makeAA.R

#' Creates the additive by additive epistatic genetic relationship matrix
#' 
#' Given a pedigree, the matrix of additive by additive genetic relatedness
#' (AA) among all individuals in the pedigree is returned.
#' 
#' Missing parents (e.g., base population) should be denoted by either 'NA',
#' '0', or '*'.
#' 
#' The function first estimates the A matrix using \code{\link{makeA}}, then it
#' calculates the Hadamard (element-wise) product of the A matrix with itself
#' (A # A).
#' 
#' @param pedigree A pedigree where the columns are ordered ID, Dam, Sire
#'
#' @return a \code{list}:
#'   \describe{
#'     \item{AA }{the AA matrix in sparse matrix form}
#'     \item{logDet }{the log determinant of the AA matrix}
#'     \item{AAinv }{the inverse of the AA matrix in sparse matrix form}
#'     \item{listAAinv }{the three column form of the non-zero elements for the
#'       inverse of the AA matrix}
#'   }
#' @author \email{matthewwolak@@gmail.com}
#' @seealso \code{\link{makeA}}
#' @examples
#' 
#'   makeAA(Mrode2)
#' 
#' @export
makeAA <- function(pedigree)
{
  A <- makeA(pedigree)
  AA <- A*A
  logDet <- determinant(AA, logarithm = TRUE)$modulus[1]
  AAinv <- solve(AA)
    AAinv@Dimnames <- list(as.character(pedigree[, 1]), NULL)
  listAAinv <- sm2list(AAinv, rownames=pedigree[,1], colnames=c("row", "column", "AAinverse"))
 return(list(AA = AA, logDet = logDet, AAinv = AAinv, listAAinv = listAAinv))    
}