python如何实现convolution neural network卷积神经网络算法

import numpy as np

def convolve(image, kernel):
    image_height, image_width = image.shape
    kernel_height, kernel_width = kernel.shape

    output_height = image_height - kernel_height + 1
    output_width = image_width - kernel_width + 1

    output = np.zeros((output_height, output_width))

    for i in range(output_height):
        for j in range(output_width):
            output[i, j] = np.sum(image[i:i+kernel_height, j:j+kernel_width] * kernel)

    return output

def relu(x):
    return np.maximum(x, 0)

def max_pool(image, pool_size):
    image_height, image_width = image.shape

    output_height = image_height // pool_size
    output_width = image_width // pool_size

    output = np.zeros((output_height, output_width))

    for i in range(output_height):
        for j in range(output_width):
            output[i, j] = np.max(image[i*pool_size:(i+1)*pool_size, j*pool_size:(j+1)*pool_size])

    return output

# 定义卷积神经网络结构
# 第一层卷积层
kernel_1 = np.random.randn(3, 3)  # 3x3的卷积核
# 第二层卷积层
kernel_2 = np.random.randn(5, 5)  # 5x5的卷积核
# 全连接层
weights = np.random.randn(64, 10)  # 权重矩阵，输入维度为64，输出维度为10

def cnn(image):
    # 第一层卷积层
    conv1 = convolve(image, kernel_1)
    relu1 = relu(conv1)
    
    # 第二层卷积层
    conv2 = convolve(relu1, kernel_2)
    relu2 = relu(conv2)
    
    # 池化层
    pool = max_pool(relu2, 2)
    
    # 展开
    flatten = pool.flatten()
    
    # 全连接层
    output = flatten.dot(weights)
    
    return output

# 测试
image = np.random.randn(28, 28)  # 输入图像，尺寸为28x28
output = cnn(image)
print(output)