#' Compute get gradient of `L(V)` given a dataset `X`.
#'
#' @param X Data matrix.
#' @param Y Responce.
#' @param V Position to compute the gradient at, aka point on Stiefl manifold.
#' @param h Bandwidth
#' @param loss.out Iff \code{TRUE} loss will be written to parent environment.
#' @param loss.only Boolean to only compute the loss, of \code{TRUE} a single
#'  value loss is returned and \code{envir} is ignored.
#' @param persistent Determines if data indices and dependent calculations shall
#'  be reused from the parent environment. ATTENTION: Do NOT set this flag, only
#'  intended for internal usage by carefully aligned functions!
#' @keywords internal
#' @export
grad <- function(X, Y, V, h,
                 loss.out = FALSE,
                 loss.only = FALSE,
                 persistent = FALSE) {
    # Get number of samples and dimension.
    n <- nrow(X)
    p <- ncol(X)

    if (!persistent) {
        # Compute lookup indexes for symmetrie, lower/upper
        # triangular parts and vectorization.
        pair.index <- elem.pairs(seq(n))
        i <- pair.index[1, ] # `i` indices of `(i, j)` pairs
        j <- pair.index[2, ] # `j` indices of `(i, j)` pairs
        # Index of vectorized matrix, for lower and upper triangular part.
        lower <- ((i - 1) * n) + j
        upper <- ((j - 1) * n) + i

        # Create all pairewise differences of rows of `X`.
        X_diff <- X[i, , drop = F] - X[j, , drop = F]
    }

    out <- .Call("grad_c", PACKAGE = "CVE",
                 X, X_diff, as.double(Y), V, as.double(h));

    if (loss.only) {
        return(out$loss)
    }
    if (loss.out) {
        loss <<- out$loss
    }

    return(out$G)
}