#' Numeric differentiation
#'
#' @example inst/examples/num_deriv.R
#'
#' @export
num.deriv <- function(F, X, h = 1e-6, sym = FALSE) {
    if (sym) {
        stopifnot(isSymmetric(X))
        p <- nrow(X)
        k <- seq_along(X) - 1
        mapply(function(i, j) {
            dx <- h * ((k == i * p + j) | (k == j * p + i))
            (F(X + dx) - F(X - dx)) / (2 * h)
        }, .row(dim(X)) - 1, .col(dim(X)) - 1)
    } else {
        sapply(seq_along(X), function(i) {
            dx <- h * (seq_along(X) == i)
            (F(X + dx) - F(X - dx)) / (2 * h)
        })
    }
}

#' Second numeric derivative
#'
#' @export
num.deriv2 <- function(F, X, Y, h = 1e-6, symX = FALSE, symY = FALSE) {
    if (missing(Y)) {
        num.deriv(function(x) {
            num.deriv(function(z) F(z), x, h = h, sym = symX)
        }, X, h = h, sym = symX)
    } else {
        num.deriv(function(y) {
            num.deriv(function(x) F(x, y), X, h = h, sym = symX)
        }, Y, h = h, sym = symY)
    }
}