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#' @title Removes IDs with NA in a list of adjacency matrices optimally
#' @description
#' The function optimally removes identifiers with NA in a list of adjacency matrices. Many combinations of rows and columns can be deleted
# before getting rid of NA. This function removes the smallest number of rows and columns.
#' removing many rows and column
#' @param network is a list of adjacency matrices
#' @param ncores is the number of cores to be used to run the program in parallel
#' @return List of adjacency matrices without missing values and a list of vectors of retained indeces
#' @importFrom parallel makeCluster stopCluster
#' @importFrom doParallel registerDoParallel
#' @importFrom foreach foreach "%dopar%"
#' @importFrom doRNG "%dorng%"
#' @examples
#' A <- matrix(1:25, 5)
#' A[1, 1] <- NA
#' A[4, 2] <- NA
#' remove.ids(A)
#'
#' B <- matrix(1:100, 10)
#' B[1, 1] <- NA
#' B[4, 2] <- NA
#' B[2, 4] <- NA
#' B[,8] <-NA
#' remove.ids(B)
#' @export
remove.ids <- function(network, ncores = 1L){
stopifnot(inherits(network, c("matrix", "data.frame", "list")))
if(inherits(network, c("matrix", "data.frame"))) network <- list(network)
# Construct cluster
cl <- makeCluster(ncores)
registerDoParallel(cl)
M <- length(network)
m <- NULL
out <- foreach(m = 1:M, .packages = "PartialNetwork") %dorng% {rem_non_fin(as.matrix(network[[m]]))}
stopCluster(cl)
network <- lapply(1:M, function(m) out[[m]]$net)
id <- lapply(1:M, function(m) c(out[[m]]$id))
list(network = network, id = id)
}
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