R/method_proper.R

In polyMatrix: Infrastructure for Manipulation Polynomial Matrices

# Title     : Row and column proper property of polyMatrix
# Created by: namezys

#' Proper polynomial matrices
#'
#' A polynomial matrix is column (row, full) proper (or reduced)
#' if the associated matrix has the same rank
#' as the number of columns (rows)
#'
#' @param pm a polyMatrix object
#' @return True if object `pm` is a (row-/column-) proper matrix
#'
#' @description Tests the proper property of a polynomial matrix.
#'   A polynomial matrix is proper if the associeted matrix has a full rank.
#'
#' @examples
#' pm <- parse.polyMatrix(
#'   "-1 + 7x     , x",
#'   " 3 - x + x^2, -1 + x^2 - 3 x^3"
#' )
#' is.column.proper(pm)
#' is.row.proper(pm)
#' is.proper(pm)
#'
#' @export
is.proper <- function (pm) {
  return(is.column.proper(pm) && is.row.proper(pm))
}

#' @describeIn is.proper tests if its argument is a column-proper matrix
#'
#' @export
is.column.proper <- function(pm) {
  col_degree <- apply(matrix.degree(pm), 2,  max)
  c_matrix <- matrix(NA, nrow(pm), ncol(pm))
  for(c in seq_len(ncol(pm))) {
    d <- col_degree[c]
    c_matrix[, c] <- pm[[d]][, c]
  }
  return(Matrix::rankMatrix(c_matrix) == ncol(pm))
}

#' @describeIn is.proper tests if its argument is a row-proper matrix
#'
#' @export
is.row.proper <- function (pm) {
  row_degree <- apply(matrix.degree(pm), 1, max)
  c_matrix <- matrix(NA, nrow(pm), ncol(pm))
  for(r in seq_len(nrow(pm))) {
    d <- row_degree[r]
    c_matrix[r, ] <- pm[[d]][r, ]
  }
  return(Matrix::rankMatrix(c_matrix) == nrow(pm))
}