C++ Library For Large Scale Eigenvalue Problems

R Interface

The RSpectra Package

RSpectra is the R interface of Spectra. It provides functions eigs() and eigs_sym() for eigenvalue problems, and svds() for truncated (partial) SVD. These functions are generic, meaning that 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)

Quick Examples

Eigenvalue Problems

We first generate some matrices:

n = 20
k = 5

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

RSpectra 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 preferred, since it is much more stable on large matrices.

SVD Problems

For SVD problems, users can 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
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)


The function-by-function reference can be found in this manual and in the built-in help system of R by typing ?RSpectra::eigs and ?RSpectra::svds