R/generate_A11.R

In YangHuiMagic: A Generalization of Yang Hui's Magic Squares

#' Generate the 2n x 2n A11 matrix (arithmetic progression form)
#'
#' @param n Parameter, final order is 4n
#' @param a11 Upper-left corner starting value
#' @param d1 Column direction common difference (horizontal increment)
#' @param d2 Row direction common difference (vertical increment)
#'
#' @return 2n x 2n matrix
#' @export
generate_A11 <- function(n, a11, d1, d2) {
  i <- 1:(2 * n)          # row indices
  j <- 1:(2 * n)          # column indices
  # Use outer to generate matrix: a11 + (i-1)*d2 + (j-1)*d1
  outer(i, j, function(r, c) a11 + (r - 1) * d2 + (c - 1) * d1)
}