# tLU: Tensor LU Decomposition Using Using Any Discrete Transform In rTensor2: MultiLinear Algebra

 tLU R Documentation

## Tensor LU Decomposition Using Using Any Discrete Transform

### Description

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

### Usage

```tLU(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 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)

### 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

```require(rTensor)
T <- rand_tensor(modes=c(2,2,4))
tLU(T,"dst")
```

rTensor2 documentation built on Aug. 14, 2022, 9:05 a.m.