Performs a tensor LU decomposition on any 3-mode tensor using any discrete transform.
: a 3-mode tensor
: 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
a Tensor-class object
If LU decomposition is performed on a n x n x k tensor, the components in the returned value are:
L: The lower triangular tensor object (n x n x k)
U: The upper triangular tensor object (n x n x k)
Kyle Caudle firstname.lastname@example.org
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.
require(rTensor) T <- rand_tensor(modes=c(2,2,4)) tLU(T,"dst")
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