python实现三维拟合的方法

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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