From 9e00d945439d801d3f4e33ed1ce57545e3310723 Mon Sep 17 00:00:00 2001
From: Benoit Jacob <jacob.benoit.1@gmail.com>
Date: Sat, 20 Dec 2008 13:36:12 +0000
Subject: * the Upper->UpperTriangular change * finally get ei_add_test right

---
 Eigen/src/Cholesky/Cholesky.h                  |  4 +-
 Eigen/src/Cholesky/CholeskyWithoutSquareRoot.h |  6 +--
 Eigen/src/Cholesky/LDLT.h                      |  4 +-
 Eigen/src/Cholesky/LLT.h                       |  4 +-
 Eigen/src/Core/MatrixBase.h                    |  4 +-
 Eigen/src/Core/Part.h                          | 58 ++++++++++----------
 Eigen/src/Core/SolveTriangular.h               | 74 +++++++++++++-------------
 Eigen/src/Core/Transpose.h                     |  4 +-
 Eigen/src/Core/util/Constants.h                | 14 ++---
 Eigen/src/LU/LU.h                              | 10 ++--
 Eigen/src/QR/HessenbergDecomposition.h         |  2 +-
 Eigen/src/QR/QR.h                              |  4 +-
 Eigen/src/QR/SelfAdjointEigenSolver.h          |  8 +--
 Eigen/src/QR/Tridiagonalization.h              | 12 ++---
 Eigen/src/Sparse/CholmodSupport.h              |  4 +-
 Eigen/src/Sparse/SparseLDLT.h                  |  2 +-
 Eigen/src/Sparse/SparseLLT.h                   |  2 +-
 Eigen/src/Sparse/SparseLU.h                    |  2 +-
 Eigen/src/Sparse/SuperLUSupport.h              |  8 +--
 Eigen/src/Sparse/TaucsSupport.h                |  6 +--
 Eigen/src/Sparse/TriangularSolver.h            |  8 +--
 Eigen/src/Sparse/UmfPackSupport.h              |  4 +-
 bench/btl/libs/eigen2/eigen2_interface.hh      |  4 +-
 bench/sparse_cholesky.cpp                      |  4 +-
 bench/sparse_trisolver.cpp                     |  8 +--
 doc/QuickStartGuide.dox                        | 20 +++----
 doc/snippets/MatrixBase_extract.cpp            |  6 +--
 doc/snippets/MatrixBase_marked.cpp             |  6 +--
 doc/snippets/MatrixBase_part.cpp               |  2 +-
 doc/snippets/class_LU_2.cpp                    |  2 +-
 test/CMakeLists.txt                            |  6 ++-
 test/sparse_solvers.cpp                        | 12 ++---
 test/triangular.cpp                            | 46 ++++++++--------
 33 files changed, 181 insertions(+), 179 deletions(-)

diff --git a/Eigen/src/Cholesky/Cholesky.h b/Eigen/src/Cholesky/Cholesky.h
index bbf24fab3..31451a6b0 100644
--- a/Eigen/src/Cholesky/Cholesky.h
+++ b/Eigen/src/Cholesky/Cholesky.h
@@ -52,7 +52,7 @@ template<typename MatrixType> class Cholesky
     }
 
 		/** \deprecated */
-    inline Part<MatrixType, Lower> matrixL(void) const { return m_matrix; }
+    inline Part<MatrixType, LowerTriangular> matrixL(void) const { return m_matrix; }
 
     /** \deprecated */
     inline bool isPositiveDefinite(void) const { return m_isPositiveDefinite; }
@@ -148,7 +148,7 @@ bool Cholesky<MatrixType>::solveInPlace(MatrixBase<Derived> &bAndX) const
   if (!m_isPositiveDefinite)
     return false;
   matrixL().solveTriangularInPlace(bAndX);
-  m_matrix.adjoint().template part<Upper>().solveTriangularInPlace(bAndX);
+  m_matrix.adjoint().template part<UpperTriangular>().solveTriangularInPlace(bAndX);
   return true;
 }
 
diff --git a/Eigen/src/Cholesky/CholeskyWithoutSquareRoot.h b/Eigen/src/Cholesky/CholeskyWithoutSquareRoot.h
index 0f3e9e07f..641f9be01 100644
--- a/Eigen/src/Cholesky/CholeskyWithoutSquareRoot.h
+++ b/Eigen/src/Cholesky/CholeskyWithoutSquareRoot.h
@@ -46,7 +46,7 @@ template<typename MatrixType> class CholeskyWithoutSquareRoot
     }
 
     /** \returns the lower triangular matrix L */
-    inline Part<MatrixType, UnitLower> matrixL(void) const { return m_matrix; }
+    inline Part<MatrixType, UnitLowerTriangular> matrixL(void) const { return m_matrix; }
 
     /** \returns the coefficients of the diagonal matrix D */
     inline DiagonalCoeffs<MatrixType> vectorD(void) const { return m_matrix.diagonal(); }
@@ -137,7 +137,7 @@ typename Derived::Eval CholeskyWithoutSquareRoot<MatrixType>::solve(const Matrix
   const int size = m_matrix.rows();
   ei_assert(size==b.rows());
 
-  return m_matrix.adjoint().template part<UnitUpper>()
+  return m_matrix.adjoint().template part<UnitUpperTriangular>()
     .solveTriangular(
       (  m_matrix.cwise().inverse().template part<Diagonal>()
        * matrixL().solveTriangular(b))
@@ -167,7 +167,7 @@ bool CholeskyWithoutSquareRoot<MatrixType>::solveInPlace(MatrixBase<Derived> &bA
     return false;
   matrixL().solveTriangularInPlace(bAndX);
   bAndX = (m_matrix.cwise().inverse().template part<Diagonal>() * bAndX).lazy();
-  m_matrix.adjoint().template part<UnitUpper>().solveTriangularInPlace(bAndX);
+  m_matrix.adjoint().template part<UnitUpperTriangular>().solveTriangularInPlace(bAndX);
   return true;
 }
 
diff --git a/Eigen/src/Cholesky/LDLT.h b/Eigen/src/Cholesky/LDLT.h
index a275e093f..4729c3621 100644
--- a/Eigen/src/Cholesky/LDLT.h
+++ b/Eigen/src/Cholesky/LDLT.h
@@ -60,7 +60,7 @@ template<typename MatrixType> class LDLT
     }
 
     /** \returns the lower triangular matrix L */
-    inline Part<MatrixType, UnitLower> matrixL(void) const { return m_matrix; }
+    inline Part<MatrixType, UnitLowerTriangular> matrixL(void) const { return m_matrix; }
 
     /** \returns the coefficients of the diagonal matrix D */
     inline DiagonalCoeffs<MatrixType> vectorD(void) const { return m_matrix.diagonal(); }
@@ -181,7 +181,7 @@ bool LDLT<MatrixType>::solveInPlace(MatrixBase<Derived> &bAndX) const
     return false;
   matrixL().solveTriangularInPlace(bAndX);
   bAndX = (m_matrix.cwise().inverse().template part<Diagonal>() * bAndX).lazy();
-  m_matrix.adjoint().template part<UnitUpper>().solveTriangularInPlace(bAndX);
+  m_matrix.adjoint().template part<UnitUpperTriangular>().solveTriangularInPlace(bAndX);
   return true;
 }
 
diff --git a/Eigen/src/Cholesky/LLT.h b/Eigen/src/Cholesky/LLT.h
index 6e412e20c..c4e7fdffd 100644
--- a/Eigen/src/Cholesky/LLT.h
+++ b/Eigen/src/Cholesky/LLT.h
@@ -67,7 +67,7 @@ template<typename MatrixType> class LLT
     }
 
     /** \returns the lower triangular matrix L */
-    inline Part<MatrixType, Lower> matrixL(void) const { return m_matrix; }
+    inline Part<MatrixType, LowerTriangular> matrixL(void) const { return m_matrix; }
 
     /** \returns true if the matrix is positive definite */
     inline bool isPositiveDefinite(void) const { return m_isPositiveDefinite; }
@@ -169,7 +169,7 @@ bool LLT<MatrixType>::solveInPlace(MatrixBase<Derived> &bAndX) const
   if (!m_isPositiveDefinite)
     return false;
   matrixL().solveTriangularInPlace(bAndX);
-  m_matrix.adjoint().template part<Upper>().solveTriangularInPlace(bAndX);
+  m_matrix.adjoint().template part<UpperTriangular>().solveTriangularInPlace(bAndX);
   return true;
 }
 
diff --git a/Eigen/src/Core/MatrixBase.h b/Eigen/src/Core/MatrixBase.h
index a9a08dc28..42d3bece3 100644
--- a/Eigen/src/Core/MatrixBase.h
+++ b/Eigen/src/Core/MatrixBase.h
@@ -470,8 +470,8 @@ template<typename Derived> class MatrixBase
     bool isIdentity(RealScalar prec = precision<Scalar>()) const;
     bool isDiagonal(RealScalar prec = precision<Scalar>()) const;
 
-    bool isUpper(RealScalar prec = precision<Scalar>()) const;
-    bool isLower(RealScalar prec = precision<Scalar>()) const;
+    bool isUpperTriangular(RealScalar prec = precision<Scalar>()) const;
+    bool isLowerTriangular(RealScalar prec = precision<Scalar>()) const;
 
     template<typename OtherDerived>
     bool isOrthogonal(const MatrixBase<OtherDerived>& other,
diff --git a/Eigen/src/Core/Part.h b/Eigen/src/Core/Part.h
index b1a0b3be9..883b92a98 100644
--- a/Eigen/src/Core/Part.h
+++ b/Eigen/src/Core/Part.h
@@ -31,8 +31,8 @@
   * \brief Expression of a triangular matrix extracted from a given matrix
   *
   * \param MatrixType the type of the object in which we are taking the triangular part
-  * \param Mode the kind of triangular matrix expression to construct. Can be Upper, StrictlyUpper,
-  *             UnitUpper, Lower, StrictlyLower, UnitLower. This is in fact a bit field; it must have either
+  * \param Mode the kind of triangular matrix expression to construct. Can be UpperTriangular, StrictlyUpperTriangular,
+  *             UnitUpperTriangular, LowerTriangular, StrictlyLowerTriangular, UnitLowerTriangular. This is in fact a bit field; it must have either
   *             UpperTriangularBit or LowerTriangularBit, and additionnaly it may have either ZeroDiagBit or
   *             UnitDiagBit.
   *
@@ -104,10 +104,10 @@ template<typename MatrixType, unsigned int Mode> class Part
     {
       EIGEN_STATIC_ASSERT(!(Flags & UnitDiagBit), WRITING_TO_TRIANGULAR_PART_WITH_UNIT_DIAGONAL_IS_NOT_SUPPORTED)
       EIGEN_STATIC_ASSERT(!(Flags & SelfAdjointBit), COEFFICIENT_WRITE_ACCESS_TO_SELFADJOINT_NOT_SUPPORTED)
-      ei_assert(   (Mode==Upper && col>=row)
-                || (Mode==Lower && col<=row)
-                || (Mode==StrictlyUpper && col>row)
-                || (Mode==StrictlyLower && col<row));
+      ei_assert(   (Mode==UpperTriangular && col>=row)
+                || (Mode==LowerTriangular && col<=row)
+                || (Mode==StrictlyUpperTriangular && col>row)
+                || (Mode==StrictlyLowerTriangular && col<row));
       return m_matrix.const_cast_derived().coeffRef(row, col);
     }
 
@@ -134,8 +134,8 @@ template<typename MatrixType, unsigned int Mode> class Part
 
 /** \returns an expression of a triangular matrix extracted from the current matrix
   *
-  * The parameter \a Mode can have the following values: \c Upper, \c StrictlyUpper, \c UnitUpper,
-  * \c Lower, \c StrictlyLower, \c UnitLower.
+  * The parameter \a Mode can have the following values: \c UpperTriangular, \c StrictlyUpperTriangular, \c UnitUpperTriangular,
+  * \c LowerTriangular, \c StrictlyLowerTriangular, \c UnitLowerTriangular.
   *
   * \addexample PartExample \label How to extract a triangular part of an arbitrary matrix
   *
@@ -187,11 +187,11 @@ struct ei_part_assignment_impl
     }
     else
     {
-      ei_assert(Mode == Upper || Mode == Lower || Mode == StrictlyUpper || Mode == StrictlyLower);
-      if((Mode == Upper && row <= col)
-      || (Mode == Lower && row >= col)
-      || (Mode == StrictlyUpper && row < col)
-      || (Mode == StrictlyLower && row > col))
+      ei_assert(Mode == UpperTriangular || Mode == LowerTriangular || Mode == StrictlyUpperTriangular || Mode == StrictlyLowerTriangular);
+      if((Mode == UpperTriangular && row <= col)
+      || (Mode == LowerTriangular && row >= col)
+      || (Mode == StrictlyUpperTriangular && row < col)
+      || (Mode == StrictlyLowerTriangular && row > col))
         dst.copyCoeff(row, col, src);
     }
   }
@@ -215,7 +215,7 @@ struct ei_part_assignment_impl<Derived1, Derived2, Mode, 0>
 };
 
 template<typename Derived1, typename Derived2>
-struct ei_part_assignment_impl<Derived1, Derived2, Upper, Dynamic>
+struct ei_part_assignment_impl<Derived1, Derived2, UpperTriangular, Dynamic>
 {
   inline static void run(Derived1 &dst, const Derived2 &src)
   {
@@ -226,7 +226,7 @@ struct ei_part_assignment_impl<Derived1, Derived2, Upper, Dynamic>
 };
 
 template<typename Derived1, typename Derived2>
-struct ei_part_assignment_impl<Derived1, Derived2, Lower, Dynamic>
+struct ei_part_assignment_impl<Derived1, Derived2, LowerTriangular, Dynamic>
 {
   inline static void run(Derived1 &dst, const Derived2 &src)
   {
@@ -237,7 +237,7 @@ struct ei_part_assignment_impl<Derived1, Derived2, Lower, Dynamic>
 };
 
 template<typename Derived1, typename Derived2>
-struct ei_part_assignment_impl<Derived1, Derived2, StrictlyUpper, Dynamic>
+struct ei_part_assignment_impl<Derived1, Derived2, StrictlyUpperTriangular, Dynamic>
 {
   inline static void run(Derived1 &dst, const Derived2 &src)
   {
@@ -247,7 +247,7 @@ struct ei_part_assignment_impl<Derived1, Derived2, StrictlyUpper, Dynamic>
   }
 };
 template<typename Derived1, typename Derived2>
-struct ei_part_assignment_impl<Derived1, Derived2, StrictlyLower, Dynamic>
+struct ei_part_assignment_impl<Derived1, Derived2, StrictlyLowerTriangular, Dynamic>
 {
   inline static void run(Derived1 &dst, const Derived2 &src)
   {
@@ -285,8 +285,8 @@ void Part<MatrixType, Mode>::lazyAssign(const Other& other)
 
 /** \returns a lvalue pseudo-expression allowing to perform special operations on \c *this.
   *
-  * The \a Mode parameter can have the following values: \c Upper, \c StrictlyUpper, \c Lower,
-  * \c StrictlyLower, \c SelfAdjoint.
+  * The \a Mode parameter can have the following values: \c UpperTriangular, \c StrictlyUpperTriangular, \c LowerTriangular,
+  * \c StrictlyLowerTriangular, \c SelfAdjoint.
   *
   * \addexample PartExample \label How to write to a triangular part of a matrix
   *
@@ -305,44 +305,44 @@ inline Part<Derived, Mode> MatrixBase<Derived>::part()
 /** \returns true if *this is approximately equal to an upper triangular matrix,
   *          within the precision given by \a prec.
   *
-  * \sa isLower(), extract(), part(), marked()
+  * \sa isLowerTriangular(), extract(), part(), marked()
   */
 template<typename Derived>
-bool MatrixBase<Derived>::isUpper(RealScalar prec) const
+bool MatrixBase<Derived>::isUpperTriangular(RealScalar prec) const
 {
   if(cols() != rows()) return false;
-  RealScalar maxAbsOnUpperPart = static_cast<RealScalar>(-1);
+  RealScalar maxAbsOnUpperTriangularPart = static_cast<RealScalar>(-1);
   for(int j = 0; j < cols(); ++j)
     for(int i = 0; i <= j; ++i)
     {
       RealScalar absValue = ei_abs(coeff(i,j));
-      if(absValue > maxAbsOnUpperPart) maxAbsOnUpperPart = absValue;
+      if(absValue > maxAbsOnUpperTriangularPart) maxAbsOnUpperTriangularPart = absValue;
     }
   for(int j = 0; j < cols()-1; ++j)
     for(int i = j+1; i < rows(); ++i)
-      if(!ei_isMuchSmallerThan(coeff(i, j), maxAbsOnUpperPart, prec)) return false;
+      if(!ei_isMuchSmallerThan(coeff(i, j), maxAbsOnUpperTriangularPart, prec)) return false;
   return true;
 }
 
 /** \returns true if *this is approximately equal to a lower triangular matrix,
   *          within the precision given by \a prec.
   *
-  * \sa isUpper(), extract(), part(), marked()
+  * \sa isUpperTriangular(), extract(), part(), marked()
   */
 template<typename Derived>
-bool MatrixBase<Derived>::isLower(RealScalar prec) const
+bool MatrixBase<Derived>::isLowerTriangular(RealScalar prec) const
 {
   if(cols() != rows()) return false;
-  RealScalar maxAbsOnLowerPart = static_cast<RealScalar>(-1);
+  RealScalar maxAbsOnLowerTriangularPart = static_cast<RealScalar>(-1);
   for(int j = 0; j < cols(); ++j)
     for(int i = j; i < rows(); ++i)
     {
       RealScalar absValue = ei_abs(coeff(i,j));
-      if(absValue > maxAbsOnLowerPart) maxAbsOnLowerPart = absValue;
+      if(absValue > maxAbsOnLowerTriangularPart) maxAbsOnLowerTriangularPart = absValue;
     }
   for(int j = 1; j < cols(); ++j)
     for(int i = 0; i < j; ++i)
-      if(!ei_isMuchSmallerThan(coeff(i, j), maxAbsOnLowerPart, prec)) return false;
+      if(!ei_isMuchSmallerThan(coeff(i, j), maxAbsOnLowerTriangularPart, prec)) return false;
   return true;
 }
 
diff --git a/Eigen/src/Core/SolveTriangular.h b/Eigen/src/Core/SolveTriangular.h
index b58dab01d..1c586b865 100644
--- a/Eigen/src/Core/SolveTriangular.h
+++ b/Eigen/src/Core/SolveTriangular.h
@@ -30,9 +30,9 @@ template<typename XprType, unsigned int Mode> struct ei_is_part<Part<XprType,Mod
 
 template<typename Lhs, typename Rhs,
   int TriangularPart = (int(Lhs::Flags) & LowerTriangularBit)
-                     ? Lower
+                     ? LowerTriangular
                      : (int(Lhs::Flags) & UpperTriangularBit)
-                     ? Upper
+                     ? UpperTriangular
                      : -1,
   int StorageOrder = ei_is_part<Lhs>::value ? -1  // this is to solve ambiguous specializations
                    : int(Lhs::Flags) & (RowMajorBit|SparseBit)
@@ -56,14 +56,14 @@ struct ei_solve_triangular_selector<Lhs,Rhs,UpLo,RowMajor|IsDense>
   typedef typename Rhs::Scalar Scalar;
   static void run(const Lhs& lhs, Rhs& other)
   {
-    const bool IsLower = (UpLo==Lower);
+    const bool IsLowerTriangular = (UpLo==LowerTriangular);
     const int size = lhs.cols();
     /* We perform the inverse product per block of 4 rows such that we perfectly match
      * our optimized matrix * vector product. blockyStart represents the number of rows
      * we have process first using the non-block version.
      */
     int blockyStart = (std::max(size-5,0)/4)*4;
-    if (IsLower)
+    if (IsLowerTriangular)
       blockyStart = size - blockyStart;
     else
       blockyStart -= 1;
@@ -72,15 +72,15 @@ struct ei_solve_triangular_selector<Lhs,Rhs,UpLo,RowMajor|IsDense>
       // process first rows using the non block version
       if(!(Lhs::Flags & UnitDiagBit))
       {
-        if (IsLower)
+        if (IsLowerTriangular)
           other.coeffRef(0,c) = other.coeff(0,c)/lhs.coeff(0, 0);
         else
           other.coeffRef(size-1,c) = other.coeff(size-1, c)/lhs.coeff(size-1, size-1);
       }
-      for(int i=(IsLower ? 1 : size-2); IsLower ? i<blockyStart : i>blockyStart; i += (IsLower ? 1 : -1) )
+      for(int i=(IsLowerTriangular ? 1 : size-2); IsLowerTriangular ? i<blockyStart : i>blockyStart; i += (IsLowerTriangular ? 1 : -1) )
       {
         Scalar tmp = other.coeff(i,c)
-          - (IsLower ? ((lhs.row(i).start(i)) * other.col(c).start(i)).coeff(0,0)
+          - (IsLowerTriangular ? ((lhs.row(i).start(i)) * other.col(c).start(i)).coeff(0,0)
                      : ((lhs.row(i).end(size-i-1)) * other.col(c).end(size-i-1)).coeff(0,0));
         if (Lhs::Flags & UnitDiagBit)
           other.coeffRef(i,c) = tmp;
@@ -89,15 +89,15 @@ struct ei_solve_triangular_selector<Lhs,Rhs,UpLo,RowMajor|IsDense>
       }
 
       // now let's process the remaining rows 4 at once
-      for(int i=blockyStart; IsLower ? i<size : i>0; )
+      for(int i=blockyStart; IsLowerTriangular ? i<size : i>0; )
       {
         int startBlock = i;
-        int endBlock = startBlock + (IsLower ? 4 : -4);
+        int endBlock = startBlock + (IsLowerTriangular ? 4 : -4);
 
         /* Process the i cols times 4 rows block, and keep the result in a temporary vector */
         // FIXME use fixed size block but take care to small fixed size matrices...
         Matrix<Scalar,Dynamic,1> btmp(4);
-        if (IsLower)
+        if (IsLowerTriangular)
           btmp = lhs.block(startBlock,0,4,i) * other.col(c).start(i);
         else
           btmp = lhs.block(i-3,i+1,4,size-1-i) * other.col(c).end(size-1-i);
@@ -106,21 +106,21 @@ struct ei_solve_triangular_selector<Lhs,Rhs,UpLo,RowMajor|IsDense>
          * btmp stores the diagonal coefficients used to update the remaining part of the result.
          */
         {
-          Scalar tmp = other.coeff(startBlock,c)-btmp.coeff(IsLower?0:3);
+          Scalar tmp = other.coeff(startBlock,c)-btmp.coeff(IsLowerTriangular?0:3);
           if (Lhs::Flags & UnitDiagBit)
             other.coeffRef(i,c) = tmp;
           else
             other.coeffRef(i,c) = tmp/lhs.coeff(i,i);
         }
 
-        i += IsLower ? 1 : -1;
-        for (;IsLower ? i<endBlock : i>endBlock; i += IsLower ? 1 : -1)
+        i += IsLowerTriangular ? 1 : -1;
+        for (;IsLowerTriangular ? i<endBlock : i>endBlock; i += IsLowerTriangular ? 1 : -1)
         {
-          int remainingSize = IsLower ? i-startBlock : startBlock-i;
+          int remainingSize = IsLowerTriangular ? i-startBlock : startBlock-i;
           Scalar tmp = other.coeff(i,c)
-            - btmp.coeff(IsLower ? remainingSize : 3-remainingSize)
-            - (   lhs.row(i).segment(IsLower ? startBlock : i+1, remainingSize)
-              * other.col(c).segment(IsLower ? startBlock : i+1, remainingSize)).coeff(0,0);
+            - btmp.coeff(IsLowerTriangular ? remainingSize : 3-remainingSize)
+            - (   lhs.row(i).segment(IsLowerTriangular ? startBlock : i+1, remainingSize)
+              * other.col(c).segment(IsLowerTriangular ? startBlock : i+1, remainingSize)).coeff(0,0);
 
           if (Lhs::Flags & UnitDiagBit)
             other.coeffRef(i,c) = tmp;
@@ -133,10 +133,10 @@ struct ei_solve_triangular_selector<Lhs,Rhs,UpLo,RowMajor|IsDense>
 };
 
 // Implements the following configurations:
-//  - inv(Lower,         ColMajor) * Column vector
-//  - inv(Lower,UnitDiag,ColMajor) * Column vector
-//  - inv(Upper,         ColMajor) * Column vector
-//  - inv(Upper,UnitDiag,ColMajor) * Column vector
+//  - inv(LowerTriangular,         ColMajor) * Column vector
+//  - inv(LowerTriangular,UnitDiag,ColMajor) * Column vector
+//  - inv(UpperTriangular,         ColMajor) * Column vector
+//  - inv(UpperTriangular,UnitDiag,ColMajor) * Column vector
 template<typename Lhs, typename Rhs, int UpLo>
 struct ei_solve_triangular_selector<Lhs,Rhs,UpLo,ColMajor|IsDense>
 {
@@ -146,7 +146,7 @@ struct ei_solve_triangular_selector<Lhs,Rhs,UpLo,ColMajor|IsDense>
 
   static void run(const Lhs& lhs, Rhs& other)
   {
-    static const bool IsLower = (UpLo==Lower);
+    static const bool IsLowerTriangular = (UpLo==LowerTriangular);
     const int size = lhs.cols();
     for(int c=0 ; c<other.cols() ; ++c)
     {
@@ -155,27 +155,27 @@ struct ei_solve_triangular_selector<Lhs,Rhs,UpLo,ColMajor|IsDense>
        * we can process using the block version.
        */
       int blockyEnd = (std::max(size-5,0)/4)*4;
-      if (!IsLower)
+      if (!IsLowerTriangular)
         blockyEnd = size-1 - blockyEnd;
-      for(int i=IsLower ? 0 : size-1; IsLower ? i<blockyEnd : i>blockyEnd;)
+      for(int i=IsLowerTriangular ? 0 : size-1; IsLowerTriangular ? i<blockyEnd : i>blockyEnd;)
       {
         /* Let's process the 4x4 sub-matrix as usual.
          * btmp stores the diagonal coefficients used to update the remaining part of the result.
          */
         int startBlock = i;
-        int endBlock = startBlock + (IsLower ? 4 : -4);
+        int endBlock = startBlock + (IsLowerTriangular ? 4 : -4);
         Matrix<Scalar,4,1> btmp;
-        for (;IsLower ? i<endBlock : i>endBlock;
-             i += IsLower ? 1 : -1)
+        for (;IsLowerTriangular ? i<endBlock : i>endBlock;
+             i += IsLowerTriangular ? 1 : -1)
         {
           if(!(Lhs::Flags & UnitDiagBit))
             other.coeffRef(i,c) /= lhs.coeff(i,i);
-          int remainingSize = IsLower ? endBlock-i-1 : i-endBlock-1;
+          int remainingSize = IsLowerTriangular ? endBlock-i-1 : i-endBlock-1;
           if (remainingSize>0)
-            other.col(c).segment((IsLower ? i : endBlock) + 1, remainingSize) -=
+            other.col(c).segment((IsLowerTriangular ? i : endBlock) + 1, remainingSize) -=
                 other.coeffRef(i,c)
-              * Block<Lhs,Dynamic,1>(lhs, (IsLower ? i : endBlock) + 1, i, remainingSize, 1);
-          btmp.coeffRef(IsLower ? i-startBlock : remainingSize) = -other.coeffRef(i,c);
+              * Block<Lhs,Dynamic,1>(lhs, (IsLowerTriangular ? i : endBlock) + 1, i, remainingSize, 1);
+          btmp.coeffRef(IsLowerTriangular ? i-startBlock : remainingSize) = -other.coeffRef(i,c);
         }
 
         /* Now we can efficiently update the remaining part of the result as a matrix * vector product.
@@ -187,11 +187,11 @@ struct ei_solve_triangular_selector<Lhs,Rhs,UpLo,ColMajor|IsDense>
         // FIXME this is cool but what about conjugate/adjoint expressions ? do we want to evaluate them ?
         // this is a more general problem though.
         ei_cache_friendly_product_colmajor_times_vector(
-          IsLower ? size-endBlock : endBlock+1,
-          &(lhs.const_cast_derived().coeffRef(IsLower ? endBlock : 0, IsLower ? startBlock : endBlock+1)),
+          IsLowerTriangular ? size-endBlock : endBlock+1,
+          &(lhs.const_cast_derived().coeffRef(IsLowerTriangular ? endBlock : 0, IsLowerTriangular ? startBlock : endBlock+1)),
           lhs.stride(),
-          btmp, &(other.coeffRef(IsLower ? endBlock : 0, c)));
-// 				if (IsLower)
+          btmp, &(other.coeffRef(IsLowerTriangular ? endBlock : 0, c)));
+// 				if (IsLowerTriangular)
 //           other.col(c).end(size-endBlock) += (lhs.block(endBlock, startBlock, size-endBlock, endBlock-startBlock)
 //                                           * other.col(c).block(startBlock,endBlock-startBlock)).lazy();
 // 				else
@@ -201,7 +201,7 @@ struct ei_solve_triangular_selector<Lhs,Rhs,UpLo,ColMajor|IsDense>
 
       /* Now we have to process the remaining part as usual */
       int i;
-      for(i=blockyEnd; IsLower ? i<size-1 : i>0; i += (IsLower ? 1 : -1) )
+      for(i=blockyEnd; IsLowerTriangular ? i<size-1 : i>0; i += (IsLowerTriangular ? 1 : -1) )
       {
         if(!(Lhs::Flags & UnitDiagBit))
           other.coeffRef(i,c) /= lhs.coeff(i,i);
@@ -209,7 +209,7 @@ struct ei_solve_triangular_selector<Lhs,Rhs,UpLo,ColMajor|IsDense>
         /* NOTE we cannot use lhs.col(i).end(size-i-1) because Part::coeffRef gets called by .col() to
          * get the address of the start of the row
          */
-        if(IsLower)
+        if(IsLowerTriangular)
           other.col(c).end(size-i-1) -= other.coeffRef(i,c) * Block<Lhs,Dynamic,1>(lhs, i+1,i, size-i-1,1);
         else
           other.col(c).start(i) -= other.coeffRef(i,c) * Block<Lhs,Dynamic,1>(lhs, 0,i, i, 1);
diff --git a/Eigen/src/Core/Transpose.h b/Eigen/src/Core/Transpose.h
index 2a9530124..1137e42dd 100644
--- a/Eigen/src/Core/Transpose.h
+++ b/Eigen/src/Core/Transpose.h
@@ -167,7 +167,7 @@ struct ei_inplace_transpose_selector;
 template<typename MatrixType>
 struct ei_inplace_transpose_selector<MatrixType,true> { // square matrix
   static void run(MatrixType& m) {
-    m.template part<StrictlyUpper>().swap(m.transpose());
+    m.template part<StrictlyUpperTriangular>().swap(m.transpose());
   }
 };
 
@@ -175,7 +175,7 @@ template<typename MatrixType>
 struct ei_inplace_transpose_selector<MatrixType,false> { // non square matrix
   static void run(MatrixType& m) {
     if (m.rows()==m.cols())
-      m.template part<StrictlyUpper>().swap(m.transpose());
+      m.template part<StrictlyUpperTriangular>().swap(m.transpose());
     else
       m.set(m.transpose().eval());
   }
diff --git a/Eigen/src/Core/util/Constants.h b/Eigen/src/Core/util/Constants.h
index 20b427df1..203f3b294 100644
--- a/Eigen/src/Core/util/Constants.h
+++ b/Eigen/src/Core/util/Constants.h
@@ -185,16 +185,16 @@ const unsigned int HereditaryBits = RowMajorBit
                                   | SparseBit;
 
 // Possible values for the Mode parameter of part() and of extract()
-const unsigned int Upper = UpperTriangularBit;
-const unsigned int StrictlyUpper = UpperTriangularBit | ZeroDiagBit;
-const unsigned int Lower = LowerTriangularBit;
-const unsigned int StrictlyLower = LowerTriangularBit | ZeroDiagBit;
+const unsigned int UpperTriangular = UpperTriangularBit;
+const unsigned int StrictlyUpperTriangular = UpperTriangularBit | ZeroDiagBit;
+const unsigned int LowerTriangular = LowerTriangularBit;
+const unsigned int StrictlyLowerTriangular = LowerTriangularBit | ZeroDiagBit;
 const unsigned int SelfAdjoint = SelfAdjointBit;
 
 // additional possible values for the Mode parameter of extract()
-const unsigned int UnitUpper = UpperTriangularBit | UnitDiagBit;
-const unsigned int UnitLower = LowerTriangularBit | UnitDiagBit;
-const unsigned int Diagonal = Upper | Lower;
+const unsigned int UnitUpperTriangular = UpperTriangularBit | UnitDiagBit;
+const unsigned int UnitLowerTriangular = LowerTriangularBit | UnitDiagBit;
+const unsigned int Diagonal = UpperTriangular | LowerTriangular;
 
 enum { Aligned, Unaligned };
 enum { ForceAligned, AsRequested };
diff --git a/Eigen/src/LU/LU.h b/Eigen/src/LU/LU.h
index 41e33b48f..f3c93a4e8 100644
--- a/Eigen/src/LU/LU.h
+++ b/Eigen/src/LU/LU.h
@@ -114,7 +114,7 @@ template<typename MatrixType> class LU
       *
       * \sa matrixLU(), matrixU()
       */
-    inline const Part<MatrixType, UnitLower> matrixL() const
+    inline const Part<MatrixType, UnitLowerTriangular> matrixL() const
     {
       return m_lu;
     }
@@ -123,7 +123,7 @@ template<typename MatrixType> class LU
       *
       * \sa matrixLU(), matrixL()
       */
-    inline const Part<MatrixType, Upper> matrixU() const
+    inline const Part<MatrixType, UpperTriangular> matrixU() const
     {
       return m_lu;
     }
@@ -441,7 +441,7 @@ void LU<MatrixType>::computeKernel(KernelMatrixType *result) const
     y(-m_lu.corner(TopRight, m_rank, dimker));
 
   m_lu.corner(TopLeft, m_rank, m_rank)
-      .template marked<Upper>()
+      .template marked<UpperTriangular>()
       .solveTriangularInPlace(y);
 
   for(int i = 0; i < m_rank; ++i)
@@ -510,7 +510,7 @@ bool LU<MatrixType>::solve(
   l.setZero();
   l.corner(Eigen::TopLeft,rows,smalldim)
     = m_lu.corner(Eigen::TopLeft,rows,smalldim);
-  l.template marked<UnitLower>().solveTriangularInPlace(c);
+  l.template marked<UnitLowerTriangular>().solveTriangularInPlace(c);
 
   // Step 3
   if(!isSurjective())
@@ -527,7 +527,7 @@ bool LU<MatrixType>::solve(
          MatrixType::MaxRowsAtCompileTime, OtherDerived::MaxColsAtCompileTime>
     d(c.corner(TopLeft, m_rank, c.cols()));
   m_lu.corner(TopLeft, m_rank, m_rank)
-      .template marked<Upper>()
+      .template marked<UpperTriangular>()
       .solveTriangularInPlace(d);
 
   // Step 4
diff --git a/Eigen/src/QR/HessenbergDecomposition.h b/Eigen/src/QR/HessenbergDecomposition.h
index 21597bb02..6d0ff794e 100644
--- a/Eigen/src/QR/HessenbergDecomposition.h
+++ b/Eigen/src/QR/HessenbergDecomposition.h
@@ -243,7 +243,7 @@ HessenbergDecomposition<MatrixType>::matrixH(void) const
   int n = m_matrix.rows();
   MatrixType matH = m_matrix;
   if (n>2)
-    matH.corner(BottomLeft,n-2, n-2).template part<Lower>().setZero();
+    matH.corner(BottomLeft,n-2, n-2).template part<LowerTriangular>().setZero();
   return matH;
 }
 
diff --git a/Eigen/src/QR/QR.h b/Eigen/src/QR/QR.h
index c19205816..88914af3a 100644
--- a/Eigen/src/QR/QR.h
+++ b/Eigen/src/QR/QR.h
@@ -60,11 +60,11 @@ template<typename MatrixType> class QR
     bool isFullRank() const { return ei_isMuchSmallerThan(m_hCoeffs.cwise().abs().minCoeff(), Scalar(1)); }
 
     /** \returns a read-only expression of the matrix R of the actual the QR decomposition */
-    const Part<NestByValue<MatrixRBlockType>, Upper>
+    const Part<NestByValue<MatrixRBlockType>, UpperTriangular>
     matrixR(void) const
     {
       int cols = m_qr.cols();
-      return MatrixRBlockType(m_qr, 0, 0, cols, cols).nestByValue().template part<Upper>();
+      return MatrixRBlockType(m_qr, 0, 0, cols, cols).nestByValue().template part<UpperTriangular>();
     }
 
     MatrixType matrixQ(void) const;
diff --git a/Eigen/src/QR/SelfAdjointEigenSolver.h b/Eigen/src/QR/SelfAdjointEigenSolver.h
index 95842c160..36188bcf9 100644
--- a/Eigen/src/QR/SelfAdjointEigenSolver.h
+++ b/Eigen/src/QR/SelfAdjointEigenSolver.h
@@ -254,22 +254,22 @@ compute(const MatrixType& matA, const MatrixType& matB, bool computeEigenvectors
   cholB.matrixL().solveTriangularInPlace(matC);
   // FIXME since we currently do not support A * inv(L'), let's do (inv(L) A')' :
   matC = matC.adjoint().eval();
-  cholB.matrixL().template marked<Lower>().solveTriangularInPlace(matC);
+  cholB.matrixL().template marked<LowerTriangular>().solveTriangularInPlace(matC);
   matC = matC.adjoint().eval();
   // this version works too:
 //   matC = matC.transpose();
-//   cholB.matrixL().conjugate().template marked<Lower>().solveTriangularInPlace(matC);
+//   cholB.matrixL().conjugate().template marked<LowerTriangular>().solveTriangularInPlace(matC);
 //   matC = matC.transpose();
   // FIXME: this should work: (currently it only does for small matrices)
 //   Transpose<MatrixType> trMatC(matC);
-//   cholB.matrixL().conjugate().eval().template marked<Lower>().solveTriangularInPlace(trMatC);
+//   cholB.matrixL().conjugate().eval().template marked<LowerTriangular>().solveTriangularInPlace(trMatC);
 
   compute(matC, computeEigenvectors);
 
   if (computeEigenvectors)
   {
     // transform back the eigen vectors: evecs = inv(U) * evecs
-    cholB.matrixL().adjoint().template marked<Upper>().solveTriangularInPlace(m_eivec);
+    cholB.matrixL().adjoint().template marked<UpperTriangular>().solveTriangularInPlace(m_eivec);
     for (int i=0; i<m_eivec.cols(); ++i)
       m_eivec.col(i) = m_eivec.col(i).normalized();
   }
diff --git a/Eigen/src/QR/Tridiagonalization.h b/Eigen/src/QR/Tridiagonalization.h
index ee7f7b84b..f56b09128 100644
--- a/Eigen/src/QR/Tridiagonalization.h
+++ b/Eigen/src/QR/Tridiagonalization.h
@@ -167,8 +167,8 @@ Tridiagonalization<MatrixType>::matrixT(void) const
   matT.corner(TopRight,n-1, n-1).diagonal() = subDiagonal().conjugate();
   if (n>2)
   {
-    matT.corner(TopRight,n-2, n-2).template part<Upper>().setZero();
-    matT.corner(BottomLeft,n-2, n-2).template part<Lower>().setZero();
+    matT.corner(TopRight,n-2, n-2).template part<UpperTriangular>().setZero();
+    matT.corner(BottomLeft,n-2, n-2).template part<LowerTriangular>().setZero();
   }
   return matT;
 }
@@ -223,17 +223,17 @@ void Tridiagonalization<MatrixType>::_compute(MatrixType& matA, CoeffVectorType&
 
       /* This is the initial algorithm which minimize operation counts and maximize
        * the use of Eigen's expression. Unfortunately, the first matrix-vector product
-       * using Part<Lower|Selfadjoint>  is very very slow */
+       * using Part<LowerTriangular|Selfadjoint>  is very very slow */
       #ifdef EIGEN_NEVER_DEFINED
       // matrix - vector product
-      hCoeffs.end(n-i-1) = (matA.corner(BottomRight,n-i-1,n-i-1).template part<Lower|SelfAdjoint>()
+      hCoeffs.end(n-i-1) = (matA.corner(BottomRight,n-i-1,n-i-1).template part<LowerTriangular|SelfAdjoint>()
                                 * (h * matA.col(i).end(n-i-1))).lazy();
       // simple axpy
       hCoeffs.end(n-i-1) += (h * Scalar(-0.5) * matA.col(i).end(n-i-1).dot(hCoeffs.end(n-i-1)))
                             * matA.col(i).end(n-i-1);
       // rank-2 update
       //Block<MatrixType,Dynamic,1> B(matA,i+1,i,n-i-1,1);
-      matA.corner(BottomRight,n-i-1,n-i-1).template part<Lower>() -=
+      matA.corner(BottomRight,n-i-1,n-i-1).template part<LowerTriangular>() -=
             (matA.col(i).end(n-i-1) * hCoeffs.end(n-i-1).adjoint()).lazy()
           + (hCoeffs.end(n-i-1) * matA.col(i).end(n-i-1).adjoint()).lazy();
       #endif
@@ -256,7 +256,7 @@ void Tridiagonalization<MatrixType>::_compute(MatrixType& matA, CoeffVectorType&
             Block<MatrixType,Dynamic,4>(matA,b+4,b,n-b-4,4).adjoint() * Block<MatrixType,Dynamic,1>(matA,b+4,i,n-b-4,1);
         // the 4x4 block diagonal:
         Block<CoeffVectorType,4,1>(hCoeffs, b, 0, 4,1) +=
-            (Block<MatrixType,4,4>(matA,b,b,4,4).template part<Lower|SelfAdjoint>()
+            (Block<MatrixType,4,4>(matA,b,b,4,4).template part<LowerTriangular|SelfAdjoint>()
              * (h * Block<MatrixType,4,1>(matA,b,i,4,1))).lazy();
       }
       #endif
diff --git a/Eigen/src/Sparse/CholmodSupport.h b/Eigen/src/Sparse/CholmodSupport.h
index c98ca2125..6689a4669 100644
--- a/Eigen/src/Sparse/CholmodSupport.h
+++ b/Eigen/src/Sparse/CholmodSupport.h
@@ -69,9 +69,9 @@ cholmod_sparse SparseMatrix<Scalar,Flags>::asCholmodMatrix()
 
   if (Flags & SelfAdjoint)
   {
-    if (Flags & Upper)
+    if (Flags & UpperTriangular)
       res.stype = 1;
-    else if (Flags & Lower)
+    else if (Flags & LowerTriangular)
       res.stype = -1;
     else
       res.stype = 0;
diff --git a/Eigen/src/Sparse/SparseLDLT.h b/Eigen/src/Sparse/SparseLDLT.h
index b29148864..b1f58b4b1 100644
--- a/Eigen/src/Sparse/SparseLDLT.h
+++ b/Eigen/src/Sparse/SparseLDLT.h
@@ -79,7 +79,7 @@ class SparseLDLT
   protected:
     typedef typename MatrixType::Scalar Scalar;
     typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
-    typedef SparseMatrix<Scalar,Lower|UnitDiagBit> CholMatrixType;
+    typedef SparseMatrix<Scalar,LowerTriangular|UnitDiagBit> CholMatrixType;
     typedef Matrix<Scalar,MatrixType::ColsAtCompileTime,1> VectorType;
 
     enum {
diff --git a/Eigen/src/Sparse/SparseLLT.h b/Eigen/src/Sparse/SparseLLT.h
index f9eb459dc..0b63f80ab 100644
--- a/Eigen/src/Sparse/SparseLLT.h
+++ b/Eigen/src/Sparse/SparseLLT.h
@@ -41,7 +41,7 @@ class SparseLLT
   protected:
     typedef typename MatrixType::Scalar Scalar;
     typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
-    typedef SparseMatrix<Scalar,Lower> CholMatrixType;
+    typedef SparseMatrix<Scalar,LowerTriangular> CholMatrixType;
 
     enum {
       SupernodalFactorIsDirty      = 0x10000,
diff --git a/Eigen/src/Sparse/SparseLU.h b/Eigen/src/Sparse/SparseLU.h
index 4eb591fe7..142592050 100644
--- a/Eigen/src/Sparse/SparseLU.h
+++ b/Eigen/src/Sparse/SparseLU.h
@@ -41,7 +41,7 @@ class SparseLU
   protected:
     typedef typename MatrixType::Scalar Scalar;
     typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
-    typedef SparseMatrix<Scalar,Lower> LUMatrixType;
+    typedef SparseMatrix<Scalar,LowerTriangular> LUMatrixType;
 
     enum {
       MatrixLUIsDirty             = 0x10000
diff --git a/Eigen/src/Sparse/SuperLUSupport.h b/Eigen/src/Sparse/SuperLUSupport.h
index aeab835aa..6f554fa6e 100644
--- a/Eigen/src/Sparse/SuperLUSupport.h
+++ b/Eigen/src/Sparse/SuperLUSupport.h
@@ -162,9 +162,9 @@ struct SluMatrixMapHelper<SparseMatrix<Scalar,Flags> >
     res.setScalarType<Scalar>();
 
     // FIXME the following is not very accurate
-    if (Flags & Upper)
+    if (Flags & UpperTriangular)
       res.Mtype = SLU_TRU;
-    if (Flags & Lower)
+    if (Flags & LowerTriangular)
       res.Mtype = SLU_TRL;
     if (Flags & SelfAdjoint)
       ei_assert(false && "SelfAdjoint matrix shape not supported by SuperLU");
@@ -213,8 +213,8 @@ class SparseLU<MatrixType,SuperLU> : public SparseLU<MatrixType>
     typedef Matrix<Scalar,Dynamic,1> Vector;
     typedef Matrix<int, 1, MatrixType::ColsAtCompileTime> IntRowVectorType;
     typedef Matrix<int, MatrixType::RowsAtCompileTime, 1> IntColVectorType;
-    typedef SparseMatrix<Scalar,Lower|UnitDiagBit> LMatrixType;
-    typedef SparseMatrix<Scalar,Upper> UMatrixType;
+    typedef SparseMatrix<Scalar,LowerTriangular|UnitDiagBit> LMatrixType;
+    typedef SparseMatrix<Scalar,UpperTriangular> UMatrixType;
     using Base::m_flags;
     using Base::m_status;
 
diff --git a/Eigen/src/Sparse/TaucsSupport.h b/Eigen/src/Sparse/TaucsSupport.h
index 22fef1ceb..15fbb83ac 100644
--- a/Eigen/src/Sparse/TaucsSupport.h
+++ b/Eigen/src/Sparse/TaucsSupport.h
@@ -50,13 +50,13 @@ taucs_ccs_matrix SparseMatrix<Scalar,Flags>::asTaucsMatrix()
     ei_assert(false && "Scalar type not supported by TAUCS");
   }
 
-  if (Flags & Upper)
+  if (Flags & UpperTriangular)
     res.flags |= TAUCS_UPPER;
-  if (Flags & Lower)
+  if (Flags & LowerTriangular)
     res.flags |= TAUCS_LOWER;
   if (Flags & SelfAdjoint)
     res.flags |= (NumTraits<Scalar>::IsComplex ? TAUCS_HERMITIAN : TAUCS_SYMMETRIC);
-  else if ((Flags & Upper) || (Flags & Lower))
+  else if ((Flags & UpperTriangular) || (Flags & LowerTriangular))
     res.flags |= TAUCS_TRIANGULAR;
 
   return res;
diff --git a/Eigen/src/Sparse/TriangularSolver.h b/Eigen/src/Sparse/TriangularSolver.h
index c32af328d..d44938273 100644
--- a/Eigen/src/Sparse/TriangularSolver.h
+++ b/Eigen/src/Sparse/TriangularSolver.h
@@ -27,7 +27,7 @@
 
 // forward substitution, row-major
 template<typename Lhs, typename Rhs>
-struct ei_solve_triangular_selector<Lhs,Rhs,Lower,RowMajor|IsSparse>
+struct ei_solve_triangular_selector<Lhs,Rhs,LowerTriangular,RowMajor|IsSparse>
 {
   typedef typename Rhs::Scalar Scalar;
   static void run(const Lhs& lhs, Rhs& other)
@@ -59,7 +59,7 @@ struct ei_solve_triangular_selector<Lhs,Rhs,Lower,RowMajor|IsSparse>
 
 // backward substitution, row-major
 template<typename Lhs, typename Rhs>
-struct ei_solve_triangular_selector<Lhs,Rhs,Upper,RowMajor|IsSparse>
+struct ei_solve_triangular_selector<Lhs,Rhs,UpperTriangular,RowMajor|IsSparse>
 {
   typedef typename Rhs::Scalar Scalar;
   static void run(const Lhs& lhs, Rhs& other)
@@ -92,7 +92,7 @@ struct ei_solve_triangular_selector<Lhs,Rhs,Upper,RowMajor|IsSparse>
 
 // forward substitution, col-major
 template<typename Lhs, typename Rhs>
-struct ei_solve_triangular_selector<Lhs,Rhs,Lower,ColMajor|IsSparse>
+struct ei_solve_triangular_selector<Lhs,Rhs,LowerTriangular,ColMajor|IsSparse>
 {
   typedef typename Rhs::Scalar Scalar;
   static void run(const Lhs& lhs, Rhs& other)
@@ -120,7 +120,7 @@ struct ei_solve_triangular_selector<Lhs,Rhs,Lower,ColMajor|IsSparse>
 
 // backward substitution, col-major
 template<typename Lhs, typename Rhs>
-struct ei_solve_triangular_selector<Lhs,Rhs,Upper,ColMajor|IsSparse>
+struct ei_solve_triangular_selector<Lhs,Rhs,UpperTriangular,ColMajor|IsSparse>
 {
   typedef typename Rhs::Scalar Scalar;
   static void run(const Lhs& lhs, Rhs& other)
diff --git a/Eigen/src/Sparse/UmfPackSupport.h b/Eigen/src/Sparse/UmfPackSupport.h
index 00fa7e57d..1bb40a7c3 100644
--- a/Eigen/src/Sparse/UmfPackSupport.h
+++ b/Eigen/src/Sparse/UmfPackSupport.h
@@ -127,8 +127,8 @@ class SparseLU<MatrixType,UmfPack> : public SparseLU<MatrixType>
     typedef Matrix<Scalar,Dynamic,1> Vector;
     typedef Matrix<int, 1, MatrixType::ColsAtCompileTime> IntRowVectorType;
     typedef Matrix<int, MatrixType::RowsAtCompileTime, 1> IntColVectorType;
-    typedef SparseMatrix<Scalar,Lower|UnitDiagBit> LMatrixType;
-    typedef SparseMatrix<Scalar,Upper> UMatrixType;
+    typedef SparseMatrix<Scalar,LowerTriangular|UnitDiagBit> LMatrixType;
+    typedef SparseMatrix<Scalar,UpperTriangular> UMatrixType;
     using Base::m_flags;
     using Base::m_status;
 
diff --git a/bench/btl/libs/eigen2/eigen2_interface.hh b/bench/btl/libs/eigen2/eigen2_interface.hh
index 0f5b6f640..40d8f9c70 100644
--- a/bench/btl/libs/eigen2/eigen2_interface.hh
+++ b/bench/btl/libs/eigen2/eigen2_interface.hh
@@ -134,11 +134,11 @@ public :
   }
 
   static inline void trisolve_lower(const gene_matrix & L, const gene_vector& B, gene_vector& X, int N){
-    X = L.template marked<Lower>().solveTriangular(B);
+    X = L.template marked<LowerTriangular>().solveTriangular(B);
   }
 
   static inline void trisolve_lower_matrix(const gene_matrix & L, const gene_matrix& B, gene_matrix& X, int N){
-    X = L.template marked<Lower>().solveTriangular(B);
+    X = L.template marked<LowerTriangular>().solveTriangular(B);
   }
 
   static inline void cholesky(const gene_matrix & X, gene_matrix & C, int N){
diff --git a/bench/sparse_cholesky.cpp b/bench/sparse_cholesky.cpp
index 5e07fac9b..ec8078e4c 100644
--- a/bench/sparse_cholesky.cpp
+++ b/bench/sparse_cholesky.cpp
@@ -37,8 +37,8 @@
         X  \
   } timer.stop(); }
 
-// typedef SparseMatrix<Scalar,Upper> EigenSparseTriMatrix;
-typedef SparseMatrix<Scalar,SelfAdjoint|Lower> EigenSparseSelfAdjointMatrix;
+// typedef SparseMatrix<Scalar,UpperTriangular> EigenSparseTriMatrix;
+typedef SparseMatrix<Scalar,SelfAdjoint|LowerTriangular> EigenSparseSelfAdjointMatrix;
 
 void fillSpdMatrix(float density, int rows, int cols,  EigenSparseSelfAdjointMatrix& dst)
 {
diff --git a/bench/sparse_trisolver.cpp b/bench/sparse_trisolver.cpp
index 021433043..158a381d8 100644
--- a/bench/sparse_trisolver.cpp
+++ b/bench/sparse_trisolver.cpp
@@ -34,8 +34,8 @@
         X  \
   } timer.stop(); }
 
-typedef SparseMatrix<Scalar,Upper> EigenSparseTriMatrix;
-typedef SparseMatrix<Scalar,RowMajorBit|Upper> EigenSparseTriMatrixRow;
+typedef SparseMatrix<Scalar,UpperTriangular> EigenSparseTriMatrix;
+typedef SparseMatrix<Scalar,RowMajorBit|UpperTriangular> EigenSparseTriMatrixRow;
 
 void fillMatrix(float density, int rows, int cols,  EigenSparseTriMatrix& dst)
 {
@@ -83,11 +83,11 @@ int main(int argc, char *argv[])
       eiToDense(sm1, m1);
       m2 = m1;
 
-      BENCH(x = m1.marked<Upper>().solveTriangular(b);)
+      BENCH(x = m1.marked<UpperTriangular>().solveTriangular(b);)
       std::cout << "   colmajor^-1 * b:\t" << timer.value() << endl;
 //       std::cerr << x.transpose() << "\n";
 
-      BENCH(x = m2.marked<Upper>().solveTriangular(b);)
+      BENCH(x = m2.marked<UpperTriangular>().solveTriangular(b);)
       std::cout << "   rowmajor^-1 * b:\t" << timer.value() << endl;
 //       std::cerr << x.transpose() << "\n";
     }
diff --git a/doc/QuickStartGuide.dox b/doc/QuickStartGuide.dox
index aa40606ed..81df4aa3d 100644
--- a/doc/QuickStartGuide.dox
+++ b/doc/QuickStartGuide.dox
@@ -513,20 +513,20 @@ Read/write access to special parts of a matrix can be achieved. See \link Matrix
 <tr><td>
 Extract triangular matrices \n from a given matrix m:
 </td><td>\code
-m.part<Eigen::Upper>()
-m.part<Eigen::StrictlyUpper>()
-m.part<Eigen::UnitUpper>()
-m.part<Eigen::Lower>()
-m.part<Eigen::StrictlyLower>()
-m.part<Eigen::UnitLower>()\endcode
+m.part<Eigen::UpperTriangular>()
+m.part<Eigen::StrictlyUpperTriangular>()
+m.part<Eigen::UnitUpperTriangular>()
+m.part<Eigen::LowerTriangular>()
+m.part<Eigen::StrictlyLowerTriangular>()
+m.part<Eigen::UnitLowerTriangular>()\endcode
 </td></tr>
 <tr><td>
 Write to triangular parts \n of a matrix m:
 </td><td>\code
-m1.part<Eigen::Upper>() = m2;
-m1.part<Eigen::StrictlyUpper>() = m2;
-m1.part<Eigen::Lower>() = m2;
-m1.part<Eigen::StrictlyLower>() = m2;\endcode
+m1.part<Eigen::UpperTriangular>() = m2;
+m1.part<Eigen::StrictlyUpperTriangular>() = m2;
+m1.part<Eigen::LowerTriangular>() = m2;
+m1.part<Eigen::StrictlyLowerTriangular>() = m2;\endcode
 </td></tr>
 <tr><td>
 Special: take advantage of symmetry \n (selfadjointness) when copying \n an expression into a matrix
diff --git a/doc/snippets/MatrixBase_extract.cpp b/doc/snippets/MatrixBase_extract.cpp
index bedf4dfbd..02f44c83f 100644
--- a/doc/snippets/MatrixBase_extract.cpp
+++ b/doc/snippets/MatrixBase_extract.cpp
@@ -1,8 +1,8 @@
 Matrix3i m = Matrix3i::Random();
 cout << "Here is the matrix m:" << endl << m << endl;
 cout << "Here is the upper-triangular matrix extracted from m:" << endl
-     << m.part<Eigen::Upper>() << endl;
+     << m.part<Eigen::UpperTriangular>() << endl;
 cout << "Here is the strictly-upper-triangular matrix extracted from m:" << endl
-     << m.part<Eigen::StrictlyUpper>() << endl;
+     << m.part<Eigen::StrictlyUpperTriangular>() << endl;
 cout << "Here is the unit-lower-triangular matrix extracted from m:" << endl
-     << m.part<Eigen::UnitLower>() << endl;
+     << m.part<Eigen::UnitLowerTriangular>() << endl;
diff --git a/doc/snippets/MatrixBase_marked.cpp b/doc/snippets/MatrixBase_marked.cpp
index d4c11c6fc..5c05ce81e 100644
--- a/doc/snippets/MatrixBase_marked.cpp
+++ b/doc/snippets/MatrixBase_marked.cpp
@@ -1,9 +1,9 @@
 Matrix3d m = Matrix3d::Zero();
-m.part<Eigen::Upper>().setOnes();
+m.part<Eigen::UpperTriangular>().setOnes();
 cout << "Here is the matrix m:" << endl << m << endl;
 Matrix3d n = Matrix3d::Ones();
-n.part<Eigen::Lower>() *= 2;
+n.part<Eigen::LowerTriangular>() *= 2;
 cout << "Here is the matrix n:" << endl << n << endl;
 cout << "And now here is m.inverse()*n, taking advantage of the fact that"
         " m is upper-triangular:" << endl
-     << m.marked<Eigen::Upper>().solveTriangular(n);
+     << m.marked<Eigen::UpperTriangular>().solveTriangular(n);
diff --git a/doc/snippets/MatrixBase_part.cpp b/doc/snippets/MatrixBase_part.cpp
index fbc55b1ca..1abbd6888 100644
--- a/doc/snippets/MatrixBase_part.cpp
+++ b/doc/snippets/MatrixBase_part.cpp
@@ -1,5 +1,5 @@
 Matrix3d m = Matrix3i::Zero();
-m.part<Eigen::StrictlyUpper>().setOnes();
+m.part<Eigen::StrictlyUpperTriangular>().setOnes();
 cout << "Here is the matrix m:" << endl << m << endl;
 cout << "And let us now compute m*m.adjoint() in a very optimized way" << endl
      << "taking advantage of the symmetry." << endl;
diff --git a/doc/snippets/class_LU_2.cpp b/doc/snippets/class_LU_2.cpp
index ccf89a995..0c72d34a4 100644
--- a/doc/snippets/class_LU_2.cpp
+++ b/doc/snippets/class_LU_2.cpp
@@ -7,7 +7,7 @@ cout << "Here is, up to permutations, its LU decomposition matrix:"
      << endl << lu.matrixLU() << endl;
 cout << "Here is the actual L matrix in this decomposition:" << endl;
 Matrix5x5 l = Matrix5x5::Identity();
-l.block<5,3>(0,0).part<StrictlyLower>() = lu.matrixLU();
+l.block<5,3>(0,0).part<StrictlyLowerTriangular>() = lu.matrixLU();
 cout << l << endl;
 cout << "Let us now reconstruct the original matrix m:" << endl;
 Matrix5x3 x = l * lu.matrixU();
diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt
index fd39dc82e..4255128ad 100644
--- a/test/CMakeLists.txt
+++ b/test/CMakeLists.txt
@@ -131,9 +131,11 @@ macro(ei_add_test testname)
 
   target_link_libraries(${targetname} ${EXTERNAL_LIBS})
   if(${ARGC} GREATER 2)
-    if(ARGV2)
+    string(STRIP "${ARGV2}" ARGV2_stripped)
+    string(LENGTH "${ARGV2_stripped}" ARGV2_stripped_length)
+    if(${ARGV2_stripped_length} GREATER 0)
       target_link_libraries(${targetname} ${ARGV2})
-    endif(ARGV2)
+    endif(${ARGV2_stripped_length} GREATER 0)
   endif(${ARGC} GREATER 2)
 
   if(WIN32)
diff --git a/test/sparse_solvers.cpp b/test/sparse_solvers.cpp
index c3050ce7d..da9a245a2 100644
--- a/test/sparse_solvers.cpp
+++ b/test/sparse_solvers.cpp
@@ -44,13 +44,13 @@ template<typename Scalar> void sparse_solvers(int rows, int cols)
 
     // lower
     initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
-    VERIFY_IS_APPROX(refMat2.template marked<Lower>().solveTriangular(vec2),
-                     m2.template marked<Lower>().solveTriangular(vec3));
+    VERIFY_IS_APPROX(refMat2.template marked<LowerTriangular>().solveTriangular(vec2),
+                     m2.template marked<LowerTriangular>().solveTriangular(vec3));
 
     // upper
     initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords);
-    VERIFY_IS_APPROX(refMat2.template marked<Upper>().solveTriangular(vec2),
-                     m2.template marked<Upper>().solveTriangular(vec3));
+    VERIFY_IS_APPROX(refMat2.template marked<UpperTriangular>().solveTriangular(vec2),
+                     m2.template marked<UpperTriangular>().solveTriangular(vec3));
 
     // TODO test row major
   }
@@ -70,7 +70,7 @@ template<typename Scalar> void sparse_solvers(int rows, int cols)
     refMat2.diagonal() *= 0.5;
 
     refMat2.llt().solve(b, &refX);
-    typedef SparseMatrix<Scalar,Lower|SelfAdjoint> SparseSelfAdjointMatrix;
+    typedef SparseMatrix<Scalar,LowerTriangular|SelfAdjoint> SparseSelfAdjointMatrix;
     x = b;
     SparseLLT<SparseSelfAdjointMatrix> (m2).solveInPlace(x);
     //VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: default");
@@ -107,7 +107,7 @@ template<typename Scalar> void sparse_solvers(int rows, int cols)
     refMat2.diagonal() *= 0.5;
 
     refMat2.ldlt().solve(b, &refX);
-    typedef SparseMatrix<Scalar,Lower|SelfAdjoint> SparseSelfAdjointMatrix;
+    typedef SparseMatrix<Scalar,LowerTriangular|SelfAdjoint> SparseSelfAdjointMatrix;
     x = b;
     SparseLDLT<SparseSelfAdjointMatrix> ldlt(m2);
     if (ldlt.succeeded())
diff --git a/test/triangular.cpp b/test/triangular.cpp
index 34afa7b3c..7021e0776 100644
--- a/test/triangular.cpp
+++ b/test/triangular.cpp
@@ -51,14 +51,14 @@ template<typename MatrixType> void triangular(const MatrixType& m)
              v2 = VectorType::Random(rows),
              vzero = VectorType::Zero(rows);
 
-  MatrixType m1up = m1.template part<Eigen::Upper>();
-  MatrixType m2up = m2.template part<Eigen::Upper>();
+  MatrixType m1up = m1.template part<Eigen::UpperTriangular>();
+  MatrixType m2up = m2.template part<Eigen::UpperTriangular>();
 
   if (rows*cols>1)
   {
-    VERIFY(m1up.isUpper());
-    VERIFY(m2up.transpose().isLower());
-    VERIFY(!m2.isLower());
+    VERIFY(m1up.isUpperTriangular());
+    VERIFY(m2up.transpose().isLowerTriangular());
+    VERIFY(!m2.isLowerTriangular());
   }
 
 //   VERIFY_IS_APPROX(m1up.transpose() * m2, m1.upper().transpose().lower() * m2);
@@ -66,20 +66,20 @@ template<typename MatrixType> void triangular(const MatrixType& m)
   // test overloaded operator+=
   r1.setZero();
   r2.setZero();
-  r1.template part<Eigen::Upper>() +=  m1;
+  r1.template part<Eigen::UpperTriangular>() +=  m1;
   r2 += m1up;
   VERIFY_IS_APPROX(r1,r2);
 
   // test overloaded operator=
   m1.setZero();
-  m1.template part<Eigen::Upper>() = (m2.transpose() * m2).lazy();
+  m1.template part<Eigen::UpperTriangular>() = (m2.transpose() * m2).lazy();
   m3 = m2.transpose() * m2;
-  VERIFY_IS_APPROX(m3.template part<Eigen::Lower>().transpose(), m1);
+  VERIFY_IS_APPROX(m3.template part<Eigen::LowerTriangular>().transpose(), m1);
 
   // test overloaded operator=
   m1.setZero();
-  m1.template part<Eigen::Lower>() = (m2.transpose() * m2).lazy();
-  VERIFY_IS_APPROX(m3.template part<Eigen::Lower>(), m1);
+  m1.template part<Eigen::LowerTriangular>() = (m2.transpose() * m2).lazy();
+  VERIFY_IS_APPROX(m3.template part<Eigen::LowerTriangular>(), m1);
 
   VERIFY_IS_APPROX(m3.template part<Diagonal>(), m3.diagonal().asDiagonal());
 
@@ -89,30 +89,30 @@ template<typename MatrixType> void triangular(const MatrixType& m)
 
   Transpose<MatrixType> trm4(m4);
   // test back and forward subsitution
-  m3 = m1.template part<Eigen::Lower>();
-  VERIFY(m3.template marked<Eigen::Lower>().solveTriangular(m3).cwise().abs().isIdentity(test_precision<RealScalar>()));
-  VERIFY(m3.transpose().template marked<Eigen::Upper>()
+  m3 = m1.template part<Eigen::LowerTriangular>();
+  VERIFY(m3.template marked<Eigen::LowerTriangular>().solveTriangular(m3).cwise().abs().isIdentity(test_precision<RealScalar>()));
+  VERIFY(m3.transpose().template marked<Eigen::UpperTriangular>()
     .solveTriangular(m3.transpose()).cwise().abs().isIdentity(test_precision<RealScalar>()));
   // check M * inv(L) using in place API
   m4 = m3;
-  m3.transpose().template marked<Eigen::Upper>().solveTriangularInPlace(trm4);
+  m3.transpose().template marked<Eigen::UpperTriangular>().solveTriangularInPlace(trm4);
   VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>()));
 
-  m3 = m1.template part<Eigen::Upper>();
-  VERIFY(m3.template marked<Eigen::Upper>().solveTriangular(m3).cwise().abs().isIdentity(test_precision<RealScalar>()));
-  VERIFY(m3.transpose().template marked<Eigen::Lower>()
+  m3 = m1.template part<Eigen::UpperTriangular>();
+  VERIFY(m3.template marked<Eigen::UpperTriangular>().solveTriangular(m3).cwise().abs().isIdentity(test_precision<RealScalar>()));
+  VERIFY(m3.transpose().template marked<Eigen::LowerTriangular>()
     .solveTriangular(m3.transpose()).cwise().abs().isIdentity(test_precision<RealScalar>()));
   // check M * inv(U) using in place API
   m4 = m3;
-  m3.transpose().template marked<Eigen::Lower>().solveTriangularInPlace(trm4);
+  m3.transpose().template marked<Eigen::LowerTriangular>().solveTriangularInPlace(trm4);
   VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>()));
 
-  m3 = m1.template part<Eigen::Upper>();
-  VERIFY(m2.isApprox(m3 * (m3.template marked<Eigen::Upper>().solveTriangular(m2)), largerEps));
-  m3 = m1.template part<Eigen::Lower>();
-  VERIFY(m2.isApprox(m3 * (m3.template marked<Eigen::Lower>().solveTriangular(m2)), largerEps));
+  m3 = m1.template part<Eigen::UpperTriangular>();
+  VERIFY(m2.isApprox(m3 * (m3.template marked<Eigen::UpperTriangular>().solveTriangular(m2)), largerEps));
+  m3 = m1.template part<Eigen::LowerTriangular>();
+  VERIFY(m2.isApprox(m3 * (m3.template marked<Eigen::LowerTriangular>().solveTriangular(m2)), largerEps));
 
-  VERIFY((m1.template part<Eigen::Upper>() * m2.template part<Eigen::Upper>()).isUpper());
+  VERIFY((m1.template part<Eigen::UpperTriangular>() * m2.template part<Eigen::UpperTriangular>()).isUpperTriangular());
 
 }
 
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