subroutine zmf5kf ( lot, ido, l1, na, cc, im1, in1, ch, im2, in2, wa )

!*****************************************************************************80
!
!! ZMF5KF is an FFTPACK5 auxiliary routine.
!
!
!
!  Modified:
!
!    26 Ausust 2009
!
!  Author:
!
!    Original complex single precision by Paul Swarztrauber, Richard Valent.
!    Complex double precision version by John Burkardt.
!
!  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 = 8 ) cc(2,in1,l1,ido,5)
  real ( kind = 8 ) ch(2,in2,l1,5,ido)
  real ( kind = 8 ) chold1
  real ( kind = 8 ) chold2
  real ( kind = 8 ) ci2
  real ( kind = 8 ) ci3
  real ( kind = 8 ) ci4
  real ( kind = 8 ) ci5
  real ( kind = 8 ) cr2
  real ( kind = 8 ) cr3
  real ( kind = 8 ) cr4
  real ( kind = 8 ) cr5
  real ( kind = 8 ) di2
  real ( kind = 8 ) di3
  real ( kind = 8 ) di4
  real ( kind = 8 ) di5
  real ( kind = 8 ) dr2
  real ( kind = 8 ) dr3
  real ( kind = 8 ) dr4
  real ( kind = 8 ) dr5
  integer ( kind = 4 ) i
  integer ( kind = 4 ) im1
  integer ( kind = 4 ) im2
  integer ( kind = 4 ) k
  integer ( kind = 4 ) lot
  integer ( kind = 4 ) m1
  integer ( kind = 4 ) m1d
  integer ( kind = 4 ) m2
  integer ( kind = 4 ) m2s
  integer ( kind = 4 ) na
  real ( kind = 8 ) sn
  real ( kind = 8 ) ti2
  real ( kind = 8 ) ti3
  real ( kind = 8 ) ti4
  real ( kind = 8 ) ti5
  real ( kind = 8 ), parameter :: ti11 = -0.9510565162951536D+00
  real ( kind = 8 ), parameter :: ti12 = -0.5877852522924731D+00
  real ( kind = 8 ) tr2
  real ( kind = 8 ) tr3
  real ( kind = 8 ) tr4
  real ( kind = 8 ) tr5
  real ( kind = 8 ), parameter :: tr11 =  0.3090169943749474D+00
  real ( kind = 8 ), parameter :: tr12 = -0.8090169943749474D+00
  real ( kind = 8 ) wa(ido,4,2)

  m1d = ( lot - 1 ) * im1 + 1
  m2s = 1 - im2

  if ( 1 < ido ) then

    do k = 1, l1
      m2 = m2s
      do m1 = 1, m1d, im1
        m2 = m2 + im2
        ti5 = cc(2,m1,k,1,2)-cc(2,m1,k,1,5)
        ti2 = cc(2,m1,k,1,2)+cc(2,m1,k,1,5)
        ti4 = cc(2,m1,k,1,3)-cc(2,m1,k,1,4)
        ti3 = cc(2,m1,k,1,3)+cc(2,m1,k,1,4)
        tr5 = cc(1,m1,k,1,2)-cc(1,m1,k,1,5)
        tr2 = cc(1,m1,k,1,2)+cc(1,m1,k,1,5)
        tr4 = cc(1,m1,k,1,3)-cc(1,m1,k,1,4)
        tr3 = cc(1,m1,k,1,3)+cc(1,m1,k,1,4)
        ch(1,m2,k,1,1) = cc(1,m1,k,1,1)+tr2+tr3
        ch(2,m2,k,1,1) = cc(2,m1,k,1,1)+ti2+ti3
        cr2 = cc(1,m1,k,1,1)+tr11*tr2+tr12*tr3
        ci2 = cc(2,m1,k,1,1)+tr11*ti2+tr12*ti3
        cr3 = cc(1,m1,k,1,1)+tr12*tr2+tr11*tr3
        ci3 = cc(2,m1,k,1,1)+tr12*ti2+tr11*ti3
        cr5 = ti11*tr5+ti12*tr4
        ci5 = ti11*ti5+ti12*ti4
        cr4 = ti12*tr5-ti11*tr4
        ci4 = ti12*ti5-ti11*ti4
        ch(1,m2,k,2,1) = cr2-ci5
        ch(1,m2,k,5,1) = cr2+ci5
        ch(2,m2,k,2,1) = ci2+cr5
        ch(2,m2,k,3,1) = ci3+cr4
        ch(1,m2,k,3,1) = cr3-ci4
        ch(1,m2,k,4,1) = cr3+ci4
        ch(2,m2,k,4,1) = ci3-cr4
        ch(2,m2,k,5,1) = ci2-cr5
      end do
    end do

    do i = 2, ido
      do k = 1, l1
        m2 = m2s
        do m1 = 1, m1d, im1
          m2 = m2 + im2
          ti5 = cc(2,m1,k,i,2)-cc(2,m1,k,i,5)
          ti2 = cc(2,m1,k,i,2)+cc(2,m1,k,i,5)
          ti4 = cc(2,m1,k,i,3)-cc(2,m1,k,i,4)
          ti3 = cc(2,m1,k,i,3)+cc(2,m1,k,i,4)
          tr5 = cc(1,m1,k,i,2)-cc(1,m1,k,i,5)
          tr2 = cc(1,m1,k,i,2)+cc(1,m1,k,i,5)
          tr4 = cc(1,m1,k,i,3)-cc(1,m1,k,i,4)
          tr3 = cc(1,m1,k,i,3)+cc(1,m1,k,i,4)
          ch(1,m2,k,1,i) = cc(1,m1,k,i,1)+tr2+tr3
          ch(2,m2,k,1,i) = cc(2,m1,k,i,1)+ti2+ti3
          cr2 = cc(1,m1,k,i,1)+tr11*tr2+tr12*tr3
          ci2 = cc(2,m1,k,i,1)+tr11*ti2+tr12*ti3
          cr3 = cc(1,m1,k,i,1)+tr12*tr2+tr11*tr3
          ci3 = cc(2,m1,k,i,1)+tr12*ti2+tr11*ti3
          cr5 = ti11*tr5+ti12*tr4
          ci5 = ti11*ti5+ti12*ti4
          cr4 = ti12*tr5-ti11*tr4
          ci4 = ti12*ti5-ti11*ti4
          dr3 = cr3-ci4
          dr4 = cr3+ci4
          di3 = ci3+cr4
          di4 = ci3-cr4
          dr5 = cr2+ci5
          dr2 = cr2-ci5
          di5 = ci2-cr5
          di2 = ci2+cr5
          ch(1,m2,k,2,i) = wa(i,1,1)*dr2+wa(i,1,2)*di2
          ch(2,m2,k,2,i) = wa(i,1,1)*di2-wa(i,1,2)*dr2
          ch(1,m2,k,3,i) = wa(i,2,1)*dr3+wa(i,2,2)*di3
          ch(2,m2,k,3,i) = wa(i,2,1)*di3-wa(i,2,2)*dr3
          ch(1,m2,k,4,i) = wa(i,3,1)*dr4+wa(i,3,2)*di4
          ch(2,m2,k,4,i) = wa(i,3,1)*di4-wa(i,3,2)*dr4
          ch(1,m2,k,5,i) = wa(i,4,1)*dr5+wa(i,4,2)*di5
          ch(2,m2,k,5,i) = wa(i,4,1)*di5-wa(i,4,2)*dr5
        end do
      end do
    end do

  else if ( na == 1 ) then

    sn = 1.0D+00 / real ( 5 * l1, kind = 8 )

    do k = 1, l1
      m2 = m2s
      do m1 = 1, m1d, im1
        m2 = m2 + im2
        ti5 = cc(2,m1,k,1,2)-cc(2,m1,k,1,5)
        ti2 = cc(2,m1,k,1,2)+cc(2,m1,k,1,5)
        ti4 = cc(2,m1,k,1,3)-cc(2,m1,k,1,4)
        ti3 = cc(2,m1,k,1,3)+cc(2,m1,k,1,4)
        tr5 = cc(1,m1,k,1,2)-cc(1,m1,k,1,5)
        tr2 = cc(1,m1,k,1,2)+cc(1,m1,k,1,5)
        tr4 = cc(1,m1,k,1,3)-cc(1,m1,k,1,4)
        tr3 = cc(1,m1,k,1,3)+cc(1,m1,k,1,4)
        ch(1,m2,k,1,1) = sn*(cc(1,m1,k,1,1)+tr2+tr3)
        ch(2,m2,k,1,1) = sn*(cc(2,m1,k,1,1)+ti2+ti3)
        cr2 = cc(1,m1,k,1,1)+tr11*tr2+tr12*tr3
        ci2 = cc(2,m1,k,1,1)+tr11*ti2+tr12*ti3
        cr3 = cc(1,m1,k,1,1)+tr12*tr2+tr11*tr3
        ci3 = cc(2,m1,k,1,1)+tr12*ti2+tr11*ti3
        cr5 = ti11*tr5+ti12*tr4
        ci5 = ti11*ti5+ti12*ti4
        cr4 = ti12*tr5-ti11*tr4
        ci4 = ti12*ti5-ti11*ti4
        ch(1,m2,k,2,1) = sn*(cr2-ci5)
        ch(1,m2,k,5,1) = sn*(cr2+ci5)
        ch(2,m2,k,2,1) = sn*(ci2+cr5)
        ch(2,m2,k,3,1) = sn*(ci3+cr4)
        ch(1,m2,k,3,1) = sn*(cr3-ci4)
        ch(1,m2,k,4,1) = sn*(cr3+ci4)
        ch(2,m2,k,4,1) = sn*(ci3-cr4)
        ch(2,m2,k,5,1) = sn*(ci2-cr5)
      end do
    end do

  else

    sn = 1.0D+00 / real ( 5 * l1, kind = 8 )

    do k = 1, l1
      do m1 = 1, m1d, im1

        ti5 = cc(2,m1,k,1,2) - cc(2,m1,k,1,5)
        ti2 = cc(2,m1,k,1,2) + cc(2,m1,k,1,5)
        ti4 = cc(2,m1,k,1,3) - cc(2,m1,k,1,4)
        ti3 = cc(2,m1,k,1,3) + cc(2,m1,k,1,4)
        tr5 = cc(1,m1,k,1,2) - cc(1,m1,k,1,5)
        tr2 = cc(1,m1,k,1,2) + cc(1,m1,k,1,5)
        tr4 = cc(1,m1,k,1,3) - cc(1,m1,k,1,4)
        tr3 = cc(1,m1,k,1,3) + cc(1,m1,k,1,4)

        chold1 = sn * ( cc(1,m1,k,1,1) + tr2 + tr3 )
        chold2 = sn * ( cc(2,m1,k,1,1) + ti2 + ti3 )

        cr2 = cc(1,m1,k,1,1) + tr11 * tr2 + tr12 * tr3
        ci2 = cc(2,m1,k,1,1) + tr11 * ti2 + tr12 * ti3
        cr3 = cc(1,m1,k,1,1) + tr12 * tr2 + tr11 * tr3
        ci3 = cc(2,m1,k,1,1) + tr12 * ti2 + tr11 * ti3

        cc(1,m1,k,1,1) = chold1
        cc(2,m1,k,1,1) = chold2

        cr5 = ti11 * tr5 + ti12 * tr4
        ci5 = ti11 * ti5 + ti12 * ti4
        cr4 = ti12 * tr5 - ti11 * tr4
        ci4 = ti12 * ti5 - ti11 * ti4

        cc(1,m1,k,1,2) = sn * ( cr2 - ci5 )
        cc(1,m1,k,1,5) = sn * ( cr2 + ci5 )
        cc(2,m1,k,1,2) = sn * ( ci2 + cr5 )
        cc(2,m1,k,1,3) = sn * ( ci3 + cr4 )
        cc(1,m1,k,1,3) = sn * ( cr3 - ci4 )
        cc(1,m1,k,1,4) = sn * ( cr3 + ci4 )
        cc(2,m1,k,1,4) = sn * ( ci3 - cr4 )
        cc(2,m1,k,1,5) = sn * ( ci2 - cr5 )

      end do
    end do

  end if

  return
end