rtran2.f90

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subroutine rtran2(data, nr, kr, ktran)
!
!     ******************************************************************
!     * interface between rft2, rfi2, and fft2.                        *
!     * the calling program should have data dimensioned with at least *
!     * (nr+1)*kr+1 elements.                                          *
!     * lasl routine may 75, called from rft2 and rfi2.                *
!     ******************************************************************

  use itm_types

  implicit none

  integer(itm_i4), intent(in) :: nr, kr, ktran
  real(r8), dimension((nr + 1) * kr + 1), intent(inout) :: data
  
  real(r8) :: theta, dc, ds, ws, wc, sumr, difr, sumi, difi, tr, ti, wca
  integer(itm_i4) :: ks, n, nmax, kmax, k, nk

  ks = 2 * kr
  n = nr / 2
  nmax = n * ks + 2
  kmax = nmax / 2
  theta = 1.5707963267949_r8 / dble(n)
  dc = 2._r8 * sin(theta)**2
  ds = sin(2._r8 * theta)
  ws = 0._r8

  if (ktran <= 0) then
    wc = -1.0_r8
    ds = -ds
  else
    wc = 1.0_r8
    data(nmax - 1) = data(1)
    data(nmax - 1 + kr) = data(kr + 1)
  end if

  do k = 1, kmax, ks
    nk = nmax - k
    sumr = .5_r8 * (data(k) + data(nk))
    difr = .5_r8 * (data(k) - data(nk))
    sumi =.5_r8 * (data(k + kr) + data(nk + kr))
    difi =.5_r8 * (data(k + kr) - data(nk + kr))
    tr =wc * sumi - ws * difr
    ti =ws * sumi + wc * difr
    data(k) = sumr + tr
    data(k + kr) = difi - ti
    data(nk) = sumr - tr
    data(nk + kr) = -difi - ti
    wca = wc - dc * wc - ds * ws
    ws = ws + ds * wc -dc * ws
    wc = wca
  end do       

  return
end subroutine rtran2