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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Tue Mar 20 14:31:15 2018
@author: rflamary
"""
import numpy as np
import pylab as pl
import ot
import scipy.linalg as linalg
#%%
n=1000
d=2
sigma=.1
# source samples
angles=np.random.rand(n,1)*2*np.pi
xs=np.concatenate((np.sin(angles),np.cos(angles)),axis=1)+sigma*np.random.randn(n,2)
xs[:n//2,1]+=2
# target samples
anglet=np.random.rand(n,1)*2*np.pi
xt=np.concatenate((np.sin(anglet),np.cos(anglet)),axis=1)+sigma*np.random.randn(n,2)
xt[:n//2,1]+=2
A=np.array([[1.5,.7],[.7,1.5]])
b=np.array([[4,2]])
xt=xt.dot(A)+b
#%%
pl.figure(1,(5,5))
pl.plot(xs[:,0],xs[:,1],'+')
pl.plot(xt[:,0],xt[:,1],'o')
#%%
Ae,be=ot.da.OT_mapping_linear(xs,xt)
Ae1=linalg.inv(Ae)
be1=-be.dot(Ae1)
xst=xs.dot(Ae)+be
xts=xt.dot(Ae1)+be1
##%%
pl.figure(1,(5,5))
pl.clf()
pl.plot(xs[:,0],xs[:,1],'+')
pl.plot(xt[:,0],xt[:,1],'o')
pl.plot(xst[:,0],xst[:,1],'+')
pl.plot(xts[:,0],xts[:,1],'o')
pl.show()
#%% Example class with on images
mapping=ot.da.LinearTransport()
mapping.fit(Xs=xs,Xt=xt)
xst=mapping.transform(Xs=xs)
xts=mapping.inverse_transform(Xt=xt)
##%%
pl.figure(1,(5,5))
pl.clf()
pl.plot(xs[:,0],xs[:,1],'+')
pl.plot(xt[:,0],xt[:,1],'o')
pl.plot(xst[:,0],xst[:,1],'+')
pl.plot(xts[:,0],xts[:,1],'o')
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