Block Lanczos SVD via block Krylov iteration

Computes a truncated SVD using a block Lanczos bidiagonalization. Each Krylov step issues one GPU GEMM per block rather than sequential GEMVs, significantly reducing kernel-launch overhead on accelerated backends.

Usage

block_lanczos(
  A,
  nv = 5L,
  nu = nv,
  block_size = NULL,
  n_steps = NULL,
  mode = "fast",
  backend = NULL
)

block_svd(
  A,
  k,
  block_size = NULL,
  n_steps = NULL,
  mode = "fast",
  backend = NULL
)

Arguments

A

Numeric matrix, adgeMatrix, or adgCMatrix. Plain matrices are coerced to adgeMatrix using mode and backend.

nv

Number of right singular vectors to return.

nu

Number of left singular vectors to return. Defaults to nv.

block_size

Integer block width for the Krylov iteration. When NULL (default), a size is chosen automatically based on nv and nu.

n_steps

Number of Krylov steps. When NULL (default), chosen automatically.

mode

Execution mode passed to adgeMatrix() when coercing plain matrices.

backend

Backend name passed to adgeMatrix() when coercing plain matrices. Ignored when A is already an aMatrix.

k

Number of singular values/vectors. Alias for nv = nu = k.

Value

A named list with components:

u

Numeric matrix [m, nu]: left singular vectors.

d

Numeric vector of length min(nu, nv): singular values in decreasing order.

v

Numeric matrix [n, nv]: right singular vectors.

iter

Integer: number of Krylov steps performed.

mprod

Integer: total matrix-vector products issued.

See also

rsvd, block_svd

Examples

A <- matrix(rnorm(200), nrow = 20)
res <- block_lanczos(A, nv = 3L)
length(res$d)
#> [1] 3