Skip to content

yixuan/rARPACK

Folders and files

NameName
Last commit message
Last commit date

Latest commit

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Repository files navigation

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rARPACK has been superseded by RSpectra to avoid the confusion on package name.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

About

Solvers for Large Scale Eigenvalue and SVD Problems

Resources

License

Stars

Watchers

Forks

Releases

No releases published

Packages

No packages published

Languages