Implicitly-restarted Lanczos methods for fast truncated singular value decomposition of sparse and dense matrices (also referred to as partial SVD). IRLBA stands for Augmented, Implicitly Restarted Lanczos Bidiagonalization Algorithm. The package provides the following functions (see help on each for details and examples).

Help documentation for each function includes extensive documentation and examples. Also see the package vignette, vignette("irlba", package="irlba").

An overview web page is here:

What’s new in Version 2.3.0?

Deprecated features

The mult argument is deprecated and will be removed in a future version. We now recommend simply defining a custom class with a custom multiplcation operator. The example below illustrates the old and new approaches.

A <- matrix(rnorm(100), 10)

# ------------------ old way ----------------------------------------------
# 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
## [1] 1.820227 1.622988 1.067185

# Compare with:
irlba(A, 3, scale=col_scale)$d
## [1] 1.820227 1.622988 1.067185

# Compare with:
svd(sweep(A, 2, col_scale, FUN=`/`))$d[1:3]
## [1] 1.820227 1.622988 1.067185

# ------------------ new way ----------------------------------------------
setClass("scaled_matrix", contains="matrix", slots=c(scale="numeric"))
setMethod("%*%", signature(x="scaled_matrix", y="numeric"), function(x ,y) x@.Data %*% (y / x@scale))
setMethod("%*%", signature(x="numeric", y="scaled_matrix"), function(x ,y) (x %*% y@.Data) / y@scale)
a <- new("scaled_matrix", A, scale=col_scale)

irlba(a, 3)$d
## [1] 1.820227 1.622988 1.067185

We have learned that using R’s existing S4 system is simpler, easier, and more flexible than using custom arguments with idiosyncratic syntax and behavior. We’ve even used the new approach to implement distributed parallel matrix products for very large problems with amazingly little code.

Wishlist / help wanted…



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