Python实现二维曲线拟合的方法

如下所示：

from numpy import *
import numpy as np
import matplotlib.pyplot as plt

plt.close()
fig=plt.figure()
plt.grid(true)
plt.axis([0,10,0,8])

#列出数据
point=[[1,2],[2,3],[3,6],[4,7],[6,5],[7,3],[8,2]]
plt.xlabel("x")
plt.ylabel("y")

#用于求出矩阵中各点的值
xsum = 0.0
x2sum = 0.0
x3sum = 0.0
x4sum = 0.0
isum = 0.0
ysum = 0.0
xysum = 0.0
x2ysum = 0.0


#列出各点的位置
for i in range(0,len(point)):

 xi=point[i][0]
 yi=point[i][1]
 plt.scatter(xi,yi,color="red")
 show_point = "("+ str(xi) +","+ str(yi) + ")"
 plt.text(xi,yi,show_point)

 xsum = xsum+xi
 x2sum = x2sum+xi**2
 x3sum = x3sum + xi**3
 x4sum = x4sum + xi**4
 isum = isum+1
 ysum = ysum+yi
 xysum = xysum+xi*yi
 x2ysum = x2ysum + xi**2*yi

# 进行矩阵运算
# _mat1 设为 mat1 的逆矩阵
m1=[[isum,xsum, x2sum],[xsum, x2sum, x3sum],[x2sum, x3sum, x4sum]]
mat1 = np.matrix(m1)
m2=[[ysum], [xysum], [x2ysum]]
mat2 = np.matrix(m2)
_mat1 =mat1.geti()
mat3 = _mat1*mat2

# 用list来提取矩阵数据
m3=mat3.tolist()
a = m3[0][0]
b = m3[1][0]
c = m3[2][0]
# 绘制回归线
x = np.linspace(0,10)
y = a + b*x + c*x**2
plt.plot(x,y)
show_line = "y="+str(a)+"+("+str(b)+"x)"+"+("+str(c)+"x2)";
plt.title(show_line)
plt.show()

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