Changeset 143


Ignore:
Timestamp:
Dec 28, 2007 9:44:53 AM (14 years ago)
Author:
raasch
Message:

first preliminary update for turbulent inflow

Location:
palm/trunk/SOURCE
Files:
8 edited

Legend:

Unmodified
Added
Removed
  • palm/trunk/SOURCE/CURRENT_MODIFICATIONS

    r142 r143  
    11New:
    22---
     3Within a job chain, the number of processors or the virtual processor grid
     4is now allowed to be changed. This modifies the domain decomposition and
     5requires that the PEs within a restart job have to know from which file(s) they
     6have to read their restart data (up to now there is a one to one relation
     7between the restart files and the PEs, i.e. processor 4 only reads data
     8from file "_0004"). Informations about the subdomain index limits of all
     9restart files are now written by PE0 (to file "_0000"). Also, all variables
     10containing global values which do not depend on the subdomain are written
     11to file "_0000" only. In a restart run, this file is opened by all PEs to
     12read these global values and the informations about the subdomain index
     13limits. Depending on these index limit information it is decided which
     14restart file(s) has/have to be opened in order to read the complete data
     15necessary for the current subdomain.
    316
     17check_open, read_var_list, read_3d_binary, write_3d_binary
    418
    519
    620Changed:
    721-------
     22-cross_ts_* (read_var_list, write_var_list)
     23-dopr_time_count, old profil parameters (cross_..., dopr_crossindex,
     24 profile_***) removed (read_3d_binary, write_3d_binary)
    825
     26hom_sum moved, volume_flow_area, volume_flow_initial moved from ..._3d_binary
     27to ..._var_list, hom_sum is now allocated in parin instead of init_3d_model
     28
     29init_3d_model, parin, read_var_list, read_3d_binary, write_var_list, write_3d_binary
    930
    1031
    1132Errors:
    1233------
     34Bugfix: remove IF statement in plant_canopy_model_ij (plant_canopy_model)
     35Bugfix: divide sums(k,8) (e) and sums(k,34) (e*) by ngp_2dh_s_inner(k,sr)
     36(like other scalars) (flow_statistics)
     37Bugfix: dopr_time_count was written on the binary file, which caused that
     38NetCDF files newly created by restart files (no append of existing files!)
     39contained uneccessary time levels. (read_3d_binary, write_3d_binary)
    1340
    14 Bugfix: remove IF statement in plant_canopy_model_ij
    15 Bugfix: divide sums(k,8) (e) and sums(k,34) (e*) by ngp_2dh_s_inner(k,sr)
    16 (like other scalars)
     41flow_statistics, plant_canopy_model, read_3d_binary, write_3d_binary
    1742
    18 flow_statistics, plant_canopy_model
    19 
  • palm/trunk/SOURCE/check_open.f90

    r139 r143  
    44! Actual revisions:
    55! -----------------
    6 !
     6! First opening of unit 13 openes file _0000 on all PEs (parallel version)
     7! because only this file contains the global variables
    78!
    89! Former revisions:
     
    9293    IF ( openfile(file_id)%opened_before )  THEN
    9394       SELECT CASE ( file_id )
    94           CASE ( 14, 21, 22, 23, 80:85 )
     95          CASE ( 13, 14, 21, 22, 23, 80:85 )
    9596             IF ( file_id == 14 .AND. openfile(file_id)%opened_before )  THEN
    9697                IF ( myid == 0 )  PRINT*, '+++ check_open: re-open of unit ', &
    9798                                   ' 14 is not verified. Please check results!'
    9899             ENDIF
    99              CONTINUE
     100
    100101          CASE DEFAULT
    101102             IF ( myid == 0 )  THEN
     
    104105             ENDIF
    105106             RETURN
     107
    106108       END SELECT
    107109    ENDIF
     
    162164                        FORM='UNFORMATTED', STATUS='OLD' )
    163165          ELSE
    164              OPEN ( 13, FILE='BININ'//TRIM( coupling_char )//'/'//myid_char, &
    165                         FORM='UNFORMATTED', STATUS='OLD' )
     166!
     167!--          First opening of unit 13 openes file _0000 on all PEs because only
     168!--          this file contains the global variables
     169             IF ( .NOT. openfile(file_id)%opened_before )  THEN
     170                OPEN ( 13, FILE='BININ'//TRIM( coupling_char )//'/_0000',&
     171                           FORM='UNFORMATTED', STATUS='OLD' )
     172             ELSE
     173                OPEN ( 13, FILE='BININ'//TRIM( coupling_char )//'/'//myid_char,&
     174                           FORM='UNFORMATTED', STATUS='OLD' )
     175             ENDIF
    166176          ENDIF
    167177
  • palm/trunk/SOURCE/init_3d_model.f90

    r139 r143  
    77! Actual revisions:
    88! -----------------
    9 !
     9! Allocation of hom_sum moved to parin
    1010!
    1111! Former revisions:
     
    101101              sums_divold_l(0:statistic_regions) )
    102102    ALLOCATE( rdf(nzb+1:nzt) )
    103     ALLOCATE( hom_sum(nzb:nzt+1,pr_palm+max_pr_user,0:statistic_regions),   &
    104               ngp_2dh_outer(nzb:nzt+1,0:statistic_regions),                 &
     103    ALLOCATE( ngp_2dh_outer(nzb:nzt+1,0:statistic_regions),                 &
    105104              ngp_2dh_outer_l(nzb:nzt+1,0:statistic_regions),               &
    106105              ngp_2dh_s_inner(nzb:nzt+1,0:statistic_regions),               &
  • palm/trunk/SOURCE/parin.f90

    r139 r143  
    44! Actual revisions:
    55! -----------------
    6 !
     6! Allocation of hom_sum moved from init_3d_model to here
    77!
    88! Former revisions:
     
    243243
    244244       ALLOCATE( ug(0:nz+1), vg(0:nz+1), &
    245                  pt_init(0:nz+1), q_init(0:nz+1), sa_init(0:nz+1), &
    246                  u_init(0:nz+1), v_init(0:nz+1),                   &
    247                  hom(0:nz+1,2,pr_palm+max_pr_user,0:statistic_regions) )
     245                 pt_init(0:nz+1), q_init(0:nz+1), sa_init(0:nz+1),          &
     246                 u_init(0:nz+1), v_init(0:nz+1),                            &
     247                 hom(0:nz+1,2,pr_palm+max_pr_user,0:statistic_regions),     &
     248                 hom_sum(nzb:nzt+1,pr_palm+max_pr_user,0:statistic_regions) )
    248249       hom = 0.0
    249250
  • palm/trunk/SOURCE/read_3d_binary.f90

    r110 r143  
    44! Actual revisions:
    55! -----------------
    6 !
     6! Restart file has to be re-opened on all PEs except PE0
     7! -dopr_time_count,
     8! hom_sum moved, volume_flow_area, volume_flow_initial moved to read_var_list,
     9! reading of old profil parameters (cross_..., dopr_crossindex, profile_***)
     10! removed
    711!
    812! Former revisions:
     
    5458    CHARACTER (LEN=10) ::  binary_version, version_on_file
    5559    CHARACTER (LEN=20) ::  field_chr
    56     CHARACTER (LEN=10),  DIMENSION(:), ALLOCATABLE ::  chdum10
    57     CHARACTER (LEN=40),  DIMENSION(:), ALLOCATABLE ::  chdum40
    58     CHARACTER (LEN=100), DIMENSION(:), ALLOCATABLE ::  chdum100
    5960
    6061    INTEGER ::  idum1, myid_on_file, numprocs_on_file, nxl_on_file, &
    6162                nxr_on_file, nyn_on_file, nys_on_file, nzb_on_file, nzt_on_file
    6263
    63     INTEGER, DIMENSION(:), ALLOCATABLE ::  idum
    64 
    65     REAL, DIMENSION(:), ALLOCATABLE ::  rdum
    66 
    6764!
    6865!-- Read data from previous model run. unit 13 already opened in parin
    6966    CALL cpu_log( log_point_s(14), 'read_3d_binary', 'start' )
     67
     68!
     69!-- Restart file has to be re-opened on all PEs except PE0
     70    CALL check_open( 13 )
    7071
    7172!
     
    173174       CALL local_stop
    174175    ENDIF
    175 
    176 !
    177 !-- Local arrays that may be required for possible temporary information
    178 !-- storage in the following
    179     ALLOCATE( chdum10(crmax), chdum40(crmax), chdum100(crmax), &
    180               idum(100*crmax), rdum(100*crmax) )
    181176
    182177!
     
    304299          CASE ( 'shf_m' )
    305300             READ ( 13 )  shf_m
    306           CASE ( 'tswst' )
    307              READ ( 13 )  tswst
    308           CASE ( 'tswst_m' )
    309              READ ( 13 )  tswst_m
    310301          CASE ( 'spectrum_x' )
    311302             READ ( 13 )  spectrum_x
     
    317308             ALLOCATE( ts_av(nys-1:nyn+1,nxl-1:nxr+1) )
    318309             READ ( 13 )  ts_av
     310          CASE ( 'tswst' )
     311             READ ( 13 )  tswst
     312          CASE ( 'tswst_m' )
     313             READ ( 13 )  tswst_m
    319314          CASE ( 'u' )
    320315             READ ( 13 )  u
     
    347342          CASE ( 'v' )
    348343             READ ( 13 )  v
    349           CASE ( 'volume_flow_area' )
    350              READ ( 13 )  volume_flow_area
    351           CASE ( 'volume_flow_initial' )
    352              READ ( 13 )  volume_flow_initial
    353344          CASE ( 'v_av' )
    354345             ALLOCATE( v_av(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) )
     
    400391             READ ( 13 )  z0_av
    401392
    402           CASE ( 'cross_linecolors' )
    403              IF ( use_prior_plot1d_parameters )  THEN
    404                 READ ( 13 )  cross_linecolors
    405              ELSE
    406                 READ ( 13 )  idum
    407              ENDIF
    408           CASE ( 'cross_linestyles' )
    409              IF ( use_prior_plot1d_parameters )  THEN
    410                 READ ( 13 )  cross_linestyles
    411              ELSE
    412                 READ ( 13 )  idum
    413              ENDIF
    414           CASE ( 'cross_normalized_x' )
    415              IF ( use_prior_plot1d_parameters )  THEN
    416                 READ ( 13 )  cross_normalized_x
    417              ELSE
    418                 READ ( 13 )  chdum10
    419              ENDIF
    420           CASE ( 'cross_normalized_y' )
    421              IF ( use_prior_plot1d_parameters )  THEN
    422                 READ ( 13 )  cross_normalized_y
    423              ELSE
    424                 READ ( 13 )  chdum10
    425              ENDIF
    426           CASE ( 'cross_normx_factor' )
    427              IF ( use_prior_plot1d_parameters )  THEN
    428                 READ ( 13 )  cross_normx_factor
    429              ELSE
    430                 READ ( 13 )  rdum
    431              ENDIF
    432           CASE ( 'cross_normy_factor' )
    433              IF ( use_prior_plot1d_parameters )  THEN
    434                 READ ( 13 )  cross_normy_factor
    435              ELSE
    436                 READ ( 13 )  rdum
    437              ENDIF
    438           CASE ( 'cross_profiles' )
    439              IF ( use_prior_plot1d_parameters )  THEN
    440                 READ ( 13 )  cross_profiles
    441              ELSE
    442                 READ ( 13 )  chdum100
    443              ENDIF
    444           CASE ( 'cross_profile_n_coun' )
    445              IF ( use_prior_plot1d_parameters )  THEN
    446                 READ ( 13 )  cross_profile_number_count
    447              ELSE
    448                 READ ( 13 )  idum(1:crmax)
    449              ENDIF
    450           CASE ( 'cross_profile_number' )
    451              IF ( use_prior_plot1d_parameters )  THEN
    452                 READ ( 13 )  cross_profile_numbers
    453              ELSE
    454                 READ ( 13 )  idum
    455              ENDIF
    456           CASE ( 'cross_uxmax' )
    457              IF ( use_prior_plot1d_parameters )  THEN
    458                 READ ( 13 )  cross_uxmax
    459              ELSE
    460                 READ ( 13 )  rdum(1:crmax)
    461              ENDIF
    462           CASE ( 'cross_uxmax_computed' )
    463              IF ( use_prior_plot1d_parameters )  THEN
    464                 READ ( 13 )  cross_uxmax_computed
    465              ELSE
    466                 READ ( 13 )  rdum(1:crmax)
    467              ENDIF
    468           CASE ( 'cross_uxmax_normaliz' )
    469              IF ( use_prior_plot1d_parameters )  THEN
    470                 READ ( 13 )  cross_uxmax_normalized
    471              ELSE
    472                 READ ( 13 )  rdum(1:crmax)
    473              ENDIF
    474           CASE ( 'cross_uxmax_norm_com' )
    475              IF ( use_prior_plot1d_parameters )  THEN
    476                 READ ( 13 )  cross_uxmax_normalized_computed
    477              ELSE
    478                 READ ( 13 )  rdum(1:crmax)
    479              ENDIF
    480           CASE ( 'cross_uxmin' )
    481              IF ( use_prior_plot1d_parameters )  THEN
    482                 READ ( 13 )  cross_uxmin
    483              ELSE
    484                 READ ( 13 )  rdum(1:crmax)
    485              ENDIF
    486           CASE ( 'cross_uxmin_computed' )
    487              IF ( use_prior_plot1d_parameters )  THEN
    488                 READ ( 13 )  cross_uxmin_computed
    489              ELSE
    490                 READ ( 13 )  rdum(1:crmax)
    491              ENDIF
    492           CASE ( 'cross_uxmin_normaliz' )
    493              IF ( use_prior_plot1d_parameters )  THEN
    494                 READ ( 13 )  cross_uxmin_normalized
    495              ELSE
    496                 READ ( 13 )  rdum(1:crmax)
    497              ENDIF
    498           CASE ( 'cross_uxmin_norm_com' )
    499              IF ( use_prior_plot1d_parameters )  THEN
    500                 READ ( 13 )  cross_uxmin_normalized_computed
    501              ELSE
    502                 READ ( 13 )  rdum(1:crmax)
    503              ENDIF
    504           CASE ( 'cross_uymax' )
    505              IF ( use_prior_plot1d_parameters )  THEN
    506                 READ ( 13 )  cross_uymax
    507              ELSE
    508                 READ ( 13 )  rdum(1:crmax)
    509              ENDIF
    510           CASE ( 'cross_uymin' )
    511              IF ( use_prior_plot1d_parameters )  THEN
    512                 READ ( 13 )  cross_uymin
    513              ELSE
    514                 READ ( 13 )  rdum(1:crmax)
    515              ENDIF
    516           CASE ( 'cross_xtext' )
    517              IF ( use_prior_plot1d_parameters )  THEN
    518                 READ ( 13 )  cross_xtext
    519              ELSE
    520                 READ ( 13 )  chdum40
    521              ENDIF
    522           CASE ( 'dopr_crossindex' )
    523              IF ( use_prior_plot1d_parameters )  THEN
    524                 READ ( 13 )  dopr_crossindex
    525              ELSE
    526                 READ ( 13 )  idum(1:100)
    527              ENDIF
    528           CASE ( 'dopr_time_count' )
    529              IF ( use_prior_plot1d_parameters )  THEN
    530                 READ ( 13 )  dopr_time_count
    531              ELSE
    532                 READ ( 13 )  idum1
    533              ENDIF
    534           CASE ( 'hom_sum' )
    535              READ ( 13 )  hom_sum
    536           CASE ( 'profile_columns' )
    537              IF ( use_prior_plot1d_parameters )  THEN
    538                 READ ( 13 )  profile_columns
    539              ELSE
    540                 READ ( 13 )  idum1
    541              ENDIF
    542           CASE ( 'profile_number' )
    543              IF ( use_prior_plot1d_parameters )  THEN
    544                 READ ( 13 )  profile_number
    545              ELSE
    546                 READ ( 13 )  idum1
    547              ENDIF
    548           CASE ( 'profile_rows' )
    549              IF ( use_prior_plot1d_parameters )  THEN
    550                 READ ( 13 )  profile_rows
    551              ELSE
    552                 READ ( 13 )  idum1
    553              ENDIF
    554 
    555393          CASE DEFAULT
    556394             PRINT*, '+++ init_3d_model: unknown field named "', &
     
    566404    ENDDO
    567405
    568     DEALLOCATE( chdum10, chdum40, chdum100, idum, rdum )
    569 
    570406!
    571407!-- End of time measuring for reading binary data
  • palm/trunk/SOURCE/read_var_list.f90

    r139 r143  
    44! Actual revisions:
    55! -----------------
    6 !
     6! After reading the global variables, unit 13 is closed for all PEs except PE0
     7! -cross_ts_*,
     8! hom_sum moved, volume_flow_area, volume_flow_initial moved from
     9! read_3d_binary to here
    710!
    811! Former revisions:
     
    4245! Description:
    4346! ------------
    44 ! Reading values of control variables from restart-file (binary format)
     47! Reading values of global control variables from restart-file (binary format)
    4548!------------------------------------------------------------------------------!
    4649
     
    6265
    6366    INTEGER            ::  max_pr_user_on_file
    64    
     67
     68
    6569    CALL check_open( 13 )
    6670
     
    245249          CASE ( 'hom' )
    246250             READ ( 13 )  hom
     251          CASE ( 'hom_sum' )
     252             READ ( 13 )  hom_sum
    247253          CASE ( 'inflow_disturbance_begin' )
    248254             READ ( 13 )  inflow_disturbance_begin
     
    485491          CASE ( 'vg_vertical_gradient_level_ind' )
    486492             READ ( 13 )  vg_vertical_gradient_level_ind
     493          CASE ( 'volume_flow_area' )
     494             READ ( 13 )  volume_flow_area
     495          CASE ( 'volume_flow_initial' )
     496             READ ( 13 )  volume_flow_initial
    487497          CASE ( 'wall_adjustment' )
    488498             READ ( 13 )  wall_adjustment
     
    491501          CASE ( 'w_max_ijk' )
    492502             READ ( 13 )  w_max_ijk
    493           CASE ( 'time-series-quantities' )
    494              READ ( 13 )  cross_ts_uymax, cross_ts_uymax_computed, &
    495                           cross_ts_uymin, cross_ts_uymin_computed
    496503
    497504          CASE DEFAULT
     
    507514    ENDDO
    508515
     516    IF ( myid /= 0 )  CALL close_file( 13 )
     517
    509518
    510519 END SUBROUTINE read_var_list
  • palm/trunk/SOURCE/write_3d_binary.f90

    r110 r143  
    44! Actual revisions:
    55! -----------------
    6 !
     6! write_var_list is only called for pe0
     7! -dopr_time_count,
     8! hom_sum moved, volume_flow_area, volume_flow_initial moved to write_var_list,
     9! writing of old profil parameters (cross_..., dopr_crossindex, profile_***)
     10! removed
    711!
    812! Former revisions:
     
    6165!
    6266!-- Write control parameters and other variables for restart.
    63     CALL write_var_list
     67    IF ( myid == 0 )  CALL write_var_list
    6468
    6569!
     
    177181       WRITE ( 14 )  'shf_m               ';  WRITE ( 14 )  shf_m
    178182    ENDIF
     183    IF ( ALLOCATED( spectrum_x ) )  THEN
     184       WRITE ( 14 )  'spectrum_x          ';  WRITE ( 14 )  spectrum_x
     185       WRITE ( 14 )  'spectrum_y          ';  WRITE ( 14 )  spectrum_y
     186    ENDIF
    179187    WRITE ( 14 )  'ts                  ';  WRITE ( 14 )  ts
    180188    IF ( ALLOCATED( ts_av ) )  THEN
     
    213221    ENDIF
    214222    WRITE ( 14 )  'v                   ';  WRITE ( 14 )  v
    215     WRITE ( 14 )  'volume_flow_area    ';  WRITE ( 14 )  volume_flow_area
    216     WRITE ( 14 )  'volume_flow_initial ';  WRITE ( 14 )  volume_flow_initial
    217223    IF ( ALLOCATED( v_av ) )  THEN
    218224       WRITE ( 14 )  'v_av                ';  WRITE ( 14 )  v_av
     
    268274    ENDIF
    269275
    270     WRITE ( 14 )  'cross_linecolors    ';  WRITE ( 14 )  cross_linecolors
    271     WRITE ( 14 )  'cross_linestyles    ';  WRITE ( 14 )  cross_linestyles
    272     WRITE ( 14 )  'cross_normalized_x  ';  WRITE ( 14 )  cross_normalized_x
    273     WRITE ( 14 )  'cross_normalized_y  ';  WRITE ( 14 )  cross_normalized_y
    274     WRITE ( 14 )  'cross_normx_factor  ';  WRITE ( 14 )  cross_normx_factor
    275     WRITE ( 14 )  'cross_normy_factor  ';  WRITE ( 14 )  cross_normy_factor
    276     WRITE ( 14 )  'cross_profiles      ';  WRITE ( 14 )  cross_profiles
    277     WRITE ( 14 )  'cross_profile_n_coun'
    278                   WRITE ( 14 )  cross_profile_number_count
    279     WRITE ( 14 )  'cross_profile_number';  WRITE ( 14 )  cross_profile_numbers
    280     WRITE ( 14 )  'cross_uxmax         ';  WRITE ( 14 )  cross_uxmax
    281     WRITE ( 14 )  'cross_uxmax_computed';  WRITE ( 14 )  cross_uxmax_computed
    282     WRITE ( 14 )  'cross_uxmax_normaliz';  WRITE ( 14 )  cross_uxmax_normalized
    283     WRITE ( 14 )  'cross_uxmax_norm_com'
    284                   WRITE ( 14 )  cross_uxmax_normalized_computed
    285     WRITE ( 14 )  'cross_uxmin         ';  WRITE ( 14 )  cross_uxmin
    286     WRITE ( 14 )  'cross_uxmin_computed';  WRITE ( 14 )  cross_uxmin_computed
    287     WRITE ( 14 )  'cross_uxmin_normaliz';  WRITE ( 14 )  cross_uxmin_normalized
    288     WRITE ( 14 )  'cross_uxmin_norm_com'
    289                   WRITE ( 14 )  cross_uxmin_normalized_computed
    290     WRITE ( 14 )  'cross_uymax         ';  WRITE ( 14 )  cross_uymax
    291     WRITE ( 14 )  'cross_uymin         ';  WRITE ( 14 )  cross_uymin
    292     WRITE ( 14 )  'cross_xtext         ';  WRITE ( 14 )  cross_xtext
    293     WRITE ( 14 )  'dopr_crossindex     ';  WRITE ( 14 )  dopr_crossindex
    294     WRITE ( 14 )  'dopr_time_count     ';  WRITE ( 14 )  dopr_time_count
    295     WRITE ( 14 )  'hom_sum             ';  WRITE ( 14 )  hom_sum
    296     WRITE ( 14 )  'profile_columns     ';  WRITE ( 14 )  profile_columns
    297     WRITE ( 14 )  'profile_number      ';  WRITE ( 14 )  profile_number
    298     WRITE ( 14 )  'profile_rows        ';  WRITE ( 14 )  profile_rows
    299     IF ( ALLOCATED( spectrum_x ) )  THEN
    300        WRITE ( 14 )  'spectrum_x          ';  WRITE ( 14 )  spectrum_x
    301        WRITE ( 14 )  'spectrum_y          ';  WRITE ( 14 )  spectrum_y
    302     ENDIF
    303 
    304276!
    305277!-- Write end label. Unit 14 is closed in the main program.
  • palm/trunk/SOURCE/write_var_list.f90

    r139 r143  
    44! Actual revisions:
    55! -----------------
    6 !
     6! -cross_ts_*,
     7! hom_sum, volume_flow_area, volume_flow_initial moved from write_3d_binary
     8! to here
    79!
    810! Former revisions:
     
    191193    WRITE ( 14 )  'hom                           '
    192194    WRITE ( 14 )  hom
     195    WRITE ( 14 )  'hom_sum                       '
     196    WRITE ( 14 )  hom_sum
    193197    WRITE ( 14 )  'inflow_disturbance_begin      '
    194198    WRITE ( 14 )  inflow_disturbance_begin
     
    431435    WRITE ( 14 )  'vg_vertical_gradient_level_ind'
    432436    WRITE ( 14 )  vg_vertical_gradient_level_ind
     437    WRITE ( 14 )  'volume_flow_area              '
     438    WRITE ( 14 )  volume_flow_area
     439    WRITE ( 14 )  'volume_flow_initial           '
     440    WRITE ( 14 )  volume_flow_initial
    433441    WRITE ( 14 )  'wall_adjustment               '
    434442    WRITE ( 14 )  wall_adjustment
     
    437445    WRITE ( 14 )  'w_max_ijk                     '
    438446    WRITE ( 14 )  w_max_ijk
    439     WRITE ( 14 )  'time-series-quantities        '
    440     WRITE ( 14 )  cross_ts_uymax, cross_ts_uymax_computed, cross_ts_uymin, &
    441                   cross_ts_uymin_computed
    442447
    443448!
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