R/B2XZG.R

In VDPO: Working with and Analyzing Functional Data of Varying Lengths

#' One dimensional B2XZG
#'
#' @param B Design matrix.
#' @param pord Order of the difference matrix.
#' @param c Polynomial order.
#'
#' @return .
#'
#' @noRd
B2XZG_1d <- function(B, pord = 2, c = 10) {
  c1 <- c[1]
  D_1 <- diff(diag(c1), differences = pord)
  P1.svd <- svd(crossprod(D_1))

  U_1s <- P1.svd$u[, 1:(c1 - pord[1])] # eigenvectors
  U_1n <- P1.svd$u[, -(1:(c1 - pord[1]))]
  d1 <- P1.svd$d[1:(c1 - pord[1])] # eigenvalues

  T_n <- U_1n
  T_s <- U_1s

  Z <- B %*% T_s
  X <- B %*% T_n

  G <- list(d1)

  T_ <- cbind(T_n, T_s)

  list(
    X    = X,
    Z    = Z,
    G    = G,
    T    = T_,
    d1   = d1,
    D_1  = D_1,
    U_1n = U_1n,
    U_1s = U_1s,
    T_n  = T_n,
    T_s  = T_s
  )
}