code: def test_constructor_dtype(self):
      # passing a dtype with a tz should localize
      idx = PeriodIndex(["2013-01", "2013-03"], dtype="period[M]")
      exp = PeriodIndex(["2013-01", "2013-03"], freq="M")
      tm.assert_index_equal(idx, exp)
      assert idx.dtype == "period[M]"
  
      idx = PeriodIndex(
          ["2013-01-05", "2013-03-05"], dtype="period[3D]"
      )
      exp = PeriodIndex(["2013-01-05", "2013-03-05"], freq="3D")
      tm.assert_index_equal(idx, exp)
      assert idx.dtype == "period[3D]"
  
      # if we already have a freq and its not the same, then asfreq
      # (not changed)
      idx = PeriodIndex(["2013-01-01", "2013-01-02"], freq="D")
  
      res = PeriodIndex(idx, dtype="period[M]")
      exp = PeriodIndex(["2013-01", "2013-01"], freq="M")
      tm.assert_index_equal(res, exp)
      assert res.dtype == "period[M]"
  
      res = PeriodIndex(idx, freq="M")
      tm.assert_index_equal(res, exp)
      assert res.dtype == "period[M]"
  
      msg = "specified freq and dtype are different"
      with pytest.raises(IncompatibleFrequency, match=msg):
          PeriodIndex(["2011-01"], freq="M", dtype="period[D]")
  
imports: import numpy
  import pytest
  from pandas._libs.tslibs.period import IncompatibleFrequency
  from pandas.core.dtypes.dtypes import PeriodDtype
  from pandas import Index, NaT, Period, PeriodIndex, Series, date_range, offsets, period_range
  import pandas._testing
  from pandas.core.arrays import PeriodArray
label_desc: Use image node_id 16 for calling the TestPeriodIndex obj's underlying member method code with example usage: obj.test_constructor_dtype() without return types