GPU-native truncated SVD via Lanczos bidiagonalization

Implements Golub-Kahan Lanczos bidiagonalization directly in ArrayFire C, keeping all matvecs and CGS2 reorthogonalization on the GPU. Only 2*work scalars and the final basis matrices cross PCIe per restart; no per-step host transfers.

Usage

irlba_native(
  A,
  nv = 5L,
  nu = nv,
  tol = sqrt(.Machine$double.eps),
  maxit = 100L,
  work = max(nv + 20L, 3L * nv),
  v0 = NULL,
  mode = "fast",
  backend = NULL
)

Arguments

A

A matrix or adgeMatrix. Coerced if necessary.

nv

Number of singular values/vectors to compute.

nu

Number of left singular vectors (default = nv).

tol

Convergence tolerance.

maxit

Maximum number of restarts.

work

Size of the Lanczos subspace per restart. Larger values converge in fewer restarts at the cost of more memory and work per restart. Default is max(nv + 20L, 3L * nv).

v0

Optional starting vector (length ncol(A)).

mode, backend

Passed to adgeMatrix() when coercing.

Value

A list with components d, u, v, iter, mprod, compatible with irlba::irlba().

Details

Compared to am_irlba, which routes each Lanczos matvec through S4 dispatch, this function:

• eliminates S4 overhead on the hot path

• replaces k sequential GEMVs for reorthogonalization with one GEMM

• uploads A once and never re-uploads it across restarts

See also

irlba, adgeMatrix