Function bosonic_single_pole 

pub fn bosonic_single_pole(
    tau: f64,
    omega: f64,
    beta: f64,
) -> Result<f64, Error>

Compute bosonic single-pole Green’s function at imaginary time τ

Evaluates G(τ) = -exp(-ω×τ) / (1 - exp(-β×ω)) for a single pole at frequency ω.

This is the imaginary-time counterpart of giwn_single_pole: G(iνn) = ∫₀^β dτ exp(iνn×τ) G(τ) = 1/(iνn - ω). G(τ) is negative for ω > 0 and positive for ω < 0, the same sign convention as fermionic_single_pole and the bosonic τ functions of DiscreteLehmannRepresentation.

Supports negative τ with periodic boundary conditions:

• G(τ + β) = G(τ) (bosonic periodicity)
• Valid for τ ∈ [-β, β]; τ is normalized with normalize_tau

ω = 0 is a genuine pole of the Bose factor, so the result is infinite there: -inf for omega = +0.0 (the ω → 0⁺ limit) and +inf for omega = -0.0. DiscreteLehmannRepresentation evaluates a zero pole through its finite, regularized limit instead.

Arguments

• tau - Imaginary time τ ∈ [-β, β]
• omega - Pole position (real frequency)
• beta - Inverse temperature

Returns

Real-valued Green’s function G(τ)

Errors

• Error::InvalidParameter if beta is not positive and finite, or omega is not finite
• Error::OutOfDomain if tau is outside [-β, β] or NaN

Example

use sparse_ir::bosonic_single_pole;

let beta = 1.0;
let omega = 5.0;
let tau = 0.5 * beta;
let g = bosonic_single_pole(tau, omega, beta).unwrap();

let expected = -(-omega * tau).exp() / (1.0 - (-beta * omega).exp());
assert!((g - expected).abs() <= 1e-14 * expected.abs());
assert!(g < 0.0);

// Periodicity: G(τ - β) = G(τ)
assert!((bosonic_single_pole(tau - beta, omega, beta).unwrap() - g).abs() < 1e-15);