R/modular.complexity.avg.r

In PABalland/EconGeo: Computing Key Indicators of the Spatial Distribution of Economic Activities

#' Compute a measure of average modular complexity of technologies
#'
#' This function computes a measure of average modular complexity of technologies (average complexity of patent documents in a given technological class) from technological classes - patents (incidence) matrices
#' @param mat A bipartite adjacency matrix (can be a sparse matrix)
#' @param sparse Logical; is the input matrix a sparse matrix? Defaults to FALSE, but can be set to TRUE if the input matrix is a sparse matrix
#' @param list Logical; is the input a list? Defaults to FALSE (input = adjacency matrix), but can be set to TRUE if the input is an edge list
#' @keywords complexity
#' @export
#' @examples
#' ## generate a technology - patent matrix
#' set.seed(31)
#' mat <- matrix(sample(0:1,30,replace=T), ncol = 5)
#' rownames(mat) <- c ("T1", "T2", "T3", "T4", "T5", "T6")
#' colnames(mat) <- c ("US1", "US2", "US3", "US4", "US5")
#'
#' ## run the function
#' modular.complexity.avg (mat)
#'
#' ## generate a technology - patent sparse matrix
#' library (Matrix)
#'
#' ## run the function
#' smat <- Matrix(mat,sparse=TRUE)
#'
#' modular.complexity.avg (smat, sparse = TRUE)
#' ## generate a regular data frame (list)
#' list <- get.list (mat)
#'
#' ## run the function
#' modular.complexity.avg (list, list = TRUE)
#' @author Pierre-Alexandre Balland \email{p.balland@uu.nl}
#' @references Fleming, L. and Sorenson, O. (2001) Technology as a complex adaptive system: evidence from patent data, \emph{Research Policy} \strong{30}: 1019-1039
#' @seealso \code{\link{ease.recombination}}, \code{\link{TCI}}, \code{\link{MORt}}

modular.complexity.avg <- function(mat, sparse = FALSE, list = FALSE) {

  library (Matrix)

  if (!list) {

  if (!sparse) {

  mat <- Matrix(mat,sparse=TRUE)
  cooc =   mat %*% Matrix::t(mat)
  diag(cooc) <- 0
  cooc[cooc > 1] <- 1

  Ease <- Matrix::rowSums(cooc, na.rm =T)/Matrix::rowSums(mat, na.rm =T)

  IntPat <- Matrix::colSums (mat, na.rm =T) / (Matrix::t(mat) %*% Ease)
  IntPat[is.infinite(IntPat)] <- 0

avgIntPat <- (mat %*% IntPat) / Matrix::rowSums(mat, na.rm =T)

  avgIntPat <- data.frame (tech = rownames (mat),
                          avg.mod.comp = round (as.numeric (avgIntPat), 2))

   } else {

  cooc =   mat %*% Matrix::t(mat)
  diag(cooc) <- 0
  cooc[cooc > 1] <- 1

  Ease <- Matrix::rowSums(cooc, na.rm =T)/Matrix::rowSums(mat, na.rm =T)

  IntPat <- Matrix::colSums (mat, na.rm =T) / (Matrix::t(mat) %*% Ease)
  IntPat[is.infinite(IntPat)] <- 0

avgIntPat <- (mat %*% IntPat) / Matrix::rowSums(mat, na.rm =T)

  avgIntPat <- data.frame (tech = rownames (mat),
                          avg.mod.comp = round (as.numeric (avgIntPat), 2))

   }

   } else {

     mat <- get.matrix(mat, sparse = TRUE)
     cooc = mat %*% Matrix::t(mat)
     diag(cooc) <- 0
     summ <- Matrix::summary(cooc)
     summ$x[summ$x>1] = 1
     x = get.matrix(summ, sparse = T)
     colnames (x) = colnames (cooc)
     rownames (x) = rownames (cooc)
     cooc = x
     Ease <- Matrix::rowSums(cooc)/Matrix::rowSums(mat)
     IntPat <- Matrix::colSums(mat)/(Matrix::t(mat) %*% Ease)
     IntPat[is.infinite(IntPat)] <- 0

avgIntPat <- (mat %*% IntPat) / Matrix::rowSums(mat, na.rm =T)

  avgIntPat <- data.frame (tech = rownames (mat),
                          avg.mod.comp = round(as.numeric (avgIntPat), 2))

}

  return(avgIntPat)
}