import numpy as np
import matplotlib.pyplot as plt
x = np.arange(10)*0.1
fx = np.array([0.97,0.83,0.65,0.54,0.46,0.36,0.29,0.25,0.21,0.17])
p = 1
N = 6 # 阶数
def Neiji(p,a,b):
'''
加权内积，p为加权值
'''
return p*np.dot(a,b)
def Nihe(x,fx,p,N):
'''
多项式拟合函数
(x,fx):给定的需要拟合的点
p:加权内积的权重值
N：多项式阶数
'''
A = np.zeros((N,N))
b = np.zeros((N,1))
for i in range(N):
for j in range(N):
A[i,j] = Neiji(p,x**i,x**j)
b[i,0] = Neiji(p,fx,x**i)
an = np.linalg.solve(A,b) # 多项式拟合模型系数
return an
an = Nihe(x,fx,p,N)
xx = np.arange(min(x),max(x),0.01) # 做图横坐标
result = np.sum([an[i]*(xx**i) for i in range(N)],axis=0) # 拟合结果曲线
plt.scatter(x,fx,c='r')
plt.plot(xx,result)
plt.show()
6阶多项式拟合.png
