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#' Reconstruction Stage of Functional Singular Spectrum Analysis
#'
#' Reconstruct univariate or multivariate functional time series
#' (\code{\link{funts}}) objects from functional singular spectrum analysis
#' (\code{\link{fssa}}) objects, including Grouping and Hankelization steps.
#' This function performs the reconstruction step for either univariate
#' functional singular spectrum analysis (ufssa) or multivariate
#' functional singular spectrum analysis (mfssa), depending on the input.
#'
#' @param U an object of class \code{\link{fssa}}.
#' @param groups a list of numeric vectors, each vector includes indices
#' of elementary components of a group used for reconstruction.
#'
#' @return A named list of objects of class \code{\link{funts}} that are
#' reconstructed according to the specified groups and a numeric vector
#' of eigenvalues.
#'
#' @note Refer to \code{\link{fssa}} for an example on how to run this
#' function starting from \code{\link{fssa}} objects.
#'
#' @seealso \code{\link{fssa}}, \code{\link{funts}}
#' @examples
#'
#' data("Callcenter")
#' L <- 28
#' U <- fssa(Callcenter, L)
#'
#' # FSSA Reconstruction step:
#' gr <- list(1, 2:3, 4:5, 6:7, 1:7)
#' Q <- freconstruct(U, gr)
#' plot(Q[[1]],
#' main = "Call Center Mean Component")
#' plot(Q[[2]],
#' main = "Call Center First Periodic Component")
#'
#' #--------------- Multivariate FSSA Example on bivariate -----------------------------
#' ## temperature curves and smoothed images of vegetation
#' \dontrun{
#' data("Montana")
#' L <- 45
#' U <- fssa(Montana, L)
#'
#' # MFSSA Reconstruction step:
#' Q <- freconstruct(U = U, groups = list(1, 2, 3))
#' plotly_funts(Q[[1]],
#' main = c("Temperature Curves Mean", "NDVI Images Mean"),
#' color_palette = "RdYlGn",
#' xticklabels = list(
#' c("00:00", "06:00", "12:00", "18:00", "24:00"),
#' c("113.40\u00B0 W", "113.30\u00B0 W")
#' ),
#' xticklocs = list(c(1, 6, 12, 18, 24), c(1, 33)),
#' yticklabels = list(NA, c("48.70\u00B0 N", "48.77\u00B0 N")),
#' yticklocs = list(NA, c(1, 33))
#' ) # mean
#'
#' plotly_funts(Q[[2]],
#' main = c("Temperature Curves Periodic", "NDVI Images Periodic"),
#' color_palette = "RdYlGn",
#' xticklabels = list(
#' c("00:00", "06:00", "12:00", "18:00", "24:00"),
#' c("113.40\u00B0 W", "113.30\u00B0 W")
#' ),
#' xticklocs = list(c(1, 6, 12, 18, 24), c(1, 33)),
#' yticklabels = list(NA, c("48.70\u00B0 N", "48.77\u00B0 N")),
#' yticklocs = list(NA, c(1, 33))
#' ) # periodic
#'
#' plot(Q[[3]],
#' obs = 3,
#' main = c("Temperature Curves Trend", "NDVI Images Trend,")
#' ) # trend
#' }
#'
#' @export
freconstruct <- function(U, groups = as.list(1L:10L)) {
if (class(U[[1]])[[1]] != "list") out <- ufreconstruct(U, groups) else out <- mfreconstruct(U, groups)
return(out)
}
#--------------------------------------ufreconstruct----------------------------------------------------
# Reconstruction stage (including Hankelization) of univariate functional singular spectrum analysis
ufreconstruct <- function(U, groups = as.list(1L:10L)) {
Y <- U$Y
N <- Y$N
basisobj <- Y$basis[[1]]
time_st <- Y$time[1]
time_en <- Y$time[N]
basis <- Y$B_mat[[1]]
d <- ncol(Y$B_mat[[1]])
L <- U$L
K <- N - L + 1L
m <- length(groups)
out <- list()
for (i in 1L:m) {
Cx <- matrix(NA, nrow = d, ncol = N)
g <- groups[[i]]
S <- 0L
for (j in 1L:length(g)) S <- S + ufproj(U, g[j], d)
S <- fH(S, d)
Cx[, 1L:L] <- S[, 1L, ]
Cx[, L:N] <- S[, , L]
recon_out <- basis %*% Cx
if (Y$dimSupp[[1]] == 2) {
x <- unique(Y$argval[[1]][, 1])
y <- unique(Y$argval[[1]][, 2])
recon_two_d <- array(data = NA, dim = c(length(x), length(y), N))
for (n in 1:N) {
count <- 1
for (i_1 in 1:length(x)) {
for (i_2 in 1:length(y)) {
recon_two_d[i_1, i_2, n] <- recon_out[count, n]
count <- count + 1L
}
}
}
recon_out <- recon_two_d
new_grid <- list(x, y)
} else {
new_grid <- Y$argval[[1]]
}
funts_out <- funts(X = recon_out, basisobj = basisobj, argval = new_grid,
start = time_st, end = time_en, vnames = Y$vnames,
dnames = Y$dnames, tname = Y$tname)
out[[i]] <- funts_out
}
out$values <- sqrt(U$values)
return(out)
}
#--------------------------------------mfreconstruct----------------------------------------------------
# Reconstruction stage (including Hankelization) of multivariate functional singular spectrum analysis.
mfreconstruct <- function(U, groups = as.list(1L:10L)) {
Y <- U$Y
N <- Y$N
basisobj <- Y$basis
time_st <- Y$time[1]
time_en <- Y$time[N]
L <- U$L
K <- N - L + 1
basis <- Y$B_mat
m <- length(groups)
recon_out <- list()
new_grid <- list()
p <- length(Y$dimSupp)
# Loop over groups
for (i in 1L:m) {
recon_group <- list()
C <- list()
S <- list()
g <- groups[[i]]
# build reconstructions
for (j in 1:p) {
d <- ncol(basis[[j]])
C[[j]] <- matrix(NA, nrow = d, ncol = N)
S[[j]] <- 0L
for (k in 1L:length(g)) {
S[[j]] <- S[[j]] + mfproj(U, g[k])[[j]]
}
S[[j]] <- fH(S[[j]], d)
C_jx <- C[[j]]
S_jx <- S[[j]]
C_jx[, 1L:L] <- S_jx[, 1L, ]
C_jx[, L:N] <- S_jx[, , L]
recon_group[[j]] <- basis[[j]] %*% C_jx
if (Y$dimSupp[[j]] == 2) {
x <- unique(Y$argval[[j]][, 1])
y <- unique(Y$argval[[j]][, 2])
recon_two_d <- array(data = NA, dim = c(length(x), length(y), N))
for (n in 1:N) {
count <- 1
for (i_1 in 1:length(x)) {
for (i_2 in 1:length(y)) {
recon_two_d[i_1, i_2, n] <- recon_group[[j]][count, n]
count <- count + 1
}
}
}
recon_group[[j]] <- recon_two_d
new_grid[[j]] <- list(x, y)
} else {
new_grid[[j]] <- Y$argval[[j]]
}
}
# output the reconstructions
funts_out <- funts(X = recon_group, basisobj = basisobj, argval = new_grid,
start = time_st, end = time_en, vnames = Y$vnames,
dnames = Y$dnames, tname = Y$tname)
recon_out[[i]] <- funts_out
}
recon_out$values <- U$values
return(recon_out)
}
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