Centering of a matricized array

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.

See Also

Cc, norm3

Examples

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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)

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