CODEWITHSUNDEEP
python
Mo Samani
Mo Samani

Reputation: 53

searching for my code error written to calculate taylor series

my homework is to write a code which contains a function that calculates the sinx taylor series and gives the amount back. the function must get (n,k) which n is the requested number for sine,and k is the digits that function must calculate after the dot. first i neglected k since its easy to limit the numbers after the dot,and wrote a function that just calculates sinx taylor,so i gave it a specific range for r(r is every sentence of the taylor series):

def taylor(n,k):

  s= ((math.pi)/180)*n
  ex = s
  sign = 1
  factorial = 1
  sum=0
  i=1
  r=1

  while r>0.00000000000000000001 or r<0.0000000000000000000001 :
     r= ex*sign/factorial
     ex = ex*s*s
     sign = sign*(-1)
     factorial=factorial*(i+1)*(i+2)
     i= i+2
     sum = sum + r

  return sum

import math
print(taylor(45,1))

i just don't know why if i set amount of r larger than this (i.e 0.1) i get this error:

Traceback (most recent call last):

File "/Users/modern/Desktop/taylor.py", line 22, in <module>

print(taylor(45))

File "/Users/modern/Desktop/taylor.py", line 12, in taylor

r= ex*sign/factorial

OverflowError: int too large to convert to float

Upvotes: 1

Views: 280

Answers (3)

0x539
0x539

Reputation: 1496

I'm not sure what you mean with

if i set amount of r larger than this (i.e 0.1)

and the condition of your while loop looks strange, but as R Nar pointed out, the error is caused by your value of factorial is getting too large. I would not recommend using decimal however since it is really slow. Rather take a look at gmpy which is built in order to get (really) fast arbitrary precision math.

Alternatively you could use Strinling's Approximation for calculating the large factorials.

Upvotes: 0

Prune
Prune

Reputation: 77910

You can handle your input with a leading question and a split, as @John Coleman suggested, although I'd do the assignment as a pair:

nums = input("Enter n, k, separated by a space")
n, k = nums.split()

Here is the cleaned-up program: the factor updates -- especially the factorial -- are reduced to changes from the previous term. I also canonized your loop limits to be more readable.

def taylor(n,k):

    s = (math.pi/180)*n
    s2 = s*s
    sum = s
    i = 1
    r = s
    converge = 1.0E-20

    while r > converge or r < converge / 100 :
        r *= -s2/((i+1)*(i+2))
        sum += r
        i = i+2

    return sum

import math
print(taylor(45,1))

Upvotes: 1

John Coleman
John Coleman

Reputation: 52008

I'm surprised that this is an issue since I would think that r gets below the error tolerance before it is a problem.

Note that what you really need is the reciprocal of the factorial. Instead of having a factorial variable that you divide by, you could have a variable, say, fact_recip which is initialized as

fact_recip = 1.0

used like r= ex*sign*fact_recp

And updated via

fact_recip /= ((i+1)*(i+2))

this will handle the error that you are seeing, but I'm not sure if the round-off error would be an issue.

Upvotes: 3

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