ENH: correlation function accepts method being a callable

- other than the listed strings for the `method` argument, accept a callable for generic correlation calculations
- minor fix of = to == in requirements file

doc/source/computation.rst

@@ -153,6 +153,21 @@ Like ``cov``, ``corr`` also supports the optional ``min_periods`` keyword:
    frame.corr(min_periods=12)
 
 
+.. versionadded:: 0.24.0
+
+The ``method`` argument can also be a callable for a generic correlation
+calculation. In this case, it should be a single function
+that produces a single value from two ndarray inputs. Suppose we wanted to
+compute the correlation based on histogram intersection:
+
+.. ipython:: python
+
+   # histogram intersection
+   histogram_intersection = lambda a, b: np.minimum(
+       np.true_divide(a, a.sum()), np.true_divide(b, b.sum())
+   ).sum()
+   frame.corr(method=histogram_intersection)
+
 A related method :meth:`~DataFrame.corrwith` is implemented on DataFrame to 
 compute the correlation between like-labeled Series contained in different 
 DataFrame objects.

doc/source/whatsnew/v0.24.0.txt

@@ -17,6 +17,9 @@ New features
 
 - ``ExcelWriter`` now accepts ``mode`` as a keyword argument, enabling append to existing workbooks when using the ``openpyxl`` engine (:issue:`3441`)
 
+- :meth:`DataFrame.corr` and :meth:`Series.corr` now accept a callable for generic calculation methods of correlation, e.g. histogram intersection (:issue:`22684`)
+
+
 .. _whatsnew_0240.enhancements.extension_array_operators:
 
 ``ExtensionArray`` operator support

pandas/core/frame.py

@@ -6652,10 +6652,14 @@ def corr(self, method='pearson', min_periods=1):
 
         Parameters
         ----------
-        method : {'pearson', 'kendall', 'spearman'}
+        method : {'pearson', 'kendall', 'spearman'} or callable
             * pearson : standard correlation coefficient
             * kendall : Kendall Tau correlation coefficient
             * spearman : Spearman rank correlation
+            * callable: callable with input two 1d ndarrays
+                and returning a float
+                .. versionadded:: 0.24.0
+
         min_periods : int, optional
             Minimum number of observations required per pair of columns
             to have a valid result. Currently only available for pearson
@@ -6675,7 +6679,7 @@ def corr(self, method='pearson', min_periods=1):
         elif method == 'spearman':
             correl = libalgos.nancorr_spearman(ensure_float64(mat),
                                                minp=min_periods)
-        elif method == 'kendall':
+        elif method == 'kendall' or callable(method):
             if min_periods is None:
                 min_periods = 1
             mat = ensure_float64(mat).T

pandas/core/nanops.py

@@ -764,6 +764,9 @@ def nancorr(a, b, method='pearson', min_periods=None):
 
 
 def get_corr_func(method):
+    if callable(method):
+        return method
+
     if method in ['kendall', 'spearman']:
         from scipy.stats import kendalltau, spearmanr
 

pandas/core/series.py

@@ -1913,10 +1913,14 @@ def corr(self, other, method='pearson', min_periods=None):
         Parameters
         ----------
         other : Series
-        method : {'pearson', 'kendall', 'spearman'}
+        method : {'pearson', 'kendall', 'spearman'} or callable
             * pearson : standard correlation coefficient
             * kendall : Kendall Tau correlation coefficient
             * spearman : Spearman rank correlation
+            * callable: callable with input two 1d ndarray
+                and returning a float
+                .. versionadded:: 0.24.0
+
         min_periods : int, optional
             Minimum number of observations needed to have a valid result
 
@@ -1929,7 +1933,7 @@ def corr(self, other, method='pearson', min_periods=None):
         if len(this) == 0:
             return np.nan
 
-        if method in ['pearson', 'spearman', 'kendall']:
+        if method in ['pearson', 'spearman', 'kendall'] or callable(method):
             return nanops.nancorr(this.values, other.values, method=method,
                                   min_periods=min_periods)
 

pandas/tests/series/test_analytics.py

@@ -789,6 +789,38 @@ def test_corr_invalid_method(self):
         with tm.assert_raises_regex(ValueError, msg):
             s1.corr(s2, method="____")
 
+    def test_corr_callable_method(self):
+        # simple correlation example
+        # returns 1 if exact equality, 0 otherwise
+        my_corr = lambda a, b: 1. if (a == b).all() else 0.
+
+        # simple example
+        s1 = Series([1, 2, 3, 4, 5])
+        s2 = Series([5, 4, 3, 2, 1])
+        expected_1 = 0
+        tm.assert_almost_equal(
+            s1.corr(s2, method=my_corr),
+            expected_1)
+
+        # full overlap
+        tm.assert_almost_equal(
+            self.ts.corr(self.ts, method=my_corr), 1.)
+
+        # partial overlap
+        tm.assert_almost_equal(
+            self.ts[:15].corr(self.ts[5:], method=my_corr), 1.)
+
+        # No overlap
+        assert np.isnan(
+            self.ts[::2].corr(self.ts[1::2], method=my_corr))
+
+        # dataframe example
+        df = pd.DataFrame([s1, s2])
+        expected_2 = pd.DataFrame([
+            {0: 1., 1: expected_1}, {0: expected_1, 1: 1.}])
+        tm.assert_almost_equal(
+            df.transpose().corr(method=my_corr), expected_2)
+
     def test_cov(self):
         # full overlap
         tm.assert_almost_equal(self.ts.cov(self.ts), self.ts.std() ** 2)