Python 最小二乘法多项式拟合曲线numpy.polyfit(),numpy.poly1d(),pylab

原文地址：http://wiki.klniu.com/zh-hans/Python/Modules/Scipy

import numpy as np
from scipy.optimize import leastsq
import pylab as pl
 
x = np.arange(1, 17, 1)
y = np.array([4.00, 6.40, 8.00, 8.80, 9.22, 9.50, 9.70, 9.86, 10.00, 10.20, 10.32, 10.42, 10.50, 10.55, 10.58, 10.60])
 
#第一个拟合，自由度为3
z1 = np.polyfit(x, y, 3)
# 生成多项式对象
p1 = np.poly1d(z1)
print(z1)
print(p1)
 
# 第二个拟合，自由度为6
z2 = np.polyfit(x, y, 6)

# 生成多项式对象

p2 = np. poly1d (z2 ) print (z2 ) print (p2 )  # 绘制曲线  # 原曲线pl. plot (x , y , 'b^-' , label = 'Origin Line' )pl. plot (x , p1 (x ) , 'gv--' , label = 'Poly Fitting Line(deg=3)' )pl. plot (x , p2 (x ) , 'r*' , label = 'Poly Fitting Line(deg=6)' )pl. axis ( [ 0 , 18 , 0 , 18 ] )pl. legend ( ) # Save figurepl. savefig ( 'scipy02.png' , dpi = 96 )

输出结果：

[ 0.00624491 -0.20371114  2.18193147  2.57208791]
          3          2
0.006245 x - 0.2037 x + 2.182 x + 2.572
[ -1.89843481e-06   1.90557772e-04  -6.80682074e-03   1.16832830e-01
  -1.04793542e+00   4.90253564e+00   1.76057692e-02]
            6             5            4          3         2
-1.898e-06 x + 0.0001906 x - 0.006807 x + 0.1168 x - 1.048 x + 4.903 x + 0.01761

图像：