!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!Calcolo numerico del volume di un' ipersfera           !
!d-dimensionale tramite il metodo "hit and miss"        !
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Program hypersphere

  Implicit none
  real,parameter :: pi = acos(-1.0)
  real, dimension(:), allocatable :: rnd
  real :: truevol, vol
  Integer :: i, Nmax, accept, dim,n
  
  print*,'Inserire la dimensione della sfera:'
  read*, dim
  allocate(rnd(dim))
  print*,'Numero massimo di punti da generare:'
  read*, Nmax
  !volume analitico dell'ipersfera
  truevol = pi**(0.5*dim)/gamma(0.5*dim) + 1)

  Open(7, File='vol.dat', Status='Replace')
  write(7,*)' n, vol, exact vol, abs(error)'
  do n=1,Nmax
  accept=0
  if (mod(n,100) == 0) then
    !metodo hit and miss
    Do i=1, n
        call random_number(rnd)
        rnd = (rnd - 0.5)*2.0   ! genero numero random tra -1 e 1
        If (dot_product(rnd,rnd) <= 1) accept = accept + 1
    end do

    !calcolo del volume numerico
    vol = (2.0**dim)*float(accept)/float(n)
    
    !salvataggio dati
    write(7,*) n,vol,truevol, abs(truevol - vol)
 end if
  end do
  Close(7)
  print*, 'Dati salvati in vol.dat '
  print*,' volume sfera numerico e esatto:',vol, truevol

End program hypersphere