R/SMMA_RH.R

In SMMA: Soft Maximin Estimation for Large Scale Array-Tensor Models

#
#     Description of this R script:
#     Rotated H-transform of an array A by a matrix M.
#
#     Intended for use with R.
#     Copyright (C) 2015 Adam Lund
#
#     This program is free software: you can redistribute it and/or modify
#     it under the terms of the GNU General Public License as published by
#     the Free Software Foundation, either version 3 of the License, or
#     (at your option) any later version.
#
#     This program is distributed in the hope that it will be useful,
#     but WITHOUT ANY WARRANTY; without even the implied warranty of
#     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#     GNU General Public License for more details.
#
#     You should have received a copy of the GNU General Public License
#     along with this program.  If not, see <http://www.gnu.org/licenses/>
#

# H-transform of an array A by a matrix X
H<-function(M, A){
  d <- dim(A)
  Amat <- matrix(A, nrow = d[1])
  MAmat <- M %*% Amat
  array(MAmat, c(nrow(MAmat), d[-1]))
}

# Rotation of an array A
Rotate <- function(A){
  d <- 1:length(dim(A))
  d1 <- c(d[-1], d[1])
  aperm(A, d1)
}

#' @name RH
#'
#' @aliases glamlasso_RH Rotate H
#'
#' @title The Rotated H-transform of a 3d Array by a Matrix
#'
#' @description  This function is an implementation of the \eqn{\rho}-operator found in
#' \cite{Currie et al 2006}. It forms the basis of the GLAM arithmetic.
#'
#' @details For details see \cite{Currie et al 2006}. Note that this particular implementation
#' is not used in the  routines underlying the optimization procedure.
#'
#' @usage RH(M, A)
#'
#' @param M a \eqn{n \times p_1} matrix.
#' @param A a 3d array of size \eqn{p_1 \times p_2 \times p_3}.
#'
#' @return A 3d array of size \eqn{p_2 \times p_3 \times n}.
#'
#' @references
#' Currie, I. D., M. Durban, and P. H. C. Eilers (2006). Generalized linear
#' array models with applications to multidimensional smoothing.
#' \emph{Journal of the Royal Statistical Society. Series B}. 68, 259-280. url = {http://dx.doi.org/10.1111/j.1467-9868.2006.00543.x}.
#'
#'
#' @author Adam Lund
#'
#' @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)))
#'
#' @export

RH <- function(M, A){

  Rotate(H(M, A))

}