BUG: fix Series.interpolate(method='index') with unsorted index

doc/source/whatsnew/v1.0.0.rst

@@ -550,6 +550,7 @@ Numeric
 - Bug in :class:`UInt64Index` precision loss while constructing from a list with values in the ``np.uint64`` range (:issue:`29526`)
 - Bug in :class:`NumericIndex` construction that caused indexing to fail when integers in the ``np.uint64`` range were used (:issue:`28023`)
 - Bug in :class:`NumericIndex` construction that caused :class:`UInt64Index` to be casted to :class:`Float64Index` when integers in the ``np.uint64`` range were used to index a :class:`DataFrame` (:issue:`28279`)
+- Bug in :meth:`Series.interpolate` when using method ``index`` with unsorted index. (:issue:`21037`)
 
 Conversion
 ^^^^^^^^^^

pandas/core/missing.py

@@ -277,7 +277,10 @@ def interpolate_1d(
                 inds = lib.maybe_convert_objects(inds)
         else:
             inds = xvalues
-        result[invalid] = np.interp(inds[invalid], inds[valid], yvalues[valid])
+        seq = np.argsort(inds[valid])
+        result[invalid] = np.interp(
+            inds[invalid], inds[valid][seq], yvalues[valid][seq]
+        )
         result[preserve_nans] = np.nan
         return result
 

pandas/tests/series/test_missing.py

@@ -1655,3 +1655,10 @@ def test_interpolate_timedelta_index(self, interp_methods_ind):
             pytest.skip(
                 "This interpolation method is not supported for Timedelta Index yet."
             )
+
+    def test_interpolate_unsorted_index(self):
+        # GH 21037
+        ts = pd.Series(data=[10, 9, np.nan, 2, 1], index=[10, 9, 3, 2, 1])
+        result = ts.interpolate(method="index").sort_index(ascending=True)
+        expected = ts.sort_index(ascending=True).interpolate(method="index")
+        tm.assert_series_equal(result, expected)