#' Generate a matrix of `n` rows of sets of probabilities 

#' generated from the Dirichlet distribution, each row 

#' summing to 1. Uses the alternative \eqn{\mu} \eqn{\phi} 

#' parameterisation for the Dirichlet distribution, 

#' representing means and precision.

#' 

#' @param n Number of sets of probabilities (defaults to 1)

#' @param mu Vector of mean values for each probability in the set

#' (defaults to c(0.001, 0.029. 0.7)). Must be greater than 0 and 

#' finite, and contain at least two values.

#' @param phi Parameter representing precision, where precision is 

#' 1/variance. Must be positive and finite. Defaults to 10.

#'

#' @examples rdirichlet_alt(n = 3, mu = c(0.001, 0.029, 0.7), phi = 10)

#' 

#' @export 

#' 

#' @import checkmate

#' @importFrom stats rgamma

#' 

rdirichlet_alt <- function(

  n = 1, 

  mu = c(0.3, 0.3, 0.3), 

  phi = 10

) {

  ### Check and convert inputs

  # True if n is "close to an integer"

  checkmate::assert_integerish(

    n, lower = 1, , upper = 10^7, len = 1, any.missing = FALSE

  )

  # mu should be a numeric vector in the range [0, 1)

  checkmate::assert_vector(

    mu, min.len = 2, strict = TRUE, any.missing = FALSE

  )

  checkmate::assert_numeric(

    mu, lower = 10^-7, upper = 1 - 10^-7

  )

  # phi should be a positive number

  checkmate::assert_number(phi, lower = 10^-7, finite = TRUE)

  # Make n actually an integer

  n <- as.integer(n)

  # Shape parameter (alpha) from mu and phi; alpha_0 = phi

  alpha <- phi * mu / mu[1]

  no_probs <- length(mu)

  # Dirichlet is a set of normalised independent gamma(alpha, 1)

  draws_mx <- matrix(

    stats::rgamma(n * no_probs, alpha), 

    ncol = no_probs, 

    byrow = TRUE

  )

  # Each set should sum to 1

  draws_mx <- draws_mx / rowSums(draws_mx)

  return(draws_mx)

}