VSH_POL_UP_ALL_DP Subroutine

private subroutine VSH_POL_UP_ALL_DP(OUT, LMAX, THETA, PHI)

All standard-VSH members VSH_POL_UP for , from one VSH_CORE pass: . Well-defined (nonzero) at -- see VSH_POL_UP for the dipole-ratio note at .

Warning

Inherits ASSOC_LEGENDRE_NORM_ALL's -dependent stability limit (safe for unconditionally) -- see STABILITY_FINDINGS.md at the repo root.

1=, 2=, 3=; mode axis indexed by YLM_INDEX(l,m).

Arguments

Type IntentOptional Attributes Name
complex(kind=dp), intent(out) :: OUT(3,(LMAX+1)**2)
integer(kind=i4), intent(in) :: LMAX

Maximum degree, .
real(kind=dp), intent(in) :: THETA

Colatitude in radians, .
real(kind=dp), intent(in) :: PHI

Longitude in radians, .

Calls

proc~~vsh_pol_up_all_dp~~CallsGraph proc~vsh_pol_up_all_dp VSH_POL_UP_ALL_DP interface~vsh_core VSH_CORE proc~vsh_pol_up_all_dp->interface~vsh_core proc~ylm_index YLM_INDEX proc~vsh_pol_up_all_dp->proc~ylm_index proc~vsh_core_dp VSH_CORE_DP interface~vsh_core->proc~vsh_core_dp proc~vsh_core_dp->proc~ylm_index dcos dcos proc~vsh_core_dp->dcos dsin dsin proc~vsh_core_dp->dsin interface~assoc_legendre_norm_all ASSOC_LEGENDRE_NORM_ALL proc~vsh_core_dp->interface~assoc_legendre_norm_all interface~ddx_assoc_legendre_norm_all DDX_ASSOC_LEGENDRE_NORM_ALL proc~vsh_core_dp->interface~ddx_assoc_legendre_norm_all proc~plm_index PLM_INDEX proc~vsh_core_dp->proc~plm_index proc~assoc_legendre_norm_all_dp ASSOC_LEGENDRE_NORM_ALL_DP interface~assoc_legendre_norm_all->proc~assoc_legendre_norm_all_dp proc~ddx_assoc_legendre_norm_all_dp DDX_ASSOC_LEGENDRE_NORM_ALL_DP interface~ddx_assoc_legendre_norm_all->proc~ddx_assoc_legendre_norm_all_dp proc~assoc_legendre_norm_all_dp->proc~plm_index proc~ddx_assoc_legendre_norm_all_dp->proc~plm_index

Called by

proc~~vsh_pol_up_all_dp~~CalledByGraph proc~vsh_pol_up_all_dp VSH_POL_UP_ALL_DP interface~vsh_pol_up_all VSH_POL_UP_ALL interface~vsh_pol_up_all->proc~vsh_pol_up_all_dp proc~batch_vsh_pol_up_cons BATCH_VSH_POL_UP_CONS proc~batch_vsh_pol_up_cons->interface~vsh_pol_up_all proc~bench_vsh_pol_up BENCH_VSH_POL_UP proc~bench_vsh_pol_up->interface~vsh_pol_up_all proc~vsh_pol_inversion VSH_POL_INVERSION proc~vsh_pol_inversion->interface~vsh_pol_up_all program~convergence_main CONVERGENCE_MAIN program~convergence_main->interface~vsh_pol_up_all program~convergence_main->proc~batch_vsh_pol_up_cons program~bench_main BENCH_MAIN program~bench_main->proc~bench_vsh_pol_up program~main MAIN program~main->proc~batch_vsh_pol_up_cons program~main->proc~vsh_pol_inversion

Source Code

  SUBROUTINE VSH_POL_UP_ALL_DP(OUT, LMAX, THETA, PHI)
  IMPLICIT NONE
  INTEGER(KIND=i4), INTENT(IN)  :: LMAX
  REAL(KIND=dp),    INTENT(IN)  :: THETA
  REAL(KIND=dp),    INTENT(IN)  :: PHI
  COMPLEX(KIND=dp), INTENT(OUT) :: OUT(3,(LMAX+1)**2)
  INTEGER(KIND=i4) :: L, M, NYLM, IDX
  REAL(KIND=dp)    :: SC_TH, SC_R
  COMPLEX(KIND=dp), ALLOCATABLE :: YLM(:), GTH(:), GPH(:)
  NYLM = (LMAX+1)**2
  ALLOCATE(YLM(NYLM), GTH(NYLM), GPH(NYLM))
  CALL VSH_CORE(YLM, GTH, GPH, LMAX, THETA, PHI)
  OUT = DCMPLX(0.d0, 0.d0)
  OUT(1, YLM_INDEX(0,0)) = -YLM(YLM_INDEX(0,0))
  DO L = 1, LMAX
    SC_TH = 1.d0/DSQRT((2*L+1.d0)*(L+1.d0))
    SC_R  = -DSQRT((L+1.d0)/(2*L+1.d0))
    DO M = -L, L
      IDX = YLM_INDEX(L, M)
      OUT(1,IDX) = SC_R  * YLM(IDX)
      OUT(2,IDX) = SC_TH * GTH(IDX)
      OUT(3,IDX) = SC_TH * GPH(IDX)
    END DO
  END DO
  DEALLOCATE(YLM, GTH, GPH)
  END SUBROUTINE VSH_POL_UP_ALL_DP