R/tSVDdwht.R

In rTensor2: MultiLinear Algebra

tSVDdwht <- function (tnsr)
{
  if (tnsr@num_modes != 3)
    stop("T-SVD only implemented for 3d so far")
  modes <- tnsr@modes
  n1 <- modes[1]
  n2 <- modes[2]
  n3 <- modes[3]
  dwhz <- aperm(apply(tnsr@data, MARGIN = 1:2, fwht), c(2,3,1))
  U_arr <- array(0, dim = c(n1, n1, n3))
  V_arr <- array(0, dim = c(n2, n2, n3))
  m <- min(n1, n2)
  S_arr <- array(0, dim = c(n1, n2, n3))
  for (j in 1:n3) {
    decomp <- svd(dwhz[, , j], nu = n1, nv = n2)
    U_arr[, , j] <- decomp$u
    V_arr[, , j] <- decomp$v
    S_arr[, , j] <- diag(decomp$d, nrow = n1, ncol = n2)
  }
  U <- as.tensor(aperm(apply(U_arr, MARGIN = 1:2,ifwht), c(2,3,1)))
  V <- as.tensor(aperm(apply(V_arr, MARGIN = 1:2,ifwht), c(2,3,1)))
  S <- as.tensor(aperm(apply(S_arr, MARGIN = 1:2,ifwht), c(2,3,1)))
  invisible(list(U = U, V = V, S = S))
}