Trevalim
Trevalim
Informatique Maths

Lagrange interpolating polynomials

par |Publié

Here is the Lagrange interpolating polynomial equation:

    \[ L_i(X)=\prod_{j=0\atop j \ne i}^n\frac{(X-a_j)}{(a_i-a_j)} \]

    \[ \boxed{P=\sum_{i=0}^nP(a_i)L_i(X)} \]

You can find a python code hosted in GitHub here: https://github.com/eddydu44/Lagrange-interpolating-polynomials

It calculates the polynomial that passes through points given interactively.

And it plots a graph like these ones :

Code :

from functools import reduce
from sympy import Symbol
X = Symbol('X')
def Lagrange(points):
P=[reduce((lambda x,y: x*y),[(X-points[j][0])/(points[i][0] - points[j][0]) for j in range(len(points)) if i != j])*points[i][1] for i in range(len(points))]
return sum(P)
print("Enter every points in this format : x y \nStop the list by entering 0")
p1=0
points=[]
while True:
p1 = [int(x) for x in input("Enter point coord: ").split()]
if p1 == [0]:
break
points+=[p1]
print(points)
P=Lagrange(points)
print("\nLagrange equation :\n")
print(P)
import matplotlib.pyplot as plt
from numpy import arange
def graph(P,points):
plt.plot([points[i][0] for i in range(len(points))], [points[i][1] for i in range(len(points))], 'ro')
plt.title('P(X)=' + str(P))
xmin=min([points[i][0] for i in range(len(points))])-1
xmax=max([points[i][0] for i in range(len(points))])+1
t1 = arange(xmin, xmax, 0.02)
def f(t):
t2 = []
for i in t :
t2 += [P.subs(X,i)]
return t2
plt.plot(t1,f(t1),'r--')
plt.show()
graph(P,points)
view raw lagrange-poly.py hosted with ❤ by GitHub

AUTEUR

eddy barraud
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