Find a few approximate largest eigenvalues and corresponding eigenvectors of a symmetric matrix.
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.
partial_eigen(x, n = 5, symmetric = TRUE, ...)
x |
numeric real-valued dense or sparse matrix. |
n |
number of largest eigenvalues and corresponding eigenvectors to compute. |
symmetric |
|
... |
optional additional parameters passed to the |
Returns a list with entries:
values n approximate largest eigenvalues
vectors n approximate corresponding eigenvectors
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.
See the RSpectra package https://cran.r-project.org/package=RSpectra for more comprehensive partial eigenvalue decomposition.
Augmented Implicitly Restarted Lanczos Bidiagonalization Methods, J. Baglama and L. Reichel, SIAM J. Sci. Comput. 2005.
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
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