code: def test_astype(self):
      pidx = pd.Index(["a", "b", "c"])
      psidx = ps.from_pandas(pidx)
  
      self.assert_eq(psidx.astype("category"), pidx.astype("category"))
      self.assert_eq(
          psidx.astype(CategoricalDtype(["c", "a", "b"])),
          pidx.astype(CategoricalDtype(["c", "a", "b"])),
      )
  
      pcidx = pidx.astype(CategoricalDtype(["c", "a", "b"]))
      pscidx = psidx.astype(CategoricalDtype(["c", "a", "b"]))
  
      self.assert_eq(
          pscidx.astype("category"), pcidx.astype("category")
      )
  
      self.assert_eq(
          pscidx.astype(CategoricalDtype(["b", "c", "a"])),
          pcidx.astype(CategoricalDtype(["b", "c", "a"])),
      )
  
      self.assert_eq(pscidx.astype(str), pcidx.astype(str))
  
imports: import unittest
  import pandas
  from pandas.api.types import CategoricalDtype
  import pyspark.pandas
  from pyspark.loose_version import LooseVersion
  from pyspark.testing.pandasutils import PandasOnSparkTestCase, TestUtils
label_desc: Use image node_id 8 for calling the CategoricalIndexTestsMixin obj's underlying member method code with example usage: obj.test_astype() without return types