tLU: LU decomposition of a 3D tensor

In TensorTools: Multilinear Algebra

LU decomposition of a 3D tensor

Description

Decomposes a 3 model tensor into a lower triangular tensor and an upper triangular tensor.

Usage

tLU(tnsr, tform)

Arguments

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

Value

L, The lower triangular tensor object

U, The upper triangular tensor object a Tensor3-class object

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

Everett Sandbo

References

M. E. Kilmer, C. D. Martin, and L. Perrone, “A third-order generalization of the matrix svd as a product of third-order tensors,” Tufts University, Department of Computer Science, Tech. Rep. TR-2008-4, 2008

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))
tLU(T,"dst")

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