From e458b7a58d9790e7c5ff40dea235402d9c4c8662 Mon Sep 17 00:00:00 2001
From: Rémi Flamary <remi.flamary@gmail.com>
Date: Fri, 2 Dec 2016 15:38:59 +0100
Subject: add doc for gallery

---
 docs/source/auto_examples/plot_barycenter_1D.py | 138 ++++++++++++++++++++++++
 1 file changed, 138 insertions(+)
 create mode 100644 docs/source/auto_examples/plot_barycenter_1D.py

(limited to 'docs/source/auto_examples/plot_barycenter_1D.py')

diff --git a/docs/source/auto_examples/plot_barycenter_1D.py b/docs/source/auto_examples/plot_barycenter_1D.py
new file mode 100644
index 0000000..30eecbf
--- /dev/null
+++ b/docs/source/auto_examples/plot_barycenter_1D.py
@@ -0,0 +1,138 @@
+# -*- coding: utf-8 -*-
+"""
+==============================
+1D Wasserstein barycenter demo
+==============================
+
+
+@author: rflamary
+"""
+
+import numpy as np
+import matplotlib.pylab as pl
+import ot
+from mpl_toolkits.mplot3d import Axes3D #necessary for 3d plot even if not used
+from matplotlib.collections import PolyCollection
+
+
+#%% parameters
+
+n=100 # nb bins
+
+# bin positions
+x=np.arange(n,dtype=np.float64)
+
+# Gaussian distributions
+a1=ot.datasets.get_1D_gauss(n,m=20,s=5) # m= mean, s= std
+a2=ot.datasets.get_1D_gauss(n,m=60,s=8)
+
+# creating matrix A containing all distributions
+A=np.vstack((a1,a2)).T
+nbd=A.shape[1]
+
+# loss matrix + normalization
+M=ot.utils.dist0(n)
+M/=M.max()
+
+#%% plot the distributions
+
+pl.figure(1)
+for i in range(nbd):
+    pl.plot(x,A[:,i])
+pl.title('Distributions')
+
+#%% 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(nbd):
+    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')
+
+
+#%% barycenter interpolation
+
+nbalpha=11
+alphalist=np.linspace(0,1,nbalpha)
+
+
+B_l2=np.zeros((n,nbalpha))
+
+B_wass=np.copy(B_l2)
+
+for i in range(0,nbalpha):
+    alpha=alphalist[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,(10,5))
+
+#pl.subplot(1,2,1)
+cmap=pl.cm.get_cmap('viridis')
+verts = []
+zs = alphalist
+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 alphalist])
+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.show()
+
+pl.figure(4,(10,5))
+
+#pl.subplot(1,2,1)
+cmap=pl.cm.get_cmap('viridis')
+verts = []
+zs = alphalist
+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 alphalist])
+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.show()
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