PRACE NPT

      Subroutine twiddle( arr, ari, m, n )

! ---------------------------------------------------------------------

! --- 'twiddle' does a complex multiplication with the appropriate

!     twiddle factors for the elements of 'arr' & 'ari' which represent

!     the Real and Imaginary parts of a 1-D 'm*(n*nodes)' length FFT, 

!     factored as a sequence of 'n*nodes' FFTs of length 'm'. 'nodes'

!     is the number of processors over which the 'm'-length FFTs are

!     distributed.

! ---------------------------------------------------------------------

      Use              mpi_module

      Use              numerics

      Implicit         None

      Integer       :: m, n

      Real(l_)      :: arr(0:m-1,0:n-1), ari(0:m-1,0:n-1)

      Integer       :: i, j, nbase

      Real(l_)      :: arg, fac, fr, fi, temp

! ---------------------------------------------------------------------

      fac   = 8.0_l_ * Atan( 1.0_l_ ) / ( m*n*nodes )

      nbase = me*n     

      Do j = 0, n - 1

         Do i = 0, m - 1

            arg      = ( i*( nbase + j ) )*fac

            fr       = Cos( arg )

            fi       = Sin( arg )

            temp     = arr(i,j)*fr - ari(i,j)*fi

            ari(i,j) = arr(i,j)*fi + ari(i,j)*fr

            arr(i,j) = temp

         End Do

      End Do

! ---------------------------------------------------------------------

      End Subroutine twiddle