import random
import copy
import numpy as np
from scipy.sparse import lil_matrix

class ATM:
    def __init__(self, K, alpha, beta, max_iter, verbose=0):
        self.K=K
        self.alpha = alpha
        self.beta = beta
        self.max_iter = max_iter
        self.verbose=verbose

    def fit(self,W,A,V,S):
        self._W = W
        self._A = A
        self._D = len(W) # number of documents
        self._V = V # number of vocabularies
        self._S = S # number of distinct authors

        self.Z = self._init_Z()
        self.Y = self._init_Y()
        self.nak = self._init_nak()
        self.nkv = self._init_nkv()
        nkv_sum = self.nkv.sum(axis=1)
        nak_sum = self.nak.sum(axis=1)

        self._max_score = -1
        self.max_Z = None
        self.max_Y = None
        remained_iter = self.max_iter
        while True:
            if self.verbose: print remained_iter
            for d in np.random.choice(self._D, self._D, replace=False):
                # Sample Z and Y
                for i in np.random.choice(len(self._W[d]), len(self._W[d]), replace=False):
                    k = self.Z[d][i] # topic
                    v = self._W[d][i] # word index
                    j = self.Y[d][i] # author_index within document d
                    a = self._A[d][j] # author

                    self.nak[a][k] -= 1
                    self.nkv[k][v] -= 1
                    nkv_sum[k] -= 1
                    nak_sum[a] -= 1

                    self.Z[d][i], self.Y[d][i] = self._sample_z_and_y(d,v,nkv_sum,nak_sum)

                    new_a = self._A[d][self.Y[d][i]]
                    new_k = self.Z[d][i]
                    self.nak[new_a][new_k] += 1
                    self.nkv[new_k][v] += 1
                    nkv_sum[new_k] += 1
                    nak_sum[new_a] += 1

            s = self.score(nkv_sum,nak_sum)
            if s > self._max_score:
                self.max_score = s
                self.max_Z = copy.copy(self.Z)
                self.max_Y = copy.copy(self.Y)
            remained_iter -= 1
            if remained_iter <= 0: break
        return self

    def _init_Z(self):
        Z = []
        for d in range(len(self._W)):
            Z.append(np.random.randint(low=0, high=self.K, size=len(self._W[d])))
        return Z

    def _init_Y(self):
        Y = []
        for d in range(len(self._W)):
            Y.append(np.random.randint(low=0, high=len(self._A[d]), size=len(self._W[d])))
        return Y

    def _init_nak(self):
        nak = np.zeros((self._S,self.K))
        for d in range(self._D):
            for i in range(len(self._W[d])):
                k = self.Z[d][i]
                j = self.Y[d][i]
                a = self._A[d][j]
                nak[a,k]+=1
        return nak

    def _init_nkv(self):
        nkv = np.zeros((self.K,self._V))
        for d in range(self._D):
            for i in range(len(self._W[d])):
                k = self.Z[d][i]
                v = self._W[d][i]
                nkv[k,v]+=1
        return nkv

    def _sample_z_and_y(self,d,v,nkv_sum,nak_sum):
        nkv = self.nkv[:,v] # k-dimensional vector
        na = len(self._A[d]) # number of authors in document d
        prob = []
        p1 = ((nkv+self.beta) / (nkv_sum+self.beta*self._V))
        for j in range(na):
            a = self._A[d][j]
            pa =  p1 * ((self.nak[a]+self.alpha) / (nak_sum[a]+self.alpha*self.K))
            prob.append(pa)
        prob = np.array(prob).flatten()
        prob = prob/prob.sum()
        zy = np.random.multinomial(n=1, pvals=prob).argmax()
        z = zy%self.K
        y = zy/self.K
        return z,y

    def score(self,nkv_sum,nak_sum):
        s = 0
        for d in range(self._D):
            for i in range(len(self._W[d])):
                v = self._W[d][i]
                k = self.Z[d][i]
                a = self._A[d][self.Y[d][i]]
                s += ((self.nkv[k,v]+self.beta) / (nkv_sum[k]+self.beta*self._V)) * ((self.nak[a,k]+self.alpha) / (nak_sum[a]+self.alpha*self.K))
        return s