import matplotlib.pyplot as plt
import numpy as np


px=[1,20,-3,10]
py=[-3,3,-23,13]

#test pour determinant =0
#px=[1,1]
#py=[-3,-3]
nbpts=len(px)
A = np.zeros((nbpts,3))
B = np.zeros((nbpts))

for i in range(0,nbpts):
    #A[i,0]=px[i]
    #A[i,1]=1
    A[i,0]=px[i]*px[i]
    A[i,1]=px[i]
    A[i,2]=1
    B[i]=py[i]
print("A:"+str(A))
print("B:"+str(B))
if nbpts==3:
    detA=np.linalg.det(A)
    #if detA==0:
    if np.abs(detA)<1e-15:
        print("le systeme d'équations n'admet pas de solution")
        exit()  
    Ainv=np.linalg.inv(A)
else:
    #calcul de la pseudo inverse
    At=np.matrix.transpose(A)
    AtA=np.dot(At,A)
    Ainv=np.dot(np.linalg.inv(AtA),At)
    
print("Ainv:"+str(Ainv))
Solution=np.dot(Ainv,np.transpose(B))
print("Solution:"+str(Solution))
a=Solution[0]
b=Solution[1]
c=Solution[2]

listx=[]
listfx=[]
 
#xmin=-4
#xmax=4
xmin=min(px)-1
xmax=max(px)+1
 
 
# https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.html
#https://matplotlib.org/3.4.3/gallery/subplots_axes_and_figures/subplot.html#sphx-glr-gallery-subplots-axes-and-figures-subplot-py
# j'aurai pu faire avec un np.linspace
for i in range(int(xmin*100),int(xmax*100),1):
            x=i/100.0
            #fx=f(x,a,b,c)
            #fx=a*x+b            
            fx=a*x*x+b*x+c            
            listx.append(x)
            listfx.append(fx)
 
plt.plot(listx, listfx,'g-')
plt.scatter(px, py)

plt.show()