# cython: boundscheck=False, cdivision=True
import numpy as np
cimport numpy as np
from libc.math cimport log, exp

DTYPE = np.float64
ctypedef np.float_t DTYPE_t

cdef DTYPE_t weight_success(int dist, int dt, DTYPE_t alpha, DTYPE_t delta, DTYPE_t lmbda,
                            DTYPE_t t_scale, DTYPE_t w1, DTYPE_t w2, DTYPE_t w3):
    """weight for successful infection, exponential time model"""
    cdef DTYPE_t structural, temporal, result
    # structural = delta ** (dist**1)
    structural = delta * lmbda**(dist-1)
    temporal = log(exp(alpha/t_scale)-1.) - alpha*dt/t_scale
    # temporal = 1. / (1. + (dt - 1.)/alpha)**0.01 - 1. / (1. + dt/alpha)**0.01
    result = log(structural) + temporal
    return result

cdef DTYPE_t weight_failure(int dist, int dt, DTYPE_t alpha, DTYPE_t delta, DTYPE_t lmbda,
                            DTYPE_t t_scale, DTYPE_t w1, DTYPE_t w2, DTYPE_t w3):
    """weight for failed infection, exponential time model"""
    cdef DTYPE_t structural, temporal, result
    # structural = delta ** (dist**1)
    structural = delta * lmbda**(dist-1)
    temporal = exp(-alpha * dt/t_scale)
    # temporal = 1.  - 1. / (1. + dt/alpha)**0.01
    result = log(1. - structural + structural * temporal)
    return result

def ml(dict root_victims, dict victims, dict non_victims,
       DTYPE_t alpha, DTYPE_t delta, DTYPE_t lmbda):
    cdef:
        int n_roots, n_victims, roots, i, dist, dt, t, l, n_days
        DTYPE_t beta, ll, beta_add, max_beta, max_beta_add
        list parents, failures, successes
    n_roots, n_victims = len(root_victims), len(victims)
    n_nodes = 148152
    n_days = 3012
    t_scale = 1.
    cdef:
        np.ndarray[DTYPE_t] probs = np.zeros(n_victims, dtype=DTYPE)
        np.ndarray[DTYPE_t] probs_fail = np.zeros(n_victims, dtype=DTYPE)
        np.ndarray[DTYPE_t] parent_dists = np.zeros(n_victims, dtype=DTYPE)
        np.ndarray[DTYPE_t] parent_dts = np.zeros(n_victims, dtype=DTYPE)
        np.ndarray[DTYPE_t] probs_nv = np.zeros(len(non_victims), dtype=DTYPE)

    # loop through victims
    for i, parents in enumerate(victims.itervalues()):
        # for each victim node i, compute the probability that all its parents
        # fail to infect it, also computes the probability that its most
        # likely parent infects it
        failures = [weight_failure(dist, dt, alpha, delta, lmbda, t_scale, w1, w2, w3)
                    for (prnt, dist, dt, w1, w2, w3) in parents]
        probs_fail[i] = sum(failures)
        successes = [weight_success(dist, dt, alpha, delta, lmbda, t_scale, w1, w2, w3)
                     for (prnt, dist, dt, w1, w2, w3) in parents]
        dists = [dist for (prnt, dist, dt, w1, w2, w3) in parents]
        dts = [dt for (prnt, dist, dt, w1, w2, w3) in parents]
        # find parent that maximizes log(p) - log(\tilde{p})
        probs[i] = float("-inf")
        for l, s in enumerate(successes):
            prob = s - failures[l]
            if prob > probs[i]:
                probs[i] = prob
                parent_dists[i] = dists[l]
                parent_dts[i] = dts[l]
                # probs_fail[i] = failures[l]

    # loop through non-victims
    for i, parents in enumerate(non_victims.itervalues()):
        # for each non victim node, compute the probability that all its
        # parents fail to infect it
        failures = [weight_failure(dist, dt, alpha, delta, lmbda, t_scale, w1, w2, w3)
                    for (prnt, dist, dt, w1, w2, w3) in parents]
        probs_nv[i] = sum(failures)

    # calculate log likelihood
    ll =  probs_fail.sum() # add probability that all edges to all victims fail
    ll += probs_nv.sum() # add probability that all edges to non_victims fail

    max_beta_add = float('-inf')
    # iterate over all victim nodes to find the optimal threshold
    for beta in np.arange(0.01, 1., 0.01):
        thresh = log(beta/(n_days*(1.-beta)))
        seeds = probs<thresh
        non_seeds = probs>=thresh
        roots = n_roots + sum(seeds)

        beta_add = 0.
        # add probability for realized edges and subtract probability these edges fail
        beta_add += (probs[non_seeds]).sum()
        # add probability for the seeds and non-seeds
        beta_add += roots * log(beta/n_days) + (n_nodes-roots) * log(1. - beta)

        if beta_add > max_beta_add:
            max_beta = beta
            max_roots = roots
            max_beta_add = beta_add
            pdists = (parent_dists[non_seeds]).mean()
            pdts = (parent_dts[non_seeds]).mean()
            # print 'beta:', max_beta, 'add:', max_beta_add, 'roots:', max_roots

    ll += max_beta_add
    roots = max_roots
    beta = max_beta
    print 'dist:', pdists
    print 'dt:', pdts
    return (beta, roots, ll)