# Coded by Nathan Wallach, May 2019
# based on Davide Cervone's recommendation from
# http://webwork.maa.org/moodle/mod/forum/discuss.php?d=3194
# as the current $Matrix->order_LR does not use fuzzy comparisons
# so does not give good results.

sub rank { # It assumes that a MathObject matrix object is sent
  my $MM1 = shift;

  if ( $MM1->class ne "Matrix") {
    return -1; # Not a matrix
  }

  # For the case it is square
  my $MM = $MM1;

  my ($Rrows,$Rcols) = $MM1->dimensions;

  if ( ( $Rrows <= 0 ) || ( $Rcols <= 0 ) ) {
    return -1; # Not a matrix
  }

  if ( $Rrows < $Rcols ) {
    # pad to make it square
    my @rows = ();
    my $i = 1;
    for ( $i = 1 ; $i <= $Rrows ; $i++ ) {
      push( @rows, $MM1->row($i) );
    }
    while ( $i <= $Rrows ) {
      # pad with zero rows
      push( @rows, ( 0 * $MM1->row(1) ) );
      $i++;
    }
    $MM = Matrix( @rows );
  } elsif ( $Rrows > $Rcols ) {
    return( rank( $MM1->transpose ) );
  }

  # Davide's approach from http://webwork.maa.org/moodle/mod/forum/discuss.php?d=3194
  my $tempR = $MM->R;
  ($Rrows,$Rcols) = $tempR->dimensions;
  my $rank;

  for ( $rank = $Rrows ; $rank >= 1; $rank-- ) {
        last if ( $tempR->element($rank,$rank) != Real("0") );
  }
  return( $rank );
}

1;