RH {SMMA}

The Rotated H-transform of a 3d Array by a Matrix

Description

This function is an implementation of the \rho-operator found in Currie et al 2006. It forms the basis of the GLAM arithmetic.

Usage

RH(M, A)

Arguments

M

a n \times p_1 matrix.

A

a 3d array of size p_1 \times p_2 \times p_3.

Details

For details see Currie et al 2006. Note that this particular implementation is not used in the routines underlying the optimization procedure.

Value

A 3d array of size p_2 \times p_3 \times n.

Author(s)

Adam Lund

References

Currie, I. D., M. Durban, and P. H. C. Eilers (2006). Generalized linear array models with applications to multidimensional smoothing. Journal of the Royal Statistical Society. Series B. 68, 259-280. url = http://dx.doi.org/10.1111/j.1467-9868.2006.00543.x.

Examples

n1 <- 65; n2 <- 26; n3 <- 13; p1 <- 13; p2 <- 5; p3 <- 4

##marginal design matrices (Kronecker components)
X1 <- matrix(rnorm(n1 * p1), n1, p1)
X2 <- matrix(rnorm(n2 * p2), n2, p2)
X3 <- matrix(rnorm(n3 * p3), n3, p3)

Beta <- array(rnorm(p1 * p2 * p3, 0, 1), c(p1 , p2, p3))
max(abs(c(RH(X3, RH(X2, RH(X1, Beta)))) - kronecker(X3, kronecker(X2, X1)) %*% c(Beta)))