Crate fpcoa 

fpcoa: Principal Coordinate Analysis (PCoA) with fixed-rank randomized SVD. Assumptions:

• dist is dense, strictly symmetric, with zeros on the diagonal. Pipeline (Halko–Martinsson–Tropp range finder + symmetric core):

1. Build B = -0.5 * J * (D ∘ D) * J (double-centering)
2. Q = subspace_iteration_full(B, rank = k + oversample, nbiter = q) (annembed/lax)
3. B_r = Qᵀ * B * Q (r × r, symmetric)
4. Symmetric eig (nalgebra): B_r = V Λ Vᵀ (Λ sorted ↓)
5. Zero-out negative eigenvalues (and their eigenvectors)
6. U ≈ Q * V_k
7. Coordinates = U * sqrt(Λ_k)

Structs

FpcoaOptions

Options for randomized PCoA.

PCoAResult

Result of PCoA.

Functions

pcoa_randomized

Perform PCoA via randomized range finder + symmetric eig on the small core.