Struct PolarTranslation 

pub struct PolarTranslation {
    terms: Vec<(i32, Complex)>,
    order: i32,
    degrees: [i32; 2],
    radial: Radial,
}

Fixed spherical mode-pair couplings shared across displacements and pullbacks.

Upstream: treams.sw.translate of one mode pair, which combines treams.special.tl_vsw_A and tl_vsw_B (tl_vsw_rA and tl_vsw_rB for regular waves).

Fields

terms: Vec<(i32, Complex)>

Degree and weight of each term.

order: i32

Order difference source.m - destination.m, shared by all terms.

degrees: [i32; 2]

Smallest and largest term degree.

radial: Radial

Implementations

impl PolarTranslation

pub fn new( destination: Mode, source: Mode, helicity: bool, radial: Radial, ) -> Result<Self>

Prepare one mode pair in helicity or parity polarization.

fn radial_row<const N: usize>(&self, z: Jet<N>) -> Result<Option<Vec<Jet<N>>>>

Spherical radial jets z_p(kr) of the term degrees, indexed by p minus the smallest degree, or None when each term evaluates its own.

Outgoing functions come from one AMOS sequence over the degree range. Regular derivatives outside the series region evaluate each single value once and share j_p between the value of degree p and the derivative of p - 1, so they equal those of crate::special::spherical_radial bitwise.

fn evaluate<const N: usize>(&self, args: [Complex; 3]) -> Result<Jet<N>>

The coefficient sum_p weight_p z_p(kr) P_p^order(cos theta) e^(i order phi) at args = [kr, theta, phi], with the derivatives with respect to the N leading arguments.

fn evaluate_jets<const N: usize>(&self, args: [Jet<N>; 3]) -> Result<Jet<N>>

One numerical kernel for value-only, coordinate and directional jets.

pub fn is_self_term(radial: Radial, kr: Complex) -> bool

Whether the polarized coefficient of radial waves at the radial argument kr is the self term, which is zero: singular waves with |kr| < 1e-16, which includes coinciding expansion centres. The tl_vsw_* coefficients have no such rule.

Upstream: treams.sw.translate, which returns zero there. Differences: treams returns this zero for any mode labels, such as l = 0 or polarization 2; the sw.translate ufunc checks the labels first and rejects those.

pub fn value(&self, args: [Complex; 3]) -> Result<Complex>

Evaluate at (kr, theta, phi); all three arguments may be complex.

pub fn pullback( &self, args: [Complex; 3], cotangent: Complex, ) -> Result<[Complex; 3]>

The gradients of the three arguments from a complex scalar cotangent.

Trait Implementations

impl Debug for PolarTranslation

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.