rARPACK has been superseded by RSpectra to avoid the confusion on package name.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.
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
)We first generate some matrices:
library(Matrix)
= 20
n = 5
k
set.seed(111)
= matrix(rnorm(n^2), n) ## class "matrix"
A1 = Matrix(A1) ## class "dgeMatrix" A2
General matrices have complex eigenvalues:
eigs(A1, k)
eigs(A2, k, opts = list(retvec = FALSE)) ## eigenvalues only
rARPACK also works on sparse matrices:
sample(n^2, n^2 / 2)] = 0
A1[= as(A1, "dgCMatrix")
A3 = as(A1, "dgRMatrix")
A4
eigs(A3, k)
eigs(A4, k)
Function interface is also supported:
= function(x, args)
f
{as.numeric(args %*% x)
}eigs(f, k, n = n, args = A3)
Symmetric matrices have real eigenvalues.
= crossprod(A1)
A5 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
).
= 100
m = 20
n = 5
k set.seed(111)
= matrix(rnorm(m * n), m)
A
svds(A, k)
svds(t(A), k, nu = 0, nv = 3)
Similar to eigs()
, svds()
supports sparse
matrices:
sample(m * n, m * n / 2)] = 0
A[= as(A, "dgCMatrix")
Asp1 = as(A, "dgRMatrix")
Asp2
svds(Asp1, k)
svds(Asp2, k, nu = 0, nv = 0)