使用辛普森规则加速集成2D gpuArray矩阵的代码

import cupy as cp

def simpson_rule_2d(matrix, dx, dy):
    """
    使用辛普森规则计算2D矩阵的积分

    :param matrix: 2D GPUArray矩阵
    :param dx: x方向的间距
    :param dy: y方向的间距
    :return: 积分值
    """
    nx, ny = matrix.shape
    integral = 0.0

    # 处理边界点
    integral += matrix[0, 0] + matrix[0, -1] + matrix[-1, 0] + matrix[-1, -1]

    # 处理内部点
    integral += cp.sum(matrix[1:-1:2, 1:-1:2]) * 4
    integral += cp.sum(matrix[1:-1:2, 2:-1:2]) * 2
    integral += cp.sum(matrix[2:-1:2, 1:-1:2]) * 2
    integral += cp.sum(matrix[2:-1:2, 2:-1:2])

    # 乘以间距的倒数
    integral *= dx * dy / 9.0

    return integral

# 示例使用
if __name__ == "__main__":
    # 创建一个2D GPUArray矩阵
    matrix = cp.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype=cp.float32)
    dx = 1.0
    dy = 1.0

    integral = simpson_rule_2d(matrix, dx, dy)
    print("积分值:", integral)