def normalize_data(a, data_mean, data_std):
  """Remove the mean from an np array and normalize by the standard deviation.

  Args:
    a: the array of data
    data_mean: the mean we want to remove (perhaps computed from different data)
    data_std: the current standard deviation to divide the data by.

  Returns:
    A new array, with the mean subtracted and divided by the data_std.
  """
  return (a - data_mean) / data_std