/// Initializing a matrix of `$x` by `$y` with its diagonal filled with 1s
/// @group init
/// @param $x      - number of rows
/// @param $y ($x) - number of columns
/// @return {Matrix}
/// @require {function} _valid-coords
/// @require {function} matrix
/// @require {function} set-entry
@function unit-matrix($x, $y: $x) {
  @if _valid-coords(($x $y)) {
    $matrix: matrix($x, $y);

    @for $i from 1 through $x {
      @for $j from 1 through $y {
        @if $i == $j {
          $matrix: set-entry($matrix, ($i $j), 1);
        }
      }
    }

    @return $matrix;
  }

  @return false;
}