import time
import main as mn
import numpy as np
import logging
import scipy.special as ssp
from itertools import product

logging.basicConfig(format='%(asctime)s - %(levelname)s - %(message)s',
                    level=logging.INFO)

def g(m):
    assert (m > 0).all()
    return np.log(1 - np.exp(-m))


def h(m):
    return -m


def ll(x, s, theta):
    """
    x : infected
    s : susceptible
    """
    res = 0
    for t in range(1, x.shape[0]):
        w = np.dot(x[t-1], theta)
        res += g(w)[x[t]].sum() + h(w)[~x[t] & s[t]].sum()
    return res


def sample(params):
    mu, v = params
    size = mu.shape
    return np.clip(np.random.beta(mu, v, size=size), 1e-3, 1e5)


def ll_full(params, x, s, nsamples=50):
    return np.mean([ll(x, s, sample(params)) for _ in xrange(nsamples)])


def kl(params1, params0):
    mu0, sig0 = params0
    mu1, sig1 = params1
    return (ssp.betaln(mu0, sig0) - ssp.betaln(mu1, sig1) + (mu0 - mu1) *
            ssp.psi(mu0) + (sig0 - sig1) * ssp.psi(sig0) + (mu1 - mu0 + sig1 -
                sig0) * ssp.psi(mu0 + sig0)).sum()


def aux(var, res, i, j, f, eps):
    var[i,j] += eps
    res[i,j] += f(var)
    var[i,j] -= 2 * eps
    res[i,j] -= f(var)
    res[i,j] /= 2 * eps
    var[i, j] += eps


def grad_ll_full(params, x, s, nsamples=50, eps=1e-5):
    mu, v = params
    n, m = mu.shape
    mugrad = np.empty((n,m))
    vgrad = np.empty((n,m))
    for (i, j) in product(xrange(n), xrange(m)):
        aux(mu, mugrad, i, j, lambda t: ll_full((t, v), x, s, nsamples), eps)
        aux(v, vgrad, i, j, lambda t: ll_full((mu, t), x, s, nsamples), eps)

    return mugrad, vgrad


def grad_kl(params1, params0, eps=1e-5):
    mu0, sig0 = params0
    mu1, sig1 = params1

    n, m = mu0.shape
    mugrad = np.empty((n,m))
    vgrad = np.empty((n,m))
    for (i, j) in product(xrange(n), xrange(m)):
        aux(mu1, mugrad, i, j, lambda t: kl((t, sig1), params0), eps)
        aux(sig1, vgrad, i, j, lambda t: kl((mu1, t), params0), eps)

    return mugrad, vgrad


def sgd(mu1, sig1, mu0, sig0, cascades, n_e=100, lr=lambda t: 1e-1, n_print=10):
    g_mu1, g_sig1 = grad_kl((mu1, sig1), (mu0, sig0))
    for t in xrange(n_e):
        lrt = lr(t)  # learning rate
        mu1 = np.clip(mu1 + lrt * g_mu1, 1e-3, 1e5)
        sig1 = np.clip(sig1 + lrt * g_sig1, 1e-3, 1e5)
        for step, (x, s) in enumerate(zip(*cascades)):
            g_mu1, g_sig1 = grad_ll_full((mu1, sig1), x, s)
            mu1 = np.clip(mu1 + lrt * g_mu1, 1e-3, 1e5)
            sig1 = np.clip(sig1 + lrt * g_sig1, 1e-3, 1e5)
            res = np.sum(ll_full((mu1, sig1), x, s) for x, s in zip(*cascades))\
                    + kl((mu1, sig1), (mu0, sig0))
            #if step % n_print == 0:
        logging.info("Epoch:{}\tStep:{}\tLB:{}\t".format(t, step, res))
        print mu1
        print sig1


if __name__ == '__main__':
    graph = np.array([[0, 0, 1], [0, 0, 0.5], [0, 0, 0]])
    #graph = np.random.binomial(2, p=.2, size=(4, 4))
    p = 0.5
    graph = np.log(1. / (1 - p * graph))
    print(graph)
    cascades = mn.build_cascade_list(mn.simulate_cascades(100, graph))
    mu0, sig0 = (1. + .2 * np.random.normal(size=graph.shape),
                 1 + .2 * np.random.normal(size=graph.shape))
    mu1, sig1 = (1. + .2 * np.random.normal(size=graph.shape),
                 1 + .2 * np.random.normal(size=graph.shape))
    sgd(mu1, sig1, mu0, sig0, cascades, n_e=30, n_print=1)