diff --git a/Eigen/src/Core/DenseBase.h b/Eigen/src/Core/DenseBase.h
index 91cfe3171..aa045686b 100644
--- a/Eigen/src/Core/DenseBase.h
+++ b/Eigen/src/Core/DenseBase.h
@@ -569,24 +569,24 @@ template<typename Derived> class DenseBase
 
     template <typename ThenDerived, typename ElseDerived>
     inline EIGEN_DEVICE_FUNC
-        CwiseTernaryOp<internal::scalar_boolean_select_op<Scalar, typename DenseBase<ThenDerived>::Scalar,
-                                                          typename DenseBase<ElseDerived>::Scalar>,
-                       Derived, ThenDerived, ElseDerived>
+        CwiseTernaryOp<internal::scalar_boolean_select_op<typename DenseBase<ThenDerived>::Scalar,
+                           typename DenseBase<ElseDerived>::Scalar, Scalar>,
+        ThenDerived, ElseDerived, Derived>
         select(const DenseBase<ThenDerived>& thenMatrix, const DenseBase<ElseDerived>& elseMatrix) const;
 
     template <typename ThenDerived>
     inline EIGEN_DEVICE_FUNC
-        CwiseTernaryOp<internal::scalar_boolean_select_op<Scalar, typename DenseBase<ThenDerived>::Scalar,
-                                                          typename DenseBase<ThenDerived>::Scalar>,
-                       Derived, ThenDerived, typename DenseBase<ThenDerived>::ConstantReturnType>
+        CwiseTernaryOp<internal::scalar_boolean_select_op<typename DenseBase<ThenDerived>::Scalar,
+                           typename DenseBase<ThenDerived>::Scalar, Scalar>,
+        ThenDerived, typename DenseBase<ThenDerived>::ConstantReturnType, Derived>
         select(const DenseBase<ThenDerived>& thenMatrix,
                const typename DenseBase<ThenDerived>::Scalar& elseScalar) const;
 
     template <typename ElseDerived>
     inline EIGEN_DEVICE_FUNC
-        CwiseTernaryOp<internal::scalar_boolean_select_op<Scalar, typename DenseBase<ElseDerived>::Scalar,
-                                                          typename DenseBase<ElseDerived>::Scalar>,
-                       Derived, typename DenseBase<ElseDerived>::ConstantReturnType, ElseDerived>
+        CwiseTernaryOp<internal::scalar_boolean_select_op<typename DenseBase<ElseDerived>::Scalar,
+                           typename DenseBase<ElseDerived>::Scalar, Scalar>,
+        typename DenseBase<ElseDerived>::ConstantReturnType, ElseDerived, Derived>
         select(const typename DenseBase<ElseDerived>::Scalar& thenScalar,
                const DenseBase<ElseDerived>& elseMatrix) const;
 
diff --git a/Eigen/src/Core/Select.h b/Eigen/src/Core/Select.h
index 1fe388efc..fdc93c5cd 100644
--- a/Eigen/src/Core/Select.h
+++ b/Eigen/src/Core/Select.h
@@ -124,14 +124,17 @@ class Select : public internal::dense_xpr_base< Select<ConditionMatrixType, Then
 template <typename Derived>
 template <typename ThenDerived, typename ElseDerived>
 inline EIGEN_DEVICE_FUNC CwiseTernaryOp<
-    internal::scalar_boolean_select_op<typename DenseBase<Derived>::Scalar, typename DenseBase<ThenDerived>::Scalar,
-                                       typename DenseBase<ElseDerived>::Scalar>,
-    Derived, ThenDerived, ElseDerived>
-DenseBase<Derived>::select(const DenseBase<ThenDerived>& thenMatrix, const DenseBase<ElseDerived>& elseMatrix) const {
-  using Op = internal::scalar_boolean_select_op<Scalar, typename DenseBase<ThenDerived>::Scalar,
-                                                typename DenseBase<ElseDerived>::Scalar>;
-  return CwiseTernaryOp<Op, Derived, ThenDerived, ElseDerived>(derived(), thenMatrix.derived(), elseMatrix.derived(),
-                                                               Op());
+    internal::scalar_boolean_select_op<typename DenseBase<ThenDerived>::Scalar,
+                                       typename DenseBase<ElseDerived>::Scalar,
+                                       typename DenseBase<Derived>::Scalar>,
+    ThenDerived, ElseDerived, Derived>
+DenseBase<Derived>::select(const DenseBase<ThenDerived>& thenMatrix,
+                           const DenseBase<ElseDerived>& elseMatrix) const {
+    using Op = internal::scalar_boolean_select_op<
+        typename DenseBase<ThenDerived>::Scalar,
+        typename DenseBase<ElseDerived>::Scalar, Scalar>;
+    return CwiseTernaryOp<Op, ThenDerived, ElseDerived, Derived>(
+        thenMatrix.derived(), elseMatrix.derived(), derived(), Op());
 }
 /** Version of DenseBase::select(const DenseBase&, const DenseBase&) with
  * the \em else expression being a scalar value.
@@ -141,16 +144,21 @@ DenseBase<Derived>::select(const DenseBase<ThenDerived>& thenMatrix, const Dense
 template <typename Derived>
 template <typename ThenDerived>
 inline EIGEN_DEVICE_FUNC CwiseTernaryOp<
-    internal::scalar_boolean_select_op<typename DenseBase<Derived>::Scalar, typename DenseBase<ThenDerived>::Scalar,
-                                       typename DenseBase<ThenDerived>::Scalar>,
-    Derived, ThenDerived, typename DenseBase<ThenDerived>::ConstantReturnType>
-DenseBase<Derived>::select(const DenseBase<ThenDerived>& thenMatrix,
-                           const typename DenseBase<ThenDerived>::Scalar& elseScalar) const {
-  using ElseConstantType = typename DenseBase<ThenDerived>::ConstantReturnType;
-  using Op = internal::scalar_boolean_select_op<Scalar, typename DenseBase<ThenDerived>::Scalar,
-                                                typename DenseBase<ThenDerived>::Scalar>;
-  return CwiseTernaryOp<Op, Derived, ThenDerived, ElseConstantType>(derived(), thenMatrix.derived(),
-                                                                    ElseConstantType(rows(), cols(), elseScalar), Op());
+    internal::scalar_boolean_select_op<typename DenseBase<ThenDerived>::Scalar,
+                                       typename DenseBase<ThenDerived>::Scalar,
+                                       typename DenseBase<Derived>::Scalar>,
+    ThenDerived, typename DenseBase<ThenDerived>::ConstantReturnType, Derived>
+DenseBase<Derived>::select(
+    const DenseBase<ThenDerived>& thenMatrix,
+    const typename DenseBase<ThenDerived>::Scalar& elseScalar) const {
+    using ElseConstantType =
+        typename DenseBase<ThenDerived>::ConstantReturnType;
+    using Op = internal::scalar_boolean_select_op<
+        typename DenseBase<ThenDerived>::Scalar,
+        typename DenseBase<ThenDerived>::Scalar, Scalar>;
+    return CwiseTernaryOp<Op, ThenDerived, ElseConstantType, Derived>(
+        thenMatrix.derived(), ElseConstantType(rows(), cols(), elseScalar),
+        derived(), Op());
 }
 /** Version of DenseBase::select(const DenseBase&, const DenseBase&) with
  * the \em then expression being a scalar value.
@@ -160,16 +168,22 @@ DenseBase<Derived>::select(const DenseBase<ThenDerived>& thenMatrix,
 template <typename Derived>
 template <typename ElseDerived>
 inline EIGEN_DEVICE_FUNC CwiseTernaryOp<
-    internal::scalar_boolean_select_op<typename DenseBase<Derived>::Scalar, typename DenseBase<ElseDerived>::Scalar,
-                                       typename DenseBase<ElseDerived>::Scalar>,
-    Derived, typename DenseBase<ElseDerived>::ConstantReturnType, ElseDerived>
-DenseBase<Derived>::select(const typename DenseBase<ElseDerived>::Scalar& thenScalar,
-                           const DenseBase<ElseDerived>& elseMatrix) const {
-  using ThenConstantType = typename DenseBase<ElseDerived>::ConstantReturnType;
-  using Op = internal::scalar_boolean_select_op<Scalar, typename DenseBase<ElseDerived>::Scalar,
-                                                typename DenseBase<ElseDerived>::Scalar>;
-  return CwiseTernaryOp<Op, Derived, ThenConstantType, ElseDerived>(
-      derived(), ThenConstantType(rows(), cols(), thenScalar), elseMatrix.derived(), Op());
+    internal::scalar_boolean_select_op<typename DenseBase<ElseDerived>::Scalar,
+                                       typename DenseBase<ElseDerived>::Scalar,
+                                       typename DenseBase<Derived>::Scalar>,
+    typename DenseBase<ElseDerived>::ConstantReturnType, ElseDerived,
+    Derived>
+DenseBase<Derived>::select(
+    const typename DenseBase<ElseDerived>::Scalar& thenScalar,
+    const DenseBase<ElseDerived>& elseMatrix) const {
+    using ThenConstantType =
+        typename DenseBase<ElseDerived>::ConstantReturnType;
+    using Op = internal::scalar_boolean_select_op<
+        typename DenseBase<ElseDerived>::Scalar,
+        typename DenseBase<ElseDerived>::Scalar, Scalar>;
+    return CwiseTernaryOp<Op, ThenConstantType, ElseDerived, Derived>(
+        ThenConstantType(rows(), cols(), thenScalar), elseMatrix.derived(),
+        derived(), Op());
 }
 
 } // end namespace Eigen
diff --git a/Eigen/src/Core/functors/TernaryFunctors.h b/Eigen/src/Core/functors/TernaryFunctors.h
index 9aadc271d..8f9492ba9 100644
--- a/Eigen/src/Core/functors/TernaryFunctors.h
+++ b/Eigen/src/Core/functors/TernaryFunctors.h
@@ -18,24 +18,23 @@ namespace internal {
 
 //---------- associative ternary functors ----------
 
-template <typename ConditionScalar, typename ThenScalar, typename ElseScalar>
+template <typename ThenScalar, typename ElseScalar, typename ConditionScalar>
 struct scalar_boolean_select_op {
   static constexpr bool ThenElseAreSame = is_same<ThenScalar, ElseScalar>::value;
   EIGEN_STATIC_ASSERT(ThenElseAreSame, THEN AND ELSE MUST BE SAME TYPE)
   using Scalar = ThenScalar;
   using result_type = Scalar;
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const ConditionScalar& cond, const ThenScalar& a,
-                                                          const ElseScalar& b) const {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const ThenScalar& a, const ElseScalar& b, const ConditionScalar& cond) const {
     return cond == ConditionScalar(0) ? b : a;
   }
   template <typename Packet>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& cond, const Packet& a, const Packet& b) const {
+      EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b, const Packet& cond) const {
     return pselect(pcmp_eq(cond, pzero(cond)), b, a);
   }
 };
 
-template <typename ConditionScalar, typename ThenScalar, typename ElseScalar>
-struct functor_traits<scalar_boolean_select_op<ConditionScalar, ThenScalar, ElseScalar>> {
+template <typename ThenScalar, typename ElseScalar, typename ConditionScalar>
+    struct functor_traits<scalar_boolean_select_op<ThenScalar, ElseScalar, ConditionScalar>> {
   using Scalar = ThenScalar;
   enum {
     Cost = 1,