fill_between(n_projections_arr, res_mean - 2 * res_std, res_mean + 2 * res_std, alpha=0.5) pl.legend() pl.xscale('log') pl.xlabel("Number of projections") pl.ylabel("Distance") pl.title('Spherical Sliced Wasserstein Distance with 95% confidence interval') pl.show() .. image-sg:: /auto_examples/sliced-wasserstein/images/sphx_glr_plot_variance_ssw_002.png :alt: Spherical Sliced Wasserstein Distance with 95% confidence interval :srcset: /auto_examples/sliced-wasserstein/images/sphx_glr_plot_variance_ssw_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 5.701 seconds) .. _sphx_glr_download_auto_examples_sliced-wasserstein_plot_variance_ssw.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_variance_ssw.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_variance_ssw.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_