BUG: Fix behavior of argmax and argmin with inf (pandas-dev#16449)

Closes pandas-dev#13595

The implementations of `nanargmin` and `nanargmax` in `nanops` were
forcing the `_get_values` utility function to always mask out infinite
values. For example, in `nanargmax`,

    >>> nanops._get_values(np.array([1, np.nan, np.inf]), True,
    isfinite=True, fill_value_typ='-inf')

    (array([  1., -inf, -inf]),
     array([False,  True,  True], dtype=bool),
     dtype('float64'),
     numpy.float64)

The first element of the result tuple (the masked version of the
values array) is used for actually finding the max or min argument. As
a result, infinite values could never be correctly recognized as the
maximum or minimum values in an array.

This also affects the behavior of `Series.idxmax` with string data (or
the `object` dtype generally). Previously, `nanargmax` would always
attempt to coerce its input to float, even when there were no missing
values. Now, it will not, and so will work correctly in the particular
case of a `Series` of strings with no missing values. However, because
it's difficult to ensure that `nanargmin` and `nanargmax` will behave
consistently for arbitrary `Series` of `object` with and without
missing values, these functions are now explicitly disallowed for
`object`.

doc/source/whatsnew/v0.21.0.txt

@@ -233,6 +233,30 @@ Dtype Conversions
 - Inconsistent behavior in ``.where()`` with datetimelikes which would raise rather than coerce to ``object`` (:issue:`16402`)
 - Bug in assignment against ``int64`` data with ``np.ndarray`` with ``float64`` dtype may keep ``int64`` dtype (:issue:`14001`)
 
+Dropping argmin/argmax support for arbitrary dtypes
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+:func:`Series.argmin` and :func:`Series.argmax` will now raise a ``TypeError`` when used with ``object`` dtypes. Previously, these functions would attempt to coerce their arguments to floats, which usually led to a ``ValueError``. Now, ``object`` dtypes are explicitly disallowed with ``argmax`` and related functions. For example, the old behavior produced a somewhat confusing message:
+
+.. code-block:: ipython
+
+  In [1]: s = pd.Series(['foo', 'bar'])
+
+  In [2]: s.argmax()
+  ...
+  ValueError: could not convert string to float: 'bar'
+
+This has now changed to
+
+.. code-block:: ipython
+
+  In [1]: s = pd.Series(['foo', 'bar'])
+
+  In [2]: s.argmax()
+  ...
+  TypeError: reduction operation 'argmax' not allowed for this dtype
+
+
 .. _whatsnew_0210.api.na_changes:
 
 NA naming Changes
@@ -369,6 +393,7 @@ Reshaping
 - Fixes regression from 0.20, :func:`Series.aggregate` and :func:`DataFrame.aggregate` allow dictionaries as return values again (:issue:`16741`)
 - Fixes dtype of result with integer dtype input, from :func:`pivot_table` when called with ``margins=True`` (:issue:`17013`)
 - Bug in :func:`crosstab` where passing two ``Series`` with the same name raised a ``KeyError`` (:issue:`13279`)
+- :func:`Series.argmin`, :func:`Series.argmax`, and their counterparts on ``DataFrame`` and groupby objects work correctly with floating point data that contains infinite values (:issue:`13595`).
 
 Numeric
 ^^^^^^^

pandas/core/nanops.py

@@ -486,23 +486,23 @@ def reduction(values, axis=None, skipna=True):
 nanmax = _nanminmax('max', fill_value_typ='-inf')
 
 
+@disallow('O')
 def nanargmax(values, axis=None, skipna=True):
     """
     Returns -1 in the NA case
     """
-    values, mask, dtype, _ = _get_values(values, skipna, fill_value_typ='-inf',
-                                         isfinite=True)
+    values, mask, dtype, _ = _get_values(values, skipna, fill_value_typ='-inf')
     result = values.argmax(axis)
     result = _maybe_arg_null_out(result, axis, mask, skipna)
     return result
 
 
+@disallow('O')
 def nanargmin(values, axis=None, skipna=True):
     """
     Returns -1 in the NA case
     """
-    values, mask, dtype, _ = _get_values(values, skipna, fill_value_typ='+inf',
-                                         isfinite=True)
+    values, mask, dtype, _ = _get_values(values, skipna, fill_value_typ='+inf')
     result = values.argmin(axis)
     result = _maybe_arg_null_out(result, axis, mask, skipna)
     return result

pandas/tests/groupby/test_groupby.py

@@ -2339,7 +2339,8 @@ def test_non_cython_api(self):
         assert_frame_equal(result, expected)
 
         # idxmax
-        expected = DataFrame([[0], [nan]], columns=['B'], index=[1, 3])
+        expected = DataFrame([[0.0], [nan]], columns=['B'],
+                             index=[1, 3])
         expected.index.name = 'A'
         result = g.idxmax()
         assert_frame_equal(result, expected)

pandas/tests/series/test_operators.py

@@ -1857,3 +1857,58 @@ def test_op_duplicate_index(self):
         result = s1 + s2
         expected = pd.Series([11, 12, np.nan], index=[1, 1, 2])
         assert_series_equal(result, expected)
+
+    def test_argminmax(self):
+        # Series.argmin, Series.argmax are aliased to Series.idxmin,
+        # Series.idxmax
+
+        # Expected behavior for empty Series
+        s = pd.Series([])
+
+        with pytest.raises(ValueError):
+            s.argmin()
+        with pytest.raises(ValueError):
+            s.argmin(skipna=False)
+        with pytest.raises(ValueError):
+            s.argmax()
+        with pytest.raises(ValueError):
+            s.argmax(skipna=False)
+
+        # For numeric data with NA and Inf (GH #13595)
+        s = pd.Series([0, -np.inf, np.inf, np.nan])
+
+        assert s.argmin() == 1
+        assert np.isnan(s.argmin(skipna=False))
+
+        assert s.argmax() == 2
+        assert np.isnan(s.argmax(skipna=False))
+
+        # Using old-style behavior that treats floating point nan, -inf, and
+        # +inf as missing
+        s = pd.Series([0, -np.inf, np.inf, np.nan])
+
+        with pd.option_context('mode.use_inf_as_na', True):
+            assert s.argmin() == 0
+            assert np.isnan(s.argmin(skipna=False))
+            assert s.argmax() == 0
+            np.isnan(s.argmax(skipna=False))
+
+        # For strings (or any Series with dtype 'O')
+        s = pd.Series(['foo', 'bar', 'baz'])
+        with pytest.raises(TypeError):
+            s.argmin()
+        with pytest.raises(TypeError):
+            s.argmax()
+
+        s = pd.Series([(1,), (2,)])
+        with pytest.raises(TypeError):
+            s.argmin()
+        with pytest.raises(TypeError):
+            s.argmax()
+
+        # For mixed data types
+        s = pd.Series(['foo', 'foo', 'bar', 'bar', None, np.nan, 'baz'])
+        with pytest.raises(TypeError):
+            s.argmin()
+        with pytest.raises(TypeError):
+            s.argmax()