Формула Лагранжа

from math import exp
 
X = [ 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5 ]
Y =  [ 2.102916, 3.467123, 5.716319, 9.424617, 15.53857,
         25.61876, 42.2382, 69.63902, 114.81534]
 
def Lagr( x, X, Y ):
    n = len( X )
    y = 0.0
    for i in range( n ):
        p = 1.0
        for j in range( n ):
            if i != j:
                p *= ( x - X[j] ) / ( X[i] -X[j] )
        y += (Y[i] *p)
    return y
 
def f(x):
    return 0.7*exp(x) + 0.1
 
x0, xn = 1.0,  5.0
h = 0.5    # шаг
 
x = x0
while x <= xn:
    print( "  %1.2f    %4.5f \t %4.5f" %  (x, Lagr(x, X, Y), f(x) ) )
    x += h

import numpy as np
 
x = [1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5]
f = [2.102916, 3.467123, 5.716319, 9.424617, 15.53857, 25.61876, 42.2382, 69.63902, 114.81534]
 
def lagrange(x_vals, y_vals, x_point):
    n = len(x_vals)
    result = 0
    for i in range(n):
        term = y_vals[i]
        for j in range(n):
            if i != j:
                term *= (x_point - x_vals[j]) / (x_vals[i] - x_vals[j])
        result += term
    return result
 
x_check = np.linspace(1, 5, 100)
f_interp = [lagrange(x, f, xi) for xi in x_check]
 
print(f_interp)

def lagrange(arrx,arry):
    def interp(x):
        q=0
        n=len(arrx)
        for i in range(n):
            num=1
            den=1
            for j in range(n):
                if j != i:
                    num=num*(x-arrx[j])
                    den=den*(arrx[i]-arrx[j])
            q=q+arry[i]*num/den
        return q        
    return interp
    
'''    
    y=2x^2+5x-7
    
    x1=0  y1=-7
    x2=1  y2=0
    x3=2  y3=11    
'''    
 
arrx=[0,1,2,3,4,5,6]
arry=[-7,0,11,13,16,19,22]
 
f=lagrange(arrx,arry)
 
for x in range(-5,5):
    print(x,f(x))