import random
import numpy as np
import math

def sigmoid(x):
    return 1. / (1 + np.exp(-x))

def sigmoid_derivative(values):
    return values*(1-values)

def tanh(x):
    return 2.0 / (1.0 + np.exp(-2 * x)) - 1.0

def tanh_derivative(values):
    return 1. - values ** 2

# createst uniform random array w/ values in [a,b) and shape args
def rand_arr(a, b, *args):
    np.random.seed(0)
    return np.random.rand(*args) * (b - a) + a

class LstmParam:
    def __init__(self, mem_cell_ct, x_dim):
        self.mem_cell_ct = mem_cell_ct
        self.x_dim = x_dim
        concat_len = x_dim + mem_cell_ct
        # weight matrices
        self.wg = rand_arr(-0.1, 0.1, mem_cell_ct, concat_len)
        self.wi = rand_arr(-0.1, 0.1, mem_cell_ct, concat_len)
        self.wf = rand_arr(-0.1, 0.1, mem_cell_ct, concat_len)
        self.wo = rand_arr(-0.1, 0.1, mem_cell_ct, concat_len)
        # bias terms
        self.bg = rand_arr(-0.1, 0.1, mem_cell_ct)
        self.bi = rand_arr(-0.1, 0.1, mem_cell_ct)
        self.bf = rand_arr(-0.1, 0.1, mem_cell_ct)
        self.bo = rand_arr(-0.1, 0.1, mem_cell_ct)
        # diffs (derivative of loss function w.r.t. all parameters)
        self.wg_diff = np.zeros((mem_cell_ct, concat_len))
        self.wi_diff = np.zeros((mem_cell_ct, concat_len))
        self.wf_diff = np.zeros((mem_cell_ct, concat_len))
        self.wo_diff = np.zeros((mem_cell_ct, concat_len))
        self.bg_diff = np.zeros(mem_cell_ct)
        self.bi_diff = np.zeros(mem_cell_ct)
        self.bf_diff = np.zeros(mem_cell_ct)
        self.bo_diff = np.zeros(mem_cell_ct)

    def apply_diff(self, lr = 1):
        self.wg -= lr * self.wg_diff
        self.wi -= lr * self.wi_diff
        self.wf -= lr * self.wf_diff
        self.wo -= lr * self.wo_diff
        self.bg -= lr * self.bg_diff
        self.bi -= lr * self.bi_diff
        self.bf -= lr * self.bf_diff
        self.bo -= lr * self.bo_diff
        # reset diffs to zero
        self.wg_diff = np.zeros_like(self.wg)
        self.wi_diff = np.zeros_like(self.wi)
        self.wf_diff = np.zeros_like(self.wf)
        self.wo_diff = np.zeros_like(self.wo)
        self.bg_diff = np.zeros_like(self.bg)
        self.bi_diff = np.zeros_like(self.bi)
        self.bf_diff = np.zeros_like(self.bf)
        self.bo_diff = np.zeros_like(self.bo)

class LstmState:
    def __init__(self, mem_cell_ct, x_dim):
        self.g = np.zeros(mem_cell_ct)
        self.i = np.zeros(mem_cell_ct)
        self.f = np.zeros(mem_cell_ct)
        self.o = np.zeros(mem_cell_ct)
        self.s = np.zeros(mem_cell_ct)
        self.h = np.zeros(mem_cell_ct)
        self.bottom_diff_h = np.zeros_like(self.h)
        self.bottom_diff_s = np.zeros_like(self.s)
   
class LstmNode:
    def __init__(self, lstm_param, lstm_state):
        # store reference to parameters and to activations
        self.state = lstm_state
        self.param = lstm_param
        # non-recurrent input concatenated with recurrent input
        self.xc = None

    def bottom_data_is(self, x, s_prev = None, h_prev = None):
        # if this is the first lstm node in the network
        if s_prev == None: s_prev = np.zeros_like(self.state.s)
        if h_prev == None: h_prev = np.zeros_like(self.state.h)
        # save data for use in backprop
        self.s_prev = s_prev
        self.h_prev = h_prev

        # concatenate x(t) and h(t-1)
        xc = np.hstack((x,  h_prev))
        #单元状态
        self.state.g = np.tanh(np.dot(self.param.wg, xc) + self.param.bg)
        #输入门
        self.state.i = sigmoid(np.dot(self.param.wi, xc) + self.param.bi)
        #遗忘门
        self.state.f = sigmoid(np.dot(self.param.wf, xc) + self.param.bf)
        #输出门
        self.state.o = sigmoid(np.dot(self.param.wo, xc) + self.param.bo)
        #更新
        self.state.s = self.state.g * self.state.i + s_prev * self.state.f
        #最终输出
        self.state.h = self.state.s * self.state.o

        self.xc = xc
   
    def top_diff_is(self, top_diff_h, top_diff_s):
        # notice that top_diff_s is carried along the constant error carousel
        ds = self.state.o * top_diff_h + top_diff_s
        do = self.state.s * top_diff_h
        di = self.state.g * ds
        dg = self.state.i * ds
        df = self.s_prev * ds

        # diffs w.r.t. vector inside sigma / tanh function
        di_input = sigmoid_derivative(self.state.i) * di
        df_input = sigmoid_derivative(self.state.f) * df
        do_input = sigmoid_derivative(self.state.o) * do
        dg_input = tanh_derivative(self.state.g) * dg

        # diffs w.r.t. inputs
        self.param.wi_diff += np.outer(di_input, self.xc)
        self.param.wf_diff += np.outer(df_input, self.xc)
        self.param.wo_diff += np.outer(do_input, self.xc)
        self.param.wg_diff += np.outer(dg_input, self.xc)
        self.param.bi_diff += di_input
        self.param.bf_diff += df_input      
        self.param.bo_diff += do_input
        self.param.bg_diff += dg_input      

        # compute bottom diff
        dxc = np.zeros_like(self.xc)
        dxc += np.dot(self.param.wi.T, di_input)
        dxc += np.dot(self.param.wf.T, df_input)
        dxc += np.dot(self.param.wo.T, do_input)
        dxc += np.dot(self.param.wg.T, dg_input)

        # save bottom diffs
        self.state.bottom_diff_s = ds * self.state.f
        self.state.bottom_diff_h = dxc[self.param.x_dim:]

class LstmNetwork():
    def __init__(self, lstm_param):
        self.lstm_param = lstm_param
        self.lstm_node_list = []
        # input sequence
        self.x_list = []

    def y_list_is(self, y_list, loss_layer):
        """
        Updates diffs by setting target sequence
        with corresponding loss layer.
        Will *NOT* update parameters.  To update parameters,
        call self.lstm_param.apply_diff()
        """
        assert len(y_list) == len(self.x_list)
        idx = len(self.x_list) - 1
        # first node only gets diffs from label ...
        loss = loss_layer.loss(self.lstm_node_list[idx].state.h, y_list[idx])
        diff_h = loss_layer.bottom_diff(self.lstm_node_list[idx].state.h, y_list[idx])
        # here s is not affecting loss due to h(t+1), hence we set equal to zero
        diff_s = np.zeros(self.lstm_param.mem_cell_ct)
        self.lstm_node_list[idx].top_diff_is(diff_h, diff_s)
        idx -= 1

        ### ... following nodes also get diffs from next nodes, hence we add diffs to diff_h
        ### we also propagate error along constant error carousel using diff_s
        while idx >= 0:
            loss += loss_layer.loss(self.lstm_node_list[idx].state.h, y_list[idx])
            diff_h = loss_layer.bottom_diff(self.lstm_node_list[idx].state.h, y_list[idx])
            diff_h += self.lstm_node_list[idx + 1].state.bottom_diff_h
            diff_s = self.lstm_node_list[idx + 1].state.bottom_diff_s
            self.lstm_node_list[idx].top_diff_is(diff_h, diff_s)
            idx -= 1

        return loss

    def x_list_clear(self):
        self.x_list = []

    def x_list_add(self, x):
        self.x_list.append(x)
        if len(self.x_list) > len(self.lstm_node_list):
            # need to add new lstm node, create new state mem
            lstm_state = LstmState(self.lstm_param.mem_cell_ct, self.lstm_param.x_dim)
            self.lstm_node_list.append(LstmNode(self.lstm_param, lstm_state))

        # get index of most recent x input
        idx = len(self.x_list) - 1
        if idx == 0:
            # no recurrent inputs yet
            self.lstm_node_list[idx].bottom_data_is(x)
        else:
            s_prev = self.lstm_node_list[idx - 1].state.s
            h_prev = self.lstm_node_list[idx - 1].state.h
            self.lstm_node_list[idx].bottom_data_is(x, s_prev, h_prev)

class LstmLayer(object):
    def __init__(self, input_width, state_width,
                 learning_rate):
        self.input_width = input_width
        self.state_width = state_width
        self.learning_rate = learning_rate
        # 门的激活函数
        self.gate_activator = SigmoidActivator()
        # 输出的激活函数
        self.output_activator = TanhActivator()
        # 当前时刻初始化为t0
        self.times = 0      
        # 各个时刻的单元状态向量c
        self.c_list = self.init_state_vec()
        # 各个时刻的输出向量h
        self.h_list = self.init_state_vec()
        # 各个时刻的遗忘门f
        self.f_list = self.init_state_vec()
        # 各个时刻的输入门i
        self.i_list = self.init_state_vec()
        # 各个时刻的输出门o
        self.o_list = self.init_state_vec()
        # 各个时刻的即时状态c~
        self.ct_list = self.init_state_vec()
        # 遗忘门权重矩阵Wfh, Wfx, 偏置项bf
        self.Wfh, self.Wfx, self.bf = (
            self.init_weight_mat())
        # 输入门权重矩阵Wfh, Wfx, 偏置项bf
        self.Wih, self.Wix, self.bi = (
            self.init_weight_mat())
        # 输出门权重矩阵Wfh, Wfx, 偏置项bf
        self.Woh, self.Wox, self.bo = (
            self.init_weight_mat())
        # 单元状态权重矩阵Wfh, Wfx, 偏置项bf
        self.Wch, self.Wcx, self.bc = (
            self.init_weight_mat())

    def init_state_vec(self):
        '''
        初始化保存状态的向量
        '''
        state_vec_list = []
        state_vec_list.append(np.zeros(
            (self.state_width, 1)))
        return state_vec_list

    def init_weight_mat(self):
        '''
        初始化权重矩阵
        '''
        Wh = np.random.uniform(-1e-4, 1e-4,
            (self.state_width, self.state_width))
        Wx = np.random.uniform(-1e-4, 1e-4,
            (self.state_width, self.input_width))
        b = np.zeros((self.state_width, 1))
        return Wh, Wx, b

    def forward(self, x):
        '''
        根据式1-式6进行前向计算
        '''
        self.times += 1
        # 遗忘门
        fg = self.calc_gate(x, self.Wfx, self.Wfh,
            self.bf, self.gate_activator)
        self.f_list.append(fg)
        # 输入门
        ig = self.calc_gate(x, self.Wix, self.Wih,
            self.bi, self.gate_activator)
        self.i_list.append(ig)
        # 输出门
        og = self.calc_gate(x, self.Wox, self.Woh,
            self.bo, self.gate_activator)
        self.o_list.append(og)
        # 即时状态
        ct = self.calc_gate(x, self.Wcx, self.Wch,
            self.bc, self.output_activator)
        self.ct_list.append(ct)
        # 单元状态
        c = fg * self.c_list[self.times - 1] + ig * ct
        self.c_list.append(c)
        # 输出
        h = og * self.output_activator.forward(c)
        self.h_list.append(h)

    def calc_gate(self, x, Wx, Wh, b, activator):
        '''
        计算门
        '''
        h = self.h_list[self.times - 1] # 上次的LSTM输出
        net = np.dot(Wh, h) + np.dot(Wx, x) + b
        gate = activator.forward(net)
        return gate


    def backward(self, x, delta_h, activator):
        '''
        实现LSTM训练算法
        '''
        self.calc_delta(delta_h, activator)
        self.calc_gradient(x)

    def update(self):
        '''
        按照梯度下降，更新权重
        '''
        self.Wfh -= self.learning_rate * self.Whf_grad
        self.Wfx -= self.learning_rate * self.Whx_grad
        self.bf -= self.learning_rate * self.bf_grad
        self.Wih -= self.learning_rate * self.Whi_grad
        self.Wix -= self.learning_rate * self.Whi_grad
        self.bi -= self.learning_rate * self.bi_grad
        self.Woh -= self.learning_rate * self.Wof_grad
        self.Wox -= self.learning_rate * self.Wox_grad
        self.bo -= self.learning_rate * self.bo_grad
        self.Wch -= self.learning_rate * self.Wcf_grad
        self.Wcx -= self.learning_rate * self.Wcx_grad
        self.bc -= self.learning_rate * self.bc_grad

    def calc_delta(self, delta_h, activator):
        # 初始化各个时刻的误差项
        self.delta_h_list = self.init_delta()  # 输出误差项
        self.delta_o_list = self.init_delta()  # 输出门误差项
        self.delta_i_list = self.init_delta()  # 输入门误差项
        self.delta_f_list = self.init_delta()  # 遗忘门误差项
        self.delta_ct_list = self.init_delta() # 即时输出误差项

        # 保存从上一层传递下来的当前时刻的误差项
        self.delta_h_list[-1] = delta_h
       
        # 迭代计算每个时刻的误差项
        for k in range(self.times, 0, -1):
            self.calc_delta_k(k)

    def init_delta(self):
        '''
        初始化误差项
        '''
        delta_list = []
        for i in range(self.times + 1):
            delta_list.append(np.zeros(
                (self.state_width, 1)))
        return delta_list

    def calc_delta_k(self, k):
        '''
        根据k时刻的delta_h，计算k时刻的delta_f、
        delta_i、delta_o、delta_ct，以及k-1时刻的delta_h
        '''
        # 获得k时刻前向计算的值
        ig = self.i_list[k]
        og = self.o_list[k]
        fg = self.f_list[k]
        ct = self.ct_list[k]
        c = self.c_list[k]
        c_prev = self.c_list[k-1]
        tanh_c = self.output_activator.forward(c)
        delta_k = self.delta_h_list[k]

        # 根据式9计算delta_o
        delta_o = (delta_k * tanh_c *
            self.gate_activator.backward(og))
        delta_f = (delta_k * og *
            (1 - tanh_c * tanh_c) * c_prev *
            self.gate_activator.backward(fg))
        delta_i = (delta_k * og *
            (1 - tanh_c * tanh_c) * ct *
            self.gate_activator.backward(ig))
        delta_ct = (delta_k * og *
            (1 - tanh_c * tanh_c) * ig *
            self.output_activator.backward(ct))
        delta_h_prev = (
                np.dot(delta_o.transpose(), self.Woh) +
                np.dot(delta_i.transpose(), self.Wih) +
                np.dot(delta_f.transpose(), self.Wfh) +
                np.dot(delta_ct.transpose(), self.Wch)
            ).transpose()

        # 保存全部delta值
        self.delta_h_list[k-1] = delta_h_prev
        self.delta_f_list[k] = delta_f
        self.delta_i_list[k] = delta_i
        self.delta_o_list[k] = delta_o
        self.delta_ct_list[k] = delta_ct

    def calc_gradient(self, x):
        # 初始化遗忘门权重梯度矩阵和偏置项
        self.Wfh_grad, self.Wfx_grad, self.bf_grad = (
            self.init_weight_gradient_mat())
        # 初始化输入门权重梯度矩阵和偏置项
        self.Wih_grad, self.Wix_grad, self.bi_grad = (
            self.init_weight_gradient_mat())
        # 初始化输出门权重梯度矩阵和偏置项
        self.Woh_grad, self.Wox_grad, self.bo_grad = (
            self.init_weight_gradient_mat())
        # 初始化单元状态权重梯度矩阵和偏置项
        self.Wch_grad, self.Wcx_grad, self.bc_grad = (
            self.init_weight_gradient_mat())

       # 计算对上一次输出h的权重梯度
        for t in range(self.times, 0, -1):
            # 计算各个时刻的梯度
            (Wfh_grad, bf_grad,
            Wih_grad, bi_grad,
            Woh_grad, bo_grad,
            Wch_grad, bc_grad) = (
                self.calc_gradient_t(t))
            # 实际梯度是各时刻梯度之和
            self.Wfh_grad += Wfh_grad
            self.bf_grad += bf_grad
            self.Wih_grad += Wih_grad
            self.bi_grad += bi_grad
            self.Woh_grad += Woh_grad
            self.bo_grad += bo_grad
            self.Wch_grad += Wch_grad
            self.bc_grad += bc_grad

        # 计算对本次输入x的权重梯度
        xt = x.transpose()
        self.Wfx_grad = np.dot(self.delta_f_list[-1], xt)
        self.Wix_grad = np.dot(self.delta_i_list[-1], xt)
        self.Wox_grad = np.dot(self.delta_o_list[-1], xt)
        self.Wcx_grad = np.dot(self.delta_ct_list[-1], xt)

    def init_weight_gradient_mat(self):
        '''
        初始化权重矩阵
        '''
        Wh_grad = np.zeros((self.state_width,
            self.state_width))
        Wx_grad = np.zeros((self.state_width,
            self.input_width))
        b_grad = np.zeros((self.state_width, 1))
        return Wh_grad, Wx_grad, b_grad

    def calc_gradient_t(self, t):
        '''
        计算每个时刻t权重的梯度
        '''
        h_prev = self.h_list[t-1].transpose()
        Wfh_grad = np.dot(self.delta_f_list[t], h_prev)
        bf_grad = self.delta_f_list[t]
        Wih_grad = np.dot(self.delta_i_list[t], h_prev)
        bi_grad = self.delta_f_list[t]
        Woh_grad = np.dot(self.delta_o_list[t], h_prev)
        bo_grad = self.delta_f_list[t]
        Wch_grad = np.dot(self.delta_ct_list[t], h_prev)
        bc_grad = self.delta_ct_list[t]
        return Wfh_grad, bf_grad, Wih_grad, bi_grad, \
               Woh_grad, bo_grad, Wch_grad, bc_grad

    def reset_state(self):
        # 当前时刻初始化为t0
        self.times = 0      
        # 各个时刻的单元状态向量c
        self.c_list = self.init_state_vec()
        # 各个时刻的输出向量h
        self.h_list = self.init_state_vec()
        # 各个时刻的遗忘门f
        self.f_list = self.init_state_vec()
        # 各个时刻的输入门i
        self.i_list = self.init_state_vec()
        # 各个时刻的输出门o
        self.o_list = self.init_state_vec()
        # 各个时刻的即时状态c~
        self.ct_list = self.init_state_vec()


def data_set():
    x = [np.array([[1], [2], [3]]),
         np.array([[2], [3], [4]])]
    d = np.array([[1], [2]])
    return x, d


def gradient_check():
    '''
    梯度检查
    '''
    # 设计一个误差函数，取所有节点输出项之和
    error_function = lambda o: o.sum()
   
    lstm = LstmLayer(3, 2, 1e-3)

    # 计算forward值
    x, d = data_set()
    lstm.forward(x[0])
    lstm.forward(x[1])
   
    # 求取sensitivity map
    sensitivity_array = np.ones(lstm.h_list[-1].shape,
                                dtype=np.float64)
    # 计算梯度
    lstm.backward(x[1], sensitivity_array, IdentityActivator())
   
    # 检查梯度
    epsilon = 10e-4
    for i in range(lstm.Wfh.shape[0]):
        for j in range(lstm.Wfh.shape[1]):
            lstm.Wfh[i,j] += epsilon
            lstm.reset_state()
            lstm.forward(x[0])
            lstm.forward(x[1])
            err1 = error_function(lstm.h_list[-1])
            lstm.Wfh[i,j] -= 2*epsilon
            lstm.reset_state()
            lstm.forward(x[0])
            lstm.forward(x[1])
            err2 = error_function(lstm.h_list[-1])
            expect_grad = (err1 - err2) / (2 * epsilon)
            lstm.Wfh[i,j] += epsilon
            print 'weights(%d,%d): expected - actural %.4e - %.4e' % (
                i, j, expect_grad, lstm.Wfh_grad[i,j])
    return lstm


def test():
    l = LstmLayer(3, 2, 1e-3)
    x, d = data_set()
    l.forward(x[0])
    l.forward(x[1])
    l.backward(x[1], d, IdentityActivator())
    return l