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derivative and newton raphson

16
i have made a code for finding a derivative and now im trying to use it to help me with a code for the newton raphson method:
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  1. def derivative (f,x,h):
  2.     import math
  3.     return float(1/(2*h)) * (f(x+h) - f(x-h))
  4.  
  5. def solve (f,x0,h):
  6.     delta= f(x(n))/fp(x(n)
  7.         for x(n+1) in solve():
  8.             x(n)-delta
the first def works fine but i cant get the second def to work can anyone see what im doing wrong?
Oct 29 '07 #1
10 8650
bvdet
2,851 Expert Mod 2GB
i have made a code for finding a derivative and now im trying to use it to help me with a code for the newton raphson method:
Expand|Select|Wrap|Line Numbers
  1. def derivative (f,x,h):
  2.     import math
  3.     return float(1/(2*h)) * (f(x+h) - f(x-h))
  4.  
  5. def solve (f,x0,h):
  6.     delta= f(x(n))/fp(x(n)
  7.         for x(n+1) in solve():
  8.             x(n)-delta
the first def works fine but i cant get the second def to work can anyone see what im doing wrong?
In function solve(), you have passed arguments 'f', 'x0' and 'h'. Where are 'x', 'fp', and 'n' defined? You are calling function 'solve()' recursively, but you are not passing any arguments to it. 'solve()' requires three arguments. The format of a 'for' loop is:
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  1. for item in iterable:
  2.     ......code......
'item' cannot be an expression.
Expand|Select|Wrap|Line Numbers
  1. >>> for x+1 in range(10):
  2. ...     print x
  3. Traceback (SyntaxError: can't assign to operator
  4. >>> 
Oct 29 '07 #2
DDCane
16
how am im supposed to fix it? fp in solve is the fisrt function. u use the first function to get the derivative of f in the first function. do u know how i fix this?

In function solve(), you have passed arguments 'f', 'x0' and 'h'. Where are 'x', 'fp', and 'n' defined? You are calling function 'solve()' recursively, but you are not passing any arguments to it. 'solve()' requires three arguments. The format of a 'for' loop is:
Expand|Select|Wrap|Line Numbers
  1. for item in iterable:
  2.     ......code......
'item' cannot be an expression.
Expand|Select|Wrap|Line Numbers
  1. >>> for x+1 in range(10):
  2. ...     print x
  3. Traceback (SyntaxError: can't assign to operator
  4. >>> 
Oct 30 '07 #3
bvdet
2,851 Expert Mod 2GB
how am im supposed to fix it? fp in solve is the fisrt function. u use the first function to get the derivative of f in the first function. do u know how i fix this?
I am not familiar with the calculation you are attempting. I know that it will not work if 'fp()' is not defined inside of 'solve()' or globally to your module.
Oct 30 '07 #4
DDCane
16
globally in the module?

I am not familiar with the calculation you are attempting. I know that it will not work if 'fp()' is not defined inside of 'solve()' or globally to your module.
Oct 30 '07 #5
bvdet
2,851 Expert Mod 2GB
globally in the module?
Let's say your code is in a file called function.py.
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  1. # code.py
  2. def fp():
  3.     ....code....
  4.  
  5. def derivative (f,x,h):
  6.     import math
  7.     return float(1/(2*h)) * (f(x+h) - f(x-h))
  8.  
  9. def solve (f,x0,h):
  10.     delta= f(x(n))/fp(x(n)
  11.         for x(n+1) in solve():
  12.             x(n)-delta
  13.  
  14. if __name__ == __main__:
  15.     ....call your functions...
Function 'fp()' is global to module 'function'.
Oct 30 '07 #6
DDCane
16
ok. is there a simpler way to write the newton raphsons method in python? ive looked at the discussions in the forums here and havent found anything that could help m efurther than what i already know. do u have any clue on how to write the method?

Let's say your code is in a file called function.py.
Expand|Select|Wrap|Line Numbers
  1. # code.py
  2. def fp():
  3.     ....code....
  4.  
  5. def derivative (f,x,h):
  6.     import math
  7.     return float(1/(2*h)) * (f(x+h) - f(x-h))
  8.  
  9. def solve (f,x0,h):
  10.     delta= f(x(n))/fp(x(n)
  11.         for x(n+1) in solve():
  12.             x(n)-delta
  13.  
  14. if __name__ == __main__:
  15.     ....call your functions...
Function 'fp()' is global to module 'function'.
Oct 30 '07 #7
bvdet
2,851 Expert Mod 2GB
ok. is there a simpler way to write the newton raphsons method in python? ive looked at the discussions in the forums here and havent found anything that could help m efurther than what i already know. do u have any clue on how to write the method?
The Newton Raphson method uses an iterative process to approximate the root of a function. That's all I know about the subject, and I had to look that up.
Oct 30 '07 #8
ok. is there a simpler way to write the newton raphsons method in python? ive looked at the discussions in the forums here and havent found anything that could help m efurther than what i already know. do u have any clue on how to write the method?
Here's what I have come up with:
import math
Expand|Select|Wrap|Line Numbers
  1. def derivative (f, x, h):
  2.     return float((f(x + h) - f(x))) / h
  3.  
  4. def solve(f, x0, h, depth):
  5.     if depth > 0:
  6.         delta = f(x0) / derivative(f, x0, h)
  7.         return solve(f, x0 - delta, h, depth - 1)
  8.     else:
  9.         return x0
I changed the formulas in your function to ones I'm more familiar with, and I had to add the parameter "depth" to tell the solve function when to stop. That's necessary because when working with the Newton-Raphson Method, you have to choose how many times you use it.
To use the solve function, you can either do something like this:
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  1. def function(x):
  2.     return math.cos(x) - x**3
  3.  
  4. solve(function, 0.5, 0.001, 6)
or:
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  1. function = lambda x: math.cos(x) - x**3
  2. solve(function, 0.5, 0.001, 6)
Either way in that example your approximating the root of "cos(3) - x**3" by applying the Newton-Raphson Method 6 times with a starting guess of "0.5". The "0.001" is the "h" value used to approximate your derivative. The lower it is the more accurate the derivative will be.
Oct 30 '07 #9
bvdet
2,851 Expert Mod 2GB
Here's what I have come up with:
import math
Expand|Select|Wrap|Line Numbers
  1. def derivative (f, x, h):
  2.     return float((f(x + h) - f(x))) / h
  3.  
  4. def solve(f, x0, h, depth):
  5.     if depth > 0:
  6.         delta = f(x0) / derivative(f, x0, h)
  7.         return solve(f, x0 - delta, h, depth - 1)
  8.     else:
  9.         return x0
I changed the formulas in your function to ones I'm more familiar with, and I had to add the parameter "depth" to tell the solve function when to stop. That's necessary because when working with the Newton-Raphson Method, you have to choose how many times you use it.
To use the solve function, you can either do something like this:
Expand|Select|Wrap|Line Numbers
  1. def function(x):
  2.     return math.cos(x) - x**3
  3.  
  4. solve(function, 0.5, 0.001, 6)
or:
Expand|Select|Wrap|Line Numbers
  1. function = lambda x: math.cos(x) - x**3
  2. solve(function, 0.5, 0.001, 6)
Either way in that example your approximating the root of "cos(3) - x**3" by applying the Newton-Raphson Method 6 times with a starting guess of "0.5". The "0.001" is the "h" value used to approximate your derivative. The lower it is the more accurate the derivative will be.
That's great KaezarRex - nice solution to an interesting problem.
BV
Oct 31 '07 #10
Hello!
(Newton-Raphson Method)
Can anyone describe how this code work?
What is depth, and how is solve working?
The function derivative only give us the derivative of a function:
for example:
Expand|Select|Wrap|Line Numbers
  1. >>> derivative(math.sin, math.pi, 0.0001)
  2. -0.9999999983354435
  3.  
But how is solve work?
solve use derivative function.
Expand|Select|Wrap|Line Numbers
  1. def derivative (f, x, h):
  2.     return float((f(x + h) - f(x))) / h
  3.  
  4. def solve(f, x0, h, depth):
  5.     if depth > 0:
  6.         delta = f(x0) / derivative(f, x0, h)
  7.         return solve(f, x0 - delta, h, depth - 1)
  8.     else:
  9.         return x0
  10.  
Sep 26 '10 #11

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