* merge

* remove a ctor in QuaternionBase as it gives a strange error with GCC 4.4.2.

Eigen/src/Array/VectorwiseOp.h

@@ -122,6 +122,7 @@ class PartialReduxExpr : ei_no_assignment_operator,
 EIGEN_MEMBER_FUNCTOR(squaredNorm, Size * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
 EIGEN_MEMBER_FUNCTOR(norm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
 EIGEN_MEMBER_FUNCTOR(sum, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(mean, (Size-1)*NumTraits<Scalar>::AddCost + NumTraits<Scalar>::MulCost);
 EIGEN_MEMBER_FUNCTOR(minCoeff, (Size-1)*NumTraits<Scalar>::AddCost);
 EIGEN_MEMBER_FUNCTOR(maxCoeff, (Size-1)*NumTraits<Scalar>::AddCost);
 EIGEN_MEMBER_FUNCTOR(all, (Size-1)*NumTraits<Scalar>::AddCost);
@@ -297,6 +298,13 @@ template<typename ExpressionType, int Direction> class VectorwiseOp
     const typename ReturnType<ei_member_sum>::Type sum() const
     { return _expression(); }
 
+    /** \returns a row (or column) vector expression of the mean
+    * of each column (or row) of the referenced expression.
+    *
+    * \sa MatrixBase::mean() */
+    const typename ReturnType<ei_member_mean>::Type mean() const
+    { return _expression(); }
+
     /** \returns a row (or column) vector expression representing
       * whether \b all coefficients of each respective column (or row) are \c true.
       *

Eigen/src/Core/Assign.h

@@ -93,7 +93,7 @@ public:
               ? ( int(MayUnrollCompletely) && int(DstIsAligned) ? int(CompleteUnrolling) : int(NoUnrolling) )
               : int(NoUnrolling)
   };
-  
+
   static void debug()
   {
     EIGEN_DEBUG_VAR(DstIsAligned)

Eigen/src/Core/Functors.h

@@ -350,7 +350,7 @@ struct ei_scalar_multiple_op {
   EIGEN_STRONG_INLINE Scalar operator() (const Scalar& a) const { return a * m_other; }
   EIGEN_STRONG_INLINE const PacketScalar packetOp(const PacketScalar& a) const
   { return ei_pmul(a, ei_pset1(m_other)); }
-  const Scalar m_other;
+  typename ei_makeconst<typename NumTraits<Scalar>::Nested>::type m_other;
 private:
   ei_scalar_multiple_op& operator=(const ei_scalar_multiple_op&);
 };
@@ -364,7 +364,7 @@ struct ei_scalar_multiple2_op {
   EIGEN_STRONG_INLINE ei_scalar_multiple2_op(const ei_scalar_multiple2_op& other) : m_other(other.m_other) { }
   EIGEN_STRONG_INLINE ei_scalar_multiple2_op(const Scalar2& other) : m_other(other) { }
   EIGEN_STRONG_INLINE result_type operator() (const Scalar1& a) const { return a * m_other; }
-  const Scalar2 m_other;
+  typename ei_makeconst<typename NumTraits<Scalar2>::Nested>::type m_other;
 };
 template<typename Scalar1,typename Scalar2>
 struct ei_functor_traits<ei_scalar_multiple2_op<Scalar1,Scalar2> >
@@ -393,7 +393,7 @@ struct ei_scalar_quotient1_impl<Scalar,false> {
   EIGEN_STRONG_INLINE ei_scalar_quotient1_impl(const ei_scalar_quotient1_impl& other) : m_other(other.m_other) { }
   EIGEN_STRONG_INLINE ei_scalar_quotient1_impl(const Scalar& other) : m_other(other) {}
   EIGEN_STRONG_INLINE Scalar operator() (const Scalar& a) const { return a / m_other; }
-  const Scalar m_other;
+  typename ei_makeconst<typename NumTraits<Scalar>::Nested>::type m_other;
 };
 template<typename Scalar>
 struct ei_functor_traits<ei_scalar_quotient1_impl<Scalar,false> >

Eigen/src/Core/MatrixBase.h

@@ -145,12 +145,6 @@ template<typename Derived> class MatrixBase
 #endif
     };
 
-    /** Default constructor. Just checks at compile-time for self-consistency of the flags. */
-    MatrixBase()
-    {
-      ei_assert(ei_are_flags_consistent<Flags>::ret);
-    }
-
 #ifndef EIGEN_PARSED_BY_DOXYGEN
     /** This is the "real scalar" type; if the \a Scalar type is already real numbers
       * (e.g. int, float or double) then \a RealScalar is just the same as \a Scalar. If
@@ -177,7 +171,7 @@ template<typename Derived> class MatrixBase
     inline int diagonalSize() const { return std::min(rows(),cols()); }
     /** \returns the number of nonzero coefficients which is in practice the number
       * of stored coefficients. */
-    inline int nonZeros() const { return derived().nonZeros(); }
+    inline int nonZeros() const { return size(); }
     /** \returns true if either the number of rows or the number of columns is equal to 1.
       * In other words, this function returns
       * \code rows()==1 || cols()==1 \endcode
@@ -645,8 +639,9 @@ template<typename Derived> class MatrixBase
     const CwiseBinaryOp<CustomBinaryOp, Derived, OtherDerived>
     binaryExpr(const MatrixBase<OtherDerived> &other, const CustomBinaryOp& func = CustomBinaryOp()) const;
 
-
+    
     Scalar sum() const;
+    Scalar mean() const;
     Scalar trace() const;
 
     Scalar prod() const;
@@ -811,6 +806,24 @@ template<typename Derived> class MatrixBase
     #ifdef EIGEN_MATRIXBASE_PLUGIN
     #include EIGEN_MATRIXBASE_PLUGIN
     #endif
+
+  protected:
+    /** Default constructor. Do nothing. */
+    MatrixBase()
+    {
+      /* Just checks for self-consistency of the flags.
+       * Only do it when debugging Eigen, as this borders on paranoiac and could slow compilation down
+       */
+#ifdef EIGEN_INTERNAL_DEBUGGING
+      EIGEN_STATIC_ASSERT(ei_are_flags_consistent<Flags>::ret,
+                          INVALID_MATRIXBASE_TEMPLATE_PARAMETERS)
+#endif
+    }
+    
+  private:
+    explicit MatrixBase(int);
+    MatrixBase(int,int);
+    template<typename OtherDerived> explicit MatrixBase(const MatrixBase<OtherDerived>&);
 };
 
 #endif // EIGEN_MATRIXBASE_H

Eigen/src/Core/NumTraits.h

@@ -52,6 +52,7 @@ template<> struct NumTraits<int>
 {
   typedef int Real;
   typedef double FloatingPoint;
+  typedef int Nested;
   enum {
     IsComplex = 0,
     HasFloatingPoint = 0,
@@ -65,6 +66,7 @@ template<> struct NumTraits<float>
 {
   typedef float Real;
   typedef float FloatingPoint;
+  typedef float Nested;
   enum {
     IsComplex = 0,
     HasFloatingPoint = 1,
@@ -78,6 +80,7 @@ template<> struct NumTraits<double>
 {
   typedef double Real;
   typedef double FloatingPoint;
+  typedef double Nested;
   enum {
     IsComplex = 0,
     HasFloatingPoint = 1,
@@ -91,6 +94,7 @@ template<typename _Real> struct NumTraits<std::complex<_Real> >
 {
   typedef _Real Real;
   typedef std::complex<_Real> FloatingPoint;
+  typedef std::complex<_Real> Nested;
   enum {
     IsComplex = 1,
     HasFloatingPoint = NumTraits<Real>::HasFloatingPoint,
@@ -104,6 +108,7 @@ template<> struct NumTraits<long long int>
 {
   typedef long long int Real;
   typedef long double FloatingPoint;
+  typedef long long int Nested;
   enum {
     IsComplex = 0,
     HasFloatingPoint = 0,
@@ -117,6 +122,7 @@ template<> struct NumTraits<long double>
 {
   typedef long double Real;
   typedef long double FloatingPoint;
+  typedef long double Nested;
   enum {
     IsComplex = 0,
     HasFloatingPoint = 1,
@@ -130,6 +136,7 @@ template<> struct NumTraits<bool>
 {
   typedef bool Real;
   typedef float FloatingPoint;
+  typedef bool Nested;
   enum {
     IsComplex = 0,
     HasFloatingPoint = 0,

Eigen/src/Core/Redux.h

@@ -342,7 +342,7 @@ MatrixBase<Derived>::maxCoeff() const
 
 /** \returns the sum of all coefficients of *this
   *
-  * \sa trace(), prod()
+  * \sa trace(), prod(), mean()
   */
 template<typename Derived>
 EIGEN_STRONG_INLINE typename ei_traits<Derived>::Scalar
@@ -351,12 +351,23 @@ MatrixBase<Derived>::sum() const
   return this->redux(Eigen::ei_scalar_sum_op<Scalar>());
 }
 
+/** \returns the mean of all coefficients of *this
+*
+* \sa trace(), prod(), sum()
+*/
+template<typename Derived>
+EIGEN_STRONG_INLINE typename ei_traits<Derived>::Scalar
+MatrixBase<Derived>::mean() const
+{
+  return this->redux(Eigen::ei_scalar_sum_op<Scalar>()) / this->size();
+}
+
 /** \returns the product of all coefficients of *this
   *
   * Example: \include MatrixBase_prod.cpp
   * Output: \verbinclude MatrixBase_prod.out
   *
-  * \sa sum()
+  * \sa sum(), mean(), trace()
   */
 template<typename Derived>
 EIGEN_STRONG_INLINE typename ei_traits<Derived>::Scalar

Eigen/src/Core/Transpose.h

@@ -69,7 +69,6 @@ template<typename MatrixType> class Transpose
 
     inline int rows() const { return m_matrix.cols(); }
     inline int cols() const { return m_matrix.rows(); }
-    inline int nonZeros() const { return m_matrix.nonZeros(); }
     inline int stride() const { return m_matrix.stride(); }
     inline Scalar* data() { return m_matrix.data(); }
     inline const Scalar* data() const { return m_matrix.data(); }
@@ -354,5 +353,5 @@ lazyAssign(const CwiseBinaryOp<ei_scalar_sum_op<Scalar>,DerivedA,CwiseUnaryOp<ei
   return lazyAssign(static_cast<const MatrixBase<CwiseBinaryOp<ei_scalar_sum_op<Scalar>,DerivedA,CwiseUnaryOp<ei_scalar_conjugate_op<Scalar>, NestByValue<Eigen::Transpose<DerivedB> > > > >& >(other));
 }
 #endif
-    
+
 #endif // EIGEN_TRANSPOSE_H

Eigen/src/Core/arch/SSE/PacketMath.h

@@ -220,8 +220,14 @@ template<> EIGEN_STRONG_INLINE void ei_pstoreu<double>(double* to, const Packet2
 template<> EIGEN_STRONG_INLINE void ei_pstoreu<float>(float*  to, const Packet4f& from) { ei_pstoreu((double*)to, _mm_castps_pd(from)); }
 template<> EIGEN_STRONG_INLINE void ei_pstoreu<int>(int*      to, const Packet4i& from) { ei_pstoreu((double*)to, _mm_castsi128_pd(from)); }
 
-#ifdef _MSC_VER
-// this fix internal compilation error
+#if defined(_MSC_VER) && (_MSC_VER <= 1500) && defined(_WIN64)
+// The temporary variable fixes an internal compilation error.
+// Direct of the struct members fixed bug #62.
+template<> EIGEN_STRONG_INLINE float  ei_pfirst<Packet4f>(const Packet4f& a) { return a.m128_f32[0]; }
+template<> EIGEN_STRONG_INLINE double ei_pfirst<Packet2d>(const Packet2d& a) { return a.m128d_f64[0]; }
+template<> EIGEN_STRONG_INLINE int    ei_pfirst<Packet4i>(const Packet4i& a) { int x = _mm_cvtsi128_si32(a); return x; }
+#elif defined(_MSC_VER) && (_MSC_VER <= 1500)
+// The temporary variable fixes an internal compilation error.
 template<> EIGEN_STRONG_INLINE float  ei_pfirst<Packet4f>(const Packet4f& a) { float x = _mm_cvtss_f32(a); return x; }
 template<> EIGEN_STRONG_INLINE double ei_pfirst<Packet2d>(const Packet2d& a) { double x = _mm_cvtsd_f64(a); return x; }
 template<> EIGEN_STRONG_INLINE int    ei_pfirst<Packet4i>(const Packet4i& a) { int x = _mm_cvtsi128_si32(a); return x; }

Eigen/src/Core/util/Memory.h

@@ -83,7 +83,7 @@ inline void* ei_aligned_malloc(size_t size)
     ei_assert(false && "heap allocation is forbidden (EIGEN_NO_MALLOC is defined)");
   #endif
 
-  void *result;  
+  void *result;
   #if !EIGEN_ALIGN
     result = malloc(size);
   #elif EIGEN_MALLOC_ALREADY_ALIGNED
@@ -97,7 +97,7 @@ inline void* ei_aligned_malloc(size_t size)
   #else
     result = ei_handmade_aligned_malloc(size);
   #endif
-    
+
   #ifdef EIGEN_EXCEPTIONS
     if(result == 0)
       throw std::bad_alloc();
@@ -324,34 +324,34 @@ public:
         typedef aligned_allocator<U> other;
     };
 
-    pointer address( reference value ) const 
+    pointer address( reference value ) const
     {
         return &value;
     }
 
-    const_pointer address( const_reference value ) const 
+    const_pointer address( const_reference value ) const
     {
         return &value;
     }
 
-    aligned_allocator() throw() 
+    aligned_allocator() throw()
     {
     }
 
-    aligned_allocator( const aligned_allocator& ) throw() 
+    aligned_allocator( const aligned_allocator& ) throw()
     {
     }
 
     template<class U>
-    aligned_allocator( const aligned_allocator<U>& ) throw() 
+    aligned_allocator( const aligned_allocator<U>& ) throw()
     {
     }
 
-    ~aligned_allocator() throw() 
+    ~aligned_allocator() throw()
     {
     }
 
-    size_type max_size() const throw() 
+    size_type max_size() const throw()
     {
         return std::numeric_limits<size_type>::max();
     }
@@ -362,24 +362,24 @@ public:
         return static_cast<pointer>( ei_aligned_malloc( num * sizeof(T) ) );
     }
 
-    void construct( pointer p, const T& value ) 
+    void construct( pointer p, const T& value )
     {
         ::new( p ) T( value );
     }
 
-    void destroy( pointer p ) 
+    void destroy( pointer p )
     {
         p->~T();
     }
 
-    void deallocate( pointer p, size_type /*num*/ ) 
+    void deallocate( pointer p, size_type /*num*/ )
     {
         ei_aligned_free( p );
     }
-    
+
     bool operator!=(const aligned_allocator<T>& other) const
     { return false; }
-    
+
     bool operator==(const aligned_allocator<T>& other) const
     { return true; }
 };

Eigen/src/Core/util/Meta.h

@@ -64,6 +64,13 @@ template<typename T> struct ei_cleantype<T&>        { typedef typename ei_cleant
 template<typename T> struct ei_cleantype<const T*>  { typedef typename ei_cleantype<T>::type type; };
 template<typename T> struct ei_cleantype<T*>        { typedef typename ei_cleantype<T>::type type; };
 
+template<typename T> struct ei_makeconst            { typedef const T type;  };
+template<typename T> struct ei_makeconst<const T>   { typedef const T type;  };
+template<typename T> struct ei_makeconst<T&>        { typedef const T& type; };
+template<typename T> struct ei_makeconst<const T&>  { typedef const T& type; };
+template<typename T> struct ei_makeconst<T*>        { typedef const T* type; };
+template<typename T> struct ei_makeconst<const T*>  { typedef const T* type; };
+
 /** \internal Allows to enable/disable an overload
   * according to a compile time condition.
   */

Eigen/src/Core/util/StaticAssert.h

@@ -76,6 +76,7 @@
         THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES,
         THIS_METHOD_IS_ONLY_FOR_ROW_MAJOR_MATRICES,
         INVALID_MATRIX_TEMPLATE_PARAMETERS,
+        INVALID_MATRIXBASE_TEMPLATE_PARAMETERS,
         BOTH_MATRICES_MUST_HAVE_THE_SAME_STORAGE_ORDER,
         THIS_METHOD_IS_ONLY_FOR_DIAGONAL_MATRIX,
         THE_MATRIX_OR_EXPRESSION_THAT_YOU_PASSED_DOES_NOT_HAVE_THE_EXPECTED_TYPE,

Eigen/src/Core/util/XprHelper.h

@@ -1,4 +1,4 @@
-// This file is part of Eigen, a lightweight C++ template library
+// // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
 // Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>

Eigen/src/Eigenvalues/ComplexSchur.h

@@ -167,10 +167,11 @@ void ComplexSchur<MatrixType>::compute(const MatrixType& matrix, bool skipU)
     //locate the range in which to iterate
     while(iu > 0)
     {
-      d = ei_norm1(m_matT.coeffRef(iu,iu)) + ei_norm1(m_matT.coeffRef(iu-1,iu-1));
-      sd = ei_norm1(m_matT.coeffRef(iu,iu-1));
+      d = ei_norm1(m_matT.coeff(iu,iu)) + ei_norm1(m_matT.coeff(iu-1,iu-1));
+      sd = ei_norm1(m_matT.coeff(iu,iu-1));
 
-      if(sd >= eps * d) break; // FIXME : precision criterion ??
+      if(!ei_isMuchSmallerThan(sd,d,eps))
+        break;
 
       m_matT.coeffRef(iu,iu-1) = Complex(0);
       iter = 0;
@@ -187,13 +188,14 @@ void ComplexSchur<MatrixType>::compute(const MatrixType& matrix, bool skipU)
     }
 
     il = iu-1;
-    while( il > 0 )
+    while(il > 0)
     {
       // check if the current 2x2 block on the diagonal is upper triangular
-      d = ei_norm1(m_matT.coeffRef(il,il)) + ei_norm1(m_matT.coeffRef(il-1,il-1));
-      sd = ei_norm1(m_matT.coeffRef(il,il-1));
+      d = ei_norm1(m_matT.coeff(il,il)) + ei_norm1(m_matT.coeff(il-1,il-1));
+      sd = ei_norm1(m_matT.coeff(il,il-1));
 
-      if(sd < eps * d) break; // FIXME : precision criterion ??
+      if(ei_isMuchSmallerThan(sd,d,eps))
+        break;
 
       --il;
     }

Eigen/src/Geometry/Quaternion.h

@@ -26,6 +26,155 @@
 #ifndef EIGEN_QUATERNION_H
 #define EIGEN_QUATERNION_H
 
+/***************************************************************************
+* Definition of QuaternionBase<Derived>
+* The implementation is at the end of the file
+***************************************************************************/
+
+template<typename Other,
+         int OtherRows=Other::RowsAtCompileTime,
+         int OtherCols=Other::ColsAtCompileTime>
+struct ei_quaternionbase_assign_impl;
+
+template<class Derived>
+class QuaternionBase : public RotationBase<Derived, 3>
+{
+  typedef RotationBase<Derived, 3> Base;
+public:
+  using Base::operator*;
+  using Base::derived;
+
+  typedef typename ei_traits<Derived>::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  typedef typename ei_traits<Derived>::Coefficients Coefficients;
+
+ // typedef typename Matrix<Scalar,4,1> Coefficients;
+  /** the type of a 3D vector */
+  typedef Matrix<Scalar,3,1> Vector3;
+  /** the equivalent rotation matrix type */
+  typedef Matrix<Scalar,3,3> Matrix3;
+  /** the equivalent angle-axis type */
+  typedef AngleAxis<Scalar> AngleAxisType;
+
+
+
+  /** \returns the \c x coefficient */
+  inline Scalar x() const { return this->derived().coeffs().coeff(0); }
+  /** \returns the \c y coefficient */
+  inline Scalar y() const { return this->derived().coeffs().coeff(1); }
+  /** \returns the \c z coefficient */
+  inline Scalar z() const { return this->derived().coeffs().coeff(2); }
+  /** \returns the \c w coefficient */
+  inline Scalar w() const { return this->derived().coeffs().coeff(3); }
+
+  /** \returns a reference to the \c x coefficient */
+  inline Scalar& x() { return this->derived().coeffs().coeffRef(0); }
+  /** \returns a reference to the \c y coefficient */
+  inline Scalar& y() { return this->derived().coeffs().coeffRef(1); }
+  /** \returns a reference to the \c z coefficient */
+  inline Scalar& z() { return this->derived().coeffs().coeffRef(2); }
+  /** \returns a reference to the \c w coefficient */
+  inline Scalar& w() { return this->derived().coeffs().coeffRef(3); }
+
+  /** \returns a read-only vector expression of the imaginary part (x,y,z) */
+  inline const VectorBlock<Coefficients,3> vec() const { return coeffs().template start<3>(); }
+
+  /** \returns a vector expression of the imaginary part (x,y,z) */
+  inline VectorBlock<Coefficients,3> vec() { return coeffs().template start<3>(); }
+
+  /** \returns a read-only vector expression of the coefficients (x,y,z,w) */
+  inline const typename ei_traits<Derived>::Coefficients& coeffs() const { return derived().coeffs(); }
+
+  /** \returns a vector expression of the coefficients (x,y,z,w) */
+  inline typename ei_traits<Derived>::Coefficients& coeffs() { return derived().coeffs(); }
+
+  template<class OtherDerived> Derived& operator=(const QuaternionBase<OtherDerived>& other);
+
+// disabled this copy operator as it is giving very strange compilation errors when compiling
+// test_stdvector with GCC 4.4.2. This looks like a GCC bug though, so feel free to re-enable it if it's
+// useful; however notice that we already have the templated operator= above and e.g. in MatrixBase
+// we didn't have to add, in addition to templated operator=, such a non-templated copy operator.
+//  Derived& operator=(const QuaternionBase& other)
+//  { return operator=<Derived>(other); }
+
+  Derived& operator=(const AngleAxisType& aa);
+  template<class OtherDerived> Derived& operator=(const MatrixBase<OtherDerived>& m);
+
+  /** \returns a quaternion representing an identity rotation
+    * \sa MatrixBase::Identity()
+    */
+  inline static Quaternion<Scalar> Identity() { return Quaternion<Scalar>(1, 0, 0, 0); }
+
+  /** \sa QuaternionBase::Identity(), MatrixBase::setIdentity()
+    */
+  inline QuaternionBase& setIdentity() { coeffs() << 0, 0, 0, 1; return *this; }
+
+  /** \returns the squared norm of the quaternion's coefficients
+    * \sa QuaternionBase::norm(), MatrixBase::squaredNorm()
+    */
+  inline Scalar squaredNorm() const { return coeffs().squaredNorm(); }
+
+  /** \returns the norm of the quaternion's coefficients
+    * \sa QuaternionBase::squaredNorm(), MatrixBase::norm()
+    */
+  inline Scalar norm() const { return coeffs().norm(); }
+
+  /** Normalizes the quaternion \c *this
+    * \sa normalized(), MatrixBase::normalize() */
+  inline void normalize() { coeffs().normalize(); }
+  /** \returns a normalized copy of \c *this
+    * \sa normalize(), MatrixBase::normalized() */
+  inline Quaternion<Scalar> normalized() const { return Quaternion<Scalar>(coeffs().normalized()); }
+
+    /** \returns the dot product of \c *this and \a other
+    * Geometrically speaking, the dot product of two unit quaternions
+    * corresponds to the cosine of half the angle between the two rotations.
+    * \sa angularDistance()
+    */
+  template<class OtherDerived> inline Scalar dot(const QuaternionBase<OtherDerived>& other) const { return coeffs().dot(other.coeffs()); }
+
+  template<class OtherDerived> inline Scalar angularDistance(const QuaternionBase<OtherDerived>& other) const;
+
+  Matrix3 toRotationMatrix() const;
+
+  template<typename Derived1, typename Derived2>
+  Derived& setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b);
+
+  template<class OtherDerived> inline Quaternion<Scalar> operator* (const QuaternionBase<OtherDerived>& q) const;
+  template<class OtherDerived> inline Derived& operator*= (const QuaternionBase<OtherDerived>& q);
+
+  Quaternion<Scalar> inverse() const;
+  Quaternion<Scalar> conjugate() const;
+
+  template<class OtherDerived> Quaternion<Scalar> slerp(Scalar t, const QuaternionBase<OtherDerived>& other) const;
+
+  /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+    * determined by \a prec.
+    *
+    * \sa MatrixBase::isApprox() */
+  template<class OtherDerived>
+  bool isApprox(const QuaternionBase<OtherDerived>& other, RealScalar prec = precision<Scalar>()) const
+  { return coeffs().isApprox(other.coeffs(), prec); }
+
+  Vector3 _transformVector(Vector3 v) const;
+
+  /** \returns \c *this with scalar type casted to \a NewScalarType
+    *
+    * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+    * then this function smartly returns a const reference to \c *this.
+    */
+  template<typename NewScalarType>
+  inline typename ei_cast_return_type<Derived,Quaternion<NewScalarType> >::type cast() const
+  {
+    return typename ei_cast_return_type<Derived,Quaternion<NewScalarType> >::type(
+      coeffs().template cast<NewScalarType>());
+  }
+};
+
+/***************************************************************************
+* Definition/implementation of Quaternion<Scalar>
+***************************************************************************/
+
 /** \geometry_module \ingroup Geometry_Module
   *
   * \class Quaternion
@@ -48,152 +197,13 @@
   * \sa  class AngleAxis, class Transform
   */
 
-template<typename Other,
-         int OtherRows=Other::RowsAtCompileTime,
-         int OtherCols=Other::ColsAtCompileTime>
-struct ei_quaternionbase_assign_impl;
-
-template<typename Scalar> class Quaternion; // [XXX] => remove when Quaternion becomes Quaternion
-
-template<typename Derived>
-struct ei_traits<QuaternionBase<Derived> >
-{
-  typedef typename ei_traits<Derived>::Scalar Scalar;
-  enum {
-    PacketAccess = ei_traits<Derived>::PacketAccess
-  };
-};
-
-template<class Derived>
-class QuaternionBase : public RotationBase<Derived, 3>
-{
-  typedef RotationBase<Derived, 3> Base;
-public:
-  using Base::operator*;
-
-  typedef typename ei_traits<QuaternionBase<Derived> >::Scalar Scalar;
-  typedef typename NumTraits<Scalar>::Real RealScalar;
-
- // typedef typename Matrix<Scalar,4,1> Coefficients;
-  /** the type of a 3D vector */
-  typedef Matrix<Scalar,3,1> Vector3;
-  /** the equivalent rotation matrix type */
-  typedef Matrix<Scalar,3,3> Matrix3;
-  /** the equivalent angle-axis type */
-  typedef AngleAxis<Scalar> AngleAxisType;
-
-  /** \returns the \c x coefficient */
-  inline Scalar x() const { return this->derived().coeffs().coeff(0); }
-  /** \returns the \c y coefficient */
-  inline Scalar y() const { return this->derived().coeffs().coeff(1); }
-  /** \returns the \c z coefficient */
-  inline Scalar z() const { return this->derived().coeffs().coeff(2); }
-  /** \returns the \c w coefficient */
-  inline Scalar w() const { return this->derived().coeffs().coeff(3); }
-
-  /** \returns a reference to the \c x coefficient */
-  inline Scalar& x() { return this->derived().coeffs().coeffRef(0); }
-  /** \returns a reference to the \c y coefficient */
-  inline Scalar& y() { return this->derived().coeffs().coeffRef(1); }
-  /** \returns a reference to the \c z coefficient */
-  inline Scalar& z() { return this->derived().coeffs().coeffRef(2); }
-  /** \returns a reference to the \c w coefficient */
-  inline Scalar& w() { return this->derived().coeffs().coeffRef(3); }
-
-  /** \returns a read-only vector expression of the imaginary part (x,y,z) */
-  inline const VectorBlock<typename ei_traits<Derived>::Coefficients,3> vec() const { return this->derived().coeffs().template start<3>(); }
-
-  /** \returns a vector expression of the imaginary part (x,y,z) */
-  inline VectorBlock<typename ei_traits<Derived>::Coefficients,3> vec() { return this->derived().coeffs().template start<3>(); }
-
-  /** \returns a read-only vector expression of the coefficients (x,y,z,w) */
-  inline const typename ei_traits<Derived>::Coefficients& coeffs() const { return this->derived().coeffs(); }
-
-  /** \returns a vector expression of the coefficients (x,y,z,w) */
-  inline typename ei_traits<Derived>::Coefficients& coeffs() { return this->derived().coeffs(); }
-
-  template<class OtherDerived> QuaternionBase& operator=(const QuaternionBase<OtherDerived>& other);
-  QuaternionBase& operator=(const AngleAxisType& aa);
-  template<class OtherDerived>
-  QuaternionBase& operator=(const MatrixBase<OtherDerived>& m);
-
-  /** \returns a quaternion representing an identity rotation
-    * \sa MatrixBase::Identity()
-    */
-  inline static Quaternion<Scalar> Identity() { return Quaternion<Scalar>(1, 0, 0, 0); }
-
-  /** \sa Quaternion2::Identity(), MatrixBase::setIdentity()
-    */
-  inline QuaternionBase& setIdentity() { coeffs() << 0, 0, 0, 1; return *this; }
-
-  /** \returns the squared norm of the quaternion's coefficients
-    * \sa Quaternion2::norm(), MatrixBase::squaredNorm()
-    */
-  inline Scalar squaredNorm() const { return coeffs().squaredNorm(); }
-
-  /** \returns the norm of the quaternion's coefficients
-    * \sa Quaternion2::squaredNorm(), MatrixBase::norm()
-    */
-  inline Scalar norm() const { return coeffs().norm(); }
-
-  /** Normalizes the quaternion \c *this
-    * \sa normalized(), MatrixBase::normalize() */
-  inline void normalize() { coeffs().normalize(); }
-  /** \returns a normalized version of \c *this
-    * \sa normalize(), MatrixBase::normalized() */
-  inline Quaternion<Scalar> normalized() const { return Quaternion<Scalar>(coeffs().normalized()); }
-
-    /** \returns the dot product of \c *this and \a other
-    * Geometrically speaking, the dot product of two unit quaternions
-    * corresponds to the cosine of half the angle between the two rotations.
-    * \sa angularDistance()
-    */
-  template<class OtherDerived> inline Scalar dot(const QuaternionBase<OtherDerived>& other) const { return coeffs().dot(other.coeffs()); }
-
-  template<class OtherDerived> inline Scalar angularDistance(const QuaternionBase<OtherDerived>& other) const;
-
-  Matrix3 toRotationMatrix(void) const;
-
-  template<typename Derived1, typename Derived2>
-  QuaternionBase& setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b);
-
-  template<class OtherDerived> inline Quaternion<Scalar> operator* (const QuaternionBase<OtherDerived>& q) const;
-  template<class OtherDerived> inline QuaternionBase& operator*= (const QuaternionBase<OtherDerived>& q);
-
-  Quaternion<Scalar> inverse(void) const;
-  Quaternion<Scalar> conjugate(void) const;
-
-  template<class OtherDerived> Quaternion<Scalar> slerp(Scalar t, const QuaternionBase<OtherDerived>& other) const;
-
-  /** \returns \c true if \c *this is approximately equal to \a other, within the precision
-    * determined by \a prec.
-    *
-    * \sa MatrixBase::isApprox() */
-  bool isApprox(const QuaternionBase& other, RealScalar prec = precision<Scalar>()) const
-  { return coeffs().isApprox(other.coeffs(), prec); }
-
-  Vector3 _transformVector(Vector3 v) const;
-
-  /** \returns \c *this with scalar type casted to \a NewScalarType
-    *
-    * Note that if \a NewScalarType is equal to the current scalar type of \c *this
-    * then this function smartly returns a const reference to \c *this.
-    */
-  template<typename NewScalarType>
-  inline typename ei_cast_return_type<Derived,Quaternion<NewScalarType> >::type cast() const
-  {
-    return typename ei_cast_return_type<Derived,Quaternion<NewScalarType> >::type(
-      coeffs().template cast<NewScalarType>());
-  }
-};
-
 template<typename _Scalar>
 struct ei_traits<Quaternion<_Scalar> >
 {
   typedef _Scalar Scalar;
   typedef Matrix<_Scalar,4,1> Coefficients;
   enum{
-    PacketAccess = Aligned 
+    PacketAccess = Aligned
   };
 };
 
@@ -239,7 +249,7 @@ public:
   explicit inline Quaternion(const MatrixBase<Derived>& other) { *this = other; }
 
   /** Copy constructor with scalar type conversion */
-  template<class Derived>
+  template<typename Derived>
   inline explicit Quaternion(const QuaternionBase<Derived>& other)
   { m_coeffs = other.coeffs().template cast<Scalar>(); }
 
@@ -250,16 +260,29 @@ protected:
   Coefficients m_coeffs;
 };
 
-/* ########### Map<Quaternion> */
+/** \ingroup Geometry_Module
+  * single precision quaternion type */
+typedef Quaternion<float> Quaternionf;
+/** \ingroup Geometry_Module
+  * double precision quaternion type */
+typedef Quaternion<double> Quaterniond;
+
+/***************************************************************************
+* Specialization of Map<Quaternion<Scalar>>
+***************************************************************************/
 
 /** \class Map<Quaternion>
   * \nonstableyet
   *
-  * \brief Expression of a quaternion
+  * \brief Expression of a quaternion from a memory buffer
   *
-  * \param Scalar the type of the vector of diagonal coefficients
+  * \param _Scalar the type of the Quaternion coefficients
+  * \param PacketAccess see class Map
   *
-  * \sa class Quaternion, class QuaternionBase
+  * This is a specialization of class Map for Quaternion. This class allows to view
+  * a 4 scalar memory buffer as an Eigen's  Quaternion object.
+  *
+  * \sa class Map, class Quaternion, class QuaternionBase
   */
 template<typename _Scalar, int _PacketAccess>
 struct ei_traits<Map<Quaternion<_Scalar>, _PacketAccess> >:
@@ -273,15 +296,23 @@ ei_traits<Quaternion<_Scalar> >
 };
 
 template<typename _Scalar, int PacketAccess>
-class Map<Quaternion<_Scalar>, PacketAccess > : public QuaternionBase<Map<Quaternion<_Scalar>, PacketAccess> >, ei_no_assignment_operator {
+class Map<Quaternion<_Scalar>, PacketAccess >
+  : public QuaternionBase<Map<Quaternion<_Scalar>, PacketAccess> >,
+    ei_no_assignment_operator
+{
   public:
-    
+
     typedef _Scalar Scalar;
+    typedef typename ei_traits<Map>::Coefficients Coefficients;
 
-    typedef typename ei_traits<Map<Quaternion<Scalar>, PacketAccess> >::Coefficients Coefficients;
+    /** Constructs a Mapped Quaternion object from the pointer \a coeffs
+      *
+      * The pointer \a coeffs must reference the four coeffecients of Quaternion in the following order:
+      * \code *coeffs == {x, y, z, w} \endcode
+      *
+      * If the template paramter PacketAccess is set to Aligned, then the pointer coeffs must be aligned. */
+    inline Map(const Scalar* coeffs) : m_coeffs(coeffs) {}
 
-    inline Map<Quaternion<Scalar>, PacketAccess >(const Scalar* coeffs) : m_coeffs(coeffs) {}
-    
     inline Coefficients& coeffs() { return m_coeffs;}
     inline const Coefficients& coeffs() const { return m_coeffs;}
 
@@ -289,15 +320,20 @@ class Map<Quaternion<_Scalar>, PacketAccess > : public QuaternionBase<Map<Quater
     Coefficients m_coeffs;
 };
 
-typedef Map<Quaternion<double> > QuaternionMapd;
-typedef Map<Quaternion<float> > QuaternionMapf;
-typedef Map<Quaternion<double>, Aligned> QuaternionMapAlignedd;
-typedef Map<Quaternion<float>, Aligned> QuaternionMapAlignedf;
+typedef Map<Quaternion<double> >          QuaternionMapd;
+typedef Map<Quaternion<float> >           QuaternionMapf;
+typedef Map<Quaternion<double>, Aligned>  QuaternionMapAlignedd;
+typedef Map<Quaternion<float>, Aligned>   QuaternionMapAlignedf;
+
+/***************************************************************************
+* Implementation of QuaternionBase methods
+***************************************************************************/
 
 // Generic Quaternion * Quaternion product
-template<int Arch, class Derived, class OtherDerived, typename Scalar, int PacketAccess> struct ei_quat_product
+// This product can be specialized for a given architecture via the Arch template argument.
+template<int Arch, class Derived1, class Derived2, typename Scalar, int PacketAccess> struct ei_quat_product
 {
-  inline static Quaternion<Scalar> run(const QuaternionBase<Derived>& a, const QuaternionBase<OtherDerived>& b){
+  inline static Quaternion<Scalar> run(const QuaternionBase<Derived1>& a, const QuaternionBase<Derived2>& b){
     return Quaternion<Scalar>
     (
       a.w() * b.w() - a.x() * b.x() - a.y() * b.y() - a.z() * b.z(),
@@ -311,21 +347,22 @@ template<int Arch, class Derived, class OtherDerived, typename Scalar, int Packe
 /** \returns the concatenation of two rotations as a quaternion-quaternion product */
 template <class Derived>
 template <class OtherDerived>
-inline Quaternion<typename ei_traits<QuaternionBase<Derived> >::Scalar> QuaternionBase<Derived>::operator* (const QuaternionBase<OtherDerived>& other) const
+inline Quaternion<typename ei_traits<Derived>::Scalar>
+QuaternionBase<Derived>::operator* (const QuaternionBase<OtherDerived>& other) const
 {
   EIGEN_STATIC_ASSERT((ei_is_same_type<typename Derived::Scalar, typename OtherDerived::Scalar>::ret),
    YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
-   return ei_quat_product<EiArch, Derived, OtherDerived, 
-                          typename ei_traits<Derived>::Scalar,
-                          ei_traits<Derived>::PacketAccess && ei_traits<OtherDerived>::PacketAccess>::run(*this, other);
+  return ei_quat_product<EiArch, Derived, OtherDerived,
+                         typename ei_traits<Derived>::Scalar,
+                         ei_traits<Derived>::PacketAccess && ei_traits<OtherDerived>::PacketAccess>::run(*this, other);
 }
 
 /** \sa operator*(Quaternion) */
 template <class Derived>
 template <class OtherDerived>
-inline QuaternionBase<Derived>& QuaternionBase<Derived>::operator*= (const QuaternionBase<OtherDerived>& other)
+inline Derived& QuaternionBase<Derived>::operator*= (const QuaternionBase<OtherDerived>& other)
 {
-  return (*this = *this * other);
+  return (derived() = derived() * other.derived());
 }
 
 /** Rotation of a vector by a quaternion.
@@ -350,21 +387,21 @@ QuaternionBase<Derived>::_transformVector(Vector3 v) const
 
 template<class Derived>
 template<class OtherDerived>
-inline QuaternionBase<Derived>& QuaternionBase<Derived>::operator=(const QuaternionBase<OtherDerived>& other)
+inline Derived& QuaternionBase<Derived>::operator=(const QuaternionBase<OtherDerived>& other)
 {
   coeffs() = other.coeffs();
-  return *this;
+  return derived();
 }
 
 /** Set \c *this from an angle-axis \a aa and returns a reference to \c *this
   */
 template<class Derived>
-inline QuaternionBase<Derived>& QuaternionBase<Derived>::operator=(const AngleAxisType& aa)
+inline Derived& QuaternionBase<Derived>::operator=(const AngleAxisType& aa)
 {
   Scalar ha = Scalar(0.5)*aa.angle(); // Scalar(0.5) to suppress precision loss warnings
   this->w() = ei_cos(ha);
   this->vec() = ei_sin(ha) * aa.axis();
-  return *this;
+  return derived();
 }
 
 /** Set \c *this from the expression \a xpr:
@@ -375,12 +412,12 @@ inline QuaternionBase<Derived>& QuaternionBase<Derived>::operator=(const AngleAx
 
 template<class Derived>
 template<class MatrixDerived>
-inline QuaternionBase<Derived>& QuaternionBase<Derived>::operator=(const MatrixBase<MatrixDerived>& xpr)
+inline Derived& QuaternionBase<Derived>::operator=(const MatrixBase<MatrixDerived>& xpr)
 {
   EIGEN_STATIC_ASSERT((ei_is_same_type<typename Derived::Scalar, typename MatrixDerived::Scalar>::ret),
    YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
   ei_quaternionbase_assign_impl<MatrixDerived>::run(*this, xpr.derived());
-  return *this;
+  return derived();
 }
 
 /** Convert the quaternion to a 3x3 rotation matrix. The quaternion is required to
@@ -434,7 +471,7 @@ QuaternionBase<Derived>::toRotationMatrix(void) const
   */
 template<class Derived>
 template<typename Derived1, typename Derived2>
-inline QuaternionBase<Derived>& QuaternionBase<Derived>::setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)
+inline Derived& QuaternionBase<Derived>::setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)
 {
   Vector3 v0 = a.normalized();
   Vector3 v1 = b.normalized();
@@ -458,7 +495,7 @@ inline QuaternionBase<Derived>& QuaternionBase<Derived>::setFromTwoVectors(const
     Scalar w2 = (Scalar(1)+c)*Scalar(0.5);
     this->w() = ei_sqrt(w2);
     this->vec() = axis * ei_sqrt(Scalar(1) - w2);
-    return *this;
+    return derived();
   }
   Vector3 axis = v0.cross(v1);
   Scalar s = ei_sqrt((Scalar(1)+c)*Scalar(2));
@@ -466,17 +503,17 @@ inline QuaternionBase<Derived>& QuaternionBase<Derived>::setFromTwoVectors(const
   this->vec() = axis * invs;
   this->w() = s * Scalar(0.5);
 
-  return *this;
+  return derived();
 }
 
 /** \returns the multiplicative inverse of \c *this
   * Note that in most cases, i.e., if you simply want the opposite rotation,
   * and/or the quaternion is normalized, then it is enough to use the conjugate.
   *
-  * \sa Quaternion2::conjugate()
+  * \sa QuaternionBase::conjugate()
   */
 template <class Derived>
-inline Quaternion<typename ei_traits<QuaternionBase<Derived> >::Scalar> QuaternionBase<Derived>::inverse() const
+inline Quaternion<typename ei_traits<Derived>::Scalar> QuaternionBase<Derived>::inverse() const
 {
   // FIXME should this function be called multiplicativeInverse and conjugate() be called inverse() or opposite()  ??
   Scalar n2 = this->squaredNorm();
@@ -485,7 +522,7 @@ inline Quaternion<typename ei_traits<QuaternionBase<Derived> >::Scalar> Quaterni
   else
   {
     // return an invalid result to flag the error
-    return Quaternion<Scalar>(ei_traits<Derived>::Coefficients::Zero());
+    return Quaternion<Scalar>(Coefficients::Zero());
   }
 }
 
@@ -496,7 +533,8 @@ inline Quaternion<typename ei_traits<QuaternionBase<Derived> >::Scalar> Quaterni
   * \sa Quaternion2::inverse()
   */
 template <class Derived>
-inline Quaternion<typename ei_traits<QuaternionBase<Derived> >::Scalar> QuaternionBase<Derived>::conjugate() const
+inline Quaternion<typename ei_traits<Derived>::Scalar>
+QuaternionBase<Derived>::conjugate() const
 {
   return Quaternion<Scalar>(this->w(),-this->x(),-this->y(),-this->z());
 }
@@ -506,11 +544,12 @@ inline Quaternion<typename ei_traits<QuaternionBase<Derived> >::Scalar> Quaterni
   */
 template <class Derived>
 template <class OtherDerived>
-inline typename ei_traits<QuaternionBase<Derived> >::Scalar QuaternionBase<Derived>::angularDistance(const QuaternionBase<OtherDerived>& other) const
+inline typename ei_traits<Derived>::Scalar
+QuaternionBase<Derived>::angularDistance(const QuaternionBase<OtherDerived>& other) const
 {
   double d = ei_abs(this->dot(other));
   if (d>=1.0)
-    return 0;
+    return Scalar(0);
   return Scalar(2) * std::acos(d);
 }
 
@@ -519,13 +558,14 @@ inline typename ei_traits<QuaternionBase<Derived> >::Scalar QuaternionBase<Deriv
   */
 template <class Derived>
 template <class OtherDerived>
-Quaternion<typename ei_traits<QuaternionBase<Derived> >::Scalar> QuaternionBase<Derived>::slerp(Scalar t, const QuaternionBase<OtherDerived>& other) const
+Quaternion<typename ei_traits<Derived>::Scalar>
+QuaternionBase<Derived>::slerp(Scalar t, const QuaternionBase<OtherDerived>& other) const
 {
   static const Scalar one = Scalar(1) - precision<Scalar>();
   Scalar d = this->dot(other);
   Scalar absD = ei_abs(d);
   if (absD>=one)
-    return Quaternion<Scalar>(*this);
+    return Quaternion<Scalar>(derived());
 
   // theta is the angle between the 2 quaternions
   Scalar theta = std::acos(absD);
@@ -549,7 +589,7 @@ struct ei_quaternionbase_assign_impl<Other,3,3>
     // This algorithm comes from  "Quaternion Calculus and Fast Animation",
     // Ken Shoemake, 1987 SIGGRAPH course notes
     Scalar t = mat.trace();
-    if (t > 0)
+    if (t > Scalar(0))
     {
       t = ei_sqrt(t + Scalar(1.0));
       q.w() = Scalar(0.5)*t;

Eigen/src/SVD/SVD.h

@@ -436,14 +436,13 @@ struct ei_solve_retval<SVD<_MatrixType>, Rhs>
 
   template<typename Dest> void evalTo(Dest& dst) const
   {
-    const int cols = this->cols();
     ei_assert(rhs().rows() == dec().rows());
 
-    for (int j=0; j<cols; ++j)
+    for (int j=0; j<cols(); ++j)
     {
       Matrix<Scalar,MatrixType::RowsAtCompileTime,1> aux = dec().matrixU().adjoint() * rhs().col(j);
 
-      for (int i = 0; i <dec().rows(); ++i)
+      for (int i = 0; i < dec().rows(); ++i)
       {
         Scalar si = dec().singularValues().coeff(i);
         if(si == RealScalar(0))
@@ -451,8 +450,10 @@ struct ei_solve_retval<SVD<_MatrixType>, Rhs>
         else
           aux.coeffRef(i) /= si;
       }
-
-      dst.col(j) = dec().matrixV() * aux;
+      const int minsize = std::min(dec().rows(),dec().cols());
+      dst.col(j).start(minsize) = aux.start(minsize);
+      if(dec().cols()>dec().rows()) dst.col(j).end(cols()-minsize).setZero();
+      dst.col(j) = dec().matrixV() * dst.col(j);
     }
   }
 };

Eigen/src/Sparse/CholmodSupport.h

@@ -126,6 +126,7 @@ class SparseLLT<MatrixType,Cholmod> : public SparseLLT<MatrixType>
     typedef SparseLLT<MatrixType> Base;
     typedef typename Base::Scalar Scalar;
     typedef typename Base::RealScalar RealScalar;
+    typedef typename Base::CholMatrixType CholMatrixType;
     using Base::MatrixLIsDirty;
     using Base::SupernodalFactorIsDirty;
     using Base::m_flags;
@@ -154,7 +155,7 @@ class SparseLLT<MatrixType,Cholmod> : public SparseLLT<MatrixType>
       cholmod_finish(&m_cholmod);
     }
 
-    inline const typename Base::CholMatrixType& matrixL(void) const;
+    inline const CholMatrixType& matrixL() const;
 
     template<typename Derived>
     bool solveInPlace(MatrixBase<Derived> &b) const;
@@ -198,7 +199,7 @@ void SparseLLT<MatrixType,Cholmod>::compute(const MatrixType& a)
 }
 
 template<typename MatrixType>
-inline const typename SparseLLT<MatrixType>::CholMatrixType&
+inline const typename SparseLLT<MatrixType,Cholmod>::CholMatrixType&
 SparseLLT<MatrixType,Cholmod>::matrixL() const
 {
   if (m_status & MatrixLIsDirty)