code: def test_map_with_string_constructor(self):
      raw = [2005, 2007, 2009]
      index = PeriodIndex(raw, freq="Y")
  
      expected = Index([str(num) for num in raw])
      res = index.map(str)
  
      # should return an Index
      assert isinstance(res, Index)
  
      # preserve element types
      assert all(isinstance(resi, str) for resi in res)
  
      # lastly, values should compare equal
      tm.assert_index_equal(res, expected)
  
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 31 for calling the TestPeriodIndex obj's underlying member method code with example usage: obj.test_map_with_string_constructor() without return types