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Generalized Eigenproblem Adaptive Power Method (GEAP)

Source: R/tensor_eigen.R
eig_geap.Rd

Computes a generalized tensor eigenpair A x^(m-1) = lambda B x^(m-1), ||x|| = 1, for symmetric A and symmetric positive definite B using the GEAP method of Kolda & Mayo (Algorithm 1), mirroring the MATLAB Tensor Toolbox eig_geap. With B = teneye(m, n) this reduces to eig_sshopm().

Usage

eig_geap(
  A,
  B,
  maximize = TRUE,
  start = NULL,
  tol = 1e-10,
  maxiters = 500L,
  tau = 1e-06
)

Arguments

A

A symmetric Tensor (all modes the same size).

B

A symmetric positive definite Tensor of the same size and order.

maximize

Logical; TRUE (default) seeks local maxima (beta = 1), FALSE seeks local minima (beta = -1).

start

Optional starting vector; random normal if omitted.

tol

Convergence tolerance on the eigenvalue change (default 1e-10).

maxiters

Maximum iterations (default 500).

tau

Positive-definiteness threshold for the adaptive shift (default 1e-6).

Value

A list with elements lambda, x, converged, iterations, and lambda_trace.

References

Kolda, T. G. and Mayo, J. R. (2014). An adaptive shifted power method for computing generalized tensor eigenpairs. SIAM J. Matrix Anal. Appl. 35(4), 1563-1581.

Examples

set.seed(1)
A <- symmetrize(tensor(array(rnorm(81), dim = c(3, 3, 3, 3))))
res <- eig_geap(A, teneye(4, 3))