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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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