如何将 function 作为参数传递

Question

I would like to find an approximate value for the number pi = 3.14.. by using the Newton method. In order to use it also for some other purpose and thus other function than sin(x) , the aim is to implement a generic function that will be passed over as an argument. I have an issue in passing a function as an argument into an other function. I also tried lambda in different variations. The code I am showing below produces the error message: IndexError: list index out of range . I will appreciate your help in solving this issue and eventually make any suggestion in the code which may not be correct. Thanks.

from sympy import *
import numpy as np
import math

x = Symbol('x')
# find the derivative of f
def deriv(f,x):
    h = 1e-5 
    return (lambda x: (f(x+h)-f(x))/h)

def newton(x0,f,err):
    A = [x0]
    n = 1
    while abs(A[n]-A[n-1])<=err:
        if n == 1:
            y = lambda x0: (math.f(x0))
            b = x0-y(x0)/(deriv(y,x0))
            A.append(b)
            n += 1             
        else:
            k = len(A)
            xk = A[k]
            y = lambda xk: (math.f(xk))
            b = newton(A[k],y,err)-y(newton(A[k],y,err))/deriv(y,k)
            A.append(b)
            n += 1
    return A, A[-1]
print(newton(3,math.sin(3),0.000001)) 

Answer 1

I don't know why you use sympy because I made it without Symbol

At the beginning you have to calculate second value and append it to list A and later you can calculate abs(A[n]-A[n-1]) (or the same without n : abs(A[-1] - A[-2]) ) because it needs two values from this list.

Other problem is that it has to check > instead of <= .

If you want to send function sin(x) then you have to use math.sin without () and arguments.

If you want to send function sin(3*x) then you would have to use lambda x: math.sin(3*x)

import math

def deriv(f, x, h=1e-5):
    return (f(x+h) - f(x)) / h

def newton(x0, f, err):
    A = [x0]

    x = A[-1]                     # get last value
    b = x - (f(x) / deriv(f, x))  # calculate new value
    A.append(b)                   # add to list

    while abs(A[-1] - A[-2]) > err:   # it has to be `>` instead of `<=`
        
        x = A[-1]                     # get last value
        b = x - (f(x) / deriv(f, x))  # calculate new value
        A.append(b)                   # add to list
        
    return A, A[-1]

# sin(x)
print(newton(3, math.sin, 0.000001))  # it needs function's name without `()`

# sin(3*x)
print(newton(3, lambda x:math.sin(3*x), 0.000001))

# sin(3*x)  # the same without `lambda`
def function(x):
    return math.sin(3*x)

print(newton(3, function, 0.000001))  

Result:

([3, 3.1425464414785056, 3.1415926532960112, 3.141592653589793], 3.141592653589793)
([3, 3.150770863559604, 3.1415903295877707, 3.1415926535897936, 3.141592653589793], 3.141592653589793)

---

EDIT:

You may write loop in newton in different way and it will need <=

def newton(x0, f, err):
    A = [x0]

    while True:
        
        x = A[-1]                     # get last value
        b = x - (f(x) / deriv(f, x))  # calculate new value
        A.append(b)                   # add to list
        
        if abs(A[-1] - A[-2]) <= err: 
            break
        
    return A, A[-1]