What's Wrong with My Monte Carlo Calculation of π Using Fortran?

[Taylor_1989]

Hi guys, I am having trouble seeing where I have actually gone wrong with my code. If I run the code I am getting approximation of 12 as my lowest is way to big. But I am really struggling to find where I have gone wrong. Any advice would be appreciated.

PROGRAM assign_10_1

IMPLICIT NONE

INTEGER, DIMENSION (1:12) :: SEED

REAL:: A,X,Y

INTEGER:: I, N, COUNTER_CIRCULE, COUNTER_SQUARE

COUNTER_CIRCULE=0

COUNTER_SQUARE=0

N=100000

WRITE(*,*)'please seclect 12 numbers for your seed'

READ(*,*) SEED

WRITE(*,*) SEED

 CALL RANDOM_SEED(PUT=SEED)

DO I=1,N
   CALL RANDOM_NUMBER(X)
   CALL RANDOM_NUMBER(Y)
   WRITE(*,*) X,Y

   IF (X**2+Y**2 < 1) THEN
   COUNTER_CIRCULE=COUNTER_CIRCULE+1
   ELSE
   COUNTER_SQUARE=COUNTER_SQUARE+1
   END IF

END DO

A=4*(COUNTER_CIRCULE/COUNTER_SQUARE)

WRITE(*,*)'ESTIMATION FOR VALUE OF PI', A
END PROGRAM

 

[BvU]

Your counter_square is not what you think it is...

 

[Baluncore]

A=4*(COUNTER_CIRCULE/COUNTER_SQUARE)

A=4*(COUNTER_CIRCULE / N)

 

[Taylor_1989]

Ok thanks guys. I got it. I just went back of the math with a bit of paper and it clicked in what you are saying. Thanks once again.

 

[Mark44]

A=4*(COUNTER_CIRCULE / N)

Not mentioned is the fact that if COUNTER_CIRCULE is 1000, then A will be assigned the value 0. In Fortran, C, C++, and many other programming languages, there are two types of division: integer division and floating point division. So for example, 2/5 is 0 while all three of the following expressions evaluate to 0.4 or something close to it.

• 2.0 / 5.0
• 2 / 5.0
• 2.0 / 5

See http://www.oc.nps.edu/~bird/oc3030_online/fortran/basics/basics.html, in Type Conversion and Mixed-Mode Arithmetic.

BTW there is no such word as "circule" in English.

 

[Taylor_1989]

Not mentioned is the fact that if COUNTER_CIRCULE is 1000, then A will be assigned the value 0. In Fortran, C, C++, and many other programming languages, there are two types of division: integer division and floating point division. So for example, 2/5 is 0 while all three of the following expressions evaluate to 0.4 or something close to it.

• 2.0 / 5.0
• 2 / 5.0
• 2.0 / 5

See http://www.oc.nps.edu/~bird/oc3030_online/fortran/basics/basics.html, in Type Conversion and Mixed-Mode Arithmetic.

BTW there is no such word as "circule" in English.

Thanks for the advice. much appreciated