使用高斯核的Nadaraya-Watson参数化三维介质的折射率，给出折射率梯度方程，用python实现

高斯核的Nadaraya-Watson参数化三维介质的折射率可以用以下代码实现： ```python import numpy as np from scipy.spatial.distance import cdist def gaussian_kernel(dist, h): return np.exp(-0.5 * (dist / h) ** 2) def nadaraya_watson(x, y, z, n, query_point, h): dist = cdist(np.array([x, y, z]).T, [query_point]) weights = gaussian_kernel(dist, h) return np.sum(n * weights) / np.sum(weights) def gradient(x, y, z, n, query_point, h): dist = cdist(np.array([x, y, z]).T, [query_point]) weights = gaussian_kernel(dist, h) grad_x = np.sum(n * weights * (x - query_point[0])) / np.sum(weights) grad_y = np.sum(n * weights * (y - query_point[1])) / np.sum(weights) grad_z = np.sum(n * weights * (z - query_point[2])) / np.sum(weights) return np.array([grad_x, grad_y, grad_z]) ``` 其中，x、y、z分别为已知点的坐标，n为对应的折射率值，query_point为待估计点的坐标，h为高斯核的带宽。 使用该函数可以得到待估计点的折射率和折射率梯度，例如： ```python # 生成随机数据 x = np.random.rand(100) y = np.random.rand(100) z = np.random.rand(100) n = np.sin(x * y * z) # 待估计点 query_point = [0.5, 0.5, 0.5] # 高斯核带宽 h = 0.1 # 计算折射率和梯度 n_hat = nadaraya_watson(x, y, z, n, query_point, h) grad_n = gradient(x, y, z, n, query_point, h) print('折射率：