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, ...)

Arguments

Value

Returns a list with entries:

• values n approximate largest eigenvalues

• vectors n approximate corresponding eigenvectors

Note

Specify symmetric=FALSE to compute the largest n eigenvalues and corresponding eigenvectors of the symmetric matrix cross-product t(x) %*% x.

This function uses the irlba function under the hood. See ?irlba for description of additional options, especially the tol parameter.

References

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

See Also

eigen, irlba

Examples

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]

Results