Struct ScaledGammaLadder 

pub(crate) struct ScaledGammaLadder {
    degree: f64,
    argument: Complex,
    modulus: f64,
    exponential: Complex,
    reflected: bool,
    upper: Option<Complex>,
    pending: Vec<Complex>,
}

Scaled incomplete gamma functions R(d) = Gamma(d, a) / a^d of one argument at descending degrees d = n, n-1, ...: downward by R(d) = (a R(d+1) - e^-a) / d, which is stable once |d| >= |a|, and above that upward from one upper_gamma evaluation up to LADDER_RUN degrees lower. At a = 0 every value is the limit -1/d. reflected selects the branch -sqrt(a) for half-integer degrees.

Fields

degree: f64

argument: Complex

modulus: f64

|a|, which every step compares with the degree.

exponential: Complex

reflected: bool

upper: Option<Complex>

R one degree higher, once one value exists.

pending: Vec<Complex>

Values of the next degrees from the upward recurrence; the last one is next.

Implementations

impl ScaledGammaLadder

pub(crate) fn new(n: f64, argument: Complex, reflected: bool) -> Self

A ladder whose first value is R(n).

pub(crate) fn next_lower(&mut self) -> Complex

The next value: R(n) first, then one degree lower each call.

fn seed(&self, degree: f64) -> Complex

R on the selected branch from one gamma evaluation, or its limit at a = 0. Where Gamma(d, a) or a^d leave the normal range of f64 (near |d| = |a| from |a| of about 120, at far evanescent orders of the lattice sums) R = e^-a h comes from the continued fraction h itself; the division scales the denominator first.

fn run_down(&self) -> Complex

R at the current, stable degree from the degree nearest zero (at most -1/2) below which every downward step is stable, so that tiny |a| never meets a^d at a large one.

fn run_up(&mut self) -> Complex

R at the current degree by the upward recurrence R(d+1) = (d R(d) + e^-a) / a, whose error shrinks by |d| / |a| per step, from one evaluation at the lowest degree with |d| < |a| (or the current one), queuing the values in between.

Trait Implementations

impl Clone for ScaledGammaLadder

fn clone(&self) -> ScaledGammaLadder

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for ScaledGammaLadder

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

Formats the value using the given formatter.