# rARPACK v0.11-0

0

0th

Percentile

## Solvers for Large Scale Eigenvalue and SVD Problems

Previously an R wrapper of the 'ARPACK' library <http://www.caam.rice.edu/software/ARPACK/>, and now a shell of the R package 'RSpectra', an R interface to the 'Spectra' library <http://yixuan.cos.name/spectra/> for solving large scale eigenvalue/vector problems. The current version of 'rARPACK' simply imports and exports the functions provided by 'RSpectra'. New users of 'rARPACK' are advised to switch to the 'RSpectra' package.

### NOTE

rARPACK has been superseded by RSpectra to avoid the confusion on package name.

rARPACK was originally an R wrapper of the ARPACK library to solve large scale eigenvalue/vector problems. From version 0.8-0, it changed the backend to the Spectra library, so theoretically it no longer depended on ARPACK since then. From version 0.11-0, rARPACK was simply a shell of the RSpectra package.

Old sources are kept in the archive branch.

New users of rARPACK are advised to switch to the RSpectra package.

## Solvers for Large Scale Eigenvalue and SVD Problems

### Introduction

rARPACK 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)
• function (implicitly specify the matrix by providing a function that calculates matrix product A %*% x)

### Example

We first generate some matrices:

library(Matrix)
n = 20
k = 5

set.seed(111)
A1 = matrix(rnorm(n^2), n)  ## class "matrix"
A2 = Matrix(A1)             ## class "dgeMatrix"


General matrices have complex eigenvalues:

eigs(A1, k)
eigs(A2, k, opts = list(retvec = FALSE))  ## eigenvalues only


rARPACK also works on sparse matrices:

A1[sample(n^2, n^2 / 2)] = 0
A3 = as(A1, "dgCMatrix")
A4 = as(A1, "dgRMatrix")

eigs(A3, k)
eigs(A4, k)


Function interface is also supported:

f = function(x, args)
{
as.numeric(args %*% x)
}
eigs(f, k, n = n, args = A3)


Symmetric matrices have real eigenvalues.

A5 = crossprod(A1)
eigs_sym(A5, k)


To find the smallest (in absolute value) k eigenvalues of A5, we have two approaches:

eigs_sym(A5, k, which = "SM")
eigs_sym(A5, k, sigma = 0)


The results should be the same, but the latter method is far more stable on large matrices.

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

m = 100
n = 20
k = 5
set.seed(111)
A = matrix(rnorm(m * n), m)

svds(A, k)
svds(t(A), k, nu = 0, nv = 3)


Similar to eigs(), svds() supports sparse matrices:

A[sample(m * n, m * n / 2)] = 0
Asp1 = as(A, "dgCMatrix")
Asp2 = as(A, "dgRMatrix")

svds(Asp1, k)
svds(Asp2, k, nu = 0, nv = 0)


## Functions in rARPACK

 Name Description eigs Find a Specified Number of Eigenvalues/vectors for Square Matrix svds Find the Largest k Singular Values/Vectors of a Matrix No Results!