MC-INTEGRATION

 ! Program name: MC-INTEGRATION

! INTEGRATION BY MONTE CARLO METHOD

! INTEGRAL BY MEAN FUNCTION

! EXAMPLE FUNCTION f= 1/(1+x**2)

! In the interval (0,1) the integral is 0.78540

Program monte_carlo

real :: f, f2, integrand, integral, sigma, a, b, x

integer :: i, n

data exact/.78540/

 

Print *, "Enter the grid of the integration, n: "

Read *, n

If (n .eq. 0) stop

 

Print *, "Enter the lower limit and upper limit of integration, a, b:"

Read *, a, b

 

! For the integral in the example, a=0 and b=1

 

f= 0.0

f2=0.0

 

call random_seed()

 

do i=1,n

   call random_number(x)

   x=x*b

   f= f+integrand(x)

   f2=f2+(integrand(x)**2)

!   print *, x, f, f2  !OPTIONAL VISUALIZATION

End do

 

f=f/n

f2=f2/n

integral=(b-a)*f

sigma=(b-a)*sqrt((f2-f**2)/n)

 

Print *,

Print *, integral, sigma, "error= ", exact-integral

 

End program monte_carlo

 

function integrand(x) result(func)

   Implicit none

   Real :: func, x

   func= 1./(1.+x**2)

End function integrand

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