空间区域：25&25正方形格子点区域，坐标原点在整个正方形区域的左下角，数据点的坐标为（ui,vi)=(0.5mod((i-1)/25),0.5int((i-1)/25)),i=1,2,...,625 模型:y = β1(ui,vi) + β2(ui,vi)*xi + εi,xi-U(0,2) ,εi-N(0,0.25) 核函数和窗宽：Gauss核；h由CV方法确定 重复次数：100次 最终估计：100次重复的平均值 取如下三组系数函数： G1:β1(u,v)=(u+v)/6 β2(u,v)=u/3 G2:β1(u,v)=4sin((Πu)/12) β2(u,v)=(36-(6-u)^2)(36-(6-v)^2)/324 G3:β1(u,v)=3sin(根号下（2(6-u)^2)+2(6-v)^2)）/根号下（2(6-u)^2)+2(6-v)^2)） β2(u,v)=2（u-2)exp(-01((6-u)^2+(6-v)^2)) 绘制原始图像，绘制GWR估计和局部GWR估计后的三维空间曲面图，python实现

首先，我们需要安装必要的库，包括`numpy`、`pandas`、`sklearn`和`plotly`。可以使用以下命令进行安装：

!pip install numpy pandas sklearn plotly

接下来，我们可以使用以下代码生成数据集：

import numpy as np
import pandas as pd

# 生成数据点的坐标
coords = []
for i in range(1, 626):
    u = 0.5 * (i - 1) % 25
    v = 0.5 * (i - 1) // 25
    coords.append((u, v))
coords = np.array(coords)

# 生成自变量和误差项
X = np.random.uniform(0, 2, size=(625,))
epsilon = np.random.normal(0, 0.25, size=(625,))

# 定义三组系数函数
def beta1_g1(u, v):
    return (u + v) / 6

def beta2_g1(u, v):
    return u / 3

def beta1_g2(u, v):
    return 4 * np.sin(np.pi * u / 12)

def beta2_g2(u, v):
    return (36 - (6 - u) ** 2) * (36 - (6 - v) ** 2) / 324

def beta1_g3(u, v):
    return 3 * np.sin(np.sqrt(2 * (6 - u) ** 2 + 2 * (6 - v) ** 2)) / np.sqrt(2 * (6 - u) ** 2 + 2 * (6 - v) ** 2)

def beta2_g3(u, v):
    return 2 * (u - 2) * np.exp(-0.1 * ((6 - u) ** 2 + (6 - v) ** 2))

# 生成因变量
y = beta1_g1(coords[:, 0], coords[:, 1]) + beta2_g1(coords[:, 0], coords[:, 1]) * X + epsilon
df = pd.DataFrame({'x':coords[:,0], 'y':coords[:,1], 'z':y})

接下来，我们可以使用以下代码来进行GWR估计和局部GWR估计，其中`h`是通过交叉验证确定的窗宽：

from sklearn.model_selection import GridSearchCV
from sklearn.neighbors import KernelDensity
from sklearn.metrics import make_scorer
from sklearn.linear_model import LinearRegression

# 定义GWR模型
class GWR:
    def __init__(self, coords, X, y, kernel='gaussian', metric='euclidean'):
        self.coords = coords
        self.X = X
        self.y = y
        self.kernel = kernel
        self.metric = metric
    
    def fit(self, h):
        self.h = h
        self.model = []
        for i in range(len(self.coords)):
            # 计算每个点的权重
            kde = KernelDensity(kernel=self.kernel, bandwidth=self.h, metric=self.metric).fit(self.coords)
            weights = np.exp(kde.score_samples([self.coords[i]]))[0]
            # 用加权最小二乘法拟合每个点的局部模型
            X_local = np.concatenate([[1], [self.coords[i][0]], [self.coords[i][1]], [self.X[i]]])
            y_local = self.y[i]
            model_local = LinearRegression().fit([X_local], [y_local], sample_weight=[weights])
            self.model.append(model_local)
    
    def predict(self, X_new):
        y_pred = []
        for i in range(len(X_new)):
            # 计算每个新点到原数据点的距离
            distances = np.linalg.norm(self.coords - X_new[i], axis=1)
            # 计算每个点的权重
            weights = np.exp(-0.5 * (distances / self.h) ** 2)
            # 用加权最小二乘法拟合每个点的局部模型
            X_local = np.concatenate([[1], [X_new[i][0]], [X_new[i][1]], [self.X[i]]])
            y_local = np.sum(weights * self.y) / np.sum(weights)
            model_local = LinearRegression().fit([X_local], [y_local], sample_weight=weights)
            y_pred.append(model_local.predict([X_local])[0])
        return y_pred

# 交叉验证确定窗宽
params = {'bandwidth': np.linspace(0.1, 2, 20)}
kde = KernelDensity(kernel='gaussian')
gwr_cv = GridSearchCV(kde, params, scoring=make_scorer(lambda y_true, y_pred: -np.mean((y_true - y_pred) ** 2)), cv=5)
gwr_cv.fit(coords)
h = gwr_cv.best_params_['bandwidth']

# 进行GWR估计和局部GWR估计
gwr_g1 = GWR(coords, X, y, kernel='gaussian')
gwr_g1.fit(h)
y_pred_g1 = gwr_g1.predict(coords)

gwr_g2 = GWR(coords, X, y, kernel='gaussian')
gwr_g2.fit(h)
y_pred_g2 = gwr_g2.predict(coords)

gwr_g3 = GWR(coords, X, y, kernel='gaussian')
gwr_g3.fit(h)
y_pred_g3 = gwr_g3.predict(coords)

最后，我们可以使用以下代码生成三维空间曲面图：

import plotly.express as px

fig = px.scatter_3d(df, x='x', y='y', z='z', opacity=0.7)
fig.add_trace(px.scatter_3d(pd.DataFrame({'x':coords[:,0], 'y':coords[:,1], 'z':y_pred_g1}), x='x', y='y', z='z', opacity=0.7).data[0])
fig.add_trace(px.scatter_3d(pd.DataFrame({'x':coords[:,0], 'y':coords[:,1], 'z':y_pred_g2}), x='x', y='y', z='z', opacity=0.7).data[0])
fig.add_trace(px.scatter_3d(pd.DataFrame({'x':coords[:,0], 'y':coords[:,1], 'z':y_pred_g3}), x='x', y='y', z='z', opacity=0.7).data[0])
fig.update_traces(marker=dict(size=2))
fig.show()

完整代码如下：