partial_eigen: Find a few approximate largest eigenvalues and corresponding eigenvectors of a symmetric matrix.

Description

Use partial_eigen to estimate a subset of the largest (most positive) eigenvalues and corresponding eigenvectors of a symmetric dense or sparse real-valued matrix.

Usage

partial_eigen(x, n = 5, symmetric = TRUE, ...)

Value

Returns a list with entries:

values n approximate largest eigenvalues
vectors n approximate corresponding eigenvectors

Arguments

x: numeric real-valued dense or sparse matrix.
n: number of largest eigenvalues and corresponding eigenvectors to compute.
symmetric: TRUE indicates x is a symmetric matrix (the default); specify symmetric=FALSE to compute the largest eigenvalues and corresponding eigenvectors of t(x) %*% x instead.
...: optional additional parameters passed to the irlba function.

References

Augmented Implicitly Restarted Lanczos Bidiagonalization Methods, J. Baglama and L. Reichel, SIAM J. Sci. Comput. 2005.

Examples

Run this code

set.seed(1)
# Construct a symmetric matrix with some positive and negative eigenvalues:
V <- qr.Q(qr(matrix(runif(100), nrow=10)))
x <- V %*% diag(c(10, -9, 8, -7, 6, -5, 4, -3, 2, -1)) %*% t(V)
partial_eigen(x, 3)$values

# Compare with eigen
eigen(x)$values[1:3]

# Use symmetric=FALSE to compute the eigenvalues of t(x) %*% x for general
# matrices x:
x <- matrix(rnorm(100), 10)
partial_eigen(x, 3, symmetric=FALSE)$values
eigen(crossprod(x))$values