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  # 階數(shù)

def Neiji(p,a,b):
    '''
    加權(quán)內(nèi)積，p為加權(quán)值
    '''
    return p*np.dot(a,b)

def Nihe(x,fx,p,N):
    '''
    多項(xiàng)式擬合函數(shù)
    (x,fx):給定的需要擬合的點(diǎn)
    p:加權(quán)內(nèi)積的權(quán)重值
    N：多項(xiàng)式階數(shù)
    '''
    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)             # 多項(xiàng)式擬合模型系數(shù)
    return an
    
an = Nihe(x,fx,p,N) 
xx = np.arange(min(x),max(x),0.01)       # 做圖橫坐標(biāo)
result = np.sum([an[i]*(xx**i) for i in range(N)],axis=0)  # 擬合結(jié)果曲線
 
plt.scatter(x,fx,c='r')
plt.plot(xx,result)
plt.show()

6階多項(xiàng)式擬合.png