R/tDWT.R

In TensorTools: Multilinear Algebra

#' Discrete Wavelet Transform
#' @description Performs the Discrete Wavelet Transform of a 3-mode Tensor.
#' @param tnsr, A 3-mode Tensor
#' @return S3 class tensor
#' @references G. Strang and T. Nguyen, Wavelets and filter banks. SIAM, 1996. A. Haar, "Zur theorie der orthogonalen funktionensysteme", Mathematische annalen, vol. 69, no. 3, pp. 331-371, 1910.
#' @examples
#' T <- t_rand(modes=c(2,3,4))
#' print(tDWT(T))
#' @author Kyle Caudle
#' @author Randy Hoover
#' @author Jackson Cates
#' @author Everett Sandbo
#' @references Jensen, A., & la Cour-Harbo, A. (2011). Ripples in mathematics: the discrete wavelet transform. Springer Science & Business Media.

tDWT <- function (tnsr) {
  # Performs the Discrete Wavelet Transform of a 3-D Tensor.
  # Input: 3D tensor
  # Output: 3D tensor where a DWT has been performed along
  # mode 3.

  modes <- tnsr$modes
  n1 <- modes[1]
  n2 <- modes[2]
  n3 <- modes[3]

  # Check to make sure n3 is more than 2.
  if (n3==2)
    stop("Mode 3 must have length 2^n where n>2")
  #  Check to see if mode 3 is a power of 2.
  if (sum(as.numeric(intToBits(n3))) != 1)
    stop("Mode 3 must be a power of 2 otherwise using 0 padding")

  dwtz = array(0,dim=c(n1,n2,n3))
  for (i in 1:n1) {
    for (j in 1:n2) {
      x <- tnsr$data[i,j,]
      # Transform mode 3 with Haar DWT
      wt <- wd(x,filter.number=1,family="DaubExPhase")
      l <- log(length(x)/2,2)
      c.in <- accessC.wd(wt,level=l)
      d.in <- accessD.wd(wt,level=l)

      dwtz[i,j,] <- c(c.in,d.in)
    }
  }
  dwtz <- as.Tensor(dwtz)
  return(dwtz)
}