norm3 {ThreeWay}

Normalization of a matricized array

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

 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 [e-mail]
Henk A.L. Kiers [e-mail]
Paolo Giordani [e-mail]

References

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

See Also

cent3, nrm2

Examples

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)