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，*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，*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：