# amprod: k-mode product. In tensr: Covariance Inference and Decompositions for Tensor Datasets

## Description

`amprod` returns the k-mode product of an array with a matrix.

## Usage

 `1` ```amprod(A, M, k) ```

## Arguments

 `A` A real valued array. `M` A real matrix. `k` An integer. The mode along which `M` is to be multiplied to `A`.

## Details

The k-mode product of a tensor A with a matrix M results in a tensor whose k-mode unfolding is M times the k-mode unfolding of A. That is `mat(amprod(A,M,k)) = M %*% mat(A,k)`. More details of the k-mode product can be found in Kolda and Bader (2009).

## Value

An array whose k-mode unfolding is ```M %*% mat(A,k)```.

Peter Hoff.

## References

Kolda, T. G., & Bader, B. W. (2009). Tensor decompositions and applications. SIAM review, 51(3), 455-500.

`atrans` for applying multiple k-mode products.

## Examples

 ```1 2 3 4 5``` ```A <- array(1:8, dim = c(2,2,2)) M <- matrix(1:4, nrow = 2, ncol = 2) Y <- amprod(A, M, 2) Y identical(M %*% mat(A,2), mat(Y,2)) ```

### Example output

```, , 1

[,1] [,2]
[1,]   10   14
[2,]   14   20

, , 2

[,1] [,2]
[1,]   26   38
[2,]   30   44

[1] TRUE
```

tensr documentation built on May 2, 2019, 2:32 p.m.