From a54775103541ea37f54269de1ba1e1396a6d7b30 Mon Sep 17 00:00:00 2001
From: Rémi Flamary <remi.flamary@gmail.com>
Date: Fri, 24 Apr 2020 17:32:57 +0200
Subject: exmaples in sections

---
 examples/barycenters/plot_barycenter_1D.py | 162 +++++++++++++++++++++++++++++
 1 file changed, 162 insertions(+)
 create mode 100644 examples/barycenters/plot_barycenter_1D.py

(limited to 'examples/barycenters/plot_barycenter_1D.py')

diff --git a/examples/barycenters/plot_barycenter_1D.py b/examples/barycenters/plot_barycenter_1D.py
new file mode 100644
index 0000000..63dc460
--- /dev/null
+++ b/examples/barycenters/plot_barycenter_1D.py
@@ -0,0 +1,162 @@
+# -*- coding: utf-8 -*-
+"""
+==============================
+1D Wasserstein barycenter demo
+==============================
+
+This example illustrates the computation of regularized Wassersyein 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.
+
+"""
+
+# Author: Remi Flamary <remi.flamary@unice.fr>
+#
+# License: MIT License
+
+# sphinx_gallery_thumbnail_number = 4
+
+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
+# -------------
+
+#%% 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)
+
+# 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
+# ---------
+
+#%% 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()
+
+##############################################################################
+# Barycenter computation
+# ----------------------
+
+#%% barycenter computation
+
+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)
+
+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()
+
+##############################################################################
+# Barycentric interpolation
+# -------------------------
+
+#%% barycenter interpolation
+
+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(0, 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)
+
+#%% plot interpolation
+
+pl.figure(3)
+
+cmap = pl.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 = pl.gcf().gca(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)
+pl.title('Barycenter interpolation with l2')
+pl.tight_layout()
+
+pl.figure(4)
+cmap = pl.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 = pl.gcf().gca(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)
+pl.title('Barycenter interpolation with Wasserstein')
+pl.tight_layout()
+
+pl.show()
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