Fortran Error: 'y' argument of 'datan2' intrinsic at (1) must be REAL

Question

I want to calculate z value as the coordinate in range of x:-50~50 and y:-50~50 like below code.

program test
implicit none
! --- [local entities]
      real*8            :: rrr,th,U0,amp,alp,Ndiv
      real*8            :: pi,alpR,NR,Rmin,Rmax,z
      integer           :: ir, i, j

do i=0, 50
  do j=0, 50
      th=datan2(i,j)
      pi=datan(1.d0)*4.d0
!
      Ndiv= 24.d0            !! Number of circumferential division
      alp = 90.d0/180.d0*pi  !! phase [rad]
      U0  = 11.4d0           !! average velocity
      amp = 0.5d0            !! amplitude of velocity
      Rmin = 10              !! [m] 
      Rmax = 50              !! [m]
      NR = 6.d0              !! Number of radial division
!
      rrr=dsqrt(i**2+j**2)
      ir=int((rrr-Rmin)/(Rmax-Rmin)*NR)
      alpR=2.d0*pi/dble(Ndiv)*dble(mod(ir,2))
      z=U0*(1.d0+amp*dsin(0.5d0*Ndiv*th+alp+alpR))

  write(*,*) 'i, j, z'
  write(*,*) i, j, z 
 end do
end do

stop
end program test

But I couldn't make it work like below error. I think because i, j are in datan(i,j). How should I change these code?

test.f90:10.16:

      th=datan2(i,j)
                1
Error: 'y' argument of 'datan2' intrinsic at (1) must be REAL
test.f90:21.16:

      rrr=dsqrt(i**2+j**2)
                1
Error: 'x' argument of 'dsqrt' intrinsic at (1) must be REAL

Answer 1

Inspired by the comments of @Rodrigo Rodrigues, @Ian Bush, and @Richard, here is a suggested rewrite of the code segment from @SW. Kim

program test
    use, intrinsic :: iso_fortran_env, only : real64
    implicit none
    ! --- [local entities]
    ! Determine the kind of your real variables (select one):
    !   for specifying a given numerical precision
    integer, parameter  :: wp = selected_real_kind(15, 307)  !15 digits, 10**307 range
    !   for specifying a given number of bits
    ! integer, parameter  :: wp = real64

    real(kind=wp), parameter    :: pi = atan(1._wp)*4._wp
    real(kind=wp)               :: rrr, th, U0, amp, alp, Ndiv
    real(kind=wp)               :: alpR, NR, Rmin, Rmax, z
    integer                     :: ir, i, j

    do i = 0, 50
        do j = 0, 50
            th = atan2(real(i, kind=wp), real(j, kind=wp))
    !
            Ndiv= 24._wp             !! Number of circumferential division
            alp = 90._wp/180._wp*pi  !! phase [rad]
            U0  = 11.4_wp            !! average velocity
            amp = 0.5_wp             !! amplitude of velocity
            Rmin = 10                !! [m]
            Rmax = 50                !! [m]
            NR = 6._wp               !! Number of radial division
    !
            rrr = sqrt(real(i, kind=wp)**2 + real(j, kind=wp)**2)
            ir = int((rrr - Rmin) / (Rmax - Rmin) * NR)
            alpR = 2._wp * pi / Ndiv * mod(ir, 2)
            z = U0 * (1._wp + amp * sin(0.5_wp * Ndiv * th + alp + alpR))
    !
            write(*,*) 'i, j, z'
            write(*,*) i, j, z
        end do
    end do

    stop
end program test

Specifically, the following changes were made with respect to the original code posted:

• Minimum change to answer the question: casting integer variables i and j to real values for using them in the real valued functions datan and dsqrt.
• Using generic names for intrinsic procedures, i.e sqrt instead of dsqrt, atan instead of datan, and sin instead of dsin. One benefit of this approach, is that the kind of working precision wp can be changed in one place, without requiring explicit changes elsewhere in the code.
• Defining the kind of real variables and calling it wp. Extended discussion of this topic, its implications and consequences can be found on this site, for example here and here. Also @Steve Lionel has an in depth post on his blog, where his general advice is to use selected_real_kind.
• Defining pi as a parameter calculating its value once, instead of calculating the same value repeatedly within the nested for loops.