From 85fb517eaf8225a607328d67ab573596b81015f1 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Tue, 6 Sep 2016 17:23:15 +0200
Subject: [PATCH] Generalize ScalarBinaryOpTraits to any complex-real
 combination as defined by NumTraits (instead of supporting std::complex
 only).

---
 Eigen/src/Core/NumTraits.h      |  3 +++
 Eigen/src/Core/util/XprHelper.h | 33 ++++++++++++++++++++-------------
 2 files changed, 23 insertions(+), 13 deletions(-)

diff --git a/Eigen/src/Core/NumTraits.h b/Eigen/src/Core/NumTraits.h
index 42cffbd3b..899dc672a 100644
--- a/Eigen/src/Core/NumTraits.h
+++ b/Eigen/src/Core/NumTraits.h
@@ -255,6 +255,9 @@ private:
   static inline std::string quiet_NaN();
 };
 
+// Empty specialization for void to allow template specialization based on NumTraits<T>::Real with T==void and SFINAE.
+template<> struct NumTraits<void> {};
+
 } // end namespace Eigen
 
 #endif // EIGEN_NUMTRAITS_H
diff --git a/Eigen/src/Core/util/XprHelper.h b/Eigen/src/Core/util/XprHelper.h
index 7e43f4fea..e26a92022 100644
--- a/Eigen/src/Core/util/XprHelper.h
+++ b/Eigen/src/Core/util/XprHelper.h
@@ -707,7 +707,7 @@ std::string demangle_flags(int f)
   * This class permits to control the scalar return type of any binary operation performed on two different scalar types through (partial) template specializations.
   *
   * For instance, let \c U1, \c U2 and \c U3 be three user defined scalar types for which most operations between instances of \c U1 and \c U2 returns an \c U3.
-  * You can let Eigen knows that by defining:
+  * You can let %Eigen knows that by defining:
     \code
     template<typename BinaryOp>
     struct ScalarBinaryOpTraits<U1,U2,BinaryOp> { typedef U3 ReturnType;  };
@@ -725,6 +725,14 @@ std::string demangle_flags(int f)
     struct ScalarBinaryOpTraits<U1,U2,internal::scalar_sum_op<U1,U2> > { typedef U1 ReturnType; };
     \endcode
   *
+  * By default, the following generic combinations are supported:
+  <table class="manual">
+  <tr><th>ScalarA</th><th>ScalarB</th><th>BinaryOp</th><th>ReturnType</th><th>Note</th></tr>
+  <tr            ><td>\c T </td><td>\c T </td><td>\c * </td><td>\c T </td><td></td></tr>
+  <tr class="alt"><td>\c NumTraits<T>::Real </td><td>\c T </td><td>\c * </td><td>\c T </td><td>Only if \c NumTraits<T>::IsComplex </td></tr>
+  <tr            ><td>\c T </td><td>\c NumTraits<T>::Real </td><td>\c * </td><td>\c T </td><td>Only if \c NumTraits<T>::IsComplex </td></tr>
+  </table>
+  *
   * \sa CwiseBinaryOp
   */
 template<typename ScalarA, typename ScalarB, typename BinaryOp=internal::scalar_product_op<ScalarA,ScalarB> >
@@ -741,6 +749,17 @@ struct ScalarBinaryOpTraits<T,T,BinaryOp>
   typedef T ReturnType;
 };
 
+template <typename T, typename BinaryOp>
+struct ScalarBinaryOpTraits<T, typename NumTraits<typename internal::enable_if<NumTraits<T>::IsComplex,T>::type>::Real, BinaryOp>
+{
+  typedef T ReturnType;
+};
+template <typename T, typename BinaryOp>
+struct ScalarBinaryOpTraits<typename NumTraits<typename internal::enable_if<NumTraits<T>::IsComplex,T>::type>::Real, T, BinaryOp>
+{
+  typedef T ReturnType;
+};
+
 // For Matrix * Permutation
 template<typename T, typename BinaryOp>
 struct ScalarBinaryOpTraits<T,void,BinaryOp>
@@ -762,18 +781,6 @@ struct ScalarBinaryOpTraits<void,void,BinaryOp>
   typedef void ReturnType;
 };
 
-template<typename T, typename BinaryOp>
-struct ScalarBinaryOpTraits<T,std::complex<T>,BinaryOp>
-{
-  typedef std::complex<T> ReturnType;
-};
-
-template<typename T, typename BinaryOp>
-struct ScalarBinaryOpTraits<std::complex<T>, T,BinaryOp>
-{
-  typedef std::complex<T> ReturnType;
-};
-
 // We require Lhs and Rhs to have "compatible" scalar types.
 // It is tempting to always allow mixing different types but remember that this is often impossible in the vectorized paths.
 // So allowing mixing different types gives very unexpected errors when enabling vectorization, when the user tries to