# Released under The MIT License (MIT)
# http://opensource.org/licenses/MIT
# Copyright (c) 2013-2016 SCoT Development Team
"""This example demonstrates that it is possible to reconstruct sources even if
we include PCA in the process.
"""
from __future__ import print_function
import numpy as np
from scot.pca import pca
from scot.var import VAR
# Set random seed for repeatable results
np.random.seed(42)
# Generate data from a VAR(1) process
model0 = VAR(1)
model0.coef = np.array([[0.3, -0.6], [0, -0.9]])
x = model0.simulate(10000).squeeze()
# Transform data with PCA
w, v = pca(x)
y = np.dot(w.T, x)
# Verify that transformed data y is decorrelated
print('Covariance of x:\n', np.cov(x.squeeze()))
print('\nCovariance of y:\n', np.cov(y.squeeze()))
model1, model2 = VAR(1), VAR(1)
# Fit model1 to the original data
model1.fit(x)
# Fit model2 to the PCA transformed data
model2.fit(y)
# The coefficients estimated on x (2) are exactly equal to the back-transformed
# coefficients estimated on y (4)
print('\n(1) True VAR coefficients:\n', model0.coef)
print('\n(2) VAR coefficients estimated on x:\n', model1.coef)
print('\n(3) VAR coefficients estimated on y:\n', model2.coef)
print('\n(4) VAR coefficients estimated on y and transformed back:\n',
w.dot(model2.coef).dot(w.T))
print('\n(5) Check if (2) and (4) are equal:\n',
np.isclose(model1.coef, w.dot(model2.coef).dot(w.T)))
