spectrum {RMAT}

Obtain the ordered eigenvalue spectrum of a matrix or ensemble of matrices.

Description

Returns a tidied dataframe of the eigenvalues of a random matrix or ensemble.

Usage

spectrum(
  array,
  norm_order = TRUE,
  singular = FALSE,
  components = TRUE,
  order = NA
)

Arguments

array

a square matrix or matrix ensemble whose eigenvalues are to be returned

norm_order

sorts the eigenvalue spectrum by its norms if TRUE, otherwise sorts them by sign

singular

return the singular values of the matrix or matrix ensemble

components

returns the array with resolved real and imaginary components if TRUE, otherwise returns complex-valued eigenvalues

order

an integer or integer vector of which eigenvalue orders to return; order 1 representing the largest, order N represents smallest (where N is the number of eigenvalues). If uninitialized, defaults to returning the entire spectrum.

Value

A tidy dataframe with the real & imaginary components of the eigenvalues and their norms along with a unique index.

Examples

# Eigenvalue spectrum of a random normal matrix
P <- RM_norm(N = 5)
spec_P <- spectrum(P)

Q <- matrix(runif(2^2), ncol = 2)
spec_Q <- spectrum(Q)

# Eigenvalue spectra of ensemble matrices
ens <- RME_norm(N = 3, size = 10)
spec_ens <- spectrum(ens)