ASSOC_LEGENDRE_NORM_ALL Interface

public interface ASSOC_LEGENDRE_NORM_ALL

Calls

interface~~assoc_legendre_norm_all~~CallsGraph interface~assoc_legendre_norm_all ASSOC_LEGENDRE_NORM_ALL proc~assoc_legendre_norm_all_dp ASSOC_LEGENDRE_NORM_ALL_DP interface~assoc_legendre_norm_all->proc~assoc_legendre_norm_all_dp proc~plm_index PLM_INDEX proc~assoc_legendre_norm_all_dp->proc~plm_index

Called by

interface~~assoc_legendre_norm_all~~CalledByGraph interface~assoc_legendre_norm_all ASSOC_LEGENDRE_NORM_ALL proc~bench_legendre BENCH_LEGENDRE proc~bench_legendre->interface~assoc_legendre_norm_all proc~ssh_all_dp SSH_ALL_DP proc~ssh_all_dp->interface~assoc_legendre_norm_all proc~vsh_core_dp VSH_CORE_DP proc~vsh_core_dp->interface~assoc_legendre_norm_all program~convergence_main CONVERGENCE_MAIN program~convergence_main->interface~assoc_legendre_norm_all interface~ssh_all SSH_ALL program~convergence_main->interface~ssh_all proc~batch_ssh_cons BATCH_SSH_CONS program~convergence_main->proc~batch_ssh_cons interface~vsh_pol_dn_all VSH_POL_DN_ALL program~convergence_main->interface~vsh_pol_dn_all interface~vsh_pol_up_all VSH_POL_UP_ALL program~convergence_main->interface~vsh_pol_up_all proc~batch_vsh_pol_dn_cons BATCH_VSH_POL_DN_CONS program~convergence_main->proc~batch_vsh_pol_dn_cons proc~batch_vsh_pol_up_cons BATCH_VSH_POL_UP_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 program~stability_main STABILITY_MAIN program~stability_main->interface~assoc_legendre_norm_all interface~ssh_all->proc~ssh_all_dp interface~vsh_core VSH_CORE interface~vsh_core->proc~vsh_core_dp program~bench_main BENCH_MAIN program~bench_main->proc~bench_legendre proc~bench_ssh BENCH_SSH program~bench_main->proc~bench_ssh proc~bench_vsh_pol_dn BENCH_VSH_POL_DN program~bench_main->proc~bench_vsh_pol_dn proc~bench_vsh_pol_up BENCH_VSH_POL_UP program~bench_main->proc~bench_vsh_pol_up proc~bench_vsh_tor BENCH_VSH_TOR program~bench_main->proc~bench_vsh_tor proc~batch_ssh_cons->interface~ssh_all proc~bench_ssh->interface~ssh_all 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->proc~vsh_pol_dn_all_dp interface~vsh_pol_up_all->proc~vsh_pol_up_all_dp program~main MAIN program~main->proc~batch_ssh_cons proc~batch_grad_ssh_cons BATCH_GRAD_SSH_CONS program~main->proc~batch_grad_ssh_cons proc~batch_l_ssh_cons BATCH_L_SSH_CONS program~main->proc~batch_l_ssh_cons proc~batch_pvsh_pol_cons BATCH_PVSH_POL_CONS program~main->proc~batch_pvsh_pol_cons proc~batch_pvsh_rad_cons BATCH_PVSH_RAD_CONS program~main->proc~batch_pvsh_rad_cons proc~batch_pvsh_tor_cons BATCH_PVSH_TOR_CONS program~main->proc~batch_pvsh_tor_cons program~main->proc~batch_vsh_pol_dn_cons program~main->proc~batch_vsh_pol_up_cons proc~pvsh_pol_tor_ortho PVSH_POL_TOR_ORTHO program~main->proc~pvsh_pol_tor_ortho proc~vsh_pol_inversion VSH_POL_INVERSION program~main->proc~vsh_pol_inversion program~main->proc~batch_vsh_tor_cons proc~batch_grad_ssh_cons->interface~grad_ssh_all proc~batch_l_ssh_cons->interface~l_ssh_all proc~batch_pvsh_pol_cons->interface~pvsh_pol_all proc~batch_pvsh_rad_cons->interface~pvsh_rad_all proc~batch_pvsh_tor_cons->interface~pvsh_tor_all proc~batch_vsh_pol_dn_cons->interface~vsh_pol_dn_all proc~batch_vsh_pol_up_cons->interface~vsh_pol_up_all proc~bench_vsh_pol_dn->interface~vsh_pol_dn_all 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->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->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 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 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

Module Procedures

private subroutine ASSOC_LEGENDRE_NORM_ALL_DP(PNORM, LMAX, X)

All -normalized associated Legendre functions , (i.e. the real-valued radial part of SSH, for ), using the Holmes & Featherstone (2002) modified forward-column recurrence. The normalization is folded directly into the recurrence coefficients, keeping every intermediate value rather than letting itself grow/shrink combinatorially like the unnormalized ASSOC_LEGENDRE_ALL/Bonnet recurrence does. This is the recurrence SSH_ALL and every batch VSH routine build on.

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Arguments

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

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

Argument, (typically ).