SUBROUTINE calc_spectra

!------------------------------------------------------------------------------!
! Current revisions:
! -----------------
! 
!
! Former revisions:
! -----------------
! $Id: calc_spectra.f90 392 2009-09-24 10:39:14Z letzel $
!
! 274 2009-03-26 15:11:21Z heinze
! Output of messages replaced by message handling routine
!
! 225 2009-01-26 14:44:20Z raasch
! Bugfix: array d is reallocated in case that multigrid is used
!
! 192 2008-08-27 16:51:49Z letzel
! bugfix in calc_spectra_x: exponent = 1.0 / ( ny + 1.0 )
! allow 100 spectra levels instead of 10 for consistency with
! define_netcdf_header
! user-defined spectra, arguments removed from transpose routines
!
! February 2007
! RCS Log replace by Id keyword, revision history cleaned up
!
! Revision 1.9  2006/04/11 14:56:00  raasch
! pl_spectra renamed data_output_sp
!
! Revision 1.1  2001/01/05 15:08:07  raasch
! Initial revision
!
!
! Description:
! ------------
! Calculate horizontal spectra along x and y. 
! ATTENTION: 1d-decomposition along y still needs improvement, because in that
!            case the gridpoint number along z still depends on the PE number
!            because transpose_xz has to be used (and possibly also
!            transpose_zyd needs modification).
!------------------------------------------------------------------------------!

#if defined( __spectra )
    USE arrays_3d
    USE control_parameters
    USE cpulog
    USE fft_xy
    USE indices
    USE interfaces
    USE pegrid
    USE spectrum

    IMPLICIT NONE

    INTEGER ::  m, pr


    CALL cpu_log( log_point(30), 'calc_spectra', 'start' )

!
!-- Initialize ffts
    CALL fft_init

!
!-- Reallocate array d in required size
    IF ( psolver == 'multigrid' )  THEN
       DEALLOCATE( d )
       ALLOCATE( d(nzb+1:nzta,nys:nyna,nxl:nxra) )
    ENDIF

!
!-- Enlarge the size of tend, used as a working array for the transpositions
    IF ( nxra > nxr  .OR.  nyna > nyn  .OR.  nza > nz )  THEN
       DEALLOCATE( tend )
       ALLOCATE( tend(1:nza,nys:nyna,nxl:nxra) )
    ENDIF

    m = 1
    DO WHILE ( data_output_sp(m) /= ' '  .AND.  m <= 10 )
!
!--    Transposition from z --> x  ( y --> x in case of a 1d-decomposition
!--    along x)
       IF ( INDEX( spectra_direction(m), 'x' ) /= 0 )  THEN

!
!--       Calculation of spectra works for cyclic boundary conditions only
          IF ( bc_lr /= 'cyclic' )  THEN

             message_string = 'non-cyclic lateral boundaries along x do not'// &
                              '& allow calculation of spectra along x'
             CALL message( 'calc_spectra', 'PA0160', 1, 2, 0, 6, 0 )
          ENDIF

          CALL preprocess_spectra( m, pr )

#if defined( __parallel )
          IF ( pdims(2) /= 1 )  THEN
             CALL transpose_zx( d, tend, d )
          ELSE
             CALL transpose_yxd( d, tend, d )
          ENDIF
          CALL calc_spectra_x( d, pr, m )
#else
          message_string = 'sorry, calculation of spectra in non parallel ' // &
                           'mode& is still not realized'
          CALL message( 'calc_spectra', 'PA0161', 1, 2, 0, 6, 0 )      
#endif

       ENDIF

!
!--    Transposition from z --> y (d is rearranged only in case of a
!--    1d-decomposition along x)
       IF ( INDEX( spectra_direction(m), 'y' ) /= 0 )  THEN

!
!--       Calculation of spectra works for cyclic boundary conditions only
          IF ( bc_ns /= 'cyclic' )  THEN
             IF ( myid == 0 )  THEN
                message_string = 'non-cyclic lateral boundaries along y do' // &
                                 ' not & allow calculation of spectra along y' 
                CALL message( 'calc_spectra', 'PA0162', 1, 2, 0, 6, 0 )
             ENDIF
             CALL local_stop
          ENDIF

          CALL preprocess_spectra( m, pr )

#if defined( __parallel )
          CALL transpose_zyd( d, tend, d )
          CALL calc_spectra_y( d, pr, m )
#else
          message_string = 'sorry, calculation of spectra in non parallel' // &
                           'mode& is still not realized'
          CALL message( 'calc_spectra', 'PA0161', 1, 2, 0, 6, 0 )
#endif

       ENDIF

!
!--    Increase counter for next spectrum
       m = m + 1
          
    ENDDO

!
!-- Increase counter for averaging process in routine plot_spectra
    average_count_sp = average_count_sp + 1

!
!-- Resize tend to its normal size
    IF ( nxra > nxr  .OR.  nyna > nyn  .OR.  nza > nz )  THEN
       DEALLOCATE( tend )
       ALLOCATE( tend(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) )
    ENDIF

    CALL cpu_log( log_point(30), 'calc_spectra', 'stop' )

#endif
 END SUBROUTINE calc_spectra


#if defined( __spectra )
 SUBROUTINE preprocess_spectra( m, pr )

    USE arrays_3d
    USE indices
    USE pegrid
    USE spectrum
    USE statistics

    IMPLICIT NONE

    INTEGER :: i, j, k, m, pr

    SELECT CASE ( TRIM( data_output_sp(m) ) )
          
    CASE ( 'u' )
       pr = 1
       d(nzb+1:nzt,nys:nyn,nxl:nxr) = u(nzb+1:nzt,nys:nyn,nxl:nxr)
       
    CASE ( 'v' )
       pr = 2
       d(nzb+1:nzt,nys:nyn,nxl:nxr) = v(nzb+1:nzt,nys:nyn,nxl:nxr)
       
    CASE ( 'w' )
       pr = 3
       d(nzb+1:nzt,nys:nyn,nxl:nxr) = w(nzb+1:nzt,nys:nyn,nxl:nxr)
       
    CASE ( 'pt' )
       pr = 4
       d(nzb+1:nzt,nys:nyn,nxl:nxr) = pt(nzb+1:nzt,nys:nyn,nxl:nxr)
       
    CASE ( 'q' )
       pr = 41
       d(nzb+1:nzt,nys:nyn,nxl:nxr) = q(nzb+1:nzt,nys:nyn,nxl:nxr)
       
    CASE DEFAULT
!
!--    The DEFAULT case is reached either if the parameter data_output_sp(m)
!--    contains a wrong character string or if the user has coded a special
!--    case in the user interface. There, the subroutine user_spectra 
!--    checks which of these two conditions applies.
       CALL user_spectra( 'preprocess', m, pr )
          
    END SELECT

!
!-- Subtract horizontal mean from the array, for which spectra have to be
!-- calculated
    DO  i = nxl, nxr
       DO  j = nys, nyn
          DO  k = nzb+1, nzt
             d(k,j,i) = d(k,j,i) - sums(k,pr)
          ENDDO
       ENDDO
    ENDDO

 END SUBROUTINE preprocess_spectra


 SUBROUTINE calc_spectra_x( ddd, pr, m )

    USE arrays_3d
    USE constants
    USE control_parameters
    USE fft_xy
    USE grid_variables
    USE indices
    USE pegrid
    USE spectrum
    USE statistics
    USE transpose_indices

    IMPLICIT NONE

    INTEGER                    ::  i, ishape(1), j, k, m, n, pr

    REAL                       ::  fac, exponent
    REAL, DIMENSION(0:nx)      ::  work
    REAL, DIMENSION(0:nx/2)    ::  sums_spectra_l
    REAL, DIMENSION(0:nx/2,100)::  sums_spectra

    REAL, DIMENSION(0:nxa,nys_x:nyn_xa,nzb_x:nzt_xa) ::  ddd

!
!-- Exponent for geometric average
    exponent = 1.0 / ( ny + 1.0 )

!
!-- Loop over all levels defined by the user
    n = 1
    DO WHILE ( comp_spectra_level(n) /= 999999  .AND.  n <= 100 )

       k = comp_spectra_level(n)

!
!--    Calculate FFT only if the corresponding level is situated on this PE
       IF ( k >= nzb_x  .AND.  k <= nzt_x )  THEN
          
          DO  j = nys_x, nyn_x

             work = ddd(0:nx,j,k)
             CALL fft_x( work, 'forward' )

             ddd(0,j,k) = dx * work(0)**2
             DO  i = 1, nx/2
                ddd(i,j,k) = dx * ( work(i)**2 + work(nx+1-i)**2 )
             ENDDO

          ENDDO

!
!--       Local sum and geometric average of these spectra
!--       (WARNING: no global sum should be performed, because floating
!--       point overflow may occur)
          DO  i = 0, nx/2

             sums_spectra_l(i) = 1.0
             DO  j = nys_x, nyn_x
                sums_spectra_l(i) = sums_spectra_l(i) * ddd(i,j,k)**exponent
             ENDDO

          ENDDO
          
       ELSE

          sums_spectra_l = 1.0

       ENDIF

!
!--    Global sum of spectra on PE0 (from where they are written on file) 
       sums_spectra(:,n) = 0.0
#if defined( __parallel )   
       CALL MPI_BARRIER( comm2d, ierr )  ! Necessary?
       CALL MPI_REDUCE( sums_spectra_l(0), sums_spectra(0,n), nx/2+1, &
                        MPI_REAL, MPI_PROD, 0, comm2d, ierr )
#else
       sums_spectra(:,n) = sums_spectra_l
#endif

       n = n + 1

    ENDDO
    n = n - 1

    IF ( myid == 0 )  THEN
!
!--    Sum of spectra for later averaging (see routine data_output_spectra)
!--    Temperton fft results need to be normalized
       IF ( fft_method == 'temperton-algorithm' )  THEN
          fac = nx + 1.0
       ELSE
          fac = 1.0
       ENDIF
       DO  i = 1, nx/2
          DO k = 1, n
             spectrum_x(i,k,m) = spectrum_x(i,k,m) + sums_spectra(i,k) * fac
          ENDDO
       ENDDO

    ENDIF

!
!-- n_sp_x is needed by data_output_spectra_x
    n_sp_x = n

 END SUBROUTINE calc_spectra_x


 SUBROUTINE calc_spectra_y( ddd, pr, m )

    USE arrays_3d
    USE constants
    USE control_parameters
    USE fft_xy
    USE grid_variables
    USE indices
    USE pegrid
    USE spectrum
    USE statistics
    USE transpose_indices

    IMPLICIT NONE

    INTEGER :: i, j, jshape(1), k, m, n, pr

    REAL                       ::  fac, exponent
    REAL, DIMENSION(0:ny)      ::  work
    REAL, DIMENSION(0:ny/2)    ::  sums_spectra_l
    REAL, DIMENSION(0:ny/2,100)::  sums_spectra

    REAL, DIMENSION(0:nya,nxl_yd:nxr_yda,nzb_yd:nzt_yda) :: ddd


!
!-- Exponent for geometric average
    exponent = 1.0 / ( nx + 1.0 )

!
!-- Loop over all levels defined by the user
    n = 1
    DO WHILE ( comp_spectra_level(n) /= 999999  .AND.  n <= 100 )

       k = comp_spectra_level(n)

!
!--    Calculate FFT only if the corresponding level is situated on this PE
       IF ( k >= nzb_yd  .AND.  k <= nzt_yd )  THEN
          
          DO  i = nxl_yd, nxr_yd

             work = ddd(0:ny,i,k)
             CALL fft_y( work, 'forward' )

             ddd(0,i,k) = dy * work(0)**2
             DO  j = 1, ny/2
                ddd(j,i,k) = dy * ( work(j)**2 + work(ny+1-j)**2 )
             ENDDO

          ENDDO

!
!--       Local sum and geometric average of these spectra
!--       (WARNING: no global sum should be performed, because floating
!--       point overflow may occur)
          DO  j = 0, ny/2

             sums_spectra_l(j) = 1.0
             DO  i = nxl_yd, nxr_yd
                sums_spectra_l(j) = sums_spectra_l(j) * ddd(j,i,k)**exponent
             ENDDO

          ENDDO
          
       ELSE

          sums_spectra_l = 1.0

       ENDIF

!
!--    Global sum of spectra on PE0 (from where they are written on file) 
       sums_spectra(:,n) = 0.0
#if defined( __parallel )   
       CALL MPI_BARRIER( comm2d, ierr )  ! Necessary?
       CALL MPI_REDUCE( sums_spectra_l(0), sums_spectra(0,n), ny/2+1, &
                        MPI_REAL, MPI_PROD, 0, comm2d, ierr )
#else
       sums_spectra(:,n) = sums_spectra_l
#endif

       n = n + 1

    ENDDO
    n = n - 1


    IF ( myid == 0 )  THEN
!
!--    Sum of spectra for later averaging (see routine data_output_spectra)
!--    Temperton fft results need to be normalized
       IF ( fft_method == 'temperton-algorithm' )  THEN
          fac = ny + 1.0
       ELSE
          fac = 1.0
       ENDIF
       DO  j = 1, ny/2
          DO k = 1, n
             spectrum_y(j,k,m) = spectrum_y(j,k,m) + sums_spectra(j,k) * fac
          ENDDO
       ENDDO

    ENDIF

!
!-- n_sp_y is needed by data_output_spectra_y
    n_sp_y = n

 END SUBROUTINE calc_spectra_y
#endif