!MNH_LIC Copyright 1994-2013 CNRS, Meteo-France and Universite Paul Sabatier
!MNH_LIC This is part of the Meso-NH software governed by the CeCILL-C licence
!MNH_LIC version 1. See LICENCE, CeCILL-C_V1-en.txt and CeCILL-C_V1-fr.txt
!MNH_LIC for details. version 1.
!-----------------------------------------------------------------
!--------------- special set of characters for RCS information
!-----------------------------------------------------------------
! $Source$ $Revision$ $Date$
!-----------------------------------------------------------------
! ################
MODULE MODI_TRIDZ
! ################
!
INTERFACE
!
SUBROUTINE TRIDZ(HLUOUT,HLBCX,HLBCY, &
PMAP,PDXHAT,PDYHAT,PDXHATM,PDYHATM,PRHOM, &
PAF,PCF,PTRIGSX,PTRIGSY,KIFAXX,KIFAXY, &
PRHODJ,PTHVREF,PZZ,PBFY,PBFB,&
PBF_SXP2_YP1_Z)!JUAN Z_SPLITING
!
IMPLICIT NONE
!
CHARACTER (LEN=*), INTENT(IN) :: HLUOUT ! output listing name
CHARACTER (LEN=4), DIMENSION(2), INTENT(IN) :: HLBCX ! x-direction LBC type
CHARACTER (LEN=4), DIMENSION(2), INTENT(IN) :: HLBCY ! y-direction LBC type
!
REAL, DIMENSION(:,:,:), INTENT(IN) :: PRHODJ ! density of reference * J
REAL, DIMENSION(:,:,:), INTENT(IN) :: PTHVREF ! Virtual Potential
! Temperature of the reference state
!
REAL, DIMENSION(:,:), INTENT(IN) :: PMAP ! scale factor
!
REAL, DIMENSION(:,:,:), INTENT(IN) :: PZZ ! height z
!
REAL, DIMENSION(:), INTENT(IN) :: PDXHAT ! Stretching in x direction
REAL, DIMENSION(:), INTENT(IN) :: PDYHAT ! Stretching in y direction
!
REAL, INTENT(OUT) :: PDXHATM ! mean grid increment in the x
! direction
REAL, INTENT(OUT) :: PDYHATM ! mean grid increment in the y
! direction
!
REAL, DIMENSION (:), INTENT(OUT) :: PRHOM ! mean of XRHODJ on the plane
! x y localized at a mass
! level
!
REAL, DIMENSION(:), INTENT(OUT) :: PAF,PCF ! vectors giving the nonvanishing
REAL, DIMENSION(:,:,:), INTENT(OUT) :: PBFY ! elements (yslice) of the tri-diag.
! matrix in the pressure eq.
!JUAN
REAL, DIMENSION(:,:,:), INTENT(OUT) :: PBFB ! elements (bsplit slide) of the tri-diag.
! matrix in the pressure eq.
REAL, DIMENSION(:,:,:), INTENT(OUT) :: PBF_SXP2_YP1_Z ! elements of the tri-diag. SXP2_YP1_Z-slide
! matrix in the pressure eq
!JUAN
!
! arrays of sin or cos values
! for the FFT :
REAL, DIMENSION(:), INTENT(OUT) :: PTRIGSX ! - along x
REAL, DIMENSION(:), INTENT(OUT) :: PTRIGSY ! - along y
!
! decomposition in prime
! numbers for the FFT:
INTEGER, DIMENSION(19), INTENT(OUT) :: KIFAXX ! - along x
INTEGER, DIMENSION(19), INTENT(OUT) :: KIFAXY ! - along y
!
END SUBROUTINE TRIDZ
!
END INTERFACE
!
END MODULE MODI_TRIDZ
!
! ###################################################################
SUBROUTINE TRIDZ(HLUOUT,HLBCX,HLBCY, &
PMAP,PDXHAT,PDYHAT,PDXHATM,PDYHATM,PRHOM, &
PAF,PCF,PTRIGSX,PTRIGSY,KIFAXX,KIFAXY, &
PRHODJ,PTHVREF,PZZ,PBFY,PBFB,&
PBF_SXP2_YP1_Z) !JUAN Z_SPLITING
! ####################################################################
!
!!**** *TRIDZ * - Compute coefficients for the flat operator
!!
!! PURPOSE
!! -------
! The purpose of this routine is to compute the vertical time independent
! coefficients a(k), b(k), c(k) required for the calculation of the "flat"
! (i.e. neglecting the orography) operator Laplacian. RHOJ is averaged on
! the whole horizontal domain. The form of the eigenvalues of the flat
! operator depends on the lateral boundary conditions. Furthermore, this
! routine initializes TRIGS and IFAX arrays required for the FFT transform
! used in the routine PRECOND.
!
!!** METHOD
!! ------
!! The forms of the eigenvalues of the horizontal Laplacian are given by:
!! Cyclic conditions:
!! -----------------
!! <rhoj> 2 ( pi ) <rhoj> 2 ( pi )
!! b(m,n) = -4 ----------- sin (----- m ) -4 ----------- sin (----- n )
!! <dxx> <dxx> ( imax ) <dyy> <dyy> ( jmax )
!!
!! Open conditions:
!! -----------------
!! <rhoj> 2 ( pi ) <rhoj> 2 ( pi )
!! b(m,n) = -4 ----------- sin (----- m ) -4 ----------- sin (----- n )
!! <dxx> <dxx> ( 2imax ) <dyy> <dyy> ( 2jmax )
!!
!! Cyclic condition along x and open condition along y:
!! ------------------------------------------------------
!! <rhoj> 2 ( pi ) <rhoj> 2 ( pi )
!! b(m,n) = -4 ----------- sin (----- m ) -4 ----------- sin (----- n )
!! <dxx> <dxx> ( imax ) <dyy> <dyy> ( 2jmax )
!!
!! Open condition along x and cyclic condition along y:
!! ------------------------------------------------------
!! <rhoj> 2 ( pi ) <rhoj> 2 ( pi )
!! b(m,n) = -4 ----------- sin (----- m ) -4 ----------- sin (----- n )
!! <dxx> <dxx> ( 2imax ) <dyy> <dyy> ( jmax )
!!
!! where m = 0,1,2....imax-1, n = 0,1,2....jmax-1
!! Note that rhoj contains the Jacobian J = Deltax*Deltay*Deltaz = volume of
!! an elementary mesh.
!!
!! EXTERNAL
!! --------
!! Function FFTFAX: initialization of TRIGSX,IFAXX,TRIGSY,IFAXY for
!! the FFT transform
!! GET_DIM_EXT_ll : get extended sub-domain sizes
!! GET_INDICE_ll : get physical sub-domain bounds
!! GET_DIM_PHYS_ll : get physical sub-domain sizes
!! GET_GLOBALDIMS_ll : get physical global domain sizes
!! GET_OR_ll : get origine coordonates of the physical sub-domain in global indices
!! REDUCESUM_ll : sum into a scalar variable
!! GET_SLICE_ll : get a slice of the global domain
!!
!! IMPLICIT ARGUMENTS
!! ------------------
!! Module MODD_CST : define constants
!! XPI : pi
!! XCPD
!! Module MODD_PARAMETERS: declaration of parameter variables
!! JPHEXT, JPVEXT: define the number of marginal points out of the
!! physical domain along horizontal and vertical directions respectively
!! Module MODD_CONF: model configurations
!! LCARTESIAN: logical for CARTESIAN geometry
!! .TRUE. = Cartesian geometry used
!! L2D: logical for 2D model version
!!
!! REFERENCE
!! ---------
!! Book2 of documentation (routine TRIDZ)
!!
!! AUTHOR
!! ------
!! P. HÅreil and J. Stein * Meteo France *
!!
!! MODIFICATIONS
!! -------------
!! Original 25/07/94
!! 14/04/95 (J. Stein) bug in the ZDZM computation
!! ( stretched case)
!! 8/07/96 (P. Jabouille) change the FFT initialization
!! which now works for odd number.
!! 14/01/97 Durran anelastic equation (Stein,Lafore)
!! 15/06/98 (D.Lugato, R.Guivarch) Parallelisation
!! 10/08/98 (N. Asencio) add parallel code
!! use PDXHAT, PDYHAT and not PXHAT,PYHAT
!! PBFY is initialized
!! 20/08/00 (J. Stein, J. Escobar) optimisation of the solver
!! PBFY transposition
!! 14/03/02 (P. Jabouille) set values for meaningless spectral coefficients
!! (to avoid problem in bouissinesq configuration)
!------------------------------------------------------------------------------
!
!* 0. DECLARATIONS
! ------------
USE MODD_CST
USE MODD_CONF
USE MODD_PARAMETERS
!
USE MODE_ll
USE MODE_IO_ll
USE MODE_FM
!JUAN P1/P2 SPLITTING
USE MODE_SPLITTINGZ_ll , ONLY : GET_DIM_EXTZ_ll,GET_ORZ_ll,LWESTZ_ll,LSOUTHZ_ll
!JUAN
!
!JUAN
USE MODE_REPRO_SUM
!JUAN
!
IMPLICIT NONE
!
!
!* 0.1 declarations of arguments
!
!
!
CHARACTER (LEN=*), INTENT(IN) :: HLUOUT ! output listing name
CHARACTER (LEN=4), DIMENSION(2), INTENT(IN) :: HLBCX ! x-direction LBC type
CHARACTER (LEN=4), DIMENSION(2), INTENT(IN) :: HLBCY ! y-direction LBC type
!
REAL, DIMENSION(:,:,:), INTENT(IN) :: PRHODJ ! density of reference * J
REAL, DIMENSION(:,:,:), INTENT(IN) :: PTHVREF ! Virtual Potential
! Temperature of the reference state
!
REAL, DIMENSION(:,:), INTENT(IN) :: PMAP ! scale factor
!
REAL, DIMENSION(:,:,:), INTENT(IN) :: PZZ ! height z
!
REAL, DIMENSION(:), INTENT(IN) :: PDXHAT ! Stretching in x direction
REAL, DIMENSION(:), INTENT(IN) :: PDYHAT ! Stretching in y direction
!
REAL, INTENT(OUT) :: PDXHATM ! mean grid increment in the x
! direction
REAL, INTENT(OUT) :: PDYHATM ! mean grid increment in the y
! direction
!
REAL, DIMENSION (:), INTENT(OUT) :: PRHOM ! mean of XRHODJ on the plane
! x y localized at a mass
! level
!
REAL, DIMENSION(:), INTENT(OUT) :: PAF,PCF ! vectors giving the nonvanishing
REAL, DIMENSION(:,:,:), INTENT(OUT) :: PBFY ! elements (yslice) of the tri-diag.
! matrix in the pressure eq. which is transposed. PBFY is a y-slices structure
!JUAN
REAL, DIMENSION(:,:,:), INTENT(OUT) :: PBFB ! elements (bsplit slide) of the tri-diag.
! matrix in the pressure eq.
REAL, DIMENSION(:,:,:), INTENT(OUT) :: PBF_SXP2_YP1_Z ! elements of the tri-diag. SXP2_YP1_Z-slide
! matrix in the pressure eq.
!JUAN
!
! arrays of sin or cos values
! for the FFT :
REAL, DIMENSION(:), INTENT(OUT) :: PTRIGSX ! - along x
REAL, DIMENSION(:), INTENT(OUT) :: PTRIGSY ! - along y
!
! decomposition in prime
! numbers for the FFT:
INTEGER, DIMENSION(19), INTENT(OUT) :: KIFAXX ! - along x
INTEGER, DIMENSION(19), INTENT(OUT) :: KIFAXY ! - along y
!
!* 0.2 declarations of local variables
!
INTEGER :: IRESP ! FM return code
INTEGER :: ILUOUT ! Logical unit number for
! output-listing
INTEGER :: IIB,IIE,IJB,IJE,IKB,IKE ! indice values of the physical subdomain
INTEGER :: IKU ! size of the arrays along z
INTEGER :: IIB_ll,IIE_ll,IJB_ll,IJE_ll ! indice values of the physical global domain
INTEGER :: IIMAX,IJMAX ! Number of points of the physical subdomain
INTEGER :: IIMAX_ll,IJMAX_ll ! Number of points of Global physical domain
!
INTEGER :: JI,JJ,JK ! loop indexes
!
INTEGER :: INN ! temporary result for the computation of array TRIGS
!
REAL, DIMENSION (:,:), ALLOCATABLE :: ZEIGEN_ll ! eigenvalues b(m,n) in global representation
REAL, DIMENSION (:), ALLOCATABLE :: ZEIGENX_ll ! used for the computation of ZEIGEN_ll
!
REAL, DIMENSION( SIZE(PDXHAT)) :: ZWORKX ! work array to compute PDXHATM
REAL, DIMENSION( SIZE(PDYHAT)) :: ZWORKY ! work array to compute PDYHATM
!
REAL :: ZGWNX,ZGWNY ! greater wave numbers allowed by the model
! configuration in x and y directions respectively
!
REAL, DIMENSION (SIZE(PZZ,3)) :: ZDZM ! mean of deltaz on the plane x y
! localized at a w-level
!
REAL :: ZANGLE,ZDEL ! needed for the initialization of the arrays used by the FFT
!
REAL :: ZINVMEAN ! inverse of inner points number in an horizontal grid
!
INTEGER :: IINFO_ll ! return code of parallel routine
REAL, DIMENSION (SIZE(PMAP,1)) :: ZXMAP ! extraction of PMAP array along x
REAL, DIMENSION (SIZE(PMAP,2)) :: ZYMAP ! extraction of PMAP array along y
INTEGER :: IORXY_ll,IORYY_ll ! origin's coordinates of the y-slices subdomain
INTEGER :: IIUY_ll,IJUY_ll ! dimensions of the y-slices subdomain
INTEGER :: IXMODE_ll,IYMODE_ll ! number of modes in the x and y direction for global point of view
INTEGER :: IXMODEY_ll,IYMODEY_ll ! number of modes in the x and y direction for y_slice point of view
!JUAN Z_SPLITTING
INTEGER :: IORXB_ll,IORYB_ll ! origin's coordinates of the b-slices subdomain
INTEGER :: IIUB_ll,IJUB_ll ! dimensions of the b-slices subdomain
INTEGER :: IXMODEB_ll,IYMODEB_ll ! number of modes in the x and y direction for b_slice point of view
!
INTEGER :: IORX_SXP2_YP1_Z_ll,IORY_SXP2_YP1_Z_ll ! origin's coordinates of the b-slices subdomain
INTEGER :: IIU_SXP2_YP1_Z_ll,IJU_SXP2_YP1_Z_ll,IKU_SXP2_YP1_Z_ll ! dimensions of the b-slices subdomain
INTEGER :: IXMODE_SXP2_YP1_Z_ll,IYMODE_SXP2_YP1_Z_ll ! number of modes in the x and y direction for b_slice point of view
!JUAN Z_SPLITTING
!JUAN16
!TYPE(DOUBLE_DOUBLE) , DIMENSION (SIZE(PZZ,3)) :: ZRHOM_ll , ZDZM_ll
REAL, ALLOCATABLE, DIMENSION(:,:) :: ZRHOM_2D , ZDZM_2D
!JUAN16
!
!
!
!
!
!------------------------------------------------------------------------------
!
!* 1. INITIALIZATION
! --------------
!
!* 1.1 retrieve a logical unit number
! ------------------------------
!
CALL FMLOOK_ll(HLUOUT,HLUOUT,ILUOUT,IRESP)
!
!* 1.2 compute loop bounds
! -------------------
!
! extended sub-domain
CALL GET_DIM_EXT_ll ('Y',IIUY_ll,IJUY_ll)
!JUAN Z_SPLITTING
CALL GET_DIM_EXT_ll ('B',IIUB_ll,IJUB_ll)
! P1/P2 splitting
CALL GET_DIM_EXTZ_ll('SXP2_YP1_Z',IIU_SXP2_YP1_Z_ll,IJU_SXP2_YP1_Z_ll,IKU_SXP2_YP1_Z_ll)
!JUAN Z_SPLITTING
IKU=SIZE(PRHODJ,3)
!
CALL GET_INDICE_ll (IIB,IJB,IIE,IJE)
IKB=1 +JPVEXT
IKE=IKU -JPVEXT
! physical sub-domain
CALL GET_DIM_PHYS_ll ( 'B',IIMAX,IJMAX)
!
! global physical domain limits
CALL GET_GLOBALDIMS_ll ( IIMAX_ll, IJMAX_ll)
IIB_ll = 1 + JPHEXT
IIE_ll = IIMAX_ll + JPHEXT
IJB_ll = 1 + JPHEXT
IJE_ll = IJMAX_ll + JPHEXT
!
! the use of local array ZEIGENX and ZEIGEN would require some technical modifications
!
ALLOCATE (ZEIGENX_ll(IIMAX_ll + 2*JPHEXT))
ALLOCATE (ZEIGEN_ll(IIMAX_ll + 2*JPHEXT, IJMAX_ll + 2*JPHEXT))
ZEIGEN_ll = 0.0
! Get the origin coordinates of the extended sub-domain in global landmarks
CALL GET_OR_ll('Y',IORXY_ll,IORYY_ll)
!JUAN Z_SPLITING
CALL GET_OR_ll('B',IORXB_ll,IORYB_ll)
! P1/P2 Splitting
CALL GET_ORZ_ll('SXP2_YP1_Z',IORX_SXP2_YP1_Z_ll,IORY_SXP2_YP1_Z_ll)
!JUAN Z_SPLITING
!
!* 1.3 allocate x-slice array
!
!* 1.4 variables for the eigenvalues computation
!
ZGWNX = XPI/REAL(IIMAX_ll)
ZGWNY = XPI/REAL(IJMAX_ll)
!
!------------------------------------------------------------------------------
!
!* 2. COMPUTE THE AVERAGE OF RHOJ*CPD*THETAVREF ALONG XY
! --------------------------------------------------
!
ZINVMEAN = 1./REAL(IIMAX_ll*IJMAX_ll)
!JUAN16
ALLOCATE(ZRHOM_2D(IIB:IIE, IJB:IJE))
!
DO JK = 1,SIZE(PZZ,3)
IF ( CEQNSYS == 'DUR' .OR. CEQNSYS == 'MAE' ) THEN
DO JJ = IJB,IJE
DO JI = IIB,IIE
ZRHOM_2D(JI,JJ) = PRHODJ(JI,JJ,JK)*XCPD*PTHVREF(JI,JJ,JK)*ZINVMEAN
END DO
END DO
ELSEIF ( CEQNSYS == 'LHE' ) THEN
DO JJ = IJB,IJE
DO JI = IIB,IIE
ZRHOM_2D(JI,JJ) = PRHODJ(JI,JJ,JK)*ZINVMEAN
END DO
END DO
END IF
! global sum
PRHOM(JK) = SUM_DD_R2_ll(ZRHOM_2D)
END DO
!
! global sum
!CALL REDUCESUM_ll(ZRHOM_ll,IINFO_ll)
!PRHOM = ZRHOM_ll
!JUAN16
!
!------------------------------------------------------------------------------
!
!* 3. COMPUTE THE MEAN INCREMENT BETWEEN Z LEVELS
! -------------------------------------------
!
!JUAN16
!ZDZM_ll = 0.
ALLOCATE(ZDZM_2D(IIB:IIE, IJB:IJE))
!
DO JK = IKB-1,IKE
DO JJ = IJB,IJE
DO JI = IIB,IIE
ZDZM_2D(JI,JJ) = (PZZ(JI,JJ,JK+1)-PZZ(JI,JJ,JK))*ZINVMEAN
END DO
END DO
ZDZM(JK) = SUM_DD_R2_ll(ZDZM_2D)
END DO
ZDZM(IKE+1) = ZDZM(IKE)
!
! global sum
!CALL REDUCESUM_ll(ZDZM_ll,IINFO_ll)
!ZDZM = ZDZM_ll
!JUAN16
!
!
! vertical average to arrive at a w-level
DO JK = IKE+1,IKB,-1
ZDZM(JK) = (ZDZM(JK) + ZDZM(JK-1))*0.5
END DO
!
ZDZM(IKB-1) = -999.
!
!------------------------------------------------------------------------------
!
!* 4. COMPUTE THE MEAN INCREMENT BETWEEN X LEVELS
! -------------------------------------------
!
PDXHATM =0.
! . local sum
IF (LCARTESIAN) THEN
PDXHATM = SUM_1DFIELD_ll ( PDXHAT,'X',IIB_ll,IIE_ll,IINFO_ll)
ELSE
! Extraction of x-slice PMAP at j=(IJB_ll+IJE_ll)/2
CALL GET_SLICE_ll (PMAP,'X',(IJB_ll+IJE_ll)/2,ZXMAP(IIB:IIE) &
,IIB,IIE,IINFO_ll)
! initialize the work array = PDXHAT/ZXMAP
ZWORKX(IIB:IIE) = PDXHAT(IIB:IIE)/ ZXMAP (IIB:IIE)
PDXHATM = SUM_1DFIELD_ll ( ZWORKX,'X',IIB_ll,IIE_ll,IINFO_ll)
END IF
! . division to complete sum
PDXHATM = PDXHATM / REAL(IIMAX_ll)
!
!------------------------------------------------------------------------------
!
!* 5. COMPUTE THE MEAN INCREMENT BETWEEN Y LEVELS
! -------------------------------------------
!
PDYHATM = 0.
IF (LCARTESIAN) THEN
PDYHATM = SUM_1DFIELD_ll ( PDYHAT,'Y',IJB_ll,IJE_ll,IINFO_ll)
ELSE
! Extraction of y-slice PMAP at i=IIB_ll+IIE_ll/2
CALL GET_SLICE_ll (PMAP,'Y',(IIB_ll+IIE_ll)/2,ZYMAP(IJB:IJE) &
,IJB,IJE,IINFO_ll)
! initialize the work array = PDYHAT / ZYMAP
ZWORKY(IJB:IJE) = PDYHAT(IJB:IJE) / ZYMAP (IJB:IJE)
PDYHATM = SUM_1DFIELD_ll ( ZWORKY,'Y',IJB_ll,IJE_ll,IINFO_ll)
END IF
! . division to complete sum
PDYHATM= PDYHATM / REAL(IJMAX_ll)
!
!------------------------------------------------------------------------------
!
!* 6. COMPUTE THE OUT-DIAGONAL ELEMENTS A AND C OF THE MATRIX
! -------------------------------------------------------
!
DO JK = IKB,IKE
PAF(JK) = 0.5 * ( PRHOM(JK-1) + PRHOM(JK) ) / ZDZM(JK) **2
PCF(JK) = 0.5 * ( PRHOM(JK) + PRHOM(JK+1) ) / ZDZM(JK+1) **2
END DO
!
! at the upper and lower levels PAF and PCF are computed using the Neumann
! conditions applying on the vertical component of the gradient
!
PAF(IKE+1) = -0.5 * ( PRHOM(IKE) + PRHOM(IKE+1) ) / ZDZM(IKE+1) **2
PCF(IKB-1) = 0.5 * ( PRHOM(IKB-1) + PRHOM(IKB) ) / ZDZM(IKB) **2
!
PAF(IKB-1) = 999.
PCF(IKE+1) = 999.
!------------------------------------------------------------------------------
!* 7. COMPUTE THE DIAGONAL ELEMENTS B OF THE MATRIX
! ---------------------------------------------
!
!* 7.1 compute the horizontal eigenvalues
!
!
!* 7.1.1 compute the eigenvalues along the x direction
!
SELECT CASE (HLBCX(1))
! in the cyclic case, the eigenvalues are the same for two following JM values:
! it corresponds to the real and complex parts of the FFT
CASE('CYCL') ! cyclic case
IXMODE_ll = IIMAX_ll+2
IXMODEY_ll = IIUY_ll
IXMODEB_ll = IIUB_ll !JUAN Z_SPLITTING
!
DO JI = 1,IXMODE_ll
ZEIGENX_ll(JI) = - ( 2. * SIN ( (JI-1)/2*ZGWNX ) / PDXHATM )**2
END DO
CASE DEFAULT ! other cases
IXMODE_ll = IIMAX_ll
!
!
IF (LEAST_ll(HSPLITTING='Y')) THEN
IXMODEY_ll = IIUY_ll - 2
ELSE
IXMODEY_ll = IIUY_ll
END IF
!JUAN Z_SPLITTING
IF (LEAST_ll(HSPLITTING='B')) THEN
IXMODEB_ll = IIUB_ll - 2
ELSE
IXMODEB_ll = IIUB_ll
END IF
!JUAN Z_SPLITTING
!
!
DO JI = 1,IXMODE_ll
ZEIGENX_ll(JI) = - ( 2. *SIN (0.5*REAL(JI-1)*ZGWNX ) / PDXHATM )**2
END DO
END SELECT
!
!* 7.1.2 compute the eventual eigenvalues along the y direction
!
IF (.NOT. L2D) THEN
!
! y lateral boundary conditions for three-dimensional cases
!
SELECT CASE (HLBCY(1))
! in the cyclic case, the eigenvalues are the same for two following JN values:
! it corresponds to the real and complex parts of the FFT result
!
CASE('CYCL') ! 3D cyclic case
IYMODE_ll = IJMAX_ll+2
IYMODEY_ll = IJUY_ll
IYMODEB_ll = IJUB_ll !JUAN Z_SPLITTING
!
DO JJ = 1,IYMODE_ll
DO JI = 1,IXMODE_ll
ZEIGEN_ll(JI,JJ) = ZEIGENX_ll(JI) - &
( 2.* SIN ( (JJ-1)/2*ZGWNY ) / PDYHATM )**2
END DO
END DO
!
CASE DEFAULT ! 3D non-cyclic cases
IYMODE_ll = IJMAX_ll
IYMODEY_ll = IJUY_ll - 2
IYMODEB_ll = IJUB_ll - 2 !JUAN Z_SPLITTING
!
DO JJ = 1,IYMODE_ll
DO JI = 1,IXMODE_ll
ZEIGEN_ll(JI,JJ) = ZEIGENX_ll(JI) - ( 2.* SIN (0.5*REAL(JJ-1)*ZGWNY ) / &
PDYHATM )**2
END DO
END DO
!
END SELECT
ELSE
!
! copy the x eigenvalue array in a 2D array for a 2D case
!
IYMODE_ll = 1
IYMODEY_ll = 1
ZEIGEN_ll(1:IXMODE_ll,1)=ZEIGENX_ll(1:IXMODE_ll)
!
END IF
!
DEALLOCATE(ZEIGENX_ll)
!
!* 7.2 compute the matrix diagonal elements
!
!
PBFY = 1.
PBFB = 1. ! JUAN Z_SLIDE
PBF_SXP2_YP1_Z = 1. ! JUAN Z_SLIDE
!
IF (L2D) THEN
DO JK= IKB,IKE
DO JJ= 1, IYMODEY_ll
DO JI= 1, IXMODEY_ll
PBFY(JI,JJ,JK) = PRHOM(JK)* ZEIGEN_ll(JI+IORXY_ll-1,JJ+IORYY_ll-1) - 0.5 * &
( ( PRHOM(JK-1) + PRHOM(JK) ) / ZDZM(JK) **2 &
+( PRHOM(JK) + PRHOM(JK+1) ) / ZDZM(JK+1)**2 )
END DO
END DO
END DO
! at the upper and lower levels PBFY is computed using the Neumann
! condition
!
PBFY(1:IXMODEY_ll,1:IYMODEY_ll,IKB-1) = -0.5 * ( PRHOM(IKB-1) + PRHOM(IKB) ) / &
ZDZM(IKB) **2
!
PBFY(1:IXMODEY_ll,1:IYMODEY_ll,IKE+1) = 0.5 * ( PRHOM(IKE) + PRHOM(IKE+1) ) / &
ZDZM(IKE+1) **2
!
ELSE
DO JK= IKB,IKE
DO JJ= 1, IYMODEY_ll
DO JI= 1, IXMODEY_ll
PBFY(JJ,JI,JK) = PRHOM(JK)* ZEIGEN_ll(JI+IORXY_ll-1,JJ+IORYY_ll-1) - 0.5 * &
( ( PRHOM(JK-1) + PRHOM(JK) ) / ZDZM(JK) **2 &
+( PRHOM(JK) + PRHOM(JK+1) ) / ZDZM(JK+1)**2 )
END DO
END DO
END DO
! at the upper and lower levels PBFY is computed using the Neumann
! condition
!
PBFY(1:IYMODEY_ll,1:IXMODEY_ll,IKB-1) = -0.5 * ( PRHOM(IKB-1) + PRHOM(IKB) ) / &
ZDZM(IKB) **2
!
PBFY(1:IYMODEY_ll,1:IXMODEY_ll,IKE+1) = 0.5 * ( PRHOM(IKE) + PRHOM(IKE+1) ) / &
ZDZM(IKE+1) **2
!
!JUAN Z_SPLITTING
!JUAN for Z splitting we need to do the vertical substitution
!JUAN in Bsplitting slides so need PBFB
DO JK= IKB,IKE
DO JJ= IJB,IJE
DO JI= IIB, IIE
PBFB(JI,JJ,JK) = PRHOM(JK)* ZEIGEN_ll(JI+IORXB_ll-IIB_ll,JJ+IORYB_ll-IJB_ll) - 0.5 * &
( ( PRHOM(JK-1) + PRHOM(JK) ) / ZDZM(JK) **2 &
+( PRHOM(JK) + PRHOM(JK+1) ) / ZDZM(JK+1)**2 )
END DO
END DO
END DO
! at the upper and lower levels PBFB is computed using the Neumann
! condition
!
PBFB(IIB:IIE,IJB:IJE,IKB-1) = -0.5 * ( PRHOM(IKB-1) + PRHOM(IKB) ) / &
ZDZM(IKB) **2
!
PBFB(IIB:IIE,IJB:IJE,IKE+1) = 0.5 * ( PRHOM(IKE) + PRHOM(IKE+1) ) / &
ZDZM(IKE+1) **2
!
IF (HLBCX(1) == 'CYCL' .AND. .NOT.(L2D) ) THEN
!JUAN
! fil unused 2 coef with NI+1 coef (lost in Z transposition elsewhere )
JI = IXMODE_ll -1
ZEIGEN_ll(2,:) = ZEIGEN_ll(JI,:)
END IF
IF (HLBCY(1) == 'CYCL' .AND. .NOT.(L2D) ) THEN
!JUAN
! fill unused (:,2,:) coef with NJ+1 coef (lost in Z transposition elsewhere )
JJ = IYMODE_ll -1
ZEIGEN_ll(:,2) = ZEIGEN_ll(:,JJ)
END IF
!
!JUAN Z_SPLITTING
!JUAN Z_SPLITTING
!JUAN for Z splitting we need to do the vertical substitution
!JUAN in _SXP2_YP1_Zsplitting slides so need PBF_SXP2_YP1_Z
DO JK=IKB,IKE
DO JJ= 1, IJU_SXP2_YP1_Z_ll
DO JI= 1, IIU_SXP2_YP1_Z_ll
PBF_SXP2_YP1_Z(JI,JJ,JK) = PRHOM(JK)* ZEIGEN_ll(JI+IORX_SXP2_YP1_Z_ll-IIB_ll,JJ+IORY_SXP2_YP1_Z_ll-IJB_ll) - 0.5 * &
( ( PRHOM(JK-1) + PRHOM(JK) ) / ZDZM(JK) **2 &
+( PRHOM(JK) + PRHOM(JK+1) ) / ZDZM(JK+1)**2 )
END DO
END DO
END DO
! at the upper and lower levels PBFB is computed using the Neumann
! condition
!
PBF_SXP2_YP1_Z(1:IIU_SXP2_YP1_Z_ll,1:IJU_SXP2_YP1_Z_ll,IKB-1) = -0.5 * ( PRHOM(IKB-1) + PRHOM(IKB) ) / &
ZDZM(IKB) **2
!
PBF_SXP2_YP1_Z(1:IIU_SXP2_YP1_Z_ll,1:IJU_SXP2_YP1_Z_ll,IKE+1) = 0.5 * ( PRHOM(IKE) + PRHOM(IKE+1) ) / &
ZDZM(IKE+1) **2
!
!JUAN Z_SPLITTING
END IF
!
! second coefficent is meaningless in cyclic case
IF (HLBCX(1) == 'CYCL' .AND. L2D .AND. SIZE(PBFY,1) .GE. 2 ) PBFY(2,:,:)=1.
IF (HLBCX(1) == 'CYCL' .AND. .NOT.(L2D) .AND. LWEST_ll(HSPLITTING='Y') .AND. SIZE(PBFY,2) .GE.2 ) &
PBFY(:,2,:)=1.
IF (HLBCY(1) == 'CYCL' .AND. .NOT.(L2D) .AND. SIZE(PBFY,1) .GE. 2 ) PBFY(2,:,:)=1.
!JUAN Z_SPLITTING
! second coefficent is meaningless in cyclic case
IF (HLBCX(1) == 'CYCL' .AND. L2D .AND. SIZE(PBFB,1) .GE. 2 ) PBFB(2,:,:)=1.
IF (HLBCX(1) == 'CYCL' .AND. .NOT.(L2D) .AND. LWEST_ll(HSPLITTING='B') .AND. SIZE(PBFB,2) .GE.2 ) &
PBFB(:,2,:)=1.
IF (HLBCY(1) == 'CYCL' .AND. .NOT.(L2D) .AND. SIZE(PBFB,1) .GE. 2 ) PBFB(2,:,:)=1.
!JUAN Z_SPLITTING
!
DEALLOCATE(ZEIGEN_ll)
!
!
!------------------------------------------------------------------------------
!* 8. INITIALIZATION OF THE TRIGS AND IFAX ARRAYS FOR THE FFT
! -------------------------------------------------------
!
! 8.1 x lateral boundary conditions
!
CALL SET99(PTRIGSX,KIFAXX,IIMAX_ll)
!
! test on the value of KIMAX: KIMAX must be factorizable as a product
! of powers of 2,3 and 5. KIFAXX(10) is equal to IIMAX if the decomposition
! is correct, then KIFAXX(1) contains the number of decomposition factors
! of KIMAX.
!
IF (KIFAXX(10) /= IIMAX_ll) THEN
WRITE(UNIT=ILUOUT,FMT="(' ERROR',/, &
&' : THE FORM OF THE FFT USED FOR THE INVERSION OF THE FLAT ',/,&
&' OPERATOR REQUIRES THAT KIMAX MUST BE FACTORIZABLE' ,/,&
& ' AS A PRODUCT OF POWERS OF 2, 3 AND 5.')")
!callabortstop
CALL CLOSE_ll(HLUOUT,IOSTAT=IRESP)
CALL ABORT
STOP
END IF
!
IF (HLBCX(1) /= 'CYCL') THEN
!
! extra trigs for shifted (co) sine transform (FFT55)
!
INN=2*(IIMAX_ll)
ZDEL=ASIN(1.0)/REAL(IIMAX_ll)
DO JI=1,IIMAX_ll
ZANGLE=REAL(JI)*ZDEL
PTRIGSX(INN+JI)=SIN(ZANGLE)
END DO
!
ENDIF
!
! 8.2 y lateral boundary conditions
!
IF (.NOT. L2D) THEN
CALL SET99(PTRIGSY,KIFAXY,IJMAX_ll)
!
! test on the value of KJMAX: KJMAX must be factorizable as a product
! of powers of 2,3 and 5. KIFAXY(10) is equal to IJMAX_ll if the decomposition
! is correct, then KIFAXX(1) contains the number of decomposition factors
! of IIMAX_ll.
!
IF (KIFAXY(10) /= IJMAX_ll) THEN
WRITE(UNIT=ILUOUT,FMT="(' ERROR',/, &
&' : THE FORM OF THE FFT USED FOR THE INVERSION OF THE FLAT ',/,&
&' OPERATOR REQUIRES THAT KJMAX MUST BE FACTORIZABLE' ,/,&
& ' AS A PRODUCT OF POWERS OF 2, 3 AND 5.')")
!callabortstop
CALL CLOSE_ll(HLUOUT,IOSTAT=IRESP)
CALL ABORT
STOP
END IF
!
!
! other cases
!
IF (HLBCY(1) /= 'CYCL') THEN
!
! extra trigs for shifted (co) sine transform
!
INN=2*(IJMAX_ll)
ZDEL=ASIN(1.0)/REAL(IJMAX_ll)
DO JJ=1,IJMAX_ll
ZANGLE=REAL(JJ)*ZDEL
PTRIGSY(INN+JJ)=SIN(ZANGLE)
END DO
!
ENDIF
!
ENDIF
!
!------------------------------------------------------------------------------
!
END SUBROUTINE TRIDZ