introduce a new LvalueBit flag and split DenseCoeffBase into three level of accessors

Eigen/src/Core/util/Constants.h

@@ -139,6 +139,14 @@ const unsigned int DirectAccessBit = 0x20;
   * means the first coefficient packet is guaranteed to be aligned */
 const unsigned int AlignedBit = 0x40;
 
+/** \ingroup flags
+  *
+  * Means the expression is writable. Note that DirectAccessBit implies LvalueBit.
+  * Internaly, it is mainly used to enable the writable coeff accessors, and makes
+  * the read-only coeff accessors to return by const reference.
+  */
+const unsigned int LvalueBit = 0x80;
+
 const unsigned int NestByRefBit = 0x100;
 
 // list of flags that are inherited by default
@@ -234,6 +242,10 @@ enum {
   IsSparse
 };
 
+enum AccessorLevels {
+  ReadOnlyAccessors, WriteAccessors, DirectAccessors
+};
+
 enum DecompositionOptions {
   Pivoting            = 0x01, // LDLT,
   NoPivoting          = 0x02, // LDLT,

Eigen/src/Core/util/ForwardDeclarations.h

@@ -36,7 +36,10 @@ template<typename Derived> struct ei_has_direct_access
 
 template<typename Derived> struct EigenBase;
 template<typename Derived> class DenseBase;
-template<typename Derived, bool EnableDirectAccessAPI = ei_has_direct_access<Derived>::ret>
+template<typename Derived,
+         AccessorLevels Level = (ei_traits<Derived>::Flags & DirectAccessBit) ? DirectAccessors
+                              : (ei_traits<Derived>::Flags & LvalueBit) ? WriteAccessors
+                              : ReadOnlyAccessors>
 class DenseCoeffsBase;
 
 template<typename _Scalar, int _Rows, int _Cols,

Eigen/src/Core/util/XprHelper.h

@@ -155,7 +155,7 @@ class ei_compute_matrix_flags
     };
 
   public:
-    enum { ret = LinearAccessBit | DirectAccessBit | NestByRefBit | packet_access_bit | row_major_bit | aligned_bit };
+    enum { ret = LinearAccessBit | LvalueBit | DirectAccessBit | NestByRefBit | packet_access_bit | row_major_bit | aligned_bit };
 };
 
 template<int _Rows, int _Cols> struct ei_size_at_compile_time
@@ -355,7 +355,7 @@ template<typename T, int n=1, typename PlainObject = typename ei_eval<T>::type>
 
 template<unsigned int Flags> struct ei_are_flags_consistent
 {
-  enum { ret = true };
+  enum { ret = EIGEN_IMPLIES(bool(Flags&DirectAccessBit), bool(Flags&LvalueBit)) };
 };
 
 template<typename Derived, typename XprKind = typename ei_traits<Derived>::XprKind>