From aaf215c15af0ae7f28ec925bc9e42edf3f72cad9 Mon Sep 17 00:00:00 2001
From: Lucy Liu <jliu176@gmail.com>
Date: Sat, 17 Feb 2024 23:00:33 +1100
Subject: [PATCH] FIX Allow alpha 0 when not using LOO in `RidgeCV` (#28425)

---
 doc/modules/linear_model.rst   | 24 +++++++++++++-----------
 sklearn/linear_model/_ridge.py | 24 +++++++++++++++++-------
 2 files changed, 30 insertions(+), 18 deletions(-)

diff --git a/doc/modules/linear_model.rst b/doc/modules/linear_model.rst
index bd074f5b326d3..ed7ea069e58b6 100644
--- a/doc/modules/linear_model.rst
+++ b/doc/modules/linear_model.rst
@@ -193,9 +193,14 @@ This method has the same order of complexity as
 Setting the regularization parameter: leave-one-out Cross-Validation
 --------------------------------------------------------------------
 
-:class:`RidgeCV` implements ridge regression with built-in
-cross-validation of the alpha parameter. The object works in the same way
-as GridSearchCV except that it defaults to Leave-One-Out Cross-Validation::
+:class:`RidgeCV` and :class:`RidgeClassifierCV` implement ridge
+regression/classification with built-in cross-validation of the alpha parameter.
+They work in the same way as :class:`~sklearn.model_selection.GridSearchCV` except
+that it defaults to efficient Leave-One-Out :term:`cross-validation`.
+When using the default :term:`cross-validation`, alpha cannot be 0 due to the
+formulation used to calculate Leave-One-Out error. See [RL2007]_ for details.
+
+Usage example::
 
     >>> import numpy as np
     >>> from sklearn import linear_model
@@ -211,16 +216,13 @@ cross-validation with :class:`~sklearn.model_selection.GridSearchCV`, for
 example `cv=10` for 10-fold cross-validation, rather than Leave-One-Out
 Cross-Validation.
 
-|details-start|
-**References**
-|details-split|
+.. topic:: References:
 
-* "Notes on Regularized Least Squares", Rifkin & Lippert (`technical report
-  <http://cbcl.mit.edu/publications/ps/MIT-CSAIL-TR-2007-025.pdf>`_,
-  `course slides
-  <https://www.mit.edu/~9.520/spring07/Classes/rlsslides.pdf>`_).
 
-|details-end|
+  .. [RL2007] "Notes on Regularized Least Squares", Rifkin & Lippert (`technical report
+    <http://cbcl.mit.edu/publications/ps/MIT-CSAIL-TR-2007-025.pdf>`_,
+    `course slides
+    <https://www.mit.edu/~9.520/spring07/Classes/rlsslides.pdf>`_).
 
 .. _lasso:
 
diff --git a/sklearn/linear_model/_ridge.py b/sklearn/linear_model/_ridge.py
index 84646f5aaf130..6c561859fdf9f 100644
--- a/sklearn/linear_model/_ridge.py
+++ b/sklearn/linear_model/_ridge.py
@@ -2188,12 +2188,21 @@ def fit(self, X, y, sample_weight=None):
         """
         cv = self.cv
 
-        check_scalar_alpha = partial(
-            check_scalar,
-            target_type=numbers.Real,
-            min_val=0.0,
-            include_boundaries="neither",
-        )
+        # `_RidgeGCV` does not work for alpha = 0
+        if cv is None:
+            check_scalar_alpha = partial(
+                check_scalar,
+                target_type=numbers.Real,
+                min_val=0.0,
+                include_boundaries="neither",
+            )
+        else:
+            check_scalar_alpha = partial(
+                check_scalar,
+                target_type=numbers.Real,
+                min_val=0.0,
+                include_boundaries="left",
+            )
 
         if isinstance(self.alphas, (np.ndarray, list, tuple)):
             n_alphas = 1 if np.ndim(self.alphas) == 0 else len(self.alphas)
@@ -2272,7 +2281,7 @@ class RidgeCV(
         Alpha corresponds to ``1 / (2C)`` in other linear models such as
         :class:`~sklearn.linear_model.LogisticRegression` or
         :class:`~sklearn.svm.LinearSVC`.
-        If using Leave-One-Out cross-validation, alphas must be positive.
+        If using Leave-One-Out cross-validation, alphas must be strictly positive.
 
     fit_intercept : bool, default=True
         Whether to calculate the intercept for this model. If set
@@ -2439,6 +2448,7 @@ class RidgeClassifierCV(_RoutingNotSupportedMixin, _RidgeClassifierMixin, _BaseR
         Alpha corresponds to ``1 / (2C)`` in other linear models such as
         :class:`~sklearn.linear_model.LogisticRegression` or
         :class:`~sklearn.svm.LinearSVC`.
+        If using Leave-One-Out cross-validation, alphas must be strictly positive.
 
     fit_intercept : bool, default=True
         Whether to calculate the intercept for this model. If set