以下是一个示例代码，展示了Kriging二维加点训练的变化过程以及3D图像可视化的方法。请注意，这只是一个基本示例，具体实现可能会根据你使用的编程语言和库而有所不同。
import numpy as npimport matplotlib.pyplot as pltfrom mpl_toolkits.mplot3d import Axes3D# 定义Kriging模型类class KrigingModel:def __init__(self, x, y):self.x = xself.y = y# 计算半方差函数（Semi-Variogram）def semivariogram(self, h, nugget, sill, range):return nugget + (sill - nugget) * (1.5 * (h / range) - 0.5 * (h / range) ** 3)# 计算两个点之间的欧氏距离def distance(self, p1, p2):return np.sqrt((p1[0] - p2[0])**2 + (p1[1] - p2[1])**2)# 训练Kriging模型def train(self):n = len(self.x)# 初始化半方差矩阵和自相关向量semivar_matrix = np.zeros((n, n))gamma_vector = np.zeros(n)# 计算半方差矩阵和自相关向量的值for i in range(n):for j in range(i+1, n):semivar_matrix[i][j] = semivar_matrix[j][i] = self.semivariogram(self.distance(self.x[i], self.x[j]),nugget=0,sill=1,range=1)gamma_vector[i] = self.y[i]# 求解Kriging模型的权重向量weights = np.linalg.solve(semivar_matrix, gamma_vector)self.weights = weights# 预测新点的值def predict(self, point):prediction = 0for i in range(len(self.x)):prediction += self.weights[i] * self.semivariogram(self.distance(point, self.x[i]),nugget=0,sill=1,range=1)return prediction# 示例数据x_train = np.random.rand(20, 2) # 训练集样本点坐标（二维）y_train = np.sin(x_train[:, 0]) + np.cos(x_train[:, 1]) # 训练集样本点对应的输出值# 构建Kriging模型并训练kriging_model = KrigingModel(x_train, y_train)kriging_model.train()# 可视化变化过程和预测结果fig = plt.figure()ax = fig.add_subplot(111, projection='3d')# 绘制原始训练数据点ax.scatter(x_train[:, 0], x_train[:, 1], y_train)# 根据模型预测网格中每个点的值，并将其可视化成3D图像resolution = 50 # 网格分辨率x_grid = np.linspace(0, 1, resolution)y_grid = np.linspace(0, 1, resolution)X, Y = np.meshgrid(x_grid, y_grid)Z = np.zeros((resolution, resolution))for i in range(resolution):for j in range(resolution):point = [x_grid[i], y_grid[j]]Z[i][j] = kriging_model.predict(point)ax.plot_surface(X, Y, Z, cmap='viridis')# 显示图形plt.show()
这段代码使用Python语言和Matplotlib库实现了Kriging二维加点训练的变化过程，并将预测结果以3D图像形式进行了可视化。你可以根据需要进行适当的修改和调整，以满足具体场景下的需求。
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