Function spectral_transfer_inverse 

fn spectral_transfer_inverse(
    a_f: DMatrix<Complex<f64>>,
) -> Option<DMatrix<Complex<f64>>>

Invert the MVAR spectral matrix A(f) to the transfer function H(f) = A(f)⁻¹ via LU factorisation, returning None when A(f) is numerically singular (|det A(f)| < 1e-30).

A(f) is non-Hermitian, so LU — not Cholesky — is the structured factorisation. A single factorisation yields both the singularity test (its determinant) and the inverse, replacing the former separate complex Gauss-Jordan inverse and Gaussian-elimination determinant.