Revert "PERF: cythonize kendall correlation (#39132)"

This reverts commit 57ccd2a.

The Kendall implementation failed to take into account ties
and was inconsistent with scipy's method

Author: zrait

pandas/_libs/algos.pyx

@@ -518,97 +518,6 @@ def nancorr_spearman(ndarray[float64_t, ndim=2] mat, Py_ssize_t minp=1) -> ndarr
     return result
 
 
-# ----------------------------------------------------------------------
-# Kendall correlation
-# Wikipedia article: https://en.wikipedia.org/wiki/Kendall_rank_correlation_coefficient
-
-@cython.boundscheck(False)
-@cython.wraparound(False)
-def nancorr_kendall(ndarray[float64_t, ndim=2] mat, Py_ssize_t minp=1) -> ndarray:
-    """
-    Perform kendall correlation on a 2d array
-
-    Parameters
-    ----------
-    mat : np.ndarray[float64_t, ndim=2]
-        Array to compute kendall correlation on
-    minp : int, default 1
-        Minimum number of observations required per pair of columns
-        to have a valid result.
-
-    Returns
-    -------
-    numpy.ndarray[float64_t, ndim=2]
-        Correlation matrix
-    """
-    cdef:
-        Py_ssize_t i, j, k, xi, yi, N, K
-        ndarray[float64_t, ndim=2] result
-        ndarray[float64_t, ndim=2] ranked_mat
-        ndarray[uint8_t, ndim=2] mask
-        float64_t currj
-        ndarray[uint8_t, ndim=1] valid
-        ndarray[int64_t] sorted_idxs
-        ndarray[float64_t, ndim=1] col
-        int64_t n_concordant
-        int64_t total_concordant = 0
-        int64_t total_discordant = 0
-        float64_t kendall_tau
-        int64_t n_obs
-
-    N, K = (<object>mat).shape
-
-    result = np.empty((K, K), dtype=np.float64)
-    mask = np.isfinite(mat)
-
-    ranked_mat = np.empty((N, K), dtype=np.float64)
-
-    for i in range(K):
-        ranked_mat[:, i] = rank_1d(mat[:, i])
-
-    for xi in range(K):
-        sorted_idxs = ranked_mat[:, xi].argsort()
-        ranked_mat = ranked_mat[sorted_idxs]
-        mask = mask[sorted_idxs]
-        for yi in range(xi + 1, K):
-            valid = mask[:, xi] & mask[:, yi]
-            if valid.sum() < minp:
-                result[xi, yi] = NaN
-                result[yi, xi] = NaN
-            else:
-                # Get columns and order second column using 1st column ranks
-                if not valid.all():
-                    col = ranked_mat[valid.nonzero()][:, yi]
-                else:
-                    col = ranked_mat[:, yi]
-                n_obs = col.shape[0]
-                total_concordant = 0
-                total_discordant = 0
-                for j in range(n_obs - 1):
-                    currj = col[j]
-                    # Count num concordant and discordant pairs
-                    n_concordant = 0
-                    for k in range(j, n_obs):
-                        if col[k] > currj:
-                            n_concordant += 1
-                    total_concordant += n_concordant
-                    total_discordant += (n_obs - 1 - j - n_concordant)
-                # Note: we do total_concordant+total_discordant here which is
-                # equivalent to the C(n, 2), the total # of pairs,
-                # listed on wikipedia
-                kendall_tau = (total_concordant - total_discordant) / \
-                              (total_concordant + total_discordant)
-                result[xi, yi] = kendall_tau
-                result[yi, xi] = kendall_tau
-
-        if mask[:, xi].sum() > minp:
-            result[xi, xi] = 1
-        else:
-            result[xi, xi] = NaN
-
-    return result
-
-
 # ----------------------------------------------------------------------
 
 ctypedef fused algos_t:

pandas/core/frame.py

@@ -9390,7 +9390,8 @@ def corr(
                 regardless of the callable's behavior.
         min_periods : int, optional
             Minimum number of observations required per pair of columns
-            to have a valid result.
+            to have a valid result. Currently only available for Pearson
+            and Spearman correlation.
 
         Returns
         -------
@@ -9424,9 +9425,7 @@ def corr(
             correl = libalgos.nancorr(mat, minp=min_periods)
         elif method == "spearman":
             correl = libalgos.nancorr_spearman(mat, minp=min_periods)
-        elif method == "kendall":
-            correl = libalgos.nancorr_kendall(mat, minp=min_periods)
-        elif callable(method):
+        elif method == "kendall" or callable(method):
             if min_periods is None:
                 min_periods = 1
             mat = mat.T