import mleNode as mn

import numpy as np
from numpy.linalg import norm
import numpy.random as nr
from scipy.optimize import minimize
import matplotlib.pyplot as plt
import seaborn
from random import random, randint

seaborn.set_style("white")


def simulate_cascade(x, graph):
    """
    Simulate an IC cascade given a graph and initial state.

    For each time step we yield:
        - susc: the nodes susceptible at the beginning of this time step
        - x: the subset of susc who became infected
    """
    susc = np.ones(graph.shape[0], dtype=bool)
    susc = susc ^ x  # t=0, the source is not susceptible
    yield x, susc
    while np.any(x):
        susc = susc ^ x  # nodes infected at previous step are now inactive
        if not np.any(susc):
            break
        x = 1 - np.exp(-np.dot(graph.T, x))
        y = nr.random(x.shape[0])
        x = (x >= y) & susc
        yield x, susc


def uniform_source(graph, *args, **kwargs):
    x0 = np.zeros(graph.shape[0], dtype=bool)
    x0[nr.randint(0, graph.shape[0])] = True
    return x0


def simulate_cascades(n, graph, source=uniform_source):
    for t in xrange(n):
        x0 = source(graph, t)
        yield simulate_cascade(x0, graph)


def build_cascade_list(cascades, collapse=False):
    x, s = [], []
    for cascade in cascades:
        xlist, slist = zip(*cascade)
        x.append(np.vstack(xlist))
        s.append(np.vstack(slist))
    if not collapse:
        return x, s
    else:
        return np.vstack(x), np.vstack(s)


def cascadeLkl(graph, infect, sus):
    # There is a problem with the current implementation
    # Note that you need to take into account the time diff between the label
    # and the values being conditioned. Note also that the matrix if stacked as
    # such will require to keep track of the state 0 of each cascade.
    a = np.dot(infect, graph)
    return np.log(1. - np.exp(-a[(infect[1:])*sus[1:]])).sum() \
            - a[(~infect[1:])*sus].sum()


if __name__ == "__main__":
    g = np.array([[0, 0, 1], [0, 0, 0.5], [0, 0, 0]])
    p = 0.5
    g = np.log(1. / (1 - p * g))
    cascades = simulate_cascades(100, g)
    cascade, y_obs = mn.build_matrix(cascades, 0)
    conf = mn.bootstrap(x, y, n_iter=100)

    estimand = np.linalg.norm(np.delete(conf - g[0], 0, axis=1), axis=1)
    error.append(mn.confidence_interval(*np.histogram(estimand, bins=50)))
    plt.semilogx(sizes, error)
    plt.show()