#' Half vectorization of a matrix (lower part)
#' @export
vech <- function(A) A[lower.tri(A, diag = TRUE)]

#' @export
vech.index <- function(p) which(.row(c(p, p)) >= .col(c(p, p)))

#' @export
vech.pinv.index <- function(p) {
    index <- matrix(NA_integer_, p, p)
    index[lower.tri(index, diag = TRUE)] <- seq_len(p * (p + 1L) / 2L)
    index[upper.tri(index)] <- t(index)[upper.tri(index)]

    index
}

#' pseudo inserse of the half vectorization
#'
#' @examples
#' # only valid for symmetric matrices
#' A <- matrix(rnorm(4^2), 4)
#' A <- A + t(A)
#' all.equal(A, vech.pinv(vech(A)))
#'
#' @export
vech.pinv <- function(a) {
    # determin original dimensions
    p <- as.integer((sqrt(8 * length(a) + 1) - 1) / 2)
    stopifnot(p * (p + 1L) == 2L * length(a))

    # de-vectorized matrix
    matrix(a[vech.pinv.index(p)], p, p)
}