update

15 files changed, 2749 insertions, 747 deletions

diff --git a/eigen/Eigen/src/Core/util/BlasUtil.h b/eigen/Eigen/src/Core/util/BlasUtil.h
index 9d03af3..b1791fb 100644
--- a/eigen/Eigen/src/Core/util/BlasUtil.h
+++ b/eigen/Eigen/src/Core/util/BlasUtil.h
@@ -18,13 +18,13 @@ namespace Eigen {
 namespace internal {
 
 // forward declarations
-template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjugateLhs=false, bool ConjugateRhs=false>
+template<typename LhsScalar, typename RhsScalar, typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs=false, bool ConjugateRhs=false>
 struct gebp_kernel;
 
-template<typename Scalar, typename Index, int nr, int StorageOrder, bool Conjugate = false, bool PanelMode=false>
+template<typename Scalar, typename Index, typename DataMapper, int nr, int StorageOrder, bool Conjugate = false, bool PanelMode=false>
 struct gemm_pack_rhs;
 
-template<typename Scalar, typename Index, int Pack1, int Pack2, int StorageOrder, bool Conjugate = false, bool PanelMode = false>
+template<typename Scalar, typename Index, typename DataMapper, int Pack1, int Pack2, int StorageOrder, bool Conjugate = false, bool PanelMode = false>
 struct gemm_pack_lhs;
 
 template<
@@ -34,7 +34,9 @@ template<
   int ResStorageOrder>
 struct general_matrix_matrix_product;
 
-template<typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs, typename RhsScalar, bool ConjugateRhs, int Version=Specialized>
+template<typename Index,
+         typename LhsScalar, typename LhsMapper, int LhsStorageOrder, bool ConjugateLhs,
+         typename RhsScalar, typename RhsMapper, bool ConjugateRhs, int Version=Specialized>
 struct general_matrix_vector_product;
 
 
@@ -42,22 +44,35 @@ template<bool Conjugate> struct conj_if;
 
 template<> struct conj_if<true> {
   template<typename T>
-  inline T operator()(const T& x) { return numext::conj(x); }
+  inline T operator()(const T& x) const { return numext::conj(x); }
   template<typename T>
-  inline T pconj(const T& x) { return internal::pconj(x); }
+  inline T pconj(const T& x) const { return internal::pconj(x); }
 };
 
 template<> struct conj_if<false> {
   template<typename T>
-  inline const T& operator()(const T& x) { return x; }
+  inline const T& operator()(const T& x) const { return x; }
   template<typename T>
-  inline const T& pconj(const T& x) { return x; }
+  inline const T& pconj(const T& x) const { return x; }
+};
+
+// Generic implementation for custom complex types.
+template<typename LhsScalar, typename RhsScalar, bool ConjLhs, bool ConjRhs>
+struct conj_helper
+{
+  typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar>::ReturnType Scalar;
+
+  EIGEN_STRONG_INLINE Scalar pmadd(const LhsScalar& x, const RhsScalar& y, const Scalar& c) const
+  { return padd(c, pmul(x,y)); }
+
+  EIGEN_STRONG_INLINE Scalar pmul(const LhsScalar& x, const RhsScalar& y) const
+  { return conj_if<ConjLhs>()(x) *  conj_if<ConjRhs>()(y); }
 };
 
 template<typename Scalar> struct conj_helper<Scalar,Scalar,false,false>
 {
-  EIGEN_STRONG_INLINE Scalar pmadd(const Scalar& x, const Scalar& y, const Scalar& c) const { return internal::pmadd(x,y,c); }
-  EIGEN_STRONG_INLINE Scalar pmul(const Scalar& x, const Scalar& y) const { return internal::pmul(x,y); }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar pmadd(const Scalar& x, const Scalar& y, const Scalar& c) const { return internal::pmadd(x,y,c); }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar pmul(const Scalar& x, const Scalar& y) const { return internal::pmul(x,y); }
 };
 
 template<typename RealScalar> struct conj_helper<std::complex<RealScalar>, std::complex<RealScalar>, false,true>
@@ -109,39 +124,147 @@ template<typename RealScalar,bool Conj> struct conj_helper<RealScalar, std::comp
 };
 
 template<typename From,typename To> struct get_factor {
-  static EIGEN_STRONG_INLINE To run(const From& x) { return x; }
+  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE To run(const From& x) { return To(x); }
 };
 
 template<typename Scalar> struct get_factor<Scalar,typename NumTraits<Scalar>::Real> {
+  EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE typename NumTraits<Scalar>::Real run(const Scalar& x) { return numext::real(x); }
 };
 
+
+template<typename Scalar, typename Index>
+class BlasVectorMapper {
+  public:
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE BlasVectorMapper(Scalar *data) : m_data(data) {}
+
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar operator()(Index i) const {
+    return m_data[i];
+  }
+  template <typename Packet, int AlignmentType>
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet load(Index i) const {
+    return ploadt<Packet, AlignmentType>(m_data + i);
+  }
+
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC bool aligned(Index i) const {
+    return (UIntPtr(m_data+i)%sizeof(Packet))==0;
+  }
+
+  protected:
+  Scalar* m_data;
+};
+
+template<typename Scalar, typename Index, int AlignmentType>
+class BlasLinearMapper {
+  public:
+  typedef typename packet_traits<Scalar>::type Packet;
+  typedef typename packet_traits<Scalar>::half HalfPacket;
+
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE BlasLinearMapper(Scalar *data) : m_data(data) {}
+
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void prefetch(int i) const {
+    internal::prefetch(&operator()(i));
+  }
+
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar& operator()(Index i) const {
+    return m_data[i];
+  }
+
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet loadPacket(Index i) const {
+    return ploadt<Packet, AlignmentType>(m_data + i);
+  }
+
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE HalfPacket loadHalfPacket(Index i) const {
+    return ploadt<HalfPacket, AlignmentType>(m_data + i);
+  }
+
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void storePacket(Index i, const Packet &p) const {
+    pstoret<Scalar, Packet, AlignmentType>(m_data + i, p);
+  }
+
+  protected:
+  Scalar *m_data;
+};
+
 // Lightweight helper class to access matrix coefficients.
-// Yes, this is somehow redundant with Map<>, but this version is much much lighter,
-// and so I hope better compilation performance (time and code quality).
-template<typename Scalar, typename Index, int StorageOrder>
-class blas_data_mapper
-{
+template<typename Scalar, typename Index, int StorageOrder, int AlignmentType = Unaligned>
+class blas_data_mapper {
   public:
-    blas_data_mapper(Scalar* data, Index stride) : m_data(data), m_stride(stride) {}
-    EIGEN_STRONG_INLINE Scalar& operator()(Index i, Index j)
-    { return m_data[StorageOrder==RowMajor ? j + i*m_stride : i + j*m_stride]; }
+  typedef typename packet_traits<Scalar>::type Packet;
+  typedef typename packet_traits<Scalar>::half HalfPacket;
+
+  typedef BlasLinearMapper<Scalar, Index, AlignmentType> LinearMapper;
+  typedef BlasVectorMapper<Scalar, Index> VectorMapper;
+
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE blas_data_mapper(Scalar* data, Index stride) : m_data(data), m_stride(stride) {}
+
+  EIGEN_DEVICE_FUNC  EIGEN_ALWAYS_INLINE blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType>
+  getSubMapper(Index i, Index j) const {
+    return blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType>(&operator()(i, j), m_stride);
+  }
+
+  EIGEN_DEVICE_FUNC  EIGEN_ALWAYS_INLINE LinearMapper getLinearMapper(Index i, Index j) const {
+    return LinearMapper(&operator()(i, j));
+  }
+
+  EIGEN_DEVICE_FUNC  EIGEN_ALWAYS_INLINE VectorMapper getVectorMapper(Index i, Index j) const {
+    return VectorMapper(&operator()(i, j));
+  }
+
+
+  EIGEN_DEVICE_FUNC
+  EIGEN_ALWAYS_INLINE Scalar& operator()(Index i, Index j) const {
+    return m_data[StorageOrder==RowMajor ? j + i*m_stride : i + j*m_stride];
+  }
+
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet loadPacket(Index i, Index j) const {
+    return ploadt<Packet, AlignmentType>(&operator()(i, j));
+  }
+
+  template <typename PacketT, int AlignmentT>
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketT load(Index i, Index j) const {
+    return ploadt<PacketT, AlignmentT>(&operator()(i, j));
+  }
+
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE HalfPacket loadHalfPacket(Index i, Index j) const {
+    return ploadt<HalfPacket, AlignmentType>(&operator()(i, j));
+  }
+
+  template<typename SubPacket>
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void scatterPacket(Index i, Index j, const SubPacket &p) const {
+    pscatter<Scalar, SubPacket>(&operator()(i, j), p, m_stride);
+  }
+
+  template<typename SubPacket>
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE SubPacket gatherPacket(Index i, Index j) const {
+    return pgather<Scalar, SubPacket>(&operator()(i, j), m_stride);
+  }
+
+  EIGEN_DEVICE_FUNC const Index stride() const { return m_stride; }
+  EIGEN_DEVICE_FUNC const Scalar* data() const { return m_data; }
+
+  EIGEN_DEVICE_FUNC Index firstAligned(Index size) const {
+    if (UIntPtr(m_data)%sizeof(Scalar)) {
+      return -1;
+    }
+    return internal::first_default_aligned(m_data, size);
+  }
+
   protected:
-    Scalar* EIGEN_RESTRICT m_data;
-    Index m_stride;
+  Scalar* EIGEN_RESTRICT m_data;
+  const Index m_stride;
 };
 
 // lightweight helper class to access matrix coefficients (const version)
 template<typename Scalar, typename Index, int StorageOrder>
-class const_blas_data_mapper
-{
+class const_blas_data_mapper : public blas_data_mapper<const Scalar, Index, StorageOrder> {
   public:
-    const_blas_data_mapper(const Scalar* data, Index stride) : m_data(data), m_stride(stride) {}
-    EIGEN_STRONG_INLINE const Scalar& operator()(Index i, Index j) const
-    { return m_data[StorageOrder==RowMajor ? j + i*m_stride : i + j*m_stride]; }
-  protected:
-    const Scalar* EIGEN_RESTRICT m_data;
-    Index m_stride;
+  EIGEN_ALWAYS_INLINE const_blas_data_mapper(const Scalar *data, Index stride) : blas_data_mapper<const Scalar, Index, StorageOrder>(data, stride) {}
+
+  EIGEN_ALWAYS_INLINE const_blas_data_mapper<Scalar, Index, StorageOrder> getSubMapper(Index i, Index j) const {
+    return const_blas_data_mapper<Scalar, Index, StorageOrder>(&(this->operator()(i, j)), this->m_stride);
+  }
 };
 
 
@@ -171,13 +294,12 @@ template<typename XprType> struct blas_traits
 };
 
 // pop conjugate
-template<typename Scalar, typename Xpr>
-struct blas_traits<CwiseUnaryOp<scalar_conjugate_op<Scalar>, Xpr> >
- : blas_traits<typename internal::remove_all<typename Xpr::Nested>::type>
+template<typename Scalar, typename NestedXpr>
+struct blas_traits<CwiseUnaryOp<scalar_conjugate_op<Scalar>, NestedXpr> >
+ : blas_traits<NestedXpr>
 {
-  typedef typename internal::remove_all<typename Xpr::Nested>::type NestedXpr;
   typedef blas_traits<NestedXpr> Base;
-  typedef CwiseUnaryOp<scalar_conjugate_op<Scalar>, Xpr> XprType;
+  typedef CwiseUnaryOp<scalar_conjugate_op<Scalar>, NestedXpr> XprType;
   typedef typename Base::ExtractType ExtractType;
 
   enum {
@@ -189,27 +311,41 @@ struct blas_traits<CwiseUnaryOp<scalar_conjugate_op<Scalar>, Xpr> >
 };
 
 // pop scalar multiple
-template<typename Scalar, typename Xpr>
-struct blas_traits<CwiseUnaryOp<scalar_multiple_op<Scalar>, Xpr> >
- : blas_traits<typename internal::remove_all<typename Xpr::Nested>::type>
+template<typename Scalar, typename NestedXpr, typename Plain>
+struct blas_traits<CwiseBinaryOp<scalar_product_op<Scalar>, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain>, NestedXpr> >
+ : blas_traits<NestedXpr>
 {
-  typedef typename internal::remove_all<typename Xpr::Nested>::type NestedXpr;
   typedef blas_traits<NestedXpr> Base;
-  typedef CwiseUnaryOp<scalar_multiple_op<Scalar>, Xpr> XprType;
+  typedef CwiseBinaryOp<scalar_product_op<Scalar>, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain>, NestedXpr> XprType;
   typedef typename Base::ExtractType ExtractType;
-  static inline ExtractType extract(const XprType& x) { return Base::extract(x.nestedExpression()); }
+  static inline ExtractType extract(const XprType& x) { return Base::extract(x.rhs()); }
   static inline Scalar extractScalarFactor(const XprType& x)
-  { return x.functor().m_other * Base::extractScalarFactor(x.nestedExpression()); }
+  { return x.lhs().functor().m_other * Base::extractScalarFactor(x.rhs()); }
 };
+template<typename Scalar, typename NestedXpr, typename Plain>
+struct blas_traits<CwiseBinaryOp<scalar_product_op<Scalar>, NestedXpr, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain> > >
+ : blas_traits<NestedXpr>
+{
+  typedef blas_traits<NestedXpr> Base;
+  typedef CwiseBinaryOp<scalar_product_op<Scalar>, NestedXpr, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain> > XprType;
+  typedef typename Base::ExtractType ExtractType;
+  static inline ExtractType extract(const XprType& x) { return Base::extract(x.lhs()); }
+  static inline Scalar extractScalarFactor(const XprType& x)
+  { return Base::extractScalarFactor(x.lhs()) * x.rhs().functor().m_other; }
+};
+template<typename Scalar, typename Plain1, typename Plain2>
+struct blas_traits<CwiseBinaryOp<scalar_product_op<Scalar>, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain1>,
+                                                            const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain2> > >
+ : blas_traits<CwiseNullaryOp<scalar_constant_op<Scalar>,Plain1> >
+{};
 
 // pop opposite
-template<typename Scalar, typename Xpr>
-struct blas_traits<CwiseUnaryOp<scalar_opposite_op<Scalar>, Xpr> >
- : blas_traits<typename internal::remove_all<typename Xpr::Nested>::type>
+template<typename Scalar, typename NestedXpr>
+struct blas_traits<CwiseUnaryOp<scalar_opposite_op<Scalar>, NestedXpr> >
+ : blas_traits<NestedXpr>
 {
-  typedef typename internal::remove_all<typename Xpr::Nested>::type NestedXpr;
   typedef blas_traits<NestedXpr> Base;
-  typedef CwiseUnaryOp<scalar_opposite_op<Scalar>, Xpr> XprType;
+  typedef CwiseUnaryOp<scalar_opposite_op<Scalar>, NestedXpr> XprType;
   typedef typename Base::ExtractType ExtractType;
   static inline ExtractType extract(const XprType& x) { return Base::extract(x.nestedExpression()); }
   static inline Scalar extractScalarFactor(const XprType& x)
@@ -217,14 +353,13 @@ struct blas_traits<CwiseUnaryOp<scalar_opposite_op<Scalar>, Xpr> >
 };
 
 // pop/push transpose
-template<typename Xpr>
-struct blas_traits<Transpose<Xpr> >
- : blas_traits<typename internal::remove_all<typename Xpr::Nested>::type>
+template<typename NestedXpr>
+struct blas_traits<Transpose<NestedXpr> >
+ : blas_traits<NestedXpr>
 {
-  typedef typename internal::remove_all<typename Xpr::Nested>::type NestedXpr;
   typedef typename NestedXpr::Scalar Scalar;
   typedef blas_traits<NestedXpr> Base;
-  typedef Transpose<Xpr> XprType;
+  typedef Transpose<NestedXpr> XprType;
   typedef Transpose<const typename Base::_ExtractType>  ExtractType; // const to get rid of a compile error; anyway blas traits are only used on the RHS
   typedef Transpose<const typename Base::_ExtractType> _ExtractType;
   typedef typename conditional<bool(Base::HasUsableDirectAccess),
@@ -234,7 +369,7 @@ struct blas_traits<Transpose<Xpr> >
   enum {
     IsTransposed = Base::IsTransposed ? 0 : 1
   };
-  static inline ExtractType extract(const XprType& x) { return Base::extract(x.nestedExpression()); }
+  static inline ExtractType extract(const XprType& x) { return ExtractType(Base::extract(x.nestedExpression())); }
   static inline Scalar extractScalarFactor(const XprType& x) { return Base::extractScalarFactor(x.nestedExpression()); }
 };
 
diff --git a/eigen/Eigen/src/Core/util/CMakeLists.txt b/eigen/Eigen/src/Core/util/CMakeLists.txt
deleted file mode 100644
index a1e2e52..0000000
--- a/eigen/Eigen/src/Core/util/CMakeLists.txt
+++ /dev/null
@@ -1,6 +0,0 @@
-FILE(GLOB Eigen_Core_util_SRCS "*.h")
-
-INSTALL(FILES 
-  ${Eigen_Core_util_SRCS}
-  DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Core/util COMPONENT Devel
-  )
diff --git a/eigen/Eigen/src/Core/util/Constants.h b/eigen/Eigen/src/Core/util/Constants.h
index 78499ff..5d37e5d 100644
--- a/eigen/Eigen/src/Core/util/Constants.h
+++ b/eigen/Eigen/src/Core/util/Constants.h
@@ -1,7 +1,7 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
-// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
 // Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
 //
 // This Source Code Form is subject to the terms of the Mozilla
@@ -25,11 +25,23 @@ const int Dynamic = -1;
   */
 const int DynamicIndex = 0xffffff;
 
+/** This value means that the increment to go from one value to another in a sequence is not constant for each step.
+  */
+const int UndefinedIncr = 0xfffffe;
+
 /** This value means +Infinity; it is currently used only as the p parameter to MatrixBase::lpNorm<int>().
   * The value Infinity there means the L-infinity norm.
   */
 const int Infinity = -1;
 
+/** This value means that the cost to evaluate an expression coefficient is either very expensive or
+  * cannot be known at compile time.
+  *
+  * This value has to be positive to (1) simplify cost computation, and (2) allow to distinguish between a very expensive and very very expensive expressions.
+  * It thus must also be large enough to make sure unrolling won't happen and that sub expressions will be evaluated, but not too large to avoid overflow.
+  */
+const int HugeCost = 10000;
+
 /** \defgroup flags Flags
   * \ingroup Core_Module
   *
@@ -48,19 +60,19 @@ const int Infinity = -1;
   * for a matrix, this means that the storage order is row-major.
   * If this bit is not set, the storage order is column-major.
   * For an expression, this determines the storage order of
-  * the matrix created by evaluation of that expression. 
-  * \sa \ref TopicStorageOrders */
+  * the matrix created by evaluation of that expression.
+  * \sa \blank  \ref TopicStorageOrders */
 const unsigned int RowMajorBit = 0x1;
 
 /** \ingroup flags
-  *
   * means the expression should be evaluated by the calling expression */
 const unsigned int EvalBeforeNestingBit = 0x2;
 
 /** \ingroup flags
-  *
+  * \deprecated
   * means the expression should be evaluated before any assignment */
-const unsigned int EvalBeforeAssigningBit = 0x4;
+EIGEN_DEPRECATED
+const unsigned int EvalBeforeAssigningBit = 0x4; // FIXME deprecated
 
 /** \ingroup flags
   *
@@ -141,17 +153,46 @@ const unsigned int LvalueBit = 0x20;
   */
 const unsigned int DirectAccessBit = 0x40;
 
-/** \ingroup flags
+/** \deprecated \ingroup flags
   *
-  * means the first coefficient packet is guaranteed to be aligned */
-const unsigned int AlignedBit = 0x80;
+  * means the first coefficient packet is guaranteed to be aligned.
+  * An expression cannot has the AlignedBit without the PacketAccessBit flag.
+  * In other words, this means we are allow to perform an aligned packet access to the first element regardless
+  * of the expression kind:
+  * \code
+  * expression.packet<Aligned>(0);
+  * \endcode
+  */
+EIGEN_DEPRECATED const unsigned int AlignedBit = 0x80;
 
 const unsigned int NestByRefBit = 0x100;
 
+/** \ingroup flags
+  *
+  * for an expression, this means that the storage order
+  * can be either row-major or column-major.
+  * The precise choice will be decided at evaluation time or when
+  * combined with other expressions.
+  * \sa \blank  \ref RowMajorBit, \ref TopicStorageOrders */
+const unsigned int NoPreferredStorageOrderBit = 0x200;
+
+/** \ingroup flags
+  *
+  * Means that the underlying coefficients can be accessed through pointers to the sparse (un)compressed storage format,
+  * that is, the expression provides:
+  * \code
+    inline const Scalar* valuePtr() const;
+    inline const Index* innerIndexPtr() const;
+    inline const Index* outerIndexPtr() const;
+    inline const Index* innerNonZeroPtr() const;
+    \endcode
+  */
+const unsigned int CompressedAccessBit = 0x400;
+
+
 // list of flags that are inherited by default
 const unsigned int HereditaryBits = RowMajorBit
-                                  | EvalBeforeNestingBit
-                                  | EvalBeforeAssigningBit;
+                                  | EvalBeforeNestingBit;
 
 /** \defgroup enums Enumerations
   * \ingroup Core_Module
@@ -160,8 +201,8 @@ const unsigned int HereditaryBits = RowMajorBit
   */
 
 /** \ingroup enums
-  * Enum containing possible values for the \p Mode parameter of 
-  * MatrixBase::selfadjointView() and MatrixBase::triangularView(). */
+  * Enum containing possible values for the \c Mode or \c UpLo parameter of
+  * MatrixBase::selfadjointView() and MatrixBase::triangularView(), and selfadjoint solvers. */
 enum UpLoType {
   /** View matrix as a lower triangular matrix. */
   Lower=0x1,                      
@@ -186,12 +227,31 @@ enum UpLoType {
 };
 
 /** \ingroup enums
-  * Enum for indicating whether an object is aligned or not. */
+  * Enum for indicating whether a buffer is aligned or not. */
 enum AlignmentType {
-  /** Object is not correctly aligned for vectorization. */
-  Unaligned=0, 
-  /** Object is aligned for vectorization. */
-  Aligned=1 
+  Unaligned=0,        /**< Data pointer has no specific alignment. */
+  Aligned8=8,         /**< Data pointer is aligned on a 8 bytes boundary. */
+  Aligned16=16,       /**< Data pointer is aligned on a 16 bytes boundary. */
+  Aligned32=32,       /**< Data pointer is aligned on a 32 bytes boundary. */
+  Aligned64=64,       /**< Data pointer is aligned on a 64 bytes boundary. */
+  Aligned128=128,     /**< Data pointer is aligned on a 128 bytes boundary. */
+  AlignedMask=255,
+  Aligned=16,         /**< \deprecated Synonym for Aligned16. */
+#if EIGEN_MAX_ALIGN_BYTES==128
+  AlignedMax = Aligned128
+#elif EIGEN_MAX_ALIGN_BYTES==64
+  AlignedMax = Aligned64
+#elif EIGEN_MAX_ALIGN_BYTES==32
+  AlignedMax = Aligned32
+#elif EIGEN_MAX_ALIGN_BYTES==16
+  AlignedMax = Aligned16
+#elif EIGEN_MAX_ALIGN_BYTES==8
+  AlignedMax = Aligned8
+#elif EIGEN_MAX_ALIGN_BYTES==0
+  AlignedMax = Unaligned
+#else
+#error Invalid value for EIGEN_MAX_ALIGN_BYTES
+#endif
 };
 
 /** \ingroup enums
@@ -297,7 +357,7 @@ enum Default_t    { Default };
 
 /** \internal \ingroup enums
   * Used in AmbiVector. */
-enum {
+enum AmbiVectorMode {
   IsDense         = 0,
   IsSparse
 };
@@ -406,10 +466,16 @@ namespace Architecture
     Generic = 0x0,
     SSE = 0x1,
     AltiVec = 0x2,
+    VSX = 0x3,
+    NEON = 0x4,
 #if defined EIGEN_VECTORIZE_SSE
     Target = SSE
 #elif defined EIGEN_VECTORIZE_ALTIVEC
     Target = AltiVec
+#elif defined EIGEN_VECTORIZE_VSX
+    Target = VSX
+#elif defined EIGEN_VECTORIZE_NEON
+    Target = NEON
 #else
     Target = Generic
 #endif
@@ -417,8 +483,9 @@ namespace Architecture
 }
 
 /** \internal \ingroup enums
-  * Enum used as template parameter in GeneralProduct. */
-enum ProductImplType { CoeffBasedProductMode, LazyCoeffBasedProductMode, OuterProduct, InnerProduct, GemvProduct, GemmProduct };
+  * Enum used as template parameter in Product and product evaluators. */
+enum ProductImplType
+{ DefaultProduct=0, LazyProduct, AliasFreeProduct, CoeffBasedProductMode, LazyCoeffBasedProductMode, OuterProduct, InnerProduct, GemvProduct, GemmProduct };
 
 /** \internal \ingroup enums
   * Enum used in experimental parallel implementation. */
@@ -427,24 +494,57 @@ enum Action {GetAction, SetAction};
 /** The type used to identify a dense storage. */
 struct Dense {};
 
+/** The type used to identify a general sparse storage. */
+struct Sparse {};
+
+/** The type used to identify a general solver (factored) storage. */
+struct SolverStorage {};
+
+/** The type used to identify a permutation storage. */
+struct PermutationStorage {};
+
+/** The type used to identify a permutation storage. */
+struct TranspositionsStorage {};
+
 /** The type used to identify a matrix expression */
 struct MatrixXpr {};
 
 /** The type used to identify an array expression */
 struct ArrayXpr {};
 
+// An evaluator must define its shape. By default, it can be one of the following:
+struct DenseShape             { static std::string debugName() { return "DenseShape"; } };
+struct SolverShape            { static std::string debugName() { return "SolverShape"; } };
+struct HomogeneousShape       { static std::string debugName() { return "HomogeneousShape"; } };
+struct DiagonalShape          { static std::string debugName() { return "DiagonalShape"; } };
+struct BandShape              { static std::string debugName() { return "BandShape"; } };
+struct TriangularShape        { static std::string debugName() { return "TriangularShape"; } };
+struct SelfAdjointShape       { static std::string debugName() { return "SelfAdjointShape"; } };
+struct PermutationShape       { static std::string debugName() { return "PermutationShape"; } };
+struct TranspositionsShape    { static std::string debugName() { return "TranspositionsShape"; } };
+struct SparseShape            { static std::string debugName() { return "SparseShape"; } };
+
 namespace internal {
-  /** \internal
-  * Constants for comparison functors
-  */
-  enum ComparisonName {
-    cmp_EQ = 0,
-    cmp_LT = 1,
-    cmp_LE = 2,
-    cmp_UNORD = 3,
-    cmp_NEQ = 4
-  };
-}
+
+  // random access iterators based on coeff*() accessors.
+struct IndexBased {};
+
+// evaluator based on iterators to access coefficients. 
+struct IteratorBased {};
+
+/** \internal
+ * Constants for comparison functors
+ */
+enum ComparisonName {
+  cmp_EQ = 0,
+  cmp_LT = 1,
+  cmp_LE = 2,
+  cmp_UNORD = 3,
+  cmp_NEQ = 4,
+  cmp_GT = 5,
+  cmp_GE = 6
+};
+} // end namespace internal
 
 } // end namespace Eigen
 
diff --git a/eigen/Eigen/src/Core/util/DisableStupidWarnings.h b/eigen/Eigen/src/Core/util/DisableStupidWarnings.h
index c53457a..4431f2f 100644
--- a/eigen/Eigen/src/Core/util/DisableStupidWarnings.h
+++ b/eigen/Eigen/src/Core/util/DisableStupidWarnings.h
@@ -4,30 +4,36 @@
 #ifdef _MSC_VER
   // 4100 - unreferenced formal parameter (occurred e.g. in aligned_allocator::destroy(pointer p))
   // 4101 - unreferenced local variable
-  // 4127 - conditional expression is constant
   // 4181 - qualifier applied to reference type ignored
   // 4211 - nonstandard extension used : redefined extern to static
   // 4244 - 'argument' : conversion from 'type1' to 'type2', possible loss of data
   // 4273 - QtAlignedMalloc, inconsistent DLL linkage
   // 4324 - structure was padded due to declspec(align())
+  // 4503 - decorated name length exceeded, name was truncated
   // 4512 - assignment operator could not be generated
   // 4522 - 'class' : multiple assignment operators specified
   // 4700 - uninitialized local variable 'xyz' used
+  // 4714 - function marked as __forceinline not inlined
   // 4717 - 'function' : recursive on all control paths, function will cause runtime stack overflow
+  // 4800 - 'type' : forcing value to bool 'true' or 'false' (performance warning)
   #ifndef EIGEN_PERMANENTLY_DISABLE_STUPID_WARNINGS
     #pragma warning( push )
   #endif
-  #pragma warning( disable : 4100 4101 4127 4181 4211 4244 4273 4324 4512 4522 4700 4717 )
+  #pragma warning( disable : 4100 4101 4181 4211 4244 4273 4324 4503 4512 4522 4700 4714 4717 4800)
+
 #elif defined __INTEL_COMPILER
   // 2196 - routine is both "inline" and "noinline" ("noinline" assumed)
   //        ICC 12 generates this warning even without any inline keyword, when defining class methods 'inline' i.e. inside of class body
   //        typedef that may be a reference type.
   // 279  - controlling expression is constant
   //        ICC 12 generates this warning on assert(constant_expression_depending_on_template_params) and frankly this is a legitimate use case.
+  // 1684 - conversion from pointer to same-sized integral type (potential portability problem)
+  // 2259 - non-pointer conversion from "Eigen::Index={ptrdiff_t={long}}" to "int" may lose significant bits
   #ifndef EIGEN_PERMANENTLY_DISABLE_STUPID_WARNINGS
     #pragma warning push
   #endif
-  #pragma warning disable 2196 279
+  #pragma warning disable 2196 279 1684 2259
+
 #elif defined __clang__
   // -Wconstant-logical-operand - warning: use of logical && with constant operand; switch to bitwise & or remove constant
   //     this is really a stupid warning as it warns on compile-time expressions involving enums
@@ -35,6 +41,9 @@
     #pragma clang diagnostic push
   #endif
   #pragma clang diagnostic ignored "-Wconstant-logical-operand"
+  #if __clang_major__ >= 3 && __clang_minor__ >= 5
+    #pragma clang diagnostic ignored "-Wabsolute-value"
+  #endif
 
 #elif defined __GNUC__ && __GNUC__>=6
 
@@ -45,4 +54,24 @@
 
 #endif
 
+#if defined __NVCC__
+  // Disable the "statement is unreachable" message
+  #pragma diag_suppress code_is_unreachable
+  // Disable the "dynamic initialization in unreachable code" message
+  #pragma diag_suppress initialization_not_reachable
+  // Disable the "invalid error number" message that we get with older versions of nvcc
+  #pragma diag_suppress 1222
+  // Disable the "calling a __host__ function from a __host__ __device__ function is not allowed" messages (yes, there are many of them and they seem to change with every version of the compiler)
+  #pragma diag_suppress 2527
+  #pragma diag_suppress 2529
+  #pragma diag_suppress 2651
+  #pragma diag_suppress 2653
+  #pragma diag_suppress 2668
+  #pragma diag_suppress 2669
+  #pragma diag_suppress 2670
+  #pragma diag_suppress 2671
+  #pragma diag_suppress 2735
+  #pragma diag_suppress 2737
+#endif
+
 #endif // not EIGEN_WARNINGS_DISABLED
diff --git a/eigen/Eigen/src/Core/util/ForwardDeclarations.h b/eigen/Eigen/src/Core/util/ForwardDeclarations.h
index f277720..1a48cff 100644
--- a/eigen/Eigen/src/Core/util/ForwardDeclarations.h
+++ b/eigen/Eigen/src/Core/util/ForwardDeclarations.h
@@ -36,6 +36,10 @@ template<typename Derived> struct accessors_level
   };
 };
 
+template<typename T> struct evaluator_traits;
+
+template< typename T> struct evaluator;
+
 } // end namespace internal
 
 template<typename T> struct NumTraits;
@@ -51,18 +55,18 @@ class DenseCoeffsBase;
 
 template<typename _Scalar, int _Rows, int _Cols,
          int _Options = AutoAlign |
-#if defined(__GNUC__) && __GNUC__==3 && __GNUC_MINOR__==4
+#if EIGEN_GNUC_AT(3,4)
     // workaround a bug in at least gcc 3.4.6
     // the innermost ?: ternary operator is misparsed. We write it slightly
     // differently and this makes gcc 3.4.6 happy, but it's ugly.
     // The error would only show up with EIGEN_DEFAULT_TO_ROW_MAJOR is defined
     // (when EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION is RowMajor)
-                          ( (_Rows==1 && _Cols!=1) ? RowMajor
+                          ( (_Rows==1 && _Cols!=1) ? Eigen::RowMajor
                           : !(_Cols==1 && _Rows!=1) ?  EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION
-                          : ColMajor ),
+                          : Eigen::ColMajor ),
 #else
-                          ( (_Rows==1 && _Cols!=1) ? RowMajor
-                          : (_Cols==1 && _Rows!=1) ? ColMajor
+                          ( (_Rows==1 && _Cols!=1) ? Eigen::RowMajor
+                          : (_Cols==1 && _Rows!=1) ? Eigen::ColMajor
                           : EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION ),
 #endif
          int _MaxRows = _Rows,
@@ -79,6 +83,7 @@ template<typename ExpressionType> class ForceAlignedAccess;
 template<typename ExpressionType> class SwapWrapper;
 
 template<typename XprType, int BlockRows=Dynamic, int BlockCols=Dynamic, bool InnerPanel = false> class Block;
+template<typename XprType, typename RowIndices, typename ColIndices> class IndexedView;
 
 template<typename MatrixType, int Size=Dynamic> class VectorBlock;
 template<typename MatrixType> class Transpose;
@@ -87,10 +92,11 @@ template<typename NullaryOp, typename MatrixType>         class CwiseNullaryOp;
 template<typename UnaryOp,   typename MatrixType>         class CwiseUnaryOp;
 template<typename ViewOp,    typename MatrixType>         class CwiseUnaryView;
 template<typename BinaryOp,  typename Lhs, typename Rhs>  class CwiseBinaryOp;
-template<typename BinOp,     typename Lhs, typename Rhs>  class SelfCwiseBinaryOp;
-template<typename Derived,   typename Lhs, typename Rhs>  class ProductBase;
-template<typename Lhs, typename Rhs, int Mode>            class GeneralProduct;
-template<typename Lhs, typename Rhs, int NestingFlags>    class CoeffBasedProduct;
+template<typename TernaryOp, typename Arg1, typename Arg2, typename Arg3>  class CwiseTernaryOp;
+template<typename Decomposition, typename Rhstype>        class Solve;
+template<typename XprType>                                class Inverse;
+
+template<typename Lhs, typename Rhs, int Option = DefaultProduct> class Product;
 
 template<typename Derived> class DiagonalBase;
 template<typename _DiagonalVectorType> class DiagonalWrapper;
@@ -108,7 +114,12 @@ template<typename Derived,
          int Level = internal::accessors_level<Derived>::has_write_access ? WriteAccessors : ReadOnlyAccessors
 > class MapBase;
 template<int InnerStrideAtCompileTime, int OuterStrideAtCompileTime> class Stride;
+template<int Value = Dynamic> class InnerStride;
+template<int Value = Dynamic> class OuterStride;
 template<typename MatrixType, int MapOptions=Unaligned, typename StrideType = Stride<0,0> > class Map;
+template<typename Derived> class RefBase;
+template<typename PlainObjectType, int Options = 0,
+         typename StrideType = typename internal::conditional<PlainObjectType::IsVectorAtCompileTime,InnerStride<1>,OuterStride<> >::type > class Ref;
 
 template<typename Derived> class TriangularBase;
 template<typename MatrixType, unsigned int Mode> class TriangularView;
@@ -119,10 +130,10 @@ template<typename MatrixType> struct CommaInitializer;
 template<typename Derived> class ReturnByValue;
 template<typename ExpressionType> class ArrayWrapper;
 template<typename ExpressionType> class MatrixWrapper;
+template<typename Derived> class SolverBase;
+template<typename XprType> class InnerIterator;
 
 namespace internal {
-template<typename DecompositionType, typename Rhs> struct solve_retval_base;
-template<typename DecompositionType, typename Rhs> struct solve_retval;
 template<typename DecompositionType> struct kernel_retval_base;
 template<typename DecompositionType> struct kernel_retval;
 template<typename DecompositionType> struct image_retval_base;
@@ -135,6 +146,21 @@ template<typename _Scalar, int Rows=Dynamic, int Cols=Dynamic, int Supers=Dynami
 
 namespace internal {
 template<typename Lhs, typename Rhs> struct product_type;
+
+template<bool> struct EnableIf;
+
+/** \internal
+  * \class product_evaluator
+  * Products need their own evaluator with more template arguments allowing for
+  * easier partial template specializations.
+  */
+template< typename T,
+          int ProductTag = internal::product_type<typename T::Lhs,typename T::Rhs>::ret,
+          typename LhsShape = typename evaluator_traits<typename T::Lhs>::Shape,
+          typename RhsShape = typename evaluator_traits<typename T::Rhs>::Shape,
+          typename LhsScalar = typename traits<typename T::Lhs>::Scalar,
+          typename RhsScalar = typename traits<typename T::Rhs>::Scalar
+        > struct product_evaluator;
 }
 
 template<typename Lhs, typename Rhs,
@@ -150,9 +176,11 @@ namespace internal {
 // with optional conjugation of the arguments.
 template<typename LhsScalar, typename RhsScalar, bool ConjLhs=false, bool ConjRhs=false> struct conj_helper;
 
-template<typename Scalar> struct scalar_sum_op;
-template<typename Scalar> struct scalar_difference_op;
-template<typename LhsScalar,typename RhsScalar> struct scalar_conj_product_op;
+template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_sum_op;
+template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_difference_op;
+template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_conj_product_op;
+template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_min_op;
+template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_max_op;
 template<typename Scalar> struct scalar_opposite_op;
 template<typename Scalar> struct scalar_conjugate_op;
 template<typename Scalar> struct scalar_real_op;
@@ -160,6 +188,7 @@ template<typename Scalar> struct scalar_imag_op;
 template<typename Scalar> struct scalar_abs_op;
 template<typename Scalar> struct scalar_abs2_op;
 template<typename Scalar> struct scalar_sqrt_op;
+template<typename Scalar> struct scalar_rsqrt_op;
 template<typename Scalar> struct scalar_exp_op;
 template<typename Scalar> struct scalar_log_op;
 template<typename Scalar> struct scalar_cos_op;
@@ -167,24 +196,29 @@ template<typename Scalar> struct scalar_sin_op;
 template<typename Scalar> struct scalar_acos_op;
 template<typename Scalar> struct scalar_asin_op;
 template<typename Scalar> struct scalar_tan_op;
-template<typename Scalar> struct scalar_pow_op;
 template<typename Scalar> struct scalar_inverse_op;
 template<typename Scalar> struct scalar_square_op;
 template<typename Scalar> struct scalar_cube_op;
 template<typename Scalar, typename NewType> struct scalar_cast_op;
-template<typename Scalar> struct scalar_multiple_op;
-template<typename Scalar> struct scalar_quotient1_op;
-template<typename Scalar> struct scalar_min_op;
-template<typename Scalar> struct scalar_max_op;
 template<typename Scalar> struct scalar_random_op;
-template<typename Scalar> struct scalar_add_op;
 template<typename Scalar> struct scalar_constant_op;
 template<typename Scalar> struct scalar_identity_op;
-
+template<typename Scalar,bool iscpx> struct scalar_sign_op;
+template<typename Scalar,typename ScalarExponent> struct scalar_pow_op;
+template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_hypot_op;
 template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_product_op;
-template<typename LhsScalar,typename RhsScalar> struct scalar_multiple2_op;
 template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_quotient_op;
 
+// SpecialFunctions module
+template<typename Scalar> struct scalar_lgamma_op;
+template<typename Scalar> struct scalar_digamma_op;
+template<typename Scalar> struct scalar_erf_op;
+template<typename Scalar> struct scalar_erfc_op;
+template<typename Scalar> struct scalar_igamma_op;
+template<typename Scalar> struct scalar_igammac_op;
+template<typename Scalar> struct scalar_zeta_op;
+template<typename Scalar> struct scalar_betainc_op;
+
 } // end namespace internal
 
 struct IOFormat;
@@ -192,18 +226,18 @@ struct IOFormat;
 // Array module
 template<typename _Scalar, int _Rows, int _Cols,
          int _Options = AutoAlign |
-#if defined(__GNUC__) && __GNUC__==3 && __GNUC_MINOR__==4
+#if EIGEN_GNUC_AT(3,4)
     // workaround a bug in at least gcc 3.4.6
     // the innermost ?: ternary operator is misparsed. We write it slightly
     // differently and this makes gcc 3.4.6 happy, but it's ugly.
     // The error would only show up with EIGEN_DEFAULT_TO_ROW_MAJOR is defined
     // (when EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION is RowMajor)
-                          ( (_Rows==1 && _Cols!=1) ? RowMajor
+                          ( (_Rows==1 && _Cols!=1) ? Eigen::RowMajor
                           : !(_Cols==1 && _Rows!=1) ?  EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION
-                          : ColMajor ),
+                          : Eigen::ColMajor ),
 #else
-                          ( (_Rows==1 && _Cols!=1) ? RowMajor
-                          : (_Cols==1 && _Rows!=1) ? ColMajor
+                          ( (_Rows==1 && _Cols!=1) ? Eigen::RowMajor
+                          : (_Cols==1 && _Rows!=1) ? Eigen::ColMajor
                           : EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION ),
 #endif
          int _MaxRows = _Rows, int _MaxCols = _Cols> class Array;
@@ -221,7 +255,9 @@ template<typename MatrixType> struct inverse_impl;
 template<typename MatrixType> class HouseholderQR;
 template<typename MatrixType> class ColPivHouseholderQR;
 template<typename MatrixType> class FullPivHouseholderQR;
+template<typename MatrixType> class CompleteOrthogonalDecomposition;
 template<typename MatrixType, int QRPreconditioner = ColPivHouseholderQRPreconditioner> class JacobiSVD;
+template<typename MatrixType> class BDCSVD;
 template<typename MatrixType, int UpLo = Lower> class LLT;
 template<typename MatrixType, int UpLo = Lower> class LDLT;
 template<typename VectorsType, typename CoeffsType, int Side=OnTheLeft> class HouseholderSequence;
@@ -234,39 +270,16 @@ template<typename Derived> class QuaternionBase;
 template<typename Scalar> class Rotation2D;
 template<typename Scalar> class AngleAxis;
 template<typename Scalar,int Dim> class Translation;
-
-// Sparse module:
-template<typename Derived> class SparseMatrixBase;
-
-#ifdef EIGEN2_SUPPORT
-template<typename Derived, int _Dim> class eigen2_RotationBase;
-template<typename Lhs, typename Rhs> class eigen2_Cross;
-template<typename Scalar> class eigen2_Quaternion;
-template<typename Scalar> class eigen2_Rotation2D;
-template<typename Scalar> class eigen2_AngleAxis;
-template<typename Scalar,int Dim> class eigen2_Transform;
-template <typename _Scalar, int _AmbientDim> class eigen2_ParametrizedLine;
-template <typename _Scalar, int _AmbientDim> class eigen2_Hyperplane;
-template<typename Scalar,int Dim> class eigen2_Translation;
-template<typename Scalar,int Dim> class eigen2_Scaling;
-#endif
-
-#if EIGEN2_SUPPORT_STAGE < STAGE20_RESOLVE_API_CONFLICTS
-template<typename Scalar> class Quaternion;
-template<typename Scalar,int Dim> class Transform;
-template <typename _Scalar, int _AmbientDim> class ParametrizedLine;
-template <typename _Scalar, int _AmbientDim> class Hyperplane;
-template<typename Scalar,int Dim> class Scaling;
-#endif
-
-#if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
+template<typename Scalar,int Dim> class AlignedBox;
 template<typename Scalar, int Options = AutoAlign> class Quaternion;
 template<typename Scalar,int Dim,int Mode,int _Options=AutoAlign> class Transform;
 template <typename _Scalar, int _AmbientDim, int Options=AutoAlign> class ParametrizedLine;
 template <typename _Scalar, int _AmbientDim, int Options=AutoAlign> class Hyperplane;
 template<typename Scalar> class UniformScaling;
 template<typename MatrixType,int Direction> class Homogeneous;
-#endif
+
+// Sparse module:
+template<typename Derived> class SparseMatrixBase;
 
 // MatrixFunctions module
 template<typename Derived> struct MatrixExponentialReturnValue;
@@ -274,7 +287,7 @@ template<typename Derived> class MatrixFunctionReturnValue;
 template<typename Derived> class MatrixSquareRootReturnValue;
 template<typename Derived> class MatrixLogarithmReturnValue;
 template<typename Derived> class MatrixPowerReturnValue;
-template<typename Derived, typename Lhs, typename Rhs> class MatrixPowerProduct;
+template<typename Derived> class MatrixComplexPowerReturnValue;
 
 namespace internal {
 template <typename Scalar>
@@ -285,18 +298,6 @@ struct stem_function
 };
 }
 
-
-#ifdef EIGEN2_SUPPORT
-template<typename ExpressionType> class Cwise;
-template<typename MatrixType> class Minor;
-template<typename MatrixType> class LU;
-template<typename MatrixType> class QR;
-template<typename MatrixType> class SVD;
-namespace internal {
-template<typename MatrixType, unsigned int Mode> struct eigen2_part_return_type;
-}
-#endif
-
 } // end namespace Eigen
 
 #endif // EIGEN_FORWARDDECLARATIONS_H
diff --git a/eigen/Eigen/src/Core/util/IndexedViewHelper.h b/eigen/Eigen/src/Core/util/IndexedViewHelper.h
new file mode 100644
index 0000000..ab01c85
--- /dev/null
+++ b/eigen/Eigen/src/Core/util/IndexedViewHelper.h
@@ -0,0 +1,187 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+#ifndef EIGEN_INDEXED_VIEW_HELPER_H
+#define EIGEN_INDEXED_VIEW_HELPER_H
+
+namespace Eigen {
+
+/** \namespace Eigen::placeholders
+  * \ingroup Core_Module
+  *
+  * Namespace containing symbolic placeholder and identifiers
+  */
+namespace placeholders {
+
+namespace internal {
+struct symbolic_last_tag {};
+}
+
+/** \var last
+  * \ingroup Core_Module
+  *
+  * Can be used as a parameter to Eigen::seq and Eigen::seqN functions to symbolically reference the last element/row/columns
+  * of the underlying vector or matrix once passed to DenseBase::operator()(const RowIndices&, const ColIndices&).
+  *
+  * This symbolic placeholder support standard arithmetic operation.
+  *
+  * A typical usage example would be:
+  * \code
+  * using namespace Eigen;
+  * using Eigen::placeholders::last;
+  * VectorXd v(n);
+  * v(seq(2,last-2)).setOnes();
+  * \endcode
+  *
+  * \sa end
+  */
+static const Symbolic::SymbolExpr<internal::symbolic_last_tag> last;
+
+/** \var end
+  * \ingroup Core_Module
+  *
+  * Can be used as a parameter to Eigen::seq and Eigen::seqN functions to symbolically reference the last+1 element/row/columns
+  * of the underlying vector or matrix once passed to DenseBase::operator()(const RowIndices&, const ColIndices&).
+  *
+  * This symbolic placeholder support standard arithmetic operation.
+  * It is essentially an alias to last+1
+  *
+  * \sa last
+  */
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+static const auto end = last+1;
+#else
+// Using a FixedExpr<1> expression is important here to make sure the compiler
+// can fully optimize the computation starting indices with zero overhead.
+static const Symbolic::AddExpr<Symbolic::SymbolExpr<internal::symbolic_last_tag>,Symbolic::ValueExpr<Eigen::internal::FixedInt<1> > > end(last+fix<1>());
+#endif
+
+} // end namespace placeholders
+
+namespace internal {
+
+ // Replace symbolic last/end "keywords" by their true runtime value
+inline Index eval_expr_given_size(Index x, Index /* size */)   { return x; }
+
+template<int N>
+FixedInt<N> eval_expr_given_size(FixedInt<N> x, Index /*size*/)   { return x; }
+
+template<typename Derived>
+Index eval_expr_given_size(const Symbolic::BaseExpr<Derived> &x, Index size)
+{
+  return x.derived().eval(placeholders::last=size-1);
+}
+
+// Extract increment/step at compile time
+template<typename T, typename EnableIf = void> struct get_compile_time_incr {
+  enum { value = UndefinedIncr };
+};
+
+// Analogue of std::get<0>(x), but tailored for our needs.
+template<typename T>
+Index first(const T& x) { return x.first(); }
+
+// IndexedViewCompatibleType/makeIndexedViewCompatible turn an arbitrary object of type T into something usable by MatrixSlice
+// The generic implementation is a no-op
+template<typename T,int XprSize,typename EnableIf=void>
+struct IndexedViewCompatibleType {
+  typedef T type;
+};
+
+template<typename T,typename Q>
+const T& makeIndexedViewCompatible(const T& x, Index /*size*/, Q) { return x; }
+
+//--------------------------------------------------------------------------------
+// Handling of a single Index
+//--------------------------------------------------------------------------------
+
+struct SingleRange {
+  enum {
+    SizeAtCompileTime = 1
+  };
+  SingleRange(Index val) : m_value(val) {}
+  Index operator[](Index) const { return m_value; }
+  Index size() const { return 1; }
+  Index first() const { return m_value; }
+  Index m_value;
+};
+
+template<> struct get_compile_time_incr<SingleRange> {
+  enum { value = 1 }; // 1 or 0 ??
+};
+
+// Turn a single index into something that looks like an array (i.e., that exposes a .size(), and operatro[](int) methods)
+template<typename T, int XprSize>
+struct IndexedViewCompatibleType<T,XprSize,typename internal::enable_if<internal::is_integral<T>::value>::type> {
+  // Here we could simply use Array, but maybe it's less work for the compiler to use
+  // a simpler wrapper as SingleRange
+  //typedef Eigen::Array<Index,1,1> type;
+  typedef SingleRange type;
+};
+
+template<typename T, int XprSize>
+struct IndexedViewCompatibleType<T, XprSize, typename enable_if<Symbolic::is_symbolic<T>::value>::type> {
+  typedef SingleRange type;
+};
+
+
+template<typename T>
+typename enable_if<Symbolic::is_symbolic<T>::value,SingleRange>::type
+makeIndexedViewCompatible(const T& id, Index size, SpecializedType) {
+  return eval_expr_given_size(id,size);
+}
+
+//--------------------------------------------------------------------------------
+// Handling of all
+//--------------------------------------------------------------------------------
+
+struct all_t { all_t() {} };
+
+// Convert a symbolic 'all' into a usable range type
+template<int XprSize>
+struct AllRange {
+  enum { SizeAtCompileTime = XprSize };
+  AllRange(Index size = XprSize) : m_size(size) {}
+  Index operator[](Index i) const { return i; }
+  Index size() const { return m_size.value(); }
+  Index first() const { return 0; }
+  variable_if_dynamic<Index,XprSize> m_size;
+};
+
+template<int XprSize>
+struct IndexedViewCompatibleType<all_t,XprSize> {
+  typedef AllRange<XprSize> type;
+};
+
+template<typename XprSizeType>
+inline AllRange<get_fixed_value<XprSizeType>::value> makeIndexedViewCompatible(all_t , XprSizeType size, SpecializedType) {
+  return AllRange<get_fixed_value<XprSizeType>::value>(size);
+}
+
+template<int Size> struct get_compile_time_incr<AllRange<Size> > {
+  enum { value = 1 };
+};
+
+} // end namespace internal
+
+
+namespace placeholders {
+
+/** \var all
+  * \ingroup Core_Module
+  * Can be used as a parameter to DenseBase::operator()(const RowIndices&, const ColIndices&) to index all rows or columns
+  */
+static const Eigen::internal::all_t all;
+
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_INDEXED_VIEW_HELPER_H
diff --git a/eigen/Eigen/src/Core/util/IntegralConstant.h b/eigen/Eigen/src/Core/util/IntegralConstant.h
new file mode 100644
index 0000000..78a4705
--- /dev/null
+++ b/eigen/Eigen/src/Core/util/IntegralConstant.h
@@ -0,0 +1,270 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+#ifndef EIGEN_INTEGRAL_CONSTANT_H
+#define EIGEN_INTEGRAL_CONSTANT_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<int N> class FixedInt;
+template<int N> class VariableAndFixedInt;
+
+/** \internal
+  * \class FixedInt
+  *
+  * This class embeds a compile-time integer \c N.
+  *
+  * It is similar to c++11 std::integral_constant<int,N> but with some additional features
+  * such as:
+  *  - implicit conversion to int
+  *  - arithmetic and some bitwise operators: -, +, *, /, %, &, |
+  *  - c++98/14 compatibility with fix<N> and fix<N>() syntax to define integral constants.
+  *
+  * It is strongly discouraged to directly deal with this class FixedInt. Instances are expcected to
+  * be created by the user using Eigen::fix<N> or Eigen::fix<N>(). In C++98-11, the former syntax does
+  * not create a FixedInt<N> instance but rather a point to function that needs to be \em cleaned-up
+  * using the generic helper:
+  * \code
+  * internal::cleanup_index_type<T>::type
+  * internal::cleanup_index_type<T,DynamicKey>::type
+  * \endcode
+  * where T can a FixedInt<N>, a pointer to function FixedInt<N> (*)(), or numerous other integer-like representations.
+  * \c DynamicKey is either Dynamic (default) or DynamicIndex and used to identify true compile-time values.
+  *
+  * For convenience, you can extract the compile-time value \c N in a generic way using the following helper:
+  * \code
+  * internal::get_fixed_value<T,DefaultVal>::value
+  * \endcode
+  * that will give you \c N if T equals FixedInt<N> or FixedInt<N> (*)(), and \c DefaultVal if T does not embed any compile-time value (e.g., T==int).
+  *
+  * \sa fix<N>, class VariableAndFixedInt
+  */
+template<int N> class FixedInt
+{
+public:
+  static const int value = N;
+  operator int() const { return value; }
+  FixedInt() {}
+  FixedInt( VariableAndFixedInt<N> other) {
+    EIGEN_ONLY_USED_FOR_DEBUG(other);
+    eigen_internal_assert(int(other)==N);
+  }
+
+  FixedInt<-N> operator-() const { return FixedInt<-N>(); }
+  template<int M>
+  FixedInt<N+M> operator+( FixedInt<M>) const { return FixedInt<N+M>(); }
+  template<int M>
+  FixedInt<N-M> operator-( FixedInt<M>) const { return FixedInt<N-M>(); }
+  template<int M>
+  FixedInt<N*M> operator*( FixedInt<M>) const { return FixedInt<N*M>(); }
+  template<int M>
+  FixedInt<N/M> operator/( FixedInt<M>) const { return FixedInt<N/M>(); }
+  template<int M>
+  FixedInt<N%M> operator%( FixedInt<M>) const { return FixedInt<N%M>(); }
+  template<int M>
+  FixedInt<N|M> operator|( FixedInt<M>) const { return FixedInt<N|M>(); }
+  template<int M>
+  FixedInt<N&M> operator&( FixedInt<M>) const { return FixedInt<N&M>(); }
+
+#if EIGEN_HAS_CXX14
+  // Needed in C++14 to allow fix<N>():
+  FixedInt operator() () const { return *this; }
+
+  VariableAndFixedInt<N> operator() (int val) const { return VariableAndFixedInt<N>(val); }
+#else
+  FixedInt ( FixedInt<N> (*)() ) {}
+#endif
+
+#if EIGEN_HAS_CXX11
+  FixedInt(std::integral_constant<int,N>) {}
+#endif
+};
+
+/** \internal
+  * \class VariableAndFixedInt
+  *
+  * This class embeds both a compile-time integer \c N and a runtime integer.
+  * Both values are supposed to be equal unless the compile-time value \c N has a special
+  * value meaning that the runtime-value should be used. Depending on the context, this special
+  * value can be either Eigen::Dynamic (for positive quantities) or Eigen::DynamicIndex (for
+  * quantities that can be negative).
+  *
+  * It is the return-type of the function Eigen::fix<N>(int), and most of the time this is the only
+  * way it is used. It is strongly discouraged to directly deal with instances of VariableAndFixedInt.
+  * Indeed, in order to write generic code, it is the responsibility of the callee to properly convert
+  * it to either a true compile-time quantity (i.e. a FixedInt<N>), or to a runtime quantity (e.g., an Index)
+  * using the following generic helper:
+  * \code
+  * internal::cleanup_index_type<T>::type
+  * internal::cleanup_index_type<T,DynamicKey>::type
+  * \endcode
+  * where T can be a template instantiation of VariableAndFixedInt or numerous other integer-like representations.
+  * \c DynamicKey is either Dynamic (default) or DynamicIndex and used to identify true compile-time values.
+  *
+  * For convenience, you can also extract the compile-time value \c N using the following helper:
+  * \code
+  * internal::get_fixed_value<T,DefaultVal>::value
+  * \endcode
+  * that will give you \c N if T equals VariableAndFixedInt<N>, and \c DefaultVal if T does not embed any compile-time value (e.g., T==int).
+  *
+  * \sa fix<N>(int), class FixedInt
+  */
+template<int N> class VariableAndFixedInt
+{
+public:
+  static const int value = N;
+  operator int() const { return m_value; }
+  VariableAndFixedInt(int val) { m_value = val; }
+protected:
+  int m_value;
+};
+
+template<typename T, int Default=Dynamic> struct get_fixed_value {
+  static const int value = Default;
+};
+
+template<int N,int Default> struct get_fixed_value<FixedInt<N>,Default> {
+  static const int value = N;
+};
+
+#if !EIGEN_HAS_CXX14
+template<int N,int Default> struct get_fixed_value<FixedInt<N> (*)(),Default> {
+  static const int value = N;
+};
+#endif
+
+template<int N,int Default> struct get_fixed_value<VariableAndFixedInt<N>,Default> {
+  static const int value = N ;
+};
+
+template<typename T, int N, int Default>
+struct get_fixed_value<variable_if_dynamic<T,N>,Default> {
+  static const int value = N;
+};
+
+template<typename T> EIGEN_DEVICE_FUNC Index get_runtime_value(const T &x) { return x; }
+#if !EIGEN_HAS_CXX14
+template<int N> EIGEN_DEVICE_FUNC Index get_runtime_value(FixedInt<N> (*)()) { return N; }
+#endif
+
+// Cleanup integer/FixedInt/VariableAndFixedInt/etc types:
+
+// By default, no cleanup:
+template<typename T, int DynamicKey=Dynamic, typename EnableIf=void> struct cleanup_index_type { typedef T type; };
+
+// Convert any integral type (e.g., short, int, unsigned int, etc.) to Eigen::Index
+template<typename T, int DynamicKey> struct cleanup_index_type<T,DynamicKey,typename internal::enable_if<internal::is_integral<T>::value>::type> { typedef Index type; };
+
+#if !EIGEN_HAS_CXX14
+// In c++98/c++11, fix<N> is a pointer to function that we better cleanup to a true FixedInt<N>:
+template<int N, int DynamicKey> struct cleanup_index_type<FixedInt<N> (*)(), DynamicKey> { typedef FixedInt<N> type; };
+#endif
+
+// If VariableAndFixedInt does not match DynamicKey, then we turn it to a pure compile-time value:
+template<int N, int DynamicKey> struct cleanup_index_type<VariableAndFixedInt<N>, DynamicKey> { typedef FixedInt<N> type; };
+// If VariableAndFixedInt matches DynamicKey, then we turn it to a pure runtime-value (aka Index):
+template<int DynamicKey> struct cleanup_index_type<VariableAndFixedInt<DynamicKey>, DynamicKey> { typedef Index type; };
+
+#if EIGEN_HAS_CXX11
+template<int N, int DynamicKey> struct cleanup_index_type<std::integral_constant<int,N>, DynamicKey> { typedef FixedInt<N> type; };
+#endif
+
+} // end namespace internal
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+
+#if EIGEN_HAS_CXX14
+template<int N>
+static const internal::FixedInt<N> fix{};
+#else
+template<int N>
+inline internal::FixedInt<N> fix() { return internal::FixedInt<N>(); }
+
+// The generic typename T is mandatory. Otherwise, a code like fix<N> could refer to either the function above or this next overload.
+// This way a code like fix<N> can only refer to the previous function.
+template<int N,typename T>
+inline internal::VariableAndFixedInt<N> fix(T val) { return internal::VariableAndFixedInt<N>(val); }
+#endif
+
+#else // EIGEN_PARSED_BY_DOXYGEN
+
+/** \var fix<N>()
+  * \ingroup Core_Module
+  *
+  * This \em identifier permits to construct an object embedding a compile-time integer \c N.
+  *
+  * \tparam N the compile-time integer value
+  *
+  * It is typically used in conjunction with the Eigen::seq and Eigen::seqN functions to pass compile-time values to them:
+  * \code
+  * seqN(10,fix<4>,fix<-3>)   // <=> [10 7 4 1]
+  * \endcode
+  *
+  * See also the function fix(int) to pass both a compile-time and runtime value.
+  *
+  * In c++14, it is implemented as:
+  * \code
+  * template<int N> static const internal::FixedInt<N> fix{};
+  * \endcode
+  * where internal::FixedInt<N> is an internal template class similar to
+  * <a href="http://en.cppreference.com/w/cpp/types/integral_constant">\c std::integral_constant </a><tt> <int,N> </tt>
+  * Here, \c fix<N> is thus an object of type \c internal::FixedInt<N>.
+  *
+  * In c++98/11, it is implemented as a function:
+  * \code
+  * template<int N> inline internal::FixedInt<N> fix();
+  * \endcode
+  * Here internal::FixedInt<N> is thus a pointer to function.
+  *
+  * If for some reason you want a true object in c++98 then you can write: \code fix<N>() \endcode which is also valid in c++14.
+  *
+  * \sa fix<N>(int), seq, seqN
+  */
+template<int N>
+static const auto fix();
+
+/** \fn fix<N>(int)
+  * \ingroup Core_Module
+  *
+  * This function returns an object embedding both a compile-time integer \c N, and a fallback runtime value \a val.
+  *
+  * \tparam N the compile-time integer value
+  * \param  val the fallback runtime integer value
+  *
+  * This function is a more general version of the \ref fix identifier/function that can be used in template code
+  * where the compile-time value could turn out to actually mean "undefined at compile-time". For positive integers
+  * such as a size or a dimension, this case is identified by Eigen::Dynamic, whereas runtime signed integers
+  * (e.g., an increment/stride) are identified as Eigen::DynamicIndex. In such a case, the runtime value \a val
+  * will be used as a fallback.
+  *
+  * A typical use case would be:
+  * \code
+  * template<typename Derived> void foo(const MatrixBase<Derived> &mat) {
+  *   const int N = Derived::RowsAtCompileTime==Dynamic ? Dynamic : Derived::RowsAtCompileTime/2;
+  *   const int n = mat.rows()/2;
+  *   ... mat( seqN(0,fix<N>(n) ) ...;
+  * }
+  * \endcode
+  * In this example, the function Eigen::seqN knows that the second argument is expected to be a size.
+  * If the passed compile-time value N equals Eigen::Dynamic, then the proxy object returned by fix will be dissmissed, and converted to an Eigen::Index of value \c n.
+  * Otherwise, the runtime-value \c n will be dissmissed, and the returned ArithmeticSequence will be of the exact same type as <tt> seqN(0,fix<N>) </tt>.
+  *
+  * \sa fix, seqN, class ArithmeticSequence
+  */
+template<int N>
+static const auto fix(int val);
+
+#endif // EIGEN_PARSED_BY_DOXYGEN
+
+} // end namespace Eigen
+
+#endif // EIGEN_INTEGRAL_CONSTANT_H
diff --git a/eigen/Eigen/src/Core/util/MKL_support.h b/eigen/Eigen/src/Core/util/MKL_support.h
index 1ef3b61..26b5966 100644
--- a/eigen/Eigen/src/Core/util/MKL_support.h
+++ b/eigen/Eigen/src/Core/util/MKL_support.h
@@ -49,7 +49,7 @@
   #define EIGEN_USE_LAPACKE
 #endif
 
-#if defined(EIGEN_USE_BLAS) || defined(EIGEN_USE_LAPACKE) || defined(EIGEN_USE_MKL_VML)
+#if defined(EIGEN_USE_MKL_VML)
   #define EIGEN_USE_MKL
 #endif
 
@@ -64,7 +64,6 @@
 #   ifndef EIGEN_USE_MKL
     /*If the MKL version is too old, undef everything*/
 #       undef   EIGEN_USE_MKL_ALL
-#       undef   EIGEN_USE_BLAS
 #       undef   EIGEN_USE_LAPACKE
 #       undef   EIGEN_USE_MKL_VML
 #       undef   EIGEN_USE_LAPACKE_STRICT
@@ -73,7 +72,7 @@
 #endif
 
 #if defined EIGEN_USE_MKL
-#include <mkl_lapacke.h>
+
 #define EIGEN_MKL_VML_THRESHOLD 128
 
 /* MKL_DOMAIN_BLAS, etc are defined only in 10.3 update 7 */
@@ -107,52 +106,23 @@
 #else
 #define EIGEN_MKL_DOMAIN_PARDISO MKL_PARDISO
 #endif
+#endif
 
 namespace Eigen {
 
 typedef std::complex<double> dcomplex;
 typedef std::complex<float>  scomplex;
 
-namespace internal {
-
-template<typename MKLType, typename EigenType>
-static inline void assign_scalar_eig2mkl(MKLType& mklScalar, const EigenType& eigenScalar) {
-  mklScalar=eigenScalar;
-}
-
-template<typename MKLType, typename EigenType>
-static inline void assign_conj_scalar_eig2mkl(MKLType& mklScalar, const EigenType& eigenScalar) {
-  mklScalar=eigenScalar;
-}
-
-template <>
-inline void assign_scalar_eig2mkl<MKL_Complex16,dcomplex>(MKL_Complex16& mklScalar, const dcomplex& eigenScalar) {
-  mklScalar.real=eigenScalar.real();
-  mklScalar.imag=eigenScalar.imag();
-}
-
-template <>
-inline void assign_scalar_eig2mkl<MKL_Complex8,scomplex>(MKL_Complex8& mklScalar, const scomplex& eigenScalar) {
-  mklScalar.real=eigenScalar.real();
-  mklScalar.imag=eigenScalar.imag();
-}
-
-template <>
-inline void assign_conj_scalar_eig2mkl<MKL_Complex16,dcomplex>(MKL_Complex16& mklScalar, const dcomplex& eigenScalar) {
-  mklScalar.real=eigenScalar.real();
-  mklScalar.imag=-eigenScalar.imag();
-}
-
-template <>
-inline void assign_conj_scalar_eig2mkl<MKL_Complex8,scomplex>(MKL_Complex8& mklScalar, const scomplex& eigenScalar) {
-  mklScalar.real=eigenScalar.real();
-  mklScalar.imag=-eigenScalar.imag();
-}
-
-} // end namespace internal
+#if defined(EIGEN_USE_MKL)
+typedef MKL_INT BlasIndex;
+#else
+typedef int BlasIndex;
+#endif
 
 } // end namespace Eigen
 
+#if defined(EIGEN_USE_BLAS)
+#include "../../misc/blas.h"
 #endif
 
 #endif // EIGEN_MKL_SUPPORT_H
diff --git a/eigen/Eigen/src/Core/util/Macros.h b/eigen/Eigen/src/Core/util/Macros.h
index 16c248c..14ec87d 100644
--- a/eigen/Eigen/src/Core/util/Macros.h
+++ b/eigen/Eigen/src/Core/util/Macros.h
@@ -1,7 +1,7 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
-// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
 // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
 //
 // This Source Code Form is subject to the terms of the Mozilla
@@ -12,26 +12,25 @@
 #define EIGEN_MACROS_H
 
 #define EIGEN_WORLD_VERSION 3
-#define EIGEN_MAJOR_VERSION 2
-#define EIGEN_MINOR_VERSION 9
+#define EIGEN_MAJOR_VERSION 3
+#define EIGEN_MINOR_VERSION 90
 
 #define EIGEN_VERSION_AT_LEAST(x,y,z) (EIGEN_WORLD_VERSION>x || (EIGEN_WORLD_VERSION>=x && \
                                       (EIGEN_MAJOR_VERSION>y || (EIGEN_MAJOR_VERSION>=y && \
                                                                  EIGEN_MINOR_VERSION>=z))))
 
-
 // Compiler identification, EIGEN_COMP_*
 
 /// \internal EIGEN_COMP_GNUC set to 1 for all compilers compatible with GCC
 #ifdef __GNUC__
-  #define EIGEN_COMP_GNUC 1
+  #define EIGEN_COMP_GNUC (__GNUC__*10+__GNUC_MINOR__)
 #else
   #define EIGEN_COMP_GNUC 0
 #endif
 
-/// \internal EIGEN_COMP_CLANG set to 1 if the compiler is clang (alias for __clang__)
+/// \internal EIGEN_COMP_CLANG set to major+minor version (e.g., 307 for clang 3.7) if the compiler is clang
 #if defined(__clang__)
-  #define EIGEN_COMP_CLANG 1
+  #define EIGEN_COMP_CLANG (__clang_major__*100+__clang_minor__)
 #else
   #define EIGEN_COMP_CLANG 0
 #endif
@@ -72,8 +71,17 @@
   #define EIGEN_COMP_MSVC 0
 #endif
 
-/// \internal EIGEN_COMP_MSVC_STRICT set to 1 if the compiler is really Microsoft Visual C++ and not ,e.g., ICC
-#if EIGEN_COMP_MSVC && !(EIGEN_COMP_ICC)
+// For the record, here is a table summarizing the possible values for EIGEN_COMP_MSVC:
+//  name  ver   MSC_VER
+//  2008    9      1500
+//  2010   10      1600
+//  2012   11      1700
+//  2013   12      1800
+//  2015   14      1900
+//  "15"   15      1900
+
+/// \internal EIGEN_COMP_MSVC_STRICT set to 1 if the compiler is really Microsoft Visual C++ and not ,e.g., ICC or clang-cl
+#if EIGEN_COMP_MSVC && !(EIGEN_COMP_ICC || EIGEN_COMP_LLVM || EIGEN_COMP_CLANG)
   #define EIGEN_COMP_MSVC_STRICT _MSC_VER
 #else
   #define EIGEN_COMP_MSVC_STRICT 0
@@ -100,9 +108,16 @@
   #define EIGEN_COMP_ARM 0
 #endif
 
+/// \internal EIGEN_COMP_ARM set to 1 if the compiler is ARM Compiler
+#if defined(__EMSCRIPTEN__)
+  #define EIGEN_COMP_EMSCRIPTEN 1
+#else
+  #define EIGEN_COMP_EMSCRIPTEN 0
+#endif
+
 
 /// \internal EIGEN_GNUC_STRICT set to 1 if the compiler is really GCC and not a compatible compiler (e.g., ICC, clang, mingw, etc.)
-#if EIGEN_COMP_GNUC && !(EIGEN_COMP_CLANG || EIGEN_COMP_ICC || EIGEN_COMP_MINGW || EIGEN_COMP_PGI || EIGEN_COMP_IBM || EIGEN_COMP_ARM )
+#if EIGEN_COMP_GNUC && !(EIGEN_COMP_CLANG || EIGEN_COMP_ICC || EIGEN_COMP_MINGW || EIGEN_COMP_PGI || EIGEN_COMP_IBM || EIGEN_COMP_ARM || EIGEN_COMP_EMSCRIPTEN)
   #define EIGEN_COMP_GNUC_STRICT 1
 #else
   #define EIGEN_COMP_GNUC_STRICT 0
@@ -299,91 +314,176 @@
 #endif
 
 
-#if EIGEN_GNUC_AT_MOST(4,3) && !defined(__clang__)
+
+#if EIGEN_GNUC_AT_MOST(4,3) && !EIGEN_COMP_CLANG
   // see bug 89
   #define EIGEN_SAFE_TO_USE_STANDARD_ASSERT_MACRO 0
 #else
   #define EIGEN_SAFE_TO_USE_STANDARD_ASSERT_MACRO 1
 #endif
 
-// 16 byte alignment is only useful for vectorization. Since it affects the ABI, we need to enable
-// 16 byte alignment on all platforms where vectorization might be enabled. In theory we could always
-// enable alignment, but it can be a cause of problems on some platforms, so we just disable it in
-// certain common platform (compiler+architecture combinations) to avoid these problems.
-// Only static alignment is really problematic (relies on nonstandard compiler extensions that don't
-// work everywhere, for example don't work on GCC/ARM), try to keep heap alignment even
-// when we have to disable static alignment.
-#if defined(__GNUC__) && !(defined(__i386__) || defined(__x86_64__) || defined(__powerpc__) || defined(__ppc__) || defined(__ia64__))
-#define EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT 1
+// This macro can be used to prevent from macro expansion, e.g.:
+//   std::max EIGEN_NOT_A_MACRO(a,b)
+#define EIGEN_NOT_A_MACRO
+
+#ifdef EIGEN_DEFAULT_TO_ROW_MAJOR
+#define EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION Eigen::RowMajor
 #else
-#define EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT 0
+#define EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION Eigen::ColMajor
 #endif
 
-// static alignment is completely disabled with GCC 3, Sun Studio, and QCC/QNX
-#if !EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT \
- && !EIGEN_GCC3_OR_OLDER \
- && !defined(__SUNPRO_CC) \
- && !defined(__QNXNTO__)
-  #define EIGEN_ARCH_WANTS_STACK_ALIGNMENT 1
-#else
-  #define EIGEN_ARCH_WANTS_STACK_ALIGNMENT 0
+#ifndef EIGEN_DEFAULT_DENSE_INDEX_TYPE
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE std::ptrdiff_t
 #endif
 
-#ifdef EIGEN_DONT_ALIGN
-  #ifndef EIGEN_DONT_ALIGN_STATICALLY
-    #define EIGEN_DONT_ALIGN_STATICALLY
-  #endif
-  #define EIGEN_ALIGN 0
+// Cross compiler wrapper around LLVM's __has_builtin
+#ifdef __has_builtin
+#  define EIGEN_HAS_BUILTIN(x) __has_builtin(x)
 #else
-  #define EIGEN_ALIGN 1
+#  define EIGEN_HAS_BUILTIN(x) 0
 #endif
 
-// EIGEN_ALIGN_STATICALLY is the true test whether we want to align arrays on the stack or not. It takes into account both the user choice to explicitly disable
-// alignment (EIGEN_DONT_ALIGN_STATICALLY) and the architecture config (EIGEN_ARCH_WANTS_STACK_ALIGNMENT). Henceforth, only EIGEN_ALIGN_STATICALLY should be used.
-#if EIGEN_ARCH_WANTS_STACK_ALIGNMENT && !defined(EIGEN_DONT_ALIGN_STATICALLY)
-  #define EIGEN_ALIGN_STATICALLY 1
-#else
-  #define EIGEN_ALIGN_STATICALLY 0
-  #ifndef EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT
-    #define EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT
-  #endif
+// A Clang feature extension to determine compiler features.
+// We use it to determine 'cxx_rvalue_references'
+#ifndef __has_feature
+# define __has_feature(x) 0
 #endif
 
-#ifdef EIGEN_DEFAULT_TO_ROW_MAJOR
-#define EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION RowMajor
+// Some old compilers do not support template specializations like:
+// template<typename T,int N> void foo(const T x[N]);
+#if !( EIGEN_COMP_CLANG && ((EIGEN_COMP_CLANG<309) || defined(__apple_build_version__)) || EIGEN_COMP_GNUC_STRICT && EIGEN_COMP_GNUC<49)
+#define EIGEN_HAS_STATIC_ARRAY_TEMPLATE 1
 #else
-#define EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION ColMajor
+#define EIGEN_HAS_STATIC_ARRAY_TEMPLATE 0
 #endif
 
-#ifndef EIGEN_DEFAULT_DENSE_INDEX_TYPE
-#define EIGEN_DEFAULT_DENSE_INDEX_TYPE std::ptrdiff_t
+// Upperbound on the C++ version to use.
+// Expected values are 03, 11, 14, 17, etc.
+// By default, let's use an arbitrarily large C++ version.
+#ifndef EIGEN_MAX_CPP_VER
+#define EIGEN_MAX_CPP_VER 99
 #endif
 
-// A Clang feature extension to determine compiler features.
-// We use it to determine 'cxx_rvalue_references'
-#ifndef __has_feature
-# define __has_feature(x) 0
+#if EIGEN_MAX_CPP_VER>=11 && (defined(__cplusplus) && (__cplusplus >= 201103L) || EIGEN_COMP_MSVC >= 1900)
+#define EIGEN_HAS_CXX11 1
+#else
+#define EIGEN_HAS_CXX11 0
+#endif
+
+#if EIGEN_MAX_CPP_VER>=14 && (defined(__cplusplus) && (__cplusplus > 201103L) || EIGEN_COMP_MSVC >= 1910)
+#define EIGEN_HAS_CXX14 1
+#else
+#define EIGEN_HAS_CXX14 0
 #endif
 
 // Do we support r-value references?
-#if (__has_feature(cxx_rvalue_references) || \
-     (defined(__cplusplus) && __cplusplus >= 201103L) || \
-     (defined(_MSC_VER) && _MSC_VER >= 1600))
-  #define EIGEN_HAVE_RVALUE_REFERENCES
+#ifndef EIGEN_HAS_RVALUE_REFERENCES
+#if EIGEN_MAX_CPP_VER>=11 && \
+    (__has_feature(cxx_rvalue_references) || \
+    (defined(__cplusplus) && __cplusplus >= 201103L) || \
+    (EIGEN_COMP_MSVC >= 1600))
+  #define EIGEN_HAS_RVALUE_REFERENCES 1
+#else
+  #define EIGEN_HAS_RVALUE_REFERENCES 0
+#endif
 #endif
 
+// Does the compiler support C99?
+#ifndef EIGEN_HAS_C99_MATH
+#if EIGEN_MAX_CPP_VER>=11 && \
+    ((defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901))       \
+  || (defined(__GNUC__) && defined(_GLIBCXX_USE_C99)) \
+  || (defined(_LIBCPP_VERSION) && !defined(_MSC_VER)) \
+  || (EIGEN_COMP_MSVC >= 1900) || defined(__SYCL_DEVICE_ONLY__))
+  #define EIGEN_HAS_C99_MATH 1
+#else
+  #define EIGEN_HAS_C99_MATH 0
+#endif
+#endif
 
-// Cross compiler wrapper around LLVM's __has_builtin
-#ifdef __has_builtin
-#  define EIGEN_HAS_BUILTIN(x) __has_builtin(x)
+// Does the compiler support result_of?
+#ifndef EIGEN_HAS_STD_RESULT_OF
+#if EIGEN_MAX_CPP_VER>=11 && ((__has_feature(cxx_lambdas) || (defined(__cplusplus) && __cplusplus >= 201103L)))
+#define EIGEN_HAS_STD_RESULT_OF 1
 #else
-#  define EIGEN_HAS_BUILTIN(x) 0
+#define EIGEN_HAS_STD_RESULT_OF 0
+#endif
+#endif
+
+// Does the compiler support variadic templates?
+#ifndef EIGEN_HAS_VARIADIC_TEMPLATES
+#if EIGEN_MAX_CPP_VER>=11 && (__cplusplus > 199711L || EIGEN_COMP_MSVC >= 1900) \
+  && (!defined(__NVCC__) || !EIGEN_ARCH_ARM_OR_ARM64 || (defined __CUDACC_VER__ && __CUDACC_VER__ >= 80000) )
+    // ^^ Disable the use of variadic templates when compiling with versions of nvcc older than 8.0 on ARM devices:
+    //    this prevents nvcc from crashing when compiling Eigen on Tegra X1
+#define EIGEN_HAS_VARIADIC_TEMPLATES 1
+#elif  EIGEN_MAX_CPP_VER>=11 && (__cplusplus > 199711L || EIGEN_COMP_MSVC >= 1900) && defined(__SYCL_DEVICE_ONLY__)
+#define EIGEN_HAS_VARIADIC_TEMPLATES 1
+#else
+#define EIGEN_HAS_VARIADIC_TEMPLATES 0
+#endif
+#endif
+
+// Does the compiler fully support const expressions? (as in c++14)
+#ifndef EIGEN_HAS_CONSTEXPR
+
+#if defined(__CUDACC__)
+// Const expressions are supported provided that c++11 is enabled and we're using either clang or nvcc 7.5 or above
+#if EIGEN_MAX_CPP_VER>=14 && (__cplusplus > 199711L && defined(__CUDACC_VER__) && (EIGEN_COMP_CLANG || __CUDACC_VER__ >= 70500))
+  #define EIGEN_HAS_CONSTEXPR 1
+#endif
+#elif EIGEN_MAX_CPP_VER>=14 && (__has_feature(cxx_relaxed_constexpr) || (defined(__cplusplus) && __cplusplus >= 201402L) || \
+  (EIGEN_GNUC_AT_LEAST(4,8) && (__cplusplus > 199711L)) || \
+  (EIGEN_COMP_CLANG >= 306 && (__cplusplus > 199711L)))
+#define EIGEN_HAS_CONSTEXPR 1
+#endif
+
+#ifndef EIGEN_HAS_CONSTEXPR
+#define EIGEN_HAS_CONSTEXPR 0
+#endif
+
+#endif
+
+// Does the compiler support C++11 math?
+// Let's be conservative and enable the default C++11 implementation only if we are sure it exists
+#ifndef EIGEN_HAS_CXX11_MATH
+  #if EIGEN_MAX_CPP_VER>=11 && ((__cplusplus > 201103L) || (__cplusplus >= 201103L) && (EIGEN_COMP_GNUC_STRICT || EIGEN_COMP_CLANG || EIGEN_COMP_MSVC || EIGEN_COMP_ICC)  \
+      && (EIGEN_ARCH_i386_OR_x86_64) && (EIGEN_OS_GNULINUX || EIGEN_OS_WIN_STRICT || EIGEN_OS_MAC))
+    #define EIGEN_HAS_CXX11_MATH 1
+  #else
+    #define EIGEN_HAS_CXX11_MATH 0
+  #endif
+#endif
+
+// Does the compiler support proper C++11 containers?
+#ifndef EIGEN_HAS_CXX11_CONTAINERS
+  #if    EIGEN_MAX_CPP_VER>=11 && \
+         ((__cplusplus > 201103L) \
+      || ((__cplusplus >= 201103L) && (EIGEN_COMP_GNUC_STRICT || EIGEN_COMP_CLANG || EIGEN_COMP_ICC>=1400)) \
+      || EIGEN_COMP_MSVC >= 1900)
+    #define EIGEN_HAS_CXX11_CONTAINERS 1
+  #else
+    #define EIGEN_HAS_CXX11_CONTAINERS 0
+  #endif
+#endif
+
+// Does the compiler support C++11 noexcept?
+#ifndef EIGEN_HAS_CXX11_NOEXCEPT
+  #if    EIGEN_MAX_CPP_VER>=11 && \
+         (__has_feature(cxx_noexcept) \
+      || (__cplusplus > 201103L) \
+      || ((__cplusplus >= 201103L) && (EIGEN_COMP_GNUC_STRICT || EIGEN_COMP_CLANG || EIGEN_COMP_ICC>=1400)) \
+      || EIGEN_COMP_MSVC >= 1900)
+    #define EIGEN_HAS_CXX11_NOEXCEPT 1
+  #else
+    #define EIGEN_HAS_CXX11_NOEXCEPT 0
+  #endif
 #endif
 
 /** Allows to disable some optimizations which might affect the accuracy of the result.
   * Such optimization are enabled by default, and set EIGEN_FAST_MATH to 0 to disable them.
   * They currently include:
-  *   - single precision Cwise::sin() and Cwise::cos() when SSE vectorization is enabled.
+  *   - single precision ArrayBase::sin() and ArrayBase::cos() for SSE and AVX vectorization.
   */
 #ifndef EIGEN_FAST_MATH
 #define EIGEN_FAST_MATH 1
@@ -395,6 +495,8 @@
 #define EIGEN_CAT2(a,b) a ## b
 #define EIGEN_CAT(a,b) EIGEN_CAT2(a,b)
 
+#define EIGEN_COMMA ,
+
 // convert a token to a string
 #define EIGEN_MAKESTRING2(a) #a
 #define EIGEN_MAKESTRING(a) EIGEN_MAKESTRING2(a)
@@ -402,7 +504,7 @@
 // EIGEN_STRONG_INLINE is a stronger version of the inline, using __forceinline on MSVC,
 // but it still doesn't use GCC's always_inline. This is useful in (common) situations where MSVC needs forceinline
 // but GCC is still doing fine with just inline.
-#if (defined _MSC_VER) || (defined __INTEL_COMPILER)
+#if EIGEN_COMP_MSVC || EIGEN_COMP_ICC
 #define EIGEN_STRONG_INLINE __forceinline
 #else
 #define EIGEN_STRONG_INLINE inline
@@ -412,24 +514,25 @@
 // attribute to maximize inlining. This should only be used when really necessary: in particular,
 // it uses __attribute__((always_inline)) on GCC, which most of the time is useless and can severely harm compile times.
 // FIXME with the always_inline attribute,
-// gcc 3.4.x reports the following compilation error:
+// gcc 3.4.x and 4.1 reports the following compilation error:
 //   Eval.h:91: sorry, unimplemented: inlining failed in call to 'const Eigen::Eval<Derived> Eigen::MatrixBase<Scalar, Derived>::eval() const'
 //    : function body not available
-#if EIGEN_GNUC_AT_LEAST(4,0)
+//   See also bug 1367
+#if EIGEN_GNUC_AT_LEAST(4,2)
 #define EIGEN_ALWAYS_INLINE __attribute__((always_inline)) inline
 #else
 #define EIGEN_ALWAYS_INLINE EIGEN_STRONG_INLINE
 #endif
 
-#if (defined __GNUC__)
+#if EIGEN_COMP_GNUC
 #define EIGEN_DONT_INLINE __attribute__((noinline))
-#elif (defined _MSC_VER)
+#elif EIGEN_COMP_MSVC
 #define EIGEN_DONT_INLINE __declspec(noinline)
 #else
 #define EIGEN_DONT_INLINE
 #endif
 
-#if (defined __GNUC__)
+#if EIGEN_COMP_GNUC
 #define EIGEN_PERMISSIVE_EXPR __extension__
 #else
 #define EIGEN_PERMISSIVE_EXPR
@@ -439,8 +542,8 @@
 //  - static is not very good because it prevents definitions from different object files to be merged.
 //           So static causes the resulting linked executable to be bloated with multiple copies of the same function.
 //  - inline is not perfect either as it unwantedly hints the compiler toward inlining the function.
-#define EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-#define EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS inline
+#define EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_DEVICE_FUNC
+#define EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_DEVICE_FUNC inline
 
 #ifdef NDEBUG
 # ifndef EIGEN_NO_DEBUG
@@ -498,15 +601,15 @@
 #endif
 
 #ifdef EIGEN_NO_DEBUG
-#define EIGEN_ONLY_USED_FOR_DEBUG(x) (void)x
+#define EIGEN_ONLY_USED_FOR_DEBUG(x) EIGEN_UNUSED_VARIABLE(x)
 #else
 #define EIGEN_ONLY_USED_FOR_DEBUG(x)
 #endif
 
 #ifndef EIGEN_NO_DEPRECATED_WARNING
-  #if (defined __GNUC__)
+  #if EIGEN_COMP_GNUC
     #define EIGEN_DEPRECATED __attribute__((deprecated))
-  #elif (defined _MSC_VER)
+  #elif EIGEN_COMP_MSVC
     #define EIGEN_DEPRECATED __declspec(deprecated)
   #else
     #define EIGEN_DEPRECATED
@@ -515,7 +618,7 @@
   #define EIGEN_DEPRECATED
 #endif
 
-#if (defined __GNUC__)
+#if EIGEN_COMP_GNUC
 #define EIGEN_UNUSED __attribute__((unused))
 #else
 #define EIGEN_UNUSED
@@ -524,19 +627,41 @@
 // Suppresses 'unused variable' warnings.
 namespace Eigen {
   namespace internal {
-    template<typename T> void ignore_unused_variable(const T&) {}
+    template<typename T> EIGEN_DEVICE_FUNC void ignore_unused_variable(const T&) {}
   }
 }
 #define EIGEN_UNUSED_VARIABLE(var) Eigen::internal::ignore_unused_variable(var);
 
 #if !defined(EIGEN_ASM_COMMENT)
-  #if (defined __GNUC__) && ( defined(__i386__) || defined(__x86_64__) )
+  #if EIGEN_COMP_GNUC && (EIGEN_ARCH_i386_OR_x86_64 || EIGEN_ARCH_ARM_OR_ARM64)
     #define EIGEN_ASM_COMMENT(X)  __asm__("#" X)
   #else
     #define EIGEN_ASM_COMMENT(X)
   #endif
 #endif
 
+
+#if EIGEN_COMP_MSVC
+  // NOTE MSVC often gives C4127 warnings with compiletime if statements. See bug 1362.
+  // This workaround is ugly, but it does the job.
+#  define EIGEN_CONST_CONDITIONAL(cond)  (void)0, cond
+#else
+#  define EIGEN_CONST_CONDITIONAL(cond)  cond
+#endif
+
+//------------------------------------------------------------------------------------------
+// Static and dynamic alignment control
+//
+// The main purpose of this section is to define EIGEN_MAX_ALIGN_BYTES and EIGEN_MAX_STATIC_ALIGN_BYTES
+// as the maximal boundary in bytes on which dynamically and statically allocated data may be alignment respectively.
+// The values of EIGEN_MAX_ALIGN_BYTES and EIGEN_MAX_STATIC_ALIGN_BYTES can be specified by the user. If not,
+// a default value is automatically computed based on architecture, compiler, and OS.
+//
+// This section also defines macros EIGEN_ALIGN_TO_BOUNDARY(N) and the shortcuts EIGEN_ALIGN{8,16,32,_MAX}
+// to be used to declare statically aligned buffers.
+//------------------------------------------------------------------------------------------
+
+
 /* EIGEN_ALIGN_TO_BOUNDARY(n) forces data to be n-byte aligned. This is used to satisfy SIMD requirements.
  * However, we do that EVEN if vectorization (EIGEN_VECTORIZE) is disabled,
  * so that vectorization doesn't affect binary compatibility.
@@ -544,28 +669,149 @@ namespace Eigen {
  * If we made alignment depend on whether or not EIGEN_VECTORIZE is defined, it would be impossible to link
  * vectorized and non-vectorized code.
  */
-#if (defined __GNUC__) || (defined __PGI) || (defined __IBMCPP__) || (defined __ARMCC_VERSION)
+#if (defined __CUDACC__)
+  #define EIGEN_ALIGN_TO_BOUNDARY(n) __align__(n)
+#elif EIGEN_COMP_GNUC || EIGEN_COMP_PGI || EIGEN_COMP_IBM || EIGEN_COMP_ARM
   #define EIGEN_ALIGN_TO_BOUNDARY(n) __attribute__((aligned(n)))
-#elif (defined _MSC_VER)
+#elif EIGEN_COMP_MSVC
   #define EIGEN_ALIGN_TO_BOUNDARY(n) __declspec(align(n))
-#elif (defined __SUNPRO_CC)
+#elif EIGEN_COMP_SUNCC
   // FIXME not sure about this one:
   #define EIGEN_ALIGN_TO_BOUNDARY(n) __attribute__((aligned(n)))
 #else
   #error Please tell me what is the equivalent of __attribute__((aligned(n))) for your compiler
 #endif
 
+// If the user explicitly disable vectorization, then we also disable alignment
+#if defined(EIGEN_DONT_VECTORIZE)
+  #define EIGEN_IDEAL_MAX_ALIGN_BYTES 0
+#elif defined(EIGEN_VECTORIZE_AVX512)
+  // 64 bytes static alignmeent is preferred only if really required
+  #define EIGEN_IDEAL_MAX_ALIGN_BYTES 64
+#elif defined(__AVX__)
+  // 32 bytes static alignmeent is preferred only if really required
+  #define EIGEN_IDEAL_MAX_ALIGN_BYTES 32
+#else
+  #define EIGEN_IDEAL_MAX_ALIGN_BYTES 16
+#endif
+
+
+// EIGEN_MIN_ALIGN_BYTES defines the minimal value for which the notion of explicit alignment makes sense
+#define EIGEN_MIN_ALIGN_BYTES 16
+
+// Defined the boundary (in bytes) on which the data needs to be aligned. Note
+// that unless EIGEN_ALIGN is defined and not equal to 0, the data may not be
+// aligned at all regardless of the value of this #define.
+
+#if (defined(EIGEN_DONT_ALIGN_STATICALLY) || defined(EIGEN_DONT_ALIGN))  && defined(EIGEN_MAX_STATIC_ALIGN_BYTES) && EIGEN_MAX_STATIC_ALIGN_BYTES>0
+#error EIGEN_MAX_STATIC_ALIGN_BYTES and EIGEN_DONT_ALIGN[_STATICALLY] are both defined with EIGEN_MAX_STATIC_ALIGN_BYTES!=0. Use EIGEN_MAX_STATIC_ALIGN_BYTES=0 as a synonym of EIGEN_DONT_ALIGN_STATICALLY.
+#endif
+
+// EIGEN_DONT_ALIGN_STATICALLY and EIGEN_DONT_ALIGN are deprectated
+// They imply EIGEN_MAX_STATIC_ALIGN_BYTES=0
+#if defined(EIGEN_DONT_ALIGN_STATICALLY) || defined(EIGEN_DONT_ALIGN)
+  #ifdef EIGEN_MAX_STATIC_ALIGN_BYTES
+    #undef EIGEN_MAX_STATIC_ALIGN_BYTES
+  #endif
+  #define EIGEN_MAX_STATIC_ALIGN_BYTES 0
+#endif
+
+#ifndef EIGEN_MAX_STATIC_ALIGN_BYTES
+
+  // Try to automatically guess what is the best default value for EIGEN_MAX_STATIC_ALIGN_BYTES
+
+  // 16 byte alignment is only useful for vectorization. Since it affects the ABI, we need to enable
+  // 16 byte alignment on all platforms where vectorization might be enabled. In theory we could always
+  // enable alignment, but it can be a cause of problems on some platforms, so we just disable it in
+  // certain common platform (compiler+architecture combinations) to avoid these problems.
+  // Only static alignment is really problematic (relies on nonstandard compiler extensions),
+  // try to keep heap alignment even when we have to disable static alignment.
+  #if EIGEN_COMP_GNUC && !(EIGEN_ARCH_i386_OR_x86_64 || EIGEN_ARCH_ARM_OR_ARM64 || EIGEN_ARCH_PPC || EIGEN_ARCH_IA64)
+  #define EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT 1
+  #elif EIGEN_ARCH_ARM_OR_ARM64 && EIGEN_COMP_GNUC_STRICT && EIGEN_GNUC_AT_MOST(4, 6)
+  // Old versions of GCC on ARM, at least 4.4, were once seen to have buggy static alignment support.
+  // Not sure which version fixed it, hopefully it doesn't affect 4.7, which is still somewhat in use.
+  // 4.8 and newer seem definitely unaffected.
+  #define EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT 1
+  #else
+  #define EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT 0
+  #endif
+
+  // static alignment is completely disabled with GCC 3, Sun Studio, and QCC/QNX
+  #if !EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT \
+  && !EIGEN_GCC3_OR_OLDER \
+  && !EIGEN_COMP_SUNCC \
+  && !EIGEN_OS_QNX
+    #define EIGEN_ARCH_WANTS_STACK_ALIGNMENT 1
+  #else
+    #define EIGEN_ARCH_WANTS_STACK_ALIGNMENT 0
+  #endif
+
+  #if EIGEN_ARCH_WANTS_STACK_ALIGNMENT
+    #define EIGEN_MAX_STATIC_ALIGN_BYTES EIGEN_IDEAL_MAX_ALIGN_BYTES
+  #else
+    #define EIGEN_MAX_STATIC_ALIGN_BYTES 0
+  #endif
+
+#endif
+
+// If EIGEN_MAX_ALIGN_BYTES is defined, then it is considered as an upper bound for EIGEN_MAX_ALIGN_BYTES
+#if defined(EIGEN_MAX_ALIGN_BYTES) && EIGEN_MAX_ALIGN_BYTES<EIGEN_MAX_STATIC_ALIGN_BYTES
+#undef EIGEN_MAX_STATIC_ALIGN_BYTES
+#define EIGEN_MAX_STATIC_ALIGN_BYTES EIGEN_MAX_ALIGN_BYTES
+#endif
+
+#if EIGEN_MAX_STATIC_ALIGN_BYTES==0 && !defined(EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT)
+  #define EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT
+#endif
+
+// At this stage, EIGEN_MAX_STATIC_ALIGN_BYTES>0 is the true test whether we want to align arrays on the stack or not.
+// It takes into account both the user choice to explicitly enable/disable alignment (by settting EIGEN_MAX_STATIC_ALIGN_BYTES)
+// and the architecture config (EIGEN_ARCH_WANTS_STACK_ALIGNMENT).
+// Henceforth, only EIGEN_MAX_STATIC_ALIGN_BYTES should be used.
+
+
+// Shortcuts to EIGEN_ALIGN_TO_BOUNDARY
 #define EIGEN_ALIGN8  EIGEN_ALIGN_TO_BOUNDARY(8)
 #define EIGEN_ALIGN16 EIGEN_ALIGN_TO_BOUNDARY(16)
+#define EIGEN_ALIGN32 EIGEN_ALIGN_TO_BOUNDARY(32)
+#define EIGEN_ALIGN64 EIGEN_ALIGN_TO_BOUNDARY(64)
+#if EIGEN_MAX_STATIC_ALIGN_BYTES>0
+#define EIGEN_ALIGN_MAX EIGEN_ALIGN_TO_BOUNDARY(EIGEN_MAX_STATIC_ALIGN_BYTES)
+#else
+#define EIGEN_ALIGN_MAX
+#endif
+
+
+// Dynamic alignment control
+
+#if defined(EIGEN_DONT_ALIGN) && defined(EIGEN_MAX_ALIGN_BYTES) && EIGEN_MAX_ALIGN_BYTES>0
+#error EIGEN_MAX_ALIGN_BYTES and EIGEN_DONT_ALIGN are both defined with EIGEN_MAX_ALIGN_BYTES!=0. Use EIGEN_MAX_ALIGN_BYTES=0 as a synonym of EIGEN_DONT_ALIGN.
+#endif
 
-#if EIGEN_ALIGN_STATICALLY
-#define EIGEN_USER_ALIGN_TO_BOUNDARY(n) EIGEN_ALIGN_TO_BOUNDARY(n)
-#define EIGEN_USER_ALIGN16 EIGEN_ALIGN16
+#ifdef EIGEN_DONT_ALIGN
+  #ifdef EIGEN_MAX_ALIGN_BYTES
+    #undef EIGEN_MAX_ALIGN_BYTES
+  #endif
+  #define EIGEN_MAX_ALIGN_BYTES 0
+#elif !defined(EIGEN_MAX_ALIGN_BYTES)
+  #define EIGEN_MAX_ALIGN_BYTES EIGEN_IDEAL_MAX_ALIGN_BYTES
+#endif
+
+#if EIGEN_IDEAL_MAX_ALIGN_BYTES > EIGEN_MAX_ALIGN_BYTES
+#define EIGEN_DEFAULT_ALIGN_BYTES EIGEN_IDEAL_MAX_ALIGN_BYTES
 #else
-#define EIGEN_USER_ALIGN_TO_BOUNDARY(n)
-#define EIGEN_USER_ALIGN16
+#define EIGEN_DEFAULT_ALIGN_BYTES EIGEN_MAX_ALIGN_BYTES
 #endif
 
+
+#ifndef EIGEN_UNALIGNED_VECTORIZE
+#define EIGEN_UNALIGNED_VECTORIZE 1
+#endif
+
+//----------------------------------------------------------------------
+
+
 #ifdef EIGEN_DONT_USE_RESTRICT_KEYWORD
   #define EIGEN_RESTRICT
 #endif
@@ -591,25 +837,26 @@ namespace Eigen {
 // just an empty macro !
 #define EIGEN_EMPTY
 
-#if defined(_MSC_VER) && (_MSC_VER < 1900) && (!defined(__INTEL_COMPILER))
-#define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
-  using Base::operator =;
-#elif defined(__clang__) // workaround clang bug (see http://forum.kde.org/viewtopic.php?f=74&t=102653)
-#define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
-  using Base::operator =; \
-  EIGEN_STRONG_INLINE Derived& operator=(const Derived& other) { Base::operator=(other); return *this; } \
-  template <typename OtherDerived> \
-  EIGEN_STRONG_INLINE Derived& operator=(const DenseBase<OtherDerived>& other) { Base::operator=(other.derived()); return *this; }
-#else
-#define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
-  using Base::operator =; \
-  EIGEN_STRONG_INLINE Derived& operator=(const Derived& other) \
-  { \
-    Base::operator=(other); \
-    return *this; \
-  }
+#if EIGEN_COMP_MSVC_STRICT && (EIGEN_COMP_MSVC < 1900 ||  defined(__CUDACC_VER__)) // for older MSVC versions, as well as 1900 && CUDA 8, using the base operator is sufficient (cf Bugs 1000, 1324)
+  #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
+    using Base::operator =;
+#elif EIGEN_COMP_CLANG // workaround clang bug (see http://forum.kde.org/viewtopic.php?f=74&t=102653)
+  #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
+    using Base::operator =; \
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const Derived& other) { Base::operator=(other); return *this; } \
+    template <typename OtherDerived> \
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const DenseBase<OtherDerived>& other) { Base::operator=(other.derived()); return *this; }
+#else
+  #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
+    using Base::operator =; \
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const Derived& other) \
+    { \
+      Base::operator=(other); \
+      return *this; \
+    }
 #endif
 
+
 /** \internal
  * \brief Macro to manually inherit assignment operators.
  * This is necessary, because the implicitly defined assignment operator gets deleted when a custom operator= is defined.
@@ -628,32 +875,13 @@ namespace Eigen {
   typedef typename Eigen::internal::traits<Derived>::Scalar Scalar; /*!< \brief Numeric type, e.g. float, double, int or std::complex<float>. */ \
   typedef typename Eigen::NumTraits<Scalar>::Real RealScalar; /*!< \brief The underlying numeric type for composed scalar types. \details In cases where Scalar is e.g. std::complex<T>, T were corresponding to RealScalar. */ \
   typedef typename Base::CoeffReturnType CoeffReturnType; /*!< \brief The return type for coefficient access. \details Depending on whether the object allows direct coefficient access (e.g. for a MatrixXd), this type is either 'const Scalar&' or simply 'Scalar' for objects that do not allow direct coefficient access. */ \
-  typedef typename Eigen::internal::nested<Derived>::type Nested; \
+  typedef typename Eigen::internal::ref_selector<Derived>::type Nested; \
   typedef typename Eigen::internal::traits<Derived>::StorageKind StorageKind; \
-  typedef typename Eigen::internal::traits<Derived>::Index Index; \
-  enum { RowsAtCompileTime = Eigen::internal::traits<Derived>::RowsAtCompileTime, \
+  typedef typename Eigen::internal::traits<Derived>::StorageIndex StorageIndex; \
+  enum CompileTimeTraits \
+      { RowsAtCompileTime = Eigen::internal::traits<Derived>::RowsAtCompileTime, \
         ColsAtCompileTime = Eigen::internal::traits<Derived>::ColsAtCompileTime, \
         Flags = Eigen::internal::traits<Derived>::Flags, \
-        CoeffReadCost = Eigen::internal::traits<Derived>::CoeffReadCost, \
-        SizeAtCompileTime = Base::SizeAtCompileTime, \
-        MaxSizeAtCompileTime = Base::MaxSizeAtCompileTime, \
-        IsVectorAtCompileTime = Base::IsVectorAtCompileTime };
-
-
-#define EIGEN_DENSE_PUBLIC_INTERFACE(Derived) \
-  typedef typename Eigen::internal::traits<Derived>::Scalar Scalar; /*!< \brief Numeric type, e.g. float, double, int or std::complex<float>. */ \
-  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar; /*!< \brief The underlying numeric type for composed scalar types. \details In cases where Scalar is e.g. std::complex<T>, T were corresponding to RealScalar. */ \
-  typedef typename Base::PacketScalar PacketScalar; \
-  typedef typename Base::CoeffReturnType CoeffReturnType; /*!< \brief The return type for coefficient access. \details Depending on whether the object allows direct coefficient access (e.g. for a MatrixXd), this type is either 'const Scalar&' or simply 'Scalar' for objects that do not allow direct coefficient access. */ \
-  typedef typename Eigen::internal::nested<Derived>::type Nested; \
-  typedef typename Eigen::internal::traits<Derived>::StorageKind StorageKind; \
-  typedef typename Eigen::internal::traits<Derived>::Index Index; \
-  enum { RowsAtCompileTime = Eigen::internal::traits<Derived>::RowsAtCompileTime, \
-        ColsAtCompileTime = Eigen::internal::traits<Derived>::ColsAtCompileTime, \
-        MaxRowsAtCompileTime = Eigen::internal::traits<Derived>::MaxRowsAtCompileTime, \
-        MaxColsAtCompileTime = Eigen::internal::traits<Derived>::MaxColsAtCompileTime, \
-        Flags = Eigen::internal::traits<Derived>::Flags, \
-        CoeffReadCost = Eigen::internal::traits<Derived>::CoeffReadCost, \
         SizeAtCompileTime = Base::SizeAtCompileTime, \
         MaxSizeAtCompileTime = Base::MaxSizeAtCompileTime, \
         IsVectorAtCompileTime = Base::IsVectorAtCompileTime }; \
@@ -661,6 +889,12 @@ namespace Eigen {
   using Base::const_cast_derived;
 
 
+// FIXME Maybe the EIGEN_DENSE_PUBLIC_INTERFACE could be removed as importing PacketScalar is rarely needed
+#define EIGEN_DENSE_PUBLIC_INTERFACE(Derived) \
+  EIGEN_GENERIC_PUBLIC_INTERFACE(Derived) \
+  typedef typename Base::PacketScalar PacketScalar;
+
+
 #define EIGEN_PLAIN_ENUM_MIN(a,b) (((int)a <= (int)b) ? (int)a : (int)b)
 #define EIGEN_PLAIN_ENUM_MAX(a,b) (((int)a >= (int)b) ? (int)a : (int)b)
 
@@ -686,24 +920,14 @@ namespace Eigen {
 #define EIGEN_SIZE_MAX(a,b) (((int)a == Dynamic || (int)b == Dynamic) ? Dynamic \
                            : ((int)a >= (int)b) ? (int)a : (int)b)
 
-#define EIGEN_ADD_COST(a,b) int(a)==Dynamic || int(b)==Dynamic ? Dynamic : int(a)+int(b)
-
 #define EIGEN_LOGICAL_XOR(a,b) (((a) || (b)) && !((a) && (b)))
 
 #define EIGEN_IMPLIES(a,b) (!(a) || (b))
 
-#define EIGEN_MAKE_CWISE_BINARY_OP(METHOD,FUNCTOR) \
-  template<typename OtherDerived> \
-  EIGEN_STRONG_INLINE const CwiseBinaryOp<FUNCTOR<Scalar>, const Derived, const OtherDerived> \
-  (METHOD)(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const \
-  { \
-    return CwiseBinaryOp<FUNCTOR<Scalar>, const Derived, const OtherDerived>(derived(), other.derived()); \
-  }
-
-// the expression type of a cwise product
-#define EIGEN_CWISE_PRODUCT_RETURN_TYPE(LHS,RHS) \
+// the expression type of a standard coefficient wise binary operation
+#define EIGEN_CWISE_BINARY_RETURN_TYPE(LHS,RHS,OPNAME) \
     CwiseBinaryOp< \
-      internal::scalar_product_op< \
+      EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)< \
           typename internal::traits<LHS>::Scalar, \
           typename internal::traits<RHS>::Scalar \
       >, \
@@ -711,4 +935,84 @@ namespace Eigen {
       const RHS \
     >
 
+#define EIGEN_MAKE_CWISE_BINARY_OP(METHOD,OPNAME) \
+  template<typename OtherDerived> \
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,OPNAME) \
+  (METHOD)(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const \
+  { \
+    return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,OPNAME)(derived(), other.derived()); \
+  }
+
+#define EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,TYPEA,TYPEB) \
+  (Eigen::internal::has_ReturnType<Eigen::ScalarBinaryOpTraits<TYPEA,TYPEB,EIGEN_CAT(EIGEN_CAT(Eigen::internal::scalar_,OPNAME),_op)<TYPEA,TYPEB>  > >::value)
+
+#define EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(EXPR,SCALAR,OPNAME) \
+  CwiseBinaryOp<EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<typename internal::traits<EXPR>::Scalar,SCALAR>, const EXPR, \
+                const typename internal::plain_constant_type<EXPR,SCALAR>::type>
+
+#define EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(SCALAR,EXPR,OPNAME) \
+  CwiseBinaryOp<EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<SCALAR,typename internal::traits<EXPR>::Scalar>, \
+                const typename internal::plain_constant_type<EXPR,SCALAR>::type, const EXPR>
+
+// Workaround for MSVC 2010 (see ML thread "patch with compile for for MSVC 2010")
+#if EIGEN_COMP_MSVC_STRICT<=1600
+#define EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(X) typename internal::enable_if<true,X>::type
+#else
+#define EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(X) X
+#endif
+
+#define EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(METHOD,OPNAME) \
+  template <typename T> EIGEN_DEVICE_FUNC inline \
+  EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,typename internal::promote_scalar_arg<Scalar EIGEN_COMMA T EIGEN_COMMA EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,Scalar,T)>::type,OPNAME))\
+  (METHOD)(const T& scalar) const { \
+    typedef typename internal::promote_scalar_arg<Scalar,T,EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,Scalar,T)>::type PromotedT; \
+    return EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,PromotedT,OPNAME)(derived(), \
+           typename internal::plain_constant_type<Derived,PromotedT>::type(derived().rows(), derived().cols(), internal::scalar_constant_op<PromotedT>(scalar))); \
+  }
+
+#define EIGEN_MAKE_SCALAR_BINARY_OP_ONTHELEFT(METHOD,OPNAME) \
+  template <typename T> EIGEN_DEVICE_FUNC inline friend \
+  EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename internal::promote_scalar_arg<Scalar EIGEN_COMMA T EIGEN_COMMA EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,T,Scalar)>::type,Derived,OPNAME)) \
+  (METHOD)(const T& scalar, const StorageBaseType& matrix) { \
+    typedef typename internal::promote_scalar_arg<Scalar,T,EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,T,Scalar)>::type PromotedT; \
+    return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(PromotedT,Derived,OPNAME)( \
+           typename internal::plain_constant_type<Derived,PromotedT>::type(matrix.derived().rows(), matrix.derived().cols(), internal::scalar_constant_op<PromotedT>(scalar)), matrix.derived()); \
+  }
+
+#define EIGEN_MAKE_SCALAR_BINARY_OP(METHOD,OPNAME) \
+  EIGEN_MAKE_SCALAR_BINARY_OP_ONTHELEFT(METHOD,OPNAME) \
+  EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(METHOD,OPNAME)
+
+
+#ifdef EIGEN_EXCEPTIONS
+#  define EIGEN_THROW_X(X) throw X
+#  define EIGEN_THROW throw
+#  define EIGEN_TRY try
+#  define EIGEN_CATCH(X) catch (X)
+#else
+#  ifdef __CUDA_ARCH__
+#    define EIGEN_THROW_X(X) asm("trap;")
+#    define EIGEN_THROW asm("trap;")
+#  else
+#    define EIGEN_THROW_X(X) std::abort()
+#    define EIGEN_THROW std::abort()
+#  endif
+#  define EIGEN_TRY if (true)
+#  define EIGEN_CATCH(X) else
+#endif
+
+
+#if EIGEN_HAS_CXX11_NOEXCEPT
+#   define EIGEN_INCLUDE_TYPE_TRAITS
+#   define EIGEN_NOEXCEPT noexcept
+#   define EIGEN_NOEXCEPT_IF(x) noexcept(x)
+#   define EIGEN_NO_THROW noexcept(true)
+#   define EIGEN_EXCEPTION_SPEC(X) noexcept(false)
+#else
+#   define EIGEN_NOEXCEPT
+#   define EIGEN_NOEXCEPT_IF(x)
+#   define EIGEN_NO_THROW throw()
+#   define EIGEN_EXCEPTION_SPEC(X) throw(X)
+#endif
+
 #endif // EIGEN_MACROS_H
diff --git a/eigen/Eigen/src/Core/util/Memory.h b/eigen/Eigen/src/Core/util/Memory.h
index 74e37a4..7d90534 100644
--- a/eigen/Eigen/src/Core/util/Memory.h
+++ b/eigen/Eigen/src/Core/util/Memory.h
@@ -1,11 +1,12 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
-// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
 // Copyright (C) 2008-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
 // Copyright (C) 2009 Kenneth Riddile <kfriddile@yahoo.com>
 // Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>
 // Copyright (C) 2010 Thomas Capricelli <orzel@freehackers.org>
+// Copyright (C) 2013 Pavel Holoborodko <pavel@holoborodko.com>
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
@@ -31,7 +32,7 @@
 // page 114, "[The] LP64 model [...] is used by all 64-bit UNIX ports" so it's indeed
 // quite safe, at least within the context of glibc, to equate 64-bit with LP64.
 #if defined(__GLIBC__) && ((__GLIBC__>=2 && __GLIBC_MINOR__ >= 8) || __GLIBC__>2) \
- && defined(__LP64__) && ! defined( __SANITIZE_ADDRESS__ )
+ && defined(__LP64__) && ! defined( __SANITIZE_ADDRESS__ ) && (EIGEN_DEFAULT_ALIGN_BYTES == 16)
   #define EIGEN_GLIBC_MALLOC_ALREADY_ALIGNED 1
 #else
   #define EIGEN_GLIBC_MALLOC_ALREADY_ALIGNED 0
@@ -41,15 +42,15 @@
 //   See http://svn.freebsd.org/viewvc/base/stable/6/lib/libc/stdlib/malloc.c?view=markup
 // FreeBSD 7 seems to have 16-byte aligned malloc except on ARM and MIPS architectures
 //   See http://svn.freebsd.org/viewvc/base/stable/7/lib/libc/stdlib/malloc.c?view=markup
-#if defined(__FreeBSD__) && !defined(__arm__) && !defined(__mips__)
+#if defined(__FreeBSD__) && !(EIGEN_ARCH_ARM || EIGEN_ARCH_MIPS) && (EIGEN_DEFAULT_ALIGN_BYTES == 16)
   #define EIGEN_FREEBSD_MALLOC_ALREADY_ALIGNED 1
 #else
   #define EIGEN_FREEBSD_MALLOC_ALREADY_ALIGNED 0
 #endif
 
-#if defined(__APPLE__) \
- || defined(_WIN64) \
- || EIGEN_GLIBC_MALLOC_ALREADY_ALIGNED \
+#if (EIGEN_OS_MAC && (EIGEN_DEFAULT_ALIGN_BYTES == 16))     \
+ || (EIGEN_OS_WIN64 && (EIGEN_DEFAULT_ALIGN_BYTES == 16))   \
+ || EIGEN_GLIBC_MALLOC_ALREADY_ALIGNED              \
  || EIGEN_FREEBSD_MALLOC_ALREADY_ALIGNED
   #define EIGEN_MALLOC_ALREADY_ALIGNED 1
 #else
@@ -58,36 +59,17 @@
 
 #endif
 
-// See bug 554 (http://eigen.tuxfamily.org/bz/show_bug.cgi?id=554)
-// It seems to be unsafe to check _POSIX_ADVISORY_INFO without including unistd.h first.
-// Currently, let's include it only on unix systems:
-#if defined(__unix__) || defined(__unix)
-  #include <unistd.h>
-  #if ((defined __QNXNTO__) || (defined _GNU_SOURCE) || (defined __PGI) || ((defined _XOPEN_SOURCE) && (_XOPEN_SOURCE >= 600))) && (defined _POSIX_ADVISORY_INFO) && (_POSIX_ADVISORY_INFO > 0)
-    #define EIGEN_HAS_POSIX_MEMALIGN 1
-  #endif
-#endif
-
-#ifndef EIGEN_HAS_POSIX_MEMALIGN
-  #define EIGEN_HAS_POSIX_MEMALIGN 0
-#endif
-
-#ifdef EIGEN_VECTORIZE_SSE
-  #define EIGEN_HAS_MM_MALLOC 1
-#else
-  #define EIGEN_HAS_MM_MALLOC 0
-#endif
-
 namespace Eigen {
 
 namespace internal {
 
+EIGEN_DEVICE_FUNC
 inline void throw_std_bad_alloc()
 {
   #ifdef EIGEN_EXCEPTIONS
     throw std::bad_alloc();
   #else
-    std::size_t huge = -1;
+    std::size_t huge = static_cast<std::size_t>(-1);
     new int[huge];
   #endif
 }
@@ -103,9 +85,9 @@ inline void throw_std_bad_alloc()
   */
 inline void* handmade_aligned_malloc(std::size_t size)
 {
-  void *original = std::malloc(size+16);
+  void *original = std::malloc(size+EIGEN_DEFAULT_ALIGN_BYTES);
   if (original == 0) return 0;
-  void *aligned = reinterpret_cast<void*>((reinterpret_cast<std::size_t>(original) & ~(std::size_t(15))) + 16);
+  void *aligned = reinterpret_cast<void*>((reinterpret_cast<std::size_t>(original) & ~(std::size_t(EIGEN_DEFAULT_ALIGN_BYTES-1))) + EIGEN_DEFAULT_ALIGN_BYTES);
   *(reinterpret_cast<void**>(aligned) - 1) = original;
   return aligned;
 }
@@ -118,7 +100,7 @@ inline void handmade_aligned_free(void *ptr)
 
 /** \internal
   * \brief Reallocates aligned memory.
-  * Since we know that our handmade version is based on std::realloc
+  * Since we know that our handmade version is based on std::malloc
   * we can use std::realloc to implement efficient reallocation.
   */
 inline void* handmade_aligned_realloc(void* ptr, std::size_t size, std::size_t = 0)
@@ -126,9 +108,9 @@ inline void* handmade_aligned_realloc(void* ptr, std::size_t size, std::size_t =
   if (ptr == 0) return handmade_aligned_malloc(size);
   void *original = *(reinterpret_cast<void**>(ptr) - 1);
   std::ptrdiff_t previous_offset = static_cast<char *>(ptr)-static_cast<char *>(original);
-  original = std::realloc(original,size+16);
+  original = std::realloc(original,size+EIGEN_DEFAULT_ALIGN_BYTES);
   if (original == 0) return 0;
-  void *aligned = reinterpret_cast<void*>((reinterpret_cast<std::size_t>(original) & ~(std::size_t(15))) + 16);
+  void *aligned = reinterpret_cast<void*>((reinterpret_cast<std::size_t>(original) & ~(std::size_t(EIGEN_DEFAULT_ALIGN_BYTES-1))) + EIGEN_DEFAULT_ALIGN_BYTES);
   void *previous_aligned = static_cast<char *>(original)+previous_offset;
   if(aligned!=previous_aligned)
     std::memmove(aligned, previous_aligned, size);
@@ -138,92 +120,46 @@ inline void* handmade_aligned_realloc(void* ptr, std::size_t size, std::size_t =
 }
 
 /*****************************************************************************
-*** Implementation of generic aligned realloc (when no realloc can be used)***
-*****************************************************************************/
-
-void* aligned_malloc(std::size_t size);
-void  aligned_free(void *ptr);
-
-/** \internal
-  * \brief Reallocates aligned memory.
-  * Allows reallocation with aligned ptr types. This implementation will
-  * always create a new memory chunk and copy the old data.
-  */
-inline void* generic_aligned_realloc(void* ptr, size_t size, size_t old_size)
-{
-  if (ptr==0)
-    return aligned_malloc(size);
-
-  if (size==0)
-  {
-    aligned_free(ptr);
-    return 0;
-  }
-
-  void* newptr = aligned_malloc(size);
-  if (newptr == 0)
-  {
-    #ifdef EIGEN_HAS_ERRNO
-    errno = ENOMEM; // according to the standard
-    #endif
-    return 0;
-  }
-
-  if (ptr != 0)
-  {
-    std::memcpy(newptr, ptr, (std::min)(size,old_size));
-    aligned_free(ptr);
-  }
-
-  return newptr;
-}
-
-/*****************************************************************************
 *** Implementation of portable aligned versions of malloc/free/realloc     ***
 *****************************************************************************/
 
 #ifdef EIGEN_NO_MALLOC
-inline void check_that_malloc_is_allowed()
+EIGEN_DEVICE_FUNC inline void check_that_malloc_is_allowed()
 {
   eigen_assert(false && "heap allocation is forbidden (EIGEN_NO_MALLOC is defined)");
 }
 #elif defined EIGEN_RUNTIME_NO_MALLOC
-inline bool is_malloc_allowed_impl(bool update, bool new_value = false)
+EIGEN_DEVICE_FUNC inline bool is_malloc_allowed_impl(bool update, bool new_value = false)
 {
   static bool value = true;
   if (update == 1)
     value = new_value;
   return value;
 }
-inline bool is_malloc_allowed() { return is_malloc_allowed_impl(false); }
-inline bool set_is_malloc_allowed(bool new_value) { return is_malloc_allowed_impl(true, new_value); }
-inline void check_that_malloc_is_allowed()
+EIGEN_DEVICE_FUNC inline bool is_malloc_allowed() { return is_malloc_allowed_impl(false); }
+EIGEN_DEVICE_FUNC inline bool set_is_malloc_allowed(bool new_value) { return is_malloc_allowed_impl(true, new_value); }
+EIGEN_DEVICE_FUNC inline void check_that_malloc_is_allowed()
 {
   eigen_assert(is_malloc_allowed() && "heap allocation is forbidden (EIGEN_RUNTIME_NO_MALLOC is defined and g_is_malloc_allowed is false)");
 }
 #else
-inline void check_that_malloc_is_allowed()
+EIGEN_DEVICE_FUNC inline void check_that_malloc_is_allowed()
 {}
 #endif
 
-/** \internal Allocates \a size bytes. The returned pointer is guaranteed to have 16 bytes alignment.
+/** \internal Allocates \a size bytes. The returned pointer is guaranteed to have 16 or 32 bytes alignment depending on the requirements.
   * On allocation error, the returned pointer is null, and std::bad_alloc is thrown.
   */
-inline void* aligned_malloc(size_t size)
+EIGEN_DEVICE_FUNC inline void* aligned_malloc(std::size_t size)
 {
   check_that_malloc_is_allowed();
 
   void *result;
-  #if !EIGEN_ALIGN
-    result = std::malloc(size);
-  #elif EIGEN_MALLOC_ALREADY_ALIGNED
+  #if (EIGEN_DEFAULT_ALIGN_BYTES==0) || EIGEN_MALLOC_ALREADY_ALIGNED
     result = std::malloc(size);
-  #elif EIGEN_HAS_POSIX_MEMALIGN
-    if(posix_memalign(&result, 16, size)) result = 0;
-  #elif EIGEN_HAS_MM_MALLOC
-    result = _mm_malloc(size, 16);
-  #elif defined(_MSC_VER) && (!defined(_WIN32_WCE))
-    result = _aligned_malloc(size, 16);
+    #if EIGEN_DEFAULT_ALIGN_BYTES==16
+    eigen_assert((size<16 || (std::size_t(result)%16)==0) && "System's malloc returned an unaligned pointer. Compile with EIGEN_MALLOC_ALREADY_ALIGNED=0 to fallback to handmade alignd memory allocator.");
+    #endif
   #else
     result = handmade_aligned_malloc(size);
   #endif
@@ -235,50 +171,27 @@ inline void* aligned_malloc(size_t size)
 }
 
 /** \internal Frees memory allocated with aligned_malloc. */
-inline void aligned_free(void *ptr)
+EIGEN_DEVICE_FUNC inline void aligned_free(void *ptr)
 {
-  #if !EIGEN_ALIGN
-    std::free(ptr);
-  #elif EIGEN_MALLOC_ALREADY_ALIGNED
+  #if (EIGEN_DEFAULT_ALIGN_BYTES==0) || EIGEN_MALLOC_ALREADY_ALIGNED
     std::free(ptr);
-  #elif EIGEN_HAS_POSIX_MEMALIGN
-    std::free(ptr);
-  #elif EIGEN_HAS_MM_MALLOC
-    _mm_free(ptr);
-  #elif defined(_MSC_VER) && (!defined(_WIN32_WCE))
-    _aligned_free(ptr);
   #else
     handmade_aligned_free(ptr);
   #endif
 }
 
 /**
-* \internal
-* \brief Reallocates an aligned block of memory.
-* \throws std::bad_alloc on allocation failure
-**/
-inline void* aligned_realloc(void *ptr, size_t new_size, size_t old_size)
+  * \internal
+  * \brief Reallocates an aligned block of memory.
+  * \throws std::bad_alloc on allocation failure
+  */
+inline void* aligned_realloc(void *ptr, std::size_t new_size, std::size_t old_size)
 {
   EIGEN_UNUSED_VARIABLE(old_size);
 
   void *result;
-#if !EIGEN_ALIGN
-  result = std::realloc(ptr,new_size);
-#elif EIGEN_MALLOC_ALREADY_ALIGNED
+#if (EIGEN_DEFAULT_ALIGN_BYTES==0) || EIGEN_MALLOC_ALREADY_ALIGNED
   result = std::realloc(ptr,new_size);
-#elif EIGEN_HAS_POSIX_MEMALIGN
-  result = generic_aligned_realloc(ptr,new_size,old_size);
-#elif EIGEN_HAS_MM_MALLOC
-  // The defined(_mm_free) is just here to verify that this MSVC version
-  // implements _mm_malloc/_mm_free based on the corresponding _aligned_
-  // functions. This may not always be the case and we just try to be safe.
-  #if defined(_MSC_VER) && (!defined(_WIN32_WCE)) && defined(_mm_free)
-    result = _aligned_realloc(ptr,new_size,16);
-  #else
-    result = generic_aligned_realloc(ptr,new_size,old_size);
-  #endif
-#elif defined(_MSC_VER) && (!defined(_WIN32_WCE))
-  result = _aligned_realloc(ptr,new_size,16);
 #else
   result = handmade_aligned_realloc(ptr,new_size,old_size);
 #endif
@@ -296,12 +209,12 @@ inline void* aligned_realloc(void *ptr, size_t new_size, size_t old_size)
 /** \internal Allocates \a size bytes. If Align is true, then the returned ptr is 16-byte-aligned.
   * On allocation error, the returned pointer is null, and a std::bad_alloc is thrown.
   */
-template<bool Align> inline void* conditional_aligned_malloc(size_t size)
+template<bool Align> EIGEN_DEVICE_FUNC inline void* conditional_aligned_malloc(std::size_t size)
 {
   return aligned_malloc(size);
 }
 
-template<> inline void* conditional_aligned_malloc<false>(size_t size)
+template<> EIGEN_DEVICE_FUNC inline void* conditional_aligned_malloc<false>(std::size_t size)
 {
   check_that_malloc_is_allowed();
 
@@ -312,22 +225,22 @@ template<> inline void* conditional_aligned_malloc<false>(size_t size)
 }
 
 /** \internal Frees memory allocated with conditional_aligned_malloc */
-template<bool Align> inline void conditional_aligned_free(void *ptr)
+template<bool Align> EIGEN_DEVICE_FUNC inline void conditional_aligned_free(void *ptr)
 {
   aligned_free(ptr);
 }
 
-template<> inline void conditional_aligned_free<false>(void *ptr)
+template<> EIGEN_DEVICE_FUNC inline void conditional_aligned_free<false>(void *ptr)
 {
   std::free(ptr);
 }
 
-template<bool Align> inline void* conditional_aligned_realloc(void* ptr, size_t new_size, size_t old_size)
+template<bool Align> inline void* conditional_aligned_realloc(void* ptr, std::size_t new_size, std::size_t old_size)
 {
   return aligned_realloc(ptr, new_size, old_size);
 }
 
-template<> inline void* conditional_aligned_realloc<false>(void* ptr, size_t new_size, size_t)
+template<> inline void* conditional_aligned_realloc<false>(void* ptr, std::size_t new_size, std::size_t)
 {
   return std::realloc(ptr, new_size);
 }
@@ -336,33 +249,43 @@ template<> inline void* conditional_aligned_realloc<false>(void* ptr, size_t new
 *** Construction/destruction of array elements                             ***
 *****************************************************************************/
 
-/** \internal Constructs the elements of an array.
-  * The \a size parameter tells on how many objects to call the constructor of T.
-  */
-template<typename T> inline T* construct_elements_of_array(T *ptr, size_t size)
-{
-  for (size_t i=0; i < size; ++i) ::new (ptr + i) T;
-  return ptr;
-}
-
 /** \internal Destructs the elements of an array.
   * The \a size parameters tells on how many objects to call the destructor of T.
   */
-template<typename T> inline void destruct_elements_of_array(T *ptr, size_t size)
+template<typename T> EIGEN_DEVICE_FUNC inline void destruct_elements_of_array(T *ptr, std::size_t size)
 {
   // always destruct an array starting from the end.
   if(ptr)
     while(size) ptr[--size].~T();
 }
 
+/** \internal Constructs the elements of an array.
+  * The \a size parameter tells on how many objects to call the constructor of T.
+  */
+template<typename T> EIGEN_DEVICE_FUNC inline T* construct_elements_of_array(T *ptr, std::size_t size)
+{
+  std::size_t i;
+  EIGEN_TRY
+  {
+      for (i = 0; i < size; ++i) ::new (ptr + i) T;
+      return ptr;
+  }
+  EIGEN_CATCH(...)
+  {
+    destruct_elements_of_array(ptr, i);
+    EIGEN_THROW;
+  }
+  return NULL;
+}
+
 /*****************************************************************************
 *** Implementation of aligned new/delete-like functions                    ***
 *****************************************************************************/
 
 template<typename T>
-EIGEN_ALWAYS_INLINE void check_size_for_overflow(size_t size)
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void check_size_for_overflow(std::size_t size)
 {
-  if(size > size_t(-1) / sizeof(T))
+  if(size > std::size_t(-1) / sizeof(T))
     throw_std_bad_alloc();
 }
 
@@ -370,24 +293,42 @@ EIGEN_ALWAYS_INLINE void check_size_for_overflow(size_t size)
   * On allocation error, the returned pointer is undefined, but a std::bad_alloc is thrown.
   * The default constructor of T is called.
   */
-template<typename T> inline T* aligned_new(size_t size)
+template<typename T> EIGEN_DEVICE_FUNC inline T* aligned_new(std::size_t size)
 {
   check_size_for_overflow<T>(size);
   T *result = reinterpret_cast<T*>(aligned_malloc(sizeof(T)*size));
-  return construct_elements_of_array(result, size);
+  EIGEN_TRY
+  {
+    return construct_elements_of_array(result, size);
+  }
+  EIGEN_CATCH(...)
+  {
+    aligned_free(result);
+    EIGEN_THROW;
+  }
+  return result;
 }
 
-template<typename T, bool Align> inline T* conditional_aligned_new(size_t size)
+template<typename T, bool Align> EIGEN_DEVICE_FUNC inline T* conditional_aligned_new(std::size_t size)
 {
   check_size_for_overflow<T>(size);
   T *result = reinterpret_cast<T*>(conditional_aligned_malloc<Align>(sizeof(T)*size));
-  return construct_elements_of_array(result, size);
+  EIGEN_TRY
+  {
+    return construct_elements_of_array(result, size);
+  }
+  EIGEN_CATCH(...)
+  {
+    conditional_aligned_free<Align>(result);
+    EIGEN_THROW;
+  }
+  return result;
 }
 
 /** \internal Deletes objects constructed with aligned_new
   * The \a size parameters tells on how many objects to call the destructor of T.
   */
-template<typename T> inline void aligned_delete(T *ptr, size_t size)
+template<typename T> EIGEN_DEVICE_FUNC inline void aligned_delete(T *ptr, std::size_t size)
 {
   destruct_elements_of_array<T>(ptr, size);
   aligned_free(ptr);
@@ -396,13 +337,13 @@ template<typename T> inline void aligned_delete(T *ptr, size_t size)
 /** \internal Deletes objects constructed with conditional_aligned_new
   * The \a size parameters tells on how many objects to call the destructor of T.
   */
-template<typename T, bool Align> inline void conditional_aligned_delete(T *ptr, size_t size)
+template<typename T, bool Align> EIGEN_DEVICE_FUNC inline void conditional_aligned_delete(T *ptr, std::size_t size)
 {
   destruct_elements_of_array<T>(ptr, size);
   conditional_aligned_free<Align>(ptr);
 }
 
-template<typename T, bool Align> inline T* conditional_aligned_realloc_new(T* pts, size_t new_size, size_t old_size)
+template<typename T, bool Align> EIGEN_DEVICE_FUNC inline T* conditional_aligned_realloc_new(T* pts, std::size_t new_size, std::size_t old_size)
 {
   check_size_for_overflow<T>(new_size);
   check_size_for_overflow<T>(old_size);
@@ -410,23 +351,43 @@ template<typename T, bool Align> inline T* conditional_aligned_realloc_new(T* pt
     destruct_elements_of_array(pts+new_size, old_size-new_size);
   T *result = reinterpret_cast<T*>(conditional_aligned_realloc<Align>(reinterpret_cast<void*>(pts), sizeof(T)*new_size, sizeof(T)*old_size));
   if(new_size > old_size)
-    construct_elements_of_array(result+old_size, new_size-old_size);
+  {
+    EIGEN_TRY
+    {
+      construct_elements_of_array(result+old_size, new_size-old_size);
+    }
+    EIGEN_CATCH(...)
+    {
+      conditional_aligned_free<Align>(result);
+      EIGEN_THROW;
+    }
+  }
   return result;
 }
 
 
-template<typename T, bool Align> inline T* conditional_aligned_new_auto(size_t size)
+template<typename T, bool Align> EIGEN_DEVICE_FUNC inline T* conditional_aligned_new_auto(std::size_t size)
 {
   if(size==0)
     return 0; // short-cut. Also fixes Bug 884
   check_size_for_overflow<T>(size);
   T *result = reinterpret_cast<T*>(conditional_aligned_malloc<Align>(sizeof(T)*size));
   if(NumTraits<T>::RequireInitialization)
-    construct_elements_of_array(result, size);
+  {
+    EIGEN_TRY
+    {
+      construct_elements_of_array(result, size);
+    }
+    EIGEN_CATCH(...)
+    {
+      conditional_aligned_free<Align>(result);
+      EIGEN_THROW;
+    }
+  }
   return result;
 }
 
-template<typename T, bool Align> inline T* conditional_aligned_realloc_new_auto(T* pts, size_t new_size, size_t old_size)
+template<typename T, bool Align> inline T* conditional_aligned_realloc_new_auto(T* pts, std::size_t new_size, std::size_t old_size)
 {
   check_size_for_overflow<T>(new_size);
   check_size_for_overflow<T>(old_size);
@@ -434,11 +395,21 @@ template<typename T, bool Align> inline T* conditional_aligned_realloc_new_auto(
     destruct_elements_of_array(pts+new_size, old_size-new_size);
   T *result = reinterpret_cast<T*>(conditional_aligned_realloc<Align>(reinterpret_cast<void*>(pts), sizeof(T)*new_size, sizeof(T)*old_size));
   if(NumTraits<T>::RequireInitialization && (new_size > old_size))
-    construct_elements_of_array(result+old_size, new_size-old_size);
+  {
+    EIGEN_TRY
+    {
+      construct_elements_of_array(result+old_size, new_size-old_size);
+    }
+    EIGEN_CATCH(...)
+    {
+      conditional_aligned_free<Align>(result);
+      EIGEN_THROW;
+    }
+  }
   return result;
 }
 
-template<typename T, bool Align> inline void conditional_aligned_delete_auto(T *ptr, size_t size)
+template<typename T, bool Align> EIGEN_DEVICE_FUNC inline void conditional_aligned_delete_auto(T *ptr, std::size_t size)
 {
   if(NumTraits<T>::RequireInitialization)
     destruct_elements_of_array<T>(ptr, size);
@@ -447,51 +418,62 @@ template<typename T, bool Align> inline void conditional_aligned_delete_auto(T *
 
 /****************************************************************************/
 
-/** \internal Returns the index of the first element of the array that is well aligned for vectorization.
+/** \internal Returns the index of the first element of the array that is well aligned with respect to the requested \a Alignment.
   *
+  * \tparam Alignment requested alignment in Bytes.
   * \param array the address of the start of the array
   * \param size the size of the array
   *
-  * \note If no element of the array is well aligned, the size of the array is returned. Typically,
-  * for example with SSE, "well aligned" means 16-byte-aligned. If vectorization is disabled or if the
+  * \note If no element of the array is well aligned or the requested alignment is not a multiple of a scalar,
+  * the size of the array is returned. For example with SSE, the requested alignment is typically 16-bytes. If
   * packet size for the given scalar type is 1, then everything is considered well-aligned.
   *
-  * \note If the scalar type is vectorizable, we rely on the following assumptions: sizeof(Scalar) is a
-  * power of 2, the packet size in bytes is also a power of 2, and is a multiple of sizeof(Scalar). On the
-  * other hand, we do not assume that the array address is a multiple of sizeof(Scalar), as that fails for
+  * \note Otherwise, if the Alignment is larger that the scalar size, we rely on the assumptions that sizeof(Scalar) is a
+  * power of 2. On the other hand, we do not assume that the array address is a multiple of sizeof(Scalar), as that fails for
   * example with Scalar=double on certain 32-bit platforms, see bug #79.
   *
   * There is also the variant first_aligned(const MatrixBase&) defined in DenseCoeffsBase.h.
+  * \sa first_default_aligned()
   */
-template<typename Scalar, typename Index>
-static inline Index first_aligned(const Scalar* array, Index size)
+template<int Alignment, typename Scalar, typename Index>
+EIGEN_DEVICE_FUNC inline Index first_aligned(const Scalar* array, Index size)
 {
-  static const Index PacketSize = packet_traits<Scalar>::size;
-  static const Index PacketAlignedMask = PacketSize-1;
+  const Index ScalarSize = sizeof(Scalar);
+  const Index AlignmentSize = Alignment / ScalarSize;
+  const Index AlignmentMask = AlignmentSize-1;
 
-  if(PacketSize==1)
+  if(AlignmentSize<=1)
   {
-    // Either there is no vectorization, or a packet consists of exactly 1 scalar so that all elements
-    // of the array have the same alignment.
+    // Either the requested alignment if smaller than a scalar, or it exactly match a 1 scalar
+    // so that all elements of the array have the same alignment.
     return 0;
   }
-  else if(size_t(array) & (sizeof(Scalar)-1))
+  else if( (UIntPtr(array) & (sizeof(Scalar)-1)) || (Alignment%ScalarSize)!=0)
   {
-    // There is vectorization for this scalar type, but the array is not aligned to the size of a single scalar.
+    // The array is not aligned to the size of a single scalar, or the requested alignment is not a multiple of the scalar size.
     // Consequently, no element of the array is well aligned.
     return size;
   }
   else
   {
-    return std::min<Index>( (PacketSize - (Index((size_t(array)/sizeof(Scalar))) & PacketAlignedMask))
-                           & PacketAlignedMask, size);
+    Index first = (AlignmentSize - (Index((UIntPtr(array)/sizeof(Scalar))) & AlignmentMask)) & AlignmentMask;
+    return (first < size) ? first : size;
   }
 }
 
+/** \internal Returns the index of the first element of the array that is well aligned with respect the largest packet requirement.
+   * \sa first_aligned(Scalar*,Index) and first_default_aligned(DenseBase<Derived>) */
+template<typename Scalar, typename Index>
+EIGEN_DEVICE_FUNC inline Index first_default_aligned(const Scalar* array, Index size)
+{
+  typedef typename packet_traits<Scalar>::type DefaultPacketType;
+  return first_aligned<unpacket_traits<DefaultPacketType>::alignment>(array, size);
+}
+
 /** \internal Returns the smallest integer multiple of \a base and greater or equal to \a size
   */
 template<typename Index>
-inline static Index first_multiple(Index size, Index base)
+inline Index first_multiple(Index size, Index base)
 {
   return ((size+base-1)/base)*base;
 }
@@ -500,15 +482,15 @@ inline static Index first_multiple(Index size, Index base)
 // use memcpy on trivial types, i.e., on types that does not require an initialization ctor.
 template<typename T, bool UseMemcpy> struct smart_copy_helper;
 
-template<typename T> void smart_copy(const T* start, const T* end, T* target)
+template<typename T> EIGEN_DEVICE_FUNC void smart_copy(const T* start, const T* end, T* target)
 {
   smart_copy_helper<T,!NumTraits<T>::RequireInitialization>::run(start, end, target);
 }
 
 template<typename T> struct smart_copy_helper<T,true> {
-  static inline void run(const T* start, const T* end, T* target)
+  EIGEN_DEVICE_FUNC static inline void run(const T* start, const T* end, T* target)
   {
-    std::ptrdiff_t size = std::ptrdiff_t(end)-std::ptrdiff_t(start);
+    IntPtr size = IntPtr(end)-IntPtr(start);
     if(size==0) return;
     eigen_internal_assert(start!=0 && end!=0 && target!=0);
     memcpy(target, start, size);
@@ -516,10 +498,44 @@ template<typename T> struct smart_copy_helper<T,true> {
 };
 
 template<typename T> struct smart_copy_helper<T,false> {
-  static inline void run(const T* start, const T* end, T* target)
+  EIGEN_DEVICE_FUNC static inline void run(const T* start, const T* end, T* target)
   { std::copy(start, end, target); }
 };
 
+// intelligent memmove. falls back to std::memmove for POD types, uses std::copy otherwise.
+template<typename T, bool UseMemmove> struct smart_memmove_helper;
+
+template<typename T> void smart_memmove(const T* start, const T* end, T* target)
+{
+  smart_memmove_helper<T,!NumTraits<T>::RequireInitialization>::run(start, end, target);
+}
+
+template<typename T> struct smart_memmove_helper<T,true> {
+  static inline void run(const T* start, const T* end, T* target)
+  {
+    IntPtr size = IntPtr(end)-IntPtr(start);
+    if(size==0) return;
+    eigen_internal_assert(start!=0 && end!=0 && target!=0);
+    std::memmove(target, start, size);
+  }
+};
+
+template<typename T> struct smart_memmove_helper<T,false> {
+  static inline void run(const T* start, const T* end, T* target)
+  {
+    if (UIntPtr(target) < UIntPtr(start))
+    {
+      std::copy(start, end, target);
+    }
+    else
+    {
+      std::ptrdiff_t count = (std::ptrdiff_t(end)-std::ptrdiff_t(start)) / sizeof(T);
+      std::copy_backward(start, end, target + count);
+    }
+  }
+};
+
+
 /*****************************************************************************
 *** Implementation of runtime stack allocation (falling back to malloc)    ***
 *****************************************************************************/
@@ -527,16 +543,16 @@ template<typename T> struct smart_copy_helper<T,false> {
 // you can overwrite Eigen's default behavior regarding alloca by defining EIGEN_ALLOCA
 // to the appropriate stack allocation function
 #ifndef EIGEN_ALLOCA
-  #if (defined __linux__) || (defined __APPLE__) || (defined alloca)
+  #if EIGEN_OS_LINUX || EIGEN_OS_MAC || (defined alloca)
     #define EIGEN_ALLOCA alloca
-  #elif defined(_MSC_VER)
+  #elif EIGEN_COMP_MSVC
     #define EIGEN_ALLOCA _alloca
   #endif
 #endif
 
 // This helper class construct the allocated memory, and takes care of destructing and freeing the handled data
 // at destruction time. In practice this helper class is mainly useful to avoid memory leak in case of exceptions.
-template<typename T> class aligned_stack_memory_handler
+template<typename T> class aligned_stack_memory_handler : noncopyable
 {
   public:
     /* Creates a stack_memory_handler responsible for the buffer \a ptr of size \a size.
@@ -545,7 +561,7 @@ template<typename T> class aligned_stack_memory_handler
      * In this case, the buffer elements will also be destructed when this handler will be destructed.
      * Finally, if \a dealloc is true, then the pointer \a ptr is freed.
      **/
-    aligned_stack_memory_handler(T* ptr, size_t size, bool dealloc)
+    aligned_stack_memory_handler(T* ptr, std::size_t size, bool dealloc)
       : m_ptr(ptr), m_size(size), m_deallocate(dealloc)
     {
       if(NumTraits<T>::RequireInitialization && m_ptr)
@@ -560,10 +576,34 @@ template<typename T> class aligned_stack_memory_handler
     }
   protected:
     T* m_ptr;
-    size_t m_size;
+    std::size_t m_size;
     bool m_deallocate;
 };
 
+template<typename T> class scoped_array : noncopyable
+{
+  T* m_ptr;
+public:
+  explicit scoped_array(std::ptrdiff_t size)
+  {
+    m_ptr = new T[size];
+  }
+  ~scoped_array()
+  {
+    delete[] m_ptr;
+  }
+  T& operator[](std::ptrdiff_t i) { return m_ptr[i]; }
+  const T& operator[](std::ptrdiff_t i) const { return m_ptr[i]; }
+  T* &ptr() { return m_ptr; }
+  const T* ptr() const { return m_ptr; }
+  operator const T*() const { return m_ptr; }
+};
+
+template<typename T> void swap(scoped_array<T> &a,scoped_array<T> &b)
+{
+  std::swap(a.ptr(),b.ptr());
+}
+
 } // end namespace internal
 
 /** \internal
@@ -583,10 +623,12 @@ template<typename T> class aligned_stack_memory_handler
   */
 #ifdef EIGEN_ALLOCA
 
-  #if defined(__arm__) || defined(_WIN32)
-    #define EIGEN_ALIGNED_ALLOCA(SIZE) reinterpret_cast<void*>((reinterpret_cast<size_t>(EIGEN_ALLOCA(SIZE+16)) & ~(size_t(15))) + 16)
+  #if EIGEN_DEFAULT_ALIGN_BYTES>0
+    // We always manually re-align the result of EIGEN_ALLOCA.
+    // If alloca is already aligned, the compiler should be smart enough to optimize away the re-alignment.
+    #define EIGEN_ALIGNED_ALLOCA(SIZE) reinterpret_cast<void*>((internal::UIntPtr(EIGEN_ALLOCA(SIZE+EIGEN_DEFAULT_ALIGN_BYTES-1)) + EIGEN_DEFAULT_ALIGN_BYTES-1) & ~(std::size_t(EIGEN_DEFAULT_ALIGN_BYTES-1)))
   #else
-    #define EIGEN_ALIGNED_ALLOCA EIGEN_ALLOCA
+    #define EIGEN_ALIGNED_ALLOCA(SIZE) EIGEN_ALLOCA(SIZE)
   #endif
 
   #define ei_declare_aligned_stack_constructed_variable(TYPE,NAME,SIZE,BUFFER) \
@@ -611,41 +653,33 @@ template<typename T> class aligned_stack_memory_handler
 *** Implementation of EIGEN_MAKE_ALIGNED_OPERATOR_NEW [_IF]                ***
 *****************************************************************************/
 
-#if EIGEN_ALIGN
-  #ifdef EIGEN_EXCEPTIONS
-    #define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign) \
-      void* operator new(size_t size, const std::nothrow_t&) noexcept { \
-        try { return Eigen::internal::conditional_aligned_malloc<NeedsToAlign>(size); } \
-        catch (...) { return 0; } \
+#if EIGEN_MAX_ALIGN_BYTES!=0
+  #define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign) \
+      void* operator new(std::size_t size, const std::nothrow_t&) EIGEN_NO_THROW { \
+        EIGEN_TRY { return Eigen::internal::conditional_aligned_malloc<NeedsToAlign>(size); } \
+        EIGEN_CATCH (...) { return 0; } \
       }
-  #else
-    #define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign) \
-      void* operator new(size_t size, const std::nothrow_t&) noexcept { \
-        return Eigen::internal::conditional_aligned_malloc<NeedsToAlign>(size); \
-      }
-  #endif
-
   #define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign) \
-      void *operator new(size_t size) { \
+      void *operator new(std::size_t size) { \
         return Eigen::internal::conditional_aligned_malloc<NeedsToAlign>(size); \
       } \
-      void *operator new[](size_t size) { \
+      void *operator new[](std::size_t size) { \
         return Eigen::internal::conditional_aligned_malloc<NeedsToAlign>(size); \
       } \
-      void operator delete(void * ptr) noexcept { Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); } \
-      void operator delete[](void * ptr) noexcept { Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); } \
-      void operator delete(void * ptr, std::size_t /* sz */) noexcept { Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); } \
-      void operator delete[](void * ptr, std::size_t /* sz */) noexcept { Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); } \
+      void operator delete(void * ptr) EIGEN_NO_THROW { Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); } \
+      void operator delete[](void * ptr) EIGEN_NO_THROW { Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); } \
+      void operator delete(void * ptr, std::size_t /* sz */) EIGEN_NO_THROW { Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); } \
+      void operator delete[](void * ptr, std::size_t /* sz */) EIGEN_NO_THROW { Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); } \
       /* in-place new and delete. since (at least afaik) there is no actual   */ \
       /* memory allocated we can safely let the default implementation handle */ \
       /* this particular case. */ \
-      static void *operator new(size_t size, void *ptr) { return ::operator new(size,ptr); } \
-      static void *operator new[](size_t size, void* ptr) { return ::operator new[](size,ptr); } \
-      void operator delete(void * memory, void *ptr) noexcept { return ::operator delete(memory,ptr); } \
-      void operator delete[](void * memory, void *ptr) noexcept { return ::operator delete[](memory,ptr); } \
+      static void *operator new(std::size_t size, void *ptr) { return ::operator new(size,ptr); } \
+      static void *operator new[](std::size_t size, void* ptr) { return ::operator new[](size,ptr); } \
+      void operator delete(void * memory, void *ptr) EIGEN_NO_THROW { return ::operator delete(memory,ptr); } \
+      void operator delete[](void * memory, void *ptr) EIGEN_NO_THROW { return ::operator delete[](memory,ptr); } \
       /* nothrow-new (returns zero instead of std::bad_alloc) */ \
       EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign) \
-      void operator delete(void *ptr, const std::nothrow_t&) noexcept { \
+      void operator delete(void *ptr, const std::nothrow_t&) EIGEN_NO_THROW { \
         Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); \
       } \
       typedef void eigen_aligned_operator_new_marker_type;
@@ -655,32 +689,31 @@ template<typename T> class aligned_stack_memory_handler
 
 #define EIGEN_MAKE_ALIGNED_OPERATOR_NEW EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(true)
 #define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar,Size) \
-  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(bool(((Size)!=Eigen::Dynamic) && ((sizeof(Scalar)*(Size))%16==0)))
+  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(bool(((Size)!=Eigen::Dynamic) && ((sizeof(Scalar)*(Size))%EIGEN_MAX_ALIGN_BYTES==0)))
 
 /****************************************************************************/
 
-
 /** \class aligned_allocator
-  * \ingroup Core_Module
-  *
-  * \brief STL compatible allocator to use with with 16 byte aligned types
-  *
-  * Example:
-  * \code
-  * // Matrix4f requires 16 bytes alignment:
-  * std::map< int, Matrix4f, std::less<int>,
-  *           aligned_allocator<std::pair<const int, Matrix4f> > > my_map_mat4;
-  * // Vector3f does not require 16 bytes alignment, no need to use Eigen's allocator:
-  * std::map< int, Vector3f > my_map_vec3;
-  * \endcode
-  *
-  * \sa \blank \ref TopicStlContainers.
-  */
+* \ingroup Core_Module
+*
+* \brief STL compatible allocator to use with with 16 byte aligned types
+*
+* Example:
+* \code
+* // Matrix4f requires 16 bytes alignment:
+* std::map< int, Matrix4f, std::less<int>,
+*           aligned_allocator<std::pair<const int, Matrix4f> > > my_map_mat4;
+* // Vector3f does not require 16 bytes alignment, no need to use Eigen's allocator:
+* std::map< int, Vector3f > my_map_vec3;
+* \endcode
+*
+* \sa \blank \ref TopicStlContainers.
+*/
 template<class T>
 class aligned_allocator : public std::allocator<T>
 {
 public:
-  typedef size_t          size_type;
+  typedef std::size_t     size_type;
   typedef std::ptrdiff_t  difference_type;
   typedef T*              pointer;
   typedef const T*        const_pointer;
@@ -718,12 +751,12 @@ public:
 //---------- Cache sizes ----------
 
 #if !defined(EIGEN_NO_CPUID)
-#  if defined(__GNUC__) && ( defined(__i386__) || defined(__x86_64__) )
-#    if defined(__PIC__) && defined(__i386__)
+#  if EIGEN_COMP_GNUC && EIGEN_ARCH_i386_OR_x86_64
+#    if defined(__PIC__) && EIGEN_ARCH_i386
        // Case for x86 with PIC
 #      define EIGEN_CPUID(abcd,func,id) \
          __asm__ __volatile__ ("xchgl %%ebx, %k1;cpuid; xchgl %%ebx,%k1": "=a" (abcd[0]), "=&r" (abcd[1]), "=c" (abcd[2]), "=d" (abcd[3]) : "a" (func), "c" (id));
-#    elif defined(__PIC__) && defined(__x86_64__)
+#    elif defined(__PIC__) && EIGEN_ARCH_x86_64
        // Case for x64 with PIC. In theory this is only a problem with recent gcc and with medium or large code model, not with the default small code model.
        // However, we cannot detect which code model is used, and the xchg overhead is negligible anyway.
 #      define EIGEN_CPUID(abcd,func,id) \
@@ -733,8 +766,8 @@ public:
 #      define EIGEN_CPUID(abcd,func,id) \
          __asm__ __volatile__ ("cpuid": "=a" (abcd[0]), "=b" (abcd[1]), "=c" (abcd[2]), "=d" (abcd[3]) : "0" (func), "2" (id) );
 #    endif
-#  elif defined(_MSC_VER)
-#    if (_MSC_VER > 1500) && ( defined(_M_IX86) || defined(_M_X64) )
+#  elif EIGEN_COMP_MSVC
+#    if (EIGEN_COMP_MSVC > 1500) && EIGEN_ARCH_i386_OR_x86_64
 #      define EIGEN_CPUID(abcd,func,id) __cpuidex((int*)abcd,func,id)
 #    endif
 #  endif
diff --git a/eigen/Eigen/src/Core/util/Meta.h b/eigen/Eigen/src/Core/util/Meta.h
index 71d5871..8de6055 100644
--- a/eigen/Eigen/src/Core/util/Meta.h
+++ b/eigen/Eigen/src/Core/util/Meta.h
@@ -1,7 +1,7 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
-// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
 // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
 //
 // This Source Code Form is subject to the terms of the Mozilla
@@ -11,8 +11,27 @@
 #ifndef EIGEN_META_H
 #define EIGEN_META_H
 
+#if defined(__CUDA_ARCH__)
+#include <cfloat>
+#include <math_constants.h>
+#endif
+
+#if EIGEN_COMP_ICC>=1600 &&  __cplusplus >= 201103L
+#include <cstdint>
+#endif
+
 namespace Eigen {
 
+typedef EIGEN_DEFAULT_DENSE_INDEX_TYPE DenseIndex;
+
+/**
+ * \brief The Index type as used for the API.
+ * \details To change this, \c \#define the preprocessor symbol \c EIGEN_DEFAULT_DENSE_INDEX_TYPE.
+ * \sa \blank \ref TopicPreprocessorDirectives, StorageIndex.
+ */
+
+typedef EIGEN_DEFAULT_DENSE_INDEX_TYPE Index;
+
 namespace internal {
 
 /** \internal
@@ -22,6 +41,16 @@ namespace internal {
   * we however don't want to add a dependency to Boost.
   */
 
+// Only recent versions of ICC complain about using ptrdiff_t to hold pointers,
+// and older versions do not provide *intptr_t types.
+#if EIGEN_COMP_ICC>=1600 &&  __cplusplus >= 201103L
+typedef std::intptr_t  IntPtr;
+typedef std::uintptr_t UIntPtr;
+#else
+typedef std::ptrdiff_t IntPtr;
+typedef std::size_t UIntPtr;
+#endif
+
 struct true_type {  enum { value = 1 }; };
 struct false_type { enum { value = 0 }; };
 
@@ -68,6 +97,23 @@ template<> struct is_arithmetic<unsigned int>  { enum { value = true }; };
 template<> struct is_arithmetic<signed long>   { enum { value = true }; };
 template<> struct is_arithmetic<unsigned long> { enum { value = true }; };
 
+#if EIGEN_HAS_CXX11
+using std::is_integral;
+#else
+template<typename T> struct is_integral               { enum { value = false }; };
+template<> struct is_integral<bool>                   { enum { value = true }; };
+template<> struct is_integral<char>                   { enum { value = true }; };
+template<> struct is_integral<signed char>            { enum { value = true }; };
+template<> struct is_integral<unsigned char>          { enum { value = true }; };
+template<> struct is_integral<signed short>           { enum { value = true }; };
+template<> struct is_integral<unsigned short>         { enum { value = true }; };
+template<> struct is_integral<signed int>             { enum { value = true }; };
+template<> struct is_integral<unsigned int>           { enum { value = true }; };
+template<> struct is_integral<signed long>            { enum { value = true }; };
+template<> struct is_integral<unsigned long>          { enum { value = true }; };
+#endif
+
+
 template <typename T> struct add_const { typedef const T type; };
 template <typename T> struct add_const<T&> { typedef T& type; };
 
@@ -80,28 +126,215 @@ template<typename T> struct add_const_on_value_type<T*>        { typedef T const
 template<typename T> struct add_const_on_value_type<T* const>  { typedef T const* const type; };
 template<typename T> struct add_const_on_value_type<T const* const>  { typedef T const* const type; };
 
+
+template<typename From, typename To>
+struct is_convertible_impl
+{
+private:
+  struct any_conversion
+  {
+    template <typename T> any_conversion(const volatile T&);
+    template <typename T> any_conversion(T&);
+  };
+  struct yes {int a[1];};
+  struct no  {int a[2];};
+
+  static yes test(const To&, int);
+  static no  test(any_conversion, ...);
+
+public:
+  static From ms_from;
+#ifdef __INTEL_COMPILER
+  #pragma warning push
+  #pragma warning ( disable : 2259 )
+#endif
+  enum { value = sizeof(test(ms_from, 0))==sizeof(yes) };
+#ifdef __INTEL_COMPILER
+  #pragma warning pop
+#endif
+};
+
+template<typename From, typename To>
+struct is_convertible
+{
+  enum { value = is_convertible_impl<typename remove_all<From>::type,
+                                     typename remove_all<To  >::type>::value };
+};
+
 /** \internal Allows to enable/disable an overload
   * according to a compile time condition.
   */
-template<bool Condition, typename T> struct enable_if;
+template<bool Condition, typename T=void> struct enable_if;
 
 template<typename T> struct enable_if<true,T>
 { typedef T type; };
 
+#if defined(__CUDA_ARCH__)
+#if !defined(__FLT_EPSILON__)
+#define __FLT_EPSILON__ FLT_EPSILON
+#define __DBL_EPSILON__ DBL_EPSILON
+#endif
 
+namespace device {
+
+template<typename T> struct numeric_limits
+{
+  EIGEN_DEVICE_FUNC
+  static T epsilon() { return 0; }
+  static T (max)() { assert(false && "Highest not supported for this type"); }
+  static T (min)() { assert(false && "Lowest not supported for this type"); }
+  static T infinity() { assert(false && "Infinity not supported for this type"); }
+  static T quiet_NaN() { assert(false && "quiet_NaN not supported for this type"); }
+};
+template<> struct numeric_limits<float>
+{
+  EIGEN_DEVICE_FUNC
+  static float epsilon() { return __FLT_EPSILON__; }
+  EIGEN_DEVICE_FUNC
+  static float (max)() { return CUDART_MAX_NORMAL_F; }
+  EIGEN_DEVICE_FUNC
+  static float (min)() { return FLT_MIN; }
+  EIGEN_DEVICE_FUNC
+  static float infinity() { return CUDART_INF_F; }
+  EIGEN_DEVICE_FUNC
+  static float quiet_NaN() { return CUDART_NAN_F; }
+};
+template<> struct numeric_limits<double>
+{
+  EIGEN_DEVICE_FUNC
+  static double epsilon() { return __DBL_EPSILON__; }
+  EIGEN_DEVICE_FUNC
+  static double (max)() { return DBL_MAX; }
+  EIGEN_DEVICE_FUNC
+  static double (min)() { return DBL_MIN; }
+  EIGEN_DEVICE_FUNC
+  static double infinity() { return CUDART_INF; }
+  EIGEN_DEVICE_FUNC
+  static double quiet_NaN() { return CUDART_NAN; }
+};
+template<> struct numeric_limits<int>
+{
+  EIGEN_DEVICE_FUNC
+  static int epsilon() { return 0; }
+  EIGEN_DEVICE_FUNC
+  static int (max)() { return INT_MAX; }
+  EIGEN_DEVICE_FUNC
+  static int (min)() { return INT_MIN; }
+};
+template<> struct numeric_limits<unsigned int>
+{
+  EIGEN_DEVICE_FUNC
+  static unsigned int epsilon() { return 0; }
+  EIGEN_DEVICE_FUNC
+  static unsigned int (max)() { return UINT_MAX; }
+  EIGEN_DEVICE_FUNC
+  static unsigned int (min)() { return 0; }
+};
+template<> struct numeric_limits<long>
+{
+  EIGEN_DEVICE_FUNC
+  static long epsilon() { return 0; }
+  EIGEN_DEVICE_FUNC
+  static long (max)() { return LONG_MAX; }
+  EIGEN_DEVICE_FUNC
+  static long (min)() { return LONG_MIN; }
+};
+template<> struct numeric_limits<unsigned long>
+{
+  EIGEN_DEVICE_FUNC
+  static unsigned long epsilon() { return 0; }
+  EIGEN_DEVICE_FUNC
+  static unsigned long (max)() { return ULONG_MAX; }
+  EIGEN_DEVICE_FUNC
+  static unsigned long (min)() { return 0; }
+};
+template<> struct numeric_limits<long long>
+{
+  EIGEN_DEVICE_FUNC
+  static long long epsilon() { return 0; }
+  EIGEN_DEVICE_FUNC
+  static long long (max)() { return LLONG_MAX; }
+  EIGEN_DEVICE_FUNC
+  static long long (min)() { return LLONG_MIN; }
+};
+template<> struct numeric_limits<unsigned long long>
+{
+  EIGEN_DEVICE_FUNC
+  static unsigned long long epsilon() { return 0; }
+  EIGEN_DEVICE_FUNC
+  static unsigned long long (max)() { return ULLONG_MAX; }
+  EIGEN_DEVICE_FUNC
+  static unsigned long long (min)() { return 0; }
+};
+
+}
+
+#endif
 
 /** \internal
   * A base class do disable default copy ctor and copy assignement operator.
   */
 class noncopyable
 {
-  noncopyable(const noncopyable&);
-  const noncopyable& operator=(const noncopyable&);
+  EIGEN_DEVICE_FUNC noncopyable(const noncopyable&);
+  EIGEN_DEVICE_FUNC const noncopyable& operator=(const noncopyable&);
 protected:
-  noncopyable() {}
-  ~noncopyable() {}
+  EIGEN_DEVICE_FUNC noncopyable() {}
+  EIGEN_DEVICE_FUNC ~noncopyable() {}
+};
+
+/** \internal
+  * Provides access to the number of elements in the object of as a compile-time constant expression.
+  * It "returns" Eigen::Dynamic if the size cannot be resolved at compile-time (default).
+  *
+  * Similar to std::tuple_size, but more general.
+  *
+  * It currently supports:
+  *  - any types T defining T::SizeAtCompileTime
+  *  - plain C arrays as T[N]
+  *  - std::array (c++11)
+  *  - some internal types such as SingleRange and AllRange
+  *
+  * The second template parameter eases SFINAE-based specializations.
+  */
+template<typename T, typename EnableIf = void> struct array_size {
+  enum { value = Dynamic };
 };
 
+template<typename T> struct array_size<T,typename internal::enable_if<((T::SizeAtCompileTime&0)==0)>::type> {
+  enum { value = T::SizeAtCompileTime };
+};
+
+template<typename T, int N> struct array_size<const T (&)[N]> {
+  enum { value = N };
+};
+template<typename T, int N> struct array_size<T (&)[N]> {
+  enum { value = N };
+};
+
+#if EIGEN_HAS_CXX11
+template<typename T, std::size_t N> struct array_size<const std::array<T,N> > {
+  enum { value = N };
+};
+template<typename T, std::size_t N> struct array_size<std::array<T,N> > {
+  enum { value = N };
+};
+#endif
+
+/** \internal
+  * Analogue of the std::size free function.
+  * It returns the size of the container or view \a x of type \c T
+  *
+  * It currently supports:
+  *  - any types T defining a member T::size() const
+  *  - plain C arrays as T[N]
+  *
+  */
+template<typename T>
+Index size(const T& x) { return x.size(); }
+
+template<typename T,std::size_t N>
+Index size(const T (&) [N]) { return N; }
 
 /** \internal
   * Convenient struct to get the result type of a unary or binary functor.
@@ -110,14 +343,20 @@ protected:
   * upcoming next STL generation (using a templated result member).
   * If none of these members is provided, then the type of the first argument is returned. FIXME, that behavior is a pretty bad hack.
   */
-template<typename T> struct result_of {};
+#if EIGEN_HAS_STD_RESULT_OF
+template<typename T> struct result_of {
+  typedef typename std::result_of<T>::type type1;
+  typedef typename remove_all<type1>::type type;
+};
+#else
+template<typename T> struct result_of { };
 
 struct has_none {int a[1];};
 struct has_std_result_type {int a[2];};
 struct has_tr1_result {int a[3];};
 
 template<typename Func, typename ArgType, int SizeOf=sizeof(has_none)>
-struct unary_result_of_select {typedef ArgType type;};
+struct unary_result_of_select {typedef typename internal::remove_all<ArgType>::type type;};
 
 template<typename Func, typename ArgType>
 struct unary_result_of_select<Func, ArgType, sizeof(has_std_result_type)> {typedef typename Func::result_type type;};
@@ -128,10 +367,10 @@ struct unary_result_of_select<Func, ArgType, sizeof(has_tr1_result)> {typedef ty
 template<typename Func, typename ArgType>
 struct result_of<Func(ArgType)> {
     template<typename T>
-    static has_std_result_type testFunctor(T const *, typename T::result_type const * = 0);
+    static has_std_result_type    testFunctor(T const *, typename T::result_type const * = 0);
     template<typename T>
-    static has_tr1_result      testFunctor(T const *, typename T::template result<T(ArgType)>::type const * = 0);
-    static has_none            testFunctor(...);
+    static has_tr1_result         testFunctor(T const *, typename T::template result<T(ArgType)>::type const * = 0);
+    static has_none               testFunctor(...);
 
     // note that the following indirection is needed for gcc-3.3
     enum {FunctorType = sizeof(testFunctor(static_cast<Func*>(0)))};
@@ -139,7 +378,7 @@ struct result_of<Func(ArgType)> {
 };
 
 template<typename Func, typename ArgType0, typename ArgType1, int SizeOf=sizeof(has_none)>
-struct binary_result_of_select {typedef ArgType0 type;};
+struct binary_result_of_select {typedef typename internal::remove_all<ArgType0>::type type;};
 
 template<typename Func, typename ArgType0, typename ArgType1>
 struct binary_result_of_select<Func, ArgType0, ArgType1, sizeof(has_std_result_type)>
@@ -152,16 +391,83 @@ struct binary_result_of_select<Func, ArgType0, ArgType1, sizeof(has_tr1_result)>
 template<typename Func, typename ArgType0, typename ArgType1>
 struct result_of<Func(ArgType0,ArgType1)> {
     template<typename T>
-    static has_std_result_type testFunctor(T const *, typename T::result_type const * = 0);
+    static has_std_result_type    testFunctor(T const *, typename T::result_type const * = 0);
     template<typename T>
-    static has_tr1_result      testFunctor(T const *, typename T::template result<T(ArgType0,ArgType1)>::type const * = 0);
-    static has_none            testFunctor(...);
+    static has_tr1_result         testFunctor(T const *, typename T::template result<T(ArgType0,ArgType1)>::type const * = 0);
+    static has_none               testFunctor(...);
 
     // note that the following indirection is needed for gcc-3.3
     enum {FunctorType = sizeof(testFunctor(static_cast<Func*>(0)))};
     typedef typename binary_result_of_select<Func, ArgType0, ArgType1, FunctorType>::type type;
 };
 
+template<typename Func, typename ArgType0, typename ArgType1, typename ArgType2, int SizeOf=sizeof(has_none)>
+struct ternary_result_of_select {typedef typename internal::remove_all<ArgType0>::type type;};
+
+template<typename Func, typename ArgType0, typename ArgType1, typename ArgType2>
+struct ternary_result_of_select<Func, ArgType0, ArgType1, ArgType2, sizeof(has_std_result_type)>
+{typedef typename Func::result_type type;};
+
+template<typename Func, typename ArgType0, typename ArgType1, typename ArgType2>
+struct ternary_result_of_select<Func, ArgType0, ArgType1, ArgType2, sizeof(has_tr1_result)>
+{typedef typename Func::template result<Func(ArgType0,ArgType1,ArgType2)>::type type;};
+
+template<typename Func, typename ArgType0, typename ArgType1, typename ArgType2>
+struct result_of<Func(ArgType0,ArgType1,ArgType2)> {
+    template<typename T>
+    static has_std_result_type    testFunctor(T const *, typename T::result_type const * = 0);
+    template<typename T>
+    static has_tr1_result         testFunctor(T const *, typename T::template result<T(ArgType0,ArgType1,ArgType2)>::type const * = 0);
+    static has_none               testFunctor(...);
+
+    // note that the following indirection is needed for gcc-3.3
+    enum {FunctorType = sizeof(testFunctor(static_cast<Func*>(0)))};
+    typedef typename ternary_result_of_select<Func, ArgType0, ArgType1, ArgType2, FunctorType>::type type;
+};
+#endif
+
+struct meta_yes { char a[1]; };
+struct meta_no  { char a[2]; };
+
+// Check whether T::ReturnType does exist
+template <typename T>
+struct has_ReturnType
+{
+  template <typename C> static meta_yes testFunctor(C const *, typename C::ReturnType const * = 0);
+  template <typename C> static meta_no  testFunctor(...);
+
+  enum { value = sizeof(testFunctor<T>(static_cast<T*>(0))) == sizeof(meta_yes) };
+};
+
+template<typename T> const T* return_ptr();
+
+template <typename T, typename IndexType=Index>
+struct has_nullary_operator
+{
+  template <typename C> static meta_yes testFunctor(C const *,typename enable_if<(sizeof(return_ptr<C>()->operator()())>0)>::type * = 0);
+  static meta_no testFunctor(...);
+
+  enum { value = sizeof(testFunctor(static_cast<T*>(0))) == sizeof(meta_yes) };
+};
+
+template <typename T, typename IndexType=Index>
+struct has_unary_operator
+{
+  template <typename C> static meta_yes testFunctor(C const *,typename enable_if<(sizeof(return_ptr<C>()->operator()(IndexType(0)))>0)>::type * = 0);
+  static meta_no testFunctor(...);
+
+  enum { value = sizeof(testFunctor(static_cast<T*>(0))) == sizeof(meta_yes) };
+};
+
+template <typename T, typename IndexType=Index>
+struct has_binary_operator
+{
+  template <typename C> static meta_yes testFunctor(C const *,typename enable_if<(sizeof(return_ptr<C>()->operator()(IndexType(0),IndexType(0)))>0)>::type * = 0);
+  static meta_no testFunctor(...);
+
+  enum { value = sizeof(testFunctor(static_cast<T*>(0))) == sizeof(meta_yes) };
+};
+
 /** \internal In short, it computes int(sqrt(\a Y)) with \a Y an integer.
   * Usage example: \code meta_sqrt<1023>::ret \endcode
   */
@@ -185,37 +491,26 @@ class meta_sqrt
 template<int Y, int InfX, int SupX>
 class meta_sqrt<Y, InfX, SupX, true> { public:  enum { ret = (SupX*SupX <= Y) ? SupX : InfX }; };
 
-/** \internal determines whether the product of two numeric types is allowed and what the return type is */
-template<typename T, typename U> struct scalar_product_traits
-{
-  enum { Defined = 0 };
-};
 
-template<typename T> struct scalar_product_traits<T,T>
+/** \internal Computes the least common multiple of two positive integer A and B
+  * at compile-time. It implements a naive algorithm testing all multiples of A.
+  * It thus works better if A>=B.
+  */
+template<int A, int B, int K=1, bool Done = ((A*K)%B)==0>
+struct meta_least_common_multiple
 {
-  enum {
-    // Cost = NumTraits<T>::MulCost,
-    Defined = 1
-  };
-  typedef T ReturnType;
+  enum { ret = meta_least_common_multiple<A,B,K+1>::ret };
 };
-
-template<typename T> struct scalar_product_traits<T,std::complex<T> >
+template<int A, int B, int K>
+struct meta_least_common_multiple<A,B,K,true>
 {
-  enum {
-    // Cost = 2*NumTraits<T>::MulCost,
-    Defined = 1
-  };
-  typedef std::complex<T> ReturnType;
+  enum { ret = A*K };
 };
 
-template<typename T> struct scalar_product_traits<std::complex<T>, T>
+/** \internal determines whether the product of two numeric types is allowed and what the return type is */
+template<typename T, typename U> struct scalar_product_traits
 {
-  enum {
-    // Cost = 2*NumTraits<T>::MulCost,
-    Defined = 1
-  };
-  typedef std::complex<T> ReturnType;
+  enum { Defined = 0 };
 };
 
 // FIXME quick workaround around current limitation of result_of
@@ -224,19 +519,31 @@ template<typename T> struct scalar_product_traits<std::complex<T>, T>
 // typedef typename scalar_product_traits<typename remove_all<ArgType0>::type, typename remove_all<ArgType1>::type>::ReturnType type;
 // };
 
-template<typename T> struct is_diagonal
-{ enum { ret = false }; };
-
-template<typename T> struct is_diagonal<DiagonalBase<T> >
-{ enum { ret = true }; };
-
-template<typename T> struct is_diagonal<DiagonalWrapper<T> >
-{ enum { ret = true }; };
+} // end namespace internal
 
-template<typename T, int S> struct is_diagonal<DiagonalMatrix<T,S> >
-{ enum { ret = true }; };
+namespace numext {
+  
+#if defined(__CUDA_ARCH__)
+template<typename T> EIGEN_DEVICE_FUNC   void swap(T &a, T &b) { T tmp = b; b = a; a = tmp; }
+#else
+template<typename T> EIGEN_STRONG_INLINE void swap(T &a, T &b) { std::swap(a,b); }
+#endif
+
+#if defined(__CUDA_ARCH__)
+using internal::device::numeric_limits;
+#else
+using std::numeric_limits;
+#endif
+
+// Integer division with rounding up.
+// T is assumed to be an integer type with a>=0, and b>0
+template<typename T>
+T div_ceil(const T &a, const T &b)
+{
+  return (a+b-1) / b;
+}
 
-} // end namespace internal
+} // end namespace numext
 
 } // end namespace Eigen
 
diff --git a/eigen/Eigen/src/Core/util/ReenableStupidWarnings.h b/eigen/Eigen/src/Core/util/ReenableStupidWarnings.h
index d573bbd..86b60f5 100644
--- a/eigen/Eigen/src/Core/util/ReenableStupidWarnings.h
+++ b/eigen/Eigen/src/Core/util/ReenableStupidWarnings.h
@@ -12,6 +12,16 @@
     #pragma GCC diagnostic pop
   #endif
 
+  #if defined __NVCC__
+//    Don't reenable the diagnostic messages, as it turns out these messages need
+//    to be disabled at the point of the template instantiation (i.e the user code)
+//    otherwise they'll be triggered by nvcc.
+//    #pragma diag_default code_is_unreachable
+//    #pragma diag_default initialization_not_reachable
+//    #pragma diag_default 2651
+//    #pragma diag_default 2653
+  #endif
+
 #endif
 
 #endif // EIGEN_WARNINGS_DISABLED
diff --git a/eigen/Eigen/src/Core/util/StaticAssert.h b/eigen/Eigen/src/Core/util/StaticAssert.h
index e53d2b8..983361a 100644
--- a/eigen/Eigen/src/Core/util/StaticAssert.h
+++ b/eigen/Eigen/src/Core/util/StaticAssert.h
@@ -26,7 +26,7 @@
 
 #ifndef EIGEN_NO_STATIC_ASSERT
 
-  #if __has_feature(cxx_static_assert) || (defined(__cplusplus) && __cplusplus >= 201103L) || (EIGEN_COMP_MSVC >= 1600)
+  #if EIGEN_MAX_CPP_VER>=11 && (__has_feature(cxx_static_assert) || (defined(__cplusplus) && __cplusplus >= 201103L) || (EIGEN_COMP_MSVC >= 1600))
 
     // if native static_assert is enabled, let's use it
     #define EIGEN_STATIC_ASSERT(X,MSG) static_assert(X,#MSG);
@@ -50,6 +50,7 @@
         THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE,
         THIS_METHOD_IS_ONLY_FOR_MATRICES_OF_A_SPECIFIC_SIZE,
         THIS_METHOD_IS_ONLY_FOR_OBJECTS_OF_A_SPECIFIC_SIZE,
+        OUT_OF_RANGE_ACCESS,
         YOU_MADE_A_PROGRAMMING_MISTAKE,
         EIGEN_INTERNAL_ERROR_PLEASE_FILE_A_BUG_REPORT,
         EIGEN_INTERNAL_COMPILATION_ERROR_OR_YOU_MADE_A_PROGRAMMING_MISTAKE,
@@ -84,6 +85,7 @@
         THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY,
         YOU_ARE_TRYING_TO_USE_AN_INDEX_BASED_ACCESSOR_ON_AN_EXPRESSION_THAT_DOES_NOT_SUPPORT_THAT,
         THIS_METHOD_IS_ONLY_FOR_1x1_EXPRESSIONS,
+        THIS_METHOD_IS_ONLY_FOR_INNER_OR_LAZY_PRODUCTS,
         THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_OF_BOOL,
         THIS_METHOD_IS_ONLY_FOR_ARRAYS_NOT_MATRICES,
         YOU_PASSED_A_ROW_VECTOR_BUT_A_COLUMN_VECTOR_WAS_EXPECTED,
@@ -92,7 +94,14 @@
         THE_STORAGE_ORDER_OF_BOTH_SIDES_MUST_MATCH,
         OBJECT_ALLOCATED_ON_STACK_IS_TOO_BIG,
         IMPLICIT_CONVERSION_TO_SCALAR_IS_FOR_INNER_PRODUCT_ONLY,
-        STORAGE_LAYOUT_DOES_NOT_MATCH
+        STORAGE_LAYOUT_DOES_NOT_MATCH,
+        EIGEN_INTERNAL_ERROR_PLEASE_FILE_A_BUG_REPORT__INVALID_COST_VALUE,
+        THIS_COEFFICIENT_ACCESSOR_TAKING_ONE_ACCESS_IS_ONLY_FOR_EXPRESSIONS_ALLOWING_LINEAR_ACCESS,
+        MATRIX_FREE_CONJUGATE_GRADIENT_IS_COMPATIBLE_WITH_UPPER_UNION_LOWER_MODE_ONLY,
+        THIS_TYPE_IS_NOT_SUPPORTED,
+        STORAGE_KIND_MUST_MATCH,
+        STORAGE_INDEX_MUST_MATCH,
+        CHOLMOD_SUPPORTS_DOUBLE_PRECISION_ONLY
       };
     };
 
@@ -103,15 +112,15 @@
     // Specialized implementation for MSVC to avoid "conditional
     // expression is constant" warnings.  This implementation doesn't
     // appear to work under GCC, hence the multiple implementations.
-    #ifdef _MSC_VER
+    #if EIGEN_COMP_MSVC
 
       #define EIGEN_STATIC_ASSERT(CONDITION,MSG) \
         {Eigen::internal::static_assertion<bool(CONDITION)>::MSG;}
 
     #else
-
+      // In some cases clang interprets bool(CONDITION) as function declaration
       #define EIGEN_STATIC_ASSERT(CONDITION,MSG) \
-        if (Eigen::internal::static_assertion<bool(CONDITION)>::MSG) {}
+        if (Eigen::internal::static_assertion<static_cast<bool>(CONDITION)>::MSG) {}
 
     #endif
 
@@ -159,7 +168,7 @@
 
 #define EIGEN_PREDICATE_SAME_MATRIX_SIZE(TYPE0,TYPE1) \
      ( \
-        (int(TYPE0::SizeAtCompileTime)==0 && int(TYPE1::SizeAtCompileTime)==0) \
+        (int(Eigen::internal::size_of_xpr_at_compile_time<TYPE0>::ret)==0 && int(Eigen::internal::size_of_xpr_at_compile_time<TYPE1>::ret)==0) \
     || (\
           (int(TYPE0::RowsAtCompileTime)==Eigen::Dynamic \
         || int(TYPE1::RowsAtCompileTime)==Eigen::Dynamic \
@@ -170,13 +179,8 @@
        ) \
      )
 
-#ifdef EIGEN2_SUPPORT
-  #define EIGEN_STATIC_ASSERT_NON_INTEGER(TYPE) \
-    eigen_assert(!NumTraits<Scalar>::IsInteger);
-#else
-  #define EIGEN_STATIC_ASSERT_NON_INTEGER(TYPE) \
+#define EIGEN_STATIC_ASSERT_NON_INTEGER(TYPE) \
     EIGEN_STATIC_ASSERT(!NumTraits<TYPE>::IsInteger, THIS_FUNCTION_IS_NOT_FOR_INTEGER_NUMERIC_TYPES)
-#endif
 
 
 // static assertion failing if it is guaranteed at compile-time that the two matrix expression types have different sizes
@@ -191,18 +195,22 @@
                           THIS_METHOD_IS_ONLY_FOR_1x1_EXPRESSIONS)
 
 #define EIGEN_STATIC_ASSERT_LVALUE(Derived) \
-      EIGEN_STATIC_ASSERT(internal::is_lvalue<Derived>::value, \
+      EIGEN_STATIC_ASSERT(Eigen::internal::is_lvalue<Derived>::value, \
                           THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY)
 
 #define EIGEN_STATIC_ASSERT_ARRAYXPR(Derived) \
-      EIGEN_STATIC_ASSERT((internal::is_same<typename internal::traits<Derived>::XprKind, ArrayXpr>::value), \
+      EIGEN_STATIC_ASSERT((Eigen::internal::is_same<typename Eigen::internal::traits<Derived>::XprKind, ArrayXpr>::value), \
                           THIS_METHOD_IS_ONLY_FOR_ARRAYS_NOT_MATRICES)
 
 #define EIGEN_STATIC_ASSERT_SAME_XPR_KIND(Derived1, Derived2) \
-      EIGEN_STATIC_ASSERT((internal::is_same<typename internal::traits<Derived1>::XprKind, \
-                                             typename internal::traits<Derived2>::XprKind \
+      EIGEN_STATIC_ASSERT((Eigen::internal::is_same<typename Eigen::internal::traits<Derived1>::XprKind, \
+                                             typename Eigen::internal::traits<Derived2>::XprKind \
                                             >::value), \
                           YOU_CANNOT_MIX_ARRAYS_AND_MATRICES)
 
+// Check that a cost value is positive, and that is stay within a reasonable range
+// TODO this check could be enabled for internal debugging only
+#define EIGEN_INTERNAL_CHECK_COST_VALUE(C) \
+      EIGEN_STATIC_ASSERT((C)>=0 && (C)<=HugeCost*HugeCost, EIGEN_INTERNAL_ERROR_PLEASE_FILE_A_BUG_REPORT__INVALID_COST_VALUE);
 
 #endif // EIGEN_STATIC_ASSERT_H
diff --git a/eigen/Eigen/src/Core/util/SymbolicIndex.h b/eigen/Eigen/src/Core/util/SymbolicIndex.h
new file mode 100644
index 0000000..bb6349e
--- /dev/null
+++ b/eigen/Eigen/src/Core/util/SymbolicIndex.h
@@ -0,0 +1,300 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SYMBOLIC_INDEX_H
+#define EIGEN_SYMBOLIC_INDEX_H
+
+namespace Eigen {
+
+/** \namespace Eigen::Symbolic
+  * \ingroup Core_Module
+  *
+  * This namespace defines a set of classes and functions to build and evaluate symbolic expressions of scalar type Index.
+  * Here is a simple example:
+  *
+  * \code
+  * // First step, defines symbols:
+  * struct x_tag {};  static const Symbolic::SymbolExpr<x_tag> x;
+  * struct y_tag {};  static const Symbolic::SymbolExpr<y_tag> y;
+  * struct z_tag {};  static const Symbolic::SymbolExpr<z_tag> z;
+  *
+  * // Defines an expression:
+  * auto expr = (x+3)/y+z;
+  *
+  * // And evaluate it: (c++14)
+  * std::cout << expr.eval(x=6,y=3,z=-13) << "\n";
+  *
+  * // In c++98/11, only one symbol per expression is supported for now:
+  * auto expr98 = (3-x)/2;
+  * std::cout << expr98.eval(x=6) << "\n";
+  * \endcode
+  *
+  * It is currently only used internally to define and minipulate the placeholders::last and placeholders::end symbols in Eigen::seq and Eigen::seqN.
+  *
+  */
+namespace Symbolic {
+
+template<typename Tag> class Symbol;
+template<typename Arg0> class NegateExpr;
+template<typename Arg1,typename Arg2> class AddExpr;
+template<typename Arg1,typename Arg2> class ProductExpr;
+template<typename Arg1,typename Arg2> class QuotientExpr;
+
+// A simple wrapper around an integral value to provide the eval method.
+// We could also use a free-function symbolic_eval...
+template<typename IndexType=Index>
+class ValueExpr {
+public:
+  ValueExpr(IndexType val) : m_value(val) {}
+  template<typename T>
+  IndexType eval_impl(const T&) const { return m_value; }
+protected:
+  IndexType m_value;
+};
+
+// Specialization for compile-time value,
+// It is similar to ValueExpr(N) but this version helps the compiler to generate better code.
+template<int N>
+class ValueExpr<internal::FixedInt<N> > {
+public:
+  ValueExpr() {}
+  template<typename T>
+  Index eval_impl(const T&) const { return N; }
+};
+
+
+/** \class BaseExpr
+  * \ingroup Core_Module
+  * Common base class of any symbolic expressions
+  */
+template<typename Derived>
+class BaseExpr
+{
+public:
+  const Derived& derived() const { return *static_cast<const Derived*>(this); }
+
+  /** Evaluate the expression given the \a values of the symbols.
+    *
+    * \param values defines the values of the symbols, it can either be a SymbolValue or a std::tuple of SymbolValue
+    *               as constructed by SymbolExpr::operator= operator.
+    *
+    */
+  template<typename T>
+  Index eval(const T& values) const { return derived().eval_impl(values); }
+
+#if EIGEN_HAS_CXX14
+  template<typename... Types>
+  Index eval(Types&&... values) const { return derived().eval_impl(std::make_tuple(values...)); }
+#endif
+
+  NegateExpr<Derived> operator-() const { return NegateExpr<Derived>(derived()); }
+
+  AddExpr<Derived,ValueExpr<> > operator+(Index b) const
+  { return AddExpr<Derived,ValueExpr<> >(derived(),  b); }
+  AddExpr<Derived,ValueExpr<> > operator-(Index a) const
+  { return AddExpr<Derived,ValueExpr<> >(derived(), -a); }
+  ProductExpr<Derived,ValueExpr<> > operator*(Index a) const
+  { return ProductExpr<Derived,ValueExpr<> >(derived(),a); }
+  QuotientExpr<Derived,ValueExpr<> > operator/(Index a) const
+  { return QuotientExpr<Derived,ValueExpr<> >(derived(),a); }
+
+  friend AddExpr<Derived,ValueExpr<> > operator+(Index a, const BaseExpr& b)
+  { return AddExpr<Derived,ValueExpr<> >(b.derived(), a); }
+  friend AddExpr<NegateExpr<Derived>,ValueExpr<> > operator-(Index a, const BaseExpr& b)
+  { return AddExpr<NegateExpr<Derived>,ValueExpr<> >(-b.derived(), a); }
+  friend ProductExpr<ValueExpr<>,Derived> operator*(Index a, const BaseExpr& b)
+  { return ProductExpr<ValueExpr<>,Derived>(a,b.derived()); }
+  friend QuotientExpr<ValueExpr<>,Derived> operator/(Index a, const BaseExpr& b)
+  { return QuotientExpr<ValueExpr<>,Derived>(a,b.derived()); }
+
+  template<int N>
+  AddExpr<Derived,ValueExpr<internal::FixedInt<N> > > operator+(internal::FixedInt<N>) const
+  { return AddExpr<Derived,ValueExpr<internal::FixedInt<N> > >(derived(), ValueExpr<internal::FixedInt<N> >()); }
+  template<int N>
+  AddExpr<Derived,ValueExpr<internal::FixedInt<-N> > > operator-(internal::FixedInt<N>) const
+  { return AddExpr<Derived,ValueExpr<internal::FixedInt<-N> > >(derived(), ValueExpr<internal::FixedInt<-N> >()); }
+  template<int N>
+  ProductExpr<Derived,ValueExpr<internal::FixedInt<N> > > operator*(internal::FixedInt<N>) const
+  { return ProductExpr<Derived,ValueExpr<internal::FixedInt<N> > >(derived(),ValueExpr<internal::FixedInt<N> >()); }
+  template<int N>
+  QuotientExpr<Derived,ValueExpr<internal::FixedInt<N> > > operator/(internal::FixedInt<N>) const
+  { return QuotientExpr<Derived,ValueExpr<internal::FixedInt<N> > >(derived(),ValueExpr<internal::FixedInt<N> >()); }
+
+  template<int N>
+  friend AddExpr<Derived,ValueExpr<internal::FixedInt<N> > > operator+(internal::FixedInt<N>, const BaseExpr& b)
+  { return AddExpr<Derived,ValueExpr<internal::FixedInt<N> > >(b.derived(), ValueExpr<internal::FixedInt<N> >()); }
+  template<int N>
+  friend AddExpr<NegateExpr<Derived>,ValueExpr<internal::FixedInt<N> > > operator-(internal::FixedInt<N>, const BaseExpr& b)
+  { return AddExpr<NegateExpr<Derived>,ValueExpr<internal::FixedInt<N> > >(-b.derived(), ValueExpr<internal::FixedInt<N> >()); }
+  template<int N>
+  friend ProductExpr<ValueExpr<internal::FixedInt<N> >,Derived> operator*(internal::FixedInt<N>, const BaseExpr& b)
+  { return ProductExpr<ValueExpr<internal::FixedInt<N> >,Derived>(ValueExpr<internal::FixedInt<N> >(),b.derived()); }
+  template<int N>
+  friend QuotientExpr<ValueExpr<internal::FixedInt<N> >,Derived> operator/(internal::FixedInt<N>, const BaseExpr& b)
+  { return QuotientExpr<ValueExpr<internal::FixedInt<N> > ,Derived>(ValueExpr<internal::FixedInt<N> >(),b.derived()); }
+
+#if (!EIGEN_HAS_CXX14)
+  template<int N>
+  AddExpr<Derived,ValueExpr<internal::FixedInt<N> > > operator+(internal::FixedInt<N> (*)()) const
+  { return AddExpr<Derived,ValueExpr<internal::FixedInt<N> > >(derived(), ValueExpr<internal::FixedInt<N> >()); }
+  template<int N>
+  AddExpr<Derived,ValueExpr<internal::FixedInt<-N> > > operator-(internal::FixedInt<N> (*)()) const
+  { return AddExpr<Derived,ValueExpr<internal::FixedInt<-N> > >(derived(), ValueExpr<internal::FixedInt<-N> >()); }
+  template<int N>
+  ProductExpr<Derived,ValueExpr<internal::FixedInt<N> > > operator*(internal::FixedInt<N> (*)()) const
+  { return ProductExpr<Derived,ValueExpr<internal::FixedInt<N> > >(derived(),ValueExpr<internal::FixedInt<N> >()); }
+  template<int N>
+  QuotientExpr<Derived,ValueExpr<internal::FixedInt<N> > > operator/(internal::FixedInt<N> (*)()) const
+  { return QuotientExpr<Derived,ValueExpr<internal::FixedInt<N> > >(derived(),ValueExpr<internal::FixedInt<N> >()); }
+
+  template<int N>
+  friend AddExpr<Derived,ValueExpr<internal::FixedInt<N> > > operator+(internal::FixedInt<N> (*)(), const BaseExpr& b)
+  { return AddExpr<Derived,ValueExpr<internal::FixedInt<N> > >(b.derived(), ValueExpr<internal::FixedInt<N> >()); }
+  template<int N>
+  friend AddExpr<NegateExpr<Derived>,ValueExpr<internal::FixedInt<N> > > operator-(internal::FixedInt<N> (*)(), const BaseExpr& b)
+  { return AddExpr<NegateExpr<Derived>,ValueExpr<internal::FixedInt<N> > >(-b.derived(), ValueExpr<internal::FixedInt<N> >()); }
+  template<int N>
+  friend ProductExpr<ValueExpr<internal::FixedInt<N> >,Derived> operator*(internal::FixedInt<N> (*)(), const BaseExpr& b)
+  { return ProductExpr<ValueExpr<internal::FixedInt<N> >,Derived>(ValueExpr<internal::FixedInt<N> >(),b.derived()); }
+  template<int N>
+  friend QuotientExpr<ValueExpr<internal::FixedInt<N> >,Derived> operator/(internal::FixedInt<N> (*)(), const BaseExpr& b)
+  { return QuotientExpr<ValueExpr<internal::FixedInt<N> > ,Derived>(ValueExpr<internal::FixedInt<N> >(),b.derived()); }
+#endif
+
+
+  template<typename OtherDerived>
+  AddExpr<Derived,OtherDerived> operator+(const BaseExpr<OtherDerived> &b) const
+  { return AddExpr<Derived,OtherDerived>(derived(),  b.derived()); }
+
+  template<typename OtherDerived>
+  AddExpr<Derived,NegateExpr<OtherDerived> > operator-(const BaseExpr<OtherDerived> &b) const
+  { return AddExpr<Derived,NegateExpr<OtherDerived> >(derived(), -b.derived()); }
+
+  template<typename OtherDerived>
+  ProductExpr<Derived,OtherDerived> operator*(const BaseExpr<OtherDerived> &b) const
+  { return ProductExpr<Derived,OtherDerived>(derived(), b.derived()); }
+
+  template<typename OtherDerived>
+  QuotientExpr<Derived,OtherDerived> operator/(const BaseExpr<OtherDerived> &b) const
+  { return QuotientExpr<Derived,OtherDerived>(derived(), b.derived()); }
+};
+
+template<typename T>
+struct is_symbolic {
+  // BaseExpr has no conversion ctor, so we only have to check whether T can be staticaly cast to its base class BaseExpr<T>.
+  enum { value = internal::is_convertible<T,BaseExpr<T> >::value };
+};
+
+// Specialization for functions, because is_convertible fails in this case.
+// Useful in c++98/11 mode when testing is_symbolic<decltype(fix<N>)>
+template<typename T>
+struct is_symbolic<T (*)()> {
+  enum { value = false };
+};
+
+/** Represents the actual value of a symbol identified by its tag
+  *
+  * It is the return type of SymbolValue::operator=, and most of the time this is only way it is used.
+  */
+template<typename Tag>
+class SymbolValue
+{
+public:
+  /** Default constructor from the value \a val */
+  SymbolValue(Index val) : m_value(val) {}
+
+  /** \returns the stored value of the symbol */
+  Index value() const { return m_value; }
+protected:
+  Index m_value;
+};
+
+/** Expression of a symbol uniquely identified by the template parameter type \c tag */
+template<typename tag>
+class SymbolExpr : public BaseExpr<SymbolExpr<tag> >
+{
+public:
+  /** Alias to the template parameter \c tag */
+  typedef tag Tag;
+
+  SymbolExpr() {}
+
+  /** Associate the value \a val to the given symbol \c *this, uniquely identified by its \c Tag.
+    *
+    * The returned object should be passed to ExprBase::eval() to evaluate a given expression with this specified runtime-time value.
+    */
+  SymbolValue<Tag> operator=(Index val) const {
+    return SymbolValue<Tag>(val);
+  }
+
+  Index eval_impl(const SymbolValue<Tag> &values) const { return values.value(); }
+
+#if EIGEN_HAS_CXX14
+  // C++14 versions suitable for multiple symbols
+  template<typename... Types>
+  Index eval_impl(const std::tuple<Types...>& values) const { return std::get<SymbolValue<Tag> >(values).value(); }
+#endif
+};
+
+template<typename Arg0>
+class NegateExpr : public BaseExpr<NegateExpr<Arg0> >
+{
+public:
+  NegateExpr(const Arg0& arg0) : m_arg0(arg0) {}
+
+  template<typename T>
+  Index eval_impl(const T& values) const { return -m_arg0.eval_impl(values); }
+protected:
+  Arg0 m_arg0;
+};
+
+template<typename Arg0, typename Arg1>
+class AddExpr : public BaseExpr<AddExpr<Arg0,Arg1> >
+{
+public:
+  AddExpr(const Arg0& arg0, const Arg1& arg1) : m_arg0(arg0), m_arg1(arg1) {}
+
+  template<typename T>
+  Index eval_impl(const T& values) const { return m_arg0.eval_impl(values) + m_arg1.eval_impl(values); }
+protected:
+  Arg0 m_arg0;
+  Arg1 m_arg1;
+};
+
+template<typename Arg0, typename Arg1>
+class ProductExpr : public BaseExpr<ProductExpr<Arg0,Arg1> >
+{
+public:
+  ProductExpr(const Arg0& arg0, const Arg1& arg1) : m_arg0(arg0), m_arg1(arg1) {}
+
+  template<typename T>
+  Index eval_impl(const T& values) const { return m_arg0.eval_impl(values) * m_arg1.eval_impl(values); }
+protected:
+  Arg0 m_arg0;
+  Arg1 m_arg1;
+};
+
+template<typename Arg0, typename Arg1>
+class QuotientExpr : public BaseExpr<QuotientExpr<Arg0,Arg1> >
+{
+public:
+  QuotientExpr(const Arg0& arg0, const Arg1& arg1) : m_arg0(arg0), m_arg1(arg1) {}
+
+  template<typename T>
+  Index eval_impl(const T& values) const { return m_arg0.eval_impl(values) / m_arg1.eval_impl(values); }
+protected:
+  Arg0 m_arg0;
+  Arg1 m_arg1;
+};
+
+} // end namespace Symbolic
+
+} // end namespace Eigen
+
+#endif // EIGEN_SYMBOLIC_INDEX_H
diff --git a/eigen/Eigen/src/Core/util/XprHelper.h b/eigen/Eigen/src/Core/util/XprHelper.h
index d05f8e5..4b337f2 100644
--- a/eigen/Eigen/src/Core/util/XprHelper.h
+++ b/eigen/Eigen/src/Core/util/XprHelper.h
@@ -14,20 +14,77 @@
 // just a workaround because GCC seems to not really like empty structs
 // FIXME: gcc 4.3 generates bad code when strict-aliasing is enabled
 // so currently we simply disable this optimization for gcc 4.3
-#if (defined __GNUG__) && !((__GNUC__==4) && (__GNUC_MINOR__==3))
+#if EIGEN_COMP_GNUC && !EIGEN_GNUC_AT(4,3)
   #define EIGEN_EMPTY_STRUCT_CTOR(X) \
-    EIGEN_STRONG_INLINE X() {} \
-    EIGEN_STRONG_INLINE X(const X& ) {}
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE X() {} \
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE X(const X& ) {}
 #else
   #define EIGEN_EMPTY_STRUCT_CTOR(X)
 #endif
 
 namespace Eigen {
 
-typedef EIGEN_DEFAULT_DENSE_INDEX_TYPE DenseIndex;
-
 namespace internal {
 
+template<typename IndexDest, typename IndexSrc>
+EIGEN_DEVICE_FUNC
+inline IndexDest convert_index(const IndexSrc& idx) {
+  // for sizeof(IndexDest)>=sizeof(IndexSrc) compilers should be able to optimize this away:
+  eigen_internal_assert(idx <= NumTraits<IndexDest>::highest() && "Index value to big for target type");
+  return IndexDest(idx);
+}
+
+
+// promote_scalar_arg is an helper used in operation between an expression and a scalar, like:
+//    expression * scalar
+// Its role is to determine how the type T of the scalar operand should be promoted given the scalar type ExprScalar of the given expression.
+// The IsSupported template parameter must be provided by the caller as: internal::has_ReturnType<ScalarBinaryOpTraits<ExprScalar,T,op> >::value using the proper order for ExprScalar and T.
+// Then the logic is as follows:
+//  - if the operation is natively supported as defined by IsSupported, then the scalar type is not promoted, and T is returned.
+//  - otherwise, NumTraits<ExprScalar>::Literal is returned if T is implicitly convertible to NumTraits<ExprScalar>::Literal AND that this does not imply a float to integer conversion.
+//  - otherwise, ExprScalar is returned if T is implicitly convertible to ExprScalar AND that this does not imply a float to integer conversion.
+//  - In all other cases, the promoted type is not defined, and the respective operation is thus invalid and not available (SFINAE).
+template<typename ExprScalar,typename T, bool IsSupported>
+struct promote_scalar_arg;
+
+template<typename S,typename T>
+struct promote_scalar_arg<S,T,true>
+{
+  typedef T type;
+};
+
+// Recursively check safe conversion to PromotedType, and then ExprScalar if they are different.
+template<typename ExprScalar,typename T,typename PromotedType,
+  bool ConvertibleToLiteral = internal::is_convertible<T,PromotedType>::value,
+  bool IsSafe = NumTraits<T>::IsInteger || !NumTraits<PromotedType>::IsInteger>
+struct promote_scalar_arg_unsupported;
+
+// Start recursion with NumTraits<ExprScalar>::Literal
+template<typename S,typename T>
+struct promote_scalar_arg<S,T,false> : promote_scalar_arg_unsupported<S,T,typename NumTraits<S>::Literal> {};
+
+// We found a match!
+template<typename S,typename T, typename PromotedType>
+struct promote_scalar_arg_unsupported<S,T,PromotedType,true,true>
+{
+  typedef PromotedType type;
+};
+
+// No match, but no real-to-integer issues, and ExprScalar and current PromotedType are different,
+// so let's try to promote to ExprScalar
+template<typename ExprScalar,typename T, typename PromotedType>
+struct promote_scalar_arg_unsupported<ExprScalar,T,PromotedType,false,true>
+   : promote_scalar_arg_unsupported<ExprScalar,T,ExprScalar>
+{};
+
+// Unsafe real-to-integer, let's stop.
+template<typename S,typename T, typename PromotedType, bool ConvertibleToLiteral>
+struct promote_scalar_arg_unsupported<S,T,PromotedType,ConvertibleToLiteral,false> {};
+
+// T is not even convertible to ExprScalar, let's stop.
+template<typename S,typename T>
+struct promote_scalar_arg_unsupported<S,T,S,false,true> {};
+
 //classes inheriting no_assignment_operator don't generate a default operator=.
 class no_assignment_operator
 {
@@ -50,19 +107,21 @@ template<typename T, int Value> class variable_if_dynamic
 {
   public:
     EIGEN_EMPTY_STRUCT_CTOR(variable_if_dynamic)
-    explicit variable_if_dynamic(T v) { EIGEN_ONLY_USED_FOR_DEBUG(v); assert(v == T(Value)); }
-    static T value() { return T(Value); }
-    void setValue(T) {}
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit variable_if_dynamic(T v) { EIGEN_ONLY_USED_FOR_DEBUG(v); eigen_assert(v == T(Value)); }
+    EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE T value() { return T(Value); }
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE operator T() const { return T(Value); }
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void setValue(T) {}
 };
 
 template<typename T> class variable_if_dynamic<T, Dynamic>
 {
     T m_value;
-    variable_if_dynamic() { assert(false); }
+    EIGEN_DEVICE_FUNC variable_if_dynamic() { eigen_assert(false); }
   public:
-    explicit variable_if_dynamic(T value) : m_value(value) {}
-    T value() const { return m_value; }
-    void setValue(T value) { m_value = value; }
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit variable_if_dynamic(T value) : m_value(value) {}
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T value() const { return m_value; }
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE operator T() const { return m_value; }
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void setValue(T value) { m_value = value; }
 };
 
 /** \internal like variable_if_dynamic but for DynamicIndex
@@ -71,19 +130,19 @@ template<typename T, int Value> class variable_if_dynamicindex
 {
   public:
     EIGEN_EMPTY_STRUCT_CTOR(variable_if_dynamicindex)
-    explicit variable_if_dynamicindex(T v) { EIGEN_ONLY_USED_FOR_DEBUG(v); assert(v == T(Value)); }
-    static T value() { return T(Value); }
-    void setValue(T) {}
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit variable_if_dynamicindex(T v) { EIGEN_ONLY_USED_FOR_DEBUG(v); eigen_assert(v == T(Value)); }
+    EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE T value() { return T(Value); }
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void setValue(T) {}
 };
 
 template<typename T> class variable_if_dynamicindex<T, DynamicIndex>
 {
     T m_value;
-    variable_if_dynamicindex() { assert(false); }
+    EIGEN_DEVICE_FUNC variable_if_dynamicindex() { eigen_assert(false); }
   public:
-    explicit variable_if_dynamicindex(T value) : m_value(value) {}
-    T value() const { return m_value; }
-    void setValue(T value) { m_value = value; }
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit variable_if_dynamicindex(T value) : m_value(value) {}
+    EIGEN_DEVICE_FUNC T EIGEN_STRONG_INLINE value() const { return m_value; }
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void setValue(T value) { m_value = value; }
 };
 
 template<typename T> struct functor_traits
@@ -101,7 +160,73 @@ template<typename T> struct packet_traits;
 template<typename T> struct unpacket_traits
 {
   typedef T type;
-  enum {size=1};
+  typedef T half;
+  enum
+  {
+    size = 1,
+    alignment = 1
+  };
+};
+
+template<int Size, typename PacketType,
+         bool Stop = Size==Dynamic || (Size%unpacket_traits<PacketType>::size)==0 || is_same<PacketType,typename unpacket_traits<PacketType>::half>::value>
+struct find_best_packet_helper;
+
+template< int Size, typename PacketType>
+struct find_best_packet_helper<Size,PacketType,true>
+{
+  typedef PacketType type;
+};
+
+template<int Size, typename PacketType>
+struct find_best_packet_helper<Size,PacketType,false>
+{
+  typedef typename find_best_packet_helper<Size,typename unpacket_traits<PacketType>::half>::type type;
+};
+
+template<typename T, int Size>
+struct find_best_packet
+{
+  typedef typename find_best_packet_helper<Size,typename packet_traits<T>::type>::type type;
+};
+
+#if EIGEN_MAX_STATIC_ALIGN_BYTES>0
+template<int ArrayBytes, int AlignmentBytes,
+         bool Match     =  bool((ArrayBytes%AlignmentBytes)==0),
+         bool TryHalf   =  bool(EIGEN_MIN_ALIGN_BYTES<AlignmentBytes) >
+struct compute_default_alignment_helper
+{
+  enum { value = 0 };
+};
+
+template<int ArrayBytes, int AlignmentBytes, bool TryHalf>
+struct compute_default_alignment_helper<ArrayBytes, AlignmentBytes, true, TryHalf> // Match
+{
+  enum { value = AlignmentBytes };
+};
+
+template<int ArrayBytes, int AlignmentBytes>
+struct compute_default_alignment_helper<ArrayBytes, AlignmentBytes, false, true> // Try-half
+{
+  // current packet too large, try with an half-packet
+  enum { value = compute_default_alignment_helper<ArrayBytes, AlignmentBytes/2>::value };
+};
+#else
+// If static alignment is disabled, no need to bother.
+// This also avoids a division by zero in "bool Match =  bool((ArrayBytes%AlignmentBytes)==0)"
+template<int ArrayBytes, int AlignmentBytes>
+struct compute_default_alignment_helper
+{
+  enum { value = 0 };
+};
+#endif
+
+template<typename T, int Size> struct compute_default_alignment {
+  enum { value = compute_default_alignment_helper<Size*sizeof(T),EIGEN_MAX_STATIC_ALIGN_BYTES>::value };
+};
+
+template<typename T> struct compute_default_alignment<T,Dynamic> {
+  enum { value = EIGEN_MAX_ALIGN_BYTES };
 };
 
 template<typename _Scalar, int _Rows, int _Cols,
@@ -127,35 +252,12 @@ template<typename _Scalar, int _Rows, int _Cols,
 template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
 class compute_matrix_flags
 {
-    enum {
-      row_major_bit = Options&RowMajor ? RowMajorBit : 0,
-      is_dynamic_size_storage = MaxRows==Dynamic || MaxCols==Dynamic,
-
-      aligned_bit =
-      (
-            ((Options&DontAlign)==0)
-        && (
-#if EIGEN_ALIGN_STATICALLY
-             ((!is_dynamic_size_storage) && (((MaxCols*MaxRows*int(sizeof(Scalar))) % 16) == 0))
-#else
-             0
-#endif
-
-          ||
-
-#if EIGEN_ALIGN
-             is_dynamic_size_storage
-#else
-             0
-#endif
-
-          )
-      ) ? AlignedBit : 0,
-      packet_access_bit = packet_traits<Scalar>::Vectorizable && aligned_bit ? PacketAccessBit : 0
-    };
-
+    enum { row_major_bit = Options&RowMajor ? RowMajorBit : 0 };
   public:
-    enum { ret = LinearAccessBit | LvalueBit | DirectAccessBit | NestByRefBit | packet_access_bit | row_major_bit | aligned_bit };
+    // FIXME currently we still have to handle DirectAccessBit at the expression level to handle DenseCoeffsBase<>
+    // and then propagate this information to the evaluator's flags.
+    // However, I (Gael) think that DirectAccessBit should only matter at the evaluation stage.
+    enum { ret = DirectAccessBit | LvalueBit | NestByRefBit | row_major_bit };
 };
 
 template<int _Rows, int _Cols> struct size_at_compile_time
@@ -163,34 +265,43 @@ template<int _Rows, int _Cols> struct size_at_compile_time
   enum { ret = (_Rows==Dynamic || _Cols==Dynamic) ? Dynamic : _Rows * _Cols };
 };
 
+template<typename XprType> struct size_of_xpr_at_compile_time
+{
+  enum { ret = size_at_compile_time<traits<XprType>::RowsAtCompileTime,traits<XprType>::ColsAtCompileTime>::ret };
+};
+
 /* plain_matrix_type : the difference from eval is that plain_matrix_type is always a plain matrix type,
  * whereas eval is a const reference in the case of a matrix
  */
 
 template<typename T, typename StorageKind = typename traits<T>::StorageKind> struct plain_matrix_type;
-template<typename T, typename BaseClassType> struct plain_matrix_type_dense;
+template<typename T, typename BaseClassType, int Flags> struct plain_matrix_type_dense;
 template<typename T> struct plain_matrix_type<T,Dense>
 {
-  typedef typename plain_matrix_type_dense<T,typename traits<T>::XprKind>::type type;
+  typedef typename plain_matrix_type_dense<T,typename traits<T>::XprKind, traits<T>::Flags>::type type;
+};
+template<typename T> struct plain_matrix_type<T,DiagonalShape>
+{
+  typedef typename T::PlainObject type;
 };
 
-template<typename T> struct plain_matrix_type_dense<T,MatrixXpr>
+template<typename T, int Flags> struct plain_matrix_type_dense<T,MatrixXpr,Flags>
 {
   typedef Matrix<typename traits<T>::Scalar,
                 traits<T>::RowsAtCompileTime,
                 traits<T>::ColsAtCompileTime,
-                AutoAlign | (traits<T>::Flags&RowMajorBit ? RowMajor : ColMajor),
+                AutoAlign | (Flags&RowMajorBit ? RowMajor : ColMajor),
                 traits<T>::MaxRowsAtCompileTime,
                 traits<T>::MaxColsAtCompileTime
           > type;
 };
 
-template<typename T> struct plain_matrix_type_dense<T,ArrayXpr>
+template<typename T, int Flags> struct plain_matrix_type_dense<T,ArrayXpr,Flags>
 {
   typedef Array<typename traits<T>::Scalar,
                 traits<T>::RowsAtCompileTime,
                 traits<T>::ColsAtCompileTime,
-                AutoAlign | (traits<T>::Flags&RowMajorBit ? RowMajor : ColMajor),
+                AutoAlign | (Flags&RowMajorBit ? RowMajor : ColMajor),
                 traits<T>::MaxRowsAtCompileTime,
                 traits<T>::MaxColsAtCompileTime
           > type;
@@ -215,6 +326,11 @@ template<typename T> struct eval<T,Dense>
 //           > type;
 };
 
+template<typename T> struct eval<T,DiagonalShape>
+{
+  typedef typename plain_matrix_type<T>::type type;
+};
+
 // for matrices, no need to evaluate, just use a const reference to avoid a useless copy
 template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
 struct eval<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>, Dense>
@@ -229,6 +345,15 @@ struct eval<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>, Dense>
 };
 
 
+/* similar to plain_matrix_type, but using the evaluator's Flags */
+template<typename T, typename StorageKind = typename traits<T>::StorageKind> struct plain_object_eval;
+
+template<typename T>
+struct plain_object_eval<T,Dense>
+{
+  typedef typename plain_matrix_type_dense<T,typename traits<T>::XprKind, evaluator<T>::Flags>::type type;
+};
+
 
 /* plain_matrix_type_column_major : same as plain_matrix_type but guaranteed to be column-major
  */
@@ -266,9 +391,6 @@ template<typename T> struct plain_matrix_type_row_major
           > type;
 };
 
-// we should be able to get rid of this one too
-template<typename T> struct must_nest_by_value { enum { ret = false }; };
-
 /** \internal The reference selector for template expressions. The idea is that we don't
   * need to use references for expressions since they are light weight proxy
   * objects which should generate no copying overhead. */
@@ -280,6 +402,12 @@ struct ref_selector
     T const&,
     const T
   >::type type;
+  
+  typedef typename conditional<
+    bool(traits<T>::Flags & NestByRefBit),
+    T &,
+    T
+  >::type non_const_type;
 };
 
 /** \internal Adds the const qualifier on the value-type of T2 if and only if T1 is a const type */
@@ -293,54 +421,41 @@ struct transfer_constness
   >::type type;
 };
 
-/** \internal Determines how a given expression should be nested into another one.
+
+// However, we still need a mechanism to detect whether an expression which is evaluated multiple time
+// has to be evaluated into a temporary.
+// That's the purpose of this new nested_eval helper:
+/** \internal Determines how a given expression should be nested when evaluated multiple times.
   * For example, when you do a * (b+c), Eigen will determine how the expression b+c should be
-  * nested into the bigger product expression. The choice is between nesting the expression b+c as-is, or
+  * evaluated into the bigger product expression. The choice is between nesting the expression b+c as-is, or
   * evaluating that expression b+c into a temporary variable d, and nest d so that the resulting expression is
   * a*d. Evaluating can be beneficial for example if every coefficient access in the resulting expression causes
   * many coefficient accesses in the nested expressions -- as is the case with matrix product for example.
   *
-  * \param T the type of the expression being nested
-  * \param n the number of coefficient accesses in the nested expression for each coefficient access in the bigger expression.
-  *
-  * Note that if no evaluation occur, then the constness of T is preserved.
-  *
-  * Example. Suppose that a, b, and c are of type Matrix3d. The user forms the expression a*(b+c).
-  * b+c is an expression "sum of matrices", which we will denote by S. In order to determine how to nest it,
-  * the Product expression uses: nested<S, 3>::ret, which turns out to be Matrix3d because the internal logic of
-  * nested determined that in this case it was better to evaluate the expression b+c into a temporary. On the other hand,
-  * since a is of type Matrix3d, the Product expression nests it as nested<Matrix3d, 3>::ret, which turns out to be
-  * const Matrix3d&, because the internal logic of nested determined that since a was already a matrix, there was no point
-  * in copying it into another matrix.
+  * \tparam T the type of the expression being nested.
+  * \tparam n the number of coefficient accesses in the nested expression for each coefficient access in the bigger expression.
+  * \tparam PlainObject the type of the temporary if needed.
   */
-template<typename T, int n=1, typename PlainObject = typename eval<T>::type> struct nested
+template<typename T, int n, typename PlainObject = typename plain_object_eval<T>::type> struct nested_eval
 {
   enum {
-    // for the purpose of this test, to keep it reasonably simple, we arbitrarily choose a value of Dynamic values.
-    // the choice of 10000 makes it larger than any practical fixed value and even most dynamic values.
-    // in extreme cases where these assumptions would be wrong, we would still at worst suffer performance issues
-    // (poor choice of temporaries).
-    // it's important that this value can still be squared without integer overflowing.
-    DynamicAsInteger = 10000,
     ScalarReadCost = NumTraits<typename traits<T>::Scalar>::ReadCost,
-    ScalarReadCostAsInteger = ScalarReadCost == Dynamic ? int(DynamicAsInteger) : int(ScalarReadCost),
-    CoeffReadCost = traits<T>::CoeffReadCost,
-    CoeffReadCostAsInteger = CoeffReadCost == Dynamic ? int(DynamicAsInteger) : int(CoeffReadCost),
-    NAsInteger = n == Dynamic ? int(DynamicAsInteger) : n,
-    CostEvalAsInteger   = (NAsInteger+1) * ScalarReadCostAsInteger + CoeffReadCostAsInteger,
-    CostNoEvalAsInteger = NAsInteger * CoeffReadCostAsInteger
+    CoeffReadCost = evaluator<T>::CoeffReadCost,  // NOTE What if an evaluator evaluate itself into a tempory?
+                                                  //      Then CoeffReadCost will be small (e.g., 1) but we still have to evaluate, especially if n>1.
+                                                  //      This situation is already taken care by the EvalBeforeNestingBit flag, which is turned ON
+                                                  //      for all evaluator creating a temporary. This flag is then propagated by the parent evaluators.
+                                                  //      Another solution could be to count the number of temps?
+    NAsInteger = n == Dynamic ? HugeCost : n,
+    CostEval   = (NAsInteger+1) * ScalarReadCost + CoeffReadCost,
+    CostNoEval = NAsInteger * CoeffReadCost,
+    Evaluate = (int(evaluator<T>::Flags) & EvalBeforeNestingBit) || (int(CostEval) < int(CostNoEval))
   };
 
-  typedef typename conditional<
-      ( (int(traits<T>::Flags) & EvalBeforeNestingBit) ||
-        int(CostEvalAsInteger) < int(CostNoEvalAsInteger)
-      ),
-      PlainObject,
-      typename ref_selector<T>::type
-  >::type type;
+  typedef typename conditional<Evaluate, PlainObject, typename ref_selector<T>::type>::type type;
 };
 
 template<typename T>
+EIGEN_DEVICE_FUNC
 inline T* const_cast_ptr(const T* ptr)
 {
   return const_cast<T*>(ptr);
@@ -364,30 +479,13 @@ struct dense_xpr_base<Derived, ArrayXpr>
   typedef ArrayBase<Derived> type;
 };
 
-/** \internal Helper base class to add a scalar multiple operator
-  * overloads for complex types */
-template<typename Derived, typename Scalar, typename OtherScalar, typename BaseType,
-         bool EnableIt = !is_same<Scalar,OtherScalar>::value >
-struct special_scalar_op_base : public BaseType
-{
-  // dummy operator* so that the
-  // "using special_scalar_op_base::operator*" compiles
-  void operator*() const;
-};
+template<typename Derived, typename XprKind = typename traits<Derived>::XprKind, typename StorageKind = typename traits<Derived>::StorageKind>
+struct generic_xpr_base;
 
-template<typename Derived,typename Scalar,typename OtherScalar, typename BaseType>
-struct special_scalar_op_base<Derived,Scalar,OtherScalar,BaseType,true>  : public BaseType
+template<typename Derived, typename XprKind>
+struct generic_xpr_base<Derived, XprKind, Dense>
 {
-  const CwiseUnaryOp<scalar_multiple2_op<Scalar,OtherScalar>, Derived>
-  operator*(const OtherScalar& scalar) const
-  {
-    return CwiseUnaryOp<scalar_multiple2_op<Scalar,OtherScalar>, Derived>
-      (*static_cast<const Derived*>(this), scalar_multiple2_op<Scalar,OtherScalar>(scalar));
-  }
-
-  inline friend const CwiseUnaryOp<scalar_multiple2_op<Scalar,OtherScalar>, Derived>
-  operator*(const OtherScalar& scalar, const Derived& matrix)
-  { return static_cast<const special_scalar_op_base&>(matrix).operator*(scalar); }
+  typedef typename dense_xpr_base<Derived,XprKind>::type type;
 };
 
 template<typename XprType, typename CastType> struct cast_return_type
@@ -405,9 +503,79 @@ template <typename A> struct promote_storage_type<A,A>
 {
   typedef A ret;
 };
+template <typename A> struct promote_storage_type<A, const A>
+{
+  typedef A ret;
+};
+template <typename A> struct promote_storage_type<const A, A>
+{
+  typedef A ret;
+};
+
+/** \internal Specify the "storage kind" of applying a coefficient-wise
+  * binary operations between two expressions of kinds A and B respectively.
+  * The template parameter Functor permits to specialize the resulting storage kind wrt to
+  * the functor.
+  * The default rules are as follows:
+  * \code
+  * A      op A      -> A
+  * A      op dense  -> dense
+  * dense  op B      -> dense
+  * sparse op dense  -> sparse
+  * dense  op sparse -> sparse
+  * \endcode
+  */
+template <typename A, typename B, typename Functor> struct cwise_promote_storage_type;
+
+template <typename A, typename Functor>                   struct cwise_promote_storage_type<A,A,Functor>                                      { typedef A      ret; };
+template <typename Functor>                               struct cwise_promote_storage_type<Dense,Dense,Functor>                              { typedef Dense  ret; };
+template <typename A, typename Functor>                   struct cwise_promote_storage_type<A,Dense,Functor>                                  { typedef Dense  ret; };
+template <typename B, typename Functor>                   struct cwise_promote_storage_type<Dense,B,Functor>                                  { typedef Dense  ret; };
+template <typename Functor>                               struct cwise_promote_storage_type<Sparse,Dense,Functor>                             { typedef Sparse ret; };
+template <typename Functor>                               struct cwise_promote_storage_type<Dense,Sparse,Functor>                             { typedef Sparse ret; };
+
+template <typename LhsKind, typename RhsKind, int LhsOrder, int RhsOrder> struct cwise_promote_storage_order {
+  enum { value = LhsOrder };
+};
+
+template <typename LhsKind, int LhsOrder, int RhsOrder>   struct cwise_promote_storage_order<LhsKind,Sparse,LhsOrder,RhsOrder>                { enum { value = RhsOrder }; };
+template <typename RhsKind, int LhsOrder, int RhsOrder>   struct cwise_promote_storage_order<Sparse,RhsKind,LhsOrder,RhsOrder>                { enum { value = LhsOrder }; };
+template <int Order>                                      struct cwise_promote_storage_order<Sparse,Sparse,Order,Order>                       { enum { value = Order }; };
+
+
+/** \internal Specify the "storage kind" of multiplying an expression of kind A with kind B.
+  * The template parameter ProductTag permits to specialize the resulting storage kind wrt to
+  * some compile-time properties of the product: GemmProduct, GemvProduct, OuterProduct, InnerProduct.
+  * The default rules are as follows:
+  * \code
+  *  K * K            -> K
+  *  dense * K        -> dense
+  *  K * dense        -> dense
+  *  diag * K         -> K
+  *  K * diag         -> K
+  *  Perm * K         -> K
+  * K * Perm          -> K
+  * \endcode
+  */
+template <typename A, typename B, int ProductTag> struct product_promote_storage_type;
+
+template <typename A, int ProductTag> struct product_promote_storage_type<A,                  A,                  ProductTag> { typedef A     ret;};
+template <int ProductTag>             struct product_promote_storage_type<Dense,              Dense,              ProductTag> { typedef Dense ret;};
+template <typename A, int ProductTag> struct product_promote_storage_type<A,                  Dense,              ProductTag> { typedef Dense ret; };
+template <typename B, int ProductTag> struct product_promote_storage_type<Dense,              B,                  ProductTag> { typedef Dense ret; };
+
+template <typename A, int ProductTag> struct product_promote_storage_type<A,                  DiagonalShape,      ProductTag> { typedef A ret; };
+template <typename B, int ProductTag> struct product_promote_storage_type<DiagonalShape,      B,                  ProductTag> { typedef B ret; };
+template <int ProductTag>             struct product_promote_storage_type<Dense,              DiagonalShape,      ProductTag> { typedef Dense ret; };
+template <int ProductTag>             struct product_promote_storage_type<DiagonalShape,      Dense,              ProductTag> { typedef Dense ret; };
+
+template <typename A, int ProductTag> struct product_promote_storage_type<A,                  PermutationStorage, ProductTag> { typedef A ret; };
+template <typename B, int ProductTag> struct product_promote_storage_type<PermutationStorage, B,                  ProductTag> { typedef B ret; };
+template <int ProductTag>             struct product_promote_storage_type<Dense,              PermutationStorage, ProductTag> { typedef Dense ret; };
+template <int ProductTag>             struct product_promote_storage_type<PermutationStorage, Dense,              ProductTag> { typedef Dense ret; };
 
 /** \internal gives the plain matrix or array type to store a row/column/diagonal of a matrix type.
-  * \param Scalar optional parameter allowing to pass a different scalar type than the one of the MatrixType.
+  * \tparam Scalar optional parameter allowing to pass a different scalar type than the one of the MatrixType.
   */
 template<typename ExpressionType, typename Scalar = typename ExpressionType::Scalar>
 struct plain_row_type
@@ -455,15 +623,201 @@ struct plain_diag_type
   >::type type;
 };
 
+template<typename Expr,typename Scalar = typename Expr::Scalar>
+struct plain_constant_type
+{
+  enum { Options = (traits<Expr>::Flags&RowMajorBit)?RowMajor:0 };
+
+  typedef Array<Scalar,  traits<Expr>::RowsAtCompileTime,   traits<Expr>::ColsAtCompileTime,
+                Options, traits<Expr>::MaxRowsAtCompileTime,traits<Expr>::MaxColsAtCompileTime> array_type;
+
+  typedef Matrix<Scalar,  traits<Expr>::RowsAtCompileTime,   traits<Expr>::ColsAtCompileTime,
+                 Options, traits<Expr>::MaxRowsAtCompileTime,traits<Expr>::MaxColsAtCompileTime> matrix_type;
+
+  typedef CwiseNullaryOp<scalar_constant_op<Scalar>, const typename conditional<is_same< typename traits<Expr>::XprKind, MatrixXpr >::value, matrix_type, array_type>::type > type;
+};
+
 template<typename ExpressionType>
 struct is_lvalue
 {
-  enum { value = !bool(is_const<ExpressionType>::value) &&
+  enum { value = (!bool(is_const<ExpressionType>::value)) &&
                  bool(traits<ExpressionType>::Flags & LvalueBit) };
 };
 
+template<typename T> struct is_diagonal
+{ enum { ret = false }; };
+
+template<typename T> struct is_diagonal<DiagonalBase<T> >
+{ enum { ret = true }; };
+
+template<typename T> struct is_diagonal<DiagonalWrapper<T> >
+{ enum { ret = true }; };
+
+template<typename T, int S> struct is_diagonal<DiagonalMatrix<T,S> >
+{ enum { ret = true }; };
+
+template<typename S1, typename S2> struct glue_shapes;
+template<> struct glue_shapes<DenseShape,TriangularShape> { typedef TriangularShape type;  };
+
+template<typename T1, typename T2>
+bool is_same_dense(const T1 &mat1, const T2 &mat2, typename enable_if<has_direct_access<T1>::ret&&has_direct_access<T2>::ret, T1>::type * = 0)
+{
+  return (mat1.data()==mat2.data()) && (mat1.innerStride()==mat2.innerStride()) && (mat1.outerStride()==mat2.outerStride());
+}
+
+template<typename T1, typename T2>
+bool is_same_dense(const T1 &, const T2 &, typename enable_if<!(has_direct_access<T1>::ret&&has_direct_access<T2>::ret), T1>::type * = 0)
+{
+  return false;
+}
+
+// Internal helper defining the cost of a scalar division for the type T.
+// The default heuristic can be specialized for each scalar type and architecture.
+template<typename T,bool Vectorized=false,typename EnableIf = void>
+struct scalar_div_cost {
+  enum { value = 8*NumTraits<T>::MulCost };
+};
+
+template<typename T,bool Vectorized>
+struct scalar_div_cost<std::complex<T>, Vectorized> {
+  enum { value = 2*scalar_div_cost<T>::value
+               + 6*NumTraits<T>::MulCost
+               + 3*NumTraits<T>::AddCost
+  };
+};
+
+
+template<bool Vectorized>
+struct scalar_div_cost<signed long,Vectorized,typename conditional<sizeof(long)==8,void,false_type>::type> { enum { value = 24 }; };
+template<bool Vectorized>
+struct scalar_div_cost<unsigned long,Vectorized,typename conditional<sizeof(long)==8,void,false_type>::type> { enum { value = 21 }; };
+
+
+#ifdef EIGEN_DEBUG_ASSIGN
+std::string demangle_traversal(int t)
+{
+  if(t==DefaultTraversal) return "DefaultTraversal";
+  if(t==LinearTraversal) return "LinearTraversal";
+  if(t==InnerVectorizedTraversal) return "InnerVectorizedTraversal";
+  if(t==LinearVectorizedTraversal) return "LinearVectorizedTraversal";
+  if(t==SliceVectorizedTraversal) return "SliceVectorizedTraversal";
+  return "?";
+}
+std::string demangle_unrolling(int t)
+{
+  if(t==NoUnrolling) return "NoUnrolling";
+  if(t==InnerUnrolling) return "InnerUnrolling";
+  if(t==CompleteUnrolling) return "CompleteUnrolling";
+  return "?";
+}
+std::string demangle_flags(int f)
+{
+  std::string res;
+  if(f&RowMajorBit)                 res += " | RowMajor";
+  if(f&PacketAccessBit)             res += " | Packet";
+  if(f&LinearAccessBit)             res += " | Linear";
+  if(f&LvalueBit)                   res += " | Lvalue";
+  if(f&DirectAccessBit)             res += " | Direct";
+  if(f&NestByRefBit)                res += " | NestByRef";
+  if(f&NoPreferredStorageOrderBit)  res += " | NoPreferredStorageOrderBit";
+  
+  return res;
+}
+#endif
+
 } // end namespace internal
 
+
+/** \class ScalarBinaryOpTraits
+  * \ingroup Core_Module
+  *
+  * \brief Determines whether the given binary operation of two numeric types is allowed and what the scalar return type is.
+  *
+  * This class permits to control the scalar return type of any binary operation performed on two different scalar types through (partial) template specializations.
+  *
+  * For instance, let \c U1, \c U2 and \c U3 be three user defined scalar types for which most operations between instances of \c U1 and \c U2 returns an \c U3.
+  * You can let %Eigen knows that by defining:
+    \code
+    template<typename BinaryOp>
+    struct ScalarBinaryOpTraits<U1,U2,BinaryOp> { typedef U3 ReturnType;  };
+    template<typename BinaryOp>
+    struct ScalarBinaryOpTraits<U2,U1,BinaryOp> { typedef U3 ReturnType;  };
+    \endcode
+  * You can then explicitly disable some particular operations to get more explicit error messages:
+    \code
+    template<>
+    struct ScalarBinaryOpTraits<U1,U2,internal::scalar_max_op<U1,U2> > {};
+    \endcode
+  * Or customize the return type for individual operation:
+    \code
+    template<>
+    struct ScalarBinaryOpTraits<U1,U2,internal::scalar_sum_op<U1,U2> > { typedef U1 ReturnType; };
+    \endcode
+  *
+  * By default, the following generic combinations are supported:
+  <table class="manual">
+  <tr><th>ScalarA</th><th>ScalarB</th><th>BinaryOp</th><th>ReturnType</th><th>Note</th></tr>
+  <tr            ><td>\c T </td><td>\c T </td><td>\c * </td><td>\c T </td><td></td></tr>
+  <tr class="alt"><td>\c NumTraits<T>::Real </td><td>\c T </td><td>\c * </td><td>\c T </td><td>Only if \c NumTraits<T>::IsComplex </td></tr>
+  <tr            ><td>\c T </td><td>\c NumTraits<T>::Real </td><td>\c * </td><td>\c T </td><td>Only if \c NumTraits<T>::IsComplex </td></tr>
+  </table>
+  *
+  * \sa CwiseBinaryOp
+  */
+template<typename ScalarA, typename ScalarB, typename BinaryOp=internal::scalar_product_op<ScalarA,ScalarB> >
+struct ScalarBinaryOpTraits
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+  // for backward compatibility, use the hints given by the (deprecated) internal::scalar_product_traits class.
+  : internal::scalar_product_traits<ScalarA,ScalarB>
+#endif // EIGEN_PARSED_BY_DOXYGEN
+{};
+
+template<typename T, typename BinaryOp>
+struct ScalarBinaryOpTraits<T,T,BinaryOp>
+{
+  typedef T ReturnType;
+};
+
+template <typename T, typename BinaryOp>
+struct ScalarBinaryOpTraits<T, typename NumTraits<typename internal::enable_if<NumTraits<T>::IsComplex,T>::type>::Real, BinaryOp>
+{
+  typedef T ReturnType;
+};
+template <typename T, typename BinaryOp>
+struct ScalarBinaryOpTraits<typename NumTraits<typename internal::enable_if<NumTraits<T>::IsComplex,T>::type>::Real, T, BinaryOp>
+{
+  typedef T ReturnType;
+};
+
+// For Matrix * Permutation
+template<typename T, typename BinaryOp>
+struct ScalarBinaryOpTraits<T,void,BinaryOp>
+{
+  typedef T ReturnType;
+};
+
+// For Permutation * Matrix
+template<typename T, typename BinaryOp>
+struct ScalarBinaryOpTraits<void,T,BinaryOp>
+{
+  typedef T ReturnType;
+};
+
+// for Permutation*Permutation
+template<typename BinaryOp>
+struct ScalarBinaryOpTraits<void,void,BinaryOp>
+{
+  typedef void ReturnType;
+};
+
+// We require Lhs and Rhs to have "compatible" scalar types.
+// It is tempting to always allow mixing different types but remember that this is often impossible in the vectorized paths.
+// So allowing mixing different types gives very unexpected errors when enabling vectorization, when the user tries to
+// add together a float matrix and a double matrix.
+#define EIGEN_CHECK_BINARY_COMPATIBILIY(BINOP,LHS,RHS) \
+  EIGEN_STATIC_ASSERT((Eigen::internal::has_ReturnType<ScalarBinaryOpTraits<LHS, RHS,BINOP> >::value), \
+    YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+    
 } // end namespace Eigen
 
 #endif // EIGEN_XPRHELPER_H