bpnn算法实现手写数字识别，要求使用mnist数据集，使用Python语言，不用keras,TensorFlow等框架

好的，我可以为您提供一个简单的bpnn算法实现手写数字识别的Python代码。这个代码使用了mnist数据集，但是没有使用任何深度学习框架，完全是手写的代码。代码如下：

import numpy as np
import struct

def load_mnist_data(data_path):
    with open(data_path + 'train-images.idx3-ubyte', 'rb') as f:
        train_images = f.read()
    with open(data_path + 'train-labels.idx1-ubyte', 'rb') as f:
        train_labels = f.read()
    with open(data_path + 't10k-images.idx3-ubyte', 'rb') as f:
        test_images = f.read()
    with open(data_path + 't10k-labels.idx1-ubyte', 'rb') as f:
        test_labels = f.read()

    # 解析数据集
    train_images = parse_images(train_images)
    train_labels = parse_labels(train_labels)
    test_images = parse_images(test_images)
    test_labels = parse_labels(test_labels)

    return train_images, train_labels, test_images, test_labels

def parse_images(data):
    magic, num, rows, cols = struct.unpack_from('>IIII', data)
    offset = struct.calcsize('>IIII')
    images = np.empty((num, rows, cols))

    for i in range(num):
        image = struct.unpack_from('>784B', data, offset)
        offset += struct.calcsize('>784B')
        images[i] = np.array(image).reshape(28, 28)

    return images

def parse_labels(data):
    magic, num = struct.unpack_from('>II', data)
    offset = struct.calcsize('>II')
    labels = np.empty(num)

    for i in range(num):
        label = struct.unpack_from('>B', data, offset)
        offset += struct.calcsize('>B')
        labels[i] = label

    return labels

def sigmoid(x):
    return 1.0 / (1.0 + np.exp(-x))

def sigmoid_derivative(x):
    return x * (1.0 - x)

class NeuralNetwork:
    def __init__(self, input_size, hidden_size, output_size):
        self.weights1 = np.random.randn(input_size, hidden_size)
        self.weights2 = np.random.randn(hidden_size, output_size)

    def forward(self, x):
        self.z2 = np.dot(x, self.weights1)
        self.a2 = sigmoid(self.z2)
        self.z3 = np.dot(self.a2, self.weights2)
        y_hat = sigmoid(self.z3)
        return y_hat

    def backward(self, x, y, y_hat, learning_rate):
        delta3 = (y_hat - y) * sigmoid_derivative(y_hat)
        d_weights2 = np.dot(self.a2.T, delta3)
        delta2 = np.dot(delta3, self.weights2.T) * sigmoid_derivative(self.a2)
        d_weights1 = np.dot(x.T, delta2)
        self.weights1 -= learning_rate * d_weights1
        self.weights2 -= learning_rate * d_weights2

    def train(self, x, y, learning_rate):
        y_hat = self.forward(x)
        self.backward(x, y, y_hat, learning_rate)

    def predict(self, x):
        y_hat = self.forward(x)
        return np.argmax(y_hat, axis=1)

if __name__ == '__main__':
    train_images, train_labels, test_images, test_labels = load_mnist_data('data/mnist/')
    train_images = train_images.reshape(train_images.shape[0], -1)
    test_images = test_images.reshape(test_images.shape[0], -1)

    input_size = train_images.shape[1]
    hidden_size = 100
    output_size = 10

    nn = NeuralNetwork(input_size, hidden_size, output_size)

    num_epochs = 100
    batch_size = 100
    learning_rate = 0.1

    num_batches = train_images.shape[0] // batch_size

    for epoch in range(num_epochs):
        for i in range(num_batches):
            batch_start = i * batch_size
            batch_end = batch_start + batch_size
            x = train_images[batch_start:batch_end]
            y = np.zeros((batch_size, output_size))
            y[np.arange(batch_size), train_labels[batch_start:batch_end].astype(int)] = 1
            nn.train(x, y, learning_rate)

        train_acc = np.mean(nn.predict(train_images) == train_labels)
        test_acc = np.mean(nn.predict(test_images) == test_labels)
        print('Epoch: %d, Train accuracy: %f, Test accuracy: %f' % (epoch, train_acc, test_acc))

这个代码的思路是：首先加载mnist数据集，然后定义一个包含一个隐层的神经网络，使用随机初始化的权重对神经网络进行训练。训练时每次读入一个batch的数据，然后使用反向传播算法对权重进行更新。最后输出训练和测试集上的准确率。