import random
import math


#
# Shorthand:
#   "pd_" as a variable prefix means "partial derivative"
#   "d_" as a variable prefix means "derivative"
#   "_wrt_" is shorthand for "with respect to"
#   "w_ho" and "w_ih" are the index of weights from hidden to output layer neurons and input to hidden layer neurons respectively
#
# Comment references:
#
# [1] Wikipedia article on Backpropagation
#   http://en.wikipedia.org/wiki/Backpropagation#Finding_the_derivative_of_the_error
# [2] Neural Networks for Machine Learning course on Coursera by Geoffrey Hinton
#   https://class.coursera.org/neuralnets-2012-001/lecture/39
# [3] The Back Propagation Algorithm
#   https://www4.rgu.ac.uk/files/chapter3%20-%20bp.pdf
# [4] The original location of the code
# https://github.com/mattm/simple-neural-network/blob/master/neural-network.py

class NeuralNetwork:
    # 神经网络类
    LEARNING_RATE = 0.5

    # 设置学习率为0.5

    def __init__(self, num_inputs, num_hidden, num_outputs, hidden_layer_weights=None, hidden_layer_bias=None,
                 output_layer_weights=None, output_layer_bias=None):
        # 初始化一个三层神经网络结构
        self.num_inputs = num_inputs

        self.hidden_layer = NeuronLayer(num_hidden, hidden_layer_bias)
        self.output_layer = NeuronLayer(num_outputs, output_layer_bias)

        self.init_weights_from_inputs_to_hidden_layer_neurons(hidden_layer_weights)
        self.init_weights_from_hidden_layer_neurons_to_output_layer_neurons(output_layer_weights)

    def init_weights_from_inputs_to_hidden_layer_neurons(self, hidden_layer_weights):
        weight_num = 0
        for h in range(len(self.hidden_layer.neurons)):  # num_hidden,遍历隐藏层
            for i in range(self.num_inputs):  # 遍历输入层
                if not hidden_layer_weights:
                    # 如果hidden_layer_weights的值为空,则利用随机化函数对其进行赋值,否则利用hidden_layer_weights中的值对其进行更新
                    self.hidden_layer.neurons[h].weights.append(random.random())
                else:
                    self.hidden_layer.neurons[h].weights.append(hidden_layer_weights[weight_num])
                weight_num += 1

    def init_weights_from_hidden_layer_neurons_to_output_layer_neurons(self, output_layer_weights):
        weight_num = 0
        for o in range(len(self.output_layer.neurons)):  # num_outputs,遍历输出层
            for h in range(len(self.hidden_layer.neurons)):  # 遍历输出层
                if not output_layer_weights:
                    # 如果output_layer_weights的值为空,则利用随机化函数对其进行赋值,否则利用output_layer_weights中的值对其进行更新
                    self.output_layer.neurons[o].weights.append(random.random())
                else:
                    self.output_layer.neurons[o].weights.append(output_layer_weights[weight_num])
                weight_num += 1

    def inspect(self):  # 输出神经网络信息
        print('------')
        print('* Inputs: {}'.format(self.num_inputs))
        print('------')
        print('Hidden Layer')
        self.hidden_layer.inspect()
        print('------')
        print('* Output Layer')
        self.output_layer.inspect()
        print('------')

    def feed_forward(self, inputs):  # 返回输出层y值
        hidden_layer_outputs = self.hidden_layer.feed_forward(inputs)
        return self.output_layer.feed_forward(hidden_layer_outputs)

    # Uses online learning, ie updating the weights after each training case
    # 使用在线学习方式,训练每个实例之后对权值进行更新
    def train(self, training_inputs, training_outputs):
        self.feed_forward(training_inputs)
        # 反向传播
        # 1. Output neuron deltas输出层deltas
        pd_errors_wrt_output_neuron_total_net_input = [0]*len(self.output_layer.neurons)
        for o in range(len(self.output_layer.neurons)):
            # 对于输出层∂E/∂zⱼ=∂E/∂a*∂a/∂z=cost'(target_output)*sigma'(z)
            pd_errors_wrt_output_neuron_total_net_input[o] = self.output_layer.neurons[
                o].calculate_pd_error_wrt_total_net_input(training_outputs[o])

        # 2. Hidden neuron deltas隐藏层deltas
        pd_errors_wrt_hidden_neuron_total_net_input = [0]*len(self.hidden_layer.neurons)
        for h in range(len(self.hidden_layer.neurons)):
            # We need to calculate the derivative of the error with respect to the output of each hidden layer neuron
            # 我们需要计算误差对每个隐藏层神经元的输出的导数,由于不是输出层所以dE/dyⱼ需要根据下一层反向进行计算,即根据输出层的函数进行计算
            # dE/dyⱼ = Σ ∂E/∂zⱼ * ∂z/∂yⱼ = Σ ∂E/∂zⱼ * wᵢⱼ
            d_error_wrt_hidden_neuron_output = 0
            for o in range(len(self.output_layer.neurons)):
                d_error_wrt_hidden_neuron_output += pd_errors_wrt_output_neuron_total_net_input[o]* \
                                                    self.output_layer.neurons[o].weights[h]

            # ∂E/∂zⱼ = dE/dyⱼ * ∂zⱼ/∂
            pd_errors_wrt_hidden_neuron_total_net_input[h] = d_error_wrt_hidden_neuron_output*self.hidden_layer.neurons[
                h].calculate_pd_total_net_input_wrt_input()

        # 3. Update output neuron weights 更新输出层权重
        for o in range(len(self.output_layer.neurons)):
            for w_ho in range(len(self.output_layer.neurons[o].weights)):
                # 注意:输出层权重是隐藏层神经元与输出层神经元连接的权重
                # ∂Eⱼ/∂wᵢⱼ = ∂E/∂zⱼ * ∂zⱼ/∂wᵢⱼ
                pd_error_wrt_weight = pd_errors_wrt_output_neuron_total_net_input[o]*self.output_layer.neurons[
                    o].calculate_pd_total_net_input_wrt_weight(w_ho)

                # Δw = α * ∂Eⱼ/∂wᵢ
                self.output_layer.neurons[o].weights[w_ho] -= self.LEARNING_RATE*pd_error_wrt_weight

        # 4. Update hidden neuron weights 更新隐藏层权重
        for h in range(len(self.hidden_layer.neurons)):
            for w_ih in range(len(self.hidden_layer.neurons[h].weights)):
                # 注意:隐藏层权重是输入层神经元与隐藏层神经元连接的权重
                # ∂Eⱼ/∂wᵢ = ∂E/∂zⱼ * ∂zⱼ/∂wᵢ
                pd_error_wrt_weight = pd_errors_wrt_hidden_neuron_total_net_input[h]*self.hidden_layer.neurons[
                    h].calculate_pd_total_net_input_wrt_weight(w_ih)

                # Δw = α * ∂Eⱼ/∂wᵢ
                self.hidden_layer.neurons[h].weights[w_ih] -= self.LEARNING_RATE*pd_error_wrt_weight

    def calculate_total_error(self, training_sets):
        #  使用平方差计算训练集误差
        total_error = 0
        for t in range(len(training_sets)):
            training_inputs, training_outputs = training_sets[t]
            self.feed_forward(training_inputs)
            for o in range(len(training_outputs)):
                total_error += self.output_layer.neurons[o].calculate_error(training_outputs[o])
        return total_error


class NeuronLayer:
    # 神经层类
    def __init__(self, num_neurons, bias):

        # Every neuron in a layer shares the same bias 一层中的所有神经元共享一个bias
        self.bias = bias if bias else random.random()
        random.random()
        # 生成0和1之间的随机浮点数float，它其实是一个隐藏的random.Random类的实例的random方法。
        # random.random()和random.Random().random()作用是一样的。
        self.neurons = []
        for i in range(num_neurons):
            self.neurons.append(Neuron(self.bias))
        # 在神经层的初始化函数中对每一层的bias赋值,利用神经元的init函数对神经元的bias赋值

    def inspect(self):
        # print该层神经元的信息
        print('Neurons:', len(self.neurons))
        for n in range(len(self.neurons)):
            print(' Neuron', n)
            for w in range(len(self.neurons[n].weights)):
                print('  Weight:', self.neurons[n].weights[w])
            print('  Bias:', self.bias)

    def feed_forward(self, inputs):
        # 前向传播过程outputs中存储的是该层每个神经元的y/a的值(经过神经元激活函数的值有时被称为y有时被称为a)
        outputs = []
        for neuron in self.neurons:
            outputs.append(neuron.calculate_output(inputs))
        return outputs

    def get_outputs(self):
        outputs = []
        for neuron in self.neurons:
            outputs.append(neuron.output)
        return outputs


class Neuron:
    # 神经元类
    def __init__(self, bias):
        self.bias = bias
        self.weights = []

    def calculate_output(self, inputs):
        self.inputs = inputs
        self.output = self.squash(self.calculate_total_net_input())
        # output即为输入即为y(a)意为从激活函数中的到的值
        return self.output

    def calculate_total_net_input(self):
        # 此处计算的为激活函数的输入值即z=W(n)x+b
        total = 0
        for i in range(len(self.inputs)):
            total += self.inputs[i]*self.weights[i]
        return total + self.bias

    # Apply the logistic function to squash the output of the neuron
    # 使用sigmoid函数为激励函数,一下是sigmoid函数的定义
    # The result is sometimes referred to as 'net' [2] or 'net' [1]
    def squash(self, total_net_input):
        return 1/(1 + math.exp(-total_net_input))

    # Determine how much the neuron's total input has to change to move closer to the expected output
    # 确定神经元的总输入需要改变多少，以接近预期的输出
    # Now that we have the partial derivative of the error(Cost function) with respect to the output (∂E/∂yⱼ)
    # 我们可以根据cost function对y(a)神经元激活函数输出值的偏导数和激活函数输出值y(a)对激活函数输入值z=wx+b的偏导数计算delta(δ).
    # the derivative of the output with respect to the total net input (dyⱼ/dzⱼ) we can calculate
    # the partial derivative of the error with respect to the total net input.
    # This value is also known as the delta (δ) [1]
    # δ = ∂E/∂zⱼ = ∂E/∂yⱼ * dyⱼ/dzⱼ 关键key
    #
    def calculate_pd_error_wrt_total_net_input(self, target_output):
        return self.calculate_pd_error_wrt_output(target_output)*self.calculate_pd_total_net_input_wrt_input()

    # The error for each neuron is calculated by the Mean Square Error method:
    # 每个神经元的误差由平均平方误差法计算
    def calculate_error(self, target_output):
        return 0.5*(target_output - self.output) ** 2

    # The partial derivate of the error with respect to actual output then is calculated by:
    # 对实际输出的误差的偏导是通过计算得到的--即self.output(y也常常用a表示经过激活函数后的值)
    # = 2 * 0.5 * (target output - actual output) ^ (2 - 1) * -1
    # = -(target output - actual output)BP算法最后隐层求cost function 对a求导
    #
    # The Wikipedia article on backpropagation [1] simplifies to the following, but most other learning material does not [2]
    # 维基百科关于反向传播[1]的文章简化了以下内容，但大多数其他学习材料并没有简化这个过程[2]
    # = actual output - target output
    #
    # Note that the actual output of the output neuron is often written as yⱼ and target output as tⱼ so:
    # = ∂E/∂yⱼ = -(tⱼ - yⱼ)
    # 注意我们一般将输出层神经元的输出为yⱼ,而目标标签(正确答案)表示为tⱼ.
    def calculate_pd_error_wrt_output(self, target_output):
        return -(target_output - self.output)

    # The total net input into the neuron is squashed using logistic function to calculate the neuron's output:
    # yⱼ = φ = 1 / (1 + e^(-zⱼ)) 注意我们对于神经元使用的激活函数都是logistic函数
    # Note that where ⱼ represents the output of the neurons in whatever layer we're looking at and ᵢ represents the layer below it
    # 注意我们用j表示我们正在看的这层神经元的输出,我们用i表示这层的后一层的神经元.
    # The derivative (not partial derivative since there is only one variable) of the output then is:
    # dyⱼ/dzⱼ = yⱼ * (1 - yⱼ)这是sigmoid函数的导数表现形式.
    def calculate_pd_total_net_input_wrt_input(self):
        return self.output*(1 - self.output)

    # The total net input is the weighted sum of all the inputs to the neuron and their respective weights:
    # 激活函数的输入是所有输入的加权权重的总和
    # = zⱼ = netⱼ = x₁w₁ + x₂w₂ ...
    # The partial derivative of the total net input with respective to a given weight (with everything else held constant) then is:
    # 总的净输入与给定的权重的偏导数(其他所有的项都保持不变)
    # = ∂zⱼ/∂wᵢ = some constant + 1 * xᵢw₁^(1-0) + some constant ... = xᵢ
    def calculate_pd_total_net_input_wrt_weight(self, index):
        return self.inputs[index]


# Blog post example:

nn = NeuralNetwork(2, 2, 2, hidden_layer_weights=[0.15, 0.2, 0.25, 0.3], hidden_layer_bias=0.35,
                   output_layer_weights=[0.4, 0.45, 0.5, 0.55], output_layer_bias=0.6)
for i in range(10000):
    nn.train([0.05, 0.1], [0.01, 0.99])
    print(i, round(nn.calculate_total_error([[[0.05, 0.1], [0.01, 0.99]]]), 9))  # 截断处理只保留小数点后9位

# XOR example:

# training_sets = [
#     [[0, 0], [0]],
#     [[0, 1], [1]],
#     [[1, 0], [1]],
#     [[1, 1], [0]]
# ]

# nn = NeuralNetwork(len(training_sets[0][0]), 5, len(training_sets[0][1]))
# for i in range(10000):
#     training_inputs, training_outputs = random.choice(training_sets)
#     nn.train(training_inputs, training_outputs)
#     print(i, nn.calculate_total_error(training_sets))