#' Lemire's improved DTW lower bound
#'
#' This function calculates an improved lower bound (LB) on the Dynamic Time Warp (DTW) distance
#' between two time series. It uses a Sakoe-Chiba constraint.
#'
#' @export
#'
#' @param x A time series (reference).
#' @param y A time series with the same length as `x` (query).
#' @param window.size Window size for envelope calculation. See details.
#' @param norm Vector norm. Either `"L1"` for Manhattan distance or `"L2"` for Euclidean.
#' @param lower.env Optionally, a pre-computed lower envelope for **`y`** can be provided (non-proxy
#'   version only). See [compute_envelope()].
#' @param upper.env Optionally, a pre-computed upper envelope for **`y`** can be provided (non-proxy
#'   version only). See [compute_envelope()].
#' @param force.symmetry If `TRUE`, a second lower bound is calculated by swapping `x` and `y`, and
#'   whichever result has a *higher* distance value is returned. The proxy version can only work if
#'   a square matrix is obtained, but use carefully.
#' @param error.check `r roxygen_error_check_param()`
#'
#' @details
#'
#' The reference time series should go in `x`, whereas the query time series should go in `y`.
#'
#' If the envelopes are provided, they should be provided together. If either one is missing, both
#' will be computed.
#'
#' `r roxygen_window_details()`
#'
#' @return The improved lower bound for the DTW distance.
#'
#' @section `r roxygen_proxy_section()`
#'
#' @section Note:
#'
#' The lower bound is only defined for time series of equal length and is **not** symmetric.
#'
#' If you wish to calculate the lower bound between several time series, it would be better to use
#' the version registered with the `proxy` package, since it includes some small optimizations. The
#' convention mentioned above for references and queries still holds. See the examples.
#'
#' The proxy version of `force.symmetry` should only be used when only `x` is provided or both `x`
#' and `y` are identical. It compares the lower and upper triangular of the resulting distance
#' matrix and forces symmetry in such a way that the tightest lower bound is obtained.
#'
#' @references
#'
#' Lemire D (2009). ``Faster retrieval with a two-pass dynamic-time-warping lower bound .'' *Pattern
#' Recognition*, **42**(9), pp. 2169 - 2180. ISSN 0031-3203,
#' \doi{10.1016/j.patcog.2008.11.030},
#' \url{https://www.sciencedirect.com/science/article/pii/S0031320308004925}.
#'
#' @examples
#'
#' # Sample data
#' data(uciCT)
#'
#' # Lower bound distance between two series
#' d.lbi <- lb_improved(CharTraj[[1]], CharTraj[[2]], window.size = 20)
#'
#' # Corresponding true DTW distance
#' d.dtw <- dtw(CharTraj[[1]], CharTraj[[2]],
#'              window.type = "sakoechiba", window.size = 20)$distance
#'
#' d.lbi <= d.dtw
#'
#' # Calculating the LB between several time series using the 'proxy' package
#' # (notice how both argments must be lists)
#' D.lbi <- proxy::dist(CharTraj[1], CharTraj[2:5], method = "LB_Improved",
#'                      window.size = 20, norm = "L2")
#'
#' # Corresponding true DTW distance
#' D.dtw <- proxy::dist(CharTraj[1], CharTraj[2:5], method = "dtw_basic",
#'                      norm = "L2", window.size = 20)
#'
#' D.lbi <= D.dtw
#'
lb_improved <- function(x, y, window.size = NULL, norm = "L1",
                        lower.env = NULL, upper.env = NULL,
                        force.symmetry = FALSE, error.check = TRUE)
{
    norm <- match.arg(norm, c("L1", "L2"))
    if (length(x) != length(y)) stop("The series must have the same length")
    window.size <- check_consistency(window.size, "window")
    if (is_multivariate(list(x, y)))
        stop("lb_improved does not support multivariate series.")
    if (error.check) {
        check_consistency(x, "ts")
        check_consistency(y, "ts")
    }

    if (is.null(lower.env) || is.null(upper.env)) {
        envelopes <- compute_envelope(y, window.size = window.size, error.check = FALSE)
        lower.env <- envelopes$lower
        upper.env <- envelopes$upper
    }
    else {
        check_consistency(lower.env, "ts")
        check_consistency(upper.env, "ts")
        if (length(lower.env) != length(x))
            stop("Length mismatch between 'x' and the lower envelope")
        if (length(upper.env) != length(x))
            stop("Length mismatch between 'x' and the upper envelope")
    }

    p <- switch(norm, L1 = 1L, L2 = 2L)
    d <- .Call(C_lbi, x, y, window.size, p, lower.env, upper.env, PACKAGE = "dtwclust")
    if (force.symmetry) {
        d2 <- lb_improved(x = y, y = x, window.size = window.size, norm = norm, error.check = FALSE)
        if (d2 > d) d <- d2 # nocov
    }
    # return
    d
}

# ==================================================================================================
# Loop without using native 'proxy' looping (to avoid multiple calculations of the envelope)
# ==================================================================================================

lb_improved_proxy <- function(x, y = NULL, window.size = NULL, norm = "L1", ...,
                              force.symmetry = FALSE, pairwise = FALSE, error.check = TRUE)
{
    x <- tslist(x)
    if (is.null(y))
        y <- x
    else
        y <- tslist(y)
    if (length(x) == 0L || length(y) == 0L) stop("Empty list received in x or y.") # nocov start
    if (error.check) check_consistency(c(x,y), "tslist")
    if (is_multivariate(c(x,y))) stop("lb_improved does not support multivariate series.") # nocov end

    fill_type <- mat_type <- dim_names <- NULL # avoid warning about undefined globals
    symmetric <- FALSE
    eval(prepare_expr) # UTILS-expressions.R

    # adjust parameters for this distance
    norm <- match.arg(norm, c("L1", "L2"))
    window.size <- check_consistency(window.size, "window")
    envelopes <- lapply(y, function(s) { compute_envelope(s, window.size, error.check = FALSE) })
    lower.env <- lapply(envelopes, "[[", "lower")
    upper.env <- lapply(envelopes, "[[", "upper")

    # calculate distance matrix
    distance <- "LBI" # read in C++, can't be temporary!
    distargs <- list(
        p = switch(norm, "L1" = 1L, "L2" = 2L),
        len = length(x[[1L]]),
        window.size = window.size,
        lower.env = lower.env,
        upper.env = upper.env
    )
    num_threads <- get_nthreads()
    .Call(C_distmat_loop,
          D, x, y, distance, distargs, fill_type, mat_type, num_threads,
          PACKAGE = "dtwclust")

    # adjust D's attributes
    if (pairwise) {
        dim(D) <- NULL
        class(D) <- "pairdist"
    }
    else {
        dimnames(D) <- dim_names
        class(D) <- "crossdist"
    }
    if (force.symmetry && !pairwise) {
        if (nrow(D) != ncol(D))
            warning("Unable to force symmetry. Resulting distance matrix is not square.") # nocov
        else
            .Call(C_force_lb_symmetry, D, PACKAGE = "dtwclust")
    }

    attr(D, "method") <- "LB_Improved"
    D
}
