subroutine r1f3kf ( ido, l1, cc, in1, ch, in2, wa1, wa2 )

!*****************************************************************************80
!
!! R1F3KF is an FFTPACK5 auxiliary routine.
!
!
!    Copyright (C) 1995-2004, Scientific Computing Division,
!    University Corporation for Atmospheric Research
!
!  Modified:
!
!    27 March 2009
!
!  Author:
!
!    Paul Swarztrauber
!    Richard Valent
!
!  Reference:
!
!    Paul Swarztrauber,
!    Vectorizing the Fast Fourier Transforms,
!    in Parallel Computations,
!    edited by G. Rodrigue,
!    Academic Press, 1982.
!
!    Paul Swarztrauber,
!    Fast Fourier Transform Algorithms for Vector Computers,
!    Parallel Computing, pages 45-63, 1984.
!
!  Parameters:
!
  implicit none

  integer ( kind = 4 ) ido
  integer ( kind = 4 ) in1
  integer ( kind = 4 ) in2
  integer ( kind = 4 ) l1

  real ( kind = 4 ) arg
  real ( kind = 4 ) cc(in1,ido,l1,3)
  real ( kind = 4 ) ch(in2,ido,3,l1)
  integer ( kind = 4 ) i
  integer ( kind = 4 ) ic
  integer ( kind = 4 ) idp2
  integer ( kind = 4 ) k
  real ( kind = 4 ) taui
  real ( kind = 4 ) taur
  real ( kind = 4 ) wa1(ido)
  real ( kind = 4 ) wa2(ido)

  arg = 2.0E+00 * 4.0E+00 * atan ( 1.0E+00 ) / 3.0E+00
  taur = cos ( arg )
  taui = sin ( arg )

  do k = 1, l1
    ch(1,1,1,k) = cc(1,1,k,1)          + ( cc(1,1,k,2) + cc(1,1,k,3) )
    ch(1,1,3,k) =                 taui * ( cc(1,1,k,3) - cc(1,1,k,2) )
    ch(1,ido,2,k) = cc(1,1,k,1) + taur * ( cc(1,1,k,2) + cc(1,1,k,3) )
  end do

  if ( ido == 1 ) then
    return
  end if

  idp2 = ido + 2

  do k = 1, l1
    do i = 3, ido, 2
      ic = idp2 - i
      ch(1,i-1,1,k) = cc(1,i-1,k,1)+((wa1(i-2)*cc(1,i-1,k,2)+ &
        wa1(i-1)*cc(1,i,k,2))+(wa2(i-2)*cc(1,i-1,k,3)+wa2(i-1)* &
        cc(1,i,k,3)))
      ch(1,i,1,k) = cc(1,i,k,1)+((wa1(i-2)*cc(1,i,k,2)- &
        wa1(i-1)*cc(1,i-1,k,2))+(wa2(i-2)*cc(1,i,k,3)-wa2(i-1)* &
        cc(1,i-1,k,3)))
      ch(1,i-1,3,k) = (cc(1,i-1,k,1)+taur*((wa1(i-2)* &
        cc(1,i-1,k,2)+wa1(i-1)*cc(1,i,k,2))+(wa2(i-2)* &
        cc(1,i-1,k,3)+wa2(i-1)*cc(1,i,k,3))))+(taui*((wa1(i-2)* &
        cc(1,i,k,2)-wa1(i-1)*cc(1,i-1,k,2))-(wa2(i-2)* &
        cc(1,i,k,3)-wa2(i-1)*cc(1,i-1,k,3))))
      ch(1,ic-1,2,k) = (cc(1,i-1,k,1)+taur*((wa1(i-2)* &
        cc(1,i-1,k,2)+wa1(i-1)*cc(1,i,k,2))+(wa2(i-2)* &
        cc(1,i-1,k,3)+wa2(i-1)*cc(1,i,k,3))))-(taui*((wa1(i-2)* &
        cc(1,i,k,2)-wa1(i-1)*cc(1,i-1,k,2))-(wa2(i-2)* &
        cc(1,i,k,3)-wa2(i-1)*cc(1,i-1,k,3))))
      ch(1,i,3,k) = (cc(1,i,k,1)+taur*((wa1(i-2)*cc(1,i,k,2)- &
        wa1(i-1)*cc(1,i-1,k,2))+(wa2(i-2)*cc(1,i,k,3)-wa2(i-1)* &
        cc(1,i-1,k,3))))+(taui*((wa2(i-2)*cc(1,i-1,k,3)+wa2(i-1)* &
        cc(1,i,k,3))-(wa1(i-2)*cc(1,i-1,k,2)+wa1(i-1)* &
        cc(1,i,k,2))))
      ch(1,ic,2,k) = (taui*((wa2(i-2)*cc(1,i-1,k,3)+wa2(i-1)* &
        cc(1,i,k,3))-(wa1(i-2)*cc(1,i-1,k,2)+wa1(i-1)* &
        cc(1,i,k,2))))-(cc(1,i,k,1)+taur*((wa1(i-2)*cc(1,i,k,2)- &
        wa1(i-1)*cc(1,i-1,k,2))+(wa2(i-2)*cc(1,i,k,3)-wa2(i-1)* &
        cc(1,i-1,k,3))))
    end do
  end do

  return
end