Struct SmallSplitKambe 

pub(crate) struct SmallSplitKambe {
    eta: Complex,
    cancellation: f64,
    coefficients: Vec<Complex>,
}

Kambe integrals I_n(z, eta) of the real-space terms of an Ewald sum at a split below every automatic one (Self::get), with the coefficients c^j / j! of their series at c = 1 / (2 eta^2), which every integral at that split shares. There the closed-form pair and its recurrence (kambe_with_bound) cancel by up to e^Re(c) (each error function loses about |a|^2 ulps to exp(-a^2) at its argument a = (z eta -+ i / eta) / sqrt 2), while the series sums terms of one phase for real z and eta; its coefficients are rounded from double-double arithmetic, since recurred in double they carry the rounding of c into every integral alike.

Fields

eta: Complex

cancellation: f64

|c| - Re c, the cancellation of the series.

coefficients: Vec<Complex>

Implementations

impl SmallSplitKambe

pub(crate) fn new(eta: Complex) -> Self

The coefficients of the series at the split eta, as many as it may take.

pub(crate) fn get<const K: usize>( &self, orders: [i32; K], z: Complex, floor: f64, ) -> [(Complex, f64); K]

I_n(z, eta) of orders (from -1 up), each with a first-order bound on its absolute rounding error in units of epsilon that counts the conditioning of the elementary functions it takes: from the closed forms where the bound of the first order stays within CLOSED_ULPS of its value or within floor (an error the caller can afford), or where the series would cancel as much; otherwise from the series where it is finite and bounds the first order at least as tightly.

fn closed(&self, n: i32, z: Complex, ulps: f64) -> (Complex, f64)

kambe_with_bound from the closed-form pair (the series pair for odd orders) and the upward recurrence, with the bounds of the pair and of the endpoint terms scaled by the conditioning of the functions they take, and ulps those of the series.

Trait Implementations

impl Clone for SmallSplitKambe

fn clone(&self) -> SmallSplitKambe

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for SmallSplitKambe

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

Formats the value using the given formatter.