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# -*- coding: utf-8 -*-
"""
====================
1D optimal transport
====================
@author: rflamary
"""
import numpy as np
import matplotlib.pylab as pl
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
pl.figure(1)
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)
ot.plot.plot1D_mat(a,b,M,'Cost matrix M')
#%% EMD
G0=ot.emd(a,b,M)
pl.figure(3)
ot.plot.plot1D_mat(a,b,G0,'OT matrix G0')
#%% Sinkhorn
lambd=1e-3
Gs=ot.sinkhorn(a,b,M,lambd)
pl.figure(4)
ot.plot.plot1D_mat(a,b,Gs,'OT matrix Sinkhorn')
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