功能输入

Question

How can I ask for user input in the nthroot function? I want the function to ask input for the power of x and the next term. (I want the program to ask for power and next term, I only used 3 and 81 respectively as a check)

def derivative(f, x, h):
   return (f(x+h) - f(x-h)) / (2.0*h)  

def nthroot(x):
   return x**3 - 81   # just a function to show it works


def newraph(f, x0, h):
   Xold = x0
   Xnew = Xold + 10* h  
   while (abs(Xold - Xnew) > h):  
      Xold = Xnew 
      Xnew = Xold - f(Xnew) / derivative(f, Xold, h)  #NewtonRaphson formula
   return Xnew

trueroot = newraph(nthroot, 1, 0.000001)    
print "The root is", trueroot

When I tried using the int(raw_input()) like this :

def derivative(f, x, h):
  return (f(x+h) - f(x-h)) / (2.0*h)  

def nthroot(x):
   root = int(raw_input("Please Enter a nth root (n) : "))
   number =  int(raw_input("Please Enter a number (x): "))
   return x**(root) - (number)

def newraph(f, x0, h):
   Xold = x0
   Xnew = Xold + 10* h  
   while (abs(Xold - Xnew) > h):  
      Xold = Xnew 
      Xnew = Xold - f(Xnew) / derivative(f, Xold, h)  #NewtonRaphson formula
   return Xnew

trueroot = newraph(nthroot, 1, 0.000001)    
print "The root is", trueroot

The prompt for the input repeats several times. How do you end that?

Answer 1

Try generating your Nthroot function on the fly with the wanted values already in there. These values will then be reused in every vall to "f" in newraph.

This method will allow you to keep using arbitrary functions for newraph (even ones where you don't need user input or completely different inputs).

def derivative(f, x, h):
  return (f(x+h) - f(x-h)) / (2.0*h)  

def generateNthrootFunc():
   root = int(raw_input("Please Enter a nth root (n) : "))
   number =  int(raw_input("Please Enter a number (x): "))
   def nthroot(x):
      return x**(root) - (number)
   return nthroot

def newraph(f, x0, h):
   Xold = x0
   Xnew = Xold + 10* h  
   while (abs(Xold - Xnew) > h):  
      Xold = Xnew 
      Xnew = Xold - f(Xnew) / derivative(f, Xold, h)  #NewtonRaphson formula
   return Xnew

root = newraph(generateNthrootFunc(), 1, 0.000001)    # call the solver
print "The root is", root

Answer 2

The prompt for the input repeats several times...

That's becouse you're calling the function several times:

root = newraph(nthroot, 1, 0.000001)    # call the solver

end then inside newraph

while (abs(Xold - Xnew) > h):  
  Xold = Xnew 
  Xnew = Xold - f(Xnew) / derivative(f, Xold, h)  #NewtonRaphson formula

where f is nthroot .

Then you call it agin in derivate (twice):

def derivative(f, x, h):
  return (f(x+h) - f(x-h)) / (2.0*h)  

Posible solution

You could make nthroot a class

class nthroot_generator:
    def __init__(self, number, root):
        self.number = number
        self.root = root
    def __call__(self, x):
        return x**(self.root) - (number)

and callit like this:

root = int(input("Please Enter a nth root (n) : "))
number =  int(input("Please Enter a number (x): "))
trueroot = newraph(nthroot_generator(root, number), 1, 0.000001)