Lagrange interpolating polynomials

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

Lagrange interpolating polynomials

AUTEUR

eddy barraud

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