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# -*- coding: utf-8 -*-
"""
====================================================
2D Wasserstein barycenters between empirical distributions
====================================================
Illustration of 2D Wasserstein barycenters between discributions that are weighted
sum of diracs.
"""
# Author: Vivien Seguy <vivien.seguy@iip.ist.i.kyoto-u.ac.jp>
#
# License: MIT License
import numpy as np
import matplotlib.pylab as pl
import ot.plot
##############################################################################
# Generate data
# -------------
#%% parameters and data generation
N = 3
d = 2
measures_locations = []
measures_weights = []
for i in range(N):
n = np.random.randint(low=1, high=20) # nb samples
mu = np.random.normal(0., 4., (d,))
A = np.random.rand(d, d)
cov = np.dot(A, A.transpose())
x_i = ot.datasets.make_2D_samples_gauss(n, mu, cov)
b_i = np.random.uniform(0., 1., (n,))
b_i = b_i / np.sum(b_i)
measures_locations.append(x_i)
measures_weights.append(b_i)
##############################################################################
# Compute free support barycenter
# -------------
k = 10
X_init = np.random.normal(0., 1., (k, d))
b = np.ones((k,)) / k
X = ot.lp.cvx.free_support_barycenter(measures_locations, measures_weights, X_init, b)
##############################################################################
# Plot data
# ---------
#%% plot samples
pl.figure(1)
for (x_i, b_i) in zip(measures_locations, measures_weights):
color = np.random.randint(low=1, high=10 * N)
pl.scatter(x_i[:, 0], x_i[:, 1], s=b * 1000, label='input measure')
pl.scatter(X[:, 0], X[:, 1], s=b * 1000, c='black', marker='^', label='2-Wasserstein barycenter')
pl.title('Data measures and their barycenter')
pl.legend(loc=0)
pl.show()
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