source: palm/trunk/SOURCE/lpm_init.f90 @ 1314

 SUBROUTINE lpm_init

!--------------------------------------------------------------------------------!
! This file is part of PALM.
!
! PALM is free software: you can redistribute it and/or modify it under the terms
! of the GNU General Public License as published by the Free Software Foundation,
! either version 3 of the License, or (at your option) any later version.
!
! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
! A PARTICULAR PURPOSE.  See the GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License along with
! PALM. If not, see <http://www.gnu.org/licenses/>.
!
! Copyright 1997-2014 Leibniz Universitaet Hannover
!--------------------------------------------------------------------------------!
!
! Current revisions:
! -----------------
! Vertical logarithmic interpolation of horizontal particle speed for particles 
! between roughness height and first vertical grid level.
!
! Former revisions:
! -----------------
! $Id: lpm_init.f90 1314 2014-03-14 18:25:17Z suehring $
!
! 1092 2013-02-02 11:24:22Z raasch
! unused variables removed
!
! 1036 2012-10-22 13:43:42Z raasch
! code put under GPL (PALM 3.9)
!
! 849 2012-03-15 10:35:09Z raasch
! routine renamed: init_particles -> lpm_init
! de_dx, de_dy, de_dz are allocated here (instead of automatic arrays in
! advec_particles),
! sort_particles renamed lpm_sort_arrays, user_init_particles renamed lpm_init
!
! 828 2012-02-21 12:00:36Z raasch
! call of init_kernels, particle feature color renamed class
!
! 824 2012-02-17 09:09:57Z raasch
! particle attributes speed_x|y|z_sgs renamed rvar1|2|3,
! array particles implemented as pointer
!
! 667 2010-12-23 12:06:00Z suehring/gryschka
! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng for allocation 
! of arrays.
!
! 622 2010-12-10 08:08:13Z raasch
! optional barriers included in order to speed up collective operations
!
! 336 2009-06-10 11:19:35Z raasch
! Maximum number of tails is calculated from maximum number of particles and
! skip_particles_for_tail,
! output of messages replaced by message handling routine
! Bugfix: arrays for tails are allocated with a minimum size of 10 tails if
! there is no tail initially
!
! 150 2008-02-29 08:19:58Z raasch
! Setting offset_ocean_* needed for calculating vertical indices within ocean
! runs
!
! 117 2007-10-11 03:27:59Z raasch
! Sorting of particles only in case of cloud droplets
!
! 106 2007-08-16 14:30:26Z raasch
! variable iran replaced by iran_part
!
! 82 2007-04-16 15:40:52Z raasch
! Preprocessor directives for old systems removed
!
! 70 2007-03-18 23:46:30Z raasch
! displacements for mpi_particle_type changed, age_m initialized,
! particles-package is now part of the default code
!
! 16 2007-02-15 13:16:47Z raasch
! Bugfix: MPI_REAL in MPI_ALLREDUCE replaced by MPI_INTEGER
!
! r4 | raasch | 2007-02-13 12:33:16 +0100 (Tue, 13 Feb 2007)
! RCS Log replace by Id keyword, revision history cleaned up
!
! Revision 1.24  2007/02/11 13:00:17  raasch
! Bugfix: allocation of tail_mask and new_tail_id in case of restart-runs
! Bugfix: __ was missing in a cpp-directive
!
! Revision 1.1  1999/11/25 16:22:38  raasch
! Initial revision
!
!
! Description:
! ------------
! This routine initializes a set of particles and their attributes (position,
! radius, ..) which are used by the Lagrangian particle model (see lpm).
!------------------------------------------------------------------------------!

    USE arrays_3d
    USE cloud_parameters
    USE control_parameters
    USE dvrp_variables
    USE grid_variables
    USE indices
    USE lpm_collision_kernels_mod
    USE particle_attributes
    USE pegrid
    USE random_function_mod


    IMPLICIT NONE

    INTEGER ::  i, j, k, n, nn
#if defined( __parallel )
    INTEGER, DIMENSION(3) ::  blocklengths, displacements, types
#endif
    LOGICAL ::  uniform_particles_l
    REAL    ::  height_int, height_p, pos_x, pos_y, pos_z, z_p,            &
                z0_av_local = 0.0


#if defined( __parallel )
!
!-- Define MPI derived datatype for FORTRAN datatype particle_type (see module
!-- particle_attributes). Integer length is 4 byte, Real is 8 byte
    blocklengths(1)  = 19;  blocklengths(2)  =   4;  blocklengths(3)  =   1
    displacements(1) =  0;  displacements(2) = 152;  displacements(3) = 168

    types(1) = MPI_REAL
    types(2) = MPI_INTEGER
    types(3) = MPI_UB
    CALL MPI_TYPE_STRUCT( 3, blocklengths, displacements, types, &
                          mpi_particle_type, ierr )
    CALL MPI_TYPE_COMMIT( mpi_particle_type, ierr )
#endif

!
!-- In case of oceans runs, the vertical index calculations need an offset,
!-- because otherwise the k indices will become negative
    IF ( ocean )  THEN
       offset_ocean_nzt    = nzt
       offset_ocean_nzt_m1 = nzt - 1
    ENDIF


!
!-- Check the number of particle groups.
    IF ( number_of_particle_groups > max_number_of_particle_groups )  THEN
       WRITE( message_string, * ) 'max_number_of_particle_groups =',      &
                                  max_number_of_particle_groups ,         &
                                  '&number_of_particle_groups reset to ', &
                                  max_number_of_particle_groups
       CALL message( 'lpm_init', 'PA0213', 0, 1, 0, 6, 0 )
       number_of_particle_groups = max_number_of_particle_groups
    ENDIF

!
!-- Set default start positions, if necessary
    IF ( psl(1) == 9999999.9 )  psl(1) = -0.5 * dx
    IF ( psr(1) == 9999999.9 )  psr(1) = ( nx + 0.5 ) * dx
    IF ( pss(1) == 9999999.9 )  pss(1) = -0.5 * dy
    IF ( psn(1) == 9999999.9 )  psn(1) = ( ny + 0.5 ) * dy
    IF ( psb(1) == 9999999.9 )  psb(1) = zu(nz/2)
    IF ( pst(1) == 9999999.9 )  pst(1) = psb(1)

    IF ( pdx(1) == 9999999.9  .OR.  pdx(1) == 0.0 )  pdx(1) = dx
    IF ( pdy(1) == 9999999.9  .OR.  pdy(1) == 0.0 )  pdy(1) = dy
    IF ( pdz(1) == 9999999.9  .OR.  pdz(1) == 0.0 )  pdz(1) = zu(2) - zu(1)

    DO  j = 2, number_of_particle_groups
       IF ( psl(j) == 9999999.9 )  psl(j) = psl(j-1)
       IF ( psr(j) == 9999999.9 )  psr(j) = psr(j-1)
       IF ( pss(j) == 9999999.9 )  pss(j) = pss(j-1)
       IF ( psn(j) == 9999999.9 )  psn(j) = psn(j-1)
       IF ( psb(j) == 9999999.9 )  psb(j) = psb(j-1)
       IF ( pst(j) == 9999999.9 )  pst(j) = pst(j-1)
       IF ( pdx(j) == 9999999.9  .OR.  pdx(j) == 0.0 )  pdx(j) = pdx(j-1)
       IF ( pdy(j) == 9999999.9  .OR.  pdy(j) == 0.0 )  pdy(j) = pdy(j-1)
       IF ( pdz(j) == 9999999.9  .OR.  pdz(j) == 0.0 )  pdz(j) = pdz(j-1)
    ENDDO

!
!-- Allocate arrays required for calculating particle SGS velocities
    IF ( use_sgs_for_particles )  THEN
       ALLOCATE( de_dx(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
                 de_dy(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
                 de_dz(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
    ENDIF

!
!-- Allocate array required for logarithmic vertical interpolation of 
!-- horizontal particle velocities between the surface and the first vertical
!-- grid level. In order to avoid repeated CPU cost-intensive CALLS of 
!-- intrinsic FORTRAN procedure LOG(z/z0), LOG(z/z0) is precalculated for 
!-- several heights. Splitting into 20 sublayers turned out to be sufficient. 
!-- To obtain exact height levels of particles, linear interpolation is applied
!-- (see lpm_advec.f90).
    IF ( prandtl_layer )  THEN
       
       ALLOCATE ( log_z_z0(0:number_of_sublayers) ) 
       z_p         = zu(nzb+1) - zw(nzb)

!
!--    Calculate horizontal mean value of z0 used for logartihmic
!--    interpolation. Note: this is not exact for heterogeneous z0. 
!--    However, sensitivity studies showed that the effect is 
!--    negligible. 
       z0_av_local  = SUM( z0(nys:nyn,nxl:nxr) )
       z0_av_global = 0.0

       CALL MPI_ALLREDUCE(z0_av_local, z0_av_global, 1, MPI_REAL, MPI_SUM, &
                          comm2d, ierr )

       z0_av_global = z0_av_global  / ( ( ny + 1 ) * ( nx + 1 ) )
!
!--    Horizontal wind speed is zero below and at z0
       log_z_z0(0) = 0.0   
!
!--    Calculate vertical depth of the sublayers
       height_int  = ( z_p - z0_av_global ) / REAL( number_of_sublayers ) 
!
!--    Precalculate LOG(z/z0)
       height_p    = 0.0
       DO  k = 1, number_of_sublayers

          height_p    = height_p + height_int
          log_z_z0(k) = LOG( height_p / z0_av_global )

       ENDDO


    ENDIF

!
!-- Initialize collision kernels
    IF ( collision_kernel /= 'none' )  CALL init_kernels

!
!-- For the first model run of a possible job chain initialize the
!-- particles, otherwise read the particle data from restart file.
    IF ( TRIM( initializing_actions ) == 'read_restart_data'  &
         .AND.  read_particles_from_restartfile )  THEN

       CALL lpm_read_restart_file

    ELSE

!
!--    Allocate particle arrays and set attributes of the initial set of
!--    particles, which can be also periodically released at later times.
!--    Also allocate array for particle tail coordinates, if needed.
       ALLOCATE( prt_count(nzb:nzt+1,nysg:nyng,nxlg:nxrg),       &
                 prt_start_index(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
                 particle_mask(maximum_number_of_particles),     &
                 part_1(maximum_number_of_particles),            &
                 part_2(maximum_number_of_particles)  )

       particles => part_1

       sort_count = 0

!
!--    Initialize all particles with dummy values (otherwise errors may
!--    occur within restart runs). The reason for this is still not clear
!--    and may be presumably caused by errors in the respective user-interface.
       particles = particle_type( 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, &
                                  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, &
                                  0.0, 0, 0, 0, 0 )
       particle_groups = particle_groups_type( 0.0, 0.0, 0.0, 0.0 )

!
!--    Set the default particle size used for dvrp plots
       IF ( dvrp_psize == 9999999.9 )  dvrp_psize = 0.2 * dx

!
!--    Set values for the density ratio and radius for all particle
!--    groups, if necessary
       IF ( density_ratio(1) == 9999999.9 )  density_ratio(1) = 0.0
       IF ( radius(1)        == 9999999.9 )  radius(1) = 0.0
       DO  i = 2, number_of_particle_groups
          IF ( density_ratio(i) == 9999999.9 )  THEN
             density_ratio(i) = density_ratio(i-1)
          ENDIF
          IF ( radius(i) == 9999999.9 )  radius(i) = radius(i-1)
       ENDDO

       DO  i = 1, number_of_particle_groups
          IF ( density_ratio(i) /= 0.0  .AND.  radius(i) == 0 )  THEN
             WRITE( message_string, * ) 'particle group #', i, 'has a', &
                                        'density ratio /= 0 but radius = 0'
             CALL message( 'lpm_init', 'PA0215', 1, 2, 0, 6, 0 )
          ENDIF
          particle_groups(i)%density_ratio = density_ratio(i)
          particle_groups(i)%radius        = radius(i)
       ENDDO

!
!--    Calculate particle positions and store particle attributes, if
!--    particle is situated on this PE
       n = 0

       DO  i = 1, number_of_particle_groups

          pos_z = psb(i)

          DO WHILE ( pos_z <= pst(i) )

             pos_y = pss(i)

             DO WHILE ( pos_y <= psn(i) )

                IF ( pos_y >= ( nys - 0.5 ) * dy  .AND.  &
                     pos_y <  ( nyn + 0.5 ) * dy )  THEN

                   pos_x = psl(i)

                   DO WHILE ( pos_x <= psr(i) )

                      IF ( pos_x >= ( nxl - 0.5 ) * dx  .AND.  &
                           pos_x <  ( nxr + 0.5 ) * dx )  THEN

                         DO  j = 1, particles_per_point

                            n = n + 1
                            IF ( n > maximum_number_of_particles )  THEN
                               WRITE( message_string, * ) 'number of initial', &
                                      'particles (', n, ') exceeds',           &
                                      '&maximum_number_of_particles (',        &
                                      maximum_number_of_particles, ') on PE ', &
                                             myid
                               CALL message( 'lpm_init', 'PA0216', 2, 2, -1, 6,&
                                             1 )
                            ENDIF
                            particles(n)%x             = pos_x
                            particles(n)%y             = pos_y
                            particles(n)%z             = pos_z
                            particles(n)%age           = 0.0
                            particles(n)%age_m         = 0.0
                            particles(n)%dt_sum        = 0.0
                            particles(n)%dvrp_psize    = dvrp_psize
                            particles(n)%e_m           = 0.0
                            IF ( curvature_solution_effects )  THEN
!
!--                            Initial values (internal timesteps, derivative)
!--                            for Rosenbrock method
                               particles(n)%rvar1      = 1.0E-12
                               particles(n)%rvar2      = 1.0E-3
                               particles(n)%rvar3      = -9999999.9
                            ELSE
!
!--                            Initial values for SGS velocities
                               particles(n)%rvar1      = 0.0
                               particles(n)%rvar2      = 0.0
                               particles(n)%rvar3      = 0.0
                            ENDIF
                            particles(n)%speed_x       = 0.0
                            particles(n)%speed_y       = 0.0
                            particles(n)%speed_z       = 0.0
                            particles(n)%origin_x      = pos_x
                            particles(n)%origin_y      = pos_y
                            particles(n)%origin_z      = pos_z
                            particles(n)%radius      = particle_groups(i)%radius
                            particles(n)%weight_factor =initial_weighting_factor
                            particles(n)%class         = 1
                            particles(n)%group         = i
                            particles(n)%tailpoints    = 0
                            IF ( use_particle_tails  .AND. &
                                 MOD( n, skip_particles_for_tail ) == 0 )  THEN
                               number_of_tails         = number_of_tails + 1
!
!--                            This is a temporary provisional setting (see
!--                            further below!)
                               particles(n)%tail_id    = number_of_tails
                            ELSE
                               particles(n)%tail_id    = 0
                            ENDIF

                         ENDDO

                      ENDIF

                      pos_x = pos_x + pdx(i)

                   ENDDO

                ENDIF

                pos_y = pos_y + pdy(i)

             ENDDO

             pos_z = pos_z + pdz(i)

          ENDDO

       ENDDO

       number_of_initial_particles = n
       number_of_particles         = n

!
!--    Calculate the number of particles and tails of the total domain
#if defined( __parallel )
       IF ( collective_wait )  CALL MPI_BARRIER( comm2d, ierr )
       CALL MPI_ALLREDUCE( number_of_particles, total_number_of_particles, 1, &
                           MPI_INTEGER, MPI_SUM, comm2d, ierr )
       IF ( collective_wait )  CALL MPI_BARRIER( comm2d, ierr )
       CALL MPI_ALLREDUCE( number_of_tails, total_number_of_tails, 1, &
                           MPI_INTEGER, MPI_SUM, comm2d, ierr )
#else
       total_number_of_particles = number_of_particles
       total_number_of_tails     = number_of_tails
#endif

!
!--    Set a seed value for the random number generator to be exclusively
!--    used for the particle code. The generated random numbers should be
!--    different on the different PEs.
       iran_part = iran_part + myid

!
!--    User modification of initial particles
       CALL user_lpm_init

!
!--    Store the initial set of particles for release at later times
       IF ( number_of_initial_particles /= 0 )  THEN
          ALLOCATE( initial_particles(1:number_of_initial_particles) )
          initial_particles(1:number_of_initial_particles) = &
                                        particles(1:number_of_initial_particles)
       ENDIF

!
!--    Add random fluctuation to particle positions
       IF ( random_start_position )  THEN

          DO  n = 1, number_of_initial_particles
             IF ( psl(particles(n)%group) /= psr(particles(n)%group) )  THEN
                particles(n)%x = particles(n)%x + &
                                 ( random_function( iran_part ) - 0.5 ) * &
                                 pdx(particles(n)%group)
                IF ( particles(n)%x  <=  ( nxl - 0.5 ) * dx )  THEN
                   particles(n)%x = ( nxl - 0.4999999999 ) * dx
                ELSEIF ( particles(n)%x  >=  ( nxr + 0.5 ) * dx )  THEN
                   particles(n)%x = ( nxr + 0.4999999999 ) * dx
                ENDIF
             ENDIF
             IF ( pss(particles(n)%group) /= psn(particles(n)%group) )  THEN
                particles(n)%y = particles(n)%y + &
                                 ( random_function( iran_part ) - 0.5 ) * &
                                 pdy(particles(n)%group)
                IF ( particles(n)%y  <=  ( nys - 0.5 ) * dy )  THEN
                   particles(n)%y = ( nys - 0.4999999999 ) * dy
                ELSEIF ( particles(n)%y  >=  ( nyn + 0.5 ) * dy )  THEN
                   particles(n)%y = ( nyn + 0.4999999999 ) * dy
                ENDIF
             ENDIF
             IF ( psb(particles(n)%group) /= pst(particles(n)%group) )  THEN
                particles(n)%z = particles(n)%z + &
                                 ( random_function( iran_part ) - 0.5 ) * &
                                 pdz(particles(n)%group)
             ENDIF
          ENDDO
       ENDIF

!
!--    Sort particles in the sequence the gridboxes are stored in the memory.
!--    Only required if cloud droplets are used.
       IF ( cloud_droplets )  CALL lpm_sort_arrays

!
!--    Open file for statistical informations about particle conditions
       IF ( write_particle_statistics )  THEN
          CALL check_open( 80 )
          WRITE ( 80, 8000 )  current_timestep_number, simulated_time, &
                              number_of_initial_particles,             &
                              maximum_number_of_particles
          CALL close_file( 80 )
       ENDIF

!
!--    Check if particles are really uniform in color and radius (dvrp_size)
!--    (uniform_particles is preset TRUE)
       IF ( uniform_particles )  THEN
          IF ( number_of_initial_particles == 0 )  THEN
             uniform_particles_l = .TRUE.
          ELSE
             n = number_of_initial_particles
             IF ( MINVAL( particles(1:n)%dvrp_psize  ) ==     &
                  MAXVAL( particles(1:n)%dvrp_psize  )  .AND. &
                  MINVAL( particles(1:n)%class ) ==     &
                  MAXVAL( particles(1:n)%class ) )  THEN
                uniform_particles_l = .TRUE.
             ELSE
                uniform_particles_l = .FALSE.
             ENDIF
          ENDIF

#if defined( __parallel )
          IF ( collective_wait )  CALL MPI_BARRIER( comm2d, ierr )
          CALL MPI_ALLREDUCE( uniform_particles_l, uniform_particles, 1, &
                              MPI_LOGICAL, MPI_LAND, comm2d, ierr )
#else
          uniform_particles = uniform_particles_l
#endif

       ENDIF

!
!--    Particles will probably become none-uniform, if their size and color
!--    will be determined by flow variables
       IF ( particle_color /= 'none'  .OR.  particle_dvrpsize /= 'none' )  THEN
          uniform_particles = .FALSE.
       ENDIF

!
!--    Set the beginning of the particle tails and their age
       IF ( use_particle_tails )  THEN
!
!--       Choose the maximum number of tails with respect to the maximum number
!--       of particles and skip_particles_for_tail
          maximum_number_of_tails = maximum_number_of_particles / &
                                    skip_particles_for_tail

!
!--       Create a minimum number of tails in case that there is no tail
!--       initially (otherwise, index errors will occur when adressing the
!--       arrays below)
          IF ( maximum_number_of_tails == 0 )  maximum_number_of_tails = 10

          ALLOCATE( particle_tail_coordinates(maximum_number_of_tailpoints,5, &
                    maximum_number_of_tails),                                 &
                    new_tail_id(maximum_number_of_tails),                     &
                    tail_mask(maximum_number_of_tails) )

          particle_tail_coordinates  = 0.0
          minimum_tailpoint_distance = minimum_tailpoint_distance**2
          number_of_initial_tails    = number_of_tails

          nn = 0
          DO  n = 1, number_of_particles
!
!--          Only for those particles marked above with a provisional tail_id
!--          tails will be created. Particles now get their final tail_id.
             IF ( particles(n)%tail_id /= 0 )  THEN

                nn = nn + 1
                particles(n)%tail_id = nn

                particle_tail_coordinates(1,1,nn) = particles(n)%x
                particle_tail_coordinates(1,2,nn) = particles(n)%y
                particle_tail_coordinates(1,3,nn) = particles(n)%z
                particle_tail_coordinates(1,4,nn) = particles(n)%class
                particles(n)%tailpoints = 1
                IF ( minimum_tailpoint_distance /= 0.0 )  THEN
                   particle_tail_coordinates(2,1,nn) = particles(n)%x
                   particle_tail_coordinates(2,2,nn) = particles(n)%y
                   particle_tail_coordinates(2,3,nn) = particles(n)%z
                   particle_tail_coordinates(2,4,nn) = particles(n)%class
                   particle_tail_coordinates(1:2,5,nn) = 0.0
                   particles(n)%tailpoints = 2
                ENDIF

             ENDIF
          ENDDO
       ENDIF

!
!--    Plot initial positions of particles (only if particle advection is
!--    switched on from the beginning of the simulation (t=0))
       IF ( particle_advection_start == 0.0 )  CALL data_output_dvrp

    ENDIF

!
!-- Check boundary condition and set internal variables
    SELECT CASE ( bc_par_b )
    
       CASE ( 'absorb' )
          ibc_par_b = 1

       CASE ( 'reflect' )
          ibc_par_b = 2
          
       CASE DEFAULT
          WRITE( message_string, * )  'unknown boundary condition ',   &
                                       'bc_par_b = "', TRIM( bc_par_b ), '"'
          CALL message( 'lpm_init', 'PA0217', 1, 2, 0, 6, 0 )
          
    END SELECT
    SELECT CASE ( bc_par_t )
    
       CASE ( 'absorb' )
          ibc_par_t = 1

       CASE ( 'reflect' )
          ibc_par_t = 2
          
       CASE DEFAULT
          WRITE( message_string, * ) 'unknown boundary condition ',   &
                                     'bc_par_t = "', TRIM( bc_par_t ), '"'
          CALL message( 'lpm_init', 'PA0218', 1, 2, 0, 6, 0 )
          
    END SELECT
    SELECT CASE ( bc_par_lr )

       CASE ( 'cyclic' )
          ibc_par_lr = 0

       CASE ( 'absorb' )
          ibc_par_lr = 1

       CASE ( 'reflect' )
          ibc_par_lr = 2
          
       CASE DEFAULT
          WRITE( message_string, * ) 'unknown boundary condition ',   &
                                     'bc_par_lr = "', TRIM( bc_par_lr ), '"'
          CALL message( 'lpm_init', 'PA0219', 1, 2, 0, 6, 0 )
          
    END SELECT
    SELECT CASE ( bc_par_ns )

       CASE ( 'cyclic' )
          ibc_par_ns = 0

       CASE ( 'absorb' )
          ibc_par_ns = 1

       CASE ( 'reflect' )
          ibc_par_ns = 2
          
       CASE DEFAULT
          WRITE( message_string, * ) 'unknown boundary condition ',   &
                                     'bc_par_ns = "', TRIM( bc_par_ns ), '"'
          CALL message( 'lpm_init', 'PA0220', 1, 2, 0, 6, 0 )
          
    END SELECT
!
!-- Formats
8000 FORMAT (I6,1X,F7.2,4X,I6,71X,I6)

 END SUBROUTINE lpm_init