code: def test_where_period_invalid_na(frame_or_series, as_cat, request):
      # GH#44697
      idx = pd.period_range("2016-01-01", periods=3, freq="D")
      if as_cat:
          idx = idx.astype("category")
      obj = frame_or_series(idx)
  
      # NA value that we should *not* cast to Period dtype
      tdnat = pd.NaT.to_numpy("m8[ns]")
  
      mask = np.array([True, True, False], ndmin=obj.ndim).T
  
      if as_cat:
          msg = (
              r"Cannot setitem on a Categorical with a new category \(NaT\), "
              "set the categories first"
          )
      else:
          msg = "value should be a 'Period'"
  
      if as_cat:
          with pytest.raises(TypeError, match=msg):
              obj.where(mask, tdnat)
  
          with pytest.raises(TypeError, match=msg):
              obj.mask(mask, tdnat)
  
          with pytest.raises(TypeError, match=msg):
              obj.mask(mask, tdnat, inplace=True)
  
      else:
          # With PeriodDtype, ser[i] = tdnat coerces instead of raising,
          #  so for consistency, ser[mask] = tdnat must as well
          expected = obj.astype(object).where(mask, tdnat)
          result = obj.where(mask, tdnat)
          tm.assert_equal(result, expected)
  
          expected = obj.astype(object).mask(mask, tdnat)
          result = obj.mask(mask, tdnat)
          tm.assert_equal(result, expected)
  
          with tm.assert_produces_warning(
              FutureWarning,
              match="Setting an item of incompatible dtype",
          ):
              obj.mask(mask, tdnat, inplace=True)
          tm.assert_equal(obj, expected)
  
imports: from datetime import datetime
  from hypothesis import given
  import numpy
  import pytest
  from pandas.core.dtypes.common import is_scalar
  import pandas
  from pandas import DataFrame, DatetimeIndex, Index, Series, StringDtype, Timestamp, date_range, isna
  import pandas._testing
  from pandas._testing._hypothesis import OPTIONAL_ONE_OF_ALL
label_desc: Use image node_id 10 for calling a global function with example usage: test_where_period_invalid_na(frame_or_series, as_cat, request) without return types