import numpy as np
import mathdef linear_transformation(matrix, vector):return vector.dot(matrix)# vector = np.array([1, 2])
# matrix = [[1, 2], [3, 4]]
# vector = linear_transformation(matrix, vector)
# print("linear_transformation:", vector)
# print("linear_transformation:", type(vector))def active(vector, f):return np.array(list(map(lambda x: f(x), vector)))def sigmoid(x): # 激活函数return 1.0 / (1.0 + math.exp(-x))# result = active(vector, sigmoid)
# print("active:", result)
# print("active:", type(result))class Bpnn:# model是一个list，例如[2, 2, 3, 1]表示输入结点2个，第一个隐含层有2个节点，第二个隐含层有3个节点，输出结点1个def initialize(self, model):# 随机生成模型对应的矩阵（网络权重）和偏置self.matrixs = []self.biases = []for i in range(len(model) - 1): # 矩阵个数为总层数减1，例如4层的网络只需要3个矩阵就可以了           self.matrixs.append(np.random.randn(model[i], model[i + 1])) # 矩阵的列数是对应输入节点的个数，矩阵的行数对应输出节点的个数for i in range(len(model) - 1):# 列表中的每个np数组代表一整层节点的偏置self.biases.append(np.random.randn(model[i + 1]))def predict(self, vector):result = np.array(vector)for i in range(len(self.matrixs)): # 其实就是对一个向量做多次线性变换result = linear_transformation(self.matrixs[i], result) + self.biases[i]result = active(result, sigmoid)return resultdef neural_net_output(self, feature): # 记录各层的输出result = []output = active(linear_transformation(self.matrixs[0], np.array(feature)) + self.biases[0], sigmoid)result.append(output)for i in range(len(self.matrixs) - 1):output = active(linear_transformation(self.matrixs[i + 1], output) + self.biases[i + 1], sigmoid)result.append(output)return result # 格式为[[代表第1层输出的向量], [代表第2层输出的向量], ...,[代表最终输出的向量]]，所有向量都是一维的np.array，向量长度为该层节点数def compute_error(self, prediction, actual): # 计算各层的误差,actual是样本标记值（期望获得的值）result = []prediction = prediction[:] # 后面的处理都不影响原始数组prediction.reverse() # 转置便于处理error = prediction[0] * (1 - prediction[0]) * (actual - prediction[0]) # 计算最终输出的误差
        result.append(error)for i in range(len(self.matrixs) - 1): # 计算每层的误差，可以通过转置矩阵计算上一层误差的一个因子error = prediction[i + 1] * (1- prediction[i + 1]) * linear_transformation(self.matrixs[-1 - i].T, error) result.append(error)result.reverse()return result # 格式为[[代表第1层输出误差的向量], [代表第2层输出误差的向量], ...,[代表最终输出误差的向量]]，所有向量都是一维的np.array，向量长度为该层节点数数def update_network(self, feature, prediction, error, LEARING_RATE):# 更新权重（手算凑出来的计算方法↓）temp = np.ones_like(self.matrixs[0]) temp = temp * LEARING_RATE * error[0]temp = temp.T * np.array(feature)temp = temp.Tself.matrixs[0] += temp;for i in range(len(self.matrixs) - 1):temp = np.ones_like(self.matrixs[i + 1]) temp = temp * LEARING_RATE * error[i + 1]temp = temp.T * prediction[i]temp = temp.Tself.matrixs[i + 1] += temp;            # 更新偏置for i in range(len(self.biases)):self.biases[i] += LEARING_RATE * error[i]def train(self, get_batch, MAX_ITERATION, LEARING_RATE, MAX_LOSS):loss = MAX_LOSS = abs(MAX_LOSS)count = MAX_ITERATIONwhile abs(loss) >= MAX_LOSS and count > 0:batch = get_batch()for example in batch:prediction = self.neural_net_output(example.feature)error = self.compute_error(prediction, example.label)self.update_network(example.feature, prediction, error, LEARING_RATE)loss = abs(np.mean(error[-1])) # 取最后一次迭代最终输出的平均值作为本批次的误差count = count - 1print("迭代次数:", MAX_ITERATION - count)print("误差:", loss)class LabeledExample:def __init__(self, feature, label):self.feature = featureself.label = label# 训练一个类似于异或（xor）运算的函数，相同为假，相异为真
labeled_examples = [LabeledExample([0, 0], [0]), LabeledExample([0, 1], [1]), LabeledExample([1, 0], [1]), LabeledExample([1, 1], [0])]def full_batch():return labeled_examplesbpnn = Bpnn()
bpnn.initialize([2, 2, 1]) # 构造一个三层的神经网络，输入节点2个，隐含层节点2个，输出节点1个
bpnn.train(full_batch, 10000, 0.6, 0.01) # 学习因子为0.6, 最大允许误差0.01
print("输入层与隐含层权值", bpnn.matrixs[0])
print("隐含层权值与输出层权值", bpnn.matrixs[1])
print("隐含层阈值", bpnn.biases[0])
print("输出层阈值", bpnn.biases[1])
sample1 = [0.05, 0.1]
sample2 = [0.2, 0.9]
sample3 = [0.86, 0.95]
print("预测样本", sample1, "的结果是:", bpnn.predict(sample1))
print("预测样本", sample2, "的结果是:", bpnn.predict(sample2))
print("预测样本", sample3, "的结果是:", bpnn.predict(sample3))