tQR: Tensor QR Decomposition Using Using Any Discrete Transform

In rTensor2: MultiLinear Algebra

Tensor QR Decomposition Using Using Any Discrete Transform

Description

Performs a tensor QR decomposition on any 3-mode tensor using any discrete transform.

Usage

tQR(tnsr,tform)

Arguments

tnsr	: a 3-mode tensor
tform	: Any discrete transform. Supported transforms are: 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

a Tensor-class object

If the QR decomposition is performed on a n \times n \times k tensor, the components in the returned value are:

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 [e-mail]

References

Kernfeld, E., Kilmer, M., & Aeron, S. (2015). Tensor-tensor products with invertible linear transforms. Linear Algebra and its Applications, 485, 545-570.

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 <- rand_tensor(modes=c(2,2,4))
tQR(T,"dst")

rTensor2 documentation built on May 29, 2024, 8:34 a.m.