Python实现三维数据拟合与可视化完整示例

Noah

发布时间：2026-10-13 | 1人浏览过

原创

本文介绍使用Python进行三维数据拟合的具体实现方法。通过定义实验数据点，利用NumPy构建正规方程矩阵并求逆，计算回归系数。结合Matplotlib库绘制3D散点图与拟合平面，直观展示拟合效果。代码包含完整的数据预处理、矩阵运算及可视化步骤，适用于需要快速实现三维线性回归的开发者参考。

具体实现代码如下所示：

from matplotlib import pyplot as plt
import numpy as np
from mpl_toolkits.mplot3d import Axes3D

fig = plt.figure()
ax = Axes3D(fig)

#列出实验数据
point=[[2,3,48],[4,5,50],[5,7,51],[8,9,55],[9,12,56]]
plt.xlabel("X1")
plt.ylabel("X2")

#表示矩阵中的值
ISum = 0.0
X1Sum = 0.0
X2Sum = 0.0
X1_2Sum = 0.0
X1X2Sum = 0.0
X2_2Sum = 0.0
YSum = 0.0
X1YSum = 0.0
X2YSum = 0.0

#在图中显示各点的位置
for i in range(0,len(point)):

 x1i=point[i][0]
 x2i=point[i][1]
 yi=point[i][2]
 ax.scatter(x1i, x2i, yi, color="red")
 show_point = "["+ str(x1i) +","+ str(x2i)+","+str(yi) + "]"
 ax.text(x1i,x2i,yi,show_point)

 ISum = ISum+1
 X1Sum = X1Sum+x1i
 X2Sum = X2Sum+x2i
 X1_2Sum = X1_2Sum+x1i**2
 X1X2Sum = X1X2Sum+x1i*x2i
 X2_2Sum = X2_2Sum+x2i**2
 YSum = YSum+yi
 X1YSum = X1YSum+x1i*yi
 X2YSum = X2YSum+x2i*yi

# 进行矩阵运算
# _mat1 设为 mat1 的逆矩阵
m1=[[ISum,X1Sum,X2Sum],[X1Sum,X1_2Sum,X1X2Sum],[X2Sum,X1X2Sum,X2_2Sum]]
mat1 = np.matrix(m1)
m2=[[YSum],[X1YSum],[X2YSum]]
mat2 = np.matrix(m2)
_mat1 =mat1.getI()
mat3 = _mat1*mat2

# 用list来提取矩阵数据
m3=mat3.tolist()
a0 = m3[0][0]
a1 = m3[1][0]
a2 = m3[2][0]

# 绘制回归线
x1 = np.linspace(0,9)
x2 = np.linspace(0,12)
y = a0+a1*x1+a2*x2
ax.plot(x1,x2,y)
show_line = "y="+str(a0)+"+"+str(a1)+"x1"+"+"+str(a2)+"x2"
plt.title(show_line)
plt.show()

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