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# -*- coding: utf-8 -*-
"""
Regularized OT with generic solver
"""
import numpy as np
import matplotlib.pylab as pl
import ot
#%% parameters
n=100 # nb bins
# bin positions
x=np.arange(n,dtype=np.float64)
# Gaussian distributions
a=ot.datasets.get_1D_gauss(n,m=20,s=5) # m= mean, s= std
b=ot.datasets.get_1D_gauss(n,m=60,s=10)
# loss matrix
M=ot.dist(x.reshape((n,1)),x.reshape((n,1)))
M/=M.max()
#%% EMD
G0=ot.emd(a,b,M)
pl.figure(3)
ot.plot.plot1D_mat(a,b,G0,'OT matrix G0')
#%% Example with Frobenius norm regularization
def f(G): return 0.5*np.sum(G**2)
def df(G): return G
reg=1e-1
Gl2=ot.optim.cg(a,b,M,reg,f,df,verbose=True)
pl.figure(3)
ot.plot.plot1D_mat(a,b,Gl2,'OT matrix Frob. reg')
#%% Example with entropic regularization
def f(G): return np.sum(G*np.log(G))
def df(G): return np.log(G)+1
reg=1e-3
Ge=ot.optim.cg(a,b,M,reg,f,df,verbose=True)
pl.figure(4)
ot.plot.plot1D_mat(a,b,Ge,'OT matrix Entrop. reg')
#%% Example with Frobenius norm + entropic regularization with gcg
def f(G): return 0.5*np.sum(G**2)
def df(G): return G
reg1=1e-1
reg2=1e-1
Gel2=ot.optim.gcg(a,b,M,reg1,reg2,f,df,verbose=True)
pl.figure(5)
ot.plot.plot1D_mat(a,b,Gel2,'OT entropic + matrix Frob. reg')
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