code: def test_constructor_pi_nat(self):
      idx = PeriodIndex(
          [
              Period("2011-01", freq="M"),
              NaT,
              Period("2011-01", freq="M"),
          ]
      )
      exp = PeriodIndex(["2011-01", "NaT", "2011-01"], freq="M")
      tm.assert_index_equal(idx, exp)
  
      idx = PeriodIndex(
          np.array(
              [
                  Period("2011-01", freq="M"),
                  NaT,
                  Period("2011-01", freq="M"),
              ]
          )
      )
      tm.assert_index_equal(idx, exp)
  
      idx = PeriodIndex(
          [
              NaT,
              NaT,
              Period("2011-01", freq="M"),
              Period("2011-01", freq="M"),
          ]
      )
      exp = PeriodIndex(["NaT", "NaT", "2011-01", "2011-01"], freq="M")
      tm.assert_index_equal(idx, exp)
  
      idx = PeriodIndex(
          np.array(
              [
                  NaT,
                  NaT,
                  Period("2011-01", freq="M"),
                  Period("2011-01", freq="M"),
              ]
          )
      )
      tm.assert_index_equal(idx, exp)
  
      idx = PeriodIndex([NaT, NaT, "2011-01", "2011-01"], freq="M")
      tm.assert_index_equal(idx, exp)
  
      with pytest.raises(ValueError, match="freq not specified"):
          PeriodIndex([NaT, NaT])
  
      with pytest.raises(ValueError, match="freq not specified"):
          PeriodIndex(np.array([NaT, NaT]))
  
      with pytest.raises(ValueError, match="freq not specified"):
          PeriodIndex(["NaT", "NaT"])
  
      with pytest.raises(ValueError, match="freq not specified"):
          PeriodIndex(np.array(["NaT", "NaT"]))
  
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 18 for calling the TestPeriodIndex obj's underlying member method code with example usage: obj.test_constructor_pi_nat() without return types