R wrapper of ARPACK for large scale eigen value/vector problems

Introduction

rARPACK is an R wrapper of the ARPACK library to solve large scale eigen value/vector problems. It is typically used to compute a few eigen values/vectors of an n by n matrix, e.g., the k largest eigen values, which is usually more efficient than eigen() if k << n.

Currently this package provides function eigs() for eigenvalue/eigenvector problems, and svds() for truncated SVD. Different matrix types in R, including sparse matrices, are supported. Below is a list of implemented ones:

• matrix (defined in base R)
• dgeMatrix (defined in Matrix package, for general matrices)
• dsyMatrix (defined in Matrix package, for symmetric matrices)
• dgCMatrix (defined in Matrix package, for column oriented sparse matrices)
• dgRMatrix (defined in Matrix package, for row oriented sparse matrices)

Example

Set up matrices.

library(rARPACK)
library(Matrix)
n = 10
k = 5
set.seed(123)
x = matrix(rnorm(n^2), n)
x[sample(n^2, floor(n^2 / 2))] = 0

xsp = as(x, "sparseMatrix");

y = crossprod(x);
ysy = as(y, "symmetricMatrix");

Compute the largest 5 eigenvalues with corresponding eigenvectors.

eigs(y, k)
eigs(ysy, k)

Compute the smallest 5 eigenvalues with corresponding eigenvectors

eigs(ysy, k, which = "SM")

or

eigs(ysy, k, sigma = 0)

Complex eigenvalues, on sparse matrix.

eigs(xsp, k)

SVD, you can specify the number of singular values(k), number of left singular vectors(nu) and number of right singular vectors(nv).

n = 10
p = 8
k = 5
set.seed(123)
x = matrix(rnorm(n * p), n)
x[sample(n * p, floor(n * p / 2))] = 0
xsp = as(x, "sparseMatrix")
xspt = t(xsp)

svds(x, k)
svds(xsp, k, nu = 0)
svds(xspt, k, nu = 0, nv = 0)