# -*- coding: utf-8 -*-
"""
Created on Thu Oct 21 15:42:18 2010

Author: josef-pktd
"""

import numpy as np
from scipy import linalg

def tiny2zero(x, eps = 1e-15):
    '''replace abs values smaller than eps by zero, makes copy
    '''
    mask = np.abs(x.copy()) <  eps
    x[mask] = 0
    return x


nobs = 5
autocov = 0.8**np.arange(nobs)
#from statsmodels.tsa import arima_process as ap
#autocov = ap.arma_acf([1, -0.8, 0.2], [1])[:10]
autocov = np.array([ 3.,  2.,  1.,  0.4,  0.12,  0.016, -0.0112,
        0.016    , -0.0112   , -0.01216  , -0.007488 , -0.0035584])/3.
autocov = autocov[:nobs]
sigma = linalg.toeplitz(autocov)
sigmainv = linalg.inv(sigma)

c = linalg.cholesky(sigma, lower=True)
ci = linalg.cholesky(sigmainv, lower=True)

print(sigma)
print(tiny2zero(ci/ci.max()))

"this is the text book transformation"
print('coefficient for first observation', np.sqrt(1-autocov[1]**2))
ci2 = ci[::-1,::-1].T
print(tiny2zero(ci2/ci2.max()))

print(np.dot(ci/ci.max(), np.ones(nobs)))

print(np.dot(ci2/ci2.max(), np.ones(nobs)))
