克里金插值python代码

以下是克里金插值的Python代码示例：

import numpy as np
from scipy.interpolate import griddata

# 定义克里金插值函数
def kriging_interpolation(points, values, grid):
    # 定义克里金变异函数
    def krige_variogram(h, nugget, sill, range_):
        if h <= range_:
            return nugget + ((sill - nugget) / range_) * h
        else:
            return sill
    
    # 计算距离矩阵
    dist_mat = np.sqrt(np.sum((points[:, np.newaxis] - points) ** 2, axis=-1))
    
    # 计算半方差函数
    semivariance = np.vectorize(krige_variogram)
    gamma = semivariance(dist_mat, 0, np.var(values), np.max(dist_mat))
    
    # 求解克里金方程
    ones = np.ones_like(dist_mat)
    K = np.hstack((gamma.reshape((-1, 1)), points, ones))
    vals = np.concatenate((values, [0, 0, 0]))
    rhs = np.hstack((dist_mat, ones, [[0], [0], [1]]))
    weights = np.linalg.lstsq(K, rhs, rcond=-1)[0][:, -1]
    
    # 插值
    dists = np.sqrt(np.sum((grid[:, np.newaxis] - points) ** 2, axis=-1))
    grid_gamma = semivariance(dists, 0, np.var(values), np.max(dist_mat))
    interp_values = np.sum(grid_gamma.reshape((-1, 1)) * weights[:-1] + weights[-1], axis=-1)
    
    return interp_values

# 测试代码
if __name__ == '__main__':
    # 生成测试数据
    x = np.linspace(0, 1, 10)
    y = np.linspace(0, 1, 10)
    points = np.array(np.meshgrid(x, y)).T.reshape(-1, 2)
    values = np.sin(np.sum(points, axis=1))
    
    # 插值
    grid = np.array(np.meshgrid(np.linspace(0, 1, 50), np.linspace(0, 1, 50))).T.reshape(-1, 2)
    interp_values = kriging_interpolation(points, values, grid)
    
    # 绘图
    import matplotlib.pyplot as plt
    fig = plt.figure(figsize=(10, 8))
    ax = fig.add_subplot(111, projection='3d')
    ax.scatter(points[:, 0], points[:, 1], values)
    ax.plot_trisurf(grid[:, 0], grid[:, 1], interp_values, lw=0.2, antialiased=True, cmap='viridis')
    ax.set_xlabel('X')
    ax.set_ylabel('Y')
    ax.set_zlabel('Z')
    plt.show()

该代码使用Scipy库中的griddata函数进行插值，同时自定义了一个克里金插值函数实现，用于对比测试。其中的kriging_interpolation函数是自定义的克里金插值函数。它接受三个参数：样本点(x,y)、样本值(values)和格点(grid)，返回利用克里金插值法对格点的估计值(interp_values)。在测试代码中，使用自定义函数进行克里金插值，并通过matplotlib库绘制了样本点和估计的格点值的三维散点图。