自定义函数实现普通克里金插值法python代码

好的，下面是自定义函数实现普通克里金插值法的Python代码：

import numpy as np
from scipy.spatial.distance import cdist

def ordinary_kriging(xyz, xy, sill, nugget):
    """Ordinary Kriging interpolation using the Hill estimator"""
    
    # Extracting coordinates and values from input arguments
    x = xyz[:, 0]
    y = xyz[:, 1]
    z = xyz[:, 2]
    xi = xy[:, 0]
    yi = xy[:, 1]
    
    # Computing Euclidean distances between input and interpolation points
    d = cdist(np.column_stack((x, y)), np.column_stack((xi, yi)))
    
    # Computing covariance matrix between input points and interpolation points
    cov_mat = (sill - nugget) * np.exp(-d) + nugget * np.identity(len(xyz))
    
    # Applying Hill estimator to covariance matrix to estimate observation variance
    var_obs = np.mean(np.diag(cov_mat))
    
    # Computing weights for interpolation points
    weights = np.linalg.solve(cov_mat, z - np.mean(z))
    
    # Computing interpolated values at interpolation points
    iz = np.dot(d.T, weights) + np.mean(z)
    
    return iz, var_obs

其中，参数说明如下：

- `xyz`：包含所有输入点的坐标和对应值的三列数组。
- `xy`：包含所有需要插值的点的坐标的二列数组。
- `sill`：变异函数的 sill 值。
- `nugget`：变异函数的 nugget 值。

函数返回值为：

- `iz`：插值点对应的插值值的一维数组。
- `var_obs`：观测方差的值。