# cent3: Centering of a matricized array In ThreeWay: Three-Way Component Analysis

## Description

Centering of a matricized array across one mode (modes indicated by 1,2, or 3).

## Usage

 `1` ``` cent3(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` Centering option (1 if `X` is centered across `A`-mode, 2 if `X` is centered across `B`-mode, 3 if `X` is centered across `C`-mode)

## Value

 `Y` Matrix of order (`n` `x` `mp`) containing the centered 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.

`Cc`, `norm3`
 ``` 1 2 3 4 5 6 7 8 9 10``` ```X <- array(c(rnorm(120)),c(6,5,4)) # matricized array Y <- supermat(X) # data centered across A-mode Z <- cent3(Y\$Xa, 6, 5, 4, 1) apply(Z,2,mean) # data centered also across B-modes (double centering) Z <- cent3(Z, 6, 5, 4, 2) apply(Z,1,mean) apply(Z,2,mean) ```