tEIG: Tensor Eigenvalue Decomposition Using any Discrete Transform

In TensorTools: Multilinear Algebra

Tensor Eigenvalue Decomposition Using any Discrete Transform

Description

The Eigenvalue decomposition of a tensor T (n x n x k) decomposes the tensor into a tensor of eigenvectors (P) and a diagonal tensor of eigenvalues (D) so that T = P D inv(P).

Usage

tEIG(tnsr, tform)

Arguments

tnsr	a 3-mode S3 tensor class object (n x n x k)
tform	Any discrete transform. fft: Fast Fourier Transorm dwt: Discrete Wavelet Transform (Haar Wavelet) dct: Discrete Cosine transform dst: Discrete Sine transform dht: Discrete Hadley transform dwht: Discrete Walsh-Hadamard transform

Value

P, a tensor of Eigenvectors (n x n x k)

D, a diagonal tensor of Eigenvalues (n x n x k)

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Everett Sandbo

References

K. Braman, "Third-order tensors as linear operators on a space of matrices", Linear Algebra and its Applications, vol. 433, no. 7, pp. 1241-1253, 2010.

Examples

T <- t_rand(modes=c(2,2,4))
tEIG(T,"dst")

TensorTools documentation built on Oct. 18, 2024, 1:07 a.m.