diff --git a/Eigen/Core b/Eigen/Core
index 7cf431320..1ec749452 100644
--- a/Eigen/Core
+++ b/Eigen/Core
@@ -391,6 +391,7 @@ using std::ptrdiff_t;
 #include "src/Core/GeneralProduct.h"
 #include "src/Core/Solve.h"
 #include "src/Core/Inverse.h"
+#include "src/Core/SolverBase.h"
 #include "src/Core/PermutationMatrix.h"
 #include "src/Core/Transpositions.h"
 #include "src/Core/TriangularMatrix.h"
diff --git a/Eigen/src/CholmodSupport/CholmodSupport.h b/Eigen/src/CholmodSupport/CholmodSupport.h
index f33aa9bf1..06421d5ed 100644
--- a/Eigen/src/CholmodSupport/CholmodSupport.h
+++ b/Eigen/src/CholmodSupport/CholmodSupport.h
@@ -170,6 +170,10 @@ class CholmodBase : public SparseSolverBase<Derived>
     typedef typename MatrixType::RealScalar RealScalar;
     typedef MatrixType CholMatrixType;
     typedef typename MatrixType::StorageIndex StorageIndex;
+    enum {
+      ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+    };
 
   public:
 
diff --git a/Eigen/src/Core/CoreEvaluators.h b/Eigen/src/Core/CoreEvaluators.h
index a8b359085..42ad452f7 100644
--- a/Eigen/src/Core/CoreEvaluators.h
+++ b/Eigen/src/Core/CoreEvaluators.h
@@ -29,6 +29,7 @@ struct storage_kind_to_evaluator_kind {
 template<typename StorageKind> struct storage_kind_to_shape;
 
 template<> struct storage_kind_to_shape<Dense>                  { typedef DenseShape Shape;           };
+template<> struct storage_kind_to_shape<SolverStorage>          { typedef SolverShape Shape;           };
 template<> struct storage_kind_to_shape<PermutationStorage>     { typedef PermutationShape Shape;     };
 template<> struct storage_kind_to_shape<TranspositionsStorage>  { typedef TranspositionsShape Shape;  };
 
diff --git a/Eigen/src/Core/Inverse.h b/Eigen/src/Core/Inverse.h
index 8ba1a12d9..f3ec84990 100644
--- a/Eigen/src/Core/Inverse.h
+++ b/Eigen/src/Core/Inverse.h
@@ -48,6 +48,7 @@ public:
   typedef typename internal::ref_selector<XprType>::type      XprTypeNested;
   typedef typename internal::remove_all<XprTypeNested>::type  XprTypeNestedCleaned;
   typedef typename internal::ref_selector<Inverse>::type Nested;
+  typedef typename internal::remove_all<XprType>::type NestedExpression;
   
   explicit Inverse(const XprType &xpr)
     : m_xpr(xpr)
@@ -62,25 +63,16 @@ protected:
   XprTypeNested m_xpr;
 };
 
-/** \internal
-  * Specialization of the Inverse expression for dense expressions.
-  * Direct access to the coefficients are discared.
-  * FIXME this intermediate class is probably not needed anymore.
-  */
-template<typename XprType>
-class InverseImpl<XprType,Dense>
-  : public MatrixBase<Inverse<XprType> >
+// Generic API dispatcher
+template<typename XprType, typename StorageKind>
+class InverseImpl
+  : public internal::generic_xpr_base<Inverse<XprType> >::type
 {
-  typedef Inverse<XprType> Derived;
-  
 public:
-  
-  typedef MatrixBase<Derived> Base;
-  EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
-  typedef typename internal::remove_all<XprType>::type NestedExpression;
-
+  typedef typename internal::generic_xpr_base<Inverse<XprType> >::type Base;
+  typedef typename XprType::Scalar Scalar;
 private:
-  
+
   Scalar coeff(Index row, Index col) const;
   Scalar coeff(Index i) const;
 };
diff --git a/Eigen/src/Core/Solve.h b/Eigen/src/Core/Solve.h
index 2d163fe2a..ba2ee53b8 100644
--- a/Eigen/src/Core/Solve.h
+++ b/Eigen/src/Core/Solve.h
@@ -34,12 +34,11 @@ template<typename Decomposition, typename RhsType,typename StorageKind> struct s
 template<typename Decomposition, typename RhsType>
 struct solve_traits<Decomposition,RhsType,Dense>
 {
-  typedef typename Decomposition::MatrixType MatrixType;
   typedef Matrix<typename RhsType::Scalar,
-                 MatrixType::ColsAtCompileTime,
+                 Decomposition::ColsAtCompileTime,
                  RhsType::ColsAtCompileTime,
                  RhsType::PlainObject::Options,
-                 MatrixType::MaxColsAtCompileTime,
+                 Decomposition::MaxColsAtCompileTime,
                  RhsType::MaxColsAtCompileTime> PlainObject;  
 };
 
@@ -145,6 +144,28 @@ struct Assignment<DstXprType, Solve<DecType,RhsType>, internal::assign_op<Scalar
   }
 };
 
+// Specialization for "dst = dec.transpose().solve(rhs)"
+template<typename DstXprType, typename DecType, typename RhsType, typename Scalar>
+struct Assignment<DstXprType, Solve<Transpose<const DecType>,RhsType>, internal::assign_op<Scalar>, Dense2Dense, Scalar>
+{
+  typedef Solve<Transpose<const DecType>,RhsType> SrcXprType;
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar> &)
+  {
+    src.dec().nestedExpression().template _solve_impl_transposed<false>(src.rhs(), dst);
+  }
+};
+
+// Specialization for "dst = dec.adjoint().solve(rhs)"
+template<typename DstXprType, typename DecType, typename RhsType, typename Scalar>
+struct Assignment<DstXprType, Solve<CwiseUnaryOp<internal::scalar_conjugate_op<typename DecType::Scalar>, const Transpose<const DecType> >,RhsType>, internal::assign_op<Scalar>, Dense2Dense, Scalar>
+{
+  typedef Solve<CwiseUnaryOp<internal::scalar_conjugate_op<typename DecType::Scalar>, const Transpose<const DecType> >,RhsType> SrcXprType;
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar> &)
+  {
+    src.dec().nestedExpression().nestedExpression().template _solve_impl_transposed<true>(src.rhs(), dst);
+  }
+};
+
 } // end namepsace internal
 
 } // end namespace Eigen
diff --git a/Eigen/src/Core/SolverBase.h b/Eigen/src/Core/SolverBase.h
new file mode 100644
index 000000000..8a4adc229
--- /dev/null
+++ b/Eigen/src/Core/SolverBase.h
@@ -0,0 +1,130 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SOLVERBASE_H
+#define EIGEN_SOLVERBASE_H
+
+namespace Eigen {
+
+namespace internal {
+
+
+
+} // end namespace internal
+
+/** \class SolverBase
+  * \brief A base class for matrix decomposition and solvers
+  *
+  * \tparam Derived the actual type of the decomposition/solver.
+  *
+  * Any matrix decomposition inheriting this base class provide the following API:
+  *
+  * \code
+  * MatrixType A, b, x;
+  * DecompositionType dec(A);
+  * x = dec.solve(b);             // solve A   * x = b
+  * x = dec.transpose().solve(b); // solve A^T * x = b
+  * x = dec.adjoint().solve(b);   // solve A'  * x = b
+  * \endcode
+  *
+  * \warning Currently, any other usage of transpose() and adjoint() are not supported and will produce compilation errors.
+  *
+  * \sa class PartialPivLU, class FullPivLU
+  */
+template<typename Derived>
+class SolverBase : public EigenBase<Derived>
+{
+  public:
+
+    typedef EigenBase<Derived> Base;
+    typedef typename internal::traits<Derived>::Scalar Scalar;
+    typedef Scalar CoeffReturnType;
+
+    enum {
+      RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
+      ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
+      SizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::RowsAtCompileTime,
+                                                          internal::traits<Derived>::ColsAtCompileTime>::ret),
+      MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,
+      MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime,
+      MaxSizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::MaxRowsAtCompileTime,
+                                                             internal::traits<Derived>::MaxColsAtCompileTime>::ret),
+      IsVectorAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime == 1
+                           || internal::traits<Derived>::MaxColsAtCompileTime == 1
+    };
+
+    /** Default constructor */
+    SolverBase()
+    {}
+
+    ~SolverBase()
+    {}
+
+    using Base::derived;
+
+    /** \returns an expression of the solution x of \f$ A x = b \f$ using the current decomposition of A.
+      */
+    template<typename Rhs>
+    inline const Solve<Derived, Rhs>
+    solve(const MatrixBase<Rhs>& b) const
+    {
+      eigen_assert(derived().rows()==b.rows() && "solve(): invalid number of rows of the right hand side matrix b");
+      return Solve<Derived, Rhs>(derived(), b.derived());
+    }
+
+    /** \internal the return type of transpose() */
+    typedef typename internal::add_const<Transpose<const Derived> >::type ConstTransposeReturnType;
+    /** \returns an expression of the transposed of the factored matrix.
+      *
+      * A typical usage is to solve for the transposed problem A^T x = b:
+      * \code x = dec.transpose().solve(b); \endcode
+      *
+      * \sa adjoint(), solve()
+      */
+    inline ConstTransposeReturnType transpose() const
+    {
+      return ConstTransposeReturnType(derived());
+    }
+
+    /** \internal the return type of adjoint() */
+    typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,
+                        CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, ConstTransposeReturnType>,
+                        ConstTransposeReturnType
+                     >::type AdjointReturnType;
+    /** \returns an expression of the adjoint of the factored matrix
+      *
+      * A typical usage is to solve for the adjoint problem A' x = b:
+      * \code x = dec.adjoint().solve(b); \endcode
+      *
+      * For real scalar types, this function is equivalent to transpose().
+      *
+      * \sa transpose(), solve()
+      */
+    inline AdjointReturnType adjoint() const
+    {
+      return AdjointReturnType(derived().transpose());
+    }
+
+  protected:
+};
+
+namespace internal {
+
+template<typename Derived>
+struct generic_xpr_base<Derived, MatrixXpr, SolverStorage>
+{
+  typedef SolverBase<Derived> type;
+
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SOLVERBASE_H
diff --git a/Eigen/src/Core/Transpose.h b/Eigen/src/Core/Transpose.h
index 2152405d5..5b66eb5e1 100644
--- a/Eigen/src/Core/Transpose.h
+++ b/Eigen/src/Core/Transpose.h
@@ -39,7 +39,7 @@ struct traits<Transpose<MatrixType> > : public traits<MatrixType>
     MaxRowsAtCompileTime = MatrixType::MaxColsAtCompileTime,
     MaxColsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
     FlagsLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,
-    Flags0 = MatrixTypeNestedPlain::Flags & ~(LvalueBit | NestByRefBit),
+    Flags0 = traits<MatrixTypeNestedPlain>::Flags & ~(LvalueBit | NestByRefBit),
     Flags1 = Flags0 | FlagsLvalueBit,
     Flags = Flags1 ^ RowMajorBit,
     InnerStrideAtCompileTime = inner_stride_at_compile_time<MatrixType>::ret,
diff --git a/Eigen/src/Core/util/Constants.h b/Eigen/src/Core/util/Constants.h
index 28852c8c3..a364f48d1 100644
--- a/Eigen/src/Core/util/Constants.h
+++ b/Eigen/src/Core/util/Constants.h
@@ -492,6 +492,9 @@ struct Dense {};
 /** The type used to identify a general sparse storage. */
 struct Sparse {};
 
+/** The type used to identify a general solver (foctored) storage. */
+struct SolverStorage {};
+
 /** The type used to identify a permutation storage. */
 struct PermutationStorage {};
 
@@ -506,6 +509,7 @@ struct ArrayXpr {};
 
 // An evaluator must define its shape. By default, it can be one of the following:
 struct DenseShape             { static std::string debugName() { return "DenseShape"; } };
+struct SolverShape            { static std::string debugName() { return "SolverShape"; } };
 struct HomogeneousShape       { static std::string debugName() { return "HomogeneousShape"; } };
 struct DiagonalShape          { static std::string debugName() { return "DiagonalShape"; } };
 struct BandShape              { static std::string debugName() { return "BandShape"; } };
diff --git a/Eigen/src/Core/util/ForwardDeclarations.h b/Eigen/src/Core/util/ForwardDeclarations.h
index 1aa81abf8..483af876f 100644
--- a/Eigen/src/Core/util/ForwardDeclarations.h
+++ b/Eigen/src/Core/util/ForwardDeclarations.h
@@ -132,6 +132,7 @@ template<typename MatrixType> struct CommaInitializer;
 template<typename Derived> class ReturnByValue;
 template<typename ExpressionType> class ArrayWrapper;
 template<typename ExpressionType> class MatrixWrapper;
+template<typename Derived> class SolverBase;
 template<typename XprType> class InnerIterator;
 
 namespace internal {
diff --git a/Eigen/src/IterativeLinearSolvers/BasicPreconditioners.h b/Eigen/src/IterativeLinearSolvers/BasicPreconditioners.h
index b850630a3..358444aff 100644
--- a/Eigen/src/IterativeLinearSolvers/BasicPreconditioners.h
+++ b/Eigen/src/IterativeLinearSolvers/BasicPreconditioners.h
@@ -39,8 +39,10 @@ class DiagonalPreconditioner
     typedef Matrix<Scalar,Dynamic,1> Vector;
   public:
     typedef typename Vector::StorageIndex StorageIndex;
-    // this typedef is only to export the scalar type and compile-time dimensions to solve_retval
-    typedef Matrix<Scalar,Dynamic,Dynamic> MatrixType;
+    enum {
+      ColsAtCompileTime = Dynamic,
+      MaxColsAtCompileTime = Dynamic
+    };
 
     DiagonalPreconditioner() : m_isInitialized(false) {}
 
diff --git a/Eigen/src/IterativeLinearSolvers/IncompleteCholesky.h b/Eigen/src/IterativeLinearSolvers/IncompleteCholesky.h
index 8f549af82..284e37f13 100644
--- a/Eigen/src/IterativeLinearSolvers/IncompleteCholesky.h
+++ b/Eigen/src/IterativeLinearSolvers/IncompleteCholesky.h
@@ -57,12 +57,15 @@ class IncompleteCholesky : public SparseSolverBase<IncompleteCholesky<Scalar,_Up
     typedef typename OrderingType::PermutationType PermutationType;
     typedef typename PermutationType::StorageIndex StorageIndex; 
     typedef SparseMatrix<Scalar,ColMajor,StorageIndex> FactorType;
-    typedef FactorType MatrixType;
     typedef Matrix<Scalar,Dynamic,1> VectorSx;
     typedef Matrix<RealScalar,Dynamic,1> VectorRx;
     typedef Matrix<StorageIndex,Dynamic, 1> VectorIx;
     typedef std::vector<std::list<StorageIndex> > VectorList; 
     enum { UpLo = _UpLo };
+    enum {
+      ColsAtCompileTime = Dynamic,
+      MaxColsAtCompileTime = Dynamic
+    };
   public:
 
     /** Default constructor leaving the object in a partly non-initialized stage.
diff --git a/Eigen/src/IterativeLinearSolvers/IncompleteLUT.h b/Eigen/src/IterativeLinearSolvers/IncompleteLUT.h
index 519472377..338e6f10a 100644
--- a/Eigen/src/IterativeLinearSolvers/IncompleteLUT.h
+++ b/Eigen/src/IterativeLinearSolvers/IncompleteLUT.h
@@ -109,11 +109,13 @@ class IncompleteLUT : public SparseSolverBase<IncompleteLUT<_Scalar, _StorageInd
     typedef Matrix<StorageIndex,Dynamic,1> VectorI;
     typedef SparseMatrix<Scalar,RowMajor,StorageIndex> FactorType;
 
+    enum {
+      ColsAtCompileTime = Dynamic,
+      MaxColsAtCompileTime = Dynamic
+    };
+
   public:
     
-    // this typedef is only to export the scalar type and compile-time dimensions to solve_retval
-    typedef Matrix<Scalar,Dynamic,Dynamic> MatrixType;
-    
     IncompleteLUT()
       : m_droptol(NumTraits<Scalar>::dummy_precision()), m_fillfactor(10),
         m_analysisIsOk(false), m_factorizationIsOk(false)
diff --git a/Eigen/src/IterativeLinearSolvers/IterativeSolverBase.h b/Eigen/src/IterativeLinearSolvers/IterativeSolverBase.h
index 5f4bcea11..e51ff7280 100644
--- a/Eigen/src/IterativeLinearSolvers/IterativeSolverBase.h
+++ b/Eigen/src/IterativeLinearSolvers/IterativeSolverBase.h
@@ -31,6 +31,11 @@ public:
   typedef typename MatrixType::StorageIndex StorageIndex;
   typedef typename MatrixType::RealScalar RealScalar;
 
+  enum {
+    ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+  };
+
 public:
 
   using Base::derived;
diff --git a/Eigen/src/LU/FullPivLU.h b/Eigen/src/LU/FullPivLU.h
index 4691efd2f..0c4d63923 100644
--- a/Eigen/src/LU/FullPivLU.h
+++ b/Eigen/src/LU/FullPivLU.h
@@ -16,6 +16,8 @@ namespace internal {
 template<typename _MatrixType> struct traits<FullPivLU<_MatrixType> >
  : traits<_MatrixType>
 {
+  typedef MatrixXpr XprKind;
+  typedef SolverStorage StorageKind;
   enum { Flags = 0 };
 };
 
@@ -53,21 +55,18 @@ template<typename _MatrixType> struct traits<FullPivLU<_MatrixType> >
   * \sa MatrixBase::fullPivLu(), MatrixBase::determinant(), MatrixBase::inverse()
   */
 template<typename _MatrixType> class FullPivLU
+  : public SolverBase<FullPivLU<_MatrixType> >
 {
   public:
     typedef _MatrixType MatrixType;
+    typedef SolverBase<FullPivLU> Base;
+
+    EIGEN_GENERIC_PUBLIC_INTERFACE(FullPivLU)
+    // FIXME StorageIndex defined in EIGEN_GENERIC_PUBLIC_INTERFACE should be int
     enum {
-      RowsAtCompileTime = MatrixType::RowsAtCompileTime,
-      ColsAtCompileTime = MatrixType::ColsAtCompileTime,
-      Options = MatrixType::Options,
       MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
       MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
     };
-    typedef typename MatrixType::Scalar Scalar;
-    typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
-    typedef typename internal::traits<MatrixType>::StorageKind StorageKind;
-    // FIXME should be int
-    typedef typename MatrixType::StorageIndex StorageIndex;
     typedef typename internal::plain_row_type<MatrixType, StorageIndex>::type IntRowVectorType;
     typedef typename internal::plain_col_type<MatrixType, StorageIndex>::type IntColVectorType;
     typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> PermutationQType;
@@ -223,6 +222,7 @@ template<typename _MatrixType> class FullPivLU
       *
       * \sa TriangularView::solve(), kernel(), inverse()
       */
+    // FIXME this is a copy-paste of the base-class member to add the isInitialized assertion.
     template<typename Rhs>
     inline const Solve<FullPivLU, Rhs>
     solve(const MatrixBase<Rhs>& b) const
diff --git a/Eigen/src/LU/PartialPivLU.h b/Eigen/src/LU/PartialPivLU.h
index 91abbc341..50e920609 100644
--- a/Eigen/src/LU/PartialPivLU.h
+++ b/Eigen/src/LU/PartialPivLU.h
@@ -17,6 +17,8 @@ namespace internal {
 template<typename _MatrixType> struct traits<PartialPivLU<_MatrixType> >
  : traits<_MatrixType>
 {
+  typedef MatrixXpr XprKind;
+  typedef SolverStorage StorageKind;
   typedef traits<_MatrixType> BaseTraits;
   enum {
     Flags = BaseTraits::Flags & RowMajorBit,
@@ -58,33 +60,29 @@ template<typename _MatrixType> struct traits<PartialPivLU<_MatrixType> >
   * \sa MatrixBase::partialPivLu(), MatrixBase::determinant(), MatrixBase::inverse(), MatrixBase::computeInverse(), class FullPivLU
   */
 template<typename _MatrixType> class PartialPivLU
+  : public SolverBase<PartialPivLU<_MatrixType> >
 {
   public:
 
     typedef _MatrixType MatrixType;
+    typedef SolverBase<PartialPivLU> Base;
+    EIGEN_GENERIC_PUBLIC_INTERFACE(PartialPivLU)
+    // FIXME StorageIndex defined in EIGEN_GENERIC_PUBLIC_INTERFACE should be int
     enum {
-      RowsAtCompileTime = MatrixType::RowsAtCompileTime,
-      ColsAtCompileTime = MatrixType::ColsAtCompileTime,
-      Options = MatrixType::Options,
       MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
       MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
     };
-    typedef typename MatrixType::Scalar Scalar;
-    typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
-    typedef typename internal::traits<MatrixType>::StorageKind StorageKind;
-    // FIXME should be int
-    typedef typename MatrixType::StorageIndex StorageIndex;
     typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> PermutationType;
     typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime> TranspositionType;
     typedef typename MatrixType::PlainObject PlainObject;
 
 
     /**
-    * \brief Default Constructor.
-    *
-    * The default constructor is useful in cases in which the user intends to
-    * perform decompositions via PartialPivLU::compute(const MatrixType&).
-    */
+      * \brief Default Constructor.
+      *
+      * The default constructor is useful in cases in which the user intends to
+      * perform decompositions via PartialPivLU::compute(const MatrixType&).
+      */
     PartialPivLU();
 
     /** \brief Default Constructor with memory preallocation
@@ -145,6 +143,7 @@ template<typename _MatrixType> class PartialPivLU
       *
       * \sa TriangularView::solve(), inverse(), computeInverse()
       */
+    // FIXME this is a copy-paste of the base-class member to add the isInitialized assertion.
     template<typename Rhs>
     inline const Solve<PartialPivLU, Rhs>
     solve(const MatrixBase<Rhs>& b) const
@@ -508,7 +507,7 @@ MatrixType PartialPivLU<MatrixType>::reconstructedMatrix() const
   return res;
 }
 
-/***** Implementation of solve() *****************************************************/
+/***** Implementation details *****************************************************/
 
 namespace internal {
 
diff --git a/Eigen/src/PaStiXSupport/PaStiXSupport.h b/Eigen/src/PaStiXSupport/PaStiXSupport.h
index cec4149e7..1999fd289 100644
--- a/Eigen/src/PaStiXSupport/PaStiXSupport.h
+++ b/Eigen/src/PaStiXSupport/PaStiXSupport.h
@@ -141,6 +141,10 @@ class PastixBase : public SparseSolverBase<Derived>
     typedef typename MatrixType::StorageIndex StorageIndex;
     typedef Matrix<Scalar,Dynamic,1> Vector;
     typedef SparseMatrix<Scalar, ColMajor> ColSpMatrix;
+    enum {
+      ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+    };
     
   public:
     
diff --git a/Eigen/src/SPQRSupport/SuiteSparseQRSupport.h b/Eigen/src/SPQRSupport/SuiteSparseQRSupport.h
index d2f053fa5..d9c3113e7 100644
--- a/Eigen/src/SPQRSupport/SuiteSparseQRSupport.h
+++ b/Eigen/src/SPQRSupport/SuiteSparseQRSupport.h
@@ -68,6 +68,10 @@ class SPQR : public SparseSolverBase<SPQR<_MatrixType> >
     typedef SuiteSparse_long StorageIndex ;
     typedef SparseMatrix<Scalar, ColMajor, StorageIndex> MatrixType;
     typedef Map<PermutationMatrix<Dynamic, Dynamic, StorageIndex> > PermutationType;
+    enum {
+      ColsAtCompileTime = Dynamic,
+      MaxColsAtCompileTime = Dynamic
+    };
   public:
     SPQR() 
       : m_ordering(SPQR_ORDERING_DEFAULT), m_allow_tol(SPQR_DEFAULT_TOL), m_tolerance (NumTraits<Scalar>::epsilon()), m_useDefaultThreshold(true)
diff --git a/Eigen/src/SparseCholesky/SimplicialCholesky.h b/Eigen/src/SparseCholesky/SimplicialCholesky.h
index ef612cf45..1343eb15c 100644
--- a/Eigen/src/SparseCholesky/SimplicialCholesky.h
+++ b/Eigen/src/SparseCholesky/SimplicialCholesky.h
@@ -71,6 +71,11 @@ class SimplicialCholeskyBase : public SparseSolverBase<Derived>
     typedef Matrix<Scalar,Dynamic,1> VectorType;
     typedef Matrix<StorageIndex,Dynamic,1> VectorI;
 
+    enum {
+      ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+    };
+
   public:
     
     using Base::derived;
diff --git a/Eigen/src/SparseLU/SparseLU.h b/Eigen/src/SparseLU/SparseLU.h
index 73368cba4..acd3ad100 100644
--- a/Eigen/src/SparseLU/SparseLU.h
+++ b/Eigen/src/SparseLU/SparseLU.h
@@ -90,6 +90,11 @@ class SparseLU : public SparseSolverBase<SparseLU<_MatrixType,_OrderingType> >,
     typedef Matrix<StorageIndex,Dynamic,1> IndexVector;
     typedef PermutationMatrix<Dynamic, Dynamic, StorageIndex> PermutationType;
     typedef internal::SparseLUImpl<Scalar, StorageIndex> Base;
+
+    enum {
+      ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+    };
     
   public:
     SparseLU():m_lastError(""),m_Ustore(0,0,0,0,0,0),m_symmetricmode(false),m_diagpivotthresh(1.0),m_detPermR(1)
diff --git a/Eigen/src/SparseQR/SparseQR.h b/Eigen/src/SparseQR/SparseQR.h
index bbd337c40..4f26c19ca 100644
--- a/Eigen/src/SparseQR/SparseQR.h
+++ b/Eigen/src/SparseQR/SparseQR.h
@@ -84,6 +84,12 @@ class SparseQR : public SparseSolverBase<SparseQR<_MatrixType,_OrderingType> >
     typedef Matrix<StorageIndex, Dynamic, 1> IndexVector;
     typedef Matrix<Scalar, Dynamic, 1> ScalarVector;
     typedef PermutationMatrix<Dynamic, Dynamic, StorageIndex> PermutationType;
+
+    enum {
+      ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+    };
+    
   public:
     SparseQR () :  m_analysisIsok(false), m_lastError(""), m_useDefaultThreshold(true),m_isQSorted(false),m_isEtreeOk(false)
     { }
diff --git a/Eigen/src/SuperLUSupport/SuperLUSupport.h b/Eigen/src/SuperLUSupport/SuperLUSupport.h
index c145e25bd..b20da37f7 100644
--- a/Eigen/src/SuperLUSupport/SuperLUSupport.h
+++ b/Eigen/src/SuperLUSupport/SuperLUSupport.h
@@ -304,6 +304,10 @@ class SuperLUBase : public SparseSolverBase<Derived>
     typedef Matrix<int, MatrixType::RowsAtCompileTime, 1> IntColVectorType;    
     typedef Map<PermutationMatrix<Dynamic,Dynamic,int> > PermutationMap;
     typedef SparseMatrix<Scalar> LUMatrixType;
+    enum {
+      ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+    };
 
   public:
 
diff --git a/Eigen/src/UmfPackSupport/UmfPackSupport.h b/Eigen/src/UmfPackSupport/UmfPackSupport.h
index caac082f3..aaec8c6f1 100644
--- a/Eigen/src/UmfPackSupport/UmfPackSupport.h
+++ b/Eigen/src/UmfPackSupport/UmfPackSupport.h
@@ -146,6 +146,10 @@ class UmfPackLU : public SparseSolverBase<UmfPackLU<_MatrixType> >
     typedef SparseMatrix<Scalar> LUMatrixType;
     typedef SparseMatrix<Scalar,ColMajor,int> UmfpackMatrixType;
     typedef Ref<const UmfpackMatrixType, StandardCompressedFormat> UmfpackMatrixRef;
+    enum {
+      ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+    };
 
   public:
 
diff --git a/test/lu.cpp b/test/lu.cpp
index f753fc74a..f14435114 100644
--- a/test/lu.cpp
+++ b/test/lu.cpp
@@ -99,6 +99,9 @@ template<typename MatrixType> void lu_non_invertible()
   m3 = MatrixType::Random(rows,cols2);
   lu.template _solve_impl_transposed<false>(m2, m3);
   VERIFY_IS_APPROX(m2, m1.transpose()*m3);
+  m3 = MatrixType::Random(rows,cols2);
+  m3 = lu.transpose().solve(m2);
+  VERIFY_IS_APPROX(m2, m1.transpose()*m3);
 
   // test solve with conjugate transposed
   m3 = MatrixType::Random(rows,cols2);
@@ -106,6 +109,9 @@ template<typename MatrixType> void lu_non_invertible()
   m3 = MatrixType::Random(rows,cols2);
   lu.template _solve_impl_transposed<true>(m2, m3);
   VERIFY_IS_APPROX(m2, m1.adjoint()*m3);
+  m3 = MatrixType::Random(rows,cols2);
+  m3 = lu.adjoint().solve(m2);
+  VERIFY_IS_APPROX(m2, m1.adjoint()*m3);
 }
 
 template<typename MatrixType> void lu_invertible()
@@ -138,12 +144,20 @@ template<typename MatrixType> void lu_invertible()
   m2 = lu.solve(m3);
   VERIFY_IS_APPROX(m3, m1*m2);
   VERIFY_IS_APPROX(m2, lu.inverse()*m3);
+
   // test solve with transposed
   lu.template _solve_impl_transposed<false>(m3, m2);
   VERIFY_IS_APPROX(m3, m1.transpose()*m2);
+  m3 = MatrixType::Random(size,size);
+  m3 = lu.transpose().solve(m2);
+  VERIFY_IS_APPROX(m2, m1.transpose()*m3);
+
   // test solve with conjugate transposed
   lu.template _solve_impl_transposed<true>(m3, m2);
   VERIFY_IS_APPROX(m3, m1.adjoint()*m2);
+  m3 = MatrixType::Random(size,size);
+  m3 = lu.adjoint().solve(m2);
+  VERIFY_IS_APPROX(m2, m1.adjoint()*m3);
 
   // Regression test for Bug 302
   MatrixType m4 = MatrixType::Random(size,size);
@@ -168,12 +182,20 @@ template<typename MatrixType> void lu_partial_piv()
   m2 = plu.solve(m3);
   VERIFY_IS_APPROX(m3, m1*m2);
   VERIFY_IS_APPROX(m2, plu.inverse()*m3);
+
   // test solve with transposed
   plu.template _solve_impl_transposed<false>(m3, m2);
   VERIFY_IS_APPROX(m3, m1.transpose()*m2);
+  m3 = MatrixType::Random(size,size);
+  m3 = plu.transpose().solve(m2);
+  VERIFY_IS_APPROX(m2, m1.transpose()*m3);
+
   // test solve with conjugate transposed
   plu.template _solve_impl_transposed<true>(m3, m2);
   VERIFY_IS_APPROX(m3, m1.adjoint()*m2);
+  m3 = MatrixType::Random(size,size);
+  m3 = plu.adjoint().solve(m2);
+  VERIFY_IS_APPROX(m2, m1.adjoint()*m3);
 }
 
 template<typename MatrixType> void lu_verify_assert()