```
#' Compute the Shannon entropy index from regions - industries matrices
#'
#' This function computes the Shannon entropy index from regions - industries matrices from (incidence) regions - industries matrices
#' @param mat An incidence matrix with regions in rows and industries in columns
#' @keywords diversity
#' @export
#' @examples
#' ## generate a region - industry matrix
#' set.seed(31)
#' mat <- matrix(sample(0:100,20,replace=T), ncol = 4)
#' rownames(mat) <- c ("R1", "R2", "R3", "R4", "R5")
#' colnames(mat) <- c ("I1", "I2", "I3", "I4")
#'
#' ## run the function
#' entropy (mat)
#' @author Pierre-Alexandre Balland \email{p.balland@uu.nl}
#' @seealso \code{\link{diversity}}
#' @references Shannon, C.E., Weaver, W. (1949) \emph{The Mathematical Theory of Communication}. Univ of Illinois Press. \cr
#' \cr
#' Frenken, K., Van Oort, F. and Verburg, T. (2007) Related variety, unrelated variety and regional economic growth, \emph{Regional studies} \strong{41} (5): 685-697.
entropy <- function(mat) {
freqs <- mat/rowSums (mat)
entropy <- - rowSums (freqs * log2(freqs+0.000000001))
entropy <- round (entropy, digits = 3)
return (entropy)
}
```

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