satellitetoolbox-legendre

name	satellitetoolbox-legendre
description	SatelliteToolboxLegendre.jl for computing associated Legendre functions and derivatives. Use when working with spherical harmonics, gravity field expansions, or geomagnetic field computations.

SatelliteToolboxLegendre.jl

Associated Legendre functions and derivatives with multiple normalization options. Repo: JuliaSpace/SatelliteToolboxLegendre.jl

Computing Legendre Functions

# P[n+1, m+1] = P_{n,m}[cos(ϕ)]
P = legendre(Val(:full), ϕ, n_max)                    # Full normalization
P = legendre(Val(:schmidt), ϕ, n_max, m_max)          # Schmidt semi-normalization
P = legendre(Val(:unnormalized), ϕ, n_max)            # Unnormalized

# In-place (zero-allocation)
legendre!(Val(:full), P, ϕ, n_max, m_max)

Computing Derivatives

(dP, P) = dlegendre(Val(:full), ϕ, n_max)             # Returns both dP and P
dlegendre!(dP, ϕ, P, n_max, m_max)                     # In-place (P must be pre-computed)

Key Conventions

• First argument N selects normalization: Val(:full), Val(:schmidt), Val(:unnormalized)
• Angle ϕ in radians
• Indexing: P[n+1, m+1] for degree n, order m
• Optional ph_term=true includes Condon-Shortley phase (-1)^m
• In-place variants infer n_max/m_max from matrix dimensions if omitted
• Zero external dependencies (pure Julia)