#!/usr/bin/env python

import numpy as np

import matplotlib.pyplot as plt

from Array import Array

from Models import NonstationaryLogistic, alpha_norm

from BinaryMatrix import approximate_conditional_nll as cond_a_nll_b

from BinaryMatrix import approximate_from_margins_weights as cond_a_sample_b

from BinaryMatrix import log_partition_is

M = 200

N = 1000

theta = 2.0

kappa_target = ('row_sum', 1)

T_fit = 20

T_grid = 1000

min_error = 0.1

theta_grid_min = 0.0

theta_grid_max = 3.0

theta_grid_G = 121

def cond_a_nll(X, w):

return cond_a_nll_b(X, w, sort_by_wopt_var = True)

def cond_a_sample(r, c, w, T = 0):

return cond_a_sample_b(r, c, w, T, sort_by_wopt_var = True)

while True:

a = Array(M, N)

alpha_norm(a, 1.0)

a.new_edge_covariate('x')[:,:] = np.random.normal(0, 1, (M, N))

d = NonstationaryLogistic()

d.beta['x'] = theta

d.match_kappa(a, kappa_target)

a.generate(d)

f = NonstationaryLogistic()

f.beta['x'] = None

f.fit_conditional(a, T = T_fit, verbose = True)

abs_err = abs(f.beta['x'] - d.beta['x'])

if abs_err > min_error:

print f.beta['x']

break

theta_vec = np.linspace(theta_grid_min, theta_grid_max, theta_grid_G)

cmle_a_vec = np.empty_like(theta_vec)

cmle_is_vec = np.empty_like(theta_vec)

logkappa_cvsq = np.empty_like(theta_vec)

A = a.array

r = A.sum(1)

c = A.sum(0)

print r

print c

X = a.edge_covariates['x'].matrix()

for l, theta_l in enumerate(theta_vec):

print l

logit_P_l = theta_l * X

w_l = np.exp(logit_P_l)

cmle_a_vec[l] = -cond_a_nll(A, w_l)

z = cond_a_sample(r, c, w_l, T_grid)

logkappa, logcvsq = log_partition_is(z, cvsq = True)

cvsq = np.exp(logcvsq)

logkappa_cvsq[l] = cvsq

print 'est. cv^2 = %.2f (T_grid = %d)' % (cvsq, T_grid)

cmle_is_vec[l] = np.sum(np.log(w_l[A])) - logkappa

print 'CMLE-A: %.2f' % theta_vec[np.argmax(cmle_a_vec)]

print 'CMLE-IS: %.2f' % theta_vec[np.argmax(cmle_is_vec)]

plt.figure()

plt.plot(theta_vec, cmle_a_vec)

plt.plot(theta_vec, cmle_is_vec)

plt.figure()

plt.plot(theta_vec, logkappa_cvsq)

plt.show()