Newton Raphson: Can the user input the function?

Question

[This image here is my python code for the Newton-Raphson method. The problem is with the mathematical function and the derivative. At the moment I am the one who specifies the function and its derivative. Is there any way to get the user to input the function that he/she desires?

import math

""" f: function, f_ : derivative of function, x0: initial guess, errortolerance: tolerance, maxIter: max number of iterations """

def newtonraphson(f, f_, x0, errortolerance=0.00001, maxIter=100):
    """

    Take a function f, its derivative f_, initial value x0, TOL and NMAX,
    and returns the root(s) of the equation using the NR method

    """

    n = 1 #initial numebr of iterations
    while n<=maxIter: # check while n less than maxIter
        x1 = x0 - (f(x0)/f_(x0)) #newtonraphson formula
        if x1 - x0 < errortolerance: 
            return x1
        else:
            x0 = x1
    return False

if __name__ == "__main__":

    def func(x): #initial function
        return 5*math.pow(x,2) - 8*math.pow(x,1) + 4

    def func_(x): #its derivative
        return 10*math.pow(x,1) - 8

    resNR = newtonraphson(func,func_,3) #result of newtonraphson
    print(resNR)

Answer 1

You can use lambda and eval to let the user input the function and its derivative. I assume you are using Python 3. If you are using Python 2, replace input with raw_input.

if __name__ == '__main__':
    f = lambda x : eval(input())
    f_ = lambda x : eval(input())

    print(newtonraphson(f, f_, 3))

Now, have your user enter an expression in x. Remember, only the already defined names are allowed in the input.