1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
|
# Validity of stirling's approximation up to N=100 and plot N vs actual, N vs approx
import math
def stirling(N): #approximation function. log(n!) = nlog(n)-n
return N*math.log(N) - N
ACTUAL=[]
APPROX=[]
factN=1
MAXNUM = 100
print('N\tActual\tApprox\t%Error')
for N in range(1,MAXNUM): # loop from N=1 to N=99
factN *= N # factorial is automatically calculated and revised per iteration.
actual = math.log(factN)
approx = stirling(N)
ACTUAL.append(actual)
APPROX.append(approx)
if(N>2): #Actual is 0 at N=1, and error is quite high for N=2 => neglect
err = 100*(actual-approx)/actual
#Print values to the screen every 5 iterations
if N<5: print ('%d\t%.2f\t%.2f\t%.4f'%(N,actual, approx, err))
elif N<100 and N%20==0: print ('%d\t%.2f\t%.2f\t%.4f'%(N,actual, approx, err))
elif N%100==0:print ('%d\t%.2f\t%.2f\t%.4f'%(N,actual, approx, err))
#Plot N vs actual, and N vs approx
from pylab import *
N = range(1,MAXNUM)
plot(N,APPROX,'-b', label = "N vs Approximation")
plot(N,ACTUAL,'-r', label = "N vs Actual")
legend(loc='lower right')
xlabel('Actual');ylabel('ln(N!) , NlnN-N')
show()
|
