Function sequential_scan 

pub fn sequential_scan<T: Float>(a: &[T], b: &[T], h0: T) -> Vec<T>

Sequential (recurrent) scan — the correctness baseline that every other scan in the crate is tested against.

Evaluates the first-order linear recurrence h_t = a_t * h_{t-1} + b_t, with h_{-1} = h0 left-to-right, returning the full state sequence [h_0, ..., h_{n-1}].

• a: per-step decay / transition coefficients
• b: per-step inputs (must be the same length as a)
• h0: the initial state fed in before the first step

Setting a_t = 1 everywhere collapses this into a plain prefix sum (running total) of b — the easiest case to eyeball, which is exactly what the test below checks.

Cost: O(n), one multiply-add per element. Inherently sequential: each step needs the previous h, so it can’t be parallelized as-is. chunked_scan exists to break that dependency for large inputs; this function is the reference it must match. Generic over the float type T (f32 for speed, f64 for numerical testing).

Example

use zilla_muf::scan::sequential_scan;
// a = 1 everywhere → plain prefix sum of b
let h = sequential_scan(&[1.0, 1.0, 1.0], &[1.0, 2.0, 3.0], 0.0);
assert_eq!(h, vec![1.0, 3.0, 6.0]);