docs: def manhattan(x, y):
      """Manhatten, taxicab, or l1 distance.
  
      ..math::
          D(x, y) = \sum_i |x_i - y_i|
      """
      result = 0.0
      for i in range(x.shape[0]):
          result += np.abs(x[i] - y[i])
  
      return result