Function fermionic_single_pole 

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

Compute fermionic 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.

Supports negative τ with anti-periodic boundary conditions:

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

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::fermionic_single_pole;

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

let expected = -(-omega * tau).exp() / (1.0 + (-beta * omega).exp());
assert!((g - expected).abs() < 1e-15);

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