BUG: Clip corr edge cases between -1.0 and 1.0

doc/source/whatsnew/v3.0.0.rst

@@ -151,10 +151,23 @@ These improvements also fixed certain bugs in groupby:
 - :meth:`.DataFrameGroupBy.sum` would have incorrect values when there are multiple groupings, unobserved groups, and non-numeric data (:issue:`43891`)
 - :meth:`.DataFrameGroupBy.value_counts` would produce incorrect results when used with some categorical and some non-categorical groupings and ``observed=False`` (:issue:`56016`)
 
-.. _whatsnew_300.notable_bug_fixes.notable_bug_fix2:
+.. _whatsnew_300.notable_bug_fixes.corr_bounded:
 
-notable_bug_fix2
-^^^^^^^^^^^^^^^^
+Improved handling of numerical precision errors in ``DataFrame.corr``
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+Fixed an issue in :meth:`.DataFrame.corr` where numerical precision errors could cause correlation values to
+exceed 1.0 when dealing with data having very small variances. Correlation coefficients are now properly
+bounded to the valid range of [-1.0, 1.0] (:issue:`61120`).
+
+Previously, the code below would return ``1.1547005383792517``. It now returns ``1.0`` as expected.
+
+.. ipython:: python
+
+    data = pd.DataFrame(dict(
+        x=[0, 1],
+        y=[1.35951, 1.3595100000000007]
+    ))
+    data.corr().max().max()
 
 .. ---------------------------------------------------------------------------
 .. _whatsnew_300.api_breaking:

pandas/_libs/algos.pyx

@@ -353,10 +353,9 @@ def nancorr(const float64_t[:, :] mat, bint cov=False, minp=None):
         float64_t[:, ::1] result
         uint8_t[:, :] mask
         int64_t nobs = 0
-        float64_t vx, vy, dx, dy, meanx, meany, divisor, ssqdmx, ssqdmy, covxy
+        float64_t vx, vy, dx, dy, meanx, meany, divisor, ssqdmx, ssqdmy, covxy, val
 
     N, K = (<object>mat).shape
-
     if minp is None:
         minpv = 1
     else:
@@ -389,8 +388,14 @@ def nancorr(const float64_t[:, :] mat, bint cov=False, minp=None):
                 else:
                     divisor = (nobs - 1.0) if cov else sqrt(ssqdmx * ssqdmy)
 
+                    # clip `covxy / divisor` to ensure coeff is within bounds
                     if divisor != 0:
-                        result[xi, yi] = result[yi, xi] = covxy / divisor
+                        val = covxy / divisor
+                        if val > 1.0:
+                            val = 1.0
+                        elif val < -1.0:
+                            val = -1.0
+                        result[xi, yi] = result[yi, xi] = val
                     else:
                         result[xi, yi] = result[yi, xi] = NaN
 

pandas/tests/frame/methods/test_cov_corr.py

@@ -485,3 +485,15 @@ def test_corrwith_min_periods_boolean(self):
         result = df_bool.corrwith(ser_bool, min_periods=3)
         expected = Series([0.57735, 0.57735], index=["A", "B"])
         tm.assert_series_equal(result, expected)
+
+    def test_corr_within_bounds(self):
+        df1 = DataFrame({"x": [0, 1], "y": [1.35951, 1.3595100000000007]})
+        result1 = df1.corr().max().max()
+        expected1 = 1.0
+        tm.assert_equal(result1, expected1)
+
+        rng = np.random.default_rng(seed=42)
+        df2 = DataFrame(rng.random((100, 4)))
+        corr_matrix = df2.corr()
+        assert corr_matrix.min().min() >= -1.0
+        assert corr_matrix.max().max() <= 1.0