TensorTools (version 1.0.0)

tEIG: 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)

Value

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

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

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

Author

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")