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# -*- coding: utf-8 -*-
"""
===============================
1D Unbalanced optimal transport
===============================
This example illustrates the computation of Unbalanced Optimal transport
using a Kullback-Leibler relaxation.
"""
# Author: Hicham Janati <hicham.janati@inria.fr>
#
# License: MIT License
import numpy as np
import matplotlib.pylab as pl
import ot
import ot.plot
from ot.datasets import make_1D_gauss as gauss
##############################################################################
# Generate data
# -------------
#%% parameters
n = 100 # nb bins
# bin positions
x = np.arange(n, dtype=np.float64)
# Gaussian distributions
a = gauss(n, m=20, s=5) # m= mean, s= std
b = gauss(n, m=60, s=10)
# make distributions unbalanced
b *= 5.
# loss matrix
M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))
M /= M.max()
##############################################################################
# Plot distributions and loss matrix
# ----------------------------------
#%% plot the distributions
pl.figure(1, figsize=(6.4, 3))
pl.plot(x, a, 'b', label='Source distribution')
pl.plot(x, b, 'r', label='Target distribution')
pl.legend()
# plot distributions and loss matrix
pl.figure(2, figsize=(5, 5))
ot.plot.plot1D_mat(a, b, M, 'Cost matrix M')
##############################################################################
# Solve Unbalanced Sinkhorn
# --------------
# Sinkhorn
epsilon = 0.1 # entropy parameter
alpha = 1. # Unbalanced KL relaxation parameter
Gs = ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, alpha, verbose=True)
pl.figure(4, figsize=(5, 5))
ot.plot.plot1D_mat(a, b, Gs, 'UOT matrix Sinkhorn')
pl.show()
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