irlba: Find a few approximate largest singular values and corresponding singular vectors of a matrix.

Description

The augmented implicitly restarted Lanczos bidiagonalization algorithm (IRLBA) finds a few approximate largest singular values and corresponding singular vectors of a sparse or dense matrix using a method of Baglama and Reichel. It is a fast and memory-efficient way to compute a partial SVD.

Usage

irlba(A, nv = 5, nu, maxit = 1000, work = nv + 7, reorth = TRUE, tol = 1e-05, v = NULL, right_only = FALSE, verbose = FALSE, scale, center, du, ds, dv, shift, mult, fastpath = TRUE)

Arguments

numeric real- or complex-valued matrix or real-valued sparse matrix.

number of right singular vectors to estimate.

number of left singular vectors to estimate (defaults to nv).

maxit

maximum number of iterations.

work

working subspace dimension, larger values can speed convergence at the cost of more memory use.

reorth

if TRUE, apply full reorthogonalization to both SVD bases, otherwise only apply reorthogonalization to the right SVD basis vectors; the latter case is cheaper per iteration but, overall, may require more iterations for convergence. Always set to TRUE when fastpath=TRUE (see below).

tol

convergence is determined when $||AV - US|| < tol*||A||$, where the spectral norm ||A|| is approximated by the largest estimated singular value, and U, V, S are the matrices corresponding to the estimated left and right singular vectors, and diagonal matrix of estimated singular values, respectively.

optional starting vector or output from a previous run of irlba used to restart the algorithm from where it left off (see the notes).

right_only

logical value indicating return only the right singular vectors (TRUE) or both sets of vectors (FALSE). The right_only option can be cheaper to compute and use much less memory when nrow(A) >> ncol(A) but note that right_only = TRUE sets fastpath = FALSE (only use this option for really large problems that run out of memory).

verbose

logical value that when TRUE prints status messages during the computation.

scale

optional column scaling vector whose values divide each column of A; must be as long as the number of columns of A (see notes).

center

optional column centering vector whose values are subtracted from each column of A; must be as long as the number of columns of A and may

DEPRECATED optional subspace deflation vector (see notes).

DEPRECATED optional subspace deflation scalar (see notes).

DEPRECATED optional subspace deflation vector (see notes).

shift

optional shift value (square matrices only, see notes).

mult

optional custom matrix multiplication function (default is %*%, see notes).

fastpath

try a fast C algorithm implementation if possible; set fastpath=FALSE to use the reference R implementation. See notes.

Value

Returns a list with entries:

References

Augmented Implicitly Restarted Lanczos Bidiagonalization Methods, J. Baglama and L. Reichel, SIAM J. Sci. Comput. 2005.

Examples

Run this code

set.seed(1)

A <- matrix(runif(400), nrow=20)
S <- irlba(A, 3)
S$d

# Compare with svd
svd(A)$d[1:3]

# Restart the algorithm to compute more singular values
# (starting with an existing solution S)
S1 <- irlba(A, 5, v=S)

# Principal components (see also prcomp_irlba)
P <- irlba(A, nv=1, center=colMeans(A))

# Compare with prcomp and prcomp_irlba (might vary up to sign)
cbind(P$v,
      prcomp(A)$rotation[, 1],
      prcomp_irlba(A)$rotation[, 1])

# A custom matrix multiplication function that scales the columns of A
# (cf the scale option). This function scales the columns of A to unit norm.
col_scale <- sqrt(apply(A, 2, crossprod))
mult <- function(x, y)
        {
          # check if x is a  vector
          if (is.vector(x))
          {
            return((x %*% y) / col_scale)
          }
          # else x is the matrix
          x %*% (y / col_scale)
        }
irlba(A, 3, mult=mult)$d

# Compare with:
irlba(A, 3, scale=col_scale)$d

# Compare with:
svd(sweep(A, 2, col_scale, FUN=`/`))$d[1:3]

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