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# -*- coding: utf-8 -*-
"""
====================
1D optimal transport
====================
@author: rflamary
"""
import numpy as np
import matplotlib.pylab as plt
import ot
from ot.datasets import get_1D_gauss as gauss
#%% 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)
# loss matrix
M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))
M /= M.max()
#%% plot the distributions
plt.figure(1)
plt.plot(x, a, 'b', label='Source distribution')
plt.plot(x, b, 'r', label='Target distribution')
plt.legend()
#%% plot distributions and loss matrix
plt.figure(2, figsize=(5, 5))
ot.plot.plot1D_mat(a, b, M, 'Cost matrix M')
#%% EMD
G0 = ot.emd(a, b, M)
plt.figure(3, figsize=(5, 5))
ot.plot.plot1D_mat(a, b, G0, 'OT matrix G0')
#%% Sinkhorn
lambd = 1e-3
Gs = ot.sinkhorn(a, b, M, lambd, verbose=True)
plt.figure(4, figsize=(5, 5))
ot.plot.plot1D_mat(a, b, Gs, 'OT matrix Sinkhorn')
plt.show()
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