hmap_axisNB_init_params Function

public function hmap_axisNB_init_params(ncfile, nvisu) result(sf)

Uses

  • proc~~hmap_axisnb_init_params~~UsesGraph proc~hmap_axisnb_init_params hmap_axisNB_init_params module~modgvec_fbase MODgvec_fBase proc~hmap_axisnb_init_params->module~modgvec_fbase module~modgvec_io_netcdf MODgvec_IO_NETCDF proc~hmap_axisnb_init_params->module~modgvec_io_netcdf module~modgvec_mpi MODgvec_MPI proc~hmap_axisnb_init_params->module~modgvec_mpi module~modgvec_globals MODgvec_Globals module~modgvec_fbase->module~modgvec_globals module~modgvec_io_netcdf->module~modgvec_globals netcdf netcdf module~modgvec_io_netcdf->netcdf iso_fortran_env iso_fortran_env module~modgvec_globals->iso_fortran_env

initialize the type hmap_axisNB and read "G-frame" from netcdf

transform from full period cartesian coordinates to one-field period "hat" cartesian coordinates, by rotating around the zaxis with the local angle zeta, with the sign given by which direction xyz(zeta=0) rotates to xyz(zeta=2pi/nfp) INVERSION OF: x=cos(zeta)xhat - sgn_rotsin(zeta)yhat, y=cos(zeta)yhat + sgn_rotsin(zeta)xhat, z <=> zhat ==> xhat=cos(zeta)x+sgn_rotsin(zeta)y, yhat=cos(zeta)y-sgn_rotsin(zeta)x, check that all points on full period are the same in the xhat,yhat,zhat coordinates NOTE THIS FUNCTION IS USING sinz=sin(zeta),cosz=cos(zeta) and sgn_rot computed above!!!!

Arguments

Type IntentOptional Attributes Name
character(len=*), intent(in) :: ncfile

netcdf file containing the group "axis" from which to read the G-frame
integer, intent(in) :: nvisu

number of visualization points for G-Frame per field period, -1: no visualization

Return Value type(t_hmap_axisNB)

self


Calls

proc~~hmap_axisnb_init_params~~CallsGraph proc~hmap_axisnb_init_params hmap_axisNB_init_params interface~par_bcast par_Bcast proc~hmap_axisnb_init_params->interface~par_bcast proc~allocate_readin_vars allocate_readin_vars proc~hmap_axisnb_init_params->proc~allocate_readin_vars proc~checkfieldperiodicity CheckFieldPeriodicity proc~hmap_axisnb_init_params->proc~checkfieldperiodicity proc~fbase_initdof t_fBase%fBase_initDOF proc~hmap_axisnb_init_params->proc~fbase_initdof proc~fbase_new fBase_new proc~hmap_axisnb_init_params->proc~fbase_new proc~hmap_axisnb_test hmap_axisNB_test proc~hmap_axisnb_init_params->proc~hmap_axisnb_test proc~ncfile_init ncfile_init proc~hmap_axisnb_init_params->proc~ncfile_init proc~par_barrier par_Barrier proc~hmap_axisnb_init_params->proc~par_barrier proc~readnetcdf ReadNETCDF proc~hmap_axisnb_init_params->proc~readnetcdf proc~rodrigues rodrigues proc~hmap_axisnb_init_params->proc~rodrigues proc~visu_axisnb Visu_axisNB proc~hmap_axisnb_init_params->proc~visu_axisnb proc~par_bcast_array1d par_Bcast_array1D interface~par_bcast->proc~par_bcast_array1d proc~par_bcast_array1d_int par_Bcast_array1D_int interface~par_bcast->proc~par_bcast_array1d_int proc~par_bcast_array1d_str par_Bcast_array1D_str interface~par_bcast->proc~par_bcast_array1d_str proc~par_bcast_array2d par_Bcast_array2D interface~par_bcast->proc~par_bcast_array2d proc~par_bcast_scalar par_Bcast_scalar interface~par_bcast->proc~par_bcast_scalar proc~par_bcast_scalar_int par_Bcast_scalar_int interface~par_bcast->proc~par_bcast_scalar_int proc~par_bcast_scalar_str par_Bcast_scalar_str interface~par_bcast->proc~par_bcast_scalar_str proc~checkfieldperiodicity->proc~rodrigues proc~hmap_axisnb_eval_tnb_hat t_hmap_axisNB%hmap_axisNB_eval_TNB_hat proc~checkfieldperiodicity->proc~hmap_axisnb_eval_tnb_hat proc~fbase_projectiptodof_tens t_fBase%fBase_projectIPtoDOF_tens proc~fbase_initdof->proc~fbase_projectiptodof_tens proc~fbase_projectxntodof t_fBase%fBase_projectxntoDOF proc~fbase_initdof->proc~fbase_projectxntodof __perfoff __perfoff proc~fbase_new->__perfoff __perfon __perfon proc~fbase_new->__perfon proc~fbase_init t_fBase%fBase_init proc~fbase_new->proc~fbase_init proc~hmap_axisnb_eval t_hmap_axisNB%hmap_axisNB_eval proc~hmap_axisnb_test->proc~hmap_axisnb_eval proc~hmap_axisnb_eval_all t_hmap_axisNB%hmap_axisNB_eval_all proc~hmap_axisnb_test->proc~hmap_axisnb_eval_all proc~hmap_axisnb_eval_dxdq t_hmap_axisNB%hmap_axisNB_eval_dxdq proc~hmap_axisnb_test->proc~hmap_axisnb_eval_dxdq proc~hmap_axisnb_eval_gij t_hmap_axisNB%hmap_axisNB_eval_gij proc~hmap_axisnb_test->proc~hmap_axisnb_eval_gij proc~hmap_axisnb_eval_gij_dq t_hmap_axisNB%hmap_axisNB_eval_gij_dq proc~hmap_axisnb_test->proc~hmap_axisnb_eval_gij_dq proc~hmap_axisnb_eval_jh t_hmap_axisNB%hmap_axisNB_eval_Jh proc~hmap_axisnb_test->proc~hmap_axisnb_eval_jh proc~hmap_axisnb_eval_jh_dq t_hmap_axisNB%hmap_axisNB_eval_Jh_dq proc~hmap_axisnb_test->proc~hmap_axisnb_eval_jh_dq proc~hmap_axisnb_get_ddx_dqij t_hmap_axisNB%hmap_axisNB_get_ddx_dqij proc~hmap_axisnb_test->proc~hmap_axisnb_get_ddx_dqij proc~hmap_axisnb_get_dx_dqi t_hmap_axisNB%hmap_axisNB_get_dx_dqi proc~hmap_axisnb_test->proc~hmap_axisnb_get_dx_dqi proc~hmap_axisnb_init_aux hmap_axisNB_init_aux proc~hmap_axisnb_test->proc~hmap_axisnb_init_aux swrite swrite proc~hmap_axisnb_test->swrite proc~mpi_check_single_access mpi_check_single_access proc~ncfile_init->proc~mpi_check_single_access proc~ncfile_openfile t_ncfile%ncfile_openfile proc~ncfile_init->proc~ncfile_openfile mpi_barrier mpi_barrier proc~par_barrier->mpi_barrier proc~readnetcdf->proc~allocate_readin_vars proc~ncfile_closefile t_ncfile%ncfile_closefile proc~readnetcdf->proc~ncfile_closefile proc~ncfile_get_array t_ncfile%ncfile_get_array proc~readnetcdf->proc~ncfile_get_array proc~ncfile_get_scalar t_ncfile%ncfile_get_scalar proc~readnetcdf->proc~ncfile_get_scalar interface~cross CROSS proc~rodrigues->interface~cross proc~visu_axisnb->proc~hmap_axisnb_eval_tnb_hat proc~writedatatonetcdf WriteDataToNETCDF proc~visu_axisnb->proc~writedatatonetcdf proc~writedatatovtk WriteDataToVTK proc~visu_axisnb->proc~writedatatovtk writedatatocsv writedatatocsv proc~visu_axisnb->writedatatocsv interface~cross->interface~cross proc~fbase_init->swrite proc~fbase_alloc fBase_alloc proc~fbase_init->proc~fbase_alloc proc~fbase_test fBase_test proc~fbase_init->proc~fbase_test __adgemm_tn __adgemm_tn proc~fbase_projectiptodof_tens->__adgemm_tn __dgemm_nt __dgemm_nt proc~fbase_projectiptodof_tens->__dgemm_nt __pamatvec_t __pamatvec_t proc~fbase_projectxntodof->__pamatvec_t proc~fbase_eval_xn t_fBase%fBase_eval_xn proc~fbase_projectxntodof->proc~fbase_eval_xn proc~hmap_axisnb_eval->proc~hmap_axisnb_eval_tnb_hat proc~hmap_axisnb_eval_all_e hmap_axisNB_eval_all_e proc~hmap_axisnb_eval_all->proc~hmap_axisnb_eval_all_e proc~hmap_axisnb_eval_dxdq->proc~hmap_axisnb_eval_tnb_hat proc~hmap_axisnb_eval_gij->proc~hmap_axisnb_eval_tnb_hat proc~hmap_axisnb_eval_gij_dq->proc~hmap_axisnb_eval_tnb_hat proc~hmap_axisnb_eval_jh->interface~cross proc~hmap_axisnb_eval_jh->proc~hmap_axisnb_eval_tnb_hat proc~hmap_axisnb_eval_jh_dq->interface~cross proc~hmap_axisnb_eval_jh_dq->proc~hmap_axisnb_eval_tnb_hat __matvec_n __matvec_n proc~hmap_axisnb_eval_tnb_hat->__matvec_n proc~fbase_eval t_fBase%fBase_eval proc~hmap_axisnb_eval_tnb_hat->proc~fbase_eval proc~hmap_axisnb_get_ddx_dqij->proc~hmap_axisnb_eval_tnb_hat proc~hmap_axisnb_get_dx_dqi->proc~hmap_axisnb_eval_tnb_hat proc~hmap_axisnb_init_aux->interface~cross proc~hmap_axisnb_init_aux->proc~hmap_axisnb_eval_tnb_hat proc~ncfile_closefile->proc~mpi_check_single_access nf90_close nf90_close proc~ncfile_closefile->nf90_close proc~ncfile_handle_error t_ncfile%ncfile_handle_error proc~ncfile_closefile->proc~ncfile_handle_error proc~ncfile_get_array->proc~mpi_check_single_access nf90_get_var nf90_get_var proc~ncfile_get_array->nf90_get_var nf90_inq_varid nf90_inq_varid proc~ncfile_get_array->nf90_inq_varid nf90_inquire_dimension nf90_inquire_dimension proc~ncfile_get_array->nf90_inquire_dimension nf90_inquire_variable nf90_inquire_variable proc~ncfile_get_array->nf90_inquire_variable proc~ncfile_enter_groups t_ncfile%ncfile_enter_groups proc~ncfile_get_array->proc~ncfile_enter_groups proc~ncfile_get_array->proc~ncfile_handle_error proc~ncfile_get_scalar->proc~mpi_check_single_access proc~ncfile_get_scalar->nf90_get_var proc~ncfile_get_scalar->nf90_inq_varid proc~ncfile_get_scalar->proc~ncfile_enter_groups proc~ncfile_get_scalar->proc~ncfile_handle_error proc~ncfile_openfile->proc~mpi_check_single_access nf90_create nf90_create proc~ncfile_openfile->nf90_create nf90_open nf90_open proc~ncfile_openfile->nf90_open proc~ncfile_openfile->proc~ncfile_handle_error mpi_bcast mpi_bcast proc~par_bcast_array1d->mpi_bcast proc~par_bcast_array1d_int->mpi_bcast proc~par_bcast_array1d_str->mpi_bcast proc~par_bcast_array2d->mpi_bcast proc~par_bcast_scalar->mpi_bcast proc~par_bcast_scalar_int->mpi_bcast proc~par_bcast_scalar_str->mpi_bcast proc~writedatatonetcdf->proc~ncfile_init proc~ncfile_def_dim t_ncfile%ncfile_def_dim proc~writedatatonetcdf->proc~ncfile_def_dim proc~ncfile_end_def_mode t_ncfile%ncfile_end_def_mode proc~writedatatonetcdf->proc~ncfile_end_def_mode proc~ncfile_put_array t_ncfile%ncfile_put_array proc~writedatatonetcdf->proc~ncfile_put_array proc~ncfile_put_attributes_char t_ncfile%ncfile_put_attributes_char proc~writedatatonetcdf->proc~ncfile_put_attributes_char proc~ncfile_put_char t_ncfile%ncfile_put_char proc~writedatatonetcdf->proc~ncfile_put_char interface~getfreeunit GETFREEUNIT proc~writedatatovtk->interface~getfreeunit sizeof_f sizeof_f proc~writedatatovtk->sizeof_f interface~getfreeunit->interface~getfreeunit proc~fbase_eval->proc~fbase_eval_xn proc~fbase_test->proc~fbase_initdof proc~fbase_test->proc~fbase_init proc~fbase_test->swrite proc~fbase_change_base t_fBase%fBase_change_base proc~fbase_test->proc~fbase_change_base proc~fbase_compare t_fBase%fBase_compare proc~fbase_test->proc~fbase_compare proc~fbase_evaldof_ip_tens t_fBase%fBase_evalDOF_IP_tens proc~fbase_test->proc~fbase_evaldof_ip_tens proc~fbase_evaldof_x t_fBase%fBase_evalDOF_x proc~fbase_test->proc~fbase_evaldof_x proc~fbase_evaldof_xn t_fBase%fBase_evalDOF_xn proc~fbase_test->proc~fbase_evaldof_xn proc~fbase_evaldof_xn_tens t_fBase%fBase_evalDOF_xn_tens proc~fbase_test->proc~fbase_evaldof_xn_tens proc~ncfile_def_dim->proc~mpi_check_single_access proc~ncfile_def_dim->proc~ncfile_handle_error nf90_def_dim nf90_def_dim proc~ncfile_def_dim->nf90_def_dim proc~ncfile_end_def_mode->proc~mpi_check_single_access proc~ncfile_end_def_mode->proc~ncfile_handle_error nf90_enddef nf90_enddef proc~ncfile_end_def_mode->nf90_enddef proc~ncfile_enter_groups->proc~mpi_check_single_access proc~ncfile_enter_groups->proc~ncfile_openfile nf90_inq_ncid nf90_inq_ncid proc~ncfile_enter_groups->nf90_inq_ncid proc~ncfile_handle_error->proc~mpi_check_single_access nf90_strerror nf90_strerror proc~ncfile_handle_error->nf90_strerror proc~ncfile_put_array->proc~mpi_check_single_access proc~ncfile_put_array->proc~ncfile_openfile proc~ncfile_put_array->nf90_inq_varid proc~ncfile_put_array->proc~ncfile_handle_error nf90_def_var nf90_def_var proc~ncfile_put_array->nf90_def_var nf90_put_var nf90_put_var proc~ncfile_put_array->nf90_put_var proc~ncfile_put_attributes_char->proc~mpi_check_single_access proc~ncfile_put_attributes_char->nf90_inq_varid proc~ncfile_put_attributes_char->proc~ncfile_handle_error nf90_put_att nf90_put_att proc~ncfile_put_attributes_char->nf90_put_att proc~ncfile_put_char->proc~mpi_check_single_access proc~ncfile_put_char->nf90_inq_varid proc~ncfile_put_char->proc~ncfile_handle_error proc~ncfile_put_char->nf90_def_var proc~ncfile_put_char->nf90_put_var proc~fbase_change_base->proc~fbase_compare proc~fbase_evaldof_ip_tens->proc~fbase_evaldof_xn __dgemm_nn __dgemm_nn proc~fbase_evaldof_ip_tens->__dgemm_nn proc~fbase_evaldof_x->proc~fbase_eval proc~fbase_evaldof_xn->__matvec_n proc~fbase_evaldof_xn->proc~fbase_eval_xn proc~fbase_evaldof_xn_tens->__dgemm_nn proc~fbase_eval1d_thet fBase_eval1d_thet proc~fbase_evaldof_xn_tens->proc~fbase_eval1d_thet proc~fbase_eval1d_zeta fBase_eval1d_zeta proc~fbase_evaldof_xn_tens->proc~fbase_eval1d_zeta

Called by

proc~~hmap_axisnb_init_params~~CalledByGraph proc~hmap_axisnb_init_params hmap_axisNB_init_params interface~t_hmap_axisnb t_hmap_axisNB interface~t_hmap_axisnb->proc~hmap_axisnb_init_params proc~hmap_axisnb_init hmap_axisNB_init interface~t_hmap_axisnb->proc~hmap_axisnb_init proc~hmap_axisnb_init->proc~hmap_axisnb_init_params

Source Code

FUNCTION hmap_axisNB_init_params(ncfile,nvisu) RESULT(sf)
! MODULES
  USE MODgvec_fbase      ,ONLY: fbase_new
  USE MODgvec_io_netcdf  ,ONLY: ncfile_init
  USE MODgvec_MPI        ,ONLY: par_BCast,par_barrier
  IMPLICIT NONE
!-----------------------------------------------------------------------------------------------------------------------------------
! INPUT VARIABLES
  CHARACTER(LEN=*),INTENT(IN) :: ncfile  !! netcdf file containing the group "axis" from which to read the G-frame
  INTEGER         ,INTENT(IN) :: nvisu   !! number of visualization points for G-Frame per field period, -1: no visualization
!-----------------------------------------------------------------------------------------------------------------------------------
! OUTPUT VARIABLES
  TYPE(t_hmap_axisNB)  :: sf !! self
!-----------------------------------------------------------------------------------------------------------------------------------
! LOCAL VARIABLES
  INTEGER :: i
  INTEGER :: error_nfp
  REAL(wp),ALLOCATABLE :: cosz(:),sinz(:)
!===================================================================================================================================
  CALL par_Barrier(beforeScreenOut='INIT HMAP :: axisNB FRAME OF A CLOSED CURVE ...')

  sf%ncfile=ncfile
  IF(MPIroot)THEN
    ! read axis from netcdf
    CALL ncfile_init(sf%nc,sf%ncfile,"r")
    CALL ReadNETCDF(sf)


    sf%sgn_rot=1
    IF(sf%nfp.GT.2)THEN !no need to check for nfp=1 and nfp=2 is either a positive or negative rotation by pi
      IF(SUM((sf%xyz(:,1+sf%nzeta) -  rodrigues(sf%xyz(:,1),TWOPI/REAL(sf%nfp,wp)))**2).LT.1.0e-12)THEN
         sf%sgn_rot=1
      ELSEIF(SUM((sf%xyz(:,1+sf%nzeta) -  rodrigues(sf%xyz(:,1),-TWOPI/REAL(sf%nfp,wp)))**2).LT.1.0e-12)THEN
         sf%sgn_rot=-1
      ELSE
        CALL abort(__STAMP__, &
           'problem with check of field period rotation: point at zeta=0 does not rotate to point at zeta= +/-2pi/nfp.')
      END IF
    END IF
    WRITE(UNIT_stdOut,'(4X,A,I2)')'INFO: sign of the rotation from zeta=0 to zeta=2pi/nfp is: ',sf%sgn_rot

    sf%n_max=(sf%nzeta-1)/2 ! maximum mode number on a field period


  END IF !MPIroot
  CALL par_BCast(sf%nzeta,0)
  CALL par_BCast(sf%nfp,0)
  CALL par_BCast(sf%n_max,0)
  CALL par_Bcast(sf%sgn_rot,0)
  IF(.NOT.MPIroot) CALL allocate_readin_vars(sf)
  CALL par_Bcast(sf%zeta,0)
  CALL par_Bcast(sf%xyz,0)
  CALL par_Bcast(sf%Nxyz,0)
  CALL par_Bcast(sf%Bxyz,0)
  !Fourier 1D base on one field period for "hat" coordinates
  CALL fbase_new(sf%fb_hat,(/0,sf%n_max/),(/1,sf%nzeta/),sf%nfp,"_sincos_",.FALSE.)
  ALLOCATE(sf%xyz_hat_modes( 3,sf%fb_hat%modes),&
           sf%Nxyz_hat_modes(3,sf%fb_hat%modes),&
           sf%Bxyz_hat_modes(3,sf%fb_hat%modes))
  IF(MPIroot)THEN
    ALLOCATE(cosz(sf%nzeta*sf%nfp),sinz(sf%nzeta*sf%nfp))
    !build cos(zeta),sin(zeta) on full torus
    DO i=1,sf%nfp
      cosz(sf%nzeta*(i-1)+1:sf%nzeta*i)=COS(sf%zeta(1:sf%nzeta)+TWOPI*(REAL(i-1,wp)/REAL(sf%nfp,wp)))
      sinz(sf%nzeta*(i-1)+1:sf%nzeta*i)=SIN(sf%zeta(1:sf%nzeta)+TWOPI*(REAL(i-1,wp)/REAL(sf%nfp,wp)))
    END DO
    sf%xyz_hat_modes =transform_to_hat(sf%xyz, "xyz to xyzhat"  )
    sf%Nxyz_hat_modes=transform_to_hat(sf%Nxyz,"Nxyz to Nxyzhat")
    sf%Bxyz_hat_modes=transform_to_hat(sf%Bxyz,"Bxyz to Bxyzhat")
    DEALLOCATE(cosz,sinz)

    IF(nvisu.GT.0) CALL Visu_axisNB(sf,nvisu*sf%nfp)

    CALL CheckFieldPeriodicity(sf,sf%sgn_rot,error_nfp)
    IF(error_nfp.LT.0) &
       CALL abort(__STAMP__, &
          "hmap_axisNB check Field Periodicity failed!")
  END IF !MPIroot

  CALL par_BCast(sf%xyz_hat_modes,0)
  CALL par_BCast(sf%Nxyz_hat_modes,0)
  CALL par_BCast(sf%Bxyz_hat_modes,0)

  sf%initialized=.TRUE.
  CALL par_barrier(afterScreenOut='...DONE')

  IF(.NOT.test_called) CALL hmap_axisNB_test(sf)

  !------------------
  CONTAINS
  !------------------
  !! transform from full period cartesian coordinates to one-field period "hat" cartesian coordinates,
  !! by rotating around the zaxis with the local angle zeta,
  !! with the sign given by which direction xyz(zeta=0) rotates to xyz(zeta=2pi/nfp)
  !! INVERSION OF: x=cos(zeta)*xhat - sgn_rot*sin(zeta)*yhat,
  !!               y=cos(zeta)*yhat + sgn_rot*sin(zeta)*xhat, z <=> zhat
  !! ==>           xhat=cos(zeta)x+sgn_rot*sin(zeta)y,
  !!               yhat=cos(zeta)y-sgn_rot*sin(zeta)x,
  !! check that all points on full period are the same in the xhat,yhat,zhat coordinates
  !! NOTE THIS FUNCTION IS USING sinz=sin(zeta),cosz=cos(zeta) and sgn_rot computed above!!!!
  FUNCTION transform_to_hat(xyz_in,msg)  RESULT(to_hat_modes)
    IMPLICIT NONE

    REAL(wp),INTENT(IN) :: xyz_in(3,sf%nzeta*sf%nfp)
    CHARACTER(*),INTENT(IN) :: msg
    REAL(wp) :: to_hat_modes(3,sf%fb_hat%modes)
    !------------------
    REAL(wp) :: to_hat(3,sf%nzeta*sf%nfp)
    REAL(wp) :: check_xhat(1:3,2:sf%nfp)
    !------------------
    to_hat(1,:)=xyz_in(1,:)*cosz(:)+sf%sgn_rot*xyz_in(2,:)*sinz(:)
    to_hat(2,:)=xyz_in(2,:)*cosz(:)-sf%sgn_rot*xyz_in(1,:)*sinz(:)
    to_hat(3,:)=xyz_in(3,:)
    !check periodicity for remaining nfp
    DO i=2,sf%nfp
      check_xhat(1,i)=MAXVAL(ABS(to_hat(1,1:sf%nzeta)-to_hat(1,sf%nzeta*(i-1)+1:sf%nzeta*i)))
      check_xhat(2,i)=MAXVAL(ABS(to_hat(2,1:sf%nzeta)-to_hat(2,sf%nzeta*(i-1)+1:sf%nzeta*i)))
      check_xhat(3,i)=MAXVAL(ABS(to_hat(3,1:sf%nzeta)-to_hat(3,sf%nzeta*(i-1)+1:sf%nzeta*i)))
    END DO
    IF(ANY(check_xhat.GT.1.0e-12))THEN
      DO i=2,sf%nfp
        WRITE(UNIT_stdout,'(A,I4,A,3E9.2)')'fp=1 vs fp=',i,', check_xyz=',check_xhat(1:3,i)
      END DO
      CALL abort(__STAMP__,&
            "transform from cartesian to hat coordinates"//TRIM(msg)//" yields non-field periodic data!")
    END IF
    DO i=1,3
      to_hat_modes(i,:)=sf%fb_hat%initDOF(to_hat(i,1:sf%nzeta),thet_zeta_start=(/0.,sf%zeta(1)/))
    END DO
  END FUNCTION transform_to_hat

END FUNCTION hmap_axisNB_init_params