Function dpss 

pub fn dpss(m: usize, nw: f64) -> FerrayResult<Array<f64, Ix1>>

Discrete prolate spheroidal sequence (Slepian taper) (#745).

Returns the dominant DPSS — the eigenvector of the canonical time–frequency concentration tridiagonal matrix corresponding to the largest eigenvalue. Equivalent to scipy.signal.windows.dpss(m, NW) with the default Kmax=None (single window, sym=True, no ratios).

nw is the standardised half bandwidth (NW = M·W), typically in the range 2..=4 for spectral analysis.

Computed by warm-up power iteration followed by Rayleigh-quotient inverse iteration (RQI) on the symmetric tridiagonal concentration matrix

  d[i]  = ((M-1)/2 − i)² · cos(2π · NW / M)
  e[i]  = (i+1)(M−i−1) / 2

Power iteration alone converges only linearly with rate λ₂/λ₁, which is far too slow for the nearly-degenerate dominant DPSS eigenvalues; RQI achieves cubic local convergence near the dominant eigenpair via tridiagonal LU (Thomas algorithm) solves of (T - σI) w = v. The result is sign-flipped if needed so the centre value is positive, and peak-normalised (matching scipy’s default norm='approximate').

Multiple Slepian sequences (Kmax > 1) need orthogonal power-iteration / deflation; tracked as a future extension.

Errors

FerrayError::InvalidValue if nw is non-finite, nw <= 0, or nw >= m / 2 (the band would degenerate).