code: def test_construction_base_constructor(self):
      # GH 13664
      arr = [
          Period("2011-01", freq="M"),
          NaT,
          Period("2011-03", freq="M"),
      ]
      tm.assert_index_equal(Index(arr), PeriodIndex(arr))
      tm.assert_index_equal(
          Index(np.array(arr)), PeriodIndex(np.array(arr))
      )
  
      arr = [np.nan, NaT, Period("2011-03", freq="M")]
      tm.assert_index_equal(Index(arr), PeriodIndex(arr))
      tm.assert_index_equal(
          Index(np.array(arr)), PeriodIndex(np.array(arr))
      )
  
      arr = [
          Period("2011-01", freq="M"),
          NaT,
          Period("2011-03", freq="D"),
      ]
      tm.assert_index_equal(Index(arr), Index(arr, dtype=object))
  
      tm.assert_index_equal(
          Index(np.array(arr)), Index(np.array(arr), dtype=object)
      )
  
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 3 for calling the TestPeriodIndex obj's underlying member method code with example usage: obj.test_construction_base_constructor() without return types