tQR: QR decomposition of a 3D tensor

In TensorTools: Multilinear Algebra

QR decomposition of a 3D tensor

Description

Decomposes a 3 mode tensor T into the product of The left singular value tensor object and a right singular value tensor object so that T = QR.

Usage

tQR(tnsr, tform)

Arguments

tnsr	a 3-mode tensor S3 class object
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

Q, The left singular value tensor object (n \times n \times k)

R, The right singular value tensor object (n \times n \times k)

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))
tQR(T,"dst")

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