| tQR {rTensor2} | R Documentation |
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 kyle.caudle@sdsmt.edu
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")