backPropagate算法实现

代码如下：

import mathimport randomimport stringrandom.seed(0)def rand(a, b):    return (b-a)*random.random() + adef makeMatrix(I, J, fill=0.0):    m = []    for i in range(I):        m.append([fill]*J)    return mdef sigmoid(x):    return math.tanh(x)def dsigmoid(y):    return 1.0 - y**2class neuralNetwork:    """三层BP网络"""    def __init__(self, ni, nh, no):        # 输入层 隐藏层 输出层        self.ni = ni + 1        self.nh = nh        self.no = no        # 激活神经网络的所有节点（向量）        self.ai = [1.0]*self.ni        self.ah = [1.0]*self.nh        self.ao = [1.0]*self.no        # 权重矩阵        self.wi = makeMatrix(self.ni, self.nh)        self.wo = makeMatrix(self.nh, self.no)        # 设置随机值        for i in range(self.ni):            for j in range(self.nh):                self.wi[i][j] = rand(-0.2, 0.2)        for j in range(self.nh):            for k in range(self.no):                self.wo[j][k] = rand(-2.0, 2.0)        # 最后建立动量因子（矩阵）        self.ci = makeMatrix(self.ni, self.nh)        self.co = makeMatrix(self.nh, self.no)    def update(self, inputs):        if len(inputs) != self.ni - 1:            raise  ValueError('与输入层节点数不符！')        # 激活输入层        for i in range(self.ni-1):            self.ai[i] = inputs[i]        # 激活隐藏层        for j in range(self.nh):            sum = 0.0            for i in range(self.ni):                sum = sum + self.ai[i] * self.wi[i][j]            self.ah[j] = sigmoid(sum)        # 激活输出层        for k in range(self.no):            sum = 0.0            for j in range(self.nh):                sum = sum + self.ah[j] * self.wo[j][k]            self.ao[k] = sigmoid(sum)        return self.ao[:]    def backPropagate(self,targets, N, M):        """反向传播"""        if len(targets) != self.no:            raise ValueError('与输出节点个数不符！')        # 计算输出层的误差        output_deltas = [0.0] * self.no        for k in range(self.no):            error = targets[k] - self.ao[k]            output_deltas[k] = dsigmoid(self.ao[k]) * error        # 计算隐藏层的误差        hidden_deltas = [0.0] * self.nh        for j in range(self.nh):            error = 0.0            for k in range(self.no):                error = error + output_deltas[k] * self.wo[j][k]            hidden_deltas[j] = dsigmoid(self.ah[j]) * error        # 更新输出层权重        for j in range(self.nh):            for k in range(self.no):                change = output_deltas[k] * self.ah[j]                self.wo[j][k] = self.wo[j][k] + N*change + M*self.co[j][k]                self.co[j][k] = change        # 更新输入层权重        for i in range(self.ni):            for j in range(self.nh):                change = hidden_deltas[j] * self.ai[i]                self.wi[i][j] = self.wi[i][j] + N*change + M*self.ci[i][j]                self.ci[i][j] = change        # 计算误差        error = 0.0        for k in range(len(targets)):            error = error + 0.5*(targets[k]-self.ao[k])**2        return error    def test(self, patterns):        for p in patterns:            print(p[0], '->', self.update(p[0]))    def weights(self):        print('输入层权重:')        for i in range(self.ni):            print(self.wi[i])        print()        print('输出层权重:')        for j in range(self.nh):            print(self.wo[j])    def train(self, patterns, epoch=10000, N=0.5, M=0.1):        # N：学习速率（learnning rate）        # M：动量因子（momentum factor）        for i in range(epoch):            error = 0.0            for p in patterns:                inputs = p[0]                targets = p[1]                self.update(inputs)                error = error + self.backPropagate(targets, N, M)            if i % 100 == 0:                print('误差 %-.5f' % error)def demo():    pat = [        [[0, 0], [0]],        [[0, 1], [1]],        [[1, 0], [1]],        [[1, 1], [0]]    ]    n = neuralNetwork(2, 2, 1)    n.train(pat)    n.test(pat)    n.weights()if __name__ == '__main__':    demo()