DDX_ASSOC_LEGENDRE_NORM_ALL_DP Subroutine

private subroutine DDX_ASSOC_LEGENDRE_NORM_ALL_DP(DPNORM, PNORM, LMAX, X)

All derivatives of the normalized associated Legendre functions, for , reusing a precomputed ASSOC_LEGENDRE_NORM_ALL table: This is the recurrence VSH_CORE (and therefore every batch VSH routine) uses for the component.

Warning

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

by PLM_INDEX(l,m); 0 at the poles (). ASSOC_LEGENDRE_NORM_ALL, same size/indexing. PNORM).

Arguments

Type IntentOptional Attributes Name
real(kind=dp), intent(out) :: DPNORM((LMAX+1)*(LMAX+2)/2)
real(kind=dp), intent(in) :: PNORM((LMAX+1)*(LMAX+2)/2)
integer(kind=i4), intent(in) :: LMAX

Maximum degree, (must match PNORM's).
real(kind=dp), intent(in) :: X

Argument, (must match the X used to build

Calls

proc~~ddx_assoc_legendre_norm_all_dp~~CallsGraph proc~ddx_assoc_legendre_norm_all_dp DDX_ASSOC_LEGENDRE_NORM_ALL_DP proc~plm_index PLM_INDEX proc~ddx_assoc_legendre_norm_all_dp->proc~plm_index

Called by

proc~~ddx_assoc_legendre_norm_all_dp~~CalledByGraph proc~ddx_assoc_legendre_norm_all_dp DDX_ASSOC_LEGENDRE_NORM_ALL_DP interface~ddx_assoc_legendre_norm_all DDX_ASSOC_LEGENDRE_NORM_ALL interface~ddx_assoc_legendre_norm_all->proc~ddx_assoc_legendre_norm_all_dp proc~vsh_core_dp VSH_CORE_DP proc~vsh_core_dp->interface~ddx_assoc_legendre_norm_all interface~vsh_core VSH_CORE interface~vsh_core->proc~vsh_core_dp proc~grad_ssh_all_dp GRAD_SSH_ALL_DP proc~grad_ssh_all_dp->interface~vsh_core proc~l_ssh_all_dp L_SSH_ALL_DP proc~l_ssh_all_dp->interface~vsh_core proc~pvsh_pol_all_dp PVSH_POL_ALL_DP proc~pvsh_pol_all_dp->interface~vsh_core proc~pvsh_rad_all_dp PVSH_RAD_ALL_DP proc~pvsh_rad_all_dp->interface~vsh_core proc~pvsh_tor_all_dp PVSH_TOR_ALL_DP proc~pvsh_tor_all_dp->interface~vsh_core proc~vsh_pol_dn_all_dp VSH_POL_DN_ALL_DP proc~vsh_pol_dn_all_dp->interface~vsh_core proc~vsh_pol_up_all_dp VSH_POL_UP_ALL_DP proc~vsh_pol_up_all_dp->interface~vsh_core interface~grad_ssh_all GRAD_SSH_ALL interface~grad_ssh_all->proc~grad_ssh_all_dp interface~l_ssh_all L_SSH_ALL interface~l_ssh_all->proc~l_ssh_all_dp interface~pvsh_pol_all PVSH_POL_ALL interface~pvsh_pol_all->proc~pvsh_pol_all_dp interface~pvsh_rad_all PVSH_RAD_ALL interface~pvsh_rad_all->proc~pvsh_rad_all_dp interface~pvsh_tor_all PVSH_TOR_ALL interface~pvsh_tor_all->proc~pvsh_tor_all_dp interface~vsh_pol_dn_all VSH_POL_DN_ALL interface~vsh_pol_dn_all->proc~vsh_pol_dn_all_dp interface~vsh_pol_up_all VSH_POL_UP_ALL interface~vsh_pol_up_all->proc~vsh_pol_up_all_dp proc~batch_grad_ssh_cons BATCH_GRAD_SSH_CONS proc~batch_grad_ssh_cons->interface~grad_ssh_all proc~batch_l_ssh_cons BATCH_L_SSH_CONS proc~batch_l_ssh_cons->interface~l_ssh_all proc~batch_pvsh_pol_cons BATCH_PVSH_POL_CONS proc~batch_pvsh_pol_cons->interface~pvsh_pol_all proc~batch_pvsh_rad_cons BATCH_PVSH_RAD_CONS proc~batch_pvsh_rad_cons->interface~pvsh_rad_all proc~batch_pvsh_tor_cons BATCH_PVSH_TOR_CONS proc~batch_pvsh_tor_cons->interface~pvsh_tor_all proc~batch_vsh_pol_dn_cons BATCH_VSH_POL_DN_CONS proc~batch_vsh_pol_dn_cons->interface~vsh_pol_dn_all 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_dn BENCH_VSH_POL_DN proc~bench_vsh_pol_dn->interface~vsh_pol_dn_all proc~bench_vsh_pol_up BENCH_VSH_POL_UP proc~bench_vsh_pol_up->interface~vsh_pol_up_all proc~decompose DECOMPOSE proc~decompose->interface~pvsh_pol_all proc~decompose->interface~pvsh_rad_all proc~decompose->interface~pvsh_tor_all proc~decompose~2 DECOMPOSE proc~decompose~2->interface~pvsh_pol_all proc~decompose~2->interface~pvsh_rad_all proc~decompose~2->interface~pvsh_tor_all proc~pvsh_pol_tor_ortho PVSH_POL_TOR_ORTHO proc~pvsh_pol_tor_ortho->interface~pvsh_pol_all proc~pvsh_pol_tor_ortho->interface~pvsh_tor_all proc~reconstruct RECONSTRUCT proc~reconstruct->interface~pvsh_pol_all proc~reconstruct->interface~pvsh_rad_all proc~reconstruct->interface~pvsh_tor_all proc~reconstruct~2 RECONSTRUCT proc~reconstruct~2->interface~pvsh_pol_all proc~reconstruct~2->interface~pvsh_rad_all proc~reconstruct~2->interface~pvsh_tor_all proc~vsh_pol_inversion VSH_POL_INVERSION proc~vsh_pol_inversion->interface~pvsh_pol_all proc~vsh_pol_inversion->interface~pvsh_rad_all proc~vsh_pol_inversion->interface~vsh_pol_dn_all proc~vsh_pol_inversion->interface~vsh_pol_up_all proc~vsh_tor_all_dp VSH_TOR_ALL_DP proc~vsh_tor_all_dp->interface~pvsh_tor_all program~convergence_main CONVERGENCE_MAIN program~convergence_main->interface~vsh_pol_dn_all program~convergence_main->interface~vsh_pol_up_all program~convergence_main->proc~batch_vsh_pol_dn_cons program~convergence_main->proc~batch_vsh_pol_up_cons interface~vsh_tor_all VSH_TOR_ALL program~convergence_main->interface~vsh_tor_all proc~batch_vsh_tor_cons BATCH_VSH_TOR_CONS program~convergence_main->proc~batch_vsh_tor_cons interface~vsh_tor_all->proc~vsh_tor_all_dp proc~run_part_a RUN_PART_A proc~run_part_a->proc~decompose proc~run_part_a~2 RUN_PART_A proc~run_part_a~2->proc~decompose~2 proc~run_part_b RUN_PART_B proc~run_part_b->proc~decompose proc~run_part_b->proc~reconstruct proc~run_part_b~2 RUN_PART_B proc~run_part_b~2->proc~decompose~2 proc~run_part_b~2->proc~reconstruct~2 program~bench_main BENCH_MAIN program~bench_main->proc~bench_vsh_pol_dn program~bench_main->proc~bench_vsh_pol_up proc~bench_vsh_tor BENCH_VSH_TOR program~bench_main->proc~bench_vsh_tor program~main MAIN program~main->proc~batch_grad_ssh_cons program~main->proc~batch_l_ssh_cons program~main->proc~batch_pvsh_pol_cons program~main->proc~batch_pvsh_rad_cons program~main->proc~batch_pvsh_tor_cons program~main->proc~batch_vsh_pol_dn_cons program~main->proc~batch_vsh_pol_up_cons program~main->proc~pvsh_pol_tor_ortho program~main->proc~vsh_pol_inversion program~main->proc~batch_vsh_tor_cons proc~batch_vsh_tor_cons->interface~vsh_tor_all proc~bench_vsh_tor->interface~vsh_tor_all program~vsh_decomposition VSH_DECOMPOSITION program~vsh_decomposition->proc~run_part_a program~vsh_decomposition->proc~run_part_b program~vsh_decomposition_tor VSH_DECOMPOSITION_TOR program~vsh_decomposition_tor->proc~run_part_a~2 program~vsh_decomposition_tor->proc~run_part_b~2

Source Code

  SUBROUTINE DDX_ASSOC_LEGENDRE_NORM_ALL_DP(DPNORM, PNORM, LMAX, X)
  IMPLICIT NONE
  INTEGER(KIND=i4), INTENT(IN)  :: LMAX
  REAL(KIND=dp),    INTENT(IN)  :: X
  REAL(KIND=dp),    INTENT(IN)  :: PNORM((LMAX+1)*(LMAX+2)/2)
  REAL(KIND=dp),    INTENT(OUT) :: DPNORM((LMAX+1)*(LMAX+2)/2)
  INTEGER(KIND=i4) :: L, M
  REAL(KIND=dp)    :: DOM, COEFF

  DOM = 1.0_dp - X**2

  DO M = 0, LMAX
    DO L = M, LMAX
      IF (ABS(X) .GE. 1.0_dp .OR. L .EQ. 0) THEN
        DPNORM(PLM_INDEX(L, M)) = 0.0_dp
      ELSE IF (L .EQ. M) THEN
        DPNORM(PLM_INDEX(L, M)) = &
          -L * X * PNORM(PLM_INDEX(L, M)) / DOM
      ELSE
        COEFF = DSQRT((2*L+1.d0)*(L**2-M**2)/(2*L-1.d0))
        DPNORM(PLM_INDEX(L, M)) = &
          (COEFF * PNORM(PLM_INDEX(L-1, M)) - &
           L * X * PNORM(PLM_INDEX(L, M))) / DOM
      END IF
    END DO
  END DO
  END SUBROUTINE DDX_ASSOC_LEGENDRE_NORM_ALL_DP