# Tensor-class

##### S4 Class for a Tensor

An S4 class for a tensor with arbitrary number of modes. The Tensor class extends the base 'array' class to include additional tensor manipulation (folding, unfolding, reshaping, subsetting) as well as a formal class definition that enables more explicit tensor algebra.

##### Details

This can be seen as a wrapper class to the base `array`

class. While it is possible to create an instance using `new`

, it is also possible to do so by passing the data into `as.tensor`

.

Each slot of a Tensor instance can be obtained using `@`

.

The following methods are overloaded for the Tensor class: `dim-methods`

, `head-methods`

, `tail-methods`

, `print-methods`

, `show-methods`

, element-wise array operations, array subsetting (extract via `['), array subset replacing (replace via `[<-'), and `tperm-methods`

, which is a wrapper around the base `aperm`

method.

To sum across any one mode of a tenor, use the function `modeSum-methods`

. To compute the mean across any one mode, use `modeMean-methods`

.

You can always unfold any Tensor into a matrix, and the `unfold-methods`

, `k_unfold-methods`

, and `matvec-methods`

methods are for that purpose. The output can be kept as a Tensor with 2 modes or a `matrix`

object. The vectorization function is also provided as `vec`

. See the attached vignette for a visualization of the different unfoldings.

Conversion from `array`

/`matrix`

to Tensor is facilitated via `as.tensor`

. To convert from a Tensor instance, simply invoke `@data`

.

The Frobenius norm of the Tensor is given by `fnorm-methods`

, while the inner product between two Tensors (of equal modes) is given by `innerProd-methods`

. You can also sum through any one mode to obtain the K-1 Tensor sum using `modeSum-methods`

. `modeMean-methods`

provides similar functionality to obtain the K-1 Tensor mean. These are primarily meant to be used internally but may be useful in doing statistics with Tensors.

For Tensors with 3 modes, we also overloaded `t`

(transpose) defined by Kilmer et.al (2013). See `t-methods`

.

To create a Tensor with i.i.d. random normal(0, 1) entries, see `rand_tensor`

.

##### Note

All of the decompositions and regression models in this package require a Tensor input.

##### Slots

- num_modes
number of modes (integer)

- modes
vector of modes (integer), aka sizes/extents/dimensions

- data
actual data of the tensor, which can be 'array' or 'vector'

##### Methods

- [
`signature(tnsr = "Tensor")`

: ...- [<-
`signature(tnsr = "Tensor")`

: ...- matvec
`signature(tnsr = "Tensor")`

: ...- dim
`signature(tnsr = "Tensor")`

: ...- fnorm
`signature(tnsr = "Tensor")`

: ...- head
`signature(tnsr = "Tensor")`

: ...- initialize
`signature(.Object = "Tensor")`

: ...- innerProd
`signature(tnsr1 = "Tensor", tnsr2 = "Tensor")`

: ...- modeMean
`signature(tnsr = "Tensor")`

: ...- modeSum
`signature(tnsr = "Tensor")`

: ...- Ops
`signature(e1 = "array", e2 = "Tensor")`

: ...- Ops
`signature(e1 = "numeric", e2 = "Tensor")`

: ...- Ops
`signature(e1 = "Tensor", e2 = "array")`

: ...- Ops
`signature(e1 = "Tensor", e2 = "numeric")`

: ...- Ops
`signature(e1 = "Tensor", e2 = "Tensor")`

: ...`signature(tnsr = "Tensor")`

: ...- k_unfold
`signature(tnsr = "Tensor")`

: ...- show
`signature(tnsr = "Tensor")`

: ...- t
`signature(tnsr = "Tensor")`

: ...- tail
`signature(tnsr = "Tensor")`

: ...- unfold
`signature(tnsr = "Tensor")`

: ...- tperm
`signature(tnsr = "Tensor")`

: ...- image
`signature(tnsr = "Tensor")`

: ...

##### References

James Li, Jacob Bien, Martin T. Wells (2018). rTensor: An R Package for Multidimensional Array (Tensor) Unfolding, Multiplication, and Decomposition. Journal of Statistical Software, 87(10), 1-31. URL http://www.jstatsoft.org/v087/i10/.

##### See Also

##### Examples

```
# NOT RUN {
tnsr <- rand_tensor()
class(tnsr)
tnsr
print(tnsr)
dim(tnsr)
tnsr@num_modes
tnsr@data
# }
```

*Documentation reproduced from package rTensor, version 1.4, License: GPL (>= 2)*