Lagrange.py

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sat Oct 30 18:11:49 2021

@author: moatasim
"""

from sympy import *
from sympy import init_printing
import numpy as np
import matplotlib.pyplot as plt

print("This script constructs the Lagrange Polynomial from data generated by a function in a specified range. Note: when inputting the function, use ** to show presence of exponent, followed by the number or variable in the power. Also, input capital E for euler's number instead of just e")
print("WARNING: when inputting function, do not use quotation marks, otherwise sympify is not able to parse the input string!")
x=symbols('x')
print("for quick checking and to avoid errors, copy paste this= (E**x)+(2**(-x))+2*cos(x) - 6")
inputfunc = input("Enter the function: ")  
func=sympify(inputfunc)
print("Since the question asks only for data points in [-2,2], we will not be asking user to input start and end points, we will just simply take [-2,2]")

datapoints=np.linspace(-2,2,10,endpoint=False)

print("Our set of x values: ", datapoints)

fx=[]

def calcfunc(a):
    return func.evalf(subs={x:a})

for val in datapoints:
    fx.append(calcfunc(val))
    
print("Our set of y values: ", fx)
    
print("By now we have constructed two lists, containing x and y values (our DATA), and the lagrange polynomial will be approximated from here")
print("Note: one of these lists is an iterable numpy array and the other is a simple python list")
n=int(input("Enter the degree of Lagrange polynomial to be calculated: "))
Px=sympify("0")
for i in range(n):
    y=fx[i]
    for j in range(n):
        if(i!=j):
            y=y*((x-datapoints[i])/(datapoints[j]-datapoints[i]))
    Px=Px+y

print(Px)

xaxis=np.linspace(-2,2,100,endpoint=False)

f=[]
for val in xaxis:
    f.append(calcfunc(val))
    
def calcpoly(a):
    return Px.evalf(subs={x:a})

lP=[]
for val in xaxis:
    lP.append(calcpoly(val))

f=np.array(f)
lP=np.array(lP)
plt.plot(xaxis,f,c='r')
#plt.plot(xaxis, lP)
plt.show()