code: def test_factorize(self):
      pidx = pd.Index(["a", "b", "a", "b"])
      psidx = ps.from_pandas(pidx)
      pcodes, puniques = pidx.factorize(sort=True)
      kcodes, kuniques = psidx.factorize()
      self.assert_eq(pcodes.tolist(), kcodes.to_list())
      self.assert_eq(puniques, kuniques)
  
      pmidx = pd.MultiIndex.from_tuples(
          [("x", "a"), ("x", "b"), ("y", "c")]
      )
      psmidx = ps.from_pandas(pmidx)
  
      self.assertRaises(
          PandasNotImplementedError, lambda: psmidx.factorize()
      )
  
imports: import unittest
  from datetime import datetime
  import numpy
  import pandas
  import pyspark.pandas
  from pyspark.pandas.exceptions import PandasNotImplementedError
  from pyspark.testing.pandasutils import PandasOnSparkTestCase, TestUtils, SPARK_CONF_ARROW_ENABLED
label_desc: Use image node_id 10 for calling the IndexBasicMixin obj's underlying member method code with example usage: obj.test_factorize() without return types