From 80e3c23bc968f866fd20344ddc443a3c7fcb3b0d Mon Sep 17 00:00:00 2001
From: Clément Bonet <32179275+clbonet@users.noreply.github.com>
Date: Thu, 23 Feb 2023 08:31:01 +0100
Subject: [WIP] Wasserstein distance on the circle and Spherical
 Sliced-Wasserstein (#434)

* W circle + SSW

* Tests + Example SSW_1

* Example Wasserstein Circle + Tests

* Wasserstein on the circle wrt Unif

* Example SSW unif

* pep8

* np.linalg.qr for numpy < 1.22 by batch + add python3.11 to tests

* np qr

* rm test python 3.11

* update names, tests, backend transpose

* Comment error batchs

* semidiscrete_wasserstein2_unif_circle example

* torch permute method instead of torch.permute for previous versions

* update comments and doc

* doc wasserstein circle model as [0,1[

* Added ot.utils.get_coordinate_circle to get coordinates on the circle in turn
---
 examples/sliced-wasserstein/plot_variance_ssw.py | 111 +++++++++++++++++++++++
 1 file changed, 111 insertions(+)
 create mode 100644 examples/sliced-wasserstein/plot_variance_ssw.py

(limited to 'examples/sliced-wasserstein/plot_variance_ssw.py')

diff --git a/examples/sliced-wasserstein/plot_variance_ssw.py b/examples/sliced-wasserstein/plot_variance_ssw.py
new file mode 100644
index 0000000..83d458f
--- /dev/null
+++ b/examples/sliced-wasserstein/plot_variance_ssw.py
@@ -0,0 +1,111 @@
+# -*- coding: utf-8 -*-
+"""
+====================================================
+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.
+
+"""
+
+# Author: Clément Bonet <clement.bonet@univ-ubs.fr>
+#
+# License: MIT License
+
+# sphinx_gallery_thumbnail_number = 2
+
+import matplotlib.pylab as pl
+import numpy as np
+
+import ot
+
+##############################################################################
+# Generate data
+# -------------
+
+# %% parameters and data generation
+
+n = 500  # 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
+
+##############################################################################
+# Plot data
+# ---------
+
+# %% plot samples
+
+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")
+
+###############################################################################
+# Spherical Sliced Wasserstein for different seeds and number of projections
+# --------------------------------------------------------------------------
+
+n_seed = 50
+n_projections_arr = np.logspace(0, 3, 25, dtype=int)
+res = np.empty((n_seed, 25))
+
+# %% Compute statistics
+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)
+
+###############################################################################
+# Plot Spherical Sliced Wasserstein
+# ---------------------------------
+
+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 inverval')
+
+pl.show()
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