# norm3: Normalization of a matricized array In ThreeWay: Three-Way Component Analysis

## Description

Normalization of a matricized array within one mode (modes indicated by 1,2, or 3) to sum of squares equal to product of size of other modes.

## Usage

 `1` ``` norm3(X, n, m, p, mode) ```

## Arguments

 `X` Matrix (or data.frame coerced to a matrix) of order (`n` `x` `mp`) containing the matricized array (frontal slices) `n` Number of `A`-mode entities `m` Number of `B`-mode entities `p` Number of `C`-mode entities `mode` Normalization option (1 if `X` is normalized within `A`-mode, 2 if `X` is normalized within `B`-mode, 3 if `X` is normalized within `C`-mode)

## Value

 `Y` Matrix of order (`n` `x` `mp`) containing the normalized matricized array (frontal slices)

## Author(s)

Maria Antonietta Del Ferraro mariaantonietta.delferraro@yahoo.it
Henk A.L. Kiers h.a.l.kiers@rug.nl
Paolo Giordani paolo.giordani@uniroma1.it

## References

H.A.L. Kiers (2000). Towards a standardized notation and terminology in multiway analysis. Journal of Chemometrics 14:105–122.

`cent3`, `nrm2`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```X <- array(c(rnorm(120)), c(6,5,4)) # matricized array Y <- supermat(X) # data normalized within A-mode Z <- norm3(Y\$Xa, 6, 5, 4, 1) apply(Z^2,1,sum) # data normalized within C-mode Z <- norm3(Y\$Xa, 6, 5, 4, 3) Z <- permnew(Z, 6, 5, 4) Z <- permnew(Z, 5, 4, 6) apply(Z^2, 1, sum) ```

### Example output

```[1] 20 20 20 20 20 20
[1] 30 30 30 30
```

ThreeWay documentation built on May 2, 2019, 9:20 a.m.