scikit-learn
diff --git a/‎doc/whats_new/v0.24.rst
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diff --git a/‎sklearn/cross_decomposition/_pls.py
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diff --git a/‎sklearn/cross_decomposition/tests/test_pls.py
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@@ -19,6 +19,12 @@ Changelog
   :term:`get_feature_names` on transformers with an empty column selection.
   :pr:`19579` by `Thomas Fan`_.
 
+:mod:`sklearn.cross_decomposition`
+..................................
+
+- |Fix| Fixed a regression in :class:`cross_decomposition.CCA`. :pr:`19646`
+  by `Thomas Fan`_.
+
 :mod:`sklearn.ensemble`
 .......................
 
 
@@ -23,6 +23,24 @@
 __all__ = ['PLSCanonical', 'PLSRegression', 'PLSSVD']
 
 
+def _pinv2_old(a):
+    # Used previous scipy pinv2 that was updated in:
+    # https://github.com/scipy/scipy/pull/10067
+    # We can not set `cond` or `rcond` for pinv2 in scipy >= 1.3 to keep the
+    # same behavior of pinv2 for scipy < 1.3, because the condition used to
+    # determine the rank is dependent on the output of svd.
+    u, s, vh = svd(a, full_matrices=False, check_finite=False)
+
+    t = u.dtype.char.lower()
+    factor = {'f': 1E3, 'd': 1E6}
+    cond = np.max(s) * factor[t] * np.finfo(t).eps
+    rank = np.sum(s > cond)
+
+    u = u[:, :rank]
+    u /= s[:rank]
+    return np.transpose(np.conjugate(np.dot(u, vh[:rank])))
+
+
 def _get_first_singular_vectors_power_method(X, Y, mode="A", max_iter=500,
                                              tol=1e-06, norm_y_weights=False):
     """Return the first left and right singular vectors of X'Y.
@@ -44,8 +62,7 @@ def _get_first_singular_vectors_power_method(X, Y, mode="A", max_iter=500,
         # As a result, and as detailed in the Wegelin's review, CCA (i.e. mode
         # B) will be unstable if n_features > n_samples or n_targets >
         # n_samples
-        X_pinv = pinv2(X, check_finite=False, cond=10*eps)
-        Y_pinv = pinv2(Y, check_finite=False, cond=10*eps)
+        X_pinv, Y_pinv = _pinv2_old(X), _pinv2_old(Y)
 
     for i in range(max_iter):
         if mode == "B":
 
@@ -552,3 +552,19 @@ def test_svd_flip_1d():
 
     assert_allclose(v, v_expected.ravel())
     assert_allclose(v, [-1, -2, -3])
+
+
+def test_loadings_converges():
+    """Test that CCA converges. Non-regression test for #19549."""
+    X, y = make_regression(n_samples=200, n_features=20, n_targets=20,
+                           random_state=20)
+
+    cca = CCA(n_components=10, max_iter=500)
+
+    with pytest.warns(None) as record:
+        cca.fit(X, y)
+    # ConvergenceWarning is not raised
+    assert not record
+
+    # Loadings converges to reasonable values
+    assert np.all(np.abs(cca.x_loadings_) < 1)