Question

I want to use the newton function loaded as

from scipy.optimize import newton

in order to find the zeros of a function enetered by the user. I write a script that first ask to the user to specify a function together with its first derivative, and also the starting point of the algorithm. First of all typing help(newton) I saw which parameters takes the function and the relative explanation:

newton(func, x0, fprime=None, args=(), tol=1.48e-08, maxiter=50)

func : function
    The function whose zero is wanted. It must be a function of a
    single variable of the form f(x,a,b,c...), where a,b,c... are extra
    arguments that can be passed in the `args` parameter.

In which way I have to pass my function? If I use for func e.g. x**3 (and its first derivative) the response is NameError: name 'x' is not defined. On the internet I find that first I have to define my function and its first derivative and pass the names as parameters. So I made the following

fie = raw_input('Enter function in terms of x (e.g. x**2 - 2*x). F= ')
dfie = raw_input('Enter first derivative of function above DF = ')
x0 = input('Enter starting point x0 = ')

def F(x,fie):
    y = eval(fie)
    return y 

def DF(x, dfie):
    dy = eval(dfie)
    return dy

print newton(F,x0,DF)

But I get the output

    102         for iter in range(maxiter):
    103             myargs = (p0,) + args
--> 104             fder = fprime(*myargs)
    105             if fder == 0:
    106                 msg = "derivative was zero."

TypeError: DF() takes exactly 2 arguments (1 given)

and the same issue for F if I omit DF. Looking at the code in /usr/local/share/src/scipy/scipy/optimize/zeros.py I see that it evaluates the first derivative with fder=fprime(*myargs) so maybe I have to put in args something that make it working. I was thinking about it but no solution comes to me.

Answer 1

First, be aware that using eval makes your program vulnerable to malicious users. If that concern does not apply, you can create F and DF like this:

F = eval('lambda x :'+fie)
DF = eval('lambda x :'+dfie)

Then both functions expect only a single argument, and you can leave the args argument empty.

EDIT. If you really want to stick to your code as closely as possible, this should also work, but it does not look very nice to me. newton will send the same args to both functions.

def F(x,fie,dfie):
    y = eval(fie)
    return y 

def DF(x,fie,dfie):
    dy = eval(dfie)
    return dy

print newton(F,x0,DF,(fie,dfie))