```
#' Compute the prody index of industries from regions - industries matrices
#'
#' This function computes the prody index of industries from (incidence) regions - industries matrices, as proposed by Hausmann, Hwang & Rodrik (2007). The index gives an associated income level for each industry. It represents a weighted average of per-capita GDPs (but GDP can be replaced by R&D, education...), where the weights correspond to the revealed comparative advantage of each region in a given industry (or sector, technology, ...).
#' @param mat An incidence matrix with regions in rows and industries in columns
#' @param vec A vector that gives GDP, R&D, education or any other relevant regional attribute that will be used to compute the weighted average for each industry
#' @keywords complexity concentration
#' @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")
#'
#' ## a vector of GDP of regions
#' vec <- c (5, 10, 15, 25, 50)
#' ## run the function
#' prody (mat, vec)
#' @author Pierre-Alexandre Balland \email{p.balland@uu.nl}
#' @seealso \code{\link{location.quotient}}
#' @references Balassa, B. (1965) Trade Liberalization and Revealed Comparative Advantage, \emph{The Manchester School} \strong{33}: 99-123 \cr
#' \cr
#' Hausmann, R., Hwang, J. & Rodrik, D. (2007) What you export matters, \emph{Journal of economic growth} \strong{12}: 1-25.
prody <- function(mat, vec) {
p = (vec %*% RCA (mat, binary = F)) / colSums (RCA (mat, binary = F))
# same as this formular
# (vec %*% (mat / rowSums (mat)) ) / colSums (mat / rowSums (mat))
return (p)
}
```

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