rank

# File lib/matrix.rb, line 720
  def rank
    if column_size > row_size
      a = transpose.to_a
      a_column_size = row_size
      a_row_size = column_size
    else
      a = to_a
      a_column_size = column_size
      a_row_size = row_size
    end
    rank = 0
    k = 0
    begin
      if (akk = a[k][k]) == 0
        i = k
        exists = true
        begin
          if (i += 1) > a_column_size - 1
            exists = false
            break
          end
        end while a[i][k] == 0
        if exists
          a[i], a[k] = a[k], a[i]
          akk = a[k][k]
        else
          i = k
          exists = true
          begin
            if (i += 1) > a_row_size - 1
              exists = false
              break
            end
          end while a[k][i] == 0
          if exists
            k.upto(a_column_size - 1) do
              |j|
              a[j][k], a[j][i] = a[j][i], a[j][k]
            end
            akk = a[k][k]
          else
            next
          end
        end
      end
      (k + 1).upto(a_row_size - 1) do
        |i|
        q = a[i][k] / akk
        (k + 1).upto(a_column_size - 1) do
          |j|
          a[i][j] -= a[k][j] * q
        end
      end
      rank += 1
    end while (k += 1) <= a_column_size - 1
    return rank
  end